cppad-20170000.3/0002755000175200017650000000000013057470543012434 5ustar coincoin-webcppad-20170000.3/README0000644000175200017650000000525012450414402013300 0ustar coincoin-webHomepage: http://www.coin-or.org/CppAD/ License: CppAD is available from Coin-OR http://www.coin-or.org with both the CPL and GPL licenses; see the CppAD download page: http://www.coin-or.org/CppAD/Doc/download.xml Documentation: The documentation is available with the math either in latex, or rendered using MathML: http://www.coin-or.org/CppAD/Doc/cppad.htm latex http://www.coin-or.org/CppAD/Doc/cppad.xml MathML Install: http://www.coin-or.org/CppAD/Doc/install.htm Mailing List: The mailing list is used for CppAD discussion and bug reporting. Only members of the mailing list can post messages (this avoids spam on the mailing list). You can join the mailing list using its general information page http://list.coin-or.org/mailman/listinfo/CppAD Sub-Directories: bin Helper shell and sed scripts used for CppAD development. build If present, used to build examples and tests. bug Directory containing demonstration of known bugs (may be empty). cmake CMake macros used by the CMakeLists.txt files. compare_c Compare speed of C and C++ on the same soruce code. cppad CppAD include directory (will be copied to prefix/include). cppad_ipopt Deprecated version of a CppAD interface to the Ipopt optimizer. doc If present, replaces http://www.coin-or.org/CppAD/Doc in links. example Most all the CppAD example files are here. introduction Contains an introduction to Algorithmic Differentiation. multi_thread Multi-threading examples and tests. omh User documentation in OMhelp format (without any source code). pkgconfig pkg-config support files. print_for Example printing during forward mode. speed Speed tests for CppAD and comparison with other AD packages. test_more Extra correctness tests that are not intended as examples. Files: AUTHORS Statement of authorship and copyright. CMakeLists.txt Top level CMake commands. COPYING Statement of user license to use this version of software. ChangeLog Pointer to logs for recent changes. INSTALL Points to install instructions. NEWS Pointer to release notes; i.e., whats new. README This file. build.sh Script used to create auto-tools distribution (deprecated). configure.ac Command for auto-tools configuration (deprecated). doc.omh Top level user documentation file. epl-v10.* Eclipse public license files in text and html. gpl-3.0.txt GNU general public license. makefile.am Top level automake input file. uw_copy*.html UW policy on intellectual property. auto-tolls created files: config.guess, config.sub, configure, decomp, install-sh, makefile.in, missing. cppad-20170000.3/speed/0002755000175200017650000000000013057470457013540 5ustar coincoin-webcppad-20170000.3/speed/add_test.sh0000755000175200017650000000442013057470456015663 0ustar coincoin-web#! /bin/bash -e # $Id: add_test.sh 2506 2012-10-24 19:36:49Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Use this shell script when a new test is added to initially create # the source code files */test_name.cpp which return false (for not available). # echo "Change this script so that it automates the omhelp commands" echo "at the beginning of the created files." echo exit 1 # if [ "$1" == "" ] then echo "usage: new_test.sh test_name" echo "where test_name is the name of the new test being added" exit 1 fi test_name="$1" if [ ! -e "link_$test_name.cpp" ] then echo "The file ./link_$test_name.cpp does not yet exist." echo "It must first be created before executing this script." exit 1 fi if ! grep "speed\/link_$test_name.cpp" main.cpp then echo "link_$test_name.cpp has not yet been added to main.cpp" exit 1 fi list=" adolc cppad double fadbad sacado " for dir in profile $list do if grep "link_$test_name.cpp" $dir/makefile.am then echo "$test_name.cpp is already in $dir/makefile.am" exit 1 fi if [ -e $dir/$test_name.cpp ] then echo "The file $dir/$test_name.cpp already exists." exit 1 fi done # sed -i main.cpp -e "s/speed\/link[^%]*\$/&%\n\tspeed\/link_$test_name.cpp/" # copy=`sed -n ../COPYING -e '/^\/\*/,/\*\/$/p'` link=`sed -n link_$test_name.cpp -e "/^ *extern *bool *link_$test_name/,/^);/p"` fun=`echo "$link" | sed -e 's/extern */\n/' -e 's/^);/)\n{\n\treturn false;\n}/'` for dir in $list do echo "$copy$fun" > $dir/$test_name.cpp sed -i $dir/makefile.am \ -e "s/\/main.cpp.*/&\n\t..\/link_$test_name.cpp \\\\/" \ -e "s/\/link_$test_name.cpp.*/&\n\t$test_name.cpp \\\\/" done sed -i profile/makefile.am \ -e "s/\/main.cpp.*/&\n\t..\/link_$test_name.cpp \\\\/" \ -e "s/\/link_$test_name.cpp.*/&\n\t..\/cppad\/$test_name.cpp \\\\/" cppad-20170000.3/speed/profile/0002755000175200017650000000000013057470456015177 5ustar coincoin-webcppad-20170000.3/speed/profile/makefile.am0000644000175200017650000000620113057470456017270 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- source_list = \ main.cpp \ ode.cpp \ det_lu.cpp \ det_minor.cpp \ mat_mul.cpp \ poly.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp \ link_det_lu.cpp \ link_det_minor.cpp \ link_mat_mul.cpp \ link_ode.cpp \ link_poly.cpp \ link_sparse_hessian.cpp \ link_sparse_jacobian.cpp \ microsoft_timer.cpp # # make separate copy of source files because building with different flags BUILT_SOURCES = $(source_list) # main.cpp: $(srcdir)/../main.cpp cp $(srcdir)/../main.cpp main.cpp ode.cpp: $(srcdir)/../cppad/ode.cpp cp $(srcdir)/../cppad/ode.cpp ode.cpp det_lu.cpp: $(srcdir)/../cppad/det_lu.cpp cp $(srcdir)/../cppad/det_lu.cpp det_lu.cpp det_minor.cpp: $(srcdir)/../cppad/det_minor.cpp cp $(srcdir)/../cppad/det_minor.cpp det_minor.cpp mat_mul.cpp: $(srcdir)/../cppad/mat_mul.cpp cp $(srcdir)/../cppad/mat_mul.cpp mat_mul.cpp poly.cpp: $(srcdir)/../cppad/poly.cpp cp $(srcdir)/../cppad/poly.cpp poly.cpp sparse_hessian.cpp: $(srcdir)/../cppad/sparse_hessian.cpp cp $(srcdir)/../cppad/sparse_hessian.cpp sparse_hessian.cpp sparse_jacobian.cpp: $(srcdir)/../cppad/sparse_jacobian.cpp cp $(srcdir)/../cppad/sparse_jacobian.cpp sparse_jacobian.cpp link_det_lu.cpp: $(srcdir)/../src/link_det_lu.cpp cp $(srcdir)/../src/link_det_lu.cpp link_det_lu.cpp link_det_minor.cpp: $(srcdir)/../src/link_det_minor.cpp cp $(srcdir)/../src/link_det_minor.cpp link_det_minor.cpp link_mat_mul.cpp: $(srcdir)/../src/link_mat_mul.cpp cp $(srcdir)/../src/link_mat_mul.cpp link_mat_mul.cpp link_ode.cpp: $(srcdir)/../src/link_ode.cpp cp $(srcdir)/../src/link_ode.cpp link_ode.cpp link_poly.cpp: $(srcdir)/../src/link_poly.cpp cp $(srcdir)/../src/link_poly.cpp link_poly.cpp link_sparse_hessian.cpp: $(srcdir)/../src/link_sparse_hessian.cpp cp $(srcdir)/../src/link_sparse_hessian.cpp link_sparse_hessian.cpp link_sparse_jacobian.cpp: $(srcdir)/../src/link_sparse_jacobian.cpp cp $(srcdir)/../src/link_sparse_jacobian.cpp link_sparse_jacobian.cpp microsoft_timer.cpp: $(srcdir)/../src/microsoft_timer.cpp cp $(srcdir)/../src/microsoft_timer.cpp microsoft_timer.cpp # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # EXTRA_DIST = \ gprof.sed # check_PROGRAMS = speed_profile # AM_CPPFLAGS = -I$(top_srcdir) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) # # BEGIN OPTIMIZE AM_CXXFLAGS = -pg -O2 -DCPPAD_PROFILE_SPEED -DNDEBUG $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) -DCPPAD_PROFILE_SPEED # END DEBUG # AM_LDFLAGS = -pg # speed_profile_SOURCES = $(source_list) # test: check ./speed_profile correct 123 cppad-20170000.3/speed/profile/gprof.sed.in0000644000175200017650000000161113057470456017413 0ustar coincoin-web#! /bin/bash -e # $Id: gprof.sed.in 2506 2012-10-24 19:36:49Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-11 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # remove template information s/<[^<>]*>//g s/<[^<>]*>//g s/<[^<>]*>//g s/<[^<>]*>//g s/<[^<>]*>//g # remove argument information s/([^()]*)//g s/([^()]*)//g # remove names space information s/[a-zA-Z0-9_]*:://g s/[a-zA-Z0-9_]*:://g s/[a-zA-Z0-9_]*:://g s/[a-zA-Z0-9_]*:://g cppad-20170000.3/speed/profile/CMakeLists.txt0000644000175200017650000000523013057470456017735 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the speed/profile directory tests # Inherit build type from ../CMakeList.txt # Adds flags to the compiler command line for sources in the current directory # and below. This command can be used to add any flags, but it was originally # intended to add preprocessor definitions. ADD_DEFINITIONS("-DCPPAD_PROFILE_SPEED ${cppad_profile_flag}") # Extra flags used by the linker when creating an executable. 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$Id: makefile.in 3839 2016-10-14 18:10:09Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- source_list = \ main.cpp \ ode.cpp \ det_lu.cpp \ det_minor.cpp \ mat_mul.cpp \ poly.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp \ link_det_lu.cpp \ link_det_minor.cpp \ link_mat_mul.cpp \ link_ode.cpp \ link_poly.cpp \ link_sparse_hessian.cpp \ link_sparse_jacobian.cpp \ microsoft_timer.cpp # # make separate copy of source files because building with different flags BUILT_SOURCES = $(source_list) # EXTRA_DIST = \ gprof.sed # AM_CPPFLAGS = -I$(top_srcdir) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) # # BEGIN OPTIMIZE AM_CXXFLAGS = -pg -O2 -DCPPAD_PROFILE_SPEED -DNDEBUG $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) -DCPPAD_PROFILE_SPEED # END DEBUG # AM_LDFLAGS = -pg # speed_profile_SOURCES = $(source_list) all: $(BUILT_SOURCES) $(MAKE) $(AM_MAKEFLAGS) all-am .SUFFIXES: .SUFFIXES: .cpp .o .obj $(srcdir)/makefile.in: @MAINTAINER_MODE_TRUE@ $(srcdir)/makefile.am $(am__configure_deps) @for dep in $?; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin fadbad_poly.cpp$$ $spell onetape std cppad cpp tadiff std ddp Taylor dz eval cppad vector Vector typedef fadbad Lu CppAD det hpp const bool $$ $section Fadbad Speed: Second Derivative of a Polynomial$$ $mindex link_poly speed$$ $head Specifications$$ See $cref link_poly$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_poly( size_t size , size_t repeat , CppAD::vector &a , // coefficients of polynomial CppAD::vector &z , // polynomial argument value CppAD::vector &ddp ) // second derivative w.r.t z { if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup size_t i; // temporary index fadbad::T Z; // domain space AD value fadbad::T P; // range space AD value // choose the polynomial coefficients CppAD::uniform_01(size, a); // AD copy of the polynomial coefficients CppAD::vector< fadbad::T > A(size); for(i = 0; i < size; i++) A[i] = a[i]; // ------------------------------------------------------ while(repeat--) { // get the next argument value CppAD::uniform_01(1, z); // independent variable value Z = z[0]; // argument value Z[1] = 1; // argument first order Taylor coefficient // AD computation of the dependent variable P = CppAD::Poly(0, A, Z); // Taylor-expand P to degree one P.eval(2); // second derivative is twice second order Taylor coefficient ddp[0] = 2. * P[2]; // Free DAG corresponding to P does not seem to improve speed. // Probably because it gets freed the next time P is assigned. // P.reset(); } // ------------------------------------------------------ return true; } /* %$$ $end */ cppad-20170000.3/speed/fadbad/sparse_jacobian.cpp0000644000175200017650000000241313057470456020565 0ustar coincoin-web// $Id: sparse_jacobian.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include /* $begin fadbad_sparse_jacobian.cpp$$ $spell const bool CppAD fadbad sparse_jacobian $$ $section fadbad Speed: sparse_jacobian$$ $srccode%cpp% */ // A fadbad version of this test is not yet available bool link_sparse_jacobian( size_t size , size_t repeat , size_t m , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& jacobian , size_t& n_sweep ) { return false; } /* %$$ $end */ cppad-20170000.3/speed/fadbad/ode.cpp0000644000175200017650000000522613057470456016216 0ustar coincoin-web// $Id: ode.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin fadbad_ode.cpp$$ $spell fadiff cassert namespace fabs const std typedef diff Jacobian cstring cppad hpp onetape Fadbad bool CppAD $$ $section Fadbad Speed: Ode$$ $mindex link_ode speed$$ $head Specifications$$ See $cref link_ode$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include # include # include // list of possible options # include extern std::map global_option; namespace fadbad { // define fabs for use by ode_evaluate fadbad::F fabs(const fadbad::F& x) { return std::max(-x, x); } } bool link_ode( size_t size , size_t repeat , CppAD::vector &x , CppAD::vector &jacobian ) { // speed test global option values if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] ) return false; // ------------------------------------------------------------- // setup assert( x.size() == size ); assert( jacobian.size() == size * size ); typedef fadbad::F ADScalar; typedef CppAD::vector ADVector; size_t i, j; size_t p = 0; // use ode to calculate function values size_t n = size; // number of independent variables size_t m = n; // number of dependent variables ADVector X(n), Y(m); // independent and dependent variables // ------------------------------------------------------------- while(repeat--) { // choose next x value CppAD::uniform_01(n, x); for(j = 0; j < n; j++) { // set value of x[j] X[j] = x[j]; // set up for X as the independent variable vector X[j].diff(j, n); } // evaluate function CppAD::ode_evaluate(X, p, Y); // return values with Y as the dependent variable vector for(i = 0; i < m; i++) { for(j = 0; j < n; j++) jacobian[ i * n + j ] = Y[i].d(j); } } return true; } /* %$$ $end */ cppad-20170000.3/speed/fadbad/sparse_hessian.cpp0000644000175200017650000000236313057470456020455 0ustar coincoin-web// $Id: sparse_hessian.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include /* $begin fadbad_sparse_hessian.cpp$$ $spell const Fadbad bool CppAD $$ $section Fadbad Speed: Sparse Hessian$$ $srccode%cpp% */ // A fadbad version of this test is not yet available bool link_sparse_hessian( size_t size , size_t repeat , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& hessian , size_t& n_sweep ) { return false; } /* %$$ $end */ cppad-20170000.3/speed/fadbad/makefile.am0000644000175200017650000000273713057470456017043 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # # Copy source file so that main.o does not end up in parent directory BUILT_SOURCES = main.cpp main.cpp: cp $(srcdir)/../main.cpp main.cpp # # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = speed_fadbad # AM_CPPFLAGS = \ -I$(top_srcdir) \ -I$(FADBAD_DIR)/include \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) # # BEGIN OPTIMIZE # Use special version of CXX_FLAGS with -Wshadow removed (if present). AM_CXXFLAGS = -O2 -DNDEBUG -DCPPAD_FADBAD_SPEED $(CXX_FLAGS_FADBAD) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g -DCPPAD_FADBAD_SPEED $(CXX_FLAGS_FADBAD) # END DEBUG # LDADD = -lspeed AM_LDFLAGS = -L../src # speed_fadbad_SOURCES = \ main.cpp \ det_lu.cpp \ det_minor.cpp \ mat_mul.cpp \ ode.cpp \ poly.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp test: check ./speed_fadbad correct 123 cppad-20170000.3/speed/fadbad/CMakeLists.txt0000644000175200017650000000376613057470456017512 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the speed/fadbad directory tests # Inherit build type from ../CMakeList.txt # assert fadbad_prefix is defined IF ( NOT fadbad_prefix ) MESSAGE(FATAL_ERROR "speed/fadbad/CMakeLists.txt: fadbad_prefix = ${fadbad_prefix}" ) ENDIF ( NOT fadbad_prefix ) # Adds flags to the compiler command line for sources in the current directory # and below. This command can be used to add any flags, but it was originally # intended to add preprocessor definitions. ADD_DEFINITIONS("-DCPPAD_FADBAD_SPEED") # Local include directories to search (not in package_prefix/includdir) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/../src ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(speed_fadbad EXCLUDE_FROM_ALL ../main.cpp det_lu.cpp det_minor.cpp mat_mul.cpp ode.cpp poly.cpp sparse_hessian.cpp sparse_jacobian.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( speed_fadbad ) # fadbad is an include file only library TARGET_LINK_LIBRARIES(speed_fadbad speed_src ) # Add the check_speed_fadbad target ADD_CUSTOM_TARGET(check_speed_fadbad speed_fadbad correct 54321 DEPENDS speed_fadbad speed_src ) MESSAGE(STATUS "make check_speed_fadbad: available") # Change check depends in parent environment add_to_list(check_speed_depends check_speed_fadbad) SET(check_speed_depends "${check_speed_depends}" PARENT_SCOPE) cppad-20170000.3/speed/fadbad/det_lu.cpp0000644000175200017650000000513013057470456016715 0ustar coincoin-web// $Id: det_lu.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin fadbad_det_lu.cpp$$ $spell onetape cppad std Lu Fadbad det badiff.hpp const CppAD typedef diff bool srand $$ $section Fadbad Speed: Gradient of Determinant Using Lu Factorization$$ $mindex link_det_lu speed matrix factor$$ $head Specifications$$ See $cref link_det_lu$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_det_lu( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ) { // speed test global option values if( global_option["onetape"] || global_option["atomic"] ) return false; if( global_option["memory"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup // // object for computing determinant typedef fadbad::B ADScalar; typedef CppAD::vector ADVector; CppAD::det_by_lu Det(size); size_t i; // temporary index size_t m = 1; // number of dependent variables size_t n = size * size; // number of independent variables ADScalar detA; // AD value of the determinant ADVector A(n); // AD version of matrix // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, matrix); // set independent variable values for(i = 0; i < n; i++) A[i] = matrix[i]; // compute the determinant detA = Det(A); // create function object f : A -> detA detA.diff(0, m); // index 0 of m dependent variables // evaluate and return gradient using reverse mode for(i =0; i < n; i++) gradient[i] = A[i].d(0); // partial detA w.r.t A[i] } // --------------------------------------------------------- return true; } /* %$$ $end */ cppad-20170000.3/speed/fadbad/mat_mul.cpp0000644000175200017650000000533513057470456017106 0ustar coincoin-web// $Id: mat_mul.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin fadbad_mat_mul.cpp$$ $spell badiff sq onetape typedef diff Fadbad Adolc cppad.hpp bool mul dz CppAD $$ $section Fadbad Speed: Matrix Multiplication$$ $mindex link_mat_mul speed multiply$$ $head Specifications$$ See $cref link_mat_mul$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_mat_mul( size_t size , size_t repeat , CppAD::vector& x , CppAD::vector& z , CppAD::vector& dz ) { // speed test global option values if( global_option["memory"] || global_option["onetape"] || global_option["atomic"] || global_option["optimize"] ) return false; // The correctness check for this test is failing, so abort (for now). return false; // ----------------------------------------------------- // setup // object for computing determinant typedef fadbad::B ADScalar; typedef CppAD::vector ADVector; size_t j; // temporary index size_t m = 1; // number of dependent variables size_t n = size * size; // number of independent variables ADVector X(n); // AD domain space vector ADVector Y(n); // Store product matrix ADVector Z(m); // AD range space vector // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, x); // set independent variable values for(j = 0; j < n; j++) X[j] = x[j]; // do the computation mat_sum_sq(size, X, Y, Z); // create function object f : X -> Z Z[0].diff(0, m); // index 0 of m dependent variables // evaluate and return gradient using reverse mode for(j = 0; j < n; j++) dz[j] = X[j].d(0); // partial Z[0] w.r.t X[j] } // return function value z[0] = Z[0].x(); // --------------------------------------------------------- return true; } /* %$$ $end */ cppad-20170000.3/speed/fadbad/det_minor.cpp0000644000175200017650000000512213057470456017422 0ustar coincoin-web// $Id: det_minor.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin fadbad_det_minor.cpp$$ $spell onetape cppad std Fadbad det badiff.hpp const CppAD typedef diff bool srand $$ $section Fadbad Speed: Gradient of Determinant by Minor Expansion$$ $mindex link_det_minor speed$$ $head Specifications$$ See $cref link_det_minor$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_det_minor( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ) { // speed test global option values if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup // object for computing determinant typedef fadbad::B ADScalar; typedef CppAD::vector ADVector; CppAD::det_by_minor Det(size); size_t i; // temporary index size_t m = 1; // number of dependent variables size_t n = size * size; // number of independent variables ADScalar detA; // AD value of the determinant ADVector A(n); // AD version of matrix // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, matrix); // set independent variable values for(i = 0; i < n; i++) A[i] = matrix[i]; // compute the determinant detA = Det(A); // create function object f : A -> detA detA.diff(0, m); // index 0 of m dependent variables // evaluate and return gradient using reverse mode for(i =0; i < n; i++) gradient[i] = A[i].d(0); // partial detA w.r.t A[i] } // --------------------------------------------------------- return true; } /* %$$ $end */ cppad-20170000.3/speed/fadbad/makefile.in0000644000175200017650000004763113057470456017056 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin adolc_poly.cpp$$ $spell alloc onetape coef cppad hos Taylor std ddp cppad adouble std vector Vector typedef adolc Lu CppAD det hpp const bool $$ $section Adolc Speed: Second Derivative of a Polynomial$$ $mindex link_poly speed$$ $head Specifications$$ See $cref link_poly$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include # include # include # include "adolc_alloc_mat.hpp" // list of possible options # include extern std::map global_option; bool link_poly( size_t size , size_t repeat , CppAD::vector &a , // coefficients of polynomial CppAD::vector &z , // polynomial argument value CppAD::vector &ddp ) // second derivative w.r.t z { if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup size_t i; int tag = 0; // tape identifier int keep = 0; // do not keep forward mode results in buffer int m = 1; // number of dependent variables int n = 1; // number of independent variables int d = 2; // highest derivative degree double f; // function value // set up for thread_alloc memory allocator (fast and checks for leaks) using CppAD::thread_alloc; // the allocator size_t capacity; // capacity of an allocation // choose a vector of polynomial coefficients CppAD::uniform_01(size, a); // AD copy of the polynomial coefficients std::vector A(size); for(i = 0; i < size; i++) A[i] = a[i]; // domain and range space AD values adouble Z, P; // allocate arguments to hos_forward double* x0 = thread_alloc::create_array(size_t(n), capacity); double* y0 = thread_alloc::create_array(size_t(m), capacity); double** x = adolc_alloc_mat(size_t(n), size_t(d)); double** y = adolc_alloc_mat(size_t(m), size_t(d)); // Taylor coefficient for argument x[0][0] = 1.; // first order x[0][1] = 0.; // second order // ---------------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose an argument value CppAD::uniform_01(1, z); // declare independent variables trace_on(tag, keep); Z <<= z[0]; // AD computation of the function value P = CppAD::Poly(0, A, Z); // create function object f : Z -> P P >>= f; trace_off(); // set the argument value x0[0] = z[0]; // evaluate the polynomial at the new argument value hos_forward(tag, m, n, d, keep, x0, x, y0, y); // second derivative is twice second order Taylor coef ddp[0] = 2. * y[0][1]; } else { // choose an argument value CppAD::uniform_01(1, z); // declare independent variables trace_on(tag, keep); Z <<= z[0]; // AD computation of the function value P = CppAD::Poly(0, A, Z); // create function object f : Z -> P P >>= f; trace_off(); while(repeat--) { // get the next argument value CppAD::uniform_01(1, z); x0[0] = z[0]; // evaluate the polynomial at the new argument value hos_forward(tag, m, n, d, keep, x0, x, y0, y); // second derivative is twice second order Taylor coef ddp[0] = 2. * y[0][1]; } } // ------------------------------------------------------ // tear down adolc_free_mat(x); adolc_free_mat(y); thread_alloc::delete_array(x0); thread_alloc::delete_array(y0); return true; } /* %$$ $end */ cppad-20170000.3/speed/adolc/sparse_jacobian.cpp0000644000175200017650000001404713057470456020454 0ustar coincoin-web// $Id: sparse_jacobian.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include /* $begin adolc_sparse_jacobian.cpp$$ $spell const sparsedrivers.cpp colpack boolsparsity adouble int int_n cppad.hpp onetape typedef alloc jac nnz cind bool CppAD adolc sparse_jacobian $$ $section adolc Speed: Sparse Jacobian$$ $mindex link_sparse_jacobian speed$$ $head Specifications$$ See $cref link_sparse_jacobian$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include # include // list of possible options # include extern std::map global_option; bool link_sparse_jacobian( size_t size , size_t repeat , size_t m , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x_return , CppAD::vector& jacobian , size_t& n_sweep ) { if( global_option["atomic"] || (! global_option["colpack"]) ) return false; if( global_option["memory"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup typedef unsigned int* SizeVector; typedef double* DblVector; typedef adouble ADScalar; typedef ADScalar* ADVector; size_t i, j, k; // temporary indices size_t n = size; // number of independent variables size_t order = 0; // derivative order corresponding to function // set up for thread_alloc memory allocator (fast and checks for leaks) using CppAD::thread_alloc; // the allocator size_t capacity; // capacity of an allocation // tape identifier int tag = 0; // AD domain space vector ADVector a_x = thread_alloc::create_array(n, capacity); // AD range space vector ADVector a_y = thread_alloc::create_array(m, capacity); // argument value in double DblVector x = thread_alloc::create_array(n, capacity); // function value in double DblVector y = thread_alloc::create_array(m, capacity); // options that control sparse_jac int options[4]; if( global_option["boolsparsity"] ) options[0] = 1; // sparsity by propagation of bit pattern else options[0] = 0; // sparsity pattern by index domains options[1] = 0; // (0 = safe mode, 1 = tight mode) options[2] = 0; // see changing to -1 and back to 0 below options[3] = 0; // (0 = column compression, 1 = row compression) // structure that holds some of the work done by sparse_jac int nnz; // number of non-zero values SizeVector rind = CPPAD_NULL; // row indices SizeVector cind = CPPAD_NULL; // column indices DblVector values = CPPAD_NULL; // Jacobian values // choose a value for x CppAD::uniform_01(n, x); // declare independent variables int keep = 0; // keep forward mode results trace_on(tag, keep); for(j = 0; j < n; j++) a_x[j] <<= x[j]; // AD computation of f (x) CppAD::sparse_jac_fun(m, n, a_x, row, col, order, a_y); // create function object f : x -> y for(i = 0; i < m; i++) a_y[i] >>= y[i]; trace_off(); // Retrieve n_sweep using undocumented feature of sparsedrivers.cpp int same_pattern = 0; options[2] = -1; n_sweep = sparse_jac(tag, int(m), int(n), same_pattern, x, &nnz, &rind, &cind, &values, options ); options[2] = 0; // ---------------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); // declare independent variables trace_on(tag, keep); for(j = 0; j < n; j++) a_x[j] <<= x[j]; // AD computation of f (x) CppAD::sparse_jac_fun(m, n, a_x, row, col, order, a_y); // create function object f : x -> y for(i = 0; i < m; i++) a_y[i] >>= y[i]; trace_off(); // is this a repeat call with the same sparsity pattern same_pattern = 0; // calculate the jacobian at this x rind = CPPAD_NULL; cind = CPPAD_NULL; values = CPPAD_NULL; sparse_jac(tag, int(m), int(n), same_pattern, x, &nnz, &rind, &cind, &values, options ); // only needed last time through loop if( repeat == 0 ) { size_t K = row.size(); for(int ell = 0; ell < nnz; ell++) { i = size_t(rind[ell]); j = size_t(cind[ell]); for(k = 0; k < K; k++) { if( row[k]==i && col[k]==j ) jacobian[k] = values[ell]; } } } // free raw memory allocated by sparse_jac free(rind); free(cind); free(values); } else { while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); // calculate the jacobian at this x sparse_jac(tag, int(m), int(n), same_pattern, x, &nnz, &rind, &cind, &values, options ); same_pattern = 1; } size_t K = row.size(); for(int ell = 0; ell < nnz; ell++) { i = size_t(rind[ell]); j = size_t(cind[ell]); for(k = 0; k < K; k++) { if( row[k]==i && col[k]==j ) jacobian[k] = values[ell]; } } // free raw memory allocated by sparse_jac free(rind); free(cind); free(values); } // -------------------------------------------------------------------- // return argument for(j = 0; j < n; j++) x_return[j] = x[j]; // tear down thread_alloc::delete_array(a_x); thread_alloc::delete_array(a_y); thread_alloc::delete_array(x); thread_alloc::delete_array(y); return true; } /* %$$ $end */ cppad-20170000.3/speed/adolc/adolc_usrparms.sh0000755000175200017650000000436013057470456020177 0ustar coincoin-web#! /bin/bash -e # $Id: adolc_usrparms.sh 3217 2014-03-19 05:09:01Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-14 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- #! /bin/bash # message=" usage: adolc_usrparms.sh adolc_usrparms.sh show adolc_usrparms.sh modify The frist usage prints the value of BUFSIZE and TBUFSIZE. The second usage show how the usrparms.h file would be modified. The third usage actually modifies the file. : The distribution directory corresponding to adolc; e.g., adolc-1.10.2. The file where the buffer sizes are specified is /adolc/usrparms.h. BUFSIZE: Buffer size for tapes. TBUFSIZE: Buffer size for temporary Taylor store. : the value we are changing the Adolc BUFSIZE parameter to. : the value we are changing the Adolc TBUFSIZE parameter to. " if [ "$1" == "" ] then echo "$message" exit 1 fi file="$1/adolc/usrparms.h" if [ ! -e $file ] then echo "adolc_usrparms.sh: cannot find the file $file" exit 1 fi # # case where we print the value of BUFSIZE and TBUFSIZE if [ "$2" == "" ] then grep "^#define T*BUFSIZE" < $file exit 0 fi same="/* Previous: \1\2 */ \3\n#define" cmd_one="s|^\(#define BUFSIZE *\)\([0-9]*\)\(.*\)|$same BUFSIZE $2|" cmd_two="s|^\(#define TBUFSIZE *\)\([0-9]*\)\(.*\)|$same TBUFSIZE $3|" if [ "$4" == "show" ] then sed < $file > adolc_usrparms.tmp \ -e "$cmd_one" -e "$cmd_two" diff $file adolc_usrparms.tmp exit 0 fi if [ "$4" == "modify" ] then sed < $file > adolc_usrparms.tmp \ -e "$cmd_one" -e "$cmd_two" diff $file adolc_usrparms.tmp mv adolc_usrparms.tmp $file echo "Execute the following commands for the change to take effect:" echo "cd $1" echo "make" echo "make install" exit 0 fi echo "$message" exit 1 cppad-20170000.3/speed/adolc/ode.cpp0000644000175200017650000000775113057470456016104 0ustar coincoin-web// $Id: ode.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin adolc_ode.cpp$$ $spell typedef adouble jacobian jacobian jac_ptr alloc cppad.hpp Jacobian Adolc bool CppAD onetape $$ $section Adolc Speed: Ode$$ $mindex link_ode speed$$ $head Specifications$$ See $cref link_ode$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_ode( size_t size , size_t repeat , CppAD::vector &x , CppAD::vector &jac ) { // speed test global option values if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["optimize"] ) return false; // ------------------------------------------------------------- // setup assert( x.size() == size ); assert( jac.size() == size * size ); typedef CppAD::vector ADVector; typedef CppAD::vector DblVector; size_t i, j; int tag = 0; // tape identifier int keep = 0; // do not keep forward mode results size_t p = 0; // use ode to calculate function values size_t n = size; // number of independent variables size_t m = n; // number of dependent variables ADVector X(n), Y(m); // independent and dependent variables DblVector f(m); // function value // set up for thread_alloc memory allocator (fast and checks for leaks) using CppAD::thread_alloc; // the allocator size_t size_min; // requested number of elements size_t size_out; // capacity of an allocation // raw memory for use with adolc size_min = n; double *x_raw = thread_alloc::create_array(size_min, size_out); size_min = m * n; double *jac_raw = thread_alloc::create_array(size_min, size_out); size_min = m; double **jac_ptr = thread_alloc::create_array(size_min, size_out); for(i = 0; i < m; i++) jac_ptr[i] = jac_raw + i * n; // ------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose next x value uniform_01(n, x); // declare independent variables trace_on(tag, keep); for(j = 0; j < n; j++) X[j] <<= x[j]; // evaluate function CppAD::ode_evaluate(X, p, Y); // create function object f : X -> Y for(i = 0; i < m; i++) Y[i] >>= f[i]; trace_off(); // evaluate the Jacobian for(j = 0; j < n; j++) x_raw[j] = x[j]; jacobian(tag, m, n, x_raw, jac_ptr); } else { // choose next x value uniform_01(n, x); // declare independent variables trace_on(tag, keep); for(j = 0; j < n; j++) X[j] <<= x[j]; // evaluate function CppAD::ode_evaluate(X, p, Y); // create function object f : X -> Y for(i = 0; i < m; i++) Y[i] >>= f[i]; trace_off(); while(repeat--) { // get next argument value uniform_01(n, x); for(j = 0; j < n; j++) x_raw[j] = x[j]; // evaluate jacobian jacobian(tag, m, n, x_raw, jac_ptr); } } // convert return value to a simple vector for(i = 0; i < m; i++) { for(j = 0; j < n; j++) jac[i * n + j] = jac_ptr[i][j]; } // ---------------------------------------------------------------------- // tear down thread_alloc::delete_array(x_raw); thread_alloc::delete_array(jac_raw); thread_alloc::delete_array(jac_ptr); return true; } /* %$$ $end */ cppad-20170000.3/speed/adolc/sparse_hessian.cpp0000644000175200017650000001317413057470456020340 0ustar coincoin-web// $Id: sparse_hessian.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin adolc_sparse_hessian.cpp$$ $spell colpack boolsparsity onetape hess int nnz cind const hes thread_alloc arg cppad adouble CppAD adolc hpp bool typedef endif $$ $section Adolc Speed: Sparse Hessian$$ $mindex link_sparse_hessian speed$$ $head Specifications$$ See $cref link_sparse_hessian$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include # include # include // list of possible options # include extern std::map global_option; bool link_sparse_hessian( size_t size , size_t repeat , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x_return , CppAD::vector& hessian , size_t& n_sweep ) { if( global_option["atomic"] || (! global_option["colpack"]) ) return false; if( global_option["memory"] || global_option["optimize"] || global_option["boolsparsity"] ) return false; // ----------------------------------------------------- // setup typedef unsigned int* SizeVector; typedef double* DblVector; typedef adouble ADScalar; typedef ADScalar* ADVector; size_t i, j, k; // temporary indices size_t order = 0; // derivative order corresponding to function size_t m = 1; // number of dependent variables size_t n = size; // number of independent variables // setup for thread_alloc memory allocator (fast and checks for leaks) using CppAD::thread_alloc; // the allocator size_t capacity; // capacity of an allocation // tape identifier int tag = 0; // AD domain space vector ADVector a_x = thread_alloc::create_array(n, capacity); // AD range space vector ADVector a_y = thread_alloc::create_array(m, capacity); // double argument value DblVector x = thread_alloc::create_array(n, capacity); // double function value double f; // options that control sparse_hess int options[2]; options[0] = 0; // safe mode options[1] = 0; // indirect recovery // structure that holds some of the work done by sparse_hess int nnz; // number of non-zero values SizeVector rind = CPPAD_NULL; // row indices SizeVector cind = CPPAD_NULL; // column indices DblVector values = CPPAD_NULL; // Hessian values // ---------------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); // declare independent variables int keep = 0; // keep forward mode results trace_on(tag, keep); for(j = 0; j < n; j++) a_x[j] <<= x[j]; // AD computation of f (x) CppAD::sparse_hes_fun(n, a_x, row, col, order, a_y); // create function object f : x -> y a_y[0] >>= f; trace_off(); // is this a repeat call with the same sparsity pattern int same_pattern = 0; // calculate the hessian at this x rind = CPPAD_NULL; cind = CPPAD_NULL; values = CPPAD_NULL; sparse_hess(tag, int(n), same_pattern, x, &nnz, &rind, &cind, &values, options ); // only needed last time through loop if( repeat == 0 ) { size_t K = row.size(); for(int ell = 0; ell < nnz; ell++) { i = size_t(rind[ell]); j = size_t(cind[ell]); for(k = 0; k < K; k++) { if( (row[k]==i && col[k]==j) || (row[k]==j && col[k]==i) ) hessian[k] = values[ell]; } } } // free raw memory allocated by sparse_hess free(rind); free(cind); free(values); } else { // choose a value for x CppAD::uniform_01(n, x); // declare independent variables int keep = 0; // keep forward mode results trace_on(tag, keep); for(j = 0; j < n; j++) a_x[j] <<= x[j]; // AD computation of f (x) CppAD::sparse_hes_fun(n, a_x, row, col, order, a_y); // create function object f : x -> y a_y[0] >>= f; trace_off(); // is this a repeat call at the same argument int same_pattern = 0; while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); // calculate the hessian at this x sparse_hess(tag, int(n), same_pattern, x, &nnz, &rind, &cind, &values, options ); same_pattern = 1; } size_t K = row.size(); for(int ell = 0; ell < nnz; ell++) { i = size_t(rind[ell]); j = size_t(cind[ell]); for(k = 0; k < K; k++) { if( (row[k]==i && col[k]==j) || (row[k]==j && col[k]==i) ) hessian[k] = values[ell]; } } // free raw memory allocated by sparse_hessian free(rind); free(cind); free(values); } // -------------------------------------------------------------------- // return argument for(j = 0; j < n; j++) x_return[j] = x[j]; // do not know how to return number of sweeps used n_sweep = 0; // tear down thread_alloc::delete_array(a_x); thread_alloc::delete_array(a_y); thread_alloc::delete_array(x); return true; } /* %$$ $end */ cppad-20170000.3/speed/adolc/makefile.am0000644000175200017650000000303013057470456016707 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # # Copy source file so that main.o does not end up in parent directory BUILT_SOURCES = main.cpp main.cpp: cp $(srcdir)/../main.cpp main.cpp # # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = speed_adolc # AM_CPPFLAGS = \ -I$(top_srcdir) \ -I$(ADOLC_DIR)/include \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) # # BEGIN OPTIMIZE AM_CXXFLAGS = -O2 -DNDEBUG -DCPPAD_ADOLC_SPEED $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) -DCPPAD_ADOLC_SPEED # END DEBUG # LDADD = -lspeed -ladolc -lColPack AM_LDFLAGS = -L../src -L$(ADOLC_DIR)/lib -L$(ADOLC_DIR)/lib64 # speed_adolc_SOURCES = \ adolc_alloc_mat.hpp \ alloc_mat.cpp \ main.cpp \ det_lu.cpp \ det_minor.cpp \ mat_mul.cpp \ ode.cpp \ poly.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp test: check ./speed_adolc correct 123 colpack ./speed_adolc correct 123 onetape colpack cppad-20170000.3/speed/adolc/alloc_mat.cpp0000644000175200017650000000356613057470456017270 0ustar coincoin-web// $Id: alloc_mat.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin adolc_alloc_mat$$ $spell adolc alloc $$ $section Adolc Test Utility: Allocate and Free Memory For a Matrix$$ $mindex adolc_alloc_mat alloc$$ $head Syntax$$ $codei%mat% = adolc_alloc_mat(%m%, %n%) %$$ $codei%adolc_free_mat(%mat%) %$$ $head Purpose$$ Use the $cref thread_alloc$$ memory allocator to allocate and free memory that can be used as a matrix with the Adolc package. $head m$$ Is the number of rows in the matrix. $head n$$ Is the number of columns in the matrix. $head mat$$ Is the matrix. To be specific, between a call to $code adolc_alloc_mat$$, and the corresponding call to $code adolc_free_mat$$, for $icode%i% = 0 , %...% , %m%-1%$$ and $icode%j% = 0 , %...% , %n%-1%$$, $icode%mat%[%i%][%j%]%$$ is the element in row $icode i$$ and column $icode j$$. $end */ # include double** adolc_alloc_mat(size_t m, size_t n) { using CppAD::thread_alloc; size_t size_min = m * n, size_out; double* vec = thread_alloc::create_array(size_min, size_out); double** mat = thread_alloc::create_array(size_min, size_out); for(size_t i = 0; i < m; i++) mat[i] = vec + i * n; return mat; } void adolc_free_mat(double** mat) { using CppAD::thread_alloc; thread_alloc::delete_array(mat[0]); thread_alloc::delete_array(mat); return; } cppad-20170000.3/speed/adolc/CMakeLists.txt0000644000175200017650000000407013057470456017360 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the speed/adolc directory tests # Inherit build type from ../CMakeList.txt # assert adolc_prefix is defined IF ( NOT adolc_prefix ) MESSAGE(FATAL_ERROR "speed/adolc/CMakeLists.txt: adolc_prefix = ${adolc_prefix}" ) ENDIF ( NOT adolc_prefix ) # Adds flags to the compiler command line for sources in the current directory # and below. This command can be used to add any flags, but it was originally # intended to add preprocessor definitions. ADD_DEFINITIONS("-DCPPAD_ADOLC_SPEED") # Local include directories to search (not in package_prefix/includdir) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/../src ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(speed_adolc EXCLUDE_FROM_ALL ../main.cpp alloc_mat.cpp det_lu.cpp det_minor.cpp mat_mul.cpp ode.cpp poly.cpp sparse_hessian.cpp sparse_jacobian.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( speed_adolc ) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES(speed_adolc speed_src ${cppad_lib} adolc ${colpack_libs} ) # Add the check_speed_adolc target ADD_CUSTOM_TARGET( check_speed_adolc speed_adolc correct 54321 colpack DEPENDS speed_adolc speed_src ) MESSAGE(STATUS "make check_speed_adolc: available") # Change check depends in parent environment add_to_list(check_speed_depends check_speed_adolc) SET(check_speed_depends "${check_speed_depends}" PARENT_SCOPE) cppad-20170000.3/speed/adolc/det_lu.cpp0000644000175200017650000000712213057470456016601 0ustar coincoin-web// $Id: det_lu.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin adolc_det_lu.cpp$$ $spell onetape thread_alloc cppad fos adouble CppAD typedef adolc Lu Adolc det hpp const bool srand $$ $section Adolc Speed: Gradient of Determinant Using Lu Factorization$$ $mindex link_det_lu speed matrix factor$$ $head Specifications$$ See $cref link_det_lu$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_det_lu( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ) { // speed test global option values if( global_option["onetape"] || global_option["atomic"] ) return false; if( global_option["memory"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup int tag = 0; // tape identifier int keep = 1; // keep forward mode results in buffer int m = 1; // number of dependent variables int n = size*size; // number of independent variables double f; // function value int j; // temporary index // set up for thread_alloc memory allocator (fast and checks for leaks) using CppAD::thread_alloc; // the allocator size_t size_min; // requested number of elements size_t size_out; // capacity of an allocation // object for computing determinant typedef adouble ADScalar; typedef ADScalar* ADVector; CppAD::det_by_lu Det(size); // AD value of determinant ADScalar detA; // AD version of matrix size_min = n; ADVector A = thread_alloc::create_array(size_min, size_out); // vectors of reverse mode weights size_min = m; double* u = thread_alloc::create_array(size_min, size_out); u[0] = 1.; // vector with matrix value size_min = n; double* mat = thread_alloc::create_array(size_min, size_out); // vector to receive gradient result size_min = n; double* grad = thread_alloc::create_array(size_min, size_out); // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, mat); // declare independent variables trace_on(tag, keep); for(j = 0; j < n; j++) A[j] <<= mat[j]; // AD computation of the determinant detA = Det(A); // create function object f : A -> detA detA >>= f; trace_off(); // evaluate and return gradient using reverse mode fos_reverse(tag, m, n, u, grad); } // ------------------------------------------------------ // return matrix and gradient for(j = 0; j < n; j++) { matrix[j] = mat[j]; gradient[j] = grad[j]; } // tear down thread_alloc::delete_array(grad); thread_alloc::delete_array(mat); thread_alloc::delete_array(u); thread_alloc::delete_array(A); return true; } /* %$$ $end */ cppad-20170000.3/speed/adolc/mat_mul.cpp0000644000175200017650000001025613057470456016765 0ustar coincoin-web// $Id: mat_mul.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin adolc_mat_mul.cpp$$ $spell sq onetape adouble typedef alloc zos fos Adolc cppad.hpp bool mul dz CppAD $$ $section Adolc Speed: Matrix Multiplication$$ $mindex link_mat_mul speed multiply$$ $head Specifications$$ See $cref link_mat_mul$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include # include // list of possible options # include extern std::map global_option; bool link_mat_mul( size_t size , size_t repeat , CppAD::vector& x , CppAD::vector& z , CppAD::vector& dz ) { // speed test global option values if( global_option["memory"] || global_option["atomic"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup typedef adouble ADScalar; typedef ADScalar* ADVector; int tag = 0; // tape identifier int m = 1; // number of dependent variables int n = size*size; // number of independent variables double f; // function value int j; // temporary index // set up for thread_alloc memory allocator (fast and checks for leaks) using CppAD::thread_alloc; // the allocator size_t capacity; // capacity of an allocation // AD domain space vector ADVector X = thread_alloc::create_array(size_t(n), capacity); // Product matrix ADVector Y = thread_alloc::create_array(size_t(n), capacity); // AD range space vector ADVector Z = thread_alloc::create_array(size_t(m), capacity); // vector with matrix value double* mat = thread_alloc::create_array(size_t(n), capacity); // vector of reverse mode weights double* u = thread_alloc::create_array(size_t(m), capacity); u[0] = 1.; // gradient double* grad = thread_alloc::create_array(size_t(n), capacity); // ---------------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose a matrix CppAD::uniform_01(n, mat); // declare independent variables int keep = 1; // keep forward mode results trace_on(tag, keep); for(j = 0; j < n; j++) X[j] <<= mat[j]; // do computations CppAD::mat_sum_sq(size, X, Y, Z); // create function object f : X -> Z Z[0] >>= f; trace_off(); // evaluate and return gradient using reverse mode fos_reverse(tag, m, n, u, grad); } else { // choose a matrix CppAD::uniform_01(n, mat); // declare independent variables int keep = 0; // do not keep forward mode results trace_on(tag, keep); for(j = 0; j < n; j++) X[j] <<= mat[j]; // do computations CppAD::mat_sum_sq(size, X, Y, Z); // create function object f : X -> Z Z[0] >>= f; trace_off(); while(repeat--) { // choose a matrix CppAD::uniform_01(n, mat); // evaluate the determinant at the new matrix value keep = 1; // keep this forward mode result zos_forward(tag, m, n, keep, mat, &f); // evaluate and return gradient using reverse mode fos_reverse(tag, m, n, u, grad); } } // return function, matrix, and gradient z[0] = f; for(j = 0; j < n; j++) { x[j] = mat[j]; dz[j] = grad[j]; } // tear down thread_alloc::delete_array(X); thread_alloc::delete_array(Y); thread_alloc::delete_array(Z); thread_alloc::delete_array(mat); thread_alloc::delete_array(u); thread_alloc::delete_array(grad); return true; } /* %$$ $end */ cppad-20170000.3/speed/adolc/det_minor.cpp0000644000175200017650000001016213057470456017303 0ustar coincoin-web// $Id: det_minor.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin adolc_det_minor.cpp$$ $spell thread_alloc onetape cppad zos fos adouble CppAD typedef adolc Lu Adolc det hpp const bool srand $$ $section Adolc Speed: Gradient of Determinant by Minor Expansion$$ $mindex link_det_minor speed$$ $head Specifications$$ See $cref link_det_minor$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_det_minor( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ) { // speed test global option values if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup typedef adouble ADScalar; typedef ADScalar* ADVector; int tag = 0; // tape identifier int m = 1; // number of dependent variables int n = size*size; // number of independent variables double f; // function value int j; // temporary index // set up for thread_alloc memory allocator (fast and checks for leaks) using CppAD::thread_alloc; // the allocator size_t capacity; // capacity of an allocation // object for computing determinant CppAD::det_by_minor Det(size); // AD value of determinant ADScalar detA; // AD version of matrix ADVector A = thread_alloc::create_array(size_t(n), capacity); // vectors of reverse mode weights double* u = thread_alloc::create_array(size_t(m), capacity); u[0] = 1.; // vector with matrix value double* mat = thread_alloc::create_array(size_t(n), capacity); // vector to receive gradient result double* grad = thread_alloc::create_array(size_t(n), capacity); // ---------------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose a matrix CppAD::uniform_01(n, mat); // declare independent variables int keep = 1; // keep forward mode results trace_on(tag, keep); for(j = 0; j < n; j++) A[j] <<= mat[j]; // AD computation of the determinant detA = Det(A); // create function object f : A -> detA detA >>= f; trace_off(); // evaluate and return gradient using reverse mode fos_reverse(tag, m, n, u, grad); } else { // choose a matrix CppAD::uniform_01(n, mat); // declare independent variables int keep = 0; // do not keep forward mode results in buffer trace_on(tag, keep); for(j = 0; j < n; j++) A[j] <<= mat[j]; // AD computation of the determinant detA = Det(A); // create function object f : A -> detA detA >>= f; trace_off(); while(repeat--) { // get the next matrix CppAD::uniform_01(n, mat); // evaluate the determinant at the new matrix value keep = 1; // keep this forward mode result zos_forward(tag, m, n, keep, mat, &f); // evaluate and return gradient using reverse mode fos_reverse(tag, m, n, u, grad); } } // -------------------------------------------------------------------- // return matrix and gradient for(j = 0; j < n; j++) { matrix[j] = mat[j]; gradient[j] = grad[j]; } // tear down thread_alloc::delete_array(grad); thread_alloc::delete_array(mat); thread_alloc::delete_array(u); thread_alloc::delete_array(A); return true; } /* %$$ $end */ cppad-20170000.3/speed/adolc/makefile.in0000644000175200017650000005072313057470456016733 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; the Free Software Foundation # gives unlimited permission to copy and/or distribute it, # with or without modifications, as long as this notice is preserved. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY, to the extent permitted by law; without # even the implied warranty of MERCHANTABILITY or FITNESS FOR A # PARTICULAR PURPOSE. @SET_MAKE@ VPATH = @srcdir@ am__is_gnu_make = { \ if test -z '$(MAKELEVEL)'; then \ false; \ elif test -n '$(MAKE_HOST)'; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # ifndef CPPAD_SPEED_ADOLC_ADOLC_ALLOC_MAT_HPP # define CPPAD_SPEED_ADOLC_ADOLC_ALLOC_MAT_HPP double** adolc_alloc_mat(size_t m, size_t n); void adolc_free_mat(double** mat); # endif cppad-20170000.3/speed/main.cpp0000644000175200017650000005246313057470456015177 0ustar coincoin-web// $Id: main.cpp 3855 2016-12-19 00:30:54Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # ifdef CPPAD_ADOLC_SPEED # define AD_PACKAGE "adolc" # endif # ifdef CPPAD_CPPAD_SPEED # define AD_PACKAGE "cppad" # endif # ifdef CPPAD_DOUBLE_SPEED # define AD_PACKAGE "double" # endif # ifdef CPPAD_FADBAD_SPEED # define AD_PACKAGE "fadbad" # endif # ifdef CPPAD_PROFILE_SPEED # define AD_PACKAGE "profile" # endif # ifdef CPPAD_SACADO_SPEED # define AD_PACKAGE "sacado" # endif /* $begin speed_main$$ $spell revsparsity colpack onetape boolsparsity optionlist underbar alloc mat_mul retaped bool ddp cppad adolc fadbad sacado CppAD det lu Jacobian $$ $section Running the Speed Test Program$$ $mindex cppad uniform_01$$ $head Syntax$$ $codei%speed/%package%/speed_%package% %test% %seed% %option_list%$$ $head Purpose$$ A version of this program runs the correctness tests or the speed tests for one AD package identified by $icode package$$. $head package$$ $subhead AD Package$$ The command line argument $icode package$$ specifies one of the AD package. The CppAD distribution comes with support for the following packages: $cref/adolc/speed_adolc/$$, $cref/cppad/speed_cppad/$$, $cref/fadbad/speed_fadbad/$$, $cref/sacado/speed_sacado/$$. You can extend this program to include other package. Such an extension need not include all the tests. For example, $cref link_sparse_hessian$$ just returns $code false$$ for the $cref/fadbad/fadbad_sparse_hessian.cpp/$$ and $cref/sacado/sacado_sparse_hessian.cpp/$$ packages. $subhead double$$ The value $icode package$$ can be $code double$$ in which case the function values (instead of derivatives) are computed using double precision operations. This enables one to compare the speed of computing function values in $code double$$ to the speed of the derivative computations. (It is often useful to divide the speed of the derivative computation by the speed of the function evaluation in $code double$$.) $subhead profile$$ In the special case where $icode package$$ is $code profile$$, the CppAD package is compiled and run with profiling to aid in determining where it is spending most of its time. $head test$$ It the argument $icode test$$ specifies which test to run and has the following possible values: $cref/correct/speed_main/test/correct/$$, $cref/speed/speed_main/test/speed/$$, $cref/det_minor/link_det_minor/$$, $cref/det_lu/link_det_lu/$$, $cref/mat_mul/link_mat_mul/$$, $cref/ode/link_ode/$$, $cref/poly/link_poly/$$, $cref/sparse_hessian/link_sparse_hessian/$$, $cref/sparse_jacobian/link_sparse_jacobian/$$. You can experiment with changing the implementation of a particular test for a particular package. $subhead correct$$ If $icode test$$ is equal to $code correct$$, all of the correctness tests are run. $subhead speed$$ If $icode test$$ is equal to $code speed$$, all of the speed tests are run. $head seed$$ The command line argument $icode seed$$ is a positive integer. The random number simulator $cref uniform_01$$ is initialized with the call $codei% uniform_01(%seed%) %$$ before any of the testing routines (listed above) are called. $head Global Options$$ This global variable has prototype $srccode%cpp% extern std::map global_option; %$$ This is true for each option that follows $icode seed$$. The order of the options does not matter and the list can be empty. Each option, must be separate command line argument to the main program. The documentation below specifics how CppAD uses these options, see the examples in $cref speed_adolc$$ for how another package might uses these options. $subhead onetape$$ If the option $code onetape$$ is present, $codep global_option["onetape"] $$ is true and otherwise it is false. If this external symbol is true, CppAD will use one taping of the operation sequence for all the repetitions of that speed test. Otherwise, the $cref/operation sequence/glossary/Operation/Sequence/$$ will be retaped for each test repetition. $pre $$ All of the tests, except $cref/det_lu/link_det_lu/$$, have a fixed operations sequence. The operation sequence for $code det_lu$$ may be different for each repetition of the test because it depends on the matrix for which the determinant is being calculated. For this reason, the CppAD test $cref cppad_det_lu.cpp$$ returns false (indicating that the test not implemented) when $code global_onetape$$ is true. $subhead optimize$$ If the option $code optimize$$ is present, $codep global_option["optimize"] $$ is true and otherwise it is false. If this external symbol is true, CppAD will optimize the operation sequence before doing computations. If it is false, this optimization will not be done. $subhead atomic$$ If the option $code atomic$$ is present, $codep global_option["atomic"] $$ is true and otherwise it is false. If this external symbol is true, CppAD will use its user defined $cref/atomic/atomic_base/$$ operation is used for the test. If no such atomic operation exists, and atomic is chosen, CppAD returns false for the test. $subhead memory$$ If the option $code memory$$ is present, $codep global_option["memory"] $$ is true and otherwise it is false. If it is true, the CppAD $cref/hold_memory/ta_hold_memory/$$ routine will be called by the main program before any of the tests are executed. This should make the CppAD $code thread_alloc$$ allocator faster. If it is false, CppAD will used standard memory allocation. $head Sparsity Options$$ The following options only apply to the $cref/sparse_jacobian/link_sparse_jacobian/$$ and $cref/sparse_hessian/link_sparse_hessian/$$ tests. The other tests will ignore these options: $subhead boolsparsity$$ If the option $code boolsparsity$$ is present, $codep global_option["boolsparsity"] $$ is true and otherwise it is false. If it is true, CppAD will use a $cref/vector of bool/glossary/Sparsity Pattern/Vector of Boolean/$$ for its sparsity patterns. Otherwise it will use a $cref/vector of sets/glossary/Sparsity Pattern/Vector of Sets/$$. $subhead revsparsity$$ If the option $code revsparsity$$ is present, $codep global_option["revsparsity"] $$ is true and otherwise it is false. If it is true, CppAD will use a $cref ForSparseJac$$ and $cref ForSparseHes$$ where possible for its sparsity patterns. Otherwise it will use $cref RevSparseJac$$ and $cref RevSparseHes$$. $subhead colpack$$ If the option $code colpack$$ is present, $codep global_option["colpack"] $$ is true and otherwise it is false. If this external symbol is true, CppAD will use $cref/colpack/colpack_prefix/$$ to do the coloring for its Otherwise, it will use it's own coloring algorithm. $head Correctness Results$$ One, but not both, of the following two output lines $codei% %package%_%test%_%optionlist%_available = false %package%_%test%_%optionlist%_ok = %flag% %$$ is generated for each correctness test where $icode package$$ and $icode test$$ are as above, $icode optionlist$$ are the options (in $icode option_list$$) separated by the underbar $code _$$ character (whereas they are separated by spaces in $icode option_list$$), and $icode flag$$ is $code true$$ or $code false$$. $head Speed Results$$ For each speed test, corresponds to three lines of the following form are generated: $codei% %package%_%test%_%optionlist%_ok = %flag% %package%_%test%_size = [ %size_1%, %...%, %size_n% ] %package%_%test%_rate = [ %rate_1%, %...%, %rate_n% ] %$$ The values $icode package$$, $icode test$$, $icode optionlist$$, and $icode flag$$ are as in the correctness results above. The values $icode size_1$$, ..., $icode size_n$$ are the size arguments used for the corresponding tests. The values $icode rate_1$$, ..., $icode rate_n$$ are the number of times per second that the corresponding size problem executed. $subhead n_sweep$$ The $cref/sparse_jacobian/link_sparse_jacobian/$$ and $cref/sparse_hessian/link_sparse_hessian/$$ tests has an extra output line with the following form $codei% %package%_sparse_%test%_n_sweep = [ %n_sweep_1%, %...%, %n_sweep_n% ] %$$ were $icode test$$ is $code jacobian$$ ($code hessian$$). The values $icode n_sweep_1$$, ..., $icode n_sweep_n$$ are the number of sweeps (colors) used for each sparse Jacobian (Hessian) calculation; see $icode n_sweep$$ for $cref/sparse_jacobian/sparse_jacobian/n_sweep/$$ and $cref/sparse_hessian/sparse_hessian/n_sweep/$$. $children% speed/src/link_det_lu.cpp% speed/src/link_det_minor.cpp% speed/src/link_mat_mul.cpp% speed/src/link_ode.cpp% speed/src/link_poly.cpp% speed/src/link_sparse_hessian.cpp% speed/src/link_sparse_jacobian.cpp% speed/src/microsoft_timer.cpp %$$ $head Link Functions$$ Each $cref/package/speed_main/package/$$ defines it's own version of one of the link functions listed below. Each of these functions links this main program to the corresponding test: $table $rref link_det_lu$$ $rref link_det_minor$$ $rref link_mat_mul$$ $rref link_ode$$ $rref link_poly$$ $rref link_sparse_hessian$$ $rref link_sparse_jacobian$$ $tend $end ----------------------------------------------------------------------------- */ // external routines # define CPPAD_DECLARE_SPEED(name) \ extern bool available_##name(void); \ extern bool correct_##name(bool is_package_double); \ extern void speed_##name(size_t size, size_t repeat) CPPAD_DECLARE_SPEED(det_lu); CPPAD_DECLARE_SPEED(det_minor); CPPAD_DECLARE_SPEED(mat_mul); CPPAD_DECLARE_SPEED(ode); CPPAD_DECLARE_SPEED(poly); CPPAD_DECLARE_SPEED(sparse_hessian); CPPAD_DECLARE_SPEED(sparse_jacobian); // info is different for each test extern void info_sparse_jacobian(size_t size, size_t& n_sweep); extern void info_sparse_hessian(size_t size, size_t& n_sweep); // -------------------------------------------------------------------------- std::map global_option; // -------------------------------------------------------------------------- namespace { using std::cout; using std::endl; const char* option_list[] = { "onetape", "optimize", "atomic", "memory", "boolsparsity", "revsparsity", "colpack", }; size_t num_option = sizeof(option_list) / sizeof( option_list[0] ); // ---------------------------------------------------------------- // not available test message void not_available_message(const char* test_name) { cout << AD_PACKAGE << ": " << test_name; cout << " is not availabe with " << endl; for(size_t i = 0; i < num_option; i++) { std::string option = option_list[i]; cout << option << " = " << global_option[option] << endl; } } // ------------------------------------------------------ // output vector in form readable by octave or matlab // convert size_t to int to avoid warning by MS compiler void output(const CppAD::vector &v) { size_t i= 0, n = v.size(); cout << "[ "; while(i < n) { cout << int(v[i++]); if( i < n ) cout << ", "; } cout << " ]"; } // ---------------------------------------------------------------- // function that runs one correctness case static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool run_correct( bool available_case(void) , bool correct_case(bool) , const char *case_name ) { bool available = available_case(); bool ok = true; if( available ) { # ifdef CPPAD_DOUBLE_SPEED ok = correct_case(true); # else ok = correct_case(false); # endif } cout << AD_PACKAGE << "_" << case_name; for(size_t i = 0; i < num_option; i++) { std::string option = option_list[i]; if( global_option[option] ) cout << "_" << option; } if( ! available ) { cout << "_available = false" << endl; return ok; } cout << "_ok = "; if( ok ) { cout << " true" << endl; Run_ok_count++; } else { cout << " false" << endl; Run_error_count++; } return ok; } // ---------------------------------------------------------------- // function that runs one speed case void run_speed( void speed_case(size_t size, size_t repeat) , const CppAD::vector& size_vec , const std::string& case_name ) { double time_min = 1.; cout << AD_PACKAGE << "_" << case_name << "_size = "; output(size_vec); cout << endl; cout << AD_PACKAGE << "_" << case_name << "_rate = "; cout << std::fixed; for(size_t i = 0; i < size_vec.size(); i++) { if( i == 0 ) cout << "[ "; else cout << ", "; cout << std::flush; size_t size = size_vec[i]; double time = CppAD::time_test(speed_case, time_min, size); double rate = 1. / time; if( rate >= 1000 ) cout << std::setprecision(0) << rate; else cout << std::setprecision(2) << rate; } cout << " ]" << endl; // // free statically allocated memory (size = repeat = 0) speed_case(0, 0); return; } } // main program that runs all the tests int main(int argc, char *argv[]) { bool ok = true; enum test_enum { test_correct, test_speed, test_det_lu, test_det_minor, test_mat_mul, test_ode, test_poly, test_sparse_hessian, test_sparse_jacobian, test_error }; struct test_struct { const char *name; const test_enum index; }; const test_struct test_list[]= { { "correct", test_correct }, { "speed", test_speed }, { "det_lu", test_det_lu }, { "det_minor", test_det_minor }, { "mat_mul", test_mat_mul }, { "ode", test_ode }, { "poly", test_poly }, { "sparse_hessian", test_sparse_hessian }, { "sparse_jacobian", test_sparse_jacobian } }; const size_t n_test = sizeof(test_list) / sizeof(test_list[0]); test_enum match = test_error; int iseed = 0; bool error = argc < 3; if( ! error ) { for(size_t i = 0; i < n_test; i++) if( strcmp(test_list[i].name, argv[1]) == 0 ) match = test_list[i].index; error = match == test_error; iseed = std::atoi( argv[2] ); error |= iseed < 0; for(size_t i = 0; i < num_option; i++) global_option[ option_list[i] ] = false; for(size_t i = 3; i < size_t(argc); i++) { error = true; for(size_t j = 0; j < num_option; j++) { if( strcmp(argv[i], option_list[j]) == 0 ) { global_option[ option_list[j] ] = true; error = false; } } } } if( error ) { cout << "usage: ./speed_" << AD_PACKAGE << " test seed option_list" << endl; cout << "test choices: " << endl; for(size_t i = 0; i < n_test; i++) cout << "\t" << test_list[i].name << endl; cout << "seed: is a positive integer used as a random seed." << endl; cout << "option: is zero, one or more of the following:" << endl; for(size_t i = 0; i < num_option; i++) cout << " " << option_list[i]; cout << endl << endl; return 1; } if( global_option["memory"] ) CppAD::thread_alloc::hold_memory(true); // initialize the random number simulator CppAD::uniform_01(size_t(iseed)); // arguments needed for speed tests size_t n_size = 5; CppAD::vector size_det_lu(n_size); CppAD::vector size_det_minor(n_size); CppAD::vector size_mat_mul(n_size); CppAD::vector size_ode(n_size); CppAD::vector size_poly(n_size); CppAD::vector size_sparse_hessian(n_size); CppAD::vector size_sparse_jacobian(n_size); for(size_t i = 0; i < n_size; i++) { size_det_minor[i] = i + 1; size_det_lu[i] = 10 * i + 1; size_mat_mul[i] = 10 * i + 1; size_ode[i] = 10 * i + 1; size_poly[i] = 10 * i + 1; size_sparse_hessian[i] = 150 * (i + 1) * (i + 1); size_sparse_jacobian[i] = 150 * (i + 1) * (i + 1); } switch(match) { // run all the correctness tests case test_correct: ok &= run_correct( available_det_lu, correct_det_lu, "det_lu" ); ok &= run_correct( available_det_minor, correct_det_minor, "det_minor" ); ok &= run_correct( available_mat_mul, correct_mat_mul, "mat_mul" ); ok &= run_correct( available_ode, correct_ode, "ode" ); ok &= run_correct( available_poly, correct_poly, "poly" ); ok &= run_correct( available_sparse_hessian, correct_sparse_hessian, "sparse_hessian" ); ok &= run_correct( available_sparse_jacobian, correct_sparse_jacobian, "sparse_jacobian" ); // summarize results assert( ok || (Run_error_count > 0) ); if( ok ) { cout << "All " << int(Run_ok_count) << " correctness tests passed." << endl; } else { cout << int(Run_error_count) << " correctness tests failed." << endl; } break; // --------------------------------------------------------- // run all the speed tests case test_speed: if( available_det_lu() ) run_speed( speed_det_lu, size_det_lu, "det_lu" ); if( available_det_minor() ) run_speed( speed_det_minor, size_det_minor, "det_minor" ); if( available_mat_mul() ) run_speed( speed_mat_mul, size_mat_mul, "mat_mul" ); if( available_ode() ) run_speed( speed_ode, size_ode, "ode" ); if( available_poly() ) run_speed( speed_poly, size_poly, "poly" ); if( available_sparse_hessian() ) run_speed( speed_sparse_hessian, size_sparse_hessian, "sparse_hessian" ); if( available_sparse_jacobian() ) run_speed( speed_sparse_jacobian, size_sparse_jacobian, "sparse_jacobian" ); ok = true; break; // --------------------------------------------------------- case test_det_lu: if( ! available_det_lu() ) { not_available_message( argv[1] ); exit(1); } ok &= run_correct( available_det_lu, correct_det_lu, "det_lu") ; run_speed(speed_det_lu, size_det_lu, "det_lu"); break; // --------------------------------------------------------- case test_det_minor: if( ! available_det_minor() ) { not_available_message( argv[1] ); exit(1); } ok &= run_correct( available_det_minor, correct_det_minor, "det_minor" ); run_speed(speed_det_minor, size_det_minor, "det_minor"); break; // --------------------------------------------------------- case test_mat_mul: if( ! available_mat_mul() ) { not_available_message( argv[1] ); exit(1); } ok &= run_correct( available_mat_mul, correct_mat_mul, "mat_mul" ); run_speed(speed_mat_mul, size_mat_mul, "mat_mul"); break; // --------------------------------------------------------- case test_ode: if( ! available_ode() ) { not_available_message( argv[1] ); exit(1); } ok &= run_correct( available_ode, correct_ode, "ode" ); run_speed(speed_ode, size_ode, "ode"); break; // --------------------------------------------------------- case test_poly: if( ! available_poly() ) { not_available_message( argv[1] ); exit(1); } ok &= run_correct( available_poly, correct_poly, "poly" ); run_speed(speed_poly, size_poly, "poly"); break; // --------------------------------------------------------- case test_sparse_hessian: if( ! available_sparse_hessian() ) { not_available_message( argv[1] ); exit(1); } ok &= run_correct( available_sparse_hessian, correct_sparse_hessian, "sparse_hessian" ); run_speed( speed_sparse_hessian, size_sparse_hessian, "sparse_hessian" ); cout << AD_PACKAGE << "_sparse_hessian_sweep = "; for(size_t i = 0; i < size_sparse_hessian.size(); i++) { if( i == 0 ) cout << "[ "; else cout << ", "; size_t n_sweep; info_sparse_hessian(size_sparse_hessian[i], n_sweep); cout << n_sweep; } cout << " ]" << endl; break; // --------------------------------------------------------- case test_sparse_jacobian: if( ! available_sparse_jacobian() ) { not_available_message( argv[1] ); exit(1); } ok &= run_correct( available_sparse_jacobian, correct_sparse_jacobian, "sparse_jacobian" ); run_speed( speed_sparse_jacobian, size_sparse_jacobian, "sparse_jacobian" ); cout << AD_PACKAGE << "_sparse_jacobian_n_sweep = "; for(size_t i = 0; i < size_sparse_jacobian.size(); i++) { if( i == 0 ) cout << "[ "; else cout << ", "; size_t n_sweep; info_sparse_jacobian(size_sparse_jacobian[i], n_sweep); cout << n_sweep; } cout << " ]" << endl; break; // --------------------------------------------------------- default: assert(0); } # ifndef NDEBUG // return memory for vectors that are still in scope size_det_lu.clear(); size_det_minor.clear(); size_mat_mul.clear(); size_ode.clear(); size_poly.clear(); size_sparse_hessian.clear(); size_sparse_jacobian.clear(); // check for memory leak if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Memory leak detected" << endl; } # endif return static_cast( ! ok ); } cppad-20170000.3/speed/cppad/0002755000175200017650000000000013057470456014626 5ustar coincoin-webcppad-20170000.3/speed/cppad/poly.cpp0000644000175200017650000000772213057470456016323 0ustar coincoin-web// $Id: poly.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_poly.cpp$$ $spell onetape coef ddp ADScalar dz ddz Taylor vector Vector typedef cppad Lu CppAD det hpp const CPPAD_TESTVECTOR bool var std cout endl $$ $section CppAD Speed: Second Derivative of a Polynomial$$ $mindex link_poly speed$$ $head Specifications$$ See $cref link_poly$$. $head Implementation$$ $srccode%cpp% */ # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_poly( size_t size , size_t repeat , CppAD::vector &a , // coefficients of polynomial CppAD::vector &z , // polynomial argument value CppAD::vector &ddp ) // second derivative w.r.t z { // speed test global option values if( global_option["atomic"] ) return false; // optimization options: no conditional skips or compare operators std::string options="no_compare_op"; // ----------------------------------------------------- // setup typedef CppAD::AD ADScalar; typedef CppAD::vector ADVector; size_t i; // temporary index size_t m = 1; // number of dependent variables size_t n = 1; // number of independent variables ADVector Z(n); // AD domain space vector ADVector P(m); // AD range space vector // choose the polynomial coefficients CppAD::uniform_01(size, a); // AD copy of the polynomial coefficients ADVector A(size); for(i = 0; i < size; i++) A[i] = a[i]; // forward mode first and second differentials CppAD::vector p(1), dp(1), dz(1), ddz(1); dz[0] = 1.; ddz[0] = 0.; // AD function object CppAD::ADFun f; // -------------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose an argument value CppAD::uniform_01(1, z); Z[0] = z[0]; // declare independent variables Independent(Z); // AD computation of the function value P[0] = CppAD::Poly(0, A, Z[0]); // create function object f : A -> detA f.Dependent(Z, P); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // pre-allocate memory for three forward mode calculations f.capacity_order(3); // evaluate the polynomial p = f.Forward(0, z); // evaluate first order Taylor coefficient dp = f.Forward(1, dz); // second derivative is twice second order Taylor coef ddp = f.Forward(2, ddz); ddp[0] *= 2.; } else { // choose an argument value CppAD::uniform_01(1, z); Z[0] = z[0]; // declare independent variables Independent(Z); // AD computation of the function value P[0] = CppAD::Poly(0, A, Z[0]); // create function object f : A -> detA f.Dependent(Z, P); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); while(repeat--) { // sufficient memory is allocated by second repetition // get the next argument value CppAD::uniform_01(1, z); // evaluate the polynomial at the new argument value p = f.Forward(0, z); // evaluate first order Taylor coefficient dp = f.Forward(1, dz); // second derivative is twice second order Taylor coef ddp = f.Forward(2, ddz); ddp[0] *= 2.; } } return true; } /* %$$ $end */ cppad-20170000.3/speed/cppad/sparse_jacobian.cpp0000644000175200017650000001343313057470456020457 0ustar coincoin-web// $Id: sparse_jacobian.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_sparse_jacobian.cpp$$ $spell const ifdef ifndef colpack boolsparsity namespace onetape work work jac CppAD cppad hpp bool typedef endif tmp std var cout endl Jacobian Fp $$ $section CppAD Speed: Sparse Jacobian$$ $mindex link_sparse_jacobian speed$$ $head Specifications$$ See $cref link_sparse_jacobian$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; namespace { using CppAD::vector; typedef vector< std::set > SetVector; typedef vector BoolVector; void calc_sparsity(SetVector& sparsity_set, CppAD::ADFun& f) { bool reverse = global_option["revsparsity"]; size_t q; if( reverse ) q = f.Range(); else q = f.Domain(); // SetVector r_set(q); for(size_t j = 0; j < q; j++) r_set[j].insert(j); if( reverse ) sparsity_set = f.RevSparseJac(q, r_set); else sparsity_set = f.ForSparseJac(q, r_set); } void calc_sparsity(BoolVector& sparsity_bool, CppAD::ADFun& f) { bool reverse = global_option["revsparsity"]; size_t q; if( reverse ) q = f.Range(); else q = f.Domain(); // BoolVector r_bool(q * q); for(size_t i = 0; i < q; i++) { for(size_t j = 0; j < q; j++) r_bool[ i * q + j] = i == j; } if( reverse ) sparsity_bool = f.RevSparseJac(q, r_bool); else sparsity_bool = f.ForSparseJac(q, r_bool); } } bool link_sparse_jacobian( size_t size , size_t repeat , size_t m , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& jacobian , size_t& n_sweep ) { if( global_option["atomic"] ) return false; # if ! CPPAD_HAS_COLPACK if( global_option["colpack"] ) return false; # endif // optimization options: no conditional skips or compare operators std::string options="no_compare_op"; // ----------------------------------------------------- // setup typedef vector< std::set > SetVector; typedef CppAD::AD ADScalar; typedef CppAD::vector ADVector; size_t j; size_t order = 0; // derivative order corresponding to function size_t n = size; // number of independent variables ADVector a_x(n); // AD domain space vector ADVector a_y(m); // AD range space vector y = g(x) CppAD::ADFun f; // AD function object // declare sparsity pattern SetVector set_sparsity(m); BoolVector bool_sparsity(m * n); // ------------------------------------------------------ if( ! global_option["onetape"] ) while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); for(j = 0; j < n; j++) a_x[j] = x[j]; // declare independent variables Independent(a_x); // AD computation of f (x) CppAD::sparse_jac_fun(m, n, a_x, row, col, order, a_y); // create function object f : X -> Y f.Dependent(a_x, a_y); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // calculate the Jacobian sparsity pattern for this function if( global_option["boolsparsity"] ) calc_sparsity(bool_sparsity, f); else calc_sparsity(set_sparsity, f); // structure that holds some of the work done by SparseJacobian CppAD::sparse_jacobian_work work; # if CPPAD_HAS_COLPACK if( global_option["colpack"] ) work.color_method = "colpack"; # endif // calculate the Jacobian at this x // (use forward mode because m > n ?) if( global_option["boolsparsity"]) n_sweep = f.SparseJacobianForward( x, bool_sparsity, row, col, jacobian, work ); else n_sweep = f.SparseJacobianForward( x, set_sparsity, row, col, jacobian, work ); } else { // choose a value for x CppAD::uniform_01(n, x); for(j = 0; j < n; j++) a_x[j] = x[j]; // declare independent variables Independent(a_x); // AD computation of f (x) CppAD::sparse_jac_fun(m, n, a_x, row, col, order, a_y); // create function object f : X -> Y f.Dependent(a_x, a_y); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // calculate the Jacobian sparsity pattern for this function if( global_option["boolsparsity"] ) calc_sparsity(bool_sparsity, f); else calc_sparsity(set_sparsity, f); // structure that holds some of the work done by SparseJacobian CppAD::sparse_jacobian_work work; # if CPPAD_HAS_COLPACK if( global_option["colpack"] ) work.color_method = "colpack"; # endif while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); // calculate the Jacobian at this x // (use forward mode because m > n ?) if( global_option["boolsparsity"] ) n_sweep = f.SparseJacobianForward( x, bool_sparsity, row, col, jacobian, work ); else n_sweep = f.SparseJacobianForward( x, set_sparsity, row, col, jacobian, work ); } } return true; } /* %$$ $end */ cppad-20170000.3/speed/cppad/ode.cpp0000644000175200017650000000615713057470456016110 0ustar coincoin-web// $Id: ode.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_ode.cpp$$ $spell jacobian jacobian endif var Jacobian std cout endl CppAD cppad hpp bool onetape typedef cassert $$ $section CppAD Speed: Gradient of Ode Solution$$ $mindex link_ode speed$$ $head Specifications$$ See $cref link_ode$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_ode( size_t size , size_t repeat , CppAD::vector &x , CppAD::vector &jacobian ) { // speed test global option values if( global_option["atomic"] ) return false; // optimization options: no conditional skips or compare operators std::string options="no_compare_op"; // -------------------------------------------------------------------- // setup assert( x.size() == size ); assert( jacobian.size() == size * size ); typedef CppAD::AD ADScalar; typedef CppAD::vector ADVector; size_t j; size_t p = 0; // use ode to calculate function values size_t n = size; // number of independent variables size_t m = n; // number of dependent variables ADVector X(n), Y(m); // independent and dependent variables CppAD::ADFun f; // AD function // ------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose next x value uniform_01(n, x); for(j = 0; j < n; j++) X[j] = x[j]; // declare the independent variable vector Independent(X); // evaluate function CppAD::ode_evaluate(X, p, Y); // create function object f : X -> Y f.Dependent(X, Y); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); jacobian = f.Jacobian(x); } else { // an x value uniform_01(n, x); for(j = 0; j < n; j++) X[j] = x[j]; // declare the independent variable vector Independent(X); // evaluate function CppAD::ode_evaluate(X, p, Y); // create function object f : X -> Y f.Dependent(X, Y); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); while(repeat--) { // get next argument value uniform_01(n, x); // evaluate jacobian jacobian = f.Jacobian(x); } } return true; } /* %$$ $end */ cppad-20170000.3/speed/cppad/sparse_hessian.cpp0000644000175200017650000001422213057470456020340 0ustar coincoin-web// $Id: sparse_hessian.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_sparse_hessian.cpp$$ $spell ifdef ifndef colpack boolsparsity namespace Jac onetape work work const hes CppAD cppad hpp bool typedef endif tmp std var cout endl $$ $section CppAD Speed: Sparse Hessian$$ $mindex link_sparse_hessian speed$$ $head Specifications$$ See $cref link_sparse_hessian$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; namespace { using CppAD::vector; typedef vector< std::set > SetVector; typedef vector BoolVector; void calc_sparsity(SetVector& sparsity_set, CppAD::ADFun& f) { size_t n = f.Domain(); size_t m = f.Range(); CPPAD_ASSERT_UNKNOWN( m == 1 ); // SetVector s_set(m); s_set[0].insert(0); // if( global_option["revsparsity"] ) { SetVector r_set(n); for(size_t i = 0; i < n; i++) r_set[i].insert(i); f.ForSparseJac(n, r_set); sparsity_set = f.RevSparseHes(n, s_set); } else { SetVector r_set(1); for(size_t i = 0; i < n; i++) r_set[0].insert(i); sparsity_set = f.ForSparseHes(r_set, s_set); } } void calc_sparsity(BoolVector& sparsity_bool, CppAD::ADFun& f) { size_t n = f.Domain(); size_t m = f.Range(); CPPAD_ASSERT_UNKNOWN( m == 1 ); // BoolVector s_bool(m); s_bool[0] = true; // if( global_option["revsparsity"] ) { BoolVector r_bool(n * n); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n; j++) r_bool[ i * n + j] = i == j; } f.ForSparseJac(n, r_bool); sparsity_bool = f.RevSparseHes(n, s_bool); } else { BoolVector r_bool(n); for(size_t i = 0; i < n; i++) r_bool[i] = true; sparsity_bool = f.ForSparseHes(r_bool, s_bool); } } } bool link_sparse_hessian( size_t size , size_t repeat , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& hessian , size_t& n_sweep ) { if( global_option["atomic"] ) return false; # if ! CPPAD_HAS_COLPACK if( global_option["colpack"] ) return false; # endif // optimization options: no conditional skips or compare operators std::string options="no_compare_op"; // ----------------------------------------------------- // setup typedef vector DblVector; typedef vector< std::set > SetVector; typedef CppAD::AD ADScalar; typedef vector ADVector; size_t j; size_t order = 0; // derivative order corresponding to function size_t m = 1; // number of dependent variables size_t n = size; // number of independent variables ADVector a_x(n); // AD domain space vector ADVector a_y(m); // AD range space vector DblVector w(m); // double range space vector CppAD::ADFun f; // AD function object // weights for hessian calculation (only one component of f) w[0] = 1.; // declare sparsity pattern SetVector set_sparsity(n); BoolVector bool_sparsity(n * n); // ------------------------------------------------------ if( ! global_option["onetape"] ) while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); for(j = 0; j < n; j++) a_x[j] = x[j]; // declare independent variables Independent(a_x); // AD computation of f(x) CppAD::sparse_hes_fun(n, a_x, row, col, order, a_y); // create function object f : X -> Y f.Dependent(a_x, a_y); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // calculate the Hessian sparsity pattern for this function if( global_option["boolsparsity"] ) calc_sparsity(bool_sparsity, f); else calc_sparsity(set_sparsity, f); // structure that holds some of work done by SparseHessian CppAD::sparse_hessian_work work; # if CPPAD_HAS_COLPACK if( global_option["colpack"] ) work.color_method = "colpack.star"; # endif // calculate this Hessian at this x if( global_option["boolsparsity"]) n_sweep = f.SparseHessian( x, w, bool_sparsity, row, col, hessian, work ); else n_sweep = f.SparseHessian( x, w, set_sparsity, row, col, hessian, work ); } else { // choose a value for x CppAD::uniform_01(n, x); for(j = 0; j < n; j++) a_x[j] = x[j]; // declare independent variables Independent(a_x); // AD computation of f(x) CppAD::sparse_hes_fun(n, a_x, row, col, order, a_y); // create function object f : X -> Y f.Dependent(a_x, a_y); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // calculate the Hessian sparsity pattern for this function if( global_option["boolsparsity"]) calc_sparsity(bool_sparsity, f); else calc_sparsity(set_sparsity, f); // declare structure that holds some of work done by SparseHessian CppAD::sparse_hessian_work work; # if CPPAD_HAS_COLPACK if( global_option["colpack"] ) work.color_method = "colpack.star"; # endif while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); // calculate hessian at this x if( global_option["boolsparsity"] ) n_sweep = f.SparseHessian( x, w, bool_sparsity, row, col, hessian, work ); else n_sweep = f.SparseHessian( x, w, set_sparsity, row, col, hessian, work ); } } return true; } /* %$$ $end */ cppad-20170000.3/speed/cppad/makefile.am0000644000175200017650000000302013057470456016713 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # # Copy source file so that main.o does not end up in parent directory BUILT_SOURCES = main.cpp main.cpp: cp $(srcdir)/../main.cpp main.cpp # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = speed_cppad # AM_CPPFLAGS = -I$(top_srcdir) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) # # BEGIN OPTIMIZE AM_CXXFLAGS = -O2 -DNDEBUG -DCPPAD_CPPAD_SPEED $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) -DCPPAD_CPPAD_SPEED # END DEBUG # LDADD = -lspeed AM_LDFLAGS = -L../src # speed_cppad_SOURCES = \ main.cpp \ det_lu.cpp \ det_minor.cpp \ mat_mul.cpp \ ode.cpp \ poly.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp test: check ./speed_cppad correct 123 ./speed_cppad correct 123 onetape ./speed_cppad correct 123 optimize ./speed_cppad correct 123 atomic ./speed_cppad correct 123 memory ./speed_cppad correct 123 boolsparsity cppad-20170000.3/speed/cppad/CMakeLists.txt0000644000175200017650000000356713057470456017377 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the speed/cppad directory tests # Inherit build type environment from ../CMakeList.txt # Adds flags to the compiler command line for sources in the current directory # and below. This command can be used to add any flags, but it was originally # intended to add preprocessor definitions. ADD_DEFINITIONS("-DCPPAD_CPPAD_SPEED") # Local include directories to search (not in package_prefix/includdir) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/../src ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(speed_cppad EXCLUDE_FROM_ALL ../main.cpp det_lu.cpp det_minor.cpp mat_mul.cpp ode.cpp poly.cpp sparse_hessian.cpp sparse_jacobian.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( speed_cppad ) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES(speed_cppad speed_src ${cppad_lib} ${colpack_libs} ) # Add the check_speed_cppad target ADD_CUSTOM_TARGET(check_speed_cppad speed_cppad correct 54321 DEPENDS speed_cppad speed_src ) MESSAGE(STATUS "make check_speed_cppad: available") # Change check depends in parent environment add_to_list(check_speed_depends check_speed_cppad) SET(check_speed_depends "${check_speed_depends}" PARENT_SCOPE) cppad-20170000.3/speed/cppad/det_lu.cpp0000644000175200017650000000542713057470456016614 0ustar coincoin-web// $Id: det_lu.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_det_lu.cpp$$ $spell onetape bool CppAD vector Vector typedef Lu cppad det hpp const srand var std cout endl $$ $section CppAD Speed: Gradient of Determinant Using Lu Factorization$$ $mindex link_det_lu speed matrix factor$$ $head Specifications$$ See $cref link_det_lu$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_det_lu( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ) { // speed test global option values if( global_option["onetape"] || global_option["atomic"] ) return false; // optimization options: no conditional skips or compare operators std::string options="no_compare_op"; // ----------------------------------------------------- // setup typedef CppAD::AD ADScalar; typedef CppAD::vector ADVector; CppAD::det_by_lu Det(size); size_t i; // temporary index size_t m = 1; // number of dependent variables size_t n = size * size; // number of independent variables ADVector A(n); // AD domain space vector ADVector detA(m); // AD range space vector CppAD::ADFun f; // AD function object // vectors of reverse mode weights CppAD::vector w(1); w[0] = 1.; // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, matrix); for( i = 0; i < n; i++) A[i] = matrix[i]; // declare independent variables Independent(A); // AD computation of the determinant detA[0] = Det(A); // create function object f : A -> detA f.Dependent(A, detA); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // evaluate and return gradient using reverse mode f.Forward(0, matrix); gradient = f.Reverse(1, w); } return true; } /* %$$ $end */ cppad-20170000.3/speed/cppad/mat_mul.cpp0000644000175200017650000001061713057470456016773 0ustar coincoin-web// $Id: mat_mul.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_mat_mul.cpp$$ $spell resize nr nc cppad mul hpp bool onetape sq var std::cout endl CppAD dz typedef boolsparsity enum $$ $section CppAD Speed, Matrix Multiplication$$ $mindex link_mat_mul multiply$$ $head Specifications$$ See $cref link_mat_mul$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_mat_mul( size_t size , size_t repeat , CppAD::vector& x , CppAD::vector& z , CppAD::vector& dz ) { // optimization options: no conditional skips or compare operators std::string options="no_compare_op"; // ----------------------------------------------------- // setup typedef CppAD::AD ADScalar; typedef CppAD::vector ADVector; size_t j; // temporary index size_t m = 1; // number of dependent variables size_t n = size * size; // number of independent variables ADVector X(n); // AD domain space vector ADVector Y(n); // Store product matrix ADVector Z(m); // AD range space vector CppAD::ADFun f; // AD function object // vectors of reverse mode weights CppAD::vector w(1); w[0] = 1.; // user atomic information CppAD::vector ax(3 + 2 * n), ay(n); atomic_mat_mul atom_mul; // if( global_option["boolsparsity"] ) atom_mul.option( CppAD::atomic_base::pack_sparsity_enum ); else atom_mul.option( CppAD::atomic_base::set_sparsity_enum ); // ------------------------------------------------------ if( ! global_option["onetape"] ) while(repeat--) { // get the next matrix CppAD::uniform_01(n, x); for( j = 0; j < n; j++) X[j] = x[j]; // declare independent variables Independent(X); // do computations if( ! global_option["atomic"] ) mat_sum_sq(size, X, Y, Z); else { ax[0] = ADScalar( size ); // number of rows in left matrix ax[1] = ADScalar( size ); // rows in left and columns in right ax[2] = ADScalar( size ); // number of columns in right matrix for(j = 0; j < n; j++) { ax[3 + j] = X[j]; ax[3 + n + j] = X[j]; } // Y = X * X atom_mul(ax, ay); Z[0] = 0.; for(j = 0; j < n; j++) Z[0] += ay[j]; } // create function object f : X -> Z f.Dependent(X, Z); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // evaluate and return gradient using reverse mode z = f.Forward(0, x); dz = f.Reverse(1, w); } else { // get a next matrix CppAD::uniform_01(n, x); for(j = 0; j < n; j++) X[j] = x[j]; // declare independent variables Independent(X); // do computations if( ! global_option["atomic"] ) mat_sum_sq(size, X, Y, Z); else { for(j = 0; j < n; j++) { ax[j] = X[j]; ax[j+n] = X[j]; } // Y = X * X atom_mul(ax, ay); Z[0] = 0.; for(j = 0; j < n; j++) Z[0] += ay[j]; } // create function object f : X -> Z f.Dependent(X, Z); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); while(repeat--) { // get a next matrix CppAD::uniform_01(n, x); // evaluate and return gradient using reverse mode z = f.Forward(0, x); dz = f.Reverse(1, w); } } // -------------------------------------------------------------------- // Free temporary work space (any future atomic_mat_mul constructors // would create new temporary work space.) CppAD::user_atomic::clear(); return true; } /* %$$ $end */ cppad-20170000.3/speed/cppad/det_minor.cpp0000644000175200017650000000714213057470456017314 0ustar coincoin-web// $Id: det_minor.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_det_minor.cpp$$ $spell onetape vector Vector typedef cppad Lu CppAD det hpp const CPPAD_TESTVECTOR bool srand var std cout endl $$ $section CppAD Speed: Gradient of Determinant by Minor Expansion$$ $mindex link_det_minor speed$$ $head Specifications$$ See $cref link_det_minor$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_det_minor( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ) { // speed test global option values if( global_option["atomic"] ) return false; // optimization options: no conditional skips or compare operators std::string options="no_compare_op"; // ----------------------------------------------------- // setup // object for computing determinant typedef CppAD::AD ADScalar; typedef CppAD::vector ADVector; CppAD::det_by_minor Det(size); size_t i; // temporary index size_t m = 1; // number of dependent variables size_t n = size * size; // number of independent variables ADVector A(n); // AD domain space vector ADVector detA(m); // AD range space vector // vectors of reverse mode weights CppAD::vector w(1); w[0] = 1.; // the AD function object CppAD::ADFun f; // --------------------------------------------------------------------- if( ! global_option["onetape"] ) while(repeat--) { // choose a matrix CppAD::uniform_01(n, matrix); for( i = 0; i < size * size; i++) A[i] = matrix[i]; // declare independent variables Independent(A); // AD computation of the determinant detA[0] = Det(A); // create function object f : A -> detA f.Dependent(A, detA); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // evaluate the determinant at the new matrix value f.Forward(0, matrix); // evaluate and return gradient using reverse mode gradient = f.Reverse(1, w); } else { // choose a matrix CppAD::uniform_01(n, matrix); for( i = 0; i < size * size; i++) A[i] = matrix[i]; // declare independent variables Independent(A); // AD computation of the determinant detA[0] = Det(A); // create function object f : A -> detA f.Dependent(A, detA); if( global_option["optimize"] ) f.optimize(options); // skip comparison operators f.compare_change_count(0); // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, matrix); // evaluate the determinant at the new matrix value f.Forward(0, matrix); // evaluate and return gradient using reverse mode gradient = f.Reverse(1, w); } } return true; } /* %$$ $end */ cppad-20170000.3/speed/cppad/makefile.in0000644000175200017650000004767013057470456016747 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; the Free Software Foundation # gives unlimited permission to copy and/or distribute it, # with or without modifications, as long as this notice is preserved. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY, to the extent permitted by law; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin link_mat_mul$$ $spell mul bool CppAD dz $$ $section Speed Testing Derivative of Matrix Multiply$$ $mindex link_mat_mul test multiple$$ $head Prototype$$ $codei%extern bool link_mat_mul( size_t %size% , size_t %repeat% , CppAD::vector& %x% , CppAD::vector& %z% , CppAD::vector& %dz% ); %$$ $head Purpose$$ Each $cref/package/speed_main/package/$$ must define a version of this routine as specified below. This is used by the $cref speed_main$$ program to run the corresponding speed and correctness tests. $head Return Value$$ If this speed test is not yet supported by a particular $icode package$$, the corresponding return value for $code link_mat_mul$$ should be $code false$$. $head n$$ The argument $icode n$$ is the number of rows and columns in the square matrix $icode x$$. $head repeat$$ The argument $icode repeat$$ is the number of different argument values that the derivative of $icode z$$ (or just the value of $icode z$$) will be computed. $head x$$ The argument $icode x$$ is a vector with $icode%x%.size() = %size% * %size%$$ elements. The input value of its elements does not matter. The output value of its elements is the last random matrix that is multiplied and then summed to form $icode z$$; $latex \[ x_{i,j} = x[ i * s + j ] \] $$ where $icode%s% = %size%$$. $head z$$ The argument $icode z$$ is a vector with one element. The input value of the element does not matter. The output of its element the sum of the elements of $icode%y% = %x% * %x%$$; i.e., $latex \[ \begin{array}{rcl} y_{i,j} & = & \sum_{k=0}^{s-1} x_{i,k} x_{k, j} \\ z & = & \sum_{i=0}^{s-1} \sum_{j=0}^{s-1} y_{i,j} \end{array} \] $$ $head dz$$ The argument $icode dz$$ is a vector with $icode%dz%.size() = %size% * %size%$$. The input values of its elements do not matter. The output value of its elements form the derivative of $icode z$$ with respect to $icode x$$. $end ----------------------------------------------------------------------------- */ # include # include extern bool link_mat_mul( size_t size , size_t repeat , CppAD::vector& x , CppAD::vector& z , CppAD::vector& dz ); bool available_mat_mul(void) { size_t size = 2; size_t repeat = 1; CppAD::vector x(size * size), z(1), dz(size * size); return link_mat_mul(size, repeat, x, z, dz); } bool correct_mat_mul(bool is_package_double) { size_t size = 2; size_t repeat = 1; CppAD::vector x(size * size), z(1), dz(size * size); link_mat_mul(size, repeat, x, z, dz); double x00 = x[0 * size + 0]; double x01 = x[0 * size + 1]; double x10 = x[1 * size + 0]; double x11 = x[1 * size + 1]; bool ok = true; double check; if( is_package_double ) { check = 0; check += x00 * x00 + x01 * x10; // y00 check += x00 * x01 + x01 * x11; // y01 check += x10 * x00 + x11 * x10; // y10 check += x10 * x01 + x11 * x11; // y11 ok &= CppAD::NearEqual(check, z[0], 1e-10, 1e-10); return ok; } // partial w.r.t. x00 check = x00 + x00 + x01 + x10; ok &= CppAD::NearEqual(check, dz[0 * size + 0], 1e-10, 1e-10); // partial w.r.t. x01 check = x10 + x00 + x11 + x10; ok &= CppAD::NearEqual(check, dz[0 * size + 1], 1e-10, 1e-10); // partial w.r.t. x10 check = x01 + x00 + x11 + x01; ok &= CppAD::NearEqual(check, dz[1 * size + 0], 1e-10, 1e-10); // partial w.r.t. x11 check = x01 + x10 + x11 + x11; ok &= CppAD::NearEqual(check, dz[1 * size + 1], 1e-10, 1e-10); return ok; } void speed_mat_mul(size_t size, size_t repeat) { // free statically allocated memory if( size == 0 && repeat == 0 ) return; // CppAD::vector x(size * size), z(1), dz(size * size); link_mat_mul(size, repeat, x, z, dz); return; } cppad-20170000.3/speed/src/CMakeLists.txt0000644000175200017650000000227613057470456017073 0ustar coincoin-web# $Id: CMakeLists.txt 3853 2016-12-14 14:40:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the cppad_ipopt/src library # Inherit build type from ../CMakeList.txt # add_library( [STATIC | SHARED | MODULE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN) # ) # Make libspeed_src a static library because this is just for testing # and is not installed (do not have to worry about library search path). ADD_LIBRARY(speed_src STATIC EXCLUDE_FROM_ALL link_det_lu.cpp link_det_minor.cpp link_mat_mul.cpp link_ode.cpp link_poly.cpp link_sparse_hessian.cpp link_sparse_jacobian.cpp microsoft_timer.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( speed_src ) cppad-20170000.3/speed/src/link_det_minor.cpp0000644000175200017650000000716713057470456020040 0ustar coincoin-web// $Id: link_det_minor.cpp 3855 2016-12-19 00:30:54Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin link_det_minor$$ $spell det bool CppAD $$ $section Speed Testing Gradient of Determinant by Minor Expansion$$ $mindex link_det_minor test$$ $head Prototype$$ $codei%extern bool link_det_minor( size_t %size% , size_t %repeat% , CppAD::vector &%matrix% , CppAD::vector &%gradient% ); %$$ $head Purpose$$ Each $cref/package/speed_main/package/$$ must define a version of this routine as specified below. This is used by the $cref speed_main$$ program to run the corresponding speed and correctness tests. $head Method$$ The same template class $cref det_by_minor$$ is used by the different AD packages. $head Return Value$$ If this speed test is not yet supported by a particular $icode package$$, the corresponding return value for $code link_det_minor$$ should be $code false$$. $head size$$ The argument $icode size$$ is the number of rows and columns in the matrix. $head repeat$$ The argument $icode repeat$$ is the number of different matrices that the gradient (or determinant) is computed for. $head matrix$$ The argument $icode matrix$$ is a vector with $icode%size%*%size%$$ elements. The input value of its elements does not matter. The output value of its elements is the last matrix that the gradient (or determinant) is computed for. $head gradient$$ The argument $icode gradient$$ is a vector with $icode%size%*%size%$$ elements. The input value of its elements does not matter. The output value of its elements is the gradient of the determinant of $icode matrix$$ with respect to its elements. $subhead double$$ In the case where $icode package$$ is $code double$$, only the first element of $icode gradient$$ is used and it is actually the determinant value (the gradient value is not computed). $end ----------------------------------------------------------------------------- */ # include # include # include extern bool link_det_minor( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ); bool available_det_minor(void) { size_t size = 3; size_t repeat = 1; CppAD::vector matrix(size * size); CppAD::vector gradient(size * size); return link_det_minor(size, repeat, matrix, gradient); } bool correct_det_minor(bool is_package_double) { size_t size = 3; size_t repeat = 1; CppAD::vector matrix(size * size); CppAD::vector gradient(size * size); link_det_minor(size, repeat, matrix, gradient); bool ok = CppAD::det_grad_33(matrix, gradient); if( is_package_double ) ok = CppAD::det_33(matrix, gradient); else ok = CppAD::det_grad_33(matrix, gradient); return ok; } void speed_det_minor(size_t size, size_t repeat) { // free statically allocated memory if( size == 0 && repeat == 0 ) return; // CppAD::vector matrix(size * size); CppAD::vector gradient(size * size); link_det_minor(size, repeat, matrix, gradient); return; } cppad-20170000.3/speed/src/link_poly.cpp0000644000175200017650000000735013057470456017035 0ustar coincoin-web// $Id: link_poly.cpp 3855 2016-12-19 00:30:54Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin link_poly$$ $spell poly bool CppAD ddp $$ $section Speed Testing Second Derivative of a Polynomial$$ $mindex link_poly test$$ $head Prototype$$ $codei%extern bool link_poly( size_t %size% , size_t %repeat% , CppAD::vector &%a% , CppAD::vector &%z% , CppAD::vector &%ddp ); %$$ $head Purpose$$ Each $cref/package/speed_main/package/$$ must define a version of this routine as specified below. This is used by the $cref speed_main$$ program to run the corresponding speed and correctness tests. $head Method$$ The same template routine $cref Poly$$ is used by the different AD packages. $head Return Value$$ If this speed test is not yet supported by a particular $icode package$$, the corresponding return value for $code link_poly$$ should be $code false$$. $head size$$ The argument $icode size$$ is the order of the polynomial (the number of coefficients in the polynomial). $head repeat$$ The argument $icode repeat$$ is the number of different argument values that the second derivative (or just the polynomial) will be computed at. $head a$$ The argument $icode a$$ is a vector with $icode%size%$$ elements. The input value of its elements does not matter. The output value of its elements is the coefficients of the polynomial that is differentiated ($th i$$ element is coefficient of order $icode i$$). $head z$$ The argument $icode z$$ is a vector with one element. The input value of the element does not matter. The output of its element is the polynomial argument value were the last second derivative (or polynomial value) was computed. $head ddp$$ The argument $icode ddp$$ is a vector with one element. The input value of its element does not matter. The output value of its element is the second derivative of the polynomial with respect to it's argument value. $subhead double$$ In the case where $icode package$$ is $code double$$, the output value of the element of $icode ddp$$ is the polynomial value (the second derivative is not computed). $end ----------------------------------------------------------------------------- */ # include # include # include extern bool link_poly( size_t size , size_t repeat , CppAD::vector &a , CppAD::vector &z , CppAD::vector &ddp ); bool available_poly(void) { size_t size = 10; size_t repeat = 1; CppAD::vector a(size), z(1), ddp(1); return link_poly(size, repeat, a, z, ddp); } bool correct_poly(bool is_package_double) { size_t size = 10; size_t repeat = 1; CppAD::vector a(size), z(1), ddp(1); link_poly(size, repeat, a, z, ddp); size_t k; double check; if( is_package_double ) k = 0; else k = 2; check = CppAD::Poly(k, a, z[0]); bool ok = CppAD::NearEqual(check, ddp[0], 1e-10, 1e-10); return ok; } void speed_poly(size_t size, size_t repeat) { // free statically allocated memory if( size == 0 && repeat == 0 ) return; // CppAD::vector a(size), z(1), ddp(1); link_poly(size, repeat, a, z, ddp); return; } cppad-20170000.3/speed/src/link_sparse_jacobian.cpp0000644000175200017650000002626213057470456021200 0ustar coincoin-web// $Id: link_sparse_jacobian.cpp 3855 2016-12-19 00:30:54Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin link_sparse_jacobian$$ $spell colpack cppad const bool CppAD Jacobian $$ $section Speed Testing Sparse Jacobian$$ $mindex link_sparse_jacobian test$$ $head Prototype$$ $codei%extern bool link_sparse_jacobian( size_t %size% , size_t %repeat% , size_t %m% , const CppAD::vector& %row% , const CppAD::vector& %col% , CppAD::vector& %x% , CppAD::vector& %jacobian% , size_t& %n_sweep% ); %$$ $head Method$$ Given a range space dimension $icode m$$ the row index vector $latex row$$, and column index vector $latex col$$, a corresponding function $latex f : \B{R}^n \rightarrow \B{R}^m $$ is defined by $cref sparse_jac_fun$$. The non-zero entries in the Jacobian of this function have the form $latex \[ \D{f[row[k]]}{x[col[k]]]} \] $$ for some $latex k$$ between zero and $icode%K% = %row%.size()-1%$$. All the other terms of the Jacobian are zero. $head size$$ The argument $icode size$$, referred to as $latex n$$ below, is the dimension of the domain space for $latex f(x)$$. $head repeat$$ The argument $icode repeat$$ is the number of times to repeat the test (with a different value for $icode x$$ corresponding to each repetition). $head m$$ Is the dimension of the range space for the function $latex f(x)$$. $head row$$ The size of the vector $icode row$$ defines the value $latex K$$. All the elements of $icode row$$ are between zero and $latex m-1$$. $head col$$ The argument $icode col$$ is a vector with size $latex K$$. The input value of its elements does not matter. On output, it has been set the column index vector for the last repetition. All the elements of $icode col$$ are between zero and $latex n-1$$. There are no duplicate row and column entires; i.e., if $icode%j% != %k%$$, $codei% %row%[%j%] != %row%[%k%] || %col%[%j%] != %col%[%k%] %$$ $head x$$ The argument $icode x$$ has prototype $codei% CppAD::vector& %x% %$$ and its size is $latex n$$; i.e., $icode%x%.size() == %size%$$. The input value of the elements of $icode x$$ does not matter. On output, it has been set to the argument value for which the function, or its derivative, is being evaluated and placed in $icode jacobian$$. The value of this vector need not change with each repetition. $head jacobian$$ The argument $icode jacobian$$ has prototype $codei% CppAD::vector& %jacobian% %$$ and its size is $icode K$$. The input value of its elements does not matter. The output value of its elements is the Jacobian of the function $latex f(x)$$. To be more specific, for $latex k = 0 , \ldots , K - 1$$, $latex \[ \D{f[ \R{row}[k] ]}{x[ \R{col}[k] ]} (x) = \R{jacobian} [k] \] $$ $head n_sweep$$ The input value of $icode n_sweep$$ does not matter. On output, it is the value $cref/n_sweep/sparse_jacobian/n_sweep/$$ corresponding to the evaluation of $icode jacobian$$. This is also the number of colors corresponding to the $cref/coloring method/sparse_jacobian/work/color_method/$$, which can be set to $cref/colpack/speed_main/Sparsity Options/colpack/$$, and is otherwise $code cppad$$. $subhead double$$ In the case where $icode package$$ is $code double$$, only the first $latex m$$ elements of $icode jacobian$$ are used and they are set to the value of $latex f(x)$$. $end ----------------------------------------------------------------------------- */ # include # include # include # include # include /*! \{ \file link_sparse_jacobian.cpp Defines and implement sparse Jacobian speed link to package specific code. */ namespace { using CppAD::vector; /*! Class used by choose_row_col to determine order of row and column indices */ class Key { public: /// row index size_t row_; /// column index size_t col_; /// default constructor Key(void) { } /*! Construct from a value for row and col \param row row value for this key \param col column value for this key */ Key(size_t row, size_t col) : row_(row), col_(col) { } /*! Compare this key with another key using < operator \param other the other key. */ bool operator<(const Key& other) const { if( row_ == other.row_ ) return col_ < other.col_; return row_ < other.row_; } }; /*! Function that randomly choose the row and column indices \param n [in] is the dimension of the domain space for the function f(x). \param m [in] is the dimension of the range space for the function f(x). \param row [out] the input size and elements of \c row do not matter. Upon return it is the chosen row indices. \param col [out] the input size and elements of \c col do not matter. Upon return it is the chosen column indices. */ void choose_row_col( size_t n , size_t m , vector& row , vector& col ) { size_t r, c, k, K = 5 * std::max(m, n); // get the random indices vector random(2 * K); CppAD::uniform_01(2 * K, random); // sort the temporary row and colunn choices vector keys(K); vector ind(K); for(k = 0; k < K; k++) { r = size_t( m * random[k] ); r = std::min(m-1, r); // c = size_t( n * random[k + K] ); c = std::min(n-1, c); // keys[k] = Key(r, c); } CppAD::index_sort(keys, ind); // remove duplicates while setting the return value for row and col row.resize(0); col.resize(0); size_t r_previous = keys[ ind[0] ].row_; size_t c_previous = keys[ ind[0] ].col_; CPPAD_ASSERT_UNKNOWN( r_previous < m && c_previous < n ); row.push_back(r_previous); col.push_back(c_previous); for(k = 1; k < K; k++) { r = keys[ ind[k] ].row_; c = keys[ ind[k] ].col_; CPPAD_ASSERT_UNKNOWN( r < m && c < n ); if( r != r_previous || c != c_previous) { row.push_back(r); col.push_back(c); } r_previous = r; c_previous = c; } } } /*! Package specific implementation of a sparse Jacobian claculation. \param size [in] is the size of the domain space; i.e. specifies \c n. \param repeat [in] number of times tha the test is repeated. \param m [in] is the dimension of the range space for f(x). \param row [in] is the row indices correpsonding to non-zero Jacobian entries. \param col [in] is the column indices corresponding to non-zero Jacobian entries. \param x [out] is a vector of size \c n containing the argument at which the Jacobian was evaluated during the last repetition. \param jacobian [out] is a vector with size row.size() containing the value of the Jacobian of f(x) corresponding to the last repetition. \param n_sweep [out] The input value of this parameter does not matter. Upon return, it is the number of sweeps (colors) corresponding to the sparse jacobian claculation. \return is true, if the sparse Jacobian speed test is implemented for this package, and false otherwise. */ extern bool link_sparse_jacobian( size_t size , size_t repeat , size_t m , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& jacobian , size_t& n_sweep ); /*! Is sparse Jacobian test avaialable. \return true, if spare Jacobian available for this package, and false otherwise. */ bool available_sparse_jacobian(void) { size_t n = 10; size_t m = 2 * n; size_t repeat = 1; vector row, col; choose_row_col(n, m, row, col); vector x(n); size_t K = row.size(); vector jacobian(K); size_t n_sweep; return link_sparse_jacobian(n, repeat, m, row, col, x, jacobian, n_sweep); } /*! Does final sparse Jacobian value pass correctness test. \param is_package_double [in] if true, we are checking function values instead of derivatives. \return true, if correctness test passes, and false otherwise. */ bool correct_sparse_jacobian(bool is_package_double) { size_t i, k; bool ok = true; double eps = 10. * CppAD::numeric_limits::epsilon(); size_t n = 5; size_t m = 2 * n; size_t repeat = 1; vector row, col; choose_row_col(n, m, row, col); size_t K = row.size(); // The double package assumes jacobian.size() >= m CPPAD_ASSERT_UNKNOWN( K >= m ); vector x(n); vector jacobian(K); size_t n_sweep; link_sparse_jacobian(n, repeat, m, row, col, x, jacobian, n_sweep); if( is_package_double) { // check f(x) size_t order = 0; vector check(m); CppAD::sparse_jac_fun(m, n, x, row, col, order, check); for(i = 0; i < m; i++) ok &= CppAD::NearEqual(check[i], jacobian[i], eps, eps); return ok; } // check f'(x) size_t order = 1; vector check(K); CppAD::sparse_jac_fun(m, n, x, row, col, order, check); for(k = 0; k < K; k++) ok &= CppAD::NearEqual(check[k], jacobian[k], eps, eps); return ok; } /*! Sparse Jacobian speed test. \param size [in] is the dimension of the argument space for this speed test. \param repeat [in] is the number of times to repeate the speed test. */ void speed_sparse_jacobian(size_t size, size_t repeat) { static size_t previous_size = 0; static vector row, col; // // free statically allocated memory if( size == 0 && repeat == 0 ) { row.clear(); col.clear(); previous_size = size; return; } size_t n = size; size_t m = 2 * n; if( size != previous_size) { choose_row_col(n, m, row, col); previous_size = size; } // note that cppad/sparse_jacobian.cpp assumes that x.size() // is the size corresponding to this test vector x(n); size_t K = row.size(); vector jacobian(K); size_t n_sweep; link_sparse_jacobian(n, repeat, m, row, col, x, jacobian, n_sweep); return; } /*! Sparse Jacobian speed test information. \param size [in] is the \c size parameter in the corresponding call to speed_sparse_jacobian. \param n_sweep [out] The input value of this parameter does not matter. 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin link_ode$$ $spell Jacobian fp bool CppAD $$ $section Speed Testing the Jacobian of Ode Solution$$ $mindex link_ode test$$ $head Prototype$$ $codei%extern bool link_ode( size_t %size% , size_t %repeat% , CppAD::vector &%x% , CppAD::vector &%jacobian% ); %$$ $head Purpose$$ Each $cref/package/speed_main/package/$$ must define a version of this routine as specified below. This is used by the $cref speed_main$$ program to run the corresponding speed and correctness tests. $head Method$$ The same template routine $cref ode_evaluate$$ is used by th different AD packages. $head f$$ The function $latex f : \B{R}^n \rightarrow \B{R}^n$$ that is defined and computed by evaluating $cref ode_evaluate$$ with a call of the form $codei% ode_evaluate(%x%, %p%, %fp%) %$$ with $icode p$$ equal to zero. Calls with the value $icode p$$ equal to one are used to check the derivative values. $head Return Value$$ If this speed test is not yet supported by a particular $icode package$$, the corresponding return value for $code link_ode$$ should be $code false$$. $head size$$ The argument $icode size$$ is the number of variables in the ordinary differential equations which is also equal to $latex n$$. $head repeat$$ The argument $icode repeat$$ is the number of times the Jacobian is computed. $head x$$ The argument $icode x$$ is a vector with $latex n$$ elements. The input value of the elements of $icode x$$ does not matter. On output, it has been set to the argument value for which the function, or its derivative, is being evaluated. The value of this vector must change with each repetition. $head jacobian$$ The argument $icode jacobian$$ is a vector with $latex n^2$$ elements. The input value of its elements does not matter. The output value of its elements is the Jacobian of the function $latex f(x)$$ that corresponds to output value of $icode x$$. To be more specific, for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , n-1$$, $latex \[ \D{f[i]}{x[j]} (x) = jacobian [ i \cdot n + j ] \] $$ $subhead double$$ In the case where $icode package$$ is $code double$$, only the first $latex n$$ element of $icode jacobian$$ are modified and they are to the function value $latex f(x)$$ corresponding to the output value of $icode x$$. $end ----------------------------------------------------------------------------- */ # include # include # include extern bool link_ode( size_t size , size_t repeat , CppAD::vector &x , CppAD::vector &jacobian ); bool available_ode(void) { size_t n = 1; size_t repeat = 1; CppAD::vector x(n); CppAD::vector jacobian(n * n); return link_ode(n, repeat, x, jacobian); } bool correct_ode(bool is_package_double) { bool ok = true; size_t n = 5; size_t repeat = 1; CppAD::vector x(n); CppAD::vector jacobian(n * n); link_ode(n, repeat, x, jacobian); size_t size = n * n; size_t p = 1; if( is_package_double ) { p = 0; // check function value size = n; } CppAD::vector check(size); CppAD::ode_evaluate(x, p, check); size_t k; for(k = 0; k < size; k++) ok &= CppAD::NearEqual(check[k], jacobian[k], 1e-6, 1e-6); return ok; } void speed_ode(size_t n, size_t repeat) { // free statically allocated memory if( n == 0 && repeat == 0 ) return; // CppAD::vector x(n); CppAD::vector jacobian(n * n); link_ode(n, repeat, x, jacobian); return; } cppad-20170000.3/speed/src/link_sparse_hessian.cpp0000644000175200017650000002447613057470456021071 0ustar coincoin-web// $Id: link_sparse_hessian.cpp 3855 2016-12-19 00:30:54Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin link_sparse_hessian$$ $spell const bool CppAD cppad colpack $$ $section Speed Testing Sparse Hessian$$ $mindex link_sparse_hessian test$$ $head Prototype$$ $codei%extern bool link_sparse_hessian( size_t %size% , size_t %repeat% , CppAD::vector& %x% , const CppAD::vector& %row% , const CppAD::vector& %col% , CppAD::vector& %hessian% , size_t %n_sweep% ); %$$ $head Method$$ Given a row index vector $latex row$$ and a second column vector $latex col$$, the corresponding function $latex f : \B{R}^n \rightarrow \B{R} $$ is defined by $cref sparse_hes_fun$$. The non-zero entries in the Hessian of this function have one of the following forms: $latex \[ \DD{f}{x[row[k]]}{x[row[k]]} \; , \; \DD{f}{x[row[k]]}{x[col[k]]} \; , \; \DD{f}{x[col[k]]}{x[row[k]]} \; , \; \DD{f}{x[col[k]]}{x[col[k]]} \] $$ for some $latex k $$ between zero and $latex K-1 $$. All the other terms of the Hessian are zero. $head size$$ The argument $icode size$$, referred to as $latex n$$ below, is the dimension of the domain space for $latex f(x)$$. $head repeat$$ The argument $icode repeat$$ is the number of times to repeat the test (with a different value for $icode x$$ corresponding to each repetition). $head x$$ The argument $icode x$$ has prototype $codei% CppAD::vector& %x% %$$ and its size is $latex n$$; i.e., $icode%x%.size() == %size%$$. The input value of the elements of $icode x$$ does not matter. On output, it has been set to the argument value for which the function, or its derivative, is being evaluated. The value of this vector need not change with each repetition. $head row$$ The argument $icode row$$ has prototype $codei% const CppAD::vector %row% %$$ Its size defines the value $latex K$$. It contains the row indices for the corresponding function $latex f(x)$$. All the elements of $icode row$$ are between zero and $latex n-1$$. $head col$$ The argument $icode col$$ has prototype $codei% const CppAD::vector %col% %$$ Its size must be the same as $icode row$$; i.e., $latex K$$. It contains the column indices for the corresponding function $latex f(x)$$. All the elements of $icode col$$ are between zero and $latex n-1$$. There are no duplicated entries requested, to be specific, if $icode%k1% != %k2%$$ then $codei% ( %row%[%k1%] , %col%[%k1%] ) != ( %row%[%k2%] , %col%[%k2%] ) %$$ $head hessian$$ The argument $icode hessian$$ has prototype $codei% CppAD::vector& hessian %$$ and its size is $icode K$$. The input value of its elements does not matter. The output value of its elements is the Hessian of the function $latex f(x)$$. To be more specific, for $latex k = 0 , \ldots , K-1$$, $latex \[ \DD{f}{ x[ \R{row}[k] ] }{ x[ \R{col}[k] ]} = \R{hessian} [k] \] $$ $head n_sweep$$ The input value of $icode n_sweep$$ does not matter. On output, it is the value $cref/n_sweep/sparse_hessian/n_sweep/$$ corresponding to the evaluation of $icode hessian$$. This is also the number of colors corresponding to the $cref/coloring method/sparse_hessian/work/color_method/$$, which can be set to $cref/colpack/speed_main/Sparsity Options/colpack/$$, and is otherwise $code cppad$$. $subhead double$$ In the case where $icode package$$ is $code double$$, only the first element of $icode hessian$$ is used and it is actually the value of $latex f(x)$$ (derivatives are not computed). $end ----------------------------------------------------------------------------- */ # include # include # include # include # include /*! \{ \file link_sparse_hessian.cpp Defines and implement sparse Hessian speed link to package specific code. */ namespace { using CppAD::vector; /*! Class used by choose_row_col to determin order of row and column indices */ class Key { public: /// row index size_t row_; /// column index size_t col_; /// default constructor Key(void) { } /*! Construct from a value for row and col \param row row value for this key \param col column value for this key */ Key(size_t row, size_t col) : row_(row), col_(col) { } /*! Compare this key with another key using < operator \param other the other key. */ bool operator<(const Key& other) const { if( row_ == other.row_ ) return col_ < other.col_; return row_ < other.row_; } }; /*! Function that randomly choose the row and column indices \param n [in] is the dimension of the argument space for the function f(x). \param row [out] the input size and elements of \c row do not matter. Upon return it is the chosen row indices. \param col [out] the input size and elements of \c col do not matter. Upon return it is the chosen column indices. */ void choose_row_col( size_t n , vector& row , vector& col ) { size_t i, j, k, ell; size_t max_per_row = 5; // generate the row and column indices row.resize(0); col.resize(0); for(i = 0; i < n; i++) { // generate max_per_row random column indices between 0 and i vector random(max_per_row); CppAD::uniform_01(max_per_row, random); // set the indices for this row size_t k_start = col.size(); for(ell = 0; ell < max_per_row; ell++) { j = std::min(i, size_t(random[ell] * i) ); bool ok = true; for(k = k_start; k < col.size(); k++) ok &= j != col[k]; if( ok ) { row.push_back(i); col.push_back(j); } } } } } /*! Package specific implementation of a sparse Hessian claculation. \param size [in] is the size of the domain space; i.e. specifies \c n. \param repeat [in] number of times tha the test is repeated. \param x [out] is a vector of size \c n containing the argument at which the Hessian was evaluated during the last repetition. \param row [in] is the row indices correpsonding to non-zero Hessian entries. \param col [in] is the column indices corresponding to non-zero Hessian entries; col.size() == row.size(). \param hessian [out] is a vector, with hessian.size() == row.size(), containing the value of the Hessian of f(x) corresponding to the last repetition. \param n_sweep [out] The input value of this parameter does not matter. Upon return, it is the number of sweeps (colors) corresponding to the sparse hessian claculation. \return is true, if the sparse Hessian speed test is implemented for this package, and false otherwise. */ extern bool link_sparse_hessian( size_t size , size_t repeat , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& hessian , size_t& n_sweep ); /*! Is sparse Hessian test avaialable. \return true, if spare Hessian available for this package, and false otherwise. */ bool available_sparse_hessian(void) { size_t n = 2; size_t repeat = 1; vector x(n); vector row, col; choose_row_col(n, row, col); size_t K = row.size(); vector hessian(K); size_t n_sweep; return link_sparse_hessian(n, repeat, row, col, x, hessian, n_sweep); } /*! Does final sparse Hessian value pass correctness test. \param is_package_double if true, we are checking function values instead of derivatives. \return true, if correctness test passes, and false otherwise. */ bool correct_sparse_hessian(bool is_package_double) { size_t n = 10; size_t repeat = 1; vector x(n); vector row, col; choose_row_col(n, row, col); size_t K = row.size(); vector hessian(K); // The double package assumes hessian.size() >= 1 CPPAD_ASSERT_UNKNOWN( K >= 1 ); size_t n_sweep; link_sparse_hessian(n, repeat, row, col, x, hessian, n_sweep); size_t order, size; if( is_package_double) { order = 0; // check function value size = 1; } else { order = 2; // check hessian value size = K; } CppAD::vector check(size); CppAD::sparse_hes_fun(n, x, row, col, order, check); bool ok = true; size_t k; for(k = 0; k < size; k++) ok &= CppAD::NearEqual(check[k], hessian[k], 1e-10, 1e-10); return ok; } /*! Sparse Hessian speed test. \param size is the dimension of the argument space for this speed test. \param repeat is the number of times to repeate the speed test. */ void speed_sparse_hessian(size_t size, size_t repeat) { static size_t previous_size = 0; static vector row, col; // // free statically allocated memory if( size == 0 && repeat == 0 ) { row.clear(); col.clear(); previous_size = size; return; } size_t n = size; vector x(n); if( size != previous_size ) { choose_row_col(n, row, col); previous_size = size; } size_t K = row.size(); vector hessian(K); // note that cppad/sparse_hessian.cpp assumes that x.size() == size size_t n_sweep; link_sparse_hessian(n, repeat, row, col, x, hessian, n_sweep); return; } /*! Sparse Hessian speed test information. \param size [in] is the \c size parameter in the corresponding call to speed_sparse_hessian. \param n_sweep [out] The input value of this parameter does not matter. Upon return, it is the value \c n_sweep retruned by the corresponding call to \c link_sparse_hessian. */ void info_sparse_hessian(size_t size, size_t& n_sweep) { size_t n = size; size_t repeat = 1; vector row, col; choose_row_col(n, row, col); // note that cppad/speed/sparse_hessian.cpp assumes that x.size() // is the size corresponding to this test vector x(n); size_t K = row.size(); vector hessian(K); link_sparse_hessian(n, repeat, row, col, x, hessian, n_sweep); return; } cppad-20170000.3/speed/src/microsoft_timer.cpp0000644000175200017650000000475013057470456020243 0ustar coincoin-web/* $Id: microsoft_timer.cpp 3724 2015-09-21 05:04:18Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin microsoft_timer$$ $spell Microsoft cpp src $$ $section Microsoft Version of Elapsed Number of Seconds$$ $head Syntax$$ $icode%s% = microsoft_timer()%$$ $head Purpose$$ This routine is accurate to within .02 seconds (see $cref elapsed_seconds$$ which uses this routine when the preprocessor symbol $code _MSC_VER$$ is defined). It does not necessary work for time intervals that are greater than a day. It uses $code ::GetSystemTime$$ for timing. $head s$$ is a $code double$$ equal to the number of seconds since the first call to $code microsoft_timer$$. $head Linking$$ The source code for this routine is located in $code speed/src/microsoft_timer.cpp$$. The preprocessor symbol $code _MSC_VER$$ must be defined, or this routine is not compiled. $end ----------------------------------------------------------------------- */ # if _MSC_VER # include # include // Note that the doxygen for this routine does not get generated because // _MSC_VER is not defined during generation. In general, it is a problem // that not all preprocessor options get documented. /*! \{ \file microsoft_timer.cpp \brief Microsoft version of elapsed_seconds. */ /*! Microsoft version of elapsed number of seconds since frist call. \copydetails elapsed_seconds */ double microsoft_timer(void) { static bool first_ = true; static SYSTEMTIME st_; SYSTEMTIME st; if( first_ ) { ::GetSystemTime(&st_); first_ = false; return 0.; } ::GetSystemTime(&st); double hour = double(st.wHour) - double(st_.wHour); double minute = double(st.wMinute) - double(st_.wMinute); double second = double(st.wSecond) - double(st_.wSecond); double milli = double(st.wMilliseconds) - double(st_.wMilliseconds); double diff = 1e-3*milli + second + 60.*minute + 3600.*hour; if( diff < 0. ) diff += 3600.*24.; assert( 0 <= diff && diff < 3600.*24. ); return diff; } # endif cppad-20170000.3/speed/src/makefile.am0000644000175200017650000000224613057470456016424 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # # BEGIN OPTIMIZE AM_CXXFLAGS = -O2 -DNDEBUG $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) # END DEBUG # AM_CPPFLAGS = \ -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) # noinst_LIBRARIES = libspeed.a libspeed_a_SOURCES = \ link_det_lu.cpp \ link_det_minor.cpp \ link_mat_mul.cpp \ link_ode.cpp \ link_poly.cpp \ link_sparse_hessian.cpp \ link_sparse_jacobian.cpp \ microsoft_timer.cpp cppad-20170000.3/speed/src/link_det_lu.cpp0000644000175200017650000000706313057470456017327 0ustar coincoin-web// $Id: link_det_lu.cpp 3855 2016-12-19 00:30:54Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin link_det_lu$$ $spell det_lu bool CppAD $$ $section Speed Testing Gradient of Determinant Using Lu Factorization$$ $mindex link_det_lu test$$ $head Prototype$$ $codei%extern bool link_det_lu( size_t %size% , size_t %repeat% , CppAD::vector &%matrix% , CppAD::vector &%gradient% ); %$$ $head Purpose$$ Each $cref/package/speed_main/package/$$ must define a version of this routine as specified below. This is used by the $cref speed_main$$ program to run the corresponding speed and correctness tests. $head Method$$ The same template routine $cref det_by_lu$$ is used by the different AD packages. $head Return Value$$ If this speed test is not yet supported by a particular $icode package$$, the corresponding return value for $code link_det_lu$$ should be $code false$$. $head size$$ The argument $icode size$$ is the number of rows and columns in the matrix. $head repeat$$ The argument $icode repeat$$ is the number of different matrices that the gradient (or determinant) is computed for. $head matrix$$ The argument $icode matrix$$ is a vector with $icode%size%*%size%$$ elements. The input value of its elements does not matter. The output value of its elements is the last matrix that the gradient (or determinant) is computed for. $head gradient$$ The argument $icode gradient$$ is a vector with $icode%size%*%size%$$ elements. The input value of its elements does not matter. The output value of its elements is the gradient of the determinant of $icode matrix$$ with respect to its elements. $subhead double$$ In the case where $icode package$$ is $code double$$, only the first element of $icode gradient$$ is used and it is actually the determinant value (the gradient value is not computed). $end ----------------------------------------------------------------------------- */ # include # include # include extern bool link_det_lu( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ); bool available_det_lu(void) { size_t size = 3; size_t repeat = 1; CppAD::vector matrix(size * size); CppAD::vector gradient(size * size); return link_det_lu(size, repeat, matrix, gradient); } bool correct_det_lu(bool is_package_double) { size_t size = 3; size_t repeat = 1; CppAD::vector matrix(size * size); CppAD::vector gradient(size * size); link_det_lu(size, repeat, matrix, gradient); bool ok; if( is_package_double ) ok = CppAD::det_33(matrix, gradient); else ok = CppAD::det_grad_33(matrix, gradient); return ok; } void speed_det_lu(size_t size, size_t repeat) { // free statically allocated memory if( size == 0 && repeat == 0 ) return; // CppAD::vector matrix(size * size); CppAD::vector gradient(size * size); link_det_lu(size, repeat, matrix, gradient); return; } cppad-20170000.3/speed/double/0002755000175200017650000000000013057470456015011 5ustar coincoin-webcppad-20170000.3/speed/double/det_minor.cpp0000644000175200017650000000341713057470456017500 0ustar coincoin-web// $Id: det_minor.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin double_det_minor.cpp$$ $spell onetape retape bool cppad det CppAD hpp $$ $section Double Speed: Determinant by Minor Expansion$$ $mindex link_det_minor speed$$ $head Specifications$$ See $cref link_det_minor$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_det_minor( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &det ) { if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]) return false; // ----------------------------------------------------- // setup CppAD::det_by_minor Det(size); size_t n = size * size; // number of independent variables // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, matrix); 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$Id: makefile.in 3839 2016-10-14 18:10:09Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # # Copy source file so that main.o does not end up in parent directory BUILT_SOURCES = main.cpp # AM_CPPFLAGS = -I$(top_srcdir) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) # # BEGIN OPTIMIZE AM_CXXFLAGS = -O2 -DNDEBUG -DCPPAD_DOUBLE_SPEED $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) -DCPPAD_DOUBLE_SPEED # END DEBUG # LDADD = -lspeed AM_LDFLAGS = -L../src # speed_double_SOURCES = \ main.cpp \ det_lu.cpp \ det_minor.cpp \ mat_mul.cpp \ ode.cpp \ poly.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp all: $(BUILT_SOURCES) $(MAKE) $(AM_MAKEFLAGS) all-am .SUFFIXES: .SUFFIXES: .cpp .o .obj $(srcdir)/makefile.in: @MAINTAINER_MODE_TRUE@ $(srcdir)/makefile.am $(am__configure_deps) @for dep in $?; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin double_poly.cpp$$ $spell onetape retape bool cppad CppAD hpp $$ $section Double Speed: Evaluate a Polynomial$$ $mindex link_poly speed$$ $head Specifications$$ See $cref link_poly$$. $head Implementation$$ $srccode%cpp% */ # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_poly( size_t size , size_t repeat , CppAD::vector &a , // coefficients of polynomial CppAD::vector &z , // polynomial argument value CppAD::vector &p ) // second derivative w.r.t z { if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]) return false; // ----------------------------------------------------- // setup // ------------------------------------------------------ while(repeat--) { // get the next argument value CppAD::uniform_01(1, z); // evaluate the polynomial at the new argument value p[0] = CppAD::Poly(0, a, z[0]); } return true; } /* %$$ $end */ cppad-20170000.3/speed/double/sparse_jacobian.cpp0000644000175200017650000000437013057470456020642 0ustar coincoin-web// $Id: sparse_jacobian.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin double_sparse_jacobian.cpp$$ $spell const onetape boolsparsity yp jac Jacobian fp bool cppad hpp CppAD cmath exp std $$ $section Double Speed: Sparse Jacobian$$ $mindex link_sparse_jacobian speed$$ $head Specifications$$ See $cref link_sparse_jacobian$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_sparse_jacobian( size_t size , size_t repeat , size_t m , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& jacobian , size_t& n_sweep ) { if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]||global_option["boolsparsity"]) return false; // ----------------------------------------------------- // setup using CppAD::vector; size_t i; size_t order = 0; // order for computing function value size_t n = size; // argument space dimension vector yp(m); // function value yp = f(x) // ------------------------------------------------------ while(repeat--) { // choose a value for x CppAD::uniform_01(n, x); // computation of the function CppAD::sparse_jac_fun(m, n, x, row, col, order, yp); } for(i = 0; i < m; i++) jacobian[i] = yp[i]; return true; } /* %$$ $end */ cppad-20170000.3/speed/double/ode.cpp0000644000175200017650000000340413057470456016263 0ustar coincoin-web// $Id: ode.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin double_ode.cpp$$ $spell onetape Jacobian CppAD cppad hpp bool cstring retape resize endif $$ $section Double Speed: Ode Solution$$ $mindex link_ode speed$$ $head Specifications$$ See $cref link_ode$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_ode( size_t size , size_t repeat , CppAD::vector &x , CppAD::vector &jacobian ) { if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]) return false; // ------------------------------------------------------------- // setup assert( x.size() == size ); size_t n = size; size_t m = 0; CppAD::vector f(n); while(repeat--) { // choose next x value uniform_01(n, x); // evaluate function CppAD::ode_evaluate(x, m, f); } size_t i; for(i = 0; i < n; i++) jacobian[i] = f[i]; return true; } /* %$$ $end */ cppad-20170000.3/speed/double/sparse_hessian.cpp0000644000175200017650000000425413057470456020527 0ustar coincoin-web// $Id: sparse_hessian.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin double_sparse_hessian.cpp$$ $spell onetape boolsparsity const hes bool cppad hpp CppAD $$ $section Double Speed: Sparse Hessian$$ $mindex link_sparse_hessian speed$$ $head Specifications$$ See $cref link_sparse_hessian$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_sparse_hessian( size_t size , size_t repeat , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& hessian , size_t& n_sweep ) { if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]||global_option["boolsparsity"]) return false; // ----------------------------------------------------- // setup using CppAD::vector; size_t order = 0; // derivative order corresponding to function size_t n = size; // argument space dimension size_t m = 1; // range space dimension vector y(m); // function value // choose a value for x CppAD::uniform_01(n, x); // ------------------------------------------------------ while(repeat--) { // computation of the function CppAD::sparse_hes_fun(n, x, row, col, order, y); } hessian[0] = y[0]; return true; } /* %$$ $end */ cppad-20170000.3/speed/double/makefile.am0000644000175200017650000000254213057470456017106 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # # Copy source file so that main.o does not end up in parent directory BUILT_SOURCES = main.cpp main.cpp: cp $(srcdir)/../main.cpp main.cpp # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = speed_double # AM_CPPFLAGS = -I$(top_srcdir) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) # # BEGIN OPTIMIZE AM_CXXFLAGS = -O2 -DNDEBUG -DCPPAD_DOUBLE_SPEED $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) -DCPPAD_DOUBLE_SPEED # END DEBUG # LDADD = -lspeed AM_LDFLAGS = -L../src # speed_double_SOURCES = \ main.cpp \ det_lu.cpp \ det_minor.cpp \ mat_mul.cpp \ ode.cpp \ poly.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp test: check ./speed_double correct 123 cppad-20170000.3/speed/double/CMakeLists.txt0000644000175200017650000000352313057470456017552 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the speed/double directory tests # Inherit build type environment from ../CMakeList.txt # Adds flags to the compiler command line for sources in the current directory # and below. This command can be used to add any flags, but it was originally # intended to add preprocessor definitions. ADD_DEFINITIONS("-DCPPAD_DOUBLE_SPEED") # Local include directories to search (not in package_prefix/includdir) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/../src ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(speed_double EXCLUDE_FROM_ALL ../main.cpp det_lu.cpp det_minor.cpp mat_mul.cpp ode.cpp poly.cpp sparse_hessian.cpp sparse_jacobian.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( speed_double ) # double does not use any external library TARGET_LINK_LIBRARIES(speed_double speed_src ) # Add the check_speed_double target ADD_CUSTOM_TARGET(check_speed_double speed_double correct 54321 DEPENDS speed_double speed_src ) MESSAGE(STATUS "make check_speed_double: available") # Change check depends in parent environment add_to_list(check_speed_depends check_speed_double) SET(check_speed_depends "${check_speed_depends}" PARENT_SCOPE) cppad-20170000.3/speed/double/det_lu.cpp0000644000175200017650000000343713057470456016776 0ustar coincoin-web// $Id: det_lu.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin double_det_lu.cpp$$ $spell onetape bool cppad hpp Lu det CppAD $$ $section Double Speed: Determinant Using Lu Factorization$$ $mindex link_det_lu speed matrix factor$$ $head Specifications$$ See $cref link_det_lu$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_det_lu( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &det ) { if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]) return false; // ----------------------------------------------------- // setup CppAD::det_by_lu Det(size); size_t n = size * size; // number of independent variables // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, matrix); // computation of the determinant det[0] = Det(matrix); } return true; } /* %$$ $end */ cppad-20170000.3/speed/double/mat_mul.cpp0000644000175200017650000000336413057470456017157 0ustar coincoin-web// $Id: mat_mul.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin double_mat_mul.cpp$$ $spell onetape CppAD cppad mul_mat hpp sq bool dz typedef $$ $section CppAD Speed: Matrix Multiplication (Double Version)$$ $mindex speed multiply link_mat_mul$$ $head Specifications$$ See $cref link_mat_mul$$. $head Implementation$$ $srccode%cpp% */ # include # include # include // Note that CppAD uses global_option["memory"] at the main program level # include extern std::map global_option; bool link_mat_mul( size_t size , size_t repeat , CppAD::vector& x , CppAD::vector& z , CppAD::vector& dz ) { if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]) return false; // ----------------------------------------------------- size_t n = size * size; // number of independent variables CppAD::vector y(n); while(repeat--) { // get the next matrix CppAD::uniform_01(n, x); // do computation mat_sum_sq(size, x, y, z); } return true; } /* %$$ $end */ cppad-20170000.3/speed/sacado/0002755000175200017650000000000013057470457014772 5ustar coincoin-webcppad-20170000.3/speed/sacado/det_minor.cpp0000644000175200017650000000477513057470456017470 0ustar coincoin-web// $Id: det_minor.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sacado_det_minor.cpp$$ $spell onetape cppad det const CppAD typedef diff bool srand Sacado.hpp ADvar Gradcomp $$ $section Sacado Speed: Gradient of Determinant by Minor Expansion$$ $mindex link_det_minor speed$$ $head Specifications$$ See $cref link_det_minor$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_det_minor( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ) { // speed test global option values if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup // object for computing determinant typedef Sacado::Rad::ADvar ADScalar; typedef CppAD::vector ADVector; CppAD::det_by_minor Det(size); size_t i; // temporary index size_t n = size * size; // number of independent variables ADScalar detA; // AD value of the determinant ADVector A(n); // AD version of matrix // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, matrix); // set independent variable values for(i = 0; i < n; i++) A[i] = matrix[i]; // compute the determinant detA = Det(A); // reverse mode compute gradient of last computed value; i.e., detA ADScalar::Gradcomp(); // return gradient for(i =0; i < n; i++) gradient[i] = A[i].adj(); // partial detA w.r.t A[i] } // --------------------------------------------------------- return true; } /* %$$ $end */ cppad-20170000.3/speed/sacado/makefile.in0000644000175200017650000004771313057470456017110 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sacado_poly.cpp$$ $spell onetape cppad cpp tadiff ddp Taylor dz eval cppad vector Vector typedef sacado Lu CppAD det hpp const bool Tay resize Coeff $$ $section Sacado Speed: Second Derivative of a Polynomial$$ $mindex link_poly speed$$ $head Specifications$$ See $cref link_poly$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_poly( size_t size , size_t repeat , CppAD::vector &a , // coefficients of polynomial CppAD::vector &z , // polynomial argument value CppAD::vector &ddp ) // second derivative w.r.t z { if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup typedef Sacado::Tay::Taylor ADScalar; CppAD::vector A(size); size_t i; // temporary index ADScalar Z; // domain space AD value ADScalar P; // range space AD value unsigned int order = 2; // order of Taylor coefficients Z.resize(order+1, false); P.resize(order+1, false); // choose the polynomial coefficients CppAD::uniform_01(size, a); // AD copy of the polynomial coefficients for(i = 0; i < size; i++) A[i] = a[i]; // ------------------------------------------------------ while(repeat--) { // get the next argument value CppAD::uniform_01(1, z); // independent variable value Z.fastAccessCoeff(0) = z[0]; // argument value Z.fastAccessCoeff(1) = 1.; // first order coefficient Z.fastAccessCoeff(2) = 0.; // second order coefficient // AD computation of the dependent variable P = CppAD::Poly(0, A, Z); // second derivative is twice second order Taylor coefficient ddp[0] = 2. * P.fastAccessCoeff(2); } // ------------------------------------------------------ return true; } /* %$$ $end */ cppad-20170000.3/speed/sacado/sparse_jacobian.cpp0000644000175200017650000000241313057470456020616 0ustar coincoin-web// $Id: sparse_jacobian.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include /* $begin sacado_sparse_jacobian.cpp$$ $spell const bool CppAD sacado sparse_jacobian $$ $section sacado Speed: sparse_jacobian$$ $srccode%cpp% */ // A sacado version of this test is not yet available bool link_sparse_jacobian( size_t size , size_t repeat , size_t m , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& jacobian , size_t& n_sweep ) { return false; } /* %$$ $end */ cppad-20170000.3/speed/sacado/ode.cpp0000644000175200017650000000473713057470456016255 0ustar coincoin-web// $Id: ode.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sacado_ode.cpp$$ $spell jacobian Sacado cppad hpp bool onetape CppAD typedef endif cassert $$ $section Sacado Speed: Gradient of Ode Solution$$ $mindex link_ode speed$$ $head Specifications$$ See $cref link_ode$$. $head Implementation$$ $srccode%cpp% */ # include // # include # include # include # include # include // list of possible options # include extern std::map global_option; bool link_ode( size_t size , size_t repeat , CppAD::vector &x , CppAD::vector &jacobian ) { // speed test global option values if( global_option["atomic"] ) return false; if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] ) return false; // ------------------------------------------------------------- // setup assert( x.size() == size ); assert( jacobian.size() == size * size ); typedef Sacado::Fad::DFad ADScalar; typedef CppAD::vector ADVector; size_t i, j; size_t p = 0; // use ode to calculate function values size_t n = size; // number of independent variables size_t m = n; // number of dependent variables ADVector X(n), Y(m); // independent and dependent variables // ------------------------------------------------------------- while(repeat--) { // choose next x value CppAD::uniform_01(n, x); for(j = 0; j < n; j++) { // set up for X as the independent variable vector X[j] = ADScalar(int(n), int(j), x[j]); } // evaluate function CppAD::ode_evaluate(X, p, Y); // return values with Y as the dependent variable vector for(i = 0; i < m; i++) { for(j = 0; j < n; j++) jacobian[ i * n + j ] = Y[i].dx(j); } } return true; } /* %$$ $end */ cppad-20170000.3/speed/sacado/sparse_hessian.cpp0000644000175200017650000000241213057470456020501 0ustar coincoin-web// $Id: sparse_hessian.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include /* $begin sacado_sparse_hessian.cpp$$ $spell boolsparsity const Sacado bool CppAD $$ $section Sacado Speed: Sparse Hessian$$ $srccode%cpp% */ // A sacado version of this test is not yet implemented extern bool link_sparse_hessian( size_t size , size_t repeat , const CppAD::vector& row , const CppAD::vector& col , CppAD::vector& x , CppAD::vector& hessian , size_t& n_sweep ) { return false; } /* %$$ $end */ cppad-20170000.3/speed/sacado/makefile.am0000644000175200017650000000302213057470457017061 0ustar coincoin-web# $Id: makefile.am 3757 2015-11-30 12:03:07Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # # Copy source file so that main.o does not end up in parent directory BUILT_SOURCES = main.cpp main.cpp: cp $(srcdir)/../main.cpp main.cpp # # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = speed_sacado # AM_CPPFLAGS = \ -I$(top_srcdir) \ -I$(SACADO_DIR)/include \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) # # BEGIN OPTIMIZE AM_CXXFLAGS = -O2 -DNDEBUG -DCPPAD_SACADO_SPEED \ -DRAD_EQ_ALIAS -DRAD_AUTO_AD_Const $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) $(CXX_FLAGS) -DCPPAD_SACADO_SPEED -DRAD_AUTO_AD_Const # END DEBUG # LDADD = -lspeed -lsacado -lteuchoscore AM_LDFLAGS = -L../src -L$(SACADO_DIR)/lib -L$(SACADO_DIR)/lib64 # speed_sacado_SOURCES = \ main.cpp \ det_lu.cpp \ det_minor.cpp \ mat_mul.cpp \ ode.cpp \ poly.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp test: check ./speed_sacado correct 123 cppad-20170000.3/speed/sacado/CMakeLists.txt0000644000175200017650000000533213057470457017533 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the speed/sacado directory tests # Inherit build type from ../CMakeList.txt # assert sacado_prefix is defined IF ( NOT sacado_prefix ) MESSAGE(FATAL_ERROR "speed/sacado/CMakeLists.txt: sacado_prefix = ${sacado_prefix}" ) ENDIF ( NOT sacado_prefix ) # Adds flags to the compiler command line for sources in the current directory # and below. This command can be used to add any flags, but it was originally # intended to add preprocessor definitions. ADD_DEFINITIONS("-DCPPAD_SACADO_SPEED -DRAD_AUTO_AD_Const") # Local include directories to search (not in package_prefix/includdir) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/../src ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(speed_sacado EXCLUDE_FROM_ALL ../main.cpp det_lu.cpp det_minor.cpp mat_mul.cpp ode.cpp poly.cpp sparse_hessian.cpp sparse_jacobian.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( speed_sacado ) # Find name used for teuchos library SET(teuchos_lib NOTFOUND) FOREACH(dir ${cmake_install_libdirs}) FILE(GLOB file_list ${sacado_prefix}/${dir}/libteuchoscore.*) IF(file_list) SET(teuchos_lib teuchoscore) ENDIF(file_list) FILE(GLOB file_list ${sacado_prefix}/${dir}/libteuchos.*) IF(file_list) SET(teuchos_lib teuchos) ENDIF(file_list) ENDFOREACH(dir) # List of libraries to be linked into the specified target IF(teuchos_lib) TARGET_LINK_LIBRARIES(speed_sacado speed_src sacado ${teuchos_lib}) ELSE(teuchos_lib) MESSAGE(FATAT_ERROR " For all dir in cmake_install_libdirs, cannot find either sacado_prefix/dir/teuchos sacado_prefix/dir/teuchoscore where sacado_prefix = ${sacado_prefix} cmake_install_libdirs = ${cmake_install_libdirs} teuchos_lib= ${teuchos_lib} " ) ENDIF(teuchos_lib) # # Add the check_speed_sacado target ADD_CUSTOM_TARGET(check_speed_sacado speed_sacado correct 54321 DEPENDS speed_sacado speed_src ) MESSAGE(STATUS "make check_speed_sacado: available") # Change check depends in parent environment add_to_list(check_speed_depends check_speed_sacado) SET(check_speed_depends "${check_speed_depends}" PARENT_SCOPE) cppad-20170000.3/speed/sacado/det_lu.cpp0000644000175200017650000000501113057470457016745 0ustar coincoin-web// $Id: det_lu.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sacado_det_lu.cpp$$ $spell onetape cppad Lu det badiff.hpp const CppAD typedef diff bool srand Sacado ADvar Tay Gradcomp $$ $section Sacado Speed: Gradient of Determinant Using Lu Factorization$$ $mindex link_det_lu speed matrix factor$$ $head Specifications$$ See $cref link_det_lu$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_det_lu( size_t size , size_t repeat , CppAD::vector &matrix , CppAD::vector &gradient ) { // speed test global option values if( global_option["onetape"] || global_option["atomic"] ) return false; if( global_option["memory"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup // // object for computing determinant typedef Sacado::Rad::ADvar ADScalar; typedef CppAD::vector ADVector; CppAD::det_by_lu Det(size); size_t i; // temporary index size_t n = size * size; // number of independent variables ADScalar detA; // AD value of the determinant ADVector A(n); // AD version of matrix // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, matrix); // set independent variable values for(i = 0; i < n; i++) A[i] = matrix[i]; // compute the determinant detA = Det(A); // compute the gradient of detA ADScalar::Gradcomp(); // evaluate and return gradient using reverse mode for(i =0; i < n; i++) gradient[i] = A[i].adj(); // partial detA w.r.t A[i] } // --------------------------------------------------------- return true; } /* %$$ $end */ cppad-20170000.3/speed/sacado/mat_mul.cpp0000644000175200017650000000524013057470457017133 0ustar coincoin-web// $Id: mat_mul.cpp 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sacado_mat_mul.cpp$$ $spell sq onetape typedef ADvar Gradcomp Sacado cppad.hpp bool mul dz CppAD $$ $section Sacado Speed: Matrix Multiplication$$ $mindex link_mat_mul speed multiply$$ $head Specifications$$ See $cref link_mat_mul$$. $head Implementation$$ $srccode%cpp% */ # include # include # include # include // list of possible options # include extern std::map global_option; bool link_mat_mul( size_t size , size_t repeat , CppAD::vector& x , CppAD::vector& z , CppAD::vector& dz ) { // speed test global option values if( global_option["memory"] || global_option["onetape"] || global_option["atomic"] || global_option["optimize"] ) return false; // ----------------------------------------------------- // setup // object for computing determinant typedef Sacado::Rad::ADvar ADScalar; typedef CppAD::vector ADVector; size_t j; // temporary index size_t m = 1; // number of dependent variables size_t n = size * size; // number of independent variables ADVector X(n); // AD domain space vector ADVector Y(n); // Store product matrix ADVector Z(m); // AD range space vector ADScalar f; // ------------------------------------------------------ while(repeat--) { // get the next matrix CppAD::uniform_01(n, x); // set independent variable values for(j = 0; j < n; j++) X[j] = x[j]; // do the computation mat_sum_sq(size, X, Y, Z); // create function object f : X -> Z f = Z[0]; // reverse mode gradient of last ADvar computed value; i.e., f ADScalar::Gradcomp(); // return gradient for(j = 0; j < n; j++) dz[j] = X[j].adj(); // partial f w.r.t X[j] } // return function value z[0] = f.val(); // --------------------------------------------------------- return true; } /* %$$ $end */ cppad-20170000.3/speed/example/0002755000175200017650000000000013057470457015173 5ustar coincoin-webcppad-20170000.3/speed/example/makefile.am0000644000175200017650000000237713057470457017276 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # EXTRA_DIST = \ speed_program.cpp # check_PROGRAMS = speed_example # AM_CPPFLAGS = -I. -I$(top_srcdir) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) # AM_CXXFLAGS = -g $(CXX_FLAGS) # LDADD = -lspeed AM_LDFLAGS = -L../src speed_example_SOURCES = \ example.cpp \ det_by_lu.cpp \ det_by_minor.cpp \ det_of_minor.cpp \ elapsed_seconds.cpp \ mat_sum_sq.cpp \ ode_evaluate.cpp \ sparse_hes_fun.cpp \ sparse_jac_fun.cpp \ speed_test.cpp \ time_test.cpp \ ../src/microsoft_timer.cpp test: check ./speed_example cppad-20170000.3/speed/example/mat_sum_sq.cpp0000644000175200017650000000332313057470457020046 0ustar coincoin-web// $Id: mat_sum_sq.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin mat_sum_sq.cpp$$ $spell sq $$ $section Sum of the Elements of the Square of a Matrix: Example and Test$$ $mindex mat_sum_sq$$ $code $srcfile%speed/example/mat_sum_sq.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include # include bool mat_sum_sq() { bool ok = true; double x_00, x_01, x_10, x_11, check; // dimension of the matrices x, y, and the result z size_t n = 2; CppAD::vector x(n * n), y(n * n), z(1); // x = [ 1 2 ; 3 4 ] x[0] = x_00 = 1.; x[1] = x_01 = 2.; x[2] = x_10 = 3.; x[3] = x_11 = 4.; // compute y = x * x and z = sum of elements in y CppAD::mat_sum_sq(n, x, y, z); // check y_00 check = x_00 * x_00 + x_01 * x_10; ok &= (check == y[0]); // check y_01 check = x_00 * x_01 + x_01 * x_11; ok &= (check == y[1]); // check y_10 check = x_10 * x_00 + x_11 * x_10; ok &= (check == y[2]); // check y_11 check = x_10 * x_01 + x_11 * x_11; ok &= (check == y[3]); // check z check = y[0] + y[1] + y[2] + y[3]; ok &= (check == z[0]); return ok; } // END C++ cppad-20170000.3/speed/example/det_by_minor.cpp0000644000175200017650000000273013057470457020351 0ustar coincoin-web// $Id: det_by_minor.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin det_by_minor.cpp$$ $spell Cpp $$ $section Determinant Using Expansion by Minors: Example and Test$$ $mindex minors$$ $code $srcfile%speed/example/det_by_minor.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool det_by_minor() { bool ok = true; // dimension of the matrix size_t n = 3; // construct the determinat object CppAD::det_by_minor Det(n); double a[] = { 1., 2., 3., // a[0] a[1] a[2] 3., 2., 1., // a[3] a[4] a[5] 2., 1., 2. // a[6] a[7] a[8] }; CPPAD_TESTVECTOR(double) A(9); size_t i; for(i = 0; i < 9; i++) A[i] = a[i]; // evaluate the determinant double det = Det(A); double check; check = a[0]*(a[4]*a[8] - a[5]*a[7]) - a[1]*(a[3]*a[8] - a[5]*a[6]) + a[2]*(a[3]*a[7] - a[4]*a[6]); ok = det == check; return ok; } // END C++ cppad-20170000.3/speed/example/elapsed_seconds.cpp0000644000175200017650000000264113057470457021033 0ustar coincoin-web// $Id: elapsed_seconds.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin elapsed_seconds.cpp$$ $spell Cpp Lu $$ $section Elapsed Seconds: Example and Test$$ $mindex seconds timer$$ $code $srcfile%speed/example/elapsed_seconds.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include # include # define CPPAD_DEBUG_ELAPSED_SECONDS 0 bool elapsed_seconds(void) { bool ok = true; double max_diff = 0.; double s0 = CppAD::elapsed_seconds(); double s1 = CppAD::elapsed_seconds(); double s2 = CppAD::elapsed_seconds(); while(s2 - s0 < 1.) { max_diff = std::max(s2 - s1, max_diff); s1 = s2; s2 = CppAD::elapsed_seconds(); } # if CPPAD_DEBUG_ELAPSED_SECONDS std::cout << "max_diff = " << max_diff << std::endl; # endif ok &= 0. < max_diff && max_diff < .04; return ok; } // END C++ cppad-20170000.3/speed/example/example.cpp0000644000175200017650000000640113057470457017331 0ustar coincoin-web// $Id: example.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin speed_example.cpp$$ $spell $$ $section Run the Speed Examples$$ $mindex program$$ $head Running Tests$$ To build this program and run its correctness tests see $cref cmake_check$$. $code $srcfile%speed/example/example.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // various example routines extern bool det_of_minor(void); extern bool det_by_lu(void); extern bool det_by_minor(void); extern bool elapsed_seconds(void); extern bool mat_sum_sq(void); extern bool ode_evaluate(void); extern bool sparse_hes_fun(void); extern bool sparse_jac_fun(void); extern bool speed_test(void); extern bool time_test(void); namespace { // function that runs one test size_t Run_ok_count = 0; size_t Run_error_count = 0; const char* exception_list[] = { "elapsed_seconds", "speed_test", "time_test" }; size_t n_exception = sizeof(exception_list) / sizeof(exception_list[0]); bool Run(bool TestOk(void), std::string name) { bool ok = true; std::streamsize width = 20; std::cout.width( width ); std::cout.setf( std::ios_base::left ); std::cout << name; bool exception = false; for(size_t i = 0; i < n_exception; i++) exception |= exception_list[i] == name; // ok &= name.size() < size_t(width); ok &= TestOk(); if( ok ) { std::cout << "OK" << std::endl; Run_ok_count++; } else if ( exception ) { std::cout << "Error: perhaps too many other programs running"; std::cout << std::endl; // no change to Run_ok_count ok = true; } else { std::cout << "Error" << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; using std::cout; using std::endl; ok &= Run(det_of_minor, "det_of_minor" ); ok &= Run(det_by_minor, "det_by_minor" ); ok &= Run(det_by_lu, "det_by_lu" ); ok &= Run(elapsed_seconds, "elapsed_seconds" ); ok &= Run(mat_sum_sq, "mat_sum_sq" ); ok &= Run(ode_evaluate, "ode_evaluate" ); ok &= Run(sparse_hes_fun, "sparse_hes_fun" ); ok &= Run(sparse_jac_fun, "sparse_jac_fun" ); ok &= Run(speed_test, "speed_test" ); ok &= Run(time_test, "time_test" ); assert( ok || (Run_error_count > 0) ); // check for memory leak in previous calculations if( ! CppAD::thread_alloc::free_all() ) { ok = false; cout << "Error: memroy leak detected" << endl; } if( ok ) { cout << "All " << int(Run_ok_count) << " tests passed "; cout << "(possibly excepting elapsed_seconds)."; } else cout << int(Run_error_count) << " tests failed."; cout << endl; return static_cast( ! ok ); } // END C++ cppad-20170000.3/speed/example/CMakeLists.txt0000644000175200017650000000314013057470457017727 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the speed/cppad directory tests # Inherit build type from ../CMakeList.txt # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) # We do not add ../src/speed_src library to avoid undefined externals. # Instead we build our own copy of ../src/microsoft_timer.cpp. ADD_EXECUTABLE(speed_example EXCLUDE_FROM_ALL example.cpp det_by_lu.cpp det_by_minor.cpp det_of_minor.cpp elapsed_seconds.cpp mat_sum_sq.cpp ode_evaluate.cpp sparse_hes_fun.cpp sparse_jac_fun.cpp speed_test.cpp time_test.cpp "../src/microsoft_timer.cpp" ) # Compiler flags for cppad source add_cppad_cxx_flags( speed_example ) # Add the check_speed_example target ADD_CUSTOM_TARGET(check_speed_example speed_example DEPENDS speed_example speed_src ) MESSAGE(STATUS "make check_speed_example: available") # Change check depends in parent environment add_to_list(check_speed_depends check_speed_example) SET(check_speed_depends "${check_speed_depends}" PARENT_SCOPE) cppad-20170000.3/speed/example/ode_evaluate.cpp0000644000175200017650000000322313057470457020332 0ustar coincoin-web// $Id: ode_evaluate.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ode_evaluate.cpp$$ $spell $$ $section ode_evaluate: Example and test$$ $mindex ode_evaluate$$ $code $srcfile%speed/example/ode_evaluate.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool ode_evaluate(void) { using CppAD::NearEqual; using CppAD::AD; bool ok = true; size_t n = 3; CppAD::vector x(n); CppAD::vector ym(n * n); CppAD::vector< AD > X(n); CppAD::vector< AD > Ym(n); // choose x size_t j; for(j = 0; j < n; j++) { x[j] = double(j + 1); X[j] = x[j]; } // declare independent variables Independent(X); // evaluate function size_t m = 0; CppAD::ode_evaluate(X, m, Ym); // evaluate derivative m = 1; CppAD::ode_evaluate(x, m, ym); // use AD to evaluate derivative CppAD::ADFun F(X, Ym); CppAD::vector dy(n * n); dy = F.Jacobian(x); size_t k; for(k = 0; k < n * n; k++) ok &= NearEqual(ym[k], dy[k] , 1e-7, 1e-7); return ok; } // END C++ cppad-20170000.3/speed/example/time_test.cpp0000644000175200017650000000405513057470457017676 0ustar coincoin-web// $Id: time_test.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin time_test.cpp$$ $spell cppad.hpp Microsoft namespace std const cout ctime ifdef const endif cpp $$ $section time_test: Example and test$$ $mindex time_test$$ $code $srcfile%speed/example/time_test.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { // empty namespace using CppAD::vector; // size for the test size_t size_; vector a, b, c; void test(size_t repeat) { // setup a.resize(size_); b.resize(size_); c.resize(size_); size_t i = size_;; while(i) { --i; a[i] = i; b[i] = 2 * i; c[i] = 0.0; } // operations we are timing while(repeat--) { i = size_;; while(i) { --i; c[i] += std::sqrt(a[i] * a[i] + b[i] * b[i]); } } } } bool time_test(void) { bool ok = true; // minimum amount of time to run test double time_min = 0.5; // size of first test case size_ = 20; // run the first test case double time_first = CppAD::time_test(test, time_min); // size of second test case is twice as large size_ = 2 * size_; // run the second test case double time_second = CppAD::time_test(test, time_min); // for this case, time should be linear w.r.t size double rel_diff = 1. - 2. * time_first / time_second; ok &= (std::fabs(rel_diff) <= .1); if( ! ok ) std::cout << std::endl << "rel_diff = " << rel_diff << std::endl; a.clear(); b.clear(); c.clear(); return ok; } // END C++ cppad-20170000.3/speed/example/speed_test.cpp0000644000175200017650000000423013057470457020033 0ustar coincoin-web// $Id: speed_test.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin speed_test.cpp$$ $spell cppad.hpp Microsoft namespace std const cout ctime ifdef const endif cpp $$ $section speed_test: Example and test$$ $mindex speed_test$$ $code $srcfile%speed/example/speed_test.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { // empty namespace using CppAD::vector; vector a, b, c; void test(size_t size, size_t repeat) { // setup a.resize(size); b.resize(size); c.resize(size); size_t i = size;; while(i) { --i; a[i] = i; b[i] = 2 * i; c[i] = 0.0; } // operations we are timing while(repeat--) { i = size;; while(i) { --i; c[i] += std::sqrt(a[i] * a[i] + b[i] * b[i]); } } } } bool speed_test(void) { bool ok = true; // size of the test cases vector size_vec(2); size_vec[0] = 40; size_vec[1] = 80; // minimum amount of time to run test double time_min = 0.5; // run the test cases vector rate_vec(2); rate_vec = CppAD::speed_test(test, size_vec, time_min); // time per repeat loop (note counting setup or teardown) double time_0 = 1. / double(rate_vec[0]); double time_1 = 1. / double(rate_vec[1]); // for this case, time should be linear w.r.t size double check = double(size_vec[1]) * time_0 / double(size_vec[0]); double rel_diff = (check - time_1) / time_1; ok &= (std::fabs(rel_diff) <= .1); if( ! 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparse_jac_fun.cpp$$ $spell jac $$ $section sparse_jac_fun: Example and test$$ $mindex sparse_jac_fun$$ $code $srcfile%speed/example/sparse_jac_fun.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool sparse_jac_fun(void) { using CppAD::NearEqual; using CppAD::AD; bool ok = true; size_t j, k; double eps = CppAD::numeric_limits::epsilon(); size_t n = 3; size_t m = 4; size_t K = 5; CppAD::vector row(K), col(K); CppAD::vector x(n), yp(K); CppAD::vector< AD > a_x(n), a_y(m); // choose x for(j = 0; j < n; j++) a_x[j] = x[j] = double(j + 1); // choose row, col for(k = 0; k < K; k++) { row[k] = k % m; col[k] = (K - k) % n; } // declare independent variables Independent(a_x); // evaluate function size_t order = 0; CppAD::sparse_jac_fun< AD >(m, n, a_x, row, col, order, a_y); // evaluate derivative order = 1; CppAD::sparse_jac_fun(m, n, x, row, col, order, yp); // use AD to evaluate derivative CppAD::ADFun f(a_x, a_y); CppAD::vector jac(m * n); jac = f.Jacobian(x); for(k = 0; k < K; k++) { size_t index = row[k] * n + col[k]; ok &= NearEqual(jac[index], yp[k] , eps, eps); } return ok; } // END C++ cppad-20170000.3/speed/example/det_of_minor.cpp0000644000175200017650000000400713057470457020342 0ustar coincoin-web// $Id: det_of_minor.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin det_of_minor.cpp$$ $spell det Cpp $$ $section Determinant of a Minor: Example and Test$$ $mindex det_of_minor$$ $code $srcfile%speed/example/det_of_minor.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool det_of_minor() { bool ok = true; size_t i; // dimension of the matrix A size_t m = 3; // index vectors set so minor is the entire matrix A std::vector r(m + 1); std::vector c(m + 1); for(i= 0; i < m; i++) { r[i] = i+1; c[i] = i+1; } r[m] = 0; c[m] = 0; // values in the matrix A double data[] = { 1., 2., 3., 3., 2., 1., 2., 1., 2. }; // construct vector a with the values of the matrix A std::vector a(data, data + 9); // evaluate the determinant of A size_t n = m; // minor has same dimension as A double det = CppAD::det_of_minor(a, m, n, r, c); // check the value of the determinant of A ok &= (det == (double) (1*(2*2-1*1) - 2*(3*2-1*2) + 3*(3*1-2*2)) ); // minor where row 0 and column 1 are removed r[m] = 1; // skip row index 0 by starting at row index 1 c[0] = 2; // skip column index 1 by pointing from index 0 to index 2 // evaluate determinant of the minor n = m - 1; // dimension of the minor det = CppAD::det_of_minor(a, m, m-1, r, c); // check the value of the determinant of the minor ok &= (det == (double) (3*2-1*2) ); return ok; } // END C++ cppad-20170000.3/speed/example/sparse_hes_fun.cpp0000644000175200017650000000415113057470457020702 0ustar coincoin-web// $Id: sparse_hes_fun.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparse_hes_fun.cpp$$ $spell hes $$ $section sparse_hes_fun: Example and test$$ $mindex sparse_hes_fun$$ $code $srcfile%speed/example/sparse_hes_fun.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool sparse_hes_fun(void) { using CppAD::NearEqual; bool ok = true; typedef CppAD::AD ADScalar; size_t j, k; double eps = 10. * CppAD::numeric_limits::epsilon(); size_t n = 5; size_t m = 1; size_t K = 2 * n; CppAD::vector row(K), col(K); CppAD::vector x(n), ypp(K); CppAD::vector a_x(n), a_y(m); // choose x for(j = 0; j < n; j++) a_x[j] = x[j] = double(j + 1); // choose row, col for(k = 0; k < K; k++) { row[k] = k % 3; col[k] = k / 3; } for(k = 0; k < K; k++) { for(size_t k1 = 0; k1 < K; k1++) assert( k == k1 || row[k] != row[k1] || col[k] != col[k1] ); } // declare independent variables Independent(a_x); // evaluate function size_t order = 0; CppAD::sparse_hes_fun(n, a_x, row, col, order, a_y); // evaluate Hessian order = 2; CppAD::sparse_hes_fun(n, x, row, col, order, ypp); // use AD to evaluate Hessian CppAD::ADFun f(a_x, a_y); CppAD::vector hes(n * n); // compoute Hessian of f_0 (x) hes = f.Hessian(x, 0); for(k = 0; k < K; k++) { size_t index = row[k] * n + col[k]; ok &= NearEqual(hes[index], ypp[k] , eps, eps); } return ok; } // END C++ cppad-20170000.3/speed/example/det_by_lu.cpp0000644000175200017650000000274513057470457017653 0ustar coincoin-web// $Id: det_by_lu.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin det_by_lu.cpp$$ $spell Cpp Lu $$ $section Determinant Using Lu Factorization: Example and Test$$ $mindex minors$$ $code $srcfile%speed/example/det_by_lu.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool det_by_lu() { bool ok = true; // dimension of the matrix size_t n = 3; // construct the determinat object CppAD::det_by_lu Det(n); double a[] = { 1., 2., 3., // a[0] a[1] a[2] 3., 2., 1., // a[3] a[4] a[5] 2., 1., 2. // a[6] a[7] a[8] }; CPPAD_TESTVECTOR(double) A(9); size_t i; for(i = 0; i < 9; i++) A[i] = a[i]; // evaluate the determinant double det = Det(A); double check; check = a[0]*(a[4]*a[8] - a[5]*a[7]) - a[1]*(a[3]*a[8] - a[5]*a[6]) + a[2]*(a[3]*a[7] - a[4]*a[6]); ok = CppAD::NearEqual(det, check, 1e-10, 1e-10); return ok; } // END C++ cppad-20170000.3/speed/example/speed_program.cpp0000644000175200017650000000424613057470457020532 0ustar coincoin-web// $Id: speed_program.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin speed_program.cpp$$ $spell speed_program.exe cppad.hpp Microsoft namespace std const cout ctime ifdef const endif cpp $$ $section Example Use of SpeedTest$$ $mindex test speed$$ $head Running This Program$$ On a Unix system that includes the $code g++$$ compiler, you can compile and run this program by changing into the $code speed/example$$ directory and executing the following commands $codep g++ -I../.. speed_program.cpp -o speed_program.exe ./speed_program.exe $$ $head Program$$ $srccode%cpp% */ # include std::string Test(size_t size, size_t repeat) { // setup double *a = new double[size]; double *b = new double[size]; double *c = new double[size]; size_t i = size;; while(i) { --i; a[i] = i; b[i] = 2 * i; } // operations we are timing while(repeat--) { i = size;; while(i) { --i; c[i] = a[i] + b[i]; } } // teardown delete [] a; delete [] b; delete [] c; // return a test name that is valid for all sizes and repeats return "double: c[*] = a[*] + b[*]"; } int main(void) { CppAD::SpeedTest(Test, 10, 10, 100); return 0; } /* %$$ $head Output$$ Executing of the program above generated the following output (the rates will be different for each particular system): $codep double: c[*] = a[*] + b[*] size = 10 rate = 14,122,236 size = 20 rate = 7,157,515 size = 30 rate = 4,972,500 size = 40 rate = 3,887,214 size = 50 rate = 3,123,086 size = 60 rate = 2,685,214 size = 70 rate = 2,314,737 size = 80 rate = 2,032,124 size = 90 rate = 1,814,145 size = 100 rate = 1,657,828 $$ $end */ cppad-20170000.3/speed/CMakeLists.txt0000644000175200017650000000341113057470457016275 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Specify build type for this directory and all its subdirectories # (subdirectories do not specify build type). # Possible values are DEBUG, RELEASE, RelWithDebInfo and MinSizeRel # CppAD developers can use DEBUG for debugging speed tests. SET(CMAKE_BUILD_TYPE RELEASE) # Initialize list of tests as empty SET(check_speed_depends "") # The CMakeLists.txt file in the specified source directory is processed # before the current input file continues beyond this command. # add_subdirectory(source_dir [binary_dir] [EXCLUDE_FROM_ALL]) ADD_SUBDIRECTORY(src) ADD_SUBDIRECTORY(cppad) ADD_SUBDIRECTORY(double) ADD_SUBDIRECTORY(example) IF ( cppad_profile_flag ) ADD_SUBDIRECTORY(profile) ENDIF ( cppad_profile_flag ) # IF ( adolc_prefix ) ADD_SUBDIRECTORY(adolc) ENDIF( adolc_prefix ) IF ( fadbad_prefix ) ADD_SUBDIRECTORY(fadbad) ENDIF( fadbad_prefix ) IF ( sacado_prefix ) ADD_SUBDIRECTORY(sacado) ENDIF( sacado_prefix ) # check_speed ADD_CUSTOM_TARGET(check_speed DEPENDS ${check_speed_depends} ) MESSAGE(STATUS "make check_speed: available") # Change check depends in parent environment add_to_list(check_depends check_speed) SET(check_depends "${check_depends}" PARENT_SCOPE) cppad-20170000.3/.gitignore0000644000175200017650000000106513032160414014406 0ustar coincoin-web# only one file git_commit.sh aclocal.m4 ar-lib autom4te.cache bin/test_one.sh commit.sh.old cppad/configure.hpp test_one.cpp test_one.exe # only one directory doc doxydoc # all directories *.err */*.err */*/*.err *.log */*.log */*/*.log *.swp */*.swp */*/*.swp *.tmp */*.tmp */*/*.tmp build */build */*/build # all directories with and without extension new new.* */new */new.* */*/new */*/new.* doxyfile doxyfile.* */doxyfile */doxyfile.* */*/doxyfile */*/doxyfile.* junk junk.* */junk */junk.* */*/junk */*/junk.* temp temp.* */temp */temp.* */*/temp */*/temp.* cppad-20170000.3/uw_copy_040507.html0000644000175200017650000011554210527074276015636 0ustar coincoin-webVol 4, Part 5, Chapter 7

Chapter 7

PATENT, INVENTION, AND COPYRIGHT POLICY

Section 1. Patent and Invention Policy

  1. This policy covers both patented and nonpatented innovations, including computer software with commercial value, and is applicable to all faculty, staff, and students. The policy is intended to show the University's positive attitude toward transfer of results of its research to the private sector.

  2. The purpose of university research is to seek new knowledge for the general benefit. Although university research is not directed intentionally toward inventions, commercially valuable inventions do often result, and it is generally in the best interests of the University and the public that patents be obtained and/or licenses granted as described in this policy. Inventions shall be promptly reported to the University's Office of Intellectual Property and Technology Transfer and all concerned shall cooperate to assure prompt initiation of appropriate technology transfer actions. The term "invention" means any invention or discovery which is or may be patentable or otherwise protectable as to ownership. An invention may be a process, machine, manufacture, composition of matter or design, or any new or useful improvement thereof. An invention is deemed to be "made" when it is conceived or first actually reduced to practice.

  3. University employees shall report all inventions and discoveries to the University's Office of Intellectual Property and Technology Transfer. As a condition of employment, and even if a specific patent agreement is not signed, University employees agree to assign all inventions in which the University has an interest to the University, to an invention management agency designated by the University, or to the sponsor if required under agreements governing the research. Employees shall execute documents of assignment and do everything reasonably required to assist the assignee(s) in obtaining, protecting, and maintaining patent or other proprietary rights. Students who are also employees, students working on a sponsored project, and students who have used University resources (other than for lecture-based coursework) shall also report all inventions and discoveries to the University's Office of Intellectual Property and Technology Transfer and shall assign all such inventions and discoveries in the same manner as University employees. Inventions in which the University has an interest but which do not meet University criteria for patenting shall be managed in accordance with policies and procedures determined by the University Office of Intellectual Property and Technology Transfer. If and to the extent permitted by state law and other University policies, those procedures may include: (a) a mechanism by which the inventor(s) may personally pay patenting costs; (b) the formation of a commercial enterprise to pursue commercialization; and, under very rare circumstances, (c) the transfer, for appropriate consideration, of the patent rights to the inventor(s). These procedures shall be implemented at the discretion of the Vice Provost for Intellectual Property and Technology Transfer.

    Although all inventions and discoveries must be reported to the Office of Intellectual Property and Technology Transfer, there are instances when the University may choose not to assert ownership. The University will not require assignment of interests for any invention for which no equipment, supplies, facilities, or trade secret information of the University was used and which was developed entirely on the employee's own time, unless (a) the inventions related (i) directly to the business of the University, or (ii) the University's actual or demonstrably anticipated research or development, or (b) the invention results from any work performed by the employee for the University.

  4. Research funded wholly or in part by an outside sponsor is subject to this policy as modified by the provisions of the agreement covering such work. Employees engaged in sponsored research are bound by the provisions of the agreement between the University and the sponsor. Title to any inventions conceived or first reduced to practice in the course of research supported by Federal agencies, industry, or other sponsors shall generally vest in the University. In rare cases, an industrial sponsor may possess a dominant patent position in a certain technology area so that any patent the University might seek would be of little or no value. For this or other reasons, an exception to the University title policy may be approved by the University's Office of Intellectual Property and Technology Transfer when to do so will honor the general principles of this policy, protect the equities involved, and satisfy the requirements of the parties.

  5. Industry supported research is valued by the University when it embraces a proper balance between the University's educational mission and industry's quest for the development of commercial products, processes, and services. Interaction with industry may take any of several forms, including grants, contracts, consortia agreements, and affiliate programs. Industry sponsors may be assured of at least a non-exclusive license to inventions conceived or developed with their support. Where the sponsor uses the invention entirely within its own operations, the license may be royalty-free. Where the sponsor, or a third party, manufactures and sells products, services, or processes based on the invention, reasonable royalty payments to the University, or its assignee, are required. If necessary for the effective development and marketing of a University invention, an exclusive license may be granted, usually for a limited time period. Where an invention is not identifiable in advance, the University may grant the sponsor an option to an exclusive license if the sponsor agrees to finance the cost of the University's patent application and observe certain diligence requirements that will assure promptly bringing the invention into public use. The patent financing may be treated as an offset against royalties payable when the invention is marketed.

  6. The University retains the right to file patents itself or to use other patent management firms. The University has agreements with the Washington Research Foundation, Research Corporation Technologies of Tucson, Arizona and Battelle Development Corporation in Columbus, Ohio as patent and license agents.

  7. Both the University and the inventor are entitled to a share of income from licensed inventions; the University on the basis of salary and facilities support for the inventor and the cost of patent or license administration; and the inventor on the basis of creative activity, documenting the invention, and assisting as necessary with commercialization. Thus, the University allocates a share of income to the inventor. The remainder is dedicated to further research by allocating shares to the college/department (or other unit) in which the invention was conceived or first reduced to practice and to the Office of the Provost.

  8. The University may take an equity position in a company whether or not license fees or royalties are paid to the University as part of a negotiated agreement. A typical circumstance under which the University might receive equity would be as part of an agreement licensing University-developed technology to a start-up or developing business venture. Another example might occur when an employee of the University utilizes the expertise and/or technology he or she has developed in the course of University employment and assists a business venture in the commercialization of an idea. (A business venture includes corporations, partnerships, or other commercial enterprises.) Such a commercial association with the University and its employees adds both value and credibility to the new business venture. To assure a balance of interests for the business venture as well as for the University, the University will generally require that it receive an equity position in such circumstances.

    9. The University's equity interests are managed and disposed of in accordance with guidelines established by the Treasury Office in consultation with the Office of the Provost and the policies and procedures stated in the University Handbook and Administrative Policy Statements. University employees may be eligible to receive a portion of the University's equity interest in accordance with the policies and procedures described in the University's Administrative Policy Statements and as allowed under state law and University conflict of interest policies. When such equities are liquidated, the net proceeds, after recovery of all University costs and after any distributions to eligible recipients, accrue to appropriate University accounts and are administered by the Provost to promote research and technology transfer across the entire University. If the proceeds from the disposition of a particular equity interest are unusually large, the Provost shall confer with the University Budget Committee, the Research Advisory Board, or other appropriate faculty bodies, on alternative uses for amounts in excess of a base figure (set at $3 million in 2000 dollars).

    There may be situations in which both the University and its employees separately own equity interests in a business venture. In such circumstances, the employee's equity interest is considered to be independent of the University's equity interest and is not held, managed, disposed of, or distributed by the University. An example would be a case in which the University receives an equity interest in a business venture as a result of licensing certain intellectual property developed by one of its employees and in which the same employee also owns a equity interest as a result of being a founder of the business venture receiving the license. In this example, the employee's equity interest is not held or managed by the University, but rather by the employee, and the employee's status as a founder having an ownership stake in the business venture renders the employee ineligible to receive a distribution of a portion of the University-owned equity.

  9. As a public institution, the University should undertake sponsored research only when the results can be published. Publication may be deferred for a reasonable time during which the University and the sponsor review the feasibility of patent coverage or other protection on an invention described in the publication. Likewise, graduate student theses or dissertations containing invention details may be withheld from the Library shelves for a limited period while this evaluation process is conducted. Some research agreements may involve University access to a sponsor's proprietary data subject to a clause defining the conditions under which such data will be identified, accepted, and used. Students should be able to participate in such research in a meaningful way without access to proprietary data. When publication of the research involving proprietary data is contemplated, the University may agree to provide the sponsor with advance copy prior to submission for publication to allow the sponsor an opportunity to identify any inadvertent disclosure of proprietary data.

  10. Employee consulting with commercial enterprises can be of significant benefit to the University, the employee, the commercial entity, and the general public. However, such involvements include the potential for conflicts of interest, for the inhibition of the free exchange of information, and for interference with the employee's primary allegiance to the University. University employees should be guided in these arrangements by the policy stated in Volume Four, Part V, Chapters 2 and 6 of the University Handbook. Invention clauses in consulting agreements must be consistent with the policy of the University and with University commitments under sponsored research agreements. Questions concerning potential conflicts should be referred to the University's Office of the Provost and the Office of Research.

  11. Conflicts of interest are of prime concern when a faculty member is involved in "deeper than consulting" arrangements with business ventures. Although the faculty member may hold an equity interest or a management position in a business venture, he or she must do so consistent with the principles and procedures of Executive Order 57 (University Handbook, Volume Four, Part V, Chapter 6, Section 6, Involvement with Commercial Enterprise, Deeper than Consulting). In situations where the employee is a board member, manager, or receives shares of stock, the option to purchase stock, or other equity interest in return for the use of his or her services and/or inventions in a business venture, approval by the Office of the Provost (after review by the dean and the chair) is required. The primary focus of the review by the Office of the Provost will be to ensure that potential conflicts of interest and exposure to liability are properly managed. For example, the interests of the graduate students involved in such cases must be protected, there must be no direct managerial involvement of the faculty member in the business venture, there must be an arms-length relationship between the faculty member's responsibilities to the business venture and the faculty member's academic responsibilities, and mechanisms must be in place to ensure that the research program of the faculty member is not distorted by his or her interests in the business venture.

Section 2. Copyright Policy

  1. Background.

    2. The University encourages the publication of scholarly works as an inherent part of its educational mission. In this connection, the University acknowledges the right of faculty, staff, and students to prepare and publish, through individual initiative, articles, pamphlets, and books that are copyrighted by the authors or their publishers and that may generate royalty income for the authors.

    The variety and number of copyrightable materials that may be created in the university community have increased significantly in recent years as have the author-university- sponsor relationships under which such materials are produced. Therefore, the following statement of University policy on ownership and use of copyrightable materials is provided to clarify the respective rights of individuals and the University in this increasingly important area. The policy will be administered by the University's Office of Intellectual Property and Technology Transfer.

  2. General Statement of University Policy on Ownership and Use of Copyrightable Materials

    3. University faculty, staff, and students retain all rights in copyrightable materials they create, including scholarly works, subject to the following exceptions and conditions:

    1. Grant and Contract Limitations. Conditions regarding rights in data or restrictions on copyright privileges contained in sponsored grants, contracts, or other awards are binding on the University and on faculty, staff, or student authors. Copyright works, with the exception of routine progress reports, prepared as required elements of such sponsored grants, contracts, or other awards shall be reported to the Office of Intellectual Property and Technology Transfer for review prior to any external dissemination of the work. If necessary to fulfill grant and contract limitations, authors shall execute an appropriate written assignment of copyrights to the University.

    2. University-Owned Materials. Materials shall be "University-owned" within the meaning of this policy statement if the work is a "work for hire" under copyright law or the author was commissioned in writing by the University (or one of its colleges, schools, departments, or other divisions) to develop the materials as a part of the author's regularly compensated duties, as for example, released time arrangements in the case of faculty members. As to a faculty member, "commissioned in writing" specifically does not refer to his or her general obligation to produce scholarly works.

    3. University-Sponsored Materials. Materials shall be "University-sponsored materials" within the meaning of this policy statement if the author developed the materials in the course of performance of his or her normal duties and utilized University staff, resources, or funding to develop the work. As to a faculty member, "normal duties" does not include his or her usual scholarly activity unless it involves extensive uncompensated use of University resources.

    4. Written Agreements. It is desirable to reach agreement in writing as to the rights of the University and of participants before work begins whenever (1) a question exists as to whether the materials will be University-owned or University-sponsored, or (2) copyrightable materials are likely to result from the joint efforts of persons in academic departments and University service departments. As to jointly-developed materials, determination of rights in written form shall be accomplished no later than prior to sale of the materials in question. Questions concerning the interpretation and administration of this policy shall be resolved in accordance with Section 3.

    5. Proportional Ownership. In case of materials developed in substantial part under commission and in substantial part through other means, the materials shall be regarded as "University-owned" in an appropriate proportion. In the case of materials developed in substantial part during the course of normal duties and with use of University staff, resources, or funding the materials shall be regarded as "University-sponsored" in an appropriate proportion.

    6. Royalty-Free Privileges to University. The University retains a right to royalty-free use of any copyrightable materials developed by University employees (other than books and materials available from a publisher through normal distribution channels) when the development of such materials was advanced through the use of University facilities, supplies, equipment, or staff services. This right exists even though the materials do not constitute University-owned or University-sponsored materials as defined above (e.g., where use of facilities by a faculty member was not extensive).

    7. Student Writings. Students employed by the University in any capacity are covered by the terms of this policy. In addition, where a student receives financial aid or remuneration under a sponsored research, training, or fellowship program, his or her rights in copyrightable materials are limited by the terms of the University agreement with the sponsoring agency. The University has no ownership rights in copyrightable materials developed by students who are not employees of the University or in materials unrelated to their employment.

  3. Types of Materials.

    4. The types of materials to which this policy is intended to apply include:

    1. Video and audio recordings, tapes, and cassettes.
    2. Film, film strips and other visual aids.
    3. Books, texts, study guides and similar published materials.
    4. Computer programs and software when copyright rather than patent or trade secret protection is relied upon as the primary source of legal protection. (When the primary commercial value of a computer program lies in its transfer in limited quantities under arrangements of confidentiality, it shall be treated as unpatented technology and be subject to the University Patent and Invention Policy.)
    5. Musical or dramatic compositions.
    6. Internet-based productions and multimedia products.
    7. Other copyrightable materials.

  4. Rights Involved in use of University-Owned or University- Sponsored Materials.

    1. Two categories of use are differentiated for purposes of this policy: internal use and external use. Internal use refers to use by any unit of the University for instruction, research, or other educational purposes. External use refers to use by other educational institutions, government and other nonprofit institutions, and use resulting from lease or other contractual arrangements for commercial distribution of the materials.

    2. Use of University-owned or University-sponsored materials under this policy shall be subject to the following conditions:

      1. Internal use

        1. Each instance of use of such materials within the University requires the approval of the author and the department or college unless advance approval is waived through a prior written understanding or the author's consent is implicit in the terms of the grant or contract supporting the work. Internal uses of such materials will not involve a transfer of funds between departments unless the lending department incurs incremental costs in order to make the materials available.

        2. As long as the author or producer of such materials remains an employee of the University, the author may: (a) request reasonable revisions of the materials prior to any instance of internal use, or (b) ask that the materials be withdrawn from internal use if revisions are not feasible.

          3. In cases where the University has invested significant funds in the production of the materials and the author/producer is unable to agree with the department head on appropriate revision or withdrawal of materials, the question will be referred to the dean of the school or college for mediation.

        3. If the author or producer terminates employment with the University, then the University retains the right to continue internal use of the material unless the author/producer and the University agree in writing on special conditions for subsequent internal use of the materials and the procedures for their revision.

      2. External use

        3. Licensing or sale of University-owned or University- sponsored materials for external use shall be preceded by a written agreement between the University and the author or producer specifying the conditions of use, and including provisions concerning the right of the author or producer to revise the materials periodically, or to withdraw them from use-- subject to existing agreements--in the event revisions are not feasible.

  1. Division of Royalties.

    1. General Policy on Royalties. As to University-owned materials, all royalties and income should inure to the University and its schools, colleges, and departments as such materials are prepared in exchange for agreed compensation. As to University-sponsored materials, a sharing of royalties and income is appropriate because of the author's provision of creative efforts on the one hand and the University's provision of salary, facilities, administrative support, and other resources.

    2. Royalties on Sales to Outside Users. Where University-owned or University-sponsored materials are to be sold or rented to outside users, the following guidelines pertaining to financial arrangements should be observed (subject to any limitations specified by granting agencies):

      1. All incremental expenses related to the distribution of copies will be recovered from each sale or rental. Original costs for production of the materials shall be recovered only if and as agreed to in writing prior to preparation of the materials by the author and the academic departments and/or other University units which incur those costs.

      2. In the case of University-owned materials, royalty and other income from sale or use of the materials (after recovery of costs as specified in 1.) shall be divided one-half to the University and one-half to the school/college/department of the author or authors. The University share shall be used to promote research across the whole University and shall normally be administered by the Office of Research. The school/college/department share shall be allocated to the dean of the college or school, and may be used for research, education, and communications. At least 75% of this share should normally go to the author's department for use there according to departmental and college goals. The dean should have discretion in distributing the remaining 25% to promote activities according to the nature and needs of the college or school in question.

      3. In the case of University-sponsored materials, royalty and other income from the sale or use of materials (after recovery of costs as specified in a.) shall be divided according to the Administrative Policy Statement 59.4, "Technology Transfer." In any given case covered by this subsection, the author may dedicate all or any portion of his/her allocation to the school/college/department, the Office of Research, or other administrative unit, subject to the provisions of Administrative Policy Statement 59.4).

      4. In certain instances it may be advantageous to market University-owned or University-sponsored materials through outside commercial sources or the University Press. Net royalty income from such sources shall be divided as specified in b. and c.

      5. Royalty and other income from updating and revision of University-sponsored materials shall be treated as income and royalty from such University-sponsored materials, unless otherwise agreed to in writing by the author/producer and the University before preparation of the original materials. The net income from such upkeep or revision shall be separately computed on an annual basis for the purpose of applying the distributions referenced in paragraph c.

  2. Protection and Liability.

    1. Protection. The Office of Intellectual Property and Technology Transfer shall investigate allegations of unauthorized use or copyright infringement of University-owned and University-sponsored materials and shall recommend appropriate action. If such action is started by the University, all costs of such action shall be borne by the University. All proceeds in excess of such costs shall be shared as provided in Subection F. (subject to sponsoring agency limitations if a grant or contract is involved).

    2. Liability. When there are allegations of violation of personal or property rights by the University, or by the author or producer of University-owned or University-sponsored materials copyrighted by the University, the University shall assume responsibility for the defense of any action and the satisfaction of any judgment rendered against the University or the author or producer.

Section 3. Interpretation and Administration of Policy.

  1. The President has designated the Vice Provost for Intellectual Property and Technology Transfer as the officer of the University to administer, apply, and interpret the provisions of this policy. The Vice Provost shall have the authority to determine whether the facts of a given case merit special consideration.

  2. Committee. The President of the University will appoint an Intellectual Property Management Advisory Committee to review periodically the policy set forth in this statement and recommend such changes to the President as the Committee deems desirable. The Committee will also advise on broader intellectual property issues that arise in the promotion and protection of research. The Committee will report to the Vice Provost for Intellectual Property and Technology Transfer and consist of no fewer than five members, a majority of whom shall be chosen from the faculty.

  3. Distribution of Statement. When this statement becomes effective as University policy, the President's office shall see that all departments and administrative offices of the University are properly informed. Thereafter, the Vice Provost for Intellectual Property and Technology Transfer shall remind deans and department heads periodically of the existence of the policy, inform them about any significant interpretations of the policy, and invite comments or questions regarding it.

  4. Duties of Vice Provost for Intellectual Property and Technology Transfer. The Vice Provost for Intellectual Property and Technology Transfer shall manage the Office of Intellectual Property and Technology Transfer, which will represent the University in negotiating agreements with inventors, authors or producers, or licensees pursuant to this policy. She or he may consult also with department heads and the heads of production units involved in a specific technology transfer transaction, and she or he shall sign or recommend all agreements for signing consistent with delegated authority. Where copyright coverage should be obtained on University-sponsored or University-owned materials, the Office of Intellectual Property and Technology Transfer will facilitate the copyright application. The faculty or staff member who is the author of University-owned or University-sponsored materials shall execute a written transfer of copyright to the University when necessary or appropriate.

  5. Inquiries on Status of Materials. Any faculty or staff member who has a question as to whether or not particular materials will be considered University-owned or University- sponsored should initiate an inquiry to the Office of Intellectual Property and Technology Transfer as to their status. This inquiry, with all relevant facts, should be forwarded via the author's department head. Thereafter, the Vice Provost for Intellectual Property and Technology Transfer shall advise the author or producer as promptly as possible as to whether or not it appears that the materials should be regarded as University-owned or University-sponsored within the meaning of this policy. The Vice Provost for Intellectual Property and Technology Transfer's decision in such cases will be considered as an advisory opinion subject to final clarification when the work is completed. At that time, the faculty or staff member should either (1) indicate concurrence in the original decision, or (2) request that the question of rights be submitted for decision to the Vice Provost for Intellectual Property and Technology Transfer. In the latter case, the decision of the Vice Provost will be final unless the faculty or staff member requests arbitration of the question.

  6. Arbitration. In the event of any differences between faculty or staff members, on the one hand, and the Vice Provost for Intellectual Property and Technology Transfer, on the other hand, and when the questions cannot be reconciled by direct negotiation, the matter shall be submitted for binding arbitration either to a single arbitrator agreed on by all parties or to a special three-person panel consisting of one person representing the faculty or staff member, one person representing the University, and a third person designated by the first two. Knowledgeable members of the University community will normally be chosen for such panels in order to expedite a decision and minimize cost. In the event costs are incurred, they shall be divided equally between the faculty/staff member and the University. Decisions of the panel will be binding on both parties. The panel shall have full access to any pertinent records over which the faculty/staff member or the University has jurisdiction.

BR, March 1969; Executive Order No. 36 of the President, June 1, 1972; revised October 3, 1977; September 26, 1983; September 21, 1992; May 2, 2000, December 20, 2000; October 27, 2003.

cppad-20170000.3/missing0000755000175200017650000001533012561675772014045 0ustar coincoin-web#! /bin/sh # Common wrapper for a few potentially missing GNU programs. scriptversion=2013-10-28.13; # UTC # Copyright (C) 1996-2014 Free Software Foundation, Inc. # Originally written by Fran,cois Pinard , 1996. # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2, or (at your option) # any later version. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # You should have received a copy of the GNU General Public License # along with this program. If not, see . # As a special exception to the GNU General Public License, if you # distribute this file as part of a program that contains a # configuration script generated by Autoconf, you may include it under # the same distribution terms that you use for the rest of that program. if test $# -eq 0; then echo 1>&2 "Try '$0 --help' for more information" exit 1 fi case $1 in --is-lightweight) # Used by our autoconf macros to check whether the available missing # script is modern enough. exit 0 ;; --run) # Back-compat with the calling convention used by older automake. shift ;; -h|--h|--he|--hel|--help) echo "\ $0 [OPTION]... PROGRAM [ARGUMENT]... Run 'PROGRAM [ARGUMENT]...', returning a proper advice when this fails due to PROGRAM being missing or too old. 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This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build and install the cppad_lib shared library # # string(REGEX REPLACE # # [...]) # # (year - 2000) dot (remove leading 0 from mmdd) dot (release) # Note that the dot (release) is optional # Also name that when mmdd is 0000 get (year - 2000) dot dot (release) STRING(REGEX REPLACE "20([0-9][0-9])0*([0-9]*)([.]?[0-9]*)" "\\1.\\2\\3" soversion ${cppad_version} ) # In case where mmdd is 0000, dot (release) is present. Convert to # (year - 2000) dot 0 dot (release) STRING(REGEX REPLACE "([.][.])" ".0." soversion ${soversion} ) print_variable(soversion) # # add_library( [STATIC | SHARED | MODULE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN) # ) ADD_LIBRARY( cppad_lib SHARED cppad_colpack.cpp ) # set_target_properties(target1 target2 ... # PROPERTIES prop1 value1 prop2 value2 ...) SET_TARGET_PROPERTIES( cppad_lib PROPERTIES SOVERSION ${soversion} ) # # install(TARGETS myExe mySharedLib myStaticLib # RUNTIME DESTINATION bin # LIBRARY DESTINATION lib # ARCHIVE DESTINATION lib/static) INSTALL(TARGETS cppad_lib DESTINATION ${cppad_abs_libdir}) cppad-20170000.3/cppad_lib/cppad_colpack.cpp0000644000175200017650000001517213057470457017650 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # include # include # if CPPAD_HAS_COLPACK == 0 namespace CppAD { namespace local { CPPAD_LIB_EXPORT void this_routine_should_never_get_called(void) { CPPAD_ASSERT_UNKNOWN(false); } } # else // CPPAD_HAS_COLPACK # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file cppad_colpack.cpp The CppAD interface to the Colpack coloring algorithms. */ /*! Determine which rows of a general sparse matrix can be computed together. \param color is a vector with color.size() == m. For i = 0 , ... , m-1, color[i] is the color for the corresponding row of the matrix. If color[i1]==color[i2], (i1, j1) is in sparsity pattern, and (i2, j2) is in sparsity pattern, then j1 is not equal to j2. \param m is the number of rows in the matrix. \param n is the number of columns in the matrix. \param adolc_pattern is a vector with adolc_pattern.size() == m. For i = 0 , ... , m-1, and for k = 1, ... ,adolc_pattern[i][0], the entry with index (i, adolc_pattern[i][k]) is a non-zero in the sparsity pattern for the matrix. */ // ---------------------------------------------------------------------- CPPAD_LIB_EXPORT void cppad_colpack_general( CppAD::vector& color , size_t m , size_t n , const CppAD::vector& adolc_pattern ) { size_t i, k; CPPAD_ASSERT_UNKNOWN( adolc_pattern.size() == m ); CPPAD_ASSERT_UNKNOWN( color.size() == m ); // Use adolc sparsity pattern to create corresponding bipartite graph ColPack::BipartiteGraphPartialColoringInterface graph( SRC_MEM_ADOLC, adolc_pattern.data(), m, n ); // row ordered Partial-Distance-Two-Coloring of the bipartite graph graph.PartialDistanceTwoColoring( "SMALLEST_LAST", "ROW_PARTIAL_DISTANCE_TWO" ); // Use coloring information to create seed matrix int n_seed_row; int n_seed_col; double** seed_matrix = graph.GetSeedMatrix(&n_seed_row, &n_seed_col); CPPAD_ASSERT_UNKNOWN( size_t(n_seed_col) == m ); // now return coloring in format required by CppAD for(i = 0; i < m; i++) color[i] = m; for(k = 0; k < size_t(n_seed_row); k++) { for(i = 0; i < m; i++) { if( seed_matrix[k][i] != 0.0 ) { // check that no row appears twice in the coloring CPPAD_ASSERT_UNKNOWN( color[i] == m ); color[i] = k; } } } # ifndef NDEBUG // check that all non-zero rows appear in the coloring for(i = 0; i < m; i++) CPPAD_ASSERT_UNKNOWN(color[i] < m || adolc_pattern[i][0] == 0); // check that no rows with the same color have overlapping entries CppAD::vector found(n); for(k = 0; k < size_t(n_seed_row); k++) { size_t j, ell; for(j = 0; j < n; j++) found[j] = false; for(i = 0; i < m; i++) if( color[i] == k ) { for(ell = 0; ell < adolc_pattern[i][0]; ell++) { j = adolc_pattern[i][1 + ell]; CPPAD_ASSERT_UNKNOWN( ! found[j] ); found[j] = true; } } } # endif return; } // ---------------------------------------------------------------------- /*! Determine which rows of a symmetrix sparse matrix can be computed together. \param color is a vector with color.size() == m. For i = 0 , ... , m-1, color[i] is the color for the corresponding row of the matrix. We say that a sparsity pattern entry (i, j) is valid if for all i1, such that i1 != i and color[i1]==color[i], and all j1, such that (i1, j1) is in sparsity pattern, j1 != j. The coloring is chosen so that for all (i, j) in the sparsity pattern; either (i, j) or (j, i) is valid (possibly both). \param m is the number of rows (and columns) in the matrix. \param adolc_pattern is a vector with adolc_pattern.size() == m. For i = 0 , ... , m-1, and for k = 1, ... ,adolc_pattern[i][0], the entry with index (i, adolc_pattern[i][k]) is in the sparsity pattern for the symmetric matrix. */ CPPAD_LIB_EXPORT void cppad_colpack_symmetric( CppAD::vector& color , size_t m , const CppAD::vector& adolc_pattern ) { size_t i; CPPAD_ASSERT_UNKNOWN( adolc_pattern.size() == m ); CPPAD_ASSERT_UNKNOWN( color.size() == m ); // Use adolc sparsity pattern to create corresponding bipartite graph ColPack::GraphColoringInterface graph( SRC_MEM_ADOLC, adolc_pattern.data(), m ); // Use STAR coloring because it has a direct recovery scheme; i.e., // not necessary to solve equations to extract values. graph.Coloring("SMALLEST_LAST", "STAR"); // Use coloring information to create seed matrix int n_seed_row; int n_seed_col; double** seed_matrix = graph.GetSeedMatrix(&n_seed_row, &n_seed_col); CPPAD_ASSERT_UNKNOWN( size_t(n_seed_row) == m ); // now return coloring for each row in format required by CppAD for(i = 0; i < m; i++) color[i] = m; for(i = 0; i < m; i++) { for(size_t k = 0; k < size_t(n_seed_col); k++) { if( seed_matrix[i][k] != 0.0 ) { CPPAD_ASSERT_UNKNOWN( color[i] == m ); color[i] = k; } } } # ifndef NDEBUG // check that every entry in the symetric matrix can be direclty recovered size_t i1, i2, j1, j2, k1, k2, nz1, nz2; for(i1 = 0; i1 < m; i1++) { nz1 = size_t(adolc_pattern[i1][0]); for(k1 = 1; k1 <= nz1; k1++) { j1 = adolc_pattern[i1][k1]; // check of a forward on color[i1] followed by a reverse // can recover entry (i1, j1) bool color_i1_ok = true; for(i2 = 0; i2 < m; i2++) if( i1 != i2 && color[i1] == color[i2] ) { nz2 = adolc_pattern[i2][0]; for(k2 = 1; k2 <= nz2; k2++) { j2 = adolc_pattern[i2][k2]; color_i1_ok &= (j1 != j2); } } // check of a forward on color[j1] followed by a reverse // can recover entry (j1, i1) bool color_j1_ok = true; for(j2 = 0; j2 < m; j2++) if( j1 != j2 && color[j1] == color[j2] ) { nz2 = adolc_pattern[j2][0]; for(k2 = 1; k2 <= nz2; k2++) { i2 = adolc_pattern[j2][k2]; color_j1_ok &= (i1 != i2); } } CPPAD_ASSERT_UNKNOWN( color_i1_ok || color_j1_ok ); } } # endif return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif // CPPAD_HAS_COLPACK cppad-20170000.3/install-sh0000755000175200017650000003452312561675772014457 0ustar coincoin-web#!/bin/sh # install - install a program, script, or datafile scriptversion=2013-12-25.23; # UTC # This originates from X11R5 (mit/util/scripts/install.sh), which was # later released in X11R6 (xc/config/util/install.sh) with the # following copyright and license. # # Copyright (C) 1994 X Consortium # # Permission is hereby granted, free of charge, to any person obtaining a copy # of this software and associated documentation files (the "Software"), to # deal in the Software without restriction, including without limitation the # rights to use, copy, modify, merge, publish, distribute, sublicense, and/or # sell copies of the Software, and to permit persons to whom the Software is # furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included in # all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 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In this case, the final cleanup might fail but the new # file should still install successfully. { test ! -f "$dst" || $doit $rmcmd -f "$dst" 2>/dev/null || { $doit $mvcmd -f "$dst" "$rmtmp" 2>/dev/null && { $doit $rmcmd -f "$rmtmp" 2>/dev/null; :; } } || { echo "$0: cannot unlink or rename $dst" >&2 (exit 1); exit 1 } } && # Now rename the file to the real destination. $doit $mvcmd "$dsttmp" "$dst" } fi || exit 1 trap '' 0 fi done # Local variables: # eval: (add-hook 'write-file-hooks 'time-stamp) # time-stamp-start: "scriptversion=" # time-stamp-format: "%:y-%02m-%02d.%02H" # time-stamp-time-zone: "UTC" # time-stamp-end: "; # UTC" # End: cppad-20170000.3/cmake/0002755000175200017650000000000013057470401013505 5ustar coincoin-webcppad-20170000.3/cmake/check_source_runs.cmake0000644000175200017650000000265612460766640020234 0ustar coincoin-web# $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # check_source_runs(source variable) # # source: (in) # contains the source for the program that will be run. # # variable: (out) # the value of this variable is 1 if the program runs and # returns a zero status. Otherwise its value is 0. # Note that this is the reverse of the status flag returned by the program. # MACRO(check_source_runs source variable) SET(CMAKE_REQUIRED_INCLUDES "" ) SET(CMAKE_REQUIRED_LIBRARIES "" ) SET(CMAKE_REQUIRED_DEFINITIONS "" ) IF( cppad_cxx_flags ) SET(CMAKE_REQUIRED_FLAGS "${cppad_cxx_flags}" ) ELSE( cppad_cxx_flags ) SET(CMAKE_REQUIRED_FLAGS "" ) ENDIF( cppad_cxx_flags ) CHECK_CXX_SOURCE_RUNS("${source}" ${variable}_result) IF( ${variable}_result ) SET(${variable} 1) ELSE( ${variable}_result ) SET(${variable} 0) ENDIF( ${variable}_result ) MESSAGE(STATUS "${variable} = ${${variable}}" ) ENDMACRO( check_source_runs ) cppad-20170000.3/cmake/add_to_list.cmake0000644000175200017650000000242712116403430016770 0ustar coincoin-web# $Id: add_to_list.cmake 2772 2013-03-08 15:43:20Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # ============================================================================= # add_to_list(variable_list constant_value) # # variables_list: (in/out) # The variable containing the list of values. # The original list may be ""; i.e., the empty list. # # constant_value: (in) # Is the value we are adding to the list. This value cannot be empty. # MACRO(add_to_list variable_list constant_value ) IF( "${${variable_list}}" STREQUAL "" ) SET( ${variable_list} ${constant_value} ) ELSE( "${${variable_list}}" STREQUAL "" ) SET( ${variable_list} ${${variable_list}} ${constant_value} ) ENDIF( "${${variable_list}}" STREQUAL "" ) ENDMACRO(add_to_list) cppad-20170000.3/cmake/dos_path_to_unix.cmake0000644000175200017650000000201412116365320020046 0ustar coincoin-web# $Id: dos_path_to_unix.cmake 2770 2013-03-08 13:42:40Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # dos_path_to_unix(dos_path unix_path) # # dos_path: (in) # is the value of the path we are converting to unix format; i.e., # all \ characters are replaced by / characters. # # unix_path: (out) # is the variable where the result of the conversion is placed. # MACRO(dos_path_to_unix dos_path unix_path) STRING(REGEX REPLACE "[\\]" "/" ${unix_path} "${dos_path}" ) ENDMACRO(dos_path_to_unix dos_path unix_path) cppad-20170000.3/cmake/sources_libs_define.cmake0000644000175200017650000000302113027220733020505 0ustar coincoin-web# $Id: sources_libs_define.cmake 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # sources_libs_define(prefix_name sources libs define) # # prefix_name: (in) # If the variable ${prefix_name}_prefix is NOTFOUND, # sources and libs are set to the empty string "" and no definition is added. # # Otherwise ${prefix_name}_sources is set to ${sources}, # ${prefix_name}_libs is set to ${libs}. If ${define} is not empty "", # the defintion -DCPPAD_${define} is added; i.e., # ADD_DEFINITIONS("-DCPPAD_${define}") # MACRO(sources_libs_define prefix_name soruces libs define) IF ( ${prefix_name}_prefix ) SET( ${prefix_name}_sources ${sources} ) SET( ${prefix_name}_libs ${libs} ) IF( NOT "${define}" STREQUAL "" ) ADD_DEFINITIONS("-DCPPAD_${define}") # MESSAGE(STATUS "-DCPPAD_${define}" ) ENDIF( NOT "${define}" STREQUAL "" ) ELSE ( ${prefix_name}_prefix ) SET( ${prefix_name}_sources "" ) SET( ${prefix_name}_libs "" ) ENDIF ( ${prefix_name}_prefix ) ENDMACRO( sources_libs_define ) cppad-20170000.3/cmake/add_cppad_cxx_flags.cmake0000644000175200017650000000222712772234250020450 0ustar coincoin-web# $Id: add_cppad_cxx_flags.cmake 3831 2016-09-26 15:03:04Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # add_cppad_cxx_flags(target_name) # # target_name: (in) # The compiler flags for this target are set to # cppad_cxx_flags. # # Side Effects: # The variable flags is used for scratch space and not # defined after the completion of this macro. # MACRO(add_cppad_cxx_flags target_name) # SET(flags ${cppad_cxx_flags}) IF( flags ) SET_TARGET_PROPERTIES( ${target_name} PROPERTIES COMPILE_FLAGS "${flags}" ) ELSE( flags ) SET_TARGET_PROPERTIES( ${target_name} PROPERTIES COMPILE_FLAGS "" ) ENDIF( flags ) ENDMACRO(add_cppad_cxx_flags) cppad-20170000.3/cmake/command_line_arg.cmake0000644000175200017650000000346412461230277017775 0ustar coincoin-web# $Id: command_line_arg.cmake 3615 2015-01-25 18:06:55Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # command_line_arg(variable default type description) # # variable: (out) # is the variable we are setting to its default value. # The varaiable can be changed on the cmake command line (or in the camke gui). # The final value of the variable is printed with the cmake output. # # default: (in) # is the default value for this variable; i.e., # if it is not set by the cmake command line or gui. # # type: (in) # must be one of the following: # STRING, if the variable holds an arbitrary string. # PATH, if the variable holds a directory. # BOOL, if the variable only has the values true or false. # # description: (in) # Is a description of how the variable affects the CppAD install procedure. # MACRO(command_line_arg variable default type description) IF( NOT ( ${type} STREQUAL "STRING" ) ) IF( NOT ( ${type} STREQUAL "PATH" ) ) IF( NOT ( ${type} STREQUAL "BOOL" ) ) MESSAGE(FATAL_ERROR, "command_line_arg: bug in CppAD cmake commands") ENDIF( NOT ( ${type} STREQUAL "BOOL" ) ) ENDIF( NOT ( ${type} STREQUAL "PATH" ) ) ENDIF( NOT ( ${type} STREQUAL "STRING" ) ) # SET(${variable} "${default}" CACHE ${type} "${description}") MESSAGE(STATUS "${variable} = ${${variable}}") ENDMACRO( command_line_arg ) cppad-20170000.3/cmake/optional_package.cmake0000644000175200017650000000510312673157244020016 0ustar coincoin-web# $Id: optional_package.cmake 3803 2016-03-19 05:07:48Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # optional_package(prefix_variable system_include description) # # prefix_variable: (out) # is a PATH variable that holds the install prefix for this optional package. # # system_include: (in) # If this is true, the include files for this package should be treated as # system files (no warnings). # # description: (in) # is a description for the install prefix for this optional package. # # If package_variable is not set by the cmake command line (or gui), # it is set to the default value NOTFOUND. # # If package_variable is set by the cmake command line, the following is done: # 1. All the valid include subdirectories are added using INCLUDE_DIRECTORIES. # 2. All the valid library subdirectories are added using LINK_DIRECTORIES. # The set of valid include and library directories are determined by # cmake_install_includedirs and cmakd_install_libdirs respectively. # # description: (in) # MACRO(optional_package prefix_variable system_include description) SET(${prefix_variable} NOTFOUND CACHE PATH "${description}") SET(prefix ${${prefix_variable}} ) MESSAGE(STATUS "${prefix_variable} = ${prefix}") IF ( prefix ) # List of preprocessor include file search directories FOREACH(dir ${cmake_install_includedirs}) IF(IS_DIRECTORY ${prefix}/${dir} ) IF( ${system_include} ) INCLUDE_DIRECTORIES( SYSTEM ${prefix}/${dir} ) MESSAGE(STATUS " Found SYSTEM ${prefix}/${dir}") ELSE( ${system_include} ) INCLUDE_DIRECTORIES( ${prefix}/${dir} ) MESSAGE(STATUS " Found ${prefix}/${dir}") ENDIF( ${system_include} ) ENDIF(IS_DIRECTORY ${prefix}/${dir} ) ENDFOREACH(dir) # Paths in which the linker will search for libraries, # only applies to targets created after it is called FOREACH(dir ${cmake_install_libdirs}) IF(IS_DIRECTORY ${prefix}/${dir} ) LINK_DIRECTORIES( ${prefix}/${dir} ) MESSAGE(STATUS " Found ${prefix}/${dir}") ENDIF(IS_DIRECTORY ${prefix}/${dir} ) ENDFOREACH(dir) ENDIF ( prefix ) ENDMACRO(optional_package) cppad-20170000.3/cmake/assert.cmake0000644000175200017650000000172113030241267016004 0ustar coincoin-web# $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # ============================================================================= # assert(variable) # # variable: (in) # The variable is checked to make sure it is true, and if it is not true # a fatal error message is printed. # MACRO(assert variable) IF( NOT ${variable} ) MESSAGE(FATAL_ERROR "Error: ${variable} is false in ${CMAKE_CURRENT_LIST_FILE}" ) ENDIF( NOT ${variable} ) ENDMACRO(assert) cppad-20170000.3/cmake/print_variable.cmake0000644000175200017650000000150413032160414017477 0ustar coincoin-web# $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # Eclipse Public License Version 1.0. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # ============================================================================= # print_variable(variable) # # variable: (in) # The variable name and value is printed # MACRO(print_variable variable) MESSAGE(STATUS "${variable} = ${${variable}}" ) ENDMACRO(print_variable) cppad-20170000.3/configure0000755000175200017650000102560013057272335014344 0ustar coincoin-web#! /bin/sh # Guess values for system-dependent variables and create Makefiles. # Generated by GNU Autoconf 2.69 for cppad 20170000.3. # # Report bugs to . # # # Copyright (C) 1992-1996, 1998-2012 Free Software Foundation, Inc. # # # This configure script is free software; the Free Software Foundation # gives unlimited permission to copy, distribute and modify it. ## -------------------- ## ## M4sh Initialization. ## ## -------------------- ## # Be more Bourne compatible DUALCASE=1; export DUALCASE # for MKS sh if test -n "${ZSH_VERSION+set}" && (emulate sh) >/dev/null 2>&1; then : emulate sh NULLCMD=: # Pre-4.2 versions of Zsh do word splitting on ${1+"$@"}, which # is contrary to our usage. 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"write failure creating $CONFIG_STATUS" "$LINENO" 5 # configure is writing to config.log, and then calls config.status. # config.status does its own redirection, appending to config.log. # Unfortunately, on DOS this fails, as config.log is still kept open # by configure, so config.status won't be able to write to it; its # output is simply discarded. So we exec the FD to /dev/null, # effectively closing config.log, so it can be properly (re)opened and # appended to by config.status. When coming back to configure, we # need to make the FD available again. if test "$no_create" != yes; then ac_cs_success=: ac_config_status_args= test "$silent" = yes && ac_config_status_args="$ac_config_status_args --quiet" exec 5>/dev/null $SHELL $CONFIG_STATUS $ac_config_status_args || ac_cs_success=false exec 5>>config.log # Use ||, not &&, to avoid exiting from the if with $? = 1, which # would make configure fail if this is the last instruction. $ac_cs_success || as_fn_exit 1 fi if test -n "$ac_unrecognized_opts" && test "$enable_option_checking" != no; then { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: unrecognized options: $ac_unrecognized_opts" >&5 $as_echo "$as_me: WARNING: unrecognized options: $ac_unrecognized_opts" >&2;} fi cppad-20170000.3/AUTHORS0000644000175200017650000000146013032160414013465 0ustar coincoin-web Statement of CppAD Authorship and Copyright =========================================== To date, 2017-01-01, Bradley M. Bell is the sole author of CppAD. While Bradley M. Bell worked for the University of Washington during the development of CppAD, the following are also true: 1. The CppAD package was not written or maintained as part of any sponsored grant at the University of Washington. 2. Bradley M. Bell was not paid by the University of Washington for the time he worked on CppAD. 3. Working on CppAD was not part of Bradley M. Bell's normal duties at for the University of Washington. Thus, in accordance with Section 2 of the University of Washington's copyright policy (see the file uw_copy_040507.html in this directory) Bradley M. Bell is the copyright holder for CppAD. cppad-20170000.3/depcomp0000755000175200017650000005601612561675772014031 0ustar coincoin-web#! /bin/sh # depcomp - compile a program generating dependencies as side-effects scriptversion=2013-05-30.07; # UTC # Copyright (C) 1999-2014 Free Software Foundation, Inc. # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2, or (at your option) # any later version. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # You should have received a copy of the GNU General Public License # along with this program. If not, see . # As a special exception to the GNU General Public License, if you # distribute this file as part of a program that contains a # configuration script generated by Autoconf, you may include it under # the same distribution terms that you use for the rest of that program. # Originally written by Alexandre Oliva . case $1 in '') echo "$0: No command. Try '$0 --help' for more information." 1>&2 exit 1; ;; -h | --h*) cat <<\EOF Usage: depcomp [--help] [--version] PROGRAM [ARGS] Run PROGRAMS ARGS to compile a file, generating dependencies as side-effects. Environment variables: depmode Dependency tracking mode. source Source file read by 'PROGRAMS ARGS'. object Object file output by 'PROGRAMS ARGS'. DEPDIR directory where to store dependencies. depfile Dependency file to output. tmpdepfile Temporary file to use when outputting dependencies. libtool Whether libtool is used (yes/no). Report bugs to . 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See the GNU # General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, see . # # As a special exception to the GNU General Public License, if you # distribute this file as part of a program that contains a # configuration script generated by Autoconf, you may include it under # the same distribution terms that you use for the rest of that # program. This Exception is an additional permission under section 7 # of the GNU General Public License, version 3 ("GPLv3"). # # Originally written by Per Bothner; maintained since 2000 by Ben Elliston. # # You can get the latest version of this script from: # http://git.savannah.gnu.org/gitweb/?p=config.git;a=blob_plain;f=config.guess;hb=HEAD # # Please send patches to . me=`echo "$0" | sed -e 's,.*/,,'` usage="\ Usage: $0 [OPTION] Output the configuration name of the system \`$me' is run on. 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ALPHA_CPU_TYPE=`/usr/sbin/psrinfo -v | sed -n -e 's/^ The alpha \(.*\) processor.*$/\1/p' | head -n 1` case "$ALPHA_CPU_TYPE" in "EV4 (21064)") UNAME_MACHINE="alpha" ;; "EV4.5 (21064)") UNAME_MACHINE="alpha" ;; "LCA4 (21066/21068)") UNAME_MACHINE="alpha" ;; "EV5 (21164)") UNAME_MACHINE="alphaev5" ;; "EV5.6 (21164A)") UNAME_MACHINE="alphaev56" ;; "EV5.6 (21164PC)") UNAME_MACHINE="alphapca56" ;; "EV5.7 (21164PC)") UNAME_MACHINE="alphapca57" ;; "EV6 (21264)") UNAME_MACHINE="alphaev6" ;; "EV6.7 (21264A)") UNAME_MACHINE="alphaev67" ;; "EV6.8CB (21264C)") UNAME_MACHINE="alphaev68" ;; "EV6.8AL (21264B)") UNAME_MACHINE="alphaev68" ;; "EV6.8CX (21264D)") UNAME_MACHINE="alphaev68" ;; "EV6.9A (21264/EV69A)") UNAME_MACHINE="alphaev69" ;; "EV7 (21364)") UNAME_MACHINE="alphaev7" ;; "EV7.9 (21364A)") UNAME_MACHINE="alphaev79" ;; esac # A Pn.n version is a patched version. # A Vn.n version is a released version. # A Tn.n version is a released field test version. # A Xn.n version is an unreleased experimental baselevel. # 1.2 uses "1.2" for uname -r. echo ${UNAME_MACHINE}-dec-osf`echo ${UNAME_RELEASE} | sed -e 's/^[PVTX]//' | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz'` # Reset EXIT trap before exiting to avoid spurious non-zero exit code. exitcode=$? trap '' 0 exit $exitcode ;; Alpha\ *:Windows_NT*:*) # How do we know it's Interix rather than the generic POSIX subsystem? # Should we change UNAME_MACHINE based on the output of uname instead # of the specific Alpha model? echo alpha-pc-interix exit ;; 21064:Windows_NT:50:3) echo alpha-dec-winnt3.5 exit ;; Amiga*:UNIX_System_V:4.0:*) echo m68k-unknown-sysv4 exit ;; *:[Aa]miga[Oo][Ss]:*:*) echo ${UNAME_MACHINE}-unknown-amigaos exit ;; *:[Mm]orph[Oo][Ss]:*:*) echo ${UNAME_MACHINE}-unknown-morphos exit ;; *:OS/390:*:*) echo i370-ibm-openedition exit ;; *:z/VM:*:*) echo s390-ibm-zvmoe exit ;; *:OS400:*:*) echo powerpc-ibm-os400 exit ;; arm:RISC*:1.[012]*:*|arm:riscix:1.[012]*:*) echo arm-acorn-riscix${UNAME_RELEASE} exit ;; arm*:riscos:*:*|arm*:RISCOS:*:*) echo arm-unknown-riscos exit ;; SR2?01:HI-UX/MPP:*:* | SR8000:HI-UX/MPP:*:*) echo hppa1.1-hitachi-hiuxmpp exit ;; Pyramid*:OSx*:*:* | MIS*:OSx*:*:* | MIS*:SMP_DC-OSx*:*:*) # akee@wpdis03.wpafb.af.mil (Earle F. Ake) contributed MIS and NILE. if test "`(/bin/universe) 2>/dev/null`" = att ; then echo pyramid-pyramid-sysv3 else echo pyramid-pyramid-bsd fi exit ;; NILE*:*:*:dcosx) echo pyramid-pyramid-svr4 exit ;; DRS?6000:unix:4.0:6*) echo sparc-icl-nx6 exit ;; DRS?6000:UNIX_SV:4.2*:7* | DRS?6000:isis:4.2*:7*) case `/usr/bin/uname -p` in sparc) echo sparc-icl-nx7; exit ;; esac ;; s390x:SunOS:*:*) echo ${UNAME_MACHINE}-ibm-solaris2`echo ${UNAME_RELEASE}|sed -e 's/[^.]*//'` exit ;; sun4H:SunOS:5.*:*) echo sparc-hal-solaris2`echo ${UNAME_RELEASE}|sed -e 's/[^.]*//'` exit ;; sun4*:SunOS:5.*:* | tadpole*:SunOS:5.*:*) echo sparc-sun-solaris2`echo ${UNAME_RELEASE}|sed -e 's/[^.]*//'` exit ;; i86pc:AuroraUX:5.*:* | i86xen:AuroraUX:5.*:*) echo i386-pc-auroraux${UNAME_RELEASE} exit ;; i86pc:SunOS:5.*:* | i86xen:SunOS:5.*:*) eval $set_cc_for_build SUN_ARCH="i386" # If there is a compiler, see if it is configured for 64-bit objects. # Note that the Sun cc does not turn __LP64__ into 1 like gcc does. # This test works for both compilers. if [ "$CC_FOR_BUILD" != 'no_compiler_found' ]; then if (echo '#ifdef __amd64'; echo IS_64BIT_ARCH; echo '#endif') | \ (CCOPTS= $CC_FOR_BUILD -E - 2>/dev/null) | \ grep IS_64BIT_ARCH >/dev/null then SUN_ARCH="x86_64" fi fi echo ${SUN_ARCH}-pc-solaris2`echo ${UNAME_RELEASE}|sed -e 's/[^.]*//'` exit ;; sun4*:SunOS:6*:*) # According to config.sub, this is the proper way to canonicalize # SunOS6. Hard to guess exactly what SunOS6 will be like, but # it's likely to be more like Solaris than SunOS4. echo sparc-sun-solaris3`echo ${UNAME_RELEASE}|sed -e 's/[^.]*//'` exit ;; sun4*:SunOS:*:*) case "`/usr/bin/arch -k`" in Series*|S4*) UNAME_RELEASE=`uname -v` ;; esac # Japanese Language versions have a version number like `4.1.3-JL'. echo sparc-sun-sunos`echo ${UNAME_RELEASE}|sed -e 's/-/_/'` exit ;; sun3*:SunOS:*:*) echo m68k-sun-sunos${UNAME_RELEASE} exit ;; sun*:*:4.2BSD:*) UNAME_RELEASE=`(sed 1q /etc/motd | awk '{print substr($5,1,3)}') 2>/dev/null` test "x${UNAME_RELEASE}" = "x" && UNAME_RELEASE=3 case "`/bin/arch`" in sun3) echo m68k-sun-sunos${UNAME_RELEASE} ;; sun4) echo sparc-sun-sunos${UNAME_RELEASE} ;; esac exit ;; aushp:SunOS:*:*) echo sparc-auspex-sunos${UNAME_RELEASE} exit ;; # The situation for MiNT is a little confusing. The machine name # can be virtually everything (everything which is not # "atarist" or "atariste" at least should have a processor # > m68000). The system name ranges from "MiNT" over "FreeMiNT" # to the lowercase version "mint" (or "freemint"). Finally # the system name "TOS" denotes a system which is actually not # MiNT. But MiNT is downward compatible to TOS, so this should # be no problem. atarist[e]:*MiNT:*:* | atarist[e]:*mint:*:* | atarist[e]:*TOS:*:*) echo m68k-atari-mint${UNAME_RELEASE} exit ;; atari*:*MiNT:*:* | atari*:*mint:*:* | atarist[e]:*TOS:*:*) echo m68k-atari-mint${UNAME_RELEASE} exit ;; *falcon*:*MiNT:*:* | *falcon*:*mint:*:* | *falcon*:*TOS:*:*) echo m68k-atari-mint${UNAME_RELEASE} exit ;; milan*:*MiNT:*:* | milan*:*mint:*:* | *milan*:*TOS:*:*) echo m68k-milan-mint${UNAME_RELEASE} exit ;; hades*:*MiNT:*:* | hades*:*mint:*:* | *hades*:*TOS:*:*) echo m68k-hades-mint${UNAME_RELEASE} exit ;; *:*MiNT:*:* | *:*mint:*:* | *:*TOS:*:*) echo m68k-unknown-mint${UNAME_RELEASE} exit ;; m68k:machten:*:*) echo m68k-apple-machten${UNAME_RELEASE} exit ;; powerpc:machten:*:*) echo powerpc-apple-machten${UNAME_RELEASE} exit ;; RISC*:Mach:*:*) echo mips-dec-mach_bsd4.3 exit ;; RISC*:ULTRIX:*:*) echo mips-dec-ultrix${UNAME_RELEASE} exit ;; VAX*:ULTRIX*:*:*) echo vax-dec-ultrix${UNAME_RELEASE} exit ;; 2020:CLIX:*:* | 2430:CLIX:*:*) echo clipper-intergraph-clix${UNAME_RELEASE} exit ;; mips:*:*:UMIPS | mips:*:*:RISCos) eval $set_cc_for_build sed 's/^ //' << EOF >$dummy.c #ifdef __cplusplus #include /* for printf() prototype */ int main (int argc, char *argv[]) { #else int main (argc, argv) int argc; char *argv[]; { #endif #if defined (host_mips) && defined (MIPSEB) #if defined (SYSTYPE_SYSV) printf ("mips-mips-riscos%ssysv\n", argv[1]); exit (0); #endif #if defined (SYSTYPE_SVR4) printf ("mips-mips-riscos%ssvr4\n", argv[1]); exit (0); #endif #if defined (SYSTYPE_BSD43) || defined(SYSTYPE_BSD) printf ("mips-mips-riscos%sbsd\n", argv[1]); exit (0); #endif #endif exit (-1); } EOF $CC_FOR_BUILD -o $dummy $dummy.c && dummyarg=`echo "${UNAME_RELEASE}" | sed -n 's/\([0-9]*\).*/\1/p'` && SYSTEM_NAME=`$dummy $dummyarg` && { echo "$SYSTEM_NAME"; exit; } echo mips-mips-riscos${UNAME_RELEASE} exit ;; Motorola:PowerMAX_OS:*:*) echo powerpc-motorola-powermax exit ;; Motorola:*:4.3:PL8-*) echo powerpc-harris-powermax exit ;; Night_Hawk:*:*:PowerMAX_OS | Synergy:PowerMAX_OS:*:*) echo powerpc-harris-powermax exit ;; Night_Hawk:Power_UNIX:*:*) echo powerpc-harris-powerunix exit ;; m88k:CX/UX:7*:*) echo m88k-harris-cxux7 exit ;; m88k:*:4*:R4*) echo m88k-motorola-sysv4 exit ;; m88k:*:3*:R3*) echo m88k-motorola-sysv3 exit ;; AViiON:dgux:*:*) # DG/UX returns AViiON for all architectures UNAME_PROCESSOR=`/usr/bin/uname -p` if [ $UNAME_PROCESSOR = mc88100 ] || [ $UNAME_PROCESSOR = mc88110 ] then if [ ${TARGET_BINARY_INTERFACE}x = m88kdguxelfx ] || \ [ ${TARGET_BINARY_INTERFACE}x = x ] then echo m88k-dg-dgux${UNAME_RELEASE} else echo m88k-dg-dguxbcs${UNAME_RELEASE} fi else echo i586-dg-dgux${UNAME_RELEASE} fi exit ;; M88*:DolphinOS:*:*) # DolphinOS (SVR3) echo m88k-dolphin-sysv3 exit ;; M88*:*:R3*:*) # Delta 88k system running SVR3 echo m88k-motorola-sysv3 exit ;; XD88*:*:*:*) # Tektronix XD88 system running UTekV (SVR3) echo m88k-tektronix-sysv3 exit ;; Tek43[0-9][0-9]:UTek:*:*) # Tektronix 4300 system running UTek (BSD) echo m68k-tektronix-bsd exit ;; *:IRIX*:*:*) echo mips-sgi-irix`echo ${UNAME_RELEASE}|sed -e 's/-/_/g'` exit ;; ????????:AIX?:[12].1:2) # AIX 2.2.1 or AIX 2.1.1 is RT/PC AIX. echo romp-ibm-aix # uname -m gives an 8 hex-code CPU id exit ;; # Note that: echo "'`uname -s`'" gives 'AIX ' i*86:AIX:*:*) echo i386-ibm-aix exit ;; ia64:AIX:*:*) if [ -x /usr/bin/oslevel ] ; then IBM_REV=`/usr/bin/oslevel` else IBM_REV=${UNAME_VERSION}.${UNAME_RELEASE} fi echo ${UNAME_MACHINE}-ibm-aix${IBM_REV} exit ;; *:AIX:2:3) if grep bos325 /usr/include/stdio.h >/dev/null 2>&1; then eval $set_cc_for_build sed 's/^ //' << EOF >$dummy.c #include main() { if (!__power_pc()) exit(1); puts("powerpc-ibm-aix3.2.5"); exit(0); } EOF if $CC_FOR_BUILD -o $dummy $dummy.c && SYSTEM_NAME=`$dummy` then echo "$SYSTEM_NAME" else echo rs6000-ibm-aix3.2.5 fi elif grep bos324 /usr/include/stdio.h >/dev/null 2>&1; then echo rs6000-ibm-aix3.2.4 else echo rs6000-ibm-aix3.2 fi exit ;; *:AIX:*:[4567]) IBM_CPU_ID=`/usr/sbin/lsdev -C -c processor -S available | sed 1q | awk '{ print $1 }'` if /usr/sbin/lsattr -El ${IBM_CPU_ID} | grep ' POWER' >/dev/null 2>&1; then IBM_ARCH=rs6000 else IBM_ARCH=powerpc fi if [ -x /usr/bin/lslpp ] ; then IBM_REV=`/usr/bin/lslpp -Lqc bos.rte.libc | awk -F: '{ print $3 }' | sed s/[0-9]*$/0/` else IBM_REV=${UNAME_VERSION}.${UNAME_RELEASE} fi echo ${IBM_ARCH}-ibm-aix${IBM_REV} exit ;; *:AIX:*:*) echo rs6000-ibm-aix exit ;; ibmrt:4.4BSD:*|romp-ibm:BSD:*) echo romp-ibm-bsd4.4 exit ;; ibmrt:*BSD:*|romp-ibm:BSD:*) # covers RT/PC BSD and echo romp-ibm-bsd${UNAME_RELEASE} # 4.3 with uname added to exit ;; # report: romp-ibm BSD 4.3 *:BOSX:*:*) echo rs6000-bull-bosx exit ;; DPX/2?00:B.O.S.:*:*) echo m68k-bull-sysv3 exit ;; 9000/[34]??:4.3bsd:1.*:*) echo m68k-hp-bsd exit ;; hp300:4.4BSD:*:* | 9000/[34]??:4.3bsd:2.*:*) echo m68k-hp-bsd4.4 exit ;; 9000/[34678]??:HP-UX:*:*) HPUX_REV=`echo ${UNAME_RELEASE}|sed -e 's/[^.]*.[0B]*//'` case "${UNAME_MACHINE}" in 9000/31? ) HP_ARCH=m68000 ;; 9000/[34]?? ) HP_ARCH=m68k ;; 9000/[678][0-9][0-9]) if [ -x /usr/bin/getconf ]; then sc_cpu_version=`/usr/bin/getconf SC_CPU_VERSION 2>/dev/null` sc_kernel_bits=`/usr/bin/getconf SC_KERNEL_BITS 2>/dev/null` case "${sc_cpu_version}" in 523) HP_ARCH="hppa1.0" ;; # CPU_PA_RISC1_0 528) HP_ARCH="hppa1.1" ;; # CPU_PA_RISC1_1 532) # CPU_PA_RISC2_0 case "${sc_kernel_bits}" in 32) HP_ARCH="hppa2.0n" ;; 64) HP_ARCH="hppa2.0w" ;; '') HP_ARCH="hppa2.0" ;; # HP-UX 10.20 esac ;; esac fi if [ "${HP_ARCH}" = "" ]; then eval $set_cc_for_build sed 's/^ //' << EOF >$dummy.c #define _HPUX_SOURCE #include #include int main () { #if defined(_SC_KERNEL_BITS) long bits = sysconf(_SC_KERNEL_BITS); #endif long cpu = sysconf (_SC_CPU_VERSION); switch (cpu) { case CPU_PA_RISC1_0: puts ("hppa1.0"); break; case CPU_PA_RISC1_1: puts ("hppa1.1"); break; case CPU_PA_RISC2_0: #if defined(_SC_KERNEL_BITS) switch (bits) { case 64: puts ("hppa2.0w"); break; case 32: puts ("hppa2.0n"); break; default: puts ("hppa2.0"); break; } break; #else /* !defined(_SC_KERNEL_BITS) */ puts ("hppa2.0"); break; #endif default: puts ("hppa1.0"); break; } exit (0); } EOF (CCOPTS= $CC_FOR_BUILD -o $dummy $dummy.c 2>/dev/null) && HP_ARCH=`$dummy` test -z "$HP_ARCH" && HP_ARCH=hppa fi ;; esac if [ ${HP_ARCH} = "hppa2.0w" ] then eval $set_cc_for_build # hppa2.0w-hp-hpux* has a 64-bit kernel and a compiler generating # 32-bit code. hppa64-hp-hpux* has the same kernel and a compiler # generating 64-bit code. GNU and HP use different nomenclature: # # $ CC_FOR_BUILD=cc ./config.guess # => hppa2.0w-hp-hpux11.23 # $ CC_FOR_BUILD="cc +DA2.0w" ./config.guess # => hppa64-hp-hpux11.23 if echo __LP64__ | (CCOPTS= $CC_FOR_BUILD -E - 2>/dev/null) | grep -q __LP64__ then HP_ARCH="hppa2.0w" else HP_ARCH="hppa64" fi fi echo ${HP_ARCH}-hp-hpux${HPUX_REV} exit ;; ia64:HP-UX:*:*) HPUX_REV=`echo ${UNAME_RELEASE}|sed -e 's/[^.]*.[0B]*//'` echo ia64-hp-hpux${HPUX_REV} exit ;; 3050*:HI-UX:*:*) eval $set_cc_for_build sed 's/^ //' << EOF >$dummy.c #include int main () { long cpu = sysconf (_SC_CPU_VERSION); /* The order matters, because CPU_IS_HP_MC68K erroneously returns true for CPU_PA_RISC1_0. CPU_IS_PA_RISC returns correct results, however. */ if (CPU_IS_PA_RISC (cpu)) { switch (cpu) { case CPU_PA_RISC1_0: puts ("hppa1.0-hitachi-hiuxwe2"); break; case CPU_PA_RISC1_1: puts ("hppa1.1-hitachi-hiuxwe2"); break; case CPU_PA_RISC2_0: puts ("hppa2.0-hitachi-hiuxwe2"); break; default: puts ("hppa-hitachi-hiuxwe2"); break; } } else if (CPU_IS_HP_MC68K (cpu)) puts ("m68k-hitachi-hiuxwe2"); else puts ("unknown-hitachi-hiuxwe2"); exit (0); } EOF $CC_FOR_BUILD -o $dummy $dummy.c && SYSTEM_NAME=`$dummy` && { echo "$SYSTEM_NAME"; exit; } echo unknown-hitachi-hiuxwe2 exit ;; 9000/7??:4.3bsd:*:* | 9000/8?[79]:4.3bsd:*:* ) echo hppa1.1-hp-bsd exit ;; 9000/8??:4.3bsd:*:*) echo hppa1.0-hp-bsd exit ;; *9??*:MPE/iX:*:* | *3000*:MPE/iX:*:*) echo hppa1.0-hp-mpeix exit ;; hp7??:OSF1:*:* | hp8?[79]:OSF1:*:* ) echo hppa1.1-hp-osf exit ;; hp8??:OSF1:*:*) echo hppa1.0-hp-osf exit ;; i*86:OSF1:*:*) if [ -x /usr/sbin/sysversion ] ; then echo ${UNAME_MACHINE}-unknown-osf1mk else echo ${UNAME_MACHINE}-unknown-osf1 fi exit ;; parisc*:Lites*:*:*) echo hppa1.1-hp-lites exit ;; C1*:ConvexOS:*:* | convex:ConvexOS:C1*:*) echo c1-convex-bsd exit ;; C2*:ConvexOS:*:* | convex:ConvexOS:C2*:*) if getsysinfo -f scalar_acc then echo c32-convex-bsd else echo c2-convex-bsd fi exit ;; C34*:ConvexOS:*:* | convex:ConvexOS:C34*:*) echo c34-convex-bsd exit ;; C38*:ConvexOS:*:* | convex:ConvexOS:C38*:*) echo c38-convex-bsd exit ;; C4*:ConvexOS:*:* | convex:ConvexOS:C4*:*) echo c4-convex-bsd exit ;; CRAY*Y-MP:*:*:*) echo ymp-cray-unicos${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; CRAY*[A-Z]90:*:*:*) echo ${UNAME_MACHINE}-cray-unicos${UNAME_RELEASE} \ | sed -e 's/CRAY.*\([A-Z]90\)/\1/' \ -e y/ABCDEFGHIJKLMNOPQRSTUVWXYZ/abcdefghijklmnopqrstuvwxyz/ \ -e 's/\.[^.]*$/.X/' exit ;; CRAY*TS:*:*:*) echo t90-cray-unicos${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; CRAY*T3E:*:*:*) echo alphaev5-cray-unicosmk${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; CRAY*SV1:*:*:*) echo sv1-cray-unicos${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; *:UNICOS/mp:*:*) echo craynv-cray-unicosmp${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; F30[01]:UNIX_System_V:*:* | F700:UNIX_System_V:*:*) FUJITSU_PROC=`uname -m | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz'` FUJITSU_SYS=`uname -p | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz' | sed -e 's/\///'` FUJITSU_REL=`echo ${UNAME_RELEASE} | sed -e 's/ /_/'` echo "${FUJITSU_PROC}-fujitsu-${FUJITSU_SYS}${FUJITSU_REL}" exit ;; 5000:UNIX_System_V:4.*:*) FUJITSU_SYS=`uname -p | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz' | sed -e 's/\///'` FUJITSU_REL=`echo ${UNAME_RELEASE} | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz' | sed -e 's/ /_/'` echo "sparc-fujitsu-${FUJITSU_SYS}${FUJITSU_REL}" exit ;; i*86:BSD/386:*:* | i*86:BSD/OS:*:* | *:Ascend\ Embedded/OS:*:*) echo ${UNAME_MACHINE}-pc-bsdi${UNAME_RELEASE} exit ;; sparc*:BSD/OS:*:*) echo sparc-unknown-bsdi${UNAME_RELEASE} exit ;; *:BSD/OS:*:*) echo ${UNAME_MACHINE}-unknown-bsdi${UNAME_RELEASE} exit ;; *:FreeBSD:*:*) UNAME_PROCESSOR=`/usr/bin/uname -p` case ${UNAME_PROCESSOR} in amd64) echo x86_64-unknown-freebsd`echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'` ;; *) echo ${UNAME_PROCESSOR}-unknown-freebsd`echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'` ;; esac exit ;; i*:CYGWIN*:*) echo ${UNAME_MACHINE}-pc-cygwin exit ;; *:MINGW64*:*) echo ${UNAME_MACHINE}-pc-mingw64 exit ;; *:MINGW*:*) echo ${UNAME_MACHINE}-pc-mingw32 exit ;; *:MSYS*:*) echo ${UNAME_MACHINE}-pc-msys exit ;; i*:windows32*:*) # uname -m includes "-pc" on this system. echo ${UNAME_MACHINE}-mingw32 exit ;; i*:PW*:*) echo ${UNAME_MACHINE}-pc-pw32 exit ;; *:Interix*:*) case ${UNAME_MACHINE} in x86) echo i586-pc-interix${UNAME_RELEASE} exit ;; authenticamd | genuineintel | EM64T) echo x86_64-unknown-interix${UNAME_RELEASE} exit ;; IA64) echo ia64-unknown-interix${UNAME_RELEASE} exit ;; esac ;; [345]86:Windows_95:* | [345]86:Windows_98:* | [345]86:Windows_NT:*) echo i${UNAME_MACHINE}-pc-mks exit ;; 8664:Windows_NT:*) echo x86_64-pc-mks exit ;; i*:Windows_NT*:* | Pentium*:Windows_NT*:*) # How do we know it's Interix rather than the generic POSIX subsystem? # It also conflicts with pre-2.0 versions of AT&T UWIN. Should we # UNAME_MACHINE based on the output of uname instead of i386? echo i586-pc-interix exit ;; i*:UWIN*:*) echo ${UNAME_MACHINE}-pc-uwin exit ;; amd64:CYGWIN*:*:* | x86_64:CYGWIN*:*:*) echo x86_64-unknown-cygwin exit ;; p*:CYGWIN*:*) echo powerpcle-unknown-cygwin exit ;; prep*:SunOS:5.*:*) echo powerpcle-unknown-solaris2`echo ${UNAME_RELEASE}|sed -e 's/[^.]*//'` exit ;; *:GNU:*:*) # the GNU system echo `echo ${UNAME_MACHINE}|sed -e 's,[-/].*$,,'`-unknown-${LIBC}`echo ${UNAME_RELEASE}|sed -e 's,/.*$,,'` exit ;; *:GNU/*:*:*) # other systems with GNU libc and userland echo ${UNAME_MACHINE}-unknown-`echo ${UNAME_SYSTEM} | sed 's,^[^/]*/,,' | tr '[A-Z]' '[a-z]'``echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'`-${LIBC} exit ;; i*86:Minix:*:*) echo ${UNAME_MACHINE}-pc-minix exit ;; aarch64:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; aarch64_be:Linux:*:*) UNAME_MACHINE=aarch64_be echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; alpha:Linux:*:*) case `sed -n '/^cpu model/s/^.*: \(.*\)/\1/p' < /proc/cpuinfo` in EV5) UNAME_MACHINE=alphaev5 ;; EV56) UNAME_MACHINE=alphaev56 ;; PCA56) UNAME_MACHINE=alphapca56 ;; PCA57) UNAME_MACHINE=alphapca56 ;; EV6) UNAME_MACHINE=alphaev6 ;; EV67) UNAME_MACHINE=alphaev67 ;; EV68*) UNAME_MACHINE=alphaev68 ;; esac objdump --private-headers /bin/sh | grep -q ld.so.1 if test "$?" = 0 ; then LIBC="gnulibc1" ; fi echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; arc:Linux:*:* | arceb:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; arm*:Linux:*:*) eval $set_cc_for_build if echo __ARM_EABI__ | $CC_FOR_BUILD -E - 2>/dev/null \ | grep -q __ARM_EABI__ then echo ${UNAME_MACHINE}-unknown-linux-${LIBC} else if echo __ARM_PCS_VFP | $CC_FOR_BUILD -E - 2>/dev/null \ | grep -q __ARM_PCS_VFP then echo ${UNAME_MACHINE}-unknown-linux-${LIBC}eabi else echo ${UNAME_MACHINE}-unknown-linux-${LIBC}eabihf fi fi exit ;; avr32*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; cris:Linux:*:*) echo ${UNAME_MACHINE}-axis-linux-${LIBC} exit ;; crisv32:Linux:*:*) echo ${UNAME_MACHINE}-axis-linux-${LIBC} exit ;; frv:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; hexagon:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; i*86:Linux:*:*) echo ${UNAME_MACHINE}-pc-linux-${LIBC} exit ;; ia64:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; m32r*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; m68*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; mips:Linux:*:* | mips64:Linux:*:*) eval $set_cc_for_build sed 's/^ //' << EOF >$dummy.c #undef CPU #undef ${UNAME_MACHINE} #undef ${UNAME_MACHINE}el #if defined(__MIPSEL__) || defined(__MIPSEL) || defined(_MIPSEL) || defined(MIPSEL) CPU=${UNAME_MACHINE}el #else #if defined(__MIPSEB__) || defined(__MIPSEB) || defined(_MIPSEB) || defined(MIPSEB) CPU=${UNAME_MACHINE} #else CPU= #endif #endif EOF eval `$CC_FOR_BUILD -E $dummy.c 2>/dev/null | grep '^CPU'` test x"${CPU}" != x && { echo "${CPU}-unknown-linux-${LIBC}"; exit; } ;; openrisc*:Linux:*:*) echo or1k-unknown-linux-${LIBC} exit ;; or32:Linux:*:* | or1k*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; padre:Linux:*:*) echo sparc-unknown-linux-${LIBC} exit ;; parisc64:Linux:*:* | hppa64:Linux:*:*) echo hppa64-unknown-linux-${LIBC} exit ;; parisc:Linux:*:* | hppa:Linux:*:*) # Look for CPU level case `grep '^cpu[^a-z]*:' /proc/cpuinfo 2>/dev/null | cut -d' ' -f2` in PA7*) echo hppa1.1-unknown-linux-${LIBC} ;; PA8*) echo hppa2.0-unknown-linux-${LIBC} ;; *) echo hppa-unknown-linux-${LIBC} ;; esac exit ;; ppc64:Linux:*:*) echo powerpc64-unknown-linux-${LIBC} exit ;; ppc:Linux:*:*) echo powerpc-unknown-linux-${LIBC} exit ;; ppc64le:Linux:*:*) echo powerpc64le-unknown-linux-${LIBC} exit ;; ppcle:Linux:*:*) echo powerpcle-unknown-linux-${LIBC} exit ;; s390:Linux:*:* | s390x:Linux:*:*) echo ${UNAME_MACHINE}-ibm-linux-${LIBC} exit ;; sh64*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; sh*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; sparc:Linux:*:* | sparc64:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; tile*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; vax:Linux:*:*) echo ${UNAME_MACHINE}-dec-linux-${LIBC} exit ;; x86_64:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; xtensa*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-${LIBC} exit ;; i*86:DYNIX/ptx:4*:*) # ptx 4.0 does uname -s correctly, with DYNIX/ptx in there. # earlier versions are messed up and put the nodename in both # sysname and nodename. echo i386-sequent-sysv4 exit ;; i*86:UNIX_SV:4.2MP:2.*) # Unixware is an offshoot of SVR4, but it has its own version # number series starting with 2... # I am not positive that other SVR4 systems won't match this, # I just have to hope. -- rms. # Use sysv4.2uw... so that sysv4* matches it. echo ${UNAME_MACHINE}-pc-sysv4.2uw${UNAME_VERSION} exit ;; i*86:OS/2:*:*) # If we were able to find `uname', then EMX Unix compatibility # is probably installed. echo ${UNAME_MACHINE}-pc-os2-emx exit ;; i*86:XTS-300:*:STOP) echo ${UNAME_MACHINE}-unknown-stop exit ;; i*86:atheos:*:*) echo ${UNAME_MACHINE}-unknown-atheos exit ;; i*86:syllable:*:*) echo ${UNAME_MACHINE}-pc-syllable exit ;; i*86:LynxOS:2.*:* | i*86:LynxOS:3.[01]*:* | i*86:LynxOS:4.[02]*:*) echo i386-unknown-lynxos${UNAME_RELEASE} exit ;; i*86:*DOS:*:*) echo ${UNAME_MACHINE}-pc-msdosdjgpp exit ;; i*86:*:4.*:* | i*86:SYSTEM_V:4.*:*) UNAME_REL=`echo ${UNAME_RELEASE} | sed 's/\/MP$//'` if grep Novell /usr/include/link.h >/dev/null 2>/dev/null; then echo ${UNAME_MACHINE}-univel-sysv${UNAME_REL} else echo ${UNAME_MACHINE}-pc-sysv${UNAME_REL} fi exit ;; i*86:*:5:[678]*) # UnixWare 7.x, OpenUNIX and OpenServer 6. case `/bin/uname -X | grep "^Machine"` in *486*) UNAME_MACHINE=i486 ;; *Pentium) UNAME_MACHINE=i586 ;; *Pent*|*Celeron) UNAME_MACHINE=i686 ;; esac echo ${UNAME_MACHINE}-unknown-sysv${UNAME_RELEASE}${UNAME_SYSTEM}${UNAME_VERSION} exit ;; i*86:*:3.2:*) if test -f /usr/options/cb.name; then UNAME_REL=`sed -n 's/.*Version //p' /dev/null >/dev/null ; then UNAME_REL=`(/bin/uname -X|grep Release|sed -e 's/.*= //')` (/bin/uname -X|grep i80486 >/dev/null) && UNAME_MACHINE=i486 (/bin/uname -X|grep '^Machine.*Pentium' >/dev/null) \ && UNAME_MACHINE=i586 (/bin/uname -X|grep '^Machine.*Pent *II' >/dev/null) \ && UNAME_MACHINE=i686 (/bin/uname -X|grep '^Machine.*Pentium Pro' >/dev/null) \ && UNAME_MACHINE=i686 echo ${UNAME_MACHINE}-pc-sco$UNAME_REL else echo ${UNAME_MACHINE}-pc-sysv32 fi exit ;; pc:*:*:*) # Left here for compatibility: # uname -m prints for DJGPP always 'pc', but it prints nothing about # the processor, so we play safe by assuming i586. # Note: whatever this is, it MUST be the same as what config.sub # prints for the "djgpp" host, or else GDB configury will decide that # this is a cross-build. echo i586-pc-msdosdjgpp exit ;; Intel:Mach:3*:*) echo i386-pc-mach3 exit ;; paragon:*:*:*) echo i860-intel-osf1 exit ;; i860:*:4.*:*) # i860-SVR4 if grep Stardent /usr/include/sys/uadmin.h >/dev/null 2>&1 ; then echo i860-stardent-sysv${UNAME_RELEASE} # Stardent Vistra i860-SVR4 else # Add other i860-SVR4 vendors below as they are discovered. echo i860-unknown-sysv${UNAME_RELEASE} # Unknown i860-SVR4 fi exit ;; mini*:CTIX:SYS*5:*) # "miniframe" echo m68010-convergent-sysv exit ;; mc68k:UNIX:SYSTEM5:3.51m) echo m68k-convergent-sysv exit ;; M680?0:D-NIX:5.3:*) echo m68k-diab-dnix exit ;; M68*:*:R3V[5678]*:*) test -r /sysV68 && { echo 'm68k-motorola-sysv'; exit; } ;; 3[345]??:*:4.0:3.0 | 3[34]??A:*:4.0:3.0 | 3[34]??,*:*:4.0:3.0 | 3[34]??/*:*:4.0:3.0 | 4400:*:4.0:3.0 | 4850:*:4.0:3.0 | SKA40:*:4.0:3.0 | SDS2:*:4.0:3.0 | SHG2:*:4.0:3.0 | S7501*:*:4.0:3.0) OS_REL='' test -r /etc/.relid \ && OS_REL=.`sed -n 's/[^ ]* [^ ]* \([0-9][0-9]\).*/\1/p' < /etc/.relid` /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4.3${OS_REL}; exit; } /bin/uname -p 2>/dev/null | /bin/grep entium >/dev/null \ && { echo i586-ncr-sysv4.3${OS_REL}; exit; } ;; 3[34]??:*:4.0:* | 3[34]??,*:*:4.0:*) /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4; exit; } ;; NCR*:*:4.2:* | MPRAS*:*:4.2:*) OS_REL='.3' test -r /etc/.relid \ && OS_REL=.`sed -n 's/[^ ]* [^ ]* \([0-9][0-9]\).*/\1/p' < /etc/.relid` /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4.3${OS_REL}; exit; } /bin/uname -p 2>/dev/null | /bin/grep entium >/dev/null \ && { echo i586-ncr-sysv4.3${OS_REL}; exit; } /bin/uname -p 2>/dev/null | /bin/grep pteron >/dev/null \ && { echo i586-ncr-sysv4.3${OS_REL}; exit; } ;; m68*:LynxOS:2.*:* | m68*:LynxOS:3.0*:*) echo m68k-unknown-lynxos${UNAME_RELEASE} exit ;; mc68030:UNIX_System_V:4.*:*) echo m68k-atari-sysv4 exit ;; TSUNAMI:LynxOS:2.*:*) echo sparc-unknown-lynxos${UNAME_RELEASE} exit ;; rs6000:LynxOS:2.*:*) echo rs6000-unknown-lynxos${UNAME_RELEASE} exit ;; PowerPC:LynxOS:2.*:* | PowerPC:LynxOS:3.[01]*:* | PowerPC:LynxOS:4.[02]*:*) echo powerpc-unknown-lynxos${UNAME_RELEASE} exit ;; SM[BE]S:UNIX_SV:*:*) echo mips-dde-sysv${UNAME_RELEASE} exit ;; RM*:ReliantUNIX-*:*:*) echo mips-sni-sysv4 exit ;; RM*:SINIX-*:*:*) echo mips-sni-sysv4 exit ;; *:SINIX-*:*:*) if uname -p 2>/dev/null >/dev/null ; then UNAME_MACHINE=`(uname -p) 2>/dev/null` echo ${UNAME_MACHINE}-sni-sysv4 else echo ns32k-sni-sysv fi exit ;; PENTIUM:*:4.0*:*) # Unisys `ClearPath HMP IX 4000' SVR4/MP effort # says echo i586-unisys-sysv4 exit ;; *:UNIX_System_V:4*:FTX*) # From Gerald Hewes . # How about differentiating between stratus architectures? -djm echo hppa1.1-stratus-sysv4 exit ;; *:*:*:FTX*) # From seanf@swdc.stratus.com. echo i860-stratus-sysv4 exit ;; i*86:VOS:*:*) # From Paul.Green@stratus.com. echo ${UNAME_MACHINE}-stratus-vos exit ;; *:VOS:*:*) # From Paul.Green@stratus.com. echo hppa1.1-stratus-vos exit ;; mc68*:A/UX:*:*) echo m68k-apple-aux${UNAME_RELEASE} exit ;; news*:NEWS-OS:6*:*) echo mips-sony-newsos6 exit ;; R[34]000:*System_V*:*:* | R4000:UNIX_SYSV:*:* | R*000:UNIX_SV:*:*) if [ -d /usr/nec ]; then echo mips-nec-sysv${UNAME_RELEASE} else echo mips-unknown-sysv${UNAME_RELEASE} fi exit ;; BeBox:BeOS:*:*) # BeOS running on hardware made by Be, PPC only. echo powerpc-be-beos exit ;; BeMac:BeOS:*:*) # BeOS running on Mac or Mac clone, PPC only. echo powerpc-apple-beos exit ;; BePC:BeOS:*:*) # BeOS running on Intel PC compatible. echo i586-pc-beos exit ;; BePC:Haiku:*:*) # Haiku running on Intel PC compatible. echo i586-pc-haiku exit ;; x86_64:Haiku:*:*) echo x86_64-unknown-haiku exit ;; SX-4:SUPER-UX:*:*) echo sx4-nec-superux${UNAME_RELEASE} exit ;; SX-5:SUPER-UX:*:*) echo sx5-nec-superux${UNAME_RELEASE} exit ;; SX-6:SUPER-UX:*:*) echo sx6-nec-superux${UNAME_RELEASE} exit ;; SX-7:SUPER-UX:*:*) echo sx7-nec-superux${UNAME_RELEASE} exit ;; SX-8:SUPER-UX:*:*) echo sx8-nec-superux${UNAME_RELEASE} exit ;; SX-8R:SUPER-UX:*:*) echo sx8r-nec-superux${UNAME_RELEASE} exit ;; Power*:Rhapsody:*:*) echo powerpc-apple-rhapsody${UNAME_RELEASE} exit ;; *:Rhapsody:*:*) echo ${UNAME_MACHINE}-apple-rhapsody${UNAME_RELEASE} exit ;; *:Darwin:*:*) UNAME_PROCESSOR=`uname -p` || UNAME_PROCESSOR=unknown eval $set_cc_for_build if test "$UNAME_PROCESSOR" = unknown ; then UNAME_PROCESSOR=powerpc fi if test `echo "$UNAME_RELEASE" | sed -e 's/\..*//'` -le 10 ; then if [ "$CC_FOR_BUILD" != 'no_compiler_found' ]; then if (echo '#ifdef __LP64__'; echo IS_64BIT_ARCH; echo '#endif') | \ (CCOPTS= $CC_FOR_BUILD -E - 2>/dev/null) | \ grep IS_64BIT_ARCH >/dev/null then case $UNAME_PROCESSOR in i386) UNAME_PROCESSOR=x86_64 ;; powerpc) UNAME_PROCESSOR=powerpc64 ;; esac fi fi elif test "$UNAME_PROCESSOR" = i386 ; then # Avoid executing cc on OS X 10.9, as it ships with a stub # that puts up a graphical alert prompting to install # developer tools. Any system running Mac OS X 10.7 or # later (Darwin 11 and later) is required to have a 64-bit # processor. This is not true of the ARM version of Darwin # that Apple uses in portable devices. UNAME_PROCESSOR=x86_64 fi echo ${UNAME_PROCESSOR}-apple-darwin${UNAME_RELEASE} exit ;; *:procnto*:*:* | *:QNX:[0123456789]*:*) UNAME_PROCESSOR=`uname -p` if test "$UNAME_PROCESSOR" = "x86"; then UNAME_PROCESSOR=i386 UNAME_MACHINE=pc fi echo ${UNAME_PROCESSOR}-${UNAME_MACHINE}-nto-qnx${UNAME_RELEASE} exit ;; *:QNX:*:4*) echo i386-pc-qnx exit ;; NEO-?:NONSTOP_KERNEL:*:*) echo neo-tandem-nsk${UNAME_RELEASE} exit ;; NSE-*:NONSTOP_KERNEL:*:*) echo nse-tandem-nsk${UNAME_RELEASE} exit ;; NSR-?:NONSTOP_KERNEL:*:*) echo nsr-tandem-nsk${UNAME_RELEASE} exit ;; *:NonStop-UX:*:*) echo mips-compaq-nonstopux exit ;; BS2000:POSIX*:*:*) echo bs2000-siemens-sysv exit ;; DS/*:UNIX_System_V:*:*) echo ${UNAME_MACHINE}-${UNAME_SYSTEM}-${UNAME_RELEASE} exit ;; *:Plan9:*:*) # "uname -m" is not consistent, so use $cputype instead. 386 # is converted to i386 for consistency with other x86 # operating systems. if test "$cputype" = "386"; then UNAME_MACHINE=i386 else UNAME_MACHINE="$cputype" fi echo ${UNAME_MACHINE}-unknown-plan9 exit ;; *:TOPS-10:*:*) echo pdp10-unknown-tops10 exit ;; *:TENEX:*:*) echo pdp10-unknown-tenex exit ;; KS10:TOPS-20:*:* | KL10:TOPS-20:*:* | TYPE4:TOPS-20:*:*) echo pdp10-dec-tops20 exit ;; XKL-1:TOPS-20:*:* | TYPE5:TOPS-20:*:*) echo pdp10-xkl-tops20 exit ;; *:TOPS-20:*:*) echo pdp10-unknown-tops20 exit ;; *:ITS:*:*) echo pdp10-unknown-its exit ;; SEI:*:*:SEIUX) echo mips-sei-seiux${UNAME_RELEASE} exit ;; *:DragonFly:*:*) echo ${UNAME_MACHINE}-unknown-dragonfly`echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'` exit ;; *:*VMS:*:*) UNAME_MACHINE=`(uname -p) 2>/dev/null` case "${UNAME_MACHINE}" in A*) echo alpha-dec-vms ; exit ;; I*) echo ia64-dec-vms ; exit ;; V*) echo vax-dec-vms ; exit ;; esac ;; *:XENIX:*:SysV) echo i386-pc-xenix exit ;; i*86:skyos:*:*) echo ${UNAME_MACHINE}-pc-skyos`echo ${UNAME_RELEASE}` | sed -e 's/ .*$//' exit ;; i*86:rdos:*:*) echo ${UNAME_MACHINE}-pc-rdos exit ;; i*86:AROS:*:*) echo ${UNAME_MACHINE}-pc-aros exit ;; x86_64:VMkernel:*:*) echo ${UNAME_MACHINE}-unknown-esx exit ;; esac cat >&2 < in order to provide the needed information to handle your system. config.guess timestamp = $timestamp uname -m = `(uname -m) 2>/dev/null || echo unknown` uname -r = `(uname -r) 2>/dev/null || echo unknown` uname -s = `(uname -s) 2>/dev/null || echo unknown` uname -v = `(uname -v) 2>/dev/null || echo unknown` /usr/bin/uname -p = `(/usr/bin/uname -p) 2>/dev/null` /bin/uname -X = `(/bin/uname -X) 2>/dev/null` hostinfo = `(hostinfo) 2>/dev/null` /bin/universe = `(/bin/universe) 2>/dev/null` /usr/bin/arch -k = `(/usr/bin/arch -k) 2>/dev/null` /bin/arch = `(/bin/arch) 2>/dev/null` /usr/bin/oslevel = `(/usr/bin/oslevel) 2>/dev/null` /usr/convex/getsysinfo = `(/usr/convex/getsysinfo) 2>/dev/null` UNAME_MACHINE = ${UNAME_MACHINE} UNAME_RELEASE = ${UNAME_RELEASE} UNAME_SYSTEM = ${UNAME_SYSTEM} UNAME_VERSION = ${UNAME_VERSION} EOF exit 1 # Local variables: # eval: (add-hook 'write-file-hooks 'time-stamp) # time-stamp-start: "timestamp='" # time-stamp-format: "%:y-%02m-%02d" # time-stamp-end: "'" # End: cppad-20170000.3/example/0002755000175200017650000000000013057470461014066 5ustar coincoin-webcppad-20170000.3/example/sparse_sub_hes.cpp0000644000175200017650000001331113057470457017601 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparse_sub_hes.cpp$$ $spell $$ $section Sparse Hessian on Subset of Variables: Example and Test$$ $head Purpose$$ This example uses a $cref/column subset/sparse_hessian/p/Column Subset/$$ of the sparsity pattern to compute the Hessian for a subset of the variables. The values in the rest of the sparsity pattern do not matter. $head See Also$$ $cref sub_sparse_hes.cpp$$ $code $srcfile%example/sparse_sub_hes.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // BEGIN_EMPTY_NAMESPACE // -------------------------------------------------------------------------- CppAD::ADFun record_function(size_t n) { // must be greater than or equal 3; see n_sweep below assert( n >= 3 ); // using CppAD::AD; typedef CppAD::vector< AD > a_vector; // // domain space vector a_vector a_x(n); for(size_t j = 0; j < n; j++) a_x[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(a_x); // range space vector size_t m = 1; a_vector a_y(m); a_y[0] = 0.0; for(size_t j = 1; j < n; j++) a_y[0] += a_x[j-1] * a_x[j] * a_x[j]; // create f: x -> y and stop tape recording // (without executing zero order forward calculation) CppAD::ADFun f; f.Dependent(a_x, a_y); // return f; } // -------------------------------------------------------------------------- bool test_set(const char* color_method) { bool ok = true; // typedef CppAD::vector< double > d_vector; typedef CppAD::vector i_vector; typedef CppAD::vector< std::set > s_vector; // size_t n = 12; CppAD::ADFun f = record_function(n); // // sparsity patteren for the sub-set of variables we are computing // the hessian w.r.t. size_t n_sub = 4; s_vector r(n); for(size_t j = 0; j < n_sub; j++) { assert( r[j].empty() ); r[j].insert(j); } // store forward sparsity for J(x) = F^{(1)} (x) * R f.ForSparseJac(n_sub, r); // compute sparsity pattern for H(x) = (S * F)^{(2)} ( x ) * R s_vector s(1); assert( s[0].empty() ); s[0].insert(0); bool transpose = true; s_vector h = f.RevSparseHes(n_sub, s, transpose); // set the row and column indices that correspond to lower triangle i_vector row, col; for(size_t i = 0; i < n_sub; i++) { if( i > 0 ) { // diagonal element row.push_back(i); col.push_back(i); // lower diagonal element row.push_back(i); col.push_back(i-1); } } // weighting for the Hessian d_vector w(1); w[0] = 1.0; // compute Hessian CppAD::sparse_hessian_work work; work.color_method = color_method; d_vector x(n), hes( row.size() ); for(size_t j = 0; j < n; j++) x[j] = double(j+1); f.SparseHessian(x, w, h, row, col, hes, work); // check the values in the sparse hessian for(size_t ell = 0; ell < row.size(); ell++) { size_t i = row[ell]; size_t j = col[ell]; if( i == j ) ok &= hes[ell] == 2.0 * x[i-1]; else { ok &= j+1 == i; ok &= hes[ell] == 2.0 * x[i]; } ell++; } return ok; } // -------------------------------------------------------------------------- bool test_bool(const char* color_method) { bool ok = true; // typedef CppAD::vector< double > d_vector; typedef CppAD::vector i_vector; typedef CppAD::vector s_vector; // size_t n = 12; CppAD::ADFun f = record_function(n); // // sparsity patteren for the sub-set of variables we are computing // the hessian w.r.t. size_t n_sub = 4; s_vector r(n * n_sub); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n_sub; j++) r[ i * n_sub + j ] = (i == j); } // store forward sparsity for J(x) = F^{(1)} (x) * R f.ForSparseJac(n_sub, r); // compute sparsity pattern for H(x) = (S * F)^{(2)} ( x ) * R s_vector s(1); s[0] = true; bool transpose = true; s_vector h = f.RevSparseHes(n_sub, s, transpose); // set the row and column indices that correspond to lower triangle i_vector row, col; for(size_t i = 0; i < n_sub; i++) { if( i > 0 ) { // diagonal element row.push_back(i); col.push_back(i); // lower diagonal element row.push_back(i); col.push_back(i-1); } } // weighting for the Hessian d_vector w(1); w[0] = 1.0; // extend sparsity pattern (values in extended columns do not matter) s_vector h_extended(n * n); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n_sub; j++) h_extended[ i * n + j ] = h[ i * n_sub + j ]; for(size_t j = n_sub; j < n; j++) h_extended[ i * n + j ] = false; } // compute Hessian CppAD::sparse_hessian_work work; work.color_method = color_method; d_vector x(n), hes( row.size() ); for(size_t j = 0; j < n; j++) x[j] = double(j+1); f.SparseHessian(x, w, h_extended, row, col, hes, work); // check the values in the sparse hessian for(size_t ell = 0; ell < row.size(); ell++) { size_t i = row[ell]; size_t j = col[ell]; if( i == j ) ok &= hes[ell] == 2.0 * x[i-1]; else { ok &= j+1 == i; ok &= hes[ell] == 2.0 * x[i]; } ell++; } return ok; } } // END_EMPTY_NAMESPACE bool sparse_sub_hes(void) { bool ok = true; ok &= test_set("cppad.symmetric"); ok &= test_set("cppad.general"); // ok &= test_bool("cppad.symmetric"); ok &= test_bool("cppad.general"); return ok; } // END C++ cppad-20170000.3/example/colpack_hes.cpp0000644000175200017650000000734713057470457017063 0ustar coincoin-web// $Id: colpack_hes.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin colpack_hes.cpp$$ $spell colpack_hes jacobian $$ $section Using ColPack: Example and Test$$ $mindex colpack hessian sparse$$ $code $srcfile%example/colpack_hes.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool colpack_hes(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; typedef CPPAD_TESTVECTOR(AD) a_vector; typedef CPPAD_TESTVECTOR(double) d_vector; typedef CppAD::vector i_vector; size_t i, j, k, ell; double eps = 10. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 5; a_vector a_x(n); for(j = 0; j < n; j++) a_x[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(a_x); // colpack example case where hessian is a spear head // i.e, H(i, j) non zero implies i = 0, j = 0, or i = j AD sum = 0.0; // partial_0 partial_j = x[j] // partial_j partial_j = x[0] for(j = 1; j < n; j++) sum += a_x[0] * a_x[j] * a_x[j] / 2.0; // // partial_i partial_i = 2 * x[i] for(i = 0; i < n; i++) sum += a_x[i] * a_x[i] * a_x[i] / 3.0; // declare dependent variables size_t m = 1; a_vector a_y(m); a_y[0] = sum; // create f: x -> y and stop tape recording CppAD::ADFun f(a_x, a_y); // new value for the independent variable vector d_vector x(n); for(j = 0; j < n; j++) x[j] = double(j + 1); /* [ 2 2 3 4 5 ] hes = [ 2 5 0 0 0 ] [ 3 0 7 0 0 ] [ 4 0 0 9 0 ] [ 5 0 0 0 11 ] */ d_vector check(n * n); for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { size_t index = i * n + j; check[index] = 0.0; if( i == 0 && 1 <= j ) check[index] += x[j]; if( 1 <= i && j == 0 ) check[index] += x[i]; if( i == j ) { check[index] += 2.0 * x[i]; if( i != 0 ) check[index] += x[0]; } } } // Normally one would use f.RevSparseHes to compute // sparsity pattern, but for this example we extract it from check. std::vector< std::set > p(n); i_vector row, col; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { ell = i * n + j; if( check[ell] != 0. ) { // insert this non-zero entry in sparsity pattern p[i].insert(j); // the Hessian is symmetric, so only upper lower triangle if( j <= i ) { row.push_back(i); col.push_back(j); } } } } size_t K = row.size(); d_vector hes(K); // contrast and check results using both cppad and colpack CppAD::sparse_hessian_work work; for(size_t i_method = 0; i_method < 3; i_method++) { // empty work structure ok &= work.color_method == "cppad.symmetric"; if( i_method == 2 ) work.color_method = "colpack.star"; // compute Hessian d_vector w(m); w[0] = 1.0; size_t n_sweep = f.SparseHessian(x, w, p, row, col, hes, work); // check result for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(check[ell], hes[k], eps, eps); } if( work.color_method != "cppad.general" ) ok &= n_sweep == 2; else ok &= n_sweep == 5; // // check that clear resets color_method to cppad.symmetric work.clear(); ok &= work.color_method == "cppad.symmetric"; } return ok; } // END C++ cppad-20170000.3/example/ad_input.cpp0000644000175200017650000000274713057470457016412 0ustar coincoin-web// $Id: ad_input.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ad_input.cpp$$ $spell Cpp cstddef $$ $section AD Output Operator: Example and Test$$ $mindex << input$$ $code $srcfile%example/ad_input.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include // std::istringstream # include // std::string bool ad_input(void) { bool ok = true; // create the input string stream is. std::string str ("123 456"); std::istringstream is(str); // start and AD recording CPPAD_TESTVECTOR( CppAD::AD ) x(1), y(1); x[0] = 1.0; CppAD::Independent(x); CppAD::AD z = x[0]; ok &= Variable(z); // read first number into z and second into y[0] is >> z >> y[0]; ok &= Parameter(z); ok &= (z == 123.); ok &= Parameter(y[0]); ok &= (y[0] == 456.); // // terminate recording starting by call to Independent CppAD::ADFun f(x, y); return ok; } // END C++ cppad-20170000.3/example/pow.cpp0000644000175200017650000000561013057470457015404 0ustar coincoin-web// $Id: pow.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin pow.cpp$$ $spell $$ $section The AD Power Function: Example and Test$$ $code $srcfile%example/pow.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool pow(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; double x = 0.5; double y = 2.; CPPAD_TESTVECTOR(AD) axy(n); axy[0] = x; axy[1] = y; // declare independent variables and start tape recording CppAD::Independent(axy); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) az(m); az[0] = CppAD::pow(axy[0], axy[1]); // pow(variable, variable) az[1] = CppAD::pow(axy[0], y); // pow(variable, parameter) az[2] = CppAD::pow(x, axy[1]); // pow(parameter, variable) // create f: axy -> az and stop tape recording CppAD::ADFun f(axy, az); // check value double check = std::pow(x, y); size_t i; for(i = 0; i < m; i++) ok &= NearEqual(az[i] , check, eps, eps); // forward computation of first partial w.r.t. x CPPAD_TESTVECTOR(double) dxy(n); CPPAD_TESTVECTOR(double) dz(m); dxy[0] = 1.; dxy[1] = 0.; dz = f.Forward(1, dxy); check = y * std::pow(x, y-1.); ok &= NearEqual(dz[0], check, eps, eps); ok &= NearEqual(dz[1], check, eps, eps); ok &= NearEqual(dz[2], 0., eps, eps); // forward computation of first partial w.r.t. y dxy[0] = 0.; dxy[1] = 1.; dz = f.Forward(1, dxy); check = std::log(x) * std::pow(x, y); ok &= NearEqual(dz[0], check, eps, eps); ok &= NearEqual(dz[1], 0., eps, eps); ok &= NearEqual(dz[2], check, eps, eps); // reverse computation of derivative of z[0] + z[1] + z[2] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 1.; w[2] = 1.; dw = f.Reverse(1, w); check = y * std::pow(x, y-1.); ok &= NearEqual(dw[0], 2. * check, eps, eps); check = std::log(x) * std::pow(x, y); ok &= NearEqual(dw[1], 2. * check, eps, eps); // use a VecAD::reference object with pow CppAD::VecAD v(2); AD zero(0); AD one(1); v[zero] = axy[0]; v[one] = axy[1]; AD result = CppAD::pow(v[zero], v[one]); ok &= NearEqual(result, az[0], eps, eps); return ok; } // END C++ cppad-20170000.3/example/interp_onetape.cpp0000644000175200017650000001013513057470457017611 0ustar coincoin-web// $Id: interp_onetape.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin interp_onetape.cpp$$ $spell retaping retape $$ $section Interpolation With Out Retaping: Example and Test$$ $mindex interpolate tape retape$$ $head See Also$$ $cref interp_retape.cpp$$ $pre $$ $code $srcfile%example/interp_onetape.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include namespace { double ArgumentValue[] = { .0 , .2 , .4 , .8 , 1. }; double FunctionValue[] = { std::sin( ArgumentValue[0] ) , std::sin( ArgumentValue[1] ) , std::sin( ArgumentValue[2] ) , std::sin( ArgumentValue[3] ) , std::sin( ArgumentValue[4] ) }; size_t TableLength = 5; size_t Index(const double &x) { // determine the index j such that x is between // ArgumentValue[j] and ArgumentValue[j+1] static size_t j = 0; while ( x < ArgumentValue[j] && j > 0 ) j--; while ( x > ArgumentValue[j+1] && j < TableLength - 2) j++; // assert conditions that must be true given logic above assert( j >= 0 && j < TableLength - 1 ); return j; } double Argument(const double &x) { size_t j = Index(x); return ArgumentValue[j]; } double Function(const double &x) { size_t j = Index(x); return FunctionValue[j]; } double Slope(const double &x) { size_t j = Index(x); double dx = ArgumentValue[j+1] - ArgumentValue[j]; double dy = FunctionValue[j+1] - FunctionValue[j]; return dy / dx; } CPPAD_DISCRETE_FUNCTION(double, Argument) CPPAD_DISCRETE_FUNCTION(double, Function) CPPAD_DISCRETE_FUNCTION(double, Slope) } bool interp_onetape(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) X(n); X[0] = .4 * ArgumentValue[1] + .6 * ArgumentValue[2]; // declare independent variables and start tape recording CppAD::Independent(X); // evaluate piecewise linear interpolant at X[0] AD A = Argument(X[0]); AD F = Function(X[0]); AD S = Slope(X[0]); AD I = F + (X[0] - A) * S; // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = I; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // vectors for arguments to the function object f CPPAD_TESTVECTOR(double) x(n); // argument values CPPAD_TESTVECTOR(double) y(m); // function values CPPAD_TESTVECTOR(double) dx(n); // differentials in x space CPPAD_TESTVECTOR(double) dy(m); // differentials in y space // to check function value we use the fact that X[0] is between // ArgumentValue[1] and ArgumentValue[2] x[0] = Value(X[0]); double delta = ArgumentValue[2] - ArgumentValue[1]; double check = FunctionValue[2] * (x[0] - ArgumentValue[1]) / delta + FunctionValue[1] * (ArgumentValue[2] - x[0]) / delta; ok &= NearEqual(Y[0], check, eps99, eps99); // evaluate f where x has different value x[0] = .7 * ArgumentValue[2] + .3 * ArgumentValue[3]; y = f.Forward(0, x); // check function value delta = ArgumentValue[3] - ArgumentValue[2]; check = FunctionValue[3] * (x[0] - ArgumentValue[2]) / delta + FunctionValue[2] * (ArgumentValue[3] - x[0]) / delta; ok &= NearEqual(y[0], check, eps99, eps99); // evaluate partials w.r.t. x[0] dx[0] = 1.; dy = f.Forward(1, dx); // check that the derivative is the slope check = (FunctionValue[3] - FunctionValue[2]) / (ArgumentValue[3] - ArgumentValue[2]); ok &= NearEqual(dy[0], check, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/print_for.cpp0000644000175200017650000000416413057470457016604 0ustar coincoin-web// $Id: print_for.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin print_for_string.cpp$$ $spell Cpp $$ $section Print During Zero Order Forward Mode: Example and Test$$ $code $srcfile%example/print_for.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using std::endl; using CppAD::AD; // use of PrintFor to check for invalid function arguments AD check_log(const AD& y, std::ostream& s_out) { // check AD value during recording if( y <= 0 ) s_out << "check_log: y == " << y << " which is <= 0\n"; // check double value during zero order forward calculation PrintFor(y, "check_log: y == ", y , " which is <= 0\n"); return log(y); } } bool print_for(void) { bool ok = true; using CppAD::PrintFor; std::stringstream stream_out; // independent variable vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 1.; // value of the independent variable during recording Independent(ax); // A log evaluations that is OK when x[0] = 1 but not when x[0] = 2. AD var = 2. - ax[0]; AD log_var = check_log(var, stream_out); ok &= stream_out.str() == ""; // dependent variable vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = log_var; // define f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // zero order forward with x[0] = 2 CPPAD_TESTVECTOR(double) x(n); x[0] = 2.; f.Forward(0, x, stream_out); std::string string_out = stream_out.str(); ok &= stream_out.str() == "check_log: y == 0 which is <= 0\n"; return ok; } // END C++ cppad-20170000.3/example/expm1.cpp0000644000175200017650000000376113057470457015636 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin expm1.cpp$$ $spell exp $$ $section The AD exp Function: Example and Test$$ $code $srcfile%example/expm1.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool expm1(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CppAD::expm1(ax[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // expx0 value double expx0 = std::exp(x0); ok &= NearEqual(ay[0], expx0-1.0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], expx0, eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], expx0, eps, eps); // use a VecAD::reference object with exp CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::expm1(v[zero]); ok &= NearEqual(result, expx0-1.0, eps, eps); return ok; } // END C++ cppad-20170000.3/example/number_skip.cpp0000644000175200017650000000374613057470457017125 0ustar coincoin-web// $Id: number_skip.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin number_skip.cpp$$ $spell Taylor $$ $section Number of Variables That Can be Skipped: Example and Test$$ $mindex number_skip optimize conditional expression condition$$ $code $srcfile%example/number_skip.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool number_skip(void) { bool ok = true; using CppAD::AD; // independent variable vector CppAD::vector< AD > ax(2); ax[0] = 0.; ax[1] = 1.; Independent(ax); // Use a conditional expression CppAD::vector< AD > ay(1); // variable that gets optimized out AD az = ax[0] * ax[0]; // conditional expression ay[0] = CondExpLt(ax[0], ax[1], ax[0] + ax[1], ax[0] - ax[1]); // create function object F : x -> ay CppAD::ADFun f; f.Dependent(ax, ay); // use zero order to evaluate F[ (3, 4) ] CppAD::vector x( f.Domain() ); CppAD::vector y( f.Range() ); x[0] = 3.; x[1] = 4.; y = f.Forward(0, x); ok &= (y[0] == x[0] + x[1]); // before call to optimize ok &= f.number_skip() == 0; size_t n_var = f.size_var(); // now optimize the operation sequence f.optimize(); // after optimize, check forward mode result x[0] = 4.; x[1] = 3.; y = f.Forward(0, x); ok &= (y[0] == x[0] - x[1]); // after optimize, check amount of optimization ok &= f.size_var() == n_var - 1; ok &= f.number_skip() == 1; return ok; } // END C++ cppad-20170000.3/example/opt_val_hes.cpp0000644000175200017650000001124013057470457017076 0ustar coincoin-web// $Id: opt_val_hes.cpp 3814 2016-04-18 14:26:10Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin opt_val_hes.cpp$$ $spell hes $$ $section opt_val_hes: Example and Test$$ $mindex opt_val_hes$$ Fix $latex z \in \B{R}^\ell$$ and define the functions $latex S_k : \B{R} \times \B{R} \rightarrow \B{R}^\ell$$ by and $latex F : \B{R} \times \B{R} \rightarrow \B{R}$$ by $latex \[ \begin{array}{rcl} S_k (x, y) & = & \frac{1}{2} [ y * \sin ( x * t_k ) - z_k ]^2 \\ F(x, y) & = & \sum_{k=0}^{\ell-1} S_k (x, y) \end{array} \] $$ It follows that $latex \[ \begin{array}{rcl} \partial_y F(x, y) & = & \sum_{k=0}^{\ell-1} [ y * \sin ( x * t_k ) - z_k ] \sin( x * t_k ) \\ \partial_y \partial_y F(x, y) & = & \sum_{k=0}^{\ell-1} \sin ( x t_k )^2 \end{array} \] $$ Furthermore if we define $latex Y(x)$$ as solving the equation $latex \partial F[ x, Y(x) ] = 0 $$ we have $latex \[ \begin{array}{rcl} 0 & = & \sum_{k=0}^{\ell-1} [ Y(x) * \sin ( x * t_k ) - z_k ] \sin( x * t_k ) \\ Y(x) \sum_{k=0}^{\ell-1} \sin ( x * t_k )^2 - \sum_{k=0}^{\ell-1} \sin ( x * t_k ) z_k \\ Y(x) & = & \frac{ \sum_{k=0}^{\ell-1} \sin( x * t_k ) z_k }{ \sum_{k=0}^{\ell-1} \sin ( x * t_k )^2 } \end{array} \] $$ $code $srcfile%example/opt_val_hes.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { using CppAD::AD; typedef CPPAD_TESTVECTOR(double) BaseVector; typedef CPPAD_TESTVECTOR(AD) ADVector; class Fun { private: const BaseVector t_; // measurement times const BaseVector z_; // measurement values public: typedef ADVector ad_vector; // constructor Fun(const BaseVector &t, const BaseVector &z) : t_(t) , z_(z) { assert( t.size() == z.size() ); } // ell size_t ell(void) const { return t_.size(); } // Fun.s AD s(size_t k, const ad_vector& x, const ad_vector& y) const { AD residual = y[0] * sin( x[0] * t_[k] ) - z_[k]; AD s_k = .5 * residual * residual; return s_k; } // Fun.sy ad_vector sy(size_t k, const ad_vector& x, const ad_vector& y) const { assert( y.size() == 1); ad_vector sy_k(1); AD residual = y[0] * sin( x[0] * t_[k] ) - z_[k]; sy_k[0] = residual * sin( x[0] * t_[k] ); return sy_k; } }; // Used to test calculation of Hessian of V AD V(const ADVector& x, const BaseVector& t, const BaseVector& z) { // compute Y(x) AD numerator = 0.; AD denominator = 0.; size_t k; for(k = 0; k < size_t(t.size()); k++) { numerator += sin( x[0] * t[k] ) * z[k]; denominator += sin( x[0] * t[k] ) * sin( x[0] * t[k] ); } AD y = numerator / denominator; // V(x) = F[x, Y(x)] AD sum = 0; for(k = 0; k < size_t(t.size()); k++) { AD residual = y * sin( x[0] * t[k] ) - z[k]; sum += .5 * residual * residual; } return sum; } } bool opt_val_hes(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // temporary indices size_t j, k; // x space vector size_t n = 1; BaseVector x(n); x[0] = 2. * 3.141592653; // y space vector size_t m = 1; BaseVector y(m); y[0] = 1.; // t and z vectors size_t ell = 10; BaseVector t(ell); BaseVector z(ell); for(k = 0; k < ell; k++) { t[k] = double(k) / double(ell); // time of measurement z[k] = y[0] * sin( x[0] * t[k] ); // data without noise } // construct the function object Fun fun(t, z); // evaluate the Jacobian and Hessian BaseVector jac(n), hes(n * n); # ifndef NDEBUG int signdet = # endif CppAD::opt_val_hes(x, y, fun, jac, hes); // we know that F_yy is positive definate for this case assert( signdet == 1 ); // create ADFun object g corresponding to V(x) ADVector a_x(n), a_v(1); for(j = 0; j < n; j++) a_x[j] = x[j]; Independent(a_x); a_v[0] = V(a_x, t, z); CppAD::ADFun g(a_x, a_v); // accuracy for checks double eps = 10. * CppAD::numeric_limits::epsilon(); // check Jacobian BaseVector check_jac = g.Jacobian(x); for(j = 0; j < n; j++) ok &= NearEqual(jac[j], check_jac[j], eps, eps); // check Hessian BaseVector check_hes = g.Hessian(x, 0); for(j = 0; j < n*n; j++) ok &= NearEqual(hes[j], check_hes[j], eps, eps); return ok; } // END C++ cppad-20170000.3/example/for_sparse_jac.cpp0000644000175200017650000001423313057470457017560 0ustar coincoin-web// $Id: for_sparse_jac.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin for_sparse_jac.cpp$$ $spell Jacobian Jac Dep Cpp $$ $section Forward Mode Jacobian Sparsity: Example and Test$$ $mindex ForSparseJac sparsity$$ $code $srcfile%example/for_sparse_jac.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { // ------------------------------------------------------------- // define the template function BoolCases template // vector class, elements of type bool bool BoolCases(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; // declare independent variables and start recording CppAD::Independent(X); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0]; Y[1] = X[0] * X[1]; Y[2] = X[1]; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // sparsity pattern for the identity matrix Vector r(n * n); size_t i, j; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) r[ i * n + j ] = (i == j); } // sparsity pattern for F'(x) Vector s(m * n); s = f.ForSparseJac(n, r); // check values ok &= (s[ 0 * n + 0 ] == true); // Y[0] does depend on X[0] ok &= (s[ 0 * n + 1 ] == false); // Y[0] does not depend on X[1] ok &= (s[ 1 * n + 0 ] == true); // Y[1] does depend on X[0] ok &= (s[ 1 * n + 1 ] == true); // Y[1] does depend on X[1] ok &= (s[ 2 * n + 0 ] == false); // Y[2] does not depend on X[0] ok &= (s[ 2 * n + 1 ] == true); // Y[2] does depend on X[1] // check that values are stored ok &= (f.size_forward_bool() > 0); ok &= (f.size_forward_set() == 0); // sparsity pattern for F'(x)^T, note R is the identity, so R^T = R bool transpose = true; Vector st(n * m); st = f.ForSparseJac(n, r, transpose); // check values ok &= (st[ 0 * m + 0 ] == true); // Y[0] does depend on X[0] ok &= (st[ 1 * m + 0 ] == false); // Y[0] does not depend on X[1] ok &= (st[ 0 * m + 1 ] == true); // Y[1] does depend on X[0] ok &= (st[ 1 * m + 1 ] == true); // Y[1] does depend on X[1] ok &= (st[ 0 * m + 2 ] == false); // Y[2] does not depend on X[0] ok &= (st[ 1 * m + 2 ] == true); // Y[2] does depend on X[1] // check that values are stored ok &= (f.size_forward_bool() > 0); ok &= (f.size_forward_set() == 0); // free values from forward calculation f.size_forward_bool(0); ok &= (f.size_forward_bool() == 0); return ok; } // define the template function SetCases template // vector class, elements of type std::set bool SetCases(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; // declare independent variables and start recording CppAD::Independent(X); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0]; Y[1] = X[0] * X[1]; Y[2] = X[1]; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // sparsity pattern for the identity matrix Vector r(n); size_t i; for(i = 0; i < n; i++) { assert( r[i].empty() ); r[i].insert(i); } // sparsity pattern for F'(x) Vector s(m); s = f.ForSparseJac(n, r); // an interator to a standard set std::set::iterator itr; bool found; // Y[0] does depend on X[0] found = s[0].find(0) != s[0].end(); ok &= ( found == true ); // Y[0] does not depend on X[1] found = s[0].find(1) != s[0].end(); ok &= ( found == false ); // Y[1] does depend on X[0] found = s[1].find(0) != s[1].end(); ok &= ( found == true ); // Y[1] does depend on X[1] found = s[1].find(1) != s[1].end(); ok &= ( found == true ); // Y[2] does not depend on X[0] found = s[2].find(0) != s[2].end(); ok &= ( found == false ); // Y[2] does depend on X[1] found = s[2].find(1) != s[2].end(); ok &= ( found == true ); // check that values are stored ok &= (f.size_forward_set() > 0); ok &= (f.size_forward_bool() == 0); // sparsity pattern for F'(x)^T bool transpose = true; Vector st(n); st = f.ForSparseJac(n, r, transpose); // Y[0] does depend on X[0] found = st[0].find(0) != st[0].end(); ok &= ( found == true ); // Y[0] does not depend on X[1] found = st[1].find(0) != st[1].end(); ok &= ( found == false ); // Y[1] does depend on X[0] found = st[0].find(1) != st[0].end(); ok &= ( found == true ); // Y[1] does depend on X[1] found = st[1].find(1) != st[1].end(); ok &= ( found == true ); // Y[2] does not depend on X[0] found = st[0].find(2) != st[0].end(); ok &= ( found == false ); // Y[2] does depend on X[1] found = st[1].find(2) != st[1].end(); ok &= ( found == true ); // check that values are stored ok &= (f.size_forward_set() > 0); ok &= (f.size_forward_bool() == 0); return ok; } } // End empty namespace # include # include bool ForSparseJac(void) { bool ok = true; // Run with Vector equal to four different cases // all of which are Simple Vectors with elements of type bool. ok &= BoolCases< CppAD::vectorBool >(); ok &= BoolCases< CppAD::vector >(); ok &= BoolCases< std::vector >(); ok &= BoolCases< std::valarray >(); // Run with Vector equal to two different cases both of which are // Simple Vectors with elements of type std::set typedef std::set set; ok &= SetCases< CppAD::vector >(); // ok &= SetCases< std::vector >(); // Do not use valarray because its element access in the const case // returns a copy instead of a reference // ok &= SetCases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/for_two.cpp0000644000175200017650000000667113057470457016266 0ustar coincoin-web// $Id: for_two.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin for_two.cpp$$ $spell Cpp $$ $section Subset of Second Order Partials: Example and Test$$ $mindex partial$$ $code $srcfile%example/for_two.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ----------------------------------------------------- // define the template function in empty namespace // bool ForTwoCases(void) template bool ForTwoCases() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); using CppAD::exp; using CppAD::sin; using CppAD::cos; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; X[1] = 2.; // declare independent variables and starting recording CppAD::Independent(X); // a calculation between the domain and range values AD Square = X[0] * X[0]; // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = Square * exp( X[1] ); Y[1] = Square * sin( X[1] ); Y[2] = Square * cos( X[1] ); // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); x[0] = 2.; x[1] = 1.; // set j and k to compute specific second partials of y size_t p = 2; VectorSize_t j(p); VectorSize_t k(p); j[0] = 0; k[0] = 0; // for second partial w.r.t. x[0] and x[0] j[1] = 0; k[1] = 1; // for second partial w.r.t x[0] and x[1] // compute the second partials VectorBase ddy(m * p); ddy = f.ForTwo(x, j, k); /* partial of y w.r.t x[0] is [ 2 * x[0] * exp(x[1]) ] [ 2 * x[0] * sin(x[1]) ] [ 2 * x[0] * cos(x[1]) ] */ // second partial of y w.r.t x[0] and x[1] ok &= NearEqual( 2.*exp(x[1]), ddy[0*p+0], eps99, eps99); ok &= NearEqual( 2.*sin(x[1]), ddy[1*p+0], eps99, eps99); ok &= NearEqual( 2.*cos(x[1]), ddy[2*p+0], eps99, eps99); // second partial of F w.r.t x[0] and x[1] ok &= NearEqual( 2.*x[0]*exp(x[1]), ddy[0*p+1], eps99, eps99); ok &= NearEqual( 2.*x[0]*cos(x[1]), ddy[1*p+1], eps99, eps99); ok &= NearEqual(-2.*x[0]*sin(x[1]), ddy[2*p+1], eps99, eps99); return ok; } } // End empty namespace # include # include bool ForTwo(void) { bool ok = true; // Run with VectorBase equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= ForTwoCases< CppAD::vector , std::vector >(); ok &= ForTwoCases< std::vector , std::vector >(); ok &= ForTwoCases< std::valarray , std::vector >(); // Run with VectorSize_t equal to two other cases // which are Simple Vectors with elements of type size_t. ok &= ForTwoCases< std::vector , CppAD::vector >(); ok &= ForTwoCases< std::vector , std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/div_eq.cpp0000644000175200017650000000444313057470457016051 0ustar coincoin-web// $Id: div_eq.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin div_eq.cpp$$ $section AD Computed Assignment Division: Example and Test$$ $mindex /= divide assign plus add$$ $code $srcfile%example/div_eq.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool DivEq(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = .5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) y(m); y[0] = x[0] * x[0]; // initial value y[0] /= 2; // AD /= int y[0] /= 4.; // AD /= double y[1] = y[0] /= x[0]; // use the result of a computed assignment // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0*x0/(2.*4.*x0), eps99, eps99); ok &= NearEqual(y[1] , y[0], eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1./8., eps99, eps99); ok &= NearEqual(dy[1], 1./8., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 0.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1./8., eps99, eps99); // use a VecAD::reference object with computed division CppAD::VecAD v(1); AD zero(0); AD result = 2; v[zero] = 1; result /= v[zero]; ok &= (result == 2); return ok; } // END C++ cppad-20170000.3/example/sparse_jacobian.cpp0000644000175200017650000001555613057470457017734 0ustar coincoin-web// $Id: sparse_jacobian.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparse_jacobian.cpp$$ $spell Cpp Jacobian $$ $section Sparse Jacobian: Example and Test$$ $mindex Jacobian spare$$ $code $srcfile%example/sparse_jacobian.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // --------------------------------------------------------- bool reverse() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; typedef CPPAD_TESTVECTOR(AD) a_vector; typedef CPPAD_TESTVECTOR(double) d_vector; typedef CPPAD_TESTVECTOR(size_t) i_vector; size_t i, j, k, ell; double eps = 10. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 4; a_vector a_x(n); for(j = 0; j < n; j++) a_x[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(a_x); size_t m = 3; a_vector a_y(m); a_y[0] = a_x[0] + a_x[1]; a_y[1] = a_x[2] + a_x[3]; a_y[2] = a_x[0] + a_x[1] + a_x[2] + a_x[3] * a_x[3] / 2.; // create f: x -> y and stop tape recording CppAD::ADFun f(a_x, a_y); // new value for the independent variable vector d_vector x(n); for(j = 0; j < n; j++) x[j] = double(j); // Jacobian of y without sparsity pattern d_vector jac(m * n); jac = f.SparseJacobian(x); /* [ 1 1 0 0 ] jac = [ 0 0 1 1 ] [ 1 1 1 x_3] */ d_vector check(m * n); check[0] = 1.; check[1] = 1.; check[2] = 0.; check[3] = 0.; check[4] = 0.; check[5] = 0.; check[6] = 1.; check[7] = 1.; check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3]; for(ell = 0; ell < size_t(check.size()); ell++) ok &= NearEqual(check[ell], jac[ell], eps, eps ); // using packed boolean sparsity patterns CppAD::vectorBool s_b(m * m), p_b(m * n); for(i = 0; i < m; i++) { for(ell = 0; ell < m; ell++) s_b[i * m + ell] = false; s_b[i * m + i] = true; } p_b = f.RevSparseJac(m, s_b); jac = f.SparseJacobian(x, p_b); for(ell = 0; ell < size_t(check.size()); ell++) ok &= NearEqual(check[ell], jac[ell], eps, eps ); // using vector of sets sparsity patterns std::vector< std::set > s_s(m), p_s(m); for(i = 0; i < m; i++) s_s[i].insert(i); p_s = f.RevSparseJac(m, s_s); jac = f.SparseJacobian(x, p_s); for(ell = 0; ell < size_t(check.size()); ell++) ok &= NearEqual(check[ell], jac[ell], eps, eps ); // using row and column indices to compute non-zero in rows 1 and 2 // (skip row 0). size_t K = 6; i_vector row(K), col(K); jac.resize(K); k = 0; for(j = 0; j < n; j++) { for(i = 1; i < m; i++) { ell = i * n + j; if( p_b[ell] ) { ok &= check[ell] != 0.; row[k] = i; col[k] = j; k++; } } } ok &= k == K; // empty work structure CppAD::sparse_jacobian_work work; // could use p_b size_t n_sweep = f.SparseJacobianReverse(x, p_s, row, col, jac, work); for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(check[ell], jac[k], eps, eps); } ok &= n_sweep == 2; // now recompute at a different x value (using work from previous call) check[11] = x[3] = 10.; std::vector< std::set > not_used; n_sweep = f.SparseJacobianReverse(x, not_used, row, col, jac, work); for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(check[ell], jac[k], eps, eps); } ok &= n_sweep == 2; return ok; } bool forward() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; typedef CPPAD_TESTVECTOR(AD) a_vector; typedef CPPAD_TESTVECTOR(double) d_vector; typedef CPPAD_TESTVECTOR(size_t) i_vector; size_t i, j, k, ell; double eps = 10. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 3; a_vector a_x(n); for(j = 0; j < n; j++) a_x[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(a_x); size_t m = 4; a_vector a_y(m); a_y[0] = a_x[0] + a_x[2]; a_y[1] = a_x[0] + a_x[2]; a_y[2] = a_x[1] + a_x[2]; a_y[3] = a_x[1] + a_x[2] * a_x[2] / 2.; // create f: x -> y and stop tape recording CppAD::ADFun f(a_x, a_y); // new value for the independent variable vector d_vector x(n); for(j = 0; j < n; j++) x[j] = double(j); // Jacobian of y without sparsity pattern d_vector jac(m * n); jac = f.SparseJacobian(x); /* [ 1 0 1 ] jac = [ 1 0 1 ] [ 0 1 1 ] [ 0 1 x_2 ] */ d_vector check(m * n); check[0] = 1.; check[1] = 0.; check[2] = 1.; check[3] = 1.; check[4] = 0.; check[5] = 1.; check[6] = 0.; check[7] = 1.; check[8] = 1.; check[9] = 0.; check[10] = 1.; check[11] = x[2]; for(ell = 0; ell < size_t(check.size()); ell++) ok &= NearEqual(check[ell], jac[ell], eps, eps ); // test using packed boolean vectors for sparsity pattern CppAD::vectorBool r_b(n * n), p_b(m * n); for(j = 0; j < n; j++) { for(ell = 0; ell < n; ell++) r_b[j * n + ell] = false; r_b[j * n + j] = true; } p_b = f.ForSparseJac(n, r_b); jac = f.SparseJacobian(x, p_b); for(ell = 0; ell < size_t(check.size()); ell++) ok &= NearEqual(check[ell], jac[ell], eps, eps ); // test using vector of sets for sparsity pattern std::vector< std::set > r_s(n), p_s(m); for(j = 0; j < n; j++) r_s[j].insert(j); p_s = f.ForSparseJac(n, r_s); jac = f.SparseJacobian(x, p_s); for(ell = 0; ell < size_t(check.size()); ell++) ok &= NearEqual(check[ell], jac[ell], eps, eps ); // using row and column indices to compute non-zero elements excluding // row 0 and column 0. size_t K = 5; i_vector row(K), col(K); jac.resize(K); k = 0; for(i = 1; i < m; i++) { for(j = 1; j < n; j++) { ell = i * n + j; if( p_b[ell] ) { ok &= check[ell] != 0.; row[k] = i; col[k] = j; k++; } } } ok &= k == K; // empty work structure CppAD::sparse_jacobian_work work; // could use p_s size_t n_sweep = f.SparseJacobianForward(x, p_b, row, col, jac, work); for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(check[ell], jac[k], eps, eps); } ok &= n_sweep == 2; // now recompute at a different x value (using work from previous call) check[11] = x[2] = 10.; n_sweep = f.SparseJacobianForward(x, p_s, row, col, jac, work); for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(check[ell], jac[k], eps, eps); } ok &= n_sweep == 2; return ok; } } // End empty namespace bool sparse_jacobian(void) { bool ok = true; ok &= forward(); ok &= reverse(); return ok; } // END C++ cppad-20170000.3/example/div.cpp0000644000175200017650000000440413057470457015361 0ustar coincoin-web// $Id: div.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin div.cpp$$ $section AD Binary Division: Example and Test$$ $mindex / divide quotient$$ $code $srcfile%example/div.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool Div(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // some binary division operations AD a = x[0] / 1.; // AD / double AD b = a / 2; // AD / int AD c = 3. / b; // double / AD AD d = 4 / c; // int / AD // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = (x[0] * x[0]) / d; // AD / AD // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0], x0*x0*3.*2.*1./(4.*x0), eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 3.*2.*1./4., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 3.*2.*1./4., eps99, eps99); // use a VecAD::reference object with division CppAD::VecAD v(1); AD zero(0); v[zero] = d; AD result = (x[0] * x[0]) / v[zero]; ok &= (result == y[0]); return ok; } // END C++ cppad-20170000.3/example/runge45_2.cpp0000644000175200017650000000733113057470457016313 0ustar coincoin-web// $Id: runge45_2.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin runge45_2.cpp$$ $spell Runge $$ $section Runge45: Example and Test$$ $mindex Runge45$$ Define $latex X : \B{R} \times \B{R} \rightarrow \B{R}^n$$ by $latex \[ X_j (b, t) = b \left( \sum_{k=0}^j t^k / k ! \right) \] $$ for $latex j = 0 , \ldots , n-1$$. It follows that $latex \[ \begin{array}{rcl} X_j (b, 0) & = & b \\ \partial_t X_j (b, t) & = & b \left( \sum_{k=0}^{j-1} t^k / k ! \right) \\ \partial_t X_j (b, t) & = & \left\{ \begin{array}{ll} 0 & {\rm if} \; j = 0 \\ X_{j-1} (b, t) & {\rm otherwise} \end{array} \right. \end{array} \] $$ For a fixed $latex t_f$$, we can use $cref Runge45$$ to define $latex f : \B{R} \rightarrow \B{R}^n$$ as an approximation for $latex f(b) = X(b, t_f )$$. We can then compute $latex f^{(1)} (b)$$ which is an approximation for $latex \[ \partial_b X(b, t_f ) = \sum_{k=0}^j t_f^k / k ! \] $$ $code $srcfile%example/runge45_2.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // for size_t # include // for machine epsilon # include // for all of CppAD namespace { template class Fun { public: // constructor Fun(void) { } // set return value to X'(t) void Ode( const Scalar &t, const CPPAD_TESTVECTOR(Scalar) &x, CPPAD_TESTVECTOR(Scalar) &f) { size_t n = x.size(); f[0] = 0.; for(size_t k = 1; k < n; k++) f[k] = x[k-1]; } }; } bool runge_45_2(void) { typedef CppAD::AD Scalar; using CppAD::NearEqual; bool ok = true; // initial return value size_t j; // temporary indices size_t n = 5; // number components in X(t) and order of method size_t M = 2; // number of Runge45 steps in [ti, tf] Scalar ad_ti = 0.; // initial time Scalar ad_tf = 2.; // final time // value of independent variable at which to record operations CPPAD_TESTVECTOR(Scalar) ad_b(1); ad_b[0] = 1.; // declare b to be the independent variable Independent(ad_b); // object to evaluate ODE Fun ad_F; // xi = X(0) CPPAD_TESTVECTOR(Scalar) ad_xi(n); for(j = 0; j < n; j++) ad_xi[j] = ad_b[0]; // compute Runge45 approximation for X(tf) CPPAD_TESTVECTOR(Scalar) ad_xf(n), ad_e(n); ad_xf = CppAD::Runge45(ad_F, M, ad_ti, ad_tf, ad_xi, ad_e); // stop recording and use it to create f : b -> xf CppAD::ADFun f(ad_b, ad_xf); // evaluate f(b) CPPAD_TESTVECTOR(double) b(1); CPPAD_TESTVECTOR(double) xf(n); b[0] = 1.; xf = f.Forward(0, b); // check that f(b) = X(b, tf) double tf = Value(ad_tf); double term = 1; double sum = 0; double eps = 10. * CppAD::numeric_limits::epsilon(); for(j = 0; j < n; j++) { sum += term; ok &= NearEqual(xf[j], b[0] * sum, eps, eps); term *= tf; term /= double(j+1); } // evalute f'(b) CPPAD_TESTVECTOR(double) d_xf(n); d_xf = f.Jacobian(b); // check that f'(b) = partial of X(b, tf) w.r.t b term = 1; sum = 0; for(j = 0; j < n; j++) { sum += term; ok &= NearEqual(d_xf[j], sum, eps, eps); term *= tf; term /= double(j+1); } return ok; } // END C++ cppad-20170000.3/example/atan.cpp0000644000175200017650000000405713057470457015526 0ustar coincoin-web// $Id: atan.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atan.cpp$$ $spell tan atan $$ $section The AD atan Function: Example and Test$$ $code $srcfile%example/atan.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool atan(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD tan_of_x0 = CppAD::tan(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::atan(tan_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps99, eps99); // use a VecAD::reference object with atan CppAD::VecAD v(1); AD zero(0); v[zero] = tan_of_x0; AD result = CppAD::atan(v[zero]); ok &= NearEqual(result, x0, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/tan.cpp0000644000175200017650000000414013057470457015356 0ustar coincoin-web// $Id: tan.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin tan.cpp$$ $spell tan tan $$ $section The AD tan Function: Example and Test$$ $code $srcfile%example/tan.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool Tan(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::tan(x[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value double check = std::tan(x0); ok &= NearEqual(y[0] , check, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); check = 1. + std::tan(x0) * std::tan(x0); ok &= NearEqual(dy[0], check, eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, eps, eps); // use a VecAD::reference object with tan CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::tan(v[zero]); check = std::tan(x0); ok &= NearEqual(result, check, eps, eps); return ok; } // END C++ cppad-20170000.3/example/ad_in_c.cpp0000644000175200017650000002721413057470457016157 0ustar coincoin-web// $Id: ad_in_c.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ad_in_c.cpp$$ $spell CppAD $$ $section Example and Test Linking CppAD to Languages Other than C++$$ $mindex C AD algorithmic differentiation automatic link$$ $code $srcfile%example/ad_in_c.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include namespace { // Begin empty namespace ***************************************** /* void debug_print(const char *label, double d) { using std::printf; unsigned char *byte = reinterpret_cast(&d); size_t n_byte = sizeof(d); printf("%s", label); for(size_t i = 0; i < n_byte; i++) printf("%x", byte[i]); printf("\n"); } */ // type in C corresponding to an AD object typedef struct { void* p_void; } cad; // type in C corresponding to a an ADFun typedef struct { void* p_void; } cad_fun; // type in C corresponding to a C AD binary operator typedef enum { op_add, op_sub, op_mul, op_div } cad_binary_op; // type in C corresponding to a C AD unary operator typedef enum { op_abs, op_acos, op_asin, op_atan, op_cos, op_cosh, op_exp, op_log, op_sin, op_sinh, op_sqrt } cad_unary_op; // -------------------------------------------------------------------------- // helper code not intended for use by C code ------------------------------ using CppAD::AD; using CppAD::ADFun; using CppAD::vector; using CppAD::NearEqual; void cad2vector(size_t n, cad* p_cad, vector< AD >& v) { assert( n == v.size() ); for(size_t j = 0; j < n; j++) { AD* p_ad = reinterpret_cast< AD* > (p_cad[j].p_void); v[j] = *p_ad; } } void vector2cad(size_t n, vector< AD >& v, cad* p_cad) { assert( n == v.size() ); for(size_t j = 0; j < n; j++) { AD* p_ad = reinterpret_cast< AD* > (p_cad[j].p_void); *p_ad = v[j]; } } void double2vector(size_t n, double* p_dbl, vector& v) { assert( n == v.size() ); for(size_t j = 0; j < n; j++) v[j] = p_dbl[j]; } void vector2double(size_t n, vector& v, double *p_dbl) { assert( n == v.size() ); for(size_t j = 0; j < n; j++) p_dbl[j] = v[j]; } std::list allocated; # ifdef NDEBUG inline void push_allocated(void *p) { } inline void pop_allocated(void *p) { } # else inline void push_allocated(void *p) { assert( p != 0 ); allocated.push_front(p); } inline void pop_allocated(void *p) { std::list::iterator i; for(i = allocated.begin(); i != allocated.end(); ++i) { if( *i == p ) { allocated.erase(i); return; } } assert( 0 ); } # endif // -------------------------------------------------------------------------- // Here is the code that links C to CppAD. You will have to add more // functions and operators to make a complete language link. // extern "C" bool cad_near_equal(double x, double y) { double eps = 10. * std::numeric_limits::epsilon(); return NearEqual(x, y, eps, 0.); } // create a C++ AD object // value is the value that the C++ AD object will have // p_cad->p_void: on input is 0, on output points to C++ AD object extern "C" void cad_new_ad(cad *p_cad, double value) { // make sure pointer is not currently allocated assert( p_cad->p_void == 0 ); AD* p_ad = new AD(value); p_cad->p_void = reinterpret_cast(p_ad); // put in list of allocate pointers push_allocated( p_cad->p_void ); } // delete a C++ AD object // p_cad->value: not used // p_cad->p_void: on input points to C++ AD object, on output is 0 extern "C" void cad_del_ad(cad* p_cad) { // make sure that p_cad has been allocated pop_allocated( p_cad->p_void ); AD* p_ad = reinterpret_cast< AD* >( p_cad->p_void ); delete p_ad; // special value for pointers that are not allocated p_cad->p_void = 0; } // extract the value from a C++ AD object // extern "C" double cad_value(cad* p_cad) { AD* p_ad = reinterpret_cast< AD* > (p_cad->p_void); return Value( Var2Par(*p_ad) ); } // preform a C AD unary operation extern "C" void cad_unary(cad_unary_op op, cad* p_operand, cad* p_result) { AD *operand, *result; result = reinterpret_cast< AD* > (p_result->p_void); operand = reinterpret_cast< AD* > (p_operand->p_void); switch(op) { case op_abs: *result = abs( *operand ); break; case op_acos: *result = acos( *operand ); break; case op_asin: *result = asin( *operand ); break; case op_atan: *result = atan( *operand ); break; case op_cos: *result = cos( *operand ); break; case op_cosh: *result = cosh( *operand ); break; case op_exp: *result = exp( *operand ); break; case op_log: *result = log( *operand ); break; case op_sin: *result = sin( *operand ); break; case op_sinh: *result = sinh( *operand ); break; case op_sqrt: *result = sqrt( *operand ); break; default: // not a unary operator assert(0); break; } return; } // perform a C AD binary operation extern "C" void cad_binary(cad_binary_op op, cad* p_left, cad* p_right, cad* p_result) { AD *result, *left, *right; result = reinterpret_cast< AD* > (p_result->p_void); left = reinterpret_cast< AD* > (p_left->p_void); right = reinterpret_cast< AD* > (p_right->p_void); assert( result != 0 ); assert( left != 0 ); assert( right != 0 ); switch(op) { case op_add: *result = *left + (*right); break; case op_sub: *result = *left - (*right); break; case op_mul: *result = *left * (*right); break; case op_div: *result = *left / (*right); break; default: // not a binary operator assert(0); } return; } // declare the independent variables in C++ extern "C" void cad_independent(size_t n, cad* px_cad) { vector< AD > x(n); cad2vector(n, px_cad, x); CppAD::Independent(x); vector2cad(n, x, px_cad); } // create an ADFun object in C++ extern "C" cad_fun cad_new_fun(size_t n, size_t m, cad* px_cad, cad* py_cad) { cad_fun fun; ADFun* p_adfun = new ADFun; vector< AD > x(n); vector< AD > y(m); cad2vector(n, px_cad, x); cad2vector(m, py_cad, y); p_adfun->Dependent(x, y); fun.p_void = reinterpret_cast( p_adfun ); // put in list of allocate pointers push_allocated( fun.p_void ); return fun; } // delete an AD function object in C extern "C" void cad_del_fun(cad_fun *fun) { // make sure this pointer has been allocated pop_allocated( fun->p_void ); ADFun* p_adfun = reinterpret_cast< ADFun* > (fun->p_void); delete p_adfun; // special value for pointers that are not allocated fun->p_void = 0; } // evaluate the Jacobian corresponding to a function object extern "C" void cad_jacobian(cad_fun fun, size_t n, size_t m, double* px, double* pjac ) { assert( fun.p_void != 0 ); ADFun* p_adfun = reinterpret_cast< ADFun* >(fun.p_void); vector x(n), jac(n * m); double2vector(n, px, x); jac = p_adfun->Jacobian(x); vector2double(n * m, jac, pjac); } // forward mode extern "C" void cad_forward(cad_fun fun, size_t order, size_t n, size_t m, double* px, double* py ) { assert( fun.p_void != 0 ); ADFun* p_adfun = reinterpret_cast< ADFun* >(fun.p_void); vector x(n), y(m); double2vector(n, px, x); y = p_adfun->Forward(order, x); vector2double(m, y, py); } // check that allocated list has been completely freed extern "C" bool cad_allocated_empty(void) { return allocated.empty(); } } // End empty namespace **************************************************** # include // used to check results in c code below # define N 2 // number of independent variables in example # define M 5 // number of dependent variables in example // ------------------------------------------------------------------------- // Here is the C code that uses the CppAD link above bool ad_in_c(void) { // This routine is intentionally coded as if it were written in C // as an example of how you can link C, and other languages to CppAD bool ok = true; // x vector of AD objects in C double value; size_t j, n = N; cad X[N]; for(j = 0; j < n; j++) { value = (double) (j+1) / (double) n; X[j].p_void = 0; cad_new_ad(X + j, value); } // y vector of AD objects in C size_t i, m = M; cad Y[M]; for(i = 0; i < m; i++) { value = 0.; // required, but not used Y[i].p_void = 0; cad_new_ad(Y + i, value); } // declare X as the independent variable vector cad_independent(n, X); // y[0] = x[0] + x[1] cad_binary(op_add, X+0, X+1, Y+0); ok &= cad_near_equal( cad_value(Y+0), cad_value(X+0)+cad_value(X+1) ); // y[1] = x[0] - x[1] cad_binary(op_sub, X+0, X+1, Y+1); ok &= cad_near_equal( cad_value(Y+1), cad_value(X+0)-cad_value(X+1) ); // y[2] = x[0] * x[1] cad_binary(op_mul, X+0, X+1, Y+2); ok &= cad_near_equal( cad_value(Y+2), cad_value(X+0)*cad_value(X+1) ); // y[3] = x[0] * x[1] cad_binary(op_div, X+0, X+1, Y+3); ok &= cad_near_equal( cad_value(Y+3), cad_value(X+0)/cad_value(X+1) ); // y[4] = sin(x[0]) + asin(sin(x[0])) cad sin_x0 = { 0 }; // initialize p_void as zero cad_new_ad( &sin_x0, 0.); cad_unary(op_sin, X+0, &sin_x0); ok &= cad_near_equal(cad_value(&sin_x0), sin(cad_value(X+0)) ); cad asin_sin_x0 = { 0 }; // initialize p_void as zero cad_new_ad( &asin_sin_x0, 0.); cad_unary(op_asin, &sin_x0, &asin_sin_x0); ok &= cad_near_equal( cad_value(&asin_sin_x0), asin( cad_value(&sin_x0) ) ); cad_binary(op_add, &sin_x0, &asin_sin_x0, Y+4); ok &= cad_near_equal( cad_value(Y+4), cad_value(&sin_x0) + cad_value(&asin_sin_x0) ); // declare y as the dependent variable vector and stop recording // and store function object in f cad_fun f = cad_new_fun(n, m, X, Y); // now use the function object double x[N], jac[N * M]; x[0] = 1.; x[1] = .5; // compute the Jacobian cad_jacobian(f, n, m, x, jac); // check the Jacobian values size_t k = 0; // partial y[0] w.r.t. x[0] ok &= cad_near_equal(jac[k++], 1.); // partial y[0] w.r.t. x[1] ok &= cad_near_equal(jac[k++], 1.); // partial y[1] w.r.t. x[0] ok &= cad_near_equal(jac[k++], 1.); // partial y[1] w.r.t. x[1] ok &= cad_near_equal(jac[k++], -1.); // partial y[2] w.r.t. x[0] ok &= cad_near_equal(jac[k++], x[1]); // partial y[2] w.r.t. x[1] ok &= cad_near_equal(jac[k++], x[0]); // partial y[3] w.r.t. x[0] ok &= cad_near_equal(jac[k++], 1./x[1]); // partial y[3] w.r.t. x[1] ok &= cad_near_equal(jac[k++], -x[0]/(x[1]*x[1])); // partial y[4] w.r.t x[0] ok &= cad_near_equal(jac[k++], cos(x[0]) + 1.); // partial y[4] w.r.t x[1] ok &= cad_near_equal(jac[k++], 0.); // evaluate the function f at a different x size_t order = 0; double y[M]; x[0] = .5; x[1] = 1.; cad_forward(f, order, n, m, x, y); // check the function values ok &= cad_near_equal(y[0] , x[0] + x[1] ); ok &= cad_near_equal(y[1] , x[0] - x[1] ); ok &= cad_near_equal(y[2] , x[0] * x[1] ); ok &= cad_near_equal(y[3] , x[0] / x[1] ); ok &= cad_near_equal(y[4] , sin(x[0]) + asin(sin(x[0])) ); // delete All C++ copies of the AD objects cad_del_fun( &f ); cad_del_ad( &sin_x0 ); cad_del_ad( &asin_sin_x0 ); for(j = 0; j < n; j++) cad_del_ad(X + j); for(i = 0; i < m; i++) cad_del_ad(Y + i); ok &= cad_allocated_empty(); return ok; } // END C++ cppad-20170000.3/example/compare.cpp0000644000175200017650000000520013057470457016220 0ustar coincoin-web// $Id: compare.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin compare.cpp$$ $spell Cpp $$ $section AD Binary Comparison Operators: Example and Test$$ $mindex compare < <= > >= == !=$$ $code $srcfile%example/compare.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool Compare(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // declare independent variables and start tape recording size_t n = 2; double x0 = 0.5; double x1 = 1.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; x[1] = x1; CppAD::Independent(x); // some binary comparision operations AD p; if( x[0] < x[1] ) p = x[0]; // values in x choose this case else p = x[1]; if( x[0] <= x[1] ) p *= x[0]; // values in x choose this case else p *= x[1]; if( x[0] > x[1] ) p *= x[0]; else p *= x[1]; // values in x choose this case if( x[0] >= x[1] ) p *= x[0]; else p *= x[1]; // values in x choose this case if( x[0] == x[1] ) p *= x[0]; else p *= x[1]; // values in x choose this case if( x[0] != x[1] ) p *= x[0]; // values in x choose this case else p *= x[1]; // dependent variable vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = p; // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0*x0*x1*x1*x1*x0, eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dx[1] = 0.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 3.*x0*x0*x1*x1*x1, eps99, eps99); // forward computation of partials w.r.t. x[1] dx[0] = 0.; dx[1] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 3.*x0*x0*x1*x1*x0, eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 3.*x0*x0*x1*x1*x1, eps99, eps99); ok &= NearEqual(dw[1], 3.*x0*x0*x1*x1*x0, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/capacity_order.cpp0000644000175200017650000000676013057470457017576 0ustar coincoin-web// $Id: capacity_order.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin capacity_order.cpp$$ $spell Taylor $$ $section Controlling Taylor Coefficient Memory Allocation: Example and Test$$ $mindex capacity_order$$ $code $srcfile%example/capacity_order.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { bool test(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; using CppAD::thread_alloc; // domain space vector size_t n(1), m(1); CPPAD_TESTVECTOR(AD) ax(n), ay(n); // declare independent variables and start tape recording ax[0] = 1.0; CppAD::Independent(ax); // Set y = x^3, use enough variables so more that the minimal amount // of memory is allocated for Taylor coefficients ay[0] = 0.; for( size_t i = 0; i < 10; i++) ay[0] += ax[0] * ax[0] * ax[0]; ay[0] = ay[0] / 10.; // create f: x -> y and stop tape recording // (without running zero order forward mode). CppAD::ADFun f; f.Dependent(ax, ay); // check that this is master thread size_t thread = thread_alloc::thread_num(); ok &= thread == 0; // this should be master thread // The highest order forward mode calculation below is first order. // This corresponds to two Taylor coefficient per variable,direction // (orders zero and one). Preallocate memory for speed. size_t inuse = thread_alloc::inuse(thread); f.capacity_order(2); ok &= thread_alloc::inuse(thread) > inuse; // zero order forward mode CPPAD_TESTVECTOR(double) x(n), y(m); x[0] = 0.5; y = f.Forward(0, x); double eps = 10. * CppAD::numeric_limits::epsilon(); ok &= NearEqual(y[0], x[0] * x[0] * x[0], eps, eps); // forward computation of partials w.r.t. x CPPAD_TESTVECTOR(double) dx(n), dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 3. * x[0] * x[0], eps, eps); // Suppose we no longer need the first order Taylor coefficients. inuse = thread_alloc::inuse(thread); f.capacity_order(1); // just keep zero order coefficients ok &= thread_alloc::inuse(thread) < inuse; // Suppose we no longer need the zero order Taylor coefficients // (could have done this first and not used f.capacity_order(1)). inuse = thread_alloc::inuse(thread); f.capacity_order(0); ok &= thread_alloc::inuse(thread) < inuse; // turn off memory holding thread_alloc::hold_memory(false); return ok; } } bool capacity_order(void) { bool ok = true; using CppAD::thread_alloc; // original amount of memory inuse size_t thread = thread_alloc::thread_num(); ok &= thread == 0; // this should be master thread size_t inuse = thread_alloc::inuse(thread); // do test in separate routine so all objects are destroyed ok &= test(); // check that the amount of memroy inuse has not changed ok &= thread_alloc::inuse(thread) == inuse; // Test above uses hold_memory, so return available memory thread_alloc::free_available(thread); return ok; } // END C++ cppad-20170000.3/example/rev_sparse_jac.cpp0000644000175200017650000001311013057470457017557 0ustar coincoin-web// $Id: rev_sparse_jac.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin rev_sparse_jac.cpp$$ $spell Jacobian Jac Dep Cpp $$ $section Reverse Mode Jacobian Sparsity: Example and Test$$ $mindex RevSparseJac sparsity$$ $code $srcfile%example/rev_sparse_jac.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ------------------------------------------------------------- // define the template function BoolCases template // vector class, elements of type bool bool BoolCases(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; // declare independent variables and start recording CppAD::Independent(ax); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = ax[0]; ay[1] = ax[0] * ax[1]; ay[2] = ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // sparsity pattern for the identity matrix Vector r(m * m); size_t i, j; for(i = 0; i < m; i++) { for(j = 0; j < m; j++) r[ i * m + j ] = (i == j); } // sparsity pattern for F'(x) Vector s(m * n); s = f.RevSparseJac(m, r); // check values ok &= (s[ 0 * n + 0 ] == true); // y[0] does depend on x[0] ok &= (s[ 0 * n + 1 ] == false); // y[0] does not depend on x[1] ok &= (s[ 1 * n + 0 ] == true); // y[1] does depend on x[0] ok &= (s[ 1 * n + 1 ] == true); // y[1] does depend on x[1] ok &= (s[ 2 * n + 0 ] == false); // y[2] does not depend on x[0] ok &= (s[ 2 * n + 1 ] == true); // y[2] does depend on x[1] // sparsity pattern for F'(x)^T, note R is the identity, so R^T = R bool transpose = true; Vector st(n * m); st = f.RevSparseJac(m, r, transpose); // check values ok &= (st[ 0 * m + 0 ] == true); // y[0] does depend on x[0] ok &= (st[ 1 * m + 0 ] == false); // y[0] does not depend on x[1] ok &= (st[ 0 * m + 1 ] == true); // y[1] does depend on x[0] ok &= (st[ 1 * m + 1 ] == true); // y[1] does depend on x[1] ok &= (st[ 0 * m + 2 ] == false); // y[2] does not depend on x[0] ok &= (st[ 1 * m + 2 ] == true); // y[2] does depend on x[1] return ok; } // define the template function SetCases template // vector class, elements of type std::set bool SetCases(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; // declare independent variables and start recording CppAD::Independent(ax); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = ax[0]; ay[1] = ax[0] * ax[1]; ay[2] = ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // sparsity pattern for the identity matrix Vector r(m); size_t i; for(i = 0; i < m; i++) { assert( r[i].empty() ); r[i].insert(i); } // sparsity pattern for F'(x) Vector s(m); s = f.RevSparseJac(m, r); // check values bool found; // y[0] does depend on x[0] found = s[0].find(0) != s[0].end(); ok &= (found == true); // y[0] does not depend on x[1] found = s[0].find(1) != s[0].end(); ok &= (found == false); // y[1] does depend on x[0] found = s[1].find(0) != s[1].end(); ok &= (found == true); // y[1] does depend on x[1] found = s[1].find(1) != s[1].end(); ok &= (found == true); // y[2] does not depend on x[0] found = s[2].find(0) != s[2].end(); ok &= (found == false); // y[2] does depend on x[1] found = s[2].find(1) != s[2].end(); ok &= (found == true); // sparsity pattern for F'(x)^T bool transpose = true; Vector st(n); st = f.RevSparseJac(m, r, transpose); // y[0] does depend on x[0] found = st[0].find(0) != st[0].end(); ok &= (found == true); // y[0] does not depend on x[1] found = st[1].find(0) != st[1].end(); ok &= (found == false); // y[1] does depend on x[0] found = st[0].find(1) != st[0].end(); ok &= (found == true); // y[1] does depend on x[1] found = st[1].find(1) != st[1].end(); ok &= (found == true); // y[2] does not depend on x[0] found = st[0].find(2) != st[0].end(); ok &= (found == false); // y[2] does depend on x[1] found = st[1].find(2) != st[1].end(); ok &= (found == true); return ok; } } // End empty namespace # include # include bool RevSparseJac(void) { bool ok = true; // Run with Vector equal to four different cases // all of which are Simple Vectors with elements of type bool. ok &= BoolCases< CppAD::vectorBool >(); ok &= BoolCases< CppAD::vector >(); ok &= BoolCases< std::vector >(); ok &= BoolCases< std::valarray >(); // Run with Vector equal to two different cases both of which are // Simple Vectors with elements of type std::set typedef std::set set; ok &= SetCases< CppAD::vector >(); ok &= SetCases< std::vector >(); // Do not use valarray because its element access in the const case // returns a copy instead of a reference // ok &= SetCases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/fun_assign.cpp0000644000175200017650000000630413057470457016734 0ustar coincoin-web// $Id: fun_assign.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin fun_assign.cpp$$ $section ADFun Assignment: Example and Test$$ $mindex assignment$$ $code $srcfile%example/fun_assign.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool fun_assign(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j; // ten times machine percision double eps = 10. * CppAD::numeric_limits::epsilon(); // two ADFun objects CppAD::ADFun g; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) x(n); for(j = 0; j < n; j++) x[j] = AD(j + 2); // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) y(m); y[0] = x[0] + x[0] * x[1]; y[1] = x[1] * x[2] + x[2]; // Store operation sequence, and order zero forward results, in f. CppAD::ADFun f(x, y); // sparsity pattern for the identity matrix CPPAD_TESTVECTOR(std::set) r(n); for(j = 0; j < n; j++) r[j].insert(j); // Store forward mode sparsity pattern in f f.ForSparseJac(n, r); // make a copy in g g = f; // check values that should be equal ok &= ( g.size_order() == f.size_order() ); ok &= ( g.size_forward_bool() == f.size_forward_bool() ); ok &= ( g.size_forward_set() == f.size_forward_set() ); // Use zero order Taylor coefficient from f for first order // calculation using g. CPPAD_TESTVECTOR(double) dx(n), dy(m); for(i = 0; i < n; i++) dx[i] = 0.; dx[1] = 1; dy = g.Forward(1, dx); ok &= NearEqual(dy[0], x[0], eps, eps); // partial y[0] w.r.t x[1] ok &= NearEqual(dy[1], x[2], eps, eps); // partial y[1] w.r.t x[1] // Use forward Jacobian sparsity pattern from f to calculate // Hessian sparsity pattern using g. CPPAD_TESTVECTOR(std::set) s(1), h(n); s[0].insert(0); // Compute sparsity pattern for Hessian of y[0] h = f.RevSparseHes(n, s); // check sparsity pattern for Hessian of y[0] = x[0] + x[0] * x[1] ok &= ( h[0].find(0) == h[0].end() ); // zero w.r.t x[0], x[0] ok &= ( h[0].find(1) != h[0].end() ); // non-zero w.r.t x[0], x[1] ok &= ( h[0].find(2) == h[0].end() ); // zero w.r.t x[0], x[2] ok &= ( h[1].find(0) != h[1].end() ); // non-zero w.r.t x[1], x[0] ok &= ( h[1].find(1) == h[1].end() ); // zero w.r.t x[1], x[1] ok &= ( h[1].find(2) == h[1].end() ); // zero w.r.t x[1], x[2] ok &= ( h[2].find(0) == h[2].end() ); // zero w.r.t x[2], x[0] ok &= ( h[2].find(1) == h[2].end() ); // zero w.r.t x[2], x[1] ok &= ( h[2].find(2) == h[2].end() ); // zero w.r.t x[2], x[2] return ok; } // END C++ cppad-20170000.3/example/ad_assign.cpp0000644000175200017650000000245313057470457016531 0ustar coincoin-web// $Id: ad_assign.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ad_assign.cpp$$ $spell Cpp $$ $section AD Assignment: Example and Test$$ $mindex assign object$$ $code $srcfile%example/ad_assign.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool ad_assign(void) { bool ok = true; // initialize test result flag using CppAD::AD; // so can use AD in place of CppAD::AD // assignment to base value AD a; a = 1.; ok &= a == 1.; // assignment to a value that converts to the base type a = 2; ok &= a == 2.; // assignment to an AD AD b(3.); a = b; ok &= a == 3.; // assignment to an VecAD element CppAD::VecAD v(1); v[0] = 4.; a = v[0]; ok &= a == 4.; return ok; } // END C++ cppad-20170000.3/example/erf.cpp0000644000175200017650000000510613057470457015353 0ustar coincoin-web// $Id: erf.cpp 3833 2016-09-29 14:31:50Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin erf.cpp$$ $spell tan erf $$ $section The AD erf Function: Example and Test$$ $code $srcfile%example/erf.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool Erf(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CppAD::erf(ax[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // check relative erorr double erf_x0 = 0.5204998778130465; ok &= NearEqual(ay[0] , erf_x0, 0., 4e-4); # if CPPAD_USE_CPLUSPLUS_2011 double tmp = std::max(1e-15, eps); ok &= NearEqual(ay[0] , erf_x0, 0., tmp); # endif // value of derivative of erf at x0 double pi = 4. * std::atan(1.); double factor = 2. / sqrt(pi); double check = factor * std::exp(-x0 * x0); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], check, 0., 1e-3); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(dy[0], check, 0., eps); # endif // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, 0., 1e-1); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(dw[0], check, 0., eps); # endif // use a VecAD::reference object with erf CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::erf(v[zero]); ok &= NearEqual(result, ay[0], eps, eps); // use a double with erf ok &= NearEqual(CppAD::erf(x0), ay[0], eps, eps); return ok; } // END C++ cppad-20170000.3/example/azmul.cpp0000644000175200017650000000424113057470457015726 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin azmul.cpp$$ $spell $$ $section AD Absolute Zero Multiplication: Example and Test$$ $code $srcfile%example/azmul.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool azmul(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double inf = std::numeric_limits::infinity(); double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; double x = 0.5; double y = 2.0; CPPAD_TESTVECTOR(AD) axy(n); axy[0] = x; axy[1] = y; // declare independent variables and start tape recording CppAD::Independent(axy); // range space vector size_t m = 5; CPPAD_TESTVECTOR(AD) az(m); az[0] = CppAD::azmul(axy[0], axy[1]); // azmul(variable, variable) az[1] = CppAD::azmul(axy[0], inf); // azmul(variable, parameter=inf) az[2] = CppAD::azmul(axy[0], 3.0); // azmul(variable, parameter=3.0) az[3] = CppAD::azmul(0.0, axy[1]); // azmul(parameter=0.0, variable) az[4] = CppAD::azmul(4.0, axy[1]); // azmul(parameter=4.0, variable) // create f: axy -> az and stop tape recording CppAD::ADFun f(axy, az); // check value when x is not zero ok &= NearEqual(az[0] , x * y, eps, eps); ok &= az[1] == inf; ok &= NearEqual(az[2] , x * 3.0, eps, eps); ok &= az[3] == 0.0; ok &= NearEqual(az[4] , 4.0 * y, eps, eps); // check value x is zero and y is infinity CPPAD_TESTVECTOR(double) xy(n), z(m); xy[0] = 0.0; xy[1] = inf; z = f.Forward(0, xy); ok &= z[0] == 0.0; ok &= z[1] == 0.0; ok &= z[2] == 0.0; ok &= z[3] == 0.0; ok &= z[4] == inf; return ok; } // END C++ cppad-20170000.3/example/dependency.cpp0000644000175200017650000001024213057470457016712 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin dependency.cpp$$ $spell CppAD Jac $$ $section Computing Dependency: Example and Test$$ $head Discussion$$ The partial of an dependent variable with respect to an independent variable might always be zero even though the dependent variable depends on the value of the dependent variable. Consider the following case $latex \[ f(x) = {\rm sign} (x) = \left\{ \begin{array}{rl} +1 & {\rm if} \; x > 0 \\ 0 & {\rm if} \; x = 0 \\ -1 & {\rm if} \; x < 0 \end{array} \right. \] $$ In this case the value of $latex f(x)$$ depends on the value of $latex x$$ but CppAD always returns zero for the derivative of the $cref sign$$ function. $head Dependency Pattern$$ If the $th i$$ dependent variables depends on the value of the $th j$$ independent variable, the corresponding entry in the dependency pattern is non-zero (true). Otherwise it is zero (false). CppAD uses $cref/sparsity patterns/glossary/Sparsity Pattern/$$ to represent dependency matrices. The $icode dependency$$ argument to $cref/ForSparseJac/ForSparseJac/dependency/$$ and $cref/RevSparseJac/RevSparseJac/dependency/$$ is a flag that signals that the dependency pattern (instead of the sparsity pattern) is computed. $code $srcfile%example/dependency.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { double heavyside(const double& x) { if( x <= 0.0 ) return 0.0; return 1.0; } CPPAD_DISCRETE_FUNCTION(double, heavyside) } bool dependency(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // VecAD object for use later CppAD::VecAD vec_ad(2); vec_ad[0] = 0.0; vec_ad[1] = 1.0; // domain space vector size_t n = 5; CPPAD_TESTVECTOR(AD) ax(n); for(size_t j = 0; j < n; j++) ax[j] = AD(j + 1); // declare independent variables and start tape recording CppAD::Independent(ax); // some AD constants AD azero(0.0), aone(1.0); // range space vector size_t m = n; size_t m1 = n - 1; CPPAD_TESTVECTOR(AD) ay(m); ay[m1-0] = sign( ax[0] ); ay[m1-1] = CondExpLe( ax[1], azero, azero, aone); ay[m1-2] = CondExpLe( azero, ax[2], azero, aone); ay[m1-3] = heavyside( ax[3] ); ay[m1-4] = vec_ad[ ax[4] - AD(4.0) ]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // ----------------------------------------------------------- // ForSparseJac and bool dependency bool transpose = false; bool dependency; // could replace CppAD::vectorBooll by CPPAD_TEST_VECTOR CppAD::vectorBool eye_bool(n * n), depend_bool(m * n); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n; j++) eye_bool[i * n + j] = (i == j); } dependency = true; depend_bool = f.ForSparseJac(n, eye_bool, transpose, dependency); for(size_t i = 0; i < m; i++) { for(size_t j = 0; j < n; j++) ok &= depend_bool[i * n + j] == (i == (m1-j)); } dependency = false; depend_bool = f.ForSparseJac(n, eye_bool, transpose, dependency); for(size_t i = 0; i < m; i++) { for(size_t j = 0; j < n; j++) ok &= depend_bool[i * n + j] == false; } // ----------------------------------------------------------- // RevSparseJac and set dependency CppAD::vector< std::set > eye_set(m), depend_set(m); for(size_t i = 0; i < m; i++) { ok &= eye_set[i].empty(); eye_set[i].insert(i); } dependency = true; depend_set = f.RevSparseJac(n, eye_set, transpose, dependency); for(size_t i = 0; i < m; i++) { std::set check; check.insert(m1 - i); ok &= depend_set[i] == check; } dependency = false; depend_set = f.RevSparseJac(n, eye_set, transpose, dependency); for(size_t i = 0; i < m; i++) ok &= depend_set[i].empty(); return ok; } // END C++ cppad-20170000.3/example/near_equal_ext.cpp0000644000175200017650000000312313057470457017570 0ustar coincoin-web// $Id: near_equal_ext.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin near_equal_ext.cpp$$ $spell cpp abs o Microsoft $$ $section Compare AD with Base Objects: Example and Test$$ $mindex NearEqualExt$$ $code $srcfile%example/near_equal_ext.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool NearEqualExt(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // double double x = 1.00000; double y = 1.00001; double a = .00005; double r = .00005; double zero = 0.; // AD AD ax(x); AD ay(y); ok &= NearEqual(ax, ay, zero, a); ok &= NearEqual(ax, y, r, zero); ok &= NearEqual(x, ay, r, a); // std::complex AD cx(x); AD cy(y); // AD< std::complex > AD acx(x); AD acy(y); ok &= NearEqual(acx, acy, zero, a); ok &= NearEqual(acx, cy, r, zero); ok &= NearEqual(acx, y, r, a); ok &= NearEqual( cx, acy, r, a); ok &= NearEqual( x, acy, r, a); return ok; } // END C++ cppad-20170000.3/example/var2par.cpp0000644000175200017650000000374113057470457016157 0ustar coincoin-web// $Id: var2par.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin var2par.cpp$$ $spell Var Cpp $$ $section Convert an AD Variable to a Parameter: Example and Test$$ $mindex Var2Par Value during taping$$ $code $srcfile%example/var2par.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool Var2Par(void) { bool ok = true; using CppAD::AD; using CppAD::Value; using CppAD::Var2Par; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) x(n); x[0] = 3.; x[1] = 4.; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = - x[1] * Var2Par(x[0]); // same as y[0] = -x[1] * 3.; // cannot call Value(x[j]) or Value(y[0]) here (currently variables) ok &= ( Value( Var2Par(x[0]) ) == 3. ); ok &= ( Value( Var2Par(x[1]) ) == 4. ); ok &= ( Value( Var2Par(y[0]) ) == -12. ); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // can call Value(x[j]) or Value(y[0]) here (currently parameters) ok &= (Value(x[0]) == 3.); ok &= (Value(x[1]) == 4.); ok &= (Value(y[0]) == -12.); // evaluate derivative of y w.r.t x CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= (dw[0] == 0.); // derivative of y[0] w.r.t x[0] is zero ok &= (dw[1] == -3.); // derivative of y[0] w.r.t x[1] is 3 return ok; } // END C++ cppad-20170000.3/example/acosh.cpp0000644000175200017650000000403113057470457015670 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin acosh.cpp$$ $spell cosh acosh $$ $section The AD acosh Function: Example and Test$$ $code $srcfile%example/acosh.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool acosh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD cosh_of_x0 = CppAD::cosh(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::acosh(cosh_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps, eps); // use a VecAD::reference object with acosh CppAD::VecAD v(1); AD zero(0); v[zero] = cosh_of_x0; AD result = CppAD::acosh(v[zero]); ok &= NearEqual(result, x0, eps, eps); return ok; } // END C++ cppad-20170000.3/example/lu_vec_ad_ok.cpp0000644000175200017650000000676513057470457017225 0ustar coincoin-web// $Id: lu_vec_ad_ok.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin lu_vec_ad_ok.cpp$$ $spell Geq Cpp Lu $$ $section Lu Factor and Solve With Recorded Pivoting: Example and Test$$ $mindex record pivot$$ $code $srcfile%example/lu_vec_ad_ok.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include "lu_vec_ad.hpp" # include bool LuVecADOk(void) { bool ok = true; using namespace CppAD; typedef AD ADdouble; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); size_t n = 3; size_t m = 2; double a1[] = { 3., 0., 0., // (1,1) is first pivot 1., 2., 1., // (2,2) is second pivot 1., 0., .5 // (3,3) is third pivot }; double a2[] = { 1., 2., 1., // (1,2) is second pivot 3., 0., 0., // (2,1) is first pivot 1., 0., .5 // (3,3) is third pivot }; double rhs[] = { 1., 3., 2., 2., 3., 1. }; VecAD Copy (n * n); VecAD Rhs (n * m); VecAD Result (n * m); ADdouble logdet; ADdouble signdet; // routine for checking determinants using expansion by minors det_by_minor Det(n); // matrix we are computing the determinant of CPPAD_TESTVECTOR(ADdouble) A(n * n); // dependent variable values CPPAD_TESTVECTOR(ADdouble) Y(1 + n * m); size_t i; size_t j; size_t k; // Original matrix for(i = 0; i < n * n; i++) A[i] = a1[i]; // right hand side for(j = 0; j < n; j++) for(k = 0; k < m; k++) Rhs[ j * m + k ] = rhs[ j * m + k ]; // Declare independent variables Independent(A); // Copy the matrix ADdouble index(0); for(i = 0; i < n*n; i++) { Copy[index] = A[i]; index += 1.; } // Solve the equation signdet = LuVecAD(n, m, Copy, Rhs, Result, logdet); // Result is the first n * m dependent variables index = 0.; for(i = 0; i < n * m; i++) { Y[i] = Result[index]; index += 1.; } // Determinant is last component of the solution Y[ n * m ] = signdet * exp( logdet ); // construct f: A -> Y ADFun f(A, Y); // check determinant using minors routine ADdouble determinant = Det( A ); ok &= NearEqual(Y[n * m], determinant, eps99, eps99); // Check solution of Rhs = A * Result double sum; for(k = 0; k < m; k++) { for(i = 0; i < n; i++) { sum = 0.; for(j = 0; j < n; j++) sum += a1[i * n + j] * Value( Y[j * m + k] ); ok &= NearEqual( rhs[i * m + k], sum, eps99, eps99); } } CPPAD_TESTVECTOR(double) y2(1 + n * m); CPPAD_TESTVECTOR(double) A2(n * n); for(i = 0; i < n * n; i++) A[i] = A2[i] = a2[i]; y2 = f.Forward(0, A2); determinant = Det(A); ok &= NearEqual(y2[ n * m], Value(determinant), eps99, eps99); // Check solution of Rhs = A2 * Result for(k = 0; k < m; k++) { for(i = 0; i < n; i++) { sum = 0.; for(j = 0; j < n; j++) sum += a2[i * n + j] * y2[j * m + k]; ok &= NearEqual( rhs[i * m + k], sum, eps99, eps99); } } return ok; } // END C++ cppad-20170000.3/example/independent.cpp0000644000175200017650000000610513057470457017074 0ustar coincoin-web// $Id: independent.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* WARNING: This file is used an an example by omh/FunConstruct.omh. $begin independent.cpp$$ $comment ! NOTE the title states that this example is used two places !$$ $section Independent and ADFun Constructor: Example and Test$$ $code $srcfile%example/independent.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // -------------------------------------------------------- // define the template function Test(void) in empty namespace template bool Test(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // domain space vector size_t n = 2; VectorAD X(n); // VectorAD is the template parameter in call to Test X[0] = 0.; X[1] = 1.; // declare independent variables and start recording // use the template parameter VectorAD for the vector type CppAD::Independent(X); AD a = X[0] + X[1]; // first AD operation AD b = X[0] * X[1]; // second AD operation // range space vector size_t m = 2; VectorAD Y(m); // VectorAD is the template paraemter in call to Test Y[0] = a; Y[1] = b; // create f: X -> Y and stop tape recording // use the template parameter VectorAD for the vector type CppAD::ADFun f(X, Y); // check value ok &= NearEqual(Y[0] , 1., 1e-10 , 1e-10); ok &= NearEqual(Y[1] , 0., 1e-10 , 1e-10); // compute f(1, 2) CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(double) y(m); x[0] = 1.; x[1] = 2.; y = f.Forward(0, x); ok &= NearEqual(y[0] , 3., 1e-10 , 1e-10); ok &= NearEqual(y[1] , 2., 1e-10 , 1e-10); // compute partial of f w.r.t x[0] at (1, 2) CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dx[1] = 0.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0] , 1., 1e-10 , 1e-10); ok &= NearEqual(dy[1] , x[1], 1e-10 , 1e-10); // compute partial of f w.r.t x[1] at (1, 2) dx[0] = 0.; dx[1] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0] , 1., 1e-10 , 1e-10); ok &= NearEqual(dy[1] , x[0], 1e-10 , 1e-10); return ok; } } // End of empty namespace ------------------------------------------- # include # include bool Independent(void) { bool ok = true; typedef CppAD::AD ADdouble; // Run with VectorAD equal to three different cases // all of which are Simple Vectors with elements of type AD. ok &= Test< CppAD::vector >(); ok &= Test< std::vector >(); ok &= Test< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/forward.cpp0000644000175200017650000000567213057470457016253 0ustar coincoin-web// $Id: forward.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin forward.cpp$$ $spell Cpp $$ $section Forward Mode: Example and Test$$ $code $srcfile%example/forward.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { // -------------------------------------------------------- // define the template function ForwardCases in empty namespace template bool ForwardCases(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = ax[0] * ax[0] * ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // initially, the variable values during taping are stored in f ok &= f.size_order() == 1; // zero order forward mode using notation in forward_zero // use the template parameter Vector for the vector type Vector x0(n), y0(m); x0[0] = 3.; x0[1] = 4.; y0 = f.Forward(0, x0); ok &= NearEqual(y0[0] , x0[0]*x0[0]*x0[1], eps, eps); ok &= f.size_order() == 1; // first order forward mode using notation in forward_one // X(t) = x0 + x1 * t // Y(t) = F[X(t)] = y0 + y1 * t + o(t) Vector x1(n), y1(m); x1[0] = 1.; x1[1] = 0.; y1 = f.Forward(1, x1); // partial F w.r.t. x_0 ok &= NearEqual(y1[0] , 2.*x0[0]*x0[1], eps, eps); ok &= f.size_order() == 2; // second order forward mode using notation in forward_order // X(t) = x0 + x1 * t + x2 * t^2 // Y(t) = F[X(t)] = y0 + y1 * t + y2 * t^2 + o(t^3) Vector x2(n), y2(m); x2[0] = 0.; x2[1] = 0.; y2 = f.Forward(2, x2); double F_00 = 2. * y2[0]; // second partial F w.r.t. x_0, x_0 ok &= NearEqual(F_00, 2.*x0[1], eps, eps); ok &= f.size_order() == 3; return ok; } } // End empty namespace # include # include bool Forward(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= ForwardCases< CppAD::vector >(); ok &= ForwardCases< std::vector >(); ok &= ForwardCases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/fun_check.cpp0000644000175200017650000000737513057470457016536 0ustar coincoin-web// $Id: fun_check.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ! WARNING: This file is used as an example by FunConstruct and Dependent $begin fun_check.cpp$$ $spell abs $$ $section ADFun Check and Re-Tape: Example and Test$$ $mindex FunCheck Dependent$$ $code $srcfile%example/fun_check.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ----------------------------------------------------------- // define the template function object Fun in empty namespace template class Fun { private: size_t n; public: // function constructor Fun(size_t n_) : n(n_) { } // function evaluator Vector operator() (const Vector &x) { Vector y(n); size_t i; for(i = 0; i < n; i++) { // This operaiton sequence depends on x if( x[i] >= 0 ) y[i] = exp(x[i]); else y[i] = exp(-x[i]); } return y; } }; // template function FunCheckCases in empty namespace template bool FunCheckCases(void) { bool ok = true; using CppAD::AD; using CppAD::ADFun; using CppAD::Independent; // use the ADFun default constructor ADFun f; // domain space vector size_t n = 2; ADVector X(n); X[0] = -1.; X[1] = 1.; // declare independent variables and starting recording Independent(X); // create function object to use with AD Fun< AD, ADVector > G(n); // range space vector size_t m = n; ADVector Y(m); Y = G(X); // stop tape and store operation sequence in f : X -> Y f.Dependent(X, Y); ok &= (f.size_order() == 0); // no implicit forward operation // create function object to use with double Fun g(n); // function values should agree when the independent variable // values are the same as during recording Vector x(n); size_t j; for(j = 0; j < n; j++) x[j] = Value(X[j]); double r = 1e-10; double a = 1e-10; ok &= FunCheck(f, g, x, a, r); // function values should not agree when the independent variable // values are the negative of values during recording for(j = 0; j < n; j++) x[j] = - Value(X[j]); ok &= ! FunCheck(f, g, x, a, r); // re-tape to obtain the new AD of double operation sequence for(j = 0; j < n; j++) X[j] = x[j]; Independent(X); Y = G(X); // stop tape and store operation sequence in f : X -> Y f.Dependent(X, Y); ok &= (f.size_order() == 0); // no implicit forward with this x // function values should agree now ok &= FunCheck(f, g, x, a, r); return ok; } } // End empty namespace # include # include bool FunCheck(void) { bool ok = true; typedef CppAD::vector Vector1; typedef CppAD::vector< CppAD::AD > ADVector1; typedef std::vector Vector2; typedef std::vector< CppAD::AD > ADVector2; typedef std::valarray Vector3; typedef std::valarray< CppAD::AD > ADVector3; // Run with Vector and ADVector equal to three different cases // all of which are Simple Vectors with elements of type // double and AD respectively. ok &= FunCheckCases< Vector1, ADVector2 >(); ok &= FunCheckCases< Vector2, ADVector3 >(); ok &= FunCheckCases< Vector3, ADVector1 >(); return ok; } // END C++ cppad-20170000.3/example/ode_taylor.cpp0000644000175200017650000001145713057470457016746 0ustar coincoin-web// $Id: ode_taylor.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ode_taylor.cpp$$ $spell Taylor Cpp const std Adolc adouble $$ $section Taylor's Ode Solver: An Example and Test$$ $mindex Taylor$$ $head Purpose$$ This example solves an ordinary differential equation using Taylor's method; i.e., $latex \[ Z(t + \Delta t) \approx Z^{(0)} (t) + \frac{ Z^{(1)} (t) }{ 1 !} \Delta t + \cdots + \frac{ Z^{(p)} (t) }{ p !} ( \Delta t )^p ) \] $$ $head ODE$$ The ODE is defined by the function $latex h : \B{R}^n \rightarrow \B{R}^n$$, which for this example is given by $latex \[ Z^{(1)} (t) = H[ Z(t) ] = \left( \begin{array}{c} 1 \\ Z_1 (t) \\ \vdots \\ Z_{n-1} (t) \end{array} \right) \] $$ and the initial condition is $latex z(0) = 0$$. $head ODE Solution$$ The solution for this example can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain $latex \[ Z(t) = \left( \begin{array}{c} t \\ t^2 / 2 \\ \vdots \\ t^n / n ! \end{array} \right) \] $$ $head Forward Mode$$ Given the Taylor coefficients for $latex k = 0 , \ldots , K$$ $latex \[ z^{(k)} = \frac{ Z^{(k)} }{ k !} (t) \]$$ we note that $latex \[ \begin{array}{rcl} Z^{(1)} (t) & = & H( z^{(0)} + z^{(1)} t + \cdots + z^{(K)} t^K ) + O( t^{K+1} ) \\ & = & h^{(0)} + h^{(1)} t + \cdots + h^{(K)} t^K + O( t^{K+1} ) \end{array} \] $$ where $latex h^{(k)}$$ is the $th k$$ order Taylor coefficient for $latex H( Z(t) )$$. Taking $th K$$ order derivatives of both sides we obtain $latex \[ \begin{array}{rcl} Z^{(K+1)} (t) & = & K ! h^{(K)} \\ z^{(K+1)} & = & h^{(K)} / K \end{array} \] $$ The code below uses this relationship to implement Taylor's method for approximating the solution of an ODE. $code $srcfile%example/ode_taylor.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end -------------------------------------------------------------------------- */ // BEGIN C++ # include // ========================================================================= // define types for each level namespace { // BEGIN empty namespace using CppAD::AD; CPPAD_TESTVECTOR( AD ) ode( const CPPAD_TESTVECTOR( AD )& Z ) { size_t n = Z.size(); CPPAD_TESTVECTOR( AD ) y(n); y[0] = 1; for(size_t k = 1; k < n; k++) y[k] = Z[k-1]; return y; } } // ------------------------------------------------------------------------- // Example that uses Taylor's method to solve ordinary differential equaitons bool ode_taylor(void) { // initialize the return value as true bool ok = true; // some temporary indices size_t i, j, k; // The ODE does not depend on the arugment values // so only tape once, also note that ode does not depend on t size_t n = 5; // number of independent and dependent variables CPPAD_TESTVECTOR( AD ) a_x(n), a_y(n); CppAD::Independent( a_x ); a_y = ode(a_x); CppAD::ADFun H(a_x, a_y); // initialize the solution vector at time zero CPPAD_TESTVECTOR( double ) z(n); for(j = 0; j < n; j++) z[j] = 0.0; size_t order = n; // order of the Taylor method size_t n_step = 4; // number of time steps double dt = 0.5; // step size in time // Taylor coefficients of order k CPPAD_TESTVECTOR( double ) hk(n), zk(n); // loop with respect to each step of Taylor's method for(size_t i_step = 0; i_step < n_step; i_step++) { // Use Taylor's method to take a step zk = z; // initialize z^{(k)} for k = 0 double dt_kp = dt; // initialize dt^(k+1) for k = 0 for(k = 0; k < order; k++) { // evaluate k-th order Taylor coefficient of H hk = H.Forward(k, zk); for(j = 0; j < n; j++) { // convert to (k+1)-Taylor coefficient for z zk[j] = hk[j] / double(k + 1); // add term for to this Taylor coefficient // to solution for y(t, x) z[j] += zk[j] * dt_kp; } // next power of t dt_kp *= dt; } } // check solution of the ODE, // Taylor's method should have no truncation error for this case double eps = 100. * std::numeric_limits::epsilon(); double check = 1.; double t = n_step * dt; for(i = 0; i < n; i++) { check *= t / double(i + 1); ok &= CppAD::NearEqual(z[i], check, eps, eps); } return ok; } // END C++ cppad-20170000.3/example/near_equal.cpp0000644000175200017650000000370513057470457016716 0ustar coincoin-web// $Id: near_equal.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin near_equal.cpp$$ $spell cpp abs o Microsoft $$ $section NearEqual Function: Example and Test$$ $head File Name$$ This file is called $code near_equal.cpp$$ instead of $code NearEqual.cpp$$ to avoid a name conflict with $code ../lib/NearEqual.cpp$$ in the corresponding Microsoft project file. $code $srcfile%example/near_equal.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool Near_Equal(void) { bool ok = true; typedef std::complex Complex; using CppAD::NearEqual; // double double x = 1.00000; double y = 1.00001; double a = .00003; double r = .00003; double zero = 0.; double inf = 1. / zero; double nan = 0. / zero; ok &= NearEqual(x, y, zero, a); ok &= NearEqual(x, y, r, zero); ok &= NearEqual(x, y, r, a); ok &= ! NearEqual(x, y, r / 10., a / 10.); ok &= ! NearEqual(inf, inf, r, a); ok &= ! NearEqual(-inf, -inf, r, a); ok &= ! NearEqual(nan, nan, r, a); // complex Complex X(x, x / 2.); Complex Y(y, y / 2.); Complex Inf(inf, zero); Complex Nan(zero, nan); ok &= NearEqual(X, Y, zero, a); ok &= NearEqual(X, Y, r, zero); ok &= NearEqual(X, Y, r, a); ok &= ! NearEqual(X, Y, r / 10., a / 10.); ok &= ! NearEqual(Inf, Inf, r, a); ok &= ! NearEqual(-Inf, -inf, r, a); ok &= ! NearEqual(Nan, Nan, r, a); return ok; } // END C++ cppad-20170000.3/example/reverse_three.cpp0000644000175200017650000000743613057470457017451 0ustar coincoin-web// $Id: reverse_three.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin reverse_three.cpp$$ $spell Taylor Cpp $$ $section Third Order Reverse Mode: Example and Test$$ $head Taylor Coefficients$$ $latex \[ \begin{array}{rcl} X(t) & = & x^{(0)} + x^{(1)} t + x^{(2)} t^2 \\ X^{(1)} (t) & = & x^{(1)} + 2 x^{(2)} t \\ X^{(2)} (t) & = & 2 x^{(2)} \end{array} \] $$ Thus, we need to be careful to properly account for the fact that $latex X^{(2)} (0) = 2 x^{(2)}$$ (and similarly $latex Y^{(2)} (0) = 2 y^{(2)}$$). $code $srcfile%example/reverse_three.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ---------------------------------------------------------- // define the template function cases in empty namespace template bool cases(void) { bool ok = true; double eps = 10. * CppAD::numeric_limits::epsilon(); using CppAD::AD; using CppAD::NearEqual; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; // declare independent variables and start recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] * X[1]; // create f : X -> Y and stop recording CppAD::ADFun f(X, Y); // define x^0 and compute y^0 using user zero order forward Vector x0(n), y0(m); x0[0] = 2.; x0[1] = 3.; y0 = f.Forward(0, x0); // y^0 = F(x^0) double check; check = x0[0] * x0[1]; ok &= NearEqual(y0[0] , check, eps, eps); // define x^1 and compute y^1 using first order forward mode Vector x1(n), y1(m); x1[0] = 4.; x1[1] = 5.; y1 = f.Forward(1, x1); // Y^1 (x) = partial_t F( x^0 + x^1 * t ) // y^1 = Y^1 (0) check = x1[0] * x0[1] + x0[0] * x1[1]; ok &= NearEqual(y1[0], check, eps, eps); // define x^2 and compute y^2 using second order forward mode Vector x2(n), y2(m); x2[0] = 6.; x2[1] = 7.; y2 = f.Forward(2, x2); // Y^2 (x) = partial_tt F( x^0 + x^1 * t + x^2 * t^2 ) // y^2 = (1/2) * Y^2 (0) check = x2[0] * x0[1] + x1[0] * x1[1] + x0[0] * x2[1]; ok &= NearEqual(y2[0], check, eps, eps); // W(x) = Y^0 (x) + 2 * Y^1 (x) + 3 * (1/2) * Y^2 (x) size_t p = 3; Vector dw(n*p), w(m*p); w[0] = 1.; w[1] = 2.; w[2] = 3.; dw = f.Reverse(p, w); // check partial w.r.t x^0_0 of W(x) check = x0[1] + 2. * x1[1] + 3. * x2[1]; ok &= NearEqual(dw[0*p+0], check, eps, eps); // check partial w.r.t x^0_1 of W(x) check = x0[0] + 2. * x1[0] + 3. * x2[0]; ok &= NearEqual(dw[1*p+0], check, eps, eps); // check partial w.r.t x^1_0 of W(x) check = 2. * x0[1] + 3. * x1[1]; ok &= NearEqual(dw[0*p+1], check, eps, eps); // check partial w.r.t x^1_1 of W(x) check = 2. * x0[0] + 3. * x1[0]; ok &= NearEqual(dw[1*p+1], check, eps, eps); // check partial w.r.t x^2_0 of W(x) check = 3. * x0[1]; ok &= NearEqual(dw[0*p+2], check, eps, eps); // check partial w.r.t x^2_1 of W(x) check = 3. * x0[0]; ok &= NearEqual(dw[1*p+2], check, eps, eps); return ok; } } // End empty namespace # include # include bool reverse_three(void) { bool ok = true; ok &= cases< CppAD::vector >(); ok &= cases< std::vector >(); ok &= cases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/mul_level.cpp0000644000175200017650000000763113057470457016570 0ustar coincoin-web// $Id: mul_level.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin mul_level.cpp$$ $spell Adolc adouble CppAD abs $$ $section Multiple Level of AD: Example and Test$$ $head Purpose$$ In this example, we use $code AD< AD >$$ (level two taping), the compute values of the function $latex f : \B{R}^n \rightarrow \B{R}$$ where $latex \[ f(x) = \frac{1}{2} \left( x_0^2 + \cdots + x_{n-1}^2 \right) \] $$ We then use $code AD$$ (level one taping) to compute the directional derivative $latex \[ f^{(1)} (x) * v = x_0 v_0 + \cdots + x_{n-1} v_{n-1} \] $$. where $latex v \in \B{R}^n$$. We then use $code double$$ (no taping) to compute $latex \[ \frac{d}{dx} \left[ f^{(1)} (x) * v \right] = v \] $$ This is only meant as an example of multiple levels of taping. The example $cref hes_times_dir.cpp$$ computes the same value more efficiently by using the identity: $latex \[ \frac{d}{dx} \left[ f^{(1)} (x) * v \right] = f^{(2)} (x) * v \] $$ The example $cref mul_level_adolc.cpp$$ computes the same values using Adolc's type $code adouble$$ and CppAD's type $code AD$$. $head Source$$ $code $srcfile%example/mul_level.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // f(x) = |x|^2 / 2 = .5 * ( x[0]^2 + ... + x[n-1]^2 ) template Type f(const CPPAD_TESTVECTOR(Type)& x) { Type sum; sum = 0.; size_t i = size_t(x.size()); for(i = 0; i < size_t(x.size()); i++) sum += x[i] * x[i]; return .5 * sum; } } bool mul_level(void) { bool ok = true; // initialize test result typedef CppAD::AD a1type; // for one level of taping typedef CppAD::AD a2type; // for two levels of taping size_t n = 5; // dimension for example size_t j; // a temporary index variable // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(a1type) a1x(n), a1v(n), a1dy(1) ; CPPAD_TESTVECTOR(a2type) a2x(n), a2y(1); // Values for the independent variables while taping the function f(x) for(j = 0; j < n; j++) a2x[j] = a1x[j] = x[j] = double(j); // Declare the independent variable for taping f(x) CppAD::Independent(a2x); // Use AD< AD > to tape the evaluation of f(x) a2y[0] = f(a2x); // Declare a1f as the corresponding ADFun< AD > // (make sure we do not run zero order forward during constructor) CppAD::ADFun a1f; a1f.Dependent(a2x, a2y); // Values for the independent variables while taping f'(x) * v // Declare the independent variable for taping f'(x) * v // (Note we did not have to tape the creationg of a1f.) CppAD::Independent(a1x); // set the argument value x for computing f'(x) * v a1f.Forward(0, a1x); // compute f'(x) * v for(j = 0; j < n; j++) a1v[j] = double(n - j); a1dy = a1f.Forward(1, a1v); // declare g as ADFun function corresponding to f'(x) * v CppAD::ADFun g; g.Dependent(a1x, a1dy); // optimize out operations not necessary for function f'(x) * v g.optimize(); // Evaluate f'(x) * v g.Forward(0, x); // compute the d/dx of f'(x) * v = f''(x) * v = v CPPAD_TESTVECTOR(double) w(1); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = g.Reverse(1, w); for(j = 0; j < n; j++) ok &= CppAD::NearEqual(dw[j], a1v[j], eps, eps); return ok; } // END C++ cppad-20170000.3/example/for_sparse_hes.cpp0000644000175200017650000001201113057470457017572 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin for_sparse_hes.cpp$$ $spell Hessian Jac Hes Dep Cpp $$ $section Forward Mode Hessian Sparsity: Example and Test$$ $mindex ForSparseHes sparsity$$ $code $srcfile%example/for_sparse_hes.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ------------------------------------------------------------- // expected sparsity pattern bool check_f0[] = { false, false, false, // partials w.r.t x0 and (x0, x1, x2) false, false, false, // partials w.r.t x1 and (x0, x1, x2) false, false, true // partials w.r.t x2 and (x0, x1, x2) }; bool check_f1[] = { false, true, false, // partials w.r.t x0 and (x0, x1, x2) true, false, false, // partials w.r.t x1 and (x0, x1, x2) false, false, false // partials w.r.t x2 and (x0, x1, x2) }; // define the template function BoolCases in empty namespace template // vector class, elements of type bool bool BoolCases(bool optimize) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; ax[2] = 2.; // declare independent variables and start recording CppAD::Independent(ax); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = sin( ax[2] ) + ax[0] + ax[1] + ax[2]; ay[1] = ax[0] * ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); if( optimize ) f.optimize(); // sparsity pattern for diagonal of identity matrix Vector r(n); size_t i, j; for(i = 0; i < n; i++) r[ i ] = true; // compute sparsity pattern for H(x) = F_0^{(2)} (x) Vector s(m); for(i = 0; i < m; i++) s[i] = false; s[0] = true; Vector h(n * n); h = f.ForSparseHes(r, s); // check values for(i = 0; i < n; i++) for(j = 0; j < n; j++) ok &= (h[ i * n + j ] == check_f0[ i * n + j ] ); // compute sparsity pattern for H(x) = F_1^{(2)} (x) for(i = 0; i < m; i++) s[i] = false; s[1] = true; h = f.ForSparseHes(r, s); // check values for(i = 0; i < n; i++) for(j = 0; j < n; j++) ok &= (h[ i * n + j ] == check_f1[ i * n + j ] ); return ok; } // define the template function SetCases in empty namespace template // vector class, elements of type std::set bool SetCases(bool optimize) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; ax[2] = 2.; // declare independent variables and start recording CppAD::Independent(ax); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = sin( ax[2] ); ay[1] = ax[0] * ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); if( optimize ) f.optimize(); // sparsity pattern for the diagonal of the identity matrix Vector r(1); size_t i; for(i = 0; i < n; i++) r[0].insert(i); // compute sparsity pattern for H(x) = F_0^{(2)} (x) Vector s(1); assert( s[0].empty() ); s[0].insert(0); Vector h(n); h = f.ForSparseHes(r, s); // check values std::set::iterator itr; size_t j; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { bool found = h[i].find(j) != h[i].end(); ok &= (found == check_f0[i * n + j]); } } // compute sparsity pattern for H(x) = F_1^{(2)} (x) s[0].clear(); assert( s[0].empty() ); s[0].insert(1); h = f.ForSparseHes(r, s); // check values for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { bool found = h[i].find(j) != h[i].end(); ok &= (found == check_f1[i * n + j]); } } return ok; } } // End empty namespace # include # include bool for_sparse_hes(void) { bool ok = true; for(size_t k = 0; k < 2; k++) { bool optimize = bool(k); // Run with Vector equal to four different cases // all of which are Simple Vectors with elements of type bool. ok &= BoolCases< CppAD::vector >(optimize); ok &= BoolCases< CppAD::vectorBool >(optimize); ok &= BoolCases< std::vector >(optimize); ok &= BoolCases< std::valarray >(optimize); // Run with Vector equal to two different cases both of which are // Simple Vectors with elements of type std::set typedef std::set set; ok &= SetCases< CppAD::vector >(optimize); ok &= SetCases< std::vector >(optimize); // Do not use valarray because its element access in the const case // returns a copy instead of a reference // ok &= SetCases< std::valarray >(optimize); } return ok; } // END C++ cppad-20170000.3/example/add_eq.cpp0000644000175200017650000000441013057470457016011 0ustar coincoin-web// $Id: add_eq.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin AddEq.cpp$$ $section AD Computed Assignment Addition: Example and Test$$ $mindex += add assign plus$$ $code $srcfile%example/add_eq.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool AddEq(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = .5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) y(m); y[0] = x[0]; // initial value y[0] += 2; // AD += int y[0] += 4.; // AD += double y[1] = y[0] += x[0]; // use the result of a computed assignment // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0+2.+4.+x0, eps99, eps99); ok &= NearEqual(y[1] , y[0], eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 2., eps99, eps99); ok &= NearEqual(dy[1], 2., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 0.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 2., eps99, eps99); // use a VecAD::reference object with computed addition CppAD::VecAD v(1); AD zero(0); AD result = 1; v[zero] = 2; result += v[zero]; ok &= (result == 3); return ok; } // END C++ cppad-20170000.3/example/atomic/0002755000175200017650000000000013057470457015347 5ustar coincoin-webcppad-20170000.3/example/atomic/reverse.cpp0000644000175200017650000002201313057470457017522 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_reverse.cpp$$ $spell Jacobian $$ $section Atomic Reverse: Example and Test$$ $head Purpose$$ This example demonstrates reverse mode derivative calculation using an atomic operation. $head function$$ For this example, the atomic function $latex f : \B{R}^3 \rightarrow \B{R}^2$$ is defined by $latex \[ f(x) = \left( \begin{array}{c} x_2 * x_2 \\ x_0 * x_1 \end{array} \right) \] $$ The corresponding Jacobian is $latex \[ f^{(1)} (x) = \left( \begin{array}{ccc} 0 & 0 & 2 x_2 \\ x_1 & x_0 & 0 \end{array} \right) \] $$ The Hessians of the component functions are $latex \[ f_0^{(2)} ( x ) = \left( \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 2 \end{array} \right) \W{,} f_1^{(2)} ( x ) = \left( \begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right) \] $$ $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // class atomic_reverse : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_reverse(const std::string& name) : // this example does not use sparsity patterns CppAD::atomic_base(name) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { size_t q1 = q + 1; # ifndef NDEBUG size_t n = tx.size() / q1; size_t m = ty.size() / q1; # endif assert( n == 3 ); assert( m == 2 ); assert( p <= q ); // this example only implements up to first order forward mode bool ok = q <= 1; if( ! ok ) return ok; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) { vy[0] = vx[2]; vy[1] = vx[0] || vx[1]; } // ------------------------------------------------------------------ // Zero forward mode. // This case must always be implemented // f(x) = [ x_2 * x_2 ] // [ x_0 * x_1 ] // y^0 = f( x^0 ) if( p <= 0 ) { // y_0^0 = x_2^0 * x_2^0 ty[0 * q1 + 0] = tx[2 * q1 + 0] * tx[2 * q1 + 0]; // y_1^0 = x_0^0 * x_1^0 ty[1 * q1 + 0] = tx[0 * q1 + 0] * tx[1 * q1 + 0]; } if( q <= 0 ) return ok; // ------------------------------------------------------------------ // First order one forward mode. // This case is needed if first order forward mode is used. // f'(x) = [ 0, 0, 2 * x_2 ] // [ x_1, x_0, 0 ] // y^1 = f'(x^0) * x^1 if( p <= 1 ) { // y_0^1 = 2 * x_2^0 * x_2^1 ty[0 * q1 + 1] = 2.0 * tx[2 * q1 + 0] * tx[2 * q1 + 1]; // y_1^1 = x_1^0 * x_0^1 + x_0^0 * x_1^1 ty[1 * q1 + 1] = tx[1 * q1 + 0] * tx[0 * q1 + 1]; ty[1 * q1 + 1] += tx[0 * q1 + 0] * tx[1 * q1 + 1]; } return ok; } /* %$$ $head reverse$$ $srccode%cpp% */ // reverse mode routine called by CppAD virtual bool reverse( size_t q , const vector& tx , const vector& ty , vector& px , const vector& py ) { size_t q1 = q + 1; size_t n = tx.size() / q1; # ifndef NDEBUG size_t m = ty.size() / q1; # endif assert( n == 3 ); assert( m == 2 ); // this example only implements up to second order reverse mode bool ok = q1 <= 2; if( ! ok ) return ok; // // initalize summation as zero for(size_t j = 0; j < n; j++) for(size_t k = 0; k < q; k++) px[j * q1 + k] = 0.0; // if( q1 == 2 ) { // -------------------------------------------------------------- // Second order reverse first compute partials of first order // We use the notation pf_ij^k for partial of F_i^1 w.r.t. x_j^k // // y_0^1 = 2 * x_2^0 * x_2^1 // pf_02^0 = 2 * x_2^1 // pf_02^1 = 2 * x_2^0 // // y_1^1 = x_1^0 * x_0^1 + x_0^0 * x_1^1 // pf_10^0 = x_1^1 // pf_11^0 = x_0^1 // pf_10^1 = x_1^0 // pf_11^1 = x_0^0 // // px_0^0 += py_0^1 * pf_00^0 + py_1^1 * pf_10^0 // += py_1^1 * x_1^1 px[0 * q1 + 0] += py[1 * q1 + 1] * tx[1 * q1 + 1]; // // px_0^1 += py_0^1 * pf_00^1 + py_1^1 * pf_10^1 // += py_1^1 * x_1^0 px[0 * q1 + 1] += py[1 * q1 + 1] * tx[1 * q1 + 0]; // // px_1^0 += py_0^1 * pf_01^0 + py_1^1 * pf_11^0 // += py_1^1 * x_0^1 px[1 * q1 + 0] += py[1 * q1 + 1] * tx[0 * q1 + 1]; // // px_1^1 += py_0^1 * pf_01^1 + py_1^1 * pf_11^1 // += py_1^1 * x_0^0 px[1 * q1 + 1] += py[1 * q1 + 1] * tx[0 * q1 + 0]; // // px_2^0 += py_0^1 * pf_02^0 + py_1^1 * pf_12^0 // += py_0^1 * 2 * x_2^1 px[2 * q1 + 0] += py[0 * q1 + 1] * 2.0 * tx[2 * q1 + 1]; // // px_2^1 += py_0^1 * pf_02^1 + py_1^1 * pf_12^1 // += py_0^1 * 2 * x_2^0 px[2 * q1 + 1] += py[0 * q1 + 1] * 2.0 * tx[2 * q1 + 0]; } // -------------------------------------------------------------- // First order reverse computes partials of zero order coefficients // We use the notation pf_ij for partial of F_i^0 w.r.t. x_j^0 // // y_0^0 = x_2^0 * x_2^0 // pf_00 = 0, pf_01 = 0, pf_02 = 2 * x_2^0 // // y_1^0 = x_0^0 * x_1^0 // pf_10 = x_1^0, pf_11 = x_0^0, pf_12 = 0 // // px_0^0 += py_0^0 * pf_00 + py_1^0 * pf_10 // += py_1^0 * x_1^0 px[0 * q1 + 0] += py[1 * q1 + 0] * tx[1 * q1 + 0]; // // px_1^0 += py_1^0 * pf_01 + py_1^0 * pf_11 // += py_1^0 * x_0^0 px[1 * q1 + 0] += py[1 * q1 + 0] * tx[0 * q1 + 0]; // // px_2^0 += py_1^0 * pf_02 + py_1^0 * pf_12 // += py_0^0 * 2.0 * x_2^0 px[2 * q1 + 0] += py[0 * q1 + 0] * 2.0 * tx[2 * q1 + 0]; // -------------------------------------------------------------- return ok; } }; } // End empty namespace /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool reverse(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // // Create the atomic_reverse object atomic_reverse afun("atomic_reverse"); // // Create the function f(u) // // domain space vector size_t n = 3; double x_0 = 1.00; double x_1 = 2.00; double x_2 = 3.00; vector< AD > au(n); au[0] = x_0; au[1] = x_1; au[2] = x_2; // declare independent variables and start tape recording CppAD::Independent(au); // range space vector size_t m = 2; vector< AD > ay(m); // call user function vector< AD > ax = au; afun(ax, ay); // create f: u -> y and stop tape recording CppAD::ADFun f; f.Dependent (au, ay); // y = f(u) // // check function value double check = x_2 * x_2; ok &= NearEqual( Value(ay[0]) , check, eps, eps); check = x_0 * x_1; ok &= NearEqual( Value(ay[1]) , check, eps, eps); // -------------------------------------------------------------------- // zero order forward // vector x0(n), y0(m); x0[0] = x_0; x0[1] = x_1; x0[2] = x_2; y0 = f.Forward(0, x0); check = x_2 * x_2; ok &= NearEqual(y0[0] , check, eps, eps); check = x_0 * x_1; ok &= NearEqual(y0[1] , check, eps, eps); // -------------------------------------------------------------------- // first order reverse // // value of Jacobian of f double check_jac[] = { 0.0, 0.0, 2.0 * x_2, x_1, x_0, 0.0 }; vector w(m), dw(n); // // check derivative of f_0 (x) for(size_t i = 0; i < m; i++) { w[i] = 1.0; w[1-i] = 0.0; dw = f.Reverse(1, w); for(size_t j = 0; j < n; j++) { // compute partial in j-th component direction ok &= NearEqual(dw[j], check_jac[i * n + j], eps, eps); } } // -------------------------------------------------------------------- // second order reverse // // value of Hessian of f_0 double check_hes_0[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0 }; // // value of Hessian of f_1 double check_hes_1[] = { 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }; vector x1(n), dw2( 2 * n ); for(size_t j = 0; j < n; j++) { for(size_t j1 = 0; j1 < n; j1++) x1[j1] = 0.0; x1[j] = 1.0; // first order forward f.Forward(1, x1); w[0] = 1.0; w[1] = 0.0; dw2 = f.Reverse(2, w); for(size_t i = 0; i < n; i++) ok &= NearEqual(dw2[i * 2 + 1], check_hes_0[i * n + j], eps, eps); w[0] = 0.0; w[1] = 1.0; dw2 = f.Reverse(2, w); for(size_t i = 0; i < n; i++) ok &= NearEqual(dw2[i * 2 + 1], check_hes_1[i * n + j], eps, eps); } // -------------------------------------------------------------------- return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/atomic.cpp0000644000175200017650000000666713057470457017344 0ustar coincoin-web// $Id: atomic.cpp 3830 2016-09-18 11:16:05Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // system include files used for I/O # include // C style asserts # include // for thread_alloc # include // external complied tests extern bool checkpoint(void); extern bool eigen_cholesky(void); extern bool eigen_mat_inv(void); extern bool eigen_mat_mul(void); extern bool extended_ode(void); extern bool for_sparse_hes(void); extern bool for_sparse_jac(void); extern bool forward(void); extern bool get_started(void); extern bool mat_mul(void); extern bool mul_level(void); extern bool norm_sq(void); extern bool ode(void); extern bool reciprocal(void); extern bool rev_sparse_hes(void); extern bool rev_sparse_jac(void); extern bool reverse(void); extern bool set_sparsity(void); extern bool tangent(void); namespace { // function that runs one test static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), const char *name) { bool ok = true; ok &= TestOk(); if( ok ) { std::cout << "OK: " << "atomic: " << name << std::endl; Run_ok_count++; } else { std::cout << "Error: " << "atomic: " << name << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; // This line is used by test_one.sh // external compiled tests ok &= Run( checkpoint, "checkpoint" ); ok &= Run( extended_ode, "extended_ode" ); ok &= Run( for_sparse_hes, "for_sparse_hes" ); ok &= Run( for_sparse_jac, "for_sparse_jac" ); ok &= Run( forward, "forward" ); ok &= Run( get_started, "get_started" ); ok &= Run( mat_mul, "mat_mul" ); ok &= Run( mul_level, "mul_level" ); ok &= Run( norm_sq, "norm_sq" ); ok &= Run( ode, "ode" ); ok &= Run( reciprocal, "reciprocal" ); ok &= Run( rev_sparse_hes, "rev_sparse_hes" ); ok &= Run( rev_sparse_jac, "rev_sparse_jac" ); ok &= Run( reverse, "reverse" ); ok &= Run( set_sparsity, "set_sparsity" ); ok &= Run( tangent, "tangent" ); # ifdef CPPAD_HAS_EIGEN ok &= Run( eigen_cholesky, "eigen_cholesky" ); ok &= Run( eigen_mat_inv, "eigen_mat_inv" ); ok &= Run( eigen_mat_mul, "eigen_mat_mul" ); # endif // check for errors using std::cout; using std::endl; assert( ok || (Run_error_count > 0) ); if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "OK: " << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Error: " << "memory leak detected" << endl; } // convert int(size_t) to avoid warning on _MSC_VER systems if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! ok ); } cppad-20170000.3/example/atomic/norm_sq.cpp0000644000175200017650000002404213057470457017531 0ustar coincoin-web// $Id: norm_sq.cpp 3821 2016-06-30 02:53:40Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_norm_sq.cpp$$ $spell sq bool enum $$ $section Atomic Euclidean Norm Squared: Example and Test$$ $mindex bool_sparsity_enum$$ $head Theory$$ This example demonstrates using $cref atomic_base$$ to define the operation $latex f : \B{R}^n \rightarrow \B{R}^m$$ where $latex n = 2$$, $latex m = 1$$, where $latex \[ f(x) = x_0^2 + x_1^2 \] $$ $head sparsity$$ This example only uses bool sparsity patterns. $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // class atomic_norm_sq : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_norm_sq(const std::string& name) : // this example only uses boolean sparsity patterns CppAD::atomic_base(name, atomic_base::bool_sparsity_enum) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { # ifndef NDEBUG size_t n = tx.size() / (q+1); size_t m = ty.size() / (q+1); # endif assert( n == 2 ); assert( m == 1 ); assert( p <= q ); // return flag bool ok = q <= 1; // Variable information must always be implemented. // y_0 is a variable if and only if x_0 or x_1 is a variable. if( vx.size() > 0 ) vy[0] = vx[0] | vx[1]; // Order zero forward mode must always be implemented. // y^0 = f( x^0 ) double x_00 = tx[ 0*(q+1) + 0]; // x_0^0 double x_10 = tx[ 1*(q+1) + 0]; // x_10 double f = x_00 * x_00 + x_10 * x_10; // f( x^0 ) if( p <= 0 ) ty[0] = f; // y_0^0 if( q <= 0 ) return ok; assert( vx.size() == 0 ); // Order one forward mode. // This case needed if first order forward mode is used. // y^1 = f'( x^0 ) x^1 double x_01 = tx[ 0*(q+1) + 1]; // x_0^1 double x_11 = tx[ 1*(q+1) + 1]; // x_1^1 double fp_0 = 2.0 * x_00; // partial f w.r.t x_0^0 double fp_1 = 2.0 * x_10; // partial f w.r.t x_1^0 if( p <= 1 ) ty[1] = fp_0 * x_01 + fp_1 * x_11; // f'( x^0 ) * x^1 if( q <= 1 ) return ok; // Assume we are not using forward mode with order > 1 assert( ! ok ); return ok; } /* %$$ $head reverse$$ $srccode%cpp% */ // reverse mode routine called by CppAD virtual bool reverse( size_t q , const vector& tx , const vector& ty , vector& px , const vector& py ) { # ifndef NDEBUG size_t n = tx.size() / (q+1); size_t m = ty.size() / (q+1); # endif assert( px.size() == n * (q+1) ); assert( py.size() == m * (q+1) ); assert( n == 2 ); assert( m == 1 ); bool ok = q <= 1; double fp_0, fp_1; switch(q) { case 0: // This case needed if first order reverse mode is used // F ( {x} ) = f( x^0 ) = y^0 fp_0 = 2.0 * tx[0]; // partial F w.r.t. x_0^0 fp_1 = 2.0 * tx[1]; // partial F w.r.t. x_0^1 px[0] = py[0] * fp_0;; // partial G w.r.t. x_0^0 px[1] = py[0] * fp_1;; // partial G w.r.t. x_0^1 assert(ok); break; default: // Assume we are not using reverse with order > 1 (q > 0) assert(!ok); } return ok; } /* %$$ $head for_sparse_jac$$ $srccode%cpp% */ // forward Jacobian bool sparsity routine called by CppAD virtual bool for_sparse_jac( size_t p , const vector& r , vector& s , const vector& x ) { // This function needed if using f.ForSparseJac size_t n = r.size() / p; # ifndef NDEBUG size_t m = s.size() / p; # endif assert( n == x.size() ); assert( n == 2 ); assert( m == 1 ); // sparsity for S(x) = f'(x) * R // where f'(x) = 2 * [ x_0, x_1 ] for(size_t j = 0; j < p; j++) { s[j] = false; for(size_t i = 0; i < n; i++) { // Visual Studio 2013 generates warning without bool below s[j] |= bool( r[i * p + j] ); } } return true; } /* %$$ $head rev_sparse_jac$$ $srccode%cpp% */ // reverse Jacobian bool sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t p , const vector& rt , vector& st , const vector& x ) { // This function needed if using RevSparseJac or optimize size_t n = st.size() / p; # ifndef NDEBUG size_t m = rt.size() / p; # endif assert( n == x.size() ); assert( n == 2 ); assert( m == 1 ); // sparsity for S(x)^T = f'(x)^T * R^T // where f'(x)^T = 2 * [ x_0, x_1]^T for(size_t j = 0; j < p; j++) for(size_t i = 0; i < n; i++) st[i * p + j] = rt[j]; return true; } /* %$$ $head rev_sparse_hes$$ $srccode%cpp% */ // reverse Hessian bool sparsity routine called by CppAD virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t p , const vector& r , const vector& u , vector& v , const vector& x ) { // This function needed if using RevSparseHes # ifndef NDEBUG size_t m = s.size(); # endif size_t n = t.size(); assert( x.size() == n ); assert( r.size() == n * p ); assert( u.size() == m * p ); assert( v.size() == n * p ); assert( n == 2 ); assert( m == 1 ); // There are no cross term second derivatives for this case, // so it is not necessary to use vx. // sparsity for T(x) = S(x) * f'(x) t[0] = s[0]; t[1] = s[0]; // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate the sparsity for U size_t j; for(j = 0; j < p; j++) for(size_t i = 0; i < n; i++) v[ i * p + j] = u[j]; // include forward Jacobian sparsity in Hessian sparsity // sparsity for g'(y) * f''(x) * R (Note f''(x) has same sparsity // as the identity matrix) if( s[0] ) { for(j = 0; j < p; j++) for(size_t i = 0; i < n; i++) { // Visual Studio 2013 generates warning without bool below v[ i * p + j] |= bool( r[ i * p + j] ); } } return true; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of atomic_norm_sq class } // End empty namespace /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool norm_sq(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); /* %$$ $subhead Constructor$$ $srccode%cpp% */ // -------------------------------------------------------------------- // Create the atomic reciprocal object atomic_norm_sq afun("atomic_norm_sq"); /* %$$ $subhead Recording$$ $srccode%cpp% */ // Create the function f(x) // // domain space vector size_t n = 2; double x0 = 0.25; double x1 = 0.75; vector< AD > ax(n); ax[0] = x0; ax[1] = x1; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; vector< AD > ay(m); // call user function and store norm_sq(x) in au[0] afun(ax, ay); // y_0 = x_0 * x_0 + x_1 * x_1 // create f: x -> y and stop tape recording CppAD::ADFun f; f.Dependent (ax, ay); /* %$$ $subhead forward$$ $srccode%cpp% */ // check function value double check = x0 * x0 + x1 * x1; ok &= NearEqual( Value(ay[0]) , check, eps, eps); // check zero order forward mode size_t q; vector x_q(n), y_q(m); q = 0; x_q[0] = x0; x_q[1] = x1; y_q = f.Forward(q, x_q); ok &= NearEqual(y_q[0] , check, eps, eps); // check first order forward mode q = 1; x_q[0] = 0.3; x_q[1] = 0.7; y_q = f.Forward(q, x_q); check = 2.0 * x0 * x_q[0] + 2.0 * x1 * x_q[1]; ok &= NearEqual(y_q[0] , check, eps, eps); /* %$$ $subhead reverse$$ $srccode%cpp% */ // first order reverse mode q = 1; vector w(m), dw(n * q); w[0] = 1.; dw = f.Reverse(q, w); check = 2.0 * x0; ok &= NearEqual(dw[0] , check, eps, eps); check = 2.0 * x1; ok &= NearEqual(dw[1] , check, eps, eps); /* %$$ $subhead for_sparse_jac$$ $srccode%cpp% */ // forward mode sparstiy pattern size_t p = n; CppAD::vectorBool r1(n * p), s1(m * p); r1[0] = true; r1[1] = false; // sparsity pattern identity r1[2] = false; r1[3] = true; // s1 = f.ForSparseJac(p, r1); ok &= s1[0] == true; // f[0] depends on x[0] ok &= s1[1] == true; // f[0] depends on x[1] /* %$$ $subhead rev_sparse_jac$$ $srccode%cpp% */ // reverse mode sparstiy pattern q = m; CppAD::vectorBool s2(q * m), r2(q * n); s2[0] = true; // compute sparsity pattern for f[0] // r2 = f.RevSparseJac(q, s2); ok &= r2[0] == true; // f[0] depends on x[0] ok &= r2[1] == true; // f[0] depends on x[1] /* %$$ $subhead rev_sparse_hes$$ $srccode%cpp% */ // Hessian sparsity (using previous ForSparseJac call) CppAD::vectorBool s3(m), h(p * n); s3[0] = true; // compute sparsity pattern for f[0] // h = f.RevSparseHes(p, s3); ok &= h[0] == true; // partial of f[0] w.r.t. x[0],x[0] is non-zero ok &= h[1] == false; // partial of f[0] w.r.t. x[0],x[1] is zero ok &= h[2] == false; // partial of f[0] w.r.t. x[1],x[0] is zero ok &= h[3] == true; // partial of f[0] w.r.t. x[1],x[1] is non-zero // return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/for_sparse_jac.cpp0000644000175200017650000001333613057470457021037 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_for_sparse_jac.cpp$$ $spell Jacobian $$ $section Atomic Forward Jacobian Sparsity: Example and Test$$ $head Purpose$$ This example demonstrates calculation of the forward Jacobian sparsity pattern for an atomic operation. $head function$$ For this example, the atomic function $latex f : \B{R}^3 \rightarrow \B{R}^2$$ is defined by $latex \[ f(x) = \left( \begin{array}{c} x_2 * x_2 \\ x_0 * x_1 \end{array} \right) \] $$ The corresponding Jacobian is $latex \[ f^{(1)} (x) = \left( \begin{array}{ccc} 0 & 0 & 2 x_2 \\ x_1 & x_0 & 0 \end{array} \right) \] $$ $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // class atomic_for_sparse_jac : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_for_sparse_jac(const std::string& name) : // this example only uses pack sparsty patterns CppAD::atomic_base(name, pack_sparsity_enum) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { # ifndef NDEBUG size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); # endif assert( n == 3 ); assert( m == 2 ); // return flag bool ok = q == 0; if( ! ok ) return ok; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) { vy[0] = vx[2]; vy[1] = vx[0] || vx[1]; } // Order zero forward mode. // This case must always be implemented // f(x) = [ x_2 * x_2 ] // [ x_0 * x_1 ] assert( p <= 0 ); if( p <= 0 ) { ty[0] = tx[2] * tx[2]; ty[1] = tx[0] * tx[1]; } return ok; } /* %$$ $head for_sparse_jac$$ $srccode%cpp% */ // forward Jacobian sparsity routine called by CppAD virtual bool for_sparse_jac( size_t q , const CppAD::vectorBool& r , CppAD::vectorBool& s , const vector& x ) { // This function needed because we are using ForSparseJac // with afun.option( CppAD::atomic_base::pack_sparsity_enum ) # ifndef NDEBUG size_t n = r.size() / q; size_t m = s.size() / q; # endif assert( x.size() == n ); assert( n == 3 ); assert( m == 2 ); // f'(x) = [ 0, 0, 2 x_2 ] // [ x_1, x_0, 0 ] // sparsity for first row of S(x) = f'(x) * R size_t i = 0; for(size_t j = 0; j < q; j++) s[ i * q + j ] = r[ 2 * q + j ]; // sparsity for second row of S(x) = f'(x) * R i = 1; for(size_t j = 0; j < q; j++) s[ i * q + j ] = r[ 0 * q + j ] | r[ 1 * q + j]; return true; } }; // End of atomic_for_sparse_jac class /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool use_atomic_for_sparse_jac(bool x_1_variable) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // // Create the atomic for_sparse_jac object atomic_for_sparse_jac afun("atomic_for_sparse_jac"); // // Create the function f(u) // // domain space vector size_t n = 3; double x_0 = 1.00; double x_1 = 2.00; double x_2 = 3.00; vector< AD > au(n); au[0] = x_0; au[1] = x_1; au[2] = x_2; // declare independent variables and start tape recording CppAD::Independent(au); // range space vector size_t m = 2; vector< AD > ay(m); // call user function vector< AD > ax(n); ax[0] = au[0]; ax[2] = au[2]; if( x_1_variable ) ax[1] = au[1]; else ax[1] = x_1; afun(ax, ay); // y = [ x_2 * x_2 , x_0 * x_1 ]^T // create f: u -> y and stop tape recording CppAD::ADFun f; f.Dependent (au, ay); // f(u) = y // // check function value double check = x_2 * x_2; ok &= NearEqual( Value(ay[0]) , check, eps, eps); check = x_0 * x_1; ok &= NearEqual( Value(ay[1]) , check, eps, eps); // check zero order forward mode size_t q; vector xq(n), yq(m); q = 0; xq[0] = x_0; xq[1] = x_1; xq[2] = x_2; yq = f.Forward(q, xq); check = x_2 * x_2; ok &= NearEqual(yq[0] , check, eps, eps); check = x_0 * x_1; ok &= NearEqual(yq[1] , check, eps, eps); // forward sparse Jacobian CppAD::vectorBool r(n * n), s(m * n); // r = identity matrix for(size_t i = 0; i < n; i++) for(size_t j = 0; j < n; j++) r[ i * n + j] = i == j; s = f.ForSparseJac(n, r); // check result CppAD::vectorBool check_s(m * n); check_s[ 0 * n + 0 ] = false; check_s[ 0 * n + 1 ] = false; check_s[ 0 * n + 2 ] = true; check_s[ 1 * n + 0 ] = true; check_s[ 1 * n + 1 ] = x_1_variable; check_s[ 1 * n + 2 ] = false; // for(size_t i = 0; i < m * n; i++) ok &= s[ i ] == check_s[ i ]; // return ok; } } // End empty namespace /* %$$ $head Test with x_1 Both a Variable and a Parameter$$ $srccode%cpp% */ bool for_sparse_jac(void) { bool ok = true; // test with x_1 a variable ok &= use_atomic_for_sparse_jac(true); // test with x_1 a parameter ok &= use_atomic_for_sparse_jac(false); return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/reciprocal.cpp0000644000175200017650000002422513057470457020201 0ustar coincoin-web// $Id: reciprocal.cpp 3821 2016-06-30 02:53:40Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_reciprocal.cpp$$ $spell enum $$ $section Reciprocal as an Atomic Operation: Example and Test$$ $mindex set_sparsity_enum$$ $head Theory$$ This example demonstrates using $cref atomic_base$$ to define the operation $latex f : \B{R}^n \rightarrow \B{R}^m$$ where $latex n = 1$$, $latex m = 1$$, and $latex f(x) = 1 / x$$. $head sparsity$$ This example only uses set sparsity patterns. $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // // a utility to compute the union of two sets. using CppAD::set_union; // class atomic_reciprocal : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_reciprocal(const std::string& name) : // this exmaple only uses set sparsity patterns CppAD::atomic_base(name, atomic_base::set_sparsity_enum) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { # ifndef NDEBUG size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); # endif assert( n == 1 ); assert( m == 1 ); assert( p <= q ); // return flag bool ok = q <= 2; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) vy[0] = vx[0]; // Order zero forward mode. // This case must always be implemented // y^0 = f( x^0 ) = 1 / x^0 double f = 1. / tx[0]; if( p <= 0 ) ty[0] = f; if( q <= 0 ) return ok; assert( vx.size() == 0 ); // Order one forward mode. // This case needed if first order forward mode is used. // y^1 = f'( x^0 ) x^1 double fp = - f / tx[0]; if( p <= 1 ) ty[1] = fp * tx[1]; if( q <= 1 ) return ok; // Order two forward mode. // This case needed if second order forward mode is used. // Y''(t) = X'(t)^\R{T} f''[X(t)] X'(t) + f'[X(t)] X''(t) // 2 y^2 = x^1 * f''( x^0 ) x^1 + 2 f'( x^0 ) x^2 double fpp = - 2.0 * fp / tx[0]; ty[2] = tx[1] * fpp * tx[1] / 2.0 + fp * tx[2]; if( q <= 2 ) return ok; // Assume we are not using forward mode with order > 2 assert( ! ok ); return ok; } /* %$$ $head reverse$$ $srccode%cpp% */ // reverse mode routine called by CppAD virtual bool reverse( size_t q , const vector& tx , const vector& ty , vector& px , const vector& py ) { # ifndef NDEBUG size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); # endif assert( px.size() == n * (q + 1) ); assert( py.size() == m * (q + 1) ); assert( n == 1 ); assert( m == 1 ); bool ok = q <= 2; double f, fp, fpp, fppp; switch(q) { case 0: // This case needed if first order reverse mode is used // reverse: F^0 ( tx ) = y^0 = f( x^0 ) f = ty[0]; fp = - f / tx[0]; px[0] = py[0] * fp;; assert(ok); break; case 1: // This case needed if second order reverse mode is used // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1 f = ty[0]; fp = - f / tx[0]; fpp = - 2.0 * fp / tx[0]; px[1] = py[1] * fp; px[0] = py[1] * fpp * tx[1]; // reverse: F^0 ( tx ) = y^0 = f( x^0 ); px[0] += py[0] * fp; assert(ok); break; case 2: // This needed if third order reverse mode is used // reverse: F^2 ( tx ) = y^2 = // = x^1 * f''( x^0 ) x^1 / 2 + f'( x^0 ) x^2 f = ty[0]; fp = - f / tx[0]; fpp = - 2.0 * fp / tx[0]; fppp = - 3.0 * fpp / tx[0]; px[2] = py[2] * fp; px[1] = py[2] * fpp * tx[1]; px[0] = py[2] * tx[1] * fppp * tx[1] / 2.0 + fpp * tx[2]; // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1 px[1] += py[1] * fp; px[0] += py[1] * fpp * tx[1]; // reverse: F^0 ( tx ) = y^0 = f( x^0 ); px[0] += py[0] * fp; assert(ok); break; default: assert(!ok); } return ok; } /* %$$ $head for_sparse_jac$$ $srccode%cpp% */ // forward Jacobian set sparsity routine called by CppAD virtual bool for_sparse_jac( size_t p , const vector< std::set >& r , vector< std::set >& s , const vector& x ) { // This function needed if using f.ForSparseJac # ifndef NDEBUG size_t n = r.size(); size_t m = s.size(); # endif assert( n == x.size() ); assert( n == 1 ); assert( m == 1 ); // sparsity for S(x) = f'(x) * R is same as sparsity for R s[0] = r[0]; return true; } /* %$$ $head rev_sparse_jac$$ $srccode%cpp% */ // reverse Jacobian set sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t p , const vector< std::set >& rt , vector< std::set >& st , const vector& x ) { // This function needed if using RevSparseJac or optimize # ifndef NDEBUG size_t n = st.size(); size_t m = rt.size(); # endif assert( n == x.size() ); assert( n == 1 ); assert( m == 1 ); // sparsity for S(x)^T = f'(x)^T * R^T is same as sparsity for R^T st[0] = rt[0]; return true; } /* %$$ $head rev_sparse_hes$$ $srccode%cpp% */ // reverse Hessian set sparsity routine called by CppAD virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t p , const vector< std::set >& r , const vector< std::set >& u , vector< std::set >& v , const vector& x ) { // This function needed if using RevSparseHes # ifndef NDEBUG size_t n = vx.size(); size_t m = s.size(); # endif assert( x.size() == n ); assert( t.size() == n ); assert( r.size() == n ); assert( u.size() == m ); assert( v.size() == n ); assert( n == 1 ); assert( m == 1 ); // There are no cross term second derivatives for this case, // so it is not necessary to vx. // sparsity for T(x) = S(x) * f'(x) is same as sparsity for S t[0] = s[0]; // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate the sparsity for U, note f'(x) may be non-zero; v[0] = u[0]; // include forward Jacobian sparsity in Hessian sparsity // (note sparsty for f''(x) * R same as for R) if( s[0] ) v[0] = set_union(v[0], r[0] ); return true; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of atomic_reciprocal class } // End empty namespace /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool reciprocal(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); /* %$$ $subhead Constructor$$ $srccode%cpp% */ // -------------------------------------------------------------------- // Create the atomic reciprocal object atomic_reciprocal afun("atomic_reciprocal"); /* %$$ $subhead Recording$$ $srccode%cpp% */ // Create the function f(x) // // domain space vector size_t n = 1; double x0 = 0.5; vector< AD > ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; vector< AD > ay(m); // call user function and store reciprocal(x) in au[0] vector< AD > au(m); afun(ax, au); // u = 1 / x // now use AD division to invert to invert the operation ay[0] = 1.0 / au[0]; // y = 1 / u = x // create f: x -> y and stop tape recording CppAD::ADFun f; f.Dependent (ax, ay); // f(x) = x /* %$$ $subhead forward$$ $srccode%cpp% */ // check function value double check = x0; ok &= NearEqual( Value(ay[0]) , check, eps, eps); // check zero order forward mode size_t q; vector x_q(n), y_q(m); q = 0; x_q[0] = x0; y_q = f.Forward(q, x_q); ok &= NearEqual(y_q[0] , check, eps, eps); // check first order forward mode q = 1; x_q[0] = 1; y_q = f.Forward(q, x_q); check = 1.; ok &= NearEqual(y_q[0] , check, eps, eps); // check second order forward mode q = 2; x_q[0] = 0; y_q = f.Forward(q, x_q); check = 0.; ok &= NearEqual(y_q[0] , check, eps, eps); /* %$$ $subhead reverse$$ $srccode%cpp% */ // third order reverse mode q = 3; vector w(m), dw(n * q); w[0] = 1.; dw = f.Reverse(q, w); check = 1.; ok &= NearEqual(dw[0] , check, eps, eps); check = 0.; ok &= NearEqual(dw[1] , check, eps, eps); ok &= NearEqual(dw[2] , check, eps, eps); /* %$$ $subhead for_sparse_jac$$ $srccode%cpp% */ // forward mode sparstiy pattern size_t p = n; CppAD::vectorBool r1(n * p), s1(m * p); r1[0] = true; // compute sparsity pattern for x[0] // s1 = f.ForSparseJac(p, r1); ok &= s1[0] == true; // f[0] depends on x[0] /* %$$ $subhead rev_sparse_jac$$ $srccode%cpp% */ // reverse mode sparstiy pattern q = m; CppAD::vectorBool s2(q * m), r2(q * n); s2[0] = true; // compute sparsity pattern for f[0] // r2 = f.RevSparseJac(q, s2); ok &= r2[0] == true; // f[0] depends on x[0] /* %$$ $subhead rev_sparse_hes$$ $srccode%cpp% */ // Hessian sparsity (using previous ForSparseJac call) CppAD::vectorBool s3(m), h(p * n); s3[0] = true; // compute sparsity pattern for f[0] // h = f.RevSparseHes(p, s3); ok &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero // return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/mul_level.cpp0000644000175200017650000000612313057470457020037 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_mul_level.cpp$$ $spell checkpointing $$ $section Atomic Operations and Multiple-Levels of AD: Example and Test$$ $head Discussion$$ One can use $cref checkpoint$$ or $cref atomic_base$$ to code an $codei%AD<%Base%>%$$ operation as atomic. This means that derivative computations that use the type $icode Base$$ will call the corresponding $code atomic_base$$ member functions. On the other hand, if $icode Base$$ is $codei%AD<%Other%>%$$ the operations recorded at the $icode Base$$ level will not be atomic. This is demonstrated in this example. $code $srcfile%example/atomic/mul_level.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::AD; typedef AD a1double; typedef AD a2double; typedef CPPAD_TESTVECTOR(a1double) a1vector; typedef CPPAD_TESTVECTOR(a2double) a2vector; void f_algo(const a2vector& x, a2vector& y) { size_t n = x.size(); y[0] = 0.0; for(size_t j = 1; j < n; j++) y[0] += x[j-1] * x[j]; return; } } // bool mul_level(void) { bool ok = true; using CppAD::checkpoint; using CppAD::ADFun; using CppAD::Independent; // domain dimension for this problem size_t n = 10; size_t m = 1; // checkpoint version of the function F(x) a2vector a2x(n), a2y(m); for(size_t j = 0; j < n; j++) a2x[j] = a2double(j + 1); // // could also use bool_sparsity_enum or set_sparsity_enum checkpoint atom_f("atom_f", f_algo, a2x, a2y); // // Record a version of y = f(x) without checkpointing Independent(a2x); f_algo(a2x, a2y); ADFun check_not(a2x, a2y); // // number of variables in a tape of f_algo that does not use checkpointing size_t size_not = check_not.size_var(); // // Record a version of y = f(x) with checkpointing Independent(a2x); atom_f(a2x, a2y); ADFun check_yes(a2x, a2y); // // f_algo is represented by one atomic operation in this tape ok &= check_yes.size_var() < size_not; // // now record operations at a1double level a1vector a1x(n), a1y(m); for(size_t j = 0; j < n; j++) a1x[j] = a1double(j + 1); // // without checkpointing Independent(a1x); a1y = check_not.Forward(0, a1x); ADFun with_not(a1x, a1y); // // should have the same size ok &= with_not.size_var() == size_not; // // with checkpointing Independent(a1x); a1y = check_yes.Forward(0, a1x); ADFun with_yes(a1x, a1y); // // f_algo is nolonger represented by one atomic operation in this tape ok &= with_yes.size_var() == size_not; // return ok; } // END C++ cppad-20170000.3/example/atomic/rev_sparse_jac.cpp0000644000175200017650000001362413057470457021045 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_rev_sparse_jac.cpp$$ $spell Jacobian Jacobians $$ $section Atomic Reverse Jacobian Sparsity: Example and Test$$ $head Purpose$$ This example demonstrates calculation of the reverse Jacobians sparsity pattern for an atomic operation. $head function$$ For this example, the atomic function $latex f : \B{R}^3 \rightarrow \B{R}^2$$ is defined by $latex \[ f( x ) = \left( \begin{array}{c} x_2 * x_2 \\ x_0 * x_1 \end{array} \right) \] $$ The corresponding Jacobian is $latex \[ f^{(1)} (x) = \left( \begin{array}{ccc} 0 & 0 & 2 x_2 \\ x_1 & x_0 & 0 \end{array} \right) \] $$ $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // class atomic_rev_sparse_jac : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_rev_sparse_jac(const std::string& name) : // this example only uses pack sparsity patterns CppAD::atomic_base(name, pack_sparsity_enum) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { # ifndef NDEBUG size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); # endif assert( n == 3 ); assert( m == 2 ); // return flag bool ok = q == 0; if( ! ok ) return ok; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) { vy[0] = vx[0]; vy[1] = vx[0] || vy[0]; } // Order zero forward mode. // This case must always be implemented // f(x) = [ x_0 * x_0 ] // [ x_0 * x_1 ] assert( p <= 0 ); if( p <= 0 ) { ty[0] = tx[2] * tx[2]; ty[1] = tx[0] * tx[1]; } return ok; } /* %$$ $head rev_sparse_jac$$ $srccode%cpp% */ // reverse Jacobian sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t q , const CppAD::vectorBool& rt , CppAD::vectorBool& st , const vector& x ) { // This function needed because we are using RevSparseHes // with afun.option( CppAD::atomic_base::pack_sparsity_enum ) # ifndef NDEBUG size_t m = rt.size() / q; size_t n = st.size() / q; # endif assert( n == x.size() ); assert( n == 3 ); assert( m == 2 ); // [ 0, x_1 ] // f'(x)^T = [ 0, x_0 ] // [ 2 x_2, 0 ] // sparsity for first row of S(x)^T = f'(x)^T * R^T size_t i = 0; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 1 * q + j ]; // sparsity for second row of S(x)^T = f'(x)^T * R^T i = 1; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 1 * q + j ]; // sparsity for third row of S(x)^T = f'(x)^T * R^T i = 2; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 0 * q + j ]; return true; } }; // End of atomic_rev_sparse_jac class /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool use_atomic_rev_sparse_jac(bool x_1_variable) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // // Create the atomic rev_sparse_jac object atomic_rev_sparse_jac afun("atomic_rev_sparse_jac"); // // Create the function f(u) // // domain space vector size_t n = 3; double x_0 = 1.00; double x_1 = 2.00; double x_2 = 3.00; vector< AD > au(n); au[0] = x_0; au[1] = x_1; au[2] = x_2; // declare independent variables and start tape recording CppAD::Independent(au); // range space vector size_t m = 2; vector< AD > ay(m); // call user function vector< AD > ax(n); ax[0] = au[0]; ax[2] = au[2]; if( x_1_variable ) ax[1] = au[1]; else ax[1] = x_1; afun(ax, ay); // y = [ x_2 * x_2 , x_0 * x_1 ]^T // create f: u -> y and stop tape recording CppAD::ADFun f; f.Dependent (au, ay); // f(u) = y // // check function value double check = x_2 * x_2; ok &= NearEqual( Value(ay[0]) , check, eps, eps); check = x_0 * x_1; ok &= NearEqual( Value(ay[1]) , check, eps, eps); // check zero order forward mode size_t q; vector xq(n), yq(m); q = 0; xq[0] = x_0; xq[1] = x_1; xq[2] = x_2; yq = f.Forward(q, xq); check = x_2 * x_2; ok &= NearEqual(yq[0] , check, eps, eps); check = x_0 * x_1; ok &= NearEqual(yq[1] , check, eps, eps); // forward sparse Jacobian CppAD::vectorBool r(m * m), s(m * n); // r = identity matrix for(size_t i = 0; i < m; i++) for(size_t j = 0; j < m; j++) r[ i * m + j] = i == j; s = f.RevSparseJac(m, r); // check result CppAD::vectorBool check_s(m * n); check_s[ 0 * n + 0 ] = false; check_s[ 0 * n + 1 ] = false; check_s[ 0 * n + 2 ] = true; check_s[ 1 * n + 0 ] = true; check_s[ 1 * n + 1 ] = x_1_variable; check_s[ 1 * n + 2 ] = false; // for(size_t i = 0; i < m * n; i++) ok &= s[ i ] == check_s[ i ]; // return ok; } } // End empty namespace /* %$$ $head Test with x_1 Both a Variable and a Parameter$$ $srccode%cpp% */ bool rev_sparse_jac(void) { bool ok = true; // test with x_1 a variable ok &= use_atomic_rev_sparse_jac(true); // test with x_1 a parameter ok &= use_atomic_rev_sparse_jac(false); return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/checkpoint.cpp0000644000175200017650000001246413057470457020207 0ustar coincoin-web// $Id: checkpoint.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin checkpoint.cpp$$ $spell checkpointing Taylor $$ $section Simple Checkpointing: Example and Test$$ $head Purpose$$ Break a large computation into pieces and only store values at the interface of the pieces. In actual applications, there may be many functions, but for this example there are only two. The functions $latex F : \B{R}^2 \rightarrow \B{R}^2$$ and $latex G : \B{R}^2 \rightarrow \B{R}^2$$ defined by $latex \[ F(y) = \left( \begin{array}{c} y_0 + y_0 + y_0 \\ y_1 + y_1 + y_1 \end{array} \right) \; , \; G(x) = \left( \begin{array}{c} x_0 \cdot x_0 \cdot x_0 \\ x_1 \cdot x_1 \cdot x_1 \end{array} \right) \] $$ $code $srcfile%example/atomic/checkpoint.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::AD; typedef CPPAD_TESTVECTOR(AD) ADVector; typedef CppAD::atomic_base::option_enum option_enum; void f_algo(const ADVector& y, ADVector& z) { z[0] = 0.0; z[1] = 0.0; for(size_t k = 0; k < 3; k++) { z[0] += y[0]; z[1] += y[1]; } return; } void g_algo(const ADVector& x, ADVector& y) { y[0] = 1.0; y[1] = 1.0; for(size_t k = 0; k < 3; k++) { y[0] *= x[0]; y[1] *= x[1]; } return; } bool test_case( option_enum f_sparsity, option_enum g_sparsity, bool optimize ) { bool ok = true; using CppAD::checkpoint; using CppAD::ADFun; using CppAD::NearEqual; size_t i, j, k, n = 2, m = n; double eps = 10. * std::numeric_limits::epsilon(); // checkpoint version of the function F(x) ADVector ax(n), ay(n), az(m); for(j = 0; j < n; j++) ax[j] = double(j + 1); // could also use bool_sparsity_enum or set_sparsity_enum checkpoint atom_f("atom_f", f_algo, ax, ay, f_sparsity); checkpoint atom_g("atom_g", g_algo, ay, az, g_sparsity); // Record a version of z = g[f(x)] without checkpointing Independent(ax); f_algo(ax, ay); g_algo(ay, az); ADFun check_not(ax, az); // Record a version of z = g[f(x)] with checkpointing Independent(ax); atom_f(ax, ay); atom_g(ay, az); ADFun check_yes(ax, az); // checkpointing should use fewer operations ok &= check_yes.size_var() < check_not.size_var(); // this does not really save space because f and g are only used once ok &= check_not.size_var() <= check_yes.size_var() + atom_f.size_var() + atom_g.size_var(); // compare forward mode results for orders 0, 1, 2 size_t q = 2; CPPAD_TESTVECTOR(double) x_q(n*(q+1)), z_not(m*(q+1)), z_yes(m*(q+1)); for(j = 0; j < n; j++) { for(k = 0; k <= q; k++) x_q[ j * (q+1) + k ] = 1.0 / (q + 1 - k); } z_not = check_not.Forward(q, x_q); z_yes = check_yes.Forward(q, x_q); for(i = 0; i < m; i++) { for(k = 0; k <= q; k++) { double zik_not = z_not[ i * (q+1) + k]; double zik_yes = z_yes[ i * (q+1) + k]; ok &= NearEqual(zik_not, zik_yes, eps, eps); } } // compare reverse mode results CPPAD_TESTVECTOR(double) w(m*(q+1)), dw_not(n*(q+1)), dw_yes(n*(q+1)); dw_not = check_not.Reverse(q+1, w); dw_yes = check_yes.Reverse(q+1, w); for(j = 0; j < n; j++) { for(k = 0; k <= q; k++) { double dwjk_not = dw_not[ j * (q+1) + k]; double dwjk_yes = dw_yes[ j * (q+1) + k]; ok &= NearEqual(dwjk_not, dwjk_yes, eps, eps); } } // compare forward mode Jacobian sparsity patterns CppAD::vector< std::set > r(n), s_not(m), s_yes(m); for(j = 0; j < n; j++) r[j].insert(j); s_not = check_not.ForSparseJac(n, r); s_yes = check_yes.ForSparseJac(n, r); for(i = 0; i < m; i++) ok &= s_not[i] == s_yes[i]; // compare reverse mode Jacobian sparsity patterns CppAD::vector< std::set > s(m), r_not(m), r_yes(m); for(i = 0; i < m; i++) s[i].insert(i); r_not = check_not.RevSparseJac(m, s); r_yes = check_yes.RevSparseJac(m, s); for(i = 0; i < m; i++) ok &= s_not[i] == s_yes[i]; // compare reverse mode Hessian sparsity patterns CppAD::vector< std::set > s_one(1), h_not(n), h_yes(n); for(i = 0; i < m; i++) s_one[0].insert(i); h_not = check_not.RevSparseHes(n, s_one); h_yes = check_yes.RevSparseHes(n, s_one); for(i = 0; i < n; i++) ok &= h_not[i] == h_yes[i]; return ok; } } bool checkpoint(void) { bool ok = true; // different types of sparsity option_enum pack_sparsity = CppAD::atomic_base::pack_sparsity_enum; option_enum bool_sparsity = CppAD::atomic_base::bool_sparsity_enum; option_enum set_sparsity = CppAD::atomic_base::set_sparsity_enum; // test some different cases ok &= test_case(pack_sparsity, pack_sparsity, true); ok &= test_case(pack_sparsity, bool_sparsity, false); ok &= test_case(bool_sparsity, set_sparsity, true); ok &= test_case(set_sparsity, set_sparsity, false); return ok; } // END C++ cppad-20170000.3/example/atomic/extended_ode.cpp0000644000175200017650000002664213057470457020512 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin checkpoint_extended_ode.cpp$$ $spell Checkpointing Runge-Kutta mul $$ $section Checkpointing an Extended ODE Solver: Example and Test$$ $index mul_level, checkpoint$$ $head See Also$$ $cref checkpoint_ode.cpp$$, $cref atomic_mul_level.cpp$$. $head Discussion$$ Suppose that we wish to extend an ODE to include derivatives with respect to some parameter in the ODE. In addition, suppose we wish to differentiate a function that depends on these derivatives. Applying checkpointing to at the second level of AD would not work; see $cref atomic_mul_level.cpp$$ In this example we show how one can do this by checkpointing an extended ODE solver. $head Problem$$ We consider the initial value problem with parameter $latex x$$ defined by, $latex z(0, x) = z_0 (x)$$, $latex \[ \partial_t z(t, x ) = h [ x , z(t, x) ] \]$$ Note that if $latex t$$ needs to be in the equation, one can define the first component of $latex z(t, x)$$ to be equal to $latex t$$. $head ODE Solver$$ For this example, we consider the Fourth order Runge-Kutta ODE solver. Given an approximation solution at time $latex t_k$$ denoted by $latex \tilde{z}_k (x)$$, and $latex \Delta t = t_{k+1} - t_k$$, it defines the approximation solution $latex \tilde{z}_{k+1} (x)$$ at time $latex t_{k+1}$$ by $latex \[ \begin{array}{rcl} h_1 & = & h [ x , \tilde{z}_k (x) ] \\ h_2 & = & h [ x , \tilde{z}_k (x) + \Delta t \; h_1 / 2 ] \\ h_3 & = & h [ x , \tilde{z}_k (x) + \Delta t \; h_2 / 2 ] \\ h_4 & = & h [ x , \tilde{z}_k (x) + \Delta t \; h_3 ] \\ \tilde{z}_{k+1} (x) & = & \tilde{z}_k (x) + \Delta t \; ( h_1 + 2 h_2 + 2 h_3 + h_4 ) / 6 \end{array} \] $$ If $latex \tilde{z}_k (x) = z_k (x)$$, then $latex \tilde{z}_{k+1} (x) = z_{k+1} (x) + O( \Delta t^5 )$$, then Other ODE solvers can use a similar method to the one used below. $head ODE$$ For this example the ODE is defined by $latex z(0, x) = 0$$ and $latex \[ h[ x, z(t, x) ] = \left( \begin{array}{c} x_0 \\ x_1 z_0 (t, x) \\ \vdots \\ x_{n-1} z_{n-2} (t, x) \end{array} \right) = \left( \begin{array}{c} \partial_t z_0 (t , x) \\ \partial_t z_1 (t , x) \\ \vdots \\ \partial_t z_{n-1} (t , x) \end{array} \right) \] $$ $head Solution$$ The solution of the ODE for this example, which is used to check the results, can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain $latex \[ z(t, x) = \left( \begin{array}{c} x_0 t \\ x_1 x_0 t^2 / 2 \\ \vdots \\ x_{n-1} x_{n-2} \ldots x_0 t^n / n ! \end{array} \right) \] $$ $code $srcfile%example/atomic/extended_ode.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::AD; typedef AD a1double; typedef AD a2double; // typedef CPPAD_TESTVECTOR( double ) a0vector; typedef CPPAD_TESTVECTOR( a1double ) a1vector; typedef CPPAD_TESTVECTOR( a2double ) a2vector; // // set once by main and kept that way double delta_t_ = std::numeric_limits::quiet_NaN(); size_t n_ = 0; // // The function h( x , y) template FloatVector h(const FloatVector& x, const FloatVector& y) { assert( size_t( x.size() ) == n_ ); assert( size_t( y.size() ) == n_ ); FloatVector result(n_); result[0] = x[0]; for(size_t i = 1; i < n_; i++) result[i] = x[i] * y[i-1]; return result; } // The 4-th Order Runge-Kutta Step template FloatVector Runge4(const FloatVector& x, const FloatVector& z0 ) { assert( size_t( x.size() ) == n_ ); assert( size_t( z0.size() ) == n_ ); // typedef typename FloatVector::value_type Float; // Float dt = Float(delta_t_); size_t m = z0.size(); // FloatVector h1(m), h2(m), h3(m), h4(m), result(m); h1 = h( x, z0 ); // for(size_t i = 0; i < m; i++) h2[i] = z0[i] + dt * h1[i] / 2.0; h2 = h( x, h2 ); // for(size_t i = 0; i < m; i++) h3[i] = z0[i] + dt * h2[i] / 2.0; h3 = h( x, h3 ); // for(size_t i = 0; i < m; i++) h4[i] = z0[i] + dt * h3[i]; h4 = h( x, h4 ); // for(size_t i = 0; i < m; i++) { Float dz = dt * ( h1[i] + 2.0*h2[i] + 2.0*h3[i] + h4[i] ) / 6.0; result[i] = z0[i] + dz; } return result; } // Derivative of 4-th Order Runge-Kutta Step w.r.t x a1vector Runge4_x(const a1vector& x, const a1vector& z0) { assert( size_t( x.size() ) == n_ ); assert( size_t( z0.size() ) == n_ ); // a2vector ax(n_); for(size_t j = 0; j < n_; j++) ax[j] = x[j]; // a2vector az0(n_); for(size_t i = 0; i < n_; i++) az0[i] = z0[i]; // CppAD::Independent(ax); a2vector az(n_); az = Runge4(ax, az0); CppAD::ADFun f(ax, az); // a1vector result = f.Jacobian(x); // return result; } // Derivative of 4-th Order Runge-Kutta Step w.r.t z0 a1vector Runge4_z0(const a1vector& x, const a1vector& z0) { assert( size_t( x.size() ) == n_ ); assert( size_t( z0.size() ) == n_ ); // a2vector ax(n_); for(size_t j = 0; j < n_; j++) ax[j] = x[j]; // a2vector az0(n_); for(size_t i = 0; i < n_; i++) az0[i] = z0[i]; // CppAD::Independent(az0); a2vector az(n_); az = Runge4(ax, az0); CppAD::ADFun f(az0, az); // a1vector result = f.Jacobian(z0); // return result; } // pack an extended ode vector template void pack( FloatVector& extended_ode , const FloatVector& x , const FloatVector& z , const FloatVector& z_x ) { assert( size_t( extended_ode.size() ) == n_ + n_ + n_ * n_ ); assert( size_t( x.size() ) == n_ ); assert( size_t( z.size() ) == n_ ); assert( size_t( z_x.size() ) == n_ * n_ ); // size_t offset = 0; for(size_t i = 0; i < n_; i++) extended_ode[offset + i] = x[i]; offset += n_; for(size_t i = 0; i < n_; i++) extended_ode[offset + i] = z[i]; offset += n_; for(size_t i = 0; i < n_; i++) { for(size_t j = 0; j < n_; j++) { // partial of z_i (t , x ) w.r.t x_j extended_ode[offset + i * n_ + j] = z_x[i * n_ + j]; } } } // unpack an extended ode vector template void unpack( const FloatVector& extended_ode , FloatVector& x , FloatVector& z , FloatVector& z_x ) { assert( size_t( extended_ode.size() ) == n_ + n_ + n_ * n_ ); assert( size_t( x.size() ) == n_ ); assert( size_t( z.size() ) == n_ ); assert( size_t( z_x.size() ) == n_ * n_ ); // size_t offset = 0; for(size_t i = 0; i < n_; i++) x[i] = extended_ode[offset + i]; offset += n_; for(size_t i = 0; i < n_; i++) z[i] = extended_ode[offset + i]; offset += n_; for(size_t i = 0; i < n_; i++) { for(size_t j = 0; j < n_; j++) { // partial of z_i (t , x ) w.r.t x_j z_x[i * n_ + j] = extended_ode[offset + i * n_ + j]; } } } // Algorithm that advances the partial of z(t, x) w.r.t x void ext_ode_algo(const a1vector& ext_ode_in, a1vector& ext_ode_out) { assert( size_t( ext_ode_in.size() ) == n_ + n_ + n_ * n_ ); assert( size_t( ext_ode_out.size() ) == n_ + n_ + n_ * n_ ); // // initial extended ode information a1vector x(n_), z0(n_), z0_x(n_ * n_); unpack(ext_ode_in, x, z0, z0_x); // // advance z(t, x) a1vector z1 = Runge4(x, z0); // // partial of z1 w.r.t. x a1vector z1_x = Runge4_x(x, z0); // // partial of z1 w.r.t. z0 a1vector z1_z0 = Runge4_z0(x, z0); // // total derivative of z1 w.r.t x for(size_t i = 0; i < n_; i++) { for(size_t j = 0; j < n_; j++) { a1double sum = 0.0; for(size_t k = 0; k < n_; k++) sum += z1_z0 [ i * n_ + k ] * z0_x [ k * n_ + j ]; z1_x[ i * n_ + j] += sum; } } // // final extended ode information pack(ext_ode_out, x, z1, z1_x); // return; } } // bool extended_ode(void) { bool ok = true; using CppAD::NearEqual; double eps = std::numeric_limits::epsilon(); // // number of terms in the differential equation n_ = 6; // // step size for the differentiail equation size_t n_step = 10; double T = 1.0; delta_t_ = T / double(n_step); // // set parameter value and initial value of the extended ode a1vector ax(n_), az0(n_), az0_x(n_ * n_); for(size_t i = 0; i < n_; i++) { ax[i] = a1double(i + 1); az0[i] = a1double(0); for(size_t j = 0; j < n_; j++) az0_x[ i * n_ + j ] = 0.0; } // // pack into extended ode information input vector size_t n_ext = n_ + n_ + n_ * n_; a1vector aext_ode_in(n_ext); pack(aext_ode_in, ax, az0, az0_x); // // create checkpoint version of the algorithm a1vector aext_ode_out(n_ext); CppAD::checkpoint ext_ode_check( "ext_ode", ext_ode_algo, aext_ode_in, aext_ode_out ); // // set the independent variables for recording CppAD::Independent( ax ); // // repack to get dependence on ax pack(aext_ode_in, ax, az0, az0_x); // // Now run the checkpoint algorithm n_step times for(size_t k = 0; k < n_step; k++) { ext_ode_check(aext_ode_in, aext_ode_out); aext_ode_in = aext_ode_out; } // // Unpack the results (must use ax1 so do not overwrite ax) a1vector ax1(n_), az1(n_), az1_x(n_ * n_); unpack(aext_ode_out, ax1, az1, az1_x); // // We could record a complicated funciton of x and z_x(T, x) in f, // but make this example simpler we record x -> z_x(T, x). CppAD::ADFun f(ax, az1_x); // // check function values a0vector x(n_), z1(n_), z1_x(n_ * n_); for(size_t j = 0; j < n_; j++) x[j] = double(j + 1); z1_x = f.Forward(0, x); // // use z(t, x) for checking solution z1[0] = x[0] * T; for(size_t i = 1; i < n_; i++) z1[i] = x[i] * T * z1[i-1] / double(i+1); // // expected accuracy for each component of of z(t, x) a0vector acc(n_); for(size_t i = 0; i < n_; i++) { if( i < 4 ) { // Runge-Kutta methos is exact for this case acc[i] = 10. * eps; } else { acc[i] = 1.0; for(size_t k = 0; k < 5; k++) acc[i] *= x[k] * delta_t_; } } // check z1(T, x) for(size_t i = 0; i < n_; i++) { for(size_t j = 0; j < n_; j++) { // check partial of z1_i w.r.t x_j double check = 0.0; if( j <= i ) check = z1[i] / x[j]; ok &= NearEqual(z1_x[ i * n_ + j ] , check, acc[i], acc[i]); } } // // Now use f to compute a derivative. For this 'simple' example it is // the derivative with respect to x of the // parital with respect to x[n-1] of z_{n-1} (t , x) a0vector w(n_ * n_), dw(n_); for(size_t i = 0; i < n_; i++) { for(size_t j = 0; j < n_; j++) { w[ i * n_ + j ] = 0.0; if( i == n_ - 1 && j == n_ - 1 ) w[ i * n_ + j ] = 1.0; } } dw = f.Reverse(1, w); for(size_t j = 0; j < n_; j++) { double check = 0.0; if( j < n_ - 1 ) check = z1[n_ - 1] / ( x[n_ - 1] * x[j] ); ok &= NearEqual(dw[j] , check, acc[n_-1], acc[n_-1]); } // return ok; } // END C++ cppad-20170000.3/example/atomic/eigen_cholesky.cpp0000644000175200017650000001676613057470457021061 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_eigen_cholesky.cpp$$ $spell Eigen Cholesky $$ $section Atomic Eigen Cholesky Factorization: Example and Test$$ $head Description$$ The $cref ADFun$$ function object $icode f$$ for this example is $latex \[ f(x) = \R{chol} \left( \begin{array}{cc} x_0 & x_1 \\ x_1 & x_2 \end{array} \right) = \frac{1}{ \sqrt{x_0} } \left( \begin{array}{cc} x_0 & 0 \\ x_1 & \sqrt{ x_0 x_2 - x_1 x_1 } \end{array} \right) \] $$ where the matrix is positive definite; i.e., $latex x_0 > 0$$, $latex x_2 > 0$$ and $latex x_0 x_2 - x_1 x_1 > 0$$. $childtable%omh/theory/cholesky.omh %cppad/example/eigen_cholesky.hpp %$$ $head Use Atomic Function$$ $srccode%cpp% */ # include # include bool eigen_cholesky(void) { typedef double scalar; typedef typename atomic_eigen_cholesky::ad_scalar ad_scalar; typedef typename atomic_eigen_cholesky::ad_matrix ad_matrix; // bool ok = true; scalar eps = 10. * std::numeric_limits::epsilon(); using CppAD::NearEqual; // /* %$$ $subhead Constructor$$ $srccode%cpp% */ // ------------------------------------------------------------------- // object that computes cholesky factor of a matrix atomic_eigen_cholesky cholesky; // ------------------------------------------------------------------- // declare independent variable vector x size_t n = 3; CPPAD_TESTVECTOR(ad_scalar) ad_x(n); ad_x[0] = 2.0; ad_x[1] = 0.5; ad_x[2] = 3.0; CppAD::Independent(ad_x); // ------------------------------------------------------------------- // A = [ x[0] x[1] ] // [ x[1] x[2] ] size_t nr = 2; ad_matrix ad_A(nr, nr); ad_A(0, 0) = ad_x[0]; ad_A(1, 0) = ad_x[1]; ad_A(0, 1) = ad_x[1]; ad_A(1, 1) = ad_x[2]; // ------------------------------------------------------------------- // use atomic operation to L such that A = L * L^T ad_matrix ad_L = cholesky.op(ad_A); // ------------------------------------------------------------------- // declare the dependent variable vector y size_t m = 3; CPPAD_TESTVECTOR(ad_scalar) ad_y(m); ad_y[0] = ad_L(0, 0); ad_y[1] = ad_L(1, 0); ad_y[2] = ad_L(1, 1); CppAD::ADFun f(ad_x, ad_y); // ------------------------------------------------------------------- // check zero order forward mode CPPAD_TESTVECTOR(scalar) x(n), y(m); x[0] = 2.0; x[1] = 0.5; x[2] = 5.0; y = f.Forward(0, x); scalar check; check = std::sqrt( x[0] ); ok &= NearEqual(y[0], check, eps, eps); check = x[1] / std::sqrt( x[0] ); ok &= NearEqual(y[1], check, eps, eps); check = std::sqrt( x[2] - x[1] * x[1] / x[0] ); ok &= NearEqual(y[2], check, eps, eps); // ------------------------------------------------------------------- // check first order forward mode CPPAD_TESTVECTOR(scalar) x1(n), y1(m); // // partial w.r.t. x[0] x1[0] = 1.0; x1[1] = 0.0; x1[2] = 0.0; // y1 = f.Forward(1, x1); check = 1.0 / (2.0 * std::sqrt( x[0] ) ); ok &= NearEqual(y1[0], check, eps, eps); // check = - x[1] / (2.0 * x[0] * std::sqrt( x[0] ) ); ok &= NearEqual(y1[1], check, eps, eps); // check = std::sqrt( x[2] - x[1] * x[1] / x[0] ); check = x[1] * x[1] / (x[0] * x[0] * 2.0 * check); ok &= NearEqual(y1[2], check, eps, eps); // // partial w.r.t. x[1] x1[0] = 0.0; x1[1] = 1.0; x1[2] = 0.0; // y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], 0.0, eps, eps); // check = 1.0 / std::sqrt( x[0] ); ok &= NearEqual(y1[1], check, eps, eps); // check = std::sqrt( x[2] - x[1] * x[1] / x[0] ); check = - 2.0 * x[1] / (2.0 * check * x[0] ); ok &= NearEqual(y1[2], check, eps, eps); // // partial w.r.t. x[2] x1[0] = 0.0; x1[1] = 0.0; x1[2] = 1.0; // y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], 0.0, eps, eps); ok &= NearEqual(y1[1], 0.0, eps, eps); // check = std::sqrt( x[2] - x[1] * x[1] / x[0] ); check = 1.0 / (2.0 * check); ok &= NearEqual(y1[2], check, eps, eps); // ------------------------------------------------------------------- // check second order forward mode CPPAD_TESTVECTOR(scalar) x2(n), y2(m); // // second partial w.r.t x[2] x2[0] = 0.0; x2[1] = 0.0; x2[2] = 0.0; y2 = f.Forward(2, x2); ok &= NearEqual(y2[0], 0.0, eps, eps); ok &= NearEqual(y2[1], 0.0, eps, eps); // check = std::sqrt( x[2] - x[1] * x[1] / x[0] ); // funciton value check = - 1.0 / ( 4.0 * check * check * check ); // second derivative check = 0.5 * check; // taylor coefficient ok &= NearEqual(y2[2], check, eps, eps); // ------------------------------------------------------------------- // check first order reverse mode CPPAD_TESTVECTOR(scalar) w(m), d1w(n); w[0] = 0.0; w[1] = 0.0; w[2] = 1.0; d1w = f.Reverse(1, w); // // partial of f[2] w.r.t x[0] scalar f2 = std::sqrt( x[2] - x[1] * x[1] / x[0] ); scalar f2_x0 = x[1] * x[1] / (2.0 * f2 * x[0] * x[0] ); ok &= NearEqual(d1w[0], f2_x0, eps, eps); // // partial of f[2] w.r.t x[1] scalar f2_x1 = - x[1] / (f2 * x[0] ); ok &= NearEqual(d1w[1], f2_x1, eps, eps); // // partial of f[2] w.r.t x[2] scalar f2_x2 = 1.0 / (2.0 * f2 ); ok &= NearEqual(d1w[2], f2_x2, eps, eps); // ------------------------------------------------------------------- // check second order reverse mode CPPAD_TESTVECTOR(scalar) d2w(2 * n); d2w = f.Reverse(2, w); // // check first order results ok &= NearEqual(d2w[0 * 2 + 0], f2_x0, eps, eps); ok &= NearEqual(d2w[1 * 2 + 0], f2_x1, eps, eps); ok &= NearEqual(d2w[2 * 2 + 0], f2_x2, eps, eps); // // check second order results scalar f2_x2_x0 = - 0.5 * f2_x0 / (f2 * f2 ); ok &= NearEqual(d2w[0 * 2 + 1], f2_x2_x0, eps, eps); scalar f2_x2_x1 = - 0.5 * f2_x1 / (f2 * f2 ); ok &= NearEqual(d2w[1 * 2 + 1], f2_x2_x1, eps, eps); scalar f2_x2_x2 = - 0.5 * f2_x2 / (f2 * f2 ); ok &= NearEqual(d2w[2 * 2 + 1], f2_x2_x2, eps, eps); // ------------------------------------------------------------------- // check third order reverse mode CPPAD_TESTVECTOR(scalar) d3w(3 * n); d3w = f.Reverse(3, w); // // check first order results ok &= NearEqual(d3w[0 * 3 + 0], f2_x0, eps, eps); ok &= NearEqual(d3w[1 * 3 + 0], f2_x1, eps, eps); ok &= NearEqual(d3w[2 * 3 + 0], f2_x2, eps, eps); // // check second order results ok &= NearEqual(d3w[0 * 3 + 1], f2_x2_x0, eps, eps); ok &= NearEqual(d3w[1 * 3 + 1], f2_x2_x1, eps, eps); ok &= NearEqual(d3w[2 * 3 + 1], f2_x2_x2, eps, eps); // ------------------------------------------------------------------- scalar f2_x2_x2_x0 = - 0.5 * f2_x2_x0 / (f2 * f2); f2_x2_x2_x0 += f2_x2 * f2_x0 / (f2 * f2 * f2); ok &= NearEqual(d3w[0 * 3 + 2], 0.5 * f2_x2_x2_x0, eps, eps); scalar f2_x2_x2_x1 = - 0.5 * f2_x2_x1 / (f2 * f2); f2_x2_x2_x1 += f2_x2 * f2_x1 / (f2 * f2 * f2); ok &= NearEqual(d3w[1 * 3 + 2], 0.5 * f2_x2_x2_x1, eps, eps); scalar f2_x2_x2_x2 = - 0.5 * f2_x2_x2 / (f2 * f2); f2_x2_x2_x2 += f2_x2 * f2_x2 / (f2 * f2 * f2); ok &= NearEqual(d3w[2 * 3 + 2], 0.5 * f2_x2_x2_x2, eps, eps); return ok; } /* %$$ $end */ cppad-20170000.3/example/atomic/makefile.am0000644000175200017650000000241013057470457017436 0ustar coincoin-web# $Id: makefile.am 3829 2016-09-13 23:10:44Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = atomic # AM_CXXFLAGS = -g $(CXX_FLAGS) # AM_CPPFLAGS = -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) # atomic_SOURCES = \ atomic.cpp \ checkpoint.cpp \ eigen_cholesky.cpp \ eigen_mat_inv.cpp \ eigen_mat_mul.cpp \ extended_ode.cpp \ for_sparse_hes.cpp \ for_sparse_jac.cpp \ forward.cpp \ get_started.cpp \ mat_mul.cpp \ mul_level.cpp \ norm_sq.cpp \ ode.cpp \ reciprocal.cpp \ rev_sparse_hes.cpp \ rev_sparse_jac.cpp \ reverse.cpp \ set_sparsity.cpp \ tangent.cpp test: check ./atomic cppad-20170000.3/example/atomic/set_sparsity.cpp0000644000175200017650000002034613057470457020607 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_set_sparsity.cpp$$ $spell enum $$ $section Atomic Sparsity with Set Patterns: Example and Test$$ $head function$$ For this example, the atomic function $latex f : \B{R}^3 \rightarrow \B{R}^2$$ is defined by $latex \[ f( x ) = \left( \begin{array}{c} x_2 \\ x_0 * x_1 \end{array} \right) \] $$ $head set_sparsity_enum$$ This example only uses set sparsity patterns. $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // vector typedef vector< std::set > set_vector; // atomic_sparsity // // a utility to compute the union of two sets. using CppAD::set_union; // class atomic_set_sparsity : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor atomic_set_sparsity(const std::string& name) : // this exampel only uses set sparsity patterns CppAD::atomic_base(name, set_sparsity_enum ) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { size_t n = tx.size() / (q + 1); # ifndef NDEBUG size_t m = ty.size() / (q + 1); # endif assert( n == 3 ); assert( m == 2 ); // only order zero bool ok = q == 0; if( ! ok ) return ok; // check for defining variable information if( vx.size() > 0 ) { ok &= vx.size() == n; vy[0] = vx[2]; vy[1] = vx[0] || vx[1]; } // Order zero forward mode. // y[0] = x[2], y[1] = x[0] * x[1] if( p <= 0 ) { ty[0] = tx[2]; ty[1] = tx[0] * tx[1]; } return ok; } /* %$$ $head for_sparse_jac$$ $srccode%cpp% */ // for_sparse_jac virtual bool for_sparse_jac( size_t p , const set_vector& r , set_vector& s , const vector& x ) { // This function needed if using f.ForSparseJac # ifndef NDEBUG size_t n = r.size(); size_t m = s.size(); # endif assert( n == x.size() ); assert( n == 3 ); assert( m == 2 ); // sparsity for S(x) = f'(x) * R = [ 0, 0, 1 ] * R s[0] = r[2]; // s[1] = union(r[0], r[1]) s[1] = set_union(r[0], r[1]); // return true; } /* %$$ $head rev_sparse_jac$$ $srccode%cpp% */ virtual bool rev_sparse_jac( size_t p , const set_vector& rt , set_vector& st , const vector& x ) { // This function needed if using RevSparseJac or optimize # ifndef NDEBUG size_t n = st.size(); size_t m = rt.size(); # endif assert( n == x.size() ); assert( n == 3 ); assert( m == 2 ); // [ 0, x1 ] // sparsity for S(x)^T = f'(x)^T * R^T = [ 0, x0 ] * R^T // [ 1, 0 ] st[0] = rt[1]; st[1] = rt[1]; st[2] = rt[0]; return true; } /* %$$ $head for_sparse_hes$$ $srccode%cpp% */ virtual bool for_sparse_hes( const vector& vx, const vector& r , const vector& s , set_vector& h , const vector& x ) { size_t n = r.size(); # ifndef NDEBUG size_t m = s.size(); # endif assert( x.size() == n ); assert( h.size() == n ); assert( n == 3 ); assert( m == 2 ); // initialize h as empty for(size_t i = 0; i < n; i++) h[i].clear(); // only f_1 has a non-zero hessian if( ! s[1] ) return true; // only the cross term between x[0] and x[1] is non-zero if( ! ( r[0] & r[1] ) ) return true; // set the possibly non-zero terms in the hessian h[0].insert(1); h[1].insert(0); return true; } /* %$$ $head rev_sparse_hes$$ $srccode%cpp% */ virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t p , const set_vector& r , const set_vector& u , set_vector& v , const vector& x ) { // This function needed if using RevSparseHes # ifndef NDEBUG size_t m = s.size(); size_t n = t.size(); # endif assert( x.size() == n ); assert( r.size() == n ); assert( u.size() == m ); assert( v.size() == n ); assert( n == 3 ); assert( m == 2 ); // sparsity for T(x) = S(x) * f'(x) = S(x) * [ 0, 0, 1 ] // [ x1, x0, 0 ] t[0] = s[1]; t[1] = s[1]; t[2] = s[0]; // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // [ 0, x1 ] // sparsity for W(x) = f'(x)^T * U(x) = [ 0, x0 ] * U(x) // [ 1, 0 ] v[0] = u[1]; v[1] = u[1]; v[2] = u[0]; // // [ 0, 1, 0 ] // sparsity for V(x) = W(x) + S_1 (x) * [ 1, 0, 0 ] * R // [ 0, 0, 0 ] if( s[1] ) { // v[0] = union( v[0], r[1] ) v[0] = set_union(v[0], r[1]); // v[1] = union( v[1], r[0] ) v[1] = set_union(v[1], r[0]); } return true; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of atomic_set_sparsity class } // End empty namespace /* %$$ $head Test Atomic Function$$ $srccode%cpp% */ bool set_sparsity(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); /* %$$ $subhead Constructor$$ $srccode%cpp% */ // Create the atomic get_started object atomic_set_sparsity afun("atomic_set_sparsity"); /* %$$ $subhead Recording$$ $srccode%cpp% */ size_t n = 3; size_t m = 2; vector< AD > ax(n), ay(m); for(size_t j = 0; j < n; j++) ax[j] = double(j + 1); // declare independent variables and start tape recording CppAD::Independent(ax); // call user function afun(ax, ay); // create f: x -> y and stop tape recording CppAD::ADFun f; f.Dependent (ax, ay); // f(x) = x // check function value ok &= NearEqual(ay[0] , ax[2], eps, eps); ok &= NearEqual(ay[1] , ax[0] * ax[1], eps, eps); /* %$$ $subhead for_sparse_jac$$ $srccode%cpp% */ // correct Jacobian result set_vector check_s(m); check_s[0].insert(2); check_s[1].insert(0); check_s[1].insert(1); // compute and test forward mode { set_vector r(n), s(m); for(size_t i = 0; i < n; i++) r[i].insert(i); s = f.ForSparseJac(n, r); for(size_t i = 0; i < m; i++) ok &= s[i] == check_s[i]; } /* %$$ $subhead rev_sparse_jac$$ $srccode%cpp% */ // compute and test reverse mode { set_vector r(m), s(m); for(size_t i = 0; i < m; i++) r[i].insert(i); s = f.RevSparseJac(m, r); for(size_t i = 0; i < m; i++) ok &= s[i] == check_s[i]; } /* %$$ $subhead for_sparse_hes$$ $srccode%cpp% */ // correct Hessian result set_vector check_h(n); check_h[0].insert(1); check_h[1].insert(0); // compute and test forward mode { set_vector r(1), s(1), h(n); for(size_t i = 0; i < m; i++) s[0].insert(i); for(size_t j = 0; j < n; j++) r[0].insert(j); h = f.ForSparseHes(r, s); for(size_t i = 0; i < n; i++) ok &= h[i] == check_h[i]; } /* %$$ $subhead rev_sparse_hes$$ Note the previous call to $code ForSparseJac$$ above stored its results in $icode f$$. $srccode%cpp% */ // compute and test reverse mode { set_vector s(1), h(n); for(size_t i = 0; i < m; i++) s[0].insert(i); h = f.RevSparseHes(n, s); for(size_t i = 0; i < n; i++) ok &= h[i] == check_h[i]; } /* %$$ $subhead Test Result$$ $srccode%cpp% */ return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/CMakeLists.txt0000644000175200017650000000321413057470457020105 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Specifies build type for this directory. Possible values are # empty, Debug, Release, RelWithDebInfo and MinSizeRel SET(CMAKE_BUILD_TYPE DEBUG) # # eigen_sources and CPPAD_HAS_EIGEN SET(sources eigen_mat_inv.cpp eigen_cholesky.cpp eigen_mat_mul.cpp) sources_libs_define(eigen "${sources}" "" HAS_EIGEN) # ADD_EXECUTABLE(example_atomic EXCLUDE_FROM_ALL ${eigen_sources} atomic.cpp checkpoint.cpp extended_ode.cpp for_sparse_hes.cpp for_sparse_jac.cpp forward.cpp get_started.cpp mat_mul.cpp mul_level.cpp norm_sq.cpp ode.cpp reciprocal.cpp rev_sparse_hes.cpp rev_sparse_jac.cpp reverse.cpp set_sparsity.cpp tangent.cpp ) # Extra compiler flags add_cppad_cxx_flags( example_atomic ) # Add the check_example_atomic target ADD_CUSTOM_TARGET(check_example_atomic example_atomic DEPENDS example_atomic ) MESSAGE(STATUS "make check_example_atomic: available") # add to check check_example_depends in parent environment add_to_list(check_example_depends check_example_atomic) SET(check_example_depends "${check_example_depends}" PARENT_SCOPE) cppad-20170000.3/example/atomic/mat_mul.cpp0000644000175200017650000001756013057470457017520 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_mat_mul.cpp$$ $spell mul $$ $section User Atomic Matrix Multiply: Example and Test$$ $head See Also$$ $cref atomic_eigen_mat_mul.cpp$$ $children% cppad/example/mat_mul.hpp %$$ $head Class Definition$$ This example uses the file $cref atomic_mat_mul.hpp$$ which defines matrix multiply as a $cref atomic_base$$ operation. $nospell $head Use Atomic Function$$ $srccode%cpp% */ # include # include bool mat_mul(void) { bool ok = true; using CppAD::AD; using CppAD::vector; size_t i, j; /* %$$ $subhead Constructor$$ $srccode%cpp% */ // ------------------------------------------------------------------- // object that multiplies 2 x 2 matrices atomic_mat_mul afun; /* %$$ $subhead Recording$$ $srccode%cpp% */ // start recording with four independent varables size_t n = 4; vector x(n); vector< AD > ax(n); for(j = 0; j < n; j++) ax[j] = x[j] = j + 1; CppAD::Independent(ax); // ------------------------------------------------------------------ size_t nr_left = 2; size_t n_middle = 2; size_t nc_right = 2; vector< AD > atom_x(3 + (nr_left + nc_right) * n_middle ); // matrix dimensions atom_x[0] = AD( nr_left ); atom_x[1] = AD( n_middle ); atom_x[2] = AD( nc_right ); // left matrix atom_x[3] = ax[0]; // left[0, 0] = x0 atom_x[4] = ax[1]; // left[0, 1] = x1 atom_x[5] = 5.; // left[1, 0] = 5 atom_x[6] = 6.; // left[1, 1] = 6 // right matix atom_x[7] = ax[2]; // right[0, 0] = x2 atom_x[8] = 7.; // right[0, 1] = 7 atom_x[9] = ax[3]; // right[1, 0] = x3 atom_x[10] = 8.; // right[1, 1] = 8 // ------------------------------------------------------------------ /* [ x0 , x1 ] * [ x2 , 7 ] = [ x0*x2 + x1*x3 , x0*7 + x1*8 ] [ 5 , 6 ] [ x3 , 8 ] [ 5*x2 + 6*x3 , 5*7 + 6*8 ] */ vector< AD > atom_y(nr_left * nc_right); afun(atom_x, atom_y); ok &= (atom_y[0] == x[0]*x[2] + x[1]*x[3]) & Variable(atom_y[0]); ok &= (atom_y[1] == x[0]*7. + x[1]*8. ) & Variable(atom_y[1]); ok &= (atom_y[2] == 5.*x[2] + 6.*x[3]) & Variable(atom_y[2]); ok &= (atom_y[3] == 5.*7. + 6.*8. ) & Parameter(atom_y[3]); // ------------------------------------------------------------------ // define the function g : x -> atom_y // g(x) = [ x0*x2 + x1*x3 , x0*7 + x1*8 , 5*x2 + 6*x3 , 5*7 + 6*8 ]^T CppAD::ADFun g(ax, atom_y); /* %$$ $subhead forward$$ $srccode%cpp% */ // Test zero order forward mode evaluation of g(x) size_t m = atom_y.size(); vector y(m); for(j = 0; j < n; j++) x[j] = j + 2; y = g.Forward(0, x); ok &= y[0] == x[0] * x[2] + x[1] * x[3]; ok &= y[1] == x[0] * 7. + x[1] * 8.; ok &= y[2] == 5. * x[2] + 6. * x[3]; ok &= y[3] == 5. * 7. + 6. * 8.; //---------------------------------------------------------------------- // Test first order forward mode evaluation of g'(x) * [1, 2, 3, 4]^T // g'(x) = [ x2, x3, x0, x1 ] // [ 7 , 8, 0, 0 ] // [ 0 , 0, 5, 6 ] // [ 0 , 0, 0, 0 ] CppAD::vector dx(n), dy(m); for(j = 0; j < n; j++) dx[j] = j + 1; dy = g.Forward(1, dx); ok &= dy[0] == 1. * x[2] + 2. * x[3] + 3. * x[0] + 4. * x[1]; ok &= dy[1] == 1. * 7. + 2. * 8. + 3. * 0. + 4. * 0.; ok &= dy[2] == 1. * 0. + 2. * 0. + 3. * 5. + 4. * 6.; ok &= dy[3] == 1. * 0. + 2. * 0. + 3. * 0. + 4. * 0.; //---------------------------------------------------------------------- // Test second order forward mode // g_0^2 (x) = [ 0, 0, 1, 0 ], g_0^2 (x) * [1] = [3] // [ 0, 0, 0, 1 ] [2] [4] // [ 1, 0, 0, 0 ] [3] [1] // [ 0, 1, 0, 0 ] [4] [2] CppAD::vector ddx(n), ddy(m); for(j = 0; j < n; j++) ddx[j] = 0.; ddy = g.Forward(2, ddx); // [1, 2, 3, 4] * g_0^2 (x) * [1, 2, 3, 4]^T = 1*3 + 2*4 + 3*1 + 4*2 ok &= 2. * ddy[0] == 1. * 3. + 2. * 4. + 3. * 1. + 4. * 2.; // for i > 0, [1, 2, 3, 4] * g_i^2 (x) * [1, 2, 3, 4]^T = 0 ok &= ddy[1] == 0.; ok &= ddy[2] == 0.; ok &= ddy[3] == 0.; /* %$$ $subhead reverse$$ $srccode%cpp% */ // Test second order reverse mode CppAD::vector w(m), dw(2 * n); for(i = 0; i < m; i++) w[i] = 0.; w[0] = 1.; dw = g.Reverse(2, w); // g_0'(x) = [ x2, x3, x0, x1 ] ok &= dw[0*2 + 0] == x[2]; ok &= dw[1*2 + 0] == x[3]; ok &= dw[2*2 + 0] == x[0]; ok &= dw[3*2 + 0] == x[1]; // g_0'(x) * [1, 2, 3, 4] = 1 * x2 + 2 * x3 + 3 * x0 + 4 * x1 // g_0^2 (x) * [1, 2, 3, 4] = [3, 4, 1, 2] ok &= dw[0*2 + 1] == 3.; ok &= dw[1*2 + 1] == 4.; ok &= dw[2*2 + 1] == 1.; ok &= dw[3*2 + 1] == 2.; /* %$$ $subhead option$$ $srccode%cpp% */ //---------------------------------------------------------------------- // Test both the boolean and set sparsity at the atomic level for(size_t sparse_index = 0; sparse_index < 2; sparse_index++) { if( sparse_index == 0 ) afun.option( CppAD::atomic_base::bool_sparsity_enum ); else afun.option( CppAD::atomic_base::set_sparsity_enum ); /* %$$ $subhead for_sparse_jac$$ $srccode%cpp% */ // Test forward Jacobian sparsity pattern /* g(x) = [ x0*x2 + x1*x3 , x0*7 + x1*8 , 5*x2 + 6*x3 , 5*7 + 6*8 ]^T so the sparsity pattern should be s[0] = {0, 1, 2, 3} s[1] = {0, 1} s[2] = {2, 3} s[3] = {} */ CppAD::vector< std::set > r(n), s(m); for(j = 0; j < n; j++) { assert( r[j].empty() ); r[j].insert(j); } s = g.ForSparseJac(n, r); for(j = 0; j < n; j++) { // s[0] = {0, 1, 2, 3} ok &= s[0].find(j) != s[0].end(); // s[1] = {0, 1} if( j == 0 || j == 1 ) ok &= s[1].find(j) != s[1].end(); else ok &= s[1].find(j) == s[1].end(); // s[2] = {2, 3} if( j == 2 || j == 3 ) ok &= s[2].find(j) != s[2].end(); else ok &= s[2].find(j) == s[2].end(); } // s[3] == {} ok &= s[3].empty(); /* %$$ $subhead rev_sparse_jac$$ $srccode%cpp% */ // Test reverse Jacobian sparsity pattern for(i = 0; i < m; i++) { s[i].clear(); s[i].insert(i); } r = g.RevSparseJac(m, s); for(j = 0; j < n ; j++) { // r[0] = {0, 1, 2, 3} ok &= r[0].find(j) != r[0].end(); // r[1] = {0, 1} if( j == 0 || j == 1 ) ok &= r[1].find(j) != r[1].end(); else ok &= r[1].find(j) == r[1].end(); // r[2] = {2, 3} if( j == 2 || j == 3 ) ok &= r[2].find(j) != r[2].end(); else ok &= r[2].find(j) == r[2].end(); } // r[3] == {} ok &= r[3].empty(); /* %$$ $subhead rev_sparse_hes$$ $srccode%cpp% */ /* Test reverse Hessian sparsity pattern g_0^2 (x) = [ 0, 0, 1, 0 ] and for i > 0, g_i^2 = 0 [ 0, 0, 0, 1 ] [ 1, 0, 0, 0 ] [ 0, 1, 0, 0 ] so for the sparsity pattern for the first component of g is h[0] = {2} h[1] = {3} h[2] = {0} h[3] = {1} */ CppAD::vector< std::set > h(n), t(1); t[0].clear(); t[0].insert(0); h = g.RevSparseHes(n, t); size_t check[] = {2, 3, 0, 1}; for(j = 0; j < n; j++) { // h[j] = { check[j] } for(i = 0; i < n; i++) { if( i == check[j] ) ok &= h[j].find(i) != h[j].end(); else ok &= h[j].find(i) == h[j].end(); } } t[0].clear(); for( j = 1; j < n; j++) t[0].insert(j); h = g.RevSparseHes(n, t); for(j = 0; j < n; j++) { // h[j] = { } for(i = 0; i < n; i++) ok &= h[j].find(i) == h[j].end(); } //----------------------------------------------------------------- } // end for(size_t sparse_index ... //----------------------------------------------------------------- return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/tangent.cpp0000644000175200017650000003332613057470457017520 0ustar coincoin-web// $Id: tangent.cpp 3821 2016-06-30 02:53:40Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_tangent.cpp$$ $spell Tanh bool $$ $section Tan and Tanh as User Atomic Operations: Example and Test$$ $mindex tangent operation$$ $head Theory$$ The code below uses the $cref tan_forward$$ and $cref tan_reverse$$ to implement the tangent and hyperbolic tangent functions as user atomic operations. $head sparsity$$ This atomic operation can use both set and bool sparsity patterns. $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // Begin empty namespace using CppAD::vector; // // a utility to compute the union of two sets. using CppAD::set_union; // class atomic_tangent : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ private: const bool hyperbolic_; // is this hyperbolic tangent public: // constructor atomic_tangent(const char* name, bool hyperbolic) : CppAD::atomic_base(name), hyperbolic_(hyperbolic) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD bool forward( size_t p , size_t q , const vector& vx , vector& vzy , const vector& tx , vector& tzy ) { size_t q1 = q + 1; # ifndef NDEBUG size_t n = tx.size() / q1; size_t m = tzy.size() / q1; # endif assert( n == 1 ); assert( m == 2 ); assert( p <= q ); size_t j, k; // check if this is during the call to old_tan(id, ax, ay) if( vx.size() > 0 ) { // set variable flag for both y an z vzy[0] = vx[0]; vzy[1] = vx[0]; } if( p == 0 ) { // z^{(0)} = tan( x^{(0)} ) or tanh( x^{(0)} ) if( hyperbolic_ ) tzy[0] = tanh( tx[0] ); else tzy[0] = tan( tx[0] ); // y^{(0)} = z^{(0)} * z^{(0)} tzy[q1 + 0] = tzy[0] * tzy[0]; p++; } for(j = p; j <= q; j++) { float j_inv = 1.f / float(j); if( hyperbolic_ ) j_inv = - j_inv; // z^{(j)} = x^{(j)} +- sum_{k=1}^j k x^{(k)} y^{(j-k)} / j tzy[j] = tx[j]; for(k = 1; k <= j; k++) tzy[j] += tx[k] * tzy[q1 + j-k] * k * j_inv; // y^{(j)} = sum_{k=0}^j z^{(k)} z^{(j-k)} tzy[q1 + j] = 0.; for(k = 0; k <= j; k++) tzy[q1 + j] += tzy[k] * tzy[j-k]; } // All orders are implemented and there are no possible errors return true; } /* %$$ $head reverse$$ $srccode%cpp% */ // reverse mode routine called by CppAD virtual bool reverse( size_t q , const vector& tx , const vector& tzy , vector& px , const vector& pzy ) { size_t q1 = q + 1; # ifndef NDEBUG size_t n = tx.size() / q1; size_t m = tzy.size() / q1; # endif assert( px.size() == n * q1 ); assert( pzy.size() == m * q1 ); assert( n == 1 ); assert( m == 2 ); size_t j, k; // copy because partials w.r.t. y and z need to change vector qzy = pzy; // initialize accumultion of reverse mode partials for(k = 0; k < q1; k++) px[k] = 0.; // eliminate positive orders for(j = q; j > 0; j--) { float j_inv = 1.f / float(j); if( hyperbolic_ ) j_inv = - j_inv; // H_{x^{(k)}} += delta(j-k) +- H_{z^{(j)} y^{(j-k)} * k / j px[j] += qzy[j]; for(k = 1; k <= j; k++) px[k] += qzy[j] * tzy[q1 + j-k] * k * j_inv; // H_{y^{j-k)} += +- H_{z^{(j)} x^{(k)} * k / j for(k = 1; k <= j; k++) qzy[q1 + j-k] += qzy[j] * tx[k] * k * j_inv; // H_{z^{(k)}} += H_{y^{(j-1)}} * z^{(j-k-1)} * 2. for(k = 0; k < j; k++) qzy[k] += qzy[q1 + j-1] * tzy[j-k-1] * 2.f; } // eliminate order zero if( hyperbolic_ ) px[0] += qzy[0] * (1.f - tzy[q1 + 0]); else px[0] += qzy[0] * (1.f + tzy[q1 + 0]); return true; } /* %$$ $head for_sparse_jac$$ $srccode%cpp% */ // forward Jacobian sparsity routine called by CppAD virtual bool for_sparse_jac( size_t p , const vector& r , vector& s , const vector& x ) { # ifndef NDEBUG size_t n = r.size() / p; size_t m = s.size() / p; # endif assert( n == x.size() ); assert( n == 1 ); assert( m == 2 ); // sparsity for S(x) = f'(x) * R for(size_t j = 0; j < p; j++) { s[0 * p + j] = r[j]; s[1 * p + j] = r[j]; } return true; } // forward Jacobian sparsity routine called by CppAD virtual bool for_sparse_jac( size_t p , const vector< std::set >& r , vector< std::set >& s , const vector& x ) { # ifndef NDEBUG size_t n = r.size(); size_t m = s.size(); # endif assert( n == x.size() ); assert( n == 1 ); assert( m == 2 ); // sparsity for S(x) = f'(x) * R s[0] = r[0]; s[1] = r[0]; return true; } /* %$$ $head rev_sparse_jac$$ $srccode%cpp% */ // reverse Jacobian sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t p , const vector& rt , vector& st , const vector& x ) { # ifndef NDEBUG size_t n = st.size() / p; size_t m = rt.size() / p; # endif assert( n == 1 ); assert( m == 2 ); assert( n == x.size() ); // sparsity for S(x)^T = f'(x)^T * R^T for(size_t j = 0; j < p; j++) st[j] = rt[0 * p + j] | rt[1 * p + j]; return true; } // reverse Jacobian sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t p , const vector< std::set >& rt , vector< std::set >& st , const vector& x ) { # ifndef NDEBUG size_t n = st.size(); size_t m = rt.size(); # endif assert( n == 1 ); assert( m == 2 ); assert( n == x.size() ); // sparsity for S(x)^T = f'(x)^T * R^T st[0] = set_union(rt[0], rt[1]); return true; } /* %$$ $head rev_sparse_hes$$ $srccode%cpp% */ // reverse Hessian sparsity routine called by CppAD virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t p , const vector& r , const vector& u , vector& v , const vector& x ) { # ifndef NDEBUG size_t m = s.size(); size_t n = t.size(); # endif assert( x.size() == n ); assert( r.size() == n * p ); assert( u.size() == m * p ); assert( v.size() == n * p ); assert( n == 1 ); assert( m == 2 ); // There are no cross term second derivatives for this case, // so it is not necessary to vx. // sparsity for T(x) = S(x) * f'(x) t[0] = s[0] | s[1]; // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate the sparsity for U, note both components // of f'(x) may be non-zero; size_t j; for(j = 0; j < p; j++) v[j] = u[ 0 * p + j ] | u[ 1 * p + j ]; // include forward Jacobian sparsity in Hessian sparsity // (note sparsty for f''(x) * R same as for R) if( s[0] | s[1] ) { for(j = 0; j < p; j++) { // Visual Studio 2013 generates warning without bool below v[j] |= bool( r[j] ); } } return true; } // reverse Hessian sparsity routine called by CppAD virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t p , const vector< std::set >& r , const vector< std::set >& u , vector< std::set >& v , const vector& x ) { # ifndef NDEBUG size_t m = s.size(); size_t n = t.size(); # endif assert( x.size() == n ); assert( r.size() == n ); assert( u.size() == m ); assert( v.size() == n ); assert( n == 1 ); assert( m == 2 ); // There are no cross term second derivatives for this case, // so it is not necessary to vx. // sparsity for T(x) = S(x) * f'(x) t[0] = s[0] | s[1]; // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate the sparsity for U, note both components // of f'(x) may be non-zero; v[0] = set_union(u[0], u[1]); // include forward Jacobian sparsity in Hessian sparsity // (note sparsty for f''(x) * R same as for R) if( s[0] | s[1] ) v[0] = set_union(v[0], r[0]); return true; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of atomic_tangent class } // End empty namespace /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool tangent(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; float eps = 10.f * CppAD::numeric_limits::epsilon(); /* %$$ $subhead Constructor$$ $srccode%cpp% */ // -------------------------------------------------------------------- // Creater a tan and tanh object atomic_tangent my_tan("my_tan", false), my_tanh("my_tanh", true); /* %$$ $subhead Recording$$ $srccode%cpp% */ // domain space vector size_t n = 1; float x0 = 0.5; CppAD::vector< AD > ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 3; CppAD::vector< AD > af(m); // temporary vector for computations // (my_tan and my_tanh computes tan or tanh and its square) CppAD::vector< AD > az(2); // call atomic tan function and store tan(x) in f[0] (ignore tan(x)^2) my_tan(ax, az); af[0] = az[0]; // call atomic tanh function and store tanh(x) in f[1] (ignore tanh(x)^2) my_tanh(ax, az); af[1] = az[0]; // put a constant in f[2] = tanh(1.) (for sparsity pattern testing) CppAD::vector< AD > one(1); one[0] = 1.; my_tanh(one, az); af[2] = az[0]; // create f: x -> f and stop tape recording CppAD::ADFun F; F.Dependent(ax, af); /* %$$ $subhead forward$$ $srccode%cpp% */ // check function value float tan = std::tan(x0); ok &= NearEqual(af[0] , tan, eps, eps); float tanh = std::tanh(x0); ok &= NearEqual(af[1] , tanh, eps, eps); // check zero order forward CppAD::vector x(n), f(m); x[0] = x0; f = F.Forward(0, x); ok &= NearEqual(f[0] , tan, eps, eps); ok &= NearEqual(f[1] , tanh, eps, eps); // compute first partial of f w.r.t. x[0] using forward mode CppAD::vector dx(n), df(m); dx[0] = 1.; df = F.Forward(1, dx); /* %$$ $subhead reverse$$ $srccode%cpp% */ // compute derivative of tan - tanh using reverse mode CppAD::vector w(m), dw(n); w[0] = 1.; w[1] = 1.; w[2] = 0.; dw = F.Reverse(1, w); // tan'(x) = 1 + tan(x) * tan(x) // tanh'(x) = 1 - tanh(x) * tanh(x) float tanp = 1.f + tan * tan; float tanhp = 1.f - tanh * tanh; ok &= NearEqual(df[0], tanp, eps, eps); ok &= NearEqual(df[1], tanhp, eps, eps); ok &= NearEqual(dw[0], w[0]*tanp + w[1]*tanhp, eps, eps); // compute second partial of f w.r.t. x[0] using forward mode CppAD::vector ddx(n), ddf(m); ddx[0] = 0.; ddf = F.Forward(2, ddx); // compute second derivative of tan - tanh using reverse mode CppAD::vector ddw(2); ddw = F.Reverse(2, w); // tan''(x) = 2 * tan(x) * tan'(x) // tanh''(x) = - 2 * tanh(x) * tanh'(x) // Note that second order Taylor coefficient for u half the // corresponding second derivative. float two = 2; float tanpp = two * tan * tanp; float tanhpp = - two * tanh * tanhp; ok &= NearEqual(two * ddf[0], tanpp, eps, eps); ok &= NearEqual(two * ddf[1], tanhpp, eps, eps); ok &= NearEqual(ddw[0], w[0]*tanp + w[1]*tanhp , eps, eps); ok &= NearEqual(ddw[1], w[0]*tanpp + w[1]*tanhpp, eps, eps); /* %$$ $subhead for_sparse_jac$$ $srccode%cpp% */ // Forward mode computation of sparsity pattern for F. size_t p = n; // user vectorBool because m and n are small CppAD::vectorBool r1(p), s1(m * p); r1[0] = true; // propagate sparsity for x[0] s1 = F.ForSparseJac(p, r1); ok &= (s1[0] == true); // f[0] depends on x[0] ok &= (s1[1] == true); // f[1] depends on x[0] ok &= (s1[2] == false); // f[2] does not depend on x[0] /* %$$ $subhead rev_sparse_jac$$ $srccode%cpp% */ // Reverse mode computation of sparsity pattern for F. size_t q = m; CppAD::vectorBool s2(q * m), r2(q * n); // Sparsity pattern for identity matrix size_t i, j; for(i = 0; i < q; i++) { for(j = 0; j < m; j++) s2[i * q + j] = (i == j); } r2 = F.RevSparseJac(q, s2); ok &= (r2[0] == true); // f[0] depends on x[0] ok &= (r2[1] == true); // f[1] depends on x[0] ok &= (r2[2] == false); // f[2] does not depend on x[0] /* %$$ $subhead rev_sparse_hes$$ $srccode%cpp% */ // Hessian sparsity for f[0] CppAD::vectorBool s3(m), h(p * n); s3[0] = true; s3[1] = false; s3[2] = false; h = F.RevSparseHes(p, s3); ok &= (h[0] == true); // Hessian is non-zero // Hessian sparsity for f[2] s3[0] = false; s3[2] = true; h = F.RevSparseHes(p, s3); 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Bell # # CppAD is distributed under multiple licenses. 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_for_sparse_hes.cpp$$ $section Atomic Forward Hessian Sparsity: Example and Test$$ $head Purpose$$ This example demonstrates calculation of the forward Hessian sparsity pattern for an atomic operation. $head function$$ For this example, the atomic function $latex f : \B{R}^3 \rightarrow \B{R}^2$$ is defined by $latex \[ f( x ) = \left( \begin{array}{c} x_2 * x_2 \\ x_0 * x_1 \end{array} \right) \] $$ The Hessians of the component functions are $latex \[ f_0^{(2)} ( x ) = \left( \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 2 \end{array} \right) \W{,} f_1^{(2)} ( x ) = \left( \begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right) \] $$ $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // class atomic_for_sparse_hes : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_for_sparse_hes(const std::string& name) : // this example only uses pack sparsity patterns CppAD::atomic_base(name, pack_sparsity_enum) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { # ifndef NDEBUG size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); # endif assert( n == 3 ); assert( m == 2 ); // return flag bool ok = q == 0; if( ! ok ) return ok; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) { vy[0] = vx[0]; vy[1] = vx[0] || vy[0]; } // Order zero forward mode. // This case must always be implemented // f(x) = [ x_0 * x_0 ] // [ x_0 * x_1 ] assert( p <= 0 ); if( p <= 0 ) { ty[0] = tx[2] * tx[2]; ty[1] = tx[0] * tx[1]; } return ok; } /* %$$ $head for_sparse_jac$$ $srccode%cpp% */ // forward Jacobian sparsity routine called by CppAD virtual bool for_sparse_jac( size_t q , const CppAD::vectorBool& r , CppAD::vectorBool& s , const vector& x ) { // This function needed because we are using ForSparseHes // with afun.option( CppAD::atomic_base::pack_sparsity_enum ) # ifndef NDEBUG size_t n = r.size() / q; size_t m = s.size() / q; # endif assert( x.size() == n ); assert( n == 3 ); assert( m == 2 ); // f'(x) = [ 0, 0, 2 x_2 ] // [ x_1, x_0, 0 ] // sparsity for first row of S(x) = f'(x) * R size_t i = 0; for(size_t j = 0; j < q; j++) s[ i * q + j ] = r[ 2 * q + j ]; // sparsity for second row of S(x) = f'(x) * R i = 1; for(size_t j = 0; j < q; j++) s[ i * q + j ] = r[ 0 * q + j ] | r[ 1 * q + j]; return true; } /* %$$ $head rev_sparse_jac$$ $srccode%cpp% */ // reverse Jacobian sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t q , const CppAD::vectorBool& rt , CppAD::vectorBool& st , const vector& x ) { // This function needed because we are using ForSparseHes // with afun.option( CppAD::atomic_base::pack_sparsity_enum ) # ifndef NDEBUG size_t m = rt.size() / q; size_t n = st.size() / q; # endif assert( x.size() == n ); assert( n == 3 ); assert( m == 2 ); // [ 0, x_1 ] // f'(x)^T = [ 0, x_0 ] // [ 2 x_2, 0 ] // sparsity for first row of S(x)^T = f'(x)^T * R^T size_t i = 0; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 1 * q + j ]; // sparsity for second row of S(x)^T = f'(x)^T * R^T i = 1; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 1 * q + j ]; // sparsity for third row of S(x)^T = f'(x)^T * R^T i = 2; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 0 * q + j ]; return true; } /* %$$ $head for_sparse_hes$$ $srccode%cpp% */ // forward Hessian sparsity routine called by CppAD virtual bool for_sparse_hes( const vector& vx, const vector& r , const vector& s , CppAD::vectorBool& h , const vector& x ) { // This function needed because we are using RevSparseHes // with afun.option( CppAD::atomic_base::pack_sparsity_enum ) size_t n = r.size(); # ifndef NDEBUG size_t m = s.size(); # endif assert( x.size() == n ); assert( n == 3 ); assert( m == 2 ); assert( h.size() == n * n ); // [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] // f_0''(x) = [ 0 , 0 , 0 ] f_1^{(2)} (x) = [ 1 , 0 , 0 ] // [ 0 , 0 , 2 ] [ 0 , 0 , 0 ] // initial entire matrix as false for(size_t i = 0; i < n * n; i++) h[i] = false; // component (2, 2) h[ 2 * n + 2 ] = s[0] & r[2]; // components (1, 0) and (0, 1) h[ 1 * n + 0 ] = s[1] & r[0] & r[1]; h[ 0 * n + 1 ] = s[1] & r[0] & r[1]; return true; } }; // End of atomic_for_sparse_hes class /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool use_atomic_for_sparse_hes(bool x_1_variable) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // // Create the atomic for_sparse_hes object atomic_for_sparse_hes afun("atomic_for_sparse_hes"); // // Create the function f(u) // // domain space vector size_t n = 3; double x_0 = 1.00; double x_1 = 2.00; double x_2 = 3.00; vector< AD > au(n); au[0] = x_0; au[1] = x_1; au[2] = x_2; // declare independent variables and start tape recording CppAD::Independent(au); // range space vector size_t m = 2; vector< AD > ay(m); // call user function vector< AD > ax(n); ax[0] = au[0]; ax[2] = au[2]; if( x_1_variable ) ax[1] = au[1]; else ax[1] = x_1; afun(ax, ay); // y = [ x_2 * x_2 , x_0 * x_1 ]^T // create f: u -> y and stop tape recording CppAD::ADFun f; f.Dependent (au, ay); // f(u) = y // // check function value double check = x_2 * x_2; ok &= NearEqual( Value(ay[0]) , check, eps, eps); check = x_0 * x_1; ok &= NearEqual( Value(ay[1]) , check, eps, eps); // check zero order forward mode size_t q; vector xq(n), yq(m); q = 0; xq[0] = x_0; xq[1] = x_1; xq[2] = x_2; yq = f.Forward(q, xq); check = x_2 * x_2; ok &= NearEqual(yq[0] , check, eps, eps); check = x_0 * x_1; ok &= NearEqual(yq[1] , check, eps, eps); // forward sparse Hessian CppAD::vectorBool r(n), s(m), h(n * n); for(size_t j = 0; j < n; j++) r[j] = true; for(size_t i = 0; i < m; i++) s[i] = true; h = f.ForSparseHes(r, s); // check result CppAD::vectorBool check_h(n * n); for(size_t i = 0; i < n * n; i++) check_h[i] = false; check_h[ 2 * n + 2 ] = true; if( x_1_variable ) { check_h[0 * n + 1] = true; check_h[1 * n + 0] = true; } for(size_t i = 0; i < n * n; i++) ok &= h[ i ] == check_h[ i ]; // return ok; } } // End empty namespace /* %$$ $head Test with x_1 Both a Variable and a Parameter$$ $srccode%cpp% */ bool for_sparse_hes(void) { bool ok = true; // test with x_1 a variable ok &= use_atomic_for_sparse_hes(true); // test with x_1 a parameter ok &= use_atomic_for_sparse_hes(false); return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/forward.cpp0000644000175200017650000001761113057470457017523 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_forward.cpp$$ $spell Jacobian $$ $section Atomic Forward: Example and Test$$ $head Purpose$$ This example demonstrates forward mode derivative calculation using an atomic operation. $head function$$ For this example, the atomic function $latex f : \B{R}^3 \rightarrow \B{R}^2$$ is defined by $latex \[ f(x) = \left( \begin{array}{c} x_2 * x_2 \\ x_0 * x_1 \end{array} \right) \] $$ The corresponding Jacobian is $latex \[ f^{(1)} (x) = \left( \begin{array}{ccc} 0 & 0 & 2 x_2 \\ x_1 & x_0 & 0 \end{array} \right) \] $$ The Hessians of the component functions are $latex \[ f_0^{(2)} ( x ) = \left( \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 2 \end{array} \right) \W{,} f_1^{(2)} ( x ) = \left( \begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right) \] $$ $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // class atomic_forward : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_forward(const std::string& name) : // this example does not use sparsity patterns CppAD::atomic_base(name) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { size_t q1 = q + 1; # ifndef NDEBUG size_t n = tx.size() / q1; size_t m = ty.size() / q1; # endif assert( n == 3 ); assert( m == 2 ); assert( p <= q ); // this example only implements up to second order forward mode bool ok = q <= 2; if( ! ok ) return ok; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) { vy[0] = vx[2]; vy[1] = vx[0] || vx[1]; } // ------------------------------------------------------------------ // Zero forward mode. // This case must always be implemented // f(x) = [ x_2 * x_2 ] // [ x_0 * x_1 ] // y^0 = f( x^0 ) if( p <= 0 ) { // y_0^0 = x_2^0 * x_2^0 ty[0 * q1 + 0] = tx[2 * q1 + 0] * tx[2 * q1 + 0]; // y_1^0 = x_0^0 * x_1^0 ty[1 * q1 + 0] = tx[0 * q1 + 0] * tx[1 * q1 + 0]; } if( q <= 0 ) return ok; // ------------------------------------------------------------------ // First order one forward mode. // This case is needed if first order forward mode is used. // f'(x) = [ 0, 0, 2 * x_2 ] // [ x_1, x_0, 0 ] // y^1 = f'(x^0) * x^1 if( p <= 1 ) { // y_0^1 = 2 * x_2^0 * x_2^1 ty[0 * q1 + 1] = 2.0 * tx[2 * q1 + 0] * tx[2 * q1 + 1]; // y_1^1 = x_1^0 * x_0^1 + x_0^0 * x_1^1 ty[1 * q1 + 1] = tx[1 * q1 + 0] * tx[0 * q1 + 1]; ty[1 * q1 + 1] += tx[0 * q1 + 0] * tx[1 * q1 + 1]; } if( q <= 1 ) return ok; // ------------------------------------------------------------------ // Second order forward mode. // This case is neede if second order forwrd mode is used. // f'(x) = [ 0, 0, 2 x_2 ] // [ x_1, x_0, 0 ] // // [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] // f_0''(x) = [ 0 , 0 , 0 ] f_1^{(2)} (x) = [ 1 , 0 , 0 ] // [ 0 , 0 , 2 ] [ 0 , 0 , 0 ] // // y_0^2 = x^1 * f_0''( x^0 ) x^1 / 2! + f_0'( x^0 ) x^2 // = ( x_2^1 * 2.0 * x_2^1 ) / 2! // + 2.0 * x_2^0 * x_2^2 ty[0 * q1 + 2] = tx[2 * q1 + 1] * tx[2 * q1 + 1]; ty[0 * q1 + 2] += 2.0 * tx[2 * q + 0] * tx[2 * q1 + 2]; // // y_1^2 = x^1 * f_1''( x^0 ) x^1 / 2! + f_1'( x^0 ) x^2 // = ( x_1^1 * x_0^1 + x_0^1 * x_1^1) / 2 // + x_1^0 * x_0^2 + x_0^0 + x_1^2 ty[1 * q1 + 2] = tx[1 * q1 + 1] * tx[0 * q1 + 1]; ty[1 * q1 + 2] += tx[1 * q1 + 0] * tx[0 * q1 + 2]; ty[1 * q1 + 2] += tx[0 * q1 + 0] * tx[1 * q1 + 2]; // ------------------------------------------------------------------ return ok; } }; } // End empty namespace /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool forward(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // // Create the atomic_forward object atomic_forward afun("atomic_forward"); // // Create the function f(u) // // domain space vector size_t n = 3; double x_0 = 1.00; double x_1 = 2.00; double x_2 = 3.00; vector< AD > au(n); au[0] = x_0; au[1] = x_1; au[2] = x_2; // declare independent variables and start tape recording CppAD::Independent(au); // range space vector size_t m = 2; vector< AD > ay(m); // call user function vector< AD > ax = au; afun(ax, ay); // create f: u -> y and stop tape recording CppAD::ADFun f; f.Dependent (au, ay); // y = f(u) // // check function value double check = x_2 * x_2; ok &= NearEqual( Value(ay[0]) , check, eps, eps); check = x_0 * x_1; ok &= NearEqual( Value(ay[1]) , check, eps, eps); // -------------------------------------------------------------------- // zero order forward // vector x0(n), y0(m); x0[0] = x_0; x0[1] = x_1; x0[2] = x_2; y0 = f.Forward(0, x0); check = x_2 * x_2; ok &= NearEqual(y0[0] , check, eps, eps); check = x_0 * x_1; ok &= NearEqual(y0[1] , check, eps, eps); // -------------------------------------------------------------------- // first order forward // // value of Jacobian of f double check_jac[] = { 0.0, 0.0, 2.0 * x_2, x_1, x_0, 0.0 }; vector x1(n), y1(m); // check first order forward mode for(size_t j = 0; j < n; j++) x1[j] = 0.0; for(size_t j = 0; j < n; j++) { // compute partial in j-th component direction x1[j] = 1.0; y1 = f.Forward(1, x1); x1[j] = 0.0; // check this direction for(size_t i = 0; i < m; i++) ok &= NearEqual(y1[i], check_jac[i * n + j], eps, eps); } // -------------------------------------------------------------------- // second order forward // // value of Hessian of f_0 double check_hes_0[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0 }; // // value of Hessian of f_1 double check_hes_1[] = { 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }; vector x2(n), y2(m); for(size_t j = 0; j < n; j++) x2[j] = 0.0; // compute diagonal elements of the Hessian for(size_t j = 0; j < n; j++) { // first order forward in j-th direction x1[j] = 1.0; f.Forward(1, x1); y2 = f.Forward(2, x2); // check this element of Hessian diagonal ok &= NearEqual(y2[0], check_hes_0[j * n + j] / 2.0, eps, eps); ok &= NearEqual(y2[1], check_hes_1[j * n + j] / 2.0, eps, eps); // for(size_t k = 0; k < n; k++) if( k != j ) { x1[k] = 1.0; f.Forward(1, x1); y2 = f.Forward(2, x2); // // y2 = (H_jj + H_kk + H_jk + H_kj) / 2.0 // y2 = (H_jj + H_kk) / 2.0 + H_jk // double H_jj = check_hes_0[j * n + j]; double H_kk = check_hes_0[k * n + k]; double H_jk = y2[0] - (H_kk + H_jj) / 2.0; ok &= NearEqual(H_jk, check_hes_0[j * n + k], eps, eps); // H_jj = check_hes_1[j * n + j]; H_kk = check_hes_1[k * n + k]; H_jk = y2[1] - (H_kk + H_jj) / 2.0; ok &= NearEqual(H_jk, check_hes_1[j * n + k], eps, eps); // x1[k] = 0.0; } x1[j] = 0.0; } // -------------------------------------------------------------------- return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/eigen_mat_inv.cpp0000644000175200017650000001401213057470457020653 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_eigen_mat_inv.cpp$$ $spell mul Eigen $$ $section Atomic Eigen Matrix Inverse: Example and Test$$ $head Description$$ The $cref ADFun$$ function object $icode f$$ for this example is $latex \[ f(x) = \left( \begin{array}{cc} x_0 & 0 \\ 0 & x_1 \end{array} \right)^{-1} \left( \begin{array}{c} 0 \\ x_2 \end{array} \right) = \left( \begin{array}{c} 0 \\ x_2 / x_1 ) \end{array} \right) \] $$ $children% cppad/example/eigen_mat_inv.hpp %$$ $head Class Definition$$ This example uses the file $cref atomic_eigen_mat_inv.hpp$$ which defines matrix multiply as a $cref atomic_base$$ operation. $nospell $head Use Atomic Function$$ $srccode%cpp% */ # include # include # include bool eigen_mat_inv(void) { typedef double scalar; typedef CppAD::AD ad_scalar; typedef typename atomic_eigen_mat_inv::ad_matrix ad_matrix; // bool ok = true; scalar eps = 10. * std::numeric_limits::epsilon(); using CppAD::NearEqual; // /* %$$ $subhead Constructor$$ $srccode%cpp% */ // ------------------------------------------------------------------- // object that multiplies matrices atomic_eigen_mat_mul mat_mul; // ------------------------------------------------------------------- // object that computes inverse of a square matrix atomic_eigen_mat_inv mat_inv; // ------------------------------------------------------------------- // declare independent variable vector x size_t n = 3; CPPAD_TESTVECTOR(ad_scalar) ad_x(n); for(size_t j = 0; j < n; j++) ad_x[j] = ad_scalar(j + 1); CppAD::Independent(ad_x); // ------------------------------------------------------------------- // left = [ x[0] 0 ] // [ 0 x[1] ] size_t nr_left = 2; ad_matrix ad_left(nr_left, nr_left); ad_left(0, 0) = ad_x[0]; ad_left(0, 1) = ad_scalar(0.0); ad_left(1, 0) = ad_scalar(0.0); ad_left(1, 1) = ad_x[1]; // ------------------------------------------------------------------- // right = [ 0 , x[2] ]^T size_t nc_right = 1; ad_matrix ad_right(nr_left, nc_right); ad_right(0, 0) = ad_scalar(0.0); ad_right(1, 0) = ad_x[2]; // ------------------------------------------------------------------- // use atomic operation to compute left^{-1} ad_matrix ad_left_inv = mat_inv.op(ad_left); // use atomic operation to multiply left^{-1} * right ad_matrix ad_result = mat_mul.op(ad_left_inv, ad_right); // ------------------------------------------------------------------- // declare the dependent variable vector y size_t m = 2; CPPAD_TESTVECTOR(ad_scalar) ad_y(2); for(size_t i = 0; i < m; i++) ad_y[i] = ad_result(i, 0); CppAD::ADFun f(ad_x, ad_y); // ------------------------------------------------------------------- // check zero order forward mode CPPAD_TESTVECTOR(scalar) x(n), y(m); for(size_t i = 0; i < n; i++) x[i] = scalar(i + 2); y = f.Forward(0, x); ok &= NearEqual(y[0], 0.0, eps, eps); ok &= NearEqual(y[1], x[2] / x[1], eps, eps); // ------------------------------------------------------------------- // check first order forward mode CPPAD_TESTVECTOR(scalar) x1(n), y1(m); x1[0] = 1.0; x1[1] = 0.0; x1[2] = 0.0; y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], 0.0, eps, eps); ok &= NearEqual(y1[1], 0.0, eps, eps); x1[0] = 0.0; x1[1] = 0.0; x1[2] = 1.0; y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], 0.0, eps, eps); ok &= NearEqual(y1[1], 1.0 / x[1], eps, eps); x1[0] = 0.0; x1[1] = 1.0; x1[2] = 0.0; y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], 0.0, eps, eps); ok &= NearEqual(y1[1], - x[2] / (x[1]*x[1]), eps, eps); // ------------------------------------------------------------------- // check second order forward mode CPPAD_TESTVECTOR(scalar) x2(n), y2(m); x2[0] = 0.0; x2[1] = 0.0; x2[2] = 0.0; scalar f1_x1_x1 = 2.0 * x[2] / (x[1] * x[1] * x[1] ); y2 = f.Forward(2, x2); ok &= NearEqual(y2[0], 0.0, eps, eps); ok &= NearEqual(y2[1], f1_x1_x1 / 2.0, eps, eps); // ------------------------------------------------------------------- // check first order reverse CPPAD_TESTVECTOR(scalar) w(m), d1w(n); w[0] = 1.0; w[1] = 0.0; d1w = f.Reverse(1, w); ok &= NearEqual(d1w[0], 0.0, eps, eps); ok &= NearEqual(d1w[1], 0.0, eps, eps); ok &= NearEqual(d1w[2], 0.0, eps, eps); w[0] = 0.0; w[1] = 1.0; d1w = f.Reverse(1, w); ok &= NearEqual(d1w[0], 0.0, eps, eps); ok &= NearEqual(d1w[1], - x[2] / (x[1]*x[1]), eps, eps); ok &= NearEqual(d1w[2], 1.0 / x[1], eps, eps); // ------------------------------------------------------------------- // check second order reverse CPPAD_TESTVECTOR(scalar) d2w(2 * n); d2w = f.Reverse(2, w); // partial f_1 w.r.t x_0 ok &= NearEqual(d2w[0 * 2 + 0], 0.0, eps, eps); // partial f_1 w.r.t x_1 ok &= NearEqual(d2w[1 * 2 + 0], - x[2] / (x[1]*x[1]), eps, eps); // partial f_1 w.r.t x_2 ok &= NearEqual(d2w[2 * 2 + 0], 1.0 / x[1], eps, eps); // partial f_1 w.r.t x_1, x_0 ok &= NearEqual(d2w[0 * 2 + 1], 0.0, eps, eps); // partial f_1 w.r.t x_1, x_1 ok &= NearEqual(d2w[1 * 2 + 1], f1_x1_x1, eps, eps); // partial f_1 w.r.t x_1, x_2 ok &= NearEqual(d2w[2 * 2 + 1], - 1.0 / (x[1]*x[1]), eps, eps); // ------------------------------------------------------------------- return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/get_started.cpp0000644000175200017650000000704213057470457020361 0ustar coincoin-web// $Id: get_started.cpp 3814 2016-04-18 14:26:10Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_get_started.cpp$$ $section Getting Started with Atomic Operations: Example and Test$$ $head Purpose$$ This example demonstrates the minimal amount of information necessary for a $cref atomic_base$$ operation. $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector class atomic_get_started : public CppAD::atomic_base { /* %$$ $head Constructor$$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_get_started(const std::string& name) : // this example does not use any sparsity patterns CppAD::atomic_base(name) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { # ifndef NDEBUG size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); # endif assert( n == 1 ); assert( m == 1 ); // return flag bool ok = q == 0; if( ! ok ) return ok; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) vy[0] = vx[0]; // Order zero forward mode. // This case must always be implemented // y^0 = f( x^0 ) = 1 / x^0 double f = 1. / tx[0]; if( p <= 0 ) ty[0] = f; return ok; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of atomic_get_started class } // End empty namespace /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool get_started(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); /* %$$ $subhead Constructor$$ $srccode%cpp% */ // Create the atomic get_started object atomic_get_started afun("atomic_get_started"); /* %$$ $subhead Recording$$ $srccode%cpp% */ // Create the function f(x) // // domain space vector size_t n = 1; double x0 = 0.5; vector< AD > ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; vector< AD > ay(m); // call user function and store get_started(x) in au[0] vector< AD > au(m); afun(ax, au); // u = 1 / x // now use AD division to invert to invert the operation ay[0] = 1.0 / au[0]; // y = 1 / u = x // create f: x -> y and stop tape recording CppAD::ADFun f; f.Dependent (ax, ay); // f(x) = x /* %$$ $subhead forward$$ $srccode%cpp% */ // check function value double check = x0; ok &= NearEqual( Value(ay[0]) , check, eps, eps); // check zero order forward mode size_t q; vector x_q(n), y_q(m); q = 0; x_q[0] = x0; y_q = f.Forward(q, x_q); ok &= NearEqual(y_q[0] , check, eps, eps); return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/eigen_mat_mul.cpp0000644000175200017650000001646513057470457020672 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_eigen_mat_mul.cpp$$ $spell mul Eigen $$ $section Atomic Eigen Matrix Multiply: Example and Test$$ $head Description$$ The $cref ADFun$$ function object $icode f$$ for this example is $latex \[ f(x) = \left( \begin{array}{cc} 0 & 0 \\ 1 & 2 \\ x_0 & x_1 \end{array} \right) \left( \begin{array}{c} x_0 \\ x_1 \end{array} \right) = \left( \begin{array}{c} 0 \\ x_0 + 2 x_1 \\ x_0 x_0 + x_1 x_1 ) \end{array} \right) \] $$ $children% cppad/example/eigen_mat_mul.hpp %$$ $head Class Definition$$ This example uses the file $cref atomic_eigen_mat_mul.hpp$$ which defines matrix multiply as a $cref atomic_base$$ operation. $nospell $head Use Atomic Function$$ $srccode%cpp% */ # include # include bool eigen_mat_mul(void) { // typedef double scalar; typedef CppAD::AD ad_scalar; typedef typename atomic_eigen_mat_mul::ad_matrix ad_matrix; // bool ok = true; scalar eps = 10. * std::numeric_limits::epsilon(); using CppAD::NearEqual; // /* %$$ $subhead Constructor$$ $srccode%cpp% */ // ------------------------------------------------------------------- // object that multiplies arbitrary matrices atomic_eigen_mat_mul mat_mul; // ------------------------------------------------------------------- // declare independent variable vector x size_t n = 2; CPPAD_TESTVECTOR(ad_scalar) ad_x(n); for(size_t j = 0; j < n; j++) ad_x[j] = ad_scalar(j); CppAD::Independent(ad_x); // ------------------------------------------------------------------- // [ 0 0 ] // left = [ 1 2 ] // [ x[0] x[1] ] size_t nr_left = 3; size_t n_middle = 2; ad_matrix ad_left(nr_left, n_middle); ad_left(0, 0) = ad_scalar(0.0); ad_left(0, 1) = ad_scalar(0.0); ad_left(1, 0) = ad_scalar(1.0); ad_left(1, 1) = ad_scalar(2.0); ad_left(2, 0) = ad_x[0]; ad_left(2, 1) = ad_x[1]; // ------------------------------------------------------------------- // right = [ x[0] , x[1] ]^T size_t nc_right = 1; ad_matrix ad_right(n_middle, nc_right); ad_right(0, 0) = ad_x[0]; ad_right(1, 0) = ad_x[1]; // ------------------------------------------------------------------- // use atomic operation to multiply left * right ad_matrix ad_result = mat_mul.op(ad_left, ad_right); // ------------------------------------------------------------------- // check that first component of result is a parameter // and the other components are varaibles. ok &= Parameter( ad_result(0, 0) ); ok &= Variable( ad_result(1, 0) ); ok &= Variable( ad_result(2, 0) ); // ------------------------------------------------------------------- // declare the dependent variable vector y size_t m = 3; CPPAD_TESTVECTOR(ad_scalar) ad_y(m); for(size_t i = 0; i < m; i++) ad_y[i] = ad_result(i, 0); CppAD::ADFun f(ad_x, ad_y); // ------------------------------------------------------------------- // check zero order forward mode CPPAD_TESTVECTOR(scalar) x(n), y(m); for(size_t i = 0; i < n; i++) x[i] = scalar(i + 2); y = f.Forward(0, x); ok &= NearEqual(y[0], 0.0, eps, eps); ok &= NearEqual(y[1], x[0] + 2.0 * x[1], eps, eps); ok &= NearEqual(y[2], x[0] * x[0] + x[1] * x[1], eps, eps); // ------------------------------------------------------------------- // check first order forward mode CPPAD_TESTVECTOR(scalar) x1(n), y1(m); x1[0] = 1.0; x1[1] = 0.0; y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], 0.0, eps, eps); ok &= NearEqual(y1[1], 1.0, eps, eps); ok &= NearEqual(y1[2], 2.0 * x[0], eps, eps); x1[0] = 0.0; x1[1] = 1.0; y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], 0.0, eps, eps); ok &= NearEqual(y1[1], 2.0, eps, eps); ok &= NearEqual(y1[2], 2.0 * x[1], eps, eps); // ------------------------------------------------------------------- // check second order forward mode CPPAD_TESTVECTOR(scalar) x2(n), y2(m); x2[0] = 0.0; x2[1] = 0.0; y2 = f.Forward(2, x2); ok &= NearEqual(y2[0], 0.0, eps, eps); ok &= NearEqual(y2[1], 0.0, eps, eps); ok &= NearEqual(y2[2], 1.0, eps, eps); // 1/2 * f_1''(x) // ------------------------------------------------------------------- // check first order reverse mode CPPAD_TESTVECTOR(scalar) w(m), d1w(n); w[0] = 0.0; w[1] = 1.0; w[2] = 0.0; d1w = f.Reverse(1, w); ok &= NearEqual(d1w[0], 1.0, eps, eps); ok &= NearEqual(d1w[1], 2.0, eps, eps); w[0] = 0.0; w[1] = 0.0; w[2] = 1.0; d1w = f.Reverse(1, w); ok &= NearEqual(d1w[0], 2.0 * x[0], eps, eps); ok &= NearEqual(d1w[1], 2.0 * x[1], eps, eps); // ------------------------------------------------------------------- // check second order reverse mode CPPAD_TESTVECTOR(scalar) d2w(2 * n); d2w = f.Reverse(2, w); // partial f_2 w.r.t. x_0 ok &= NearEqual(d2w[0 * 2 + 0], 2.0 * x[0], eps, eps); // partial f_2 w.r.t x_1 ok &= NearEqual(d2w[1 * 2 + 0], 2.0 * x[1], eps, eps); // partial f_2 w.r.t x_1, x_0 ok &= NearEqual(d2w[0 * 2 + 1], 0.0, eps, eps); // partial f_2 w.r.t x_1, x_1 ok &= NearEqual(d2w[1 * 2 + 1], 2.0, eps, eps); // ------------------------------------------------------------------- // check forward Jacobian sparsity CPPAD_TESTVECTOR( std::set ) r(n), s(m); std::set check_set; for(size_t j = 0; j < n; j++) r[j].insert(j); s = f.ForSparseJac(n, r); check_set.clear(); ok &= s[0] == check_set; check_set.insert(0); check_set.insert(1); ok &= s[1] == check_set; ok &= s[2] == check_set; // ------------------------------------------------------------------- // check reverse Jacobian sparsity r.resize(m); for(size_t i = 0; i < m; i++) r[i].insert(i); s = f.RevSparseJac(m, r); check_set.clear(); ok &= s[0] == check_set; check_set.insert(0); check_set.insert(1); ok &= s[1] == check_set; ok &= s[2] == check_set; // ------------------------------------------------------------------- // check forward Hessian sparsity for f_2 (x) CPPAD_TESTVECTOR( std::set ) r2(1), s2(1), h(n); for(size_t j = 0; j < n; j++) r2[0].insert(j); s2[0].clear(); s2[0].insert(2); h = f.ForSparseHes(r2, s2); check_set.clear(); check_set.insert(0); ok &= h[0] == check_set; check_set.clear(); check_set.insert(1); ok &= h[1] == check_set; // ------------------------------------------------------------------- // check reverse Hessian sparsity for f_2 (x) CPPAD_TESTVECTOR( std::set ) s3(1); s3[0].clear(); s3[0].insert(2); h = f.RevSparseHes(n, s3); check_set.clear(); check_set.insert(0); ok &= h[0] == check_set; check_set.clear(); check_set.insert(1); ok &= h[1] == check_set; // ------------------------------------------------------------------- return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atomic/ode.cpp0000644000175200017650000002047013057470457016623 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin checkpoint_ode.cpp$$ $spell Checkpointing Runge-Kutta $$ $section Checkpointing an ODE Solver: Example and Test$$ $head See Also$$ $cref checkpoint_extended_ode.cpp$$, $head Purpose$$ In this example we $cref checkpoint$$ one step of an ODE solver. $head Problem$$ We consider the initial value problem with parameter $latex x$$ defined by, $latex z(0, x) = z_0 (x)$$, $latex \[ \partial_t z(t, x ) = h [ x , z(t, x) ] \]$$ Note that if $latex t$$ needs to be in the equation, one can define the first component of $latex z(t, x)$$ to be equal to $latex t$$. $head ODE Solver$$ For this example, we consider the Fourth order Runge-Kutta ODE solver. Given an approximation solution at time $latex t_k$$ denoted by $latex \tilde{z}_k (x)$$, and $latex \Delta t = t_{k+1} - t_k$$, it defines the approximation solution $latex \tilde{z}_{k+1} (x)$$ at time $latex t_{k+1}$$ by $latex \[ \begin{array}{rcl} h_1 & = & h [ x , \tilde{z}_k (x) ] \\ h_2 & = & h [ x , \tilde{z}_k (x) + \Delta t \; h_1 / 2 ] \\ h_3 & = & h [ x , \tilde{z}_k (x) + \Delta t \; h_2 / 2 ] \\ h_4 & = & h [ x , \tilde{z}_k (x) + \Delta t \; h_3 ] \\ \tilde{z}_{k+1} (x) & = & \tilde{z}_k (x) + \Delta t \; ( h_1 + 2 h_2 + 2 h_3 + h_4 ) / 6 \end{array} \] $$ If $latex \tilde{z}_k (x) = z_k (x)$$, $latex \tilde{z}_{k+1} (x) = z_{k+1} (x) + O( \Delta t^5 )$$. Other ODE solvers can use a similar method to the one used below. $head ODE$$ For this example the ODE is defined by $latex z(0, x) = 0$$ and $latex \[ h[ x, z(t, x) ] = \left( \begin{array}{c} x_0 \\ x_1 z_0 (t, x) \\ \vdots \\ x_{n-1} z_{n-2} (t, x) \end{array} \right) = \left( \begin{array}{c} \partial_t z_0 (t , x) \\ \partial_t z_1 (t , x) \\ \vdots \\ \partial_t z_{n-1} (t , x) \end{array} \right) \] $$ $head Solution$$ The solution of the ODE for this example, which is used to check the results, can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain $latex \[ z(t, x) = \left( \begin{array}{c} x_0 t \\ x_1 x_0 t^2 / 2 \\ \vdots \\ x_{n-1} x_{n-2} \ldots x_0 t^n / n ! \end{array} \right) \] $$ $code $srcfile%example/atomic/ode.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::AD; typedef AD a1double; typedef AD a2double; // typedef CPPAD_TESTVECTOR( double ) a0vector; typedef CPPAD_TESTVECTOR( a1double ) a1vector; typedef CPPAD_TESTVECTOR( a2double ) a2vector; // // set once by main and kept that way double delta_t_ = std::numeric_limits::quiet_NaN(); size_t n_ = 0; // // The function h( x , y) template FloatVector h(const FloatVector& x, const FloatVector& y) { assert( size_t( x.size() ) == n_ ); assert( size_t( y.size() ) == n_ ); FloatVector result(n_); result[0] = x[0]; for(size_t i = 1; i < n_; i++) result[i] = x[i] * y[i-1]; return result; } // The 4-th Order Runge-Kutta Step template FloatVector Runge4(const FloatVector& x, const FloatVector& z0 ) { assert( size_t( x.size() ) == n_ ); assert( size_t( z0.size() ) == n_ ); // typedef typename FloatVector::value_type Float; // Float dt = Float(delta_t_); size_t m = z0.size(); // FloatVector h1(m), h2(m), h3(m), h4(m), result(m); h1 = h( x, z0 ); // for(size_t i = 0; i < m; i++) h2[i] = z0[i] + dt * h1[i] / 2.0; h2 = h( x, h2 ); // for(size_t i = 0; i < m; i++) h3[i] = z0[i] + dt * h2[i] / 2.0; h3 = h( x, h3 ); // for(size_t i = 0; i < m; i++) h4[i] = z0[i] + dt * h3[i]; h4 = h( x, h4 ); // for(size_t i = 0; i < m; i++) { Float dz = dt * ( h1[i] + 2.0*h2[i] + 2.0*h3[i] + h4[i] ) / 6.0; result[i] = z0[i] + dz; } return result; } // pack x and z into an ode_info vector template void pack( FloatVector& ode_info , const FloatVector& x , const FloatVector& z ) { assert( size_t( ode_info.size() ) == n_ + n_ ); assert( size_t( x.size() ) == n_ ); assert( size_t( z.size() ) == n_ ); // size_t offset = 0; for(size_t i = 0; i < n_; i++) ode_info[offset + i] = x[i]; offset += n_; for(size_t i = 0; i < n_; i++) ode_info[offset + i] = z[i]; } // unpack an ode_info vector template void unpack( const FloatVector& ode_info , FloatVector& x , FloatVector& z ) { assert( size_t( ode_info.size() ) == n_ + n_ ); assert( size_t( x.size() ) == n_ ); assert( size_t( z.size() ) == n_ ); // size_t offset = 0; for(size_t i = 0; i < n_; i++) x[i] = ode_info[offset + i]; offset += n_; for(size_t i = 0; i < n_; i++) z[i] = ode_info[offset + i]; } // Algorithm that z(t, x) void ode_algo(const a1vector& ode_info_in, a1vector& ode_info_out) { assert( size_t( ode_info_in.size() ) == n_ + n_ ); assert( size_t( ode_info_out.size() ) == n_ + n_ ); // // initial ode information a1vector x(n_), z0(n_); unpack(ode_info_in, x, z0); // // advance z(t, x) a1vector z1 = Runge4(x, z0); // // final ode information pack(ode_info_out, x, z1); // return; } } // bool ode(void) { bool ok = true; using CppAD::NearEqual; double eps = std::numeric_limits::epsilon(); // // number of terms in the differential equation n_ = 6; // // step size for the differentiail equation size_t n_step = 10; double T = 1.0; delta_t_ = T / double(n_step); // // set parameter value and initial value of the ode a1vector ax(n_), az0(n_); for(size_t i = 0; i < n_; i++) { ax[i] = a1double(i + 1); az0[i] = a1double(0); } // // pack ode information input vector a1vector ode_info_in(2 * n_); pack(ode_info_in, ax, az0); // // create checkpoint version of the algorithm a1vector ode_info_out(2 * n_); CppAD::checkpoint ode_check( "ode", ode_algo, ode_info_in, ode_info_out ); // // set the independent variables for recording CppAD::Independent( ax ); // // repack to get dependence on ax pack(ode_info_in, ax, az0); // // Now run the checkpoint algorithm n_step times for(size_t k = 0; k < n_step; k++) { ode_check(ode_info_in, ode_info_out); ode_info_in = ode_info_out; } // // Unpack the results (must use ax1 so do not overwrite ax) a1vector ax1(n_), az1(n_); unpack(ode_info_out, ax1, az1); // // We could record a complicated funciton of x and z(T, x) in f, // but make this example simpler we record x -> z(T, x). CppAD::ADFun f(ax, az1); // // check function values a0vector x(n_), z1(n_); for(size_t j = 0; j < n_; j++) x[j] = double(j + 1); z1 = f.Forward(0, x); // // separate calculation of z(t, x) a0vector check_z1(n_); check_z1[0] = x[0] * T; for(size_t i = 1; i < n_; i++) check_z1[i] = x[i] * T * check_z1[i-1] / double(i+1); // // expected accuracy for each component of of z(t, x) a0vector acc(n_); for(size_t i = 0; i < n_; i++) { if( i < 4 ) { // Runge-Kutta methos is exact for this case acc[i] = 10. * eps; } else { acc[i] = 1.0; for(size_t k = 0; k < 5; k++) acc[i] *= x[k] * delta_t_; } } // check z1(T, x) for(size_t i = 0; i < n_; i++) ok &= NearEqual(z1[i] , check_z1[i], acc[i], acc[i]); // // Now use f to compute a derivative. For this 'simple' example it is // the derivative of z_{n-1} (T, x) respect to x of the a0vector w(n_), dw(n_); for(size_t i = 0; i < n_; i++) { w[i] = 0.0; if( i == n_ - 1 ) w[i] = 1.0; } dw = f.Reverse(1, w); for(size_t j = 0; j < n_; j++) { double check = z1[n_ - 1] / x[j]; ok &= NearEqual(dw[j] , check, 100.*eps, 100.*eps); } // return ok; } // END C++ cppad-20170000.3/example/atomic/rev_sparse_hes.cpp0000644000175200017650000002211313057470457021060 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_rev_sparse_hes.cpp$$ $section Atomic Reverse Hessian Sparsity: Example and Test$$ $head Purpose$$ This example demonstrates calculation of the reverse Hessian sparsity pattern for an atomic operation. $head function$$ For this example, the atomic function $latex f : \B{R}^3 \rightarrow \B{R}^2$$ is defined by $latex \[ f( x ) = \left( \begin{array}{c} x_2 * x_2 \\ x_0 * x_1 \end{array} \right) \] $$ The Hessians of the component functions are $latex \[ f_0^{(2)} ( x ) = \left( \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 2 \end{array} \right) \W{,} f_1^{(2)} ( x ) = \left( \begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right) \] $$ $nospell $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // class atomic_rev_sparse_hes : public CppAD::atomic_base { /* %$$ $head Constructor $$ $srccode%cpp% */ public: // constructor (could use const char* for name) atomic_rev_sparse_hes(const std::string& name) : // this example only uses pack sparsity patterns CppAD::atomic_base(name, pack_sparsity_enum) { } private: /* %$$ $head forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { # ifndef NDEBUG size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); # endif assert( n == 3 ); assert( m == 2 ); // return flag bool ok = q == 0; if( ! ok ) return ok; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) { vy[0] = vx[0]; vy[1] = vx[0] || vy[0]; } // Order zero forward mode. // This case must always be implemented // f(x) = [ x_0 * x_0 ] // [ x_0 * x_1 ] assert( p <= 0 ); if( p <= 0 ) { ty[0] = tx[2] * tx[2]; ty[1] = tx[0] * tx[1]; } return ok; } /* %$$ $head for_sparse_jac$$ $srccode%cpp% */ // forward Jacobian sparsity routine called by CppAD virtual bool for_sparse_jac( size_t q , const CppAD::vectorBool& r , CppAD::vectorBool& s , const vector& x ) { // This function needed because we are using ForSparseHes // with afun.option( CppAD::atomic_base::pack_sparsity_enum ) # ifndef NDEBUG size_t n = r.size() / q; size_t m = s.size() / q; # endif assert( n == x.size() ); assert( n == 3 ); assert( m == 2 ); // f'(x) = [ 0, 0, 2 x_2 ] // [ x_1, x_0, 0 ] // sparsity for first row of S(x) = f'(x) * R size_t i = 0; for(size_t j = 0; j < q; j++) s[ i * q + j ] = r[ 2 * q + j ]; // sparsity for second row of S(x) = f'(x) * R i = 1; for(size_t j = 0; j < q; j++) s[ i * q + j ] = r[ 0 * q + j ] | r[ 1 * q + j]; return true; } /* %$$ $head rev_sparse_jac$$ $srccode%cpp% */ // reverse Jacobian sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t q , const CppAD::vectorBool& rt , CppAD::vectorBool& st , const vector& x ) { // This function needed because we are using ForSparseHes // with afun.option( CppAD::atomic_base::pack_sparsity_enum ) # ifndef NDEBUG size_t m = rt.size() / q; size_t n = st.size() / q; # endif assert( n == x.size() ); assert( n == 3 ); assert( m == 2 ); // [ 0, x_1 ] // f'(x)^T = [ 0, x_0 ] // [ 2 x_2, 0 ] // sparsity for first row of S(x)^T = f'(x)^T * R^T size_t i = 0; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 1 * q + j ]; // sparsity for second row of S(x)^T = f'(x)^T * R^T i = 1; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 1 * q + j ]; // sparsity for third row of S(x)^T = f'(x)^T * R^T i = 2; for(size_t j = 0; j < q; j++) st[ i * q + j ] = rt[ 0 * q + j ]; return true; } /* %$$ $head rev_sparse_hes$$ $srccode%cpp% */ // reverse Hessian sparsity routine called by CppAD virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t q , const CppAD::vectorBool& r , const CppAD::vectorBool& u , CppAD::vectorBool& v , const vector& x ) { // This function needed because we are using RevSparseHes // with afun.option( CppAD::atomic_base::pack_sparsity_enum ) # ifndef NDEBUG size_t m = s.size(); size_t n = t.size(); # endif assert( x.size() == n ); assert( r.size() == n * q ); assert( u.size() == m * q ); assert( v.size() == n * q ); assert( n == 3 ); assert( m == 2 ); // // f'(x) = [ 0, 0, 2 x_2 ] // [ x_1, x_0, 0 ] // // [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] // f_0''(x) = [ 0 , 0 , 0 ] f_1^{(2)} (x) = [ 1 , 0 , 0 ] // [ 0 , 0 , 2 ] [ 0 , 0 , 0 ] // ------------------------------------------------------------------ // sparsity pattern for row vector T(x) = S(x) * f'(x) t[0] = s[1]; t[1] = s[1]; t[2] = s[0]; // ------------------------------------------------------------------ // sparsity pattern for W(x) = f'(x)^T * U(x) for(size_t j = 0; j < q; j++) { v[ 0 * q + j ] = u[ 1 * q + j ]; v[ 1 * q + j ] = u[ 1 * q + j ]; v[ 2 * q + j ] = u[ 0 * q + j ]; } // ------------------------------------------------------------------ // sparsity pattern for Q(x) = W(x) + S_0 (x) * f_0^{(2)} (x) * R if( s[0] ) { for(size_t j = 0; j < q; j++) { // cannot use |= with vectorBool v[ 2 * q + j ] = bool(v[ 2 * q + j ]) | bool(r[ 2 * q + j ]); } } // ------------------------------------------------------------------ // sparsity pattern for V(x) = Q(x) + S_1 (x) * f_1^{(2)} (x) * R if( s[1] ) { for(size_t j = 0; j < q; j++) { // cannot use |= with vectorBool v[ 0 * q + j ] = bool(v[ 0 * q + j ]) | bool(r[ 1 * q + j ]); v[ 1 * q + j ] = bool(v[ 1 * q + j ]) | bool(r[ 0 * q + j ]); } } return true; } }; // End of atomic_rev_sparse_hes class /* %$$ $head Use Atomic Function$$ $srccode%cpp% */ bool use_atomic_rev_sparse_hes(bool x_1_variable) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // // Create the atomic rev_sparse_hes object atomic_rev_sparse_hes afun("atomic_rev_sparse_hes"); // // Create the function f(u) // // domain space vector size_t n = 3; double x_0 = 1.00; double x_1 = 2.00; double x_2 = 3.00; vector< AD > au(n); au[0] = x_0; au[1] = x_1; au[2] = x_2; // declare independent variables and start tape recording CppAD::Independent(au); // range space vector size_t m = 2; vector< AD > ay(m); // call user function vector< AD > ax(n); ax[0] = au[0]; ax[2] = au[2]; if( x_1_variable ) ax[1] = au[1]; else ax[1] = x_1; afun(ax, ay); // y = [ x_2 * x_2 , x_0 * x_1 ]^T // create f: u -> y and stop tape recording CppAD::ADFun f; f.Dependent (au, ay); // f(u) = y // // check function value double check = x_2 * x_2; ok &= NearEqual( Value(ay[0]) , check, eps, eps); check = x_0 * x_1; ok &= NearEqual( Value(ay[1]) , check, eps, eps); // check zero order forward mode size_t q; vector xq(n), yq(m); q = 0; xq[0] = x_0; xq[1] = x_1; xq[2] = x_2; yq = f.Forward(q, xq); check = x_2 * x_2; ok &= NearEqual(yq[0] , check, eps, eps); check = x_0 * x_1; ok &= NearEqual(yq[1] , check, eps, eps); // reverse sparse Hessian CppAD::vectorBool r(n * n), s(m), h(n * n); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n; j++) r[i * n + j] = i == j; } for(size_t i = 0; i < m; i++) s[i] = true; f.ForSparseJac(n, r); h = f.RevSparseHes(n, s); // check result CppAD::vectorBool check_h(n * n); for(size_t i = 0; i < n * n; i++) check_h[i] = false; check_h[ 2 * n + 2 ] = true; if( x_1_variable ) { check_h[0 * n + 1] = true; check_h[1 * n + 0] = true; } for(size_t i = 0; i < n * n; i++) ok &= h[ i ] == check_h[ i ]; // return ok; } } // End empty namespace /* %$$ $head Test with x_1 Both a Variable and a Parameter$$ $srccode%cpp% */ bool rev_sparse_hes(void) { bool ok = true; // test with x_1 a variable ok &= use_atomic_rev_sparse_hes(true); // test with x_1 a parameter ok &= use_atomic_rev_sparse_hes(false); return ok; } /* %$$ $$ $comment end nospell$$ $end */ cppad-20170000.3/example/atan2.cpp0000644000175200017650000000427413057470457015611 0ustar coincoin-web// $Id: atan2.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atan2.cpp$$ $spell tan atan $$ $section The AD atan2 Function: Example and Test$$ $code $srcfile%example/atan2.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool atan2(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD sin_of_x0 = CppAD::sin(x[0]); AD cos_of_x0 = CppAD::cos(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::atan2(sin_of_x0, cos_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps99, eps99); // use a VecAD::reference object with atan2 CppAD::VecAD v(2); AD zero(0); AD one(1); v[zero] = sin_of_x0; v[one] = cos_of_x0; AD result = CppAD::atan2(v[zero], v[one]); ok &= NearEqual(result, x0, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/sparsity_sub.cpp0000644000175200017650000000534613057470457017334 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparsity_sub.cpp$$ $spell Jac Jacobian Hes $$ $section Sparsity Patterns For a Subset of Variables: Example and Test$$ $head See Also$$ $cref sparse_sub_hes.cpp$$, $cref sub_sparse_hes.cpp$$. $head ForSparseJac$$ The routine $cref ForSparseJac$$ is used to compute the sparsity for both the full Jacobian (see $icode s$$) and a subset of the Jacobian (see $icode s2$$). $head RevSparseHes$$ The routine $cref RevSparseHes$$ is used to compute both sparsity for both the full Hessian (see $icode h$$) and a subset of the Hessian (see $icode h2$$). $code $srcfile%example/sparsity_sub.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool sparsity_sub(void) { // C++ source code bool ok = true; // using std::cout; using CppAD::vector; using CppAD::AD; using CppAD::vectorBool; size_t n = 4; size_t m = n-1; vector< AD > ax(n), ay(m); for(size_t j = 0; j < n; j++) ax[j] = double(j+1); CppAD::Independent(ax); for(size_t i = 0; i < m; i++) ay[i] = (ax[i+1] - ax[i]) * (ax[i+1] - ax[i]); CppAD::ADFun f(ax, ay); // Evaluate the full Jacobian sparsity pattern for f vectorBool r(n * n), s(m * n); for(size_t j = 0 ; j < n; j++) { for(size_t i = 0; i < n; i++) r[i * n + j] = (i == j); } s = f.ForSparseJac(n, r); // evaluate the sparsity for the Hessian of f_0 + ... + f_{m-1} vectorBool t(m), h(n * n); for(size_t i = 0; i < m; i++) t[i] = true; h = f.RevSparseHes(n, t); // evaluate the Jacobian sparsity pattern for first n/2 components of x size_t n2 = n / 2; vectorBool r2(n * n2), s2(m * n2); for(size_t j = 0 ; j < n2; j++) { for(size_t i = 0; i < n; i++) r2[i * n2 + j] = (i == j); } s2 = f.ForSparseJac(n2, r2); // evaluate the sparsity for the subset of Hessian of // f_0 + ... + f_{m-1} where first partial has only first n/2 components vectorBool h2(n2 * n); h2 = f.RevSparseHes(n2, t); // check sparsity pattern for Jacobian for(size_t i = 0; i < m; i++) { for(size_t j = 0; j < n2; j++) ok &= s2[i * n2 + j] == s[i * n + j]; } // check sparsity pattern for Hessian for(size_t i = 0; i < n2; i++) { for(size_t j = 0; j < n; j++) ok &= h2[i * n + j] == h[i * n + j]; } return ok; } // END C++ cppad-20170000.3/example/jacobian.cpp0000644000175200017650000000552513057470457016352 0ustar coincoin-web// $Id: jacobian.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin jacobian.cpp$$ $spell Cpp Jacobian $$ $section Jacobian: Example and Test$$ $mindex Jacobian$$ $code $srcfile%example/jacobian.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // --------------------------------------------------------- // define the template function JacobianCases in empty namespace template bool JacobianCases() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); using CppAD::exp; using CppAD::sin; using CppAD::cos; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; X[1] = 2.; // declare independent variables and starting recording CppAD::Independent(X); // a calculation between the domain and range values AD Square = X[0] * X[0]; // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = Square * exp( X[1] ); Y[1] = Square * sin( X[1] ); Y[2] = Square * cos( X[1] ); // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector Vector x(n); x[0] = 2.; x[1] = 1.; // compute the derivative at this x Vector jac( m * n ); jac = f.Jacobian(x); /* F'(x) = [ 2 * x[0] * exp(x[1]) , x[0] * x[0] * exp(x[1]) ] [ 2 * x[0] * sin(x[1]) , x[0] * x[0] * cos(x[1]) ] [ 2 * x[0] * cos(x[1]) , -x[0] * x[0] * sin(x[i]) ] */ ok &= NearEqual( 2.*x[0]*exp(x[1]), jac[0*n+0], eps99, eps99); ok &= NearEqual( 2.*x[0]*sin(x[1]), jac[1*n+0], eps99, eps99); ok &= NearEqual( 2.*x[0]*cos(x[1]), jac[2*n+0], eps99, eps99); ok &= NearEqual( x[0] * x[0] *exp(x[1]), jac[0*n+1], eps99, eps99); ok &= NearEqual( x[0] * x[0] *cos(x[1]), jac[1*n+1], eps99, eps99); ok &= NearEqual(-x[0] * x[0] *sin(x[1]), jac[2*n+1], eps99, eps99); return ok; } } // End empty namespace # include # include bool Jacobian(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= JacobianCases< CppAD::vector >(); ok &= JacobianCases< std::vector >(); ok &= JacobianCases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/lu_solve.cpp0000644000175200017650000000517613057470457016436 0ustar coincoin-web// $Id: lu_solve.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin lu_solve.cpp$$ $spell Geq Cpp Lu $$ $section LuSolve With Complex Arguments: Example and Test$$ $code $srcfile%example/lu_solve.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // for CppAD::LuSolve # include // for CppAD::NearEqual # include // for CppAD::vector # include // for std::complex typedef std::complex Complex; // define the Complex type bool LuSolve(void) { bool ok = true; using namespace CppAD; size_t n = 3; // number rows in A and B size_t m = 2; // number columns in B, X and S // A is an n by n matrix, B, X, and S are n by m matrices CppAD::vector A(n * n), B(n * m), X(n * m) , S(n * m); Complex logdet; // log of determinant of A int signdet; // zero if A is singular Complex det; // determinant of A size_t i, j, k; // some temporary indices // set A equal to the n by n Hilbert Matrix for(i = 0; i < n; i++) for(j = 0; j < n; j++) A[i * n + j] = 1. / (double) (i + j + 1); // set S to the solution of the equation we will solve for(j = 0; j < n; j++) for(k = 0; k < m; k++) S[ j * m + k ] = Complex(j, j + k); // set B = A * S size_t ik; Complex sum; for(k = 0; k < m; k++) { for(i = 0; i < n; i++) { sum = 0.; for(j = 0; j < n; j++) sum += A[i * n + j] * S[j * m + k]; B[i * m + k] = sum; } } // solve the equation A * X = B and compute determinant of A signdet = CppAD::LuSolve(n, m, A, B, X, logdet); det = Complex( signdet ) * exp( logdet ); double cond = 4.62963e-4; // condition number of A when n = 3 double determinant = 1. / 2160.; // determinant of A when n = 3 double delta = 1e-14 / cond; // accuracy expected in X // check determinant ok &= CppAD::NearEqual(det, determinant, delta, delta); // check solution for(ik = 0; ik < n * m; ik++) ok &= CppAD::NearEqual(X[ik], S[ik], delta, delta); return ok; } // END C++ cppad-20170000.3/example/to_string.cpp0000644000175200017650000000515513057470457016613 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin to_string.cpp$$ $section to_string: Example and Test$$ $code $srcfile%example/to_string.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ // Examples with fundamental types # include namespace { template Integer string2int(const std::string& s) { Integer result = 0; size_t index = 0; if( s[0] == '-' ) ++index; while( index < s.size() ) result = 10 * result + Integer( s[index++] - '0'); if( s[0] == '-' ) return - result; return result; } template bool integer(void) { bool ok = true; // Integer max = std::numeric_limits::max(); std::string s = CppAD::to_string(max); Integer check = string2int(s); ok &= max == check; // Integer min = std::numeric_limits::min(); s = CppAD::to_string(min); check = string2int(s); ok &= min == check; // return ok; } template bool floating(void) { bool ok = true; Float eps = std::numeric_limits::epsilon(); Float pi = 4.0 * std::atan(1.); // std::string s = CppAD::to_string( pi ); Float check = std::atof( s.c_str() ); ok &= std::fabs( check - pi ) <= 2.0 * eps; // return ok; } } // Examples with AD types # include namespace { template bool ad_floating(void) { bool ok = true; Base eps = std::numeric_limits::epsilon(); Base pi = 4.0 * std::atan(1.); // std::string s = CppAD::to_string( CppAD::AD( pi ) ); Base check = std::atof( s.c_str() ); ok &= std::fabs( check - pi ) <= 2.0 * eps; // return ok; } } // Test driver bool to_string(void) { bool ok = true; ok &= integer(); ok &= integer(); ok &= integer(); # if CPPAD_USE_CPLUSPLUS_2011 ok &= integer(); # endif // ok &= floating(); ok &= floating(); ok &= floating(); // ok &= ad_floating(); ok &= ad_floating(); // return ok; } // END C++ cppad-20170000.3/example/acos.cpp0000644000175200017650000000407213057470457015525 0ustar coincoin-web// $Id: acos.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin acos.cpp$$ $spell cos acos $$ $section The AD acos Function: Example and Test$$ $code $srcfile%example/acos.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool acos(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD cos_of_x0 = CppAD::cos(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::acos(cos_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps, eps); // use a VecAD::reference object with acos CppAD::VecAD v(1); AD zero(0); v[zero] = cos_of_x0; AD result = CppAD::acos(v[zero]); ok &= NearEqual(result, x0, eps, eps); return ok; } // END C++ cppad-20170000.3/example/rev_sparse_hes.cpp0000644000175200017650000001317313057470457017612 0ustar coincoin-web// $Id: rev_sparse_hes.cpp 3793 2016-02-29 18:18:32Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin rev_sparse_hes.cpp$$ $spell Hessian Jac Hes Dep Cpp $$ $section Reverse Mode Hessian Sparsity: Example and Test$$ $mindex RevSparseHes sparsity$$ $code $srcfile%example/rev_sparse_hes.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ------------------------------------------------------------- // expected sparsity pattern bool check_f0[] = { false, false, false, // partials w.r.t x0 and (x0, x1, x2) false, false, false, // partials w.r.t x1 and (x0, x1, x2) false, false, true // partials w.r.t x2 and (x0, x1, x2) }; bool check_f1[] = { false, true, false, // partials w.r.t x0 and (x0, x1, x2) true, false, false, // partials w.r.t x1 and (x0, x1, x2) false, false, false // partials w.r.t x2 and (x0, x1, x2) }; // define the template function BoolCases in empty namespace template // vector class, elements of type bool bool BoolCases(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; ax[2] = 2.; // declare independent variables and start recording CppAD::Independent(ax); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = sin( ax[2] ); ay[1] = ax[0] * ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // sparsity pattern for the identity matrix Vector r(n * n); size_t i, j; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) r[ i * n + j ] = (i == j); } // compute sparsity pattern for J(x) = F^{(1)} (x) f.ForSparseJac(n, r); // compute sparsity pattern for H(x) = F_0^{(2)} (x) Vector s(m); for(i = 0; i < m; i++) s[i] = false; s[0] = true; Vector h(n * n); h = f.RevSparseHes(n, s); // check values for(i = 0; i < n; i++) for(j = 0; j < n; j++) ok &= (h[ i * n + j ] == check_f0[ i * n + j ] ); // compute sparsity pattern for H(x) = F_1^{(2)} (x) for(i = 0; i < m; i++) s[i] = false; s[1] = true; h = f.RevSparseHes(n, s); // check values for(i = 0; i < n; i++) for(j = 0; j < n; j++) ok &= (h[ i * n + j ] == check_f1[ i * n + j ] ); // call that transposed the result bool transpose = true; h = f.RevSparseHes(n, s, transpose); // This h is symmetric, because R is symmetric, not really testing here for(i = 0; i < n; i++) for(j = 0; j < n; j++) ok &= (h[ j * n + i ] == check_f1[ i * n + j ] ); return ok; } // define the template function SetCases in empty namespace template // vector class, elements of type std::set bool SetCases(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; ax[2] = 2.; // declare independent variables and start recording CppAD::Independent(ax); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = sin( ax[2] ); ay[1] = ax[0] * ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // sparsity pattern for the identity matrix Vector r(n); size_t i; for(i = 0; i < n; i++) { assert( r[i].empty() ); r[i].insert(i); } // compute sparsity pattern for J(x) = F^{(1)} (x) f.ForSparseJac(n, r); // compute sparsity pattern for H(x) = F_0^{(2)} (x) Vector s(1); assert( s[0].empty() ); s[0].insert(0); Vector h(n); h = f.RevSparseHes(n, s); // check values std::set::iterator itr; size_t j; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { bool found = h[i].find(j) != h[i].end(); ok &= (found == check_f0[i * n + j]); } } // compute sparsity pattern for H(x) = F_1^{(2)} (x) s[0].clear(); assert( s[0].empty() ); s[0].insert(1); h = f.RevSparseHes(n, s); // check values for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { bool found = h[i].find(j) != h[i].end(); ok &= (found == check_f1[i * n + j]); } } // call that transposed the result bool transpose = true; h = f.RevSparseHes(n, s, transpose); // This h is symmetric, because R is symmetric, not really testing here for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { bool found = h[j].find(i) != h[j].end(); ok &= (found == check_f1[i * n + j]); } } return ok; } } // End empty namespace # include # include bool rev_sparse_hes(void) { bool ok = true; // Run with Vector equal to four different cases // all of which are Simple Vectors with elements of type bool. ok &= BoolCases< CppAD::vector >(); ok &= BoolCases< CppAD::vectorBool >(); ok &= BoolCases< std::vector >(); ok &= BoolCases< std::valarray >(); // Run with Vector equal to two different cases both of which are // Simple Vectors with elements of type std::set typedef std::set set; ok &= SetCases< CppAD::vector >(); ok &= SetCases< std::vector >(); // Do not use valarray because its element access in the const case // returns a copy instead of a reference // ok &= SetCases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/pow_int.cpp0000644000175200017650000000415313057470457016257 0ustar coincoin-web// $Id: pow_int.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin pow_int.cpp$$ $spell tan atan $$ $section The Pow Integer Exponent: Example and Test$$ $mindex int$$ $code $srcfile%example/pow_int.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool pow_int(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // declare independent variables and start tape recording size_t n = 1; double x0 = -0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; CppAD::Independent(x); // dependent variable vector size_t m = 7; CPPAD_TESTVECTOR(AD) y(m); int i; for(i = 0; i < int(m); i++) y[i] = CppAD::pow(x[0], i - 3); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value double check; for(i = 0; i < int(m); i++) { check = std::pow(x0, double(i - 3)); ok &= NearEqual(y[i] , check, 1e-10 , 1e-10); } // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); for(i = 0; i < int(m); i++) { check = double(i-3) * std::pow(x0, double(i - 4)); ok &= NearEqual(dy[i] , check, 1e-10 , 1e-10); } // reverse computation of derivative of y[i] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); for(i = 0; i < int(m); i++) w[i] = 0.; for(i = 0; i < int(m); i++) { w[i] = 1.; dw = f.Reverse(1, w); check = double(i-3) * std::pow(x0, double(i - 4)); ok &= NearEqual(dw[0] , check, 1e-10 , 1e-10); w[i] = 0.; } return ok; } // END C++ cppad-20170000.3/example/ad_output.cpp0000644000175200017650000000361613057470457016607 0ustar coincoin-web// $Id: ad_output.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ad_output.cpp$$ $spell Cpp cstddef $$ $section AD Output Operator: Example and Test$$ $mindex <<$$ $code $srcfile%example/ad_output.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include // std::ostringstream # include // std::string # include // std::setprecision, setw, setfill, right namespace { template void set_ostream(S &os) { os << std::setprecision(4) // 4 digits of precision << std::setw(6) // 6 characters per field << std::setfill(' ') // fill with spaces << std::right; // adjust value to the right } } bool ad_output(void) { bool ok = true; // This output stream is an ostringstream for testing purposes. // You can use << with other types of streams; i.e., std::cout. std::ostringstream stream; // ouput an AD object CppAD::AD pi = 4. * atan(1.); // 3.1415926536 set_ostream(stream); stream << pi; // ouput a VecAD::reference object CppAD::VecAD v(1); CppAD::AD zero(0); v[zero] = exp(1.); // 2.7182818285 set_ostream(stream); stream << v[zero]; // convert output from stream to string std::string str = stream.str(); // check the output ok &= (str == " 3.142 2.718"); return ok; } // END C++ cppad-20170000.3/example/unary_minus.cpp0000644000175200017650000000357313057470457017156 0ustar coincoin-web// $Id: unary_minus.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin unary_minus.cpp$$ $spell Cpp cstddef $$ $section AD Unary Minus Operator: Example and Test$$ $code $srcfile%example/unary_minus.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool UnaryMinus(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) x(n); x[0] = 3.; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = - x[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check values ok &= ( y[0] == -3. ); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); size_t p = 1; dx[0] = 1.; dy = f.Forward(p, dx); ok &= ( dy[0] == -1. ); // dy[0] / dx[0] // reverse computation of dertivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(p, w); ok &= ( dw[0] == -1. ); // dy[0] / dx[0] // use a VecAD::reference object with unary minus CppAD::VecAD v(1); AD zero(0); v[zero] = x[0]; AD result = - v[zero]; ok &= (result == y[0]); return ok; } // END C++ cppad-20170000.3/example/eigen_array.cpp0000644000175200017650000000374713057470457017075 0ustar coincoin-web// $Id: eigen_array.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin eigen_array.cpp$$ $spell Eigen $$ $section Using Eigen Arrays: Example and Test$$ $mindex array$$ $code $srcfile%example/eigen_array.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool eigen_array(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; using Eigen::Matrix; using Eigen::Dynamic; // typedef Matrix< AD , Dynamic, 1 > a_vector; // // some temporary indices size_t i, j; // domain and range space vectors size_t n = 10, m = n; a_vector a_x(n), a_y(m); // set and declare independent variables and start tape recording for(j = 0; j < n; j++) a_x[j] = double(1 + j); CppAD::Independent(a_x); // evaluate a component wise function a_y = a_x.array() + a_x.array().sin(); // create f: x -> y and stop tape recording CppAD::ADFun f(a_x, a_y); // compute the derivative of y w.r.t x using CppAD CPPAD_TESTVECTOR(double) x(n); for(j = 0; j < n; j++) x[j] = double(j) + 1.0 / double(j+1); CPPAD_TESTVECTOR(double) jac = f.Jacobian(x); // check Jacobian double eps = 100. * CppAD::numeric_limits::epsilon(); for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { double check = 1.0 + cos(x[i]); if( i != j ) check = 0.0; ok &= NearEqual(jac[i * n + j], check, eps, eps); } } return ok; } // END C++ cppad-20170000.3/example/reverse_one.cpp0000644000175200017650000000533513057470457017117 0ustar coincoin-web// $Id: reverse_one.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin reverse_one.cpp$$ $spell Cpp $$ $section First Order Reverse Mode: Example and Test$$ $code $srcfile%example/reverse_one.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ---------------------------------------------------------- // define the template function reverse_one_cases in empty namespace template bool reverse_one_cases(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; // declare independent variables and start recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] * X[0] * X[1]; // create f : X -> Y and stop recording CppAD::ADFun f(X, Y); // use first order reverse mode to evaluate derivative of y[0] // and use the values in X for the independent variables. CPPAD_TESTVECTOR(double) w(m), dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0] , 2.*X[0]*X[1], eps99, eps99); ok &= NearEqual(dw[1] , X[0]*X[0], eps99, eps99); // use zero order forward mode to evaluate y at x = (3, 4) // and use the template parameter Vector for the vector type Vector x(n), y(m); x[0] = 3.; x[1] = 4.; y = f.Forward(0, x); ok &= NearEqual(y[0] , x[0]*x[0]*x[1], eps99, eps99); // use first order reverse mode to evaluate derivative of y[0] // and using the values in x for the independent variables. w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0] , 2.*x[0]*x[1], eps99, eps99); ok &= NearEqual(dw[1] , x[0]*x[0], eps99, eps99); return ok; } } // End empty namespace # include # include bool reverse_one(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= reverse_one_cases< CppAD::vector >(); ok &= reverse_one_cases< std::vector >(); ok &= reverse_one_cases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/interface2c.cpp0000644000175200017650000001116413057470457016765 0ustar coincoin-web// $Id: interface2c.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin interface2c.cpp$$ $spell $$ $section Interfacing to C: Example and Test$$ $mindex C interface difference central$$ $code $srcfile%example/interface2c.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // CppAD utilities # include // assert macro namespace { // Begin empty namespace /* Compute the value of a sum of Gaussians defined by a and evaluated at x y = sum_{i=1}^n a[3*i] exp( (x - a[3*i+1])^2 / a[3*i+2])^2 ) where the floating point type is a template parameter */ template Float sumGauss(const Float &x, const CppAD::vector &a) { // number of components in a size_t na = a.size(); // number of Gaussians size_t n = na / 3; // check the restricitons on na assert( na == n * 3 ); // declare temporaries used inside of loop Float ex, arg; // initialize sum Float y = 0.; // loop with respect to Gaussians size_t i; for(i = 0; i < n; i++) { arg = (x - a[3*i+1]) / a[3*i+2]; ex = exp(-arg * arg); y += a[3*i] * ex; } return y; } /* Create a C function interface that computes both y = sum_{i=1}^n a[3*i] exp( (x - a[3*i+1])^2 / a[3*i+2])^2 ) and its derivative with respect to the parameter vector a. */ extern "C" void sumGauss(float x, float a[], float *y, float dyda[], size_t na) { // Note that any simple vector could replace CppAD::vector; // for example, std::vector, std::valarray // check the restrictions on na assert( na % 3 == 0 ); // mod(na, 3) = 0 // use the shorthand ADfloat for the type CppAD::AD typedef CppAD::AD ADfloat; // vector for indpendent variables CppAD::vector A(na); // used with template function above CppAD::vector acopy(na); // used for derivative calculations // vector for the dependent variables (there is only one) CppAD::vector Y(1); // copy the independent variables from C vector to CppAD vectors size_t i; for(i = 0; i < na; i++) A[i] = acopy[i] = a[i]; // declare that A is the independent variable vector CppAD::Independent(A); // value of x as an ADfloat object ADfloat X = x; // Evaluate template version of sumGauss with ADfloat as the template // parameter. Set the independent variable to the resulting value Y[0] = sumGauss(X, A); // create the AD function object F : A -> Y CppAD::ADFun F(A, Y); // use Value to convert Y[0] to float and return y = F(a) *y = CppAD::Value(Y[0]); // evaluate the derivative F'(a) CppAD::vector J(na); J = F.Jacobian(acopy); // return the value of dyda = F'(a) as a C vector for(i = 0; i < na; i++) dyda[i] = J[i]; return; } /* Link CppAD::NearEqual so do not have to use namespace notation in Interface2C */ bool NearEqual(float x, float y, float r, float a) { return CppAD::NearEqual(x, y, r, a); } } // End empty namespace bool Interface2C(void) { // This routine is intentionally coded as if it were a C routine // except for the fact that it uses the predefined type bool. bool ok = true; // declare variables float x, a[6], y, dyda[6], tmp[6]; size_t na, i; // number of parameters (3 for each Gaussian) na = 6; // number of Gaussians: n = na / 3; // value of x x = 1.; // value of the parameter vector a for(i = 0; i < na; i++) a[i] = (float) (i+1); // evaulate function and derivative sumGauss(x, a, &y, dyda, na); // compare dyda to central difference approximation for deriative for(i = 0; i < na; i++) { // local variables float small, ai, yp, ym, dy_da; // We assume that the type float has at least 7 digits of // precision, so we choose small to be about pow(10., -7./2.). small = (float) 3e-4; // value of this component of a ai = a[i]; // evaluate F( a + small * ei ) a[i] = ai + small; sumGauss(x, a, &yp, tmp, na); // evaluate F( a - small * ei ) a[i] = ai - small; sumGauss(x, a, &ym, tmp, na); // evaluate central difference approximates for partial dy_da = (yp - ym) / (2 * small); // restore this component of a a[i] = ai; ok &= NearEqual(dyda[i], dy_da, small, small); } return ok; } // END C++ cppad-20170000.3/example/vector_bool.cpp0000644000175200017650000000541213057470457017114 0ustar coincoin-web// $Id: vector_bool.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin vector_bool.cpp$$ $spell Cpp bool $$ $section CppAD::vectorBool Class: Example and Test$$ $mindex bool vectorBool CppAD$$ $code $srcfile%example/vector_bool.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include // sstream and string are used to test output operation # include bool vectorBool(void) { bool ok = true; using CppAD::vectorBool; vectorBool x; // default constructor ok &= (x.size() == 0); x.resize(2); // resize and set element assignment to bool ok &= (x.size() == 2); x[0] = false; x[1] = true; vectorBool y(2); // sizing constructor ok &= (y.size() == 2); const vectorBool z(x); // copy constructor and const element access ok &= (z.size() == 2); ok &= ( (z[0] == false) && (z[1] == true) ); x[0] = true; // modify, assignment changes x ok &= (x[0] == true); // resize x to zero and check that vector assignment works for both // size zero and mathching sizes x.resize(0); ok &= (x.size() == 0); ok &= (y.size() == z.size()); // x = y = z; ok &= ( (x[0] == false) && (x[1] == true) ); ok &= ( (y[0] == false) && (y[1] == true) ); ok &= ( (z[0] == false) && (z[1] == true) ); // test of push_vector y.push_vector(z); ok &= y.size() == 4; ok &= ( (y[0] == false) && (y[1] == true) ); ok &= ( (y[2] == false) && (y[3] == true) ); y[1] = false; // element assignment to another element x[0] = y[1]; ok &= (x[0] == false); // test of output std::string correct= "01"; std::string str; std::ostringstream buf; buf << z; str = buf.str(); ok &= (str == correct); // test resize(0), capacity, and clear size_t i = x.capacity(); ok &= i > 0; x.resize(0); ok &= i == x.capacity(); x.clear(); ok &= 0 == x.capacity(); // test of push_back element for(i = 0; i < 100; i++) x.push_back( (i % 3) != 0 ); ok &= (x.size() == 100); for(i = 0; i < 100; i++) ok &= ( x[i] == ((i % 3) != 0) ); // is that boolvector is // a simple vector class with elements of type bool CppAD::CheckSimpleVector< bool, vectorBool >(); return ok; } // END C++ cppad-20170000.3/example/conj_grad.cpp0000644000175200017650000001557213057470457016535 0ustar coincoin-web// $Id: conj_grad.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin conj_grad.cpp$$ $spell checkpointing goto $$ $section Differentiate Conjugate Gradient Algorithm: Example and Test$$ $head Purpose$$ The conjugate gradient algorithm is sparse linear solver and a good example where checkpointing can be applied (for each iteration). This example is a preliminary version of a new library routine for the conjugate gradient algorithm. $head Algorithm$$ Given a positive definite matrix $latex A \in \B{R}^{n \times n}$$, a vector $latex b \in \B{R}^n$$, and tolerance $latex \varepsilon$$, the conjugate gradient algorithm finds an $latex x \in \B{R}^n$$ such that $latex \| A x - b \|^2 / n \leq \varepsilon^2$$ (or it terminates at a specified maximum number of iterations). $list number$$ Input: $pre $$ The matrix $latex A \in \B{R}^{n \times n}$$, the vector $latex b \in \B{R}^n$$, a tolerance $latex \varepsilon \geq 0$$, a maximum number of iterations $latex m$$, and the initial approximate solution $latex x^0 \in \B{R}^n$$ (can use zero for $latex x^0$$). $lnext Initialize: $pre $$ $latex g^0 = A * x^0 - b$$, $latex d^0 = - g^0$$, $latex s_0 = ( g^0 )^\R{T} g^0$$, $latex k = 0$$. $lnext Convergence Check: $pre $$ if $latex k = m$$ or $latex \sqrt{ s_k / n } < \varepsilon $$, return $latex k$$ as the number of iterations and $latex x^k$$ as the approximate solution. $lnext Next $latex x$$: $pre $$ $latex \mu_{k+1} = s_k / [ ( d^k )^\R{T} A d^k ]$$, $latex x^{k+1} = x^k + \mu_{k+1} d^k$$. $lnext Next $latex g$$: $pre $$ $latex g^{k+1} = g^k + \mu_{k+1} A d^k$$, $latex s_{k+1} = ( g^{k+1} )^\R{T} g^{k+1}$$. $lnext Next $latex d$$: $pre $$ $latex d^{k+1} = - g^k + ( s_{k+1} / s_k ) d^k$$. $lnext Iterate: $pre $$ $latex k = k + 1$$, goto Convergence Check. $lend $code $srcfile%example/conj_grad.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include namespace { // Begin empty namespace using CppAD::AD; // A simple matrix multiply c = a * b , where a has n columns // and b has n rows. This should be changed to a function so that // it can efficiently handle the case were A is large and sparse. template // a simple vector class void mat_mul(size_t n, const Vector& a, const Vector& b, Vector& c) { typedef typename Vector::value_type scalar; size_t m, p; m = a.size() / n; p = b.size() / n; assert( m * n == a.size() ); assert( n * p == b.size() ); assert( m * p == c.size() ); size_t i, j, k, ij; for(i = 0; i < m; i++) { for(j = 0; j < p; j++) { ij = i * p + j; c[ij] = scalar(0); for(k = 0; k < n; k++) c[ij] = c[ij] + a[i * m + k] * b[k * p + j]; } } return; } // Solve A * x == b to tolerance epsilon or terminate at m interations. template // a simple vector class size_t conjugate_gradient( size_t m , // input double epsilon , // input const Vector& A , // input const Vector& b , // input Vector& x ) // input / output { typedef typename Vector::value_type scalar; scalar mu, s_previous; size_t i, k; size_t n = x.size(); assert( A.size() == n * n ); assert( b.size() == n ); Vector g(n), d(n), s(1), Ad(n), dAd(1); // g = A * x mat_mul(n, A, x, g); for(i = 0; i < n; i++) { // g = A * x - b g[i] = g[i] - b[i]; // d = - g d[i] = -g[i]; } // s = g^T * g mat_mul(n, g, g, s); for(k = 0; k < m; k++) { s_previous = s[0]; if( s_previous < epsilon ) return k; // Ad = A * d mat_mul(n, A, d, Ad); // dAd = d^T * A * d mat_mul(n, d, Ad, dAd); // mu = s / d^T * A * d mu = s_previous / dAd[0]; // g = g + mu * A * d for(i = 0; i < n; i++) { x[i] = x[i] + mu * d[i]; g[i] = g[i] + mu * Ad[i]; } // s = g^T * g mat_mul(n, g, g, s); // d = - g + (s / s_previous) * d for(i = 0; i < n; i++) d[i] = - g[i] + ( s[0] / s_previous) * d[i]; } return m; } } // End empty namespace bool conj_grad(void) { bool ok = true; // ---------------------------------------------------------------------- // Setup // ---------------------------------------------------------------------- using CppAD::AD; using CppAD::NearEqual; using CppAD::vector; using std::cout; using std::endl; size_t i, j; // size of the vectors size_t n = 40; vector D(n * n), Dt(n * n), A(n * n), x(n), b(n), c(n); vector< AD > a_A(n * n), a_x(n), a_b(n); // D = diagonally dominant matrix // c = vector of ones for(i = 0; i < n; i++) { c[i] = 1.; double sum = 0; for(j = 0; j < n; j++) if( i != j ) { D[ i * n + j ] = std::rand() / double(RAND_MAX); Dt[j * n + i ] = D[i * n + j ]; sum += D[i * n + j ]; } Dt[ i * n + i ] = D[ i * n + i ] = sum * 1.1; } // A = D^T * D mat_mul(n, Dt, D, A); // b = D^T * c mat_mul(n, Dt, c, b); // copy from double to AD for(i = 0; i < n; i++) { a_b[i] = b[i]; for(j = 0; j < n; j++) a_A[ i * n + j ] = A[ i * n + j ]; } // --------------------------------------------------------------------- // Record the function f : b -> x // --------------------------------------------------------------------- // Make b the independent variable vector Independent(a_b); // Solve A * x = b using conjugate gradient method double epsilon = 1e-7; for(i = 0; i < n; i++) a_x[i] = AD(0); size_t m = n + 1; size_t k = conjugate_gradient(m, epsilon, a_A, a_b, a_x); // create f_cg: b -> x and stop tape recording CppAD::ADFun f(a_b, a_x); // --------------------------------------------------------------------- // Check for correctness // --------------------------------------------------------------------- // conjugate gradient should converge with in n iterations ok &= (k <= n); // accuracy to which we expect values to agree double delta = 10. * epsilon * std::sqrt( double(n) ); // copy x from AD to double for(i = 0; i < n; i++) x[i] = Value( a_x[i] ); // check c = A * x mat_mul(n, A, x, c); for(i = 0; i < n; i++) ok &= NearEqual(c[i] , b[i], delta , delta); // forward computation of partials w.r.t. b[0] vector db(n), dx(n); for(j = 0; j < n; j++) db[j] = 0.; db[0] = 1.; // check db = A * dx delta = 5. * delta; dx = f.Forward(1, db); mat_mul(n, A, dx, c); for(i = 0; i < n; i++) ok &= NearEqual(c[i], db[i], delta, delta); return ok; } // END C++ cppad-20170000.3/example/bool_fun.cpp0000644000175200017650000000344213057470460016375 0ustar coincoin-web// $Id: bool_fun.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin bool_fun.cpp$$ $spell bool Geq Cpp $$ $section AD Boolean Functions: Example and Test$$ $mindex bool$$ $code $srcfile%example/bool_fun.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include // define abbreviation for double precision complex typedef std::complex Complex; namespace { // a unary bool function with Complex argument static bool IsReal(const Complex &x) { return x.imag() == 0.; } // a binary bool function with Complex arguments static bool AbsGeq(const Complex &x, const Complex &y) { double axsq = x.real() * x.real() + x.imag() * x.imag(); double aysq = y.real() * y.real() + y.imag() * y.imag(); return axsq >= aysq; } // Create version of IsReal with AD argument // inside of namespace and outside of any other function. CPPAD_BOOL_UNARY(Complex, IsReal) // Create version of AbsGeq with AD arguments // inside of namespace and outside of any other function. CPPAD_BOOL_BINARY(Complex, AbsGeq) } bool BoolFun(void) { bool ok = true; CppAD::AD x = Complex(1., 0.); CppAD::AD y = Complex(1., 1.); ok &= IsReal(x); ok &= ! AbsGeq(x, y); return ok; } // END C++ cppad-20170000.3/example/sub_eq.cpp0000644000175200017650000000444313057470460016052 0ustar coincoin-web// $Id: sub_eq.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sub_eq.cpp$$ $section AD Computed Assignment Subtraction: Example and Test$$ $mindex -= subtract assign plus add$$ $code $srcfile%example/sub_eq.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool SubEq(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = .5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) y(m); y[0] = 3. * x[0]; // initial value y[0] -= 2; // AD -= int y[0] -= 4.; // AD -= double y[1] = y[0] -= x[0]; // use the result of a computed assignment // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , 3.*x0-(2.+4.+x0), eps99, eps99); ok &= NearEqual(y[1] , y[0], eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 2., eps99, eps99); ok &= NearEqual(dy[1], 2., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 0.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 2., eps99, eps99); // use a VecAD::reference object with computed subtraction CppAD::VecAD v(1); AD zero(0); AD result = 1; v[zero] = 2; result -= v[zero]; ok &= (result == -1); return ok; } // END C++ cppad-20170000.3/example/lu_vec_ad.hpp0000644000175200017650000000177213057470460016524 0ustar coincoin-web// $Id: lu_vec_ad.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_EXAMPLE_LU_VEC_AD_HPP # define CPPAD_EXAMPLE_LU_VEC_AD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace CppAD { extern CppAD::AD LuVecAD( size_t n, size_t m, CppAD::VecAD &Matrix, CppAD::VecAD &Rhs, CppAD::VecAD &Result, CppAD::AD &logdet ); } # endif cppad-20170000.3/example/nan.cpp0000644000175200017650000000252413057470460015346 0ustar coincoin-web// $Id: nan.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin nan.cpp$$ $section nan: Example and Test$$ $code $srcfile%example/nan.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool nan(void) { bool ok = true; // get a nan double double_zero = 0.; double double_nan = std::numeric_limits::quiet_NaN(); // create a simple vector with no nans std::vector v(2); v[0] = double_zero; v[1] = double_zero; // check that zero is not nan ok &= ! CppAD::isnan(double_zero); ok &= ! CppAD::hasnan(v); // check that nan is a nan v[1] = double_nan; ok &= CppAD::isnan(double_nan); ok &= CppAD::hasnan(v); // check that nan is not equal to itself ok &= (double_nan != double_nan); return ok; } // END C++ cppad-20170000.3/example/hes_minor_det.cpp0000644000175200017650000000433713057470460017415 0ustar coincoin-web// $Id: hes_minor_det.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin hes_minor_det.cpp$$ $spell Cpp $$ $section Gradient of Determinant Using Expansion by Minors: Example and Test$$ $mindex minors$$ $code $srcfile%example/hes_minor_det.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include typedef std::complex Complex; typedef CppAD::AD ADComplex; typedef CPPAD_TESTVECTOR(ADComplex) ADVector; // ---------------------------------------------------------------------------- bool HesMinorDet(void) { bool ok = true; using namespace CppAD; size_t n = 2; // object for computing determinants det_by_minor Det(n); // independent and dependent variable vectors CPPAD_TESTVECTOR(ADComplex) X(n * n); CPPAD_TESTVECTOR(ADComplex) D(1); // value of the independent variable size_t i; for(i = 0; i < n * n; i++) X[i] = Complex(int(i), -int(i)); // set the independent variables Independent(X); // comupute the determinant D[0] = Det(X); // create the function object ADFun f(X, D); // argument value CPPAD_TESTVECTOR(Complex) x( n * n ); for(i = 0; i < n * n; i++) x[i] = Complex(2 * i, i); // first derivative of the determinant CPPAD_TESTVECTOR(Complex) H( n * n * n * n); H = f.Hessian(x, 0); /* f(x) = x[0] * x[3] - x[1] * x[2] f'(x) = ( x[3], -x[2], -x[1], x[0] ) */ Complex zero(0., 0.); Complex one(1., 0.); Complex Htrue[] = { zero, zero, zero, one, zero, zero, -one, zero, zero, -one, zero, zero, one, zero, zero, zero }; for( i = 0; i < n*n*n*n; i++) ok &= Htrue[i] == H[i]; return ok; } // END C++ cppad-20170000.3/example/value.cpp0000644000175200017650000000326013057470460015704 0ustar coincoin-web// $Id: value.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin value.cpp$$ $spell Cpp cstddef $$ $section Convert From AD to its Base Type: Example and Test$$ $mindex Value record$$ $code $srcfile%example/value.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool Value(void) { bool ok = true; using CppAD::AD; using CppAD::Value; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) x(n); x[0] = 3.; x[1] = 4.; // check value before recording ok &= (Value(x[0]) == 3.); ok &= (Value(x[1]) == 4.); // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = - x[1]; // cannot call Value(x[j]) or Value(y[0]) here (currently variables) AD p = 5.; // p is a parameter (does not depend on x) ok &= (Value(p) == 5.); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // can call Value(x[j]) or Value(y[0]) here (currently parameters) ok &= (Value(x[0]) == 3.); ok &= (Value(x[1]) == 4.); ok &= (Value(y[0]) == -4.); return ok; } // END C++ cppad-20170000.3/example/log1p.cpp0000644000175200017650000000403613057470460015614 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin log1p.cpp$$ $spell expm1 log1p $$ $section The AD log1p Function: Example and Test$$ $code $srcfile%example/log1p.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool log1p(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD expm1_of_x0 = CppAD::expm1(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::log1p(expm1_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps, eps); // use a VecAD::reference object with log1p CppAD::VecAD v(1); AD zero(0); v[zero] = expm1_of_x0; AD result = CppAD::log1p(v[zero]); ok &= NearEqual(result, x0, eps, eps); return ok; } // END C++ cppad-20170000.3/example/jac_lu_det.cpp0000644000175200017650000000347013057470460016664 0ustar coincoin-web// $Id: jac_lu_det.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin jac_lu_det.cpp$$ $spell Lu Cpp $$ $section Gradient of Determinant Using Lu Factorization: Example and Test$$ $code $srcfile%example/jac_lu_det.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool JacLuDet(void) { bool ok = true; using namespace CppAD; size_t n = 2; // object for computing determinants det_by_lu Det(n); // independent and dependent variable vectors CPPAD_TESTVECTOR(ADComplex) X(n * n); CPPAD_TESTVECTOR(ADComplex) D(1); // value of the independent variable size_t i; for(i = 0; i < n * n; i++) X[i] = Complex(int(i), -int(i)); // set the independent variables Independent(X); // compute the determinant D[0] = Det(X); // create the function object ADFun f(X, D); // argument value CPPAD_TESTVECTOR(Complex) x( n * n ); for(i = 0; i < n * n; i++) x[i] = Complex(2 * i, i); // first derivative of the determinant CPPAD_TESTVECTOR(Complex) J( n * n ); J = f.Jacobian(x); /* f(x) = x[0] * x[3] - x[1] * x[2] */ Complex Jtrue[] = { x[3], -x[2], -x[1], x[0] }; for( i = 0; i < n*n; i++) ok &= NearEqual( Jtrue[i], J[i], 1e-10 , 1e-10 ); return ok; } // END C++ cppad-20170000.3/example/mul_eq.cpp0000644000175200017650000000446013057470460016055 0ustar coincoin-web// $Id: mul_eq.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin mul_eq.cpp$$ $section AD Computed Assignment Multiplication: Example and Test$$ $mindex *= multiply assign plus add$$ $code $srcfile%example/mul_eq.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool MulEq(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = .5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) y(m); y[0] = x[0]; // initial value y[0] *= 2; // AD *= int y[0] *= 4.; // AD *= double y[1] = y[0] *= x[0]; // use the result of a computed assignment // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0*2.*4.*x0, eps99, eps99); ok &= NearEqual(y[1] , y[0], eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 8.*2.*x0, eps99, eps99); ok &= NearEqual(dy[1], 8.*2.*x0, eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 0.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 8.*2.*x0, eps99, eps99); // use a VecAD::reference object with computed multiplication CppAD::VecAD v(1); AD zero(0); AD result = 1; v[zero] = 2; result *= v[zero]; ok &= (result == 2); return ok; } // END C++ cppad-20170000.3/example/tanh.cpp0000644000175200017650000000415113057470460015522 0ustar coincoin-web// $Id: tanh.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin tanh.cpp$$ $spell tanh $$ $section The AD tanh Function: Example and Test$$ $code $srcfile%example/tanh.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool Tanh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::tanh(x[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value double check = std::tanh(x0); ok &= NearEqual(y[0] , check, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); check = 1. - std::tanh(x0) * std::tanh(x0); ok &= NearEqual(dy[0], check, eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, eps, eps); // use a VecAD::reference object with tan CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::tanh(v[zero]); check = std::tanh(x0); ok &= NearEqual(result, check, eps, eps); return ok; } // END C++ cppad-20170000.3/example/lu_factor.cpp0000644000175200017650000000576213057470460016557 0ustar coincoin-web// $Id: lu_factor.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin lu_factor.cpp$$ $spell Geq Cpp Lu $$ $section LuFactor: Example and Test$$ $mindex LuFactor$$ $code $srcfile%example/lu_factor.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // for rand function # include // for CppAD::LuFactor # include // for CppAD::NearEqual # include // for CppAD::vector bool LuFactor(void) { bool ok = true; # ifndef _MSC_VER using std::rand; using std::srand; # endif using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); size_t n = 5; // number rows in A double rand_max = double(RAND_MAX); // maximum rand value double sum; // element of L * U double pij; // element of permuted A size_t i, j, k; // temporary indices // A is an n by n matrix CppAD::vector A(n*n), LU(n*n), L(n*n), U(n*n); // set A equal to an n by n random matrix for(i = 0; i < n; i++) for(j = 0; j < n; j++) A[i * n + j] = rand() / rand_max; // pivot vectors CppAD::vector ip(n); CppAD::vector jp(n); // factor the matrix A LU = A; CppAD::LuFactor(ip, jp, LU); // check that ip and jp are permutations of the indices 0, ... , n-1 for(i = 0; i < n; i++) { ok &= (ip[i] < n); ok &= (jp[i] < n); for(j = 0; j < n; j++) { if( i != j ) { ok &= (ip[i] != ip[j]); ok &= (jp[i] != jp[j]); } } } // Extract L from LU for(i = 0; i < n; i++) { // elements along and below the diagonal for(j = 0; j <= i; j++) L[i * n + j] = LU[ ip[i] * n + jp[j] ]; // elements above the diagonal for(j = i+1; j < n; j++) L[i * n + j] = 0.; } // Extract U from LU for(i = 0; i < n; i++) { // elements below the diagonal for(j = 0; j < i; j++) U[i * n + j] = 0.; // elements along the diagonal U[i * n + i] = 1.; // elements above the diagonal for(j = i+1; j < n; j++) U[i * n + j] = LU[ ip[i] * n + jp[j] ]; } // Compute L * U for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { // compute element (i,j) entry in L * U sum = 0.; for(k = 0; k < n; k++) sum += L[i * n + k] * U[k * n + j]; // element (i,j) in permuted version of A pij = A[ ip[i] * n + jp[j] ]; // compare ok &= NearEqual(pij, sum, eps99, eps99); } } return ok; } // END C++ cppad-20170000.3/example/rev_two.cpp0000644000175200017650000000652713057470460016266 0ustar coincoin-web// $Id: rev_two.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin rev_two.cpp$$ $spell Cpp $$ $section Second Partials Reverse Driver: Example and Test$$ $code $srcfile%example/rev_two.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ----------------------------------------------------- // define the template function in empty namespace // bool RevTwoCases(void) template bool RevTwoCases() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); using CppAD::exp; using CppAD::sin; using CppAD::cos; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; X[1] = 2.; // declare independent variables and starting recording CppAD::Independent(X); // a calculation between the domain and range values AD Square = X[0] * X[0]; // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = Square * exp( X[1] ); Y[1] = Square * sin( X[1] ); Y[2] = Square * cos( X[1] ); // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); x[0] = 2.; x[1] = 1.; // set i and j to compute specific second partials of y size_t p = 2; VectorSize_t i(p); VectorSize_t j(p); i[0] = 0; j[0] = 0; // for partials y[0] w.r.t x[0] and x[k] i[1] = 1; j[1] = 1; // for partials y[1] w.r.t x[1] and x[k] // compute the second partials VectorBase ddw(n * p); ddw = f.RevTwo(x, i, j); // partials of y[0] w.r.t x[0] is 2 * x[0] * exp(x[1]) // check partials of y[0] w.r.t x[0] and x[k] for k = 0, 1 ok &= NearEqual( 2.*exp(x[1]), ddw[0*p+0], eps99, eps99); ok &= NearEqual( 2.*x[0]*exp(x[1]), ddw[1*p+0], eps99, eps99); // partials of y[1] w.r.t x[1] is x[0] * x[0] * cos(x[1]) // check partials of F_1 w.r.t x[1] and x[k] for k = 0, 1 ok &= NearEqual( 2.*x[0]*cos(x[1]), ddw[0*p+1], eps99, eps99); ok &= NearEqual( -x[0]*x[0]*sin(x[1]), ddw[1*p+1], eps99, eps99); return ok; } } // End empty namespace # include # include bool RevTwo(void) { bool ok = true; // Run with VectorBase equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= RevTwoCases< CppAD::vector , std::vector >(); ok &= RevTwoCases< std::vector , std::vector >(); ok &= RevTwoCases< std::valarray , std::vector >(); // Run with VectorSize_t equal to two other cases // which are Simple Vectors with elements of type size_t. ok &= RevTwoCases< std::vector , CppAD::vector >(); ok &= RevTwoCases< std::vector , std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/hessian.cpp0000644000175200017650000000536513057470460016232 0ustar coincoin-web// $Id: hessian.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin hessian.cpp$$ $spell Cpp Hessian $$ $section Hessian: Example and Test$$ $mindex Hessian$$ $code $srcfile%example/hessian.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // --------------------------------------------------------- // define the template function HessianCases in empty namespace template bool HessianCases() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); using CppAD::exp; using CppAD::sin; using CppAD::cos; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; X[1] = 2.; // declare independent variables and starting recording CppAD::Independent(X); // a calculation between the domain and range values AD Square = X[0] * X[0]; // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = Square * exp( X[1] ); Y[1] = Square * sin( X[1] ); Y[2] = Square * cos( X[1] ); // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector Vector x(n); x[0] = 2.; x[1] = 1.; // second derivative of y[1] Vector hes( n * n ); hes = f.Hessian(x, 1); /* F_1 = x[0] * x[0] * sin(x[1]) F_1^{(1)} = [ 2 * x[0] * sin(x[1]) , x[0] * x[0] * cos(x[1]) ] F_1^{(2)} = [ 2 * sin(x[1]) , 2 * x[0] * cos(x[1]) ] [ 2 * x[0] * cos(x[1]) , - x[0] * x[0] * sin(x[1]) ] */ ok &= NearEqual( 2.*sin(x[1]), hes[0*n+0], eps99, eps99); ok &= NearEqual( 2.*x[0]*cos(x[1]), hes[0*n+1], eps99, eps99); ok &= NearEqual( 2.*x[0]*cos(x[1]), hes[1*n+0], eps99, eps99); ok &= NearEqual( - x[0]*x[0]*sin(x[1]), hes[1*n+1], eps99, eps99); return ok; } } // End empty namespace # include # include bool Hessian(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= HessianCases< CppAD::vector >(); ok &= HessianCases< std::vector >(); ok &= HessianCases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/eigen_det.cpp0000644000175200017650000000530513057470460016515 0ustar coincoin-web// $Id: eigen_det.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin eigen_det.cpp$$ $spell Eigen $$ $section Using Eigen To Compute Determinant: Example and Test$$ $mindex determinant$$ $code $srcfile%example/eigen_det.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include bool eigen_det(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; using Eigen::Matrix; using Eigen::Dynamic; // typedef Matrix< double , Dynamic, Dynamic > matrix; typedef Matrix< AD , Dynamic, Dynamic > a_matrix; // typedef Matrix< double , Dynamic , 1> vector; typedef Matrix< AD , Dynamic , 1> a_vector; // some temporary indices size_t i, j; // domain and range space vectors size_t size = 3, n = size * size, m = 1; a_vector a_x(n), a_y(m); vector x(n); // set and declare independent variables and start tape recording for(i = 0; i < size; i++) { for(j = 0; j < size; j++) { // lower triangular matrix a_x[i * size + j] = x[i * size + j] = 0.0; if( j <= i ) a_x[i * size + j] = x[i * size + j] = double(1 + i + j); } } CppAD::Independent(a_x); // copy independent variable vector to a matrix a_matrix a_X(size, size); matrix X(size, size); for(i = 0; i < size; i++) { for(j = 0; j < size; j++) { X(i, j) = x[i * size + j]; // If we used a_X(i, j) = X(i, j), a_X would not depend on a_x. a_X(i, j) = a_x[i * size + j]; } } // Compute the log of determinant of X a_y[0] = log( a_X.determinant() ); // create f: x -> y and stop tape recording CppAD::ADFun f(a_x, a_y); // check function value double eps = 100. * CppAD::numeric_limits::epsilon(); CppAD::det_by_minor det(size); ok &= NearEqual(Value(a_y[0]) , log(det(x)), eps, eps); // compute the derivative of y w.r.t x using CppAD vector jac = f.Jacobian(x); // check the derivative using the formula // d/dX log(det(X)) = transpose( inv(X) ) matrix inv_X = X.inverse(); for(i = 0; i < size; i++) { for(j = 0; j < size; j++) ok &= NearEqual(jac[i * size + j], inv_X(j, i), eps, eps); } return ok; } // END C++ cppad-20170000.3/example/makefile.am0000644000175200017650000001151513057470460016162 0ustar coincoin-web# $Id: makefile.am 3853 2016-12-14 14:40:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD puts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # ------------------------------------------------------------------------- if CppAD_ADOLC ADOLC_SRC_FILES = mul_level_adolc.cpp mul_level_adolc_ode.cpp ADOLC_EXTRA_FILES = ADOLC_LIB = -ladolc -lColPack -L$(ADOLC_DIR)/lib -L$(ADOLC_DIR)/lib64 ADOLC_FLAGS = -DCPPAD_HAS_ADOLC -I$(ADOLC_DIR)/include else ADOLC_EXTRA_FILES = mul_level_adolc.cpp mul_level_adolc_ode.cpp ADOLC_SRC_FILES = ADOLC_LIB = ADOLC_FLAGS = endif # ------------------------------------------------------------------------- if CppAD_HAVE_AR if CppAD_EIGEN_DIR # make a special library so can have it's own compile flags (see configure.ac) EIGEN_EXTRA_FILES = noinst_LIBRARIES = libeigen.a libeigen_a_SOURCES = eigen_det.cpp eigen_array.cpp EIGEN_LIB = -L. -leigen EIGEN_FLAGS = -DCPPAD_HAS_EIGEN libeigen_a_CXXFLAGS = \ -g $(CXX_FLAGS_EIGEN) \ -DCPPAD_HAS_EIGEN \ -I$(EIGEN_DIR)/include else EIGEN_EXTRA_FILES = eigen_det.cpp eigen_array.cpp EIGEN_LIB = EIGEN_FLAGS = endif else EIGEN_EXTRA_FILES = eigen_det.cpp eigen_array.cpp EIGEN_LIB = EIGEN_FLAGS = endif # ------------------------------------------------------------------------- # auto-tools does not support use of colpack EXTRA_DIST = \ colpack_hes.cpp \ colpack_jac.cpp \ $(ADOLC_EXTRA_FILES) \ $(EIGEN_EXTRA_FILES) # check_PROGRAMS = example # if CppAD_MS_COMPILER AM_CXXFLAGS = -EHsc -g $(ADOLC_FLAGS) $(EIGEN_FLAGS) $(CXX_FLAGS) else AM_CXXFLAGS = -g $(ADOLC_FLAGS) $(EIGEN_FLAGS) $(CXX_FLAGS) endif # AM_CPPFLAGS = \ -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ $(ADOLC_FLAGS) \ $(EIGEN_FLAGS) # LDADD = $(ADOLC_LIB) $(BTHREAD_LIB) $(EIGEN_LIB) $(PTHREAD_LIB) # example_SOURCES = \ $(ADOLC_SRC_FILES) \ \ abort_recording.cpp \ abs.cpp \ acos.cpp \ acosh.cpp \ ad_assign.cpp \ ad_ctor.cpp \ add.cpp \ add_eq.cpp \ ad_fun.cpp \ ad_in_c.cpp \ ad_input.cpp \ ad_output.cpp \ asin.cpp \ asinh.cpp \ atan2.cpp \ atan.cpp \ atanh.cpp \ azmul.cpp \ base_alloc.hpp \ base_require.cpp \ bender_quad.cpp \ bool_fun.cpp \ bool_sparsity.cpp \ capacity_order.cpp \ change_param.cpp \ check_for_nan.cpp \ check_numeric_type.cpp \ check_simple_vector.cpp \ compare_change.cpp \ compare.cpp \ complex_poly.cpp \ cond_exp.cpp \ conj_grad.cpp \ cos.cpp \ cosh.cpp \ cppad_vector.cpp \ dependency.cpp \ div.cpp \ div_eq.cpp \ equal_op_seq.cpp \ erf.cpp \ error_handler.cpp \ example.cpp \ exp.cpp \ expm1.cpp \ for_one.cpp \ for_sparse_hes.cpp \ for_sparse_jac.cpp \ for_two.cpp \ forward.cpp \ forward_dir.cpp \ forward_order.cpp \ fun_assign.cpp \ fun_check.cpp \ hes_lagrangian.cpp \ hes_lu_det.cpp \ hes_minor_det.cpp \ hessian.cpp \ hes_times_dir.cpp \ independent.cpp \ index_sort.cpp \ integer.cpp \ interface2c.cpp\ interp_onetape.cpp\ interp_retape.cpp\ jac_lu_det.cpp \ jac_minor_det.cpp \ jacobian.cpp \ log10.cpp \ log1p.cpp \ log.cpp \ lu_factor.cpp \ lu_invert.cpp \ lu_ratio.cpp \ lu_solve.cpp \ lu_vec_ad.cpp \ lu_vec_ad.hpp \ lu_vec_ad_ok.cpp \ mul.cpp \ mul_eq.cpp \ mul_level.cpp \ mul_level_ode.cpp \ nan.cpp \ near_equal.cpp \ near_equal_ext.cpp \ number_skip.cpp \ numeric_type.cpp \ num_limits.cpp \ ode_err_control.cpp \ ode_err_maxabs.cpp \ ode_gear_control.cpp\ ode_gear.cpp \ ode_stiff.cpp \ ode_taylor.cpp \ opt_val_hes.cpp \ par_var.cpp \ poly.cpp \ pow.cpp \ pow_int.cpp \ print_for.cpp \ reverse_checkpoint.cpp \ reverse_one.cpp \ reverse_three.cpp \ reverse_two.cpp \ rev_one.cpp \ rev_sparse_hes.cpp \ rev_sparse_jac.cpp \ rev_two.cpp \ romberg_mul.cpp \ romberg_one.cpp \ rosen_34.cpp \ runge45_1.cpp \ runge45_2.cpp \ seq_property.cpp \ set_union.cpp \ sign.cpp \ simple_vector.cpp \ sin.cpp \ sinh.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp \ sparse_sub_hes.cpp \ sparsity_sub.cpp \ sqrt.cpp \ stack_machine.cpp \ sub.cpp \ sub_eq.cpp \ sub_sparse_hes.cpp \ tan.cpp \ tanh.cpp \ tape_index.cpp \ thread_alloc.cpp \ to_string.cpp \ unary_minus.cpp \ unary_plus.cpp \ value.cpp \ var2par.cpp \ vec_ad.cpp \ vector_bool.cpp test: check ./example cppad-20170000.3/example/example.cpp0000644000175200017650000003351513057470460016231 0ustar coincoin-web// $Id: example.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin example.cpp$$ $spell Cpp $$ $section CppAD Examples and Tests$$ $head Running Tests$$ To build this program and run its correctness tests see $cref cmake_check$$. $code $srcfile%example/example.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ // system include files used for I/O # include // C style asserts # include // standard string # include // memory utility # include // prototype external compiled tests (this line expected by bin/new_test.sh) extern bool abort_recording(void); extern bool abs(void); extern bool acosh(void); extern bool acos(void); extern bool ad_assign(void); extern bool ad_ctor(void); extern bool AddEq(void); extern bool Add(void); extern bool ad_fun(void); extern bool ad_in_c(void); extern bool ad_input(void); extern bool ad_output(void); extern bool asinh(void); extern bool asin(void); extern bool atan2(void); extern bool atanh(void); extern bool atan(void); extern bool azmul(void); extern bool base_require(void); extern bool BenderQuad(void); extern bool BoolFun(void); extern bool bool_sparsity(void); extern bool capacity_order(void); extern bool change_param(void); extern bool check_for_nan(void); extern bool CheckNumericType(void); extern bool CheckSimpleVector(void); extern bool colpack_hes(void); extern bool colpack_jac(void); extern bool compare_change(void); extern bool Compare(void); extern bool complex_poly(void); extern bool CondExp(void); extern bool conj_grad(void); extern bool Cosh(void); extern bool Cos(void); extern bool CppAD_vector(void); extern bool dependency(void); extern bool DivEq(void); extern bool Div(void); extern bool eigen_array(void); extern bool eigen_det(void); extern bool EqualOpSeq(void); extern bool Erf(void); extern bool ErrorHandler(void); extern bool expm1(void); extern bool exp(void); extern bool ForOne(void); extern bool for_sparse_hes(void); extern bool ForSparseJac(void); extern bool ForTwo(void); extern bool forward_dir(void); extern bool forward_order(void); extern bool Forward(void); extern bool fun_assign(void); extern bool FunCheck(void); extern bool HesLagrangian(void); extern bool HesLuDet(void); extern bool HesMinorDet(void); extern bool Hessian(void); extern bool HesTimesDir(void); extern bool Independent(void); extern bool index_sort(void); extern bool Integer(void); extern bool Interface2C(void); extern bool interp_onetape(void); extern bool interp_retape(void); extern bool JacLuDet(void); extern bool JacMinorDet(void); extern bool Jacobian(void); extern bool log10(void); extern bool log1p(void); extern bool log(void); extern bool LuFactor(void); extern bool LuInvert(void); extern bool LuRatio(void); extern bool LuSolve(void); extern bool LuVecADOk(void); extern bool MulEq(void); extern bool mul_level_adolc_ode(void); extern bool mul_level_adolc(void); extern bool mul_level_ode(void); extern bool mul_level(void); extern bool Mul(void); extern bool nan(void); extern bool NearEqualExt(void); extern bool Near_Equal(void); extern bool number_skip(void); extern bool NumericType(void); extern bool num_limits(void); extern bool OdeErrControl(void); extern bool OdeErrMaxabs(void); extern bool OdeGearControl(void); extern bool OdeGear(void); extern bool OdeStiff(void); extern bool ode_taylor(void); extern bool opt_val_hes(void); extern bool ParVar(void); extern bool Poly(void); extern bool pow_int(void); extern bool pow(void); extern bool print_for(void); extern bool reverse_any(void); extern bool reverse_one(void); extern bool reverse_three(void); extern bool reverse_two(void); extern bool RevOne(void); extern bool rev_sparse_hes(void); extern bool RevSparseJac(void); extern bool RevTwo(void); extern bool RombergMul(void); extern bool RombergOne(void); extern bool Rosen34(void); extern bool runge_45_1(void); extern bool runge_45_2(void); extern bool seq_property(void); extern bool set_union(void); extern bool sign(void); extern bool SimpleVector(void); extern bool Sinh(void); extern bool Sin(void); extern bool sparse_hessian(void); extern bool sparse_jacobian(void); extern bool sparse_sub_hes(void); extern bool sparsity_sub(void); extern bool Sqrt(void); extern bool StackMachine(void); extern bool SubEq(void); extern bool sub_sparse_hes(void); extern bool Sub(void); extern bool Tanh(void); extern bool Tan(void); extern bool TapeIndex(void); extern bool thread_alloc(void); extern bool to_string(void); extern bool UnaryMinus(void); extern bool UnaryPlus(void); extern bool Value(void); extern bool Var2Par(void); extern bool vec_ad(void); extern bool vectorBool(void); namespace { // function that runs one test static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), std::string name) { bool ok = true; std::streamsize width = 20; std::cout.width( width ); std::cout.setf( std::ios_base::left ); std::cout << name; // ok &= name.size() < size_t(width); ok &= TestOk(); if( ok ) { std::cout << "OK" << std::endl; Run_ok_count++; } else { std::cout << "Error" << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; // This line is used by test_one.sh // run external compiled tests (this line expected by bin/new_test.sh) ok &= Run( abort_recording, "abort_recording" ); ok &= Run( abs, "abs" ); ok &= Run( acos, "acos" ); ok &= Run( acosh, "acosh" ); ok &= Run( ad_assign, "ad_assign" ); ok &= Run( ad_ctor, "ad_ctor" ); ok &= Run( Add, "Add" ); ok &= Run( AddEq, "AddEq" ); ok &= Run( ad_fun, "ad_fun" ); ok &= Run( ad_in_c, "ad_in_c" ); ok &= Run( ad_input, "ad_input" ); ok &= Run( ad_output, "ad_output" ); ok &= Run( asin, "asin" ); ok &= Run( asinh, "asinh" ); ok &= Run( atan2, "atan2" ); ok &= Run( atan, "atan" ); ok &= Run( atanh, "atanh" ); ok &= Run( azmul, "azmul" ); ok &= Run( BenderQuad, "BenderQuad" ); ok &= Run( BoolFun, "BoolFun" ); ok &= Run( bool_sparsity, "bool_sparsity" ); ok &= Run( capacity_order, "capacity_order" ); ok &= Run( change_param, "change_param" ); ok &= Run( check_for_nan, "check_for_nan" ); ok &= Run( CheckNumericType, "CheckNumericType" ); ok &= Run( CheckSimpleVector, "CheckSimpleVector"); ok &= Run( compare_change, "compare_change" ); ok &= Run( Compare, "Compare" ); ok &= Run( complex_poly, "complex_poly" ); ok &= Run( CondExp, "CondExp" ); ok &= Run( conj_grad, "conj_grad" ); ok &= Run( Cos, "Cos" ); ok &= Run( Cosh, "Cosh" ); ok &= Run( CppAD_vector, "CppAD_vector" ); ok &= Run( dependency, "dependency" ); ok &= Run( Div, "Div" ); ok &= Run( DivEq, "DivEq" ); ok &= Run( EqualOpSeq, "EqualOpSeq" ); ok &= Run( Erf, "Erf" ); ok &= Run( ErrorHandler, "ErrorHandler" ); ok &= Run( exp, "exp" ); ok &= Run( expm1, "expm1" ); ok &= Run( ForOne, "ForOne" ); ok &= Run( for_sparse_hes, "for_sparse_hes" ); ok &= Run( ForSparseJac, "ForSparseJac" ); ok &= Run( ForTwo, "ForTwo" ); ok &= Run( forward_dir, "forward_dir" ); ok &= Run( Forward, "Forward" ); ok &= Run( forward_order, "forward_order" ); ok &= Run( fun_assign, "fun_assign" ); ok &= Run( FunCheck, "FunCheck" ); ok &= Run( HesLagrangian, "HesLagrangian" ); ok &= Run( HesLuDet, "HesLuDet" ); ok &= Run( HesMinorDet, "HesMinorDet" ); ok &= Run( Hessian, "Hessian" ); ok &= Run( HesTimesDir, "HesTimesDir" ); ok &= Run( Independent, "Independent" ); ok &= Run( index_sort, "index_sort" ); ok &= Run( Integer, "Integer" ); ok &= Run( Interface2C, "Interface2C" ); ok &= Run( interp_onetape, "interp_onetape" ); ok &= Run( interp_retape, "interp_retape" ); ok &= Run( JacLuDet, "JacLuDet" ); ok &= Run( JacMinorDet, "JacMinorDet" ); ok &= Run( Jacobian, "Jacobian" ); ok &= Run( log10, "log10" ); ok &= Run( log1p, "log1p" ); ok &= Run( log, "log" ); ok &= Run( LuFactor, "LuFactor" ); ok &= Run( LuInvert, "LuInvert" ); ok &= Run( LuRatio, "LuRatio" ); ok &= Run( LuSolve, "LuSolve" ); ok &= Run( LuVecADOk, "LuVecADOk" ); ok &= Run( MulEq, "MulEq" ); ok &= Run( mul_level, "mul_level" ); ok &= Run( mul_level_ode, "mul_level_ode" ); ok &= Run( Mul, "Mul" ); ok &= Run( nan, "nan" ); ok &= Run( NearEqualExt, "NearEqualExt" ); ok &= Run( Near_Equal, "Near_Equal" ); ok &= Run( number_skip, "number_skip" ); ok &= Run( NumericType, "NumericType" ); ok &= Run( num_limits, "num_limits" ); ok &= Run( OdeErrControl, "OdeErrControl" ); ok &= Run( OdeErrMaxabs, "OdeErrMaxabs" ); ok &= Run( OdeGearControl, "OdeGearControl" ); ok &= Run( OdeGear, "OdeGear" ); ok &= Run( OdeStiff, "OdeStiff" ); ok &= Run( ode_taylor, "ode_taylor" ); ok &= Run( opt_val_hes, "opt_val_hes" ); ok &= Run( ParVar, "ParVar" ); ok &= Run( Poly, "Poly" ); ok &= Run( pow_int, "pow_int" ); ok &= Run( pow, "pow" ); ok &= Run( reverse_any, "reverse_any" ); ok &= Run( reverse_one, "reverse_one" ); ok &= Run( reverse_three, "reverse_three" ); ok &= Run( reverse_two, "reverse_two" ); ok &= Run( RevOne, "RevOne" ); ok &= Run( rev_sparse_hes, "rev_sparse_hes" ); ok &= Run( RevSparseJac, "RevSparseJac" ); ok &= Run( RevTwo, "RevTwo" ); ok &= Run( RombergMul, "RombergMul" ); ok &= Run( RombergOne, "RombergOne" ); ok &= Run( Rosen34, "Rosen34" ); ok &= Run( runge_45_1, "runge_45_1" ); ok &= Run( runge_45_2, "runge_45_2" ); ok &= Run( seq_property, "seq_property" ); ok &= Run( set_union, "set_union" ); ok &= Run( sign, "sign" ); ok &= Run( SimpleVector, "SimpleVector" ); ok &= Run( Sinh, "Sinh" ); ok &= Run( Sin, "Sin" ); ok &= Run( sparse_hessian, "sparse_hessian" ); ok &= Run( sparse_jacobian, "sparse_jacobian" ); ok &= Run( sparse_sub_hes, "sparse_sub_hes" ); ok &= Run( sparsity_sub, "sparsity_sub" ); ok &= Run( Sqrt, "Sqrt" ); ok &= Run( StackMachine, "StackMachine" ); ok &= Run( SubEq, "SubEq" ); ok &= Run( sub_sparse_hes, "sub_sparse_hes" ); ok &= Run( Sub, "Sub" ); ok &= Run( Tanh, "Tanh" ); ok &= Run( Tan, "Tan" ); ok &= Run( TapeIndex, "TapeIndex" ); ok &= Run( thread_alloc, "thread_alloc" ); ok &= Run( to_string, "to_string" ); ok &= Run( UnaryMinus, "UnaryMinus" ); ok &= Run( UnaryPlus, "UnaryPlus" ); ok &= Run( Value, "Value" ); ok &= Run( Var2Par, "Var2Par" ); ok &= Run( vec_ad, "vec_ad" ); ok &= Run( vectorBool, "vectorBool" ); # ifdef CPPAD_HAS_ADOLC ok &= Run( mul_level_adolc, "mul_level_adolc" ); ok &= Run( mul_level_adolc_ode, "mul_level_adolc_ode" ); # endif # ifdef CPPAD_COLPACK_EXAMPLES ok &= Run( colpack_hes, "colpack_hes" ); ok &= Run( colpack_jac, "colpack_jac" ); # endif # ifdef CPPAD_HAS_EIGEN ok &= Run( eigen_array, "eigen_array" ); ok &= Run( eigen_det, "eigen_det" ); # endif // check for errors using std::cout; using std::endl; assert( ok || (Run_error_count > 0) ); if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "OK: " << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Error: " << "memory leak detected" << endl; } // Run base_require after memory leak check because base_alloc.hpp uses // thread_alloc to allocate memory for static copies of nan. ok &= Run( base_require, "base_require" ); // convert int(size_t) to avoid warning on _MSC_VER systems if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! ok ); } // END C++ cppad-20170000.3/example/log10.cpp0000644000175200017650000000413613057470460015515 0ustar coincoin-web// $Id: log10.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin log10.cpp$$ $spell log $$ $section The AD log10 Function: Example and Test$$ $code $srcfile%example/log10.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool log10(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // ten raised to the x0 power AD ten = 10.; AD pow_10_x0 = CppAD::pow(ten, x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::log10(pow_10_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps99, eps99); // use a VecAD::reference object with log10 CppAD::VecAD v(1); AD zero(0); v[zero] = pow_10_x0; AD result = CppAD::log10(v[zero]); ok &= NearEqual(result, x0, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/stack_machine.cpp0000644000175200017650000001232413057470460017362 0ustar coincoin-web// $Id: stack_machine.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin stack_machine.cpp$$ $spell $$ $section Example Differentiating a Stack Machine Interpreter$$ $mindex test$$ $code $srcfile%example/stack_machine.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include # include # include # include # include namespace { // Begin empty namespace ------------------------------------------------ bool is_number( const std::string &s ) { char ch = s[0]; bool number = (std::strchr("0123456789.", ch) != 0); return number; } bool is_binary( const std::string &s ) { char ch = s[0]; bool binary = (strchr("+-*/.", ch) != 0); return binary; } bool is_variable( const std::string &s ) { char ch = s[0]; bool variable = ('a' <= ch) & (ch <= 'z'); return variable; } void StackMachine( std::stack< std::string > &token_stack , CppAD::vector< CppAD::AD > &variable ) { using std::string; using std::stack; using CppAD::AD; stack< AD > value_stack; string token; AD value_one; AD value_two; while( ! token_stack.empty() ) { string s = token_stack.top(); token_stack.pop(); if( is_number(s) ) { value_one = std::atof( s.c_str() ); value_stack.push( value_one ); } else if( is_variable(s) ) { value_one = variable[ size_t(s[0]) - size_t('a') ]; value_stack.push( value_one ); } else if( is_binary(s) ) { assert( value_stack.size() >= 2 ); value_one = value_stack.top(); value_stack.pop(); value_two = value_stack.top(); value_stack.pop(); switch( s[0] ) { case '+': value_stack.push(value_one + value_two); break; case '-': value_stack.push(value_one - value_two); break; case '*': value_stack.push(value_one * value_two); break; case '/': value_stack.push(value_one / value_two); break; default: assert(0); } } else if( s[0] == '=' ) { assert( value_stack.size() >= 1 ); assert( token_stack.size() >= 1 ); // s = token_stack.top(); token_stack.pop(); // assert( is_variable( s ) ); value_one = value_stack.top(); value_stack.pop(); // variable[ size_t(s[0]) - size_t('a') ] = value_one; } else assert(0); } return; } // End empty namespace ------------------------------------------------------- } bool StackMachine(void) { bool ok = true; using std::string; using std::stack; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); using CppAD::vector; // The users program in that stack machine language const char *program[] = { "1.0", "a", "+", "=", "b", // b = a + 1 "2.0", "b", "*", "=", "c", // c = b * 2 "3.0", "c", "-", "=", "d", // d = c - 3 "4.0", "d", "/", "=", "e" // e = d / 4 }; size_t n_program = sizeof( program ) / sizeof( program[0] ); // put the program in the token stack stack< string > token_stack; size_t i = n_program; while(i--) token_stack.push( program[i] ); // domain space vector size_t n = 1; vector< AD > X(n); X[0] = 0.; // declare independent variables and start tape recording CppAD::Independent(X); // x[0] corresponds to a in the stack machine vector< AD > variable(26); variable[0] = X[0]; // calculate the resutls of the program StackMachine( token_stack , variable); // range space vector size_t m = 4; vector< AD > Y(m); Y[0] = variable[1]; // b = a + 1 Y[1] = variable[2]; // c = (a + 1) * 2 Y[2] = variable[3]; // d = (a + 1) * 2 - 3 Y[3] = variable[4]; // e = ( (a + 1) * 2 - 3 ) / 4 // create f : X -> Y and stop tape recording CppAD::ADFun f(X, Y); // use forward mode to evaluate function at different argument value size_t p = 0; vector x(n); vector y(m); x[0] = 1.; y = f.Forward(p, x); // check function values ok &= (y[0] == x[0] + 1.); ok &= (y[1] == (x[0] + 1.) * 2.); ok &= (y[2] == (x[0] + 1.) * 2. - 3.); ok &= (y[3] == ( (x[0] + 1.) * 2. - 3.) / 4.); // Use forward mode (because x is shorter than y) to calculate Jacobian p = 1; vector dx(n); vector dy(m); dx[0] = 1.; dy = f.Forward(p, dx); ok &= NearEqual(dy[0], 1., eps99, eps99); ok &= NearEqual(dy[1], 2., eps99, eps99); ok &= NearEqual(dy[2], 2., eps99, eps99); ok &= NearEqual(dy[3], .5, eps99, eps99); // Use Jacobian routine (which automatically decides which mode to use) dy = f.Jacobian(x); ok &= NearEqual(dy[0], 1., eps99, eps99); ok &= NearEqual(dy[1], 2., eps99, eps99); ok &= NearEqual(dy[2], 2., eps99, eps99); ok &= NearEqual(dy[3], .5, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/CMakeLists.txt0000644000175200017650000001034313057470460016624 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the example directory tests # Inherit environment from ../CMakeList.txt # Specifies build type for this directory. Possible values are # empty, Debug, Release, RelWithDebInfo and MinSizeRel SET(CMAKE_BUILD_TYPE DEBUG) # initialize check_depends SET(check_example_depends example) # atomic examples ADD_SUBDIRECTORY(atomic) # optimize examples ADD_SUBDIRECTORY(optimize) # adolc_sources, adolc_libs, and CPPAD_HAS_ADOLC SET(sources mul_level_adolc.cpp mul_level_adolc_ode.cpp) sources_libs_define(adolc "${sources}" adolc HAS_ADOLC) # eigen_sources and CPPAD_HAS_EIGEN SET(sources eigen_det.cpp eigen_array.cpp) sources_libs_define(eigen "${sources}" "" HAS_EIGEN) # colpack_prefix SET(colpack_sources colpack_hes.cpp colpack_jac.cpp ) # ipopt_prefix IF( ipopt_prefix ) ADD_SUBDIRECTORY(ipopt_solve) add_to_list(check_depends check_example_ipopt_solve) ENDIF( ipopt_prefix ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(example EXCLUDE_FROM_ALL example.cpp ${adolc_sources} ${eigen_sources} ${colpack_sources} abort_recording.cpp abs.cpp acos.cpp acosh.cpp ad_assign.cpp ad_ctor.cpp add.cpp add_eq.cpp ad_fun.cpp ad_in_c.cpp ad_input.cpp ad_output.cpp asin.cpp asinh.cpp atan2.cpp atan.cpp atanh.cpp azmul.cpp base_alloc.hpp base_require.cpp bender_quad.cpp bool_fun.cpp bool_sparsity.cpp capacity_order.cpp change_param.cpp check_for_nan.cpp check_numeric_type.cpp check_simple_vector.cpp compare_change.cpp compare.cpp complex_poly.cpp cond_exp.cpp conj_grad.cpp cos.cpp cosh.cpp cppad_vector.cpp dependency.cpp div.cpp div_eq.cpp equal_op_seq.cpp erf.cpp error_handler.cpp exp.cpp expm1.cpp for_one.cpp for_sparse_hes.cpp for_sparse_jac.cpp for_two.cpp forward.cpp forward_dir.cpp forward_order.cpp fun_assign.cpp fun_check.cpp hes_lagrangian.cpp hes_lu_det.cpp hes_minor_det.cpp hessian.cpp hes_times_dir.cpp independent.cpp index_sort.cpp integer.cpp interface2c.cpp interp_onetape.cpp interp_retape.cpp jac_lu_det.cpp jac_minor_det.cpp jacobian.cpp log10.cpp log1p.cpp log.cpp lu_factor.cpp lu_invert.cpp lu_ratio.cpp lu_solve.cpp lu_vec_ad.cpp lu_vec_ad.hpp lu_vec_ad_ok.cpp mul.cpp mul_eq.cpp mul_level.cpp mul_level_ode.cpp nan.cpp near_equal.cpp near_equal_ext.cpp number_skip.cpp numeric_type.cpp num_limits.cpp ode_err_control.cpp ode_err_maxabs.cpp ode_gear_control.cpp ode_gear.cpp ode_stiff.cpp ode_taylor.cpp opt_val_hes.cpp par_var.cpp poly.cpp pow.cpp pow_int.cpp print_for.cpp reverse_checkpoint.cpp reverse_one.cpp reverse_three.cpp reverse_two.cpp rev_one.cpp rev_sparse_hes.cpp rev_sparse_jac.cpp rev_two.cpp romberg_mul.cpp romberg_one.cpp rosen_34.cpp runge45_1.cpp runge45_2.cpp seq_property.cpp set_union.cpp sign.cpp simple_vector.cpp sin.cpp sinh.cpp sparse_hessian.cpp sparse_jacobian.cpp sparse_sub_hes.cpp sparsity_sub.cpp sqrt.cpp stack_machine.cpp sub.cpp sub_eq.cpp sub_sparse_hes.cpp tan.cpp tanh.cpp tape_index.cpp thread_alloc.cpp to_string.cpp unary_minus.cpp unary_plus.cpp value.cpp var2par.cpp vec_ad.cpp vector_bool.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags(example) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES(example ${cppad_lib} ${adolc_libs} ${colpack_libs} ) # Add the check_example target ADD_CUSTOM_TARGET(check_example example DEPENDS ${check_example_depends}) MESSAGE(STATUS "make check_example: available") # Change check depends in parent environment add_to_list(check_depends check_example) SET(check_depends "${check_depends}" PARENT_SCOPE) cppad-20170000.3/example/sub.cpp0000644000175200017650000000433213057470460015362 0ustar coincoin-web// $Id: sub.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sub.cpp$$ $section AD Binary Subtraction: Example and Test$$ $mindex - subtract minus$$ $code $srcfile%example/sub.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool Sub(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = .5; CPPAD_TESTVECTOR(AD) x(1); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); AD a = 2. * x[0] - 1.; // AD - double AD b = a - 2; // AD - int AD c = 3. - b; // double - AD AD d = 4 - c; // int - AD // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = x[0] - d; // AD - AD // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0], x0-4.+3.+2.-2.*x0+1., eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], -1., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], -1., eps99, eps99); // use a VecAD::reference object with subtraction CppAD::VecAD v(1); AD zero(0); v[zero] = b; AD result = 3. - v[zero]; ok &= (result == c); return ok; } // END C++ cppad-20170000.3/example/rosen_34.cpp0000644000175200017650000001113513057470460016224 0ustar coincoin-web// $Id: rosen_34.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin rosen_34.cpp$$ $spell Rosen $$ $section Rosen34: Example and Test$$ $mindex Rosen34$$ Define $latex X : \B{R} \rightarrow \B{R}^n$$ by $latex \[ X_i (t) = t^{i+1} \] $$ for $latex i = 1 , \ldots , n-1$$. It follows that $latex \[ \begin{array}{rclr} X_i(0) & = & 0 & {\rm for \; all \;} i \\ X_i ' (t) & = & 1 & {\rm if \;} i = 0 \\ X_i '(t) & = & (i+1) t^i = (i+1) X_{i-1} (t) & {\rm if \;} i > 0 \end{array} \] $$ The example tests Rosen34 using the relations above: $code $srcfile%example/rosen_34.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // For automatic differentiation namespace { class Fun { public: // constructor Fun(bool use_x_) : use_x(use_x_) { } // compute f(t, x) both for double and AD template void Ode( const Scalar &t, const CPPAD_TESTVECTOR(Scalar) &x, CPPAD_TESTVECTOR(Scalar) &f) { size_t n = x.size(); Scalar ti(1); f[0] = Scalar(1); size_t i; for(i = 1; i < n; i++) { ti *= t; // convert int(size_t) to avoid warning // on _MSC_VER systems if( use_x ) f[i] = int(i+1) * x[i-1]; else f[i] = int(i+1) * ti; } } // compute partial of f(t, x) w.r.t. t using AD void Ode_ind( const double &t, const CPPAD_TESTVECTOR(double) &x, CPPAD_TESTVECTOR(double) &f_t) { using namespace CppAD; size_t n = x.size(); CPPAD_TESTVECTOR(AD) T(1); CPPAD_TESTVECTOR(AD) X(n); CPPAD_TESTVECTOR(AD) F(n); // set argument values T[0] = t; size_t i; for(i = 0; i < n; i++) X[i] = x[i]; // declare independent variables Independent(T); // compute f(t, x) this->Ode(T[0], X, F); // define AD function object ADFun fun(T, F); // compute partial of f w.r.t t CPPAD_TESTVECTOR(double) dt(1); dt[0] = 1.; f_t = fun.Forward(1, dt); } // compute partial of f(t, x) w.r.t. x using AD void Ode_dep( const double &t, const CPPAD_TESTVECTOR(double) &x, CPPAD_TESTVECTOR(double) &f_x) { using namespace CppAD; size_t n = x.size(); CPPAD_TESTVECTOR(AD) T(1); CPPAD_TESTVECTOR(AD) X(n); CPPAD_TESTVECTOR(AD) F(n); // set argument values T[0] = t; size_t i, j; for(i = 0; i < n; i++) X[i] = x[i]; // declare independent variables Independent(X); // compute f(t, x) this->Ode(T[0], X, F); // define AD function object ADFun fun(X, F); // compute partial of f w.r.t x CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) df(n); for(j = 0; j < n; j++) dx[j] = 0.; for(j = 0; j < n; j++) { dx[j] = 1.; df = fun.Forward(1, dx); for(i = 0; i < n; i++) f_x [i * n + j] = df[i]; dx[j] = 0.; } } private: const bool use_x; }; } bool Rosen34(void) { bool ok = true; // initial return value size_t i; // temporary indices using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); size_t n = 4; // number components in X(t) and order of method size_t M = 2; // number of Rosen34 steps in [ti, tf] double ti = 0.; // initial time double tf = 2.; // final time // xi = X(0) CPPAD_TESTVECTOR(double) xi(n); for(i = 0; i 0); // compute Rosen34 approximation for X(tf) CPPAD_TESTVECTOR(double) xf(n), e(n); xf = CppAD::Rosen34(F, M, ti, tf, xi, e); double check = tf; for(i = 0; i < n; i++) { // check that error is always positive ok &= (e[i] >= 0.); // 4th order method is exact for i < 4 if( i < 4 ) ok &= NearEqual(xf[i], check, eps99, eps99); // 3rd order method is exact for i < 3 if( i < 3 ) ok &= (e[i] <= 1e-10); // check value for next i check *= tf; } } return ok; } // END C++ cppad-20170000.3/example/poly.cpp0000644000175200017650000000236613057470460015561 0ustar coincoin-web// $Id: poly.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin poly.cpp$$ $section Polynomial Evaluation: Example and Test$$ $code $srcfile%example/poly.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool Poly(void) { bool ok = true; // degree of the polynomial size_t deg = 3; // set the polynomial coefficients CPPAD_TESTVECTOR(double) a(deg + 1); size_t i; for(i = 0; i <= deg; i++) a[i] = 1.; // evaluate this polynomial size_t k = 0; double z = 2.; double p = CppAD::Poly(k, a, z); ok &= (p == 1. + z + z*z + z*z*z); // evaluate derivative k = 1; p = CppAD::Poly(k, a, z); ok &= (p == 1 + 2.*z + 3.*z*z); return ok; } // END C++ cppad-20170000.3/example/cond_exp.cpp0000644000175200017650000000642713057470460016377 0ustar coincoin-web// $Id: cond_exp.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cond_exp.cpp$$ $spell Cpp cstddef CondExp $$ $section Conditional Expressions: Example and Test$$ $head See Also$$ $cref optimize_conditional_skip.cpp$$ $head Description$$ Use $code CondExp$$ to compute $latex \[ f(x) = \sum_{j=0}^{m-1} x_j \log( x_j ) \] $$ and its derivative at various argument values ( where $latex x_j \geq 0$$ ) with out having to re-tape; i.e., using only one $cref ADFun$$ object. Note that $latex x_j \log ( x_j ) \rightarrow 0 $$ as $latex x_j \downarrow 0$$ and we need to handle the case $latex x_j = 0$$ in a special way to avoid multiplying zero by infinity. $code $srcfile%example/cond_exp.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool CondExp(void) { bool ok = true; using CppAD::isnan; using CppAD::AD; using CppAD::NearEqual; using CppAD::log; using CppAD::abs; double eps = 100. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 5; CPPAD_TESTVECTOR(AD) ax(n); size_t j; for(j = 0; j < n; j++) ax[j] = 1.; // declare independent variables and start tape recording CppAD::Independent(ax); AD asum = 0.; AD azero = 0.; for(j = 0; j < n; j++) { // if x_j > 0, add x_j * log( x_j ) to the sum asum += CppAD::CondExpGt(ax[j], azero, ax[j] * log(ax[j]), azero); } // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = asum; // create f: x -> ay and stop tape recording CppAD::ADFun f(ax, ay); // vectors for arguments to the function object f CPPAD_TESTVECTOR(double) x(n); // argument values CPPAD_TESTVECTOR(double) y(m); // function values CPPAD_TESTVECTOR(double) w(m); // function weights CPPAD_TESTVECTOR(double) dw(n); // derivative of weighted function // a case where x[j] > 0 for all j double check = 0.; for(j = 0; j < n; j++) { x[j] = double(j + 1); check += x[j] * log( x[j] ); } // function value y = f.Forward(0, x); ok &= NearEqual(y[0], check, eps, eps); // compute derivative of y[0] w[0] = 1.; dw = f.Reverse(1, w); for(j = 0; j < n; j++) ok &= NearEqual(dw[j], log(x[j]) + 1., eps, eps); // a case where x[3] is equal to zero check -= x[3] * log( x[3] ); x[3] = 0.; // function value y = f.Forward(0, x); ok &= NearEqual(y[0], check, eps, eps); // check derivative of y[0] f.check_for_nan(false); w[0] = 1.; dw = f.Reverse(1, w); for(j = 0; j < n; j++) { if( x[j] > 0 ) ok &= NearEqual(dw[j], log(x[j]) + 1., eps, eps); else { // Note that in case where dw has type AD and is a variable // this dw[j] can be nan (zero times nan is not zero). ok &= NearEqual(dw[j], 0.0, eps, eps); } } return ok; } // END C++ cppad-20170000.3/example/exp.cpp0000644000175200017650000000401413057470460015362 0ustar coincoin-web// $Id: exp.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp.cpp$$ $spell exp $$ $section The AD exp Function: Example and Test$$ $code $srcfile%example/exp.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool exp(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CppAD::exp(ax[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // check value double check = std::exp(x0); ok &= NearEqual(ay[0], check, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], check, eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, eps, eps); // use a VecAD::reference object with exp CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::exp(v[zero]); ok &= NearEqual(result, check, eps, eps); return ok; } // END C++ cppad-20170000.3/example/cos.cpp0000644000175200017650000000411013057470460015347 0ustar coincoin-web// $Id: cos.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cos.cpp$$ $spell cos $$ $section The AD cos Function: Example and Test$$ $code $srcfile%example/cos.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool Cos(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::cos(x[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value double check = std::cos(x0); ok &= NearEqual(y[0] , check, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); check = - std::sin(x0); ok &= NearEqual(dy[0], check, eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, eps99, eps99); // use a VecAD::reference object with cos CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::cos(v[zero]); check = std::cos(x0); ok &= NearEqual(result, check, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/check_numeric_type.cpp0000644000175200017650000001042013057470460020424 0ustar coincoin-web// $Id: check_numeric_type.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin check_numeric_type.cpp$$ $section The CheckNumericType Function: Example and Test$$ $mindex check NumericType$$ $code $srcfile%example/check_numeric_type.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include // Chosing a value between 1 and 10 selects a numeric class properity to be // omitted and result in an error message being generated # define CppADMyTypeOmit 0 namespace { // Empty namespace // ------------------------------------------------------------------- class MyType { private: double d; public: // constructor from void MyType(void) : d(0.) { } // constructor from an int MyType(int d_) : d(d_) { } // copy constuctor MyType(const MyType &x) { d = x.d; } // assignment operator void operator = (const MyType &x) { d = x.d; } // member function that converts to double double Double(void) const { return d; } # if CppADMyTypeOmit != 1 // unary plus MyType operator + (void) const { MyType x; x.d = d; return x; } # endif # if CppADMyTypeOmit != 2 // unary plus MyType operator - (void) const { MyType x; x.d = - d; return x; } # endif # if CppADMyTypeOmit != 3 // binary addition MyType operator + (const MyType &x) const { MyType y; y.d = d + x.d ; return y; } # endif # if CppADMyTypeOmit != 4 // binary subtraction MyType operator - (const MyType &x) const { MyType y; y.d = d - x.d ; return y; } # endif # if CppADMyTypeOmit != 5 // binary multiplication MyType operator * (const MyType &x) const { MyType y; y.d = d * x.d ; return y; } # endif # if CppADMyTypeOmit != 6 // binary division MyType operator / (const MyType &x) const { MyType y; y.d = d / x.d ; return y; } # endif # if CppADMyTypeOmit != 7 // computed assignment addition void operator += (const MyType &x) { d += x.d; } # endif # if CppADMyTypeOmit != 8 // computed assignment subtraction void operator -= (const MyType &x) { d -= x.d; } # endif # if CppADMyTypeOmit != 9 // computed assignment multiplication void operator *= (const MyType &x) { d *= x.d; } # endif # if CppADMyTypeOmit != 10 // computed assignment division void operator /= (const MyType &x) { d /= x.d; } # endif }; // ------------------------------------------------------------------- /* Solve: A[0] * x[0] + A[1] * x[1] = b[0] A[2] * x[0] + A[3] * x[1] = b[1] */ template void Solve(NumericType *A, NumericType *x, NumericType *b) { // make sure NumericType satisfies its conditions CppAD::CheckNumericType(); // copy b to x x[0] = b[0]; x[1] = b[1]; // copy A to work space NumericType W[4]; W[0] = A[0]; W[1] = A[1]; W[2] = A[2]; W[3] = A[3]; // divide first row by W(1,1) W[1] /= W[0]; x[0] /= W[0]; W[0] = NumericType(1); // subtract W(2,1) times first row from second row W[3] -= W[2] * W[1]; x[1] -= W[2] * x[0]; W[2] = NumericType(0); // divide second row by W(2, 2) x[1] /= W[3]; W[3] = NumericType(1); // use first row to solve for x[0] x[0] -= W[1] * x[1]; } } // End Empty namespace bool CheckNumericType(void) { bool ok = true; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); MyType A[4]; A[0] = MyType(1); A[1] = MyType(2); A[2] = MyType(3); A[3] = MyType(4); MyType b[2]; b[0] = MyType(1); b[1] = MyType(2); MyType x[2]; Solve(A, x, b); MyType sum; sum = A[0] * x[0] + A[1] * x[1]; ok &= NearEqual(sum.Double(), b[0].Double(), eps99, eps99); sum = A[2] * x[0] + A[3] * x[1]; ok &= NearEqual(sum.Double(), b[1].Double(), eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/jac_minor_det.cpp0000644000175200017650000000412613057470460017367 0ustar coincoin-web// $Id: jac_minor_det.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin jac_minor_det.cpp$$ $spell Cpp $$ $section Gradient of Determinant Using Expansion by Minors: Example and Test$$ $mindex minors$$ $code $srcfile%example/jac_minor_det.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include typedef std::complex Complex; typedef CppAD::AD ADComplex; typedef CPPAD_TESTVECTOR(ADComplex) ADVector; // ---------------------------------------------------------------------------- bool JacMinorDet(void) { bool ok = true; using namespace CppAD; size_t n = 2; // object for computing determinant det_by_minor Det(n); // independent and dependent variable vectors CPPAD_TESTVECTOR(ADComplex) X(n * n); CPPAD_TESTVECTOR(ADComplex) D(1); // value of the independent variable size_t i; for(i = 0; i < n * n; i++) X[i] = Complex(int(i), -int(i)); // set the independent variables Independent(X); // comupute the determinant D[0] = Det(X); // create the function object ADFun f(X, D); // argument value CPPAD_TESTVECTOR(Complex) x( n * n ); for(i = 0; i < n * n; i++) x[i] = Complex(2 * i, i); // first derivative of the determinant CPPAD_TESTVECTOR(Complex) J( n * n ); J = f.Jacobian(x); /* f(x) = x[0] * x[3] - x[1] * x[2] f'(x) = ( x[3], -x[2], -x[1], x[0] ) */ Complex Jtrue[] = { x[3], -x[2], -x[1], x[0] }; for(i = 0; i < n * n; i++) ok &= Jtrue[i] == J[i]; return ok; } // END C++ cppad-20170000.3/example/unary_plus.cpp0000644000175200017650000000356213057470460016776 0ustar coincoin-web// $Id: unary_plus.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin unary_plus.cpp$$ $spell Cpp cstddef $$ $section AD Unary Plus Operator: Example and Test$$ $code $srcfile%example/unary_plus.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool UnaryPlus(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) x(n); x[0] = 3.; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = + x[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check values ok &= ( y[0] == 3. ); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); size_t p = 1; dx[0] = 1.; dy = f.Forward(p, dx); ok &= ( dy[0] == 1. ); // dy[0] / dx[0] // reverse computation of dertivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(p, w); ok &= ( dw[0] == 1. ); // dy[0] / dx[0] // use a VecAD::reference object with unary plus CppAD::VecAD v(1); AD zero(0); v[zero] = x[0]; AD result = + v[zero]; ok &= (result == y[0]); return ok; } // END C++ cppad-20170000.3/example/ode_stiff.cpp0000644000175200017650000001222613057470460016534 0ustar coincoin-web// $Id: ode_stiff.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ode_stiff.cpp$$ $spell Rosen $$ $section A Stiff Ode: Example and Test$$ $mindex ode$$ Define $latex x : \B{R} \rightarrow \B{R}^2$$ by $latex \[ \begin{array}{rcl} x_0 (0) & = & 1 \\ x_1 (0) & = & 0 \\ x_0^\prime (t) & = & - a_0 x_0 (t) \\ x_1^\prime (t) & = & + a_0 x_0 (t) - a_1 x_1 (t) \end{array} \] $$ If $latex a_0 \gg a_1 > 0$$, this is a stiff Ode and the analytic solution is $latex \[ \begin{array}{rcl} x_0 (t) & = & \exp( - a_0 t ) \\ x_1 (t) & = & a_0 [ \exp( - a_1 t ) - \exp( - a_0 t ) ] / ( a_0 - a_1 ) \end{array} \] $$ The example tests Rosen34 using the relations above: $code $srcfile%example/ode_stiff.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // To print the comparision, change the 0 to 1 on the next line. # define CPPAD_ODE_STIFF_PRINT 0 namespace { // -------------------------------------------------------------- class Fun { private: CPPAD_TESTVECTOR(double) a; public: // constructor Fun(const CPPAD_TESTVECTOR(double)& a_) : a(a_) { } // compute f(t, x) void Ode( const double &t, const CPPAD_TESTVECTOR(double) &x, CPPAD_TESTVECTOR(double) &f) { f[0] = - a[0] * x[0]; f[1] = + a[0] * x[0] - a[1] * x[1]; } // compute partial of f(t, x) w.r.t. t void Ode_ind( const double &t, const CPPAD_TESTVECTOR(double) &x, CPPAD_TESTVECTOR(double) &f_t) { f_t[0] = 0.; f_t[1] = 0.; } // compute partial of f(t, x) w.r.t. x void Ode_dep( const double &t, const CPPAD_TESTVECTOR(double) &x, CPPAD_TESTVECTOR(double) &f_x) { f_x[0] = -a[0]; f_x[1] = 0.; f_x[2] = +a[0]; f_x[3] = -a[1]; } }; // -------------------------------------------------------------- class RungeMethod { private: Fun F; public: // constructor RungeMethod(const CPPAD_TESTVECTOR(double) &a_) : F(a_) { } void step( double ta , double tb , CPPAD_TESTVECTOR(double) &xa , CPPAD_TESTVECTOR(double) &xb , CPPAD_TESTVECTOR(double) &eb ) { xb = CppAD::Runge45(F, 1, ta, tb, xa, eb); } size_t order(void) { return 5; } }; class RosenMethod { private: Fun F; public: // constructor RosenMethod(const CPPAD_TESTVECTOR(double) &a_) : F(a_) { } void step( double ta , double tb , CPPAD_TESTVECTOR(double) &xa , CPPAD_TESTVECTOR(double) &xb , CPPAD_TESTVECTOR(double) &eb ) { xb = CppAD::Rosen34(F, 1, ta, tb, xa, eb); } size_t order(void) { return 4; } }; } bool OdeStiff(void) { bool ok = true; // initial return value CPPAD_TESTVECTOR(double) a(2); a[0] = 1e3; a[1] = 1.; RosenMethod rosen(a); RungeMethod runge(a); Fun gear(a); CPPAD_TESTVECTOR(double) xi(2); xi[0] = 1.; xi[1] = 0.; CPPAD_TESTVECTOR(double) eabs(2); eabs[0] = 1e-6; eabs[1] = 1e-6; CPPAD_TESTVECTOR(double) ef(2); CPPAD_TESTVECTOR(double) xf(2); CPPAD_TESTVECTOR(double) maxabs(2); size_t nstep; size_t k; for(k = 0; k < 3; k++) { size_t M = 5; double ti = 0.; double tf = 1.; double smin = 1e-7; double sini = 1e-7; double smax = 1.; double scur = .5; double erel = 0.; if( k == 0 ) { xf = CppAD::OdeErrControl(rosen, ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep); } else if( k == 1 ) { xf = CppAD::OdeErrControl(runge, ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep); } else if( k == 2 ) { xf = CppAD::OdeGearControl(gear, M, ti, tf, xi, smin, smax, sini, eabs, erel, ef, maxabs, nstep); } double x0 = exp(-a[0]*tf); ok &= CppAD::NearEqual(x0, xf[0], 0., eabs[0]); ok &= CppAD::NearEqual(0., ef[0], 0., eabs[0]); double x1 = a[0] * (exp(-a[1]*tf) - exp(-a[0]*tf))/(a[0] - a[1]); ok &= CppAD::NearEqual(x1, xf[1], 0., eabs[1]); ok &= CppAD::NearEqual(0., ef[1], 0., eabs[0]); # if CPPAD_ODE_STIFF_PRINT const char* method[]={ "Rosen34", "Runge45", "Gear5" }; std::cout << std::endl; std::cout << "method = " << method[k] << std::endl; std::cout << "nstep = " << nstep << std::endl; std::cout << "x0 = " << x0 << std::endl; std::cout << "xf[0] = " << xf[0] << std::endl; std::cout << "x0 - xf[0] = " << x0 - xf[0] << std::endl; std::cout << "ef[0] = " << ef[0] << std::endl; std::cout << "x1 = " << x1 << std::endl; std::cout << "xf[1] = " << xf[1] << std::endl; std::cout << "x1 - xf[1] = " << x1 - xf[1] << std::endl; std::cout << "ef[1] = " << ef[1] << std::endl; # endif } return ok; } // END C++ cppad-20170000.3/example/for_one.cpp0000644000175200017650000000504013057470460016215 0ustar coincoin-web// $Id: for_one.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin for_one.cpp$$ $spell Cpp $$ $section First Order Partial Driver: Example and Test$$ $code $srcfile%example/for_one.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ------------------------------------------------------- // define the template function ForOneCases in empty namespace template bool ForOneCases() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); using CppAD::exp; using CppAD::sin; using CppAD::cos; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; X[1] = 2.; // declare independent variables and starting recording CppAD::Independent(X); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] * exp( X[1] ); Y[1] = X[0] * sin( X[1] ); Y[2] = X[0] * cos( X[1] ); // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector Vector x(n); x[0] = 2.; x[1] = 1.; // compute partial of y w.r.t x[0] Vector dy(m); dy = f.ForOne(x, 0); ok &= NearEqual( dy[0], exp(x[1]), eps99, eps99); // for y[0] ok &= NearEqual( dy[1], sin(x[1]), eps99, eps99); // for y[1] ok &= NearEqual( dy[2], cos(x[1]), eps99, eps99); // for y[2] // compute partial of F w.r.t x[1] dy = f.ForOne(x, 1); ok &= NearEqual( dy[0], x[0]*exp(x[1]), eps99, eps99); ok &= NearEqual( dy[1], x[0]*cos(x[1]), eps99, eps99); ok &= NearEqual( dy[2], -x[0]*sin(x[1]), eps99, eps99); return ok; } } // End empty namespace # include # include bool ForOne(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= ForOneCases< CppAD::vector >(); ok &= ForOneCases< std::vector >(); ok &= ForOneCases< std::valarray >(); return ok; } // END C++ 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin add.cpp$$ $section AD Binary Addition: Example and Test$$ $mindex + add plus$$ $code $srcfile%example/add.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool Add(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // some binary addition operations AD a = x[0] + 1.; // AD + double AD b = a + 2; // AD + int AD c = 3. + b; // double + AD AD d = 4 + c; // int + AD // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = d + x[0]; // AD + AD // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , 2. * x0 + 10, eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 2., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 2., eps99, eps99); // use a VecAD::reference object with addition CppAD::VecAD v(1); AD zero(0); v[zero] = a; AD result = v[zero] + 2; ok &= (result == b); return ok; } // END C++ cppad-20170000.3/example/set_union.cpp0000644000175200017650000000231113057470460016567 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin set_union.cpp$$ $section Set Union: Example and Test$$ $code $srcfile%example/set_union.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool set_union(void) { bool ok = true; // create empty sets std::set left, right, result; // set left = {1, 2} left.insert(1); left.insert(2); // set right = {2, 3} right.insert(2); right.insert(3); // set result = {1, 2} U {2, 3} result = CppAD::set_union(left, right); // expected result size_t check_vec[] = {1, 2, 3}; std::set check_set(check_vec, check_vec + 3); // check result ok &= result == check_set; return ok; } // END C++ cppad-20170000.3/example/ad_fun.cpp0000644000175200017650000000654313057470460016033 0ustar coincoin-web// $Id: ad_fun.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ad_fun.cpp$$ $spell $$ $section Creating Your Own Interface to an ADFun Object$$ $mindex example test$$ $code $srcfile%example/ad_fun.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // This class is an example of a different interface to an AD function object template class my_ad_fun { private: CppAD::ADFun f; public: // default constructor my_ad_fun(void) { } // destructor ~ my_ad_fun(void) { } // Construct an my_ad_fun object with an operation sequence. // This is the same as for ADFun except that no zero // order forward sweep is done. Note Hessian and Jacobian do // their own zero order forward mode sweep. template my_ad_fun(const ADvector& x, const ADvector& y) { f.Dependent(x, y); } // same as ADFun::Jacobian template VectorBase jacobian(const VectorBase& x) { return f.Jacobian(x); } // same as ADFun::Hessian template VectorBase hessian(const VectorBase &x, const VectorBase &w) { return f.Hessian(x, w); } }; } // End empty namespace bool ad_fun(void) { // This example is similar to example/jacobian.cpp, except that it // uses my_ad_fun instead of ADFun. bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); using CppAD::exp; using CppAD::sin; using CppAD::cos; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; X[1] = 2.; // declare independent variables and starting recording CppAD::Independent(X); // a calculation between the domain and range values AD Square = X[0] * X[0]; // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = Square * exp( X[1] ); Y[1] = Square * sin( X[1] ); Y[2] = Square * cos( X[1] ); // create f: X -> Y and stop tape recording my_ad_fun f(X, Y); // new value for the independent variable vector CPPAD_TESTVECTOR(double) x(n); x[0] = 2.; x[1] = 1.; // compute the derivative at this x CPPAD_TESTVECTOR(double) jac( m * n ); jac = f.jacobian(x); /* F'(x) = [ 2 * x[0] * exp(x[1]) , x[0] * x[0] * exp(x[1]) ] [ 2 * x[0] * sin(x[1]) , x[0] * x[0] * cos(x[1]) ] [ 2 * x[0] * cos(x[1]) , -x[0] * x[0] * sin(x[i]) ] */ ok &= NearEqual( 2.*x[0]*exp(x[1]), jac[0*n+0], eps99, eps99); ok &= NearEqual( 2.*x[0]*sin(x[1]), jac[1*n+0], eps99, eps99); ok &= NearEqual( 2.*x[0]*cos(x[1]), jac[2*n+0], eps99, eps99); ok &= NearEqual( x[0] * x[0] *exp(x[1]), jac[0*n+1], eps99, eps99); ok &= NearEqual( x[0] * x[0] *cos(x[1]), jac[1*n+1], eps99, eps99); ok &= NearEqual(-x[0] * x[0] *sin(x[1]), jac[2*n+1], eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/change_param.cpp0000644000175200017650000000767513057470460017213 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include /* $begin change_param.cpp$$ $spell Jacobian $$ $section Computing a Jacobian With Constants that Change$$ $mindex multiple AD level$$ $head Purpose$$ In this example we use two levels of taping so that a derivative can have constant parameters that can be changed. To be specific, we consider the function $latex f : \B{R}^2 \rightarrow \B{R}^2$$ $latex \[ f(x) = p \left( \begin{array}{c} \sin( x_0 ) \\ \sin( x_1 ) \end{array} \right) \]$$ were $latex p \in \B{R}$$ is a parameter. The Jacobian of this function is $latex \[ g(x,p) = p \left( \begin{array}{cc} \cos( x_0 ) & 0 \\ 0 & \cos( x_1 ) \end{array} \right) \] $$ In this example we use two levels of AD to avoid computing the partial of $latex f(x)$$ with respect to $latex p$$, but still allow for the evaluation of $latex g(x, p)$$ at different values of $latex p$$. $end */ bool change_param(void) { bool ok = true; // initialize test result typedef CppAD::AD a1type; // for first level of taping typedef CppAD::AD a2type; // for second level of taping size_t nu = 3; // number components in u size_t nx = 2; // number components in x size_t ny = 2; // num components in f(x) size_t nJ = ny * nx; // number components in Jacobian of f(x) // temporary indices size_t j; // declare first level of independent variables // (Start taping now so can record dependency of a1f on a1p.) CPPAD_TESTVECTOR(a1type) a1u(nu); for(j = 0; j < nu; j++) a1u[j] = 0.; CppAD::Independent(a1u); // parameter in computation of Jacobian a1type a1p = a1u[2]; // declare second level of independent variables CPPAD_TESTVECTOR(a2type) a2x(nx); for(j = 0; j < nx; j++) a2x[j] = 0.; CppAD::Independent(a2x); // compute dependent variables at second level CPPAD_TESTVECTOR(a2type) a2y(ny); a2y[0] = sin( a2x[0] ) * a1p; a2y[1] = sin( a2x[1] ) * a1p; // declare function object that computes values at the first level // (make sure we do not run zero order forward during constructor) CppAD::ADFun a1f; a1f.Dependent(a2x, a2y); // compute the Jacobian of a1f at a1u[0], a1u[1] CPPAD_TESTVECTOR(a1type) a1x(nx); a1x[0] = a1u[0]; a1x[1] = a1u[1]; CPPAD_TESTVECTOR(a1type) a1J(nJ); a1J = a1f.Jacobian( a1x ); // declare function object that maps u = (x, p) to Jacobian of f // (make sure we do not run zero order forward during constructor) CppAD::ADFun g; g.Dependent(a1u, a1J); // remove extra variables used during the reconding of a1f, // but not needed any more. g.optimize(); // compute the Jacobian of f using zero order forward // sweep with double values CPPAD_TESTVECTOR(double) J(nJ), u(nu); for(j = 0; j < nu; j++) u[j] = double(j+1); J = g.Forward(0, u); // accuracy for tests double eps = 100. * CppAD::numeric_limits::epsilon(); // y[0] = sin( x[0] ) * p // y[1] = sin( x[1] ) * p CPPAD_TESTVECTOR(double) x(nx); x[0] = u[0]; x[1] = u[1]; double p = u[2]; // J[0] = partial y[0] w.r.t x[0] = cos( x[0] ) * p double check = cos( x[0] ) * p; ok &= fabs( check - J[0] ) <= eps; // J[1] = partial y[0] w.r.t x[1] = 0.; check = 0.; ok &= fabs( check - J[1] ) <= eps; // J[2] = partial y[1] w.r.t. x[0] = 0. check = 0.; ok &= fabs( check - J[2] ) <= eps; // J[3] = partial y[1] w.r.t x[1] = cos( x[1] ) * p check = cos( x[1] ) * p; ok &= fabs( check - J[3] ) <= eps; return ok; } // END PROGRAM cppad-20170000.3/example/reverse_two.cpp0000644000175200017650000000556113057470460017142 0ustar coincoin-web// $Id: reverse_two.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin reverse_two.cpp$$ $spell Cpp $$ $section Second Order Reverse ModeExample and Test$$ $mindex example$$ $code $srcfile%example/reverse_two.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ---------------------------------------------------------- // define the template function reverse_two_cases in empty namespace template bool reverse_two_cases(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; // declare independent variables and start recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] * X[0] * X[1]; // create f : X -> Y and stop recording CppAD::ADFun f(X, Y); // use zero order forward mode to evaluate y at x = (3, 4) // use the template parameter Vector for the vector type Vector x(n), y(m); x[0] = 3.; x[1] = 4.; y = f.Forward(0, x); ok &= NearEqual(y[0] , x[0]*x[0]*x[1], eps99, eps99); // use first order forward mode in x[0] direction // (all second order partials below involve x[0]) Vector dx(n), dy(m); dx[0] = 1.; dx[1] = 1.; dy = f.Forward(1, dx); double check = 2.*x[0]*x[1]*dx[0] + x[0]*x[0]*dx[1]; ok &= NearEqual(dy[0], check, eps99, eps99); // use second order reverse mode to evalaute second partials of y[0] // with respect to (x[0], x[0]) and with respect to (x[0], x[1]) Vector w(m), dw( n * 2 ); w[0] = 1.; dw = f.Reverse(2, w); // check derivative of f ok &= NearEqual(dw[0*2+0] , 2.*x[0]*x[1], eps99, eps99); ok &= NearEqual(dw[1*2+0] , x[0]*x[0], eps99, eps99); // check derivative of f^{(1)} (x) * dx check = 2.*x[1]*dx[1] + 2.*x[0]*dx[1]; ok &= NearEqual(dw[0*2+1] , check, eps99, eps99); check = 2.*x[0]*dx[1]; ok &= NearEqual(dw[1*2+1] , check, eps99, eps99); return ok; } } // End empty namespace # include # include bool reverse_two(void) { bool ok = true; ok &= reverse_two_cases< CppAD::vector >(); ok &= reverse_two_cases< std::vector >(); ok &= reverse_two_cases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/abs.cpp0000644000175200017650000000607213057470460015341 0ustar coincoin-web// $Id: abs.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin abs.cpp$$ $spell fabs abs $$ $section AD Absolute Value Function: Example and Test$$ $mindex abs fabs$$ $code $srcfile%example/abs.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool abs(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) x(n); x[0] = 0.; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 6; CPPAD_TESTVECTOR(AD) y(m); y[0] = abs(x[0] - 1.); y[1] = abs(x[0]); y[2] = abs(x[0] + 1.); // y[3] = fabs(x[0] - 1.); y[4] = fabs(x[0]); y[5] = fabs(x[0] + 1.); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check values ok &= (y[0] == 1.); ok &= (y[1] == 0.); ok &= (y[2] == 1.); // ok &= (y[3] == 1.); ok &= (y[4] == 0.); ok &= (y[5] == 1.); // forward computation of partials w.r.t. a positive x[0] direction size_t p = 1; CPPAD_TESTVECTOR(double) dx(n), dy(m); dx[0] = 1.; dy = f.Forward(p, dx); ok &= (dy[0] == - dx[0]); ok &= (dy[1] == 0. ); // used to be (dy[1] == + dx[0]); ok &= (dy[2] == + dx[0]); // ok &= (dy[3] == - dx[0]); ok &= (dy[4] == 0. ); // used to be (dy[1] == + dx[0]); ok &= (dy[5] == + dx[0]); // forward computation of partials w.r.t. a negative x[0] direction dx[0] = -1.; dy = f.Forward(p, dx); ok &= (dy[0] == - dx[0]); ok &= (dy[1] == 0. ); // used to be (dy[1] == - dx[0]); ok &= (dy[2] == + dx[0]); // ok &= (dy[3] == - dx[0]); ok &= (dy[4] == 0. ); // used to be (dy[1] == - dx[0]); ok &= (dy[5] == + dx[0]); // reverse computation of derivative of y[0] p = 1; CPPAD_TESTVECTOR(double) w(m), dw(n); w[0] = 1.; w[1] = 0.; w[2] = 0.; w[3] = 0.; w[4] = 0.; w[5] = 0.; dw = f.Reverse(p, w); ok &= (dw[0] == -1.); // reverse computation of derivative of y[1] w[0] = 0.; w[1] = 1.; dw = f.Reverse(p, w); ok &= (dw[0] == 0.); // reverse computation of derivative of y[5] w[1] = 0.; w[5] = 1.; dw = f.Reverse(p, w); ok &= (dw[0] == 1.); // use a VecAD::reference object with abs and fabs CppAD::VecAD v(1); AD zero(0); v[zero] = -1; AD result = abs(v[zero]); ok &= NearEqual(result, 1., eps99, eps99); result = fabs(v[zero]); ok &= NearEqual(result, 1., eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/lu_invert.cpp0000644000175200017650000000637313057470460016607 0ustar coincoin-web// $Id: lu_invert.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin lu_invert.cpp$$ $spell Geq Cpp Lu $$ $section LuInvert: Example and Test$$ $mindex LuInvert$$ $code $srcfile%example/lu_invert.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // for rand function # include // for CppAD::LuInvert # include // for CppAD::NearEqual # include // for CppAD::vector bool LuInvert(void) { bool ok = true; # ifndef _MSC_VER using std::rand; using std::srand; # endif size_t n = 7; // number rows in A size_t m = 3; // number columns in B double rand_max = double(RAND_MAX); // maximum rand value double sum; // element of L * U size_t i, j, k; // temporary indices // dimension matrices CppAD::vector A(n*n), X(n*m), B(n*m), LU(n*n), L(n*n), U(n*n); // seed the random number generator srand(123); // pivot vectors CppAD::vector ip(n); CppAD::vector jp(n); // set pivot vectors for(i = 0; i < n; i++) { ip[i] = (i + 2) % n; // ip = 2 , 3, ... , n-1, 0, 1 jp[i] = (n + 2 - i) % n; // jp = 2 , 1, n-1, n-2, ... , 3 } // chose L, a random lower triangular matrix for(i = 0; i < n; i++) { for(j = 0; j <= i; j++) L [i * n + j] = rand() / rand_max; for(j = i+1; j < n; j++) L [i * n + j] = 0.; } // chose U, a random upper triangular matrix with ones on diagonal for(i = 0; i < n; i++) { for(j = 0; j < i; j++) U [i * n + j] = 0.; U[ i * n + i ] = 1.; for(j = i+1; j < n; j++) U [i * n + j] = rand() / rand_max; } // chose X, a random matrix for(i = 0; i < n; i++) { for(k = 0; k < m; k++) X[i * m + k] = rand() / rand_max; } // set LU to a permuted combination of both L and U for(i = 0; i < n; i++) { for(j = 0; j <= i; j++) LU [ ip[i] * n + jp[j] ] = L[i * n + j]; for(j = i+1; j < n; j++) LU [ ip[i] * n + jp[j] ] = U[i * n + j]; } // set A to a permuted version of L * U for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { // compute (i,j) entry in permuted matrix sum = 0.; for(k = 0; k < n; k++) sum += L[i * n + k] * U[k * n + j]; A[ ip[i] * n + jp[j] ] = sum; } } // set B to A * X for(i = 0; i < n; i++) { for(k = 0; k < m; k++) { // compute (i,k) entry of B sum = 0.; for(j = 0; j < n; j++) sum += A[i * n + j] * X[j * m + k]; B[i * m + k] = sum; } } // solve for X CppAD::LuInvert(ip, jp, LU, B); // check result for(i = 0; i < n; i++) { for(k = 0; k < m; k++) { ok &= CppAD::NearEqual( X[i * m + k], B[i * m + k], 1e-10, 1e-10 ); } } return ok; } // END C++ cppad-20170000.3/example/runge45_1.cpp0000644000175200017650000000630313057470460016302 0ustar coincoin-web// $Id: runge45_1.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin runge45_1.cpp$$ $spell Runge $$ $section Runge45: Example and Test$$ $mindex Runge45$$ Define $latex X : \B{R} \rightarrow \B{R}^n$$ by $latex \[ X_i (t) = t^{i+1} \] $$ for $latex i = 1 , \ldots , n-1$$. It follows that $latex \[ \begin{array}{rclr} X_i(0) & = & 0 & {\rm for \; all \;} i \\ X_i ' (t) & = & 1 & {\rm if \;} i = 0 \\ X_i '(t) & = & (i+1) t^i = (i+1) X_{i-1} (t) & {\rm if \;} i > 0 \end{array} \] $$ The example tests Runge45 using the relations above: $code $srcfile%example/runge45_1.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // for size_t # include // for CppAD::NearEqual # include // for CppAD::vector # include // for CppAD::Runge45 // Runge45 requires fabs to be defined (not std::fabs) // defines this for doubles, but runge_45.hpp does not. # include // for fabs without std in front namespace { class Fun { public: // constructor Fun(bool use_x_) : use_x(use_x_) { } // set f = x'(t) void Ode( const double &t, const CppAD::vector &x, CppAD::vector &f) { size_t n = x.size(); double ti = 1.; f[0] = 1.; size_t i; for(i = 1; i < n; i++) { ti *= t; if( use_x ) f[i] = (i+1) * x[i-1]; else f[i] = (i+1) * ti; } } private: const bool use_x; }; } bool runge_45_1(void) { bool ok = true; // initial return value size_t i; // temporary indices using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); size_t n = 5; // number components in X(t) and order of method size_t M = 2; // number of Runge45 steps in [ti, tf] double ti = 0.; // initial time double tf = 2.; // final time // xi = X(0) CppAD::vector xi(n); for(i = 0; i 0); // compute Runge45 approximation for X(tf) CppAD::vector xf(n), e(n); xf = CppAD::Runge45(F, M, ti, tf, xi, e); double check = tf; for(i = 0; i < n; i++) { // check that error is always positive ok &= (e[i] >= 0.); // 5th order method is exact for i < 5 if( i < 5 ) ok &= NearEqual(xf[i], check, eps99, eps99); // 4th order method is exact for i < 4 if( i < 4 ) ok &= (e[i] <= 1e-10); // check value for next i check *= tf; } } return ok; } // END C++ cppad-20170000.3/example/ode_err_maxabs.cpp0000644000175200017650000000711713057470460017547 0ustar coincoin-web// $Id: ode_err_maxabs.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ode_err_maxabs.cpp$$ $spell Runge Maxabs $$ $section OdeErrControl: Example and Test Using Maxabs Argument$$ $mindex OdeErrControl$$ Define $latex X : \B{R} \rightarrow \B{R}^2$$ by $latex \[ \begin{array}{rcl} X_0 (t) & = & - \exp ( - w_0 t ) \\ X_1 (t) & = & \frac{w_0}{w_1 - w_0} [ \exp ( - w_0 t ) - \exp( - w_1 t )] \end{array} \] $$ It follows that $latex X_0 (0) = 1$$, $latex X_1 (0) = 0$$ and $latex \[ \begin{array}{rcl} X_0^{(1)} (t) & = & - w_0 X_0 (t) \\ X_1^{(1)} (t) & = & + w_0 X_0 (t) - w_1 X_1 (t) \end{array} \] $$ Note that $latex X_1 (0)$$ is zero an if $latex w_0 t$$ is large, $latex X_0 (t)$$ is near zero. This example tests OdeErrControl using the $icode maxabs$$ argument. $code $srcfile%example/ode_err_maxabs.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // for size_t # include // for exp # include // CppAD::OdeErrControl # include // CppAD::NearEqual # include // CppAD::vector # include // CppAD::Runge45 namespace { // -------------------------------------------------------------- class Fun { private: CppAD::vector w; public: // constructor Fun(const CppAD::vector &w_) : w(w_) { } // set f = x'(t) void Ode( const double &t, const CppAD::vector &x, CppAD::vector &f) { f[0] = - w[0] * x[0]; f[1] = + w[0] * x[0] - w[1] * x[1]; } }; // -------------------------------------------------------------- class Method { private: Fun F; public: // constructor Method(const CppAD::vector &w_) : F(w_) { } void step( double ta, double tb, CppAD::vector &xa , CppAD::vector &xb , CppAD::vector &eb ) { xb = CppAD::Runge45(F, 1, ta, tb, xa, eb); } size_t order(void) { return 4; } }; } bool OdeErrMaxabs(void) { bool ok = true; // initial return value CppAD::vector w(2); w[0] = 10.; w[1] = 1.; Method method(w); CppAD::vector xi(2); xi[0] = 1.; xi[1] = 0.; CppAD::vector eabs(2); eabs[0] = 0.; eabs[1] = 0.; CppAD::vector ef(2); CppAD::vector xf(2); CppAD::vector maxabs(2); double ti = 0.; double tf = 1.; double smin = .5; double smax = 1.; double scur = .5; double erel = 1e-4; bool accurate = false; while( ! accurate ) { xf = OdeErrControl(method, ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs); accurate = true; size_t i; for(i = 0; i < 2; i++) accurate &= ef[i] <= erel * maxabs[i]; if( ! accurate ) smin = smin / 2; } double x0 = exp(-w[0]*tf); ok &= CppAD::NearEqual(x0, xf[0], erel, 0.); ok &= CppAD::NearEqual(0., ef[0], erel, erel); double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]); ok &= CppAD::NearEqual(x1, xf[1], erel, 0.); ok &= CppAD::NearEqual(0., ef[1], erel, erel); return ok; } // END C++ cppad-20170000.3/example/ode_err_control.cpp0000644000175200017650000000721613057470460017754 0ustar coincoin-web// $Id: ode_err_control.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ode_err_control.cpp$$ $spell $$ $section OdeErrControl: Example and Test$$ Define $latex X : \B{R} \rightarrow \B{R}^2$$ by $latex \[ \begin{array}{rcl} X_0 (0) & = & 1 \\ X_1 (0) & = & 0 \\ X_0^{(1)} (t) & = & - \alpha X_0 (t) \\ X_1^{(1)} (t) & = & 1 / X_0 (t) \end{array} \] $$ It follows that $latex \[ \begin{array}{rcl} X_0 (t) & = & \exp ( - \alpha t ) \\ X_1 (t) & = & [ \exp( \alpha t ) - 1 ] / \alpha \end{array} \] $$ This example tests OdeErrControl using the relations above. $head Nan$$ Note that $latex X_0 (t) > 0$$ for all $latex t$$ and that the ODE goes through a singularity between $latex X_0 (t) > 0$$ and $latex X_0 (t) < 0$$. If $latex X_0 (t) < 0$$, we return $code nan$$ in order to inform $code OdeErrControl$$ that its is taking to large a step. $code $srcfile%example/ode_err_control.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // for quiet_NaN # include // for size_t # include // for exp # include // CppAD::OdeErrControl # include // CppAD::NearEqual # include // CppAD::vector # include // CppAD::Runge45 namespace { // -------------------------------------------------------------- class Fun { private: const double alpha_; public: // constructor Fun(double alpha) : alpha_(alpha) { } // set f = x'(t) void Ode( const double &t, const CppAD::vector &x, CppAD::vector &f) { f[0] = - alpha_ * x[0]; f[1] = 1. / x[0]; // case where ODE does not make sense if( x[0] < 0. ) f[1] = std::numeric_limits::quiet_NaN(); } }; // -------------------------------------------------------------- class Method { private: Fun F; public: // constructor Method(double alpha) : F(alpha) { } void step( double ta, double tb, CppAD::vector &xa , CppAD::vector &xb , CppAD::vector &eb ) { xb = CppAD::Runge45(F, 1, ta, tb, xa, eb); } size_t order(void) { return 4; } }; } bool OdeErrControl(void) { bool ok = true; // initial return value double alpha = 10.; Method method(alpha); CppAD::vector xi(2); xi[0] = 1.; xi[1] = 0.; CppAD::vector eabs(2); eabs[0] = 1e-4; eabs[1] = 1e-4; // inputs double ti = 0.; double tf = 1.; double smin = 1e-4; double smax = 1.; double scur = 1.; double erel = 0.; // outputs CppAD::vector ef(2); CppAD::vector xf(2); CppAD::vector maxabs(2); size_t nstep; xf = OdeErrControl(method, ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep); double x0 = exp(-alpha*tf); ok &= CppAD::NearEqual(x0, xf[0], 1e-4, 1e-4); ok &= CppAD::NearEqual(0., ef[0], 1e-4, 1e-4); double x1 = (exp(alpha*tf) - 1) / alpha; ok &= CppAD::NearEqual(x1, xf[1], 1e-4, 1e-4); ok &= CppAD::NearEqual(0., ef[1], 1e-4, 1e-4); return ok; } // END C++ cppad-20170000.3/example/ad_ctor.cpp0000644000175200017650000000260013057470460016200 0ustar coincoin-web// $Id: ad_ctor.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ad_ctor.cpp$$ $spell Cpp $$ $section AD Constructors: Example and Test$$ $mindex constructor object$$ $code $srcfile%example/ad_ctor.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool ad_ctor(void) { bool ok = true; // initialize test result flag using CppAD::AD; // so can use AD in place of CppAD::AD // default constructor AD a; a = 0.; ok &= a == 0.; // constructor from base type AD b(1.); ok &= b == 1.; // constructor from another type that converts to the base type AD c(2); ok &= c == 2.; // constructor from AD AD d(c); ok &= d == 2.; // constructor from a VecAD element CppAD::VecAD v(1); v[0] = 3.; AD e( v[0] ); ok &= e == 3.; return ok; } // END C++ cppad-20170000.3/example/vec_ad.cpp0000644000175200017650000001236613057470460016020 0ustar coincoin-web// $Id: vec_ad.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin vec_ad.cpp$$ $spell Vec Cpp cstddef $$ $section AD Vectors that Record Index Operations: Example and Test$$ $mindex VecAD vec_ad.cpp$$ $code $srcfile%example/vec_ad.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { // return the vector x that solves the following linear system // a[0] * x[0] + a[1] * x[1] = b[0] // a[2] * x[0] + a[3] * x[1] = b[1] // in a way that will record pivot operations on the AD tape typedef CPPAD_TESTVECTOR(CppAD::AD) Vector; Vector Solve(const Vector &a , const Vector &b) { using namespace CppAD; assert(a.size() == 4 && b.size() == 2); // copy the vector b into the VecAD object B VecAD B(2); AD u; for(u = 0; u < 2; u += 1.) B[u] = b[ Integer(u) ]; // copy the matrix a into the VecAD object A VecAD A(4); for(u = 0; u < 4; u += 1.) A[u] = a [ Integer(u) ]; // tape AD operation sequence that determines the row of A // with maximum absolute element in column zero AD zero(0), one(1); AD rmax = CondExpGt(abs(a[0]), abs(a[2]), zero, one); // divide row rmax by A(rmax, 0) A[rmax * 2 + 1] = A[rmax * 2 + 1] / A[rmax * 2 + 0]; B[rmax] = B[rmax] / A[rmax * 2 + 0]; A[rmax * 2 + 0] = one; // subtract A(other,0) times row A(rmax, *) from row A(other,*) AD other = one - rmax; A[other * 2 + 1] = A[other * 2 + 1] - A[other * 2 + 0] * A[rmax * 2 + 1]; B[other] = B[other] - A[other * 2 + 0] * B[rmax]; A[other * 2 + 0] = zero; // back substitute to compute the solution vector x. // Note that the columns of A correspond to rows of x. // Also note that A[rmax * 2 + 0] is equal to one. CPPAD_TESTVECTOR(AD) x(2); x[1] = B[other] / A[other * 2 + 1]; x[0] = B[rmax] - A[rmax * 2 + 1] * x[1]; return x; } } bool vec_ad(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 4; CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(AD) X(n); // 2 * identity matrix (rmax in Solve will be 0) X[0] = x[0] = 2.; X[1] = x[1] = 0.; X[2] = x[2] = 0.; X[3] = x[3] = 2.; // declare independent variables and start tape recording CppAD::Independent(X); // define the vector b CPPAD_TESTVECTOR(double) b(2); CPPAD_TESTVECTOR(AD) B(2); B[0] = b[0] = 0.; B[1] = b[1] = 1.; // range space vector solves X * Y = b size_t m = 2; CPPAD_TESTVECTOR(AD) Y(m); Y = Solve(X, B); // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // By Cramer's rule: // y[0] = [ b[0] * x[3] - x[1] * b[1] ] / [ x[0] * x[3] - x[1] * x[2] ] // y[1] = [ x[0] * b[1] - b[0] * x[2] ] / [ x[0] * x[3] - x[1] * x[2] ] double den = x[0] * x[3] - x[1] * x[2]; double dsq = den * den; double num0 = b[0] * x[3] - x[1] * b[1]; double num1 = x[0] * b[1] - b[0] * x[2]; // check value ok &= NearEqual(Y[0] , num0 / den, eps99, eps99); ok &= NearEqual(Y[1] , num1 / den, eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dx[1] = 0.; dx[2] = 0.; dx[3] = 0.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 0. - num0 * x[3] / dsq, eps99, eps99); ok &= NearEqual(dy[1], b[1] / den - num1 * x[3] / dsq, eps99, eps99); // compute the solution for a new x matrix such that pivioting // on the original rmax row would divide by zero CPPAD_TESTVECTOR(double) y(m); x[0] = 0.; x[1] = 2.; x[2] = 2.; x[3] = 0.; // new values for Cramer's rule den = x[0] * x[3] - x[1] * x[2]; dsq = den * den; num0 = b[0] * x[3] - x[1] * b[1]; num1 = x[0] * b[1] - b[0] * x[2]; // check values y = f.Forward(0, x); ok &= NearEqual(y[0] , num0 / den, eps99, eps99); ok &= NearEqual(y[1] , num1 / den, eps99, eps99); // forward computation of partials w.r.t. x[1] dx[0] = 0.; dx[1] = 1.; dx[2] = 0.; dx[3] = 0.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0],-b[1] / den + num0 * x[2] / dsq, eps99, eps99); ok &= NearEqual(dy[1], 0. + num1 * x[2] / dsq, eps99, eps99); // reverse computation of derivative of y[0] w.r.t x CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 0.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 0. - num0 * x[3] / dsq, eps99, eps99); ok &= NearEqual(dw[1],-b[1] / den + num0 * x[2] / dsq, eps99, eps99); ok &= NearEqual(dw[2], 0. + num0 * x[1] / dsq, eps99, eps99); ok &= NearEqual(dw[3], b[0] / den - num0 * x[0] / dsq, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/hes_times_dir.cpp0000644000175200017650000000456613057470460017420 0ustar coincoin-web// $Id: hes_times_dir.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin hes_times_dir.cpp$$ $spell $$ $section Hessian Times Direction: Example and Test$$ $mindex direction$$ $code $srcfile%example/hes_times_dir.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ // Example and test of computing the Hessian times a direction; i.e., // given F : R^n -> R and a direction dx in R^n, we compute F''(x) * dx # include namespace { // put this function in the empty namespace // F(x) = |x|^2 = x[0]^2 + ... + x[n-1]^2 template Type F(CPPAD_TESTVECTOR(Type) &x) { Type sum = 0; size_t i = x.size(); while(i--) sum += x[i] * x[i]; return sum; } } bool HesTimesDir(void) { bool ok = true; // initialize test result size_t j; // a domain variable variable using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 5; CPPAD_TESTVECTOR(AD) X(n); for(j = 0; j < n; j++) X[j] = AD(j); // declare independent variables and start recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = F(X); // create f : X -> Y and stop recording CppAD::ADFun f(X, Y); // choose a direction dx and compute dy(x) = F'(x) * dx CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); for(j = 0; j < n; j++) dx[j] = double(n - j); dy = f.Forward(1, dx); // compute ddw = F''(x) * dx CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) ddw(2 * n); w[0] = 1.; ddw = f.Reverse(2, w); // F(x) = x[0]^2 + x[1]^2 + ... + x[n-1]^2 // F''(x) = 2 * Identity_Matrix // F''(x) * dx = 2 * dx for(j = 0; j < n; j++) ok &= NearEqual(ddw[j * 2 + 1], 2.*dx[j], eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/lu_vec_ad.cpp0000644000175200017650000002024313057470460016511 0ustar coincoin-web// $Id: lu_vec_ad.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin lu_vec_ad.cpp$$ $escape #$$ $spell signdet Lu Vec Rhs logdet Cpp $$ $section Lu Factor and Solve with Recorded Pivoting$$ $mindex LuVecAD linear equation determinant$$ $pre $$ $head Syntax$$ $codei%int LuVecAD( size_t %n%, size_t %m%, VecAD<%double%> &%Matrix%, VecAD<%double%> &%Rhs%, VecAD<%double%> &%Result%, AD<%double%> &%logdet%)%$$ $head Purpose$$ Solves the linear equation $latex \[ Matrix * Result = Rhs \] $$ where $icode Matrix$$ is an $latex n \times n$$ matrix, $icode Rhs$$ is an $latex n x m$$ matrix, and $icode Result$$ is an $latex n x m$$ matrix. $pre $$ The routine $cref LuSolve$$ uses an arbitrary vector type, instead of $cref VecAD$$, to hold its elements. The pivoting operations for a $code ADFun$$ object corresponding to an $code LuVecAD$$ solution will change to be optimal for the matrix being factored. $pre $$ It is often the case that $code LuSolve$$ is faster than $code LuVecAD$$ when $code LuSolve$$ uses a simple vector class with $cref/elements of type double/SimpleVector/Elements of Specified Type/$$, but the corresponding $cref ADFun$$ objects have a fixed set of pivoting operations. $head Storage Convention$$ The matrices stored in row major order. To be specific, if $latex A$$ contains the vector storage for an $latex n x m$$ matrix, $latex i$$ is between zero and $latex n-1$$, and $latex j$$ is between zero and $latex m-1$$, $latex \[ A_{i,j} = A[ i * m + j ] \] $$ (The length of $latex A$$ must be equal to $latex n * m $$.) $head n$$ is the number of rows in $icode Matrix$$, $icode Rhs$$, and $icode Result$$. $head m$$ is the number of columns in $icode Rhs$$ and $icode Result$$. It is ok for $icode m$$ to be zero which is reasonable when you are only interested in the determinant of $icode Matrix$$. $head Matrix$$ On input, this is an $latex n \times n$$ matrix containing the variable coefficients for the equation we wish to solve. On output, the elements of $icode Matrix$$ have been overwritten and are not specified. $head Rhs$$ On input, this is an $latex n \times m$$ matrix containing the right hand side for the equation we wish to solve. On output, the elements of $icode Rhs$$ have been overwritten and are not specified. If $icode m$$ is zero, $icode Rhs$$ is not used. $head Result$$ On input, this is an $latex n \times m$$ matrix and the value of its elements do not matter. On output, the elements of $icode Rhs$$ contain the solution of the equation we wish to solve (unless the value returned by $code LuVecAD$$ is equal to zero). If $icode m$$ is zero, $icode Result$$ is not used. $head logdet$$ On input, the value of $icode logdet$$ does not matter. On output, it has been set to the log of the determinant of $icode Matrix$$ (but not quite). To be more specific, if $icode signdet$$ is the value returned by $code LuVecAD$$, the determinant of $icode Matrix$$ is given by the formula $latex \[ det = signdet \exp( logdet ) \] $$ This enables $code LuVecAD$$ to use logs of absolute values. $head Example$$ $children% example/lu_vec_ad_ok.cpp %$$ The file $cref lu_vec_ad_ok.cpp$$ contains an example and test of $code LuVecAD$$. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------ */ # include "lu_vec_ad.hpp" # include // BEGIN CppAD namespace namespace CppAD { AD LuVecAD( size_t n, size_t m, CppAD::VecAD &Matrix, CppAD::VecAD &Rhs, CppAD::VecAD &Result, CppAD::AD &logdet) { using namespace CppAD; typedef AD Type; // temporary index Type index; Type jndex; // index and maximum element value Type imax; Type jmax; Type itmp; Type jtmp; Type emax; // some temporary indices Type i; Type j; Type k; // count pivots Type p; // sign of the determinant Type signdet; // temporary values Type etmp; Type diff; // pivot element Type pivot; // singular matrix Type singular = 0.; // some constants Type M(m); Type N(n); Type One(1); Type Zero(0); // pivot row and column order in the matrix VecAD ip(n); VecAD jp(n); // ------------------------------------------------------- // initialize row and column order in matrix not yet pivoted for(i = 0; i < N; i += 1.) { ip[i] = i; jp[i] = i; } // initialize the log determinant logdet = 0.; signdet = 1; for(p = 0; p < N; p += 1.) { // determine row and column corresponding to element of // maximum absolute value in remaining part of Matrix imax = N; jmax = N; emax = 0.; for(i = p; i < N; i += 1.) { itmp = ip[i] * N; for(j = p; j < N; j += 1.) { assert( (ip[i] < N) & (jp[j] < N) ); index = itmp + jp[j]; etmp = Matrix[ index ]; // compute absolute value of element etmp = abs(etmp); // update maximum absolute value so far emax = CondExpGe(etmp, emax, etmp, emax); imax = CondExpGe(etmp, emax, i, imax); jmax = CondExpGe(etmp, emax, j, jmax); } } assert( (imax < N) & (jmax < N) ); // switch rows so max absolute element is in row p index = ip[p]; ip[p] = ip[imax]; ip[imax] = index; // if imax != p, switch sign of determinant signdet = CondExpEq(imax, p, signdet, -signdet); // switch columns so max absolute element is in column p jndex = jp[p]; jp[p] = jp[jmax]; jp[jmax] = jndex; // if imax != p, switch sign of determinant signdet = CondExpEq(jmax, p, signdet, -signdet); // pivot using the max absolute element itmp = ip[p] * N; index = itmp + jp[p]; pivot = Matrix[ index ]; // update the singular matrix flag singular = CondExpEq(pivot, Zero, One, singular); // update the log of absolute determinant and its sign etmp = abs(pivot); logdet = logdet + log( etmp ); signdet = CondExpGe(pivot, Zero, signdet, - signdet); /* Reduce by the elementary transformations that maps Matrix( ip[p], jp[p] ) to one and Matrix( ip[i], jp[p] ) to zero for i = p + 1., ... , n-1 */ // divide row number ip[p] by pivot element for(j = p + 1.; j < N; j += 1.) { index = itmp + jp[j]; Matrix[ index ] = Matrix[ index ] / pivot; } // not used anymore so no need to set to 1 // Matrix[ ip[p] * N + jp[p] ] = Type(1); // divide corresponding row of right hand side by pivot element itmp = ip[p] * M; for(k = 0; k < M; k += 1.) { index = itmp + k; Rhs[ index ] = Rhs[ index ] / pivot; } for(i = p + 1.; i < N; i += 1. ) { itmp = ip[i] * N; jtmp = ip[p] * N; index = itmp + jp[p]; etmp = Matrix[ index ]; for(j = p + 1.; j < N; j += 1.) { index = itmp + jp[j]; jndex = jtmp + jp[j]; Matrix[ index ] = Matrix[ index ] - etmp * Matrix[ jndex ]; } itmp = ip[i] * M; jtmp = ip[p] * M; for(k = 0; k < M; k += 1.) { index = itmp + k; jndex = jtmp + k; Rhs[ index ] = Rhs[ index ] - etmp * Rhs[ jndex ]; } // not used any more so no need to set to zero // Matrix[ ip[i] * N + jp[p] ] = 0.; } } // loop over equations for(k = 0; k < M; k += 1.) { // loop over variables p = N; while( p > 0. ) { p -= 1.; index = ip[p] * M + k; jndex = jp[p] * M + k; etmp = Rhs[ index ]; Result[ jndex ] = etmp; for(i = 0; i < p; i += 1. ) { index = ip[i] * M + k; jndex = ip[i] * N + jp[p]; Rhs[ index ] = Rhs[ index ] - etmp * Matrix[ jndex ]; } } } // make sure return zero in the singular case return (1. - singular) * signdet; } } // END CppAD namespace cppad-20170000.3/example/reverse_checkpoint.cpp0000644000175200017650000001612113057470460020452 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin reverse_checkpoint.cpp$$ $spell Checkpointing Taylor $$ $section Reverse Mode General Case (Checkpointing): Example and Test$$ $head See Also$$ $cref checkpoint$$ $head Purpose$$ Break a large computation into pieces and only store values at the interface of the pieces (this is much easier to do using $cref checkpoint$$). In actual applications, there may be many functions, but for this example there are only two. The functions $latex F : \B{R}^2 \rightarrow \B{R}^2$$ and $latex G : \B{R}^2 \rightarrow \B{R}^2$$ defined by $latex \[ F(x) = \left( \begin{array}{c} x_0 x_1 \\ x_1 - x_0 \end{array} \right) \; , \; G(y) = \left( \begin{array}{c} y_0 - y_1 \\ y_1 y_0 \end{array} \right) \] $$ $head Processing Steps$$ We apply reverse mode to compute the derivative of $latex H : \B{R}^2 \rightarrow \B{R}$$ is defined by $latex \[ \begin{array}{rcl} H(x) & = & G_0 [ F(x) ] + G_1 [ F(x) ] \\ & = & x_0 x_1 - ( x_1 - x_0 ) + x_0 x_1 ( x_1 - x_0 ) \\ & = & x_0 x_1 ( 1 - x_0 + x_1 ) - x_1 + x_0 \end{array} \] $$ Given the zero and first order Taylor coefficients $latex x^{(0)} $$ and $latex x^{(1)}$$, we use $latex X(t)$$, $latex Y(t)$$ and $latex Z(t)$$ for the corresponding functions; i.e., $latex \[ \begin{array}{rcl} X(t) & = & x^{(0)} + x^{(1)} t \\ Y(t) & = & F[X(t)] = y^{(0)} + y^{(1)} t + O(t^2) \\ Z(t) & = & G \{ F [ X(t) ] \} = z^{(0)} + z^{(1)} t + O(t^2) \\ h^{(0)} & = & z^{(0)}_0 + z^{(0)}_1 \\ h^{(1)} & = & z^{(1)}_0 + z^{(1)}_1 \end{array} \] $$ Here are the processing steps: $list number$$ Use forward mode on $latex F(x)$$ to compute $latex y^{(0)}$$ and $latex y^{(1)}$$. $lnext Free some, or all, of the memory corresponding to $latex F(x)$$. $lnext Use forward mode on $latex G(y)$$ to compute $latex z^{(0)}$$ and $latex z^{(1)}$$ $lnext Use reverse mode on $latex G(y)$$ to compute the derivative of $latex h^{(1)}$$ with respect to $latex y^{(0)}$$ and $latex y^{(1)}$$. $lnext Free all the memory corresponding to $latex G(y)$$. $lnext Use reverse mode on $latex F(x)$$ to compute the derivative of $latex h^{(1)}$$ with respect to $latex x^{(0)}$$ and $latex x^{(1)}$$. $lend This uses the following relations: $latex \[ \begin{array}{rcl} \partial_{x(0)} h^{(1)} [ x^{(0)} , x^{(1)} ] & = & \partial_{y(0)} h^{(1)} [ y^{(0)} , y^{(1)} ] \partial_{x(0)} y^{(0)} [ x^{(0)} , x^{(1)} ] \\ & + & \partial_{y(1)} h^{(1)} [ y^{(0)} , y^{(1)} ] \partial_{x(0)} y^{(1)} [ x^{(0)} , x^{(1)} ] \\ \partial_{x(1)} h^{(1)} [ x^{(0)} , x^{(1)} ] & = & \partial_{y(0)} h^{(1)} [ y^{(0)} , y^{(1)} ] \partial_{x(1)} y^{(0)} [ x^{(0)} , x^{(1)} ] \\ & + & \partial_{y(1)} h^{(1)} [ y^{(0)} , y^{(1)} ] \partial_{x(1)} y^{(1)} [ x^{(0)} , x^{(1)} ] \end{array} \] $$ where $latex \partial_{x(0)}$$ denotes the partial with respect to $latex x^{(0)}$$. $code $srcfile%example/reverse_checkpoint.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { template Vector F(const Vector& x) { Vector y(2); y[0] = x[0] * x[1]; y[1] = x[1] - x[0]; return y; } template Vector G(const Vector& y) { Vector z(2); z[0] = y[0] - y[1]; z[1] = y[1] * y[0]; return z; } } namespace { bool reverse_any_case(bool free_all) { bool ok = true; double eps = 10. * CppAD::numeric_limits::epsilon(); using CppAD::AD; using CppAD::NearEqual; CppAD::ADFun f, g, empty; // specify the Taylor coefficients for X(t) size_t n = 2; CPPAD_TESTVECTOR(double) x0(n), x1(n); x0[0] = 1.; x0[1] = 2.; x1[0] = 3.; x1[1] = 4.; // record the function F(x) CPPAD_TESTVECTOR(AD) X(n), Y(n); size_t i; for(i = 0; i < n; i++) X[i] = x0[i]; CppAD::Independent(X); Y = F(X); f.Dependent(X, Y); // a fucntion object with an almost empty operation sequence CppAD::Independent(X); empty.Dependent(X, X); // compute the Taylor coefficients for Y(t) CPPAD_TESTVECTOR(double) y0(n), y1(n); y0 = f.Forward(0, x0); y1 = f.Forward(1, x1); if( free_all ) f = empty; else { // free all the Taylor coefficients stored in f f.capacity_order(0); } // record the function G(x) CPPAD_TESTVECTOR(AD) Z(n); CppAD::Independent(Y); Z = G(Y); g.Dependent(Y, Z); // compute the Taylor coefficients for Z(t) CPPAD_TESTVECTOR(double) z0(n), z1(n); z0 = g.Forward(0, y0); z1 = g.Forward(1, y1); // check zero order Taylor coefficient for h^0 = z_0^0 + z_1^0 double check = x0[0] * x0[1] * (1. - x0[0] + x0[1]) - x0[1] + x0[0]; double h0 = z0[0] + z0[1]; ok &= NearEqual(h0, check, eps, eps); // check first order Taylor coefficient h^1 check = x0[0] * x0[1] * (- x1[0] + x1[1]) - x1[1] + x1[0]; check += x1[0] * x0[1] * (1. - x0[0] + x0[1]); check += x0[0] * x1[1] * (1. - x0[0] + x0[1]); double h1 = z1[0] + z1[1]; ok &= NearEqual(h1, check, eps, eps); // compute the derivative with respect to y^0 and y^0 of h^1 size_t p = 2; CPPAD_TESTVECTOR(double) w(n*p), dw(n*p); w[0*p+0] = 0.; // coefficient for z_0^0 w[0*p+1] = 1.; // coefficient for z_0^1 w[1*p+0] = 0.; // coefficient for z_1^0 w[1*p+1] = 1.; // coefficient for z_1^1 dw = g.Reverse(p, w); // We are done using g, so we can free its memory. g = empty; // We need to use f next. if( free_all ) { // we must again record the operation sequence for F(x) CppAD::Independent(X); Y = F(X); f.Dependent(X, Y); } // now recompute the Taylor coefficients corresponding to F(x) // (we already know the result; i.e., y0 and y1). f.Forward(0, x0); f.Forward(1, x1); // compute the derivative with respect to x^0 and x^0 of // h^1 = z_0^1 + z_1^1 CPPAD_TESTVECTOR(double) dv(n*p); dv = f.Reverse(p, dw); // check partial of h^1 w.r.t x^0_0 check = x0[1] * (- x1[0] + x1[1]); check -= x1[0] * x0[1]; check += x1[1] * (1. - x0[0] + x0[1]) - x0[0] * x1[1]; ok &= NearEqual(dv[0*p+0], check, eps, eps); // check partial of h^1 w.r.t x^0_1 check = x0[0] * (- x1[0] + x1[1]); check += x1[0] * (1. - x0[0] + x0[1]) + x1[0] * x0[1]; check += x0[0] * x1[1]; ok &= NearEqual(dv[1*p+0], check, eps, eps); // check partial of h^1 w.r.t x^1_0 check = 1. - x0[0] * x0[1]; check += x0[1] * (1. - x0[0] + x0[1]); ok &= NearEqual(dv[0*p+1], check, eps, eps); // check partial of h^1 w.r.t x^1_1 check = x0[0] * x0[1] - 1.; check += x0[0] * (1. - x0[0] + x0[1]); ok &= NearEqual(dv[1*p+1], check, eps, eps); return ok; } } bool reverse_any(void) { bool ok = true; ok &= reverse_any_case(true); ok &= reverse_any_case(false); return ok; } // END C++ cppad-20170000.3/example/thread_alloc.cpp0000644000175200017650000001515313057470460017215 0ustar coincoin-web// $Id: thread_alloc.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin thread_alloc.cpp$$ $spell pthread openmp $$ $section Fast Multi-Threading Memory Allocator: Example and Test$$ $mindex openmp allocation pthread boost multi-thread$$ $code $srcfile%example/thread_alloc.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include # include namespace { // Begin empty namespace bool raw_allocate(void) { bool ok = true; using CppAD::thread_alloc; size_t thread; // check that no memory is initilaly inuse ok &= thread_alloc::free_all(); // amount of static memory used by thread zero size_t static_inuse = 0; // repeatedly allocate enough memory for at least two size_t values. size_t min_size_t = 2; size_t min_bytes = min_size_t * sizeof(size_t); size_t n_outter = 10; size_t n_inner = 5; for(size_t i = 0; i < n_outter; i++) { // Do not use CppAD::vector here because its use of thread_alloc // complicates the inuse and avaialble results. std::vector v_ptr(n_inner); // cap_bytes will be set by get_memory size_t cap_bytes = 0; // set here to avoid MSC warning for(size_t j = 0; j < n_inner; j++) { // allocate enough memory for min_size_t size_t objects v_ptr[j] = thread_alloc::get_memory(min_bytes, cap_bytes); size_t* ptr = reinterpret_cast(v_ptr[j]); // determine the number of size_t values we have obtained size_t cap_size_t = cap_bytes / sizeof(size_t); ok &= min_size_t <= cap_size_t; // use placement new to call the size_t copy constructor for(size_t k = 0; k < cap_size_t; k++) new(ptr + k) size_t(i + j + k); // check that the constructor worked for(size_t k = 0; k < cap_size_t; k++) ok &= ptr[k] == (i + j + k); } // check that n_inner * cap_bytes are inuse and none are available thread = thread_alloc::thread_num(); ok &= thread_alloc::inuse(thread) == n_inner*cap_bytes + static_inuse; ok &= thread_alloc::available(thread) == 0; // return the memrory to thread_alloc for(size_t j = 0; j < n_inner; j++) thread_alloc::return_memory(v_ptr[j]); // check that now n_inner * cap_bytes are now available // and none are in use ok &= thread_alloc::inuse(thread) == static_inuse; ok &= thread_alloc::available(thread) == n_inner * cap_bytes; } thread_alloc::free_available(thread); // check that the tests have not held onto memory ok &= ! CppAD::memory_leak(); return ok; } class my_char { public: char ch_ ; my_char(void) : ch_(' ') { } my_char(const my_char& my_ch) : ch_(my_ch.ch_) { } }; bool type_allocate(void) { bool ok = true; using CppAD::thread_alloc; size_t i; // check initial memory values size_t thread = thread_alloc::thread_num(); ok &= thread == 0; ok &= thread_alloc::free_all(); size_t static_inuse = 0; // initial allocation of an array size_t size_min = 3; size_t size_one; my_char *array_one = thread_alloc::create_array(size_min, size_one); // check the values and change them to null 'x' for(i = 0; i < size_one; i++) { ok &= array_one[i].ch_ == ' '; array_one[i].ch_ = 'x'; } // now create a longer array size_t size_two; my_char *array_two = thread_alloc::create_array(2 * size_min, size_two); // check the values in array one for(i = 0; i < size_one; i++) ok &= array_one[i].ch_ == 'x'; // check the values in array two for(i = 0; i < size_two; i++) ok &= array_two[i].ch_ == ' '; // check the amount of inuse and available memory // (an extra size_t value is used for each memory block). size_t check = static_inuse + sizeof(my_char)*(size_one + size_two); ok &= thread_alloc::inuse(thread) - check < sizeof(my_char); ok &= thread_alloc::available(thread) == 0; // delete the arrays thread_alloc::delete_array(array_one); thread_alloc::delete_array(array_two); ok &= thread_alloc::inuse(thread) == static_inuse; check = sizeof(my_char)*(size_one + size_two); ok &= thread_alloc::available(thread) - check < sizeof(my_char); // free the memory for use by this thread thread_alloc::free_available(thread); // check that the tests have not held onto memory ok &= ! CppAD::memory_leak(); return ok; } } // End empty namespace bool check_alignment(void) { bool ok = true; using CppAD::thread_alloc; // number of binary digits in a size_t value size_t n_digit = std::numeric_limits::digits; // must be a multiple of 8 ok &= (n_digit % 8) == 0; // number of bytes in a size_t value size_t n_byte = n_digit / 8; // check raw allocation ------------------------------------------------- size_t min_bytes = 1; size_t cap_bytes; void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes); // convert to a size_t value size_t v_size_t = reinterpret_cast(v_ptr); // check that it is aligned ok &= (v_size_t % n_byte) == 0; // return memory to available pool thread_alloc::return_memory(v_ptr); // check array allocation ---------------------------------------------- size_t size_min = 1; size_t size_out; my_char *array_ptr = thread_alloc::create_array(size_min, size_out); // convert to a size_t value size_t array_size_t = reinterpret_cast(array_ptr); // check that it is aligned ok &= (array_size_t % n_byte) == 0; // return memory to avialable pool thread_alloc::delete_array(array_ptr); return ok; } bool thread_alloc(void) { bool ok = true; using CppAD::thread_alloc; // check that there is only on thread ok &= thread_alloc::num_threads() == 1; // so thread number must be zero ok &= thread_alloc::thread_num() == 0; // and we are in sequential execution mode ok &= thread_alloc::in_parallel() == false; // Instruct thread_alloc to hold onto memory. This makes memory // allocation faster (especially when there are multiple threads). thread_alloc::hold_memory(true); // run raw allocation tests ok &= raw_allocate(); // run typed allocation tests ok &= type_allocate(); // check alignment ok &= check_alignment(); // return allocator to its default mode thread_alloc::hold_memory(false); return ok; } // END C++ cppad-20170000.3/example/sqrt.cpp0000644000175200017650000000413713057470460015565 0ustar coincoin-web// $Id: sqrt.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sqrt.cpp$$ $spell sqrt $$ $section The AD sqrt Function: Example and Test$$ $code $srcfile%example/sqrt.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool Sqrt(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::sqrt(x[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value double check = std::sqrt(x0); ok &= NearEqual(y[0] , check, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); check = 1. / (2. * std::sqrt(x0) ); ok &= NearEqual(dy[0], check, eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, eps99, eps99); // use a VecAD::reference object with sqrt CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::sqrt(v[zero]); check = std::sqrt(x0); ok &= NearEqual(result, check, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/log.cpp0000644000175200017650000000405613057470460015355 0ustar coincoin-web// $Id: log.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin log.cpp$$ $spell exp log $$ $section The AD log Function: Example and Test$$ $code $srcfile%example/log.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool log(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD exp_of_x0 = CppAD::exp(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::log(exp_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps99, eps99); // use a VecAD::reference object with log CppAD::VecAD v(1); AD zero(0); v[zero] = exp_of_x0; AD result = CppAD::log(v[zero]); ok &= NearEqual(result, x0, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/asin.cpp0000644000175200017650000000407213057470460015524 0ustar coincoin-web// $Id: asin.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin asin.cpp$$ $spell sin asin $$ $section The AD asin Function: Example and Test$$ $code $srcfile%example/asin.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool asin(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD sin_of_x0 = CppAD::sin(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::asin(sin_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps, eps); // use a VecAD::reference object with asin CppAD::VecAD v(1); AD zero(0); v[zero] = sin_of_x0; AD result = CppAD::asin(v[zero]); ok &= NearEqual(result, x0, eps, eps); return ok; } // END C++ cppad-20170000.3/example/error_handler.cpp0000644000175200017650000000403413057470460017416 0ustar coincoin-web// $Id: error_handler.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin error_handler.cpp$$ $spell CppAD $$ $section Replacing The CppAD Error Handler: Example and Test$$ $mindex handler$$ $code $srcfile%example/error_handler.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { void myhandler( bool known , int line , const char *file , const char *exp , const char *msg ) { // error handler must not return, so throw an exception throw line; } } bool ErrorHandler(void) { using CppAD::ErrorHandler; int lineMinusFive = 0; // replace the default CppAD error handler ErrorHandler info(myhandler); // set ok to false unless catch block is executed bool ok = false; // use try / catch because handler throws an exception try { // set the static variable Line to next source code line lineMinusFive = __LINE__; // can call myhandler anywhere that ErrorHandler is defined ErrorHandler::Call( true , // reason for the error is known __LINE__ , // current source code line number __FILE__ , // current source code file name "1 > 0" , // an intentional error condition "Testing ErrorHandler" // reason for error ); } catch ( int line ) { // check value of the line number that was passed to handler ok = (line == lineMinusFive + 5); } // info drops out of scope and the default CppAD error handler // is restored when this routine returns. return ok; } // END C++ cppad-20170000.3/example/par_var.cpp0000644000175200017650000000371313057470460016225 0ustar coincoin-web// $Id: par_var.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin par_var.cpp$$ $section AD Parameter and Variable Functions: Example and Test$$ $code $srcfile%example/par_var.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool ParVar(void) { bool ok = true; using CppAD::AD; using CppAD::VecAD; using CppAD::Parameter; using CppAD::Variable; // declare independent variables and start tape recording size_t n = 1; CPPAD_TESTVECTOR(AD) x(n); x[0] = 0.; ok &= Parameter(x[0]); // x[0] is a paraemter here CppAD::Independent(x); ok &= Variable(x[0]); // now x[0] is a variable // dependent variable vector size_t m = 2; CPPAD_TESTVECTOR(AD) y(m); y[0] = 2.; ok &= Parameter(y[0]); // y[0] does not depend on x[0] y[1] = abs(x[0]); ok &= Variable(y[1]); // y[1] does depends on x[0] // VecAD objects VecAD z(2); z[0] = 0.; z[1] = 1.; ok &= Parameter(z); // z does not depend on x[0] z[x[0]] = 2.; ok &= Variable(z); // z depends on x[0] // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check that now all AD objects are parameters ok &= Parameter(x[0]); ok &= ! Variable(x[0]); ok &= Parameter(y[0]); ok &= ! Variable(y[0]); ok &= Parameter(y[1]); ok &= ! Variable(y[1]); // check that the VecAD object is a parameter ok &= Parameter(z); return ok; } // END C++ cppad-20170000.3/example/atanh.cpp0000644000175200017650000000403113057470460015660 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atanh.cpp$$ $spell tanh atanh $$ $section The AD atanh Function: Example and Test$$ $code $srcfile%example/atanh.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool atanh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD tanh_of_x0 = CppAD::tanh(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::atanh(tanh_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps, eps); // use a VecAD::reference object with atanh CppAD::VecAD v(1); AD zero(0); v[zero] = tanh_of_x0; AD result = CppAD::atanh(v[zero]); ok &= NearEqual(result, x0, eps, eps); return ok; } // END C++ cppad-20170000.3/example/ipopt_solve/0002755000175200017650000000000013057470460016430 5ustar coincoin-webcppad-20170000.3/example/ipopt_solve/makefile.am0000644000175200017650000000224113057470460020521 0ustar coincoin-web# $Id: makefile.am 3803 2016-03-19 05:07:48Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = solve # AM_CXXFLAGS = -g $(CXX_FLAGS) # AM_CPPFLAGS = -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ -I$(IPOPT_DIR)/include # LDADD = \ $(CPPAD_IPOPT_LIBS) \ $(FCLIBS) \ $(PTHREAD_LIB) \ $(DL_LIB) # solve_SOURCES = \ get_started.cpp \ ipopt_solve.cpp \ ode_inverse.cpp \ retape.cpp test: check ./test.sh cppad-20170000.3/example/ipopt_solve/CMakeLists.txt0000644000175200017650000000273713057470460021177 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the example/ipopt_solve directory tests # Specifies build type for this directory. Possible values are # empty, Debug, Release, RelWithDebInfo and MinSizeRel SET(CMAKE_BUILD_TYPE DEBUG) # Local link directories to search, as determined by pkg-config for ipopt LINK_DIRECTORIES( ${ipopt_LIBRARY_DIRS} ) # ADD_EXECUTABLE(example_ipopt_solve EXCLUDE_FROM_ALL get_started.cpp ipopt_solve.cpp ode_inverse.cpp retape.cpp ) # Extra compiler flags add_cppad_cxx_flags( example_ipopt_solve ) # libraries to be linked into the specified target, # as determined by pkg-config for ipopt TARGET_LINK_LIBRARIES(example_ipopt_solve ${cppad_lib} ${ipopt_LIBRARIES} ${colpack_libs} ) # Add the check_example_ipopt_solve target ADD_CUSTOM_TARGET(check_example_ipopt_solve example_ipopt_solve DEPENDS example_ipopt_solve ) MESSAGE(STATUS "make check_example_ipopt_solve: available") cppad-20170000.3/example/ipopt_solve/test.sh.in0000644000175200017650000000125213057470460020346 0ustar coincoin-web#! /bin/bash -e # $Id: test.sh.in 2655 2012-12-27 13:51:34Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- export LD_LIBRARY_PATH=@CPPAD_IPOPT_LD_PATH@ ./solve cppad-20170000.3/example/ipopt_solve/retape.cpp0000644000175200017650000000630313057470460020414 0ustar coincoin-web// $Id: retape.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_solve_retape.cpp$$ $spell Retaping retape cppad_nlp IpoptDir CppAD $$ $section Nonlinear Programming Retaping: Example and Test$$ $mindex retape ipopt_solve$$ $head Purpose$$ This example program demonstrates a case were the $code ipopt::solve$$ argument $cref/retape/ipopt_solve/options/Retape/$$ should be true. $code $srcfile%example/ipopt_solve/retape.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::AD; class FG_eval { public: typedef CPPAD_TESTVECTOR( AD ) ADvector; void operator()(ADvector& fg, const ADvector& x) { assert( fg.size() == 1 ); assert( x.size() == 1 ); // compute the Huber function using a conditional // statement that depends on the value of x. double eps = 0.1; if( abs(x[0]) <= eps ) fg[0] = x[0] * x[0] / (2.0 * eps); else fg[0] = abs(x[0]) - eps / 2.0; return; } }; } bool retape(void) { bool ok = true; typedef CPPAD_TESTVECTOR( double ) Dvector; // number of independent variables (domain dimension for f and g) size_t nx = 1; // number of constraints (range dimension for g) size_t ng = 0; // initial value, lower and upper limits, for the independent variables Dvector xi(nx), xl(nx), xu(nx); xi[0] = 2.0; xl[0] = -1e+19; xu[0] = +1e+19; // lower and upper limits for g Dvector gl(ng), gu(ng); // object that computes objective and constraints FG_eval fg_eval; // options std::string options; // retape operation sequence for each new x options += "Retape true\n"; // turn off any printing options += "Integer print_level 0\n"; options += "String sb yes\n"; // maximum number of iterations options += "Integer max_iter 10\n"; // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) options += "Numeric tol 1e-9\n"; // derivative testing options += "String derivative_test second-order\n"; // maximum amount of random pertubation; e.g., // when evaluation finite diff options += "Numeric point_perturbation_radius 0.\n"; // place to return solution CppAD::ipopt::solve_result solution; // solve the problem CppAD::ipopt::solve( options, xi, xl, xu, gl, gu, fg_eval, solution ); // // Check some of the solution values // ok &= solution.status == CppAD::ipopt::solve_result::success; double rel_tol = 1e-6; // relative tolerance double abs_tol = 1e-6; // absolute tolerance ok &= CppAD::NearEqual( solution.x[0], 0.0, rel_tol, abs_tol); return ok; } // END C++ cppad-20170000.3/example/ipopt_solve/makefile.in0000644000175200017650000004635113057470460020544 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; the Free Software Foundation # gives unlimited permission to copy and/or distribute it, # with or without modifications, as long as this notice is preserved. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY, to the extent permitted by law; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_solve_ode_inverse.cpp$$ $spell $$ $section ODE Inverse Problem Definitions: Source Code$$ $mindex example$$ $head Purpose$$ This example demonstrates how to invert for parameters in a ODE where the solution of the ODE is numerically approximated. $head Forward Problem$$ We consider the following ordinary differential equation: $latex \[ \begin{array}{rcl} \partial_t y_0 ( t , a ) & = & - a_1 * y_0 (t, a ) \\ \partial_t y_1 (t , a ) & = & + a_1 * y_0 (t, a ) - a_2 * y_1 (t, a ) \end{array} \] $$ with the initial conditions $latex \[ y_0 (0 , a) = ( a_0 , 0 )^\R{T} \] $$ Our forward problem is stated as follows: Given $latex a \in \B{R}^3$$ determine the value of $latex y ( t , a ) $$, for $latex t \in R$$, that solves the initial value problem above. $head Measurements$$ Suppose we are also given measurement times $latex s \in \B{R}^5$$ and a measurement vector $latex z \in \B{R}^4$$ and for $latex i = 0, \ldots, 3$$, we model $latex z_i$$ by $latex \[ z_i = y_1 ( s_{i+1} , a) + e_i \] $$ where $latex e_{i-1} \sim {\bf N} (0 , \sigma^2 )$$ is the measurement noise, and $latex \sigma > 0$$ is the standard deviation of the noise. $subhead Simulation Analytic Solution$$ The following analytic solution to the forward problem is used to simulate a data set: $latex \[ \begin{array}{rcl} y_0 (t , a) & = & a_0 * \exp( - a_1 * t ) \\ y_1 (t , a) & = & a_0 * a_1 * \frac{\exp( - a_2 * t ) - \exp( -a_1 * t )}{ a_1 - a_2 } \end{array} \] $$ $subhead Simulation Parameter Values$$ $table $latex \bar{a}_0 = 1$$ $pre $$ $cnext initial value of $latex y_0 (t, a)$$ $rnext $latex \bar{a}_1 = 2$$ $pre $$ $cnext transfer rate from compartment zero to compartment one $rnext $latex \bar{a}_2 = 1$$ $pre $$ $cnext transfer rate from compartment one to outside world $rnext $latex \sigma = 0$$ $pre $$ $cnext standard deviation of measurement noise $rnext $latex e_i = 0$$ $pre $$ $cnext simulated measurement noise, $latex i = 1 , \ldots , Nz$$ $rnext $latex s_i = i * .5$$ $pre $$ $cnext time corresponding to the $th i$$ measurement, $latex i = 0 , \ldots , 3$$ $tend $subhead Simulated Measurement Values$$ The simulated measurement values are given by the equation $latex \[ \begin{array}{rcl} z_i & = & e_i + y_1 ( s_{i+1} , \bar{a} ) \\ & = & \bar{a}_0 * \bar{a}_1 * \frac{\exp( - \bar{a}_2 * s_i ) - \exp( -\bar{a}_1 * s_i )} { \bar{a}_1 - \bar{a}_2 } \end{array} \] $$ for $latex i = 0, \ldots , 3$$. $head Inverse Problem$$ The maximum likelihood estimate for $latex a$$ given $latex z$$ solves the following optimization problem $latex \[ \begin{array}{rcl} {\rm minimize} \; & \sum_{i=0}^3 ( z_i - y_1 ( s_{i+1} , a ) )^2 & \;{\rm w.r.t} \; a \in \B{R}^3 \end{array} \] $$ $head Trapezoidal Approximation$$ We are given a number of approximation points per measurement interval $latex np$$ and define the time grid $latex t \in \B{R}^{4 \cdot np + 1}$$ as follows: $latex t_0 = s_0$$ and for $latex i = 0 , 1 , 2, 3$$, $latex j = 1 , \ldots , np$$ $latex \[ t_{i \cdot np + j} = s_i + (s_{i+1} - s{i}) \frac{i}{np} \] $$ We note that for $latex i = 1 , \ldots , 4$$, $latex t_{i \cdot np} = s_i$$. This example uses a trapezoidal approximation to solve the ODE. Given $latex a \in \B{R}^3$$ and $latex y^{k-1} \approx y( t_{k-1} , a )$$, the a trapezoidal method approximates $latex y ( t_j , a )$$ by the value $latex y^k \in \B{R}^2$$ ) that solves the equation $latex \[ y^k = y^{k-1} + \frac{G( y^k , a ) + G( y^{k-1} , a ) }{2} * (t_k - t_{k-1}) \] $$ where $latex G : \B{R}^2 \times \B{R}^3 \rightarrow \B{R}^2$$ is defined by $latex \[ \begin{array}{rcl} G_0 ( y , a ) & = & - a_1 * y_0 \\ G_1 ( y , a ) & = & + a_1 * y_0 - a_2 * y_1 \end{array} \] $$ $head Solution Method$$ We use constraints to embed the forward problem in the inverse problem. To be specific, we solve the optimization problem $latex \[ \begin{array}{rcl} {\rm minimize} & \sum_{i=0}^3 ( z_i - y_1^{(i+1) \cdot np} )^2 & \; {\rm w.r.t} \; a \in \B{R}^3 \; y^0 \in \B{R}^2 , \ldots , y^{3 \cdot np -1} \in \B{R}^2 \\ {\rm subject \; to} 0 = y^0 - ( a_0 , 0 )^\R{T} \\ & 0 = y^k - y^{k-1} - \frac{G( y^k , a ) + G( y^{k-1} , a ) }{2} (t_k - t_{k-1}) & \; {\rm for} \; k = 1 , \ldots , 4 \cdot np \end{array} \] $$ The code below we using the notation $latex x \in \B{3 + (4 \cdot np + 1) \cdot 2}$$ defined by $latex \[ x = \left( a_0, a_1, a_2 , y_0^0, y_1^0, \ldots , y_0^{4 \cdot np}, y_1^{4 \cdots np} \right) \] $$ $head Source$$ The following source code implements the ODE inversion method proposed above: $code $srcfile%example/ipopt_solve/ode_inverse.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include namespace { using CppAD::AD; // value of a during simulation a[0], a[1], a[2] double a_[] = {2.0, 1.0, 0.5}; // number of components in a size_t na_ = sizeof(a_) / sizeof(a_[0]); // function used to simulate data double yone(double t) { return a_[0]*a_[1] * (exp(-a_[2]*t) - exp(-a_[1]*t)) / (a_[1] - a_[2]); } // time points were we have data (no data at first point) double s_[] = {0.0, 0.5, 1.0, 1.5, 2.0 }; // Simulated data for case with no noise (first point is not used) double z_[] = {yone(s_[1]), yone(s_[2]), yone(s_[3]), yone(s_[4])}; size_t nz_ = sizeof(z_) / sizeof(z_[0]); // number of trapozoidal approximation points per measurement interval size_t np_ = 40; class FG_eval { private: public: // derived class part of constructor typedef CPPAD_TESTVECTOR( AD ) ADvector; // Evaluation of the objective f(x), and constraints g(x) void operator()(ADvector& fg, const ADvector& x) { CPPAD_TESTVECTOR( AD ) a(na_); size_t i, j, k; // extract the vector a for(i = 0; i < na_; i++) a[i] = x[i]; // compute the object f(x) fg[0] = 0.0; for(i = 0; i < nz_; i++) { k = (i + 1) * np_; AD y_1 = x[na_ + 2 * k + 1]; AD dif = z_[i] - y_1; fg[0] += dif * dif; } // constraint corresponding to initial value y(0, a) // Note that this constraint is invariant with size of dt fg[1] = x[na_+0] - a[0]; fg[2] = x[na_+1] - 0.0; // constraints corresponding to trapozoidal approximation for(i = 0; i < nz_; i++) { // spacing between grid point double dt = (s_[i+1] - s_[i]) / static_cast(np_); for(j = 1; j <= np_; j++) { k = i * np_ + j; // compute derivative at y^k AD y_0 = x[na_ + 2 * k + 0]; AD y_1 = x[na_ + 2 * k + 1]; AD G_0 = - a[1] * y_0; AD G_1 = + a[1] * y_0 - a[2] * y_1; // compute derivative at y^{k-1} AD ym_0 = x[na_ + 2 * (k-1) + 0]; AD ym_1 = x[na_ + 2 * (k-1) + 1]; AD Gm_0 = - a[1] * ym_0; AD Gm_1 = + a[1] * ym_0 - a[2] * ym_1; // constraint should be zero fg[1 + 2*k ] = y_0 - ym_0 - dt*(G_0 + Gm_0)/2.; fg[2 + 2*k ] = y_1 - ym_1 - dt*(G_1 + Gm_1)/2.; // scale g(x) so it has similar size as f(x) fg[1 + 2*k ] /= dt; fg[2 + 2*k ] /= dt; } } } }; } bool ode_inverse(void) { bool ok = true; size_t i; typedef CPPAD_TESTVECTOR( double ) Dvector; // number of components in the function g size_t ng = (np_ * nz_ + 1) * 2; // number of independent variables size_t nx = na_ + ng; // initial vlaue for the variables we are optimizing w.r.t Dvector xi(nx), xl(nx), xu(nx); for(i = 0; i < nx; i++) { xi[i] = 0.0; // initial value xl[i] = -1e19; // no lower limit xu[i] = +1e19; // no upper limit } for(i = 0; i < na_; i++) xi[0] = 1.5; // initial value for a // all the difference equations are constrainted to be zero Dvector gl(ng), gu(ng); for(i = 0; i < ng; i++) { gl[i] = 0.0; gu[i] = 0.0; } // object defining both f(x) and g(x) FG_eval fg_eval; // options std::string options; // Use sparse matrices for calculation of Jacobians and Hessians // with forward mode for Jacobian (seems to be faster for this case). options += "Sparse true forward\n"; // turn off any printing options += "Integer print_level 0\n"; options += "String sb yes\n"; // maximum number of iterations options += "Integer max_iter 30\n"; // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) options += "Numeric tol 1e-6\n"; // place to return solution CppAD::ipopt::solve_result solution; // solve the problem CppAD::ipopt::solve( options, xi, xl, xu, gl, gu, fg_eval, solution ); // // Check some of the solution values // ok &= solution.status == CppAD::ipopt::solve_result::success; // double rel_tol = 1e-4; // relative tolerance double abs_tol = 1e-4; // absolute tolerance for(i = 0; i < na_; i++) ok &= CppAD::NearEqual( a_[i], solution.x[i], rel_tol, abs_tol); return ok; } // END C++ cppad-20170000.3/example/ipopt_solve/ipopt_solve.cpp0000644000175200017650000000434013057470460021476 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // system include files used for I/O # include // C style asserts # include // ipopt solve include file # include // external complied tests extern bool get_started(void); extern bool ode_inverse(void); extern bool retape(void); namespace { // function that runs one test static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), const char *name) { bool ok = true; double s0 = CppAD::elapsed_seconds(); ok &= TestOk(); double s1 = CppAD::elapsed_seconds(); double sec = std::floor(100*(s1 - s0) + 0.5) / 100.; if( ok ) { std::cout << "OK: " << "ipopt_solve: " << name; std::cout << ", seconds = " << sec << std::endl; Run_ok_count++; } else { std::cout << "Error: " << "ipopt_solve: " << name << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; // This line is used by test_one.sh // external compiled tests ok &= Run( get_started, "get_started" ); ok &= Run( ode_inverse, "ode_inverse" ); ok &= Run( retape, "retape" ); // check for errors using std::cout; using std::endl; assert( ok || (Run_error_count > 0) ); if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "OK: " << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Error: " << "memory leak detected" << endl; } // convert int(size_t) to avoid warning on _MSC_VER systems if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! ok ); } cppad-20170000.3/example/ipopt_solve/get_started.cpp0000644000175200017650000001027213057470460021441 0ustar coincoin-web// $Id: get_started.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_solve_get_started.cpp$$ $spell cppad_nlp IpoptDir CppAD $$ $section Nonlinear Programming Using CppAD and Ipopt: Example and Test$$ $mindex ipopt AD$$ $head Purpose$$ This example program demonstrates how to use $cref ipopt_solve$$ to solve the example problem in the Ipopt documentation; i.e., the problem $latex \[ \begin{array}{lc} {\rm minimize \; } & x_1 * x_4 * (x_1 + x_2 + x_3) + x_3 \\ {\rm subject \; to \; } & x_1 * x_2 * x_3 * x_4 \geq 25 \\ & x_1^2 + x_2^2 + x_3^2 + x_4^2 = 40 \\ & 1 \leq x_1, x_2, x_3, x_4 \leq 5 \end{array} \] $$ $head Configuration Requirement$$ This example will be compiled and tested provided that $cref ipopt_prefix$$ is specified on the $cref cmake$$ command line. $code $srcfile%example/ipopt_solve/get_started.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::AD; class FG_eval { public: typedef CPPAD_TESTVECTOR( AD ) ADvector; void operator()(ADvector& fg, const ADvector& x) { assert( fg.size() == 3 ); assert( x.size() == 4 ); // Fortran style indexing AD x1 = x[0]; AD x2 = x[1]; AD x3 = x[2]; AD x4 = x[3]; // f(x) fg[0] = x1 * x4 * (x1 + x2 + x3) + x3; // g_1 (x) fg[1] = x1 * x2 * x3 * x4; // g_2 (x) fg[2] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4; // return; } }; } bool get_started(void) { bool ok = true; size_t i; typedef CPPAD_TESTVECTOR( double ) Dvector; // number of independent variables (domain dimension for f and g) size_t nx = 4; // number of constraints (range dimension for g) size_t ng = 2; // initial value of the independent variables Dvector xi(nx); xi[0] = 1.0; xi[1] = 5.0; xi[2] = 5.0; xi[3] = 1.0; // lower and upper limits for x Dvector xl(nx), xu(nx); for(i = 0; i < nx; i++) { xl[i] = 1.0; xu[i] = 5.0; } // lower and upper limits for g Dvector gl(ng), gu(ng); gl[0] = 25.0; gu[0] = 1.0e19; gl[1] = 40.0; gu[1] = 40.0; // object that computes objective and constraints FG_eval fg_eval; // options std::string options; // turn off any printing options += "Integer print_level 0\n"; options += "String sb yes\n"; // maximum number of iterations options += "Integer max_iter 10\n"; // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) options += "Numeric tol 1e-6\n"; // derivative testing options += "String derivative_test second-order\n"; // maximum amount of random pertubation; e.g., // when evaluation finite diff options += "Numeric point_perturbation_radius 0.\n"; // place to return solution CppAD::ipopt::solve_result solution; // solve the problem CppAD::ipopt::solve( options, xi, xl, xu, gl, gu, fg_eval, solution ); // // Check some of the solution values // ok &= solution.status == CppAD::ipopt::solve_result::success; // double check_x[] = { 1.000000, 4.743000, 3.82115, 1.379408 }; double check_zl[] = { 1.087871, 0., 0., 0. }; double check_zu[] = { 0., 0., 0., 0. }; double rel_tol = 1e-6; // relative tolerance double abs_tol = 1e-6; // absolute tolerance for(i = 0; i < nx; i++) { ok &= CppAD::NearEqual( check_x[i], solution.x[i], rel_tol, abs_tol ); ok &= CppAD::NearEqual( check_zl[i], solution.zl[i], rel_tol, abs_tol ); ok &= CppAD::NearEqual( check_zu[i], solution.zu[i], rel_tol, abs_tol ); } return ok; } // END C++ cppad-20170000.3/example/cosh.cpp0000644000175200017650000000411413057470460015523 0ustar coincoin-web// $Id: cosh.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cosh.cpp$$ $spell $$ $section The AD cosh Function: Example and Test$$ $code $srcfile%example/cosh.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool Cosh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::cosh(x[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value double check = std::cosh(x0); ok &= NearEqual(y[0] , check, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); check = std::sinh(x0); ok &= NearEqual(dy[0], check, eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, eps99, eps99); // use a VecAD::reference object with cosh CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::cosh(v[zero]); check = std::cosh(x0); ok &= NearEqual(result, check, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/rev_one.cpp0000644000175200017650000000516013057470460016226 0ustar coincoin-web// $Id: rev_one.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin rev_one.cpp$$ $spell Cpp $$ $section First Order Derivative Driver: Example and Test$$ $code $srcfile%example/rev_one.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // ------------------------------------------------------- // define the template function RevOneCases in empty namespace template bool RevOneCases() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); using CppAD::exp; using CppAD::sin; using CppAD::cos; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; X[1] = 2.; // declare independent variables and starting recording CppAD::Independent(X); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] * exp( X[1] ); Y[1] = X[0] * sin( X[1] ); Y[2] = X[0] * cos( X[1] ); // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector Vector x(n); x[0] = 2.; x[1] = 1.; // compute and check derivative of y[0] Vector dw(n); dw = f.RevOne(x, 0); ok &= NearEqual(dw[0], exp(x[1]), eps99, eps99); // w.r.t x[0] ok &= NearEqual(dw[1], x[0]*exp(x[1]), eps99, eps99); // w.r.t x[1] // compute and check derivative of y[1] dw = f.RevOne(x, 1); ok &= NearEqual(dw[0], sin(x[1]), eps99, eps99); ok &= NearEqual(dw[1], x[0]*cos(x[1]), eps99, eps99); // compute and check derivative of y[2] dw = f.RevOne(x, 2); ok &= NearEqual(dw[0], cos(x[1]), eps99, eps99); ok &= NearEqual(dw[1], - x[0]*sin(x[1]), eps99, eps99); return ok; } } // End empty namespace # include # include bool RevOne(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= RevOneCases< CppAD::vector >(); ok &= RevOneCases< std::vector >(); ok &= RevOneCases< std::valarray >(); return ok; } // END C++ cppad-20170000.3/example/romberg_one.cpp0000644000175200017650000000377413057470460017100 0ustar coincoin-web// $Id: romberg_one.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin romberg_one.cpp$$ $spell Romberg $$ $section One Dimensional Romberg Integration: Example and Test$$ $code $srcfile%example/romberg_one.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include namespace { class Fun { private: const size_t degree; public: // constructor Fun(size_t degree_) : degree(degree_) { } // function F(x) = x^degree template Type operator () (const Type &x) { size_t i; Type f = 1; for(i = 0; i < degree; i++) f *= x; return f; } }; } bool RombergOne(void) { bool ok = true; size_t i; size_t degree = 4; Fun F(degree); // arguments to RombergOne double a = 0.; double b = 1.; size_t n = 4; size_t p; double r, e; // int_a^b F(x) dx = [ b^(degree+1) - a^(degree+1) ] / (degree+1) double bpow = 1.; double apow = 1.; for(i = 0; i <= degree; i++) { bpow *= b; apow *= a; } double check = (bpow - apow) / (degree+1); // step size corresponding to r double step = (b - a) / exp(log(2.)*(n-1)); // step size corresponding to error estimate step *= 2.; // step size raised to a power double spow = 1; for(p = 0; p < n; p++) { spow = spow * step * step; r = CppAD::RombergOne(F, a, b, n, p, e); ok &= e < (degree+1) * spow; ok &= CppAD::NearEqual(check, r, 0., e); } return ok; } // END C++ cppad-20170000.3/example/sin.cpp0000644000175200017650000000410613057470460015361 0ustar coincoin-web// $Id: sin.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sin.cpp$$ $spell sin $$ $section The AD sin Function: Example and Test$$ $code $srcfile%example/sin.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool Sin(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::sin(x[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value double check = std::sin(x0); ok &= NearEqual(y[0] , check, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); check = std::cos(x0); ok &= NearEqual(dy[0], check, eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, eps99, eps99); // use a VecAD::reference object with sin CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::sin(v[zero]); check = std::sin(x0); ok &= NearEqual(result, check, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/sign.cpp0000644000175200017650000000372513057470460015536 0ustar coincoin-web// $Id: sign.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sign.cpp$$ $spell $$ $section Sign Function: Example and Test$$ $code $srcfile%example/sign.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool sign(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // create f: x -> y where f(x) = sign(x) size_t n = 1; size_t m = 1; CPPAD_TESTVECTOR(AD) ax(n), ay(m); ax[0] = 0.; CppAD::Independent(ax); ay[0] = sign(ax[0]); CppAD::ADFun f(ax, ay); // check value during recording ok &= (ay[0] == 0.); // use f(x) to evaluate the sign function and its derivatives CPPAD_TESTVECTOR(double) x(n), y(m), dx(n), dy(m), w(m), dw(n); dx[0] = 1.; w[0] = 1.; // x[0] = 2.; y = f.Forward(0, x); ok &= (y[0] == 1.); dy = f.Forward(1, dx); ok &= (dy[0] == 0.); dw = f.Reverse(1, w); ok &= (dw[0] == 0.); // x[0] = 0.; y = f.Forward(0, x); ok &= (y[0] == 0.); dy = f.Forward(1, dx); ok &= (dy[0] == 0.); dw = f.Reverse(1, w); ok &= (dw[0] == 0.); // x[0] = -2.; y = f.Forward(0, x); ok &= (y[0] == -1.); dy = f.Forward(1, dx); ok &= (dy[0] == 0.); dw = f.Reverse(1, w); ok &= (dw[0] == 0.); // use a VecAD::reference object with sign CppAD::VecAD v(1); AD zero(0); v[zero] = 2.; AD result = sign(v[zero]); ok &= (result == 1.); return ok; } // END C++ cppad-20170000.3/example/ode_gear.cpp0000644000175200017650000000771513057470460016346 0ustar coincoin-web// $Id: ode_gear.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ode_gear.cpp$$ $spell Rosen $$ $section OdeGear: Example and Test$$ $mindex OdeGear$$ Define $latex x : \B{R} \rightarrow \B{R}^n$$ by $latex \[ x_i (t) = t^{i+1} \] $$ for $latex i = 1 , \ldots , n-1$$. It follows that $latex \[ \begin{array}{rclr} x_i(0) & = & 0 & {\rm for \; all \;} i \\ x_i ' (t) & = & 1 & {\rm if \;} i = 0 \\ x_i '(t) & = & (i+1) t^i = (i+1) x_{i-1} (t) & {\rm if \;} i > 0 \end{array} \] $$ The example tests OdeGear using the relations above: $code $srcfile%example/ode_gear.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include // For automatic differentiation namespace { class Fun { public: // constructor Fun(bool use_x_) : use_x(use_x_) { } // compute f(t, x) both for double and AD template void Ode( const Scalar &t, const CPPAD_TESTVECTOR(Scalar) &x, CPPAD_TESTVECTOR(Scalar) &f) { size_t n = x.size(); Scalar ti(1); f[0] = Scalar(1); size_t i; for(i = 1; i < n; i++) { ti *= t; // convert int(size_t) to avoid warning // on _MSC_VER systems if( use_x ) f[i] = int(i+1) * x[i-1]; else f[i] = int(i+1) * ti; } } void Ode_dep( const double &t, const CPPAD_TESTVECTOR(double) &x, CPPAD_TESTVECTOR(double) &f_x) { using namespace CppAD; size_t n = x.size(); CPPAD_TESTVECTOR(AD) T(1); CPPAD_TESTVECTOR(AD) X(n); CPPAD_TESTVECTOR(AD) F(n); // set argument values T[0] = t; size_t i, j; for(i = 0; i < n; i++) X[i] = x[i]; // declare independent variables Independent(X); // compute f(t, x) this->Ode(T[0], X, F); // define AD function object ADFun fun(X, F); // compute partial of f w.r.t x CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) df(n); for(j = 0; j < n; j++) dx[j] = 0.; for(j = 0; j < n; j++) { dx[j] = 1.; df = fun.Forward(1, dx); for(i = 0; i < n; i++) f_x [i * n + j] = df[i]; dx[j] = 0.; } } private: const bool use_x; }; } bool OdeGear(void) { bool ok = true; // initial return value size_t i, j; // temporary indices size_t m = 4; // index of next value in X size_t n = m; // number of components in x(t) // vector of times CPPAD_TESTVECTOR(double) T(m+1); double step = .1; T[0] = 0.; for(j = 1; j <= m; j++) { T[j] = T[j-1] + step; step = 2. * step; } // initial values for x( T[m-j] ) CPPAD_TESTVECTOR(double) X((m+1) * n); for(j = 0; j < m; j++) { double ti = T[j]; for(i = 0; i < n; i++) { X[ j * n + i ] = ti; ti *= T[j]; } } // error bound CPPAD_TESTVECTOR(double) e(n); size_t use_x; for( use_x = 0; use_x < 2; use_x++) { // function object depends on value of use_x Fun F(use_x > 0); // compute OdeGear approximation for x( T[m] ) CppAD::OdeGear(F, m, n, T, X, e); double check = T[m]; for(i = 0; i < n; i++) { // method is exact up to order m and x[i] = t^{i+1} if( i + 1 <= m ) ok &= CppAD::NearEqual( X[m * n + i], check, 1e-10, 1e-10 ); // error bound should be zero up to order m-1 if( i + 1 < m ) ok &= CppAD::NearEqual( e[i], 0., 1e-10, 1e-10 ); // check value for next i check *= T[m]; } } return ok; } // END C++ cppad-20170000.3/example/mul.cpp0000644000175200017650000000432413057470460015367 0ustar coincoin-web// $Id: mul.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin mul.cpp$$ $section AD Binary Multiplication: Example and Test$$ $mindex * multiply times$$ $code $srcfile%example/mul.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool Mul(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // domain space vector size_t n = 1; double x0 = .5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // some binary multiplication operations AD a = x[0] * 1.; // AD * double AD b = a * 2; // AD * int AD c = 3. * b; // double * AD AD d = 4 * c; // int * AD // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = x[0] * d; // AD * AD // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0*(4.*3.*2.*1.)*x0, 1e-10 , 1e-10); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10); // use a VecAD::reference object with multiplication CppAD::VecAD v(1); AD zero(0); v[zero] = c; AD result = 4 * v[zero]; ok &= (result == d); return ok; } // END C++ cppad-20170000.3/example/ode_gear_control.cpp0000644000175200017650000000721413057470460020100 0ustar coincoin-web// $Id: ode_gear_control.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ode_gear_control.cpp$$ $spell Runge $$ $section OdeGearControl: Example and Test$$ $mindex OdeGearControl$$ Define $latex X : \B{R} \rightarrow \B{R}^2$$ by $latex \[ \begin{array}{rcl} X_0 (t) & = & - \exp ( - w_0 t ) \\ X_1 (t) & = & \frac{w_0}{w_1 - w_0} [ \exp ( - w_0 t ) - \exp( - w_1 t )] \end{array} \] $$ It follows that $latex X_0 (0) = 1$$, $latex X_1 (0) = 0$$ and $latex \[ \begin{array}{rcl} X_0^{(1)} (t) & = & - w_0 X_0 (t) \\ X_1^{(1)} (t) & = & + w_0 X_0 (t) - w_1 X_1 (t) \end{array} \] $$ The example tests OdeGearControl using the relations above: $code $srcfile%example/ode_gear_control.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include // CppAD::OdeGearControl namespace { // -------------------------------------------------------------- class Fun { private: CPPAD_TESTVECTOR(double) w; public: // constructor Fun(const CPPAD_TESTVECTOR(double) &w_) : w(w_) { } // set f = x'(t) template void Ode( const Scalar &t, const CPPAD_TESTVECTOR(Scalar) &x, CPPAD_TESTVECTOR(Scalar) &f) { f[0] = - w[0] * x[0]; f[1] = + w[0] * x[0] - w[1] * x[1]; } void Ode_dep( const double &t, const CPPAD_TESTVECTOR(double) &x, CPPAD_TESTVECTOR(double) &f_x) { using namespace CppAD; size_t n = x.size(); CPPAD_TESTVECTOR(AD) T(1); CPPAD_TESTVECTOR(AD) X(n); CPPAD_TESTVECTOR(AD) F(n); // set argument values T[0] = t; size_t i, j; for(i = 0; i < n; i++) X[i] = x[i]; // declare independent variables Independent(X); // compute f(t, x) this->Ode(T[0], X, F); // define AD function object ADFun fun(X, F); // compute partial of f w.r.t x CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) df(n); for(j = 0; j < n; j++) dx[j] = 0.; for(j = 0; j < n; j++) { dx[j] = 1.; df = fun.Forward(1, dx); for(i = 0; i < n; i++) f_x [i * n + j] = df[i]; dx[j] = 0.; } } }; } bool OdeGearControl(void) { bool ok = true; // initial return value using CppAD::NearEqual; CPPAD_TESTVECTOR(double) w(2); w[0] = 10.; w[1] = 1.; Fun F(w); CPPAD_TESTVECTOR(double) xi(2); xi[0] = 1.; xi[1] = 0.; CPPAD_TESTVECTOR(double) eabs(2); eabs[0] = 1e-4; eabs[1] = 1e-4; // return values CPPAD_TESTVECTOR(double) ef(2); CPPAD_TESTVECTOR(double) maxabs(2); CPPAD_TESTVECTOR(double) xf(2); size_t nstep; // input values size_t M = 5; double ti = 0.; double tf = 1.; double smin = 1e-8; double smax = 1.; double sini = 1e-10; double erel = 0.; xf = CppAD::OdeGearControl(F, M, ti, tf, xi, smin, smax, sini, eabs, erel, ef, maxabs, nstep); double x0 = exp(-w[0]*tf); ok &= NearEqual(x0, xf[0], 1e-4, 1e-4); ok &= NearEqual(0., ef[0], 1e-4, 1e-4); double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]); ok &= NearEqual(x1, xf[1], 1e-4, 1e-4); ok &= NearEqual(0., ef[1], 1e-4, 1e-4); return ok; } // END C++ cppad-20170000.3/example/sub_sparse_hes.cpp0000644000175200017650000000772513057470460017607 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sub_sparse_hes.cpp$$ $section Computing Sparse Hessian for a Subset of Variables$$ $head Purpose$$ This example uses $cref/multiple levels of AD/mul_level/$$ to compute the Hessian for a subset of the variables without having to compute the sparsity pattern for the entire function. $head See Also$$ $cref sparse_sub_hes.cpp$$, $cref sparsity_sub.cpp$$, $head Function$$ We consider the function $latex f : \B{R}^{nu} \times \B{R}^{nv} \rightarrow \B{R}$$ defined by $latex \[ f (u, v) = \left( \sum_{j=0}^{nu-1} u_j^3 \right) \left( \sum_{j=0}^{nv-1} v_j \right) \] $$ $head Subset$$ Suppose that we are only interested computing the function $latex \[ H(u, v) = \partial_u \partial_u f (u, v) \] $$ where this Hessian is sparse. $head Example$$ The following code shows one way to compute this subset of the Hessian of $latex f$$. $code $srcfile%example/sub_sparse_hes.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::vector; template Scalar f(const vector& u,const vector& v) { size_t i; Scalar sum_v = Scalar(0); for(i = 0; i < v.size(); i++) sum_v += v[i]; Scalar sum_cube_u = Scalar(0); for(i = 0; i < u.size(); i++) sum_cube_u += u[i] * u[i] * u[i] / 6.0; return sum_v * sum_cube_u; } } bool sub_sparse_hes(void) { bool ok = true; using CppAD::AD; typedef AD adouble; typedef AD a2double; typedef vector< std::set > pattern; double eps = 10. * std::numeric_limits::epsilon(); size_t i, j; // start recording with x = (u , v) size_t nu = 10; size_t nv = 5; size_t n = nu + nv; vector ax(n); for(j = 0; j < n; j++) ax[j] = adouble(j + 2); CppAD::Independent(ax); // extract u as independent variables vector a2u(nu); for(j = 0; j < nu; j++) a2u[j] = a2double(j + 2); CppAD::Independent(a2u); // extract v as parameters vector a2v(nv); for(j = 0; j < nv; j++) a2v[j] = ax[nu+j]; // record g(u) vector a2y(1); a2y[0] = f(a2u, a2v); CppAD::ADFun g; g.Dependent(a2u, a2y); // compue sparsity pattern for Hessian of g(u) pattern r(nu), s(1); for(j = 0; j < nu; j++) r[j].insert(j); g.ForSparseJac(nu, r); s[0].insert(0); pattern p = g.RevSparseHes(nu, s); // Row and column indices for non-zeros in lower triangle of Hessian vector row, col; for(i = 0; i < nu; i++) { std::set::const_iterator itr; for(itr = p[i].begin(); itr != p[i].end(); itr++) { j = *itr; if( j <= i ) { row.push_back(i); col.push_back(j); } } } size_t K = row.size(); CppAD::sparse_hessian_work work; vector au(nu), ahes(K), aw(1); aw[0] = 1.0; for(j = 0; j < nu; j++) au[j] = ax[j]; size_t n_sweep = g.SparseHessian(au, aw, p, row, col, ahes, work); // The Hessian w.r.t u is diagonal ok &= n_sweep == 1; // record H(u, v) = Hessian of f w.r.t u CppAD::ADFun H(ax, ahes); // remove unecessary operations H.optimize(); // Now evaluate the Hessian at a particular value for u, v vector u(nu), v(nv), x(n); for(j = 0; j < n; j++) x[j] = double(j + 2); vector hes = H.Forward(0, x); // Now check the Hessian double sum_v = 0.0; for(j = 0; j < nv; j++) sum_v += x[nu + j]; for(size_t k = 0; k < K; k++) { i = row[k]; j = col[k]; ok &= i == j; double check = sum_v * x[i]; ok &= CppAD::NearEqual(hes[k], check, eps, eps); } return ok; } // END C++ cppad-20170000.3/example/base_require.cpp0000644000175200017650000000377513057470460017251 0ustar coincoin-web// $Id: base_require.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_require.cpp$$ $spell alloc $$ $section Using a User Defined AD Base Type: Example and Test$$ $mindex type$$ $code $srcfile%example/base_require.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $head Purpose$$ The type $code base_alloc$$, defined in $cref base_alloc.hpp$$, meets the requirements specified by $cref base_require$$ for $icode Base$$ in $codei%AD<%Base%>%$$. The program below is an example use of $codei%AD%$$. $end */ // BEGIN C++ # include "base_alloc.hpp" # include bool base_require(void) { bool ok = true; using CppAD::thread_alloc; typedef CppAD::AD ad_base_alloc; // check the amount of memory inuse by this thread (thread zero) size_t thread = thread_alloc::thread_num(); ok &= thread == 0; // y = x^2 size_t n = 1, m = 1; CPPAD_TESTVECTOR(ad_base_alloc) a_x(n), a_y(m); a_x[0] = ad_base_alloc(1.); CppAD::Independent(a_x); a_y[0] = a_x[0] * a_x[0]; CppAD::ADFun f(a_x, a_y); // check function value f(x) = x^2 CPPAD_TESTVECTOR(base_alloc) x(n), y(m); base_alloc eps = base_alloc(100.) * CppAD::numeric_limits::epsilon(); x[0] = base_alloc(3.); y = f.Forward(0, x); ok &= CppAD::NearEqual(y[0], x[0] * x[0], eps, eps); // check derivative value f'(x) = 2 * x CPPAD_TESTVECTOR(base_alloc) dy(m * n); dy = f.Jacobian(x); ok &= CppAD::NearEqual(dy[0], base_alloc(2.) * x[0], eps, eps); return ok; } // END C++ cppad-20170000.3/example/integer.cpp0000644000175200017650000000334513057470460016231 0ustar coincoin-web// $Id: integer.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin integer.cpp$$ $spell Cpp cstddef $$ $section Convert From AD to Integer: Example and Test$$ $mindex Integer$$ $code $srcfile%example/integer.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool Integer(void) { bool ok = true; using CppAD::AD; using CppAD::Integer; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) x(n); x[0] = 3.5; x[1] = 4.5; // check integer before recording ok &= (Integer(x[0]) == 3); ok &= (Integer(x[1]) == 4); // start recording // declare independent variables and start tape recording CppAD::Independent(x); // check integer during recording ok &= (Integer(x[0]) == 3); ok &= (Integer(x[1]) == 4); // check integer for VecAD element CppAD::VecAD v(1); AD zero(0); v[zero] = 2; ok &= (Integer(v[zero]) == 2); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = - x[1]; // create f: x -> y and stop recording CppAD::ADFun f(x, y); // check integer after recording ok &= (Integer(x[0]) == 3.); ok &= (Integer(x[1]) == 4.); ok &= (Integer(y[0]) == -4.); return ok; } // END C++ cppad-20170000.3/example/hes_lu_det.cpp0000644000175200017650000000400013057470460016674 0ustar coincoin-web// $Id: hes_lu_det.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin hes_lu_det.cpp$$ $spell Lu Cpp $$ $section Gradient of Determinant Using LU Factorization: Example and Test$$ $code $srcfile%example/hes_lu_det.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool HesLuDet(void) { bool ok = true; using namespace CppAD; typedef std::complex Complex; size_t n = 2; // object for computing determinants det_by_lu< AD > Det(n); // independent and dependent variable vectors CPPAD_TESTVECTOR(AD) X(n * n); CPPAD_TESTVECTOR(AD) D(1); // value of the independent variable size_t i; for(i = 0; i < n * n; i++) X[i] = Complex(int(i), -int(i) ); // set the independent variables Independent(X); D[0] = Det(X); // create the function object ADFun f(X, D); // argument value CPPAD_TESTVECTOR(Complex) x( n * n ); for(i = 0; i < n * n; i++) x[i] = Complex(2 * i, i); // first derivative of the determinant CPPAD_TESTVECTOR(Complex) H( n * n * n * n ); H = f.Hessian(x, 0); /* f(x) = x[0] * x[3] - x[1] * x[2] f'(x) = ( x[3], -x[2], -x[1], x[0] ) */ Complex zero(0., 0.); Complex one(1., 0.); Complex Htrue[] = { zero, zero, zero, one, zero, zero, -one, zero, zero, -one, zero, zero, one, zero, zero, zero }; for( i = 0; i < n*n*n*n; i++) ok &= NearEqual( Htrue[i], H[i], 1e-10 , 1e-10 ); return ok; } // END C++ cppad-20170000.3/example/forward_order.cpp0000644000175200017650000000466613057470460017442 0ustar coincoin-web// $Id: forward_order.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin forward_order.cpp$$ $spell Cpp $$ $section Forward Mode: Example and Test of Multiple Orders$$ $code $srcfile%example/forward_order.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool forward_order(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = ax[0] * ax[0] * ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // initially, the variable values during taping are stored in f ok &= f.size_order() == 1; // Compute three forward orders at one size_t q = 2, q1 = q+1; CPPAD_TESTVECTOR(double) xq(n*q1), yq; xq[q1*0 + 0] = 3.; xq[q1*1 + 0] = 4.; // x^0 (order zero) xq[q1*0 + 1] = 1.; xq[q1*1 + 1] = 0.; // x^1 (order one) xq[q1*0 + 2] = 0.; xq[q1*1 + 2] = 0.; // x^2 (order two) // X(t) = x^0 + x^1 * t + x^2 * t^2 // = [ 3 + t, 4 ] yq = f.Forward(q, xq); ok &= size_t( yq.size() ) == m*q1; // Y(t) = F[X(t)] // = (3 + t) * (3 + t) * 4 // = y^0 + y^1 * t + y^2 * t^2 + o(t^3) // // check y^0 (order zero) CPPAD_TESTVECTOR(double) x0(n); x0[0] = xq[q1*0 + 0]; x0[1] = xq[q1*1 + 0]; ok &= NearEqual(yq[q1*0 + 0] , x0[0]*x0[0]*x0[1], eps, eps); // // check y^1 (order one) ok &= NearEqual(yq[q1*0 + 1] , 2.*x0[0]*x0[1], eps, eps); // // check y^2 (order two) double F_00 = 2. * yq[q1*0 + 2]; // second partial F w.r.t. x_0, x_0 ok &= NearEqual(F_00, 2.*x0[1], eps, eps); // check number of orders per variable ok &= f.size_order() == 3; return ok; } // END C++ cppad-20170000.3/example/lu_ratio.cpp0000644000175200017650000001134613057470460016412 0ustar coincoin-web// $Id: lu_ratio.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin lu_ratio.cpp$$ $spell Geq Cpp Lu $$ $section LuRatio: Example and Test$$ $mindex LuRatio$$ $code $srcfile%example/lu_ratio.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include // for rand function # include # include namespace { // Begin empty namespace CppAD::ADFun *NewFactor( size_t n , const CPPAD_TESTVECTOR(double) &x , bool &ok , CPPAD_TESTVECTOR(size_t) &ip , CPPAD_TESTVECTOR(size_t) &jp ) { using CppAD::AD; using CppAD::ADFun; size_t i, j, k; // values for independent and dependent variables CPPAD_TESTVECTOR(AD) Y(n*n+1), X(n*n); // values for the LU factor CPPAD_TESTVECTOR(AD) LU(n*n); // record the LU factorization corresponding to this value of x AD Ratio; for(k = 0; k < n*n; k++) X[k] = x[k]; Independent(X); for(k = 0; k < n*n; k++) LU[k] = X[k]; CppAD::LuRatio(ip, jp, LU, Ratio); for(k = 0; k < n*n; k++) Y[k] = LU[k]; Y[n*n] = Ratio; // use a function pointer so can return ADFun object ADFun *FunPtr = new ADFun(X, Y); // check value of ratio during recording ok &= (Ratio == 1.); // check that ip and jp are permutations of the indices 0, ... , n-1 for(i = 0; i < n; i++) { ok &= (ip[i] < n); ok &= (jp[i] < n); for(j = 0; j < n; j++) { if( i != j ) { ok &= (ip[i] != ip[j]); ok &= (jp[i] != jp[j]); } } } return FunPtr; } bool CheckLuFactor( size_t n , const CPPAD_TESTVECTOR(double) &x , const CPPAD_TESTVECTOR(double) &y , const CPPAD_TESTVECTOR(size_t) &ip , const CPPAD_TESTVECTOR(size_t) &jp ) { bool ok = true; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); double sum; // element of L * U double pij; // element of permuted x size_t i, j, k; // temporary indices // L and U factors CPPAD_TESTVECTOR(double) L(n*n), U(n*n); // Extract L from LU factorization for(i = 0; i < n; i++) { // elements along and below the diagonal for(j = 0; j <= i; j++) L[i * n + j] = y[ ip[i] * n + jp[j] ]; // elements above the diagonal for(j = i+1; j < n; j++) L[i * n + j] = 0.; } // Extract U from LU factorization for(i = 0; i < n; i++) { // elements below the diagonal for(j = 0; j < i; j++) U[i * n + j] = 0.; // elements along the diagonal U[i * n + i] = 1.; // elements above the diagonal for(j = i+1; j < n; j++) U[i * n + j] = y[ ip[i] * n + jp[j] ]; } // Compute L * U for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { // compute element (i,j) entry in L * U sum = 0.; for(k = 0; k < n; k++) sum += L[i * n + k] * U[k * n + j]; // element (i,j) in permuted version of A pij = x[ ip[i] * n + jp[j] ]; // compare ok &= NearEqual(pij, sum, eps99, eps99); } } return ok; } } // end Empty namespace bool LuRatio(void) { bool ok = true; size_t n = 2; // number rows in A double ratio; // values for independent and dependent variables CPPAD_TESTVECTOR(double) x(n*n), y(n*n+1); // pivot vectors CPPAD_TESTVECTOR(size_t) ip(n), jp(n); // set x equal to the identity matrix x[0] = 1.; x[1] = 0; x[2] = 0.; x[3] = 1.; // create a fnction object corresponding to this value of x CppAD::ADFun *FunPtr = NewFactor(n, x, ok, ip, jp); // use function object to factor matrix y = FunPtr->Forward(0, x); ratio = y[n*n]; ok &= (ratio == 1.); ok &= CheckLuFactor(n, x, y, ip, jp); // set x so that the pivot ratio will be infinite x[0] = 0. ; x[1] = 1.; x[2] = 1. ; x[3] = 0.; // try to use old function pointer to factor matrix y = FunPtr->Forward(0, x); ratio = y[n*n]; // check to see if we need to refactor matrix ok &= (ratio > 10.); if( ratio > 10. ) { delete FunPtr; // to avoid a memory leak FunPtr = NewFactor(n, x, ok, ip, jp); } // now we can use the function object to factor matrix y = FunPtr->Forward(0, x); ratio = y[n*n]; ok &= (ratio == 1.); ok &= CheckLuFactor(n, x, y, ip, jp); delete FunPtr; // avoid memory leak return ok; } // END C++ cppad-20170000.3/example/optimize/0002755000175200017650000000000013057470460015725 5ustar coincoin-webcppad-20170000.3/example/optimize/reverse_active.cpp0000644000175200017650000000607613057470460021446 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin optimize_reverse_active.cpp$$ $section Example Optimization and Reverse Activity Analysis$$ $code $srcfile%example/optimize/reverse_active.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { struct tape_size { size_t n_var; size_t n_op; }; template void fun( const Vector& x, Vector& y, tape_size& before, tape_size& after ) { typedef typename Vector::value_type scalar; // phantom variable with index 0 and independent variables // begin operator, independent variable operators and end operator before.n_var = 1 + x.size(); before.n_op = 2 + x.size(); after.n_var = 1 + x.size(); after.n_op = 2 + x.size(); // initilized product of even and odd variables scalar prod_even = x[0]; scalar prod_odd = x[1]; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; // // compute product of even and odd variables for(size_t i = 2; i < x.size(); i++) { if( i % 2 == 0 ) { // prod_even will affect dependent variable prod_even = prod_even * x[i]; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; } else { // prod_odd will not affect dependent variable prod_odd = prod_odd * x[i]; before.n_var += 1; before.n_op += 1; after.n_var += 0; after.n_op += 0; } } // dependent variable for this operation sequence y[0] = prod_even; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; } } bool reverse_active(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 6; CPPAD_TESTVECTOR(AD) ax(n); for(size_t i = 0; i < n; i++) ax[i] = AD(i + 1); // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); tape_size before, after; fun(ax, ay, before, after); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); ok &= f.size_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence f.optimize(); ok &= f.size_var() == after.n_var; ok &= f.size_op() == after.n_op; // check zero order forward with different argument value CPPAD_TESTVECTOR(double) x(n), y(m), check(m); for(size_t i = 0; i < n; i++) x[i] = double(i + 2); y = f.Forward(0, x); fun(x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); return ok; } // END C++ cppad-20170000.3/example/optimize/makefile.am0000644000175200017650000000202613057470460020017 0ustar coincoin-web# $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = optimize # AM_CXXFLAGS = -g $(CXX_FLAGS) # AM_CPPFLAGS = -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) # optimize_SOURCES = \ compare_op.cpp \ conditional_skip.cpp \ cumulative_sum.cpp \ forward_active.cpp \ nest_conditional.cpp \ optimize.cpp \ print_for.cpp \ reverse_active.cpp test: check ./optimize cppad-20170000.3/example/optimize/conditional_skip.cpp0000644000175200017650000001063413057470460021764 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin optimize_conditional_skip.cpp$$ $section Example Optimization and Conditional Expressions$$ $head See Also$$ $cref cond_exp.cpp$$ $code $srcfile%example/optimize/conditional_skip.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { struct tape_size { size_t n_var; size_t n_op; }; template void fun( const std::string& options , const Vector& x, Vector& y, tape_size& before, tape_size& after ) { typedef typename Vector::value_type scalar; // phantom variable with index 0 and independent variables // begin operator, independent variable operators and end operator before.n_var = 1 + x.size(); before.n_op = 2 + x.size(); after.n_var = 1 + x.size(); after.n_op = 2 + x.size(); // Create a variable that is is only used as left operand // in the comparision operation scalar left = 1. / x[0]; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // right operand in comparison operation scalar right = x[0]; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; // Note that the left and right operand in the CondExpLt comparison // are determined at this point. Hence the conditional skip operator // will be inserted here so that the operations mentioned below can // also be skipped during zero order foward mode. if( options.find("no_conditional_skip") == std::string::npos ) after.n_op += 1; // for conditional skip operation // Create a variable that is only used when comparison result is true // (can be skipped when the comparison result is false) scalar if_true = x[0] * 5.0; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // Create two variables only used when the comparison result is false // (can be skipped when the comparison result is true) scalar temp = 5.0 + x[0]; scalar if_false = temp * 3.0; before.n_var += 2; before.n_op += 2; after.n_var += 2; after.n_op += 2; // conditional comparision is 1 / x[0] < x[0] scalar value = CppAD::CondExpLt(left, right, if_true, if_false); before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // results for this operation sequence y[0] = value; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; } } bool conditional_skip(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); for(size_t k = 0; k < 2; k++) { // optimization options std::string options = ""; if( k == 0 ) options = "no_conditional_skip"; // declare independent variables and start tape recording CppAD::Independent(ax); // compute function computation tape_size before, after; fun(options, ax, ay, before, after); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); ok &= f.size_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence f.optimize(options); ok &= f.size_var() == after.n_var; ok &= f.size_op() == after.n_op; // Check case where result of the comparison is true (x[0] > 1.0). CPPAD_TESTVECTOR(double) x(n), y(m), check(m); x[0] = 1.75; y = f.Forward(0, x); fun(options, x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); if( options == "" ) ok &= f.number_skip() == 2; else ok &= f.number_skip() == 0; // Check case where result of the comparision is false (x[0] <= 1.0) x[0] = 0.5; y = f.Forward(0, x); fun(options, x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); if( options == "" ) ok &= f.number_skip() == 1; else ok &= f.number_skip() == 0; } return ok; } // END C++ cppad-20170000.3/example/optimize/CMakeLists.txt0000644000175200017650000000256013057470460020466 0ustar coincoin-web# $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the example/optimize directory tests # Specifies build type for this directory. Possible values are # empty, Debug, Release, RelWithDebInfo and MinSizeRel SET(CMAKE_BUILD_TYPE DEBUG) # ADD_EXECUTABLE(example_optimize EXCLUDE_FROM_ALL conditional_skip.cpp compare_op.cpp cumulative_sum.cpp forward_active.cpp nest_conditional.cpp print_for.cpp optimize.cpp reverse_active.cpp ) # Extra compiler flags add_cppad_cxx_flags( example_optimize ) # Add the check_example_optimize target ADD_CUSTOM_TARGET(check_example_optimize example_optimize DEPENDS example_optimize ) MESSAGE(STATUS "make check_example_optimize: available") # add to check check_example_depends in parent environment add_to_list(check_example_depends check_example_optimize) SET(check_example_depends "${check_example_depends}" PARENT_SCOPE) cppad-20170000.3/example/optimize/nest_conditional.cpp0000644000175200017650000001247013057470460021767 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin optimize_nest_conditional.cpp$$ $section Example Optimization and Nested Conditional Expressions$$ $head See Also$$ $cref cond_exp.cpp$$ $code $srcfile%example/optimize/nest_conditional.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { struct tape_size { size_t n_var; size_t n_op; }; template void fun( const std::string& options , const Vector& x, Vector& y, tape_size& before, tape_size& after ) { typedef typename Vector::value_type scalar; // phantom variable with index 0 and independent variables // begin operator, independent variable operators and end operator before.n_var = 1 + x.size(); before.n_op = 2 + x.size(); after.n_var = 1 + x.size(); after.n_op = 2 + x.size(); // Create a variable that is is only used in the second comparision scalar two = 1. + x[0]; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // Conditional skip for second comparison will be inserted here. if( options.find("no_conditional_skip") == std::string::npos ) after.n_op += 1; // for conditional skip operation // Create a variable that is is only used in the first comparision // (can be skipped when second comparison result is false) scalar one = 1. / x[0]; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // Conditional skip for first comparison will be inserted here. if( options.find("no_conditional_skip") == std::string::npos ) after.n_op += 1; // for conditional skip operation // value when first comparison if false scalar one_false = 5.0; // Create a variable that is only used when second comparison is true // (can be skipped when it is false) scalar one_true = x[0] / 5.0; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // value when second comparison is false scalar two_false = 3.0; // First conditional compaison is 1 / x[0] < x[0] // is only used when second conditional expression is true // (can be skipped when it is false) scalar two_true = CppAD::CondExpLt(one, x[0], one_true, one_false); before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // Second conditional compaison is 1 + x[0] < x[1] scalar two_value = CppAD::CondExpLt(two, x[1], two_true, two_false); before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // results for this operation sequence y[0] = two_value; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; } } bool nest_conditional(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; ax[1] = 0.5; // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); for(size_t k = 0; k < 2; k++) { // optimization options std::string options = ""; if( k == 0 ) options = "no_conditional_skip"; // declare independent variables and start tape recording CppAD::Independent(ax); // compute function computation tape_size before, after; fun(options, ax, ay, before, after); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); ok &= f.size_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence f.optimize(options); ok &= f.size_var() == after.n_var; ok &= f.size_op() == after.n_op; // Check case where result of the second comparison is true // and first comparison is true CPPAD_TESTVECTOR(double) x(n), y(m), check(m); x[0] = 1.75; x[1] = 4.0; y = f.Forward(0, x); fun(options, x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); ok &= f.number_skip() == 0; // Check case where result of the second comparison is true // and first comparison is false x[0] = 0.5; x[1] = 4.0; y = f.Forward(0, x); fun(options, x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); if( options == "" ) ok &= f.number_skip() == 1; else ok &= f.number_skip() == 0; // Check case where result of the second comparison is false // and first comparison is true x[0] = 1.75; x[1] = 0.0; y = f.Forward(0, x); fun(options, x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); if( options == "" ) ok &= f.number_skip() == 3; else ok &= f.number_skip() == 0; // Check case where result of the second comparison is false // and first comparison is false x[0] = 0.5; x[1] = 0.0; y = f.Forward(0, x); fun(options, x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); if( options == "" ) ok &= f.number_skip() == 3; else ok &= f.number_skip() == 0; } return ok; } // END C++ cppad-20170000.3/example/optimize/forward_active.cpp0000644000175200017650000000773713057470460021444 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin optimize_forward_active.cpp$$ $section Example Optimization and Forward Activity Analysis$$ $code $srcfile%example/optimize/forward_active.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { struct tape_size { size_t n_var; size_t n_op; }; template void fun( const Vector& x, Vector& y, tape_size& before, tape_size& after ) { typedef typename Vector::value_type scalar; // phantom variable with index 0 and independent variables // begin operator, independent variable operators and end operator before.n_var = 1 + x.size(); before.n_op = 2 + x.size(); after.n_var = 1 + x.size(); after.n_op = 2 + x.size(); // adding the constant zero does not take any operations scalar zero = 0.0 + x[0]; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; // multiplication by the constant one does not take any operations scalar one = 1.0 * x[1]; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; // multiplication by the constant zero does not take any operations // and results in the constant zero. scalar two = 0.0 * x[0]; // operations that only involve constants do not take any operations scalar three = (1.0 + two) * 3.0; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; // The optimizer will reconize that zero + one = one + zero // for all values of x. scalar four = zero + one; scalar five = one + zero; before.n_var += 2; before.n_op += 2; after.n_var += 1; after.n_op += 1; // The optimizer will reconize that sin(x[3]) = sin(x[3]) // for all values of x. Note that, for computation of derivatives, // sin(x[3]) and cos(x[3]) are stored on the tape as a pair. scalar six = sin(x[2]); scalar seven = sin(x[2]); before.n_var += 4; before.n_op += 2; after.n_var += 2; after.n_op += 1; // If we used addition here, five + seven = zero + one + seven // which would get converted to a cumulative summation operator. scalar eight = five * seven; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // results for this operation sequence y[0] = eight; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; } } bool forward_active(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; ax[1] = 1.5; ax[2] = 2.0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); tape_size before, after; fun(ax, ay, before, after); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); ok &= f.size_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence // Note that, for this case, all the optimization was done during // the recording and there is no benifit to the optimization. f.optimize(); ok &= f.size_var() == after.n_var; ok &= f.size_op() == after.n_op; // check zero order forward with different argument value CPPAD_TESTVECTOR(double) x(n), y(m), check(m); for(size_t i = 0; i < n; i++) x[i] = double(i + 2); y = f.Forward(0, x); fun(x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); return ok; } // END C++ cppad-20170000.3/example/optimize/optimize.cpp0000644000175200017650000000466213057470460020277 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // system include files used for I/O # include // C style asserts # include // for thread_alloc # include // external complied tests extern bool compare_op(void); extern bool conditional_skip(void); extern bool cumulative_sum(void); extern bool forward_active(void); extern bool nest_conditional(void); extern bool print_for(void); extern bool reverse_active(void); namespace { // function that runs one test static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), const char *name) { bool ok = true; ok &= TestOk(); if( ok ) { std::cout << "OK: " << "optimize: " << name << std::endl; Run_ok_count++; } else { std::cout << "Error: " << "optimize: " << name << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; // This line is used by test_one.sh // external compiled tests ok &= Run( cumulative_sum, "compare_op" ); ok &= Run( cumulative_sum, "cumulative_sum" ); ok &= Run( conditional_skip, "conditional_skip" ); ok &= Run( forward_active, "forward_active" ); ok &= Run( nest_conditional, "nest_conditional" ); ok &= Run( print_for, "print_for" ); ok &= Run( reverse_active, "reverse_active" ); // check for errors using std::cout; using std::endl; assert( ok || (Run_error_count > 0) ); if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "OK: " << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Error: " << "memory leak detected" << endl; } // convert int(size_t) to avoid warning on _MSC_VER systems if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin optimize_cumulative_sum.cpp$$ $section Example Optimization and Cumulative Sum Operations$$ $code $srcfile%example/optimize/cumulative_sum.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { struct tape_size { size_t n_var; size_t n_op; }; template void fun( const Vector& x, Vector& y, tape_size& before, tape_size& after ) { typedef typename Vector::value_type scalar; // phantom variable with index 0 and independent variables // begin operator, independent variable operators and end operator before.n_var = 1 + x.size(); before.n_op = 2 + x.size(); after.n_var = 1 + x.size(); after.n_op = 2 + x.size(); // operators that are identical, and that will be made part of the // cummulative summation. Make sure do not replace second variable // using the first and then remove the first as part of the // cumulative summation. scalar first = x[0] + x[1]; scalar second = x[0] + x[1]; before.n_var += 2; before.n_op += 2; after.n_var += 0; after.n_op += 0; // test that subtractions are also included in cumulative summations scalar third = x[1] - 2.0; before.n_var += 1; before.n_op += 1; after.n_var += 0; after.n_op += 0; // the finial summation is converted to a cumulative summation // the other is removed. scalar csum = first + second + third; before.n_var += 2; before.n_op += 2; after.n_var += 1; after.n_op += 1; // results for this operation sequence y[0] = csum; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; } } bool cumulative_sum(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; ax[1] = 1.5; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); tape_size before, after; fun(ax, ay, before, after); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); ok &= f.size_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence f.optimize(); ok &= f.size_var() == after.n_var; ok &= f.size_op() == after.n_op; // Check result for a zero order calculation for a different x, CPPAD_TESTVECTOR(double) x(n), y(m), check(m); x[0] = 0.75; x[1] = 2.25; y = f.Forward(0, x); fun(x, check, before, after); ok &= CppAD::NearEqual(y[0], check[0], eps10, eps10); return ok; } // END C++ cppad-20170000.3/example/optimize/print_for.cpp0000644000175200017650000000634513057470460020441 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin optimize_print_for.cpp$$ $spell Cpp $$ $section Example Optimization and Print Forward Operators$$ $code $srcfile%example/optimize/print_for.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { struct tape_size { size_t n_var; size_t n_op; }; void PrintFor( double pos, const char* before, double var, const char* after ) { if( pos <= 0.0 ) std::cout << before << var << after; return; } template void fun( const std::string& options , const Vector& x, Vector& y, tape_size& before, tape_size& after ) { typedef typename Vector::value_type scalar; // phantom variable with index 0 and independent variables // begin operator, independent variable operators and end operator before.n_var = 1 + x.size(); before.n_op = 2 + x.size(); after.n_var = 1 + x.size(); after.n_op = 2 + x.size(); // Argument to PrintFor is only needed // if we are keeping print forward operators scalar minus_one = x[0] - 1.0; before.n_var += 1; before.n_op += 1; if( options.find("no_print_for_op") == std::string::npos ) { after.n_var += 1; after.n_op += 1; } // print argument to log function minus one, if it is <= 0 PrintFor(minus_one, "minus_one == ", minus_one , " is <= 0\n"); before.n_var += 0; before.n_op += 1; if( options.find("no_print_for_op") == std::string::npos ) { after.n_var += 0; after.n_op += 1; } // now compute log y[0] = log( x[0] ); before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; } } bool print_for(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 1.5; // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); for(size_t k = 0; k < 2; k++) { // optimization options std::string options = ""; if( k == 0 ) options = "no_print_for_op"; // declare independent variables and start tape recording CppAD::Independent(ax); // compute function value tape_size before, after; fun(options, ax, ay, before, after); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); ok &= f.size_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence f.optimize(options); ok &= f.size_var() == after.n_var; ok &= f.size_op() == after.n_op; // Check result for a zero order calculation for a different x CPPAD_TESTVECTOR(double) x(n), y(m), check(m); x[0] = 2.75; y = f.Forward(0, x); fun(options, x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); } return ok; } // END C++ cppad-20170000.3/example/optimize/compare_op.cpp0000644000175200017650000001021113057470460020546 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin optimize_compare_op.cpp$$ $section Example Optimization and Comparison Operators$$ $head See Also$$ $cref cond_exp.cpp$$ $code $srcfile%example/optimize/compare_op.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { struct tape_size { size_t n_var; size_t n_op; }; template void fun( const std::string& options , const Vector& x, Vector& y, tape_size& before, tape_size& after ) { typedef typename Vector::value_type scalar; // phantom variable with index 0 and independent variables // begin operator, independent variable operators and end operator before.n_var = 1 + x.size(); before.n_op = 2 + x.size(); after.n_var = 1 + x.size(); after.n_op = 2 + x.size(); // Create a variable that is is only used in the comparision operation // It is not used when the comparison operator is not included scalar one = 1. / x[0]; before.n_var += 1; before.n_op += 1; after.n_var += 0; after.n_op += 0; // If we keep comparision operators, we must compute their operands if( options.find("no_compare_op") == std::string::npos ) { after.n_var += 1; after.n_op += 1; } // Create a variable that is used by the result scalar two = x[0] * 5.; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // Only one variable created for this comparison operation // but the value depends on which branch is taken. scalar three; if( one < x[0] ) // comparison operator three = two / 2.0; // division operator else three = 2.0 * two; // multiplication operator // comparison and either division of multiplication operator before.n_var += 1; before.n_op += 2; // comparison operator depends on optimization options after.n_var += 1; after.n_op += 1; // check if we are keeping the comparison operator if( options.find("no_compare_op") == std::string::npos ) after.n_op += 1; // results for this operation sequence y[0] = three; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; } } bool compare_op(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); for(size_t k = 0; k < 2; k++) { // optimization options std::string options = ""; if( k == 0 ) options = "no_compare_op"; // declare independent variables and start tape recording CppAD::Independent(ax); // compute function value tape_size before, after; fun(options, ax, ay, before, after); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); ok &= f.size_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence f.optimize(options); ok &= f.size_var() == after.n_var; ok &= f.size_op() == after.n_op; // Check result for a zero order calculation for a different x, // where the result of the comparison is he same. CPPAD_TESTVECTOR(double) x(n), y(m), check(m); x[0] = 0.75; y = f.Forward(0, x); if ( options == "" ) ok &= f.CompareChange() == 0; fun(options, x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); // Check case where result of the comparision is differnent // (hence one needs to re-tape to get correct result) x[0] = 2.0; y = f.Forward(0, x); if ( options == "" ) ok &= f.CompareChange() == 1; fun(options, x, check, before, after); ok &= std::fabs(y[0] - check[0]) > 0.5; } return ok; } // END C++ cppad-20170000.3/example/asinh.cpp0000644000175200017650000000403113057470460015667 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin asinh.cpp$$ $spell sinh asinh $$ $section The AD asinh Function: Example and Test$$ $code $srcfile%example/asinh.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool asinh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD sinh_of_x0 = CppAD::sinh(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::asinh(sinh_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps, eps); // use a VecAD::reference object with asinh CppAD::VecAD v(1); AD zero(0); v[zero] = sinh_of_x0; AD result = CppAD::asinh(v[zero]); ok &= NearEqual(result, x0, eps, eps); return ok; } // END C++ cppad-20170000.3/example/sinh.cpp0000644000175200017650000000412213057470460015527 0ustar coincoin-web// $Id: sinh.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sinh.cpp$$ $spell sinh $$ $section The AD sinh Function: Example and Test$$ $code $srcfile%example/sinh.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool Sinh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = CppAD::sinh(x[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value double check = std::sinh(x0); ok &= NearEqual(y[0] , check, eps99, eps99); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); check = std::cosh(x0); ok &= NearEqual(dy[0], check, eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], check, eps99, eps99); // use a VecAD::reference object with sinh CppAD::VecAD v(1); AD zero(0); v[zero] = x0; AD result = CppAD::sinh(v[zero]); check = std::sinh(x0); ok &= NearEqual(result, check, eps99, eps99); return ok; } // END C++ cppad-20170000.3/example/numeric_type.cpp0000644000175200017650000000515213057470460017275 0ustar coincoin-web// $Id: numeric_type.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin numeric_type.cpp$$ $section The NumericType: Example and Test$$ $mindex NumericType$$ $code $srcfile%example/numeric_type.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // Empty namespace // ------------------------------------------------------------------- class MyType { private: double d; public: // constructor from void MyType(void) : d(0.) { } // constructor from an int MyType(int d_) : d(d_) { } // copy constructor MyType(const MyType &x) { d = x.d; } // assignment operator void operator = (const MyType &x) { d = x.d; } // member function that converts to double double Double(void) const { return d; } // unary plus MyType operator + (void) const { MyType x; x.d = d; return x; } // unary plus MyType operator - (void) const { MyType x; x.d = - d; return x; } // binary addition MyType operator + (const MyType &x) const { MyType y; y.d = d + x.d ; return y; } // binary subtraction MyType operator - (const MyType &x) const { MyType y; y.d = d - x.d ; return y; } // binary multiplication MyType operator * (const MyType &x) const { MyType y; y.d = d * x.d ; return y; } // binary division MyType operator / (const MyType &x) const { MyType y; y.d = d / x.d ; return y; } // computed assignment addition void operator += (const MyType &x) { d += x.d; } // computed assignment subtraction void operator -= (const MyType &x) { d -= x.d; } // computed assignment multiplication void operator *= (const MyType &x) { d *= x.d; } // computed assignment division void operator /= (const MyType &x) { d /= x.d; } }; } bool NumericType(void) { bool ok = true; using CppAD::AD; using CppAD::CheckNumericType; CheckNumericType (); CheckNumericType (); CheckNumericType (); CheckNumericType< AD > (); CheckNumericType< AD< AD > >(); return ok; } // END C++ cppad-20170000.3/example/romberg_mul.cpp0000644000175200017650000000510613057470460017103 0ustar coincoin-web// $Id: romberg_mul.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Rombergmul.cpp$$ $spell Romberg $$ $section One Dimensional Romberg Integration: Example and Test$$ $code $srcfile%example/romberg_mul.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include namespace { class TestFun { private: const CppAD::vector deg; public: // constructor TestFun(const CppAD::vector deg_) : deg(deg_) { } // function F(x) = x[0]^deg[0] * x[1]^deg[1] double operator () (const CppAD::vector &x) { size_t i; double f = 1; for(i = 0; i < deg[0]; i++) f *= x[0]; for(i = 0; i < deg[1]; i++) f *= x[1]; return f; } }; } bool RombergMul(void) { bool ok = true; size_t i; size_t k; CppAD::vector deg(2); deg[0] = 5; deg[1] = 3; TestFun F(deg); CppAD::RombergMul< TestFun , CppAD::vector, CppAD::vector, 2 > RombergMulTest; // arugments to RombergMul CppAD::vector a(2); CppAD::vector b(2); CppAD::vector n(2); CppAD::vector p(2); for(i = 0; i < 2; i++) { a[i] = 0.; b[i] = 1.; } n[0] = 4; n[1] = 3; double r, e; // int_a1^b1 dx1 int_a0^b0 F(x0,x1) dx0 // = [ b0^(deg[0]+1) - a0^(deg[0]+1) ] / (deg[0]+1) // * [ b1^(deg[1]+1) - a1^(deg[1]+1) ] / (deg[1]+1) double bpow = 1.; double apow = 1.; for(i = 0; i <= deg[0]; i++) { bpow *= b[0]; apow *= a[0]; } double check = (bpow - apow) / (deg[0]+1); bpow = 1.; apow = 1.; for(i = 0; i <= deg[1]; i++) { bpow *= b[1]; apow *= a[1]; } check *= (bpow - apow) / (deg[1]+1); double step = (b[1] - a[1]) / exp(log(2.)*(n[1]-1)); double spow = 1; for(k = 0; k <= n[1]; k++) { spow = spow * step * step; double bnd = 3 * (deg[1] + 1) * spow; for(i = 0; i < 2; i++) p[i] = k; r = RombergMulTest(F, a, b, n, p, e); ok &= e < bnd; ok &= CppAD::NearEqual(check, r, 0., e); } return ok; } // END C++ cppad-20170000.3/example/mul_level_ode.cpp0000644000175200017650000002243713057470460017412 0ustar coincoin-web// $Id: mul_level_ode.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin mul_level_ode.cpp$$ $spell Taylor Cpp const std Adolc adouble $$ $section Taylor's Ode Solver: A Multi-Level AD Example and Test$$ $head Purpose$$ This is a realistic example using two levels of AD; see $cref mul_level$$. The first level uses $code AD$$ to tape the solution of an ordinary differential equation. This solution is then differentiated with respect to a parameter vector. The second level uses $code AD< AD >$$ to take derivatives during the solution of the differential equation. These derivatives are used in the application of Taylor's method to the solution of the ODE. The example $cref mul_level_adolc_ode.cpp$$ computes the same values using Adolc's type $code adouble$$ and CppAD's type $code AD$$. The example $cref ode_taylor.cpp$$ is a simpler applications of Taylor's method for solving an ODE. $head ODE$$ For this example the ODE's are defined by the function $latex h : \B{R}^n \times \B{R}^n \rightarrow \B{R}^n$$ where $latex \[ h[ x, y(t, x) ] = \left( \begin{array}{c} x_0 \\ x_1 y_0 (t, x) \\ \vdots \\ x_{n-1} y_{n-2} (t, x) \end{array} \right) = \left( \begin{array}{c} \partial_t y_0 (t , x) \\ \partial_t y_1 (t , x) \\ \vdots \\ \partial_t y_{n-1} (t , x) \end{array} \right) \] $$ and the initial condition $latex y(0, x) = 0$$. The value of $latex x$$ is fixed during the solution of the ODE and the function $latex g : \B{R}^n \rightarrow \B{R}^n$$ is used to define the ODE where $latex \[ g(y) = \left( \begin{array}{c} x_0 \\ x_1 y_0 \\ \vdots \\ x_{n-1} y_{n-2} \end{array} \right) \] $$ $head ODE Solution$$ The solution for this example can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain $latex \[ y(t, x ) = \left( \begin{array}{c} x_0 t \\ x_1 x_0 t^2 / 2 \\ \vdots \\ x_{n-1} x_{n-2} \ldots x_0 t^n / n ! \end{array} \right) \] $$ $head Derivative of ODE Solution$$ Differentiating the solution above, with respect to the parameter vector $latex x$$, we notice that $latex \[ \partial_x y(t, x ) = \left( \begin{array}{cccc} y_0 (t,x) / x_0 & 0 & \cdots & 0 \\ y_1 (t,x) / x_0 & y_1 (t,x) / x_1 & 0 & \vdots \\ \vdots & \vdots & \ddots & 0 \\ y_{n-1} (t,x) / x_0 & y_{n-1} (t,x) / x_1 & \cdots & y_{n-1} (t,x) / x_{n-1} \end{array} \right) \] $$ $head Taylor's Method Using AD$$ An $th m$$ order Taylor method for approximating the solution of an ordinary differential equations is $latex \[ y(t + \Delta t , x) \approx \sum_{k=0}^p \partial_t^k y(t , x ) \frac{ \Delta t^k }{ k ! } = y^{(0)} (t , x ) + y^{(1)} (t , x ) \Delta t + \cdots + y^{(p)} (t , x ) \Delta t^p \] $$ where the Taylor coefficients $latex y^{(k)} (t, x)$$ are defined by $latex \[ y^{(k)} (t, x) = \partial_t^k y(t , x ) / k ! \] $$ We define the function $latex z(t, x)$$ by the equation $latex \[ z ( t , x ) = g[ y ( t , x ) ] = h [ x , y( t , x ) ] \] $$ It follows that $latex \[ \begin{array}{rcl} \partial_t y(t, x) & = & z (t , x) \\ \partial_t^{k+1} y(t , x) & = & \partial_t^k z (t , x) \\ y^{(k+1)} ( t , x) & = & z^{(k)} (t, x) / (k+1) \end{array} \] $$ where $latex z^{(k)} (t, x)$$ is the $th k$$ order Taylor coefficient for $latex z(t, x)$$. In the example below, the Taylor coefficients $latex \[ y^{(0)} (t , x) , \ldots , y^{(k)} ( t , x ) \] $$ are used to calculate the Taylor coefficient $latex z^{(k)} ( t , x )$$ which in turn gives the value for $latex y^{(k+1)} y ( t , x)$$. $head Source$$ $code $srcfile%example/mul_level_ode.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end -------------------------------------------------------------------------- */ // BEGIN C++ # include // ========================================================================= // define types for each level namespace { // BEGIN empty namespace typedef CppAD::AD a1type; typedef CppAD::AD a2type; // ------------------------------------------------------------------------- // class definition for C++ function object that defines ODE class Ode { private: // copy of a that is set by constructor and used by g(y) CPPAD_TESTVECTOR(a1type) a1x_; public: // constructor Ode(const CPPAD_TESTVECTOR(a1type)& a1x) : a1x_(a1x) { } // the function g(y) is evaluated with two levels of taping CPPAD_TESTVECTOR(a2type) operator() ( const CPPAD_TESTVECTOR(a2type)& a2y) const { size_t n = a2y.size(); CPPAD_TESTVECTOR(a2type) a2g(n); size_t i; a2g[0] = a1x_[0]; for(i = 1; i < n; i++) a2g[i] = a1x_[i] * a2y[i-1]; return a2g; } }; // ------------------------------------------------------------------------- // Routine that uses Taylor's method to solve ordinary differential equaitons // and allows for algorithmic differentiation of the solution. CPPAD_TESTVECTOR(a1type) taylor_ode( Ode G , // function that defines the ODE size_t order , // order of Taylor's method used size_t nstep , // number of steps to take const a1type& a1dt , // Delta t for each step const CPPAD_TESTVECTOR(a1type)& a1y_ini) // y(t) at the initial time { // some temporary indices size_t i, k, ell; // number of variables in the ODE size_t n = a1y_ini.size(); // copies of x and g(y) with two levels of taping CPPAD_TESTVECTOR(a2type) a2y(n), a2z(n); // y, y^{(k)} , z^{(k)}, and y^{(k+1)} CPPAD_TESTVECTOR(a1type) a1y(n), a1y_k(n), a1z_k(n), a1y_kp(n); // initialize x for(i = 0; i < n; i++) a1y[i] = a1y_ini[i]; // loop with respect to each step of Taylors method for(ell = 0; ell < nstep; ell++) { // prepare to compute derivatives using a1type for(i = 0; i < n; i++) a2y[i] = a1y[i]; CppAD::Independent(a2y); // evaluate ODE in a2type a2z = G(a2y); // define differentiable version of a1g: y -> z // that computes its derivatives using a1type objects CppAD::ADFun a1g(a2y, a2z); // Use Taylor's method to take a step a1y_k = a1y; // initialize y^{(k)} a1type a1dt_kp = a1dt; // initialize dt^(k+1) for(k = 0; k <= order; k++) { // evaluate k-th order Taylor coefficient of y a1z_k = a1g.Forward(k, a1y_k); for(i = 0; i < n; i++) { // convert to (k+1)-Taylor coefficient for x a1y_kp[i] = a1z_k[i] / a1type(k + 1); // add term for to this Taylor coefficient // to solution for y(t, x) a1y[i] += a1y_kp[i] * a1dt_kp; } // next power of t a1dt_kp *= a1dt; // next Taylor coefficient a1y_k = a1y_kp; } } return a1y; } } // END empty namespace // ========================================================================== // Routine that tests alogirhtmic differentiation of solutions computed // by the routine taylor_ode. bool mul_level_ode(void) { bool ok = true; double eps = 100. * std::numeric_limits::epsilon(); // number of components in differential equation size_t n = 4; // some temporary indices size_t i, j; // parameter vector in both double and a1type CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(a1type) a1x(n); for(i = 0; i < n; i++) a1x[i] = x[i] = double(i + 1); // declare the parameters as the independent variable CppAD::Independent(a1x); // arguments to taylor_ode Ode G(a1x); // function that defines the ODE size_t order = n; // order of Taylor's method used size_t nstep = 2; // number of steps to take a1type a1dt = double(1.); // Delta t for each step // value of y(t, x) at the initial time CPPAD_TESTVECTOR(a1type) a1y_ini(n); for(i = 0; i < n; i++) a1y_ini[i] = 0.; // integrate the differential equation CPPAD_TESTVECTOR(a1type) a1y_final(n); a1y_final = taylor_ode(G, order, nstep, a1dt, a1y_ini); // define differentiable fucntion object f : x -> y_final // that computes its derivatives in double CppAD::ADFun f(a1x, a1y_final); // check function values double check = 1.; double t = nstep * Value(a1dt); for(i = 0; i < n; i++) { check *= x[i] * t / double(i + 1); ok &= CppAD::NearEqual(Value(a1y_final[i]), check, eps, eps); } // evaluate the Jacobian of h at a CPPAD_TESTVECTOR(double) jac ( f.Jacobian(x) ); // There appears to be a bug in g++ version 4.4.2 because it generates // a warning for the equivalent form // CPPAD_TESTVECTOR(double) jac = f.Jacobian(x); // check Jacobian for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { double jac_ij = jac[i * n + j]; if( i < j ) check = 0.; else check = Value( a1y_final[i] ) / x[j]; ok &= CppAD::NearEqual(jac_ij, check, eps, eps); } } return ok; } // END C++ cppad-20170000.3/example/simple_vector.cpp0000644000175200017650000000555713057470460017456 0ustar coincoin-web// $Id: simple_vector.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin simple_vector.cpp$$ $spell Cpp $$ $section Simple Vector Template Class: Example and Test$$ $code $srcfile%example/simple_vector.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end -------------------------------------------------------------------------- */ // BEGIN C++ # include // std::cout and std::endl # include // std::vector # include // std::valarray # include // CppAD::vector # include // CppAD::CheckSimpleVector namespace { template bool Ok(void) { // type corresponding to elements of Vector typedef typename Vector::value_type Scalar; bool ok = true; // initialize testing flag Vector x; // use the default constructor ok &= (x.size() == 0); // test size for an empty vector Vector y(2); // use the sizing constructor ok &= (y.size() == 2); // size for an vector with elements // non-const access to the elements of y size_t i; for(i = 0; i < 2; i++) y[i] = Scalar(i); const Vector z(y); // copy constructor x.resize(2); // resize x = z; // vector assignment // use the const access to the elements of x // and test the values of elements of x, y, z for(i = 0; i < 2; i++) { ok &= (x[i] == Scalar(i)); ok &= (y[i] == Scalar(i)); ok &= (z[i] == Scalar(i)); } return ok; } } bool SimpleVector (void) { bool ok = true; // use routine above to check these cases ok &= Ok< std::vector >(); ok &= Ok< std::valarray >(); ok &= Ok< CppAD::vector >(); # ifndef _MSC_VER // Avoid Microsoft following compiler warning: 'size_t' : // forcing value to bool 'true' or 'false' (performance warning) ok &= Ok< std::vector >(); ok &= Ok< CppAD::vector >(); # endif // use CheckSimpleVector for more extensive testing CppAD::CheckSimpleVector >(); CppAD::CheckSimpleVector >(); CppAD::CheckSimpleVector >(); CppAD::CheckSimpleVector >(); CppAD::CheckSimpleVector >(); return ok; } // END C++ cppad-20170000.3/example/mul_level_adolc_ode.cpp0000644000175200017650000002552613057470460020556 0ustar coincoin-web// $Id: mul_level_adolc_ode.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin mul_level_adolc_ode.cpp$$ $spell hpp Taylor Cpp const std AdolcDir adouble Vec $$ $section Taylor's Ode Solver: A Multi-Level Adolc Example and Test$$ $head Purpose$$ This is a realistic example using two levels of AD; see $cref mul_level$$. The first level uses Adolc's $code adouble$$ type to tape the solution of an ordinary differential equation. This solution is then differentiated with respect to a parameter vector. The second level uses CppAD's type $code AD$$ to take derivatives during the solution of the differential equation. These derivatives are used in the application of Taylor's method to the solution of the ODE. The example $cref mul_level_ode.cpp$$ computes the same values using $code AD$$ and $code AD< AD >$$. The example $cref ode_taylor.cpp$$ is a simpler applications of Taylor's method for solving an ODE. $head ODE$$ For this example the ODE's are defined by the function $latex h : \B{R}^n \times \B{R}^n \rightarrow \B{R}^n$$ where $latex \[ h[ x, y(t, x) ] = \left( \begin{array}{c} x_0 \\ x_1 y_0 (t, x) \\ \vdots \\ x_{n-1} y_{n-2} (t, x) \end{array} \right) = \left( \begin{array}{c} \partial_t y_0 (t , x) \\ \partial_t y_1 (t , x) \\ \vdots \\ \partial_t y_{n-1} (t , x) \end{array} \right) \] $$ and the initial condition $latex y(0, x) = 0$$. The value of $latex x$$ is fixed during the solution of the ODE and the function $latex g : \B{R}^n \rightarrow \B{R}^n$$ is used to define the ODE where $latex \[ g(y) = \left( \begin{array}{c} x_0 \\ x_1 y_0 \\ \vdots \\ x_{n-1} y_{n-2} \end{array} \right) \] $$ $head ODE Solution$$ The solution for this example can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain $latex \[ y(t, x ) = \left( \begin{array}{c} x_0 t \\ x_1 x_0 t^2 / 2 \\ \vdots \\ x_{n-1} x_{n-2} \ldots x_0 t^n / n ! \end{array} \right) \] $$ $head Derivative of ODE Solution$$ Differentiating the solution above, with respect to the parameter vector $latex x$$, we notice that $latex \[ \partial_x y(t, x ) = \left( \begin{array}{cccc} y_0 (t,x) / x_0 & 0 & \cdots & 0 \\ y_1 (t,x) / x_0 & y_1 (t,x) / x_1 & 0 & \vdots \\ \vdots & \vdots & \ddots & 0 \\ y_{n-1} (t,x) / x_0 & y_{n-1} (t,x) / x_1 & \cdots & y_{n-1} (t,x) / x_{n-1} \end{array} \right) \] $$ $head Taylor's Method Using AD$$ An $th m$$ order Taylor method for approximating the solution of an ordinary differential equations is $latex \[ y(t + \Delta t , x) \approx \sum_{k=0}^p \partial_t^k y(t , x ) \frac{ \Delta t^k }{ k ! } = y^{(0)} (t , x ) + y^{(1)} (t , x ) \Delta t + \cdots + y^{(p)} (t , x ) \Delta t^p \] $$ where the Taylor coefficients $latex y^{(k)} (t, x)$$ are defined by $latex \[ y^{(k)} (t, x) = \partial_t^k y(t , x ) / k ! \] $$ We define the function $latex z(t, x)$$ by the equation $latex \[ z ( t , x ) = g[ y ( t , x ) ] = h [ x , y( t , x ) ] \] $$ It follows that $latex \[ \begin{array}{rcl} \partial_t y(t, x) & = & z (t , x) \\ \partial_t^{k+1} y(t , x) & = & \partial_t^k z (t , x) \\ y^{(k+1)} ( t , x) & = & z^{(k)} (t, x) / (k+1) \end{array} \] $$ where $latex z^{(k)} (t, x)$$ is the $th k$$ order Taylor coefficient for $latex z(t, x)$$. In the example below, the Taylor coefficients $latex \[ y^{(0)} (t , x) , \ldots , y^{(k)} ( t , x ) \] $$ are used to calculate the Taylor coefficient $latex z^{(k)} ( t , x )$$ which in turn gives the value for $latex y^{(k+1)} y ( t , x)$$. $head base_adolc.hpp$$ The file $cref base_adolc.hpp$$ is implements the $cref/Base type requirements/base_require/$$ where $icode Base$$ is $code adolc$$. $head Memory Management$$ Adolc uses raw memory arrays that depend on the number of dependent and independent variables. The $cref thread_alloc$$ memory management utilities $cref/create_array/ta_create_array/$$ and $cref/delete_array/ta_delete_array/$$ are used to manage this memory allocation. $head Configuration Requirement$$ This example will be compiled and tested provided that the value $cref ipopt_prefix$$ is specified on the $cref cmake$$ command line. $head Source$$ $code $srcfile%example/mul_level_adolc_ode.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end -------------------------------------------------------------------------- */ // BEGIN C++ # include # include # include // definitions not in Adolc distribution and required to use CppAD::AD # include # include // ========================================================================== namespace { // BEGIN empty namespace // define types for each level typedef adouble a1type; typedef CppAD::AD a2type; // ------------------------------------------------------------------------- // class definition for C++ function object that defines ODE class Ode { private: // copy of a that is set by constructor and used by g(y) CPPAD_TESTVECTOR(a1type) a1x_; public: // constructor Ode(const CPPAD_TESTVECTOR(a1type)& a1x) : a1x_(a1x) { } // the function g(y) is evaluated with two levels of taping CPPAD_TESTVECTOR(a2type) operator() ( const CPPAD_TESTVECTOR(a2type)& a2y) const { size_t n = a2y.size(); CPPAD_TESTVECTOR(a2type) a2g(n); size_t i; a2g[0] = a1x_[0]; for(i = 1; i < n; i++) a2g[i] = a1x_[i] * a2y[i-1]; return a2g; } }; // ------------------------------------------------------------------------- // Routine that uses Taylor's method to solve ordinary differential equaitons // and allows for algorithmic differentiation of the solution. CPPAD_TESTVECTOR(a1type) taylor_ode_adolc( Ode G , // function that defines the ODE size_t order , // order of Taylor's method used size_t nstep , // number of steps to take const a1type &a1dt , // Delta t for each step const CPPAD_TESTVECTOR(a1type) &a1y_ini) // y(t) at the initial time { // some temporary indices size_t i, k, ell; // number of variables in the ODE size_t n = a1y_ini.size(); // copies of x and g(y) with two levels of taping CPPAD_TESTVECTOR(a2type) a2y(n), Z(n); // y, y^{(k)} , z^{(k)}, and y^{(k+1)} CPPAD_TESTVECTOR(a1type) a1y(n), a1y_k(n), a1z_k(n), a1y_kp(n); // initialize x for(i = 0; i < n; i++) a1y[i] = a1y_ini[i]; // loop with respect to each step of Taylors method for(ell = 0; ell < nstep; ell++) { // prepare to compute derivatives using a1type for(i = 0; i < n; i++) a2y[i] = a1y[i]; CppAD::Independent(a2y); // evaluate ODE using a2type Z = G(a2y); // define differentiable version of g: X -> Y // that computes its derivatives using a1type CppAD::ADFun a1g(a2y, Z); // Use Taylor's method to take a step a1y_k = a1y; // initialize y^{(k)} a1type dt_kp = a1dt; // initialize dt^(k+1) for(k = 0; k <= order; k++) { // evaluate k-th order Taylor coefficient of y a1z_k = a1g.Forward(k, a1y_k); for(i = 0; i < n; i++) { // convert to (k+1)-Taylor coefficient for x a1y_kp[i] = a1z_k[i] / a1type(k + 1); // add term for to this Taylor coefficient // to solution for y(t, x) a1y[i] += a1y_kp[i] * dt_kp; } // next power of t dt_kp *= a1dt; // next Taylor coefficient a1y_k = a1y_kp; } } return a1y; } } // END empty namespace // ========================================================================== // Routine that tests algorithmic differentiation of solutions computed // by the routine taylor_ode. bool mul_level_adolc_ode(void) { bool ok = true; double eps = 100. * std::numeric_limits::epsilon(); // number of components in differential equation size_t n = 4; // some temporary indices size_t i, j; // set up for thread_alloc memory allocator using CppAD::thread_alloc; // the allocator size_t capacity; // capacity of an allocation // the vector x with lenght n (or greater) in double double* x = thread_alloc::create_array(n, capacity); // the vector x with lenght n in a1type CPPAD_TESTVECTOR(a1type) a1x(n); for(i = 0; i < n; i++) a1x[i] = x[i] = double(i + 1); // declare the parameters as the independent variable int tag = 0; // Adolc setup int keep = 1; trace_on(tag, keep); for(i = 0; i < n; i++) a1x[i] <<= double(i + 1); // a1x is independent for adouble type // arguments to taylor_ode_adolc Ode G(a1x); // function that defines the ODE size_t order = n; // order of Taylor's method used size_t nstep = 2; // number of steps to take a1type a1dt = 1.; // Delta t for each step // value of y(t, x) at the initial time CPPAD_TESTVECTOR(a1type) a1y_ini(n); for(i = 0; i < n; i++) a1y_ini[i] = 0.; // integrate the differential equation CPPAD_TESTVECTOR(a1type) a1y_final(n); a1y_final = taylor_ode_adolc(G, order, nstep, a1dt, a1y_ini); // declare the differentiable fucntion f : x -> y_final // (corresponding to the tape of adouble operations) double* y_final = thread_alloc::create_array(n, capacity); for(i = 0; i < n; i++) a1y_final[i] >>= y_final[i]; trace_off(); // check function values double check = 1.; double t = nstep * a1dt.value(); for(i = 0; i < n; i++) { check *= x[i] * t / double(i + 1); ok &= CppAD::NearEqual(y_final[i], check, eps, eps); } // memory where Jacobian will be returned double* jac_ = thread_alloc::create_array(n * n, capacity); double** jac = thread_alloc::create_array(n, capacity); for(i = 0; i < n; i++) jac[i] = jac_ + i * n; // evaluate Jacobian of h at a size_t m = n; // # dependent variables jacobian(tag, int(m), int(n), x, jac); // check Jacobian for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { if( i < j ) check = 0.; else check = y_final[i] / x[j]; ok &= CppAD::NearEqual(jac[i][j], check, eps, eps); } } // make memroy avaiable for other use by this thread thread_alloc::delete_array(x); thread_alloc::delete_array(y_final); thread_alloc::delete_array(jac_); thread_alloc::delete_array(jac); return ok; } // END C++ cppad-20170000.3/example/equal_op_seq.cpp0000644000175200017650000000332313057470460017245 0ustar coincoin-web// $Id: equal_op_seq.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin equal_op_seq.cpp$$ $spell Op $$ $section EqualOpSeq: Example and Test$$ $mindex EqualOpSeq$$ $code $srcfile%example/equal_op_seq.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool EqualOpSeq(void) { bool ok = true; using CppAD::AD; using CppAD::EqualOpSeq; // domain space vector size_t n = 1; double x0 = 1.; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); AD a = 1. + x[0]; // this variable is 1 + x0 AD b = 2. * x[0]; // this variable is 2 * x0 // both a and b are variables ok &= (a == b); // 1 + 1 == 2 * 1 ok &= ! EqualOpSeq(a, b); // 1 + x[0] != 2 * x[0] // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = a; // both y[0] and a are variables EqualOpSeq(y[0], a); // 2 * x[0] == 2 * x[0] // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // both a and b are parameters (after the creation of f above) ok &= EqualOpSeq(a, b); // 1 + 1 == 2 * 1 return ok; } // END C++ cppad-20170000.3/example/tape_index.cpp0000644000175200017650000000500513057470460016707 0ustar coincoin-web// $Id: tape_index.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin tape_index.cpp$$ $section Taping Array Index Operation: Example and Test$$ $mindex tape operation$$ $code $srcfile%example/tape_index.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { double Array(const double &index) { static double array[] = { 5., 4., 3., 2., 1. }; static size_t number = sizeof(array) / sizeof(array[0]); if( index < 0. ) return array[0]; size_t i = static_cast(index); if( i >= number ) return array[number-1]; return array[i]; } // in empty namespace and outside any other routine CPPAD_DISCRETE_FUNCTION(double, Array) } bool TapeIndex(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 2.; // array index value X[1] = 3.; // multiplier of array index value // declare independent variables and start tape recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[1] * Array( X[0] ); // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // vectors for arguments to the function object f CPPAD_TESTVECTOR(double) x(n); // argument values CPPAD_TESTVECTOR(double) y(m); // function values CPPAD_TESTVECTOR(double) w(m); // function weights CPPAD_TESTVECTOR(double) dw(n); // derivative of weighted function // check function value x[0] = Value(X[0]); x[1] = Value(X[1]); y[0] = Value(Y[0]); ok &= y[0] == x[1] * Array(x[0]); // evaluate f where x has different values x[0] = x[0] + 1.; // new array index value x[1] = x[1] + 1.; // new multiplier value y = f.Forward(0, x); ok &= y[0] == x[1] * Array(x[0]); // evaluate derivaitve of y[0] w[0] = 1.; dw = f.Reverse(1, w); ok &= dw[0] == 0.; // partial w.r.t array index ok &= dw[1] == Array(x[0]); // partial w.r.t multiplier return ok; } // END C++ cppad-20170000.3/example/mul_level_adolc.cpp0000644000175200017650000001146513057470460017724 0ustar coincoin-web// $Id: mul_level_adolc.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin mul_level_adolc.cpp$$ $spell CppAD AdolcDir adouble Vec $$ $section Using Adolc with Multiple Levels of Taping: Example and Test$$ $head Purpose$$ In this example, we use $code AD< adouble> >$$ (level two taping), the compute values of the function $latex f : \B{R}^n \rightarrow \B{R}$$ where $latex \[ f(x) = \frac{1}{2} \left( x_0^2 + \cdots + x_{n-1}^2 \right) \] $$ We then use Adolc's $code adouble$$ (level one taping) to compute the directional derivative $latex \[ f^{(1)} (x) * v = x_0 v_0 + \cdots + x_{n-1} v_{n-1} \] $$. where $latex v \in \B{R}^n$$. We then use $code double$$ (no taping) to compute $latex \[ \frac{d}{dx} \left[ f^{(1)} (x) * v \right] = v \] $$ This is only meant as an example of multiple levels of taping. The example $cref hes_times_dir.cpp$$ computes the same value more efficiently by using the identity: $latex \[ \frac{d}{dx} \left[ f^{(1)} (x) * v \right] = f^{(2)} (x) * v \] $$ The example $cref mul_level.cpp$$ computes the same values using $code AD< AD >$$ and $code AD$$. $head Memory Management$$ Adolc uses raw memory arrays that depend on the number of dependent and independent variables. The memory management utility $cref thread_alloc$$ is used to manage this memory allocation. $head Configuration Requirement$$ This example will be compiled and tested provided that the value $cref adolc_prefix$$ is specified on the $cref cmake$$ command line. $head Source$$ $code $srcfile%example/mul_level_adolc.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include // adouble definitions not in Adolc distribution and // required in order to use CppAD::AD # include # include namespace { // f(x) = |x|^2 / 2 = .5 * ( x[0]^2 + ... + x[n-1]^2 ) template Type f(const CPPAD_TESTVECTOR(Type)& x) { Type sum; sum = 0.; size_t i = size_t(x.size()); for(i = 0; i < size_t(x.size()); i++) sum += x[i] * x[i]; return .5 * sum; } } bool mul_level_adolc(void) { bool ok = true; // initialize test result using CppAD::thread_alloc; // The CppAD memory allocator typedef adouble a1type; // for first level of taping typedef CppAD::AD a2type; // for second level of taping size_t n = 5; // number independent variables size_t j; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(a1type) a1x(n); CPPAD_TESTVECTOR(a2type) a2x(n); // Values for the independent variables while taping the function f(x) for(j = 0; j < n; j++) a2x[j] = double(j); // Declare the independent variable for taping f(x) CppAD::Independent(a2x); // Use AD to tape the evaluation of f(x) CPPAD_TESTVECTOR(a2type) a2y(1); a2y[0] = f(a2x); // Declare a1f as the corresponding ADFun function f(x) // (make sure we do not run zero order forward during constructor) CppAD::ADFun a1f; a1f.Dependent(a2x, a2y); // Value of the independent variables whitle taping f'(x) * v int tag = 0; int keep = 1; trace_on(tag, keep); for(j = 0; j < n; j++) a1x[j] <<= double(j); // set the argument value x for computing f'(x) * v a1f.Forward(0, a1x); // compute f'(x) * v CPPAD_TESTVECTOR(a1type) a1v(n); CPPAD_TESTVECTOR(a1type) a1df(1); for(j = 0; j < n; j++) a1v[j] = double(n - j); a1df = a1f.Forward(1, a1v); // declare Adolc function corresponding to f'(x) * v double df; a1df[0] >>= df; trace_off(); // compute the d/dx of f'(x) * v = f''(x) * v size_t m = 1; // # dependent in f'(x) * v // w = new double[capacity] where capacity >= m size_t capacity; double* w = thread_alloc::create_array(m, capacity); // dw = new double[capacity] where capacity >= n double* dw = thread_alloc::create_array(n, capacity); w[0] = 1.; fos_reverse(tag, int(m), int(n), w, dw); for(j = 0; j < n; j++) { double vj = a1v[j].value(); ok &= CppAD::NearEqual(dw[j], vj, eps, eps); } // make memory avaialble for other use by this thread thread_alloc::delete_array(w); thread_alloc::delete_array(dw); return ok; } // END C++ cppad-20170000.3/example/bool_sparsity.cpp0000644000175200017650000001215013057470460017457 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin bool_sparsity.cpp$$ $spell Bool $$ $section Using vectorBool Sparsity To Conserve Memory: Example and Test$$ $head Purpose$$ This example show how to conserve memory when computing sparsity patterns. $code $srcfile%example/bool_sparsity.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::vector; using std::cout; using CppAD::vectorBool; using CppAD::AD; using CppAD::ADFun; // function f(x) that we are computing sparsity patterns for template vector fun(const vector& x) { size_t n = x.size(); vector ret(n + 1); for(size_t j = 0; j < n; j++) { size_t k = (j + 1) % n; ret[j] = x[j] * x[j] * x[k]; } ret[n] = 0.0; return ret; } // check sparsity pattern for f(x) bool check_jac(const vectorBool& pattern, size_t n) { bool ok = true; for(size_t i = 0; i < n; i++) { size_t k = (i + 1) % n; for(size_t j = 0; j < n; j++) { bool non_zero = (i == j) || (j == k); ok &= pattern[ i * n + j] == non_zero; } } for(size_t j = 0; j < n; j++) ok &= pattern[ n * n + j] == false; return ok; } // check sparsity pattern for the Hessian of sum_i f_i(x) bool check_hes(const vectorBool& pattern, size_t n) { bool ok = true; for(size_t i = 0; i < n; i++) { size_t k1 = (i + 1) % n; size_t k2 = (n + i - 1) % n; for(size_t j = 0; j < n; j++) { bool non_zero = (i == j) || (j == k1) || (j == k2); ok &= pattern[ i * n + j] == non_zero; } } return ok; } // compute sparsity for Jacobian of f(x) using forward mode bool for_sparse_jac(ADFun& f) { bool ok = true; size_t n = f.Domain(); size_t m = f.Range(); // // number of columns of the sparsity patter to compute at a time size_t n_col = vectorBool::bit_per_unit(); vectorBool pattern(m * n), s(m * n_col), r(n * n_col); // size_t n_loop = (n - 1) / n_col + 1; for(size_t i_loop = 0; i_loop < n_loop; i_loop++) { size_t j_col = i_loop * n_col; for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n_col; j++) r[i * n_col + j] = (i == j_col + j); } s = f.ForSparseJac(n_col, r); for(size_t i = 0; i < m; i++) { for(size_t j = 0; j < n_col; j++) if( j_col + j < n ) pattern[ i * n + j_col + j ] = s[ i * n_col + j]; } } ok &= check_jac(pattern, n); // return ok; } // compute sparsity for Jacobian of f(x) using reverse mode bool rev_sparse_jac(ADFun& f) { bool ok = true; size_t n = f.Domain(); size_t m = f.Range(); // // number of rows of the sparsity patter to compute at a time size_t n_row = vectorBool::bit_per_unit(); vectorBool pattern(m * n), s(n_row * n), r(n_row * m); // size_t n_loop = (m - 1) / n_row + 1; for(size_t i_loop = 0; i_loop < n_loop; i_loop++) { size_t i_row = i_loop * n_row; for(size_t i = 0; i < n_row; i++) { for(size_t j = 0; j < m; j++) r[i * m + j] = (i_row + i == j); } s = f.RevSparseJac(n_row, r); for(size_t i = 0; i < n_row; i++) { for(size_t j = 0; j < n; j++) if( i_row + i < m ) pattern[ (i_row + i) * n + j ] = s[ i * n + j]; } } ok &= check_jac(pattern, n); // return ok; } // compute sparsity for Hessian of sum_i f_i (x) bool rev_sparse_hes(ADFun& f) { bool ok = true; size_t n = f.Domain(); size_t m = f.Range(); // // number of columns of the sparsity patter to compute at a time size_t n_col = vectorBool::bit_per_unit(); vectorBool pattern(n * n), r(n * n_col), h(n * n_col); // consider case where Hessian for sum of f_i(x) w.r.t i vectorBool s(m); for(size_t i = 0; i < m; i++) s[i] = true; // size_t n_loop = (n - 1) / n_col + 1; for(size_t i_loop = 0; i_loop < n_loop; i_loop++) { size_t j_col = i_loop * n_col; for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n_col; j++) r[i * n_col + j] = (i == j_col + j); } // f.ForSparseJac(n_col, r); bool transpose = true; h = f.RevSparseHes(n_col, s, transpose); // for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n_col; j++) if( j_col + j < n ) pattern[ i * n + j_col + j ] = h[ i * n_col + j]; } } ok &= check_hes(pattern, n); // return ok; } } // driver for all of the cases above bool bool_sparsity(void) { bool ok = true; // // record the funcion size_t n = 100; size_t m = n + 1; vector< AD > x(n), y(m); for(size_t j = 0; j < n; j++) x[j] = AD(j+1); CppAD::Independent(x); y = fun(x); ADFun f(x, y); // // run the three example / tests ok &= for_sparse_jac(f); ok &= rev_sparse_jac(f); ok &= rev_sparse_hes(f); return ok; } // END C++ cppad-20170000.3/example/base_alloc.hpp0000644000175200017650000002353713057470460016672 0ustar coincoin-web// $Id: base_alloc.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_EXAMPLE_BASE_ALLOC_HPP # define CPPAD_EXAMPLE_BASE_ALLOC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_alloc.hpp$$ $spell azmul expm1 atanh acosh asinh Rel Lt Le Eq Ge Gt Cond enum geq cos sqrt cppad.hpp alloc op const ptrdbl bool CppAD sizeof inline atan ostream namespace exp tanh acos asin std fabs erf endif $$ $section Example AD Where Base Constructor Allocates Memory$$ $head Purpose$$ Demonstrate use of $codei%AD<%Base%>%$$ where memory is allocated for each element of the type $icode Base$$. In addition, this is a complete example where all the $cref/required Base/base_require/$$ type operations are defined (as apposed to other examples where some of the operations for the Base type are already defined). $head Include File$$ This file uses some of the definitions in $cref base_require$$ and $cref thread_alloc$$. $srccode%cpp% */ # include # include /* %$$ $head Computed Assignment Macro$$ This macro is used for the $code base_alloc$$ computed assignment operators; to be specific, used with $icode op $$ equal to $code +=$$, $code -=$$, $code *=$$, $code /=$$. $srccode%cpp% */ # define BASE_ALLOC_ASSIGN_OPERATOR(op) \ void operator op (const base_alloc& x) \ { *ptrdbl_ op *x.ptrdbl_; } /* %$$ $head Binary Operator Macro$$ This macro is used for the $code base_alloc$$ binary operators (as member functions); to be specific, used with $icode op $$ equal to $code +$$, $code -$$, $code *$$, $code /$$. $srccode%cpp% */ # define BASE_ALLOC_BINARY_OPERATOR(op) const \ base_alloc operator op (const base_alloc& x) const \ { base_alloc result; \ double dbl = *ptrdbl_; \ double x_dbl = *x.ptrdbl_; \ *result.ptrdbl_ = dbl op x_dbl; \ return result; \ } /* %$$ $head Boolean Operator Macro$$ This macro can be used for the $code base_alloc$$ binary operators that have a $code bool$$ result; to be specific, used with $icode op $$ equal to $code ==$$, $code !=$$, $code <$$, $code <=$$, $code >=$$, and $code >$$, $srccode%cpp% */ # define BASE_ALLOC_BOOL_OPERATOR(op) const \ bool operator op (const base_alloc& x) const \ { double dbl = *ptrdbl_; \ double x_dbl = *x.ptrdbl_; \ return dbl op x_dbl; \ } /* %$$ $head Class Definition$$ The following example class defines the necessary $cref base_member$$ functions. It is made more complicated by storing a pointer to a $code double$$ instead of the $code double$$ value itself. $srccode%cpp% */ class base_alloc { public: double* ptrdbl_; base_alloc(void) { size_t cap; void* v = CppAD::thread_alloc::get_memory(sizeof(double), cap); ptrdbl_ = static_cast(v); } base_alloc(double dbl) { size_t cap; void *v = CppAD::thread_alloc::get_memory(sizeof(double), cap); ptrdbl_ = static_cast(v); *ptrdbl_ = dbl; } base_alloc(const base_alloc& x) { size_t cap; void *v = CppAD::thread_alloc::get_memory(sizeof(double), cap); ptrdbl_ = static_cast(v); *ptrdbl_ = *x.ptrdbl_; } ~base_alloc(void) { void* v = static_cast(ptrdbl_); CppAD::thread_alloc::return_memory(v); } base_alloc operator-(void) const { base_alloc result; *result.ptrdbl_ = - *ptrdbl_; return result; } base_alloc operator+(void) const { return *this; } void operator=(const base_alloc& x) { *ptrdbl_ = *x.ptrdbl_; } BASE_ALLOC_ASSIGN_OPERATOR(+=) BASE_ALLOC_ASSIGN_OPERATOR(-=) BASE_ALLOC_ASSIGN_OPERATOR(*=) BASE_ALLOC_ASSIGN_OPERATOR(/=) BASE_ALLOC_BINARY_OPERATOR(+) BASE_ALLOC_BINARY_OPERATOR(-) BASE_ALLOC_BINARY_OPERATOR(*) BASE_ALLOC_BINARY_OPERATOR(/) BASE_ALLOC_BOOL_OPERATOR(==) BASE_ALLOC_BOOL_OPERATOR(!=) // The <= operator is not necessary for the base type requirements // (needed so we can use NearEqual with base_alloc arguments). BASE_ALLOC_BOOL_OPERATOR(<=) }; /* %$$ $head CondExpOp$$ The type $code base_alloc$$ does not use $cref CondExp$$ operations. Hence its $code CondExpOp$$ function is defined by $srccode%cpp% */ namespace CppAD { inline base_alloc CondExpOp( enum CompareOp cop , const base_alloc& left , const base_alloc& right , const base_alloc& exp_if_true , const base_alloc& exp_if_false ) { // not used assert(false); // to void compiler error return base_alloc(); } } /* %$$ $head CondExpRel$$ The $cref/CPPAD_COND_EXP_REL/base_cond_exp/CondExpRel/$$ macro invocation $srccode%cpp% */ namespace CppAD { CPPAD_COND_EXP_REL(base_alloc) } /* %$$ uses $code CondExpOp$$ above to define $codei%CondExp%Rel%$$ for $code base_alloc$$ arguments and $icode%Rel%$$ equal to $code Lt$$, $code Le$$, $code Eq$$, $code Ge$$, and $code Gt$$. $head EqualOpSeq$$ The type $code base_alloc$$ is simple (in this respect) and so we define $srccode%cpp% */ namespace CppAD { inline bool EqualOpSeq(const base_alloc& x, const base_alloc& y) { return *x.ptrdbl_ == *y.ptrdbl_; } } /* %$$ $head Identical$$ The type $code base_alloc$$ is simple (in this respect) and so we define $srccode%cpp% */ namespace CppAD { inline bool IdenticalPar(const base_alloc& x) { return true; } inline bool IdenticalZero(const base_alloc& x) { return (*x.ptrdbl_ == 0.0); } inline bool IdenticalOne(const base_alloc& x) { return (*x.ptrdbl_ == 1.0); } inline bool IdenticalEqualPar(const base_alloc& x, const base_alloc& y) { return (*x.ptrdbl_ == *y.ptrdbl_); } } /* %$$ $head Output Operator$$ $srccode%cpp% */ namespace CppAD { std::ostream& operator << (std::ostream &os, const base_alloc& x) { os << *x.ptrdbl_; return os; } } /* %$$ $head Integer$$ $srccode%cpp% */ namespace CppAD { inline int Integer(const base_alloc& x) { return static_cast(*x.ptrdbl_); } } /* %$$ $head azmul$$ $srccode%cpp% */ namespace CppAD { CPPAD_AZMUL( base_alloc ) } /* %$$ $head Ordered$$ The $code base_alloc$$ type supports ordered comparisons $srccode%cpp% */ namespace CppAD { inline bool GreaterThanZero(const base_alloc& x) { return *x.ptrdbl_ > 0.0; } inline bool GreaterThanOrZero(const base_alloc& x) { return *x.ptrdbl_ >= 0.0; } inline bool LessThanZero(const base_alloc& x) { return *x.ptrdbl_ < 0.0; } inline bool LessThanOrZero(const base_alloc& x) { return *x.ptrdbl_ <= 0.f; } inline bool abs_geq(const base_alloc& x, const base_alloc& y) { return std::fabs(*x.ptrdbl_) >= std::fabs(*y.ptrdbl_); } } /* %$$ $head Unary Standard Math$$ The macro $cref/CPPAD_STANDARD_MATH_UNARY/base_std_math/CPPAD_STANDARD_MATH_UNARY/$$ would not work with the type $code base_alloc$$ so we define a special macro for this type: $srccode%cpp% */ # define BASE_ALLOC_STD_MATH(fun) \ inline base_alloc fun (const base_alloc& x) \ { return std::fun(*x.ptrdbl_); } /* %$$ The following invocations of the macro above define the $cref/unary standard math/base_std_math/Unary Standard Math/$$ functions (except for $code abs$$): $srccode%cpp% */ namespace CppAD { BASE_ALLOC_STD_MATH(acos) BASE_ALLOC_STD_MATH(asin) BASE_ALLOC_STD_MATH(atan) BASE_ALLOC_STD_MATH(cos) BASE_ALLOC_STD_MATH(cosh) BASE_ALLOC_STD_MATH(exp) BASE_ALLOC_STD_MATH(log) BASE_ALLOC_STD_MATH(log10) BASE_ALLOC_STD_MATH(sin) BASE_ALLOC_STD_MATH(sinh) BASE_ALLOC_STD_MATH(sqrt) BASE_ALLOC_STD_MATH(tan) BASE_ALLOC_STD_MATH(tanh) } /* %$$ The absolute value function is special because its $code std$$ name is $code fabs$$ $srccode%cpp% */ namespace CppAD { inline base_alloc abs(const base_alloc& x) { return std::fabs(*x.ptrdbl_); } } /* %$$ $head erf, asinh, acosh, atanh, expm1, log1p$$ The following defines the $cref/erf, asinh, acosh, atanh, expm1, log1p /base_std_math /erf, asinh, acosh, atanh, expm1, log1p /$$ functions required by $code AD$$: $srccode%cpp% */ # if CPPAD_USE_CPLUSPLUS_2011 BASE_ALLOC_STD_MATH(erf) BASE_ALLOC_STD_MATH(asinh) BASE_ALLOC_STD_MATH(acosh) BASE_ALLOC_STD_MATH(atanh) BASE_ALLOC_STD_MATH(expm1) BASE_ALLOC_STD_MATH(log1p) # endif /* %$$ $head sign$$ The following defines the $code CppAD::sign$$ function that is required to use $code AD$$: $srccode%cpp% */ namespace CppAD { inline base_alloc sign(const base_alloc& x) { if( *x.ptrdbl_ > 0.0 ) return 1.0; if( *x.ptrdbl_ == 0.0 ) return 0.0; return -1.0; } } /* %$$ $head pow $$ The following defines a $code CppAD::pow$$ function that is required to use $code AD$$: $srccode%cpp% */ namespace CppAD { inline base_alloc pow(const base_alloc& x, const base_alloc& y) { return std::pow(*x.ptrdbl_, *y.ptrdbl_); } } /* %$$ $head numeric_limits$$ The following defines the CppAD $cref numeric_limits$$ for the type $code base_alloc$$: $srccode%cpp% */ namespace CppAD { CPPAD_NUMERIC_LIMITS(double, base_alloc) } /* %$$ $head to_string$$ The following defines the CppAD $cref to_string$$ function for the type $code base_alloc$$: $srccode%cpp% */ namespace CppAD { CPPAD_TO_STRING(base_alloc) } /* %$$ $head hash_code$$ The $cref/default/base_hash/Default/$$ hashing function does not work well for this case because two different pointers can have the same value. $srccode|cpp| */ namespace CppAD { inline unsigned short hash_code(const base_alloc& x) { unsigned short code = 0; if( *x.ptrdbl_ == 0.0 ) return code; double log_x = log( abs( *x.ptrdbl_ ) ); // assume log( std::numeric_limits::max() ) is near 700 code = static_cast( (CPPAD_HASH_TABLE_SIZE / 700 + 1) * log_x ); code = code % CPPAD_HASH_TABLE_SIZE; return code; } } /* |$$ $end */ # endif cppad-20170000.3/example/seq_property.cpp0000644000175200017650000001043713057470460017330 0ustar coincoin-web// $Id: seq_property.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin seq_property.cpp$$ $spell op arg abs var VecAD $$ $section ADFun Sequence Properties: Example and Test$$ $mindex Domain Range Parameter size_var size_par size_op_arg size_VecAD$$ $code $srcfile%example/seq_property.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool seq_property(void) { bool ok = true; using CppAD::AD; // Use nvar to track the number of variables in the operation sequence. // Start with one for the phantom variable at tape address zero. size_t nvar = 1; // Use npar to track the number of parameters in the operation sequence. size_t npar = 0; // Start with one for operator corresponding to phantom variable size_t nop = 1; // Start with one for operator corresponding to phantom argument size_t narg = 1; // Use ntext to track the number of characters used to label // output generated using PrintFor commands. size_t ntext = 0; // Use nvecad to track the number of VecAD vectors, plus the number // of VecAD vector elements, in the operation sequence. size_t nvecad = 0; // a VecAD vector CppAD::VecAD v(2); v[0] = 0; // requires the parameter 0, when becomes a variable v[1] = 1; // requires the parameter 1, when becomes a variable // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) x(n); x[0] = 0.; x[1] = 1.; // declare independent variables and start tape recording CppAD::Independent(x); nvar += n; nop += n; // a computation that adds to the operation sequence AD I = 0; v[I] = x[0]; nvecad += 3; // one for vector, two for its elements npar += 2; // need parameters 0 and 1 for initial v nop += 1; // operator for storing in a VecAD object narg += 3; // the three arguments are v, I, and x[0] // some operations that do not add to the operation sequence AD u = x[0]; // use same variable as x[0] AD w = x[1]; // use same variable as x[1] // a computation that adds to the operation sequence w = w * (u + w); nop += 2; // requires two new operators, an add and a multiply nvar += 2; // each operator results in its own variable narg += 4; // each operator has two arguments // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) y(m); // operations that do not add to the operation sequence y[0] = 1.; // re-use the parameter 1 y[1] = u; // use same variable as u // a computation that adds to the operation sequence y[2] = w + 2.; nop += 1; // requires a new add operator npar += 1; // new parameter 2 is new, so it must be included nvar += 1; // variable corresponding to the result narg += 2; // operator has two arguments // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); nop += 1; // special operator for y[0] because it is a parameter nvar += 1; // special variable for y[0] because it is a parameter narg += 1; // identifies which parameter corresponds to y[0] nop += 1; // special operator at the end of operation sequence // check the sequence property functions ok &= f.Domain() == n; ok &= f.Range() == m; ok &= f.Parameter(0) == true; ok &= f.Parameter(1) == false; ok &= f.Parameter(2) == false; ok &= f.size_var() == nvar; ok &= f.size_op() == nop; ok &= f.size_op_arg() == narg; ok &= f.size_par() == npar; ok &= f.size_text() == ntext; ok &= f.size_VecAD() == nvecad; size_t sum = 0; sum += nop * sizeof(CppAD::local::OpCode); sum += narg * sizeof(CPPAD_TAPE_ADDR_TYPE); sum += npar * sizeof(double); sum += ntext * sizeof(char); sum += nvecad * sizeof(CPPAD_TAPE_ADDR_TYPE); ok &= f.size_op_seq() == sum; return ok; } // END C++ cppad-20170000.3/example/interp_retape.cpp0000644000175200017650000000747513057470460017445 0ustar coincoin-web// $Id: interp_retape.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin interp_retape.cpp$$ $spell Retaping retape $$ $section Interpolation With Retaping: Example and Test$$ $mindex interpolate tape retape$$ $head See Also$$ $cref interp_onetape.cpp$$ $pre $$ $code $srcfile%example/interp_retape.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include namespace { double ArgumentValue[] = { .0 , .2 , .4 , .8 , 1. }; double FunctionValue[] = { std::sin( ArgumentValue[0] ) , std::sin( ArgumentValue[1] ) , std::sin( ArgumentValue[2] ) , std::sin( ArgumentValue[3] ) , std::sin( ArgumentValue[4] ) }; size_t TableLength = 5; size_t Index(const CppAD::AD &x) { // determine the index j such that x is between // ArgumentValue[j] and ArgumentValue[j+1] static size_t j = 0; while ( x < ArgumentValue[j] && j > 0 ) j--; while ( x > ArgumentValue[j+1] && j < TableLength - 2) j++; // assert conditions that must be true given logic above assert( j >= 0 && j < TableLength - 1 ); return j; } double Argument(const CppAD::AD &x) { size_t j = Index(x); return ArgumentValue[j]; } double Function(const CppAD::AD &x) { size_t j = Index(x); return FunctionValue[j]; } double Slope(const CppAD::AD &x) { size_t j = Index(x); double dx = ArgumentValue[j+1] - ArgumentValue[j]; double dy = FunctionValue[j+1] - FunctionValue[j]; return dy / dx; } } bool interp_retape(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) X(n); // loop over argument values size_t k; for(k = 0; k < TableLength - 1; k++) { X[0] = .4 * ArgumentValue[k] + .6 * ArgumentValue[k+1]; // declare independent variables and start tape recording // (use a different tape for each argument value) CppAD::Independent(X); // evaluate piecewise linear interpolant at X[0] AD A = Argument(X[0]); AD F = Function(X[0]); AD S = Slope(X[0]); AD I = F + (X[0] - A) * S; // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = I; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // vectors for arguments to the function object f CPPAD_TESTVECTOR(double) x(n); // argument values CPPAD_TESTVECTOR(double) y(m); // function values CPPAD_TESTVECTOR(double) dx(n); // differentials in x space CPPAD_TESTVECTOR(double) dy(m); // differentials in y space // to check function value we use the fact that X[0] is between // ArgumentValue[k] and ArgumentValue[k+1] double delta, check; x[0] = Value(X[0]); delta = ArgumentValue[k+1] - ArgumentValue[k]; check = FunctionValue[k+1] * (x[0]-ArgumentValue[k]) / delta + FunctionValue[k] * (ArgumentValue[k+1]-x[0]) / delta; ok &= NearEqual(Y[0], check, eps99, eps99); // evaluate partials w.r.t. x[0] dx[0] = 1.; dy = f.Forward(1, dx); // check that the derivative is the slope check = (FunctionValue[k+1] - FunctionValue[k]) / (ArgumentValue[k+1] - ArgumentValue[k]); ok &= NearEqual(dy[0], check, eps99, eps99); } return ok; } // END C++ cppad-20170000.3/example/forward_dir.cpp0000644000175200017650000000561513057470460017100 0ustar coincoin-web// $Id: forward_dir.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin forward_dir.cpp$$ $spell Cpp $$ $section Forward Mode: Example and Test of Multiple Directions$$ $mindex orders order$$ $code $srcfile%example/forward_dir.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool forward_dir(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.; ax[1] = 1.; ax[2] = 2.; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = ax[0] * ax[1] * ax[2]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // initially, the variable values during taping are stored in f ok &= f.size_order() == 1; // zero order Taylor coefficients CPPAD_TESTVECTOR(double) x0(n), y0; for(j = 0; j < n; j++) x0[j] = double(j+1); y0 = f.Forward(0, x0); ok &= size_t( y0.size() ) == m; double y_0 = 1.*2.*3.; ok &= NearEqual(y0[0], y_0, eps, eps); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + 1 + ell); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = 0.0; } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = (1 + 1t)(2 + 2t)(3 + 3t) double y_1_0 = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.; double y_2_0 = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.; // // Y_1 (t) = F[X_1(t)] // = (1 + 2t)(2 + 3t)(3 + 4t) double y_1_1 = 2.*2.*3. + 3.*1.*3. + 4.*1.*2.; double y_2_1 = 1.*3.*4. + 2.*2.*4. + 3.*2.*3.; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // // check number of orders ok &= f.size_order() == 3; // // check number of directions ok &= f.size_direction() == 2; // return ok; } // END C++ cppad-20170000.3/example/abort_recording.cpp0000644000175200017650000000410713057470460017734 0ustar coincoin-web// $Id: abort_recording.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin abort_recording.cpp$$ $spell $$ $section Abort Current Recording: Example and Test$$ $mindex recording$$ $code $srcfile%example/abort_recording.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool abort_recording(void) { bool ok = true; double eps = 10. * CppAD::numeric_limits::epsilon(); using CppAD::AD; try { // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) x(n); x[0] = 0.; // declare independent variables and start tape recording CppAD::Independent(x); // simulate an error during calculation of y and the execution // stream was aborted throw 1; } catch (int e) { ok &= (e == 1); // do this incase throw occured after the call to Independent // (for case above this is known, but in general it is unknown) AD::abort_recording(); } /* Now make sure that we can start another recording */ // declare independent variables and start tape recording size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); y[0] = 2 * x[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= CppAD::NearEqual(dy[0], 2., eps, eps); return ok; } // END C++ cppad-20170000.3/example/sparse_hessian.cpp0000644000175200017650000001133413057470460017600 0ustar coincoin-web// $Id: sparse_hessian.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparse_hessian.cpp$$ $spell Cpp Hessian $$ $section Sparse Hessian: Example and Test$$ $mindex Hessian spare$$ $code $srcfile%example/sparse_hessian.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool sparse_hessian(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j, k, ell; typedef CPPAD_TESTVECTOR(AD) a_vector; typedef CPPAD_TESTVECTOR(double) d_vector; typedef CPPAD_TESTVECTOR(size_t) i_vector; typedef CPPAD_TESTVECTOR(bool) b_vector; typedef CPPAD_TESTVECTOR(std::set) s_vector; double eps = 10. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 12; // must be greater than or equal 3; see n_sweep below a_vector a_x(n); for(j = 0; j < n; j++) a_x[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(a_x); // range space vector size_t m = 1; a_vector a_y(m); a_y[0] = a_x[0]*a_x[1]; for(j = 0; j < n; j++) a_y[0] += a_x[j] * a_x[j] * a_x[j]; // create f: x -> y and stop tape recording // (without executing zero order forward calculation) CppAD::ADFun f; f.Dependent(a_x, a_y); // new value for the independent variable vector, and weighting vector d_vector w(m), x(n); for(j = 0; j < n; j++) x[j] = double(j); w[0] = 1.0; // vector used to check the value of the hessian d_vector check(n * n); for(ell = 0; ell < n * n; ell++) check[ell] = 0.0; ell = 0 * n + 1; check[ell] = 1.0; ell = 1 * n + 0; check[ell] = 1.0 ; for(j = 0; j < n; j++) { ell = j * n + j; check[ell] = 6.0 * x[j]; } // ------------------------------------------------------------------- // second derivative of y[0] w.r.t x d_vector hes(n * n); hes = f.SparseHessian(x, w); for(ell = 0; ell < n * n; ell++) ok &= NearEqual(w[0] * check[ell], hes[ell], eps, eps ); // -------------------------------------------------------------------- // example using vectors of bools to compute sparsity pattern for Hessian b_vector r_bool(n * n); for(i = 0; i < n; i++) { for(j = 0; j < n; j++) r_bool[i * n + j] = false; r_bool[i * n + i] = true; } f.ForSparseJac(n, r_bool); // b_vector s_bool(m); for(i = 0; i < m; i++) s_bool[i] = w[i] != 0; b_vector p_bool = f.RevSparseHes(n, s_bool); hes = f.SparseHessian(x, w, p_bool); for(ell = 0; ell < n * n; ell++) ok &= NearEqual(w[0] * check[ell], hes[ell], eps, eps ); // -------------------------------------------------------------------- // example using vectors of sets to compute sparsity pattern for Hessian s_vector r_set(n); for(i = 0; i < n; i++) r_set[i].insert(i); f.ForSparseJac(n, r_set); // s_vector s_set(m); for(i = 0; i < m; i++) if( w[i] != 0. ) s_set[0].insert(i); s_vector p_set = f.RevSparseHes(n, s_set); // example passing sparsity pattern to SparseHessian hes = f.SparseHessian(x, w, p_set); for(ell = 0; ell < n * n; ell++) ok &= NearEqual(w[0] * check[ell], hes[ell], eps, eps ); // -------------------------------------------------------------------- // use row and column indices to specify upper triangle of // non-zero elements of Hessian size_t K = n + 1; i_vector row(K), col(K); hes.resize(K); k = 0; for(j = 0; j < n; j++) { // diagonal of Hessian row[k] = j; col[k] = j; k++; } // only off diagonal non-zero elemenet in upper triangle row[k] = 0; col[k] = 1; k++; ok &= k == K; CppAD::sparse_hessian_work work; // can use p_set or p_bool. size_t n_sweep = f.SparseHessian(x, w, p_set, row, col, hes, work); for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(w[0] * check[ell], hes[k], eps, eps ); } ok &= n_sweep == 2; // now recompute at a different x and w (using work from previous call w[0] = 2.0; x[1] = 0.5; ell = 1 * n + 1; check[ell] = 6.0 * x[1]; s_vector not_used; n_sweep = f.SparseHessian(x, w, not_used, row, col, hes, work); for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(w[0] * check[ell], hes[k], eps, eps ); } ok &= n_sweep == 2; return ok; } // END C++ cppad-20170000.3/example/check_simple_vector.cpp0000644000175200017650000001047113057470460020602 0ustar coincoin-web// $Id: check_simple_vector.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin check_simple_vector.cpp$$ $section The CheckSimpleVector Function: Example and Test$$ $mindex check SimpleVector$$ $code $srcfile%example/check_simple_vector.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include // Chosing a value between 1 and 9 selects a simple vector properity to be // omitted and result in an error message being generated # define CppADMyVectorOmit 0 // ------------------------------------------------------------------------- // example class used for non-constant elements (different from Scalar) template class MyElement { private: Scalar *element; public: // element constructor MyElement(Scalar *e) { element = e; } // an example element assignment that returns void void operator = (const Scalar &s) { *element = s; } // conversion to Scalar operator Scalar() const { return *element; } }; // example simple vector class template class MyVector { private: size_t length; Scalar * data; public: # if CppADMyVectorOmit != 1 // type of the elements in the vector typedef Scalar value_type; # endif # if CppADMyVectorOmit != 2 // default constructor inline MyVector(void) : length(0) , data(0) { } # endif # if CppADMyVectorOmit != 3 // constructor with a specified size inline MyVector(size_t n) : length(n) { if( length == 0 ) data = 0; else data = new Scalar[length]; } # endif # if CppADMyVectorOmit != 4 // copy constructor inline MyVector(const MyVector &x) : length(x.length) { size_t i; if( length == 0 ) data = 0; else data = new Scalar[length]; for(i = 0; i < length; i++) data[i] = x.data[i]; } # endif # if CppADMyVectorOmit != 4 # if CppADMyVectorOmit != 7 // destructor (it is not safe to delete the pointer in cases 4 and 7) ~MyVector(void) { delete [] data; } # endif # endif # if CppADMyVectorOmit != 5 // size function inline size_t size(void) const { return length; } # endif # if CppADMyVectorOmit != 6 // resize function inline void resize(size_t n) { if( length > 0 ) delete [] data; length = n; if( length > 0 ) data = new Scalar[length]; else data = 0; } # endif # if CppADMyVectorOmit != 7 // assignment operator inline MyVector & operator=(const MyVector &x) { size_t i; for(i = 0; i < length; i++) data[i] = x.data[i]; return *this; } # endif # if CppADMyVectorOmit != 8 // non-constant element access MyElement operator[](size_t i) { return data + i; } # endif # if CppADMyVectorOmit != 9 // constant element access const Scalar & operator[](size_t i) const { return data[i]; } # endif }; // ------------------------------------------------------------------------- /* Compute r = a * v, where a is a scalar with same type as the elements of the Simple Vector v. This routine uses the CheckSimpleVector function to ensure that the types agree. */ namespace { // Empty namespace template Vector Sscal(const Scalar &a, const Vector &v) { // invoke CheckSimpleVector function CppAD::CheckSimpleVector(); size_t n = v.size(); Vector r(n); size_t i; for(i = 0; i < n; i++) r[i] = a * v[i]; return r; } } bool CheckSimpleVector(void) { bool ok = true; using CppAD::vector; // -------------------------------------------------------- // If you change double to float in the next statement, // CheckSimpleVector will generate an error message at compile time. double a = 3.; // -------------------------------------------------------- size_t n = 2; MyVector v(n); v[0] = 1.; v[1] = 2.; MyVector r = Sscal(a, v); ok &= (r[0] == 3.); ok &= (r[1] == 6.); return ok; } // END C++ cppad-20170000.3/example/bender_quad.cpp0000644000175200017650000001127313057470460017044 0ustar coincoin-web// $Id: bender_quad.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin bender_quad.cpp$$ $spell argmin $$ $section BenderQuad: Example and Test$$ $mindex BenderQuad$$ Define $latex F : \B{R} \times \B{R} \rightarrow \B{R}$$ by $latex \[ F(x, y) = \frac{1}{2} \sum_{i=1}^N [ y * \sin ( x * t_i ) - z_i ]^2 \] $$ where $latex z \in \B{R}^N$$ is a fixed vector. It follows that $latex \[ \begin{array}{rcl} \partial_y F(x, y) & = & \sum_{i=1}^N [ y * \sin ( x * t_i ) - z_i ] \sin( x * t_i ) \\ \partial_y \partial_y F(x, y) & = & \sum_{i=1}^N \sin ( x t_i )^2 \end{array} \] $$ Furthermore if we define $latex Y(x)$$ as the argmin of $latex F(x, y)$$ with respect to $latex y$$, $latex \[ \begin{array}{rcl} Y(x) & = & y - [ \partial_y \partial_y F(x, y) ]^{-1} \partial_y F[x, y] \\ & = & \left. \sum_{i=1}^N z_i \sin ( x t_i ) \right/ \sum_{i=1}^N z_i \sin ( x * t_i )^2 \end{array} \] $$ $code $srcfile%example/bender_quad.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using CppAD::AD; typedef CPPAD_TESTVECTOR(double) BAvector; typedef CPPAD_TESTVECTOR(AD) ADvector; class Fun { private: BAvector t_; // measurement times BAvector z_; // measurement values public: // constructor Fun(const BAvector &t, const BAvector &z) : t_(t), z_(z) { } // Fun.f(x, y) = F(x, y) ADvector f(const ADvector &x, const ADvector &y) { size_t i; size_t N = size_t(z_.size()); ADvector F(1); F[0] = 0.; AD residual; for(i = 0; i < N; i++) { residual = y[0] * sin( x[0] * t_[i] ) - z_[i]; F[0] += .5 * residual * residual; } return F; } // Fun.h(x, y) = H(x, y) = F_y (x, y) ADvector h(const ADvector &x, const BAvector &y) { size_t i; size_t N = size_t(z_.size()); ADvector fy(1); fy[0] = 0.; AD residual; for(i = 0; i < N; i++) { residual = y[0] * sin( x[0] * t_[i] ) - z_[i]; fy[0] += residual * sin( x[0] * t_[i] ); } return fy; } // Fun.dy(x, y, h) = - H_y (x,y)^{-1} * h // = - F_yy (x, y)^{-1} * h ADvector dy( const BAvector &x , const BAvector &y , const ADvector &H ) { size_t i; size_t N = size_t(z_.size()); ADvector Dy(1); AD fyy = 0.; for(i = 0; i < N; i++) { fyy += sin( x[0] * t_[i] ) * sin( x[0] * t_[i] ); } Dy[0] = - H[0] / fyy; return Dy; } }; // Used to test calculation of Hessian of G AD G(const ADvector& x, const BAvector& t, const BAvector& z) { // compute Y(x) AD numerator = 0.; AD denominator = 0.; size_t k; for(k = 0; k < size_t(t.size()); k++) { numerator += sin( x[0] * t[k] ) * z[k]; denominator += sin( x[0] * t[k] ) * sin( x[0] * t[k] ); } AD y = numerator / denominator; // V(x) = F[x, Y(x)] AD sum = 0; for(k = 0; k < size_t(t.size()); k++) { AD residual = y * sin( x[0] * t[k] ) - z[k]; sum += .5 * residual * residual; } return sum; } } bool BenderQuad(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // temporary indices size_t i, j; // x space vector size_t n = 1; BAvector x(n); x[0] = 2. * 3.141592653; // y space vector size_t m = 1; BAvector y(m); y[0] = 1.; // t and z vectors size_t N = 10; BAvector t(N); BAvector z(N); for(i = 0; i < N; i++) { t[i] = double(i) / double(N); // time of measurement z[i] = y[0] * sin( x[0] * t[i] ); // data without noise } // construct the function object Fun fun(t, z); // evaluate the G(x), G'(x) and G''(x) BAvector g(1), gx(n), gxx(n * n); CppAD::BenderQuad(x, y, fun, g, gx, gxx); // create ADFun object Gfun corresponding to G(x) ADvector a_x(n), a_g(1); for(j = 0; j < n; j++) a_x[j] = x[j]; Independent(a_x); a_g[0] = G(a_x, t, z); CppAD::ADFun Gfun(a_x, a_g); // accuracy for checks double eps = 10. * CppAD::numeric_limits::epsilon(); // check Jacobian BAvector check_gx = Gfun.Jacobian(x); for(j = 0; j < n; j++) ok &= NearEqual(gx[j], check_gx[j], eps, eps); // check Hessian BAvector check_gxx = Gfun.Hessian(x, 0); for(j = 0; j < n*n; j++) ok &= NearEqual(gxx[j], check_gxx[j], eps, eps); return ok; } // END C++ cppad-20170000.3/example/index_sort.cpp0000644000175200017650000000453313057470460016752 0ustar coincoin-web// $Id: index_sort.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin index_sort.cpp$$ $section Index Sort: Example and Test$$ $mindex index_sort$$ $code $srcfile%example/index_sort.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include # include namespace{ // class that uses < to compare a pair of size_t values class Key { public: size_t first_; size_t second_; // Key(void) { } // Key(size_t first, size_t second) : first_(first), second_(second) { } // bool operator<(const Key& other) const { if( first_ == other.first_ ) return second_ < other.second_; return first_ < other.first_; } }; template bool vector_case(void) { bool ok = true; size_t i, j; size_t first[] = { 4, 4, 3, 3, 2, 2, 1, 1}; size_t second[] = { 0, 1, 0, 1, 0, 1, 0, 1}; size_t size = sizeof(first) / sizeof(first[0]); VectorKey keys(size); for(i = 0; i < size; i++) keys[i] = Key(first[i], second[i]); VectorSize ind(size); CppAD::index_sort(keys, ind); // check that all the indices are different for(i = 0; i < size; i++) { for(j = 0; j < size; j++) ok &= (i == j) | (ind[i] != ind[j]); } // check for increasing order for(i = 0; i < size-1; i++) { if( first[ ind[i] ] == first[ ind[i+1] ] ) ok &= second[ ind[i] ] <= second[ ind[i+1] ]; else ok &= first[ ind[i] ] < first[ ind[i+1] ]; } return ok; } } bool index_sort(void) { bool ok = true; // some example simple vector template classes ok &= vector_case< std::vector, std::valarray >(); ok &= vector_case< std::valarray, CppAD::vector >(); ok &= vector_case< CppAD::vector, std::vector >(); return ok; } // END C++ cppad-20170000.3/example/check_for_nan.cpp0000644000175200017650000000600413057470460017346 0ustar coincoin-web// $Id: check_for_nan.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin check_for_nan.cpp$$ $section ADFun Checking For Nan: Example and Test$$ $code $srcfile%example/check_for_nan.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { void myhandler( bool known , int line , const char *file , const char *exp , const char *msg ) { // error handler must not return, so throw an exception std::string message = msg; throw message; } } bool check_for_nan(void) { bool ok = true; using CppAD::AD; using std::string; double eps = 10. * std::numeric_limits::epsilon(); // replace the default CppAD error handler CppAD::ErrorHandler info(myhandler); CPPAD_TESTVECTOR(AD) ax(2), ay(2); ax[0] = 2.0; ax[1] = 1.0; CppAD::Independent(ax); ay[0] = sqrt( ax[0] ); ay[1] = sqrt( ax[1] ); CppAD::ADFun f(ax, ay); CPPAD_TESTVECTOR(double) x(2), y(2); x[0] = 2.0; x[1] = -1.0; // use try / catch because this causes an exception // (assuming that NDEBUG is not defined) f.check_for_nan(true); try { y = f.Forward(0, x); # ifndef NDEBUG // When compiled with NDEBUG defined, // CppAD does not spend time checking for nan. ok = false; # endif } catch(std::string msg) { // get and check size of the independent variable vector string pattern = "vector_size = "; size_t start = msg.find(pattern) + pattern.size(); string number; for(size_t i = start; msg[i] != '\n'; i++) number += msg[i]; size_t vector_size = std::atoi(number.c_str()); ok &= vector_size == 2; // get and check first dependent variable index that is nan pattern = "index = "; start = msg.find(pattern) + pattern.size(); number = ""; for(size_t i = start; msg[i] != '\n'; i++) number += msg[i]; size_t index = std::atoi(number.c_str()); ok &= index == 1; // get the name of the file pattern = "file_name = "; start = msg.find(pattern) + pattern.size(); string file_name; for(size_t i = start; msg[i] != '\n'; i++) file_name += msg[i]; // get and check independent variable vector that resulted in the nan CppAD::vector vec(vector_size); CppAD::get_check_for_nan(vec, file_name); for(size_t i = 0; i < vector_size; i++) ok &= vec[i] == x[i]; } // now do calculation without an exception f.check_for_nan(false); y = f.Forward(0, x); ok &= CppAD::NearEqual(y[0], std::sqrt(x[0]), eps, eps); ok &= CppAD::isnan( y[1] ); return ok; } // END C++ cppad-20170000.3/example/num_limits.cpp0000644000175200017650000000521013057470460016745 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin num_limits.cpp$$ $spell $$ $section Numeric Limits: Example and Test$$ $code $srcfile%example/num_limits.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # ifdef _MSC_VER // Supress Microsoft compiler warning about possible loss of precision, // in the constructors (when converting to std::complex) // Float one = 1 // Float two = 2 // 1 and 2 are small enough so no loss of precision when converting to float. # pragma warning(disable:4244) # endif # include # include namespace { typedef CppAD::AD Float; // // ----------------------------------------------------------------- bool check_epsilon(void) { bool ok = true; Float eps = CppAD::numeric_limits::epsilon(); Float eps2 = eps / 2.0; Float check = 1.0 + eps; ok &= 1.0 != check; check = 1.0 + eps2; ok &= 1.0 == check; return ok; } // ----------------------------------------------------------------- bool check_min(void) { bool ok = true; Float min = CppAD::numeric_limits::min(); Float eps = CppAD::numeric_limits::epsilon(); // Float match = (min / 100.) * 100.; ok &= abs(match / min - 1.0) > 3.0 * eps; // match = (min * 100.) / 100.; ok &= abs(match / min - 1.0) < 3.0 * eps; return ok; } // ----------------------------------------------------------------- bool check_max(void) { bool ok = true; Float max = CppAD::numeric_limits::max(); Float eps = CppAD::numeric_limits::epsilon(); // Float match = (max * 100.) / 100.; ok &= abs(match / max - 1.0) > 3.0 * eps; // match = (max / 100.) * 100.; ok &= abs(match / max - 1.0) < 3.0 * eps; return ok; } // ----------------------------------------------------------------- bool check_nan(void) { bool ok = true; Float nan = CppAD::numeric_limits::quiet_NaN(); ok &= nan != nan; return ok; } } bool num_limits(void) { bool ok = true; ok &= check_epsilon(); ok &= check_min(); ok &= check_max(); ok &= check_nan(); return ok; } // END C++ cppad-20170000.3/example/colpack_jac.cpp0000644000175200017650000000610013057470460017015 0ustar coincoin-web// $Id: colpack_jac.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin colpack_jac.cpp$$ $spell colpack_jac jacobian $$ $section Using ColPack: Example and Test$$ $mindex colpack jacobian sparse$$ $code $srcfile%example/colpack_jac.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool colpack_jac(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; typedef CPPAD_TESTVECTOR(AD) a_vector; typedef CPPAD_TESTVECTOR(double) d_vector; typedef CppAD::vector i_vector; size_t i, j, k, ell; double eps = 10. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 4; a_vector a_x(n); for(j = 0; j < n; j++) a_x[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(a_x); size_t m = 3; a_vector a_y(m); a_y[0] = a_x[0] + a_x[1]; a_y[1] = a_x[2] + a_x[3]; a_y[2] = a_x[0] + a_x[1] + a_x[2] + a_x[3] * a_x[3] / 2.; // create f: x -> y and stop tape recording CppAD::ADFun f(a_x, a_y); // new value for the independent variable vector d_vector x(n); for(j = 0; j < n; j++) x[j] = double(j); /* [ 1 1 0 0 ] jac = [ 0 0 1 1 ] [ 1 1 1 x_3] */ d_vector check(m * n); check[0] = 1.; check[1] = 1.; check[2] = 0.; check[3] = 0.; check[4] = 0.; check[5] = 0.; check[6] = 1.; check[7] = 1.; check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3]; // Normally one would use f.ForSparseJac or f.RevSparseJac to compute // sparsity pattern, but for this example we extract it from check. std::vector< std::set > p(m); // using row and column indices to compute non-zero in rows 1 and 2 i_vector row, col; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { ell = i * n + j; if( check[ell] != 0. ) { row.push_back(i); col.push_back(j); p[i].insert(j); } } } size_t K = row.size(); d_vector jac(K); // empty work structure CppAD::sparse_jacobian_work work; ok &= work.color_method == "cppad"; // choose to use ColPack work.color_method = "colpack"; // forward mode size_t n_sweep = f.SparseJacobianForward(x, p, row, col, jac, work); for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(check[ell], jac[k], eps, eps); } ok &= n_sweep == 4; // reverse mode work.clear(); work.color_method = "colpack"; n_sweep = f.SparseJacobianReverse(x, p, row, col, jac, work); for(k = 0; k < K; k++) { ell = row[k] * n + col[k]; ok &= NearEqual(check[ell], jac[k], eps, eps); } ok &= n_sweep == 2; return ok; } // END C++ cppad-20170000.3/example/compare_change.cpp0000644000175200017650000001144113057470460017523 0ustar coincoin-web// $Id: compare_change.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin compare_change.cpp$$ $spell Cpp $$ $section CompareChange and Re-Tape: Example and Test$$ $mindex compare change re-tape$$ $code $srcfile%example/compare_change.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // put this function in the empty namespace template Type Minimum(const Type &x, const Type &y) { // Use a comparision to compute the min(x, y) // (note that CondExp would never require retaping). if( x < y ) return x; return y; } struct error_info { bool known; int line; std::string file; std::string exp; std::string msg; }; void error_handler( bool known , int line , const char *file , const char *exp , const char *msg ) { // error handler must not return, so throw an exception error_info info; info.known = known; info.line = line; info.file = file; info.exp = exp; info.msg = msg; throw info; } } bool compare_change(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 3.; ax[1] = 4.; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = Minimum(ax[0], ax[1]); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // set count to one (not necessry because is its default value) f.compare_change_count(1); // evaluate zero mode Forward where comparison has the same result // as during taping; i.e., x[0] < x[1]. CPPAD_TESTVECTOR(double) x(n), y(m); x[0] = 2.; x[1] = 3.; y = f.Forward(0, x); ok &= (y[0] == x[0]); ok &= (y[0] == Minimum(x[0], x[1])); ok &= (f.compare_change_number() == 0); ok &= (f.compare_change_op_index() == 0); // evaluate zero mode Forward where comparison has different result // as during taping; i.e., x[0] >= x[1]. x[0] = 3.; x[1] = 2.; y = f.Forward(0, x); ok &= (y[0] == x[0]); ok &= (y[0] != Minimum(x[0], x[1])); ok &= (f.compare_change_number() == 1); ok &= (f.compare_change_op_index() > 0 ); size_t op_index = f.compare_change_op_index(); // Local block during which default CppAD error handler is replaced. // If you do not replace the default CppAD error handler, // and you run in the debugger, you will be able to inspect the // call stack and see that 'if( x < y )' is where the comparison is. bool missed_error = true; { CppAD::ErrorHandler local_error_handler(error_handler); std::string check_msg = "Operator index equals abort_op_index in Independent"; try { // determine the operation index where the change occurred CppAD::Independent(ax, op_index); ay[0] = Minimum(ax[0], ax[1]); # ifdef NDEBUG // CppAD does not spend time checking operator index when // NDEBUG is defined missed_error = false; AD::abort_recording(); # endif } catch( error_info info ) { missed_error = false; ok &= info.known; ok &= info.msg == check_msg; // Must abort the recording so we can start a new one // (and to avoid a memory leak). AD::abort_recording(); } } ok &= ! missed_error; // set count to zero to demonstrate case where comparisons are not checked f.compare_change_count(0); y = f.Forward(0, x); ok &= (y[0] == x[0]); ok &= (y[0] != Minimum(x[0], x[1])); ok &= (f.compare_change_number() == 0); ok &= (f.compare_change_op_index() == 0); // now demonstrate that compare_change_number works for an optimized // tape (note that compare_change_op_index is always zero after optimize) f.optimize(); f.compare_change_count(1); y = f.Forward(0, x); ok &= (y[0] == x[0]); ok &= (y[0] != Minimum(x[0], x[1])); ok &= (f.compare_change_number() == 1); ok &= (f.compare_change_op_index() == 0); // now retape to get the a tape that agrees with the algorithm ax[0] = x[0]; ax[1] = x[1]; Independent(ax); ay[0] = Minimum(ax[0], ax[1]); f.Dependent(ax, ay); y = f.Forward(0, x); ok &= (y[0] == x[1]); ok &= (y[0] == Minimum(x[0], x[1])); ok &= (f.compare_change_number() == 0); ok &= (f.compare_change_op_index() == 0); return ok; } // END C++ cppad-20170000.3/example/hes_lagrangian.cpp0000644000175200017650000001404413057470460017534 0ustar coincoin-web// $Id: hes_lagrangian.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin hes_lagrangian.cpp$$ $spell Cpp HesLagrangian $$ $comment ! NOTE the title states that this example is used two places !$$ $section Hessian of Lagrangian and ADFun Default Constructor: Example and Test$$ $mindex HesLagrangian constructor$$ $code $srcfile%example/hes_lagrangian.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include namespace { CppAD::AD Lagragian( const CppAD::vector< CppAD::AD > &xyz ) { using CppAD::AD; assert( xyz.size() == 6 ); AD x0 = xyz[0]; AD x1 = xyz[1]; AD x2 = xyz[2]; AD y0 = xyz[3]; AD y1 = xyz[4]; AD z = xyz[5]; // compute objective function AD f = x0 * x0; // compute constraint functions AD g0 = 1. + 2.*x1 + 3.*x2; AD g1 = log( x0 * x2 ); // compute the Lagragian AD L = y0 * g0 + y1 * g1 + z * f; return L; } CppAD::vector< CppAD::AD > fg( const CppAD::vector< CppAD::AD > &x ) { using CppAD::AD; using CppAD::vector; assert( x.size() == 3 ); vector< AD > fg(3); fg[0] = x[0] * x[0]; fg[1] = 1. + 2. * x[1] + 3. * x[2]; fg[2] = log( x[0] * x[2] ); return fg; } bool CheckHessian( CppAD::vector H , double x0, double x1, double x2, double y0, double y1, double z ) { using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); bool ok = true; size_t n = 3; assert( H.size() == n * n ); /* L = z*x0*x0 + y0*(1 + 2*x1 + 3*x2) + y1*log(x0*x2) L_0 = 2 * z * x0 + y1 / x0 L_1 = y0 * 2 L_2 = y0 * 3 + y1 / x2 */ // L_00 = 2 * z - y1 / ( x0 * x0 ) double check = 2. * z - y1 / (x0 * x0); ok &= NearEqual(H[0 * n + 0], check, eps99, eps99); // L_01 = L_10 = 0 ok &= NearEqual(H[0 * n + 1], 0., eps99, eps99); ok &= NearEqual(H[1 * n + 0], 0., eps99, eps99); // L_02 = L_20 = 0 ok &= NearEqual(H[0 * n + 2], 0., eps99, eps99); ok &= NearEqual(H[2 * n + 0], 0., eps99, eps99); // L_11 = 0 ok &= NearEqual(H[1 * n + 1], 0., eps99, eps99); // L_12 = L_21 = 0 ok &= NearEqual(H[1 * n + 2], 0., eps99, eps99); ok &= NearEqual(H[2 * n + 1], 0., eps99, eps99); // L_22 = - y1 / (x2 * x2) check = - y1 / (x2 * x2); ok &= NearEqual(H[2 * n + 2], check, eps99, eps99); return ok; } bool UseL() { using CppAD::AD; using CppAD::vector; // double values corresponding to XYZ vector double x0(.5), x1(1e3), x2(1), y0(2.), y1(3.), z(4.); // domain space vector size_t n = 3; vector< AD > XYZ(n); XYZ[0] = x0; XYZ[1] = x1; XYZ[2] = x2; // declare X as independent variable vector and start recording CppAD::Independent(XYZ); // add the Lagragian multipliers to XYZ // (note that this modifies the vector XYZ) XYZ.push_back(y0); XYZ.push_back(y1); XYZ.push_back(z); // range space vector size_t m = 1; vector< AD > L(m); L[0] = Lagragian(XYZ); // create K: X -> L and stop tape recording // We cannot use the ADFun sequence constructor because XYZ has // changed between the call to Independent and here. CppAD::ADFun K; K.Dependent(L); // Operation sequence corresponding to K does depends on // value of y0, y1, and z. Must redo calculations above when // y0, y1, or z changes. // declare independent variable vector and Hessian vector x(n); vector H( n * n ); // point at which we are computing the Hessian // (must redo calculations below each time x changes) x[0] = x0; x[1] = x1; x[2] = x2; H = K.Hessian(x, 0); // check this Hessian calculation return CheckHessian(H, x0, x1, x2, y0, y1, z); } bool Usefg() { using CppAD::AD; using CppAD::vector; // parameters defining problem double x0(.5), x1(1e3), x2(1), y0(2.), y1(3.), z(4.); // domain space vector size_t n = 3; vector< AD > X(n); X[0] = x0; X[1] = x1; X[2] = x2; // declare X as independent variable vector and start recording CppAD::Independent(X); // range space vector size_t m = 3; vector< AD > FG(m); FG = fg(X); // create K: X -> FG and stop tape recording CppAD::ADFun K; K.Dependent(FG); // Operation sequence corresponding to K does not depend on // value of x0, x1, x2, y0, y1, or z. // forward and reverse mode arguments and results vector x(n); vector H( n * n ); vector dx(n); vector w(m); vector dw(2*n); // compute Hessian at this value of x // (must redo calculations below each time x changes) x[0] = x0; x[1] = x1; x[2] = x2; K.Forward(0, x); // set weights to Lagrange multiplier values // (must redo calculations below each time y0, y1, or z changes) w[0] = z; w[1] = y0; w[2] = y1; // initialize dx as zero size_t i, j; for(i = 0; i < n; i++) dx[i] = 0.; // loop over components of x for(i = 0; i < n; i++) { dx[i] = 1.; // dx is i-th elementary vector K.Forward(1, dx); // partial w.r.t dx dw = K.Reverse(2, w); // deritavtive of partial for(j = 0; j < n; j++) H[ i * n + j ] = dw[ j * 2 + 1 ]; dx[i] = 0.; // dx is zero vector } // check this Hessian calculation return CheckHessian(H, x0, x1, x2, y0, y1, z); } } bool HesLagrangian(void) { bool ok = true; // UseL is simpler, but must retape every time that y of z changes ok &= UseL(); // Usefg does not need to retape unless operation sequence changes ok &= Usefg(); return ok; } // END C++ cppad-20170000.3/example/cppad_vector.cpp0000644000175200017650000000577013057470461017252 0ustar coincoin-web// $Id: cppad_vector.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_vector.cpp$$ $spell Cpp $$ $section CppAD::vector Template Class: Example and Test$$ $mindex vector CppAD$$ $code $srcfile%example/cppad_vector.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include // sstream and string are used to test output operation # include bool CppAD_vector(void) { bool ok = true; using CppAD::vector; // so can use vector instead of CppAD::vector typedef double Type; // change double to test other types // check Simple Vector specifications CppAD::CheckSimpleVector< Type, vector >(); vector x; // default constructor ok &= (x.size() == 0); x.resize(2); // resize and set element assignment ok &= (x.size() == 2); x[0] = Type(1); x[1] = Type(2); vector y(2); // sizing constructor ok &= (y.size() == 2); const vector z(x); // copy constructor and const element access ok &= (z.size() == 2); ok &= ( (z[0] == Type(1)) && (z[1] == Type(2)) ); x[0] = Type(2); // modify, assignment changes x ok &= (x[0] == Type(2)); x = y = z; // vector assignment ok &= ( (x[0] == Type(1)) && (x[1] == Type(2)) ); ok &= ( (y[0] == Type(1)) && (y[1] == Type(2)) ); ok &= ( (z[0] == Type(1)) && (z[1] == Type(2)) ); // test of output std::string correct= "{ 1, 2 }"; std::string str; std::ostringstream buf; buf << z; str = buf.str(); ok &= (str == correct); // test resize(1), resize(0), capacity, and clear size_t i = x.capacity(); ok &= i >= 2; x.resize(1); ok &= x[0] == Type(1); ok &= i == x.capacity(); x.resize(0); ok &= i == x.capacity(); x.clear(); ok &= 0 == x.capacity(); // test of push_back scalar and capacity size_t N = 100; for(i = 0; i < N; i++) { size_t old_capacity = x.capacity(); x.push_back( Type(i) ); ok &= (i+1) == x.size(); ok &= i < x.capacity(); ok &= (i == old_capacity) || old_capacity == x.capacity(); } for(i = 0; i < N; i++) ok &= ( x[i] == Type(i) ); // test of data Type* data = x.data(); for(i = 0; i < N; i++) { ok &= data[i] == Type(i); data[i] = Type(N - i); ok &= x[i] == Type(N - i); } // test of push_vector x.push_vector(x); ok &= (x.size() == 2 * N); for(i = 0; i < N; i++) { ok &= x[i] == Type(N - i); ok &= x[i+N] == Type(N - i); } return ok; } // END C++ cppad-20170000.3/example/complex_poly.cpp0000644000175200017650000000402613057470461017304 0ustar coincoin-web// $Id: complex_poly.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin complex_poly.cpp$$ $spell Cpp $$ $section Complex Polynomial: Example and Test$$ $mindex polynomial$$ $head Poly$$ Select this link to view specifications for $cref Poly$$: $code $srcfile%example/complex_poly.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include bool complex_poly(void) { bool ok = true; size_t deg = 4; using CppAD::AD; using CppAD::Poly; typedef std::complex Complex; // polynomial coefficients CPPAD_TESTVECTOR( Complex ) a (deg + 1); // coefficients for p(z) CPPAD_TESTVECTOR(AD) A (deg + 1); size_t i; for(i = 0; i <= deg; i++) A[i] = a[i] = Complex(i, i); // independent variable vector CPPAD_TESTVECTOR(AD) Z(1); Complex z = Complex(1., 2.); Z[0] = z; Independent(Z); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) P(1); // dependent variable values P[0] = Poly(0, A, Z[0]); // create f: Z -> P and vectors used for derivative calculations CppAD::ADFun f(Z, P); CPPAD_TESTVECTOR(Complex) v( f.Domain() ); CPPAD_TESTVECTOR(Complex) w( f.Range() ); // check first derivative w.r.t z v[0] = 1.; w = f.Forward(1, v); Complex p = Poly(1, a, z); ok &= ( w[0] == p ); // second derivative w.r.t z is 2 times its second order Taylor coeff v[0] = 0.; w = f.Forward(2, v); p = Poly(2, a, z); ok &= ( 2. * w[0] == p ); return ok; } // END C++ cppad-20170000.3/config.sub0000755000175200017650000010624612561675772014440 0ustar coincoin-web#! /bin/sh # Configuration validation subroutine script. # Copyright 1992-2015 Free Software Foundation, Inc. timestamp='2015-01-01' # This file is free software; you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 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This Exception is an additional permission under section 7 # of the GNU General Public License, version 3 ("GPLv3"). # Please send patches to . # # Configuration subroutine to validate and canonicalize a configuration type. # Supply the specified configuration type as an argument. # If it is invalid, we print an error message on stderr and exit with code 1. # Otherwise, we print the canonical config type on stdout and succeed. # You can get the latest version of this script from: # http://git.savannah.gnu.org/gitweb/?p=config.git;a=blob_plain;f=config.sub;hb=HEAD # This file is supposed to be the same for all GNU packages # and recognize all the CPU types, system types and aliases # that are meaningful with *any* GNU software. # Each package is responsible for reporting which valid configurations # it does not support. The user should be able to distinguish # a failure to support a valid configuration from a meaningless # configuration. # The goal of this file is to map all the various variations of a given # machine specification into a single specification in the form: # CPU_TYPE-MANUFACTURER-OPERATING_SYSTEM # or in some cases, the newer four-part form: # CPU_TYPE-MANUFACTURER-KERNEL-OPERATING_SYSTEM # It is wrong to echo any other type of specification. me=`echo "$0" | sed -e 's,.*/,,'` usage="\ Usage: $0 [OPTION] CPU-MFR-OPSYS $0 [OPTION] ALIAS Canonicalize a configuration name. Operation modes: -h, --help print this help, then exit -t, --time-stamp print date of last modification, then exit -v, --version print version number, then exit Report bugs and patches to ." version="\ GNU config.sub ($timestamp) Copyright 1992-2015 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE." help=" Try \`$me --help' for more information." # Parse command line while test $# -gt 0 ; do case $1 in --time-stamp | --time* | -t ) echo "$timestamp" ; exit ;; --version | -v ) echo "$version" ; exit ;; --help | --h* | -h ) echo "$usage"; exit ;; -- ) # Stop option processing shift; break ;; - ) # Use stdin as input. break ;; -* ) echo "$me: invalid option $1$help" exit 1 ;; *local*) # First pass through any local machine types. echo $1 exit ;; * ) break ;; esac done case $# in 0) echo "$me: missing argument$help" >&2 exit 1;; 1) ;; *) echo "$me: too many arguments$help" >&2 exit 1;; esac # Separate what the user gave into CPU-COMPANY and OS or KERNEL-OS (if any). # Here we must recognize all the valid KERNEL-OS combinations. maybe_os=`echo $1 | sed 's/^\(.*\)-\([^-]*-[^-]*\)$/\2/'` case $maybe_os in nto-qnx* | linux-gnu* | linux-android* | linux-dietlibc | linux-newlib* | \ linux-musl* | linux-uclibc* | uclinux-uclibc* | uclinux-gnu* | kfreebsd*-gnu* | \ knetbsd*-gnu* | netbsd*-gnu* | \ kopensolaris*-gnu* | \ storm-chaos* | os2-emx* | rtmk-nova*) os=-$maybe_os basic_machine=`echo $1 | sed 's/^\(.*\)-\([^-]*-[^-]*\)$/\1/'` ;; android-linux) os=-linux-android basic_machine=`echo $1 | sed 's/^\(.*\)-\([^-]*-[^-]*\)$/\1/'`-unknown ;; *) basic_machine=`echo $1 | sed 's/-[^-]*$//'` if [ $basic_machine != $1 ] then os=`echo $1 | sed 's/.*-/-/'` else os=; fi ;; esac ### Let's recognize common machines as not being operating systems so ### that things like config.sub decstation-3100 work. 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-mint | -mint[0-9]*) basic_machine=m68k-atari os=-mint ;; esac # Decode aliases for certain CPU-COMPANY combinations. case $basic_machine in # Recognize the basic CPU types without company name. # Some are omitted here because they have special meanings below. 1750a | 580 \ | a29k \ | aarch64 | aarch64_be \ | alpha | alphaev[4-8] | alphaev56 | alphaev6[78] | alphapca5[67] \ | alpha64 | alpha64ev[4-8] | alpha64ev56 | alpha64ev6[78] | alpha64pca5[67] \ | am33_2.0 \ | arc | arceb \ | arm | arm[bl]e | arme[lb] | armv[2-8] | armv[3-8][lb] | armv7[arm] \ | avr | avr32 \ | be32 | be64 \ | bfin \ | c4x | c8051 | clipper \ | d10v | d30v | dlx | dsp16xx \ | epiphany \ | fido | fr30 | frv | ft32 \ | h8300 | h8500 | hppa | hppa1.[01] | hppa2.0 | hppa2.0[nw] | hppa64 \ | hexagon \ | i370 | i860 | i960 | ia64 \ | ip2k | iq2000 \ | k1om \ | le32 | le64 \ | lm32 \ | m32c | m32r | m32rle | m68000 | m68k | m88k \ | maxq | mb | microblaze | microblazeel | mcore | mep | metag \ | mips | mipsbe | mipseb | mipsel | mipsle \ | mips16 \ | mips64 | mips64el \ | mips64octeon | mips64octeonel \ | mips64orion | mips64orionel \ | mips64r5900 | mips64r5900el \ | mips64vr | mips64vrel \ | mips64vr4100 | mips64vr4100el \ | mips64vr4300 | mips64vr4300el \ | mips64vr5000 | mips64vr5000el \ | mips64vr5900 | mips64vr5900el \ | mipsisa32 | mipsisa32el \ | mipsisa32r2 | mipsisa32r2el \ | mipsisa32r6 | mipsisa32r6el \ | mipsisa64 | mipsisa64el \ | mipsisa64r2 | mipsisa64r2el \ | mipsisa64r6 | mipsisa64r6el \ | mipsisa64sb1 | mipsisa64sb1el \ | mipsisa64sr71k | mipsisa64sr71kel \ | mipsr5900 | mipsr5900el \ | mipstx39 | mipstx39el \ | mn10200 | mn10300 \ | moxie \ | mt \ | msp430 \ | nds32 | nds32le | nds32be \ | nios | nios2 | nios2eb | nios2el \ | ns16k | ns32k \ | open8 | or1k | or1knd | or32 \ | pdp10 | pdp11 | pj | pjl \ | powerpc | powerpc64 | powerpc64le | powerpcle \ | pyramid \ | riscv32 | riscv64 \ | rl78 | rx \ | score \ | sh | sh[1234] | sh[24]a | sh[24]aeb | sh[23]e | sh[34]eb | sheb | shbe | shle | sh[1234]le | sh3ele \ | sh64 | sh64le \ | sparc | sparc64 | sparc64b | sparc64v | sparc86x | sparclet | sparclite \ | sparcv8 | sparcv9 | sparcv9b | sparcv9v \ | spu \ | tahoe | tic4x | tic54x | tic55x | tic6x | tic80 | tron \ | ubicom32 \ | v850 | v850e | v850e1 | v850e2 | v850es | v850e2v3 \ | visium \ | we32k \ | x86 | xc16x | xstormy16 | xtensa \ | z8k | z80) basic_machine=$basic_machine-unknown ;; c54x) basic_machine=tic54x-unknown ;; c55x) basic_machine=tic55x-unknown ;; c6x) basic_machine=tic6x-unknown ;; leon|leon[3-9]) basic_machine=sparc-$basic_machine ;; m6811 | m68hc11 | m6812 | m68hc12 | m68hcs12x | nvptx | picochip) basic_machine=$basic_machine-unknown os=-none ;; m88110 | m680[12346]0 | m683?2 | m68360 | m5200 | v70 | w65 | z8k) ;; ms1) basic_machine=mt-unknown ;; strongarm | thumb | xscale) basic_machine=arm-unknown ;; xgate) basic_machine=$basic_machine-unknown os=-none ;; xscaleeb) basic_machine=armeb-unknown ;; xscaleel) basic_machine=armel-unknown ;; # We use `pc' rather than `unknown' # because (1) that's what they normally are, and # (2) the word "unknown" tends to confuse beginning users. i*86 | x86_64) basic_machine=$basic_machine-pc ;; # Object if more than one company name word. *-*-*) echo Invalid configuration \`$1\': machine \`$basic_machine\' not recognized 1>&2 exit 1 ;; # Recognize the basic CPU types with company name. 580-* \ | a29k-* \ | aarch64-* | aarch64_be-* \ | alpha-* | alphaev[4-8]-* | alphaev56-* | alphaev6[78]-* \ | alpha64-* | alpha64ev[4-8]-* | alpha64ev56-* | alpha64ev6[78]-* \ | alphapca5[67]-* | alpha64pca5[67]-* | arc-* | arceb-* \ | arm-* | armbe-* | armle-* | armeb-* | armv*-* \ | avr-* | avr32-* \ | be32-* | be64-* \ | bfin-* | bs2000-* \ | c[123]* | c30-* | [cjt]90-* | c4x-* \ | c8051-* | clipper-* | craynv-* | cydra-* \ | d10v-* | d30v-* | dlx-* \ | elxsi-* \ | f30[01]-* | f700-* | fido-* | fr30-* | frv-* | fx80-* \ | h8300-* | h8500-* \ | hppa-* | hppa1.[01]-* | hppa2.0-* | hppa2.0[nw]-* | hppa64-* \ | hexagon-* \ | i*86-* | i860-* | i960-* | ia64-* \ | ip2k-* | iq2000-* \ | k1om-* \ | le32-* | le64-* \ | lm32-* \ | m32c-* | m32r-* | m32rle-* \ | m68000-* | m680[012346]0-* | m68360-* | m683?2-* | m68k-* \ | m88110-* | m88k-* | maxq-* | mcore-* | metag-* \ | microblaze-* | microblazeel-* \ | mips-* | mipsbe-* | mipseb-* | mipsel-* | mipsle-* \ | mips16-* \ | mips64-* | mips64el-* \ | mips64octeon-* | mips64octeonel-* \ | mips64orion-* | mips64orionel-* \ | mips64r5900-* | mips64r5900el-* \ | mips64vr-* | mips64vrel-* \ | mips64vr4100-* | mips64vr4100el-* \ | mips64vr4300-* | mips64vr4300el-* \ | mips64vr5000-* | mips64vr5000el-* \ | mips64vr5900-* | mips64vr5900el-* \ | mipsisa32-* | mipsisa32el-* \ | mipsisa32r2-* | mipsisa32r2el-* \ | mipsisa32r6-* | mipsisa32r6el-* \ | mipsisa64-* | mipsisa64el-* \ | mipsisa64r2-* | mipsisa64r2el-* \ | mipsisa64r6-* | mipsisa64r6el-* \ | mipsisa64sb1-* | mipsisa64sb1el-* \ | mipsisa64sr71k-* | mipsisa64sr71kel-* \ | mipsr5900-* | mipsr5900el-* \ | mipstx39-* | mipstx39el-* \ | mmix-* \ | mt-* \ | msp430-* \ | nds32-* | nds32le-* | nds32be-* \ | nios-* | nios2-* | nios2eb-* | nios2el-* \ | none-* | np1-* | ns16k-* | ns32k-* \ | open8-* \ | or1k*-* \ | orion-* \ | pdp10-* | pdp11-* | pj-* | pjl-* | pn-* | power-* \ | powerpc-* | powerpc64-* | powerpc64le-* | powerpcle-* \ | pyramid-* \ | rl78-* | romp-* | rs6000-* | rx-* \ | sh-* | sh[1234]-* | sh[24]a-* | sh[24]aeb-* | sh[23]e-* | sh[34]eb-* | sheb-* | shbe-* \ | shle-* | sh[1234]le-* | sh3ele-* | sh64-* | sh64le-* \ | sparc-* | sparc64-* | sparc64b-* | sparc64v-* | sparc86x-* | sparclet-* \ | sparclite-* \ | sparcv8-* | sparcv9-* | sparcv9b-* | sparcv9v-* | sv1-* | sx?-* \ | tahoe-* \ | tic30-* | tic4x-* | tic54x-* | tic55x-* | tic6x-* | tic80-* \ | tile*-* \ | tron-* \ | ubicom32-* \ | v850-* | v850e-* | v850e1-* | v850es-* | v850e2-* | v850e2v3-* \ | vax-* \ | visium-* \ | we32k-* \ | x86-* | x86_64-* | xc16x-* | xps100-* \ | xstormy16-* | xtensa*-* \ | ymp-* \ | z8k-* | z80-*) ;; # Recognize the basic CPU types without company name, with glob match. xtensa*) basic_machine=$basic_machine-unknown ;; # Recognize the various machine names and aliases which stand # for a CPU type and a company and sometimes even an OS. 386bsd) basic_machine=i386-unknown os=-bsd ;; 3b1 | 7300 | 7300-att | att-7300 | pc7300 | safari | unixpc) basic_machine=m68000-att ;; 3b*) basic_machine=we32k-att ;; a29khif) basic_machine=a29k-amd os=-udi ;; abacus) basic_machine=abacus-unknown ;; adobe68k) basic_machine=m68010-adobe os=-scout ;; alliant | fx80) basic_machine=fx80-alliant ;; altos | altos3068) basic_machine=m68k-altos ;; am29k) basic_machine=a29k-none os=-bsd ;; amd64) basic_machine=x86_64-pc ;; amd64-*) basic_machine=x86_64-`echo $basic_machine | sed 's/^[^-]*-//'` ;; amdahl) basic_machine=580-amdahl os=-sysv ;; amiga | amiga-*) basic_machine=m68k-unknown ;; amigaos | amigados) basic_machine=m68k-unknown os=-amigaos ;; amigaunix | amix) basic_machine=m68k-unknown os=-sysv4 ;; apollo68) basic_machine=m68k-apollo os=-sysv ;; apollo68bsd) basic_machine=m68k-apollo os=-bsd ;; aros) basic_machine=i386-pc os=-aros ;; aux) basic_machine=m68k-apple os=-aux ;; balance) basic_machine=ns32k-sequent os=-dynix ;; blackfin) basic_machine=bfin-unknown os=-linux ;; blackfin-*) basic_machine=bfin-`echo $basic_machine | sed 's/^[^-]*-//'` os=-linux ;; bluegene*) basic_machine=powerpc-ibm os=-cnk ;; c54x-*) basic_machine=tic54x-`echo $basic_machine | sed 's/^[^-]*-//'` ;; c55x-*) basic_machine=tic55x-`echo $basic_machine | sed 's/^[^-]*-//'` ;; c6x-*) basic_machine=tic6x-`echo $basic_machine | sed 's/^[^-]*-//'` ;; c90) basic_machine=c90-cray os=-unicos ;; cegcc) basic_machine=arm-unknown os=-cegcc ;; convex-c1) basic_machine=c1-convex os=-bsd ;; convex-c2) basic_machine=c2-convex os=-bsd ;; convex-c32) basic_machine=c32-convex os=-bsd ;; convex-c34) basic_machine=c34-convex os=-bsd ;; convex-c38) basic_machine=c38-convex os=-bsd ;; cray | j90) basic_machine=j90-cray os=-unicos ;; craynv) basic_machine=craynv-cray os=-unicosmp ;; cr16 | cr16-*) basic_machine=cr16-unknown os=-elf ;; crds | unos) basic_machine=m68k-crds ;; crisv32 | crisv32-* | etraxfs*) basic_machine=crisv32-axis ;; cris | cris-* | etrax*) basic_machine=cris-axis ;; crx) basic_machine=crx-unknown os=-elf ;; da30 | da30-*) basic_machine=m68k-da30 ;; decstation | decstation-3100 | pmax | pmax-* | pmin | dec3100 | decstatn) basic_machine=mips-dec ;; decsystem10* | dec10*) basic_machine=pdp10-dec os=-tops10 ;; decsystem20* | dec20*) basic_machine=pdp10-dec os=-tops20 ;; delta | 3300 | motorola-3300 | motorola-delta \ | 3300-motorola | delta-motorola) basic_machine=m68k-motorola ;; delta88) basic_machine=m88k-motorola os=-sysv3 ;; dicos) basic_machine=i686-pc os=-dicos ;; djgpp) basic_machine=i586-pc os=-msdosdjgpp ;; dpx20 | dpx20-*) basic_machine=rs6000-bull os=-bosx ;; dpx2* | dpx2*-bull) basic_machine=m68k-bull os=-sysv3 ;; ebmon29k) basic_machine=a29k-amd os=-ebmon ;; elxsi) basic_machine=elxsi-elxsi os=-bsd ;; encore | umax | mmax) basic_machine=ns32k-encore ;; es1800 | OSE68k | ose68k | ose | OSE) basic_machine=m68k-ericsson os=-ose ;; fx2800) basic_machine=i860-alliant ;; genix) basic_machine=ns32k-ns ;; gmicro) basic_machine=tron-gmicro os=-sysv ;; go32) basic_machine=i386-pc os=-go32 ;; h3050r* | hiux*) basic_machine=hppa1.1-hitachi os=-hiuxwe2 ;; h8300hms) basic_machine=h8300-hitachi os=-hms ;; h8300xray) basic_machine=h8300-hitachi os=-xray ;; h8500hms) basic_machine=h8500-hitachi os=-hms ;; harris) basic_machine=m88k-harris os=-sysv3 ;; hp300-*) basic_machine=m68k-hp ;; hp300bsd) basic_machine=m68k-hp os=-bsd ;; hp300hpux) basic_machine=m68k-hp os=-hpux ;; hp3k9[0-9][0-9] | hp9[0-9][0-9]) basic_machine=hppa1.0-hp ;; hp9k2[0-9][0-9] | hp9k31[0-9]) basic_machine=m68000-hp ;; hp9k3[2-9][0-9]) basic_machine=m68k-hp ;; hp9k6[0-9][0-9] | hp6[0-9][0-9]) basic_machine=hppa1.0-hp ;; hp9k7[0-79][0-9] | hp7[0-79][0-9]) basic_machine=hppa1.1-hp ;; hp9k78[0-9] | hp78[0-9]) # FIXME: really hppa2.0-hp basic_machine=hppa1.1-hp ;; hp9k8[67]1 | hp8[67]1 | hp9k80[24] | hp80[24] | hp9k8[78]9 | hp8[78]9 | hp9k893 | hp893) # FIXME: really hppa2.0-hp basic_machine=hppa1.1-hp ;; hp9k8[0-9][13679] | hp8[0-9][13679]) basic_machine=hppa1.1-hp ;; hp9k8[0-9][0-9] | hp8[0-9][0-9]) basic_machine=hppa1.0-hp ;; hppa-next) os=-nextstep3 ;; hppaosf) basic_machine=hppa1.1-hp os=-osf ;; hppro) basic_machine=hppa1.1-hp os=-proelf ;; i370-ibm* | ibm*) basic_machine=i370-ibm ;; i*86v32) basic_machine=`echo $1 | sed -e 's/86.*/86-pc/'` os=-sysv32 ;; i*86v4*) basic_machine=`echo $1 | sed -e 's/86.*/86-pc/'` os=-sysv4 ;; i*86v) basic_machine=`echo $1 | sed -e 's/86.*/86-pc/'` os=-sysv ;; i*86sol2) basic_machine=`echo $1 | sed -e 's/86.*/86-pc/'` os=-solaris2 ;; i386mach) basic_machine=i386-mach os=-mach ;; i386-vsta | vsta) basic_machine=i386-unknown os=-vsta ;; iris | iris4d) basic_machine=mips-sgi case $os in -irix*) ;; *) os=-irix4 ;; esac ;; isi68 | isi) basic_machine=m68k-isi os=-sysv ;; leon-*|leon[3-9]-*) basic_machine=sparc-`echo $basic_machine | sed 's/-.*//'` ;; m68knommu) basic_machine=m68k-unknown os=-linux ;; m68knommu-*) basic_machine=m68k-`echo $basic_machine | sed 's/^[^-]*-//'` os=-linux ;; m88k-omron*) basic_machine=m88k-omron ;; magnum | m3230) basic_machine=mips-mips os=-sysv ;; merlin) basic_machine=ns32k-utek os=-sysv ;; microblaze*) basic_machine=microblaze-xilinx ;; mingw64) basic_machine=x86_64-pc os=-mingw64 ;; mingw32) basic_machine=i686-pc os=-mingw32 ;; mingw32ce) basic_machine=arm-unknown os=-mingw32ce ;; miniframe) basic_machine=m68000-convergent ;; *mint | -mint[0-9]* | *MiNT | *MiNT[0-9]*) basic_machine=m68k-atari os=-mint ;; mips3*-*) basic_machine=`echo $basic_machine | sed -e 's/mips3/mips64/'` ;; mips3*) basic_machine=`echo $basic_machine | sed -e 's/mips3/mips64/'`-unknown ;; monitor) basic_machine=m68k-rom68k os=-coff ;; morphos) basic_machine=powerpc-unknown os=-morphos ;; moxiebox) basic_machine=moxie-unknown os=-moxiebox ;; msdos) basic_machine=i386-pc os=-msdos ;; ms1-*) basic_machine=`echo $basic_machine | sed -e 's/ms1-/mt-/'` ;; msys) basic_machine=i686-pc os=-msys ;; mvs) basic_machine=i370-ibm os=-mvs ;; nacl) basic_machine=le32-unknown os=-nacl ;; ncr3000) basic_machine=i486-ncr os=-sysv4 ;; netbsd386) basic_machine=i386-unknown os=-netbsd ;; netwinder) basic_machine=armv4l-rebel os=-linux ;; news | news700 | news800 | news900) basic_machine=m68k-sony os=-newsos ;; news1000) basic_machine=m68030-sony os=-newsos ;; news-3600 | risc-news) basic_machine=mips-sony os=-newsos ;; necv70) basic_machine=v70-nec os=-sysv ;; next | m*-next ) basic_machine=m68k-next case $os in -nextstep* ) ;; -ns2*) os=-nextstep2 ;; *) os=-nextstep3 ;; esac ;; nh3000) basic_machine=m68k-harris os=-cxux ;; nh[45]000) basic_machine=m88k-harris os=-cxux ;; nindy960) basic_machine=i960-intel os=-nindy ;; mon960) basic_machine=i960-intel os=-mon960 ;; nonstopux) basic_machine=mips-compaq os=-nonstopux ;; np1) basic_machine=np1-gould ;; neo-tandem) basic_machine=neo-tandem ;; nse-tandem) basic_machine=nse-tandem ;; nsr-tandem) basic_machine=nsr-tandem ;; op50n-* | op60c-*) basic_machine=hppa1.1-oki os=-proelf ;; openrisc | openrisc-*) basic_machine=or32-unknown ;; os400) basic_machine=powerpc-ibm os=-os400 ;; OSE68000 | ose68000) basic_machine=m68000-ericsson os=-ose ;; os68k) basic_machine=m68k-none os=-os68k ;; pa-hitachi) basic_machine=hppa1.1-hitachi os=-hiuxwe2 ;; paragon) basic_machine=i860-intel os=-osf ;; parisc) basic_machine=hppa-unknown os=-linux ;; parisc-*) basic_machine=hppa-`echo $basic_machine | sed 's/^[^-]*-//'` os=-linux ;; pbd) basic_machine=sparc-tti ;; pbb) basic_machine=m68k-tti ;; pc532 | pc532-*) basic_machine=ns32k-pc532 ;; pc98) basic_machine=i386-pc ;; pc98-*) basic_machine=i386-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pentium | p5 | k5 | k6 | nexgen | viac3) basic_machine=i586-pc ;; pentiumpro | p6 | 6x86 | athlon | athlon_*) basic_machine=i686-pc ;; pentiumii | pentium2 | pentiumiii | pentium3) basic_machine=i686-pc ;; pentium4) basic_machine=i786-pc ;; pentium-* | p5-* | k5-* | k6-* | nexgen-* | viac3-*) basic_machine=i586-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pentiumpro-* | p6-* | 6x86-* | athlon-*) basic_machine=i686-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pentiumii-* | pentium2-* | pentiumiii-* | pentium3-*) basic_machine=i686-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pentium4-*) basic_machine=i786-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pn) basic_machine=pn-gould ;; power) basic_machine=power-ibm ;; ppc | ppcbe) basic_machine=powerpc-unknown ;; ppc-* | ppcbe-*) basic_machine=powerpc-`echo $basic_machine | sed 's/^[^-]*-//'` ;; ppcle | powerpclittle | ppc-le | powerpc-little) basic_machine=powerpcle-unknown ;; ppcle-* | powerpclittle-*) basic_machine=powerpcle-`echo $basic_machine | sed 's/^[^-]*-//'` ;; ppc64) basic_machine=powerpc64-unknown ;; ppc64-* | ppc64p7-*) basic_machine=powerpc64-`echo $basic_machine | sed 's/^[^-]*-//'` ;; ppc64le | powerpc64little | ppc64-le | powerpc64-little) basic_machine=powerpc64le-unknown ;; ppc64le-* | powerpc64little-*) basic_machine=powerpc64le-`echo $basic_machine | sed 's/^[^-]*-//'` ;; ps2) basic_machine=i386-ibm ;; pw32) basic_machine=i586-unknown os=-pw32 ;; rdos | rdos64) basic_machine=x86_64-pc os=-rdos ;; rdos32) basic_machine=i386-pc os=-rdos ;; rom68k) basic_machine=m68k-rom68k os=-coff ;; rm[46]00) basic_machine=mips-siemens ;; rtpc | rtpc-*) basic_machine=romp-ibm ;; s390 | s390-*) basic_machine=s390-ibm ;; s390x | s390x-*) basic_machine=s390x-ibm ;; sa29200) basic_machine=a29k-amd os=-udi ;; sb1) basic_machine=mipsisa64sb1-unknown ;; sb1el) basic_machine=mipsisa64sb1el-unknown ;; sde) basic_machine=mipsisa32-sde os=-elf ;; sei) basic_machine=mips-sei os=-seiux ;; sequent) basic_machine=i386-sequent ;; sh) basic_machine=sh-hitachi os=-hms ;; sh5el) basic_machine=sh5le-unknown ;; sh64) basic_machine=sh64-unknown ;; sparclite-wrs | simso-wrs) basic_machine=sparclite-wrs os=-vxworks ;; sps7) basic_machine=m68k-bull os=-sysv2 ;; spur) basic_machine=spur-unknown ;; st2000) basic_machine=m68k-tandem ;; stratus) basic_machine=i860-stratus os=-sysv4 ;; strongarm-* | thumb-*) basic_machine=arm-`echo $basic_machine | sed 's/^[^-]*-//'` ;; sun2) basic_machine=m68000-sun ;; sun2os3) basic_machine=m68000-sun os=-sunos3 ;; sun2os4) basic_machine=m68000-sun os=-sunos4 ;; sun3os3) basic_machine=m68k-sun os=-sunos3 ;; sun3os4) basic_machine=m68k-sun os=-sunos4 ;; sun4os3) basic_machine=sparc-sun os=-sunos3 ;; sun4os4) basic_machine=sparc-sun os=-sunos4 ;; sun4sol2) basic_machine=sparc-sun os=-solaris2 ;; sun3 | sun3-*) basic_machine=m68k-sun ;; sun4) basic_machine=sparc-sun ;; sun386 | sun386i | roadrunner) basic_machine=i386-sun ;; sv1) basic_machine=sv1-cray os=-unicos ;; symmetry) basic_machine=i386-sequent os=-dynix ;; t3e) basic_machine=alphaev5-cray os=-unicos ;; t90) basic_machine=t90-cray os=-unicos ;; tile*) basic_machine=$basic_machine-unknown os=-linux-gnu ;; tx39) basic_machine=mipstx39-unknown ;; tx39el) basic_machine=mipstx39el-unknown ;; toad1) basic_machine=pdp10-xkl os=-tops20 ;; tower | tower-32) basic_machine=m68k-ncr ;; tpf) basic_machine=s390x-ibm os=-tpf ;; udi29k) basic_machine=a29k-amd os=-udi ;; ultra3) basic_machine=a29k-nyu os=-sym1 ;; v810 | necv810) basic_machine=v810-nec os=-none ;; vaxv) basic_machine=vax-dec os=-sysv ;; vms) basic_machine=vax-dec os=-vms ;; vpp*|vx|vx-*) basic_machine=f301-fujitsu ;; vxworks960) basic_machine=i960-wrs os=-vxworks ;; vxworks68) basic_machine=m68k-wrs os=-vxworks ;; vxworks29k) basic_machine=a29k-wrs os=-vxworks ;; w65*) basic_machine=w65-wdc os=-none ;; w89k-*) basic_machine=hppa1.1-winbond os=-proelf ;; xbox) basic_machine=i686-pc os=-mingw32 ;; xps | xps100) basic_machine=xps100-honeywell ;; xscale-* | xscalee[bl]-*) basic_machine=`echo $basic_machine | sed 's/^xscale/arm/'` ;; ymp) basic_machine=ymp-cray os=-unicos ;; z8k-*-coff) basic_machine=z8k-unknown os=-sim ;; z80-*-coff) basic_machine=z80-unknown os=-sim ;; none) basic_machine=none-none os=-none ;; # Here we handle the default manufacturer of certain CPU types. It is in # some cases the only manufacturer, in others, it is the most popular. w89k) basic_machine=hppa1.1-winbond ;; op50n) basic_machine=hppa1.1-oki ;; op60c) basic_machine=hppa1.1-oki ;; romp) basic_machine=romp-ibm ;; mmix) basic_machine=mmix-knuth ;; rs6000) basic_machine=rs6000-ibm ;; vax) basic_machine=vax-dec ;; pdp10) # there are many clones, so DEC is not a safe bet basic_machine=pdp10-unknown ;; pdp11) basic_machine=pdp11-dec ;; we32k) basic_machine=we32k-att ;; sh[1234] | sh[24]a | sh[24]aeb | sh[34]eb | sh[1234]le | sh[23]ele) basic_machine=sh-unknown ;; sparc | sparcv8 | sparcv9 | sparcv9b | sparcv9v) basic_machine=sparc-sun ;; cydra) basic_machine=cydra-cydrome ;; orion) basic_machine=orion-highlevel ;; orion105) basic_machine=clipper-highlevel ;; mac | mpw | mac-mpw) basic_machine=m68k-apple ;; pmac | pmac-mpw) basic_machine=powerpc-apple ;; *-unknown) # Make sure to match an already-canonicalized machine name. ;; *) echo Invalid configuration \`$1\': machine \`$basic_machine\' not recognized 1>&2 exit 1 ;; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old DivEq example now used just for valiadation testing */ # include namespace { // BEGIN empty namespace bool DivEqTestOne(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 2.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; // some constants AD zero = 0.; AD one = 1.; // dependent variable values Z[x] = U[s]; Z[y] = U[t]; Z[x] /= U[t]; // AD *= AD Z[y] /= 5.; // AD *= double zero /= Z[y]; // divide into a parameter equal to zero Z[y] /= one; // divide by a parameter equal to one Z[y] /= 1.; // divide by a double equal to one // check that zero is still a parameter // (must do this before creating f because it erases the tape) ok &= Parameter(zero); // create f : U -> Z and vectors for derivative calcualtions ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check that none of the components of f are parameters size_t i; for(i = 0; i < f.Range(); i++) ok &= ! f.Parameter(i); // check functin values ok &= NearEqual(Z[x] , 3. / 2. , eps99, eps99); ok &= NearEqual(Z[y] , 2. / 5. , eps99, eps99); // forward computation of partials w.r.t. t v[s] = 0.; v[t] = 1.; w = f.Forward(1, v); ok &= NearEqual(w[x] , -1.*U[s]/(U[t]*U[t]) , eps99, eps99); // dx/dt ok &= NearEqual(w[y] , 1. / 5. , eps99, eps99); // dy/dt // reverse computation of second partials of x CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 1.; w[y] = 0.; r = f.Reverse(2, w); ok &= NearEqual(r[2 * s + 1] // d^2 x / (dt ds) , - 1. / (U[t] * U[t]) , 1e-10 , 1e-10 ); ok &= NearEqual(r[2 * t + 1] // d^2 x / (dt dt) , 2. * U[s] / (U[t] * U[t] * U[t]) , 1e-10 , 1e-10 ); return ok; } bool DivEqTestTwo(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // independent variable vector double u0 = .5; CPPAD_TESTVECTOR(AD) U(1); U[0] = u0; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = U[0] * U[0]; // initial value Z[0] /= 2; // AD /= int Z[0] /= 4.; // AD /= double Z[0] /= U[0]; // AD /= AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(Z[0] , u0*u0/(2*4*u0), eps99, eps99); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 1./8.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, eps99, eps99); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 1./8.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, eps99, eps99); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } } // END empty namespace bool DivEq(void) { bool ok = true; ok &= DivEqTestOne(); ok &= DivEqTestTwo(); return ok; } cppad-20170000.3/test_more/old_tan.cpp0000644000175200017650000002667613057470461016577 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin old_tan.cpp$$ $spell Tanh $$ $section Old Tan and Tanh as User Atomic Operations: Example and Test$$ $head Deprecated 2013-05-27$$ This example has not deprecated; see $cref atomic_tangent.cpp$$ instead. $head Theory$$ The code below uses the $cref tan_forward$$ and $cref tan_reverse$$ to implement the tangent ($icode%id% == 0%$$) and hyperbolic tangent ($icode%id% == 1%$$) functions as user atomic operations. $code $srcfile%test_more/old_tan.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // Begin empty namespace using CppAD::vector; // a utility to compute the union of two sets. using CppAD::set_union; // ---------------------------------------------------------------------- // forward mode routine called by CppAD bool old_tan_forward( size_t id , size_t order , size_t n , size_t m , const vector& vx , vector& vzy , const vector& tx , vector& tzy ) { assert( id == 0 || id == 1 ); assert( n == 1 ); assert( m == 2 ); assert( tx.size() >= (order+1) * n ); assert( tzy.size() >= (order+1) * m ); size_t n_order = order + 1; size_t j = order; size_t k; // check if this is during the call to old_tan(id, ax, ay) if( vx.size() > 0 ) { assert( vx.size() >= n ); assert( vzy.size() >= m ); // now setvzy vzy[0] = vx[0]; vzy[1] = vx[0]; } if( j == 0 ) { // z^{(0)} = tan( x^{(0)} ) or tanh( x^{(0)} ) if( id == 0 ) tzy[0] = tan( tx[0] ); else tzy[0] = tanh( tx[0] ); // y^{(0)} = z^{(0)} * z^{(0)} tzy[n_order + 0] = tzy[0] * tzy[0]; } else { float j_inv = 1.f / float(j); if( id == 1 ) j_inv = - j_inv; // z^{(j)} = x^{(j)} +- sum_{k=1}^j k x^{(k)} y^{(j-k)} / j tzy[j] = tx[j]; for(k = 1; k <= j; k++) tzy[j] += tx[k] * tzy[n_order + j-k] * k * j_inv; // y^{(j)} = sum_{k=0}^j z^{(k)} z^{(j-k)} tzy[n_order + j] = 0.; for(k = 0; k <= j; k++) tzy[n_order + j] += tzy[k] * tzy[j-k]; } // All orders are implemented and there are no possible errors return true; } // ---------------------------------------------------------------------- // reverse mode routine called by CppAD bool old_tan_reverse( size_t id , size_t order , size_t n , size_t m , const vector& tx , const vector& tzy , vector& px , const vector& pzy ) { assert( id == 0 || id == 1 ); assert( n == 1 ); assert( m == 2 ); assert( tx.size() >= (order+1) * n ); assert( tzy.size() >= (order+1) * m ); assert( px.size() >= (order+1) * n ); assert( pzy.size() >= (order+1) * m ); size_t n_order = order + 1; size_t j, k; // copy because partials w.r.t. y and z need to change vector qzy = pzy; // initialize accumultion of reverse mode partials for(k = 0; k < n_order; k++) px[k] = 0.; // eliminate positive orders for(j = order; j > 0; j--) { float j_inv = 1.f / float(j); if( id == 1 ) j_inv = - j_inv; // H_{x^{(k)}} += delta(j-k) +- H_{z^{(j)} y^{(j-k)} * k / j px[j] += qzy[j]; for(k = 1; k <= j; k++) px[k] += qzy[j] * tzy[n_order + j-k] * k * j_inv; // H_{y^{j-k)} += +- H_{z^{(j)} x^{(k)} * k / j for(k = 1; k <= j; k++) qzy[n_order + j-k] += qzy[j] * tx[k] * k * j_inv; // H_{z^{(k)}} += H_{y^{(j-1)}} * z^{(j-k-1)} * 2. for(k = 0; k < j; k++) qzy[k] += qzy[n_order + j-1] * tzy[j-k-1] * 2.f; } // eliminate order zero if( id == 0 ) px[0] += qzy[0] * (1.f + tzy[n_order + 0]); else px[0] += qzy[0] * (1.f - tzy[n_order + 0]); return true; } // ---------------------------------------------------------------------- // forward Jacobian sparsity routine called by CppAD bool old_tan_for_jac_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , vector< std::set >& s ) { assert( n == 1 ); assert( m == 2 ); assert( id == 0 || id == 1 ); assert( r.size() >= n ); assert( s.size() >= m ); // sparsity for z and y are the same as for x s[0] = r[0]; s[1] = r[0]; return true; } // ---------------------------------------------------------------------- // reverse Jacobian sparsity routine called by CppAD bool old_tan_rev_jac_sparse( size_t id , size_t n , size_t m , size_t p , vector< std::set >& r , const vector< std::set >& s ) { assert( n == 1 ); assert( m == 2 ); assert( id == 0 || id == 1 ); assert( r.size() >= n ); assert( s.size() >= m ); // note that, if the users code only uses z, and not y, // we could just set r[0] = s[0] r[0] = set_union(s[0], s[1]); return true; } // ---------------------------------------------------------------------- // reverse Hessian sparsity routine called by CppAD bool old_tan_rev_hes_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , const vector& s , vector& t , const vector< std::set >& u , vector< std::set >& v ) { assert( n == 1 ); assert( m == 2 ); assert( id == 0 || id == 1 ); assert( r.size() >= n ); assert( s.size() >= m ); assert( t.size() >= n ); assert( u.size() >= m ); assert( v.size() >= n ); // back propagate Jacobian sparsity. If users code only uses z, // we could just set t[0] = s[0]; t[0] = s[0] | s[1]; // back propagate Hessian sparsity, ... v[0] = set_union(u[0], u[1]); // convert forward Jacobian sparsity to Hessian sparsity // because tan and tanh are nonlinear if( t[0] ) v[0] = set_union(v[0], r[0]); return true; } // --------------------------------------------------------------------- // Declare the AD routine old_tan(id, ax, ay) CPPAD_USER_ATOMIC( old_tan , CppAD::vector , float , old_tan_forward , old_tan_reverse , old_tan_for_jac_sparse , old_tan_rev_jac_sparse , old_tan_rev_hes_sparse ) } // End empty namespace bool old_tan(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; float eps = 10.f * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 1; float x0 = 0.5; CppAD::vector< AD > ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 3; CppAD::vector< AD > af(m); // temporary vector for old_tan computations // (old_tan computes tan or tanh and its square) CppAD::vector< AD > az(2); // call user tan function and store tan(x) in f[0] (ignore tan(x)^2) size_t id = 0; old_tan(id, ax, az); af[0] = az[0]; // call user tanh function and store tanh(x) in f[1] (ignore tanh(x)^2) id = 1; old_tan(id, ax, az); af[1] = az[0]; // put a constant in f[2] = tanh(1.) (for sparsity pattern testing) CppAD::vector< AD > one(1); one[0] = 1.; old_tan(id, one, az); af[2] = az[0]; // create f: x -> f and stop tape recording CppAD::ADFun F; F.Dependent(ax, af); // check function value float tan = std::tan(x0); ok &= NearEqual(af[0] , tan, eps, eps); float tanh = std::tanh(x0); ok &= NearEqual(af[1] , tanh, eps, eps); // check zero order forward CppAD::vector x(n), f(m); x[0] = x0; f = F.Forward(0, x); ok &= NearEqual(f[0] , tan, eps, eps); ok &= NearEqual(f[1] , tanh, eps, eps); // compute first partial of f w.r.t. x[0] using forward mode CppAD::vector dx(n), df(m); dx[0] = 1.; df = F.Forward(1, dx); // compute derivative of tan - tanh using reverse mode CppAD::vector w(m), dw(n); w[0] = 1.; w[1] = 1.; w[2] = 0.; dw = F.Reverse(1, w); // tan'(x) = 1 + tan(x) * tan(x) // tanh'(x) = 1 - tanh(x) * tanh(x) float tanp = 1.f + tan * tan; float tanhp = 1.f - tanh * tanh; ok &= NearEqual(df[0], tanp, eps, eps); ok &= NearEqual(df[1], tanhp, eps, eps); ok &= NearEqual(dw[0], w[0]*tanp + w[1]*tanhp, eps, eps); // compute second partial of f w.r.t. x[0] using forward mode CppAD::vector ddx(n), ddf(m); ddx[0] = 0.; ddf = F.Forward(2, ddx); // compute second derivative of tan - tanh using reverse mode CppAD::vector ddw(2); ddw = F.Reverse(2, w); // tan''(x) = 2 * tan(x) * tan'(x) // tanh''(x) = - 2 * tanh(x) * tanh'(x) // Note that second order Taylor coefficient for u half the // corresponding second derivative. float two = 2; float tanpp = two * tan * tanp; float tanhpp = - two * tanh * tanhp; ok &= NearEqual(two * ddf[0], tanpp, eps, eps); ok &= NearEqual(two * ddf[1], tanhpp, eps, eps); ok &= NearEqual(ddw[0], w[0]*tanp + w[1]*tanhp , eps, eps); ok &= NearEqual(ddw[1], w[0]*tanpp + w[1]*tanhpp, eps, eps); // Forward mode computation of sparsity pattern for F. size_t p = n; // user vectorBool because m and n are small CppAD::vectorBool r1(p), s1(m * p); r1[0] = true; // propagate sparsity for x[0] s1 = F.ForSparseJac(p, r1); ok &= (s1[0] == true); // f[0] depends on x[0] ok &= (s1[1] == true); // f[1] depends on x[0] ok &= (s1[2] == false); // f[2] does not depend on x[0] // Reverse mode computation of sparsity pattern for F. size_t q = m; CppAD::vectorBool s2(q * m), r2(q * n); // Sparsity pattern for identity matrix size_t i, j; for(i = 0; i < q; i++) { for(j = 0; j < m; j++) s2[i * q + j] = (i == j); } r2 = F.RevSparseJac(q, s2); ok &= (r2[0] == true); // f[0] depends on x[0] ok &= (r2[1] == true); // f[1] depends on x[0] ok &= (r2[2] == false); // f[2] does not depend on x[0] // Hessian sparsity for f[0] CppAD::vectorBool s3(m), h(p * n); s3[0] = true; s3[1] = false; s3[2] = false; h = F.RevSparseHes(p, s3); ok &= (h[0] == true); // Hessian is non-zero // Hessian sparsity for f[2] s3[0] = false; s3[2] = true; h = F.RevSparseHes(p, s3); ok &= (h[0] == false); // Hessian is zero // check tanh results for a large value of x x[0] = std::numeric_limits::max() / two; f = F.Forward(0, x); tanh = 1.; ok &= NearEqual(f[1], tanh, eps, eps); df = F.Forward(1, dx); tanhp = 0.; ok &= NearEqual(df[1], tanhp, eps, eps); // -------------------------------------------------------------------- // Free all temporary work space associated with old_atomic objects. // (If there are future calls to user atomic functions, they will // create new temporary work space.) CppAD::user_atomic::clear(); return ok; } // END C++ cppad-20170000.3/test_more/for_sparse_hes.cpp0000644000175200017650000000622013057470461020140 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // Begin empty namespace bool test_one() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 14; // dimension of the range space size_t m = 1; // temporary indices size_t i, j; // for testing load and store operations CppAD::VecAD ad_vec(2); ad_vec[0] = 3.0; ad_vec[1] = 4.0; // initialize check values to false CPPAD_TESTVECTOR(bool) check(n * n); for(j = 0; j < n * n; j++) check[j] = false; // independent variable vector CPPAD_TESTVECTOR(AD) ax(n); for(j = 0; j < n; j++) ax[j] = AD(j); Independent(ax); // accumulate sum here AD sum(0.); // first operand size_t F = 0; // ad_vec[variable] when ad_vec is a parameter sum += ad_vec[ax[F]]; // use fact ax[F] is zero F += 1; // ad_vec[parameter] when ad_vec depends on a variable // (CppAD sparsity does not separate elements of ad_vec) ad_vec[ AD(0) ] = ax[F] * ax[F]; sum += ad_vec[ ax[F] ]; // user fact that ax[F] is one check[F * n + F] = true; F += 1; // parameter / variable sum += 2.0 / ax[F]; check[F * n + F] = true; F += 1; // erf(variable) sum += erf( ax[F] ); check[F * n + F] = true; F += 1; // pow(parameter, variable) sum += pow( 2.0 , ax[F] ); check[F * n + F] = true; F += 1; // pow(variable, parameter) sum += pow( ax[F] , 2.0 ); check[F * n + F] = true; F += 1; // second operand size_t S = F + 1; // variable * variable sum += ax[F] * ax[S]; check[F * n + S] = check[S * n + F] = true; F += 2; S += 2; // azmul(variable, variable) sum += azmul(ax[F], ax[S]); check[F * n + S] = check[S * n + F] = true; F += 2; S += 2; // variable / variable sum += ax[F] / ax[S]; check[F * n + S] = check[S * n + F] = check[S * n + S] = true; F += 2; S += 2; // pow( variable , variable ) sum += pow( ax[F] , ax[S] ); check[F * n + F] = check[S * n + S] = true; check[F * n + S] = check[S * n + F] = true; F += 2; S += 2; ok &= F == n; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = sum; // create function object f : x -> y ADFun f(ax, ay); // ------------------------------------------------------------------ // compute sparsity CPPAD_TESTVECTOR(bool) r(n), s(m), h(n * n); for(j = 0; j < n; j++) r[j] = true; for(i = 0; i < m; i++) s[i] = true; h = f.ForSparseHes(r, s); // check result for(i = 0; i < n; i++) for(j = 0; j < n; j++) ok &= h[i * n + j] == check[i * n + j]; // ------------------------------------------------------------------ return ok; } } // End of empty namespace bool for_sparse_hes(void) { bool ok = true; ok &= test_one(); return ok; } cppad-20170000.3/test_more/vec_ad.cpp0000644000175200017650000001460313057470461016363 0ustar coincoin-web// $Id: vec_ad.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old examples now only used for validation testing */ // BEGIN C++ # include # include namespace { // Begin empty namespace bool VecADTestOne(void) { bool ok = true; using namespace CppAD; using CppAD::sin; using CppAD::cos; size_t n = 3; AD N(n); AD a; size_t i; // create the array CppAD::VecAD V(n); // check assignment from double (while not taping) for(i = 0; i < n; i++) V[i] = double(n - i); // check assignment from an AD (while not taping) for(i = 0; i < n; i++) V[i] = 2. * V[i]; // check array values (while not taping) for(i = 0; i < n; i++) ok &= ( V[i] == 2. * double(n - i) ); // independent variable CPPAD_TESTVECTOR(AD) X(1); X[0] = double(n - 1); Independent(X); // check assignment from double during taping a = -1.; for(i = 0; i < n; i++) { a += 1.; V[a] = double(n - i); } // check assignment from AD during taping a = -1.; for(i = 0; i < n; i++) { a += 1.; V[a] = sin( X[0] ) * V[a]; } // dependent variable CPPAD_TESTVECTOR(AD) Z(1); Z[0] = V[ X[0] ]; // create f: X -> Z ADFun f(X, Z); CPPAD_TESTVECTOR(double) x( f.Domain() ); CPPAD_TESTVECTOR(double) dx( f.Domain() ); CPPAD_TESTVECTOR(double) z( f.Range() ); CPPAD_TESTVECTOR(double) dz( f.Range() ); double vx; for(i = 0; i < n; i++) { // check that the indexing operation was taped x[0] = double(i); z = f.Forward(0, x); vx = double(n - i); ok &= NearEqual(z[0], sin(x[0]) * vx, 1e-10, 1e-10); // note that derivative of v[x] w.r.t. x is zero dx[0] = 1.; dz = f.Forward(1, dx); ok &= NearEqual(dz[0], cos(x[0]) * vx, 1e-10, 1e-10); // reverse mode calculation of same value dz[0] = 1.; dx = f.Reverse(1, dz); ok &= NearEqual(dx[0], cos(x[0]) * vx, 1e-10, 1e-10); } return ok; } // create the discrete function AD Floor(const AD &X) double Floor(const double &x) { return std::floor(x); } CPPAD_DISCRETE_FUNCTION(double, Floor) bool VecADTestTwo(void) { bool ok = true; using namespace CppAD; double pi = 4. * CppAD::atan(1.); size_t nx = 10; // number of x grid point double xLow = 0; // minimum value for x double xUp = 2 * pi; // maximum value for x double xStep = (xUp - xLow) / (nx - 1); // step size in x double xCur; // current value for x // fill in the data vector on a uniform grid VecAD Data(nx); size_t i; for(i = 0; i < nx; i++) { xCur = xLow + double(i) * xStep; // use size_t indexing of Data while not taping Data[i] = CppAD::sin(xCur); } // declare independent variable CPPAD_TESTVECTOR(AD) X(1); X[0] = 2.; Independent(X); // compute index corresponding to current value of X[0] AD I = X[0] / xStep; AD Ifloor = Floor(I); // make sure Ifloor >= 0 (during taping) AD Zero(0); Ifloor = CondExpLt(Ifloor, Zero, Zero, Ifloor); // make sure Ifloor <= nx - 2 (during taping) AD Nxminus2(nx - 2); Ifloor = CondExpGt(Ifloor, Nxminus2, Nxminus2, Ifloor); // Iceil is Ifloor + 1 AD Iceil = Ifloor + 1.; // linear interpolate Data CPPAD_TESTVECTOR(AD) Y(1); Y[0] = Data[Ifloor] + (I - Ifloor) * (Data[Iceil] - Data[Ifloor]); // create f: X -> Y that linearly interpolates the data vector ADFun f(X, Y); // evaluate the linear interpolant at the mid point for first interval CPPAD_TESTVECTOR(double) x(1); CPPAD_TESTVECTOR(double) y(1); x[0] = xStep / 2.; y = f.Forward(0, x); ok &= NearEqual(y[0], (Data[0] + Data[1])/2., 1e-10, 1e-10); // evalute the derivative with respect to x CPPAD_TESTVECTOR(double) dx(1); CPPAD_TESTVECTOR(double) dy(1); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], (Data[1] - Data[0]) / xStep, 1e-10, 1e-10); return ok; } # include bool SecondOrderReverse(void) { // Bradley M. Bell 2009-07-06 // Reverse mode for LdpOp was only modifying the highest order partial // This test demonstrated the bug bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); size_t n = 1; CPPAD_TESTVECTOR(AD) X(n); X[0] = 2.; CppAD::Independent(X); size_t m = 2; CPPAD_TESTVECTOR(AD) Y(m); // The LdpOp instruction corresponds to operations with VecAD vectors. CppAD::VecAD Z(2); AD zero = 0; Z[zero] = X[0] + 1; // The LdvOp instruction corresponds to the index being a variable. AD one = X[0] - 1; // one in a variable here Z[one] = X[0] + 1.; // Compute a function where the second order partial for y // depends on the first order partials for z // This will use the LdpOp instruction because the index // access to z is the parameter zero. Y[0] = Z[zero] * Z[zero]; Y[1] = Z[one] * Z[one]; CppAD::ADFun f(X, Y); // first order forward CPPAD_TESTVECTOR(double) dx(n); size_t p = 1; dx[0] = 1.; f.Forward(p, dx); // Test LdpOp // second order reverse (test exp_if_true case) CPPAD_TESTVECTOR(double) w(m), dw(2 * n); w[0] = 1.; w[1] = 0.; p = 2; dw = f.Reverse(p, w); // check first derivative in dw double check = 2. * (Value( X[0] ) + 1.); ok &= NearEqual(dw[0], check, eps, eps); // check second derivative in dw check = 2.; ok &= NearEqual(dw[1], check, eps, eps); // Test LdvOp // second order reverse (test exp_if_true case) w[0] = 0.; w[1] = 1.; p = 2; dw = f.Reverse(p, w); // check first derivative in dw check = 2. * (Value( X[0] ) + 1.); ok &= NearEqual(dw[0], check, eps, eps); // check second derivative in dw check = 2.; ok &= NearEqual(dw[1], check, eps, eps); return ok; } } // END empty namespace bool VecAD(void) { bool ok = true; ok &= VecADTestOne(); ok &= VecADTestTwo(); ok &= SecondOrderReverse(); return ok; } cppad-20170000.3/test_more/log1p.cpp0000644000175200017650000000374613057470461016172 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include bool log1p(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // a temporary value AD expm1_of_x0 = CppAD::expm1(ax[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CppAD::log1p(expm1_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // check value ok &= NearEqual(ay[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // forward computation of higher order partials w.r.t. x[0] size_t n_order = 5; for(size_t order = 2; order < n_order; order++) { dx[0] = 0.; dy = f.Forward(order, dx); ok &= NearEqual(dy[0], 0., eps, eps); } // reverse computation of derivatives CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n_order * n); w[0] = 1.; dw = f.Reverse(n_order, w); ok &= NearEqual(dw[0], 1., eps, eps); for(size_t order = 1; order < n_order; order++) ok &= NearEqual(dw[order * n + 0], 0., eps, eps); return ok; } // END C++ cppad-20170000.3/test_more/rev_two.cpp0000644000175200017650000000257313057470461016632 0ustar coincoin-web// $Id: rev_two.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include bool RevTwo() { bool ok = true; using CppAD::AD; using CppAD::vector; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); size_t n = 2; vector< AD > X(n); X[0] = 1.; X[1] = 1.; Independent(X); size_t m = 1; vector< AD > Y(m); Y[0] = X[0] * X[0] + X[0] * X[1] + 2. * X[1] * X[1]; CppAD::ADFun F(X,Y); vector x(n); x[0] = .5; x[1] = 1.5; size_t L = 1; vector I(L); vector J(L); vector H(n); I[0] = 0; J[0] = 0; H = F.RevTwo(x, I, J); ok &= NearEqual(H[0], 2., eps99, eps99); ok &= NearEqual(H[1], 1., eps99, eps99); J[0] = 1; H = F.RevTwo(x, I, J); ok &= NearEqual(H[0], 1., eps99, eps99); ok &= NearEqual(H[1], 4., eps99, eps99); return ok; } cppad-20170000.3/test_more/neg.cpp0000644000175200017650000000344313057470461015713 0ustar coincoin-web// $Id: neg.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* old example and test now only used for testing */ // BEGIN C++ # include bool Neg(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 4.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(1); size_t x = 0; // dependent variable values Z[x] = - U[t]; // - AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check values ok &= ( Z[x] == -4. ); // forward computation of partials w.r.t. s v[s] = 1.; v[t] = 0.; w = f.Forward(1, v); ok &= ( w[x] == 0. ); // dx/ds // forward computation of partials w.r.t. t v[s] = 0.; v[t] = 1.; w = f.Forward(1, v); ok &= ( w[x] == -1. ); // dx/dt // reverse computation of second partials of z CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 1.; r = f.Reverse(2, w); ok &= ( r[2 * s + 1] == 0. ); // d^2 x / (ds ds) ok &= ( r[2 * t + 1] == 0. ); // d^2 x / (ds dt) return ok; } // END C++ cppad-20170000.3/test_more/div.cpp0000644000175200017650000001307013057470461015721 0ustar coincoin-web// $Id: div.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old Div examples now used just for valiadation testing */ # include namespace { // BEGIN empty namespace bool DivTestOne(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // assign some parameters AD zero = 0.; AD one = 1.; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 2.; U[t] = 3.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(6); size_t x = 0; size_t y = 1; size_t z = 2; size_t u = 3; size_t v = 4; size_t w = 5; // dependent variables Z[x] = U[s] / U[t]; // AD / AD Z[y] = Z[x] / 4.; // AD / double Z[z] = 5. / Z[y]; // double / AD Z[u] = Z[z] / one; // division by a parameter equal to one Z[v] = Z[z] / 1.; // division by a double equal to one Z[w] = zero / Z[z]; // division into a parameter equal to zero // check division into a zero valued parameter results in a parameter // (must do this before creating f because it erases the tape) ok &= Parameter(Z[w]); // create f : U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) q( f.Domain() ); CPPAD_TESTVECTOR(double) r( f.Range() ); // check parameter flag ok &= f.Parameter(w); // check values ok &= NearEqual( Z[x] , 2. / 3. , eps99, eps99); ok &= NearEqual( Z[y] , 2. / ( 3. * 4. ) , eps99, eps99); ok &= NearEqual( Z[z] , 5. * 3. * 4. / 2. , eps99, eps99); ok &= ( Z[w] == 0. ); ok &= ( Z[u] == Z[z] ); // forward computation of partials w.r.t. s q[s] = 1.; q[t] = 0.; r = f.Forward(1, q); ok &= NearEqual(r[x], 1./U[t], eps99, eps99); // dx/ds ok &= NearEqual(r[y], 1./(U[t]*4.), eps99, eps99); // dy/ds ok &= NearEqual(r[z], -5.*U[t]*4./(U[s]*U[s]), eps99, eps99); // dz/ds ok &= ( r[u] == r[z] ); // du/ds ok &= ( r[v] == r[z] ); // dv/ds ok &= ( r[w] == 0. ); // dw/ds // forward computation in the direction (1, 1) q[s] = 1.; q[t] = 1.; r = f.Forward(1, q); ok &= NearEqual(r[x], 1./U[t] - U[s]/(U[t] * U[t]), eps99, eps99); // second order reverse mode computation CPPAD_TESTVECTOR(double) Q( f.Domain() * 2 ); r[x] = 1.; r[y] = r[z] = r[u] = r[v] = r[w] = 0.; Q = f.Reverse(2, r); ok &= NearEqual( Q[s * f.Domain() + 1], - 1. / (U[t] * U[t]), 1e-10, 1e-10 ); return ok; } bool DivTestTwo(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // independent variable vector double u0 = .5; CPPAD_TESTVECTOR(AD) U(1); U[0] = u0; Independent(U); AD a = U[0] / 1.; // AD / double AD b = a / 2; // AD / int AD c = 3. / b; // double / AD AD d = 4 / c; // int / AD // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = U[0] * U[0] / d; // AD / AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(Value(Z[0]) , u0*u0/(4/(3/(u0/2))), eps99, eps99); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; double value = 6. / 4.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, eps99, eps99); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 6. / 4.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, eps99, eps99); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } bool DivTestThree(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // more testing of variable / variable case double x0 = 2.; double x1 = 3.; size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = x0; X[1] = x1; Independent(X); size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] / X[1]; ADFun f(X, Y); CPPAD_TESTVECTOR(double) dx(n), dy(m); double check; dx[0] = 1.; dx[1] = 1.; dy = f.Forward(1, dx); check = 1. / x1 - x0 / (x1 * x1); ok &= NearEqual(dy[0], check, eps99, eps99); CPPAD_TESTVECTOR(double) w(m), dw(n); w[0] = 1.; dw = f.Reverse(1, w); check = 1. / x1; ok &= NearEqual(dw[0], check, eps99, eps99); check = - x0 / (x1 * x1); ok &= NearEqual(dw[1], check, eps99, eps99); return ok; } } // END empty namespace bool Div(void) { bool ok = true; ok &= DivTestOne(); ok &= DivTestTwo(); ok &= DivTestThree(); return ok; } cppad-20170000.3/test_more/assign.cpp0000644000175200017650000000467313057470461016434 0ustar coincoin-web// $Id: assign.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example, now used just for validation testing */ # include bool assign(void) { bool ok = true; using CppAD::AD; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) x(n); x[0] = 2; // AD = int x[1] = 3.; // AD = double x[2] = x[1]; // AD = AD // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) y(m); // assign an AD object equal to an independent variable // (choose the first independent variable to check a special case) // use the value returned by the assignment (for another assignment) y[0] = y[1] = x[0]; // assign an AD object equal to an expression y[1] = x[1] + 1.; y[2] = x[2] + 2.; // check that all the resulting components of y depend on x ok &= Variable(y[0]); // y[0] = x[0] ok &= Variable(y[1]); // y[1] = x[1] + 1 ok &= Variable(y[2]); // y[2] = x[2] + 2 // construct f : x -> y and stop the tape recording CppAD::ADFun f(x, y); // check variable values ok &= ( y[0] == 2.); ok &= ( y[1] == 4.); ok &= ( y[2] == 5.); // compute partials w.r.t x[1] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 0.; dx[1] = 1.; dx[2] = 0.; dy = f.Forward(1, dx); ok &= (dy[0] == 0.); // dy[0] / dx[1] ok &= (dy[1] == 1.); // dy[1] / dx[1] ok &= (dy[2] == 0.); // dy[2] / dx[1] // compute the derivative y[2] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 0.; w[1] = 0.; w[2] = 1.; dw = f.Reverse(1, w); ok &= (dw[0] == 0.); // dy[2] / dx[0] ok &= (dw[1] == 0.); // dy[2] / dx[1] ok &= (dw[2] == 1.); // dy[2] / dx[2] // assign a VecAD::reference CppAD::VecAD v(1); AD zero(0); v[zero] = 5.; ok &= (v[0] == 5.); return ok; } cppad-20170000.3/test_more/copy.cpp0000644000175200017650000001020713057470461016110 0ustar coincoin-web// $Id: copy.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old Copy example now used just for valiadation testing */ # include namespace { // begin empty namespace bool copy_older(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(1); size_t is = 0; U[is] = 2.; Independent(U); // create an AD that does not depend on s AD t = 3.; // use copy constructor AD x(U[is]); AD y(t); // check which are parameters ok &= ! Parameter(x); ok &= Parameter(y); // dependent variable vector, indices, and values CPPAD_TESTVECTOR(AD) Z(2); size_t ix = 0; size_t iy = 1; Z[ix] = x; Z[iy] = y; // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check parameters flags ok &= ! f.Parameter(ix); ok &= f.Parameter(iy); // check function values ok &= ( Z[ix] == 2. ); ok &= ( Z[iy] == 3. ); // forward computation of partials w.r.t. s v[is] = 1.; w = f.Forward(1, v); ok &= ( w[ix] == 1. ); // dx/ds ok &= ( w[iy] == 0. ); // dy/ds return ok; } bool copy_ad(void) { bool ok = true; // initialize test result flag using CppAD::AD; // so can use AD in place of CppAD::AD // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) x(n); x[0] = 2.; // declare independent variables and start tape recording CppAD::Independent(x); // create an AD that does not depend on x AD b = 3.; // use copy constructor AD u(x[0]); AD v = b; // check which are parameters ok &= Variable(u); ok &= Parameter(v); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) y(m); y[0] = u; y[1] = v; // create f: x -> y and vectors used for derivative calculations CppAD::ADFun f(x, y); CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); // check parameters flags ok &= ! f.Parameter(0); ok &= f.Parameter(1); // check function values ok &= ( y[0] == 2. ); ok &= ( y[1] == 3. ); // forward computation of partials w.r.t. x[0] dx[0] = 1.; dy = f.Forward(1, dx); ok &= ( dy[0] == 1. ); // du / dx ok &= ( dy[1] == 0. ); // dv / dx return ok; } bool copy_base(void) { bool ok = true; // initialize test result flag using CppAD::AD; // so can use AD in place of CppAD::AD // construct directly from Base where Base is double AD x(1.); // construct from a type that converts to Base where Base is double AD y = 2; // construct from a type that converts to Base where Base = AD AD< AD > z(3); // check that resulting objects are parameters ok &= Parameter(x); ok &= Parameter(y); ok &= Parameter(z); // check values of objects (compare AD with double) ok &= ( x == 1.); ok &= ( y == 2.); ok &= ( Value(z) == 3.); // user constructor through the static_cast template function x = static_cast < AD >( 4 ); z = static_cast < AD< AD > >( 5 ); ok &= ( x == 4. ); ok &= ( Value(z) == 5. ); return ok; } bool default_ctor(void) { bool ok = true; using CppAD::AD; // default AD constructor AD x, y; // check that they are parameters ok &= Parameter(x); ok &= Parameter(y); // assign them values x = 3.; y = 4.; // just check a simple operation ok &= (x + y == 7.); return ok; } // END PROGRAM } // end empty namespace bool copy(void) { bool ok = true; ok &= copy_older(); ok &= copy_ad(); ok &= copy_base(); ok &= default_ctor(); return ok; } cppad-20170000.3/test_more/tan.cpp0000644000175200017650000001114313057470461015720 0ustar coincoin-web/* $Id: tan.cpp 3683 2015-05-10 02:24:16Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test higher order derivatives for tan(x) function. */ # include namespace { bool tan_two(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = tan( ax[0] ); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficient CPPAD_TESTVECTOR(double) x1(n), y1; x1[0] = 2.0; y1 = f.Forward(1, x1); ok &= size_t( y1.size() ) == m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(n), y2; x2[0] = 0.0; y2 = f.Forward(2, x2); ok &= size_t( y2.size() ) == m; // // Y (t) = F[X_0(t)] // = tan(0.5 + 2t ) // Y' (t) = 2 * cos(0.5 + 2t )^(-2) double sec_sq = 1.0 / ( cos(0.5) * cos(0.5) ); double check = 2.0 * sec_sq; ok &= NearEqual(y1[0] , check, eps, eps); // // Y''(0) = 8*cos(0.5)^(-3)*sin(0.5) check = 8.0 * tan(0.5) * sec_sq / 2.0; ok &= NearEqual(y2[0] , check, eps, eps); // return ok; } bool tan_case(bool tan_first) { bool ok = true; double eps = 100. * std::numeric_limits::epsilon(); using CppAD::AD; using CppAD::NearEqual; // independent variable vector, indices, values, and declaration size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = .7; Independent(ax); // dependent variable vector and indices size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); if( tan_first ) ay[0] = atan( tan( ax[0] ) ); else ay[0] = tan( atan( ax[0] ) ); // check value ok &= NearEqual(ax[0] , ay[0], eps, eps); // create f: x -> y and vectors used for derivative calculations CppAD::ADFun f(ax, ay); CPPAD_TESTVECTOR(double) dx(n), dy(m); // forward computation of partials w.r.t. x dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1e0, eps, eps); size_t p, order = 5; dx[0] = 0.; for(p = 2; p < order; p++) { dy = f.Forward(p, dx); ok &= NearEqual(dy[0], 0e0, eps, eps); } // reverse computation of order partial CPPAD_TESTVECTOR(double) w(m), dw(n * order); w[0] = 1.; dw = f.Reverse(order, w); ok &= NearEqual(dw[0], 1e0, eps, eps); for(p = 1; p < order; p++) ok &= NearEqual(dw[p], 0e0, eps, eps); return ok; } bool tanh_case(bool tanh_first) { bool ok = true; double eps = 100. * std::numeric_limits::epsilon(); using CppAD::AD; using CppAD::NearEqual; // independent variable vector, indices, values, and declaration size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = .5; Independent(ax); // dependent variable vector and indices size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); AD z; if( tanh_first ) { z = tanh( ax[0] ); ay[0] = .5 * log( (1. + z) / (1. - z) ); } else { z = .5 * log( (1. + ax[0]) / (1. - ax[0]) ); ay[0] = tanh(z); } // check value ok &= NearEqual(ax[0] , ay[0], eps, eps); // create f: x -> y and vectors used for derivative calculations CppAD::ADFun f(ax, ay); CPPAD_TESTVECTOR(double) dx(n), dy(m); // forward computation of partials w.r.t. x dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1e0, eps, eps); size_t p, order = 5; dx[0] = 0.; for(p = 2; p < order; p++) { dy = f.Forward(p, dx); ok &= NearEqual(dy[0], 0e0, eps, eps); } // reverse computation of order partial CPPAD_TESTVECTOR(double) w(m), dw(n * order); w[0] = 1.; dw = f.Reverse(order, w); ok &= NearEqual(dw[0], 1e0, eps, eps); for(p = 1; p < order; p++) ok &= NearEqual(dw[p], 0e0, eps, eps); return ok; } } bool tan(void) { bool ok = true; // ok &= tan_case(true); ok &= tan_case(false); ok &= tanh_case(true); ok &= tanh_case(false); // ok &= tan_two(); return ok; } cppad-20170000.3/test_more/rev_sparse_jac.cpp0000644000175200017650000003005113057470461020123 0ustar coincoin-web// $Id: rev_sparse_jac.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # define CheckOp(Op) \ Y[index] = X[0] Op 2.; \ Check[index * n + 0] = true; \ Check[index * n + 1] = false; \ Check[index * n + 2] = false; \ index++; \ Y[index] = X[0] Op X[1]; \ Check[index * n + 0] = true; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; \ Y[index] = 3. Op X[1]; \ Check[index * n + 0] = false; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; # define CheckUnaryFun(Fun) \ Y[index] = Fun(X[0]); \ Check[index * n + 0] = true; \ Check[index * n + 1] = false; \ Check[index * n + 2] = false; \ index++; \ Y[index] = Fun(X[0] + X[1]); \ Check[index * n + 0] = true; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; \ Y[index] = Fun(X[1]); \ Check[index * n + 0] = false; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; # define CheckBinaryFun(Fun) \ Y[index] = Fun( X[0] , 2.); \ Check[index * n + 0] = true; \ Check[index * n + 1] = false; \ Check[index * n + 2] = false; \ index++; \ Y[index] = Fun( X[0] , X[1]); \ Check[index * n + 0] = true; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; \ Y[index] = Fun( 3. , X[1]); \ Check[index * n + 0] = false; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; namespace { // BEGIN empty namespace bool case_one() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; // dimension of the range space size_t m = (4 + 11 + 1) * 3 + 4; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = .1; X[1] = .2; X[2] = .3; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // initialize index into Y size_t index = 0; // 4 binary operators CheckOp(+); CheckOp(-); CheckOp(*); CheckOp(/); // 11 unary functions CheckUnaryFun(abs); CheckUnaryFun(acos); CheckUnaryFun(asin); CheckUnaryFun(atan); CheckUnaryFun(cos); CheckUnaryFun(cosh); CheckUnaryFun(exp); CheckUnaryFun(log); CheckUnaryFun(sin); CheckUnaryFun(sinh); CheckUnaryFun(sqrt); // 1 binary function CheckBinaryFun(pow); // conditional expression Y[index] = CondExpLt(X[0], X[1], X[0], AD(2.)); Check[index * n + 0] = true; Check[index * n + 1] = false; Check[index * n + 2] = false; index++; Y[index] = CondExpLt(X[0], X[1], X[0], X[1]); Check[index * n + 0] = true; Check[index * n + 1] = true; Check[index * n + 2] = false; index++; Y[index] = CondExpLt(X[0], X[1], AD(3.), X[1]); Check[index * n + 0] = false; Check[index * n + 1] = true; Check[index * n + 2] = false; index++; // non-trival composition Y[index] = Y[0] + Y[1] + X[2]; Check[index * n + 0] = true; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); // -------------------------------------------------------- // dependency matrix for the identity function U(y) = y CPPAD_TESTVECTOR( bool ) Py(m * m); size_t i, j; for(i = 0; i < m; i++) { for(j = 0; j < m; j++) Py[ i * m + j ] = false; Py[ i * m + i ] = true; } // evaluate the dependency matrix for F(x) CPPAD_TESTVECTOR( bool ) Px(m * n); Px = F.RevSparseJac(m, Py); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Px[i * n + j] == Check[i * n + j]); } // -------------------------------------------------------- // dependency matrix for the identity function U(y) = y CPPAD_TESTVECTOR(std::set) Sy(m); for(i = 0; i < m; i++) { assert( Sy[i].empty() ); Sy[i].insert(i); } // evaluate the dependency matrix for U(F(x)) CPPAD_TESTVECTOR(std::set) Sx(m); Sx = F.RevSparseJac(m, Sy); // check values std::set::iterator itr; bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sx[i].find(j) != Sx[i].end(); ok &= (found == Check[i * n + j]); } } return ok; } bool case_two() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; // dimension of the range space size_t m = 3; // inialize the vector as zero CppAD::VecAD Z(n - 1); size_t k; for(k = 0; k < n-1; k++) Z[k] = 0.; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; X[2] = 2.; Independent(X); // VecAD vector is going to depend on X[1] and X[2] Z[ X[0] ] = X[1]; Z[ X[1] ] = X[2]; // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // initialize index into Y size_t index = 0; // First component only depends on X[0]; Y[index] = X[0]; Check[index * n + 0] = true; Check[index * n + 1] = false; Check[index * n + 2] = false; index++; // Second component depends on the vector Z AD zero(0); Y[index] = Z[zero]; // Load by a parameter Check[index * n + 0] = false; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // Third component depends on the vector Z Y[index] = Z[ X[0] ]; // Load by a variable Check[index * n + 0] = false; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); // dependency matrix for the identity function S(y) = y CPPAD_TESTVECTOR( bool ) Py(m * m); size_t i, j; for(i = 0; i < m; i++) { for(j = 0; j < m; j++) Py[ i * m + j ] = false; Py[ i * m + i ] = true; } // evaluate the dependency matrix for S [ F(x) ] CPPAD_TESTVECTOR( bool ) Px(m * n); Px = F.RevSparseJac(m, Py); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Px[i * n + j] == Check[i * n + j]); } // -------------------------------------------------------- // dependency matrix for the identity function U(y) = y CPPAD_TESTVECTOR(std::set) Sy(m); for(i = 0; i < m; i++) { assert( Sy[i].empty() ); Sy[i].insert(i); } // evaluate the dependency matrix for U(F(x)) CPPAD_TESTVECTOR(std::set) Sx(m); Sx = F.RevSparseJac(m, Sy); // check values std::set::iterator itr; bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sx[i].find(j) != Sx[i].end(); ok &= (found == Check[i * n + j]); } } return ok; } bool case_three() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 2; // dimension of the range space size_t m = 3; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = 2.; X[1] = 3.; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // initialize index into Y size_t index = 0; // Y[0] only depends on X[0]; Y[index] = pow(X[0], 2.); Check[index * n + 0] = true; Check[index * n + 1] = false; index++; // Y[1] depends on X[1] Y[index] = pow(2., X[1]); Check[index * n + 0] = false; Check[index * n + 1] = true; index++; // Y[2] depends on X[0] and X[1] Y[index] = pow(X[0], X[1]); Check[index * n + 0] = true; Check[index * n + 1] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); // ----------------------------------------------------------------- // dependency matrix for the identity function CPPAD_TESTVECTOR( bool ) Py(m * m); size_t i, j; for(i = 0; i < m; i++) { for(j = 0; j < m; j++) Py[ i * m + j ] = (i == j); } // evaluate the dependency matrix for F(x) CPPAD_TESTVECTOR( bool ) Px(m * n); Px = F.RevSparseJac(m, Py); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Px[i * n + j] == Check[i * n + j]); } // --------------------------------------------------------- // dependency matrix for the identity function CPPAD_TESTVECTOR(std::set) Sy(m); for(i = 0; i < m; i++) { assert( Sy[i].empty() ); Sy[i].insert(i); } // evaluate the dependency matrix for F(x) CPPAD_TESTVECTOR(std::set) Sx(m); Sx = F.RevSparseJac(m, Sy); // check values bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sx[i].find(j) != Sx[i].end(); ok &= (found == Check[i * n + j]); } } return ok; } // case where s is not identity matrix bool case_four() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 2; // dimension of the range space size_t m = n; // independent and variable vectors CPPAD_TESTVECTOR(AD) ax(n), ay(m); ax[0] = 2.; ax[1] = 3.; Independent(ax); ay[0] = ax[1]; ay[1] = ax[0]; // create function object F : x -> y ADFun F(ax, ay); // evaluate the dependency matrix for F(x) size_t q = 1; CPPAD_TESTVECTOR( bool ) s(q * m), r(q * n); s[0] = true; s[1] = false; r = F.RevSparseJac(q, s); ok &= size_t( r.size() ) == q * n; ok &= r[0] == false; ok &= r[1] == true; return ok; } bool case_five() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 2; // dimension of the range space size_t m = 3; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = 2.; X[1] = 3.; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // initialize index into Y size_t index = 0; // Y[0] only depends on X[0]; Y[index] = pow(X[0], 2.); Check[index * n + 0] = true; Check[index * n + 1] = false; index++; // Y[1] depends on X[1] Y[index] = pow(2., X[1]); Check[index * n + 0] = false; Check[index * n + 1] = true; index++; // Y[2] depends on X[0] and X[1] Y[index] = pow(X[0], X[1]); Check[index * n + 0] = true; Check[index * n + 1] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); // ----------------------------------------------------------------- // dependency matrix for the identity function CPPAD_TESTVECTOR( bool ) Py(m * m); size_t i, j; for(i = 0; i < m; i++) { for(j = 0; j < m; j++) Py[ i * m + j ] = (i == j); } // evaluate the dependency matrix for F(x) bool transpose = true; CPPAD_TESTVECTOR( bool ) Px(n * m); Px = F.RevSparseJac(m, Py, transpose); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Px[j * m + i] == Check[i * n + j]); } // --------------------------------------------------------- // dependency matrix for the identity function CPPAD_TESTVECTOR(std::set) Sy(m); for(i = 0; i < m; i++) { assert( Sy[i].empty() ); Sy[i].insert(i); } // evaluate the dependency matrix for F(x) CPPAD_TESTVECTOR(std::set) Sx(n); Sx = F.RevSparseJac(m, Sy, transpose); // check values bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sx[j].find(i) != Sx[j].end(); ok &= (found == Check[i * n + j]); } } return ok; } } // END empty namespace bool rev_sparse_jac(void) { bool ok = true; ok &= case_one(); ok &= case_two(); ok &= case_three(); ok &= case_four(); ok &= case_five(); return ok; } cppad-20170000.3/test_more/atan.cpp0000644000175200017650000000667213057470461016074 0ustar coincoin-web/* $Id: atan.cpp 3682 2015-05-08 21:59:05Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old atan examples now used just for validation testing. */ # include namespace { // BEGIN empty namespace bool AtanTestOne(void) { bool ok = true; using CppAD::atan; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(1); size_t s = 0; U[s] = 1.; Independent(U); // some temporary values AD x = cos(U[s]); AD y = sin(U[s]); AD z = y / x; // tan(s) // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(1); size_t a = 0; // dependent variable values Z[a] = atan(z); // atan( tan(s) ) // create f: U -> Z and vectors used for dierivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check value ok &= NearEqual(U[s] , Z[a], 1e-10 , 1e-10); // forward computation of partials w.r.t. s v[s] = 1.; w = f.Forward(1, v); ok &= NearEqual(w[a], 1e0, 1e-10 , 1e-10); // da/ds // reverse computation of first order partial of a w[a] = 1.; v = f.Reverse(1, w); ok &= NearEqual(v[s], 1e0, 1e-10 , 1e-10); // da/ds // forward computation of second partials w.r.t. s and s v[s] = 1.; f.Forward(1, v); v[s] = 0.; w = f.Forward(2, v); ok &= NearEqual(2. * w[a], 0e0, 1e-10 , 1e-10); // d^2 a / (ds ds) // reverse computation of second partials of a CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[a] = 1.; r = f.Reverse(2, w); ok &= NearEqual(r[2 * s + 1] ,0e0, 1e-10 , 1e-10 ); // d^2 a / (ds ds) return ok; } bool AtanTestTwo(void) { bool ok = true; using CppAD::atan; using CppAD::sin; using CppAD::cos; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 1.; Independent(U); // a temporary values AD x = sin(U[0]) / cos(U[0]); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = atan(x); // atan( tan(u) ) // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(U[0] , Z[0], 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 1.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 1.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } } // END empty namespace bool atan(void) { bool ok = true; ok &= AtanTestOne(); ok &= AtanTestTwo(); return ok; } cppad-20170000.3/test_more/adfun_copy.cpp0000644000175200017650000000265613057470461017276 0ustar coincoin-web// $Id: adfun_copy.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test that ADFun copy constructor generates an error message. */ # include # include namespace { // error handler to catch the error void myhandler( bool known , int line , const char *file , const char *exp , const char *msg ) { // error handler must not return, so throw an exception throw std::string("myhandler"); } } bool adfun_copy(void) { // error handler for this routine CppAD::ErrorHandler info(myhandler); // an ADFun object CppAD::ADFun f; // value of ok if no error occurs bool ok = false; try { // This operation uses the ADFun copy constructor which is defined, // but should not be used and should generate an error CppAD::ADFun g(f); } catch ( std::string msg ) { // check for expected return ok = (msg == "myhandler"); } return ok; } cppad-20170000.3/test_more/cos.cpp0000644000175200017650000000411213057470461015720 0ustar coincoin-web// $Id: cos.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example now just used for validation testing */ # include bool Cos(void) { bool ok = true; using CppAD::sin; using CppAD::cos; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 1.; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = cos(U[0]); // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value double sin_u = sin( Value(U[0]) ); double cos_u = cos( Value(U[0]) ); ok &= NearEqual(cos_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; for(j = 1; j < p; j++) { w = f.Forward(j, v); double value; if( j % 4 == 1 ) value = -sin_u; else if( j % 4 == 2 ) value = -cos_u; else if( j % 4 == 3 ) value = sin_u; else value = cos_u; jfac *= j; ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; for(j = 0; j < p; j++) { double value; if( j % 4 == 0 ) value = -sin_u; else if( j % 4 == 1 ) value = -cos_u; else if( j % 4 == 2 ) value = sin_u; else value = cos_u; ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); } return ok; } cppad-20170000.3/test_more/add_zero.cpp0000644000175200017650000000360413057470461016730 0ustar coincoin-web// $Id: add_zero.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test the use of the special parameters zero and one with the multiply operator */ # include typedef CppAD::AD ADdouble; typedef CppAD::AD< ADdouble > ADDdouble; bool AddZero(void) { using namespace CppAD; bool ok = true; size_t i; for(i = 0; i < 2; i++) { // run through the cases x = 0, 1 size_t j; for(j = 0; j < 2; j++) { // run through the cases y = 0, 1 CPPAD_TESTVECTOR( ADdouble ) x(1); x[0] = double(i); Independent(x); CPPAD_TESTVECTOR( ADDdouble ) y(1); y[0] = ADDdouble(j); Independent(y); CPPAD_TESTVECTOR( ADDdouble ) z(2); z[0] = x[0] + y[0]; z[1] = y[0] + x[0]; z[1] += x[0]; // f(y) = z = { x + y , y + x + x } ADFun< ADdouble > f(y, z); CPPAD_TESTVECTOR( ADdouble ) u( f.Domain() ); CPPAD_TESTVECTOR( ADdouble ) v( f.Range() ); // v = f(y) u[0] = ADdouble(j); v = f.Forward(0, u); // check value of f ok &= v[0] == x[0] + ADdouble(j); ok &= v[1] == ADdouble(j) + x[0] + x[0]; // g(x) = f(y) = {x + y , y + x + x} ADFun g(x, v); CPPAD_TESTVECTOR( double ) a( g.Domain() ); CPPAD_TESTVECTOR( double ) b( g.Range() ); // b = g'(x) a[0] = 1.; b = g.Forward(1, a); // check derivatives of g ok &= (b[0] == 1.); ok &= (b[1] == 2.); } } return ok; } cppad-20170000.3/test_more/reverse.cpp0000644000175200017650000003260013057470461016612 0ustar coincoin-web// $Id: reverse.cpp 3799 2016-03-12 12:33:53Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old Reverse example now used just for valiadation testing */ # include namespace { // ---------------------------------------------------------- bool reverse_one(void) { bool ok = true; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(3); U[0] = 0.; U[1] = 1.; U[2] = 2.; Independent(U); // compute sum and product of elements in U AD Sum = 0.; AD Prod = 1.; size_t i; for(i = 0; i < 3; i++) { Sum += U[i]; Prod *= U[i]; } // dependent variable vector CPPAD_TESTVECTOR(AD) V(2); V[0] = Sum; V[1] = Prod; // V = f(U) ADFun f(U, V); // Evaluate ( v[0] * f_0 + v[1] * f_1 )^(1) [ u0 ] --------------- size_t p = 1; CPPAD_TESTVECTOR(double) v( f.Range() ); CPPAD_TESTVECTOR(double) u0( f.Domain() ); CPPAD_TESTVECTOR(double) r1( f.Domain() * p ); v[0] = 1.; v[1] = -1.; r1 = f.Reverse(p, v); // direct evaluation of gradients of components of f CPPAD_TESTVECTOR(double) g0(3), g1(3); u0[0] = Value(U[0]); u0[1] = Value(U[1]); u0[2] = Value(U[2]); g0[0] = 1.; g0[1] = 1.; g0[2] = 1.; g1[0] = u0[1]*u0[2]; g1[1] = u0[0]*u0[2]; g1[2] = u0[0]*u0[1]; // compare values for(i = 0; i < 3; i++) { ok &= NearEqual(r1[i] , v[0] * g0[i] + v[1] * g1[i], 1e-10, 1e-10); } // ------------------------------------------------------------------- // Define the function z(t, u0, u1) = f( u0 + u1 * t ) and evaluate // the first order Taylor coefficient column vector z(*, u0, u1) p = 1; CPPAD_TESTVECTOR(double) u1( f.Domain() ); u1[0] = 2.; u1[1] = -1.; u1[2] = 3.; f.Forward(p, u1); // Evaluate the derivaties with respect to u0 of the functions // order 0: v[0] * z_0 (0, u0, u1) + v[1] * z_1 (0, u0, u1) // order 1: v[0] * d/dt z_0 (0, u0, u1) + v[1] * d/dt z_1 (0, u0, u1) p = 2; CPPAD_TESTVECTOR(double) r2( f.Domain() * p ); v[0] = -.5; v[1] = .5; r2 = f.Reverse(p, v); // check derivative of the zero order term for(i = 0; i < 3; i++) { ok &= NearEqual(r2[p * i + 0] , v[0] * g0[i] + v[1] * g1[i], 1e-10, 1e-10); } /* The j-th component of the first order term is d/dt z_j(0, u0, u1) = f_j^{(1)} (u0) * u1 We use ei to denote the vector with its i-th component one and all the other components zero. The partial derivative of the j-th component of the first order term with respect u0[i] is ei * f_j^{(2)} ( u0 ) * u1 */ // direct evaluation of the Hessian f_1^{(2)} (u0) // (the Hessian f_0^{(2)} is identically zero) CPPAD_TESTVECTOR(double) H1(9); H1[0] = 0.; H1[1] = u0[2]; H1[2] = u0[1]; H1[3] = u0[2]; H1[4] = 0.; H1[5] = u0[0]; H1[6] = u0[1]; H1[7] = u0[0]; H1[8] = 0.; size_t j; for(i = 0; i < 3; i++) { double sum = 0.; for(j = 0; j < 3; j++) sum += H1[i * 3 + j] * u1[j]; // note term corresponding to v[0] is zero ok &= NearEqual(r2[p * i + 1], v[1] * sum, 1e-10, 1e-10); } return ok; } // define the template function reverse_any_cases in empty namespace template bool reverse_any_cases(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; X[2] = 2.; // declare independent variables and start recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] * X[1] * X[2]; // create f : X -> Y and stop recording CppAD::ADFun f(X, Y); // define W(t, u) = (u_0 + dx_0*t)*(u_1 + dx_1*t)*(u_2 + dx_2*t) // use zero order forward to evaluate W0(u) = W(0, u) Vector u(n), W0(m); u[0] = 2.; u[1] = 3.; u[2] = 4.; W0 = f.Forward(0, u); double check; check = u[0]*u[1]*u[2]; ok &= NearEqual(W0[0] , check, 1e-10, 1e-10); // define W_t(t, u) = partial W(t, u) w.r.t t // W_t(t, u) = (u_0 + dx_0*t)*(u_1 + dx_1*t)*dx_2 // + (u_0 + dx_0*t)*(u_2 + dx_2*t)*dx_1 // + (u_1 + dx_1*t)*(u_2 + dx_2*t)*dx_0 // use first order forward mode to evaluate W1(u) = W_t(0, u) Vector dx(n), W1(m); dx[0] = .2; dx[1] = .3; dx[2] = .4; W1 = f.Forward(1, dx); check = u[0]*u[1]*dx[2] + u[0]*u[2]*dx[1] + u[1]*u[2]*dx[0]; ok &= NearEqual(W1[0], check, 1e-10, 1e-10); // define W_tt (t, u) = partial W_t(t, u) w.r.t t // W_tt(t, u) = 2*(u_0 + dx_0*t)*dx_1*dx_2 // + 2*(u_1 + dx_1*t)*dx_0*dx_2 // + 2*(u_3 + dx_3*t)*dx_0*dx_1 // use second order forward to evaluate W2(u) = 1/2 * W_tt(0, u) Vector ddx(n), W2(m); ddx[0] = ddx[1] = ddx[2] = 0.; W2 = f.Forward(2, ddx); check = u[0]*dx[1]*dx[2] + u[1]*dx[0]*dx[2] + u[2]*dx[0]*dx[1]; ok &= NearEqual(W2[0], check, 1e-10, 1e-10); // use third order reverse mode to evaluate derivatives size_t p = 3; Vector w(m), dw(n * p); w[0] = 1.; dw = f.Reverse(p, w); // check derivative of W0(u) w.r.t. u ok &= NearEqual(dw[0*p+0], u[1]*u[2], 1e-10, 1e-10); ok &= NearEqual(dw[1*p+0], u[0]*u[2], 1e-10, 1e-10); ok &= NearEqual(dw[2*p+0], u[0]*u[1], 1e-10, 1e-10); // check derivative of W1(u) w.r.t. u ok &= NearEqual(dw[0*p+1], u[1]*dx[2] + u[2]*dx[1], 1e-10, 1e-10); ok &= NearEqual(dw[1*p+1], u[0]*dx[2] + u[2]*dx[0], 1e-10, 1e-10); ok &= NearEqual(dw[2*p+1], u[0]*dx[1] + u[1]*dx[0], 1e-10, 1e-10); // check derivative of W2(u) w.r.t u ok &= NearEqual(dw[0*p+2], dx[1]*dx[2], 1e-10, 1e-10); ok &= NearEqual(dw[1*p+2], dx[0]*dx[2], 1e-10, 1e-10); ok &= NearEqual(dw[2*p+2], dx[0]*dx[1], 1e-10, 1e-10); return ok; } /* $comment reverse_checkpoint.cpp$$ $spell Taylor $$ $section Reverse Mode General Case: Example and Test$$ $index general, reverse example$$ $index reverse, general example$$ $index example, general reverse$$ $index test, general reverse$$ $index composition, example$$ $index example, composition$$ $index test, composition$$ $head Purpose$$ Break a derivative computation into pieces and only store values at the interface of the pieces. In actual applications, there may be many functions, but for this example there are only two. The functions $latex F : \B{R}^2 \rightarrow \B{R}^2$$ and $latex G : \B{R}^2 \rightarrow \B{R}^2$$ defined by $latex \[ F(x) = \left( \begin{array}{c} x_0 x_1 \\ x_1 - x_0 \end{array} \right) \; , \; G(y) = \left( \begin{array}{c} y_0 - y_1 \\ y_1 y_0 \end{array} \right) \] $$ Another difference is that in actual applications, the memory corresponding to function objects not currently being used is sometimes returned to the system (see $cref checkpoint.cpp$$). $head Processing Steps$$ We apply reverse mode to compute the derivative of $latex H : \B{R}^2 \rightarrow \B{R}$$ is defined by $latex \[ \begin{array}{rcl} H(x) & = & G_0 [ F(x) ] + G_1 [ F(x) ] \\ & = & x_0 x_1 - ( x_1 - x_0 ) + x_0 x_1 ( x_1 - x_0 ) \\ & = & x_0 x_1 ( 1 - x_0 + x_1 ) - x_1 + x_0 \end{array} \] $$ Given the zero and first order Taylor coefficients $latex x^{(0)} $$ and $latex x^{(1)}$$, we use $latex X(t)$$, $latex Y(t)$$ and $latex Z(t)$$ for the corresponding functions; i.e., $latex \[ \begin{array}{rcl} X(t) & = & x^{(0)} + x^{(1)} t \\ Y(t) & = & F[X(t)] = y^{(0)} + y^{(1)} t + O(t^2) \\ Z(t) & = & G \{ F [ X(t) ] \} = z^{(0)} + z^{(1)} t + O(t^2) \\ h^{(0)} & = & z^{(0)}_0 + z^{(0)}_1 \\ h^{(1)} & = & z^{(1)}_0 + z^{(1)}_1 \end{array} \] $$ Here are the processing steps: $list number$$ Use forward mode on $latex F(x)$$ to compute $latex y^{(0)}$$ and $latex y^{(1)}$$ $lnext Use forward mode on $latex G(y)$$ to compute $latex z^{(0)}$$ and $latex z^{(1)}$$ $lnext Use reverse mode on $latex G(y)$$ to compute the derivative of $latex h^{(k)}$$ with respect to $latex y^{(0)}$$ and $latex y^{(1)}$$. $lnext Use reverse mode on $latex F(x)$$ to compute the derivative of $latex h^{(k)}$$ with respect to $latex x^{(0)}$$ and $latex x^{(1)}$$. $lend This uses the following relations for $latex k = 0 , 1$$: $latex \[ \begin{array}{rcl} \partial_{x(0)} h^{(k)} [ x^{(0)} , x^{(1)} ] & = & \partial_{y(0)} h^{(k)} [ y^{(0)} , y^{(1)} ] \partial_{x(0)} y^{(0)} [ x^{(0)} , x^{(1)} ] \\ & + & \partial_{y(1)} h^{(k)} [ y^{(0)} , y^{(1)} ] \partial_{x(0)} y^{(1)} [ x^{(0)} , x^{(1)} ] \\ \partial_{x(1)} h^{(k)} [ x^{(0)} , x^{(1)} ] & = & \partial_{y(0)} h^{(k)} [ y^{(0)} , y^{(1)} ] \partial_{x(1)} y^{(0)} [ x^{(0)} , x^{(1)} ] \\ & + & \partial_{y(1)} h^{(k)} [ y^{(0)} , y^{(1)} ] \partial_{x(1)} y^{(1)} [ x^{(0)} , x^{(1)} ] \end{array} \] $$ where $latex \partial_{x(0)}$$ denotes the partial with respect to $latex x^{(0)}$$. $code $comment%example/reverse_checkpoint.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ template Vector F_reverse_mul(const Vector& x) { Vector y(2); y[0] = x[0] * x[1]; y[1] = x[1] - x[0]; return y; } template Vector G_reverse_mul(const Vector& y) { Vector z(2); z[0] = y[0] - y[1]; z[1] = y[1] * y[0]; return z; } bool reverse_mul(void) { bool ok = true; double eps = 10. * CppAD::numeric_limits::epsilon(); using CppAD::AD; using CppAD::NearEqual; CppAD::ADFun f, g; // Record the function F(x) size_t n = 2; CPPAD_TESTVECTOR(AD) X(n), Y(n); X[0] = X[1] = 0.; CppAD::Independent(X); Y = F_reverse_mul(X); f.Dependent(X, Y); // Record the function G(x) CPPAD_TESTVECTOR(AD) Z(n); Y[0] = Y[1] = 0.; CppAD::Independent(Y); Z = G_reverse_mul(Y); g.Dependent(Y, Z); // argument and function values CPPAD_TESTVECTOR(double) x0(n), y0(n), z0(n); x0[0] = 1.; x0[1] = 2.; y0 = f.Forward(0, x0); z0 = g.Forward(0, y0); // check function value double check = x0[0] * x0[1] * (1. - x0[0] + x0[1]) - x0[1] + x0[0]; double h0 = z0[0] + z0[1]; ok &= NearEqual(h0, check, eps, eps); // first order Taylor coefficients CPPAD_TESTVECTOR(double) x1(n), y1(n), z1(n); x1[0] = 3.; x1[1] = 4.; y1 = f.Forward(1, x1); z1 = g.Forward(1, y1); // check first order Taylor coefficients check = x0[0] * x0[1] * (- x1[0] + x1[1]) - x1[1] + x1[0]; check += x1[0] * x0[1] * (1. - x0[0] + x0[1]); check += x0[0] * x1[1] * (1. - x0[0] + x0[1]); double h1 = z1[0] + z1[1]; ok &= NearEqual(h1, check, eps, eps); // ---------------------------------------------------------------- // dw^0 (y) = \partial_y^0 h^0 (y) // dw^1 (y) = \partial_y^1 h^0 (y) size_t p = 2; CPPAD_TESTVECTOR(double) w(n*p), dw(n*p); w[0*p+0] = 1.; // coefficient for z^0_0 w[1*p+0] = 1.; // coefficient for z^0_1 w[0*p+1] = 0.; // coefficient for z^1_0 w[1*p+1] = 0.; // coefficient for z^1_1 dw = g.Reverse(p, w); // dv^0 = dw^0 * \partial_x^0 y^0 (x) + dw^1 * \partial_x^0 y^1 (x) // dv^1 = dw^0 * \partial_x^1 y^0 (x) + dw^1 * \partial_x^1 y^1 (x) CPPAD_TESTVECTOR(double) dv(n*p); dv = f.Reverse(p, dw); // check partial of h^0 w.r.t x^0_0 check = x0[1] * (1. - x0[0] + x0[1]) + 1.; check -= x0[0] * x0[1]; ok &= NearEqual(dv[0*p+0], check, eps, eps); // check partial of h^0 w.r.t x^0_1 check = x0[0] * (1. - x0[0] + x0[1]) - 1.; check += x0[0] * x0[1]; ok &= NearEqual(dv[1*p+0], check, eps, eps); // check partial of h^0 w.r.t x^1_0 and x^1_1 check = 0.; ok &= NearEqual(dv[0*p+1], check, eps, eps); ok &= NearEqual(dv[1*p+1], check, eps, eps); // ---------------------------------------------------------------- // dw^0 (y) = \partial_y^0 h^1 (y) // dw^1 (y) = \partial_y^1 h^1 (y) w[0*p+0] = 0.; // coefficient for z^0_0 w[1*p+0] = 0.; // coefficient for z^0_1 w[0*p+1] = 1.; // coefficient for z^1_0 w[1*p+1] = 1.; // coefficient for z^1_1 dw = g.Reverse(p, w); // dv^0 = dw^0 * \partial_x^0 y^0 (x) + dw^1 * \partial_x^0 y^1 (x) // dv^1 = dw^0 * \partial_x^1 y^0 (x) + dw^1 * \partial_x^1 y^1 (x) dv = f.Reverse(p, dw); // check partial of h^1 w.r.t x^0_0 check = x0[1] * (- x1[0] + x1[1]); check -= x1[0] * x0[1]; check += x1[1] * (1. - x0[0] + x0[1]) - x0[0] * x1[1]; ok &= NearEqual(dv[0*p+0], check, eps, eps); // check partial of h^1 w.r.t x^0_1 check = x0[0] * (- x1[0] + x1[1]); check += x1[0] * (1. - x0[0] + x0[1]) + x1[0] * x0[1]; check += x0[0] * x1[1]; ok &= NearEqual(dv[1*p+0], check, eps, eps); // check partial of h^1 w.r.t x^1_0 // (by reverse mode identity is equal to partial h^0 w.r.t. x^0_0) check = 1. - x0[0] * x0[1]; check += x0[1] * (1. - x0[0] + x0[1]); ok &= NearEqual(dv[0*p+1], check, eps, eps); // check partial of h^1 w.r.t x^1_1 // (by reverse mode identity is equal to partial h^0 w.r.t. x^0_1) check = x0[0] * x0[1] - 1.; check += x0[0] * (1. - x0[0] + x0[1]); ok &= NearEqual(dv[1*p+1], check, eps, eps); return ok; } // ---------------------------------------------------------------------------- } // End empty namespace # include # include bool reverse(void) { bool ok = true; ok &= reverse_one(); ok &= reverse_mul(); ok &= reverse_any_cases< CppAD::vector >(); ok &= reverse_any_cases< std::vector >(); ok &= reverse_any_cases< std::valarray >(); return ok; } cppad-20170000.3/test_more/acos.cpp0000644000175200017650000000345413057470461016071 0ustar coincoin-web/* $Id: acos.cpp 3680 2015-05-07 19:17:37Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old acos examples now used just for valiadation testing */ # include bool acos(void) { bool ok = true; using CppAD::acos; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = .5; Independent(U); // a temporary values AD x = cos(U[0]); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = acos(x); // acos( cos(u) ) // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(U[0] , Z[0], 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 1.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 1.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } cppad-20170000.3/test_more/mul.cpp0000644000175200017650000001026213057470461015734 0ustar coincoin-web// $Id: mul.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old Mul examples now used just for valiadation testing */ # include namespace { // BEGIN empty namespace bool MulTestOne(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 2.; Independent(U); // assign some parameters AD zero = 0.; AD one = 1.; // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(5); size_t x = 0; size_t y = 1; size_t z = 2; size_t u = 3; size_t v = 4; // assign the dependent variables Z[x] = U[s] * U[t]; // AD * AD Z[y] = Z[x] * 4.; // AD * double Z[z] = 4. * Z[y]; // double * AD Z[u] = one * Z[z]; // multiplication by parameter equal to one Z[v] = zero * Z[z]; // multiplication by parameter equal to zero // check multipilcation by zero results in a parameter ok &= Parameter(Z[v]); // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) q( f.Domain() ); CPPAD_TESTVECTOR(double) r( f.Range() ); // check parameter flag ok &= f.Parameter(v); // check values ok &= ( Z[x] == 3. * 2. ); ok &= ( Z[y] == 3. * 2. * 4. ); ok &= ( Z[z] == 4. * 3. * 2. * 4. ); ok &= ( Z[u] == Z[z] ); ok &= ( Z[v] == 0. ); // forward computation of partials w.r.t. s q[s] = 1.; q[t] = 0.; r = f.Forward(1, q); ok &= ( r[x] == U[t] ); // dx/ds ok &= ( r[y] == U[t] * 4. ); // dy/ds ok &= ( r[z] == 4. * U[t] * 4. ); // dz/ds ok &= ( r[u] == r[z] ); // du/ds ok &= ( r[v] == 0. ); // dv/ds // reverse computation of second partials of z CPPAD_TESTVECTOR(double) d2( f.Domain() * 2 ); r[x] = 0.; r[y] = 0.; r[z] = 1.; r[u] = 0.; r[v] = 0.; d2 = f.Reverse(2, r); // check second order partials ok &= ( d2[2 * s + 1] == 0. ); // d^2 z / (ds ds) ok &= ( d2[2 * t + 1] == 4. * 4. ); // d^2 z / (ds dt) return ok; } bool MulTestTwo(void) { bool ok = true; using namespace CppAD; // independent variable vector double u0 = .5; CPPAD_TESTVECTOR(AD) U(1); U[0] = u0; Independent(U); AD a = U[0] * 1.; // AD * double AD b = a * 2; // AD * int AD c = 3. * b; // double * AD AD d = 4 * c; // int * AD // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = U[0] * d; // AD * AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(Value(Z[0]) , u0*4*3*2*u0, 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; for(j = 1; j < p; j++) { double value; if( j == 1 ) value = 48. * u0; else if( j == 2 ) value = 48.; else value = 0.; jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; for(j = 0; j < p; j++) { double value; if( j == 0 ) value = 48. * u0; else if( j == 1 ) value = 48.; else value = 0.; ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); } return ok; } } // END empty namespace bool Mul(void) { bool ok = true; ok &= MulTestOne(); ok &= MulTestTwo(); return ok; } cppad-20170000.3/test_more/checkpoint.cpp0000644000175200017650000001231113057470461017263 0ustar coincoin-web// $Id: checkpoint.cpp 3784 2016-01-22 10:46:29Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { using CppAD::AD; typedef CPPAD_TESTVECTOR(AD) ADVector; bool f_algo(const ADVector& x, ADVector& y) { size_t n = x.size(); size_t m = y.size(); assert( n == m + 1); for(size_t i = 0; i < m; i++) y[i] = x[i] * x[i+1]; return true; } bool g_algo(const ADVector& y, ADVector& z) { size_t n = y.size(); size_t m = z.size(); assert( n + 1 == m ); z[0] = 0.0; for(size_t i = 1; i < m; i++) { z[0] += y[i-1]; z[i] = y[i-1]; } return true; } bool test_one(void) { bool ok = true; using CppAD::checkpoint; using CppAD::ADFun; using CppAD::NearEqual; size_t i, j, k, n = 4, ell = n-1 , m = ell + 1; double eps = 10. * std::numeric_limits::epsilon(); // checkpoint version of the function F(x) ADVector ax(n), ay(ell), az(m); for(j = 0; j < n; j++) ax[j] = double(j); checkpoint f_check("f_check", f_algo, ax, ay); checkpoint g_check("g_check", g_algo, ay, az); // Record a version of z = g[f(x)] without checkpointing Independent(ax); f_algo(ax, ay); g_algo(ay, az); ADFun check_not(ax, az); // Record a version of z = g[f(x)] with checkpointing Independent(ax); f_check(ax, ay); g_check(ay, az); ADFun check_yes(ax, az); // compare forward mode results for orders 0, 1, 2 size_t p = 2; CPPAD_TESTVECTOR(double) x_p(n*(p+1)), z_not(m*(p+1)), z_yes(m*(p+1)); for(j = 0; j < n; j++) { for(k = 0; k <= p; k++) x_p[ j * (p+1) + k ] = 1.0 / (p + 1 - k); } z_not = check_not.Forward(p, x_p); z_yes = check_yes.Forward(p, x_p); for(i = 0; i < m; i++) { for(k = 0; k <= p; k++) { double zik_not = z_not[ i * (p+1) + k]; double zik_yes = z_yes[ i * (p+1) + k]; ok &= NearEqual(zik_not, zik_yes, eps, eps); } } // compare reverse mode results CPPAD_TESTVECTOR(double) w(m*(p+1)), dw_not(n*(p+1)), dw_yes(n*(p+1)); for(i = 0; i < m; i++) { for(k = 0; k <= p; k++) w[ i * (p+1) + k ] = 2.0 / (p + 1 - k ); } dw_not = check_not.Reverse(p+1, w); dw_yes = check_yes.Reverse(p+1, w); for(j = 0; j < n; j++) { for(k = 0; k <= p; k++) { double dwjk_not = dw_not[ j * (p+1) + k]; double dwjk_yes = dw_yes[ j * (p+1) + k]; ok &= NearEqual(dwjk_not, dwjk_yes, eps, eps); } } // mix sparsity so test both cases f_check.option( CppAD::atomic_base::bool_sparsity_enum ); g_check.option( CppAD::atomic_base::set_sparsity_enum ); // compare forward mode Jacobian sparsity patterns size_t q = n - 1; CppAD::vector< std::set > r(n), s_not(m), s_yes(m); for(j = 0; j < n; j++) { if( j < q ) r[j].insert(j); else { r[j].insert(0); r[j].insert(1); } } s_not = check_not.ForSparseJac(q, r); s_yes = check_yes.ForSparseJac(q, r); for(i = 0; i < m; i++) ok &= s_not[i] == s_yes[i]; // compare reverse mode Jacobian sparsity patterns CppAD::vector< std::set > s(m), r_not(m), r_yes(m); for(i = 0; i < m; i++) s[i].insert(i); r_not = check_not.RevSparseJac(m, s); r_yes = check_yes.RevSparseJac(m, s); for(i = 0; i < m; i++) ok &= s_not[i] == s_yes[i]; // compare reverse mode Hessian sparsity patterns CppAD::vector< std::set > s_one(1), h_not(q), h_yes(q); for(i = 0; i < m; i++) s_one[0].insert(i); h_not = check_not.RevSparseHes(q, s_one); h_yes = check_yes.RevSparseHes(q, s_one); for(i = 0; i < q; i++) ok &= h_not[i] == h_yes[i]; checkpoint::clear(); return ok; } bool h_algo(const ADVector& ax, ADVector& ay) { ay[0] = ax[0]; ay[1] = ax[1] + ax[2]; return true; } bool test_two(void) { bool ok = true; using CppAD::checkpoint; using CppAD::ADFun; using CppAD::NearEqual; // checkpoint version of H(x) size_t m = 2; size_t n = 3; ADVector ax(n), ay(m); for(size_t j = 0; j < n; j++) ax[j] = double(j); checkpoint h_check("h_check", h_algo, ax, ay); // record function using h_check Independent(ax); h_check(ax, ay); ADFun h(ax, ay); for(size_t k = 0; k < 3; k++) { if( k == 0 ) h_check.option(CppAD::atomic_base::pack_sparsity_enum); if( k == 1 ) h_check.option(CppAD::atomic_base::bool_sparsity_enum); if( k == 2 ) h_check.option(CppAD::atomic_base::set_sparsity_enum); // compute sparsity pattern h_1(x) = x[1] + x[2] CppAD::vector< std::set > r(1), s(1); r[0].insert(1); s = h.RevSparseJac(1, r); // check result std::set check; check.insert(1); check.insert(2); ok &= s[0] == check; } return ok; } } bool checkpoint(void) { bool ok = true; ok &= test_one(); ok &= test_two(); return ok; } // END C++ cppad-20170000.3/test_more/cosh.cpp0000644000175200017650000000365513057470461016103 0ustar coincoin-web// $Id: cosh.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example now just used for validation testing. */ # include bool Cosh(void) { bool ok = true; using CppAD::sinh; using CppAD::cosh; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 1.; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = cosh(U[0]); // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value double sinh_u = sinh( Value(U[0]) ); double cosh_u = cosh( Value(U[0]) ); ok &= NearEqual(cosh_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; for(j = 1; j < p; j++) { w = f.Forward(j, v); double value; if( j % 2 == 1 ) value = sinh_u; else value = cosh_u; jfac *= j; ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; for(j = 0; j < p; j++) { double value; if( j % 2 == 0 ) value = sinh_u; else value = cosh_u; ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); } return ok; } cppad-20170000.3/test_more/add.cpp0000644000175200017650000000665013057470461015675 0ustar coincoin-web// $Id: add.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old Add examples now used just for valiadation testing */ # include namespace { // BEGIN empty namespace bool AddTestOne(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 2.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(3); size_t x = 0; size_t y = 1; size_t z = 2; // dependent variable values Z[x] = U[s] + U[t]; // AD + AD Z[y] = Z[x] + 1.; // AD + double Z[z] = 1. + Z[y]; // double + AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check function values ok &= ( Z[x] == 3. + 2. ); ok &= ( Z[y] == 3. + 2. + 1. ); ok &= ( Z[z] == 1. + 3. + 2. + 1. ); // forward computation of partials w.r.t. s v[s] = 1.; v[t] = 0.; w = f.Forward(1, v); ok &= ( w[x] == 1. ); // dx/ds ok &= ( w[y] == 1. ); // dy/ds ok &= ( w[z] == 1. ); // dz/ds // reverse computation of second partials of z CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 0.; w[y] = 0.; w[z] = 1.; r = f.Reverse(2, w); ok &= ( r[2 * s + 1] == 0. ); // d^2 z / (ds ds) ok &= ( r[2 * t + 1] == 0. ); // d^2 z / (ds dt) return ok; } bool AddTestTwo(void) { bool ok = true; using namespace CppAD; // independent variable vector double u0 = .5; CPPAD_TESTVECTOR(AD) U(1); U[0] = u0; Independent(U); AD a = U[0] + 1.; // AD + double AD b = a + 2; // AD + int AD c = 3. + b; // double + AD AD d = 4 + c; // int + AD // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = d + U[0]; // AD + AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(Z[0] , 2 * u0 + 10, 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 2.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 2.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } } // END empty namespace bool Add(void) { bool ok = true; ok &= AddTestOne(); ok &= AddTestTwo(); return ok; } cppad-20170000.3/test_more/from_base.cpp0000644000175200017650000000263313057470461017077 0ustar coincoin-web// $Id: from_base.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old FromBase example now used just for valiadation testing */ # include bool FromBase(void) { bool ok = true; using namespace CppAD; // construct directly form Base where Base = double AD x(1.); AD y = 2.; // construct from a type that can be converted to Base // where Base = AD AD< AD > X(1.); AD< AD > Y(2); // check that resulting objects are parameters ok &= Parameter(x); ok &= Parameter(y); ok &= Parameter(X); ok &= Parameter(Y); // check values of objects ok &= (x == 1.); ok &= (X == x); ok &= (y == 2.); ok &= (Y == y); // user constructor through the static_cast template function x = static_cast < AD >( 4 ); X = static_cast < AD< AD > >( 4 ); ok &= (x == 4.); ok &= (X == x); return ok; } // END PROGRAM cppad-20170000.3/test_more/dbl_epsilon.cpp0000644000175200017650000000164613057470461017437 0ustar coincoin-web// $Id: dbl_epsilon.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Check the value of machine epsilon is accurate enough for the correctness tests */ # include # include bool dbl_epsilon(void) { bool ok = true; // CppAD correctness tests assume machine epsilon is less than 1e-13 ok &= DBL_EPSILON < 1e-13; ok &= std::numeric_limits::digits10 >= 13; return ok; } cppad-20170000.3/test_more/cppad_eigen.cpp0000644000175200017650000000425013057470461017375 0ustar coincoin-web// $Id: cppad_eigen.cpp 3760 2015-12-01 04:12:28Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test of Eigen Interface to CppAD Scalar Types $end */ # include bool cppad_eigen(void) { bool ok = true; using CppAD::AD; using Eigen::Dynamic; using Eigen::Matrix; typedef Eigen::NumTraits > traits; ok &= traits::IsComplex == 0; ok &= traits::IsInteger == 0; ok &= traits::IsSigned == 1; ok &= traits::RequireInitialization == 1; ok &= traits::ReadCost == 1; ok &= traits::AddCost == 2; ok &= traits::MulCost == 2; ok &= traits::epsilon() == std::numeric_limits::epsilon(); ok &= traits::dummy_precision() == 100.* std::numeric_limits::epsilon(); ok &= traits::highest() == std::numeric_limits::max(); ok &= traits::lowest() == std::numeric_limits::min(); AD x = 2.0; ok &= conj(x) == x; ok &= real(x) == x; ok &= imag(x) == 0.0; ok &= abs2(x) == 4.0; // Outputing a matrix used to fail before partial specialization of // struct significant_decimals_default_impl in cppad_eigen.hpp. Matrix< AD, 1, 1> X; X(0, 0) = AD(1); std::stringstream stream_out; stream_out << X; ok &= "1" == stream_out.str(); # if ! CPPAD_DEPRECATED // multiplying three matrices together used to cause warning // before making ctor from arbitrary type to AD explicit. typedef CppAD::AD AScalar; Matrix A(1,1), B(1,1), C(1,1), D(1,1); A(0,0) = 1.0; B(0,0) = 2.0; C(0,0) = 3.0; D = A * B * C; ok &= D(0,0) == 6.0 ; # endif return ok; } cppad-20170000.3/test_more/rosen_34.cpp0000644000175200017650000000714313057470461016577 0ustar coincoin-web// $Id: rosen_34.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old OdeImplicit example now used just for valiadation testing of Rosen34 */ // BEGIN C++ # include # include # include /* Case where x[0](0) = 1, x[0]'(t) = - w[0] * x[0](t) x[1](0) = 1, x[1]'(t) = - w[1] * x[1](t) x[2](0) = 0, x[2]'(t) = w[2] * t x[0](t) = exp( - w[0] * t ) x[1](t) = exp( - w[1] * t ) x[2](t) = w[2] * t^2 / 2 */ namespace { // BEGIN Empty namespace class TestFun { public: TestFun(const CPPAD_TESTVECTOR(CppAD::AD) &w_) { w.resize( w_.size() ); w = w_; } void Ode( const CppAD::AD &t, const CPPAD_TESTVECTOR(CppAD::AD) &x, CPPAD_TESTVECTOR(CppAD::AD) &f) { f[0] = - w[0] * x[0]; f[1] = - w[1] * x[1]; f[2] = w[2] * t; } void Ode_ind( const CppAD::AD &t, const CPPAD_TESTVECTOR(CppAD::AD) &x, CPPAD_TESTVECTOR(CppAD::AD) &f_t) { f_t[0] = 0.; f_t[1] = 0.; f_t[2] = w[2]; } void Ode_dep( const CppAD::AD &t, const CPPAD_TESTVECTOR(CppAD::AD) &x, CPPAD_TESTVECTOR(CppAD::AD) &f_x) { f_x[0] = - w[0]; f_x[1] = 0.; f_x[2] = 0.; f_x[3] = 0.; f_x[4] = - w[1]; f_x[5] = 0.; f_x[6] = 0.; f_x[7] = 0.; f_x[8] = 0.; } private: CPPAD_TESTVECTOR(CppAD::AD) w; }; } // END empty namespace bool Rosen34(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); CPPAD_TESTVECTOR(AD) x(3); CPPAD_TESTVECTOR(AD) w(3); size_t n = 3; size_t nstep = 20; AD t0 = 0.; AD t1 = 1.; // set independent variables size_t i; for(i = 0; i < n; i++) w[i] = 100 * i + 1.; Independent(w); // construct the function object using the independent variables TestFun fun(w); // initial value of x CPPAD_TESTVECTOR(AD) xini(3); xini[0] = 1.; xini[1] = 1.; xini[2] = 0.; // integrate the differential equation x = Rosen34(fun, nstep, t0, t1, xini); // create f : w -> x and vectors for evaluating derivatives ADFun f(w, x); CPPAD_TESTVECTOR(double) q( f.Domain() ); CPPAD_TESTVECTOR(double) r( f.Range() ); // check function values AD x0 = exp( - w[0] * t1 ); ok &= NearEqual(x[0], x0, 0., 1. / (nstep * nstep) ); AD x1 = exp( - w[1] * t1 ); ok &= NearEqual(x[1], x1, 0., 1. / (nstep * nstep) ); AD x2 = w[2] * t1 * t1 / 2.; ok &= NearEqual(x[2], x2, eps99, eps99); // check dx[0] / dw[0] for(i = 0; i < size_t(w.size()); i++) q[i] = 0.; q[0] = 1.; r = f.Forward(1, q); ok &= NearEqual(r[0], - w[0] * x0, 0., 1. / (nstep * nstep) ); // check dx[1] / dw[1] q[0] = 0.; q[1] = 1.; r = f.Forward(1, q); ok &= NearEqual(r[1], - w[1] * x1, 0., 1. / (nstep * nstep) ); // check dx[2] / dw[2] q[1] = 0.; q[2] = 1.; r = f.Forward(1, q); ok &= NearEqual(r[2], x2 / w[2], eps99, eps99); return ok; } // END C++ cppad-20170000.3/test_more/sparse_vec_ad.cpp0000644000175200017650000000566613057470461017751 0ustar coincoin-web// $Id: sparse_vec_ad.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include bool sparse_vec_ad(void) { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; size_t i, j; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); for(j = 0; j < n; j++) X[j] = AD(j); Independent(X); // dependent variable vector size_t m = n; CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // Create a VecAD so that there are two in the tape and the sparsity // pattern depends on the second one (checks addressing VecAD objects) VecAD W(n); // VecAD equal to X VecAD Z(n); AD J; for(j = 0; j < n; j++) { J = AD(j); W[J] = X[0]; Z[J] = X[j]; // y[i] depends on x[j] for j <= i // (and is non-linear for j <= 1). if( j == 1 ) Y[j] = Z[J] * Z[J]; else Y[j] = Z[J]; } // compute dependent variables values AD P = 1; J = AD(0); for(j = 0; j < n; j++) { for(i = 0; i < m; i++) Check[ i * m + j ] = (j <= i); } // create function object F : X -> Y ADFun F(X, Y); // dependency matrix for the identity function W(x) = x CPPAD_TESTVECTOR( bool ) Identity(n * n); for(i = 0; i < n; i++) { for(j = 0; j < n; j++) Identity[ i * n + j ] = false; Identity[ i * n + i ] = true; } // evaluate the dependency matrix for Identity(F(x)) CPPAD_TESTVECTOR( bool ) Px(m * n); Px = F.RevSparseJac(n, Identity); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Px[i * m + j] == Check[i * m + j]); } // evaluate the dependency matrix for F(Identity(x)) CPPAD_TESTVECTOR( bool ) Py(m * n); Py = F.ForSparseJac(n, Identity); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Py[i * m + j] == Check[i * m + j]); } // test sparsity pattern for Hessian of F_2 ( Identity(x) ) CPPAD_TESTVECTOR(bool) Hy(m); for(i = 0; i < m; i++) Hy[i] = false; Hy[2] = true; CPPAD_TESTVECTOR(bool) Pxx(n * n); Pxx = F.RevSparseHes(n, Hy); for(i = 0; i < n; i++) { for(j = 0; j < n; j++) ok &= (Pxx[i * n + j] == false ); } // test sparsity pattern for Hessian of F_1 ( Identity(x) ) for(i = 0; i < m; i++) Hy[i] = false; Hy[1] = true; Pxx = F.RevSparseHes(n, Hy); for(i = 0; i < n; i++) { for(j = 0; j < n; j++) ok &= (Pxx[i * n + j] == ( (i <= 1) & (j <= 1) ) ); } return ok; } cppad-20170000.3/test_more/forward_order.cpp0000644000175200017650000001246313057470461020003 0ustar coincoin-web// $Id: forward_order.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* */ // BEGIN C++ # include namespace { double my_discrete(const double& x) { return static_cast ( x ); } CPPAD_DISCRETE_FUNCTION(double, my_discrete) } bool forward_order(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t j, k; double eps = 10. * CppAD::numeric_limits::epsilon(); // domain space vector size_t n = 23, m = n; CPPAD_TESTVECTOR(AD) X(n), Y(m); for(j = 0; j < n; j++) X[j] = 0.0; // declare independent variables and starting recording CppAD::Independent(X); // identity function values size_t i = 0; size_t identity_begin = i; Y[i] = cos( acos( X[i] ) ); i++; // AcosOp, CosOp Y[i] = sin( asin( X[i] ) ); i++; // AsinOp, SinOp Y[i] = tan( atan( X[i] ) ); i++; // AtanOp, TanOp Y[i] = CondExpGt(X[i], X[i-1], X[i], X[i-2]); i++; // CExpOp Y[i] = X[i-1] * X[i] / X[i-1]; i++; // DivvvOp, MulvvOp Y[i] = X[i] * X[i] * 1.0 / X[i]; i++; // DivpvOp Y[i] = 5.0 * X[i] / 5.0; i++; // DivvpOp, MulpvOp Y[i] = exp( log( X[i] ) ); i++; // ExpOp, LogOp Y[i] = pow( sqrt( X[i] ), 2.0); i++; // PowvpOp, SqrtOp Y[i] = log( pow( std::exp(1.), X[i] ) ); i++; // PowpvOp Y[i] = log( pow( X[i], X[i] ) ) / log( X[i]); i++; // PowvvOp Y[i] = -2. - ((X[i-1] - X[i]) - 2.) + X[i-1]; i++; // Sub*Op: pv, vv, vp size_t identity_end = i; // other functions Y[i] = abs( X[i] ); i++; // AbsOp Y[i] = X[i-1] + X[i] + 2.0; i++; // AddvvOp, AddvpOp Y[i] = cosh( X[i] ); i++; // CoshOp Y[i] = my_discrete( X[i] ); i++; // DisOp Y[i] = 4.0; i++; // ParOp Y[i] = sign( X[i] ); i++; // SignOp Y[i] = sinh( X[i] ); i++; // SinhOp Y[i] = tanh(X[i]); i++; // TanhOp // VecAD operations CppAD::VecAD V(n); AD index = 1.; V[index] = 3.0; Y[i] = V[index]; i++; // StppOp, LdpOp V[index] = X[0]; Y[i] = V[index]; i++; // StpvOp, LdpOp index = double(n) * X[3]; V[index] = X[1]; Y[i] = V[index]; i++; // StvvOp, LdvOp // create f: X -> Y and stop tape recording assert( i == m ); CppAD::ADFun f; f.Dependent(X, Y); // initially, no values stored in f ok &= f.size_order() == 0; // Set X_j (t) = x + t size_t p = 2, p1 = p+1; CPPAD_TESTVECTOR(double) x(n), x_p(n * p1), y_p(m * p1); for(j = 0; j < n; j++) { x[j] = double(j) / double(n); x_p[j * p1 + 0] = x[j]; // order 0 x_p[j * p1 + 1] = 1.; // order 1 x_p[j * p1 + 2] = 0.; // order 2 } // compute orders 0, 1, 2 y_p = f.Forward(p, x_p); // identity functions CPPAD_TESTVECTOR(double) y(p1); i = 0; for(j = identity_begin; j != identity_end; j++) { y[0] = x[j]; y[1] = 1.0; y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); i++; } // y_i = abs( x_i ) y[0] = CppAD::abs( x[i] ); y[1] = CppAD::sign( x[i] ); y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = x_[i-1] + x_i + 2 i++; y[0] = x[i-1] + x[i] + 2.0; y[1] = 2.0; y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = cosh( x_i ) i++; y[0] = CppAD::cosh( x[i] ); y[1] = CppAD::sinh( x[i] ); y[2] = CppAD::cosh( x[i] ) / 2.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = my_discrete( x_i ) i++; y[0] = my_discrete( x[i] ); y[1] = 0.0; y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = 4 i++; y[0] = 4.0; y[1] = 0.0; y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = sign( x_i ) i++; y[0] = CppAD::sign( x[i] ); y[1] = 0.0; y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = sinh( x_i ) i++; y[0] = CppAD::sinh( x[i] ); y[1] = CppAD::cosh( x[i] ); y[2] = CppAD::sinh( x[i] ) / 2.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = tanh( x_i ) i++; y[0] = CppAD::tanh( x[i] ); y[1] = 1.0 - y[0] * y[0]; y[2] = - 2.0 * y[0] * y[1] / 2.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = 3.0; i++; y[0] = 3.0; y[1] = 0.0; y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = x_0 i++; y[0] = x[0]; y[1] = 1.0; y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); // y_i = x_1 i++; y[0] = x[1]; y[1] = 1.0; y[2] = 0.0; for(k = 0; k < p1; k++) ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps); return ok; } // END C++ cppad-20170000.3/test_more/optimize.cpp0000644000175200017650000014775113057470461017015 0ustar coincoin-web/* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // 2DO: Test that optimize.hpp use of base_atomic::rev_sparse_jac works. # include # include namespace { // include conditional skip optimization bool conditional_skip_; // accuracy for almost equal checks using CppAD::NearEqual; // note this enum type is not part of the API (but its values are) CppAD::atomic_base::option_enum atomic_sparsity_option_; // ---------------------------------------------------------------- class ode_evaluate_fun { public: // Given that y_i (0) = x_i, // the following y_i (t) satisfy the ODE below: // y_0 (t) = x[0] // y_1 (t) = x[1] + x[0] * t // y_2 (t) = x[2] + x[1] * t + x[0] * t^2/2 // y_3 (t) = x[3] + x[2] * t + x[1] * t^2/2 + x[0] * t^3 / 3! // ... void Ode( const CppAD::AD& t, const CppAD::vector< CppAD::AD >& y, CppAD::vector< CppAD::AD >& f) { size_t n = y.size(); f[0] = 0.; for(size_t k = 1; k < n; k++) f[k] = y[k-1]; } }; bool optimize_ode(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; // independent variable vector size_t n = 2; vector< AD > ax(n); for(size_t j = 0; j < n; j++) ax[j] = AD(j+1); Independent(ax); // function that defines the ode ode_evaluate_fun F; // initial and final time AD ati = 0.0; AD atf = 0.5; // initial value for y(x, t); i.e. y(x, 0) // (is a reference to x) size_t m = n; vector< AD > ayi = ax; // final value for y(x, t); i.e., y(x, 1) vector< AD > ayf(m); // Use one fourth order Runge-Kutta step to solve ODE size_t M = 1; ayf = CppAD::Runge45(F, M, ati, atf, ayi); // function f(x) = y(x, tf) CppAD::ADFun f(ax, ayf); // optimize f(x) f.optimize(); // compute f'(x) vector x(n), jac(m * n); for(size_t j = 0; j < n; j++) x[j] = double(j+1); jac = f.Jacobian(x); // check f'(x) double tj = 1.0; for(size_t j = 0; j < n; j++) { for(size_t i = j; i < m; i++) ok &= CppAD::NearEqual( tj , jac[ i * n * j], eps10, eps10); tj *= Value( atf - ati ); } return ok; } // ---------------------------------------------------------------- // Test nested conditional expressions. bool nested_cond_exp(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; // independent variable vector vector< AD > ax(2), ay(1); ax[0] = 1.0; ax[1] = 2.0; Independent(ax); // first conditional expression AD ac1 = CondExpLe(ax[0], ax[1], 2.0 * ax[0], 3.0 * ax[1] ); // second conditional expression AD ac2 = CondExpGe(ax[0], ax[1], 4.0 * ax[0], 5.0 * ax[1] ); // third conditional expression AD ac3 = CondExpLt(ax[0], ax[1], 6.0 * ac1, 7.0 * ac2 ); // create function object f : ax -> ay ay[0] = ac3; CppAD::ADFun f(ax, ay); // now optimize the operation sequence if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); // now zero order forward vector x(2), y(1); for(size_t i = 0; i < 3; i++) { x[0] = 1.0 - double(i); x[1] = - x[0]; y = f.Forward(0, x); // // first conditional expression double c1; if( x[0] <= x[1] ) c1 = 2.0 * x[0]; else c1 = 3.0 * x[1]; // // second conditional expression double c2; if( x[0] >= x[1] ) c2 = 4.0 * x[0]; else c2 = 5.0 * x[1]; // third conditional expression double c3; if( x[0] < x[1] ) c3 = 6.0 * c1; else c3 = 7.0 * c2; ok &= NearEqual(y[0], c3, eps10, eps10); } return ok; } // ---------------------------------------------------------------- // Test for bug where checkpoint function did not depend on // the operands in the logical comparison because of the CondExp // sparsity pattern. void j_algo( const CppAD::vector< CppAD::AD >& ax , CppAD::vector< CppAD::AD >& ay ) { ay[0] = CondExpGt(ax[0], ax[1], ax[2], ax[3]); } bool atomic_cond_exp_sparsity(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; // Create a checkpoint version of the function g vector< AD > au(4), av(1); for(size_t i = 0; i < 4; i++) au[i] = AD(i); CppAD::checkpoint j_check("j_check", j_algo, au, av); // independent variable vector vector< AD > ax(2), ay(1); ax[0] = 1.; ax[1] = 1.; Independent(ax); // call atomic function that does not get used for(size_t i = 0; i < 4; i++) au[i] = ax[0] + AD(i + 1) * ax[1]; j_check(au, ay); // create function object f : ax -> ay CppAD::ADFun f(ax, ay); // now optimize the operation sequence j_check.option( atomic_sparsity_option_ ); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); // check result where true case is used; i.e., au[0] > au[1] vector x(2), y(1); x[0] = 1.; x[1] = -1; y = f.Forward(0, x); ok &= NearEqual(y[0], x[0] + double(3) * x[1], eps10, eps10); // check result where false case is used; i.e., au[0] <= au[1] x[0] = 1.; x[1] = 1; y = f.Forward(0, x); ok &= NearEqual(y[0], x[0] + double(4) * x[1], eps10, eps10); return ok; } // ------------------------------------------------------------------- // Test conditional optimizing out call to an atomic function call void k_algo( const CppAD::vector< CppAD::AD >& x , CppAD::vector< CppAD::AD >& y ) { y[0] = x[0] + x[1]; } void h_algo( const CppAD::vector< CppAD::AD >& x , CppAD::vector< CppAD::AD >& y ) { y[0] = x[0] - x[1]; } bool atomic_cond_exp(void) { bool ok = true; typedef CppAD::vector< CppAD::AD > ADVector; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // Create a checkpoint version of the function g ADVector ax(2), ag(1), ah(1), ay(1); ax[0] = 0.; ax[1] = 1.; CppAD::checkpoint k_check("k_check", k_algo, ax, ag); CppAD::checkpoint h_check("h_check", h_algo, ax, ah); // independent variable vector Independent(ax); // atomic function calls that get conditionally used k_check(ax, ag); h_check(ax, ah); // conditional expression ay[0] = CondExpLt(ax[0], ax[1], ag[0], ah[0]); // create function object f : ax -> ay CppAD::ADFun f; f.Dependent(ax, ay); // use zero order to evaluate when condition is true CppAD::vector x(2), dx(2); CppAD::vector y(1), dy(1), w(1); x[0] = 3.; x[1] = 4.; y = f.Forward(0, x); ok &= NearEqual(y[0], x[0] + x[1], eps10, eps10); // before optimize k_check.option( atomic_sparsity_option_ ); h_check.option( atomic_sparsity_option_ ); ok &= f.number_skip() == 0; // now optimize the operation sequence if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); // optimized zero order forward when condition is false x[0] = 4.; x[1] = 3.; y = f.Forward(0, x); ok &= NearEqual(y[0], x[0] - x[1], eps10, eps10); // after optimize can skip either call to g or call to h ok &= f.number_skip() == 1; // optimized first order forward dx[0] = 2.; dx[1] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], dx[0] - dx[1], eps10, eps10); // optimized first order reverse w[0] = 1.; dx = f.Reverse(1, w); ok &= NearEqual(dx[0], 1., eps10, eps10); ok &= NearEqual(dx[1], -1., eps10, eps10); return ok; } // ------------------------------------------------------------------- // Test of optimizing out arguments to an atomic function void g_algo( const CppAD::vector< CppAD::AD >& ax , CppAD::vector< CppAD::AD >& ay ) { ay = ax; } bool atomic_no_used(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; // Create a checkpoint version of the function g vector< AD > ax(2), ay(2), az(1); ax[0] = 0.; ax[1] = 1.; CppAD::checkpoint g_check("g_check", g_algo, ax, ay); // independent variable vector Independent(ax); // call atomic function that does not get used g_check(ax, ay); // conditional expression az[0] = CondExpLt(ax[0], ax[1], ax[0] + ax[1], ax[0] - ax[1]); // create function object f : ax -> az CppAD::ADFun f(ax, az); // number of variables before optimization // (include ay[0] and ay[1]) size_t n_before = f.size_var(); // now optimize the operation sequence g_check.option( atomic_sparsity_option_ ); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); // number of variables after optimization // (does not include ay[0] and ay[1]) size_t n_after = f.size_var(); ok &= n_after + 2 == n_before; // check optimization works ok vector x(2), z(1); x[0] = 4.; x[1] = 3.; z = f.Forward(0, x); ok &= NearEqual(z[0], x[0] - x[1], eps10, eps10); return ok; } bool atomic_arguments(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; vector< AD > au(2), aw(2), ax(2), ay(1); // create atomic function corresponding to g_algo au[0] = 1.0; au[1] = 2.0; CppAD::checkpoint g_check("g_algo", g_algo, au, ax); // start recording a new function CppAD::Independent(ax); // now use g_check during the recording au[0] = ax[0] + ax[1]; // this argument requires a new variable au[1] = ax[0] - ax[1]; // this argument also requires a new variable g_check(au, aw); // now create f(x) = x_0 - x_1 ay[0] = aw[0]; CppAD::ADFun f(ax, ay); // number of variables before optimization size_t n_before = f.size_var(); // now optimize f so that the calculation of au[1] is removed g_check.option( atomic_sparsity_option_ ); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); // check difference in number of variables size_t n_after = f.size_var(); ok &= n_before == n_after + 1; // now compute and check a forward mode calculation vector x(2), y(1); x[0] = 5.0; x[1] = 6.0; y = f.Forward(0, x); ok &= NearEqual(y[0], x[0] + x[1], eps10, eps10); return ok; } // ------------------------------------------------------------------- // Test the reverse dependency analysis optimization template void depend_fun (const Vector& x, Vector& y, size_t& original, size_t& opt) { typedef typename Vector::value_type Scalar; Scalar not_used; Scalar one(1), two(2), three(3); // independent variable and phantom at beginning original = 1 + x.size(); opt = 1 + x.size(); // unary operator where operand is arg[0] // (note that sin corresponds to two tape variables) not_used = fabs(x[0]); y[0] = sin(x[0]); original += 3; opt += 2; // binary operator where left operand is a variable // and right operand is a parameter not_used = not_used + 2.; y[1] = x[1] * 3.; original += 2; opt += 1; // binary operator where left operand is a parameter // and right operation is a variable not_used = 2. - not_used; y[2] = 3. / x[2]; original += 2; opt += 1; // binary operator where both operands are variables not_used = x[3] - not_used; y[3] = x[3] / x[2]; original += 2; opt += 1; // conditional expression that will be optimized out not_used = CppAD::CondExpLt(x[0], x[1], x[2], x[3]) + not_used; y[4] = CppAD::CondExpLt(x[4], one, two, three); original += 3; opt += 1; // y[5] does not depend on the value of not_used. // Make sure a parameter, corresponding to a dependent variable, // is not optimized out of the operation sequence. y[5] = 0.0 * not_used; original += 1; opt += 1; // Wwe do not use the argument x[5], to // make sure it is not optimized out. return; } bool depend_one(void) { // Test all except for VecAD operations bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); size_t original; size_t opt; size_t i, j; // domain space vector size_t n = 6; CppAD::vector< AD > X(n); for(j = 0; j < n; j++) X[j] = 1. / double(j + 1); // declare independent variables and start tape recording CppAD::Independent(X); // range space vector size_t m = n; CppAD::vector< AD > Y(m); depend_fun(X, Y, original, opt); // create f: X -> Y and stop tape recording CppAD::ADFun F; F.Dependent(X, Y); CppAD::vector x(n), y(m), check(m); for(j = 0; j < n; j++) x[j] = Value(X[j]); y = F.Forward(0, x); depend_fun(x, check, original, opt); for(i = 0; i < m; i++) ok &= NearEqual(y[i], check[i], eps10, eps10); // Check size before optimization ok &= F.size_var() == original; // Optimize the operation sequence if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // Check size after optimization ok &= F.size_var() == opt; // check result now // (should have already been checked if NDEBUG not defined) y = F.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(y[i], check[i], eps10, eps10); return ok; } bool depend_two(void) { // Test VecAD operations bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); size_t i, j; // domain space vector size_t n = 2; CppAD::vector< AD > X(n); for(j = 0; j < n; j++) X[j] = double(j); // range space vector size_t m = 3; CppAD::vector< AD > Y(m); CppAD::VecAD U(m); CppAD::VecAD V(n); for(i = 0; i < m; i++) U[i] = 0; for(j = 0; j < n; j++) V[j] = 0; // declare independent variables and start tape recording CppAD::Independent(X); // first vecad vector that is a variable U[ X[0] ] = X[1]; // second vecad vector that is a variable V[ X[0] ] = X[1]; // Make dependency for vecad vectors different that for // variables because original code used worng dependency info. // Y does not depend on the first variable in the tape; i.e. // the one corresponding to the BeginOp. So make it depend // on the first vecad vector in the tape. for(i = 0; i < m; i++) { AD I(i); Y[i] = U[I]; } // create f: X -> Y and stop tape recording // Y[ X[0] ] = X[1] and other components of Y are zero. CppAD::ADFun F; F.Dependent(X, Y); // Check number of VecAD vectors plus number of VecAD elements ok &= (F.size_VecAD() == 2 + n + m); CppAD::vector x(n), y(m); for(j = 0; j < n; j++) x[j] = double(j); y = F.Forward(0, x); for(i = 0; i < m; i++) { if( i != static_cast(x[0]) ) ok &= NearEqual(y[i], 0., eps10, eps10); else ok &= NearEqual(y[i], x[1], eps10, eps10); } if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // Check number of VecAD vectors plus number of VecAD elements ok &= (F.size_VecAD() == 1 + m); y = F.Forward(0, x); for(i = 0; i < m; i++) { if( i != static_cast(x[0]) ) ok &= NearEqual(y[i], 0., eps10, eps10); else ok &= NearEqual(y[i], x[1], eps10, eps10); } return ok; } bool depend_three(void) { // Power function is a special case for optimize bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; size_t n = 3; size_t j; vector< AD > X(n), Y(n); vector x(n), y(n); for(j = 0; j < n; j++) X[j] = x[j] = double(j+2); CppAD::Independent(X); Y[0] = pow(X[0], 2.0); Y[1] = pow(2.0, X[1]); Y[2] = pow(X[0], X[1]); CppAD::ADFun F(X, Y); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); y = F.Forward(0, x); // Use identically equal because the result of the operations // have been stored as double and gaurd bits have been dropped. // (This may not be true for some compiler in the future). for(j = 0; j < n; j++) ok &= NearEqual(y[j], Value(Y[j]), eps10, eps10); // check reverse mode derivative vector w(n), dw(n); w[0] = 0.; w[1] = 0.; w[2] = 1.; dw = F.Reverse(1, w); double check = x[1] * pow( x[0], x[1] - 1. ); ok &= NearEqual( dw[0], check, eps10, eps10 ); check = log( x[0] ) * pow( x[0], x[1] ); ok &= NearEqual( dw[1], check, eps10, eps10 ); check = 0.; ok &= NearEqual( dw[2], check, eps10, eps10 ); return ok; } bool depend_four(void) { // erf function is a special case for optimize bool ok = true; # if CPPAD_USE_CPLUSPLUS_2011 using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; size_t n = 1; size_t m = 1; vector< AD > X(n), Y(m); vector x(n); X[0] = x[0] = double(0.5); CppAD::Independent(X); Y[0] = erf(X[0]) + erf(X[0]); CppAD::ADFun F(X, Y); vector y_original = F.Forward(0, x); size_t size_original = F.size_var(); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); ok &= F.size_var() + 5 == size_original; vector y = F.Forward(0, x); ok &= NearEqual(y[0], y_original[0], eps10, eps10); # endif return ok; } // =================================================================== // Test duplicate operation analysis template void duplicate_fun (const Vector& x, Vector& y, size_t& original, size_t& opt) { typedef typename Vector::value_type Scalar; original = 0; opt = 0; // unary operator where operand is arg[0] and one result Scalar a1 = CppAD::exp(x[0]); original += 1; opt += 1; // unary operator where operand is arg[0] and two results Scalar b1 = CppAD::sin(x[1]); original += 2; opt += 2; // non-commutative binary operator where left is a variable // and right is a parameter Scalar c1 = x[2] - 3.; original += 1; opt += 1; // non-commutative binary operator where left is a parameter // and right is a variable Scalar d1 = 3. / x[3]; original += 1; opt += 1; // non-commutative binary operator where left is a variable // and right is a variable Scalar e1 = pow(x[3], x[4]); original += 3; opt += 3; // commutative binary operator where left is a variable // and right is a parameter Scalar f1 = x[5] * 5.; original += 1; opt += 1; // commutative binary operator where left is a variable // and right is a variable Scalar g1 = x[5] + x[6]; original += 1; opt += 1; // duplicate variables Scalar a2 = CppAD::exp(x[0]); Scalar b2 = CppAD::sin(x[1]); // counts for 2 variables Scalar c2 = x[2] - 3.; Scalar d2 = 3. / x[3]; Scalar e2 = pow(x[3], x[4]); // counts for 3 variables Scalar f2 = 5. * x[5]; Scalar g2 = x[6] + x[5]; original += 10; // result vector y[0] = a1 * a2; y[1] = b1 * b2; y[2] = c1 * c2; y[3] = d1 * d2; y[4] = e1 * e2; y[5] = f1 * f2; y[6] = g1 * g2; original += 7; opt += 7; return; } bool duplicate_one(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); size_t original; size_t opt; size_t i, j; // domain space vector size_t n = 7; CppAD::vector< AD > X(n); for(j = 0; j < n; j++) X[j] = 1. / double(j + 1); // declare independent variables and start tape recording CppAD::Independent(X); // range space vector size_t m = n; CppAD::vector< AD > Y(m); duplicate_fun(X, Y, original, opt); // create f: X -> Y and stop tape recording CppAD::ADFun F; F.Dependent(X, Y); CppAD::vector x(n), y(m), check(m); for(j = 0; j < n; j++) x[j] = Value(X[j]); y = F.Forward(0, x); duplicate_fun(x, check, original, opt); for(i = 0; i < m; i++) ok &= NearEqual(y[i], check[i], eps10, eps10); // Check size before optimization ok &= F.size_var() == (n + 1 + original); // Optimize the operation sequence if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // Check size after optimization ok &= F.size_var() == (n + 1 + opt); // check result now // (should have already been checked if NDEBUG not defined) y = F.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(y[i], check[i], eps10, eps10); return ok; } // ------------------------------------------------------------------- bool duplicate_two(void) { // test that duplicate expression removal is relative to // new and not just old argument indices. bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); size_t i, j; // domain space vector size_t n = 1; CppAD::vector< AD > X(n); for(j = 0; j < n; j++) X[j] = double(j + 2); // range space vector size_t m = 1; CppAD::vector< AD > Y(m); // declare independent variables and start tape recording CppAD::Independent(X); // create a new variable AD A1 = X[0] - 2.; // create a duplicate variable AD A2 = X[0] - 2.; // create a new variable using first version of duplicate AD B1 = A1 / 2.; // create a duplicate that can only be dectected using new // argument indices AD B2 = A2 / 2.; // Make a new variable for result // and make it depend on all the variables Y[0] = B1 + B2; // create f: X -> Y and stop tape recording CppAD::ADFun F; F.Dependent(X, Y); // check number of variables in original function ok &= (F.size_var() == 1 + n + m + 4 ); CppAD::vector x(n), y(m); for(j = 0; j < n; j++) x[j] = double(j + 2); y = F.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(y[i], Value(Y[i]), eps10, eps10); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // check number of variables in optimized version ok &= (F.size_var() == 1 + n + m + 2 ); y = F.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(y[i], Value(Y[i]), eps10, eps10); return ok; } // ------------------------------------------------------------------- bool duplicate_three(void) { // test that duplicate expression removal is relative to // new and not just old argument indices (commutative case). bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); size_t i, j; // domain space vector size_t n = 1; CppAD::vector< AD > X(n); for(j = 0; j < n; j++) X[j] = double(j + 2); // range space vector size_t m = 1; CppAD::vector< AD > Y(m); // declare independent variables and start tape recording CppAD::Independent(X); // create a new variable AD A1 = X[0] + 2.; // create a duplicate variable AD A2 = 2. + X[0]; // create a new variable using first version of duplicate AD B1 = A1 * 2.; // create a duplicate that can only be dectected using new // argument indices AD B2 = 2. * A2; // Make a new variable for result // and make it depend on all the variables Y[0] = B1 + B2; // create f: X -> Y and stop tape recording CppAD::ADFun F; F.Dependent(X, Y); // check number of variables in original function ok &= (F.size_var() == 1 + n + m + 4 ); CppAD::vector x(n), y(m); for(j = 0; j < n; j++) x[j] = double(j + 2); y = F.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(y[i], Value(Y[i]), eps10, eps10); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // check number of variables in optimized version ok &= (F.size_var() == 1 + n + m + 2 ); y = F.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(y[i], Value(Y[i]), eps10, eps10); return ok; } // ------------------------------------------------------------------- bool duplicate_four(void) { // Check that unary expression matching not only checks hash code, // and operator, but also operand (old bug that has been fixed). bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CppAD::vector< AD > X(n); X[0] = 1.; // range space vector size_t m = 1; CppAD::vector< AD > Y(m); // declare independent variables and start tape recording CppAD::Independent(X); // check a huge number of same operation with different operands size_t n_operations = std::min( size_t(CPPAD_HASH_TABLE_SIZE) + 5, size_t(std::numeric_limits::max()) - 5 ); Y[0] = X[0]; for(j = 0; j < n_operations; j++) Y[0] = fabs(Y[0]); // create f: X -> Y and stop tape recording CppAD::ADFun F; F.Dependent(X, Y); // check number of variables in original function ok &= (F.size_var() == 1 + n + n_operations ); CppAD::vector x(n), y(m); x[0] = 1.; y = F.Forward(0, x); ok &= NearEqual(y[0], Value(Y[0]), eps10, eps10); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // check same number of variables in optimized version ok &= (F.size_var() == 1 + n + n_operations ); y = F.Forward(0, x); ok &= NearEqual(y[0], Value(Y[0]), eps10, eps10); return ok; } // ==================================================================== bool cummulative_sum(void) { // test conversion of a sequence of additions and subtraction // to a cummulative summation sequence. bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); size_t i, j; // domain space vector size_t n = 7; CppAD::vector< AD > X(n); for(j = 0; j < n; j++) X[j] = double(j + 2); size_t n_original = 1 + n; size_t n_optimize = 1 + n; // range space vector size_t m = 2; CppAD::vector< AD > Y(m); // declare independent variables and start tape recording CppAD::Independent(X); // Operations inside of optimize_cadd Y[0] = 5. + (X[0] + X[1]) + (X[1] - X[2]) // Addvv, Subvv + (X[2] - 1.) + (2. - X[3]) // Subvp, Subpv + (X[4] + 3.) + (4. + X[5]); // Addpv, Addpv (no Addvp) n_original += 12; n_optimize += 1; // Operations inside of optimize_csub Y[1] = 5. - (X[1] + X[2]) - (X[2] - X[3]) // Addvv, Subvv - (X[3] - 1.) - (2. - X[4]) // Subvp, Subpv - (X[5] + 3.) - (4. + X[6]); // Addpv, Addpv (no Addvp) n_original += 12; n_optimize += 1; CppAD::ADFun F; F.Dependent(X, Y); // check number of variables in original function ok &= (F.size_var() == n_original ); CppAD::vector x(n), y(m); for(j = 0; j < n; j++) x[j] = double(j + 2); y = F.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(y[i], Value(Y[i]), eps10, eps10); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // check number of variables in optimized version ok &= (F.size_var() == n_optimize ); y = F.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(y[i], Value(Y[i]), eps10, eps10); return ok; } // ------------------------------------------------------------------- bool forward_csum(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // independent variable vector CppAD::vector< AD > X(2); X[0] = 0.; X[1] = 1.; Independent(X); // compute sum of elements in X CppAD::vector< AD > Y(1); Y[0] = X[0] + X[0] + X[1]; // create function object F : X -> Y ADFun F(X, Y); // now optimize the operation sequence if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // use zero order to evaluate F[ (3, 4) ] CppAD::vector x0( F.Domain() ); CppAD::vector y0( F.Range() ); x0[0] = 3.; x0[1] = 4.; y0 = F.Forward(0, x0); ok &= NearEqual(y0[0] , x0[0]+x0[0]+x0[1], eps10, eps10); // evaluate derivative of F in X[0] direction CppAD::vector x1( F.Domain() ); CppAD::vector y1( F.Range() ); x1[0] = 1.; x1[1] = 0.; y1 = F.Forward(1, x1); ok &= NearEqual(y1[0] , x1[0]+x1[0]+x1[1], eps10, eps10); // evaluate second derivative of F in X[0] direction CppAD::vector x2( F.Domain() ); CppAD::vector y2( F.Range() ); x2[0] = 0.; x2[1] = 0.; y2 = F.Forward(2, x2); double F_00 = 2. * y2[0]; ok &= NearEqual(F_00, 0., eps10, eps10); return ok; } // ------------------------------------------------------------------- bool reverse_csum(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // independent variable vector CppAD::vector< AD > X(2); X[0] = 0.; X[1] = 1.; Independent(X); // compute sum of elements in X CppAD::vector< AD > Y(1); Y[0] = X[0] - (X[0] - X[1]); // create function object F : X -> Y ADFun F(X, Y); // now optimize the operation sequence if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // use zero order to evaluate F[ (3, 4) ] CppAD::vector x0( F.Domain() ); CppAD::vector y0( F.Range() ); x0[0] = 3.; x0[1] = 4.; y0 = F.Forward(0, x0); ok &= NearEqual(y0[0] , x0[0]-x0[0]+x0[1], eps10, eps10); // evaluate derivative of F CppAD::vector dF( F.Domain() ); CppAD::vector w( F.Range() ); w[0] = 1.; dF = F.Reverse(1, w); ok &= NearEqual(dF[0] , 0., eps10, eps10); ok &= NearEqual(dF[1] , 1., eps10, eps10); return ok; } bool forward_sparse_jacobian() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; // dimension of the range space size_t m = 3; // independent variable vector CppAD::vector< AD > X(n); X[0] = 2.; X[1] = 3.; X[2] = 4.; Independent(X); // dependent variable vector CppAD::vector< AD > Y(m); // check results vector CppAD::vector< bool > Check(m * n); // initialize index into Y size_t index = 0; // Y[0] Y[index] = X[0] + X[1] + 5.; Check[index * n + 0] = true; Check[index * n + 1] = true; Check[index * n + 2] = false; index++; // Y[1] Y[index] = Y[0] - (X[1] + X[2]); Check[index * n + 0] = true; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // Y[2] // 2DO: There is a subtitle issue that has to do with using reverse // jacobian sparsity patterns during the optimization process. // We need an option to include X[0] in the sparsity pattern // so the optimizer can know it affects the results. Y[index] = CondExpLe(X[0], X[1], X[1]+X[1], X[2]-X[2]); Check[index * n + 0] = false; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // --------------------------------------------------------- // dependency matrix for the identity function CppAD::vector< std::set > Sx(n); size_t i, j; for(i = 0; i < n; i++) { assert( Sx[i].empty() ); Sx[i].insert(i); } // evaluate the dependency matrix for F(x) CppAD::vector< std::set > Sy(m); Sy = F.ForSparseJac(n, Sx); // check values bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sy[i].find(j) != Sy[i].end(); ok &= (found == Check[i * n + j]); } } return ok; } bool reverse_sparse_jacobian() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; // dimension of the range space size_t m = 3; // independent variable vector CppAD::vector< AD > X(n); X[0] = 2.; X[1] = 3.; X[2] = 4.; Independent(X); // dependent variable vector CppAD::vector< AD > Y(m); // check results vector CppAD::vector< bool > Check(m * n); // initialize index into Y size_t index = 0; // Y[0] Y[index] = X[0] + X[1] + 5.; Check[index * n + 0] = true; Check[index * n + 1] = true; Check[index * n + 2] = false; index++; // Y[1] Y[index] = Y[0] - (X[1] + X[2]); Check[index * n + 0] = true; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // Y[2] Y[index] = CondExpLe(X[0], X[1], X[1]+X[1], X[2]-X[2]); Check[index * n + 0] = false; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // ---------------------------------------------------------- // dependency matrix for the identity function CppAD::vector< bool > Py(m * m); size_t i, j; for(i = 0; i < m; i++) { for(j = 0; j < m; j++) Py[ i * m + j ] = i == j; } // evaluate the dependency matrix for F(x) CppAD::vector< bool > Px(m * n); Px = F.RevSparseJac(m, Py); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= Px[i * n + j] == Check[i * n + j]; } return ok; } bool reverse_sparse_hessian(void) { bool ok = true; using CppAD::AD; size_t i, j; size_t n = 3; CppAD::vector< AD > X(n); X[0] = 1.; X[1] = 2.; X[2] = 3.; CppAD::Independent(X); size_t m = 1; CppAD::vector< AD > Y(m); Y[0] = CondExpGe( X[0], X[1], X[0] + (2. + X[1] + 3.) * X[1], X[0] + (2. + X[2] + 3.) * X[1] ); CppAD::vector check(n * n); check[0 * n + 0] = false; // partial w.r.t. x[0], x[0] check[0 * n + 1] = false; // x[0], x[1] check[0 * n + 2] = false; // x[0], x[2] check[1 * n + 0] = false; // partial w.r.t. x[1], x[0] check[1 * n + 1] = true; // x[1], x[1] check[1 * n + 2] = true; // x[1], x[2] check[2 * n + 0] = false; // partial w.r.t. x[2], x[0] check[2 * n + 1] = true; // x[2], x[1] check[2 * n + 2] = false; // x[2], x[2] // create function object F : X -> Y CppAD::ADFun F(X, Y); if( conditional_skip_ ) F.optimize(); else F.optimize("no_conditional_skip"); // sparsity pattern for the identity function U(x) = x CppAD::vector Px(n * n); for(i = 0; i < n; i++) for(j = 0; j < n; j++) Px[ i * n + j ] = i == j; // compute sparsity pattern for Jacobian of F(U(x)) CppAD::vector P_jac(m * n); P_jac = F.ForSparseJac(n, Px); // compute sparsity pattern for Hessian of F_k ( U(x) ) CppAD::vector Py(m); CppAD::vector Pxx(n * n); Py[0] = true; Pxx = F.RevSparseHes(n, Py); // check values for(i = 0; i < n * n; i++) ok &= (Pxx[i] == check[i]); return ok; } // check that CondExp properly detects dependencies bool cond_exp_depend(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); AD zero(0.), one(1.), two(2.), three(3.); size_t n = 4; CppAD::vector< AD > X(n); X[0] = zero; X[1] = one; X[2] = two; X[3] = three; CppAD::Independent(X); size_t m = 4; CppAD::vector< AD > Y(m); Y[0] = CondExpLt(X[0] + .5, one, two, three); Y[1] = CondExpLt(zero, X[1] + .5, two, three); Y[2] = CondExpLt(zero, one, X[2] + .5, three); Y[3] = CondExpLt(zero, one, two, X[3] + .5); CppAD::ADFun f(X, Y); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); CppAD::vector x(n), y(m); size_t i; for(i = 0; i < n; i++) x[i] = double(n - i); y = f.Forward(0, x); if( x[0] + .5 < 1. ) ok &= NearEqual(y[0], 2., eps10, eps10); else ok &= NearEqual(y[0], 3., eps10, eps10); if( 0. < x[1] + .5 ) ok &= NearEqual(y[1], 2., eps10, eps10); else ok &= NearEqual(y[1], 3., eps10, eps10); ok &= NearEqual(y[2], x[2] + .5, eps10, eps10);; ok &= NearEqual(y[3], 2., eps10, eps10); return ok; } // check that CondExp properly handels expressions that get // removed during opitmization bool cond_exp_removed(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); AD zero(0.); size_t n = 1; CppAD::vector< AD > X(n); X[0] = 1.0; CppAD::Independent(X); size_t m = 1; CppAD::vector< AD > Y(m); AD true_case = sin(X[0]) + sin(X[0]); AD false_case = cos(X[0]) + cos(X[0]); Y[0] = CondExpLt(X[0], zero, true_case, false_case); CppAD::ADFun f(X, Y); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); CppAD::vector x(n), y(m), w(m), dw(n); x[0] = 1.0; y = f.Forward(0, x); ok &= NearEqual(y[0], false_case, eps10, eps10); w[0] = 1.0; dw = f.Reverse(1, w); // derivative of cos is minus sin ok &= NearEqual(dw[0], - true_case, eps10, eps10); return ok; } // ------------------------------------------------------------------- using CppAD::set_union; bool old_atomic_forward( size_t id , size_t k , size_t n , size_t m , const CppAD::vector& vx , CppAD::vector& vy , const CppAD::vector& tx , CppAD::vector& ty ) { assert(n == 3 && m == 2); if( k > 0 ) return false; // y[0] = x[0] + x[1] ty[0] = tx[0] + tx[1]; // y[1] = x[1] + x[2] ty[1] = tx[1] + tx[2]; if( vy.size() > 0 ) { vy[0] = vx[0] | vx[1]; vy[1] = vx[1] | vx[2]; } return true; } bool old_atomic_reverse( size_t id , size_t k , size_t n , size_t m , const CppAD::vector& tx , const CppAD::vector& ty , CppAD::vector& px , const CppAD::vector& py ) { return false; } bool old_atomic_for_jac_sparse( size_t id , size_t n , size_t m , size_t q , const CppAD::vector< std::set >& r , CppAD::vector< std::set >& s ) { return false; } bool old_atomic_rev_jac_sparse( size_t id , size_t n , size_t m , size_t q , CppAD::vector< std::set >& r , const CppAD::vector< std::set >& s ) { assert(n == 3 && m == 2); r[0].clear(); r[1].clear(); r[2].clear(); // y[0] = x[0] + x[1] r[0] = set_union(r[0], s[0]); r[1] = set_union(r[1], s[0]); // y[1] = x[1] + x[2] r[1] = set_union(r[1], s[1]); r[2] = set_union(r[2], s[1]); return true; } bool old_atomic_rev_hes_sparse( size_t id , size_t n , size_t m , size_t q , const CppAD::vector< std::set >& r , const CppAD::vector& s , CppAD::vector& t , const CppAD::vector< std::set >& u , CppAD::vector< std::set >& v ) { return false; } CPPAD_USER_ATOMIC( my_old_atomic , CppAD::vector , double , old_atomic_forward , old_atomic_reverse , old_atomic_for_jac_sparse , old_atomic_rev_jac_sparse , old_atomic_rev_hes_sparse ) bool old_atomic_test(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); size_t j; size_t n = 3; size_t m = 2; CppAD::vector< AD > ax(n), ay(m), az(m); for(j = 0; j < n; j++) ax[j] = AD(j + 1); CppAD::Independent(ax); size_t id = 0; // first call should stay in the tape my_old_atomic(id++, ax, ay); // second call will not get used my_old_atomic(id++, ax, az); // create function CppAD::ADFun g(ax, ay); // should have 1 + n + m + m varaibles ok &= g.size_var() == (1 + n + m + m); g.optimize(); // should have 1 + n + m varaibles ok &= g.size_var() == (1 + n + m); // now test that the optimized function gives same results CppAD::vector x(n), y(m); for(j = 0; j < n; j++) x[j] = (j + 1) * (j + 1); y = g.Forward(0, x); // y[0] = x[0] + x[1] ok &= NearEqual(y[0], x[0] + x[1], eps10, eps10); // y[1] = x[1] + x[2] ok &= NearEqual(y[0], x[0] + x[1], eps10, eps10); return ok; } bool not_identically_equal(void) { bool ok = true; using CppAD::AD; // independent variable vector size_t n = 5; CppAD::vector< AD > ax(n); size_t j; for(j = 0; j < n; j++) ax[j] = 1. / 3.; CppAD::Independent(ax); // dependent variable vector size_t m = 1; CppAD::vector< AD > ay(m); ay[0] = 0.; for(j = 0; j < n; j++) { if( j % 2 == 0 ) ay[0] += ax[j]; else ay[0] -= ax[j]; } CppAD::ADFun f(ax, ay); // Used to fail assert in optimize that forward mode results // are identically equal if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); return ok; } // ----------------------------------------------------------------------- double floor(const double& x) { return std::floor(x); } CPPAD_DISCRETE_FUNCTION(double, floor) bool discrete_function(void) { bool ok = true; using CppAD::vector; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); vector< CppAD::AD > ax(1), ay(1); ax[0] = 0.0; CppAD::Independent(ax); ay[0] = floor(ax[0]) + floor(ax[0]); CppAD::ADFun f(ax, ay); size_t size_before = f.size_var(); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); size_t size_after = f.size_var(); ok &= size_after + 1 == size_before; vector x(1), y(1); x[0] = -2.2; y = f.Forward(0, x); ok &= NearEqual(y[0], -6.0, eps10, eps10); return ok; } // ---------------------------------------------------------------- void i_algo( const CppAD::vector< CppAD::AD >& ax , CppAD::vector< CppAD::AD >& ay ) { ay[0] = 1.0 / ax[0]; } // // Test bug where atomic functions were not properly conditionally skipped. bool cond_exp_skip_atomic(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; // Create a checkpoint version of the function i_algo vector< AD > au(1), av(1), aw(1); au[0] = 1.0; CppAD::checkpoint i_check("i_check", i_algo, au, av); // independent variable vector vector< AD > ax(2), ay(1); ax[0] = 1.0; ax[1] = 2.0; Independent(ax); // call atomic function that does not get used au[0] = ax[0]; i_check(au, av); au[0] = ax[1]; i_check(au, aw); AD zero = 0.0; ay[0] = CondExpGt(av[0], zero, av[0], aw[0]); // create function object f : ax -> ay CppAD::ADFun f(ax, ay); // run case that skips the second call to afun // (can use trace in forward0sweep.hpp to see this). vector x(2), y_before(1), y_after(1); x[0] = 1.0; x[1] = 2.0; y_before = f.Forward(0, x); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); y_after = f.Forward(0, x); ok &= NearEqual(y_before[0], y_after[0], eps10, eps10); return ok; } // // Test bug where conditional dependence did not pass through // atomic functions bool cond_exp_atomic_dependence(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); using CppAD::vector; // Create a checkpoint version of the function i_algo vector< AD > au(1), av(1), aw(1); au[0] = 1.0; CppAD::checkpoint i_check("i_check", i_algo, au, av); vector< AD > ax(2), ay(1); AD zero = 0.0; ax[0] = 1.0; ax[1] = 1.0; Independent(ax); av[0] = ax[0] + ax[1]; i_check(av, aw); ay[0] = CondExpGt(aw[0], zero, zero, aw[0]); CppAD::ADFun f; f.Dependent(ax, ay); // run case that skips the second call to afun // (but not for order zero) vector x(2), y_before(1), y_after(1); vector dx(2), dy_before(1), dy_after(1); x[0] = 1.0; x[1] = 1.0; y_before = f.Forward(0, x); dx[0] = 2.0; dx[1] = 2.0; dy_before = f.Forward(1, dx); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); y_after = f.Forward(0, x); dy_after = f.Forward(1, dx); ok &= NearEqual(y_before[0] , y_after[0], eps10, eps10); ok &= NearEqual(dy_before[0], dy_after[0], eps10, eps10); return ok; } // ----------------------------------------------------------------------- // Test reverse mode conditionalay skipping commands. template Type my_max(const CppAD::vector& arg) { Type res = arg[0]; for(size_t j = 0;j < arg.size(); j++) res = CondExpGt(res, arg[j], res, arg[j]); return res; } bool cond_exp_reverse(void) { bool ok = true; size_t n = 3; using CppAD::vector; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); vector< AD > ax(n), ay(1); for(size_t j = 0; j < n; j++) ax[j] = 1.0; Independent(ax); ay[0] = my_max(ax) + my_max(ax); CppAD::ADFun f(ax, ay); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); vector x(n), w(1), dx(n); for(size_t j = 0;j < n; j++) x[j] = double(j); f.Forward(0, x); w[0] = 1.0; dx = f.Reverse(1, w); for(size_t j = 0; j < n; j++) { if( j == n-1 ) ok &= NearEqual(dx[j], 2.0, eps10, eps10); else ok &= NearEqual(dx[j], 0.0, eps10, eps10); } return ok; } // Test case where an expression depends on both the true // and false cases (bug fixed 2014-12-22) bool cond_exp_both_true_and_false(void) { bool ok = true; using CppAD::vector; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); // f(x) = x[0] + x[0] if x[0] >= 3 // = x[0] + x[1] otherwise vector< AD > ax(2), ay(3); ax[0] = 1.0; ax[1] = 2.0; Independent(ax); AD three(3); AD value = ax[0] + ax[1]; // a simple value ay[0] = CppAD::CondExpGe(ax[0], three, value, value); // a binary exprpression ay[1] = CppAD::CondExpGe(ax[0], three, ax[0]-ax[1], ax[0]-ax[1]); // a unary expression ay[2] = CppAD::CondExpGe(ax[0], three, exp(ax[0]), exp(ax[0]) ); CppAD::ADFun f(ax, ay); if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); // check case where x[0] >= 3 vector x(2), y(3); x[0] = 4.0; x[1] = 2.0; y = f.Forward(0, x); ok &= NearEqual(y[0], x[0] + x[1], eps10, eps10); ok &= NearEqual(y[1], x[0] - x[1], eps10, eps10); ok &= NearEqual(y[2], exp(x[0]), eps10, eps10); // check case where x[0] < 3 x[0] = 1.0; x[1] = 2.0; y = f.Forward(0, x); ok &= NearEqual(y[0], x[0] + x[1], eps10, eps10); ok &= NearEqual(y[1], x[0] - x[1], eps10, eps10); ok &= NearEqual(y[2], exp(x[0]), eps10, eps10); return ok; } // Test case where a variable is removed during optimization // (bug fixed 2017-03-04) bool cond_exp_skip_remove_var(void) { bool ok = true; using CppAD::vector; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits::epsilon(); vector< AD > ax(2), ay(2); ax[0] = 1.0; ax[1] = 2.0; Independent(ax); // AD var_1 = ax[0] + ax[1]; AD var_2 = ax[0] + ax[1]; // gets removed during optimization AD var_3 = ax[0] + ax[1]; // gets removed during optimization AD var_4 = ax[0] - ax[1]; AD par_1 = 1.0; // // first conditional expression depends on var_1 // 6 * x_0 if x_0 + x_1 >= 1.0, 7 * x_1 otherwise ay[0] = CppAD::CondExpGe(var_1, par_1, 6.0 * ax[0], 7.0 * ax[1]); // // second conditional expression depends on var_4 // 8 * x_0 if x_0 - x_1 >= x_0 + x_1, 9 * x_1 otherwise ay[1] = CppAD::CondExpGe(var_4, par_1, 8.0 * ax[0], 9.0 * ax[1]); CppAD::ADFun f(ax, ay); // if( conditional_skip_ ) f.optimize(); else f.optimize("no_conditional_skip"); // check case where x[0] = 2, x[1] = 4 vector x(2), y(2); x[0] = 2.0; x[1] = 4.0; y = f.Forward(0, x); ok &= NearEqual(y[0], 6.0 * x[0], eps10, eps10); ok &= NearEqual(y[1], 9.0 * x[1], eps10, eps10); return ok; } } bool optimize(void) { bool ok = true; conditional_skip_ = true; atomic_sparsity_option_ = CppAD::atomic_base::bool_sparsity_enum; // optimize an example ODE ok &= optimize_ode(); // atomic sparsity loop for(size_t i = 0; i < 3; i++) { if( i == 0 ) atomic_sparsity_option_ = CppAD::atomic_base::pack_sparsity_enum; else if( i == 1 ) atomic_sparsity_option_ = CppAD::atomic_base::bool_sparsity_enum; else if( i == 2 ) atomic_sparsity_option_ = CppAD::atomic_base::set_sparsity_enum; else ok &= false; // // check conditional expression sparsity pattern // (used to optimize calls to atomic functions). ok &= atomic_cond_exp_sparsity(); // check optimizing out entire atomic function ok &= atomic_cond_exp(); // check optimizing out atomic arguments ok &= atomic_no_used(); ok &= atomic_arguments(); } // conditional skip loop for(size_t i = 0; i < 2; i++) { conditional_skip_ = i == 0; // // check nested conditional expressions ok &= nested_cond_exp(); // check reverse dependency analysis optimization ok &= depend_one(); ok &= depend_two(); ok &= depend_three(); ok &= depend_four(); // check removal of duplicate expressions ok &= duplicate_one(); ok &= duplicate_two(); ok &= duplicate_three(); ok &= duplicate_four(); // convert sequence of additions to cummulative summation ok &= cummulative_sum(); ok &= forward_csum(); ok &= reverse_csum(); // sparsity patterns ok &= forward_sparse_jacobian(); ok &= reverse_sparse_jacobian(); ok &= reverse_sparse_hessian(); // check that CondExp properly detects dependencies ok &= cond_exp_depend(); // check that it properly handles expressions that have been removed ok &= cond_exp_removed(); // check old_atomic functions ok &= old_atomic_test(); // case where results are not identically equal ok &= not_identically_equal(); // case where a discrete function is used ok &= discrete_function(); // check conditional skip of an atomic function ok &= cond_exp_skip_atomic(); // check conditional dependence through atomic function ok &= cond_exp_atomic_dependence(); // check reverse mode conditional skipping ok &= cond_exp_reverse(); // check case where an expresion needed by both true and false case ok &= cond_exp_both_true_and_false(); // check case were a variable in left or right expressions // is removed during the optimization ok &= cond_exp_skip_remove_var(); } // CppAD::user_atomic::clear(); return ok; } cppad-20170000.3/test_more/forward.cpp0000644000175200017650000001500713057470461016605 0ustar coincoin-web// $Id: forward.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old Forward example now used just for valiadation testing */ # include namespace { // Begin empty namespace template // vector class, elements of type double bool ForwardCases(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // independent variable vector CPPAD_TESTVECTOR(AD) X(2); X[0] = 0.; X[1] = 1.; Independent(X); // compute product of elements in X CPPAD_TESTVECTOR(AD) Y(1); Y[0] = X[0] * X[0] * X[1]; // create function object F : X -> Y ADFun F(X, Y); // use zero order to evaluate F[ (3, 4) ] VectorDouble x0( F.Domain() ); VectorDouble y0( F.Range() ); x0[0] = 3.; x0[1] = 4.; y0 = F.Forward(0, x0); ok &= NearEqual(y0[0] , x0[0]*x0[0]*x0[1], eps99, eps99); // evaluate derivative of F in X[0] direction VectorDouble x1( F.Domain() ); VectorDouble y1( F.Range() ); x1[0] = 1.; x1[1] = 0.; y1 = F.Forward(1, x1); ok &= NearEqual(y1[0] , 2.*x0[0]*x0[1], eps99, eps99); // evaluate second derivative of F in X[0] direction VectorDouble x2( F.Domain() ); VectorDouble y2( F.Range() ); x2[0] = 0.; x2[1] = 0.; y2 = F.Forward(2, x2); double F_00 = 2. * y2[0]; ok &= NearEqual(F_00, 2.*x0[1], eps99, eps99); // evalute derivative of F in X[1] direction x1[0] = 0.; x1[1] = 1.; y1 = F.Forward(1, x1); ok &= NearEqual(y1[0] , x0[0]*x0[0], eps99, eps99); // evaluate second derivative of F in X[1] direction y2 = F.Forward(2, x2); double F_11 = 2. * y2[0]; ok &= NearEqual(F_11, 0., eps99, eps99); // evalute derivative of F in X[0] + X[1] direction x1[0] = 1.; x1[1] = 1.; y1 = F.Forward(1, x1); ok &= NearEqual(y1[0], 2.*x0[0]*x0[1] + x0[0]*x0[0], eps99, eps99); // use second derivative of F in X[0] direction to // compute second partial of F w.r.t X[1] w.r.t X[2] y2 = F.Forward(2, x2); double F_01 = y2[0] - F_00 / 2. - F_11 / 2.; ok &= NearEqual(F_01 , 2.*x0[0], eps99, eps99); return ok; } bool ForwardOlder(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // independent variable vector CPPAD_TESTVECTOR(AD) U(3); U[0] = 0.; U[1] = 1.; U[2] = 2.; Independent(U); // compute sum and product of elements in U AD sum = 0.; AD prod = 1.; size_t i; for(i = 0; i < 3; i++) { sum += U[i]; prod *= U[i]; } // dependent variable vector CPPAD_TESTVECTOR(AD) V(2); V[0] = sum; V[1] = prod; // V = f(U) ADFun f(U, V); // use ADFun object to evaluate f[ (1, 2, 3)^T ] ----------------- CPPAD_TESTVECTOR(double) u0( f.Domain() ); CPPAD_TESTVECTOR(double) v0( f.Range() ); size_t p; p = 0; u0[0] = 1.; u0[1] = 2.; u0[2] = 3.; v0 = f.Forward(p, u0); // direct evaluation of f[ u0 ] CPPAD_TESTVECTOR(double) f0(2); f0[0] = u0[0] + u0[1] + u0[2]; f0[1] = u0[0] * u0[1] * u0[2]; // compare values ok &= NearEqual(v0[0] , f0[0], eps99, eps99); ok &= NearEqual(v0[1] , f0[1], eps99, eps99); // use ADFun object to evaluate f^(1) [ u0 ] * u1 ----------------- CPPAD_TESTVECTOR(double) u1( f.Domain() ); CPPAD_TESTVECTOR(double) v1( f.Range() ); p = 1; u1[0] = 1.; u1[1] = 1.; u1[2] = 1.; v1 = f.Forward(p, u1); // direct evaluation of gradients of components of f CPPAD_TESTVECTOR(double) g0(3), g1(3); g0[0] = 1.; g0[1] = 1.; g0[2] = 1.; g1[0] = u0[1]*u0[2]; g1[1] = u0[0]*u0[2]; g1[2] = u0[0]*u0[1]; // compare values ok &= NearEqual(v1[0] , g0[0]*u1[0] + g0[1]*u1[1] + g0[2]*u1[2] , 1e-10, 1e-10); ok &= NearEqual(v1[1] , g1[0]*u1[0] + g1[1]*u1[1] + g1[2]*u1[2] , 1e-10, 1e-10); // use ADFun object to evaluate ------------------------------------ // (1/2) * { f^(1)[ u0 ] * u2 + u1^T * f^(2)[ u0 ] * u1 } CPPAD_TESTVECTOR(double) u2( f.Domain() ); CPPAD_TESTVECTOR(double) v2( f.Range() ); p = 2; u2[0] = .5; u2[1] = .4; u2[2] = .3; v2 = f.Forward(p, u2); // direct evaluation of Hessian of second components of f // (the Hessian of the first component is zero) CPPAD_TESTVECTOR(double) H1(9); H1[0] = 0.; H1[1] = u0[2]; H1[2] = u0[1]; H1[3] = u0[2]; H1[4] = 0.; H1[5] = u0[0]; H1[6] = u0[1]; H1[7] = u0[0]; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // --------------------------------------------------------- template Vector eval_g(const Vector& x) { Vector g(2); g[0] = x[0] * x[1] * x[2] * x[3]; g[1] = x[0] * x[0] + x[1] * x[1] + x[2] * x[2] + x[3] * x[3]; return g; } template Vector eval_jac_g(const Vector& x) { Vector jac_g(8); // g[0] = x[0] * x[1] * x[2] * x[3]; jac_g[0] = x[1] * x[2] * x[3]; jac_g[1] = x[0] * x[2] * x[3]; jac_g[2] = x[0] * x[1] * x[3]; jac_g[3] = x[0] * x[1] * x[2]; // g[1] = x[0] * x[0] + x[1] * x[1] + x[2] * x[2] + x[3] * x[3]; jac_g[4+0] = 2. * x[0]; jac_g[4+1] = 2. * x[1]; jac_g[4+2] = 2. * x[2]; jac_g[4+3] = 2. * x[3]; return jac_g; } } // End empty namespace bool jacobian(void) { bool ok = true; using CppAD::vector; size_t i, j, k; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); size_t n = 4; size_t m = 2; vector< CppAD::AD > ad_x(n); vector< CppAD::AD > ad_g(m); vector x(n); x[0] = 1.; x[1] = 5.0; x[2] = 5.0; x[3] = 1.0; for(j = 0; j < n; j++) ad_x[j] = x[j]; // CppAD::Independent(ad_x); ad_g = eval_g(ad_x); CppAD::ADFun fun_g(ad_x, ad_g); vector check(m * n); check = eval_jac_g(x); // regular jacobian vector jac_g = fun_g.Jacobian(x); for(k = 0; k < m *n; k++) ok &= NearEqual(jac_g[k], check[k], eps99, eps99); // one argument sparse jacobian jac_g = fun_g.SparseJacobian(x); for(k = 0; k < m *n; k++) ok &= NearEqual(jac_g[k], check[k], eps99, eps99); // sparse jacobian using bool vectors CPPAD_TESTVECTOR(bool) p_b(m * n) , r_b(n * n); for(i = 0; i < n; i++) for(j = 0; j < n; j++) r_b[i * n + j] = (i == j); p_b = fun_g.ForSparseJac(n, r_b); jac_g = fun_g.SparseJacobian(x, p_b); for(k = 0; k < m *n; k++) ok &= NearEqual(jac_g[k], check[k], eps99, eps99); // sparse jacobian using vectors of sets std::vector< std::set > p_s(m) , r_s(n); for(i = 0; i < n; i++) for(j = 0; j < n; j++) r_s[i].insert(j); p_s = fun_g.ForSparseJac(n, r_s); jac_g = fun_g.SparseJacobian(x, p_s); for(k = 0; k < m *n; k++) ok &= NearEqual(jac_g[k], check[k], eps99, eps99); return ok; } // END PROGRAM cppad-20170000.3/test_more/track_new_del.cpp0000644000175200017650000000321713057470461017742 0ustar coincoin-web// $Id: track_new_del.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin TrackNewDel.cpp$$ $section Tracking Use of New and Delete: Example and Test$$ $mindex delete$$ $code $srcfile%test_more/track_new_del.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include bool track_new_del(void) { bool ok = true; // initial count size_t count = CPPAD_TRACK_COUNT(); // allocate an array of lenght 5 double *ptr = CPPAD_NULL; size_t newlen = 5; ptr = CPPAD_TRACK_NEW_VEC(newlen, ptr); // copy data into the array size_t ncopy = newlen; size_t i; for(i = 0; i < ncopy; i++) ptr[i] = double(i); // extend the buffer to be lenght 10 newlen = 10; ptr = CPPAD_TRACK_EXTEND(newlen, ncopy, ptr); // copy data into the new part of the array for(i = ncopy; i < newlen; i++) ptr[i] = double(i); // check the values in the array for(i = 0; i < newlen; i++) ok &= (ptr[i] == double(i)); // free the memory allocated since previous call to TrackCount CPPAD_TRACK_DEL_VEC(ptr); // check for memory leak ok &= (count == CPPAD_TRACK_COUNT()); return ok; } // END C++ cppad-20170000.3/test_more/sparse_hessian.cpp0000644000175200017650000001532713057470461020155 0ustar coincoin-web// $Id: sparse_hessian.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old SparseHessian example */ # include namespace { // --------------------------------------------------------- bool rc_tridiagonal(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j, k, ell; double eps10 = 10. * CppAD::epsilon(); size_t n = 12; // must be greater than or equal 3; see n_sweep. size_t m = n - 1; CPPAD_TESTVECTOR(AD) a_x(n), a_y(m); CPPAD_TESTVECTOR(double) x(n), check(n * n), w(m); for(j = 0; j < n; j++) a_x[j] = x[j] = double(j+1); // declare independent variables and start taping CppAD::Independent(a_x); for(ell = 0; ell < n * n; ell++) check[ell] = 0.0; for(i = 0; i < m; i++) { AD diff = a_x[i+1] - a_x[i]; a_y[i] = 0.5 * diff * diff / double(i+2); w[i] = double(i+1); ell = i * n + i; check[ell] += w[i] / double(i+2); ell = (i+1) * n + i+1; check[ell] += w[i] / double(i+2); ell = (i+1) * n + i; check[ell] -= w[i] / double(i+2); ell = i * n + i+1; check[ell] -= w[i] / double(i+2); } // create f: x -> y CppAD::ADFun f(a_x, a_y); // determine the sparsity pattern p for Hessian of w^T f typedef CppAD::vector< std::set > VectorSet; VectorSet p_r(n); for(j = 0; j < n; j++) p_r[j].insert(j); f.ForSparseJac(n, p_r); // VectorSet p_s(1); for(i = 0; i < m; i++) if( w[i] != 0 ) p_s[0].insert(i); VectorSet p_h = f.RevSparseHes(n, p_s); // requres the upper triangle of the Hessian size_t K = 2 * n - 1; CPPAD_TESTVECTOR(size_t) r(K), c(K); CPPAD_TESTVECTOR(double) hes(K); k = 0; for(i = 0; i < n; i++) { r[k] = i; c[k] = i; k++; if( i < n-1 ) { r[k] = i; c[k] = i+1; k++; } } ok &= k == K; // test computing sparse Hessian CppAD::sparse_hessian_work work; size_t n_sweep = f.SparseHessian(x, w, p_h, r, c, hes, work); ok &= n_sweep == 3; for(k = 0; k < K; k++) { ell = r[k] * n + c[k]; ok &= NearEqual(check[ell], hes[k], eps10, eps10); ell = c[k] * n + r[k]; ok &= NearEqual(check[ell], hes[k], eps10, eps10); } return ok; } template bool bool_case() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j, k; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) X(n); for(i = 0; i < n; i++) X[i] = AD (0); // declare independent variables and starting recording CppAD::Independent(X); size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] * X[0] + X[0] * X[1] + X[1] * X[1] + X[2] * X[2]; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); for(i = 0; i < n; i++) x[i] = double(i); // second derivative of y[1] VectorBase w(m); w[0] = 1.; VectorBase h( n * n ); h = f.SparseHessian(x, w); /* [ 2 1 0 ] h = [ 1 2 0 ] [ 0 0 2 ] */ VectorBase check(n * n); check[0] = 2.; check[1] = 1.; check[2] = 0.; check[3] = 1.; check[4] = 2.; check[5] = 0.; check[6] = 0.; check[7] = 0.; check[8] = 2.; for(k = 0; k < n * n; k++) ok &= NearEqual(check[k], h[k], 1e-10, 1e-10 ); // determine the sparsity pattern p for Hessian of w^T F VectorBool r(n * n); for(j = 0; j < n; j++) { for(k = 0; k < n; k++) r[j * n + k] = false; r[j * n + j] = true; } f.ForSparseJac(n, r); // VectorBool s(m); for(i = 0; i < m; i++) s[i] = w[i] != 0; VectorBool p = f.RevSparseHes(n, s); // test passing sparsity pattern h = f.SparseHessian(x, w, p); for(k = 0; k < n * n; k++) ok &= NearEqual(check[k], h[k], 1e-10, 1e-10 ); return ok; } template bool set_case() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j, k; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) X(n); for(i = 0; i < n; i++) X[i] = AD (0); // declare independent variables and starting recording CppAD::Independent(X); size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] * X[0] + X[0] * X[1] + X[1] * X[1] + X[2] * X[2]; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); for(i = 0; i < n; i++) x[i] = double(i); // second derivative of y[1] VectorBase w(m); w[0] = 1.; VectorBase h( n * n ); h = f.SparseHessian(x, w); /* [ 2 1 0 ] h = [ 1 2 0 ] [ 0 0 2 ] */ VectorBase check(n * n); check[0] = 2.; check[1] = 1.; check[2] = 0.; check[3] = 1.; check[4] = 2.; check[5] = 0.; check[6] = 0.; check[7] = 0.; check[8] = 2.; for(k = 0; k < n * n; k++) ok &= NearEqual(check[k], h[k], 1e-10, 1e-10 ); // determine the sparsity pattern p for Hessian of w^T F VectorSet r(n); for(j = 0; j < n; j++) r[j].insert(j); f.ForSparseJac(n, r); // VectorSet s(1); for(i = 0; i < m; i++) if( w[i] != 0 ) s[0].insert(i); VectorSet p = f.RevSparseHes(n, s); // test passing sparsity pattern h = f.SparseHessian(x, w, p); for(k = 0; k < n * n; k++) ok &= NearEqual(check[k], h[k], 1e-10, 1e-10 ); return ok; } } // End empty namespace # include # include bool sparse_hessian(void) { bool ok = true; ok &= rc_tridiagonal(); // --------------------------------------------------------------- // vector of bool cases ok &= bool_case< CppAD::vector , CppAD::vectorBool >(); ok &= bool_case< std::vector , CppAD::vector >(); ok &= bool_case< std::valarray , std::vector >(); // --------------------------------------------------------------- // vector of set cases typedef std::vector< std::set > std_vector_set; typedef CppAD::vector< std::set > cppad_vector_set; // ok &= set_case< CppAD::vector, std_vector_set >(); ok &= set_case< std::valarray, std_vector_set >(); ok &= set_case< std::vector, cppad_vector_set >(); ok &= set_case< CppAD::vector, cppad_vector_set >(); // // According to section 26.3.2.3 of the 1998 C++ standard // a const valarray does not return references to its elements. // so do not include it in the testing for sets. // --------------------------------------------------------------- return ok; } cppad-20170000.3/test_more/eigen_mat_inv.cpp0000644000175200017650000001433713057470461017752 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace { // BEGIN_EMPTY_NAMESPACE typedef double scalar; typedef CppAD::AD ad_scalar; typedef typename atomic_eigen_mat_inv::ad_matrix ad_matrix; scalar eps = 10. * std::numeric_limits::epsilon(); using CppAD::NearEqual; // -------------------------------------------------------------------------- /* Test atomic_eigen_mat_inv using a non-symetric matrix f(x) = [ x[0] -1 ]^{-1} [ 2 x[1] ] = [ x[1] 1 ] / (x[0] * x[1] + 2) [ -2 x[0] ] y[0] = x[1] / (x[0] * x[1] + 2) y[1] = 1.0 / (x[0] * x[1] + 2) y[2] = -2.0 / (x[0] * x[1] + 2) y[3] = x[0] / (x[0] * x[1] + 2) */ bool non_symmetric(void) { bool ok = true; // ------------------------------------------------------------------- // object that computes inverse of a 2x2 matrix atomic_eigen_mat_inv mat_inv; // ------------------------------------------------------------------- // declare independent variable vector x size_t n = 2; CPPAD_TESTVECTOR(ad_scalar) ad_x(n); for(size_t j = 0; j < n; j++) ad_x[j] = ad_scalar(j); CppAD::Independent(ad_x); // ------------------------------------------------------------------- // arg = [ x[0] -1 ] // [ 2 x[1] ] size_t nr = 2; ad_matrix ad_arg(nr, nr); ad_arg(0, 0) = ad_x[0]; ad_arg(0, 1) = ad_scalar(-1.0); ad_arg(1, 0) = ad_scalar(2.0); ad_arg(1, 1) = ad_x[1]; // ------------------------------------------------------------------- // use atomic operation to compute arg^{-1} ad_matrix ad_result = mat_inv.op(ad_arg); // ------------------------------------------------------------------- // declare the dependent variable vector y size_t m = 4; CPPAD_TESTVECTOR(ad_scalar) ad_y(4); for(size_t i = 0; i < nr; i++) for(size_t j = 0; j < nr; j++) ad_y[ i * nr + j ] = ad_result(i, j); /* Used to test hand calculated derivaives CppAD::AD ad_dinv = 1.0 / (ad_x[0] * ad_x[1] + 2.0); ad_y[0] = ad_x[1] * ad_dinv; ad_y[1] = 1.0 * ad_dinv; ad_y[2] = -2.0 * ad_dinv; ad_y[3] = ad_x[0] * ad_dinv; */ CppAD::ADFun f(ad_x, ad_y); // ------------------------------------------------------------------- // check zero order forward mode CPPAD_TESTVECTOR(scalar) x(n), y(m); for(size_t i = 0; i < n; i++) x[i] = scalar(i + 2); scalar dinv = 1.0 / (x[0] * x[1] + 2.0); y = f.Forward(0, x); ok &= NearEqual(y[0], x[1] * dinv, eps, eps); ok &= NearEqual(y[1], 1.0 * dinv, eps, eps); ok &= NearEqual(y[2], -2.0 * dinv, eps, eps); ok &= NearEqual(y[3], x[0] * dinv, eps, eps); // ------------------------------------------------------------------- // check first order forward mode CPPAD_TESTVECTOR(scalar) x1(n), y1(m); scalar dinv_x0 = - x[1] * dinv * dinv; x1[0] = 1.0; x1[1] = 0.0; y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], x[1] * dinv_x0, eps, eps); ok &= NearEqual(y1[1], 1.0 * dinv_x0, eps, eps); ok &= NearEqual(y1[2], -2.0 * dinv_x0, eps, eps); ok &= NearEqual(y1[3], dinv + x[0] * dinv_x0, eps, eps); // scalar dinv_x1 = - x[0] * dinv * dinv; x1[0] = 0.0; x1[1] = 1.0; y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], dinv + x[1] * dinv_x1, eps, eps); ok &= NearEqual(y1[1], 1.0 * dinv_x1, eps, eps); ok &= NearEqual(y1[2], -2.0 * dinv_x1, eps, eps); ok &= NearEqual(y1[3], x[0] * dinv_x1, eps, eps); // ------------------------------------------------------------------- // check second order forward mode CPPAD_TESTVECTOR(scalar) x2(n), y2(m); scalar dinv_x1_x1 = 2.0 * x[0] * x[0] * dinv * dinv * dinv; x2[0] = 0.0; x2[1] = 0.0; y2 = f.Forward(2, x2); ok &= NearEqual(2.0*y2[0], 2.0*dinv_x1 + x[1]*dinv_x1_x1, eps, eps); ok &= NearEqual(2.0*y2[1], 1.0 * dinv_x1_x1, eps, eps); ok &= NearEqual(2.0*y2[2], -2.0 * dinv_x1_x1, eps, eps); ok &= NearEqual(2.0*y2[3], x[0] * dinv_x1_x1, eps, eps); // ------------------------------------------------------------------- // check first order reverse CPPAD_TESTVECTOR(scalar) w(m), d1w(n); for(size_t i = 0; i < m; i++) w[i] = 0.0; w[0] = 1.0; d1w = f.Reverse(1, w); ok &= NearEqual(d1w[0], x[1] * dinv_x0, eps, eps); ok &= NearEqual(d1w[1], dinv + x[1] * dinv_x1, eps, eps); w[0] = 0.0; w[1] = 1.0; d1w = f.Reverse(1, w); ok &= NearEqual(d1w[0], 1.0 * dinv_x0, eps, eps); ok &= NearEqual(d1w[1], 1.0 * dinv_x1, eps, eps); w[1] = 0.0; w[2] = 1.0; d1w = f.Reverse(1, w); ok &= NearEqual(d1w[0], -2.0 * dinv_x0, eps, eps); ok &= NearEqual(d1w[1], -2.0 * dinv_x1, eps, eps); w[2] = 0.0; w[3] = 1.0; d1w = f.Reverse(1, w); ok &= NearEqual(d1w[0], dinv + x[0] * dinv_x0, eps, eps); ok &= NearEqual(d1w[1], x[0] * dinv_x1, eps, eps); // ------------------------------------------------------------------- // check second order reverse CPPAD_TESTVECTOR(scalar) d2w(2 * n); // dinv_x1 = - x[0] * dinv * dinv; scalar dinv_x1_x0 = 2.0 * x[0] * x[1] * dinv * dinv * dinv - dinv * dinv; d2w = f.Reverse(2, w); // partial f_3 w.r.t x_0 ok &= NearEqual(d2w[0 * 2 + 0], dinv + x[0] * dinv_x0, eps, eps); // partial f_3 w.r.t x_1 ok &= NearEqual(d2w[1 * 2 + 0], x[0] * dinv_x1, eps, eps); // partial f_3 w.r.t. x_1, x_0 ok &= NearEqual(d2w[0 * 2 + 1], dinv_x1 + x[0] * dinv_x1_x0, eps, eps); // partial f_3 w.r.t. x_1, x_1 ok &= NearEqual(d2w[1 * 2 + 1], x[0] * dinv_x1_x1, eps, eps); // ------------------------------------------------------------------- return ok; } } // END_EMPTY_NAMESPACE bool eigen_mat_inv(void) { bool ok = true; ok &= non_symmetric(); return ok; } cppad-20170000.3/test_more/for_hess.cpp0000644000175200017650000000630313057470461016750 0ustar coincoin-web// $Id: for_hess.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old ForHess example now used just for valiadation testing */ # include bool ForHess(void) { bool ok = true; using namespace CppAD; using CppAD::exp; using CppAD::sin; using CppAD::cos; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); size_t i; // create independent variable vector with assigned values CPPAD_TESTVECTOR(double) u0(3); CPPAD_TESTVECTOR(AD) U(3); for(i = 0; i < 3; i++) U[i] = u0[i] = double(i+1); Independent( U ); // define the function CPPAD_TESTVECTOR(AD) Y(2); Y[0] = U[0] * exp( U[1] ); Y[1] = U[1] * sin( U[2] ); // create the function y = F(u) ADFun F(U, Y); // formulas for the upper triangle of Hessian of F_0 CPPAD_TESTVECTOR(double) H0(9); H0[0] = 0.; // d^2 y[0] / d_u[0] d_u[0] H0[1] = exp( u0[1] ); // d^2 y[0] / d_u[0] d_u[1] H0[2] = 0.; // d^2 y[0] / d_u[0] d_u[2] H0[4] = u0[0] * exp( u0[1] ); // d^2 y[0] / d_u[1] d_u[1] H0[5] = 0.; // d^2 y[0] / d_u[1] d_u[2] H0[8] = 0.; // d^2 y[0] / d_u[2] d_u[2] // formulas for the upper triangle of Hessian of F_1 CPPAD_TESTVECTOR(double) H1(9); H1[0] = 0.; // d^2 Y[1] / d_U[0] d_U[0] H1[1] = 0.; // d^2 Y[1] / d_U[0] d_U[1] H1[2] = 0.; // d^2 Y[1] / d_U[0] d_U[2] H1[4] = 0.; // d^2 Y[1] / d_U[1] d_U[1] H1[5] = cos( u0[2] ); // d^2 Y[1] / d_U[1] d_U[2] H1[8] = - u0[1] * sin( u0[2] );// d^2 Y[1] / d_U[2] d_U[2] // Define U(t) = u0 + u1 t + u2 t^2 / 2 CPPAD_TESTVECTOR(double) u1(3); CPPAD_TESTVECTOR(double) u2(3); for(i = 0; i < 3; i++) u1[i] = u2[i] = 0.; size_t j; for(i = 0; i < 3; i++) { // diagonal of Hessians in i-th coordiante direction u1[i] = 1.; F.Forward(1, u1); CPPAD_TESTVECTOR(double) Di = F.Forward(2, u2); ok &= NearEqual( 2. * Di[0] , H0[ i + 3 * i], eps99, eps99); ok &= NearEqual( 2. * Di[1] , H1[ i + 3 * i], eps99, eps99); // for(j = i+1; j < 3; j++) { // cross term in i and j direction u1[j] = 1.; F.Forward(1, u1); CPPAD_TESTVECTOR(double) Cij = F.Forward(2, u2); // diagonal of Hessian in j-th coordinate direction u1[i] = 0.; F.Forward(1, u1); CPPAD_TESTVECTOR(double) Dj = F.Forward(2, u2); // (i, j) elements of the Hessians double H0ij = Cij[0] - Di[0] - Dj[0]; ok &= NearEqual( H0ij, H0[j + 3 * i], eps99, eps99); double H1ij = Cij[1] - Di[1] - Dj[1]; ok &= NearEqual( H1ij, H1[j + 3 * i], eps99, eps99); // reset all components of u1 to zero u1[j] = 0.; } } return ok; } cppad-20170000.3/test_more/cond_exp_rev.cpp0000644000175200017650000000673213057470461017621 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // Test that reverse mode handles conditional expressions properly // in that infinity and nans do not propagate thouh un-used case. # include bool cond_exp_rev(void) { bool ok = true; using CppAD::vector; using CppAD::AD; AD anan = std::numeric_limits::quiet_NaN(); AD azero = 0.0; size_t n = 2; vector< AD > ax(n), ay; ax[0] = 1.0; ax[1] = anan; Independent(ax); // AbsOp ay.push_back( CondExpGt(ax[0], azero, ax[0], abs(ax[1]) )); // AcosOp ay.push_back( CondExpGt(ax[0], azero, ax[0], acos(ax[1]) )); // AddvvOp ay.push_back( CondExpGt(ax[0], azero, ax[0], ax[0] + ax[1] )); // AddpvOp ay.push_back( CondExpGt(ax[0], azero, ax[0], 1.0 + ax[1] )); // AsinOp ay.push_back( CondExpGt(ax[0], azero, ax[0], asin(ax[1]) )); // AtanOp ay.push_back( CondExpGt(ax[0], azero, ax[0], atan(ax[1]) )); // CosOp ay.push_back( CondExpGt(ax[0], azero, ax[0], cos(ax[1]) )); // CoshOp ay.push_back( CondExpGt(ax[0], azero, ax[0], cosh(ax[1]) )); // DivvvOp ay.push_back( CondExpGt(ax[0], azero, ax[0], ax[0] / ax[1] )); // DivpvOp ay.push_back( CondExpGt(ax[0], azero, ax[0], 1.0 / ax[1] )); // DivvpOp ay.push_back( CondExpGt(ax[0], azero, ax[0], ax[1] / 2.0 )); // ErfOp ay.push_back( CondExpGt(ax[0], azero, ax[0], erf(ax[1]) )); // ExpOp ay.push_back( CondExpGt(ax[0], azero, ax[0], exp(ax[1]) )); // LogOp ay.push_back( CondExpGt(ax[0], azero, ax[0], log(ax[1]) )); // MulvvOp ay.push_back( CondExpGt(ax[0], azero, ax[0], ax[0] * ax[1] )); // MulpvOp ay.push_back( CondExpGt(ax[0], azero, ax[0], 2.0 * ax[1] )); // PowvvOP // uses check in log, mul, and exp ay.push_back( CondExpGt(ax[0], azero, ax[0], pow(ax[1], ax[1]) )); // PowvpOP // uses check in log, mul, and exp ay.push_back( CondExpGt(ax[0], azero, ax[0], pow(ax[1], 2.0) )); // PowpvOP // uses check in log, mul, and exp ay.push_back( CondExpGt(ax[0], azero, ax[0], pow(2.0, ax[1]) )); // SignOp ay.push_back( CondExpGt(ax[0], azero, ax[0], sign(ax[1]) )); // SinOp ay.push_back( CondExpGt(ax[0], azero, ax[0], sin(ax[1]) )); // SinhOp ay.push_back( CondExpGt(ax[0], azero, ax[0], sinh(ax[1]) )); // SqrtOp ay.push_back( CondExpGt(ax[0], azero, ax[0], sqrt(ax[1]) )); // SubvvOp ay.push_back( CondExpGt(ax[0], azero, ax[0], ax[0] - ax[1] )); // SubpvOp ay.push_back( CondExpGt(ax[0], azero, ax[0], 1.0 - ax[1] )); // SubvpOp ay.push_back( CondExpGt(ax[0], azero, ax[0], ax[1] - 1.0 )); // TanOp ay.push_back( CondExpGt(ax[0], azero, ax[0], tan(ax[1]) )); // TanhOp ay.push_back( CondExpGt(ax[0], azero, ax[0], tanh(ax[1]) )); // create f : x -> y size_t m = ay.size(); CppAD::ADFun f(ax, ay); // weighting vector and reverse mode derivative vector w(m), dw(n); for(size_t i = 0; i < m; i++) w[i] = 0.0; // check DivvOp for(size_t i = 0; i < m; i++) { w[i] = 1.0; dw = f.Reverse(1, w); ok &= dw[0] == 1.0; ok &= dw[1] == 0.0; w[i] = 0.0; } return ok; } cppad-20170000.3/test_more/asinh.cpp0000644000175200017650000000374313057470461016247 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include bool asinh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // a temporary value AD sinh_of_x0 = CppAD::sinh(ax[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CppAD::asinh(sinh_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // check value ok &= NearEqual(ay[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // forward computation of higher order partials w.r.t. x[0] size_t n_order = 5; for(size_t order = 2; order < n_order; order++) { dx[0] = 0.; dy = f.Forward(order, dx); ok &= NearEqual(dy[0], 0., eps, eps); } // reverse computation of derivatives CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n_order * n); w[0] = 1.; dw = f.Reverse(n_order, w); ok &= NearEqual(dw[0], 1., eps, eps); for(size_t order = 1; order < n_order; order++) ok &= NearEqual(dw[order * n + 0], 0., eps, eps); return ok; } // END C++ cppad-20170000.3/test_more/simple_vector.cpp0000644000175200017650000000575713057470461020027 0ustar coincoin-web// $Id: simple_vector.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old simple vector example now used just for validation testing */ // BEGIN C++ // need this to define size_t # include // # include // # define MySimpleVector std::vector // # include // # define MySimpleVector std::valarray // Assuming CppAD (http://www.seanet.com/~bradbell/cppad) is installed # include # define MySimpleVector CppAD::vector // Assuming Boost (http://www.boost.org) is installed // # include // # define MySimpleVector boost::numeric::ublas::vector // A special type of element that counts assignment operations class MyInt { public: // constructors MyInt(void) : count(0), value(0) { } MyInt(int _value) : count(0), value(_value) { } // assignment operator MyInt& operator=(const MyInt &x) { value = x.value; count++; return *this; } // equality operator bool operator==(const MyInt &x) const { return value == x.value; } int Value(void) const { return value; } size_t Count(void) const { return count; } private: size_t count; // count number of assignments int value; // value of this object }; // Test of a Simple Vector template class bool SimpleVector(void) { bool ok = true; typedef MySimpleVector vector; // class we are testing typedef vector::value_type myInt; // type of elements vector x; // default constructor ok &= (x.size() == 0); x.resize(2); // resize and set element assignment ok &= (x.size() == 2); x[0] = myInt(0); x[1] = myInt(1); vector y(2); // sizing constructor ok &= (y.size() == 2); const vector z(x); // copy constructor and const element access ok &= (z.size() == 2); ok &= ( (z[0] == myInt(0)) && (z[1] == myInt(1)) ); // check that vector assignment x[0] = 2; // modify so that assignment changes x size_t x0count = x[0].Count(); // store initial counts size_t y1count = y[1].Count(); size_t z0count = z[0].Count(); x = y = z; // vector assignment // check resulting values ok &= ( (x[0] == myInt(0)) && (x[1] == myInt(1)) ); ok &= ( (y[0] == myInt(0)) && (y[1] == myInt(1)) ); ok &= ( (z[0] == myInt(0)) && (z[1] == myInt(1)) ); // check that MyInt assignment was called (not raw memory copy) ok &= (x[0].Count() == x0count + 1); ok &= (y[1].Count() == y1count + 1); ok &= (z[0].Count() == z0count); return ok; } // END C++ cppad-20170000.3/test_more/atomic_sparsity.cpp0000644000175200017650000001627613057470461020364 0ustar coincoin-web/* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Atomic function g( x ) = [ x_2, x_0 * x_1 ] f(u) = g( u_0 + u_1, u_0 + u_1, u_2 ) \] $$ */ # include namespace { // isolate items below to this file using CppAD::vector; // vector typedef vector< std::set > set_vector; // atomic_sparsity // // a utility to compute the union of two sets. using CppAD::set_union; // class atomic_set_sparsity : public CppAD::atomic_base { public: // constructor atomic_set_sparsity(const std::string& name) : // this exampel only uses set sparsity patterns CppAD::atomic_base(name, set_sparsity_enum ) { } private: // forward virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { size_t n = tx.size() / (q + 1); # ifndef NDEBUG size_t m = ty.size() / (q + 1); # endif assert( n == 3 ); assert( m == 2 ); // only order zero bool ok = q == 0; if( ! ok ) return ok; // check for defining variable information if( vx.size() > 0 ) { ok &= vx.size() == n; vy[0] = vx[2]; vy[1] = vx[0] || vx[1]; } // Order zero forward mode. // y[0] = x[2], y[1] = x[0] * x[1] if( p <= 0 ) { ty[0] = tx[2]; ty[1] = tx[0] * tx[1]; } return ok; } // for_sparse_jac virtual bool for_sparse_jac( size_t p , const set_vector& r , set_vector& s , const vector& x ) { // This function needed if using f.ForSparseJac # ifndef NDEBUG size_t n = r.size(); size_t m = s.size(); # endif assert( n == x.size() ); assert( n == 3 ); assert( m == 2 ); // sparsity for S(x) = f'(x) * R = [ 0, 0, 1 ] * R s[0] = r[2]; // s[1] = union(r[0], r[1]) s[1] = set_union(r[0], r[1]); // return true; } virtual bool rev_sparse_jac( size_t p , const set_vector& rt , set_vector& st , const vector& x ) { // This function needed if using RevSparseJac or optimize # ifndef NDEBUG size_t n = st.size(); size_t m = rt.size(); # endif assert( n == x.size() ); assert( n == 3 ); assert( m == 2 ); // [ 0, x1 ] // sparsity for S(x)^T = f'(x)^T * R^T = [ 0, x0 ] * R^T // [ 1, 0 ] st[0] = rt[1]; st[1] = rt[1]; st[2] = rt[0]; return true; } virtual bool for_sparse_hes( const vector& vx, const vector& r , const vector& s , set_vector& h , const vector& x ) { size_t n = r.size(); # ifndef NDEBUG size_t m = s.size(); # endif assert( x.size() == n ); assert( h.size() == n ); assert( n == 3 ); assert( m == 2 ); // initialize h as empty for(size_t i = 0; i < n; i++) h[i].clear(); // only f_1 has a non-zero hessian if( ! s[1] ) return true; // only the cross term between x[0] and x[1] is non-zero if( ! ( r[0] & r[1] ) ) return true; // set the possibly non-zero terms in the hessian h[0].insert(1); h[1].insert(0); return true; } virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t p , const set_vector& r , const set_vector& u , set_vector& v , const vector& x ) { // This function needed if using RevSparseHes # ifndef NDEBUG size_t m = s.size(); size_t n = t.size(); # endif assert( x.size() == n ); assert( r.size() == n ); assert( u.size() == m ); assert( v.size() == n ); assert( n == 3 ); assert( m == 2 ); // sparsity for T(x) = S(x) * f'(x) = S(x) * [ 0, 0, 1 ] // [ x1, x0, 0 ] t[0] = s[1]; t[1] = s[1]; t[2] = s[0]; // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // [ 0, x1 ] // sparsity for W(x) = f'(x)^T * U(x) = [ 0, x0 ] * U(x) // [ 1, 0 ] v[0] = u[1]; v[1] = u[1]; v[2] = u[0]; // // [ 0, 1, 0 ] // sparsity for V(x) = W(x) + S_1 (x) * [ 1, 0, 0 ] * R // [ 0, 0, 0 ] if( s[1] ) { // v[0] = union( v[0], r[1] ) v[0] = set_union(v[0], r[1]); // v[1] = union( v[1], r[0] ) v[1] = set_union(v[1], r[0]); } return true; } }; // End of atomic_set_sparsity class } // End empty namespace bool atomic_sparsity(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // Create the atomic get_started object atomic_set_sparsity afun("atomic_set_sparsity"); size_t n = 3; size_t m = 2; vector< AD > au(n), ay(m); for(size_t j = 0; j < n; j++) au[j] = double(j + 1); // declare independent variables and start tape recording CppAD::Independent(au); // ax vector< AD > ax(n); ax[0] = au[0] + au[1]; ax[1] = au[0] + au[1]; ax[2] = au[2]; // call user function afun(ax, ay); // create f: u -> y and stop tape recording CppAD::ADFun f(au, ay); // check function value ok &= NearEqual(ay[0] , au[2], eps, eps); ok &= NearEqual(ay[1] , (au[0] + au[1]) * (au[0] + au[1]), eps, eps); // correct Jacobian result set_vector check_s(m); check_s[0].insert(2); check_s[1].insert(0); check_s[1].insert(1); // compute and test forward mode { set_vector r(n), s(m); for(size_t i = 0; i < n; i++) r[i].insert(i); s = f.ForSparseJac(n, r); for(size_t i = 0; i < m; i++) ok &= s[i] == check_s[i]; } // compute and test reverse mode { set_vector r(m), s(m); for(size_t i = 0; i < m; i++) r[i].insert(i); s = f.RevSparseJac(m, r); for(size_t i = 0; i < m; i++) ok &= s[i] == check_s[i]; } // correct Hessian result set_vector check_h(n); check_h[0].insert(0); check_h[0].insert(1); check_h[1].insert(0); check_h[1].insert(1); // compute and test forward mode { set_vector r(1), s(1), h(n); for(size_t i = 0; i < m; i++) s[0].insert(i); for(size_t j = 0; j < n; j++) r[0].insert(j); h = f.ForSparseHes(r, s); for(size_t i = 0; i < n; i++) ok &= h[i] == check_h[i]; } // compute and test reverse mode { set_vector s(1), h(n); for(size_t i = 0; i < m; i++) s[0].insert(i); h = f.RevSparseHes(n, s); for(size_t i = 0; i < n; i++) ok &= h[i] == check_h[i]; } return ok; } cppad-20170000.3/test_more/base_adolc.cpp0000644000175200017650000000646513057470461017225 0ustar coincoin-web// $Id: base_adolc.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include // adouble definitions not in Adolc distribution and // required in order to use CppAD::AD # include # include bool base_adolc(void) { bool ok = true; // initialize test result typedef adouble ADdouble; // for first level of taping typedef CppAD::AD ADDdouble; // for second level of taping size_t n = 4; // number independent variables CPPAD_TESTVECTOR(ADdouble) a_x(n); CPPAD_TESTVECTOR(ADDdouble) aa_x(n); // value of the independent variables int tag = 0; // Adolc setup int keep = 1; trace_on(tag, keep); size_t j; for(j = 0; j < n; j++) a_x[j] <<= double(n - j); // a_x is independent for ADdouble for(j = 0; j < n; j++) aa_x[j] = a_x[j]; // track how aa_x depends on a_x CppAD::Independent(aa_x); // aa_x is independent for ADDdouble // compute function size_t m = 5; CPPAD_TESTVECTOR(ADDdouble) aa_f(m); // dependent variables // different cases of conditional expressions aa_f[0] = CondExpLt(aa_x[0], aa_x[1], aa_x[2], aa_x[3]); aa_f[1] = CondExpLe(aa_x[0], aa_x[1], aa_x[2], aa_x[3]); aa_f[2] = CondExpEq(aa_x[0], aa_x[1], aa_x[2], aa_x[3]); aa_f[3] = CondExpGe(aa_x[0], aa_x[1], aa_x[2], aa_x[3]); aa_f[4] = CondExpGt(aa_x[0], aa_x[1], aa_x[2], aa_x[3]); // declare inner function (just to stop inner taping) CppAD::ADFun a_F(aa_x, aa_f); // set values for outer function same as inner function // (corresponding to the tape of adobule operations) double f_j; for(j = 0; j < m; j++) Value(aa_f[j]) >>= f_j; trace_off(); // arrays for Adolc zos_forward double *x = CPPAD_NULL, *y = CPPAD_NULL; x = CPPAD_TRACK_NEW_VEC(n, x); y = CPPAD_TRACK_NEW_VEC(m, y); // switch order of arguments from when taping was done for(j = 0; j < n; j++) x[j] = double(j); zos_forward(tag, int(m), int(n), keep, x, y); // CondExpLt(0, 1, 2, 3) ok &= (y[0] == double(2)); // CondExpLe(0, 1, 2, 3) ok &= (y[1] == double(2)); // CondExpEq(0, 1, 2, 3) ok &= (y[2] == double(3)); // CondExpGe(0, 1, 2, 3) ok &= (y[3] == double(3)); // CondExpGt(0, 1, 2, 3) ok &= (y[4] == double(3)); // set left = right and true < false x[0] = x[1] = 1.; x[2] = 2.; x[3] = 3.; zos_forward(tag, int(m), int(n), keep, x, y); // CondExpLt(1, 1, 2, 3) ok &= (y[0] == double(3)); // CondExpLe(1, 1, 2, 3) ok &= (y[1] == double(2)); // CondExpEq(1, 1, 2, 3) ok &= (y[2] == double(2)); // CondExpGe(1, 1, 2, 3) ok &= (y[3] == double(2)); // CondExpGt(1, 1, 2, 3) ok &= (y[4] == double(3)); CPPAD_TRACK_DEL_VEC(x); CPPAD_TRACK_DEL_VEC(y); return ok; } // END PROGRAM cppad-20170000.3/test_more/old_usead_1.cpp0000644000175200017650000002442613057470461017325 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin old_usead_1.cpp$$ $spell checkpoint var $$ $section Using AD to Compute Atomic Function Derivatives$$ $mindex inside user checkpoint$$ $head Deprecated 2013-05-27$$ This example has been deprecated because it is easier to use the $cref checkpoint$$ class instead. $head Purpose$$ Consider the case where an inner function is used repeatedly in the definition of an outer function. In this case, it may reduce the number of variables $cref/size_var/seq_property/size_var/$$, and hence the required memory. $head Simple Case$$ This example is the same as $cref old_reciprocal.cpp$$, except that it uses AD to compute the derivatives needed by an atomic function. This is a simple example of an inner function, and hence not really useful for the purpose above; see $cref old_usead_2.cpp$$ for a more complete example. $code $srcfile%test_more/old_usead_1.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // Begin empty namespace using CppAD::AD; using CppAD::ADFun; using CppAD::vector; // ---------------------------------------------------------------------- // function that computes reciprocal ADFun* r_ptr_; void create_r(void) { vector< AD > ax(1), ay(1); ax[0] = 1; CppAD::Independent(ax); ay[0] = 1.0 / ax[0]; r_ptr_ = new ADFun(ax, ay); } void destroy_r(void) { delete r_ptr_; r_ptr_ = CPPAD_NULL; } // ---------------------------------------------------------------------- // forward mode routine called by CppAD bool reciprocal_forward( size_t id , size_t k , size_t n , size_t m , const vector& vx , vector& vy , const vector& tx , vector& ty ) { assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); assert( k == 0 || vx.size() == 0 ); bool ok = true; vector x_q(1), y_q(1); // check for special case if( vx.size() > 0 ) vy[0] = vx[0]; // make sure r_ has proper lower order Taylor coefficients stored // then compute ty[k] for(size_t q = 0; q <= k; q++) { x_q[0] = tx[q]; y_q = r_ptr_->Forward(q, x_q); if( q == k ) ty[k] = y_q[0]; assert( q == k || ty[q] == y_q[0] ); } return ok; } // ---------------------------------------------------------------------- // reverse mode routine called by CppAD bool reciprocal_reverse( size_t id , size_t k , size_t n , size_t m , const vector& tx , const vector& ty , vector& px , const vector& py ) { assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); bool ok = true; vector x_q(1), w(k+1), dw(k+1); // make sure r_ has proper forward mode coefficients size_t q; for(q = 0; q <= k; q++) { x_q[0] = tx[q]; # ifdef NDEBUG r_ptr_->Forward(q, x_q); # else vector y_q(1); y_q = r_ptr_->Forward(q, x_q); assert( ty[q] == y_q[0] ); # endif } for(q = 0; q <=k; q++) w[q] = py[q]; dw = r_ptr_->Reverse(k+1, w); for(q = 0; q <=k; q++) px[q] = dw[q]; return ok; } // ---------------------------------------------------------------------- // forward Jacobian sparsity routine called by CppAD bool reciprocal_for_jac_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , vector< std::set >& s ) { assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); bool ok = true; vector< std::set > R(1), S(1); R[0] = r[0]; S = r_ptr_->ForSparseJac(p, R); s[0] = S[0]; return ok; } // ---------------------------------------------------------------------- // reverse Jacobian sparsity routine called by CppAD bool reciprocal_rev_jac_sparse( size_t id , size_t n , size_t m , size_t p , vector< std::set >& r , const vector< std::set >& s ) { assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); bool ok = true; vector< std::set > R(p), S(p); size_t q; for(q = 0; q < p; q++) S[q] = s[q]; R = r_ptr_->RevSparseJac(p, S); for(q = 0; q < p; q++) r[q] = R[q]; return ok; } // ---------------------------------------------------------------------- // reverse Hessian sparsity routine called by CppAD bool reciprocal_rev_hes_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , const vector& s , vector& t , const vector< std::set >& u , vector< std::set >& v ) { // Can just return false if not use RevSparseHes. assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); bool ok = true; // compute sparsity pattern for T(x) = S(x) * f'(x) vector T(1), S(1); S[0] = s[0]; T = r_ptr_->RevSparseJac(1, S); t[0] = T[0]; // compute sparsity pattern for A(x) = U(x)^T * f'(x) vector Ut(p), A(p); size_t q; for(q = 0; q < p; q++) Ut[q] = false; std::set::iterator itr; for(itr = u[0].begin(); itr != u[0].end(); itr++) Ut[*itr] = true; A = r_ptr_-> RevSparseJac(p, Ut); // compute sparsity pattern for H(x) = R^T * (S * F)''(x) vector H(p), R(n); for(q = 0; q < p; q++) R[q] = false; for(itr = r[0].begin(); itr != r[0].end(); itr++) R[*itr] = true; r_ptr_->ForSparseJac(p, R); H = r_ptr_->RevSparseHes(p, S); // compute sparsity pattern for V(x) = A(x)^T + H(x)^T v[0].clear(); for(q = 0; q < p; q++) if( A[q] | H[q] ) v[0].insert(q); return ok; } // --------------------------------------------------------------------- // Declare the AD routine reciprocal(id, ax, ay) CPPAD_USER_ATOMIC( reciprocal , CppAD::vector , double , reciprocal_forward , reciprocal_reverse , reciprocal_for_jac_sparse , reciprocal_rev_jac_sparse , reciprocal_rev_hes_sparse ) } // End empty namespace bool old_usead_1(void) { bool ok = true; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // -------------------------------------------------------------------- // Create the ADFun r_ create_r(); // -------------------------------------------------------------------- // Create the function f(x) // // domain space vector size_t n = 1; double x0 = 0.5; vector< AD > ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; vector< AD > ay(m); // call user function and store reciprocal(x) in au[0] vector< AD > au(m); size_t id = 0; // not used reciprocal(id, ax, au); // u = 1 / x // call user function and store reciprocal(u) in ay[0] reciprocal(id, au, ay); // y = 1 / u = x // create f: x -> y and stop tape recording ADFun f; f.Dependent(ax, ay); // f(x) = x // -------------------------------------------------------------------- // Check function value results // // check function value double check = x0; ok &= NearEqual( Value(ay[0]) , check, eps, eps); // check zero order forward mode size_t q; vector x_q(n), y_q(m); q = 0; x_q[0] = x0; y_q = f.Forward(q, x_q); ok &= NearEqual(y_q[0] , check, eps, eps); // check first order forward mode q = 1; x_q[0] = 1; y_q = f.Forward(q, x_q); check = 1.; ok &= NearEqual(y_q[0] , check, eps, eps); // check second order forward mode q = 2; x_q[0] = 0; y_q = f.Forward(q, x_q); check = 0.; ok &= NearEqual(y_q[0] , check, eps, eps); // -------------------------------------------------------------------- // Check reverse mode results // // third order reverse mode q = 3; vector w(m), dw(n * q); w[0] = 1.; dw = f.Reverse(q, w); check = 1.; ok &= NearEqual(dw[0] , check, eps, eps); check = 0.; ok &= NearEqual(dw[1] , check, eps, eps); ok &= NearEqual(dw[2] , check, eps, eps); // -------------------------------------------------------------------- // forward mode sparstiy pattern size_t p = n; CppAD::vectorBool r1(n * p), s1(m * p); r1[0] = true; // compute sparsity pattern for x[0] s1 = f.ForSparseJac(p, r1); ok &= s1[0] == true; // f[0] depends on x[0] // -------------------------------------------------------------------- // reverse mode sparstiy pattern q = m; CppAD::vectorBool s2(q * m), r2(q * n); s2[0] = true; // compute sparsity pattern for f[0] r2 = f.RevSparseJac(q, s2); ok &= r2[0] == true; // f[0] depends on x[0] // -------------------------------------------------------------------- // Hessian sparsity (using previous ForSparseJac call) CppAD::vectorBool s3(m), h(p * n); s3[0] = true; // compute sparsity pattern for f[0] h = f.RevSparseJac(p, s3); ok &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero // ----------------------------------------------------------------- // Free all memory associated with the object r_ptr destroy_r(); // ----------------------------------------------------------------- // Free all temporary work space associated with old_atomic objects. // (If there are future calls to user atomic functions, they will // create new temporary work space.) CppAD::user_atomic::clear(); return ok; } // END C++ cppad-20170000.3/test_more/ipopt_solve.cpp0000644000175200017650000000715513057470461017511 0ustar coincoin-web// $Id: ipopt_solve.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Testing ipopt::solve */ # ifdef CPPAD_IPOPT_TEST # include namespace { using CppAD::AD; class FG_eval { public: typedef CPPAD_TESTVECTOR( AD ) ADvector; void operator()(ADvector& fg, const ADvector& x) { assert( fg.size() == 3 ); assert( x.size() == 4 ); // Fortran style indexing AD x1 = x[0]; AD x2 = x[1]; AD x3 = x[2]; AD x4 = x[3]; // f(x) fg[0] = x1 * x4 * (x1 + x2 + x3) + x3; // g_1 (x) fg[1] = x1 * x2 * x3 * x4; // g_2 (x) fg[2] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4; // return; } }; } bool ipopt_solve(void) { bool ok = true; size_t i, j; typedef CPPAD_TESTVECTOR( double ) Dvector; // number of independent variables (domain dimension for f and g) size_t nx = 4; // number of constraints (range dimension for g) size_t ng = 2; // initial value of the independent variables Dvector xi(nx); xi[0] = 1.0; xi[1] = 5.0; xi[2] = 5.0; xi[3] = 1.0; // lower and upper limits for x Dvector xl(nx), xu(nx); for(j = 0; j < nx; j++) { xl[j] = 1.0; xu[j] = 5.0; } // lower and upper limits for g Dvector gl(ng), gu(ng); gl[0] = 25.0; gu[0] = 1.0e19; gl[1] = 40.0; gu[1] = 40.0; // object that computes objective and constraints FG_eval fg_eval; // options std::string base_options; // turn off any printing base_options += "Integer print_level 0\n"; base_options += "String sb yes\n"; // maximum number of iterations base_options += "Integer max_iter 10\n"; // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) base_options += "Numeric tol 1e-6\n"; // derivative testing base_options += "String derivative_test second-order\n"; // maximum amount of random pertubation; e.g., // when evaluation finite diff base_options += "Numeric point_perturbation_radius 0.\n"; // place to return solution CppAD::ipopt::solve_result solution; // solution values and tolerances double check_x[] = { 1.000000, 4.743000, 3.82115, 1.379408 }; double check_zl[] = { 1.087871, 0., 0., 0. }; double check_zu[] = { 0., 0., 0., 0. }; double rel_tol = 1e-6; // relative tolerance double abs_tol = 1e-6; // absolute tolerance for(i = 0; i < 3; i++) { std::string options( base_options ); if( i == 1 ) options += "Sparse true forward\n"; if( i == 2 ) options += "Sparse true reverse\n"; // solve the problem CppAD::ipopt::solve( options, xi, xl, xu, gl, gu, fg_eval, solution ); ok &= solution.status==CppAD::ipopt::solve_result::success; // // Check some of the solution values for(j = 0; j < nx; j++) { ok &= CppAD::NearEqual( check_x[j], solution.x[j], rel_tol, abs_tol ); ok &= CppAD::NearEqual( check_zl[j], solution.zl[j], rel_tol, abs_tol ); ok &= CppAD::NearEqual( check_zu[j], solution.zu[j], rel_tol, abs_tol ); } } return ok; } # endif cppad-20170000.3/test_more/pow_int.cpp0000644000175200017650000000340213057470461016614 0ustar coincoin-web// $Id: pow_int.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example now just used for validation testing. */ # include bool PowInt(void) { bool ok = true; using CppAD::pow; using CppAD::exp; using CppAD::log; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(1); U[0] = 2.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(2); // dependent variable values Z[0] = pow(U[0], 5); // x = u^5 Z[1] = pow(U[0], -5); // y = u^{-5} // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); /* x_u = 5 * u^4 y_u = - 5 * u^{-6} */ // check function values values double u = Value(U[0]); ok &= NearEqual(Z[0] , exp( log(u) * 5.), 1e-10 , 1e-10); ok &= NearEqual(Z[1] , exp( - log(u) * 5.), 1e-10 , 1e-10); // forward computation of partials v[0] = 1.; w = f.Forward(1, v); ok &= NearEqual(w[0] , 5. * exp( log(u) * 4.), 1e-10 , 1e-10); ok &= NearEqual(w[1] , - 5. * exp( - log(u) * 6.), 1e-10 , 1e-10); return ok; } cppad-20170000.3/test_more/num_limits.cpp0000644000175200017650000001372513057470461017326 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* old num_limits.cpp example / test $spell $$ $section Numeric Limits: Example and Test$$ $index limits$$ $index example, limits$$ $index test, limits$$ $head Assumption$$ This code assumes that the decimal point is infront of the mantissa. Hence dividing the minimum normalized value looses precision, while multiplying the maximum normalized value results in infinity. $head Externals$$ This example using external routines to get and set values so that the complier does not set the correspdong code and optimize it out. $code old verbatim%example/num_limits.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # ifdef _MSC_VER // Supress Microsoft compiler warning about possible loss of precision, // in the constructors (when converting to std::complex) // Type one = 1 // Type two = 2 // 1 and 2 are small enough so no loss of precision when converting to float. # pragma warning(disable:4244) # endif # include # include # include "extern_value.hpp" namespace { using CppAD::vector; using CppAD::abs_geq; template Type add_one(const Type& value) { return( Type(1) + value ); } // ----------------------------------------------------------------- template bool check_epsilon(void) { bool ok = true; typedef extern_value value; value eps( CppAD::numeric_limits::epsilon() ); value one( Type(1) ); value two( Type(2) ); value tmp( Type(0) ); // tmp.set( add_one( eps.get() / two.get() ) ); ok &= one.get() == tmp.get(); // tmp.set( add_one( eps.get() ) ); ok &= one.get() != tmp.get(); return ok; } // ----------------------------------------------------------------- template bool check_min(void) { bool ok = true; typedef extern_value value; value min( CppAD::numeric_limits::min() ); value eps3( Type(3) * CppAD::numeric_limits::epsilon() ); value one( Type(1) ); value hun( Type(100) ); value tmp( Type(0) ); // tmp.set( min.get() / hun.get() ); tmp.set( tmp.get() * hun.get() ); ok &= abs_geq(tmp.get()/min.get() - one.get(), eps3.get()); // tmp.set( min.get() * hun.get() ); tmp.set( tmp.get() / hun.get() ); ok &= ! abs_geq(tmp.get()/min.get() - one.get(), eps3.get()); return ok; } // ----------------------------------------------------------------- template bool check_max(void) { bool ok = true; typedef extern_value value; value max2( CppAD::numeric_limits::max() / Type(2) ); value eps3( Type(3) * CppAD::numeric_limits::epsilon() ); value one( Type(1) ); value hun( Type(100) ); value tmp( Type(0) ); // In complex case, this operaiton can result in (inf, 0) tmp.set( max2.get() * hun.get() ); // In complex case, this operaiotn can result in (inf,-nan) // (where nan corresponds to inf * 0) tmp.set( tmp.get() / hun.get() ); if( ! CppAD::isnan( tmp.get() ) ) ok &= abs_geq( tmp.get() / max2.get() - one.get(), eps3.get() ); // tmp.set( max2.get() / hun.get() ); tmp.set( tmp.get() * hun.get() ); ok &= ! abs_geq(tmp.get() / max2.get() - one.get(), eps3.get() ); return ok; } // ----------------------------------------------------------------- template bool check_quiet_NaN(void) { bool ok = true; typedef extern_value value; value nan( CppAD::numeric_limits::quiet_NaN() ); value same( nan.get() ); // ok &= nan.get() != same.get(); ok &= ! (nan.get() == same.get() ); // return ok; } } bool num_limits(void) { bool ok = true; using CppAD::AD; // ------------------------------------------------------------------- // epsilon for Base types defined by CppAD ok &= check_epsilon(); ok &= check_epsilon(); ok &= check_epsilon< std::complex >(); ok &= check_epsilon< std::complex >(); // epsilon for some AD types. ok &= check_epsilon< AD >(); ok &= check_epsilon< AD >(); ok &= check_epsilon< AD > >(); ok &= check_epsilon< AD > >(); // ------------------------------------------------------------------- // min for Base types defined by CppAD ok &= check_min(); ok &= check_min(); ok &= check_min< std::complex >(); ok &= check_min< std::complex >(); // min for some AD types. ok &= check_min< AD >(); ok &= check_min< AD >(); ok &= check_min< AD > >(); ok &= check_min< AD > >(); // ------------------------------------------------------------------- // max for Base types defined by CppAD ok &= check_max(); ok &= check_max(); ok &= check_max< std::complex >(); ok &= check_max< std::complex >(); // max for some AD types. ok &= check_max< AD >(); ok &= check_max< AD >(); ok &= check_max< AD< std::complex > >(); ok &= check_max< AD< std::complex > >(); // ------------------------------------------------------------------- // quiet_NaN for Base types defined by CppAD ok &= check_quiet_NaN(); ok &= check_quiet_NaN(); ok &= check_quiet_NaN< std::complex >(); ok &= check_quiet_NaN< std::complex >(); // quiet_NaN for some AD types. ok &= check_quiet_NaN< AD >(); ok &= check_quiet_NaN< AD >(); ok &= check_quiet_NaN< AD< std::complex > >(); ok &= check_quiet_NaN< AD< std::complex > >(); return ok; } // END C++ cppad-20170000.3/test_more/old_usead_2.cpp0000644000175200017650000003476313057470461017333 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin old_usead_2.cpp$$ $spell checkpoint var $$ $section Using AD to Compute Atomic Function Derivatives$$ $mindex inside user checkpoint$$ $head Deprecated 2013-05-27$$ This example has been deprecated because it is easier to use the $cref checkpoint$$ class instead. $head Purpose$$ Consider the case where an inner function is used repeatedly in the definition of an outer function. In this case, it may reduce the number of variables $cref/size_var/seq_property/size_var/$$, and hence the required memory. $code $srcfile%test_more/old_usead_2.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // Begin empty namespace using CppAD::AD; using CppAD::ADFun; using CppAD::vector; // ---------------------------------------------------------------------- // ODE for [t, t^2 / 2 ] in form required by Runge45 class Fun { public: void Ode( const AD &t, const vector< AD > &z, vector< AD > &f) { assert( z.size() == 2 ); assert( f.size() == 2 ); f[0] = 1.0; f[1] = z[0]; } }; // ---------------------------------------------------------------------- // Create function that takes on Runge45 step for the ODE above ADFun* r_ptr_; void create_r(void) { size_t n = 3, m = 2; vector< AD > x(n), zi(m), y(m), e(m); // The value of x does not matter because the operation sequence // does not depend on x. x[0] = 0.0; // initial value z_0 (t) at t = ti x[1] = 0.0; // initial value z_1 (t) at t = ti x[2] = 0.1; // final time for this integration CppAD::Independent(x); zi[0] = x[0]; // z_0 (t) at t = ti zi[1] = x[1]; // z_1 (t) at t = ti AD ti = 0.0; // t does not appear in ODE so does not matter AD tf = x[2]; // final time size_t M = 3; // number of Runge45 steps to take Fun F; y = CppAD::Runge45(F, M, ti, tf, zi, e); r_ptr_ = new ADFun(x, y); } void destroy_r(void) { delete r_ptr_; r_ptr_ = CPPAD_NULL; } // ---------------------------------------------------------------------- // forward mode routine called by CppAD bool solve_ode_forward( size_t id , size_t k , size_t n , size_t m , const vector& vx , vector& vy , const vector& tx , vector& ty ) { assert( id == 0 ); assert( n == 3 ); assert( m == 2 ); assert( k == 0 || vx.size() == 0 ); bool ok = true; vector xp(n), yp(m); size_t i, j; // check for special case if( vx.size() > 0 ) { //Compute r, a Jacobian sparsity pattern. // Use reverse mode because m < n. vector< std::set > s(m), r(m); for(i = 0; i < m; i++) s[i].insert(i); r = r_ptr_->RevSparseJac(m, s); std::set::const_iterator itr; for(i = 0; i < m; i++) { vy[i] = false; for(itr = s[i].begin(); itr != s[i].end(); itr++) { j = *itr; assert( j < n ); // y[i] depends on the value of x[j] // Visual Studio 2013 generates warning without bool below vy[i] |= bool( vx[j] ); } } } // make sure r_ has proper lower order Taylor coefficients stored // then compute ty[k] for(size_t q = 0; q <= k; q++) { for(j = 0; j < n; j++) xp[j] = tx[j * (k+1) + q]; yp = r_ptr_->Forward(q, xp); if( q == k ) { for(i = 0; i < m; i++) ty[i * (k+1) + q] = yp[i]; } # ifndef NDEBUG else { for(i = 0; i < m; i++) assert( ty[i * (k+1) + q] == yp[i] ); } # endif } // no longer need the Taylor coefficients in r_ptr_ // (have to reconstruct them every time) r_ptr_->capacity_order(0); return ok; } // ---------------------------------------------------------------------- // reverse mode routine called by CppAD bool solve_ode_reverse( size_t id , size_t k , size_t n , size_t m , const vector& tx , const vector& ty , vector& px , const vector& py ) { assert( id == 0 ); assert( n == 3 ); assert( m == 2 ); bool ok = true; vector xp(n), w( (k+1) * m ), dw( (k+1) * n ); // make sure r_ has proper forward mode coefficients size_t i, j, q; for(q = 0; q <= k; q++) { for(j = 0; j < n; j++) xp[j] = tx[j * (k+1) + q]; # ifdef NDEBUG r_ptr_->Forward(q, xp); # else vector yp(m); yp = r_ptr_->Forward(q, xp); for(i = 0; i < m; i++) assert( ty[i * (k+1) + q] == yp[i] ); # endif } for(i = 0; i < m; i++) { for(q = 0; q <=k; q++) w[ i * (k+1) + q] = py[ i * (k+1) + q]; } dw = r_ptr_->Reverse(k+1, w); for(j = 0; j < n; j++) { for(q = 0; q <=k; q++) px[ j * (k+1) + q] = dw[ j * (k+1) + q]; } // no longer need the Taylor coefficients in r_ptr_ // (have to reconstruct them every time) r_ptr_->capacity_order(0); return ok; } // ---------------------------------------------------------------------- // forward Jacobian sparsity routine called by CppAD bool solve_ode_for_jac_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , vector< std::set >& s ) { assert( id == 0 ); assert( n == 3 ); assert( m == 2 ); bool ok = true; vector< std::set > R(n), S(m); for(size_t j = 0; j < n; j++) R[j] = r[j]; S = r_ptr_->ForSparseJac(p, R); for(size_t i = 0; i < m; i++) s[i] = S[i]; // no longer need the forward mode sparsity pattern // (have to reconstruct them every time) r_ptr_->size_forward_set(0); return ok; } // ---------------------------------------------------------------------- // reverse Jacobian sparsity routine called by CppAD bool solve_ode_rev_jac_sparse( size_t id , size_t n , size_t m , size_t p , vector< std::set >& r , const vector< std::set >& s ) { assert( id == 0 ); assert( n == 3 ); assert( m == 2 ); bool ok = true; vector< std::set > R(p), S(p); std::set::const_iterator itr; size_t i; // untranspose s for(i = 0; i < m; i++) { for(itr = s[i].begin(); itr != s[i].end(); itr++) S[*itr].insert(i); } R = r_ptr_->RevSparseJac(p, S); // transpose r for(i = 0; i < m; i++) r[i].clear(); for(i = 0; i < p; i++) { for(itr = R[i].begin(); itr != R[i].end(); itr++) r[*itr].insert(i); } return ok; } // ---------------------------------------------------------------------- // reverse Hessian sparsity routine called by CppAD bool solve_ode_rev_hes_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , const vector& s , vector& t , const vector< std::set >& u , vector< std::set >& v ) { // Can just return false if not use RevSparseHes. assert( id == 0 ); assert( n == 3 ); assert( m == 2 ); bool ok = true; std::set::const_iterator itr; // compute sparsity pattern for T(x) = S(x) * f'(x) vector< std::set > S(1); size_t i, j; S[0].clear(); for(i = 0; i < m; i++) if( s[i] ) S[0].insert(i); t = r_ptr_->RevSparseJac(1, s); // compute sparsity pattern for A(x)^T = U(x)^T * f'(x) vector< std::set > Ut(p), At(p); for(i = 0; i < m; i++) { for(itr = u[i].begin(); itr != u[i].end(); itr++) Ut[*itr].insert(i); } At = r_ptr_->RevSparseJac(p, Ut); // compute sparsity pattern for H(x)^T = R^T * (S * F)''(x) vector< std::set > R(n), Ht(p); for(j = 0; j < n; j++) R[j] = r[j]; r_ptr_->ForSparseJac(p, R); Ht = r_ptr_->RevSparseHes(p, S); // compute sparsity pattern for V(x) = A(x) + H(x)^T for(j = 0; j < n; j++) v[j].clear(); for(i = 0; i < p; i++) { for(itr = At[i].begin(); itr != At[i].end(); itr++) v[*itr].insert(i); for(itr = Ht[i].begin(); itr != Ht[i].end(); itr++) v[*itr].insert(i); } // no longer need the forward mode sparsity pattern // (have to reconstruct them every time) r_ptr_->size_forward_set(0); return ok; } // --------------------------------------------------------------------- // Declare the AD routine solve_ode(id, ax, ay) CPPAD_USER_ATOMIC( solve_ode , CppAD::vector , double , solve_ode_forward , solve_ode_reverse , solve_ode_for_jac_sparse , solve_ode_rev_jac_sparse , solve_ode_rev_hes_sparse ) } // End empty namespace bool old_usead_2(void) { bool ok = true; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // -------------------------------------------------------------------- // Create the ADFun r_ create_r(); // -------------------------------------------------------------------- // domain and range space vectors size_t n = 3, m = 2; vector< AD > au(n), ax(n), ay(m); au[0] = 0.0; // value of z_0 (t) = t, at t = 0 ax[1] = 0.0; // value of z_1 (t) = t^2/2, at t = 0 au[2] = 1.0; // final t CppAD::Independent(au); size_t M = 2; // number of r steps to take ax[0] = au[0]; // value of z_0 (t) = t, at t = 0 ax[1] = au[1]; // value of z_1 (t) = t^2/2, at t = 0 AD dt = au[2] / M; // size of each r step ax[2] = dt; for(size_t i_step = 0; i_step < M; i_step++) { size_t id = 0; // not used solve_ode(id, ax, ay); ax[0] = ay[0]; ax[1] = ay[1]; } // create f: u -> y and stop tape recording // y_0(t) = u_0 + t = u_0 + u_2 // y_1(t) = u_1 + u_0 * t + t^2 / 2 = u_1 + u_0 * u_2 + u_2^2 / 2 // where t = u_2 ADFun f; f.Dependent(au, ay); // -------------------------------------------------------------------- // Check forward mode results // // zero order forward vector up(n), yp(m); size_t q = 0; double u0 = 0.5; double u1 = 0.25; double u2 = 0.75; double check; up[0] = u0; up[1] = u1; up[2] = u2; yp = f.Forward(q, up); check = u0 + u2; ok &= NearEqual( yp[0], check, eps, eps); check = u1 + u0 * u2 + u2 * u2 / 2.0; ok &= NearEqual( yp[1], check, eps, eps); // // forward mode first derivative w.r.t t q = 1; up[0] = 0.0; up[1] = 0.0; up[2] = 1.0; yp = f.Forward(q, up); check = 1.0; ok &= NearEqual( yp[0], check, eps, eps); check = u0 + u2; ok &= NearEqual( yp[1], check, eps, eps); // // forward mode second order Taylor coefficient w.r.t t q = 2; up[0] = 0.0; up[1] = 0.0; up[2] = 0.0; yp = f.Forward(q, up); check = 0.0; ok &= NearEqual( yp[0], check, eps, eps); check = 1.0 / 2.0; ok &= NearEqual( yp[1], check, eps, eps); // -------------------------------------------------------------------- // reverse mode derivatives of \partial_t y_1 (t) vector w(m * q), dw(n * q); w[0 * q + 0] = 0.0; w[1 * q + 0] = 0.0; w[0 * q + 1] = 0.0; w[1 * q + 1] = 1.0; dw = f.Reverse(q, w); // derivative of y_1(u) = u_1 + u_0 * u_2 + u_2^2 / 2, w.r.t. u // is equal deritative of \partial_u2 y_1(u) w.r.t \partial_u2 u check = u2; ok &= NearEqual( dw[0 * q + 1], check, eps, eps); check = 1.0; ok &= NearEqual( dw[1 * q + 1], check, eps, eps); check = u0 + u2; ok &= NearEqual( dw[2 * q + 1], check, eps, eps); // derivative of \partial_t y_1 w.r.t u = u_0 + t, w.r.t u check = 1.0; ok &= NearEqual( dw[0 * q + 0], check, eps, eps); check = 0.0; ok &= NearEqual( dw[1 * q + 0], check, eps, eps); check = 1.0; ok &= NearEqual( dw[2 * q + 0], check, eps, eps); // -------------------------------------------------------------------- // forward mode sparsity pattern for the Jacobian // f_u = [ 1, 0, 1 ] // [ u_2, 1, u_2 ] size_t i, j, p = n; CppAD::vectorBool r(n * p), s(m * p); // r = identity sparsity pattern for(i = 0; i < n; i++) for(j = 0; j < p; j++) r[i*n +j] = (i == j); s = f.ForSparseJac(p, r); ok &= s[ 0 * p + 0] == true; ok &= s[ 0 * p + 1] == false; ok &= s[ 0 * p + 2] == true; ok &= s[ 1 * p + 0] == true; ok &= s[ 1 * p + 1] == true; ok &= s[ 1 * p + 2] == true; // -------------------------------------------------------------------- // reverse mode sparsity pattern for the Jacobian q = m; s.resize(q * m); r.resize(q * n); // s = identity sparsity pattern for(i = 0; i < q; i++) for(j = 0; j < m; j++) s[i*m +j] = (i == j); r = f.RevSparseJac(q, s); ok &= r[ 0 * n + 0] == true; ok &= r[ 0 * n + 1] == false; ok &= r[ 0 * n + 2] == true; ok &= r[ 1 * n + 0] == true; ok &= r[ 1 * n + 1] == true; ok &= r[ 1 * n + 2] == true; // -------------------------------------------------------------------- // Hessian sparsity for y_1 (u) = u_1 + u_0 * u_2 + u_2^2 / 2 s.resize(m); s[0] = false; s[1] = true; r.resize(n * n); for(i = 0; i < n; i++) for(j = 0; j < n; j++) r[ i * n + j ] = (i == j); CppAD::vectorBool h(n * n); h = f.RevSparseHes(n, s); ok &= h[0 * n + 0] == false; ok &= h[0 * n + 1] == false; ok &= h[0 * n + 2] == true; ok &= h[1 * n + 0] == false; ok &= h[1 * n + 1] == false; ok &= h[1 * n + 2] == false; ok &= h[2 * n + 0] == true; ok &= h[2 * n + 1] == false; ok &= h[2 * n + 2] == true; // -------------------------------------------------------------------- destroy_r(); // Free all temporary work space associated with old_atomic objects. // (If there are future calls to user atomic functions, they will // create new temporary work space.) CppAD::user_atomic::clear(); return ok; } // END C++ cppad-20170000.3/test_more/mul_zdouble.cpp0000644000175200017650000001036313057470461017462 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // Check that multilevel reverse with conditial expressions works properly // when using AD< AD >. # include namespace { using CppAD::AD; using CppAD::zdouble; using CppAD::ADFun; using CppAD::vector; typedef AD a1type; typedef AD a2type; typedef vector (*a2fun)(const vector& a2x); // zdouble eps = 10. * std::numeric_limits::epsilon(); size_t n_ = 2; size_t m_ = 1; // void record(a2fun fun, ADFun& g) { vector x(n_); vector a1x(n_), a1w(m_), a1z(m_ * n_); vector a2x(n_), a2y(m_); // for(size_t j = 0; j < n_; j++) { x[j] = 0.0; a1x[j] = a1type( x[j] ); a2x[j] = a2type( a1x[j] ); } Independent(a2x); // f(x) = x[0] / x[1] if x[1] > 0.0 else 0.0 a2y = fun(a2x); ADFun a1f; a1f.Dependent(a2x, a2y); // use reverse mode to calculate g(x) = f'(x) a1w[0] = a1type(1.0); Independent(a1x); a1f.Forward(0, a1x); a1z = a1f.Reverse(1, a1w); g.Dependent(a1x, a1z); // return; } // ---------------------------------------------------------------------- vector div(const vector& a2x) { vector a2y(m_); a2type a2zero = a2type(0.0); a2type a2four = a2type(4.0); a2y[0] = CondExpGt(a2x[1], a2zero, a2x[0] / a2x[1], a2zero); a2y[0] += CondExpGt(a2x[1], a2zero, a2four / a2x[1], a2zero); return a2y; } bool check_div(void) { bool ok = true; // record division operations ADFun g; record(div, g); vector x(n_), z(n_); // check result where x[1] <= 0.0 (would be nan without absoute zero) x[0] = 0.0; x[1] = 0.0; z = g.Forward(0, x); z = g.Forward(0, x); ok &= z[0] == 0.0; ok &= z[1] == 0.0; // check result where x[1] > 0.0 x[0] = 2.0; x[1] = 3.0; z = g.Forward(0, x); ok &= CppAD::NearEqual(z[0], 1.0/x[1], eps, eps); ok &= CppAD::NearEqual(z[1], - (x[0]+4.0)/(x[1]*x[1]), eps, eps); // return ok; } // ---------------------------------------------------------------------- vector mul(const vector& a2x) { vector a2y(m_); a2type a2zero = a2type(0.0); a2type a2four = a2type(4.0); a2y[0] = CondExpLt(a2x[0], a2four, a2x[0] * a2x[1], a2zero); a2y[0] += CondExpLt(a2x[0], a2four, a2four * a2x[1], a2zero); a2y[0] += CondExpLt(a2x[0], a2four, a2x[1] * a2four, a2zero); return a2y; } bool check_mul(void) { bool ok = true; // record multiplication operations ADFun g; record(mul, g); vector x(n_), z(n_); // check result where x[0] > 4 (would be nan without absoute zero) ok &= std::numeric_limits::has_infinity; x[0] = std::numeric_limits::infinity(); x[1] = 0.0; z = g.Forward(0, x); ok &= z[0] == 0.0; ok &= z[1] == 0.0; // check result where x[0] < 4 x[0] = 2.0; x[1] = 3.0; z = g.Forward(0, x); ok &= CppAD::NearEqual(z[0], x[1], eps, eps); ok &= CppAD::NearEqual(z[1], x[0]+8.0, eps, eps); // return ok; } // ---------------------------------------------------------------------- bool check_numeric_limits(void) { bool ok = true; // double double_eps = std::numeric_limits::epsilon(); zdouble zdouble_eps = CppAD::numeric_limits::epsilon(); ok &= double_eps == zdouble_eps; // double double_min = std::numeric_limits::min(); zdouble zdouble_min = CppAD::numeric_limits::min(); ok &= double_min == zdouble_min; // double double_max = std::numeric_limits::max(); zdouble zdouble_max = CppAD::numeric_limits::max(); ok &= double_max == zdouble_max; // return ok; } } bool mul_zdouble(void) { bool ok = true; ok &= check_div(); ok &= check_mul(); ok &= check_numeric_limits(); return ok; } cppad-20170000.3/test_more/pow.cpp0000644000175200017650000002474213057470461015754 0ustar coincoin-web// $Id: pow.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old examples now just used for validation testing. */ # include namespace { // BEGIN empty namespace bool PowTestOne(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 2; double x = 0.5; double y = 2.; CPPAD_TESTVECTOR(AD) XY(n); XY[0] = x; XY[1] = y; // declare independent variables and start tape recording CppAD::Independent(XY); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD) Z(m); Z[0] = CppAD::pow(XY[0], XY[1]); // pow(variable, variable) Z[1] = CppAD::pow(XY[0], y); // pow(variable, parameter) Z[2] = CppAD::pow(x, XY[1]); // pow(parameter, variable) // create f: XY -> Z and stop tape recording CppAD::ADFun f(XY, Z); // check value double check = std::pow(x, y); size_t i; for(i = 0; i < m; i++) ok &= NearEqual(Z[i] , check, eps99, eps99); // forward computation of first partial w.r.t. x CPPAD_TESTVECTOR(double) dxy(n); CPPAD_TESTVECTOR(double) dz(m); dxy[0] = 1.; dxy[1] = 0.; dz = f.Forward(1, dxy); check = y * std::pow(x, y-1.); ok &= NearEqual(dz[0], check, eps99, eps99); ok &= NearEqual(dz[1], check, eps99, eps99); ok &= NearEqual(dz[2], 0., eps99, eps99); // forward computation of first partial w.r.t. y dxy[0] = 0.; dxy[1] = 1.; dz = f.Forward(1, dxy); check = std::log(x) * std::pow(x, y); ok &= NearEqual(dz[0], check, eps99, eps99); ok &= NearEqual(dz[1], 0., eps99, eps99); ok &= NearEqual(dz[2], check, eps99, eps99); // reverse computation of derivative of z[0] + z[1] + z[2] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 1.; w[2] = 1.; dw = f.Reverse(1, w); check = y * std::pow(x, y-1.); ok &= NearEqual(dw[0], 2. * check, eps99, eps99); check = std::log(x) * std::pow(x, y); ok &= NearEqual(dw[1], 2. * check, eps99, eps99); // use a VecAD::reference object with pow CppAD::VecAD v(2); AD zero(0); AD one(1); v[zero] = XY[0]; v[one] = XY[1]; AD result = CppAD::pow(v[zero], v[one]); ok &= NearEqual(result, Z[0], eps99, eps99); return ok; } bool PowTestTwo(void) { bool ok = true; using CppAD::pow; using CppAD::exp; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 2.; U[t] = 3.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; // dependent variable values AD u = exp(U[s]); // u = exp(s) Z[x] = pow(u, U[t]); // x = exp(s * t) Z[y] = pow(Z[x], u); // y = exp( s * t * exp(s) ) // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); /* u_s (s, t) = u u_t (s, t) = 0 y_s (s, t) = (1 + s) t * u * y y_t (s, t) = s * u * y y_st (s, t) = ( u + s * u ) * y + ( t * u + s * t * u ) * s * u * y */ // check values ok &= NearEqual(Z[x] , exp(2. * 3.), eps99, eps99); ok &= NearEqual(Z[y] , exp( 2. * 3. * exp(2.) ), eps99, eps99); // forward computation of partials w.r.t. s v[s] = 1.; v[t] = 0.; w = f.Forward(1, v); ok &= ( w[x] == U[t] * Z[x] ); // dx/ds ok &= ( w[y] == (1. + U[s]) * U[t] * u * Z[y] ); // dy/ds // forward computation of partials w.r.t. t v[s] = 0.; v[t] = 1.; w = f.Forward(1, v); ok &= ( w[y] == U[s] * u * Z[y] ); // dy/dt // forward computation of second Taylor coefficient w.r.t. t v[t] = 1.; w = f.Forward(1, v); v[t] = 0.; CPPAD_TESTVECTOR(double) f_tt = f.Forward(2, v); // forward computation of second Taylor coefficient w.r.t. s v[s] = 1.; w = f.Forward(1, v); v[s] = 0.; CPPAD_TESTVECTOR(double) f_ss = f.Forward(2, v); // second Taylor coefficient w.r.t. direction r = (s,t) v[s] = 1.; v[t] = 1.; w = f.Forward(1, v); v[s] = 0.; v[t] = 0.; CPPAD_TESTVECTOR(double) f_rr = f.Forward(2, v); // check second order partial of y ok &= NearEqual( f_rr[y] - f_ss[y] - f_tt[y], (1. + U[s]) * u * Z[y] + (1. + U[s]) * U[t] * u * U[s] * u * Z[y], 1e-10 , 1e-10 ); return ok; } bool PowTestThree(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) x(n); x[0] = 2.; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 4; CPPAD_TESTVECTOR(AD) y(m); // some special cases y[0] = pow(x[0], 0.); y[1] = pow(0., x[0]); y[2] = pow(x[0], 1.); y[3] = pow(1., x[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check function values ok &= (Value(y[0]) == 1.); ok &= (Value(y[1]) == 0.); ok &= (Value(y[2]) == Value(x[0])); ok &= (Value(y[3]) == 1.); // forward computation of first partial w.r.t. x CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= (dy[0] == 0.); ok &= (dy[1] == 0.); ok &= NearEqual(dy[2], 1., eps99, eps99); ok &= (dy[3] == 0.); // reverse mode computation of derivative of y[0]+y[1]+y[2]+y[3] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 1.; w[2] = 1.; w[3] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 1., eps99, eps99); return ok; } bool PowTestFour(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = -2; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 5; CPPAD_TESTVECTOR(AD) y(m); // some special cases (skip zero raised to a negative power) y[0] = pow(1., x[0]); size_t i; for(i = 1; i < m; i++) y[i] = pow(x[0], i-1); // pow(AD, int) // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); ok &= (Value(y[0]) == 1.); double check; for(i = 1; i < m; i++) { check = std::pow(x0, double(i-1)); ok &= NearEqual(y[i], check, eps99, eps99); } // forward computation of first partial w.r.t. x CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= (dy[0] == 0.); double sum = 0; for(i = 1; i < m; i++) { if( i == 1 ) check = 0.; else check = double(i-1) * std::pow(x0, double(i-2)); ok &= NearEqual(dy[i], check, eps99, eps99); sum += check; } // reverse mode computation of derivative of y[0] + .. y[m-1]; CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); for(i = 0; i < m; i++) w[i] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], sum, eps99, eps99); return ok; } bool PowTestFive(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = -1.; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) y(m); // case of zero raised to a positive integer power double e = 2.; y[0] = pow(x[0], int(e)); // use pow(AD, int) // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check function value ok &= (Value(y[0]) == pow(x0, e) ); // forward computation of first partial w.r.t. x[1] double d1 = e * pow(x0, (e-1)); CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], d1, eps99, eps99); // reverse mode computation of second partials // x.r.t. x[1],x[0] and x[1], x[1] double d2 = e * (e-1) * pow(x0, (e-2)); CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) ddw(2*n); w[0] = 1.; ddw = f.Reverse(2, w); ok &= NearEqual(ddw[0], d1, eps99, eps99); ok &= NearEqual(ddw[1], d2, eps99, eps99); return ok; } bool PowTestSix(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 1.5; CPPAD_TESTVECTOR(AD) x(n); x[0] = x0; // domain space vector CPPAD_TESTVECTOR(AD< AD >) X(n); X[0] = x[0]; // declare independent variables and start tape recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD< AD >) Y(m); // case of AD< AD > raised to a double power double e = 2.5; Y[0] = pow(X[0], e); // create F: X -> Y and stop tape recording CppAD::ADFun< AD > F(X, Y); // check function value ok &= NearEqual(Value(Value(Y[0])), pow(x0, e), eps99, eps99); // forward computation of first partial w.r.t. x[1] double d1 = e * pow(x0, (e-1)); CPPAD_TESTVECTOR(AD) dx(n); CPPAD_TESTVECTOR(AD) dy(m); dx[0] = 1.; dy = F.Forward(1, dx); ok &= NearEqual(dy[0], d1, eps99, eps99); // reverse mode computation of second partials // x.r.t. x[1],x[0] and x[1], x[1] double d2 = e * (e-1) * pow(x0, (e-2)); CPPAD_TESTVECTOR(AD) w(m); CPPAD_TESTVECTOR(AD) ddw(2*n); w[0] = 1.; ddw = F.Reverse(2, w); ok &= NearEqual(ddw[0], d1, eps99, eps99); ok &= NearEqual(ddw[1], d2, eps99, eps99); return ok; } } // END empty namespace bool Pow(void) { bool ok = true; ok &= PowTestOne(); ok &= PowTestTwo(); ok &= PowTestThree(); ok &= PowTestFour(); ok &= PowTestFive(); ok &= PowTestSix(); return ok; } cppad-20170000.3/test_more/sparse_jacobian.cpp0000644000175200017650000003613613057470461020272 0ustar coincoin-web// $Id: sparse_jacobian.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old sparse Jacobian example */ # include namespace { // --------------------------------------------------------- bool rc_tridiagonal(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j, k, ell; double eps10 = 10. * CppAD::epsilon(); // domain space vector size_t n = 13; // must be greater than or equal 3 (see n_sweep below) CPPAD_TESTVECTOR(AD) X(n); CPPAD_TESTVECTOR(double) x(n); for(j = 0; j < n; j++) X[j] = x[j] = double(j+1); // declare independent variables and starting recording CppAD::Independent(X); size_t m = n; CPPAD_TESTVECTOR(AD) Y(m); CPPAD_TESTVECTOR(double) check(m * n ); for(ell = 0; ell < m * n; ell++) check[ell] = 0.0; size_t K = 0; for(i = 0; i < n; i++) { ell = i * n + i; Y[i] = (ell+1) * 0.5 * X[i] * X[i]; check[ell] = (ell+1) * x[i]; K++; if( i < n-1 ) { j = i + 1; ell = i * n + j; Y[i] += (ell+1) * 0.5 * X[i+1] * X[i+1]; check[ell] = (ell+1) * x[i+1]; K++; } if(i > 0 ) { j = i - 1; ell = i * n + j; Y[i] += (ell+1) * 0.5 * X[i-1] * X[i-1]; check[ell] = (ell+1) * x[i-1]; } } // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // sparsity pattern CppAD::vector< std::set > s(m), p(m); for(i = 0; i < m; i++) s[i].insert(i); p = f.RevSparseJac(m, s); // Request the upper triangle of the array CPPAD_TESTVECTOR(size_t) r(K), c(K); CPPAD_TESTVECTOR(double) jac(K); k = 0; for(i = 0; i < n; i++) { r[k] = i; c[k] = i; k++; if( i < n-1 ) { r[k] = i; c[k] = i+1; k++; } } ok &= K == k; CppAD::sparse_jacobian_work work; size_t n_sweep = f.SparseJacobianForward(x, p, r, c, jac, work); ok &= n_sweep == 3; for(k = 0; k < K; k++) { ell = r[k] * n + c[k]; ok &= NearEqual(check[ell], jac[k], eps10, eps10); } work.clear(); n_sweep = f.SparseJacobianReverse(x, p, r, c, jac, work); ok &= n_sweep == 3; for(k = 0; k < K; k++) { ell = r[k] * n + c[k]; ok &= NearEqual(check[ell], jac[k], eps10, eps10); } return ok; } template bool rc_set(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j, k, ell; double eps10 = 10. * CppAD::epsilon(); // domain space vector size_t n = 4; CPPAD_TESTVECTOR(AD) X(n); for(j = 0; j < n; j++) X[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(X); size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = 1.0*X[0] + 2.0*X[1]; Y[1] = 3.0*X[2] + 4.0*X[3]; Y[2] = 5.0*X[0] + 6.0*X[1] + 7.0*X[3]*X[3]/2.; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); for(j = 0; j < n; j++) x[j] = double(j); // Jacobian of y /* [ 1 2 0 0 ] jac = [ 0 0 3 4 ] [ 5 6 0 7*x_3] */ VectorBase check(m * n); check[0] = 1.; check[1] = 2.; check[2] = 0.; check[3] = 0.; check[4] = 0.; check[5] = 0.; check[6] = 3.; check[7] = 4.; check[8] = 5.; check[9] = 6.; check[10] = 0.; check[11] = 7.*x[3]; // sparsity pattern VectorSet s(m), p(m); for(i = 0; i < m; i++) s[i].insert(i); p = f.RevSparseJac(m, s); // Use forward mode to compute columns 0 and 2 // (make sure order of rows and columns does not matter) CPPAD_TESTVECTOR(size_t) r(3), c(3); VectorBase jac(3); r[0] = 2; c[0] = 0; r[1] = 1; c[1] = 2; r[2] = 0; c[2] = 0; CppAD::sparse_jacobian_work work; size_t n_sweep = f.SparseJacobianForward(x, p, r, c, jac, work); for(k = 0; k < 3; k++) { ell = r[k] * n + c[k]; ok &= NearEqual(check[ell], jac[k], eps10, eps10); } ok &= (n_sweep == 1); // Use reverse mode to compute rows 0 and 1 // (make sure order of rows and columns does not matter) r.resize(4), c.resize(4); jac.resize(4); r[0] = 0; c[0] = 0; r[1] = 1; c[1] = 2; r[2] = 0; c[2] = 1; r[3] = 1; c[3] = 3; work.clear(); n_sweep = f.SparseJacobianReverse(x, p, r, c, jac, work); for(k = 0; k < 4; k++) { ell = r[k] * n + c[k]; ok &= NearEqual(check[ell], jac[k], eps10, eps10); } ok &= (n_sweep == 1); return ok; } template bool rc_bool(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t j, k, ell; double eps10 = 10. * CppAD::epsilon(); // domain space vector size_t n = 4; CPPAD_TESTVECTOR(AD) X(n); for(j = 0; j < n; j++) X[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(X); size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = 1.0*X[0] + 2.0*X[1]; Y[1] = 3.0*X[2] + 4.0*X[3]; Y[2] = 5.0*X[0] + 6.0*X[1] + 7.0*X[3]*X[3]/2.; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); for(j = 0; j < n; j++) x[j] = double(j); // Jacobian of y /* [ 1 2 0 0 ] jac = [ 0 0 3 4 ] [ 5 6 0 7*x_3] */ VectorBase check(m * n); check[0] = 1.; check[1] = 2.; check[2] = 0.; check[3] = 0.; check[4] = 0.; check[5] = 0.; check[6] = 3.; check[7] = 4.; check[8] = 5.; check[9] = 6.; check[10] = 0.; check[11] = 7.*x[3]; VectorBool s(m * n); s[0] = true; s[1] = true; s[2] = false; s[3] = false; s[4] = false; s[5] = false; s[6] = true; s[7] = true; s[8] = true; s[9] = true; s[10] = false; s[11] = true; // Use forward mode to compute columns 0 and 2 // (make sure order of rows and columns does not matter) CPPAD_TESTVECTOR(size_t) r(3), c(3); VectorBase jac(3); r[0] = 2; c[0] = 0; r[1] = 1; c[1] = 2; r[2] = 0; c[2] = 0; CppAD::sparse_jacobian_work work; size_t n_sweep = f.SparseJacobianForward(x, s, r, c, jac, work); for(k = 0; k < 3; k++) { ell = r[k] * n + c[k]; ok &= NearEqual(check[ell], jac[k], eps10, eps10); } ok &= (n_sweep == 1); // Use reverse mode to compute rows 0 and 1 // (make sure order of rows and columns does not matter) r.resize(4), c.resize(4); jac.resize(4); r[0] = 0; c[0] = 0; r[1] = 1; c[1] = 2; r[2] = 0; c[2] = 1; r[3] = 1; c[3] = 3; work.clear(); n_sweep = f.SparseJacobianReverse(x, s, r, c, jac, work); for(k = 0; k < 4; k++) { ell = r[k] * n + c[k]; ok &= NearEqual(check[ell], jac[k], eps10, eps10); } ok &= (n_sweep == 1); return ok; } template bool reverse_bool(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j, k; // domain space vector size_t n = 4; CPPAD_TESTVECTOR(AD) X(n); for(j = 0; j < n; j++) X[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(X); size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = 1.0*X[0] + 2.0*X[1]; Y[1] = 3.0*X[2] + 4.0*X[3]; Y[2] = 5.0*X[0] + 6.0*X[1] + 7.0*X[2] + 8.0*X[3]*X[3]/2.; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); for(j = 0; j < n; j++) x[j] = double(j); // Jacobian of y without sparsity pattern VectorBase jac(m * n); jac = f.SparseJacobian(x); /* [ 1 2 0 0 ] jac = [ 0 0 3 4 ] [ 5 6 7 8*x_3] */ VectorBase check(m * n); check[0] = 1.; check[1] = 2.; check[2] = 0.; check[3] = 0.; check[4] = 0.; check[5] = 0.; check[6] = 3.; check[7] = 4.; check[8] = 5.; check[9] = 6.; check[10] = 7.; check[11] = 8.*x[3]; for(k = 0; k < 12; k++) ok &= NearEqual(check[k], jac[k], 1e-10, 1e-10 ); // test passing sparsity pattern VectorBool s(m * m); VectorBool p(m * n); for(i = 0; i < m; i++) { for(k = 0; k < m; k++) s[i * m + k] = false; s[i * m + i] = true; } p = f.RevSparseJac(m, s); jac = f.SparseJacobian(x, p); for(k = 0; k < 12; k++) ok &= NearEqual(check[k], jac[k], 1e-10, 1e-10 ); return ok; } template bool reverse_set(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t i, j, k; // domain space vector size_t n = 4; CPPAD_TESTVECTOR(AD) X(n); for(j = 0; j < n; j++) X[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(X); size_t m = 3; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] + X[1]; Y[1] = X[2] + X[3]; Y[2] = X[0] + X[1] + X[2] + X[3] * X[3] / 2.; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); for(j = 0; j < n; j++) x[j] = double(j); // Jacobian of y without sparsity pattern VectorBase jac(m * n); jac = f.SparseJacobian(x); /* [ 1 1 0 0 ] jac = [ 0 0 1 1 ] [ 1 1 1 x_3] */ VectorBase check(m * n); check[0] = 1.; check[1] = 1.; check[2] = 0.; check[3] = 0.; check[4] = 0.; check[5] = 0.; check[6] = 1.; check[7] = 1.; check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3]; for(k = 0; k < 12; k++) ok &= NearEqual(check[k], jac[k], 1e-10, 1e-10 ); // test passing sparsity pattern VectorSet s(m), p(m); for(i = 0; i < m; i++) s[i].insert(i); p = f.RevSparseJac(m, s); jac = f.SparseJacobian(x, p); for(k = 0; k < 12; k++) ok &= NearEqual(check[k], jac[k], 1e-10, 1e-10 ); return ok; } template bool forward_bool(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t j, k; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) X(n); for(j = 0; j < n; j++) X[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(X); size_t m = 4; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] + X[2]; Y[1] = X[0] + X[2]; Y[2] = X[1] + X[2]; Y[3] = X[1] + X[2] * X[2] / 2.; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); for(j = 0; j < n; j++) x[j] = double(j); // Jacobian of y without sparsity pattern VectorBase jac(m * n); jac = f.SparseJacobian(x); /* [ 1 0 1 ] jac = [ 1 0 1 ] [ 0 1 1 ] [ 0 1 x_2 ] */ VectorBase check(m * n); check[0] = 1.; check[1] = 0.; check[2] = 1.; check[3] = 1.; check[4] = 0.; check[5] = 1.; check[6] = 0.; check[7] = 1.; check[8] = 1.; check[9] = 0.; check[10] = 1.; check[11] = x[2]; for(k = 0; k < 12; k++) ok &= NearEqual(check[k], jac[k], 1e-10, 1e-10 ); // test passing sparsity pattern VectorBool r(n * n); VectorBool p(m * n); for(j = 0; j < n; j++) { for(k = 0; k < n; k++) r[j * n + k] = false; r[j * n + j] = true; } p = f.ForSparseJac(n, r); jac = f.SparseJacobian(x, p); for(k = 0; k < 12; k++) ok &= NearEqual(check[k], jac[k], 1e-10, 1e-10 ); return ok; } template bool forward_set(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; size_t j, k; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) X(n); for(j = 0; j < n; j++) X[j] = AD (0); // declare independent variables and starting recording CppAD::Independent(X); size_t m = 4; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[0] + X[2]; Y[1] = X[0] + X[2]; Y[2] = X[1] + X[2]; Y[3] = X[1] + X[2] * X[2] / 2.; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // new value for the independent variable vector VectorBase x(n); for(j = 0; j < n; j++) x[j] = double(j); // Jacobian of y without sparsity pattern VectorBase jac(m * n); jac = f.SparseJacobian(x); /* [ 1 0 1 ] jac = [ 1 0 1 ] [ 0 1 1 ] [ 0 1 x_2 ] */ VectorBase check(m * n); check[0] = 1.; check[1] = 0.; check[2] = 1.; check[3] = 1.; check[4] = 0.; check[5] = 1.; check[6] = 0.; check[7] = 1.; check[8] = 1.; check[9] = 0.; check[10] = 1.; check[11] = x[2]; for(k = 0; k < 12; k++) ok &= NearEqual(check[k], jac[k], 1e-10, 1e-10 ); // test passing sparsity pattern VectorSet r(n), p(m); for(j = 0; j < n; j++) r[j].insert(j); p = f.ForSparseJac(n, r); jac = f.SparseJacobian(x, p); for(k = 0; k < 12; k++) ok &= NearEqual(check[k], jac[k], 1e-10, 1e-10 ); return ok; } bool multiple_of_n_bit(void) { bool ok = true; using CppAD::AD; using CppAD::vector; size_t i, j; // should be the same as the corresponding typedef in // cppad/local/sparse_pack.hpp typedef size_t Pack; // number of bits per packed value size_t n_bit = std::numeric_limits::digits; // check case where number of variables is equal to n_bit vector< AD > x(n_bit); vector< AD > y(n_bit); // create an AD function with domain and range dimension equal to n_bit CppAD::Independent(x); for(i = 0; i < n_bit; i++) y[i] = x[n_bit - i - 1]; CppAD::ADFun f(x, y); // Jacobian sparsity patterns vector r(n_bit * n_bit); vector s(n_bit * n_bit); for(i = 0; i < n_bit; i++) { for(j = 0; j < n_bit; j++) r[ i * n_bit + j ] = (i == j); } s = f.ForSparseJac(n_bit, r); // check the result for(i = 0; i < n_bit; i++) { for(j = 0; j < n_bit; j++) { if( i == n_bit - j - 1 ) ok = ok & s[ i * n_bit + j ]; else ok = ok & (! s[i * n_bit + j] ); } } return ok; } } // End empty namespace # include # include bool sparse_jacobian(void) { bool ok = true; ok &= rc_tridiagonal(); ok &= multiple_of_n_bit(); // --------------------------------------------------------------- // vector of bool cases ok &= rc_bool< CppAD::vector, CppAD::vectorBool >(); ok &= forward_bool< CppAD::vector, CppAD::vector >(); // ok &= reverse_bool< std::vector, std::vector >(); ok &= rc_bool< std::vector, std::valarray >(); // ok &= forward_bool< std::valarray, CppAD::vectorBool >(); ok &= reverse_bool< std::valarray, CppAD::vector >(); // --------------------------------------------------------------- // vector of set cases typedef std::vector< std::set > std_vector_set; typedef CppAD::vector< std::set > cppad_vector_set; // ok &= rc_set< CppAD::vector, std_vector_set >(); ok &= forward_set< std::valarray, std_vector_set >(); // ok &= reverse_set< std::vector, cppad_vector_set >(); ok &= rc_set< CppAD::vector, cppad_vector_set >(); // // According to section 26.3.2.3 of the 1998 C++ standard // a const valarray does not return references to its elements. // typedef std::valarray< std::set > std_valarray_set; // ok &= forward_set< std::valarray, std_valarray_set >(); // ok &= reverse_set< std::valarray, std_valarray_set >(); // --------------------------------------------------------------- // return ok; } cppad-20170000.3/test_more/abs.cpp0000644000175200017650000000375013057470461015710 0ustar coincoin-web// $Id: abs.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test of directional derivative in AD< AD< double > > case. */ # include bool abs(void) { // test if CppAD::abs uses if statement during forward computations bool ok = true; using CppAD::Independent; using CppAD::ADFun; typedef CppAD::AD ADdouble; typedef CppAD::AD< ADdouble > ADDdouble; // af(x) = |x| CPPAD_TESTVECTOR( ADDdouble ) aax(1), aay(1); aax[0] = ADDdouble(0.); CppAD::Independent(aax); aay[0] = CppAD::abs(aax[0]); CppAD::ADFun< ADdouble > af(aax, aay); // f(x) = |x| CPPAD_TESTVECTOR( ADdouble ) ax(1), ay(1); ax[0] = ADdouble(0.); CppAD::Independent(ax); ay = af.Forward(0, ax); CppAD::ADFun f(ax, ay); // compute derivative of af at a positive argument CPPAD_TESTVECTOR( ADdouble ) adx(1), ady(1); ax[0] = 1.; ay = af.Forward(0, ax); adx[0] = 1; ady = af.Forward(1, adx); ok &= (ady[0] == 1.); // compute derivative of af at a zero argument ax[0] = 0.; ay = af.Forward(0, ax); adx[0] = 1; ady = af.Forward(1, adx); ok &= (ady[0] == 0.); // compute derivative of f at zero argument CPPAD_TESTVECTOR(double) x(1), y(1), dx(1), dy(1); x[0] = 0.; y = f.Forward(0, x); dx[0] = 1; dy = f.Forward(1, dx); ok &= (dy[0] == 0.); // compute derivative of af at a negative argument x[0] = -1.; y = f.Forward(0, x); dx[0] = 1; dy = f.Forward(1, dx); ok &= (dy[0] == -1.); return ok; } cppad-20170000.3/test_more/mul_level.cpp0000644000175200017650000002305013057470461017122 0ustar coincoin-web// $Id: mul_level.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # ifdef CPPAD_ADOLC_TEST # include # include # include // adouble definitions not in Adolc distribution and // required in order to use CppAD::AD # include # endif # include # include namespace { // BEGIN empty namespace bool One(void) { bool ok = true; // initialize test result using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); typedef CppAD::AD ADdouble; // for one level of taping typedef CppAD::AD ADDdouble; // for two levels of taping size_t n = 2; // dimension for example // value of the independent variables CPPAD_TESTVECTOR(ADDdouble) aa_x(n); aa_x[0] = 1.; aa_x[1] = 3.; // test conversion double to AD< AD > aa_x[0] = 2. * aa_x[0]; // test double * AD< AD > CppAD::Independent(aa_x); // compute the function f(x) = 2 * x[0] * x[1] CPPAD_TESTVECTOR(ADDdouble) aa_f(1); aa_f[0] = 2. * aa_x[0] * aa_x[1]; CppAD::ADFun F(aa_x, aa_f); // value of the independent variables CPPAD_TESTVECTOR(ADdouble) a_x(n); a_x[0] = 2.; a_x[1] = 3.; Independent(a_x); // re-evaluate f(2, 3) (must get deepedence on a_x). size_t p = 0; CPPAD_TESTVECTOR(ADdouble) a_fp(1); a_fp = F.Forward(p, a_x); ok &= NearEqual(a_fp[0], 2. * a_x[0] * a_x[1], eps, eps); // compute the function g(x) = 2 * partial_x[0] f(x) = 4 * x[1] p = 1; CPPAD_TESTVECTOR(ADdouble) a_dx(n), a_g(1); a_dx[0] = 1.; a_dx[1] = 0.; a_fp = F.Forward(p, a_dx); a_g[0] = 2. * a_fp[0]; CppAD::ADFun G(a_x, a_g); // compute partial_x[1] g(x) CPPAD_TESTVECTOR(double) xp(n), gp(1); p = 0; xp[0] = 4.; xp[1] = 5.; gp = G.Forward(p, xp); ok &= NearEqual(gp[0], 4. * xp[1], eps, eps); p = 1; xp[0] = 0.; xp[1] = 1.; gp = G.Forward(p, xp); ok &= NearEqual(gp[0], 4., eps, eps); return ok; } // f(x) = |x|^2 = .5 * ( x[0]^2 + ... + x[n-1]^2 ) template Type f_Two(CPPAD_TESTVECTOR(Type) &x) { Type sum; // check assignment of AD< AD > = double sum = .5; sum += .5; size_t i = x.size(); while(i--) sum += x[i] * x[i]; // check computed assignment AD< AD > -= int sum -= 1; // check double * AD< AD > return .5 * sum; } bool Two(void) { bool ok = true; // initialize test result typedef CppAD::AD ADdouble; // for one level of taping typedef CppAD::AD ADDdouble; // for two levels of taping size_t n = 5; // dimension for example size_t j; // a temporary index variable CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(ADdouble) a_x(n); CPPAD_TESTVECTOR(ADDdouble) aa_x(n); // value of the independent variables for(j = 0; j < n; j++) a_x[j] = x[j] = double(j); // x[j] = j Independent(a_x); // a_x is indedendent for ADdouble for(j = 0; j < n; j++) aa_x[j] = a_x[j]; // track how aa_x depends on a_x CppAD::Independent(aa_x); // aa_x is independent for ADDdouble // compute function CPPAD_TESTVECTOR(ADDdouble) aa_f(1); // scalar valued function aa_f[0] = f_Two(aa_x); // has only one component // declare inner function (corresponding to ADDdouble calculation) CppAD::ADFun a_F(aa_x, aa_f); // compute f'(x) size_t p = 1; // order of derivative of a_F CPPAD_TESTVECTOR(ADdouble) a_w(1); // weight vector for a_F CPPAD_TESTVECTOR(ADdouble) a_df(n); // value of derivative a_w[0] = 1; // weighted function same as a_F a_df = a_F.Reverse(p, a_w); // gradient of f // declare outter function (corresponding to ADdouble calculation) CppAD::ADFun df(a_x, a_df); // compute the d/dx of f'(x) * v = f''(x) * v CPPAD_TESTVECTOR(double) v(n); CPPAD_TESTVECTOR(double) ddf_v(n); for(j = 0; j < n; j++) v[j] = double(n - j); ddf_v = df.Reverse(p, v); // f(x) = .5 * ( x[0]^2 + x[1]^2 + ... + x[n-1]^2 ) // f'(x) = (x[0], x[1], ... , x[n-1]) // f''(x) * v = ( v[0], v[1], ... , x[n-1] ) for(j = 0; j < n; j++) ok &= CppAD::NearEqual(ddf_v[j], v[j], 1e-10, 1e-10); return ok; } # ifdef CPPAD_ADOLC_TEST bool adolc(void) { bool ok = true; // initialize test result typedef adouble ADdouble; // for first level of taping typedef CppAD::AD ADDdouble; // for second level of taping size_t n = 5; // number independent variables CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(ADdouble) a_x(n); CPPAD_TESTVECTOR(ADDdouble) aa_x(n); // value of the independent variables int tag = 0; // Adolc setup int keep = 1; trace_on(tag, keep); size_t j; for(j = 0; j < n; j++) { x[j] = double(j); // x[j] = j a_x[j] <<= x[j]; // a_x is independent for ADdouble } for(j = 0; j < n; j++) aa_x[j] = a_x[j]; // track how aa_x depends on a_x CppAD::Independent(aa_x); // aa_x is independent for ADDdouble // compute function CPPAD_TESTVECTOR(ADDdouble) aa_f(1); // scalar valued function aa_f[0] = f_Two(aa_x); // has only one component // declare inner function (corresponding to ADDdouble calculation) CppAD::ADFun a_F(aa_x, aa_f); // compute f'(x) size_t p = 1; // order of derivative of a_F CPPAD_TESTVECTOR(ADdouble) a_w(1); // weight vector for a_F CPPAD_TESTVECTOR(ADdouble) a_df(n); // value of derivative a_w[0] = 1; // weighted function same as a_F a_df = a_F.Reverse(p, a_w); // gradient of f // declare outter function // (corresponding to the tape of adouble operations) double df_j; for(j = 0; j < n; j++) a_df[j] >>= df_j; trace_off(); // compute the d/dx of f'(x) * v = f''(x) * v size_t m = n; // # dependent in f'(x) double *v = CPPAD_NULL, *ddf_v = CPPAD_NULL; v = CPPAD_TRACK_NEW_VEC(m, v); // track v = new double[m] ddf_v = CPPAD_TRACK_NEW_VEC(n, ddf_v); // track ddf_v = new double[n] for(j = 0; j < n; j++) v[j] = double(n - j); fos_reverse(tag, int(m), int(n), v, ddf_v); // f(x) = .5 * ( x[0]^2 + x[1]^2 + ... + x[n-1]^2 ) // f'(x) = (x[0], x[1], ... , x[n-1]) // f''(x) * v = ( v[0], v[1], ... , x[n-1] ) for(j = 0; j < n; j++) ok &= CppAD::NearEqual(ddf_v[j], v[j], 1e-10, 1e-10); CPPAD_TRACK_DEL_VEC(v); // check usage of delete CPPAD_TRACK_DEL_VEC(ddf_v); return ok; } # endif // CPPAD_ADOLC_TEST bool std_math(void) { bool ok = true; using CppAD::AD; using CppAD::Independent; using CppAD::ADFun; double eps = std::numeric_limits::epsilon(); typedef AD ADdouble; // for first level of taping typedef AD ADDdouble; // for second level of taping size_t n = 1; // number independent variables size_t m = 1; // number dependent and independent variables CPPAD_TESTVECTOR(double) x(n), y(m); CPPAD_TESTVECTOR(ADdouble) ax(n), ay(m); CPPAD_TESTVECTOR(ADDdouble) aax(n), aay(m); // create af(x) = tanh(x) aax[0] = 1.; Independent( aax ); aay[0] = tanh(aax[0]); ADFun af(aax, aay); // create g(x) = af(x) ax[0] = 1.; Independent( ax ); ay = af.Forward(0, ax); ADFun g(ax, ay); // evaluate h(x) = g(x) x[0] = 1.; y = g.Forward(0, x); // check result double check = tanh(x[0]); ok &= CppAD::NearEqual(y[0], check, eps, eps); return ok; } // supress this test until ../bug/abs.sh is fixed # ifdef CPPAD_NOT_DEFINED bool abs(void) { bool ok = true; using CppAD::AD; using CppAD::Independent; using CppAD::ADFun; double eps = std::numeric_limits::epsilon(); typedef AD ADdouble; // for first level of taping typedef AD ADDdouble; // for second level of taping size_t n = 1; // number independent variables size_t m = 1; // number dependent and independent variables CPPAD_TESTVECTOR(double) x(n), y(m); CPPAD_TESTVECTOR(ADdouble) ax(n), ay(m); CPPAD_TESTVECTOR(ADDdouble) aax(n), aay(m); // create af(x) = abs(x) aax[0] = 1.; Independent( aax ); aay[0] = abs(aax[0]); ADFun af(aax, aay); // create g(x) = af'(x) ax[0] = 1.; Independent( ax ); ay = af.Jacobian(ax); ADFun g(ax, ay); // evaluate g(x) at same x as recording x[0] = 1.; y = g.Forward(0, x); // check result double check = 1.; ok &= CppAD::NearEqual(y[0], check, eps, eps); // evaluate g(x) at different x from recording // (but abs is an atomic operation so derivative should work) x[0] = -1.; y = g.Forward(0, x); // check result check = -1.; ok &= CppAD::NearEqual(y[0], check, eps, eps); return ok; } # endif } // END empty namespace bool mul_level(void) { bool ok = true; ok &= One(); ok &= Two(); # ifdef CPPAD_ADOLC_TEST ok &= adolc(); # endif ok &= std_math(); # ifdef CPPAD_NOT_DEFINED ok &= abs(); # endif return ok; } cppad-20170000.3/test_more/old_reciprocal.cpp0000644000175200017650000002435613057470461020131 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin old_reciprocal.cpp$$ $section Old Atomic Operation Reciprocal: Example and Test$$ $head Deprecated 2013-05-27$$ This example has been deprecated; see $cref atomic_reciprocal.cpp$$ instead. $head Theory$$ The example below defines the user atomic function $latex f : \B{R}^n \rightarrow \B{R}^m$$ where $latex n = 1$$, $latex m = 1$$, and $latex f(x) = 1 / x$$. $code $srcfile%test_more/old_reciprocal.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { // Begin empty namespace using CppAD::vector; // ---------------------------------------------------------------------- // a utility to compute the union of two sets. using CppAD::set_union; // ---------------------------------------------------------------------- // forward mode routine called by CppAD bool reciprocal_forward( size_t id , size_t k , size_t n , size_t m , const vector& vx , vector& vy , const vector& tx , vector& ty ) { assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); assert( k == 0 || vx.size() == 0 ); bool ok = false; double f, fp, fpp; // Must always define the case k = 0. // Do not need case k if not using f.Forward(q, xp) for q >= k. switch(k) { case 0: // this case must be implemented if( vx.size() > 0 ) vy[0] = vx[0]; // y^0 = f( x^0 ) = 1 / x^0 ty[0] = 1. / tx[0]; ok = true; break; case 1: // needed if first order forward mode is used assert( vx.size() == 0 ); // y^1 = f'( x^0 ) x^1 f = ty[0]; fp = - f / tx[0]; ty[1] = fp * tx[1]; ok = true; break; case 2: // needed if second order forward mode is used assert( vx.size() == 0 ); // Y''(t) = X'(t)^\R{T} f''[X(t)] X'(t) + f'[X(t)] X''(t) // 2 y^2 = x^1 * f''( x^0 ) x^1 + 2 f'( x^0 ) x^2 f = ty[0]; fp = - f / tx[0]; fpp = - 2.0 * fp / tx[0]; ty[2] = tx[1] * fpp * tx[1] / 2.0 + fp * tx[2]; ok = true; break; } return ok; } // ---------------------------------------------------------------------- // reverse mode routine called by CppAD bool reciprocal_reverse( size_t id , size_t k , size_t n , size_t m , const vector& tx , const vector& ty , vector& px , const vector& py ) { // Do not need case k if not using f.Reverse(k+1, w). assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); bool ok = false; double f, fp, fpp, fppp; switch(k) { case 0: // needed if first order reverse mode is used // reverse: F^0 ( tx ) = y^0 = f( x^0 ) f = ty[0]; fp = - f / tx[0]; px[0] = py[0] * fp;; ok = true; break; case 1: // needed if second order reverse mode is used // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1 f = ty[0]; fp = - f / tx[0]; fpp = - 2.0 * fp / tx[0]; px[1] = py[1] * fp; px[0] = py[1] * fpp * tx[1]; // reverse: F^0 ( tx ) = y^0 = f( x^0 ); px[0] += py[0] * fp; ok = true; break; case 2: // needed if third order reverse mode is used // reverse: F^2 ( tx ) = y^2 = // = x^1 * f''( x^0 ) x^1 / 2 + f'( x^0 ) x^2 f = ty[0]; fp = - f / tx[0]; fpp = - 2.0 * fp / tx[0]; fppp = - 3.0 * fpp / tx[0]; px[2] = py[2] * fp; px[1] = py[2] * fpp * tx[1]; px[0] = py[2] * tx[1] * fppp * tx[1] / 2.0 + fpp * tx[2]; // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1 px[1] += py[1] * fp; px[0] += py[1] * fpp * tx[1]; // reverse: F^0 ( tx ) = y^0 = f( x^0 ); px[0] += py[0] * fp; ok = true; break; } return ok; } // ---------------------------------------------------------------------- // forward Jacobian sparsity routine called by CppAD bool reciprocal_for_jac_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , vector< std::set >& s ) { // Can just return false if not using f.ForSparseJac assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); // sparsity for S(x) = f'(x) * R is same as sparsity for R s[0] = r[0]; return true; } // ---------------------------------------------------------------------- // reverse Jacobian sparsity routine called by CppAD bool reciprocal_rev_jac_sparse( size_t id , size_t n , size_t m , size_t p , vector< std::set >& r , const vector< std::set >& s ) { // Can just return false if not using RevSparseJac. assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); // sparsity for R(x) = S * f'(x) is same as sparsity for S for(size_t q = 0; q < p; q++) r[q] = s[q]; return true; } // ---------------------------------------------------------------------- // reverse Hessian sparsity routine called by CppAD bool reciprocal_rev_hes_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , const vector& s , vector& t , const vector< std::set >& u , vector< std::set >& v ) { // Can just return false if not use RevSparseHes. assert( id == 0 ); assert( n == 1 ); assert( m == 1 ); // sparsity for T(x) = S(x) * f'(x) is same as sparsity for S t[0] = s[0]; // V(x) = [ f'(x)^T * g''(y) * f'(x) + g'(y) * f''(x) ] * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate the sparsity for U because derivative of // reciprocal may be non-zero v[0] = u[0]; // convert forward Jacobian sparsity to Hessian sparsity // because second derivative of reciprocal may be non-zero if( s[0] ) v[0] = set_union(v[0], r[0] ); return true; } // --------------------------------------------------------------------- // Declare the AD routine reciprocal(id, ax, ay) CPPAD_USER_ATOMIC( reciprocal , CppAD::vector , double , reciprocal_forward , reciprocal_reverse , reciprocal_for_jac_sparse , reciprocal_rev_jac_sparse , reciprocal_rev_hes_sparse ) } // End empty namespace bool old_reciprocal(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits::epsilon(); // -------------------------------------------------------------------- // Create the function f(x) // // domain space vector size_t n = 1; double x0 = 0.5; vector< AD > ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; vector< AD > ay(m); // call user function and store reciprocal(x) in au[0] vector< AD > au(m); size_t id = 0; // not used reciprocal(id, ax, au); // u = 1 / x // call user function and store reciprocal(u) in ay[0] reciprocal(id, au, ay); // y = 1 / u = x // create f: x -> y and stop tape recording CppAD::ADFun f; f.Dependent (ax, ay); // f(x) = x // -------------------------------------------------------------------- // Check forward mode results // // check function value double check = x0; ok &= NearEqual( Value(ay[0]) , check, eps, eps); // check zero order forward mode size_t q; vector x_q(n), y_q(m); q = 0; x_q[0] = x0; y_q = f.Forward(q, x_q); ok &= NearEqual(y_q[0] , check, eps, eps); // check first order forward mode q = 1; x_q[0] = 1; y_q = f.Forward(q, x_q); check = 1.; ok &= NearEqual(y_q[0] , check, eps, eps); // check second order forward mode q = 2; x_q[0] = 0; y_q = f.Forward(q, x_q); check = 0.; ok &= NearEqual(y_q[0] , check, eps, eps); // -------------------------------------------------------------------- // Check reverse mode results // // third order reverse mode q = 3; vector w(m), dw(n * q); w[0] = 1.; dw = f.Reverse(q, w); check = 1.; ok &= NearEqual(dw[0] , check, eps, eps); check = 0.; ok &= NearEqual(dw[1] , check, eps, eps); ok &= NearEqual(dw[2] , check, eps, eps); // -------------------------------------------------------------------- // forward mode sparstiy pattern size_t p = n; CppAD::vectorBool r1(n * p), s1(m * p); r1[0] = true; // compute sparsity pattern for x[0] s1 = f.ForSparseJac(p, r1); ok &= s1[0] == true; // f[0] depends on x[0] // -------------------------------------------------------------------- // reverse mode sparstiy pattern q = m; CppAD::vectorBool s2(q * m), r2(q * n); s2[0] = true; // compute sparsity pattern for f[0] r2 = f.RevSparseJac(q, s2); ok &= r2[0] == true; // f[0] depends on x[0] // -------------------------------------------------------------------- // Hessian sparsity (using previous ForSparseJac call) CppAD::vectorBool s3(m), h(p * n); s3[0] = true; // compute sparsity pattern for f[0] h = f.RevSparseHes(p, s3); ok &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero // ----------------------------------------------------------------- // Free all temporary work space associated with old_atomic objects. // (If there are future calls to user atomic functions, they will // create new temporary work space.) CppAD::user_atomic::clear(); return ok; } // END C++ cppad-20170000.3/test_more/fun_check.cpp0000644000175200017650000000705413057470461017071 0ustar coincoin-web// $Id: fun_check.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* old example, now just used for testing deprecated syntax f.Dependent(y) */ // BEGIN C++ # include namespace { // ----------------------------------------------------------- // define the template function object Fun in empty namespace template class Fun { private: size_t n; public: // function constructor Fun(size_t n_) : n(n_) { } // function evaluator Vector operator() (const Vector &x) { Vector y(n); size_t i; for(i = 0; i < n; i++) { // This operaiton sequence depends on x if( x[i] >= 0 ) y[i] = exp(x[i]); else y[i] = exp(-x[i]); } return y; } }; // template function FunCheckCases in empty namespace template bool FunCheckCases(void) { bool ok = true; using CppAD::AD; using CppAD::ADFun; using CppAD::Independent; // use the ADFun default constructor ADFun f; // domain space vector size_t n = 2; ADVector X(n); X[0] = -1.; X[1] = 1.; // declare independent variables and starting recording Independent(X); // create function object to use with AD Fun< AD, ADVector > G(n); // range space vector size_t m = n; ADVector Y(m); Y = G(X); // stop tape and store operation sequence in f : X -> Y f.Dependent(Y); ok &= (f.size_order() == 0); // no implicit forward operation // create function object to use with double Fun g(n); // function values should agree when the independent variable // values are the same as during recording Vector x(n); size_t j; for(j = 0; j < n; j++) x[j] = Value(X[j]); double r = 1e-10; double a = 1e-10; ok &= FunCheck(f, g, x, a, r); // function values should not agree when the independent variable // values are the negative of values during recording for(j = 0; j < n; j++) x[j] = - Value(X[j]); ok &= ! FunCheck(f, g, x, a, r); // re-tape to obtain the new AD of double operation sequence for(j = 0; j < n; j++) X[j] = x[j]; Independent(X); Y = G(X); // stop tape and store operation sequence in f : X -> Y f.Dependent(Y); ok &= (f.size_order() == 0); // no implicit forward with this x // function values should agree now ok &= FunCheck(f, g, x, a, r); return ok; } } // End empty namespace # include # include bool FunCheck(void) { bool ok = true; typedef CppAD::vector Vector1; typedef CppAD::vector< CppAD::AD > ADVector1; typedef std::vector Vector2; typedef std::vector< CppAD::AD > ADVector2; typedef std::valarray Vector3; typedef std::valarray< CppAD::AD > ADVector3; // Run with Vector and ADVector equal to three different cases // all of which are Simple Vectors with elements of type // double and AD respectively. ok &= FunCheckCases< Vector1, ADVector2 >(); ok &= FunCheckCases< Vector2, ADVector3 >(); ok &= FunCheckCases< Vector3, ADVector1 >(); return ok; } // END C++ cppad-20170000.3/test_more/mul_cskip.cpp0000644000175200017650000000363013057470461017126 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include // Test multiple level conditional skip where value of comparision is // uncertain during forward mode base Base value can be a variable. bool mul_cskip(void) { bool ok = true; using namespace CppAD; using CppAD::vector; typedef AD a1type; typedef AD a2type; size_t n = 2; size_t m = 1; vector x(n), y(m); x[0] = 0.0; x[1] = 1.0; // start recording a2type operations vector a2x(n), a2y(m); for (size_t j = 0; j < n; j++) a2x[j] = a2type( a1type(x[j]) ); Independent(a2x); // a1f(x) = x_0 * x_1 if x[0] == 1 // 0.0 otherwise a2type a2zero = a2type(0.0); a2type a2one = a2type(1.0); a2type a2p = a2x[0] * a2x[1]; a2y[0] = CondExpEq(a2x[0], a2one, a2p, a2zero); ADFun a1f(a2x, a2y); // Optimization will check to see if we can skip part of conditional // expression that is not used. a1f.optimize(); // f(x) = x_0 * x_1 if x[0] == 1 // 0.0 otherwise vector a1x(n), a1y(m); for (size_t j = 0; j < n; j++) a1x[j] = a1type(x[j]); Independent(a1x); a1y = a1f.Forward(0, a1x); CppAD::ADFun f(a1x, a1y); // check case where x[0] == 1 x[0] = 1.0; x[1] = 2.0; y = f.Forward(0, x); ok &= y[0] == x[1]; // check case where x[0] != 1 x[0] = 3.0; x[1] = 2.0; y = f.Forward(0, x); ok &= y[0] == 0.0; return ok; } cppad-20170000.3/test_more/mul_cond_rev.cpp0000644000175200017650000001615613057470461017623 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test of multi-level conditional expressions reverse mode */ # include bool mul_cond_rev(void) { bool ok = true; using CppAD::vector; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); // typedef CppAD::AD a1double; typedef CppAD::AD a2double; // a1double a1zero = 0.0; a2double a2zero = a1zero; a1double a1one = 1.0; a2double a2one = a1one; // // -------------------------------------------------------------------- // create a1f = f(x) size_t n = 1; size_t m = 25; // vector a2x(n), a2y(m); a2x[0] = a2double( 5.0 ); Independent(a2x); // size_t i = 0; // variable that is greater than one when x[0] is zero // and less than one when x[0] is 1.0 or greater a2double a2switch = a2one / (a2x[0] + a2double(0.5)); // variable that is infinity when x[0] is zero // and a normal number when x[0] is 1.0 or greater a2double a2inf_var = a2one / a2x[0]; // variable that is nan when x[0] is zero // and a normal number when x[0] is 1.0 or greater a2double a2nan_var = ( a2one / a2inf_var ) / a2x[0]; // variable that is one when x[0] is zero // and less then one when x[0] is 1.0 or greater a2double a2one_var = a2one / ( a2one + a2x[0] ); // div a2y[i++] = CondExpGt(a2x[0], a2zero, a2nan_var, a2zero); // abs a2y[i++] = CondExpGt(a2x[0], a2zero, abs( a2y[0] ), a2zero); // add a2y[i++] = CondExpGt(a2x[0], a2zero, a2nan_var + a2nan_var, a2zero); // acos a2y[i++] = CondExpGt(a2x[0], a2zero, acos(a2switch), a2zero); // asin a2y[i++] = CondExpGt(a2x[0], a2zero, asin(a2switch), a2zero); // atan a2y[i++] = CondExpGt(a2x[0], a2zero, atan(a2nan_var), a2zero); // cos a2y[i++] = CondExpGt(a2x[0], a2zero, cos(a2nan_var), a2zero); // cosh a2y[i++] = CondExpGt(a2x[0], a2zero, cosh(a2nan_var), a2zero); // exp a2y[i++] = CondExpGt(a2x[0], a2zero, exp(a2nan_var), a2zero); // log a2y[i++] = CondExpGt(a2x[0], a2zero, log(a2x[0]), a2zero); // mul a2y[i++] = CondExpGt(a2x[0], a2zero, a2x[0] * a2inf_var, a2zero); // pow a2y[i++] = CondExpGt(a2x[0], a2zero, pow(a2inf_var, a2x[0]), a2zero); // sin a2y[i++] = CondExpGt(a2x[0], a2zero, sin(a2nan_var), a2zero); // sinh a2y[i++] = CondExpGt(a2x[0], a2zero, sinh(a2nan_var), a2zero); // sqrt a2y[i++] = CondExpGt(a2x[0], a2zero, sqrt(a2x[0]), a2zero); // sub a2y[i++] = CondExpGt(a2x[0], a2zero, a2inf_var - a2nan_var, a2zero); // tan a2y[i++] = CondExpGt(a2x[0], a2zero, tan(a2nan_var), a2zero); // tanh a2y[i++] = CondExpGt(a2x[0], a2zero, tanh(a2nan_var), a2zero); // azmul a2y[i++] = CondExpGt(a2x[0], a2zero, azmul(a2x[0], a2inf_var), a2zero); // // Operations that are C+11 atomic // // acosh a2y[i++] = CondExpGt(a2x[0], a2zero, acosh( a2x[0] ), a2zero); // asinh a2y[i++] = CondExpGt(a2x[0], a2zero, asinh( a2nan_var ), a2zero); // atanh a2y[i++] = CondExpGt(a2x[0], a2zero, atanh( a2one_var ), a2zero); // erf a2y[i++] = CondExpGt(a2x[0], a2zero, erf( a2nan_var ), a2zero); // expm1 a2y[i++] = CondExpGt(a2x[0], a2zero, expm1(a2nan_var), a2zero); // log1p a2y[i++] = CondExpGt(a2x[0], a2zero, log1p(- a2one_var ), a2zero); // ok &= i == m; CppAD::ADFun a1f; a1f.Dependent(a2x, a2y); // -------------------------------------------------------------------- // create h = f(x) vector a1x(n), a1y(m); a1x[0] = 5.0; // Independent(a1x); i = 0; a1double a1switch = a1one / (a1x[0] + a1double(0.5)); a1double a1inf_var = a1one / a1x[0]; a1double a1nan_var = ( a1one / a1inf_var ) / a1x[0]; a1double a1one_var = a1one / ( a1one + a1x[0] ); // div a1y[i++] = CondExpGt(a1x[0], a1zero, a1nan_var, a1zero); // abs a1y[i++] = CondExpGt(a1x[0], a1zero, abs( a1y[0] ), a1zero); // add a1y[i++] = CondExpGt(a1x[0], a1zero, a1nan_var + a1nan_var, a1zero); // acos a1y[i++] = CondExpGt(a1x[0], a1zero, acos(a1switch), a1zero); // asin a1y[i++] = CondExpGt(a1x[0], a1zero, asin(a1switch), a1zero); // atan a1y[i++] = CondExpGt(a1x[0], a1zero, atan(a1nan_var), a1zero); // cos a1y[i++] = CondExpGt(a1x[0], a1zero, cos(a1nan_var), a1zero); // cosh a1y[i++] = CondExpGt(a1x[0], a1zero, cosh(a1nan_var), a1zero); // exp a1y[i++] = CondExpGt(a1x[0], a1zero, exp(a1nan_var), a1zero); // log a1y[i++] = CondExpGt(a1x[0], a1zero, log(a1x[0]), a1zero); // mul a1y[i++] = CondExpGt(a1x[0], a1zero, a1x[0] * a1inf_var, a1zero); // pow a1y[i++] = CondExpGt(a1x[0], a1zero, pow(a1inf_var, a1x[0]), a1zero); // sin a1y[i++] = CondExpGt(a1x[0], a1zero, sin(a1nan_var), a1zero); // sinh a1y[i++] = CondExpGt(a1x[0], a1zero, sinh(a1nan_var), a1zero); // sqrt a1y[i++] = CondExpGt(a1x[0], a1zero, sqrt(a1x[0]), a1zero); // sub a1y[i++] = CondExpGt(a1x[0], a1zero, a1inf_var - a1nan_var, a1zero); // tan a1y[i++] = CondExpGt(a1x[0], a1zero, tan(a1nan_var), a1zero); // tanh a1y[i++] = CondExpGt(a1x[0], a1zero, tanh(a1nan_var), a1zero); // azmul a1y[i++] = CondExpGt(a1x[0], a1zero, azmul(a1x[0], a1inf_var), a1zero); // // Operations that are C+11 atomic // // acosh a1y[i++] = CondExpGt(a1x[0], a1zero, acosh( a1x[0] ), a1zero); // asinh a1y[i++] = CondExpGt(a1x[0], a1zero, asinh( a1nan_var ), a1zero); // atanh a1y[i++] = CondExpGt(a1x[0], a1zero, atanh( a1one_var ), a1zero); // erf a1y[i++] = CondExpGt(a1x[0], a1zero, erf( a1nan_var ), a1zero); // expm1 a1y[i++] = CondExpGt(a1x[0], a1zero, expm1(a1nan_var), a1zero); // log1p a1y[i++] = CondExpGt(a1x[0], a1zero, log1p(- a1one_var ), a1zero); // ok &= i == m; CppAD::ADFun h; h.Dependent(a1x, a1y); // -------------------------------------------------------------------- // create g = f'(x) vector a1dy(m), a1w(m); a1x[0] = 2.0; for(i = 0; i < m; i++) a1w[i] = 0.0; // Independent(a1x); a1f.Forward(0, a1x); // for(i = 0; i < m; i++) { a1w[i] = 1.0; vector dyi_dx = a1f.Reverse(1, a1w); a1dy[i] = dyi_dx[0]; a1w[i] = 0.0; } CppAD::ADFun g; // g uses reverse mode derivatives g.Dependent(a1x, a1dy); // -------------------------------------------------------------------- // check case where x[0] > 0 vector x(1), dx(1), dg(m), dh(m); x[0] = 2.0; dx[0] = 1.0; h.Forward(0, x); dh = h.Forward(1, dx); // dh uses forward mode derivatives dg = g.Forward(0, x); for(i = 0; i < m; i++) ok &= NearEqual(dg[i], dh[i], eps, eps); // -------------------------------------------------------------------- // check case where x[0] = 0 x[0] = 0.0; dg = g.Forward(0, x); h.Forward(0, x); dh = h.Forward(1, dx); for(i = 0; i < m; i++) { ok &= dg[i] == 0.0; ok &= dh[i] == 0.0; } // -------------------------------------------------------------------- return ok; } cppad-20170000.3/test_more/compare.cpp0000644000175200017650000000365613057470461016576 0ustar coincoin-web// $Id: compare.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Check comparison operators between AD< AD > and Base, int */ # include namespace { template bool Compare(void) { bool ok = true; using CppAD::AD; Type middle = 4; AD three = 3; AD four = 4; AD five = 5; // AD > Type ok &= ! (three > middle); ok &= ! (four > middle); ok &= (five > middle); // Type > AD ok &= (middle > three ); ok &= ! (middle > four ); ok &= ! (middle > five ); // AD >= Type ok &= ! (three >= middle); ok &= (four >= middle); ok &= (five >= middle); // Type > AD ok &= (middle >= three ); ok &= (middle >= four ); ok &= ! (middle >= five ); // AD < Type ok &= (three < middle); ok &= ! (four < middle); ok &= ! (five < middle); // Type > AD ok &= ! (middle < three ); ok &= ! (middle < four ); ok &= (middle < five ); // AD <= Type ok &= (three <= middle); ok &= (four <= middle); ok &= ! (five <= middle); // Type > AD ok &= ! (middle <= three ); ok &= (middle <= four ); ok &= (middle <= five ); return ok; } } bool Compare(void) { bool ok = true; ok &= Compare(); ok &= Compare(); ok &= Compare< CppAD::AD >(); return ok; } cppad-20170000.3/test_more/sub_eq.cpp0000644000175200017650000000631113057470461016415 0ustar coincoin-web// $Id: sub_eq.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old SubEq examples now used just for valiadation testing */ # include namespace { // BEGIN empty namespace bool SubEqTestOne(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 2.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; // dependent variable values Z[x] = U[s]; Z[y] = U[t]; Z[x] -= U[t]; // AD -= AD Z[y] -= 5.; // AD -= double // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check function values ok &= ( Z[x] == 3. - 2. ); ok &= ( Z[y] == 2. - 5. ); // forward computation of partials w.r.t. t v[s] = 0.; v[t] = 1.; w = f.Forward(1, v); ok &= ( w[x] == -1. ); // dx/dt ok &= ( w[y] == 1. ); // dy/dt // reverse computation of second partials of x CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 1.; w[y] = 0.; r = f.Reverse(2, w); ok &= ( r[2 * s + 1] == 0. ); // d^2 x / (ds ds) ok &= ( r[2 * t + 1] == 0. ); // d^2 x / (ds dt) return ok; } bool SubEqTestTwo(void) { bool ok = true; using namespace CppAD; // independent variable vector double u0 = .5; CPPAD_TESTVECTOR(AD) U(1); U[0] = u0; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = U[0]; // initial value Z[0] -= 2; // AD -= int Z[0] -= 4.; // AD -= double Z[0] -= 2 * U[0]; // AD -= AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(Z[0] , u0-2-4-2*u0, 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = -1.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = -1.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } } // END empty namespace bool SubEq(void) { bool ok = true; ok &= SubEqTestOne(); ok &= SubEqTestTwo(); return ok; } cppad-20170000.3/test_more/runge_45.cpp0000644000175200017650000000711413057470461016571 0ustar coincoin-web// $Id: runge_45.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old OdeRunge example now used just for valiadation testing of Runge45 */ # include # include # include namespace { // BEGIN Empty namespace class TestFun { public: TestFun(const CPPAD_TESTVECTOR(CppAD::AD) &w_) { w.resize( w_.size() ); w = w_; } void Ode( const CppAD::AD &t, const CPPAD_TESTVECTOR(CppAD::AD) &x, CPPAD_TESTVECTOR(CppAD::AD) &f) { using CppAD::exp; size_t n = x.size(); size_t i; f[0] = 0.; for(i = 1; i < n-1; i++) f[i] = w[i] * x[i-1]; f[n-1] = x[0] * x[1]; } private: CPPAD_TESTVECTOR(CppAD::AD) w; }; } // END Empty namespace bool Runge45(void) { bool ok = true; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); size_t i; size_t j; size_t k; size_t n = 6; size_t m = n - 1; CPPAD_TESTVECTOR(AD) x(n); AD t0 = 0.; AD t1 = 2.; size_t nstep = 2; // vector of independent variables CPPAD_TESTVECTOR(AD) w(m); for(i = 0; i < m; i++) w[i] = double(i); Independent(w); // construct function object using independent variables TestFun fun(w); // initial value of x CPPAD_TESTVECTOR(AD) x0(n); for(i = 0; i < n; i++) x0[i] = 0.; x0[0] = exp( w[0] ); // solve the differential equation x = Runge45(fun, nstep, t0, t1, x0); // create f : w -> x and vectors for evaluating derivatives ADFun f(w, x); CPPAD_TESTVECTOR(double) q( f.Domain() ); CPPAD_TESTVECTOR(double) r( f.Range() ); // for i < n-1, // x[i](2) = exp( w[0] ) * (w[1] / 1) * ... * (w[i] / i) * 2^i AD xi2 = exp(w[0]); for(i = 0; i < n-1; i++) { ok &= NearEqual(x[i], xi2, eps99, eps99); if( i < n-2 ) xi2 *= w[i+1] * 2. / double(i+1); } // x[n-1](2) = exp(2 * w[0]) * w[1] * 2^2 / 2 xi2 = exp(2. * w[0]) * w[1] * 2.; ok &= NearEqual(x[n-1], xi2, eps99, eps99); // the partial of x[i](2) with respect to w[j] is // x[i](2) / w[j] if 0 < j <= i < n-1 // x[i](2) if j == 0 and i < n-1 // 2*x[i](2) if j == 0 and i = n-1 // x[i](2) / w[j] if j == 1 and i = n-1 // zero otherwise for(i = 0; i < n-1; i++) { // compute partials of x[i] for(k = 0; k < n; k++) r[k] = 0.; r[i] = 1.; q = f.Reverse(1,r); for(j = 0; j < m; j++) { // check partial of x[i] w.r.t w[j] if (j == 0 ) ok &= NearEqual(q[j], x[i], eps99, eps99); else if( j <= i ) ok &= NearEqual( q[j], x[i]/w[j], 1e-14, 1e-14); else ok &= NearEqual(q[j], 0., eps99, eps99); } } // compute partials of x[n-1] i = n-1; for(k = 0; k < n; k++) r[k] = 0.; r[i] = 1.; q = f.Reverse(1,r); for(j = 0; j < m; j++) { // check partial of x[n-1] w.r.t w[j] if (j == 0 ) ok &= NearEqual(q[j], 2.*x[i], eps99, eps99); else if( j == 1 ) ok &= NearEqual( q[j], x[i]/w[1], 1e-14, 1e-14); else ok &= NearEqual(q[j], 0., eps99, eps99); } return ok; } cppad-20170000.3/test_more/erf.cpp0000644000175200017650000001560513057470461015721 0ustar coincoin-web// $Id: erf.cpp 3833 2016-09-29 14:31:50Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // --------------------------------------------------------------------- bool old_example(void) { bool ok = true; using namespace CppAD; using CppAD::atan; using CppAD::exp; using CppAD::sqrt; # if CPPAD_USE_CPLUSPLUS_2011 double eps = 100.0 * std::numeric_limits::epsilon(); # endif // Construct function object corresponding to erf CPPAD_TESTVECTOR(AD) ax(1); CPPAD_TESTVECTOR(AD) ay(1); ax[0] = 0.; Independent(ax); ay[0] = erf(ax[0]); ADFun f(ax, ay); // Construct function object corresponding to derivative of erf Independent(ax); double pi = 4.0 * atan(1.0); ay[0] = exp( - ax[0] * ax[0] ) * 2.0 / sqrt(pi); ADFun df(ax, ay); // vectors to use with function object CPPAD_TESTVECTOR(double) x0(1), y0(1), x1(1), y1(1), check(1); // check value at zero x0[0] = 1.5; y0 = f.Forward(0, x0); check[0] = 0.96611; ok &= std::fabs(check[0] - y0[0]) <= 4e-4; // check the derivative of error function x1[0] = 1.0; y1 = f.Forward(1, x1); check = df.Forward(0, x0); ok &= NearEqual(check[0], y1[0], 0., 2e-3); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(check[0], y1[0], eps, eps); # endif // check second derivative CPPAD_TESTVECTOR(double) x2(1), y2(1); x2[0] = 0.0; y2 = f.Forward(2, x2); check = df.Forward(1, x1); ok &= NearEqual(check[0] / 2.0, y2[0], 0., 2e-3); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(check[0] / 2.0, y2[0], eps, eps); # endif // check third derivative CPPAD_TESTVECTOR(double) x3(1), y3(1); x3[0] = 0.0; y3 = f.Forward(3, x3); check = df.Forward(2, x2); ok &= NearEqual(check[0] / 3.0, y3[0], 0., 2e-3); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(check[0] / 3.0, y3[0], eps, eps); # endif // check 4-th order of reverse mode CPPAD_TESTVECTOR(double) w(1), dy(4), x4(1), y4(1); x4[0] = 0.0; w[0] = 1.0; dy = f.Reverse(4, w); y4 = f.Forward(4, x4); // ok &= NearEqual(dy[0], y1[0], 0., 2e-3); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(dy[0], y1[0], eps, eps); # endif // ok &= NearEqual(dy[1], 2.0 * y2[0], 0., 2e-3); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(dy[1], 2.0 * y2[0], eps, eps); # endif // ok &= NearEqual(dy[2], 3.0 * y3[0], 0., 2e-3); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(dy[2], 3.0 * y3[0], eps, eps); # endif // ok &= NearEqual(dy[3], 4.0 * y4[0], 0., 2e-3); # if CPPAD_USE_CPLUSPLUS_2011 ok &= NearEqual(dy[3], 4.0 * y4[0], eps, eps); # endif return ok; } # if CPPAD_USE_CPLUSPLUS_2011 // --------------------------------------------------------------------- bool hessian(void) { bool ok = true; double eps = 1.0 * std::numeric_limits::epsilon(); using CppAD::vector; using CppAD::AD; size_t n = 2; size_t m = 1; vector x(n), w(m); w[0] = 1.0; vector< AD > ax(n), ay(m); ax[0] = x[0] = 0.5; ax[1] = x[1] = 0.0; // construct function CppAD::Independent(ax); ay[0] = erf( 2.0 * ax[0] ); CppAD::ADFun f(ax, ay); // dense hessian vector dense_hess = f.Hessian(x, 0); // sparse_hessian vector sparse_hess = f.SparseHessian(x, w); // Define g(u) = erf(2 * u) // g'(u) = 2 * erf'(2 * u) // = 2 * exp( - 2 * u * 2 * u ) * 2 / sqrt(pi) // = exp( - 4 * u * u ) * 4 / sqrt(pi) // g''(u) = - exp( - 4 * u * u ) * 32 * u / sqrt(pi) double root_pi = std::sqrt( 4.0 * atan(1.0) ); double check = -std::exp(-4.0 * x[0] * x[0]) * 32.0 * x[0] / root_pi; ok &= CppAD::NearEqual(dense_hess[0], check, eps, eps); ok &= CppAD::NearEqual(sparse_hess[0], check, eps, eps); for(size_t k = 1; k < n * n; k++) { ok &= CppAD::NearEqual(dense_hess[k], 0.0, eps, eps); ok &= CppAD::NearEqual(sparse_hess[k], 0.0, eps, eps); } return ok; } // --------------------------------------------------------------------- bool mul_dir(void) { bool ok = true; using namespace CppAD; using CppAD::atan; using CppAD::exp; using CppAD::sqrt; double eps = 100.0 * std::numeric_limits::epsilon(); // Construct function object corresponding to erf CPPAD_TESTVECTOR(AD) ax(1); CPPAD_TESTVECTOR(AD) ay(1); ax[0] = 0.; Independent(ax); ay[0] = erf(ax[0]); ADFun f(ax, ay); // Construct function object corresponding to derivative of erf Independent(ax); double pi = 4.0 * atan(1.0); ay[0] = exp( - ax[0] * ax[0] ) * 2.0 / sqrt(pi); ADFun df(ax, ay); // number of directions size_t r = 1; // vectors to use with objects CPPAD_TESTVECTOR(double) x0(1), y0(1), x1(1), y1(1), y2(1), y3(1); CPPAD_TESTVECTOR(double) zero(1), check(1); CPPAD_TESTVECTOR(double) xq(r), yq(r), checkq(r), zeroq(r); // check function value x0[0] = 1.5; y0 = f.Forward(0, x0); check[0] = 0.9661051464753108; double tmp = std::max(1e-15, eps); ok &= NearEqual(check[0], y0[0], 0.0, tmp); // check first order derivative x1[0] = 1.0; y1 = f.Forward(1, x1); check = df.Forward(0, x0); ok &= NearEqual(check[0], y1[0], eps, eps); for(size_t ell = 0.0; ell < r; ell++) { xq[ell] = x1[ell] / (ell + 1.0); zeroq[ell] = 0.0; } yq = f.Forward(1, r, xq); for(size_t ell = 0.0; ell < r; ell++) { checkq[ell] = check[0] * xq[ell]; ok &= NearEqual(checkq[ell], yq[ell], eps, eps); } // check second order derivative zero[0] = 0.0; y2 = f.Forward(2, zero); check = df.Forward(1, x1); check[0] /= 2.0; ok &= NearEqual(check[0], y2[0], eps, eps); yq = f.Forward(2, r, zeroq); for(size_t ell = 0.0; ell < r; ell++) { checkq[ell] = check[0] * xq[ell]; ok &= NearEqual(checkq[ell], yq[ell], eps, eps); } // check third order derivative zero[0] = 0.0; y3 = f.Forward(3, zero); check = df.Forward(2, zero); check[0] /= 3.0; ok &= NearEqual(check[0], y3[0], eps, eps); yq = f.Forward(3, r, zeroq); for(size_t ell = 0.0; ell < r; ell++) { checkq[ell] = check[0] * xq[ell]; ok &= NearEqual(checkq[ell], yq[ell], eps, eps); } return ok; } // ------------------------------------------------------------------- # endif } bool erf(void) { bool ok = true; ok &= old_example(); # if CPPAD_USE_CPLUSPLUS_2011 ok &= hessian(); ok &= mul_dir(); # endif return ok; } cppad-20170000.3/test_more/sub_zero.cpp0000644000175200017650000000360513057470461016772 0ustar coincoin-web// $Id: sub_zero.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test the use of the special parameters zero and one with the multiply operator */ # include typedef CppAD::AD ADdouble; typedef CppAD::AD< ADdouble > ADDdouble; bool SubZero(void) { using namespace CppAD; bool ok = true; size_t i; for(i = 0; i < 2; i++) { // run through the cases x = 0, 1 size_t j; for(j = 0; j < 2; j++) { // run through the cases y = 0, 1 CPPAD_TESTVECTOR( ADdouble ) x(1); x[0] = double(i); Independent(x); CPPAD_TESTVECTOR( ADDdouble ) y(1); y[0] = ADDdouble(j); Independent(y); CPPAD_TESTVECTOR( ADDdouble ) z(2); z[0] = x[0] - y[0]; z[1] = y[0] - x[0]; z[1] -= x[0]; // f(y) = z = { x - y , y - x - x } ADFun< ADdouble > f(y, z); CPPAD_TESTVECTOR( ADdouble ) u( f.Domain() ); CPPAD_TESTVECTOR( ADdouble ) v( f.Range() ); // v = f(y) u[0] = ADdouble(j); v = f.Forward(0, u); // check value of f ok &= v[0] == x[0] - ADdouble(j); ok &= v[1] == ADdouble(j) - x[0] - x[0]; // g(x) = f(y) = {x - y , y - x - x} ADFun g(x, v); CPPAD_TESTVECTOR( double ) a( g.Domain() ); CPPAD_TESTVECTOR( double ) b( g.Range() ); // b = g'(x) a[0] = 1.; b = g.Forward(1, a); // check derivatives of g ok &= (b[0] == 1.); ok &= (b[1] == -2.); } } return ok; } cppad-20170000.3/test_more/expm1.cpp0000644000175200017650000000374013057470461016174 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include bool expm1(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // a temporary value AD log_p1 = CppAD::log(ax[0] + 1.0); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CppAD::expm1(log_p1); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // check value ok &= NearEqual(ay[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // forward computation of higher order partials w.r.t. x[0] size_t n_order = 5; for(size_t order = 2; order < n_order; order++) { dx[0] = 0.; dy = f.Forward(order, dx); ok &= NearEqual(dy[0], 0., eps, eps); } // reverse computation of derivatives CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n_order * n); w[0] = 1.; dw = f.Reverse(n_order, w); ok &= NearEqual(dw[0], 1., eps, eps); for(size_t order = 1; order < n_order; order++) ok &= NearEqual(dw[order * n + 0], 0., eps, eps); return ok; } // END C++ cppad-20170000.3/test_more/ode_err_control.cpp0000644000175200017650000002475713057470461020334 0ustar coincoin-web// $Id: ode_err_control.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include // for size_t # include // for exp # include // CppAD::OdeErrControl # include // CppAD::NearEqual # include // CppAD::vector # include // CppAD::Runge45 /* ------------------------------------------------------------------------- Test relative error with zero initial conditions. (Uses minimum step size to integrate). */ namespace { // -------------------------------------------------------------- class Fun_one { private: size_t n; // dimension of the state space public: // constructor Fun_one(size_t n_) : n(n_) { } // given x(0) = 0 // solution is x_i (t) = t^(i+1) void Ode( const double &t, const CppAD::vector &x, CppAD::vector &f) { size_t i; f[0] = 1.; for(i = 1; i < n; i++) f[i] = (i+1) * x[i-1]; } }; // -------------------------------------------------------------- class Method_one { private: Fun_one F; public: // constructor Method_one(size_t n_) : F(n_) { } void step( double ta, double tb, CppAD::vector &xa , CppAD::vector &xb , CppAD::vector &eb ) { xb = CppAD::Runge45(F, 1, ta, tb, xa, eb); } size_t order(void) { return 4; } }; } bool OdeErrControl_one(void) { bool ok = true; // initial return value using CppAD::NearEqual; // Runge45 should yield exact results for x_i (t) = t^(i+1), i < 4 size_t n = 6; // construct method for n component solution Method_one method(n); // inputs to OdeErrControl double ti = 0.; double tf = .9; double smin = 1e-2; double smax = 1.; double scur = .5; double erel = 1e-7; CppAD::vector xi(n); CppAD::vector eabs(n); size_t i; for(i = 0; i < n; i++) { xi[i] = 0.; eabs[i] = 0.; } // outputs from OdeErrControl CppAD::vector ef(n); CppAD::vector xf(n); xf = OdeErrControl(method, ti, tf, xi, smin, smax, scur, eabs, erel, ef); double check = 1.; for(i = 0; i < n; i++) { check *= tf; ok &= NearEqual(check, xf[i], erel, 0.); } return ok; } /* Old example now just a test Define $latex X : \B{R} \rightarrow \B{R}^2$$ by $latex \[ \begin{array}{rcl} X_0 (t) & = & - \exp ( - w_0 t ) \\ X_1 (t) & = & \frac{w_0}{w_1 - w_0} [ \exp ( - w_0 t ) - \exp( - w_1 t )] \end{array} \] $$ It follows that $latex X_0 (0) = 1$$, $latex X_1 (0) = 0$$ and $latex \[ \begin{array}{rcl} X_0^{(1)} (t) & = & - w_0 X_0 (t) \\ X_1^{(1)} (t) & = & + w_0 X_0 (t) - w_1 X_1 (t) \end{array} \] $$ */ namespace { // -------------------------------------------------------------- class Fun_two { private: CppAD::vector w; public: // constructor Fun_two(const CppAD::vector &w_) : w(w_) { } // set f = x'(t) void Ode( const double &t, const CppAD::vector &x, CppAD::vector &f) { f[0] = - w[0] * x[0]; f[1] = + w[0] * x[0] - w[1] * x[1]; } }; // -------------------------------------------------------------- class Method_two { private: Fun_two F; public: // constructor Method_two(const CppAD::vector &w_) : F(w_) { } void step( double ta, double tb, CppAD::vector &xa , CppAD::vector &xb , CppAD::vector &eb ) { xb = CppAD::Runge45(F, 1, ta, tb, xa, eb); } size_t order(void) { return 4; } }; } bool OdeErrControl_two(void) { bool ok = true; // initial return value using CppAD::NearEqual; CppAD::vector w(2); w[0] = 10.; w[1] = 1.; Method_two method(w); CppAD::vector xi(2); xi[0] = 1.; xi[1] = 0.; CppAD::vector eabs(2); eabs[0] = 1e-4; eabs[1] = 1e-4; // inputs double ti = 0.; double tf = 1.; double smin = 1e-4; double smax = 1.; double scur = .5; double erel = 0.; // outputs CppAD::vector ef(2); CppAD::vector xf(2); CppAD::vector maxabs(2); size_t nstep; xf = OdeErrControl(method, ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep); double x0 = exp(-w[0]*tf); ok &= NearEqual(x0, xf[0], 1e-4, 1e-4); ok &= NearEqual(0., ef[0], 1e-4, 1e-4); double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]); ok &= NearEqual(x1, xf[1], 1e-4, 1e-4); ok &= NearEqual(0., ef[1], 1e-4, 1e-4); return ok; } /* Define $latex X : \B{R} \rightarrow \B{R}^2$$ by $latex \[ \begin{array}{rcl} X_0 (0) & = & 1 \\ X_1 (0) & = & 0 \\ X_0^{(1)} (t) & = & 2 \alpha t X_0 (t) \\ X_1^{(1)} (t) & = & 1 / X_0 (t) \end{array} \] $$ It follows that $latex \[ \begin{array}{rcl} X_0 (t) & = & \exp ( \alpha t^2 ) \\ X_1 (t) & = & \int_0^t \exp( - \alpha s^2 ) {\bf d} s \\ & = & \frac{1}{ \sqrt{\alpha} \int_0^{\sqrt{\alpha} t} \exp( - r^2 ) {\bf d} r \\ & = & \frac{\sqrt{\pi}}{ 2 \sqrt{\alpha} {\rm erf} ( \sqrt{\alpha} t ) \end{array} \] $$ If $latex X_0 (t) < 0$$, we return $code nan$$ in order to inform $code OdeErrControl$$ that its is taking to large a step. */ # include // CppAD::Rosen34 # include namespace { // -------------------------------------------------------------- class Fun_three { private: const double alpha_; bool was_negative_; public: // constructor Fun_three(double alpha) : alpha_(alpha), was_negative_(false) { } // set f = x'(t) void Ode( const double &t, const CppAD::vector &x, CppAD::vector &f) { f[0] = 2. * alpha_ * t * x[0]; f[1] = 1. / x[0]; // case where ODE does not make sense if( x[0] < 0. || x[1] < 0. ) { was_negative_ = true; f[0] = CppAD::nan(0.); } } // set f_t = df / dt void Ode_ind( const double &t, const CppAD::vector &x, CppAD::vector &f_t) { f_t[0] = 2. * alpha_ * x[0]; f_t[1] = 0.; if( x[0] < 0. || x[1] < 0. ) { was_negative_ = true; f_t[0] = CppAD::nan(0.); } } // set f_x = df / dx void Ode_dep( const double &t, const CppAD::vector &x, CppAD::vector &f_x) { double x0_sq = x[0] * x[0]; f_x[0 * 2 + 0] = 2. * alpha_ * t; // f0 w.r.t. x0 f_x[0 * 2 + 1] = 0.; // f0 w.r.t. x1 f_x[1 * 2 + 0] = -1./x0_sq; // f1 w.r.t. x0 f_x[1 * 2 + 1] = 0.; // f1 w.r.t. x1 if( x[0] < 0. || x[1] < 0. ) { was_negative_ = true; f_x[0] = CppAD::nan(0.); } } bool was_negative(void) { return was_negative_; } }; // -------------------------------------------------------------- class Method_three { public: Fun_three F; // constructor Method_three(double alpha) : F(alpha) { } void step( double ta, double tb, CppAD::vector &xa , CppAD::vector &xb , CppAD::vector &eb ) { xb = CppAD::Rosen34(F, 1, ta, tb, xa, eb); } size_t order(void) { return 3; } }; } bool OdeErrControl_three(void) { bool ok = true; // initial return value using CppAD::NearEqual; double alpha = 10.; Method_three method(alpha); CppAD::vector xi(2); xi[0] = 1.; xi[1] = 0.; CppAD::vector eabs(2); eabs[0] = 1e-4; eabs[1] = 1e-4; // inputs double ti = 0.; double tf = 1.; double smin = 1e-4; double smax = 1.; double scur = 1.; double erel = 0.; // outputs CppAD::vector ef(2); CppAD::vector xf(2); CppAD::vector maxabs(2); size_t nstep; xf = OdeErrControl(method, ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep); double x0 = exp( alpha * tf * tf ); ok &= NearEqual(x0, xf[0], 1e-4, 1e-4); ok &= NearEqual(0., ef[0], 1e-4, 1e-4); double root_pi = sqrt( 4. * atan(1.)); double root_alpha = sqrt( alpha ); double x1 = CppAD::erf(alpha * tf) * root_pi / (2 * root_alpha); ok &= NearEqual(x1, xf[1], 1e-4, 1e-4); ok &= NearEqual(0., ef[1], 1e-4, 1e-4); ok &= method.F.was_negative(); return ok; } namespace { // -------------------------------------------------------------- class Fun_four { private: size_t n; // dimension of the state space public: // constructor Fun_four(size_t n_) : n(n_) { } // given x(0) = 0 // solution is x_i (t) = t^(i+1) void Ode( const double &t, const CppAD::vector &x, CppAD::vector &f) { size_t i; f[0] = CppAD::nan(0.); for(i = 1; i < n; i++) f[i] = (i+1) * x[i-1]; } }; // -------------------------------------------------------------- class Method_four { private: Fun_four F; public: // constructor Method_four(size_t n_) : F(n_) { } void step( double ta, double tb, CppAD::vector &xa , CppAD::vector &xb , CppAD::vector &eb ) { xb = CppAD::Runge45(F, 1, ta, tb, xa, eb); } size_t order(void) { return 4; } }; } bool OdeErrControl_four(void) { bool ok = true; // initial return value // construct method for n component solution size_t n = 6; Method_four method(n); // inputs to OdeErrControl // special case where scur is converted to ti - tf // (so it is not equal to smin) double ti = 0.; double tf = .9; double smin = .8; double smax = 1.; double scur = smin; double erel = 1e-7; CppAD::vector xi(n); CppAD::vector eabs(n); size_t i; for(i = 0; i < n; i++) { xi[i] = 0.; eabs[i] = 0.; } // outputs from OdeErrControl CppAD::vector ef(n); CppAD::vector xf(n); xf = OdeErrControl(method, ti, tf, xi, smin, smax, scur, eabs, erel, ef); // check that Fun_four always returning nan results in nan for(i = 0; i < n; i++) { ok &= CppAD::isnan(xf[i]); ok &= CppAD::isnan(ef[i]); } return ok; } // ========================================================================== bool ode_err_control(void) { bool ok = true; ok &= OdeErrControl_one(); ok &= OdeErrControl_two(); ok &= OdeErrControl_three(); ok &= OdeErrControl_four(); return ok; } cppad-20170000.3/test_more/vec_unary.cpp0000644000175200017650000000425613057470461017140 0ustar coincoin-web// $Id: vec_unary.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test the use of VecADelem with unary operators */ # include bool VecUnary(void) { using namespace CppAD; using CppAD::abs; using CppAD::sin; using CppAD::atan; using CppAD::cos; using CppAD::exp; using CppAD::log; using CppAD::sqrt; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); bool ok = true; size_t n = 8; size_t i; CPPAD_TESTVECTOR(AD) X(n); VecAD Y(n); CPPAD_TESTVECTOR(AD) Z(n); for(i = 0; i < n; i++) X[i] = int(i); // some compilers require the int here Independent(X); AD j; j = 0.; Y[j] = X[0]; Z[0] = -Y[j]; j = 1.; Y[j] = X[1]; Z[1] = sin( Y[j] ); j = 2.; Y[j] = X[2]; Z[2] = abs( Y[j] ); j = 3.; Y[j] = X[3]; Z[3] = atan( Y[j] ); j = 4.; Y[j] = X[4]; Z[4] = cos( Y[j] ); j = 5.; Y[j] = X[5]; Z[5] = exp( Y[j] ); j = 6.; Y[j] = X[6]; Z[6] = log( Y[j] ); j = 7.; Y[j] = X[7]; Z[7] = sqrt( Y[j] ); ADFun f(X, Z); CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(double) z(n); for(i = 0; i < n; i++) x[i] = 2. / double(i + 1); x[7] = abs( x[7] ); z = f.Forward(0, x); ok &= NearEqual(z[0], - x[0], eps99, eps99); ok &= NearEqual(z[1], sin( x[1] ), eps99, eps99); ok &= NearEqual(z[2], abs( x[2] ), eps99, eps99); ok &= NearEqual(z[3], atan(x[3] ), eps99, eps99); ok &= NearEqual(z[4], cos( x[4] ), eps99, eps99); ok &= NearEqual(z[5], exp( x[5] ), eps99, eps99); ok &= NearEqual(z[6], log( x[6] ), eps99, eps99); ok &= NearEqual(z[7], sqrt(x[7] ), eps99, eps99); return ok; } cppad-20170000.3/test_more/atanh.cpp0000644000175200017650000000374313057470461016240 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include bool atanh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // a temporary value AD tanh_of_x0 = CppAD::tanh(ax[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CppAD::atanh(tanh_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // check value ok &= NearEqual(ay[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // forward computation of higher order partials w.r.t. x[0] size_t n_order = 5; for(size_t order = 2; order < n_order; order++) { dx[0] = 0.; dy = f.Forward(order, dx); ok &= NearEqual(dy[0], 0., eps, eps); } // reverse computation of derivatives CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n_order * n); w[0] = 1.; dw = f.Reverse(n_order, w); ok &= NearEqual(dw[0], 1., eps, eps); for(size_t order = 1; order < n_order; order++) ok &= NearEqual(dw[order * n + 0], 0., eps, eps); return ok; } // END C++ cppad-20170000.3/test_more/parameter.cpp0000644000175200017650000000311313057470461017114 0ustar coincoin-web// $Id: parameter.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // Test hash coding of parameter during recording # include namespace { // BEGIN empty namespace template bool test(void) { bool ok = true; using namespace CppAD; // number of different parameter values size_t n_parameter = 13; // number of parameter repeats size_t n_repeat = 17; // independent variable vector size_t j, n = n_parameter * n_repeat; CPPAD_TESTVECTOR(AD) ax(n); for(j = 0; j < n; j++) ax[j] = Float(j); Independent(ax); // dependent variable vector and indices size_t i, m = n; CPPAD_TESTVECTOR(AD) ay(m); for(i = 0; i < m; i++) { // must avoid Float(k) = 0 because it would get optimized out size_t k = (i % n_parameter); k = k * k * 10 + 1; j = i; ay[i] = ax[j] + Float(k); } // create f: ax -> ay ADFun f(ax, ay); ok = f.size_par() == n_parameter; return ok; } } // END empty namespace bool parameter(void) { bool ok = true; ok &= test(); ok &= test(); return ok; } cppad-20170000.3/test_more/compare_change.cpp0000644000175200017650000002301413057470461020071 0ustar coincoin-web/* $Id: compare_change.cpp 3607 2015-01-20 16:20:41Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old CompareChange examples and tests, now just used for validation testing */ # include namespace { // ---------------------------------------------------------------------- bool CompareChange_one(void) { bool ok = true; using namespace CppAD; // ------------------------------- < ---------------------------- // create independent variables CPPAD_TESTVECTOR(AD) X(2); X[0] = 3.; X[1] = 4.; Independent(X); // create dependent variables CPPAD_TESTVECTOR(AD) Y(6); // CondExp would never require retaping if( X[0] < X[1] ) // True variable < variable Y[0] = X[0]; else Y[0] = X[1]; if( X[1] < X[0] ) // False variable < variable Y[1] = X[0]; else Y[1] = X[1]; if( 3.5 < X[1] ) // True parameter < variable Y[2] = X[0]; else Y[2] = X[1]; if( 3.5 < X[0] ) // False parameter < variable Y[3] = X[0]; else Y[3] = X[1]; if( X[0] < 4. ) // True variable < parameter Y[4] = X[0]; else Y[4] = X[1]; if( X[1] < 4. ) // False variable < parameter Y[5] = X[0]; else Y[5] = X[1]; // f : X -> Y ADFun *f; f = new ADFun(X, Y); // new argument value CPPAD_TESTVECTOR(double) x( X.size() ); x[0] = 4.; x[1] = 3.; // evaluate the function at new argument CPPAD_TESTVECTOR(double) y( Y.size() ); y = f->Forward(0, x); // check results ok &= (y[0] == x[0]); // this is what the was taped ok &= (y[1] == x[1]); ok &= (y[2] == x[0]); ok &= (y[3] == x[1]); ok &= (y[4] == x[0]); ok &= (y[5] == x[1]); ok &= (f->CompareChange() == 6); // all comparisions have changed // done with this function delete f; // ------------------------------- > ---------------------------- // create independent variables Independent(X); if( X[0] > X[1] ) // False variable > variable Y[0] = X[0]; else Y[0] = X[1]; if( X[1] > X[0] ) // True variable > variable Y[1] = X[0]; else Y[1] = X[1]; if( 3.5 > X[1] ) // False parameter > variable Y[2] = X[0]; else Y[2] = X[1]; if( 3.5 > X[0] ) // True parameter > variable Y[3] = X[0]; else Y[3] = X[1]; if( X[0] > 3. ) // False variable > parameter Y[4] = X[0]; else Y[4] = X[1]; if( X[1] > 3. ) // True variable > parameter Y[5] = X[0]; else Y[5] = X[1]; // f : X -> Y f = new ADFun (X, Y); // evaluate the function at new argument y = f->Forward(0, x); // check results ok &= (y[0] == x[1]); // this is what the was taped ok &= (y[1] == x[0]); ok &= (y[2] == x[1]); ok &= (y[3] == x[0]); ok &= (y[4] == x[1]); ok &= (y[5] == x[0]); ok &= (f->CompareChange() == 6); // all comparisions have changed // done with this function delete f; // ------------------------------- <= ---------------------------- // create independent variables Independent(X); if( X[0] <= X[1] ) // True variable <= variable Y[0] = X[0]; else Y[0] = X[1]; if( X[1] <= X[0] ) // False variable <= variable Y[1] = X[0]; else Y[1] = X[1]; if( 4. <= X[1] ) // True parameter <= variable Y[2] = X[0]; else Y[2] = X[1]; if( 4. <= X[0] ) // False parameter <= variable Y[3] = X[0]; else Y[3] = X[1]; if( X[0] <= 3.5 ) // True variable <= parameter Y[4] = X[0]; else Y[4] = X[1]; if( X[1] <= 3.5 ) // False variable <= parameter Y[5] = X[0]; else Y[5] = X[1]; // f : X -> Y f = new ADFun (X, Y); // evaluate the function at new argument y = f->Forward(0, x); // check results ok &= (y[0] == x[0]); // this is what the was taped ok &= (y[1] == x[1]); ok &= (y[2] == x[0]); ok &= (y[3] == x[1]); ok &= (y[4] == x[0]); ok &= (y[5] == x[1]); ok &= (f->CompareChange() == 6); // all comparisions have changed // done with this function delete f; // ------------------------------- >= ---------------------------- // create independent variables Independent(X); if( X[0] >= X[1] ) // False variable >= variable Y[0] = X[0]; else Y[0] = X[1]; if( X[1] >= X[0] ) // True variable >= variable Y[1] = X[0]; else Y[1] = X[1]; if( 3.5 >= X[1] ) // False parameter >= variable Y[2] = X[0]; else Y[2] = X[1]; if( 3.5 >= X[0] ) // True parameter >= variable Y[3] = X[0]; else Y[3] = X[1]; if( X[0] >= 4. ) // False variable >= parameter Y[4] = X[0]; else Y[4] = X[1]; if( X[1] >= 4. ) // True variable >= parameter Y[5] = X[0]; else Y[5] = X[1]; // f : X -> Y f = new ADFun (X, Y); // evaluate the function at new argument y = f->Forward(0, x); // check results ok &= (y[0] == x[1]); // this is what the was taped ok &= (y[1] == x[0]); ok &= (y[2] == x[1]); ok &= (y[3] == x[0]); ok &= (y[4] == x[1]); ok &= (y[5] == x[0]); ok &= (f->CompareChange() == 6); // all comparisions have changed // done with this function delete f; // ------------------------------- == ---------------------------- // create independent variables Independent(X); if( X[0] == X[1] ) // False variable == variable Y[0] = X[0]; else Y[0] = X[1]; if( X[0] == X[0] ) // True variable == variable Y[1] = X[0]; else Y[1] = X[1]; if( 3. == X[1] ) // False parameter == variable Y[2] = X[0]; else Y[2] = X[1]; if( 3. == X[0] ) // True parameter == variable Y[3] = X[0]; else Y[3] = X[1]; if( X[0] == 4. ) // False variable == parameter Y[4] = X[0]; else Y[4] = X[1]; if( X[1] == 4. ) // True variable == parameter Y[5] = X[0]; else Y[5] = X[1]; // f : X -> Y f = new ADFun (X, Y); // evaluate the function at new argument y = f->Forward(0, x); // check results ok &= (y[0] == x[1]); // this is what the was taped ok &= (y[1] == x[0]); ok &= (y[2] == x[1]); ok &= (y[3] == x[0]); ok &= (y[4] == x[1]); ok &= (y[5] == x[0]); // the first two comparisions do not change ok &= (f->CompareChange() == 4); // done with this function delete f; // ------------------------------- != ---------------------------- // create independent variables Independent(X); if( X[0] != X[1] ) // True variable != variable Y[0] = X[0]; else Y[0] = X[1]; if( X[0] != X[0] ) // False variable != variable Y[1] = X[0]; else Y[1] = X[1]; if( 3. != X[1] ) // True parameter != variable Y[2] = X[0]; else Y[2] = X[1]; if( 3. != X[0] ) // False parameter != variable Y[3] = X[0]; else Y[3] = X[1]; if( X[0] != 4. ) // True variable != parameter Y[4] = X[0]; else Y[4] = X[1]; if( X[1] != 4. ) // False variable != parameter Y[5] = X[0]; else Y[5] = X[1]; // f : X -> Y f = new ADFun (X, Y); // evaluate the function at new argument y = f->Forward(0, x); // check results ok &= (y[0] == x[0]); // this is what the was taped ok &= (y[1] == x[1]); ok &= (y[2] == x[0]); ok &= (y[3] == x[1]); ok &= (y[4] == x[0]); ok &= (y[5] == x[1]); // the first two comparisions do not change ok &= (f->CompareChange() == 4); // done with this function delete f; return ok; } // ---------------------------------------------------------------------- template Type Minimum(const Type &x, const Type &y) { // Use a comparision to compute the min(x, y) // (note that CondExp would never require retaping). if( x < y ) return x; return y; } bool CompareChange_two(void) { bool ok = true; using CppAD::AD; using CppAD::ADFun; using CppAD::Independent; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 3.; X[1] = 4.; // declare independent variables and start tape recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = Minimum(X[0], X[1]); // create f: x -> y and stop tape recording ADFun f(X, Y); // evaluate zero mode Forward where conditional has the same result // note that f.CompareChange is not defined when NDEBUG is true CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(double) y(m); x[0] = 3.5; x[1] = 4.; y = f.Forward(0, x); ok &= (y[0] == x[0]); ok &= (y[0] == Minimum(x[0], x[1])); ok &= (f.CompareChange() == 0); // evaluate zero mode Forward where conditional has different result x[0] = 4.; x[1] = 3.; y = f.Forward(0, x); ok &= (y[0] == x[0]); ok &= (y[0] != Minimum(x[0], x[1])); ok &= (f.CompareChange() == 1); // re-tape to obtain the new AD operation sequence X[0] = 4.; X[1] = 3.; Independent(X); Y[0] = Minimum(X[0], X[1]); // stop tape and store result in f f.Dependent(Y); // evaluate the function at new argument values y = f.Forward(0, x); ok &= (y[0] == x[1]); ok &= (y[0] == Minimum(x[0], x[1])); ok &= (f.CompareChange() == 0); return ok; } } bool compare_change(void) { bool ok = true; ok &= CompareChange_one(); ok &= CompareChange_two(); return ok; } // END C++ cppad-20170000.3/test_more/azmul.cpp0000644000175200017650000001572013057470461016273 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace { bool test_forward(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double inf = std::numeric_limits::infinity(); double eps = 10. * std::numeric_limits::epsilon(); typedef AD a1double; typedef AD a2double; // domain space vector size_t n = 2; size_t m = 3; // double level CPPAD_TESTVECTOR(double) x(n), z(m); x[0] = 3.0; x[1] = 4.0; // start a1 level recording CPPAD_TESTVECTOR(a1double) a1x(n), a1dx(n), a1y(m), a1z(m); for(size_t j = 0; j < n; j++) a1x[j] = x[j]; CppAD::Independent(a1x); // start a2 level recording CPPAD_TESTVECTOR(a2double) a2x(n), a2y(m); for(size_t j = 0; j < n; j++) a2x[j] = a1x[j]; CppAD::Independent(a2x); // y a2y[0] = CppAD::azmul(a2x[0], a2x[1]); // azmul(variable, variable) a2y[1] = CppAD::azmul(a1x[0], a2x[1]); // azmul(parameter, variable) a2y[2] = CppAD::azmul(a2x[0], a1x[1]); // azmul(variable, parameter) // create f: x -> y and stop a2 recording CppAD::ADFun a1f; a1f.Dependent(a2x, a2y); // check y a1y = a1f.Forward(0, a1x); // azmul(variable, variable) only for(size_t i = 0; i < m; i++) ok &= NearEqual(a1y[i] , x[0] * x[1], eps, eps); for(size_t j = 0; j < n; j++) a1dx[j] = a1double(1.0); a1z = a1f.Forward(1, a1dx); // create g: x -> z and stop a1 recording CppAD::ADFun g; g.Dependent(a1x, a1z); // check value when x[0] is not zero z = g.Forward(0, x); // z_0 = d_lambda [ ( x[0] + lambda ) * ( x[1] + lambda ) ] ok &= NearEqual(z[0] , x[0] + x[1], eps, eps); // z_1 = d_lambda [ x[0] * ( x[1] + lambda ) ] ok &= NearEqual(z[1] , x[0], eps, eps); // z_2 = d_lambda [ ( x[0] + lambda ) * x[1] ] ok &= NearEqual(z[2] , x[1], eps, eps); // check value x[0] is zero and x[1] is infinity x[0] = 0.0; x[1] = inf; z = g.Forward(0, x); ok &= z[0] == inf; ok &= z[1] == 0.0; ok &= z[2] == inf; return ok; } bool test_reverse(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double inf = std::numeric_limits::infinity(); double eps = 10. * std::numeric_limits::epsilon(); typedef AD a1double; typedef AD a2double; // domain space vector size_t n = 2; size_t m = 3; // double level CPPAD_TESTVECTOR(double) x(n), z(n); x[0] = 3.0; x[1] = 4.0; // start a1 level recording CPPAD_TESTVECTOR(a1double) a1x(n), a1dx(n), a1w(m), a1z(n); for(size_t j = 0; j < n; j++) a1x[j] = x[j]; CppAD::Independent(a1x); // start a2 level recording CPPAD_TESTVECTOR(a2double) a2x(n), a2y(m); for(size_t j = 0; j < n; j++) a2x[j] = a1x[j]; CppAD::Independent(a2x); // y a2y[0] = CppAD::azmul(a2x[0], a2x[1]); // azmul(variable, variable) a2y[1] = CppAD::azmul(a1x[0], a2x[1]); // azmul(parameter, variable) a2y[2] = CppAD::azmul(a2x[0], a1x[1]); // azmul(variable, parameter) // create f: x -> y and stop a2 recording CppAD::ADFun a1f; a1f.Dependent(a2x, a2y); // w(x) = y[0] + y[1] + y[2] for(size_t i = 0; i < m; i++) a1w[i] = a1double(1.0); a1f.Forward(0, a1x); a1dx = a1f.Reverse(1, a1w); // create g: x -> z and stop a1 recording CppAD::ADFun g; g.Dependent(a1x, a1dx); // check value when x[0] is not zero z = g.Forward(0, x); // partial y[0] w.r.t x[0] = x[1] // partial y[1] w.r.t x[0] = 0 // partial y[2] w.r.t x[0] = x[1] ok &= NearEqual(z[0] , x[1] + x[1], eps, eps); // partial y[0] w.r.t x[1] = x[0] // partial y[1] w.r.t x[1] = x[0] // partial y[2] w.r.t x[1] = 0 ok &= NearEqual(z[1] , x[0] + x[0], eps, eps); // check value x[0] is zero and x[1] is infinity x[0] = 0.0; x[1] = inf; z = g.Forward(0, x); ok &= z[0] == inf; ok &= z[1] == 0.0; return ok; } bool test_forward_dir(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double inf = std::numeric_limits::infinity(); double eps = 10. * std::numeric_limits::epsilon(); typedef AD a1double; typedef AD a2double; // domain space vector size_t n = 2; size_t m = 3; size_t r = 2; // double level CPPAD_TESTVECTOR(double) x(n), z(r * m); x[0] = 3.0; x[1] = 4.0; // start a1 level recording CPPAD_TESTVECTOR(a1double) a1x(n), a1dx(r * n), a1y(m), a1z(r * m); for(size_t j = 0; j < n; j++) a1x[j] = x[j]; CppAD::Independent(a1x); // start a2 level recording CPPAD_TESTVECTOR(a2double) a2x(n), a2y(m); for(size_t j = 0; j < n; j++) a2x[j] = a1x[j]; CppAD::Independent(a2x); // y a2y[0] = CppAD::azmul(a2x[0], a2x[1]); // azmul(variable, variable) a2y[1] = CppAD::azmul(a1x[0], a2x[1]); // azmul(parameter, variable) a2y[2] = CppAD::azmul(a2x[0], a1x[1]); // azmul(variable, parameter) // create f: x -> y and stop a2 recording CppAD::ADFun a1f; a1f.Dependent(a2x, a2y); // check y a1y = a1f.Forward(0, a1x); // azmul(variable, variable) only for(size_t i = 0; i < m; i++) ok &= NearEqual(a1y[i] , x[0] * x[1], eps, eps); for(size_t j = 0; j < n; j++) { for(size_t ell = 0; ell < r; ell++) a1dx[r * j + ell] = a1double(1.0 + ell); } a1z = a1f.Forward(1, r, a1dx); // create g: x -> z and stop a1 recording CppAD::ADFun g; g.Dependent(a1x, a1z); // check value when x[0] is not zero z = g.Forward(0, x); // z_00 = d_lambda [ ( x[0] + lambda ) * ( x[1] + lambda ) ] ok &= NearEqual(z[r * 0 + 0] , x[0] + x[1], eps, eps); // z_01 = d_lambda [ ( x[0] + 2 * lambda ) * ( x[1] + 2 * lambda ) ] ok &= NearEqual(z[r * 0 + 1] , 2.0*(x[0] + x[1]), eps, eps); // z_10 = d_lambda [ x[0] * ( x[1] + lambda ) ] ok &= NearEqual(z[r * 1 + 0] , x[0], eps, eps); // z_11 = d_lambda [ x[0] * ( x[1] + 2 * lambda ) ] ok &= NearEqual(z[r * 1 + 1] , 2.0 * x[0], eps, eps); // z_20 = d_lambda [ ( x[0] + lambda ) * x[1] ] ok &= NearEqual(z[r * 2 + 0] , x[1], eps, eps); // z_21 = d_lambda [ ( x[0] + 2 * lambda ) * x[1] ] ok &= NearEqual(z[r * 2 + 1] , 2.0 * x[1], eps, eps); // check value x[0] is zero and x[1] is infinity x[0] = 0.0; x[1] = inf; z = g.Forward(0, x); ok &= z[r * 0 + 0] == inf; ok &= z[r * 0 + 1] == inf; ok &= z[r * 1 + 0] == 0.0; ok &= z[r * 1 + 1] == 0.0; ok &= z[r * 2 + 0] == inf; ok &= z[r * 2 + 1] == inf; return ok; } } bool azmul(void) { bool ok = true; ok &= test_forward(); ok &= test_reverse(); ok &= test_forward_dir(); return ok; } cppad-20170000.3/test_more/exp.cpp0000644000175200017650000000667413057470461015747 0ustar coincoin-web// $Id: exp.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old exp example now used just for validation testing. */ # include # include namespace { // BEGIN empty namespace bool ExpTestOne(void) { bool ok = true; using CppAD::exp; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(1); size_t s = 0; U[s] = 1.; Independent(U); // dependent variable vector, indices, and values CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; Z[x] = exp(U[s]); Z[y] = exp(Z[x]); // define f : U -> Z and vectors for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check values ok &= NearEqual(Z[x] , exp(1.), 1e-10 , 1e-10); ok &= NearEqual(Z[y] , exp( exp(1.) ), 1e-10 , 1e-10); // forward computation of partials w.r.t. s v[s] = 1.; w = f.Forward(1, v); ok &= NearEqual(w[x], Z[x], 1e-10 , 1e-10); // dx/ds ok &= NearEqual(w[y], Z[y] * Z[x], 1e-10 , 1e-10); // dy/ds // reverse computation of partials of y w[x] = 0.; w[y] = 1.; v = f.Reverse(1,w); ok &= NearEqual(v[s], Z[y] * Z[x], 1e-10 , 1e-10); // dy/ds // forward computation of second partials w.r.t s v[s] = 1.; w = f.Forward(1, v); v[s] = 0.; w = f.Forward(2, v); ok &= NearEqual( // d^2 y / (ds ds) 2. * w[y] , Z[y] * Z[x] * Z[x] + Z[y] * Z[x], 1e-10 , 1e-10 ); // reverse computation of second partials of y CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 0.; w[y] = 1.; r = f.Reverse(2, w); ok &= NearEqual( // d^2 y / (ds ds) r[2 * s + 1] , Z[y] * Z[x] * Z[x] + Z[y] * Z[x], 1e-10 , 1e-10 ); return ok; } bool ExpTestTwo(void) { bool ok = true; using CppAD::exp; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 1.; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = exp(U[0]); // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value double exp_u = exp( Value(U[0]) ); ok &= NearEqual(exp_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; for(j = 1; j < p; j++) { w = f.Forward(j, v); jfac *= j; ok &= NearEqual(jfac*w[0], exp_u, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], exp_u, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); } return ok; } } // END empty namespace bool Exp(void) { bool ok = true; ok &= ExpTestOne(); ok &= ExpTestTwo(); return ok; } cppad-20170000.3/test_more/poly.cpp0000644000175200017650000000423513057470461016125 0ustar coincoin-web// $Id: poly.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* // Old GetStarted example now used just for validation testing */ // BEGIN C++ // directory where cppad/cppad.hpp is stored must be searched by compiler # include bool Poly(void) { bool ok = true; // make CppAD routines visible without CppAD:: infront of names using namespace CppAD; // degree of the polynomial that we will differentiate size_t deg = 4; // vector that will hold polynomial coefficients for p(z) CPPAD_TESTVECTOR(AD) A(deg + 1); // AD elements CPPAD_TESTVECTOR(double) a(deg + 1); // double elements // set the polynomial coefficients A[0] = 1.; size_t k; for(k = 1; k <= deg; k++) A[k] = a[k] = 1.; // independent variables CPPAD_TESTVECTOR(AD) Z(1); // one independent variable Z[0] = 3.; // value of independent variable Independent(Z); // declare independent variable // dependent variables CPPAD_TESTVECTOR(AD) P(1); // one dependent variable P[0] = Poly(0, A, Z[0]); // value of polynomial at Z[0] // define f : Z -> P as a function mapping independent to dependent ADFun f(Z, P); // ADFun corresponding to polynomial // compute derivative of polynomial CPPAD_TESTVECTOR(double) z(1); // vector length f.Domain() CPPAD_TESTVECTOR(double) J(1); // vector length f.Range * f.Domain() z[0] = 3.; // point at which to compute derivative J = f.Jacobian(z); // value of derivative // compare with derivative as computed by Poly ok &= (Poly(1, a, z[0]) == J[0]); return ok; } // END C++ cppad-20170000.3/test_more/sin_cos.cpp0000644000175200017650000002125013057470461016573 0ustar coincoin-web// $Id: sin_cos.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Comprehensive test of Trigonometric and Hyperbolic Sine and Cosine */ # include # include namespace { // Begin empty namespace bool Sin(void) { bool ok = true; using CppAD::sin; using CppAD::cos; using namespace CppAD; // independent variable vector double x = .5; double y = .8; CPPAD_TESTVECTOR(AD) X(2); X[0] = x; X[1] = y; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); AD U = X[0] * X[1]; Z[0] = sin( U ); // create f: X -> Z and vectors used for derivative calculations // f(x, y) = sin(x, y) ADFun f(X, Z); CPPAD_TESTVECTOR(double) v( 2 ); CPPAD_TESTVECTOR(double) w( 1 ); // check value double sin_u = sin( Value(U) ); double cos_u = cos( Value(U) ); ok &= NearEqual(sin_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; // differential w.r.t. x v[1] = 0; // differential w.r.t. y double yj = 1; // y^j for(j = 1; j < p; j++) { w = f.Forward(j, v); // compute j-th power of y yj *= y ; // compute j-th derivartive of sin function double sinj; if( j % 4 == 1 ) sinj = cos_u; else if( j % 4 == 2 ) sinj = -sin_u; else if( j % 4 == 3 ) sinj = -cos_u; else sinj = sin_u; jfac *= j; // check j-th derivative of z w.r.t x ok &= NearEqual(jfac*w[0], sinj * yj, 1e-10 , 1e-10); v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r( 2 * p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; yj = 1.; double sinjp = 0.; for(j = 0; j < p; j++) { double sinj = sinjp; // compute j+1 derivative of sin funciton if( j % 4 == 0 ) sinjp = cos_u; else if( j % 4 == 1 ) sinjp = -sin_u; else if( j % 4 == 2 ) sinjp = -cos_u; else sinjp = sin_u; // derivative w.r.t x of sin^{(j)} (x * y) * y^j ok &= NearEqual(jfac*r[0+j], sinjp * yj * y, 1e-10 , 1e-10); // derivative w.r.t y of sin^{(j)} (x * y) * y^j double value = sinjp * yj * x + j * sinj * yj / y; ok &= NearEqual(jfac*r[p+j], value , 1e-10 , 1e-10); jfac *= (j + 1); yj *= y; } return ok; } bool Cos(void) { bool ok = true; using CppAD::sin; using CppAD::cos; using namespace CppAD; // independent variable vector double x = .5; double y = .8; CPPAD_TESTVECTOR(AD) X(2); X[0] = x; X[1] = y; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); AD U = X[0] * X[1]; Z[0] = cos( U ); // create f: X -> Z and vectors used for derivative calculations // f(x, y) = cos(x, y) ADFun f(X, Z); CPPAD_TESTVECTOR(double) v( 2 ); CPPAD_TESTVECTOR(double) w( 1 ); // check value double sin_u = sin( Value(U) ); double cos_u = cos( Value(U) ); ok &= NearEqual(cos_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; // differential w.r.t. x v[1] = 0; // differential w.r.t. y double yj = 1; // y^j for(j = 1; j < p; j++) { w = f.Forward(j, v); // compute j-th power of y yj *= y ; // compute j-th derivartive of cos function double cosj; if( j % 4 == 1 ) cosj = -sin_u; else if( j % 4 == 2 ) cosj = -cos_u; else if( j % 4 == 3 ) cosj = sin_u; else cosj = cos_u; jfac *= j; // check j-th derivative of z w.r.t x ok &= NearEqual(jfac*w[0], cosj * yj, 1e-10 , 1e-10); v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r( 2 * p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; yj = 1.; double cosjp = 0.; for(j = 0; j < p; j++) { double cosj = cosjp; // compute j+1 derivative of cos funciton if( j % 4 == 0 ) cosjp = -sin_u; else if( j % 4 == 1 ) cosjp = -cos_u; else if( j % 4 == 2 ) cosjp = sin_u; else cosjp = cos_u; // derivative w.r.t x of cos^{(j)} (x * y) * y^j ok &= NearEqual(jfac*r[0+j], cosjp * yj * y, 1e-10 , 1e-10); // derivative w.r.t y of cos^{(j)} (x * y) * y^j double value = cosjp * yj * x + j * cosj * yj / y; ok &= NearEqual(jfac*r[p+j], value , 1e-10 , 1e-10); jfac *= (j + 1); yj *= y; } return ok; } bool Cosh(void) { bool ok = true; using CppAD::sinh; using CppAD::cosh; using namespace CppAD; // independent variable vector double x = .5; double y = .8; CPPAD_TESTVECTOR(AD) X(2); X[0] = x; X[1] = y; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); AD U = X[0] * X[1]; Z[0] = cosh( U ); // create f: X -> Z and vectors used for derivative calculations // f(x, y) = cosh(x, y) ADFun f(X, Z); CPPAD_TESTVECTOR(double) v( 2 ); CPPAD_TESTVECTOR(double) w( 1 ); // check value double sinh_u = sinh( Value(U) ); double cosh_u = cosh( Value(U) ); ok &= NearEqual(cosh_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; // differential w.r.t. x v[1] = 0; // differential w.r.t. y double yj = 1; // y^j for(j = 1; j < p; j++) { w = f.Forward(j, v); // compute j-th power of y yj *= y ; // compute j-th derivartive of cosh function double coshj; if( j % 2 == 1 ) coshj = sinh_u; else coshj = cosh_u; jfac *= j; // check j-th derivative of z w.r.t x ok &= NearEqual(jfac*w[0], coshj * yj, 1e-10 , 1e-10); v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r( 2 * p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; yj = 1.; double coshjp = 0.; for(j = 0; j < p; j++) { double coshj = coshjp; // compute j+1 derivative of cosh funciton if( j % 2 == 0 ) coshjp = sinh_u; else coshjp = cosh_u; // derivative w.r.t x of cosh^{(j)} (x * y) * y^j ok &= NearEqual(jfac*r[0+j], coshjp * yj * y, 1e-10 , 1e-10); // derivative w.r.t y of cosh^{(j)} (x * y) * y^j double value = coshjp * yj * x + j * coshj * yj / y; ok &= NearEqual(jfac*r[p+j], value , 1e-10 , 1e-10); jfac *= (j + 1); yj *= y; } return ok; } bool Sinh(void) { bool ok = true; using CppAD::sinh; using CppAD::cosh; using namespace CppAD; // independent variable vector double x = .5; double y = .8; CPPAD_TESTVECTOR(AD) X(2); X[0] = x; X[1] = y; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); AD U = X[0] * X[1]; Z[0] = sinh( U ); // create f: X -> Z and vectors used for derivative calculations // f(x, y) = sinh(x, y) ADFun f(X, Z); CPPAD_TESTVECTOR(double) v( 2 ); CPPAD_TESTVECTOR(double) w( 1 ); // check value double sinh_u = sinh( Value(U) ); double cosh_u = cosh( Value(U) ); ok &= NearEqual(sinh_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; // differential w.r.t. x v[1] = 0; // differential w.r.t. y double yj = 1; // y^j for(j = 1; j < p; j++) { w = f.Forward(j, v); // compute j-th power of y yj *= y ; // compute j-th derivartive of sinh function double sinhj; if( j % 2 == 1 ) sinhj = cosh_u; else sinhj = sinh_u; jfac *= j; // check j-th derivative of z w.r.t x ok &= NearEqual(jfac*w[0], sinhj * yj, 1e-10 , 1e-10); v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r( 2 * p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; yj = 1.; double sinhjp = 0.; for(j = 0; j < p; j++) { double sinhj = sinhjp; // compute j+1 derivative of sinh funciton if( j % 2 == 0 ) sinhjp = cosh_u; else sinhjp = sinh_u; // derivative w.r.t x of sinh^{(j)} (x * y) * y^j ok &= NearEqual(jfac*r[0+j], sinhjp * yj * y, 1e-10 , 1e-10); // derivative w.r.t y of sinh^{(j)} (x * y) * y^j double value = sinhjp * yj * x + j * sinhj * yj / y; ok &= NearEqual(jfac*r[p+j], value , 1e-10 , 1e-10); jfac *= (j + 1); yj *= y; } return ok; } } // End empty namespace bool SinCos(void) { bool ok = Sin() & Cos() & Cosh() & Sinh(); return ok; } cppad-20170000.3/test_more/mul_eq.cpp0000644000175200017650000000701713057470461016425 0ustar coincoin-web// $Id: mul_eq.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old MulEq examples now used just for valiadation testing */ # include namespace { // BEGIN empty namespace bool MulEqTestOne(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 2.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; // some initial values AD zero = 0.; AD one = 1.; // dependent variable values Z[x] = U[s]; Z[y] = U[t]; Z[x] *= U[t]; // AD *= AD Z[y] *= 5.; // AD *= double zero *= Z[x]; one *= Z[x]; // check that zero is a parameter ok &= Parameter(zero); // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check values ok &= ( Z[x] == 3. * 2. ); ok &= ( Z[y] == 2. * 5. ); ok &= ( zero == 0. ); ok &= ( one == Z[x] ); // forward computation of partials w.r.t. t v[s] = 0.; v[t] = 1.; w = f.Forward(1, v); ok &= ( w[x] == U[s] ); // dx/dt ok &= ( w[y] == 5. ); // dy/dt // reverse computation of second partials of x CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 1.; w[y] = 0.; r = f.Reverse(2, w); ok &= ( r[2 * s + 1] == 1. ); ok &= ( r[2 * t + 1] == 0. ); return ok; } bool MulEqTestTwo(void) { bool ok = true; using namespace CppAD; // independent variable vector double u0 = .5; CPPAD_TESTVECTOR(AD) U(1); U[0] = u0; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = U[0]; // initial value Z[0] *= 2; // AD *= int Z[0] *= 4.; // AD *= double Z[0] *= U[0]; // AD *= AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(Z[0] , u0*2*4*u0, 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; for(j = 1; j < p; j++) { double value; if( j == 1 ) value = 16. * u0; else if( j == 2 ) value = 16.; else value = 0.; jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; for(j = 0; j < p; j++) { double value; if( j == 0 ) value = 16. * u0; else if( j == 1 ) value = 16.; else value = 0.; ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); } return ok; } } // END empty namespace bool MulEq(void) { bool ok = true; ok &= MulEqTestOne(); ok &= MulEqTestTwo(); return ok; } cppad-20170000.3/test_more/cond_exp.cpp0000644000175200017650000002724213057470461016744 0ustar coincoin-web/* $Id: cond_exp.cpp 3666 2015-02-28 16:54:17Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Comprehensive test built on 08/07 for new user interface to CondExp */ // BEGIN C++ # include namespace { // Begin empty namespace bool CondExp_pvvv(void) { bool ok = true; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) X(3); X[0] = 0.; X[1] = 1.; X[2] = 2.; Independent(X); // parameter value AD one = 1.; // dependent variable vector CPPAD_TESTVECTOR(AD) Y(5); // CondExp(parameter, variable, variable, variable) Y[0] = CondExpLt(one, X[0], X[1], X[2]); Y[1] = CondExpLe(one, X[0], X[1], X[2]); Y[2] = CondExpEq(one, X[0], X[1], X[2]); Y[3] = CondExpGe(one, X[0], X[1], X[2]); Y[4] = CondExpGt(one, X[0], X[1], X[2]); // create f: X -> Y ADFun f(X, Y); // vectors for function values CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // vectors for derivative values CPPAD_TESTVECTOR(double) dv( f.Domain() ); CPPAD_TESTVECTOR(double) dw( f.Range() ); // check original function values ok &= Y[0] == X[2]; ok &= Y[1] == X[2]; ok &= Y[2] == X[2]; ok &= Y[3] == X[1]; ok &= Y[4] == X[1]; // function values v[0] = 2.; v[1] = 1.; v[2] = 0.; w = f.Forward(0, v); ok &= ( w[0] == v[1] ); ok &= ( w[1] == v[1] ); ok &= ( w[2] == v[2] ); ok &= ( w[3] == v[2] ); ok &= ( w[4] == v[2] ); // forward mode derivative values dv[0] = 1.; dv[1] = 2.; dv[2] = 3.; dw = f.Forward(1, dv); ok &= (dw[0] == dv[1] ); ok &= (dw[1] == dv[1] ); ok &= (dw[2] == dv[2] ); ok &= (dw[3] == dv[2] ); ok &= (dw[4] == dv[2] ); // reverse mode derivative values dw[0] = 1.; dw[1] = 2.; dw[2] = 3.; dw[3] = 4.; dw[4] = 5.; dv = f.Reverse(1, dw); ok &= (dv[0] == 0.); ok &= (dv[1] == dw[0] + dw[1] ); ok &= (dv[2] == dw[2] + dw[3] + dw[4] ); return ok; } bool CondExp_vpvv(void) { bool ok = true; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) X(3); X[0] = 0.; X[1] = 1.; X[2] = 2.; Independent(X); // parameter value AD one = 1.; // dependent variable vector CPPAD_TESTVECTOR(AD) Y(5); // CondExp(variable, parameter, variable, variable) Y[0] = CondExpLt(X[0], one, X[1], X[2]); Y[1] = CondExpLe(X[0], one, X[1], X[2]); Y[2] = CondExpEq(X[0], one, X[1], X[2]); Y[3] = CondExpGe(X[0], one, X[1], X[2]); Y[4] = CondExpGt(X[0], one, X[1], X[2]); // create f: X -> Y ADFun f(X, Y); // vectors for function values CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // vectors for derivative values CPPAD_TESTVECTOR(double) dv( f.Domain() ); CPPAD_TESTVECTOR(double) dw( f.Range() ); // check original function values ok &= Y[0] == X[1]; ok &= Y[1] == X[1]; ok &= Y[2] == X[2]; ok &= Y[3] == X[2]; ok &= Y[4] == X[2]; // function values v[0] = 2.; v[1] = 1.; v[2] = 0.; w = f.Forward(0, v); ok &= ( w[0] == v[2] ); ok &= ( w[1] == v[2] ); ok &= ( w[2] == v[2] ); ok &= ( w[3] == v[1] ); ok &= ( w[4] == v[1] ); // forward mode derivative values dv[0] = 1.; dv[1] = 2.; dv[2] = 3.; dw = f.Forward(1, dv); ok &= (dw[0] == dv[2] ); ok &= (dw[1] == dv[2] ); ok &= (dw[2] == dv[2] ); ok &= (dw[3] == dv[1] ); ok &= (dw[4] == dv[1] ); // reverse mode derivative values dw[0] = 1.; dw[1] = 2.; dw[2] = 3.; dw[3] = 4.; dw[4] = 5.; dv = f.Reverse(1, dw); ok &= (dv[0] == 0.); ok &= (dv[1] == dw[3] + dw[4] ); ok &= (dv[2] == dw[0] + dw[1] + dw[2] ); return ok; } bool CondExp_vvpv(void) { bool ok = true; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) X(3); X[0] = 0.; X[1] = 1.; X[2] = 2.; Independent(X); // parameter value AD three = 3.; // dependent variable vector CPPAD_TESTVECTOR(AD) Y(5); // CondExp(variable, variable, parameter, variable) Y[0] = CondExpLt(X[0], X[1], three, X[2]); Y[1] = CondExpLe(X[0], X[1], three, X[2]); Y[2] = CondExpEq(X[0], X[1], three, X[2]); Y[3] = CondExpGe(X[0], X[1], three, X[2]); Y[4] = CondExpGt(X[0], X[1], three, X[2]); // create f: X -> Y ADFun f(X, Y); // vectors for function values CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // vectors for derivative values CPPAD_TESTVECTOR(double) dv( f.Domain() ); CPPAD_TESTVECTOR(double) dw( f.Range() ); // check original function values ok &= Y[0] == three; ok &= Y[1] == three; ok &= Y[2] == X[2]; ok &= Y[3] == X[2]; ok &= Y[4] == X[2]; // function values v[0] = 2.; v[1] = 1.; v[2] = 0.; w = f.Forward(0, v); ok &= ( w[0] == v[2] ); ok &= ( w[1] == v[2] ); ok &= ( w[2] == v[2] ); ok &= ( w[3] == three ); ok &= ( w[4] == three ); // forward mode derivative values dv[0] = 1.; dv[1] = 2.; dv[2] = 3.; dw = f.Forward(1, dv); ok &= (dw[0] == dv[2] ); ok &= (dw[1] == dv[2] ); ok &= (dw[2] == dv[2] ); ok &= (dw[3] == 0. ); ok &= (dw[4] == 0. ); // reverse mode derivative values dw[0] = 1.; dw[1] = 2.; dw[2] = 3.; dw[3] = 4.; dw[4] = 5.; dv = f.Reverse(1, dw); ok &= (dv[0] == 0.); ok &= (dv[1] == 0.); ok &= (dv[2] == dw[0] + dw[1] + dw[2] ); return ok; } bool CondExp_vvvp(void) { bool ok = true; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) X(3); X[0] = 0.; X[1] = 1.; X[2] = 2.; Independent(X); // parameter value AD three = 3.; // dependent variable vector CPPAD_TESTVECTOR(AD) Y(5); // CondExp(variable, variable, variable, parameter) Y[0] = CondExpLt(X[0], X[1], X[2], three); Y[1] = CondExpLe(X[0], X[1], X[2], three); Y[2] = CondExpEq(X[0], X[1], X[2], three); Y[3] = CondExpGe(X[0], X[1], X[2], three); Y[4] = CondExpGt(X[0], X[1], X[2], three); // create f: X -> Y ADFun f(X, Y); // vectors for function values CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // vectors for derivative values CPPAD_TESTVECTOR(double) dv( f.Domain() ); CPPAD_TESTVECTOR(double) dw( f.Range() ); // check original function values ok &= Y[0] == X[2]; ok &= Y[1] == X[2]; ok &= Y[2] == three; ok &= Y[3] == three; ok &= Y[4] == three; // function values v[0] = 2.; v[1] = 1.; v[2] = 0.; w = f.Forward(0, v); ok &= ( w[0] == three ); ok &= ( w[1] == three ); ok &= ( w[2] == three ); ok &= ( w[3] == v[2] ); ok &= ( w[4] == v[2] ); // forward mode derivative values dv[0] = 1.; dv[1] = 2.; dv[2] = 3.; dw = f.Forward(1, dv); ok &= (dw[0] == 0. ); ok &= (dw[1] == 0. ); ok &= (dw[2] == 0. ); ok &= (dw[3] == dv[2] ); ok &= (dw[4] == dv[2] ); // reverse mode derivative values dw[0] = 1.; dw[1] = 2.; dw[2] = 3.; dw[3] = 4.; dw[4] = 5.; dv = f.Reverse(1, dw); ok &= (dv[0] == 0.); ok &= (dv[1] == 0.); ok &= (dv[2] == dw[3] + dw[4] ); return ok; } # include bool SecondOrderReverse(void) { // Bradley M. Bell 2009-07-04 // Reverse mode for CExpOp was only modifying the highest order partial // This test demonstrated the bug bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits::epsilon(); size_t n = 1; CPPAD_TESTVECTOR(AD) X(n); X[0] = 2.; CppAD::Independent(X); size_t m = 2; CPPAD_TESTVECTOR(AD) Y(m); AD left = X[0]; AD right = X[0] * X[0]; AD exp_if_true = left; AD exp_if_false = right; // Test of reverse mode using exp_if_true case // For this value of X, should be the same as Z = X[0] AD Z = CondExpLt(left, right, exp_if_true, exp_if_false); Y[0] = Z * Z; // Test of reverse mode using exp_if_false case exp_if_false = left; exp_if_true = right; Z = CondExpGt(left, right, exp_if_true, exp_if_false); Y[1] = Z * Z; CppAD::ADFun f(X, Y); // first order forward CPPAD_TESTVECTOR(double) dx(n); size_t p = 1; dx[0] = 1.; f.Forward(p, dx); // second order reverse (test exp_if_true case) CPPAD_TESTVECTOR(double) w(m), dw(2 * n); w[0] = 1.; w[1] = 0.; p = 2; dw = f.Reverse(p, w); // check first derivative in dw double check = 2. * Value( X[0] ); ok &= NearEqual(dw[0], check, eps, eps); // check second derivative in dw check = 2.; ok &= NearEqual(dw[1], check, eps, eps); // test exp_if_false case w[0] = 0.; w[1] = 1.; p = 2; dw = f.Reverse(p, w); // check first derivative in dw check = 2. * Value( X[0] ); ok &= NearEqual(dw[0], check, eps, eps); // check second derivative in dw check = 2.; ok &= NearEqual(dw[1], check, eps, eps); return ok; } double Infinity(double zero) { return 1. / zero; } bool OldExample(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; using CppAD::log; using CppAD::abs; double eps = 100. * std::numeric_limits::epsilon(); // domain space vector size_t n = 5; CPPAD_TESTVECTOR(AD) X(n); size_t j; for(j = 0; j < n; j++) X[j] = 1.; // declare independent variables and start tape recording CppAD::Independent(X); // sum with respect to j of log of absolute value of X[j] // sould be - infinity if any of the X[j] are zero AD MinusInfinity = - Infinity(0.); AD Sum = 0.; AD Zero(0); for(j = 0; j < n; j++) { // if X[j] > 0 Sum += CppAD::CondExpGt(X[j], Zero, log(X[j]), Zero); // if X[j] < 0 Sum += CppAD::CondExpLt(X[j], Zero, log(-X[j]), Zero); // if X[j] == 0 Sum += CppAD::CondExpEq(X[j], Zero, MinusInfinity, Zero); } // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = Sum; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // vectors for arguments to the function object f CPPAD_TESTVECTOR(double) x(n); // argument values CPPAD_TESTVECTOR(double) y(m); // function values CPPAD_TESTVECTOR(double) w(m); // function weights CPPAD_TESTVECTOR(double) dw(n); // derivative of weighted function // a case where abs( x[j] ) > 0 for all j double check = 0.; double sign = 1.; for(j = 0; j < n; j++) { sign *= -1.; x[j] = sign * double(j + 1); check += log( abs( x[j] ) ); } // function value y = f.Forward(0, x); ok &= ( y[0] == check ); // compute derivative of y[0] w[0] = 1.; dw = f.Reverse(1, w); for(j = 0; j < n; j++) { if( x[j] > 0. ) ok &= NearEqual(dw[j], 1./abs( x[j] ), eps, eps); else ok &= NearEqual(dw[j], -1./abs( x[j] ), eps, eps); } // a case where x[0] is equal to zero sign = 1.; for(j = 0; j < n; j++) { sign *= -1.; x[j] = sign * double(j); } // function value y = f.Forward(0, x); ok &= ( y[0] == -Infinity(0.) ); // compute derivative of y[0] f.check_for_nan(false); w[0] = 1.; dw = f.Reverse(1, w); for(j = 0; j < n; j++) { if( x[j] > 0. ) ok &= NearEqual(dw[j], 1./abs( x[j] ), eps, eps); else if( x[j] < 0. ) ok &= NearEqual(dw[j], -1./abs( x[j] ), eps, eps); else ok &= NearEqual(dw[j], 0.0, eps, eps); } return ok; } } // end empty namespace bool CondExp(void) { bool ok = true; ok &= CondExp_pvvv(); ok &= CondExp_vpvv(); ok &= CondExp_vvpv(); ok &= CondExp_vvvp(); ok &= SecondOrderReverse(); ok &= OldExample(); return ok; } // END C++ cppad-20170000.3/test_more/vec_ad_par.cpp0000644000175200017650000000352113057470461017222 0ustar coincoin-web// $Id: vec_ad_par.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test the use of the parameters in VecAD element assignments */ # include typedef CppAD::AD ADdouble; typedef CppAD::AD< ADdouble > ADDdouble; bool VecADPar(void) { using namespace CppAD; bool ok = true; CPPAD_TESTVECTOR( ADdouble ) x(2); x[0] = 0; x[1] = 0; Independent(x); CPPAD_TESTVECTOR( ADDdouble ) y(1); y[0] = 1; Independent(y); VecAD< ADdouble > v(2); ADDdouble zero(0); ADDdouble one(1); v[zero] = x[0]; // these two parameter values are equal, v[one] = x[1]; // but they are not identically equal CPPAD_TESTVECTOR( ADDdouble ) z(1); z[0] = v[zero] + v[one]; // f(y) = x[0] + x[1] ADFun< ADdouble > f(y, z); CPPAD_TESTVECTOR( ADdouble ) a( f.Domain() ); CPPAD_TESTVECTOR( ADdouble ) b( f.Range() ); // fy = f(y) = x[0] + x[1] a[0] = 0.; b = f.Forward(0, a); // check value of f ok &= b[0] == (x[0] + x[1]); // g(x) = x[0] + x[1]; ADFun g(x, b); CPPAD_TESTVECTOR( double ) c( g.Domain() ); CPPAD_TESTVECTOR( double ) d( g.Range() ); // d = g(1, 2) c[0] = 1.; // these tow values are not equal and correspond c[1] = 2.; // to replacements for the equal parameter values above d = g.Forward(0, c); // check function value ok &= (d[0] == c[0] + c[1]); return ok; } cppad-20170000.3/test_more/sinh.cpp0000644000175200017650000000364613057470461016110 0ustar coincoin-web// $Id: sinh.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example now just used for validation testing. */ # include bool Sinh(void) { bool ok = true; using CppAD::sinh; using CppAD::cosh; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 1.; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = sinh(U[0]); // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value double sin_u = sinh( Value(U[0]) ); double cos_u = cosh( Value(U[0]) ); ok &= NearEqual(sin_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; for(j = 1; j < p; j++) { w = f.Forward(j, v); double value; if( j % 2 == 1 ) value = cos_u; else value = sin_u; jfac *= j; ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; for(j = 0; j < p; j++) { double value; if( j % 2 == 0 ) value = cos_u; else value = sin_u; ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); } return ok; } cppad-20170000.3/test_more/old_mat_mul.hpp0000644000175200017650000003020513057470461017437 0ustar coincoin-web// $Id$ # ifndef CPPAD_TEST_MORE_OLD_MAT_MUL_HPP # define CPPAD_TEST_MORE_OLD_MAT_MUL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin old_mat_mul.hpp$$ $spell old_mat_mul.hpp cppad CppAD namespace struct nr nc bool vx const im mj ij px py std tx ty resize nz var jac Jacobian hes vy $$ $section Define Matrix Multiply as a User Atomic Operation$$ $mindex old_mat_mul old_atomic test$$ $head Syntax$$ This file is located in the $code example$$ directory. It can be copied to the current working directory and included with the syntax $codei% # include "old_mat_mul.hpp" %$$ $head Example$$ The file $cref old_mat_mul.cpp$$ contains an example use of $code old_mat_mul.hpp$$. It returns true if it succeeds and false otherwise. $head Begin Source$$ $srccode%cpp% */ # include // Include CppAD definitions namespace { // Begin empty namespace using CppAD::vector; // Let vector denote CppAD::vector /* %$$ $head Extra Call Information$$ $srccode%cpp% */ // Information we will attach to each mat_mul call struct call_info { size_t nr_result; size_t n_middle; size_t nc_result; vector vx; }; vector info_; // vector of call information // number of orders for this operation (k + 1) size_t n_order_ = 0; // number of rows in the result matrix size_t nr_result_ = 0; // number of columns in left matrix and number of rows in right matrix size_t n_middle_ = 0; // number of columns in the result matrix size_t nc_result_ = 0; // which components of x are variables vector* vx_ = CPPAD_NULL; // get the information corresponding to this call void get_info(size_t id, size_t k, size_t n, size_t m) { n_order_ = k + 1; nr_result_ = info_[id].nr_result; n_middle_ = info_[id].n_middle; nc_result_ = info_[id].nc_result; vx_ = &(info_[id].vx); assert(n == nr_result_ * n_middle_ + n_middle_ * nc_result_); assert(m == nr_result_ * nc_result_); } /* %$$ $head Matrix Indexing$$ $srccode%cpp% */ // Convert left matrix index pair and order to a single argument index size_t left(size_t i, size_t j, size_t ell) { assert( i < nr_result_ ); assert( j < n_middle_ ); return (i * n_middle_ + j) * n_order_ + ell; } // Convert right matrix index pair and order to a single argument index size_t right(size_t i, size_t j, size_t ell) { assert( i < n_middle_ ); assert( j < nc_result_ ); size_t offset = nr_result_ * n_middle_; return (offset + i * nc_result_ + j) * n_order_ + ell; } // Convert result matrix index pair and order to a single result index size_t result(size_t i, size_t j, size_t ell) { assert( i < nr_result_ ); assert( j < nc_result_ ); return (i * nc_result_ + j) * n_order_ + ell; } /* %$$ $head One Matrix Multiply$$ Forward mode matrix multiply left times right and sum into result: $srccode%cpp% */ void multiply_and_sum( size_t order_left , size_t order_right, const vector& tx , vector& ty ) { size_t i, j; size_t order_result = order_left + order_right; for(i = 0; i < nr_result_; i++) { for(j = 0; j < nc_result_; j++) { double sum = 0.; size_t middle, im_left, mj_right, ij_result; for(middle = 0; middle < n_middle_; middle++) { im_left = left(i, middle, order_left); mj_right = right(middle, j, order_right); sum += tx[im_left] * tx[mj_right]; } ij_result = result(i, j, order_result); ty[ ij_result ] += sum; } } return; } /* %$$ $head Reverse Partials One Order$$ Compute reverse mode partials for one order and sum into px: $srccode%cpp% */ void reverse_multiply( size_t order_left , size_t order_right, const vector& tx , const vector& ty , vector& px , const vector& py ) { size_t i, j; size_t order_result = order_left + order_right; for(i = 0; i < nr_result_; i++) { for(j = 0; j < nc_result_; j++) { size_t middle, im_left, mj_right, ij_result; for(middle = 0; middle < n_middle_; middle++) { ij_result = result(i, j, order_result); im_left = left(i, middle, order_left); mj_right = right(middle, j, order_right); // sum += tx[im_left] * tx[mj_right]; px[im_left] += tx[mj_right] * py[ij_result]; px[mj_right] += tx[im_left] * py[ij_result]; } } } return; } /* %$$ $head Set Union$$ $srccode%cpp% */ using CppAD::set_union; /* %$$ $head CppAD User Atomic Callback Functions$$ $srccode%cpp% */ // ---------------------------------------------------------------------- // forward mode routine called by CppAD bool mat_mul_forward( size_t id , size_t k , size_t n , size_t m , const vector& vx , vector& vy , const vector& tx , vector& ty ) { size_t i, j, ell; get_info(id, k, n, m); // check if this is during the call to mat_mul(id, ax, ay) if( vx.size() > 0 ) { assert( k == 0 && vx.size() > 0 ); // store the vx information in info_ assert( vx_->size() == 0 ); info_[id].vx.resize(n); for(j = 0; j < n; j++) info_[id].vx[j] = vx[j]; assert( vx_->size() == n ); // now compute vy for(i = 0; i < nr_result_; i++) { for(j = 0; j < nc_result_; j++) { // compute vy[ result(i, j, 0) ] bool var = false; bool nz_left, nz_right; size_t middle, im_left, mj_right, ij_result; for(middle = 0; middle < n_middle_; middle++) { im_left = left(i, middle, k); mj_right = right(middle, j, k); nz_left = vx[im_left] | (tx[im_left] != 0.); nz_right = vx[mj_right] | (tx[mj_right]!= 0.); // if not multiplying by the constant zero if( nz_left & nz_right ) var |= (vx[im_left] | vx[mj_right]); } ij_result = result(i, j, k); vy[ij_result] = var; } } } // initialize result as zero for(i = 0; i < nr_result_; i++) { for(j = 0; j < nc_result_; j++) ty[ result(i, j, k) ] = 0.; } // sum the product of proper orders for(ell = 0; ell <=k; ell++) multiply_and_sum(ell, k-ell, tx, ty); // All orders are implemented and there are no possible error // conditions, so always return true. return true; } // ---------------------------------------------------------------------- // reverse mode routine called by CppAD bool mat_mul_reverse( size_t id , size_t k , size_t n , size_t m , const vector& tx , const vector& ty , vector& px , const vector& py ) { get_info(id, k, n, m); size_t ell = n * n_order_; while(ell--) px[ell] = 0.; size_t order = n_order_; while(order--) { // reverse sum the products for specified order for(ell = 0; ell <=order; ell++) reverse_multiply(ell, order-ell, tx, ty, px, py); } // All orders are implemented and there are no possible error // conditions, so always return true. return true; } // ---------------------------------------------------------------------- // forward Jacobian sparsity routine called by CppAD bool mat_mul_for_jac_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , vector< std::set >& s ) { size_t i, j, k, im_left, middle, mj_right, ij_result; k = 0; get_info(id, k, n, m); for(i = 0; i < nr_result_; i++) { for(j = 0; j < nc_result_; j++) { ij_result = result(i, j, k); s[ij_result].clear(); for(middle = 0; middle < n_middle_; middle++) { im_left = left(i, middle, k); mj_right = right(middle, j, k); // s[ij_result] = union( s[ij_result], r[im_left] ) s[ij_result] = set_union(s[ij_result], r[im_left]); // s[ij_result] = union( s[ij_result], r[mj_right] ) s[ij_result] = set_union(s[ij_result], r[mj_right]); } } } return true; } // ---------------------------------------------------------------------- // reverse Jacobian sparsity routine called by CppAD bool mat_mul_rev_jac_sparse( size_t id , size_t n , size_t m , size_t p , vector< std::set >& r , const vector< std::set >& s ) { size_t i, j, k, im_left, middle, mj_right, ij_result; k = 0; get_info(id, k, n, m); for(j = 0; j < n; j++) r[j].clear(); for(i = 0; i < nr_result_; i++) { for(j = 0; j < nc_result_; j++) { ij_result = result(i, j, k); for(middle = 0; middle < n_middle_; middle++) { im_left = left(i, middle, k); mj_right = right(middle, j, k); // r[im_left] = union( r[im_left], s[ij_result] ) r[im_left] = set_union(r[im_left], s[ij_result]); // r[mj_right] = union( r[mj_right], s[ij_result] ) r[mj_right] = set_union(r[mj_right], s[ij_result]); } } } return true; } // ---------------------------------------------------------------------- // reverse Hessian sparsity routine called by CppAD bool mat_mul_rev_hes_sparse( size_t id , size_t n , size_t m , size_t p , const vector< std::set >& r , const vector& s , vector& t , const vector< std::set >& u , vector< std::set >& v ) { size_t i, j, k, im_left, middle, mj_right, ij_result; k = 0; get_info(id, k, n, m); for(j = 0; j < n; j++) { t[j] = false; v[j].clear(); } assert( vx_->size() == n ); for(i = 0; i < nr_result_; i++) { for(j = 0; j < nc_result_; j++) { ij_result = result(i, j, k); for(middle = 0; middle < n_middle_; middle++) { im_left = left(i, middle, k); mj_right = right(middle, j, k); // back propagate Jacobian sparsity t[im_left] = (t[im_left] | s[ij_result]); t[mj_right] = (t[mj_right] | s[ij_result]); // Visual Studio C++ 2008 warns unsafe mix of int and // bool if we use the following code directly above: // t[im_left] |= s[ij_result]; // t[mj_right] |= s[ij_result]; // back propagate Hessian sparsity // v[im_left] = union( v[im_left], u[ij_result] ) // v[mj_right] = union( v[mj_right], u[ij_result] ) v[im_left] = set_union(v[im_left], u[ij_result] ); v[mj_right] = set_union(v[mj_right], u[ij_result] ); // Check for case where the (i,j) result element // is in reverse Jacobian and both left and right // operands in multiplication are variables if(s[ij_result] & (*vx_)[im_left] & (*vx_)[mj_right]) { // v[im_left] = union( v[im_left], r[mj_right] ) v[im_left] = set_union(v[im_left], r[mj_right] ); // v[mj_right] = union( v[mj_right], r[im_left] ) v[mj_right] = set_union(v[mj_right], r[im_left] ); } } } } return true; } /* %$$ $head Declare mat_mul Function$$ Declare the $code AD$$ routine $codei%mat_mul(%id%, %ax%, %ay%)%$$ and end empty namespace (we could use any $cref/simple vector template class/SimpleVector/$$ instead of $code CppAD::vector$$): $srccode%cpp% */ CPPAD_USER_ATOMIC( mat_mul , CppAD::vector , double , mat_mul_forward , mat_mul_reverse , mat_mul_for_jac_sparse , mat_mul_rev_jac_sparse , mat_mul_rev_hes_sparse ) } // End empty namespace /* %$$ $end */ # endif cppad-20170000.3/test_more/acosh.cpp0000644000175200017650000000374413057470461016243 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include bool acosh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 200. * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::Independent(ax); // a temporary value AD cosh_of_x0 = CppAD::cosh(ax[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CppAD::acosh(cosh_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // check value ok &= NearEqual(ay[0] , x0, eps, eps); // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 1., eps, eps); // forward computation of higher order partials w.r.t. x[0] size_t n_order = 5; for(size_t order = 2; order < n_order; order++) { dx[0] = 0.; dy = f.Forward(order, dx); ok &= NearEqual(dy[0], 0., eps, eps); } // reverse computation of derivatives CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n_order * n); w[0] = 1.; dw = f.Reverse(n_order, w); ok &= NearEqual(dw[0], 1., eps, eps); for(size_t order = 1; order < n_order; order++) ok &= NearEqual(dw[order * n + 0], 0., eps, eps); return ok; } // END C++ cppad-20170000.3/test_more/print_for.cpp0000644000175200017650000000524013057470461017141 0ustar coincoin-web// $Id: print_for.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // modified version of test that used to be in ../print_for/print_for.cpp # include namespace { using std::endl; using CppAD::AD; // use of PrintFor to check for invalid function arguments AD check_log(const AD& y) { // check during recording CPPAD_ASSERT_UNKNOWN( y > 0. ); // check during zero order forward calculation PrintFor(y, "check_log: y == ", y , " which is <= 0\n"); return log(y); } } bool print_for(void) { bool ok = true; using CppAD::PrintFor; std::stringstream stream_out; // stream that output is written to std::string string_check; // what we expect the output to be // independent variable vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 1.; Independent(ax); // print a VecAD::reference object that is a parameter CppAD::VecAD av(1); AD Zero(0); av[Zero] = 0.; PrintFor("v[0] = ", av[Zero]); string_check += "v[0] = 0"; // v[0] == 0 during Forward(0, x) // Print a newline to separate this from previous output, // then print an AD object that is a variable. PrintFor("\nv[0] + x[0] = ", av[0] + ax[0]); string_check += "\nv[0] + x[0] = 2"; // x[0] == 2 during Forward(0, x) // A conditional print that will not generate output when x[0] = 2. PrintFor(ax[0], "\n 2. + x[0] = ", 2. + ax[0], "\n"); // A conditional print that will generate output when x[0] = 2. PrintFor(ax[0] - 2., "\n 3. + x[0] = ", 3. + ax[0], "\n"); string_check += "\n 3. + x[0] = 5\n"; // A log evaluations that will result in an error message when x[0] = 2. AD var = 2. - ax[0]; AD log_var = check_log(var); string_check += "check_log: y == 0 which is <= 0\n"; // dependent variable vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = av[Zero] + ax[0]; // define f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // zero order forward with x[0] = 2 CPPAD_TESTVECTOR(double) x(n); x[0] = 2.; f.Forward(0, x, stream_out); std::string string_out = stream_out.str(); ok &= string_out == string_check; return ok; } cppad-20170000.3/test_more/old_mat_mul.cpp0000644000175200017650000002017113057470461017433 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin old_mat_mul.cpp$$ $spell mul $$ $section Old Matrix Multiply as a User Atomic Operation: Example and Test$$ $head Deprecated 2013-05-27$$ This example has been deprecated; use $cref atomic_mat_mul.cpp$$ instead. $children% test_more/old_mat_mul.hpp %$$ $head Include File$$ This routine uses the include file $cref old_mat_mul.hpp$$. $code $srcfile%test_more/old_mat_mul.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include "old_mat_mul.hpp" bool old_mat_mul(void) { bool ok = true; using CppAD::AD; // matrix sizes for this test size_t nr_result = 2; size_t n_middle = 2; size_t nc_result = 2; // declare the AD vectors ax and ay and X size_t n = nr_result * n_middle + n_middle * nc_result; size_t m = nr_result * nc_result; CppAD::vector< AD > X(4), ax(n), ay(m); size_t i, j; for(j = 0; j < X.size(); j++) X[j] = (j + 1); // X is the vector of independent variables CppAD::Independent(X); // left matrix ax[0] = X[0]; // left[0,0] = x[0] = 1 ax[1] = X[1]; // left[0,1] = x[1] = 2 ax[2] = 5.; // left[1,0] = 5 ax[3] = 6.; // left[1,1] = 6 // right matrix ax[4] = X[2]; // right[0,0] = x[2] = 3 ax[5] = 7.; // right[0,1] = 7 ax[6] = X[3]; // right[1,0] = x[3] = 4 ax[7] = 8.; // right[1,1] = 8 /* [ x0 , x1 ] * [ x2 , 7 ] = [ x0*x2 + x1*x3 , x0*7 + x1*8 ] [ 5 , 6 ] [ x3 , 8 ] [ 5*x2 + 6*x3 , 5*7 + 6*8 ] */ // The call back routines need to know the dimensions of the matrices. // Store information about the matrix multiply for this call to mat_mul. call_info info; info.nr_result = nr_result; info.n_middle = n_middle; info.nc_result = nc_result; // info.vx gets set by forward during call to mat_mul below assert( info.vx.size() == 0 ); size_t id = info_.size(); info_.push_back(info); // user defined AD version of matrix multiply mat_mul(id, ax, ay); //---------------------------------------------------------------------- // check AD results ok &= ay[0] == (1*3 + 2*4); ok &= Variable( ay[0] ); ok &= ay[1] == (1*7 + 2*8); ok &= Variable( ay[1] ); ok &= ay[2] == (5*3 + 6*4); ok &= Variable( ay[2] ); ok &= ay[3] == (5*7 + 6*8); ok &= Parameter( ay[3] ); //---------------------------------------------------------------------- // use mat_mul to define a function g : X -> ay CppAD::ADFun G; G.Dependent(X, ay); // g(x) = [ x0*x2 + x1*x3 , x0*7 + x1*8 , 5*x2 + 6*x3 , 5*7 + 6*8 ]^T //---------------------------------------------------------------------- // Test zero order forward mode evaluation of g(x) CppAD::vector x( X.size() ), y(m); for(j = 0; j < X.size() ; j++) x[j] = j + 2; y = G.Forward(0, x); ok &= y[0] == x[0] * x[2] + x[1] * x[3]; ok &= y[1] == x[0] * 7. + x[1] * 8.; ok &= y[2] == 5. * x[2] + 6. * x[3]; ok &= y[3] == 5. * 7. + 6. * 8.; //---------------------------------------------------------------------- // Test first order forward mode evaluation of g'(x) * [1, 2, 3, 4]^T // g'(x) = [ x2, x3, x0, x1 ] // [ 7 , 8, 0, 0 ] // [ 0 , 0, 5, 6 ] // [ 0 , 0, 0, 0 ] CppAD::vector dx( X.size() ), dy(m); for(j = 0; j < X.size() ; j++) dx[j] = j + 1; dy = G.Forward(1, dx); ok &= dy[0] == 1. * x[2] + 2. * x[3] + 3. * x[0] + 4. * x[1]; ok &= dy[1] == 1. * 7. + 2. * 8. + 3. * 0. + 4. * 0.; ok &= dy[2] == 1. * 0. + 2. * 0. + 3. * 5. + 4. * 6.; ok &= dy[3] == 1. * 0. + 2. * 0. + 3. * 0. + 4. * 0.; //---------------------------------------------------------------------- // Test second order forward mode // g_0^2 (x) = [ 0, 0, 1, 0 ], g_0^2 (x) * [1] = [3] // [ 0, 0, 0, 1 ] [2] [4] // [ 1, 0, 0, 0 ] [3] [1] // [ 0, 1, 0, 0 ] [4] [2] CppAD::vector ddx( X.size() ), ddy(m); for(j = 0; j < X.size() ; j++) ddx[j] = 0.; ddy = G.Forward(2, ddx); // [1, 2, 3, 4] * g_0^2 (x) * [1, 2, 3, 4]^T = 1*3 + 2*4 + 3*1 + 4*2 ok &= 2. * ddy[0] == 1. * 3. + 2. * 4. + 3. * 1. + 4. * 2.; // for i > 0, [1, 2, 3, 4] * g_i^2 (x) * [1, 2, 3, 4]^T = 0 ok &= ddy[1] == 0.; ok &= ddy[2] == 0.; ok &= ddy[3] == 0.; //---------------------------------------------------------------------- // Test second order reverse mode CppAD::vector w(m), dw(2 * X.size() ); for(i = 0; i < m; i++) w[i] = 0.; w[0] = 1.; dw = G.Reverse(2, w); // g_0'(x) = [ x2, x3, x0, x1 ] ok &= dw[0*2 + 0] == x[2]; ok &= dw[1*2 + 0] == x[3]; ok &= dw[2*2 + 0] == x[0]; ok &= dw[3*2 + 0] == x[1]; // g_0'(x) * [1, 2, 3, 4] = 1 * x2 + 2 * x3 + 3 * x0 + 4 * x1 // g_0^2 (x) * [1, 2, 3, 4] = [3, 4, 1, 2] ok &= dw[0*2 + 1] == 3.; ok &= dw[1*2 + 1] == 4.; ok &= dw[2*2 + 1] == 1.; ok &= dw[3*2 + 1] == 2.; //---------------------------------------------------------------------- // Test forward and reverse Jacobian sparsity pattern /* [ x0 , x1 ] * [ x2 , 7 ] = [ x0*x2 + x1*x3 , x0*7 + x1*8 ] [ 5 , 6 ] [ x3 , 8 ] [ 5*x2 + 6*x3 , 5*7 + 6*8 ] so the sparsity pattern should be s[0] = {0, 1, 2, 3} s[1] = {0, 1} s[2] = {2, 3} s[3] = {} */ CppAD::vector< std::set > r( X.size() ), s(m); for(j = 0; j < X.size() ; j++) { assert( r[j].empty() ); r[j].insert(j); } s = G.ForSparseJac( X.size() , r); for(j = 0; j < X.size() ; j++) { // s[0] = {0, 1, 2, 3} ok &= s[0].find(j) != s[0].end(); // s[1] = {0, 1} if( j == 0 || j == 1 ) ok &= s[1].find(j) != s[1].end(); else ok &= s[1].find(j) == s[1].end(); // s[2] = {2, 3} if( j == 2 || j == 3 ) ok &= s[2].find(j) != s[2].end(); else ok &= s[2].find(j) == s[2].end(); } // s[3] == {} ok &= s[3].empty(); //---------------------------------------------------------------------- // Test reverse Jacobian sparsity pattern /* [ x0 , x1 ] * [ x2 , 7 ] = [ x0*x2 + x1*x3 , x0*7 + x1*8 ] [ 5 , 6 ] [ x3 , 8 ] [ 5*x2 + 6*x3 , 5*7 + 6*8 ] so the sparsity pattern should be r[0] = {0, 1, 2, 3} r[1] = {0, 1} r[2] = {2, 3} r[3] = {} */ for(i = 0; i < m; i++) { s[i].clear(); s[i].insert(i); } r = G.RevSparseJac(m, s); for(j = 0; j < X.size() ; j++) { // r[0] = {0, 1, 2, 3} ok &= r[0].find(j) != r[0].end(); // r[1] = {0, 1} if( j == 0 || j == 1 ) ok &= r[1].find(j) != r[1].end(); else ok &= r[1].find(j) == r[1].end(); // r[2] = {2, 3} if( j == 2 || j == 3 ) ok &= r[2].find(j) != r[2].end(); else ok &= r[2].find(j) == r[2].end(); } // r[3] == {} ok &= r[3].empty(); //---------------------------------------------------------------------- /* Test reverse Hessian sparsity pattern g_0^2 (x) = [ 0, 0, 1, 0 ] and for i > 0, g_i^2 = 0 [ 0, 0, 0, 1 ] [ 1, 0, 0, 0 ] [ 0, 1, 0, 0 ] so for the sparsity pattern for the first component of g is h[0] = {2} h[1] = {3} h[2] = {0} h[3] = {1} */ CppAD::vector< std::set > h( X.size() ), t(1); t[0].clear(); t[0].insert(0); h = G.RevSparseHes(X.size() , t); size_t check[] = {2, 3, 0, 1}; for(j = 0; j < X.size() ; j++) { // h[j] = { check[j] } for(i = 0; i < n; i++) { if( i == check[j] ) ok &= h[j].find(i) != h[j].end(); else ok &= h[j].find(i) == h[j].end(); } } t[0].clear(); for( j = 1; j < X.size(); j++) t[0].insert(j); h = G.RevSparseHes(X.size() , t); for(j = 0; j < X.size() ; j++) { // h[j] = { } for(i = 0; i < X.size(); i++) ok &= h[j].find(i) == h[j].end(); } // -------------------------------------------------------------------- // Free temporary work space. (If there are future calls to // old_mat_mul they would create new temporary work space.) CppAD::user_atomic::clear(); info_.clear(); return ok; } // END C++ cppad-20170000.3/test_more/extern_value.hpp0000644000175200017650000000151113057470461017642 0ustar coincoin-web// $Id: extern_value.hpp 3804 2016-03-20 15:08:46Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # ifndef CPPAD_TEST_MORE_EXTERN_VALUE_HPP # define CPPAD_TEST_MORE_EXTERN_VALUE_HPP template class extern_value { private: Type value_; public: extern_value(Type value); void set(Type value); Type get(void); }; # endif cppad-20170000.3/test_more/local/0002755000175200017650000000000013057470461015526 5ustar coincoin-webcppad-20170000.3/test_more/local/vector_set.cpp0000644000175200017650000001000613057470461020402 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // BEGIN empty namespace template bool test_no_other(void) { bool ok = true; VectorSet vec_set; size_t n_set = 4; size_t end = 5; vec_set.resize(n_set, end); // ok &= end == vec_set.end(); ok &= n_set == vec_set.n_set(); // // add the element i+1 to set i for(size_t i = 1; i < n_set; i++) vec_set.add_element(i, i+1); // // check for element i and i+1 in set i for(size_t i = 0; i < n_set; i++) { ok &= ! vec_set.is_element(i, i); if( i == 0 ) ok &= ! vec_set.is_element(i, i+1); else ok &= vec_set.is_element(i, i+1); } // // set an empty set to value of set 2 size_t target = 0; size_t source = 2; vec_set.assignment(target, source, vec_set); ok &= ! vec_set.is_element(target, source); ok &= vec_set.is_element(target, source+1); // // set a non-empty set to the value of set 2 target = 1; vec_set.assignment(target, source, vec_set); ok &= ! vec_set.is_element(target, source); ok &= vec_set.is_element(target, source+1); // // add an element to set 1, one of the three vectors equal to set 2 target = 1; vec_set.add_element(target, source); ok &= vec_set.is_element(target, source); ok &= vec_set.is_element(target, source+1); ok &= ! vec_set.is_element(source, source); ok &= vec_set.is_element(source, source+1); // // now take the union of set 2 and set 3 and place in set 0 // (wich is sharing a list with set 2) target = 0; vec_set.binary_union(target, source, source+1, vec_set); ok &= vec_set.is_element(target, source+1); ok &= vec_set.is_element(target, source+2); ok &= vec_set.is_element(source, source+1); ok &= ! vec_set.is_element(source, source+2); // // now check the elements in set 0 by iterating over them typename VectorSet::const_iterator itr(vec_set, target); ok &= *itr == source+1; ok &= *(++itr) == source+2; ok &= *(++itr) == end; // // now test clear vec_set.clear(1); ok &= ! vec_set.is_element(1, source+1); ok &= vec_set.is_element(0, source+1); // // now force sparse_list garbage collection by setting all sets // equal to set 0 for(size_t i = 1; i < n_set; i++) { vec_set.assignment(i, 0, vec_set); ok &= vec_set.is_element(i, source+1); ok &= vec_set.is_element(i, source+2); } // return ok; } template bool test_yes_other(void) { bool ok = true; VectorSet vec_set, other_vec; size_t n_set = 4; size_t end = 5; vec_set.resize(n_set, end); other_vec.resize(n_set, end); // // add element i to set i in vec_set // add element i+1 to set i in other for(size_t i = 1; i < n_set; i++) { vec_set.add_element(i, i); other_vec.add_element(i, i+1); } // // assignment from other size_t target = 0; size_t source = 1; vec_set.assignment(target, source, other_vec); ok &= ! vec_set.is_element(target, source); ok &= vec_set.is_element(target, source+1); // // now take the union of a set from vec_set and from other_vec target = 2; // where result goes in vec_set size_t left = 2; // left operand in vec_set size_t right = 2; // right operand in other vec_set.binary_union(target, left, right, other_vec); ok &= vec_set.is_element(target, left); ok &= vec_set.is_element(target, right+1); // return ok; } } // END empty namespace bool vector_set(void) { bool ok = true; ok &= test_no_other(); ok &= test_no_other(); // ok &= test_yes_other(); ok &= test_yes_other(); // return ok; } cppad-20170000.3/test_more/zdouble.cpp0000644000175200017650000000556113057470461016611 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin zdouble.cpp$$ $spell zdouble $$ $section zdouble: Example and Test$$ $code $srcfile%test_more/zdouble.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { template bool test(bool is_double) { bool ok = true; Base eps = 10. * std::numeric_limits::epsilon(); typedef CppAD::AD a1type; typedef CppAD::AD a2type; // value during taping size_t n = 2; CPPAD_TESTVECTOR(Base) x(n); x[0] = 0.0; x[1] = 0.0; // declare independent variable CPPAD_TESTVECTOR(a2type) a2x(n); for (size_t j = 0; j < n; j++) a2x[j] = a2type( a1type(x[j]) ); Independent(a2x); // zero and one as a2type values a2type a2zero = a2type(0.0); a2type a2one = a2type(1.0); // h(x) = x[0] / x[1] if x[1] > x[0] else 1.0 a2type h_x = CondExpGt(a2x[1], a2x[0], a2x[0] / a2x[1], a2one); // f(x) = h(x) if x[0] > 0.0 else 0.0 // = x[0] / x[1] if x[1] > x[0] and x[0] > 0.0 // = 1.0 if x[0] >= x[1] and x[0] > 0.0 // = 0.0 if x[0] <= 0.0 a2type f_x = CondExpGt(a2x[0], a2zero, h_x, a2one); // define the function f(x) size_t m = 1; CPPAD_TESTVECTOR(a2type) a2y(m); a2y[0] = f_x; CppAD::ADFun af1; af1.Dependent(a2x, a2y); // Define function g(x) = gradient of f(x) CPPAD_TESTVECTOR(a1type) a1x(n), a1z(n), a1w(m); for (size_t j = 0; j < n; j++) a1x[j] = a1type(x[j]); a1w[0] = a1type(1.0); Independent(a1x); af1.Forward(0, a1x); a1z = af1.Reverse(1, a1w); CppAD::ADFun g; g.Dependent(a1x, a1z); // check result for a case where f(x) = 0.0; CPPAD_TESTVECTOR(Base) z(2); x[0] = 0.0; x[1] = 0.0; z = g.Forward(0, x); ok &= z[0] == 0.0; ok &= z[1] == 0.0; // check result for a case where f(x) = 1.0; x[0] = 1.0; x[1] = 0.5; z = g.Forward(0, x); ok &= z[0] == 0.0; ok &= z[1] == 0.0; // check result for a case where f(x) = x[0] / x[1]; x[0] = 1.0; x[1] = 2.0; z = g.Forward(0, x); ok &= CppAD::NearEqual(z[0], 1.0/x[1], eps, eps); ok &= CppAD::NearEqual(z[1], - x[0]/(x[1]*x[1]), eps, eps); return ok; } } bool zdouble(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; using CppAD::zdouble; // bool is_double = false; ok &= test(is_double); // is_double = true; ok &= test(is_double); // return ok; } // END C++ cppad-20170000.3/test_more/value.cpp0000644000175200017650000000303713057470461016255 0ustar coincoin-web// $Id: value.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old Value example now used just for valiadation testing */ // BEGIN C++ # include bool Value(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 4.; Independent(U); // cannot call Value after Independent (tape is recording) // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(1); size_t x = 0; // dependent variable values Z[x] = - U[t]; // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // can call Value after ADFun constructor (tape is no longer recording) // check value of s double sValue = Value(U[s]); ok &= ( sValue == 3. ); // check value of x double xValue = Value(Z[x]); ok &= ( xValue == -4. ); return ok; } // END C++ cppad-20170000.3/test_more/mul_zero_one.cpp0000644000175200017650000000357413057470461017644 0ustar coincoin-web// $Id: mul_zero_one.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test the use of the special parameters zero and one with the multiply operator */ # include typedef CppAD::AD ADdouble; typedef CppAD::AD< ADdouble > ADDdouble; bool MulZeroOne(void) { using namespace CppAD; bool ok = true; size_t i; for(i = 0; i < 3; i++) { // run through the cases x = 0, 1, 2 size_t j; for(j = 0; j < 3; j++) { // run through the cases y = 0, 1, 2 CPPAD_TESTVECTOR( ADdouble ) x(1); x[0] = double(i); Independent(x); CPPAD_TESTVECTOR( ADDdouble ) y(1); y[0] = ADDdouble(j); Independent(y); CPPAD_TESTVECTOR( ADDdouble ) z(2); z[0] = x[0] * y[0]; z[1] = y[0] * x[0]; z[1] *= x[0]; // f(y) = z = { x * y , y * x * x } ADFun< ADdouble > f(y, z); CPPAD_TESTVECTOR( ADdouble ) u( f.Domain() ); CPPAD_TESTVECTOR( ADdouble ) v( f.Range() ); // v = f'(y) u[0] = ADdouble(1.); v = f.Forward(1, u); // check derivatives of f ok &= v[0] == x[0]; ok &= v[1] == x[0] * x[0]; // g(x) = f'(y) = {x , x * x} ADFun g(x, v); CPPAD_TESTVECTOR( double ) a( g.Domain() ); CPPAD_TESTVECTOR( double ) b( g.Range() ); // b = g'(x) a[0] = 1.; b = g.Forward(1, a); // check derivatives of g ok &= (b[0] == 1.); ok &= (b[1] == 2. * x[0]); } } return ok; } cppad-20170000.3/test_more/add_eq.cpp0000644000175200017650000000652413057470461016362 0ustar coincoin-web// $Id: add_eq.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old example now used just for valiadation testing */ # include namespace { // BEGIN empty namespace bool AddEqOne(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 2.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; // dependent variable values Z[x] = 4.; Z[y] = U[t]; Z[x] += U[s]; // parameter += variable Z[x] += U[t]; // variable += variable Z[y] += .5; // variable += double // use .5 because it is represented exactly in binary and // because it makes sure that += does not slice the double to an int // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check function values ok &= ( Z[x] == 4. + 3. + 2. ); ok &= ( Z[y] == 2. + .5 ); // forward computation of partials w.r.t. s v[s] = 1.; v[t] = 0.; w = f.Forward(1, v); ok &= ( w[x] == 1. ); // dx/ds ok &= ( w[y] == 0. ); // dy/ds // reverse computation of second partials of x CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 1.; w[y] = 0.; r = f.Reverse(2, w); ok &= ( r[2 * s + 1] == 0. ); ok &= ( r[2 * t + 1] == 0. ); return ok; } bool AddEqTwo(void) { bool ok = true; using namespace CppAD; // independent variable vector double u0 = .5; CPPAD_TESTVECTOR(AD) U(1); U[0] = u0; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = U[0]; // initial value Z[0] += 2; // AD += int Z[0] += 4.; // AD += double Z[0] += U[0]; // AD += AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(Z[0] , u0+2+4+u0, 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 2.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 2.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } } // END empty namespace bool AddEq(void) { bool ok = true; ok &= AddEqOne(); ok &= AddEqTwo(); return ok; } // END PROGRAM cppad-20170000.3/test_more/hes_sparsity.cpp0000644000175200017650000002407113057470461017657 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // Begin empty namespace void forward_sparse_jacobian_bool(CppAD::ADFun& f) { size_t n = f.Domain(); CPPAD_TESTVECTOR(bool) eye(n * n); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n; j++) eye[ i * n + j] = (i == j); } f.ForSparseJac(n, eye); return; } void forward_sparse_jacobian_set(CppAD::ADFun& f) { size_t n = f.Domain(); CPPAD_TESTVECTOR(std::set) eye(n); for(size_t i = 0; i < n; i++) eye[i].insert(i); f.ForSparseJac(n, eye); return; } bool sparse_hessian_test( CppAD::ADFun& f , size_t index , CPPAD_TESTVECTOR(bool)& check ) { bool ok = true; size_t n = f.Domain(); size_t m = f.Range(); // boolean sparsity patterns CPPAD_TESTVECTOR(bool) r_bool(n), s_bool(m), h_bool(n * n); for(size_t j = 0; j < n; j++) r_bool[j] = true; for(size_t i = 0; i < m; i++) s_bool[i] = i == index; // // bool ForSparseHes h_bool = f.ForSparseHes(r_bool, s_bool); for(size_t i = 0; i < n * n; i++) ok &= h_bool[i] == check[i]; // // bool RevSparseHes forward_sparse_jacobian_bool(f); h_bool = f.RevSparseHes(n, s_bool); for(size_t i = 0; i < n * n; i++) ok &= h_bool[i] == check[i]; // // set sparsity patterns CPPAD_TESTVECTOR( std::set ) r_set(1), s_set(1), h_set(n); for(size_t j = 0; j < n; j++) r_set[0].insert(j); s_set[0].insert(index); // // set ForSparseHes h_set = f.ForSparseHes(r_set, s_set); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n; j++) { bool found = h_set[i].find(j) != h_set[i].end(); ok &= found == check[i * n + j]; } } // // set RevSparseHes forward_sparse_jacobian_set(f); h_set = f.RevSparseHes(n, s_set); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n; j++) { bool found = h_set[i].find(j) != h_set[i].end(); ok &= found == check[i * n + j]; } } // return ok; } bool case_one() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 10; // dimension of the range space size_t m = 2; // temporary indices // initialize check values to false CPPAD_TESTVECTOR(bool) Check(n * n); for(size_t j = 0; j < n * n; j++) Check[j] = false; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); for(size_t j = 0; j < n; j++) X[j] = AD(j); Independent(X); // accumulate sum here AD sum(0.); // variable * variable sum += X[2] * X[3]; Check[2 * n + 3] = Check[3 * n + 2] = true; // variable / variable sum += X[4] / X[5]; Check[4 * n + 5] = Check[5 * n + 4] = Check[5 * n + 5] = true; // CondExpLt(variable, variable, variable, variable) sum += CondExpLt(X[1], X[2], sin(X[6]), cos(X[7]) ); Check[6 * n + 6] = true; Check[7 * n + 7] = true; // pow(variable, variable) sum += pow(X[8], X[9]); Check[8 * n + 8] = Check[8 * n + 9] = true; Check[9 * n + 8] = Check[9 * n + 9] = true; // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); Y[0] = sum; // variable - variable Y[1] = X[0] - X[1]; // create function object F : X -> Y ADFun F(X, Y); // check Hessian of F_0 ok &= sparse_hessian_test(F, 0, Check); // check Hessian of F_1 for(size_t j = 0; j < n * n; j++) Check[j] = false; ok &= sparse_hessian_test(F, 1, Check); // ----------------------------------------------------------------------- return ok; } bool case_two() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 4; // dimension of the range space size_t m = 1; // initialize check values to false CPPAD_TESTVECTOR(bool) Check(n * n); for(size_t j = 0; j < n * n; j++) Check[j] = false; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); for(size_t j = 0; j < n; j++) X[j] = AD(j); Independent(X); // Test the case where dependent variable is a non-linear function // of the result of a conditional expression. CPPAD_TESTVECTOR(AD) Y(m); Y[0] = CondExpLt(X[0], X[1], X[2], X[3]); Y[0] = cos(Y[0]) + X[0] + X[1]; // Hessian with respect to x[0] and x[1] is zero. // Hessian with respect to x[2] and x[3] is full // (although we know that there are no cross terms, this is an // inefficiency of the conditional expression operator). Check[2 * n + 2] = Check[ 2 * n + 3 ] = true; Check[3 * n + 2] = Check[ 3 * n + 3 ] = true; // create function object F : X -> Y ADFun F(X, Y); // ----------------------------------------------------------------- sparse_hessian_test(F, 0, Check); // return ok; } bool case_three() { bool ok = true; using CppAD::AD; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; // declare independent variables and start recording CppAD::Independent(X); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); // make sure reverse jacobian is propagating dependency to // intermediate values (not just final ones). Y[0] = X[0] * X[0] + 2; // create f: X -> Y and stop tape recording CppAD::ADFun f(X, Y); // ------------------------------------------------------------------ CPPAD_TESTVECTOR(bool) check(n * n); check[0] = true; sparse_hessian_test(f, 0, check); // return ok; } bool case_four() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; // dimension of the range space size_t m = 1; // inialize the vector as zero CppAD::VecAD Z(n - 1); size_t k; for(k = 0; k < n-1; k++) Z[k] = 0.; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; X[2] = 2.; Independent(X); // VecAD vector z depends on both x[1] and x[2] // (component indices do not matter because they can change). Z[ X[0] ] = X[1] * X[2]; Z[ X[1] ] = 0.; // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(n * n); // y = z[j] where j might be zero or one. Y[0] = Z[ X[1] ]; Check[0 * n + 0] = false; // partial w.r.t x[0], x[0] Check[0 * n + 1] = false; // partial w.r.t x[0], x[1] Check[0 * n + 2] = false; // partial w.r.t x[0], x[2] Check[1 * n + 0] = false; // partial w.r.t x[1], x[0] Check[1 * n + 1] = false; // partial w.r.t x[1], x[1] Check[1 * n + 2] = true; // partial w.r.t x[1], x[2] Check[2 * n + 0] = false; // partial w.r.t x[2], x[0] Check[2 * n + 1] = true; // partial w.r.t x[2], x[1] Check[2 * n + 2] = false; // partial w.r.t x[2], x[2] // create function object F : X -> Y ADFun F(X, Y); // ----------------------------------------------------- sparse_hessian_test(F, 0, Check); // return ok; } bool case_five(void) { bool ok = true; using CppAD::AD; size_t n = 2; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; X[1] = 2.; CppAD::Independent(X); size_t m = 2; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = pow(X[0], 2.); Y[1] = pow(2., X[1]); // create function object F : X -> Y CppAD::ADFun F(X, Y); // Test F_0 and F_1 for(size_t index = 0; index < n; index++) { CPPAD_TESTVECTOR(bool) check(n * n); for(size_t i = 0; i < n; i++) for(size_t j = 0; j < n; j++) check[i * n + j] = (i == index) & (j == index); sparse_hessian_test(F, index, check); } // return ok; } // Note ForSparseHes does not work for this case because R not diagonal. bool case_six() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; // dimension of the range space size_t m = 1; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; X[2] = 2.; Independent(X); // y = z[j] where j might be zero or one. CPPAD_TESTVECTOR(AD) Y(m); Y[0] = X[1] * X[2]; // create function object F : X -> Y ADFun F(X, Y); // sparsity pattern for hessian of F^2 CPPAD_TESTVECTOR(bool) F2(n * n); F2[0 * n + 0] = false; // partial w.r.t x[0], x[0] F2[0 * n + 1] = false; // partial w.r.t x[0], x[1] F2[0 * n + 2] = false; // partial w.r.t x[0], x[2] F2[1 * n + 0] = false; // partial w.r.t x[1], x[0] F2[1 * n + 1] = false; // partial w.r.t x[1], x[1] F2[1 * n + 2] = true; // partial w.r.t x[1], x[2] F2[2 * n + 0] = false; // partial w.r.t x[2], x[0] F2[2 * n + 1] = true; // partial w.r.t x[2], x[1] F2[2 * n + 2] = false; // partial w.r.t x[2], x[2] // choose a non-symmetric sparsity pattern for R CPPAD_TESTVECTOR( bool ) r(n * n); size_t i, j, k; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) r[ i * n + j ] = false; j = n - i - 1; r[ j * n + j ] = true; } // sparsity pattern for H^T CPPAD_TESTVECTOR(bool) Check(n * n); for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { Check[ i * n + j] = false; for(k = 0; k < n; k++) { // some gcc versions std::vector do not support |= // on elements (because they pack the bits). bool tmp = Check[i * n + j]; Check[i * n + j] = tmp | (F2[i * n + k] & r[ k * n + j]); } } } // compute the reverse Hessian sparsity pattern for F^2 * R F.ForSparseJac(n, r); CPPAD_TESTVECTOR( bool ) s(m), h(n * n); s[0] = 1.; bool transpose = true; h = F.RevSparseHes(n, s, transpose); // check values for(i = 0; i < n; i++) { for(j = 0; j < n; j++) ok &= (h[i * n + j] == Check[i * n + j]); } // compute the reverse Hessian sparsity pattern for R^T * F^2 transpose = false; h = F.RevSparseHes(n, s, transpose); // check values for(i = 0; i < n; i++) { for(j = 0; j < n; j++) ok &= (h[j * n + i] == Check[i * n + j]); } return ok; } } // End of empty namespace bool hes_sparsity(void) { bool ok = true; ok &= case_one(); ok &= case_two(); ok &= case_three(); ok &= case_four(); ok &= case_five(); ok &= case_six(); return ok; } cppad-20170000.3/test_more/test_vector.cpp0000644000175200017650000000430113057470461017475 0ustar coincoin-web// $Id: test_vector.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test deprecated CPPAD_TEST_VECTOR macro (should use CPPAD_TESTVECTOR instead */ # include // this test is coppied from example/add.cpp on 2012-06-06 bool test_vector(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TEST_VECTOR< AD > x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // some binary addition operations AD a = x[0] + 1.; // AD + double AD b = a + 2; // AD + int AD c = 3. + b; // double + AD AD d = 4 + c; // int + AD // range space vector size_t m = 1; CPPAD_TEST_VECTOR< AD > y(m); y[0] = d + x[0]; // AD + AD // create f: x -> y and stop tape recording CppAD::ADFun f(x, y); // check value ok &= NearEqual(y[0] , 2. * x0 + 10, eps99, eps99); // forward computation of partials w.r.t. x[0] CPPAD_TEST_VECTOR< double > dx(n); CPPAD_TEST_VECTOR< double > dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 2., eps99, eps99); // reverse computation of derivative of y[0] CPPAD_TEST_VECTOR< double > w(m); CPPAD_TEST_VECTOR< double > dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], 2., eps99, eps99); // use a VecAD::reference object with addition CppAD::VecAD v(1); AD zero(0); v[zero] = a; AD result = v[zero] + 2; ok &= (result == b); return ok; } cppad-20170000.3/test_more/for_sparse_jac.cpp0000644000175200017650000002672613057470461020133 0ustar coincoin-web// $Id: for_sparse_jac.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # define CheckOp(Op) \ Y[index] = X[0] Op 2.; \ Check[index * n + 0] = true; \ Check[index * n + 1] = false; \ Check[index * n + 2] = false; \ index++; \ Y[index] = X[0] Op X[1]; \ Check[index * n + 0] = true; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; \ Y[index] = 3. Op X[1]; \ Check[index * n + 0] = false; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; # define CheckUnaryFun(Fun) \ Y[index] = Fun(X[0]); \ Check[index * n + 0] = true; \ Check[index * n + 1] = false; \ Check[index * n + 2] = false; \ index++; \ Y[index] = Fun(X[0] + X[1]); \ Check[index * n + 0] = true; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; \ Y[index] = Fun(X[1]); \ Check[index * n + 0] = false; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; # define CheckBinaryFun(Fun) \ Y[index] = Fun( X[0] , 2.); \ Check[index * n + 0] = true; \ Check[index * n + 1] = false; \ Check[index * n + 2] = false; \ index++; \ Y[index] = Fun( X[0] , X[1]); \ Check[index * n + 0] = true; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; \ Y[index] = Fun( 3. , X[1]); \ Check[index * n + 0] = false; \ Check[index * n + 1] = true; \ Check[index * n + 2] = false; \ index++; namespace { // Begin empty namespace bool case_one() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; // dimension of the range space size_t m = (4 + 11 + 1) * 3 + 4; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = .1; X[1] = .2; X[2] = .3; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // initialize index into Y size_t index = 0; // 4 binary operators CheckOp(+); CheckOp(-); CheckOp(*); CheckOp(/); // 11 unary functions CheckUnaryFun(abs); CheckUnaryFun(acos); CheckUnaryFun(asin); CheckUnaryFun(atan); CheckUnaryFun(cos); CheckUnaryFun(cosh); CheckUnaryFun(exp); CheckUnaryFun(log); CheckUnaryFun(sin); CheckUnaryFun(sinh); CheckUnaryFun(sqrt); // 1 binary function CheckBinaryFun(pow); // conditional expression (value of comparision does not matter) Y[index] = CondExpLt(X[0], X[1], X[0], AD(2.)); Check[index * n + 0] = true; Check[index * n + 1] = false; Check[index * n + 2] = false; index++; Y[index] = CondExpLt(X[0], X[1], X[0], X[1]); Check[index * n + 0] = true; Check[index * n + 1] = true; Check[index * n + 2] = false; index++; Y[index] = CondExpLt(X[0], X[1], AD(3.), X[1]); Check[index * n + 0] = false; Check[index * n + 1] = true; Check[index * n + 2] = false; index++; // non-trival composition Y[index] = X[0] * X[1] + X[1] * X[2]; Check[index * n + 0] = true; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); // --------------------------------------------------------- // dependency matrix for the identity function W(x) = x CPPAD_TESTVECTOR( bool ) Px(n * n); size_t i, j; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) Px[ i * n + j ] = false; Px[ i * n + i ] = true; } // evaluate the dependency matrix for F(X(x)) CPPAD_TESTVECTOR( bool ) Py(m * n); Py = F.ForSparseJac(n, Px); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Py[i * n + j] == Check[i * n + j]); } // --------------------------------------------------------- // dependency matrix for the identity function W(x) = x CPPAD_TESTVECTOR(std::set) Sx(n); for(i = 0; i < n; i++) { assert( Sx[i].empty() ); Sx[i].insert(i); } // evaluate the dependency matrix for F(X(x)) CPPAD_TESTVECTOR(std::set) Sy(m); Sy = F.ForSparseJac(n, Sx); // check values bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sy[i].find(j) != Sy[i].end(); ok &= (found == Check[i * n + j]); } } return ok; } bool case_two() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 3; // dimension of the range space size_t m = 3; // inialize the vector as zero CppAD::VecAD Z(n - 1); size_t k; for(k = 0; k < n-1; k++) Z[k] = 0.; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = 0.; X[1] = 1.; X[2] = 2.; Independent(X); // VecAD vector is going to depend on X[1] and X[2] Z[ X[0] ] = X[1]; Z[ X[1] ] = X[2]; // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // initialize index into Y size_t index = 0; // First component only depends on X[0]; Y[index] = X[0]; Check[index * n + 0] = true; Check[index * n + 1] = false; Check[index * n + 2] = false; index++; // Second component depends on the vector Z AD zero(0); Y[index] = Z[zero]; // Load by a parameter Check[index * n + 0] = false; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // Third component depends on the vector Z Y[index] = Z[ X[0] ]; // Load by a variable Check[index * n + 0] = false; Check[index * n + 1] = true; Check[index * n + 2] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); // ----------------------------------------------------------------- // dependency matrix for the identity function W(x) = x CPPAD_TESTVECTOR( bool ) Px(n * n); size_t i, j; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) Px[ i * n + j ] = false; Px[ i * n + i ] = true; } // evaluate the dependency matrix for F(X(x)) CPPAD_TESTVECTOR( bool ) Py(m * n); Py = F.ForSparseJac(n, Px); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Py[i * n + j] == Check[i * n + j]); } // --------------------------------------------------------- // dependency matrix for the identity function W(x) = x CPPAD_TESTVECTOR(std::set) Sx(n); for(i = 0; i < n; i++) { assert( Sx[i].empty() ); Sx[i].insert(i); } // evaluate the dependency matrix for F(X(x)) CPPAD_TESTVECTOR(std::set) Sy(m); Sy = F.ForSparseJac(n, Sx); // check values bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sy[i].find(j) != Sy[i].end(); ok &= (found == Check[i * n + j]); } } return ok; } bool case_three() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 2; // dimension of the range space size_t m = 3; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = 2.; X[1] = 3.; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // initialize index into Y size_t index = 0; // Y[0] only depends on X[0]; Y[index] = pow(X[0], 2.); Check[index * n + 0] = true; Check[index * n + 1] = false; index++; // Y[1] depends on X[1] Y[index] = pow(2., X[1]); Check[index * n + 0] = false; Check[index * n + 1] = true; index++; // Y[2] depends on X[0] and X[1] Y[index] = pow(X[0], X[1]); Check[index * n + 0] = true; Check[index * n + 1] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); // ----------------------------------------------------------------- // dependency matrix for the identity function CPPAD_TESTVECTOR( bool ) Px(n * n); size_t i, j; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) Px[ i * n + j ] = false; Px[ i * n + i ] = true; } // evaluate the dependency matrix for F(X(x)) CPPAD_TESTVECTOR( bool ) Py(m * n); Py = F.ForSparseJac(n, Px); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Py[i * n + j] == Check[i * n + j]); } // --------------------------------------------------------- // dependency matrix for the identity function CPPAD_TESTVECTOR(std::set) Sx(n); for(i = 0; i < n; i++) { assert( Sx[i].empty() ); Sx[i].insert(i); } // evaluate the dependency matrix for F(X(x)) CPPAD_TESTVECTOR(std::set) Sy(m); Sy = F.ForSparseJac(n, Sx); // check values bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sy[i].find(j) != Sy[i].end(); ok &= (found == Check[i * n + j]); } } return ok; } bool case_four() { bool ok = true; using namespace CppAD; // dimension of the domain space size_t n = 2; // dimension of the range space size_t m = 3; // independent variable vector CPPAD_TESTVECTOR(AD) X(n); X[0] = 2.; X[1] = 3.; Independent(X); // dependent variable vector CPPAD_TESTVECTOR(AD) Y(m); // check results vector CPPAD_TESTVECTOR( bool ) Check(m * n); // initialize index into Y size_t index = 0; // Y[0] only depends on X[0]; Y[index] = pow(X[0], 2.); Check[index * n + 0] = true; Check[index * n + 1] = false; index++; // Y[1] depends on X[1] Y[index] = pow(2., X[1]); Check[index * n + 0] = false; Check[index * n + 1] = true; index++; // Y[2] depends on X[0] and X[1] Y[index] = pow(X[0], X[1]); Check[index * n + 0] = true; Check[index * n + 1] = true; index++; // check final index assert( index == m ); // create function object F : X -> Y ADFun F(X, Y); // ----------------------------------------------------------------- // dependency matrix for the identity function CPPAD_TESTVECTOR( bool ) Px(n * n); size_t i, j; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) Px[ i * n + j ] = false; Px[ i * n + i ] = true; } // evaluate the dependency matrix for F(X(x)) bool transpose = true; CPPAD_TESTVECTOR( bool ) Py(n * m); Py = F.ForSparseJac(n, Px, transpose); // check values for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= (Py[j * m + i] == Check[i * n + j]); } // --------------------------------------------------------- // dependency matrix for the identity function CPPAD_TESTVECTOR(std::set) Sx(n); for(i = 0; i < n; i++) { assert( Sx[i].empty() ); Sx[i].insert(i); } // evaluate the dependency matrix for F(X(x)) CPPAD_TESTVECTOR(std::set) Sy(n); Sy = F.ForSparseJac(n, Sx, transpose); // check values bool found; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) { found = Sy[j].find(i) != Sy[j].end(); ok &= (found == Check[i * n + j]); } } return ok; } } // End empty namespace bool for_sparse_jac(void) { bool ok = true; ok &= case_one(); ok &= case_two(); ok &= case_three(); ok &= case_four(); return ok; } cppad-20170000.3/test_more/romberg_one.cpp0000644000175200017650000000445213057470461017441 0ustar coincoin-web/* $Id: romberg_one.cpp 3747 2015-11-09 14:25:41Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* old romberg_one.cpp example / test $spell Romberg $$ $section One Dimensional Romberg Integration: Example and Test$$ $index Romberg, example$$ $index example, Romberg$$ $index test, Romberg$$ $code old verbatim%example/romberg_one.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { class Fun { private: const size_t degree; public: // constructor Fun(size_t degree_) : degree(degree_) { } // function F(x) = x^degree template Float operator () (const Float &x) { size_t i; Float f(1); for(i = 0; i < degree; i++) f *= x; return f; } }; template bool RombergOneCase(void) { bool ok = true; size_t i; size_t degree = 4; Fun F(degree); // arguments to RombergOne Float a(0); Float b(1); Float r; size_t n = 4; Float e; size_t p; // int_a^b F(x) dx = // [ b^(degree+1) - a^(degree+1) ] / (degree+1) Float bpow(1); Float apow(1); for(i = 0; i <= degree; i++) { bpow *= b; apow *= a; } Float check = (bpow - apow) / Float(degree+1); // step size corresponding to r Float step = (b - a) / exp(log(Float(2.))*Float(n-1)); // step size corresponding to error estimate step *= Float(2.); // step size raised to a power Float spow = Float(1); for(p = 0; p < n; p++) { spow = spow * step * step; r = CppAD::RombergOne(F, a, b, n, p, e); ok &= e < (degree+1) * spow; ok &= CppAD::NearEqual(check, r, Float(0.), e); } return ok; } } bool RombergOne(void) { bool ok = true; using CppAD::AD; ok &= RombergOneCase(); ok &= RombergOneCase< AD >(); ok &= RombergOneCase< AD< AD > >(); return ok; } // END C++ cppad-20170000.3/test_more/log.cpp0000644000175200017650000000700113057470461015715 0ustar coincoin-web/* $Id: log.cpp 3684 2015-05-10 14:01:21Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old log examples now used just for validation testing */ # include namespace { // BEGIN empty namespace bool LogTestOne(void) { bool ok = true; using CppAD::log; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(1); size_t s = 0; U[s] = 2.; Independent(U); // dependent variable vector, indices, and values CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; Z[x] = log(U[s]); Z[y] = log(Z[x]); // define f : U -> Z and vectors for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check values ok &= NearEqual(Z[x] , log(2.), 1e-10 , 1e-10); ok &= NearEqual(Z[y] , log( log(2.) ), 1e-10 , 1e-10); // forward computation of partials w.r.t. s v[s] = 1.; w = f.Forward(1, v); ok &= NearEqual(w[x], 1. / U[s], 1e-10 , 1e-10); // dx/ds ok &= NearEqual(w[y], 1. / (U[s] * Z[x]), 1e-10 , 1e-10); // dy/ds // reverse computation of partials of y w[x] = 0.; w[y] = 1.; v = f.Reverse(1,w); ok &= NearEqual(v[s], 1. / (U[s] * Z[x]), 1e-10 , 1e-10); // dy/ds // forward computation of second partials w.r.t. s v[s] = 1.; w = f.Forward(1, v); v[s] = 0.; w = f.Forward(2, v); ok &= NearEqual( 2. * w[y] , - 1. / (Z[x]*Z[x]*U[s]*U[s]) - 1. / (Z[x]*U[s]*U[s]), 1e-10 , 1e-10 ); // reverse computation of second partials of y CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 0.; w[y] = 1.; r = f.Reverse(2, w); ok &= NearEqual( r[2 * s + 1] , - 1. / (Z[x]*Z[x]*U[s]*U[s]) - 1. / (Z[x]*U[s]*U[s]), 1e-10 , 1e-10 ); return ok; } bool LogTestTwo(void) { bool ok = true; using CppAD::log; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 1.; Independent(U); // a temporary values AD x = exp(U[0]); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = log(x); // log( exp(u) ) // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(U[0] , Z[0], 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 1.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 1.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } } // END empty namespace bool log(void) { bool ok = true; ok &= LogTestOne(); ok &= LogTestTwo(); return ok; } cppad-20170000.3/test_more/extern_value.cpp0000644000175200017650000000236013057470461017640 0ustar coincoin-web// $Id: extern_value.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include "extern_value.hpp" # define INSTANTIATE(Type) template class extern_value< Type > template extern_value::extern_value(Type value) { value_ = value; } template void extern_value::set(Type value) { value_ = value; } template Type extern_value::get(void) { return value_; } INSTANTIATE( float ); INSTANTIATE( double ); INSTANTIATE( std::complex ); INSTANTIATE( std::complex ); // INSTANTIATE( CppAD::AD< float > ); INSTANTIATE( CppAD::AD< double > ); INSTANTIATE( CppAD::AD< std::complex > ); INSTANTIATE( CppAD::AD< std::complex > ); cppad-20170000.3/test_more/log10.cpp0000644000175200017650000000342313057470461016062 0ustar coincoin-web/* $Id: log10.cpp 3684 2015-05-10 14:01:21Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example now used just for validation testing. */ # include bool log10(void) { bool ok = true; using CppAD::log10; using CppAD::log; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(1); size_t s = 0; U[s] = 10.; Independent(U); // dependent variable vector, indices, and values CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; Z[x] = log10(U[s]); Z[y] = log10(Z[x]); // define f : U -> Z and vectors for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check values ok &= NearEqual(Z[x] , 1., 1e-10 , 1e-10); ok &= NearEqual(Z[y] , 0., 1e-10 , 1e-10); // forward computation of partials w.r.t. s double l10 = log(10.); v[s] = 1.; w = f.Forward(1, v); ok &= NearEqual(w[x], 1./(U[s]*l10) , 1e-10 , 1e-10); // dx/ds ok &= NearEqual(w[y], 1./(U[s]*Z[x]*l10*l10), 1e-10 , 1e-10); // dy/ds // reverse computation of partials of y w[x] = 0.; w[y] = 1.; v = f.Reverse(1,w); ok &= NearEqual(v[s], 1./(U[s]*Z[x]*l10*l10), 1e-10 , 1e-10); // dy/ds return ok; } cppad-20170000.3/test_more/test_more.cpp0000644000175200017650000002405513057470461017145 0ustar coincoin-web/* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // system include files used for I/O # include // memory leak checker # include // prototype external compiled tests (this line expected by bin/new_test.sh) extern bool abs(void); extern bool acos(void); extern bool acosh(void); extern bool adfun_copy(void); extern bool Add(void); extern bool AddEq(void); extern bool AddZero(void); extern bool alloc_openmp(void); extern bool asin(void); extern bool asinh(void); extern bool assign(void); extern bool atan(void); extern bool atanh(void); extern bool atan2(void); extern bool atomic_sparsity(void); extern bool azmul(void); extern bool base_adolc(void); extern bool base_alloc_test(void); extern bool check_simple_vector(void); extern bool checkpoint(void); extern bool Compare(void); extern bool compare_change(void); extern bool CondExp(void); extern bool CondExpAD(void); extern bool cond_exp_rev(void); extern bool copy(void); extern bool Cos(void); extern bool Cosh(void); extern bool cppad_eigen(void); extern bool dbl_epsilon(void); extern bool Div(void); extern bool DivEq(void); extern bool DivZeroOne(void); extern bool eigen_mat_inv(void); extern bool erf(void); extern bool Exp(void); extern bool expm1(void); extern bool ForHess(void); extern bool for_sparse_hes(void); extern bool for_sparse_jac(void); extern bool Forward(void); extern bool forward_dir(void); extern bool forward_order(void); extern bool FromBase(void); extern bool FunCheck(void); extern bool hes_sparsity(void); extern bool ipopt_solve(void); extern bool jacobian(void); extern bool log(void); extern bool log10(void); extern bool log1p(void); extern bool Mul(void); extern bool mul_level(void); extern bool mul_cond_rev(void); extern bool mul_cskip(void); extern bool MulEq(void); extern bool mul_zdouble(void); extern bool MulZeroOne(void); extern bool NearEqualExt(void); extern bool Neg(void); extern bool num_limits(void); extern bool ode_err_control(void); extern bool old_mat_mul(void); extern bool old_reciprocal(void); extern bool old_tan(void); extern bool old_usead_1(void); extern bool old_usead_2(void); extern bool omp_alloc(void); extern bool optimize(void); extern bool parameter(void); extern bool Poly(void); extern bool Pow(void); extern bool PowInt(void); extern bool print_for(void); extern bool reverse(void); extern bool rev_sparse_jac(void); extern bool RevTwo(void); extern bool RombergOne(void); extern bool Rosen34(void); extern bool Runge45(void); extern bool SimpleVector(void); extern bool Sin(void); extern bool SinCos(void); extern bool Sinh(void); extern bool sparse_hessian(void); extern bool sparse_jacobian(void); extern bool sparse_vec_ad(void); extern bool Sqrt(void); extern bool std_math(void); extern bool Sub(void); extern bool SubEq(void); extern bool SubZero(void); extern bool tan(void); extern bool to_string(void); extern bool test_vector(void); extern bool track_new_del(void); extern bool Value(void); extern bool VecAD(void); extern bool VecADPar(void); extern bool VecUnary(void); extern bool zdouble(void); // tests in local subdirectory extern bool vector_set(void); namespace { // function that runs one test static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), std::string name) { bool ok = true; std::streamsize width = 20; std::cout.width( width ); std::cout.setf( std::ios_base::left ); std::cout << name; // ok &= name.size() < size_t(width); ok &= TestOk(); if( ok ) { std::cout << "OK" << std::endl; Run_ok_count++; } else { std::cout << "Error" << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; using namespace std; // This line is used by test_one.sh // run external compiled tests (this line expected by bin/new_test.sh) ok &= Run( abs, "abs" ); ok &= Run( acos, "acos" ); ok &= Run( acosh, "acosh" ); ok &= Run( adfun_copy, "adfun_copy" ); ok &= Run( Add, "Add" ); ok &= Run( AddEq, "AddEq" ); ok &= Run( AddZero, "AddZero" ); ok &= Run( asin, "asin" ); ok &= Run( asinh, "asinh" ); ok &= Run( assign, "assign" ); ok &= Run( atan, "atan" ); ok &= Run( atanh, "atanh" ); ok &= Run( atan2, "atan2" ); ok &= Run( atomic_sparsity, "atomic_sparsity"); ok &= Run( azmul, "azmul" ); ok &= Run( check_simple_vector, "check_simple_vector" ); ok &= Run( checkpoint, "checkpoint" ); ok &= Run( Compare, "Compare" ); ok &= Run( compare_change, "compare_change" ); ok &= Run( CondExp, "CondExp" ); ok &= Run( CondExpAD, "CondExpAD" ); ok &= Run( cond_exp_rev, "cond_exp_rev" ); ok &= Run( copy, "copy" ); ok &= Run( Cos, "Cos" ); ok &= Run( Cosh, "Cosh" ); ok &= Run( dbl_epsilon, "dbl_epsilon" ); ok &= Run( Div, "Div" ); ok &= Run( DivEq, "DivEq" ); ok &= Run( DivZeroOne, "DivZeroOne" ); ok &= Run( erf, "erf" ); ok &= Run( Exp, "Exp" ); ok &= Run( expm1, "expm1" ); ok &= Run( ForHess, "ForHess" ); ok &= Run( for_sparse_hes, "for_sparse_hes" ); ok &= Run( for_sparse_jac, "for_sparse_jac" ); ok &= Run( Forward, "Forward" ); ok &= Run( forward_dir, "forward_dir" ); ok &= Run( forward_order, "forward_order" ); ok &= Run( FromBase, "FromBase" ); ok &= Run( FunCheck, "FunCheck" ); ok &= Run( hes_sparsity, "hes_sparsity" ); ok &= Run( jacobian, "jacobian" ); ok &= Run( log, "log" ); ok &= Run( log10, "log10" ); ok &= Run( log1p, "log1p" ); ok &= Run( Mul, "Mul" ); ok &= Run( mul_level, "mul_level" ); ok &= Run( mul_cond_rev, "mul_cond_rev" ); ok &= Run( mul_cskip, "Mul_cskip" ); ok &= Run( MulEq, "MulEq" ); ok &= Run( mul_zdouble, "mul_zdouble" ); ok &= Run( MulZeroOne, "MulZeroOne" ); ok &= Run( NearEqualExt, "NearEqualExt" ); ok &= Run( Neg, "Neg" ); ok &= Run( num_limits, "num_limits" ); ok &= Run( ode_err_control, "ode_err_control"); ok &= Run( old_mat_mul, "old_mat_mul" ); ok &= Run( old_reciprocal, "old_reciprocal" ); ok &= Run( old_tan, "old_tan" ); ok &= Run( old_usead_1, "old_usead_1" ); ok &= Run( old_usead_2, "old_usead_2" ); ok &= Run( omp_alloc, "omp_alloc" ); ok &= Run( optimize, "optimize" ); ok &= Run( parameter, "parameter" ); ok &= Run( Poly, "Poly" ); ok &= Run( Pow, "Pow" ); ok &= Run( PowInt, "PowInt" ); ok &= Run( print_for, "print_for" ); ok &= Run( reverse, "reverse" ); ok &= Run( rev_sparse_jac, "rev_sparse_jac" ); ok &= Run( RevTwo, "RevTwo" ); ok &= Run( RombergOne, "RombergOne" ); ok &= Run( Rosen34, "Rosen34" ); ok &= Run( Runge45, "Runge45" ); ok &= Run( SimpleVector, "SimpleVector" ); ok &= Run( Sin, "Sin" ); ok &= Run( SinCos, "SinCos" ); ok &= Run( Sinh, "Sinh" ); ok &= Run( sparse_hessian, "sparse_hessian" ); ok &= Run( sparse_jacobian, "sparse_jacobian"); ok &= Run( sparse_vec_ad, "sparse_vec_ad" ); ok &= Run( Sqrt, "Sqrt" ); ok &= Run( std_math, "std_math" ); ok &= Run( Sub, "Sub" ); ok &= Run( SubEq, "SubEq" ); ok &= Run( SubZero, "SubZero" ); ok &= Run( tan, "tan" ); ok &= Run( to_string, "to_string" ); ok &= Run( track_new_del, "track_new_del" ); ok &= Run( Value, "Value" ); ok &= Run( VecAD, "VecAD" ); ok &= Run( VecADPar, "VecADPar" ); ok &= Run( VecUnary, "VecUnary" ); ok &= Run( zdouble, "zdouble" ); # ifdef CPPAD_ADOLC_TEST ok &= Run( base_adolc, "base_adolc" ); # endif # ifdef CPPAD_IPOPT_TEST ok &= Run( ipopt_solve, "ipopt_solve" ); # endif # ifdef CPPAD_OPENMP_TEST ok &= Run( alloc_openmp, "alloc_openmp" ); # endif # ifdef CPPAD_EIGEN_TEST ok &= Run( cppad_eigen, "cppad_eigen" ); ok &= Run( eigen_mat_inv, "eigen_mat_inv" ); # endif # if ! CPPAD_EIGENVECTOR ok &= Run( test_vector, "test_vector" ); # endif // local sub-directory ok &= Run( test_vector, "test_vector" ); // check for errors using std::cout; using std::endl; assert( ok || (Run_error_count > 0) ); if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "OK: " << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Error: " << "memory leak detected" << endl; } // Run base_require after memory leak check because base_alloc.hpp uses // thread_alloc to allocate memory for static copies of nan. ok &= Run( base_alloc_test, "base_alloc" ); // convert int(size_t) to avoid warning on _MSC_VER systems if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! ok ); } // END PROGRAM cppad-20170000.3/test_more/div_zero_one.cpp0000644000175200017650000000436213057470461017625 0ustar coincoin-web// $Id: div_zero_one.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test the use of the special parameters zero and one with the multiply operator */ # include typedef CppAD::AD ADdouble; typedef CppAD::AD< ADdouble > ADDdouble; bool DivZeroOne(void) { using namespace CppAD; bool ok = true; size_t i; for(i = 0; i < 3; i++) { // run through the cases x = 0, 1, 2 size_t j; for(j = 0; j < 3; j++) { // run through the cases y = 0, 1, 2 CPPAD_TESTVECTOR( ADdouble ) x(1); x[0] = double(i); Independent(x); CPPAD_TESTVECTOR( ADDdouble ) y(1); y[0] = ADDdouble(j); Independent(y); CPPAD_TESTVECTOR( ADDdouble ) z(2); if( j == 0 ) z[0] = ADDdouble(0); else z[0] = x[0] / y[0]; if( i == 0 ) z[1] = ADDdouble(0); else { z[1] = y[0] / x[0]; z[1] /= x[0]; } // f(y) = z = { x / y , y / (x * x) } ADFun< ADdouble > f(y, z); CPPAD_TESTVECTOR( ADdouble ) u( f.Domain() ); CPPAD_TESTVECTOR( ADdouble ) v( f.Range() ); // v = f'(y) u[0] = ADdouble(1.); v = f.Forward(1, u); // check derivatives of f ADdouble check = - double(i) / double(j * j); if( j != 0 ) ok &= NearEqual( v[0], check, 1e-10, 1e-10 ); check = 1. / double(i * i); if( i != 0 ) ok &= NearEqual( v[1], check, 1e-10, 1e-10); // g(x) = f'(y) = {-x/y^2 , 1/(x * x)} ADFun g(x, v); CPPAD_TESTVECTOR( double ) a( g.Domain() ); CPPAD_TESTVECTOR( double ) b( g.Range() ); // b = g'(x) a[0] = 1.; b = g.Forward(1, a); // check derivatives of g if( j != 0 ) ok &= NearEqual( b[0], - 1./double(j*j), 1e-10, 1e-10 ); if( i != 0 ) ok &= NearEqual( b[1], -2./double(i*i*i), 1e-10, 1e-10); } } return ok; } cppad-20170000.3/test_more/forward_dir.cpp0000644000175200017650000012652113057470461017447 0ustar coincoin-web/* $Id: forward_dir.cpp 3683 2015-05-10 02:24:16Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // test multiple directions operators // MulvvOp is tested by example/forward_dir.cpp # include # include # include namespace { using CppAD::AD; using CppAD::NearEqual; // --------------------------------------------------------------------- // Used the check that fun is an idenity funciton typedef AD (*adfun)(const AD&); bool check_identity(adfun identity, double argument) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = argument; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = identity(ax[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] = X_0(t) // = 0.5 + 1t + 2t^2 double y_1_0 = 1.0; double y_2_0 = 2.0; // // Y_1 (t) = F[X_1(t)] = X_1(t) // = 0.5 + 2t + 3t^2 double y_1_1 = 2.0; double y_2_1 = 3.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // AbsOp bool abs_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; ax[1] = -1.0; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = abs( ax[0] ) + abs( 2.0 * ax[1] ); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = abs(0.5 + 1t + 2t^2) + abs( 2*(-1.0 + 2t + 3t^2 ) ) double y_1_0 = -3.0; double y_2_0 = -4.0; // // Y_1 (t) = F[X_1(t)] // = abs(0.5 + 2t + 3t^2) + abs( 2*(-1.0 + 3t + 4t^2 ) ) double y_1_1 = -4.0; double y_2_1 = -5.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // AddpvOp bool addpv_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = 2.0 + ax[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 3); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = 2.0 + (0.5 + 1t + 3t^2) double y_1_0 = 1.0; double y_2_0 = 3.0; // // Y_1 (t) = F[X_1(t)] // = 2.0 + (0.5 + 2t + 4t^2) double y_1_1 = 2.0; double y_2_1 = 4.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // AddvvOp bool addvv_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; ax[1] = 2.0; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = ax[0] + ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = (0.5 + 1t + 2t^2) + (2.0 + 2t + 3t^2) double y_1_0 = 1.0 + 2.0; double y_2_0 = 2.0 + 3.0; // // Y_1 (t) = F[X_1(t)] // = (2.0 + 2t + 3t^2) + (2.0 + 3t + 4t^2) double y_1_1 = 2.0 + 3.0; double y_2_1 = 3.0 + 4.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // CosOp bool cos_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = cos( ax[0] ); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = cos( 0.5 + 1t + 2t^2 ) // Y_0' (t) = -sin( 0.5 + 1t + 2t^2) * (1 + 4t) double y_1_0 = - sin(0.5); double y_2_0 = - ( cos(0.5) + 4.0 * sin(0.5) ) / 2.0; // // Y_1 (t) = F[X_1(t)] // = cos( 0.5 + 2t + 3t^2 ) // Y_1' (t) = -sin( 0.5 + 2t + 3t^2) * (2 + 6t) double y_1_1 = - sin(0.5) * 2.0; double y_2_1 = - ( cos(0.5) * 4.0 + 6.0 * sin(0.5) ) / 2.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // CoshOp bool cosh_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = cosh( ax[0] ); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = cosh( 0.5 + 1t + 2t^2 ) // Y_0' (t) = sinh( 0.5 + 1t + 2t^2) * (1 + 4t) double y_1_0 = sinh(0.5); double y_2_0 = ( sinh(0.5) * 4.0 + cosh(0.5) ) / 2.0; // // Y_1 (t) = F[X_1(t)] // = cosh( 0.5 + 2t + 3t^2 ) // Y_1' (t) = sinh( 0.5 + 2t + 3t^2) * (2 + 6t) double y_1_1 = sinh(0.5) * 2.0; double y_2_1 = ( sinh(0.5) * 6.0 + cosh(0.5) * 4.0 ) / 2.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // CExpOp bool cexp_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 4; CPPAD_TESTVECTOR(AD) ax(n); for(j = 0; j < n; j++) ax[j] = double(j); // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = CondExpLt(ax[0], ax[1], ax[2], ax[3]); ay[1] = CondExpGt(ax[0], ax[1], ax[2], ax[3]); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y0_0 (t) = X2_0(t) // = 2.0 + 3t + 4t^2 double y0_1_0 = 3.0; double y0_2_0 = 4.0; // // Y1_0 (t) = X3_0(t) // = 3.0 + 4t + 5t^2 double y1_1_0 = 4.0; double y1_2_0 = 5.0; // // Y0_1 (t) = X2_1(t) // = 2.0 + 4t + 5t^2 double y0_1_1 = 4.0; double y0_2_1 = 5.0; // // Y1_1 (t) = X3_0(t) // = 3.0 + 5t + 6t^2 double y1_1_1 = 5.0; double y1_2_1 = 6.0; // ok &= NearEqual(y1[0*r+0] , y0_1_0, eps, eps); ok &= NearEqual(y1[1*r+0] , y1_1_0, eps, eps); ok &= NearEqual(y1[0*r+1] , y0_1_1, eps, eps); ok &= NearEqual(y1[1*r+1] , y1_1_1, eps, eps); // ok &= NearEqual(y2[0*r+0] , y0_2_0, eps, eps); ok &= NearEqual(y2[1*r+0] , y1_2_0, eps, eps); ok &= NearEqual(y2[0*r+1] , y0_2_1, eps, eps); ok &= NearEqual(y2[1*r+1] , y1_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // CSumOp bool csum_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD) ax(n); for(j = 0; j < n; j++) ax[j] = double(j); // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = 0.0; for(j = 0; j < n; j++) ay[0] += ax[j]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // optmize the tape so converts summation to on CSumOp operator f.optimize(); // zero order CPPAD_TESTVECTOR(double) x0(n); for(j = 0; j < n; j++) x0[j] = double(j); f.Forward(0, x0); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 3); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // double check = 0.0; for(j = 0; j < n; j++) check += x1[ r * j + 0]; ok &= NearEqual(y1[0] , check, eps, eps); // check = 0.0; for(j = 0; j < n; j++) check += x1[ r * j + 1]; ok &= NearEqual(y1[1] , check, eps, eps); // check = 0.0; for(j = 0; j < n; j++) check += x2[ r * j + 0]; ok &= NearEqual(y2[0] , check, eps, eps); // check = 0.0; for(j = 0; j < n; j++) check += x2[ r * j + 1]; ok &= NearEqual(y2[1] , check, eps, eps); // return ok; } // --------------------------------------------------------------------- // DisOp (test assuming that AddvvOp is correct) double round_off(const double& x) { // std::round(x); is C++11, so we avoid using it return std::floor( x + 0.5 ); } CPPAD_DISCRETE_FUNCTION(double, round_off) bool dis_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = round_off( ax[0] ) + ax[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // zero order CPPAD_TESTVECTOR(double) x0(n), y0; x0[0] = 2.2; y0 = f.Forward(0, x0); ok &= size_t( y0.size() ) == m; ok &= NearEqual(y0[0], round_off(x0[0]) + x0[0], eps, eps); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // // Y_0 (t) = F[X_0(t)] // = 2.0 + (2.2 + 1t + 2t^2) double y_1_0 = 1.0; double y_2_0 = 2.0; // // Y_1 (t) = F[X_1(t)] // = 2.0 + (2.2 + 2t + 3t^2) double y_1_1 = 2.0; double y_2_1 = 3.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // DivpvOp (testing assumping MulpvOp is correct) bool divpv_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = (2.0 / ax[0]) * (ax[0] * ax[0]); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = 2.0 * (0.5 + 1t + 2t^2) double y_1_0 = 2.0; double y_2_0 = 4.0; // // Y_1 (t) = F[X_1(t)] // = 2.0 * (0.5 + 2t + 3t^2)/2.0 double y_1_1 = 4.0; double y_2_1 = 6.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // DivvpOp bool divvp_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = ax[0] / 2.0; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 3); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = (0.5 + 1t + 3t^2)/2.0 double y_1_0 = 1.0 / 2.0; double y_2_0 = 3.0 / 2.0; // // Y_1 (t) = F[X_1(t)] // = (0.5 + 2t + 4t^2)/2.0 double y_1_1 = 2.0 / 2.0; double y_2_1 = 4.0 / 2.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // ExpOp bool exp_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = exp( ax[0] ); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = exp(0.5 + 1t + 2t^2) // Y_0' (t) = exp(0.5 + 1t + 2t^2)*(1 + 4t) double y_1_0 = exp(0.5); double y_2_0 = ( exp(0.5)*4.0 + exp(0.5) ) / 2.0; // // Y_1 (t) = F[X_1(t)] // = exp(0.5 + 2t + 3t^2) // Y_1' (t) = exp(0.5 + 2t + 3t^2)*(2 + 6t) double y_1_1 = exp(0.5)*2.0; double y_2_1 = ( exp(0.5)*6.0 + exp(0.5)*2.0*2.0 ) / 2.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // LdpOp and LdvOp (test assuming AdvvOp is correct) bool load_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.0; ax[1] = 1.0; // declare independent variables and starting recording CppAD::Independent(ax); // Store operations CppAD::VecAD avec(3); avec[ AD(0) ] = ax[0]; // store a variable avec[ AD(1) ] = ax[1]; // store a variable avec[ AD(2) ] = 5.0; // store a parameter // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = avec[ AD(0) ]; // load using parameter index ay[1] = avec[ ax[0] ]; // load using variable index // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // zero order Taylor coefficients CPPAD_TESTVECTOR(double) x0(n), y0; x0[0] = 2; x0[1] = 3; y0 = f.Forward(0, x0); ok &= size_t( y0.size() ) == m; // y[0] = avec[0] = x[0] ok &= y0[0] == x0[0]; // y[1] = avec[ x[0] ] = avec[2] = 5.0 ok &= y0[1] == 5.0; // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y0_0 (t) = 2.0 + 1t + 2t^2 double y0_1_0 = 1.0; double y0_2_0 = 2.0; // // Y1_0 (t) = 5.0 double y1_1_0 = 0.0; double y1_2_0 = 0.0; // // Y0_1 (t) = 2.0 + 2t + 3t^2 double y0_1_1 = 2.0; double y0_2_1 = 3.0; // // Y1_1 (t) = 5.0 double y1_1_1 = 0.0; double y1_2_1 = 0.0; // ok &= NearEqual(y1[0*r+0] , y0_1_0, eps, eps); ok &= NearEqual(y1[1*r+0] , y1_1_0, eps, eps); ok &= NearEqual(y1[0*r+1] , y0_1_1, eps, eps); ok &= NearEqual(y1[1*r+1] , y1_1_1, eps, eps); // ok &= NearEqual(y2[0*r+0] , y0_2_0, eps, eps); ok &= NearEqual(y2[1*r+0] , y1_2_0, eps, eps); ok &= NearEqual(y2[0*r+1] , y0_2_1, eps, eps); ok &= NearEqual(y2[1*r+1] , y1_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // MulpvOp bool mulpv_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = 2.0 * ax[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 3); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = 2.0 * (0.5 + 1t + 3t^2) double y_1_0 = 2.0 * 1.0; double y_2_0 = 2.0 * 3.0; // // Y_1 (t) = F[X_1(t)] // = 2.0 * (0.5 + 2t + 4t^2) double y_1_1 = 2.0 * 2.0; double y_2_1 = 2.0 * 4.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // ParOp bool par_op(void) { bool ok = true; size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = 0.0 * ax[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = 0.0 for(ell = 0; ell < r; ell++) { ok &= y1[ell] == 0.0; ok &= y2[ell] == 0.0; } return ok; } // --------------------------------------------------------------------- // PowvvOp (test assuming LogOp, ExpOp and DivvvOp are correct) bool powvv_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; ax[1] = 2.0; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = log( pow( exp(ax[0]) , ax[1] ) ) / ax[1] ; ay[1] = log( pow( exp(ax[0]) , ax[1] ) ) / ax[0] ; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y0_0 (t) = 0.5 + 1t + 2t^2 double y0_1_0 = 1.0; double y0_2_0 = 2.0; // // Y0_1 (t) = 0.5 + 2t + 3t^2 double y0_1_1 = 2.0; double y0_2_1 = 3.0; // // Y1_0 (t) = 2.0 + 2t + 3t^2 double y1_1_0 = 2.0; double y1_2_0 = 3.0; // // Y1_1 (t) = 2.0 + 3t + 4t^2 double y1_1_1 = 3.0; double y1_2_1 = 4.0; // ok &= NearEqual(y1[0*r+0] , y0_1_0, eps, eps); ok &= NearEqual(y1[1*r+0] , y1_1_0, eps, eps); ok &= NearEqual(y1[0*r+1] , y0_1_1, eps, eps); ok &= NearEqual(y1[1*r+1] , y1_1_1, eps, eps); // ok &= NearEqual(y2[0*r+0] , y0_2_0, eps, eps); ok &= NearEqual(y2[1*r+0] , y1_2_0, eps, eps); ok &= NearEqual(y2[0*r+1] , y0_2_1, eps, eps); ok &= NearEqual(y2[1*r+1] , y1_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // SignOp (test assuming that MulvvOp is correct) bool sign_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = sign( ax[0] ) * ax[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // zero order CPPAD_TESTVECTOR(double) x0(n), y0; x0[0] = -3.0; y0 = f.Forward(0, x0); ok &= size_t( y0.size() ) == m; ok &= NearEqual(y0[0], CppAD::abs(x0[0]), eps, eps); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // // Y_0 (t) = F[X_0(t)] // = -(-3.0 + 1t + 2t^2) double y_1_0 = -1.0; double y_2_0 = -2.0; // // Y_1 (t) = F[X_1(t)] // = -(-3.0 + 2t + 3t^2) double y_1_1 = -2.0; double y_2_1 = -3.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // SinOp bool sin_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = sin( ax[0] ); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = sin( 0.5 + 1t + 2t^2 ) // Y_0' (t) = cos( 0.5 + 1t + 2t^2) * (1 + 4t) double y_1_0 = cos(0.5); double y_2_0 = ( cos(0.5) * 4.0 - sin(0.5) ) / 2.0; // // Y_1 (t) = F[X_1(t)] // = sin( 0.5 + 2t + 3t^2 ) // Y_1' (t) = cos( 0.5 + 2t + 3t^2) * (2 + 6t) double y_1_1 = cos(0.5) * 2.0; double y_2_1 = ( cos(0.5) * 6.0 - sin(0.5) * 4.0 ) / 2.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // SinhOp bool sinh_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = sinh( ax[0] ); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = sinh( 0.5 + 1t + 2t^2 ) // Y_0' (t) = cosh( 0.5 + 1t + 2t^2) * (1 + 4t) double y_1_0 = cosh(0.5); double y_2_0 = ( cosh(0.5) * 4.0 + sinh(0.5) ) / 2.0; // // Y_1 (t) = F[X_1(t)] // = sinh( 0.5 + 2t + 3t^2 ) // Y_1' (t) = cosh( 0.5 + 2t + 3t^2) * (2 + 6t) double y_1_1 = cosh(0.5) * 2.0; double y_2_1 = ( cosh(0.5) * 6.0 + sinh(0.5) * 4.0 ) / 2.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // SubpvOp bool subpv_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = 2.0 - ax[0]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 3); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = 2.0 - (0.5 + 1t + 3t^2)/2.0 double y_1_0 = - 1.0; double y_2_0 = - 3.0; // // Y_1 (t) = F[X_1(t)] // = 3.0 - (0.5 + 2t + 4t^2)/2.0 double y_1_1 = - 2.0; double y_2_1 = - 4.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // SubvvOp bool subvv_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; ax[1] = 2.0; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = ax[0] - 2.0 * ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = (0.5 + 1t + 2t^2) - 2.0 * (2.0 + 2t + 3t^2) double y_1_0 = 1.0 - 4.0; double y_2_0 = 2.0 - 6.0; // // Y_1 (t) = F[X_1(t)] // = (2.0 + 2t + 3t^2) - 2.0 * (2.0 + 3t + 4t^2) double y_1_1 = 2.0 - 6.0; double y_2_1 = 3.0 - 8.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // TanOp bool tan_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // domain space vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 0.5; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = tan( ax[0] ); // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = tan(0.5 + 1t + 2t^2) // Y_0' (t) = cos(0.5 + 1t + 2t^2)^(-2)*(1 + 4t) // Y_0''(0) = 2*cos(0.5)^(-3)*sin(0.5) + 4*cos(0.5)^(-2) double sec_sq = 1.0 / ( cos(0.5) * cos(0.5) ); double y_1_0 = sec_sq; double y_2_0 = (2.0 * tan(0.5) + 4.0) * sec_sq / 2.0; // // Y_1 (t) = F[X_1(t)] // = tan(0.5 + 2t + 3t^2) // Y_1' (t) = cos(0.5 + 2t + 3t^2)^(-2)*(2 + 6t) // Y_1''(0) = 2*cos(0.5)^(-3)*sin(0.5)*2*2 + 6*cos(0.5)^(-2) double y_1_1 = 2.0 * sec_sq; double y_2_1 = (8.0 * tan(0.5) + 6.0) * sec_sq / 2.0; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // Usr*Op typedef CPPAD_TESTVECTOR(AD) avector; void usr_algo(const avector& x, avector& z) { z[0] = ( x[0] + x[1] ) / 2.0; z[1] = x[0] * x[1]; z[2] = ( x[0] - x[1] ) / 2.0; return; } bool usr_op(void) { bool ok = true; double eps = 10. * std::numeric_limits::epsilon(); size_t j; // define checkpoint function size_t n = 2; avector ax(n), az(3); ax[0] = 0.5; ax[1] = 2.0; CppAD::checkpoint usr_check("usr_check", usr_algo, ax, az); // declare independent variables and starting recording CppAD::Independent(ax); // record checkpoint function usr_check(ax, az); // range space vector size_t m = 2; avector ay(m); ay[0] = az[0] + az[2]; // = ax[0] ay[1] = az[0] - az[2]; // = ax[1] // create f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + ell + 1); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = double(j + ell + 2); } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y0_0 (t) = 0.5 + 1t + 2t^2 double y0_1_0 = 1.0; double y0_2_0 = 2.0; // // Y0_1 (t) = 0.5 + 2t + 3t^2 double y0_1_1 = 2.0; double y0_2_1 = 3.0; // // Y1_0 (t) = 2.0 + 2t + 3t^2 double y1_1_0 = 2.0; double y1_2_0 = 3.0; // // Y1_1 (t) = 2.0 + 3t + 4t^2 double y1_1_1 = 3.0; double y1_2_1 = 4.0; // ok &= NearEqual(y1[0*r+0] , y0_1_0, eps, eps); ok &= NearEqual(y1[1*r+0] , y1_1_0, eps, eps); ok &= NearEqual(y1[0*r+1] , y0_1_1, eps, eps); ok &= NearEqual(y1[1*r+1] , y1_1_1, eps, eps); // ok &= NearEqual(y2[0*r+0] , y0_2_0, eps, eps); ok &= NearEqual(y2[1*r+0] , y1_2_0, eps, eps); ok &= NearEqual(y2[0*r+1] , y0_2_1, eps, eps); ok &= NearEqual(y2[1*r+1] , y1_2_1, eps, eps); // return ok; } // --------------------------------------------------------------------- // Inverse functions assume the following already tested: // CosOp, SinOp, TanOp, ExpOp, MulvvOp, DivvpOp, AddpvOp // // AcosOp AD acos_fun(const AD& x) { return acos( cos(x) ); } bool acos_op(void) { return check_identity(acos_fun, 0.5); } // // AcoshOp AD acosh_fun(const AD& x) { return acosh( cosh(x) ); } bool acosh_op(void) { return check_identity(acosh_fun, 0.5); } // // AsinOp AD asin_fun(const AD& x) { return asin( sin(x) ); } bool asin_op(void) { return check_identity(asin_fun, 0.5); } // // AsinhOp AD asinh_fun(const AD& x) { return asinh( sinh(x) ); } bool asinh_op(void) { return check_identity(asinh_fun, 0.5); } // // AtanOp AD atan_fun(const AD& x) { return atan( tan(x) ); } bool atan_op(void) { return check_identity(atan_fun, 0.5); } // // AtanhOp AD atanh_fun(const AD& x) { return atanh( tanh(x) ); } bool atanh_op(void) { return check_identity(atanh_fun, 0.5); } // // LogOp AD log_fun(const AD& x) { return log( exp(x) ); } bool log_op(void) { return check_identity(log_fun, 0.5); } // // DivvvOp AD divvv_fun(const AD& x) { return (x * x) / x; } bool divvv_op(void) { return check_identity(divvv_fun, 0.5); } // // PowpvOp AD powpv_fun(const AD& x ) { return log( pow( exp(3.0) , x ) ) / 3.0; } bool powpv_op(void) { return check_identity(powpv_fun, 0.5); } // // PowvpOp AD powvp_fun(const AD& x ) { return log( pow( exp(x) , 3.0 ) ) / 3.0; } bool powvp_op(void) { return check_identity(powvp_fun, 0.5); } // // SqrtOp AD sqrt_fun(const AD& x ) { return sqrt( x * x ); } bool sqrt_op(void) { return check_identity(sqrt_fun, 0.5); } // // SubvpOp AD subvp_fun(const AD& x ) { return 3.0 + ( x - 3.0 ); } bool subvp_op(void) { return check_identity(subvp_fun, 0.5); } // // TanhOp AD tanh_fun(const AD& x ) { AD z = tanh(x); return log( (1.0 + z) / (1.0 - z) ) / 2.0; } bool tanh_op(void) { return check_identity(tanh_fun, 0.5); } } bool forward_dir(void) { bool ok = true; // ok &= abs_op(); ok &= acos_op(); ok &= acosh_op(); ok &= asin_op(); ok &= asinh_op(); ok &= atan_op(); ok &= atanh_op(); ok &= addpv_op(); ok &= addvv_op(); ok &= cexp_op(); ok &= cosh_op(); ok &= cos_op(); ok &= csum_op(); ok &= dis_op(); ok &= divpv_op(); ok &= divvp_op(); ok &= divvv_op(); ok &= exp_op(); ok &= load_op(); ok &= log_op(); ok &= mulpv_op(); ok &= par_op(); ok &= powpv_op(); ok &= powvp_op(); ok &= powvv_op(); ok &= sign_op(); ok &= sin_op(); ok &= sinh_op(); ok &= subpv_op(); ok &= subvp_op(); ok &= subvv_op(); ok &= sqrt_op(); ok &= tan_op(); ok &= tanh_op(); ok &= usr_op(); // return ok; } cppad-20170000.3/test_more/base_alloc.cpp0000644000175200017650000000211613057470461017222 0ustar coincoin-web// $Id: base_alloc.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "../example/base_alloc.hpp" # include bool base_alloc_test(void) { bool ok = true; using CppAD::thread_alloc; typedef CppAD::AD my_ad; // y = x^2 CppAD::vector a_x, a_y; a_x.resize(1); a_x[0] = my_ad(1.); CppAD::Independent(a_x); a_y.resize(1); a_y[0] = a_x[0]; // create a new parameter for each iteration of this loop size_t i, N = 50; for(i = 0; i < N; i++) a_y[0] += double(i); CppAD::ADFun f(a_x, a_y); return ok; } cppad-20170000.3/test_more/makefile.am0000644000175200017650000001055613057470461016535 0ustar coincoin-web# ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # # ------------------------------------------------------------------------- if CppAD_OPENMP OPENMP_SRC_FILES = alloc_openmp.cpp else OPENMP_SRC_FILES = endif # ------------------------------------------------------------------------- if CppAD_ADOLC ADOLC_SRC_FILES = base_adolc.cpp ADOLC_EXTRA_FILES = ADOLC_LIB = -ladolc -lColPack -L$(ADOLC_DIR)/lib -L$(ADOLC_DIR)/lib64 ADOLC_FLAGS = -DCPPAD_ADOLC_TEST -I$(ADOLC_DIR)/include else ADOLC_EXTRA_FILES = base_adolc.cpp ADOLC_SRC_FILES = ADOLC_LIB = ADOLC_FLAGS = endif # ------------------------------------------------------------------------- if CppAD_IPOPT IPOPT_SRC_FILES = ipopt_solve.cpp IPOPT_EXTRA_FILES = IPOPT_LIB = -lipopt \ $(CPPAD_IPOPT_LIBS) $(FCLIBS) $(PTHREAD_LIB) $(DL_LIB) IPOPT_FLAGS = -DCPPAD_IPOPT_TEST -I$(IPOPT_DIR)/include else IPOPT_EXTRA_FILES = ipopt_solve.cpp IPOPT_SRC_FILES = IPOPT_LIB = IPOPT_FLAGS = endif # ------------------------------------------------------------------------- if CppAD_EIGEN_DIR # make a special library so can have it's own compile flags (see configure.ac) EIGEN_EXTRA_FILES = noinst_LIBRARIES = libeigen.a libeigen_a_SOURCES = cppad_eigen.cpp eigen_mat_inv.cpp EIGEN_LIB = -L. -leigen libeigen_a_CXXFLAGS = \ -g \ $(CXX_FLAGS_EIGEN) \ -DCPPAD_EIGEN_TEST \ -I$(EIGEN_DIR)/include else EIGEN_EXTRA_FILES = cppad_eigen.cpp eigen_mat_inv.cpp EIGEN_LIB = endif # ------------------------------------------------------------------------- # Microsoft project files and script to run a single test EXTRA_DIST = \ $(ADOLC_EXTRA_FILES) \ $(IPOPT_EXTRA_FILES) \ $(EIGEN_EXTRA_FILES) # check_PROGRAMS = test_more # AM_CPPFLAGS = -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ $(ADOLC_FLAGS) \ $(IPOPT_FLAGS) \ $(OPENMP_FLAGS) # AM_CXXFLAGS = -g $(ADOLC_FLAGS) $(IPOPT_FLAGS) $(CXX_FLAGS) # AM_LDFLAGS = $(OPENMP_FLAGS) LDADD = $(ADOLC_LIB) $(IPOPT_LIB) $(EIGEN_LIB) $(OPENMP_FLAGS) # test_more_SOURCES = \ $(ADOLC_SRC_FILES) \ $(IPOPT_SRC_FILES) \ $(OPENMP_SRC_FILES) \ test_more.cpp \ abs.cpp \ acos.cpp \ acosh.cpp \ adfun_copy.cpp \ asin.cpp \ asinh.cpp \ assign.cpp \ add.cpp \ add_eq.cpp \ add_zero.cpp \ atan.cpp \ atanh.cpp \ atan2.cpp \ atomic_sparsity.cpp \ azmul.cpp \ base_alloc.cpp \ check_simple_vector.cpp \ checkpoint.cpp \ compare.cpp \ compare_change.cpp \ cond_exp.cpp \ cond_exp_ad.cpp \ cond_exp_rev.cpp \ copy.cpp \ cos.cpp \ cosh.cpp \ dbl_epsilon.cpp \ div.cpp \ div_eq.cpp \ div_zero_one.cpp \ erf.cpp \ exp.cpp \ expm1.cpp \ extern_value.cpp \ extern_value.hpp \ for_hess.cpp \ for_sparse_hes.cpp \ for_sparse_jac.cpp \ forward.cpp \ forward_dir.cpp \ forward_order.cpp \ from_base.cpp \ fun_check.cpp \ hes_sparsity.cpp \ jacobian.cpp \ num_limits.cpp \ log.cpp \ log1p.cpp \ log10.cpp \ mul.cpp \ mul_cskip.cpp \ mul_eq.cpp \ mul_level.cpp \ mul_cond_rev.cpp \ mul_zdouble.cpp \ mul_zero_one.cpp \ near_equal_ext.cpp \ neg.cpp \ ode_err_control.cpp \ old_usead_2.cpp \ old_usead_1.cpp \ old_tan.cpp \ old_reciprocal.cpp \ old_mat_mul.cpp \ old_mat_mul.hpp \ omp_alloc.cpp \ optimize.cpp \ parameter.cpp \ poly.cpp \ pow.cpp \ pow_int.cpp \ print_for.cpp \ romberg_one.cpp \ rosen_34.cpp \ runge_45.cpp \ reverse.cpp \ rev_sparse_jac.cpp \ rev_two.cpp \ simple_vector.cpp \ sin.cpp \ sin_cos.cpp \ sinh.cpp \ sparse_hessian.cpp \ sparse_jacobian.cpp \ sparse_vec_ad.cpp \ sqrt.cpp \ std_math.cpp \ sub.cpp \ sub_eq.cpp \ sub_zero.cpp \ tan.cpp \ test_vector.cpp \ to_string.cpp \ track_new_del.cpp \ value.cpp \ vec_ad.cpp \ vec_ad_par.cpp \ vec_unary.cpp \ zdouble.cpp test: check ./test_more cppad-20170000.3/test_more/cond_exp_ad.cpp0000644000175200017650000001661513057470461017412 0ustar coincoin-web// $Id: cond_exp_ad.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test of CondExp with AD< AD< Base > > types */ # include typedef CppAD::AD< double > ADdouble; typedef CppAD::AD< ADdouble > ADADdouble; namespace { // BEGIN empty namespace bool CondExpADOne(void) { bool ok = true; using namespace CppAD; size_t n = 3; size_t m = 8; // ADdouble independent variable vector CPPAD_TESTVECTOR( ADdouble ) Xa(n); Xa[0] = -1.; Xa[1] = 0.; Xa[2] = 1.; Independent(Xa); // ADdouble independent variable vector CPPAD_TESTVECTOR( ADADdouble ) Xaa(n); Xaa[0] = Xa[0]; Xaa[1] = Xa[1]; Xaa[2] = Xa[2]; Independent(Xaa); // ADADdouble parameter ADADdouble p = ADADdouble(Xa[0]); ADADdouble q = ADADdouble(Xa[1]); ADADdouble r = ADADdouble(Xa[2]); // ADADdouble dependent variable vector CPPAD_TESTVECTOR( ADADdouble ) Yaa(m); // CondExp(parameter, parameter, parameter) Yaa[0] = CondExp(p, q, r); // CondExp(parameter, parameter, variable) Yaa[1] = CondExp(p, q, Xaa[2]); // CondExp(parameter, varaible, parameter) Yaa[2] = CondExp(p, Xaa[1], r); // CondExp(parameter, variable, variable) Yaa[3] = CondExp(p, Xaa[1], Xaa[2]); // CondExp(variable, variable, variable) Yaa[5] = CondExp(Xaa[0], Xaa[1], Xaa[2]); // CondExp(variable, variable, parameter) Yaa[4] = CondExp(Xaa[0], Xaa[1], r); // CondExp(variable, parameter, variable) Yaa[6] = CondExp(Xaa[0], q, Xaa[2]); // CondExp(variable, parameter, parameter) Yaa[7] = CondExp(Xaa[0], q, r); // create fa: Xaa -> Yaa function object ADFun< ADdouble > fa(Xaa, Yaa); // function values CPPAD_TESTVECTOR( ADdouble ) Ya(m); Ya = fa.Forward(0, Xa); // create f: Xa -> Ya function object ADFun f(Xa, Ya); // check result of function evaluation CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(double) y(m); x[0] = 1.; x[1] = 0.; x[2] = -1.; y = f.Forward(0, x); size_t i; for(i = 0; i < m; i++) { // y[i] = CondExp(x[0], x[1], x[2]) if( x[0] > 0 ) ok &= (y[i] == x[1]); else ok &= (y[i] == x[2]); } // check forward mode derivatives CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dx[1] = 2.; dx[2] = 3.; dy = f.Forward(1, dx); for(i = 0; i < m; i++) { if( x[0] > 0. ) ok &= (dy[i] == dx[1]); else ok &= (dy[i] == dx[2]); } // calculate Jacobian CPPAD_TESTVECTOR(double) J(m * n); size_t j; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) J[i * n + j] = 0.; if( x[0] > 0. ) J[i * n + 1] = 1.; else J[i * n + 2] = 1.; } // check reverse mode derivatives for(i = 0; i < m; i++) dy[i] = double(i); dx = f.Reverse(1, dy); double sum; for(j = 0; j < n; j++) { sum = 0; for(i = 0; i < m; i++) sum += dy[i] * J[i * n + j]; ok &= (sum == dx[j]); } // forward mode computation of sparsity pattern CPPAD_TESTVECTOR(bool) Px(n * n); for(i = 0; i < n; i++) { for(j = 0; j < n; j++) Px[i * n + j] = false; Px[i * n + i] = true; } CPPAD_TESTVECTOR(bool) Py(m * n); Py = f.ForSparseJac(n, Px); for(i = 0; i < m; i++) { ok &= Py[ i * n + 0 ] == false; ok &= Py[ i * n + 1 ] == true; ok &= Py[ i * n + 2 ] == true; } // reverse mode computation of sparsity pattern Py.resize(m * m); for(i = 0; i < m; i++) { for(j = 0; j < m; j++) Py[i * m + j] = false; Py[i * m + i] = true; } Px.resize(m * n); Px = f.RevSparseJac(m, Py); for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= ( Px[i * n + j] == ( j > 0 ) ); } return ok; } bool CondExpADTwo(void) { bool ok = true; using namespace CppAD; size_t n = 3; size_t m = 8; // ADdouble independent variable vector CPPAD_TESTVECTOR( ADdouble ) Xa(n); Xa[0] = -1.; Xa[1] = 0.; Xa[2] = 1.; Independent(Xa); // use VecAD so that sparsity results are local VecAD Va(1); ADdouble zero = 0.; Va[zero] = Xa[0]; // ADdouble independent variable vector CPPAD_TESTVECTOR( ADADdouble ) Xaa(n); Xaa[0] = ADdouble( Va[zero] ); Xaa[1] = Xa[1]; Xaa[2] = Xa[2]; Independent(Xaa); // ADADdouble parameter ADADdouble p = ADADdouble(Xa[0]); ADADdouble q = ADADdouble(Xa[1]); ADADdouble r = ADADdouble(Xa[2]); // ADADdouble dependent variable vector CPPAD_TESTVECTOR( ADADdouble ) Yaa(m); // CondExp(parameter, parameter, parameter) Yaa[0] = CondExp(p, q, r); // CondExp(parameter, parameter, variable) Yaa[1] = CondExp(p, q, Xaa[2]); // CondExp(parameter, varaible, parameter) Yaa[2] = CondExp(p, Xaa[1], r); // CondExp(parameter, variable, variable) Yaa[3] = CondExp(p, Xaa[1], Xaa[2]); // CondExp(variable, variable, variable) Yaa[5] = CondExp(Xaa[0], Xaa[1], Xaa[2]); // CondExp(variable, variable, parameter) Yaa[4] = CondExp(Xaa[0], Xaa[1], r); // CondExp(variable, parameter, variable) Yaa[6] = CondExp(Xaa[0], q, Xaa[2]); // CondExp(variable, parameter, parameter) Yaa[7] = CondExp(Xaa[0], q, r); // create fa: Xaa -> Yaa function object ADFun< ADdouble > fa(Xaa, Yaa); // function values CPPAD_TESTVECTOR( ADdouble ) Ya(m); Ya = fa.Forward(0, Xa); // create f: Xa -> Ya function object ADFun f(Xa, Ya); // check use_VecAD ok &= f.use_VecAD(); // check result of function evaluation CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(double) y(m); x[0] = 1.; x[1] = 0.; x[2] = -1.; y = f.Forward(0, x); size_t i; for(i = 0; i < m; i++) { // y[i] = CondExp(x[0], x[1], x[2]) if( x[0] > 0 ) ok &= (y[i] == x[1]); else ok &= (y[i] == x[2]); } // check forward mode derivatives CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dx[1] = 2.; dx[2] = 3.; dy = f.Forward(1, dx); for(i = 0; i < m; i++) { if( x[0] > 0. ) ok &= (dy[i] == dx[1]); else ok &= (dy[i] == dx[2]); } // calculate Jacobian CPPAD_TESTVECTOR(double) J(m * n); size_t j; for(i = 0; i < m; i++) { for(j = 0; j < n; j++) J[i * n + j] = 0.; if( x[0] > 0. ) J[i * n + 1] = 1.; else J[i * n + 2] = 1.; } // check reverse mode derivatives for(i = 0; i < m; i++) dy[i] = double(i); dx = f.Reverse(1, dy); double sum; for(j = 0; j < n; j++) { sum = 0; for(i = 0; i < m; i++) sum += dy[i] * J[i * n + j]; ok &= (sum == dx[j]); } // forward mode computation of sparsity pattern CPPAD_TESTVECTOR(bool) Px(n * n); for(i = 0; i < n; i++) { for(j = 0; j < n; j++) Px[i * n + j] = false; Px[i * n + i] = true; } CPPAD_TESTVECTOR(bool) Py(m * n); Py = f.ForSparseJac(n, Px); for(i = 0; i < m; i++) { for(j = 0; j < n; j++) // sparsity pattern works for both true and false cases. ok &= ( Py[i * n + j] == (j > 0) ); } // reverse mode computation of sparsity pattern Py.resize(m * m); for(i = 0; i < m; i++) { for(j = 0; j < m; j++) Py[i * m + j] = false; Py[i * m + i] = true; } Px.resize(m * n); Px = f.RevSparseJac(m, Py); for(i = 0; i < m; i++) { for(j = 0; j < n; j++) ok &= ( Px[i * n + j] == (j > 0) ); } return ok; } } // END empty namespace bool CondExpAD(void) { bool ok = true; ok &= CondExpADOne(); ok &= CondExpADTwo(); return ok; } cppad-20170000.3/test_more/sub.cpp0000644000175200017650000001076513057470461015740 0ustar coincoin-web// $Id: sub.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old Sub examples now used just for valiadation testing */ # include namespace { // BEGIN empty namespace bool One(void) { bool ok = true; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(2); size_t s = 0; size_t t = 1; U[s] = 3.; U[t] = 2.; Independent(U); // dependent variable vector and indices CPPAD_TESTVECTOR(AD) Z(3); size_t x = 0; size_t y = 1; size_t z = 2; // dependent variable values Z[x] = U[s] - U[t]; // AD - AD Z[y] = Z[x] - 1.; // AD - double Z[z] = 1. - Z[y]; // double - AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check function values ok &= ( Z[x] == 3. - 2. ); ok &= ( Z[y] == 3. - 2. - 1. ); ok &= ( Z[z] == 1. - 3. + 2. + 1. ); // forward computation of partials w.r.t. s v[s] = 1.; v[t] = 0.; w = f.Forward(1, v); ok &= ( w[x] == 1. ); // dx/ds ok &= ( w[y] == 1. ); // dy/ds ok &= ( w[z] == -1. ); // dz/ds // reverse computation of second partials of z CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 0.; w[y] = 0.; w[z] = 1.; r = f.Reverse(2, w); ok &= ( r[2 * s + 1] == 0. ); // d^2 z / (ds ds) ok &= ( r[2 * t + 1] == 0. ); // d^2 z / (ds dt) return ok; } bool Two(void) { bool ok = true; using namespace CppAD; // independent variable vector double u0 = .5; CPPAD_TESTVECTOR(AD) U(1); U[0] = u0; Independent(U); AD a = 2. * U[0] - 1.; // AD - double AD b = a - 2; // AD - int AD c = 3. - b; // double - AD AD d = 4 - c; // int - AD // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = U[0] - d; // AD - AD // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(Value(Z[0]) , u0-4+3-2*u0+1+2, 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = -1.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = -1.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } bool Three(void) { bool ok = true; using namespace CppAD; // special cases where tests above check OK and SubpvOp // implementation is known to be worng. // Probably two minuses make a plus. size_t n = 1; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; Independent(X); size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); Y[0] = 1. - X[0]; ADFun f(X, Y); CPPAD_TESTVECTOR(double) w(m), dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= (dw[0] == -1.); return ok; } bool Four(void) { bool ok = true; using namespace CppAD; // special cases where parameter number is equal to // variable index in result. size_t n = 1; CPPAD_TESTVECTOR(AD) X(n); X[0] = 1.; Independent(X); size_t m = 1; CPPAD_TESTVECTOR(AD) Y(m); if( 0. < X[0] && X[0] < 10. ) Y[0] = X[0] - 2.; else Y[0] = X[0] - 2.; ADFun f(X, Y); CPPAD_TESTVECTOR(double) y(m), x(n); x[0] = 1.; y = f.Forward(0, x); ok &= (y[0] == -1.); CPPAD_TESTVECTOR(double) dy(m), dx(n); dx[0] = 1.; dy = f.Forward(1, dx); ok &= (dy[0] == 1.); return ok; } } // END empty namespace bool Sub(void) { bool ok = true; ok &= One(); ok &= Two(); ok &= Three(); ok &= Four(); return ok; } cppad-20170000.3/test_more/std_math.cpp0000644000175200017650000000331013057470461016736 0ustar coincoin-web// $Id: std_math.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Test the using standard math functions with AD< AD > */ # include typedef CppAD::AD ADdouble; typedef CppAD::AD< ADdouble > ADDdouble; bool std_math(void) { using CppAD::NearEqual; bool ok = true; ADDdouble half(.5); ADDdouble one(1.); ADDdouble two(2.); ADDdouble ten(10.); ADDdouble small(1e-6); ADDdouble pi_4(3.141592653 / 4.); ADDdouble root_2( sqrt(two) ); ADDdouble y( acos(one / root_2) ); ok &= NearEqual( pi_4, y, small, small ); y = cos(pi_4); ok &= NearEqual( one / root_2, y, small, small ); y = asin(one / root_2); ok &= NearEqual( pi_4, y, small, small ); y = sin(pi_4); ok &= NearEqual( one / root_2, y, small, small ); y = atan(one); ok &= NearEqual( pi_4, y, small, small ); y = tan(pi_4); ok &= NearEqual( one, y, small, small ); y = two * cosh(one); ok &= NearEqual( exp(one) + exp(-one), y, small, small ); y = two * sinh(one); ok &= NearEqual( exp(one) - exp(-one), y, small, small ); y = log( exp(one) ); ok &= NearEqual( one, y, small, small ); y = log10( exp( log(ten) ) ); ok &= NearEqual( one, y, small, small ); return ok; } cppad-20170000.3/test_more/sin.cpp0000644000175200017650000000411313057470461015726 0ustar coincoin-web// $Id: sin.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example now just used for validation testing. */ # include bool Sin(void) { bool ok = true; using CppAD::sin; using CppAD::cos; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 1.; Independent(U); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = sin(U[0]); // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value double sin_u = sin( Value(U[0]) ); double cos_u = cos( Value(U[0]) ); ok &= NearEqual(sin_u, Value(Z[0]), 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; v[0] = 1.; for(j = 1; j < p; j++) { w = f.Forward(j, v); double value; if( j % 4 == 1 ) value = cos_u; else if( j % 4 == 2 ) value = -sin_u; else if( j % 4 == 3 ) value = -cos_u; else value = sin_u; jfac *= j; ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; for(j = 0; j < p; j++) { double value; if( j % 4 == 0 ) value = cos_u; else if( j % 4 == 1 ) value = -sin_u; else if( j % 4 == 2 ) value = -cos_u; else value = sin_u; ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); } return ok; } cppad-20170000.3/test_more/sqrt.cpp0000644000175200017650000001217613057470461016136 0ustar coincoin-web// $Id: sqrt.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Two old sqrt examples now used just for validation testing. */ # include # include namespace { // BEGIN empty namespace bool SqrtTestOne(void) { bool ok = true; using CppAD::sqrt; using CppAD::pow; using namespace CppAD; // independent variable vector, indices, values, and declaration CPPAD_TESTVECTOR(AD) U(1); size_t s = 0; U[s] = 4.; Independent(U); // dependent variable vector, indices, and values CPPAD_TESTVECTOR(AD) Z(2); size_t x = 0; size_t y = 1; Z[x] = sqrt(U[s]); Z[y] = sqrt(Z[x]); // define f : U -> Z and vectors for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v( f.Domain() ); CPPAD_TESTVECTOR(double) w( f.Range() ); // check values ok &= NearEqual(Z[x] , 2., 1e-10 , 1e-10); ok &= NearEqual(Z[y] , sqrt(2.), 1e-10 , 1e-10); // forward computation of partials w.r.t. s v[s] = 1.; w = f.Forward(1, v); ok &= NearEqual(w[x], .5 * pow(4., -.5), 1e-10 , 1e-10); // dx/ds ok &= NearEqual(w[y], .25 * pow(4., -.75), 1e-10 , 1e-10); // dy/ds // reverse computation of partials of y w[x] = 0.; w[y] = 1.; v = f.Reverse(1,w); ok &= NearEqual(v[s], .25 * pow(4., -.75), 1e-10 , 1e-10); // dy/ds // forward computation of second partials w.r.t s v[s] = 1.; w = f.Forward(1, v); v[s] = 0.; w = f.Forward(2, v); ok &= NearEqual( // d^2 y / (ds ds) 2. * w[y] , -.75 * .25 * pow(4., -1.75), 1e-10 , 1e-10 ); // reverse computation of second partials of y CPPAD_TESTVECTOR(double) r( f.Domain() * 2 ); w[x] = 0.; w[y] = 1.; r = f.Reverse(2, w); ok &= NearEqual( // d^2 y / (ds ds) r[2 * s + 1] , -.75 * .25 * pow(4., -1.75), 1e-10 , 1e-10 ); return ok; } bool SqrtTestTwo(void) { bool ok = true; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 2.; Independent(U); // a temporary values AD x = U[0] * U[0]; // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = sqrt( x ); // z = sqrt( u * u ) // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(U[0] , Z[0], 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 1.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 1.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } bool SqrtTestThree(void) { bool ok = true; using CppAD::sqrt; using CppAD::exp; using namespace CppAD; // independent variable vector, indices, values, and declaration double x = 4.; CPPAD_TESTVECTOR(AD) X(1); X[0] = x; Independent(X); // dependent variable vector, indices, and values CPPAD_TESTVECTOR(AD) Y(1); Y[0] = sqrt( exp(X[0]) ); // define f : X -> Y and vectors for derivative calculations ADFun f(X, Y); // forward computation of first Taylor coefficient CPPAD_TESTVECTOR(double) x1( f.Domain() ); CPPAD_TESTVECTOR(double) y1( f.Range() ); x1[0] = 1.; y1 = f.Forward(1, x1); ok &= NearEqual(y1[0], exp(x/2.)/2., 1e-10 , 1e-10); // forward computation of second Taylor coefficient CPPAD_TESTVECTOR(double) x2( f.Domain() ); CPPAD_TESTVECTOR(double) y2( f.Range() ); x2[0] = 0.; y2 = f.Forward(2, x2); ok &= NearEqual(2.*y2[0] , exp(x/2.)/4., 1e-10 , 1e-10 ); // forward computation of third Taylor coefficient CPPAD_TESTVECTOR(double) x3( f.Domain() ); CPPAD_TESTVECTOR(double) y3( f.Range() ); x3[0] = 0.; y3 = f.Forward(3, x3); ok &= NearEqual(6.*y3[0] , exp(x/2.)/8., 1e-10 , 1e-10 ); // reverse computation of deritavitve of Taylor coefficients CPPAD_TESTVECTOR(double) r( f.Domain() * 4 ); CPPAD_TESTVECTOR(double) w(1); w[0] = 1.; r = f.Reverse(4, w); ok &= NearEqual(r[0], exp(x/2.)/2., 1e-10 , 1e-10); ok &= NearEqual(r[1], exp(x/2.)/4., 1e-10 , 1e-10 ); ok &= NearEqual(2.*r[2], exp(x/2.)/8., 1e-10 , 1e-10 ); ok &= NearEqual(6.*r[3], exp(x/2.)/16., 1e-10 , 1e-10 ); return ok; } } // END empty namespace bool Sqrt(void) { bool ok = true; ok &= SqrtTestOne(); ok &= SqrtTestTwo(); ok &= SqrtTestThree(); return ok; } cppad-20170000.3/test_more/omp_alloc.cpp0000644000175200017650000001263113057470461017106 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin omp_alloc.cpp$$ $spell openmp $$ $section OpenMP Memory Allocator: Example and Test$$ $mindex allocation multi thread$$ $head Deprecated 2011-08-31$$ This example is only intended to help convert calls to $cref omp_alloc$$ to calls to $cref thread_alloc$$. $code $srcfile%test_more/omp_alloc.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include namespace { // Begin empty namespace bool omp_alloc_bytes(void) { bool ok = true; using CppAD::omp_alloc; size_t thread; // check initial memory values ok &= ! CppAD::memory_leak(); // amount of static memory used by thread zero size_t static_inuse = omp_alloc::inuse(0); // determine the currently executing thread // (should be zero because not in parallel mode) thread = omp_alloc::get_thread_num(); // repeatedly allocate enough memory for at least two size_t values. size_t min_size_t = 2; size_t min_bytes = min_size_t * sizeof(size_t); size_t n_outter = 10; size_t n_inner = 5; size_t cap_bytes(0), i, j, k; for(i = 0; i < n_outter; i++) { // Do not use CppAD::vector here because its use of omp_alloc // complicates the inuse and avaialble results. std::vector v_ptr(n_inner); for( j = 0; j < n_inner; j++) { // allocate enough memory for min_size_t size_t objects v_ptr[j] = omp_alloc::get_memory(min_bytes, cap_bytes); size_t* ptr = reinterpret_cast(v_ptr[j]); // determine the number of size_t values we have obtained size_t cap_size_t = cap_bytes / sizeof(size_t); ok &= min_size_t <= cap_size_t; // use placement new to call the size_t copy constructor for(k = 0; k < cap_size_t; k++) new(ptr + k) size_t(i + j + k); // check that the constructor worked for(k = 0; k < cap_size_t; k++) ok &= ptr[k] == (i + j + k); } // check that n_inner * cap_bytes are inuse and none are available ok &= omp_alloc::inuse(thread) == n_inner*cap_bytes + static_inuse; ok &= omp_alloc::available(thread) == 0; // return the memrory to omp_alloc for(j = 0; j < n_inner; j++) omp_alloc::return_memory(v_ptr[j]); // check that now n_inner * cap_bytes are now available // and none are in use ok &= omp_alloc::inuse(thread) == static_inuse; ok &= omp_alloc::available(thread) == n_inner * cap_bytes; } // return all the available memory to the system omp_alloc::free_available(thread); ok &= ! CppAD::memory_leak(); return ok; } class my_char { public: char ch_ ; my_char(void) : ch_(' ') { } my_char(const my_char& my_ch) : ch_(my_ch.ch_) { } }; bool omp_alloc_array(void) { bool ok = true; using CppAD::omp_alloc; size_t i; // check initial memory values size_t thread = omp_alloc::get_thread_num(); ok &= thread == 0; ok &= ! CppAD::memory_leak(); size_t static_inuse = omp_alloc::inuse(0); // initial allocation of an array size_t size_min = 3; size_t size_one; my_char *array_one = omp_alloc::create_array(size_min, size_one); // check the values and change them to null 'x' for(i = 0; i < size_one; i++) { ok &= array_one[i].ch_ == ' '; array_one[i].ch_ = 'x'; } // now create a longer array size_t size_two; my_char *array_two = omp_alloc::create_array(2 * size_min, size_two); // check the values in array one for(i = 0; i < size_one; i++) ok &= array_one[i].ch_ == 'x'; // check the values in array two for(i = 0; i < size_two; i++) ok &= array_two[i].ch_ == ' '; // check the amount of inuse and available memory // (an extra size_t value is used for each memory block). size_t check = static_inuse + sizeof(my_char)*(size_one + size_two); ok &= omp_alloc::inuse(thread) - check < sizeof(my_char); ok &= omp_alloc::available(thread) == 0; // delete the arrays omp_alloc::delete_array(array_one); omp_alloc::delete_array(array_two); ok &= omp_alloc::inuse(thread) == static_inuse; check = sizeof(my_char)*(size_one + size_two); ok &= omp_alloc::available(thread) - check < sizeof(my_char); // free the memory for use by this thread omp_alloc::free_available(thread); ok &= ! CppAD::memory_leak(); return ok; } } // End empty namespace bool omp_alloc(void) { bool ok = true; using CppAD::omp_alloc; // check initial state of allocator ok &= omp_alloc::get_max_num_threads() == 1; // set the maximum number of threads greater than one // so that omp_alloc holds onto memory CppAD::omp_alloc::set_max_num_threads(2); ok &= omp_alloc::get_max_num_threads() == 2; ok &= ! CppAD::memory_leak(); // now use memory allocator in state where it holds onto memory ok &= omp_alloc_bytes(); ok &= omp_alloc_array(); // check that the tests have not held onto memory ok &= ! CppAD::memory_leak(); // set the maximum number of threads back to one // so that omp_alloc no longer holds onto memory CppAD::omp_alloc::set_max_num_threads(1); return ok; } // END C++ cppad-20170000.3/test_more/asin.cpp0000644000175200017650000000344713057470461016100 0ustar coincoin-web/* $Id: asin.cpp 3675 2015-05-05 14:26:18Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example now only used for validation testing. */ # include bool asin(void) { bool ok = true; using CppAD::asin; using namespace CppAD; // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = .5; Independent(U); // a temporary values AD x = sin(U[0]); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = asin(x); // asin( sin(u) ) // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check value ok &= NearEqual(U[0] , Z[0], 1e-10 , 1e-10); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 1.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(jfac*w[0], value, 1e-10 , 1e-10); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 1.; for(j = 0; j < p; j++) { ok &= NearEqual(jfac*r[j], value, 1e-10 , 1e-10); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } cppad-20170000.3/test_more/atan2.cpp0000644000175200017650000000544313057470461016151 0ustar coincoin-web// $Id: atan2.cpp 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example and test now just used for validation testing. */ # include # include namespace { // begin empty namespace bool ad_ad(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); AD< AD > x(2.), y(2.); AD< AD > z = atan2(y, x); NearEqual( Value( Value(z) ), atan(1.), eps99, eps99); return ok; } bool general(void) { bool ok = true; using CppAD::atan; using CppAD::sin; using CppAD::cos; using namespace CppAD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits::epsilon(); // independent variable vector CPPAD_TESTVECTOR(AD) U(1); U[0] = 1.; Independent(U); // a temporary values AD x = cos(U[0]); AD y = sin(U[0]); // dependent variable vector CPPAD_TESTVECTOR(AD) Z(1); Z[0] = atan2(y, x); // create f: U -> Z and vectors used for derivative calculations ADFun f(U, Z); CPPAD_TESTVECTOR(double) v(1); CPPAD_TESTVECTOR(double) w(1); // check original value (u in first quadrant) ok &= NearEqual(U[0] , Z[0], eps99, eps99); // check case where u is in second quadrant v[0] = 3.; w = f.Forward(0, v); ok &= NearEqual(w[0] , v[0], eps99, eps99); // check case where u is in third quadrant v[0] = -3.; w = f.Forward(0, v); ok &= NearEqual(w[0] , v[0], eps99, eps99); // check case where u is in fourth quadrant v[0] = -1.; w = f.Forward(0, v); ok &= NearEqual(w[0] , v[0], eps99, eps99); // forward computation of partials w.r.t. u size_t j; size_t p = 5; double jfac = 1.; double value = 1.; v[0] = 1.; for(j = 1; j < p; j++) { jfac *= j; w = f.Forward(j, v); ok &= NearEqual(w[0], value/jfac, eps99, eps99); // d^jz/du^j v[0] = 0.; value = 0.; } // reverse computation of partials of Taylor coefficients CPPAD_TESTVECTOR(double) r(p); w[0] = 1.; r = f.Reverse(p, w); jfac = 1.; value = 1.; for(j = 0; j < p; j++) { ok &= NearEqual(r[j], value/jfac, eps99, eps99); // d^jz/du^j jfac *= (j + 1); value = 0.; } return ok; } } // end empty namespace bool atan2(void) { bool ok = true; ok &= ad_ad(); ok &= general(); return ok; } cppad-20170000.3/test_more/near_equal_ext.cpp0000644000175200017650000000347513057470461020143 0ustar coincoin-web// $Id: near_equal_ext.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* Old example now just used for validation testing */ # include # include bool NearEqualExt(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // double double x = 1.00000; double y = 1.00001; double a = .00005; double r = .00005; double zero = 0.; double inf = 1. / zero; double nan = 0. / zero; // AD AD X(x); AD Y(y); AD Inf(inf); AD Nan(nan); ok &= NearEqual(X, Y, zero, a); ok &= NearEqual(X, y, zero, a); ok &= NearEqual(x, Y, zero, a); ok &= ! NearEqual(X, Y, zero, a/25.); ok &= ! NearEqual(X, y, zero, a/25.); ok &= ! NearEqual(x, Y, zero, a/25.); ok &= NearEqual(X, Y, r, zero); ok &= NearEqual(X, y, r, zero); ok &= NearEqual(x, Y, r, zero); ok &= ! NearEqual(X, Y, r/25., zero); ok &= ! NearEqual(X, y, r/25., zero); ok &= ! NearEqual(x, Y, r/25., zero); ok &= ! NearEqual(Inf, Inf, r, a); ok &= ! NearEqual(Inf, inf, r, a); ok &= ! NearEqual(inf, Inf, r, a); ok &= ! NearEqual(-Inf, -Inf, r, a); ok &= ! NearEqual(-Inf, -inf, r, a); ok &= ! NearEqual(-inf, -Inf, r, a); ok &= ! NearEqual(Nan, Nan, r, a); ok &= ! NearEqual(Nan, nan, r, a); ok &= ! NearEqual(nan, Nan, r, a); return ok; } cppad-20170000.3/test_more/to_string.cpp0000644000175200017650000000276313057470461017156 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // check complex case # include namespace { template bool test(void) { bool ok = true; Float eps = std::numeric_limits::epsilon(); Float pi = 4.0 * std::atan(1.0); Float e = std::exp(1.0); typedef std::complex Base; Base c = Base(pi, e); std::string s = CppAD::to_string( CppAD::AD(c) ); // // get strings corresponding to real and imaginary parts std::string real = ""; std::string imag = ""; size_t index = 1; // skip ( at front while( s[index] != ',' ) real += s[index++]; index++; while( s[index] != ')' ) imag += s[index++]; // Float check = std::atof( real.c_str() ); ok &= std::fabs( check - pi ) <= 2.0 * eps; // check = std::atof( imag.c_str() ); ok &= std::fabs( check - e ) <= 2.0 * eps; // return ok; } } bool to_string(void) { bool ok = true; ok &= test(); ok &= test(); return ok; } // END C++ cppad-20170000.3/test_more/CMakeLists.txt0000644000175200017650000000651713057470461017203 0ustar coincoin-web# ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the test_more directory tests # Inherit environment from ../CMakeList.txt # Specifies build type for this directory. Possible values are # empty, Debug, Release, RelWithDebInfo and MinSizeRel SET(CMAKE_BUILD_TYPE DEBUG) # This directory now contains omp_alloc.cpp which uses multi-threading, so # so no longer can set CPPAD_MAX_NUM_THREADS equal to one (its smallest value) # ADD_DEFINITIONS("-DCPPAD_MAX_NUM_THREADS=1") # adolc_sources, adolc_libs and CPPAD_ADOLC_TEST SET(sources base_adolc.cpp) sources_libs_define(adolc "${sources}" adolc ADOLC_TEST) # eigen_sources and CPPAD_EIGEN_TEST SET(sources cppad_eigen.cpp eigen_mat_inv.cpp) sources_libs_define(eigen "${sources}" "" EIGEN_TEST) # ipopt_prefix SET(sources ipopt_solve.cpp) sources_libs_define(ipopt "${sources}" "${ipopt_LIBRARIES}" IPOPT_TEST) # ) ADD_EXECUTABLE(test_more EXCLUDE_FROM_ALL test_more.cpp ${adolc_sources} ${eigen_sources} ${ipopt_sources} old_usead_2.cpp old_usead_1.cpp old_tan.cpp old_reciprocal.cpp old_mat_mul.cpp abs.cpp acos.cpp acosh.cpp adfun_copy.cpp asin.cpp asinh.cpp assign.cpp add.cpp add_eq.cpp add_zero.cpp atan.cpp atanh.cpp atan2.cpp atomic_sparsity.cpp azmul.cpp base_alloc.cpp check_simple_vector.cpp checkpoint.cpp compare.cpp compare_change.cpp cond_exp.cpp cond_exp_ad.cpp cond_exp_rev.cpp copy.cpp cos.cpp cosh.cpp dbl_epsilon.cpp div.cpp div_eq.cpp div_zero_one.cpp erf.cpp exp.cpp expm1.cpp extern_value.cpp for_hess.cpp for_sparse_hes.cpp for_sparse_jac.cpp forward.cpp forward_dir.cpp forward_order.cpp from_base.cpp fun_check.cpp hes_sparsity.cpp jacobian.cpp num_limits.cpp log.cpp log1p.cpp log10.cpp mul.cpp mul_cskip.cpp mul_eq.cpp mul_level.cpp mul_cond_rev.cpp mul_zdouble.cpp mul_zero_one.cpp near_equal_ext.cpp neg.cpp ode_err_control.cpp omp_alloc.cpp optimize.cpp parameter.cpp poly.cpp pow.cpp pow_int.cpp print_for.cpp romberg_one.cpp rosen_34.cpp runge_45.cpp reverse.cpp rev_sparse_jac.cpp rev_two.cpp simple_vector.cpp sin.cpp sin_cos.cpp sinh.cpp sparse_hessian.cpp sparse_jacobian.cpp sparse_vec_ad.cpp sqrt.cpp std_math.cpp sub.cpp sub_eq.cpp sub_zero.cpp tan.cpp test_vector.cpp to_string.cpp track_new_del.cpp value.cpp vec_ad.cpp vec_ad_par.cpp vec_unary.cpp zdouble.cpp local/vector_set.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags(test_more) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES(test_more ${cppad_lib} ${adolc_libs} ${ipopt_libs} ${colpack_libs} ) # Add the check_test_more target ADD_CUSTOM_TARGET( check_test_more test_more DEPENDS test_more ) MESSAGE(STATUS "make check_test_more: available") # Change check depends in parent environment add_to_list(check_depends check_test_more) SET(check_depends "${check_depends}" PARENT_SCOPE) cppad-20170000.3/test_more/check_simple_vector.cpp0000644000175200017650000000247613057470461021157 0ustar coincoin-web// $Id: check_simple_vector.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # include namespace { template void Case(const Scalar& x, const Scalar& y) { using CppAD::CheckSimpleVector; CheckSimpleVector > (x, y); CheckSimpleVector > (x, y); CheckSimpleVector > (x, y); typedef CPPAD_TESTVECTOR(Scalar) testvector; CheckSimpleVector (x, y); } } bool check_simple_vector(void) { // Unusal test in that CheckSimpleVector will abort if an error occurs Case(float(0), float(1)); Case(double(0), double(1)); // std::set x, y; x.insert(1); y.insert(2); Case(x, y); // return true; } cppad-20170000.3/test_more/alloc_openmp.cpp0000644000175200017650000000466613057470461017622 0ustar coincoin-web// $Id: alloc_openmp.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN C++ # include # include # define NUMBER_THREADS 2 namespace { using CppAD::thread_alloc; // used to inform CppAD when we are in parallel execution mode bool in_parallel(void) { return static_cast( omp_in_parallel() ); } // used to inform CppAD of current thread number thread_number() size_t thread_number(void) { return static_cast( omp_get_thread_num() ); } // structure with information for one thread typedef struct { // function object (worker input) CppAD::vector x; } thread_one_t; // vector with information for all threads thread_one_t thread_all_[NUMBER_THREADS]; // -------------------------------------------------------------------- // function that does the work for one thread void worker(void) { size_t thread_num = thread_number(); thread_all_[thread_num].x.resize(1); thread_all_[thread_num].x[0]=static_cast(thread_num); } } // Test routine called by the master thread (thread_num = 0). bool alloc_openmp(void) { bool ok = true; int num_threads = NUMBER_THREADS; // call setup for using thread_alloc in parallel mode. thread_alloc::parallel_setup( size_t(num_threads), in_parallel, thread_number ); // Execute the worker function in parallel int thread_num; # pragma omp parallel for for(thread_num = 0; thread_num < num_threads; thread_num++) worker(); // end omp parallel for // now inform CppAD that there is only one thread thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL); for(thread_num = 0; thread_num < num_threads; thread_num++) { // check calculations by this thread in parallel model ok &= thread_all_[thread_num].x[0] == static_cast(thread_num); // test having master thread (thread number zero) // free memory that was allocated by thread number thread_num. thread_all_[thread_num].x.clear(); } return ok; } cppad-20170000.3/cppad_ipopt/0002755000175200017650000000000013057470462014736 5ustar coincoin-webcppad-20170000.3/cppad_ipopt/speed/0002755000175200017650000000000013057470461016035 5ustar coincoin-webcppad-20170000.3/cppad_ipopt/speed/CMakeLists.txt0000644000175200017650000000401413057470461020572 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the cppad_ipopt/speed directory tests # Inherit build type from ../CMakeList.txt # Local include directories to search (not in package_prefix/include) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/../src ) # Local link directories to search (not in external packages) # (cannot use ../src/cppad_ipopt library because it is linke with debugging) LINK_DIRECTORIES( ${ipopt_LIBRARY_DIRS} ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) # Include source for cppad_ipopt library so we build it without debugging ADD_EXECUTABLE(cppad_ipopt_speed EXCLUDE_FROM_ALL speed.cpp ../src/cppad_ipopt_nlp.cpp ../src/fun_record.hpp ../src/hes_fg_map.cpp ../src/jac_g_map.cpp ../src/sparse_map2vec.cpp ../src/vec_fun_pattern.cpp ode_speed.cpp ) # Add extra compiler flags add_cppad_cxx_flags( cppad_ipopt_speed ) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES( cppad_ipopt_speed cppad_ipopt ${cppad_lib} ${ipopt_LIBRARIES} ${colpack_libs} ) # Add the check_cppad_ipopt_speed target ADD_CUSTOM_TARGET(check_cppad_ipopt_speed cppad_ipopt_speed DEPENDS cppad_ipopt_speed cppad_ipopt ) MESSAGE(STATUS "make check_cppad_ipopt_speed: available") # Change check depends in parent environment add_to_list(check_cppad_ipopt_depends check_cppad_ipopt_speed) SET(check_cppad_ipopt_depends "${check_cppad_ipopt_depends}" PARENT_SCOPE) cppad-20170000.3/cppad_ipopt/speed/test.sh.in0000644000175200017650000000125213057470461017753 0ustar coincoin-web#! /bin/bash -e # $Id: test.sh.in 2506 2012-10-24 19:36:49Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- export LD_LIBRARY_PATH=@CPPAD_IPOPT_LD_PATH@ ./speed cppad-20170000.3/cppad_ipopt/speed/speed.cpp0000644000175200017650000000303513057470461017640 0ustar coincoin-web// $Id: speed.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include // system include files used for I/O # include // std::string // external complied tests extern double ode_speed(const char* name, size_t& count); // main program that runs all the cppad_ipopt speed tests int main(void) { using std::printf; const char* name; double seconds; size_t count; name = "simple_retape_yes"; seconds = ode_speed(name, count); printf("ode %20s: seconds = %5.2f: eval_r_count = %d\n", name, seconds, int(count) ); name = "simple_retape_no"; seconds = ode_speed(name, count); printf("ode %20s: seconds = %5.2f: eval_r_count = %d\n", name, seconds, int(count) ); name = "fast_retape_yes"; seconds = ode_speed(name, count); printf("ode %20s: seconds = %5.2f: eval_r_count = %d\n", name, seconds, int(count) ); name = "fast_retape_no"; seconds = ode_speed(name, count); printf("ode %20s: seconds = %5.2f: eval_r_count = %d\n", name, seconds, int(count) ); 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uninstall-am .PRECIOUS: makefile test: check ./test.sh # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: cppad-20170000.3/cppad_ipopt/speed/ode_speed.cpp0000644000175200017650000000455713057470461020501 0ustar coincoin-web// $Id: ode_speed.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_ode_speed.cpp$$ $section Speed Test for Both Simple and Fast Representations$$ $code $srcfile%cppad_ipopt/speed/ode_speed.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include "../example/ode_run.hpp" # include "../example/ode_simple.hpp" # include "../example/ode_fast.hpp" # include # include # if CPPAD_HAS_GETTIMEOFDAY & CPPAD_NO_MICROSOFT # include # else # include # endif namespace { double current_second(void) { # if CPPAD_HAS_GETTIMEOFDAY & CPPAD_NOT_MICOROSOFT struct timeval value; gettimeofday(&value, 0); return double(value.tv_sec) + double(value.tv_usec) * 1e-6; # else return (double) clock() / (double) CLOCKS_PER_SEC; # endif } } double ode_speed(const char* name, size_t& count) { // determine simple and retape flags bool simple = true, retape = true; if( std::strcmp(name, "simple_retape_no") == 0 ) { simple = true; retape = false; } else if( std::strcmp(name, "simple_retape_yes") == 0 ) { simple = true; retape = true; } else if( std::strcmp(name, "fast_retape_no") == 0 ) { simple = false; retape = false; } else if( std::strcmp(name, "fast_retape_yes") == 0 ) { simple = false; retape = true; } else assert(false); size_t i; double s0, s1; size_t c0, c1; // solution vector NumberVector x; // number of time grid intervals between measurement values SizeVector N(Nz + 1); N[0] = 0; for(i = 1; i <= Nz; i++) { N[i] = 10; // n += N[i] * Ny; } // n += Na; s0 = current_second(); c0 = count_eval_r(); if( simple ) ipopt_ode_case(retape, N, x); else ipopt_ode_case(retape, N, x); s1 = current_second(); c1 = count_eval_r(); count = c1 - c0 - 1; return s1 - s0; } // END C++ cppad-20170000.3/cppad_ipopt/speed/makefile.am0000644000175200017650000000313413057470461020130 0ustar coincoin-web# $Id: makefile.am 3853 2016-12-14 14:40:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # EXTRA_DIST = test.sh.in # check_PROGRAMS = speed # # BEGIN OPTIMIZE AM_CXXFLAGS = -O2 -DNDEBUG $(CXX_FLAGS) # END OPTIMIZE # # BEGIN DEBUG # AM_CXXFLAGS = -g $(CXX_FLAGS) # END DEBUG # AM_CPPFLAGS = -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ -I$(IPOPT_DIR)/include # LDADD = \ -lcppad_ipopt \ $(CPPAD_IPOPT_LIBS) \ $(FCLIBS) \ $(PTHREAD_LIB) \ $(DL_LIB) AM_LDFLAGS = -L../src # # Cannot use ../src/libcppad_ipopt.a because it is compiled for debugging # so build an optimized version here to use here. speed_SOURCES = \ speed.cpp \ ../src/cppad_ipopt_nlp.cpp \ ../src/fun_record.hpp \ ../src/hes_fg_map.cpp \ ../src/jac_g_map.cpp \ ../src/sparse_map2vec.cpp \ ../src/vec_fun_pattern.cpp \ ode_speed.cpp test: check ./test.sh cppad-20170000.3/cppad_ipopt/src/0002755000175200017650000000000013057470462015525 5ustar coincoin-webcppad-20170000.3/cppad_ipopt/src/vec_fun_pattern.cpp0000644000175200017650000001207513057470461021415 0ustar coincoin-web// $Id: vec_fun_pattern.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "cppad_ipopt_nlp.hpp" # include "vec_fun_pattern.hpp" // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /*! \{ \file vec_fun_pattern.cpp \brief Determine a sparsity pattern for a vector of AD function objects. */ /*! Determine a sparsity patterns for each function in a vector of functions. \param K is the number of functions that we are computing the sparsity pattern for. \param p is a vector with size \c K. For k = 0 , ... , K-1, p[k] is dimension of the range space for \f$ r_k (u) \f$; i.e., \f$ r_k (u) \in {\bf R}^{p(k)} \f$. \param q is a vector with size \c K. For k = 0 , ... , K-1, q[k] is dimension of the domain space for \f$ r_k (u) \f$; i.e., \f$ u \in {\bf R}^{q(k)} \f$. \param retape is a vector with size \c K. For k = 0 , ... , K-1, if retape[k] is true, the function object r[k] is a valid representation for \f$ r_k (u) \f$ for all \f$ u \in {\bf R}^{q(k)} \f$. Otherwise, the function object must be retaped for each value of \f$ u \f$. \param r_fun is the vector of AD function objects which has size size \c K. For k = 0 , ... , K-1, if retape[k] is true, r_fun[k] is not used. If retape[k] is false, r_fun[k] is not used. is a CppAD function object correspopnding to the function \f$ r_k : {\bf R}^{q[k]} \rightarrow {\bf R}^{p[k]} \f$. The following non-constant member functions will be called: \verbatim r_fun[k].ForSparseJac(q[k], pattern_domain) r_fun[k].RevSparseHes(p[k], pattern_range) \endverbatim The following \c const member functions r_fun[k].Range() and r_fun[k].Domain() may also be called. \param pattern_jac_r is a vector with size \c K. On input, For k = 0 , ... , K-1, pattern_jac_r[k] is a vector of length p[k] * q[k] and the value of its elements does not matter. On output it is a CppAD sparsity pattern for the Jacobian of \f$ r_k (u) \f$. \param pattern_hes_r is a vector with size \c K. On input, For k = 0 , ... , K-1, pattern_hes_r[k] is a vector of length q[k] * q[k] and the value of its elements does not matter. On output it is a CppAD sparsity pattern for the Hessian of \f$ R : {\bf R}^{q[k]} \rightarrow {\bf R} \f$ which is defined by \f[ R(u) = \sum_{i=0}^{p[k]-1} r_k (u)_i \f] */ void vec_fun_pattern( size_t K , const CppAD::vector& p , const CppAD::vector& q , const CppAD::vectorBool& retape , CppAD::vector< CppAD::ADFun >& r_fun , CppAD::vector& pattern_jac_r , CppAD::vector& pattern_hes_r ) { // check some assumptions CPPAD_ASSERT_UNKNOWN( K == p.size() ); CPPAD_ASSERT_UNKNOWN( K == q.size() ); CPPAD_ASSERT_UNKNOWN( K == retape.size() ); CPPAD_ASSERT_UNKNOWN( K == r_fun.size() ); CPPAD_ASSERT_UNKNOWN( K == pattern_jac_r.size() ); CPPAD_ASSERT_UNKNOWN( K == pattern_hes_r.size() ); using CppAD::vectorBool; size_t i, j, k; for(k = 0; k < K; k++) { // check some k specific assumptions CPPAD_ASSERT_UNKNOWN( pattern_jac_r[k].size() == p[k] * q[k] ); CPPAD_ASSERT_UNKNOWN( pattern_hes_r[k].size() == q[k] * q[k] ); if( retape[k] ) { for(i = 0; i < p[k]; i++) { for(j = 0; j < q[k]; j++) pattern_jac_r[k][i*q[k] + j] = true; } for(i = 0; i < q[k]; i++) { for(j = 0; j < q[k]; j++) pattern_hes_r[k][i*q[k] + j] = true; } } else { // check assumptions about r_k CPPAD_ASSERT_UNKNOWN( r_fun[k].Range() == p[k] ); CPPAD_ASSERT_UNKNOWN( r_fun[k].Domain() == q[k] ); // pattern for the identity matrix CppAD::vectorBool pattern_domain(q[k] * q[k]); for(i = 0; i < q[k]; i++) { for(j = 0; j < q[k]; j++) pattern_domain[i*q[k] + j] = (i == j); } // use forward mode to compute Jacobian sparsity pattern_jac_r[k] = r_fun[k].ForSparseJac(q[k], pattern_domain); // user reverse mode to compute Hessian sparsity CppAD::vectorBool pattern_ones(p[k]); for(i = 0; i < p[k]; i++) pattern_ones[i] = true; pattern_hes_r[k] = r_fun[k].RevSparseHes(q[k], pattern_ones); } } } // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- cppad-20170000.3/cppad_ipopt/src/jac_g_map.hpp0000644000175200017650000000366413057470462020145 0ustar coincoin-web// $Id: jac_g_map.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_SRC_JAC_G_MAP_HPP # define CPPAD_CPPAD_IPOPT_SRC_JAC_G_MAP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "cppad_ipopt_nlp.hpp" /*! \file jac_g_map.hpp \brief Create a mapping between two representations for Jacobian of g. \ingroup jac_g_map_cpp */ // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- extern void jac_g_map( cppad_ipopt_fg_info* fg_info , size_t m , size_t n , size_t K , const CppAD::vector& L , const CppAD::vector& p , const CppAD::vector& q , const CppAD::vector& pattern_jac_r , CppAD::vector& I , CppAD::vector& J , CppAD::vector< std::map >& index_jac_g ); // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- # endif cppad-20170000.3/cppad_ipopt/src/vec_fun_pattern.hpp0000644000175200017650000000331713057470462021422 0ustar coincoin-web// $Id: vec_fun_pattern.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_SRC_VEC_FUN_PATTERN_HPP # define CPPAD_CPPAD_IPOPT_SRC_VEC_FUN_PATTERN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "cppad_ipopt_nlp.hpp" // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /*! \file vec_fun_pattern.hpp \brief Determine sparsity pattern for a vector of AD fuction objects. \ingroup vec_fun_pattern_cpp */ extern void vec_fun_pattern( size_t K , const CppAD::vector& p , const CppAD::vector& q , const CppAD::vectorBool& retape , CppAD::vector< CppAD::ADFun >& r_fun , CppAD::vector& pattern_jac_r , CppAD::vector& pattern_hes_r ); // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- # endif cppad-20170000.3/cppad_ipopt/src/hes_fg_map.cpp0000644000175200017650000001351713057470462020326 0ustar coincoin-web// $Id: hes_fg_map.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "cppad_ipopt_nlp.hpp" # include "hes_fg_map.hpp" // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /*! \{ \file hes_fg_map.cpp \brief Creates a mapping between two representations for Hessian of fg. */ /*! Create mapping from CppAD to Ipopt sparse representations of Hessian of F(x). The functions \f$ f : {\bf R}^n \rightarrow {\bf R} \f$ and \f$ g : {\bf R}^n \rightarrow {\bf R}^m \f$ are defined by the \ref Users_Representation. We define the function \f$ F : {\bf R}^n \rightarrow {\bf R} \f$ by \f[ F(x) = \sum_{i=0}^m fg(x)_i \f] \param fg_info For k = 0 , ... , K-1, for ell = 0 , ... , L[k], the function call \verbatim fg_info->index(k, ell, I, J); \endverbatim is made by \c hes_fg_map. The values \c k and \c ell are inputs. The input size of \c I ( \c J ) is greater than or equal p[k] ( q[k] ) and this size is not changed. The input values of the elements of \c I and \c J are not specified. The output value of the elements of \c I define \f[ I_{k, \ell} = ( {\rm I[0]} , \cdots , {\rm I[p[k]-1]} ) \f] The output value of the elements of \c J define \f[ J_{k, \ell} = ( {\rm J[0]} , \cdots , {\rm J[q[k]-1]} ) \f] \param m is the dimension of the range space for \f$ g(x) \f$; i.e., \f$ g(x) \in {\bf R}^m \f$. \param n is the dimension of the domain space for \f$ f(x) \f$ and \f$ g(x) \f$; i.e., \f$ x \in {\bf R}^n \f$. \param K is the number of functions \f$ r_k ( u ) \f$ used for the representation of \f$ f(x) \f$ and \f$ g(x) \f$. \param L is a vector with size \c K. For k = 0 , ... , K-1, L[k] is the number of terms that use \f$ r_k (u) \f$ in the representation of \f$ f(x) \f$ and \f$ g(x) \f$. \param p is a vector with size \c K. For k = 0 , ... , K-1, p[k] is dimension of the range space for \f$ r_k (u) \f$; i.e., \f$ r_k (u) \in {\bf R}^{p(k)} \f$. \param q is a vector with size \c K. For k = 0 , ... , K-1, q[k] is dimension of the domain space for \f$ r_k (u) \f$; i.e., \f$ u \in {\bf R}^{q(k)} \f$. \param pattern_hes_r is a vector with size \c K. For k = 0 , ... , K-1, pattern_jac_r[k] is a CppAD sparsity pattern for the Hessian of the function \f[ R(u) = \sum_{i=0}^{p[k]-1} r_k (u)_i \f] As such, pattern_hes_r[k].size() == q[k] * q[k]. \param I is a work vector of length greater than or equal p[k] for all \c k. The input and output value of its elements are unspecified. The size of \c I is not changed. \param J is a work vector of length greater than or equal q[k] for all \c k. The input and output value of its elements are unspecified. The size of \c J is not changed. \param index_hes_fg: On input, this is empty; i.e., index_jac_g.size() == 0. On output, it is the index mapping from \f$ (i, j) \f$ in the Jacobian of \f$ g(x) \f$ to the corresponding index value used by Ipopt to represent the Jacobian. Furthermore, if index_jac_g[i].find(j) == index_jac_g[i].end(), then the \f$ (i, j)\f$ entry in the Jacobian of \f$ g(x) \f$ is always zero. */ void hes_fg_map( cppad_ipopt_fg_info* fg_info , size_t m , size_t n , size_t K , const CppAD::vector& L , const CppAD::vector& p , const CppAD::vector& q , const CppAD::vector& pattern_hes_r , CppAD::vector& I , CppAD::vector& J , CppAD::vector< std::map >& index_hes_fg ) { using CppAD::vectorBool; size_t i, j, ij, k, ell; CPPAD_ASSERT_UNKNOWN( K == L.size() ); CPPAD_ASSERT_UNKNOWN( K == p.size() ); CPPAD_ASSERT_UNKNOWN( K == q.size() ); CPPAD_ASSERT_UNKNOWN( K == pattern_hes_r.size() ); # ifndef NDEBUG for(k = 0; k < K; k++) { CPPAD_ASSERT_UNKNOWN( p[k] <= I.size() ); CPPAD_ASSERT_UNKNOWN( q[k] <= J.size() ); CPPAD_ASSERT_UNKNOWN( q[k]*q[k] == pattern_hes_r[k].size() ); } # endif // Now compute pattern for fg // (use standard set representation because can be huge). CppAD::vector< std::set > pattern_hes_fg(n); for(k = 0; k < K; k++) for(ell = 0; ell < L[k]; ell++) { fg_info->index(k, ell, I, J); for(i = 0; i < q[k]; i++) { for(j = 0; j < q[k]; j++) { ij = i * q[k] + j; if( pattern_hes_r[k][ij] ) pattern_hes_fg[J[i]].insert(J[j]); } } } // Now compute the mapping from (i, j) in the Hessian of fg to the // corresponding index value used by Ipopt to represent the Hessian. CPPAD_ASSERT_UNKNOWN( index_hes_fg.size() == 0 ); index_hes_fg.resize(n); std::set::const_iterator itr; ell = 0; for(i = 0; i < n; i++) { for( itr = pattern_hes_fg[i].begin(); itr != pattern_hes_fg[i].end(); itr++) { index_hes_fg[i][*itr] = ell++; } } return; } // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- cppad-20170000.3/cppad_ipopt/src/makefile.am0000644000175200017650000000240713057470462017622 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # # AM_CXXFLAGS = -g $(CXX_FLAGS) # AM_CPPFLAGS = \ -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ -I$(IPOPT_DIR)/include # # make building the library conditional on having IPOPT_DIR specified if CppAD_IPOPT lib_LIBRARIES = libcppad_ipopt.a libcppad_ipopt_a_SOURCES = \ cppad_ipopt_nlp.cpp \ cppad_ipopt_nlp.hpp \ fun_record.hpp \ hes_fg_map.cpp \ hes_fg_map.hpp \ jac_g_map.cpp \ jac_g_map.hpp \ sparse_map2vec.cpp \ sparse_map2vec.hpp \ vec_fun_pattern.cpp \ vec_fun_pattern.hpp endif cppad-20170000.3/cppad_ipopt/src/sparse_map2vec.cpp0000644000175200017650000000576713057470462021160 0ustar coincoin-web// $Id: sparse_map2vec.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "cppad_ipopt_nlp.hpp" # include "sparse_map2vec.hpp" // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /*! \{ \file sparse_map2vec.cpp \brief Create a two vector sparsity representation from a vector of maps. */ /*! Create a two vector sparsity representation from a vector of maps. \param sparse Is a vector of maps representation of sparsity as well as the index in the two vector representation. To be specific; \verbatim for(i = 0; i < sparse.size(); i++) { for(itr = sparse[i].begin(); itr != sparse[i].end(); itr++) { j = itr->first; // (i, j) is a possibly non-zero entry in sparsity pattern // k == itr->second, is corresponding index in i_row and j_col k++; } } \endverbatim \param n_nz is the total number of possibly non-zero entries. \param i_row The input size and element values for \c i_row do not matter. On output, it has size \c n_nz and i_row[k] contains the row index corresponding to the \c k-th possibly non-zero entry. \param j_col The input size and element values for \c j_col do not matter. On output, it has size \c n_nz and j_col[k] contains the column index corresponding to the \c k-th possibly non-zero entry. */ void sparse_map2vec( const CppAD::vector< std::map > sparse, size_t& n_nz , CppAD::vector& i_row , CppAD::vector& j_col ) { size_t i, j, k, m; // number of rows in sparse m = sparse.size(); // itererator for one row std::map::const_iterator itr; // count the number of possibly non-zeros in sparse n_nz = 0; for(i = 0; i < m; i++) for(itr = sparse[i].begin(); itr != sparse[i].end(); itr++) ++n_nz; // resize the return vectors to accomidate n_nz entries i_row.resize(n_nz); j_col.resize(n_nz); // set the row and column indices and check assumptions on sparse k = 0; for(i = 0; i < m; i++) { for(itr = sparse[i].begin(); itr != sparse[i].end(); itr++) { j = itr->first; CPPAD_ASSERT_UNKNOWN( k == itr->second ); i_row[k] = i; j_col[k] = j; ++k; } } return; } // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- cppad-20170000.3/cppad_ipopt/src/cppad_ipopt_nlp.cpp0000644000175200017650000007514613057470462021417 0ustar coincoin-web// $Id: cppad_ipopt_nlp.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include "cppad_ipopt_nlp.hpp" # include "sparse_map2vec.hpp" # include "jac_g_map.hpp" # include "hes_fg_map.hpp" # include "vec_fun_pattern.hpp" # include "fun_record.hpp" /// If 0 tracing is off, otherwise tracing is on. # define CPPAD_IPOPT_NLP_TRACE 0 # if CPPAD_IPOPT_NLP_TRACE # include # endif // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /*! \{ \file cppad_ipopt_nlp.cpp \brief Member functions for the cppad_ipopt_nlp class. */ /*! Constructor for the \ref Nonlinear_Programming_Problem. \param n dimension of the domain space for f(x) and g(x). \param m dimension of the range space for g(x) \param x_i initial value of x during the optimization procedure (size n). \param x_l lower limit for x (size n). \param x_u upper limit for x (size n). \param g_l lower limit for g(x) (size m). \param g_u upper limit for g(x) (size m). \param fg_info pointer to base class version of derived class object used to get information about the user's representation for f(x) and g(x). (The object pointed to must not be deleted before this cppad_ipopt_nlp object). \param solution pointer to object where final results are stored. (The object pointed to must not be deleted before this cppad_ipopt_nlp object). \par Constants The following values are set by the constructor and are \c const or effectively \c const; i.e., they are set by the constructor and should not be changed: \verbatim n_, m_, x_i_, x_l_, x_u_, g_l_, g_u_, K_, L_, p_, q_, retape_, pattern_jac_r_, pattern_hes_r_, index_jac_g_, index_hes_fg_, nnz_jac_g_, iRow_jac_g_, jCol_jac_g_, nnz_h_lag_, iRow_h_lag_, jCol_h_lag_, \endverbatim In addition, the function calls fg_info->set_n(n) and fg_info->set_m(m) are used to set the values of \c n and \c m in \c fg_info. \par Variables The following arrays have fixed size which is set during this constructor: \li \c tape_ok_ has size \c K_. It is initialized as true for indices \c k such that retape[k] is false. \li \c r_fun_ has size \c K_. It is initilaize with the default \c ADFun constructor. Then, for indices \c k such that retape[k] is false, the operation sequence corresponding to \f$ r_k (u) \f$ is stored in r_fun_[k]. \li \c I_ has size equal to the maximum of p[k] w.r.t \c k. \li \c J_ has size equal to the maximum of q[k] w.r.t \c k. \par NDEBUG If the preprocessor symbol \c NEBUG is not defined, certain of the assumptions about the function calls of the form \verbatim fg_info->index(k, ell, I, J) \endverbatim are checked to make sure they hold. */ cppad_ipopt_nlp::cppad_ipopt_nlp( size_t n , size_t m , const NumberVector &x_i , const NumberVector &x_l , const NumberVector &x_u , const NumberVector &g_l , const NumberVector &g_u , cppad_ipopt_fg_info* fg_info , cppad_ipopt_solution* solution ) : n_ ( n ), m_ ( m ), x_i_ ( x_i ), x_l_ ( x_l ), x_u_ ( x_u ), g_l_ ( g_l ), g_u_ ( g_u ), fg_info_ ( fg_info ) , solution_ (solution) , infinity_ ( std::numeric_limits::infinity() ) { size_t k; // set information needed in cppad_ipopt_fg_info fg_info_->set_n(n); fg_info_->set_m(m); // get information from derived class version of fg_info K_ = fg_info_->number_functions(); L_.resize(K_); p_.resize(K_); q_.resize(K_); r_fun_.resize(K_); retape_.resize(K_); tape_ok_.resize(K_); pattern_jac_r_.resize(K_); pattern_hes_r_.resize(K_); size_t max_p = 0; size_t max_q = 0; for(k = 0; k < K_; k++) { L_[k] = fg_info_->number_terms(k); p_[k] = fg_info_->range_size(k); q_[k] = fg_info_->domain_size(k); retape_[k] = fg_info_->retape(k); max_p = std::max(max_p, p_[k]); max_q = std::max(max_q, q_[k]); pattern_jac_r_[k].resize( p_[k] * q_[k] ); pattern_hes_r_[k].resize( q_[k] * q_[k] ); } I_.resize(max_p); J_.resize(max_q); # ifndef NDEBUG size_t i, j, ell; // check for valid range and domain indices for(k = 0; k < K_; k++) for(ell = 0; ell < L_[k]; ell++) { for( i = 0; i < p_[k]; i++) I_[i] = m+1; // an invalid range index for( j = 0; j < q_[k]; j++) J_[j] = n; // an invalid domain index fg_info_->index(k, ell, I_, J_); for( i = 0; i < p_[k]; i++) if( I_[i] > m ) { std::cerr << "k=" << k << ", ell=" << ell << ", I[" << i << "]=" << I_[i] << std::endl; CPPAD_ASSERT_KNOWN( I_[i] <= m, "cppad_ipopt_nlp: invalid value in index vector I" ); } for( j = 0; j < q_[k]; j++) if( J_[j] >= n ) { std::cerr << "k=" << k << ", ell=" << ell << ", J[" << j << "]=" << J_[j] << std::endl; CPPAD_ASSERT_KNOWN( J_[j] < n, "cppad_ipopt_nlp: invalid value in index vector J" ); } } # endif // record r[k] for functions that do not need retaping for(k = 0; k < K_; k++) { tape_ok_[k] = false; if( ! retape_[k] ) { // Operation sequence does not depend on value // of u so record it once here in the constructor. fg_info_->index(k, 0, I_, J_); fun_record( fg_info_ , // inputs k , p_ , q_ , n_ , x_i_ , J_ , r_fun_ // output ); // take time to optimize because only recording once r_fun_[k].optimize(); // ok and will stay that way tape_ok_[k] = true; } } // compute a sparsity patterns for each r_k (u) vec_fun_pattern( K_, p_, q_, retape_, r_fun_, // inputs pattern_jac_r_, pattern_hes_r_ // outputs ); // mapping from (i,j) to Ipopt sparsity index for Jacobian of g jac_g_map( fg_info_, m_, n_, K_, L_, p_, q_, pattern_jac_r_, // inputs I_, J_, // work index_jac_g_ // outputs ); // mapping from (i,j) to Ipopt sparsity index for Hessian of Lagragian hes_fg_map( fg_info_, m_, n_, K_, L_, p_, q_, pattern_hes_r_, // inputs I_, J_, // work index_hes_fg_ // outputs ); // Compute Ipopt sparsity structure for Jacobian of g sparse_map2vec( index_jac_g_, // inputs nnz_jac_g_, iRow_jac_g_, jCol_jac_g_ // outputs ); // Compute Ipopt sparsity structure for Hessian of Lagragian sparse_map2vec( index_hes_fg_, // inputs nnz_h_lag_, iRow_h_lag_, jCol_h_lag_ // outputs ); } /// The destructor takes no special action. cppad_ipopt_nlp::~cppad_ipopt_nlp() {} /*! Return dimension information about optimization problem. \param[out] n is set to the value \c n_. \param[out] m is set to the value \c m_. \param[out] nnz_jac_g is set to the value of \c nnz_jac_g_. \param[out] nnz_h_lag is set to the vlaue of \c nnz_h_lag_. \param[out] index_style is set to C_STYLE; i.e., zeoro based indexing is used in the information passed to Ipopt. */ bool cppad_ipopt_nlp::get_nlp_info(Index& n, Index& m, Index& nnz_jac_g, Index& nnz_h_lag, IndexStyleEnum& index_style) { n = n_; m = m_; nnz_jac_g = nnz_jac_g_; nnz_h_lag = nnz_h_lag_; // use the fortran index style for row/col entries index_style = C_STYLE; return true; } /*! Return bound information about optimization problem. \param[in] n is the dimension of the domain space for f(x) and g(x); i.e., it must be equal to \c n_. \param[out] x_l is a vector of size \c n. The input value of its elements does not matter. On output, it is a copy of the lower bound for \f$ x \f$; i.e., \c x_l_. \param[out] x_u is a vector of size \c n. The input value of its elements does not matter. On output, it is a copy of the upper bound for \f$ x \f$; i.e., \c x_u_. \param[in] m is the dimension of the range space for g(x). i.e., it must be equal to \c m_. \param[out] g_l is a vector of size \c m. The input value of its elements does not matter. On output, it is a copy of the lower bound for \f$ g(x) \f$; i.e., \c g_l_. \param[out] g_u is a vector of size \c m. The input value of its elements does not matter. On output, it is a copy of the upper bound for \f$ g(x) \f$; i.e, \c g_u_. */ bool cppad_ipopt_nlp::get_bounds_info(Index n, Number* x_l, Number* x_u, Index m, Number* g_l, Number* g_u) { size_t i, j; // here, the n and m we gave IPOPT in get_nlp_info are passed back CPPAD_ASSERT_UNKNOWN(size_t(n) == n_); CPPAD_ASSERT_UNKNOWN(size_t(m) == m_); // pass back bounds for(j = 0; j < n_; j++) { x_l[j] = x_l_[j]; x_u[j] = x_u_[j]; } for(i = 0; i < m_; i++) { g_l[i] = g_l_[i]; g_u[i] = g_u_[i]; } return true; } /*! Return initial x value where optimiation is started. \param[in] n must be equal to the domain dimension for f(x) and g(x); i.e., it must be equal to \c n_. \param[in] init_x must be equal to true. \param[out] x is a vector of size \c n. The input value of its elements does not matter. On output, it is a copy of the initial value for \f$ x \f$; i.e. \c x_i_. \param[in] init_z must be equal to false. \param z_L is not used. \param z_U is not used. \param[in] m must be equal to the range dimension for g(x); i.e., it must be equal to \c m_. \param init_lambda must be equal to false. \param lambda is not used. */ bool cppad_ipopt_nlp::get_starting_point(Index n, bool init_x, Number* x, bool init_z, Number* z_L, Number* z_U, Index m, bool init_lambda, Number* lambda) { size_t j; CPPAD_ASSERT_UNKNOWN(size_t(n) == n_ ); CPPAD_ASSERT_UNKNOWN(size_t(m) == m_ ); CPPAD_ASSERT_UNKNOWN(init_x == true); CPPAD_ASSERT_UNKNOWN(init_z == false); CPPAD_ASSERT_UNKNOWN(init_lambda == false); for(j = 0; j < n_; j++) x[j] = x_i_[j]; return true; } /*! Evaluate the objective fucntion f(x). \param[in] n is the dimension of the argument space for f(x); i.e., must be equal \c n_. \param[in] x is a vector of size \c n containing the point at which to evaluate the function f(x). \param[in] new_x is false if the previous call to any one of the \ref Deprecated_Evaluation_Methods used the same value for \c x. \param[out] obj_value is the value of the objective f(x) at this value of \c x. \return The return value is always true; see \ref Deprecated_Evaluation_Methods. \par Efficiency This routine could be more efficient (for certain when when L[k] > 1 and retape[k] is true) if the users also provided a version of the function fg_info->eval_r(k, u) where \c u was of type \c NumberVector. */ bool cppad_ipopt_nlp::eval_f( Index n, const Number* x, bool new_x, Number& obj_value ) { CPPAD_ASSERT_UNKNOWN(size_t(n) == n_ ); size_t iobj, j, k, ell; // initialize summation obj_value = 0.; // update tape_ok_ flag for(k = 0; k < K_; k++) { if( retape_[k] && (new_x || L_[k] > 1) ) tape_ok_[k] = false; } for(k = 0; k < K_; k++) for(ell = 0; ell < L_[k]; ell++) { fg_info_->index(k, ell, I_, J_); for(iobj = 0; iobj < p_[k]; iobj++) if( I_[iobj] == 0 ) { if( ! tape_ok_[k] ) { // Record r_k for value of u corresponding to x fun_record( fg_info_ , // inputs k , p_ , q_ , n_ , x , J_ , r_fun_ // output ); tape_ok_[k] = ! (retape_[k] || L_[k] > 1); } NumberVector u(q_[k]); NumberVector r(p_[k]); for(j = 0; j < q_[k]; j++) { CPPAD_ASSERT_UNKNOWN( J_[j] < n_ ); u[j] = x[ J_[j] ]; } r = r_fun_[k].Forward(0, u); obj_value += r[iobj]; } } # if CPPAD_IPOPT_NLP_TRACE using std::printf; for(j = 0; j < n_; j++) printf("cppad_ipopt_nlp::eval_f::x[%d] = %20.14g\n", j, x[j]); printf("cppad_ipopt_nlp::eval_f::obj_value = %20.14g\n", obj_value); # endif # ifndef NDEBUG CPPAD_ASSERT_KNOWN( (-infinity_ < obj_value) && (obj_value < infinity_), "cppad_ipopt_nlp::eval_f:: objective value is not finite" ); # endif return true; } /*! Evaluate the gradient of f(x). \param[in] n is the dimension of the argument space for f(x); i.e., must be equal \c n_. \param[in] x has a vector of size \c n containing the point at which to evaluate the gradient of f(x). \param[in] new_x is false if the previous call to any one of the \ref Deprecated_Evaluation_Methods used the same value for \c x. \param[out] grad_f is a vector of size \c n. The input value of its elements does not matter. The output value of its elements is the gradient of f(x) at this value of. \return The return value is always true; see \ref Deprecated_Evaluation_Methods. */ bool cppad_ipopt_nlp::eval_grad_f( Index n, const Number* x, bool new_x, Number* grad_f ) { CPPAD_ASSERT_UNKNOWN(size_t(n) == n_ ); size_t iobj, i, j, k, ell; // initialize summation for(j = 0; j < n_; j++) grad_f[j] = 0.; // update tape_ok_ flag for(k = 0; k < K_; k++) { if( retape_[k] && (new_x || L_[k] > 1) ) tape_ok_[k] = false; } for(k = 0; k < K_; k++) for(ell = 0; ell < L_[k]; ell++) { fg_info_->index(k, ell, I_, J_); for(iobj = 0; iobj < p_[k]; iobj++) if( I_[iobj] == 0 ) { if( ! tape_ok_[k] ) { // Record r_k for value of u corresponding to x fun_record( fg_info_ , // inputs k , p_ , q_ , n_ , x , J_ , r_fun_ // output ); tape_ok_[k] = ! (retape_[k] || L_[k] > 1); } NumberVector u(q_[k]); NumberVector w(p_[k]); NumberVector r_grad(q_[k]); for(j = 0; j < q_[k]; j++) { CPPAD_ASSERT_UNKNOWN( J_[j] < n_ ); u[j] = x[ J_[j] ]; } r_fun_[k].Forward(0, u); for(i = 0; i < p_[k]; i++) w[i] = 0.; w[iobj] = 1.; r_grad = r_fun_[k].Reverse(1, w); for(j = 0; j < q_[k]; j++) { CPPAD_ASSERT_UNKNOWN( J_[j] < n_ ); grad_f[ J_[j] ] += r_grad[j]; } } } # if CPPAD_IPOPT_NLP_TRACE using std::printf; for(j = 0; j < n_; j++) printf( "cppad_ipopt_nlp::eval_grad_f::x[%d] = %20.14g\n", j, x[j] ); for(j = 0; j < n_; j++) printf( "cppad_ipopt_nlp::eval_grad_f::grad_f[%d] = %20.14g\n", j, grad_f[j] ); # endif # ifndef NDEBUG for(j = 0; j < n_; j++) CPPAD_ASSERT_KNOWN( (-infinity_ < grad_f[j]) && (grad_f[j] < infinity_), "cppad_ipopt_nlp::grad_f:: gradient of objective is not finite" ); # endif return true; } /*! Evaluate the function g(x). \param[in] n is the dimension of the argument space for g(x); i.e., must be equal \c n_. \param[in] x has a vector of size \c n containing the point at which to evaluate the constraint function g(x). \param[in] new_x is false if the previous call to any one of the \ref Deprecated_Evaluation_Methods used the same value for \c x. \param[in] m is the dimension of the range space for g(x); i.e., must be equal to \c m_. \param[out] g is a vector of size \c m. The input value of its elements does not matter. The output value of its elements is the value of the function g(x) at this value of \c x. \return The return value is always true; see \ref Deprecated_Evaluation_Methods. */ bool cppad_ipopt_nlp::eval_g( Index n, const Number* x, bool new_x, Index m, Number* g ) { CPPAD_ASSERT_UNKNOWN(size_t(n) == n_ ); size_t i, j, k, ell; // initialize summation for(i = 0; i < m_; i++) g[i] = 0.; // update tape_ok_ flag for(k = 0; k < K_; k++) { if( retape_[k] && (new_x || L_[k] > 1) ) tape_ok_[k] = false; } for(k = 0; k < K_; k++) for(ell = 0; ell < L_[k]; ell++) { fg_info_->index(k, ell, I_, J_); if( ! tape_ok_[k] ) { // Record r_k for value of u corresponding to x fun_record( fg_info_ , // inputs k , p_ , q_ , n_ , x , J_ , r_fun_ // output ); } tape_ok_[k] = ! (retape_[k] || L_[k] > 1); NumberVector u(q_[k]); NumberVector r(p_[k]); for(j = 0; j < q_[k]; j++) { CPPAD_ASSERT_UNKNOWN( J_[j] < n_ ); u[j] = x[ J_[j] ]; } r = r_fun_[k].Forward(0, u); for(i = 0; i < p_[k]; i++) { CPPAD_ASSERT_UNKNOWN( I_[i] <= m_ ); if( I_[i] >= 1 ) g[ I_[i] - 1 ] += r[i]; } } # if CPPAD_IPOPT_NLP_TRACE using std::printf; for(j = 0; j < n_; j++) printf("cppad_ipopt_nlp::eval_g::x[%d] = %20.14g\n", j, x[j]); for(i = 0; i < m_; i++) printf("cppad_ipopt_nlp::eval_g::g[%d] = %20.14g\n", i, g[i]); # endif # ifndef NDEBUG for(i = 0; i < m_; i++) CPPAD_ASSERT_KNOWN( (-infinity_ < g[i]) && (g[i] < infinity_), "cppad_ipopt_nlp::eval_g:: not all constraints are not finite" ); # endif return true; } /*! Evaluate the Jacobian of g(x). \param[in] n is the dimension of the argument space for g(x); i.e., must be equal \c n_. \param x if \c values is not \c NULL, \c x is a vector of size \c n containing the point at which to evaluate the gradient of g(x). \param[in] new_x is false if the previous call to any one of the \ref Deprecated_Evaluation_Methods used the same value for \c x. \param[in] m is the dimension of the range space for g(x); i.e., must be equal to \c m_. \param[in] nele_jac is the number of possibly non-zero elements in the Jacobian of g(x); i.e., must be equal to \c nnz_jac_g_. \param iRow if \c values is not \c NULL, \c iRow is not defined. if \c values is \c NULL, \c iRow is a vector with size \c nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, iRow[k] is the base zero row index for the k-th possibly non-zero entry in the Jacobian of g(x). \param jCol if \c values is not \c NULL, \c jCol is not defined. if \c values is \c NULL, \c jCol is a vector with size \c nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, jCol[k] is the base zero column index for the k-th possibly non-zero entry in the Jacobian of g(x). \param values if \c values is not \c NULL, \c values is a vector with size \c nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, values[k] is the value for the k-th possibly non-zero entry in the Jacobian of g(x). \return The return value is always true; see \ref Deprecated_Evaluation_Methods. */ bool cppad_ipopt_nlp::eval_jac_g(Index n, const Number* x, bool new_x, Index m, Index nele_jac, Index* iRow, Index *jCol, Number* values) { CPPAD_ASSERT_UNKNOWN(size_t(m) == m_ ); CPPAD_ASSERT_UNKNOWN(size_t(n) == n_ ); CPPAD_ASSERT_UNKNOWN( size_t(nele_jac) == nnz_jac_g_ ); size_t i, j, k, ell, l; std::map::iterator index_ij; if (values == NULL) { for(k = 0; k < nnz_jac_g_; k++) { iRow[k] = iRow_jac_g_[k]; jCol[k] = jCol_jac_g_[k]; } return true; } // initialize summation l = nnz_jac_g_; while(l--) values[l] = 0.; // update tape_ok_ flag for(k = 0; k < K_; k++) { if( retape_[k] && (new_x || L_[k] > 1) ) tape_ok_[k] = false; } for(k = 0; k < K_; k++) for(ell = 0; ell < L_[k]; ell++) { fg_info_->index(k, ell, I_, J_); if( ! tape_ok_[k] ) { // Record r_k for value of u corresponding to x fun_record( fg_info_ , // inputs k , p_ , q_ , n_ , x , J_ , r_fun_ // output ); } tape_ok_[k] = ! (retape_[k] || L_[k] > 1); NumberVector u(q_[k]); NumberVector jac_r(p_[k] * q_[k]); for(j = 0; j < q_[k]; j++) { CPPAD_ASSERT_UNKNOWN( J_[j] < n_ ); u[j] = x[ J_[j] ]; } if( retape_[k] ) jac_r = r_fun_[k].Jacobian(u); else jac_r = r_fun_[k].SparseJacobian(u, pattern_jac_r_[k]); for(i = 0; i < p_[k]; i++) if( I_[i] != 0 ) { CPPAD_ASSERT_UNKNOWN( I_[i] <= m_ ); for(j = 0; j < q_[k]; j++) { index_ij = index_jac_g_[I_[i]-1].find(J_[j]); if( index_ij != index_jac_g_[I_[i]-1].end() ) { l = index_ij->second; values[l] += jac_r[i * q_[k] + j]; } else CPPAD_ASSERT_UNKNOWN( jac_r[i * q_[k] + j] == 0. ); } } } # ifndef NDEBUG for(l = 0; l < nnz_jac_g_; l++) CPPAD_ASSERT_KNOWN( (-infinity_ < values[l]) && (values[l] < infinity_), "cppad_ipopt_nlp::eval_jac_g:: a component of " "gradient of g is not finite" ); # endif return true; } /*! Evaluate the Hessian of the Lagragian \section Deprecated_Hessian_of_the_Lagragian The Hessian of the Lagragian The Hessian of the Lagragian is defined as \f[ H(x, \sigma, \lambda ) = \sigma \nabla^2 f(x) + \sum_{i=0}^{m-1} \lambda_i \nabla^2 g(x)_i \f] \param[in] n is the dimension of the argument space for g(x); i.e., must be equal \c n_. \param x if \c values is not \c NULL, \c x is a vector of size \c n containing the point at which to evaluate the Hessian of the Lagrangian. \param[in] new_x is false if the previous call to any one of the \ref Deprecated_Evaluation_Methods used the same value for \c x. \param[in] obj_factor the value \f$ \sigma \f$ multiplying the Hessian of f(x) in the expression for \ref Deprecated_Hessian_of_the_Lagragian. \param[in] m is the dimension of the range space for g(x); i.e., must be equal to \c m_. \param[in] lambda if \c values is not \c NULL, \c lambda is a vector of size \c m specifing the value of \f$ \lambda \f$ in the expression for \ref Deprecated_Hessian_of_the_Lagragian. \param[in] new_lambda is true if the previous call to \c eval_h had the same value for \c lambda and false otherwise. (Not currently used.) \param[in] nele_hess is the number of possibly non-zero elements in the Hessian of the Lagragian; i.e., must be equal to \c nnz_h_lag_. \param iRow if \c values is not \c NULL, \c iRow is not defined. if \c values is \c NULL, \c iRow is a vector with size \c nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, iRow[k] is the base zero row index for the k-th possibly non-zero entry in the Hessian of the Lagragian. \param jCol if \c values is not \c NULL, \c jCol is not defined. if \c values is \c NULL, \c jCol is a vector with size \c nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, jCol[k] is the base zero column index for the k-th possibly non-zero entry in the Hessian of the Lagragian. \param values if \c values is not \c NULL, it is a vector with size \c nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, values[k] is the value for the k-th possibly non-zero entry in the Hessian of the Lagragian. \return The return value is always true; see \ref Deprecated_Evaluation_Methods. */ bool cppad_ipopt_nlp::eval_h(Index n, const Number* x, bool new_x, Number obj_factor, Index m, const Number* lambda, bool new_lambda, Index nele_hess, Index* iRow, Index* jCol, Number* values) { CPPAD_ASSERT_UNKNOWN(size_t(m) == m_ ); CPPAD_ASSERT_UNKNOWN(size_t(n) == n_ ); size_t i, j, k, ell, l; std::map::iterator index_ij; if (values == NULL) { for(k = 0; k < nnz_h_lag_; k++) { iRow[k] = iRow_h_lag_[k]; jCol[k] = jCol_h_lag_[k]; } return true; } // initialize summation l = nnz_h_lag_; while(l--) values[l] = 0.; // update tape_ok_ flag for(k = 0; k < K_; k++) { if( retape_[k] && (new_x || L_[k] > 1) ) tape_ok_[k] = false; } for(k = 0; k < K_; k++) for(ell = 0; ell < L_[k]; ell++) { fg_info_->index(k, ell, I_, J_); bool in_use = false; for(i = 0; i < p_[k]; i++) { if( I_[i] == 0 ) in_use |= obj_factor > 0.; else in_use |= lambda[ I_[i] - 1 ] > 0; } if( in_use ) { if( ! tape_ok_[k] ) { // Record r_k for value of u corresponding to x fun_record( fg_info_ , // inputs k , p_ , q_ , n_ , x , J_ , r_fun_ // output ); tape_ok_[k] = ! (retape_[k] || L_[k] > 1); } NumberVector w(p_[k]); NumberVector r_hes(q_[k] * q_[k]); NumberVector u(q_[k]); for(j = 0; j < q_[k]; j++) { CPPAD_ASSERT_UNKNOWN( J_[j] < n_ ); u[j] = x[ J_[j] ]; } for(i = 0; i < p_[k]; i++) { CPPAD_ASSERT_UNKNOWN( I_[i] <= m_ ); if( I_[i] == 0 ) w[i] = obj_factor; else w[i] = lambda[ I_[i] - 1 ]; } if( retape_[k] ) r_hes = r_fun_[k].Hessian(u, w); else r_hes = r_fun_[k].SparseHessian( u, w, pattern_hes_r_[k] ); for(i = 0; i < q_[k]; i++) for(j = 0; j < q_[k]; j++) if( J_[j] <= J_[i] ) { index_ij = index_hes_fg_[J_[i]].find(J_[j]); if( index_ij != index_hes_fg_[J_[i]].end() ) { l = index_ij->second; values[l] += r_hes[i * q_[k] + j]; } else CPPAD_ASSERT_UNKNOWN( r_hes[i * q_[k] + j] == 0. ); } } } # ifndef NDEBUG for(l = 0; l < nnz_h_lag_; l++) CPPAD_ASSERT_KNOWN( (-infinity_ < values[l]) && (values[l] < infinity_), "cppad_ipopt_nlp::eval_h:: a component of " "Hessian of Lagragian is not finite" ); # endif return true; } /*! Pass solution information from Ipopt to users solution structure. \param[in] status is value that the Ipopt solution status which gets mapped to a correponding value for \n solution_->status. \param[in] n is the dimension of the domain space for f(x) and g(x); i.e., it must be equal to \c n_. \param[in] x is a vector with size \c n specifing the final solution. \n solution_->x is set to be a vector with size \c n and to have the same element values. \param[in] z_L is a vector with size \c n specifing the Lagragian multipliers for the constraint \f$ x^l \leq x \f$. \n solution_->z_l is set to be a vector with size \c n and to have the same element values. \param[in] z_U is a vector with size \c n specifing the Lagragian multipliers for the constraint \f$ x \leq x^u \f$. \n solution_->z_u is set to be a vector with size \c n and to have the same element values. \param[in] m is the dimension of the range space for g(x). i.e., it must be equal to \c m_. \param[in] g is a vector with size \c m containing the value of the constraint function g(x) at the final solution for \c x. \n solution_->g is set to be a vector with size \c m and to have the same element values. \param[in] lambda is a vector with size \c m specifing the Lagragian multipliers for the constraints \f$ g^l \leq g(x) \leq g^u \f$. \n solution_->lambda is set to be a vector with size \c m and to have the same element values. \param[in] obj_value is the value of the objective function f(x) at the final solution for \c x. \n solution_->obj_value is set to have the same value. \param[in] ip_data is unspecified (by Ipopt) and hence not used. \param[in] ip_cq is unspecified (by Ipopt) and hence not used. \par solution_[out] the pointer \c solution_ , which is equal to the pointer \c solution in the constructor for \c cppad_ipopt_nlp, is used to set output values (see documentation above). */ void cppad_ipopt_nlp::finalize_solution( Ipopt::SolverReturn status , Index n , const Number* x , const Number* z_L , const Number* z_U , Index m , const Number* g , const Number* lambda , Number obj_value , const Ipopt::IpoptData* ip_data , Ipopt::IpoptCalculatedQuantities* ip_cq ) { size_t i, j; CPPAD_ASSERT_UNKNOWN(size_t(n) == n_ ); CPPAD_ASSERT_UNKNOWN(size_t(m) == m_ ); switch(status) { // convert status from Ipopt enum to cppad_ipopt_solution enum case Ipopt::SUCCESS: solution_->status = cppad_ipopt_solution::success; break; case Ipopt::MAXITER_EXCEEDED: solution_->status = cppad_ipopt_solution::maxiter_exceeded; break; case Ipopt::STOP_AT_TINY_STEP: solution_->status = cppad_ipopt_solution::stop_at_tiny_step; break; case Ipopt::STOP_AT_ACCEPTABLE_POINT: solution_->status = cppad_ipopt_solution::stop_at_acceptable_point; break; case Ipopt::LOCAL_INFEASIBILITY: solution_->status = cppad_ipopt_solution::local_infeasibility; break; case Ipopt::USER_REQUESTED_STOP: solution_->status = cppad_ipopt_solution::user_requested_stop; break; case Ipopt::DIVERGING_ITERATES: solution_->status = cppad_ipopt_solution::diverging_iterates; break; case Ipopt::RESTORATION_FAILURE: solution_->status = cppad_ipopt_solution::restoration_failure; break; case Ipopt::ERROR_IN_STEP_COMPUTATION: solution_->status = cppad_ipopt_solution::error_in_step_computation; break; case Ipopt::INVALID_NUMBER_DETECTED: solution_->status = cppad_ipopt_solution::invalid_number_detected; break; case Ipopt::INTERNAL_ERROR: solution_->status = cppad_ipopt_solution::internal_error; break; default: solution_->status = cppad_ipopt_solution::unknown; } solution_->x.resize(n_); solution_->z_l.resize(n_); solution_->z_u.resize(n_); for(j = 0; j < n_; j++) { solution_->x[j] = x[j]; solution_->z_l[j] = z_L[j]; solution_->z_u[j] = z_U[j]; } solution_->g.resize(m_); solution_->lambda.resize(m_); for(i = 0; i < m_; i++) { solution_->g[i] = g[i]; solution_->lambda[i] = lambda[i]; } solution_->obj_value = obj_value; return; } // This routine is defined, but not yet used // (trying to figure out a problem with Ipopt-3.9.1 and dismod4). bool cppad_ipopt_nlp::intermediate_callback( Ipopt::AlgorithmMode mode, Index iter, Number obj_value, Number inf_pr, Number inf_du, Number mu, Number d_norm, Number regularization_size, Number alpha_du, Number alpha_pr, Index ls_trials, const Ipopt::IpoptData* ip_data, Ipopt::IpoptCalculatedQuantities* ip_cq ) { // std::cout << "intermediate_callback called" << std::endl; return true; } // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- cppad-20170000.3/cppad_ipopt/src/fun_record.hpp0000644000175200017650000000746113057470462020372 0ustar coincoin-web// $Id: fun_record.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_SRC_FUN_RECORD_HPP # define CPPAD_CPPAD_IPOPT_SRC_FUN_RECORD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "cppad_ipopt_nlp.hpp" // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /*! \{ \file fun_record.hpp \brief Records operation sequence for r_k (u) */ /*! Records operation sequence for \f$ r_k (u) \f$ at \f$u = [ J \circ n ] (x)\f$. \tparam NumVector is the type of the argumen \c x. It can either be Ipopt::Number* or CppAD::vector; i.e., NumberVector. \param fg_info Given a value \f$ u \in {\bf R}^{q[k]} \f$, \c fg_info returns the value \f$ r_k (u) \in {\bf R}^{p[k]} \f$. using the syntax \verbatim fg_info->eval_r(k, u); \endverbatim No other use is made of \c fg_info. \param k is a value less that \c K specifying the index value for \c k in the evaluation eval_r. \param p p[k] is dimension of the range space for \f$ r_k (u) \f$; i.e., \f$ r_k (u) \in {\bf R}^{p(k)} \f$. \param q q[k] is dimension of the domain space for \f$ r_k (u) \f$; i.e., \f$ u \in {\bf R}^{q(k)} \f$. \param n is the lenght of the vector \c x. \param x the length of \c x is equal to \c n and the point \f[ u = [ J \circ n ] (x) \f] is the point at which the operation sequence for \f$ r_k \f$ is recorded. \param J is a vector with lenght q[k] that projects from \f$ {\bf R}^n \f$ to \f$ {\bf R}^{q[k]} \f$ by selecting an ordered subset of the possible indices \f$ \{ 0 , \ldots , n-1 \} \f$. Hence, 0 <= J[j] < n for j = 0 , ... , q[k]-1. \param r_fun is the vector of AD function objects which has size size greater than \c k. Only the function object r_fun[k] is referenced. The input value of this function object does not matter. On output it is a recording of the function \f$ r_k (u) \f$ at the value of \f$ u \f$ specified by \c x and \c J. */ template void fun_record( cppad_ipopt_fg_info* fg_info , size_t k , const SizeVector& p , const SizeVector& q , size_t n , const NumVector& x , const SizeVector& J , CppAD::vector< CppAD::ADFun >& r_fun ) { size_t j; // extract u from x ADVector u(q[k]); for(j = 0; j < q[k]; j++) { // when NDEBUG is not defined, this error should be caught // during the cppad_ipopt_nlp constructor. CPPAD_ASSERT_UNKNOWN( J[j] < n ); u[j] = x[ J[j] ]; } // start the recording CppAD::Independent(u); // record the evaulation of r_k (u) ADVector r_k = fg_info->eval_r(k, u); CPPAD_ASSERT_KNOWN( r_k.size() == p[k] , "cppad_ipopt_nlp: eval_r return value size not equal to p[k]." ); // stop the recording and store operation sequence in r_fun[k].Dependent(u, r_k); } // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- # endif cppad-20170000.3/cppad_ipopt/src/CMakeLists.txt0000644000175200017650000000261213057470462020264 0ustar coincoin-web# $Id: CMakeLists.txt 3853 2016-12-14 14:40:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the cppad_ipopt/src library # Inherit build type from ../CMakeList.txt # add_library( [STATIC | SHARED | MODULE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN) # ) ADD_LIBRARY(cppad_ipopt cppad_ipopt_nlp.cpp hes_fg_map.cpp jac_g_map.cpp sparse_map2vec.cpp vec_fun_pattern.cpp ) # Add extra compiler flags add_cppad_cxx_flags( cppad_ipopt ) # install(FILES files... DESTINATION # [PERMISSIONS permissions...] # [CONFIGURATIONS [Debug|Release|...]] # [COMPONENT ] # [RENAME ] [OPTIONAL]) INSTALL(FILES cppad_ipopt_nlp.hpp DESTINATION ${cppad_abs_includedir}) # install(TARGETS myExe mySharedLib myStaticLib # RUNTIME DESTINATION bin # LIBRARY DESTINATION lib # ARCHIVE DESTINATION lib/static) INSTALL(TARGETS cppad_ipopt DESTINATION ${cppad_abs_libdir}) cppad-20170000.3/cppad_ipopt/src/hes_fg_map.hpp0000644000175200017650000000367313057470462020335 0ustar coincoin-web// $Id: hes_fg_map.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_SRC_HES_FG_MAP_HPP # define CPPAD_CPPAD_IPOPT_SRC_HES_FG_MAP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "cppad_ipopt_nlp.hpp" /*! \file hes_fg_map.hpp \brief Create a mapping between two representations for Hessian of fg. \ingroup hes_fg_map_cpp */ // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- extern void hes_fg_map( cppad_ipopt_fg_info* fg_info , size_t m , size_t n , size_t K , const CppAD::vector& L , const CppAD::vector& p , const CppAD::vector& q , const CppAD::vector& pattern_hes_r , CppAD::vector& I , CppAD::vector& J , CppAD::vector< std::map >& index_hes_fg ); // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- # endif cppad-20170000.3/cppad_ipopt/src/sparse_map2vec.hpp0000644000175200017650000000270513057470462021152 0ustar coincoin-web// $Id: sparse_map2vec.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_SRC_SPARSE_MAP2VEC_HPP # define CPPAD_CPPAD_IPOPT_SRC_SPARSE_MAP2VEC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /*! \file sparse_map2vec.hpp \brief Create a two vector sparsity representation from a vector of maps. \ingroup sparese_map2vec_cpp */ extern void sparse_map2vec( const CppAD::vector< std::map > sparse, size_t& n_nz , CppAD::vector& i_row , CppAD::vector& j_col ); // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- # endif cppad-20170000.3/cppad_ipopt/src/cppad_ipopt_nlp.hpp0000644000175200017650000010225313057470462021412 0ustar coincoin-web// $Id: cppad_ipopt_nlp.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_SRC_CPPAD_IPOPT_NLP_HPP # define CPPAD_CPPAD_IPOPT_SRC_CPPAD_IPOPT_NLP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_ipopt_nlp$$ $dollar @$$ $spell libipopt namespace dir cppad bool doesn't nan inf naninf std maxiter infeasibility obj const optimizer cppad_ipopt_nlp.hpp fg_info.eval retape CppAD $$ $section Nonlinear Programming Using the CppAD Interface to Ipopt$$ $mindex AD$$ $head Deprecated 2012-11-28$$ This interface to Ipopt is deprecated, use $cref ipopt_solve$$ instead. $head Syntax$$ $codei%# include "cppad_ipopt_nlp.hpp" %$$ $codei%cppad_ipopt_solution %solution%; %$$ $codei%cppad_ipopt_nlp %cppad_nlp%( %n%, %m%, %x_i%, %x_l%, %x_u%, %g_l%, %g_u%, &%fg_info%, &%solution% )%$$ $codei% export LD_LIBRARY_PATH=@LD_LIBRARY_PATH:%ipopt_library_paths%$$ $head Purpose$$ The class $code cppad_ipopt_nlp$$ is used to solve nonlinear programming problems of the form $latex \[ \begin{array}{rll} {\rm minimize} & f(x) \\ {\rm subject \; to} & g^l \leq g(x) \leq g^u \\ & x^l \leq x \leq x^u \end{array} \] $$ This is done using $href% http://www.coin-or.org/projects/Ipopt.xml% Ipopt %$$ optimizer and $href% http://www.coin-or.org/CppAD/% CppAD %$$ Algorithmic Differentiation package. $head cppad_ipopt namespace$$ All of the declarations for these routines are in the $code cppad_ipopt$$ namespace (not the $code CppAD$$ namespace). For example; $cref/SizeVector/cppad_ipopt_nlp/SizeVector/$$ below actually denotes the type $code cppad_ipopt::SizeVector$$. $head ipopt_library_paths$$ If you are linking to a shared version of the Ipopt library, you may have to add some paths the $code LD_LIBRARY_PATH$$ shell variable using the $code export$$ command in the syntax above. For example, if the file the ipopt library is $codei% %ipopt_prefix%/lib64/libipopt.a %$$ you will need to add the corresponding directory; e.g., $codei% export LD_LIBRARY_PATH="%ipopt_prefix%/lib64%:@LD_LIBRARY_PATH" %$$ see $cref ipopt_prefix$$. $head fg(x)$$ The function $latex fg : \B{R}^n \rightarrow \B{R}^{m+1}$$ is defined by $latex \[ \begin{array}{rcl} fg_0 (x) & = & f(x) \\ fg_1 (x) & = & g_0 (x) \\ & \vdots & \\ fg_m (x) & = & g_{m-1} (x) \end{array} \] $$ $subhead Index Vector$$ We define an $icode index vector$$ as a vector of non-negative integers for which none of the values are equal; i.e., it is both a vector and a set. If $latex I$$ is an index vector $latex |I|$$ is used to denote the number of elements in $latex I$$ and $latex \| I \|$$ is used to denote the value of the maximum element in $latex I$$. $subhead Projection$$ Given an index vector $latex J$$ and a positive integer $latex n$$ where $latex n > \| J \|$$, we use $latex J \otimes n $$ for the mapping $latex ( J \otimes n ) : \B{R}^n \rightarrow \B{R}^{|J|}$$ defined by $latex \[ [ J \otimes n ] (x)_j = x_{J(j)} \] $$ for $latex j = 0 , \ldots |J| - 1$$. $subhead Injection$$ Given an index vector $latex I$$ and a positive integer $latex m$$ where $latex m > \| I \|$$, we use $latex m \otimes I$$ for the mapping $latex ( m \otimes I ): \B{R}^{|I|} \rightarrow \B{R}^m$$ defined by $latex \[ [ m \otimes I ] (y)_i = \left\{ \begin{array}{ll} y_k & {\rm if} \; i = I(k) \; {\rm for \; some} \; k \in \{ 0 , \cdots, |I|-1 \} \\ 0 & {\rm otherwise} \end{array} \right. \] $$ $subhead Representation$$ In many applications, each of the component functions of $latex fg(x)$$ only depend on a few of the components of $latex x$$. In this case, expressing $latex fg(x)$$ in terms of simpler functions with fewer arguments can greatly reduce the amount of work required to compute its derivatives. $pre $$ We use the functions $latex r_k : \B{R}^{q(k)} \rightarrow \B{R}^{p(k)}$$ for $latex k = 0 , \ldots , K$$ to express our representation of $latex fg(x)$$ in terms of simpler functions as follows $latex \[ fg(x) = \sum_{k=0}^{K-1} \; \sum_{\ell=0}^{L(k) - 1} [ (m+1) \otimes I_{k,\ell} ] \; \circ \; r_k \; \circ \; [ J_{k,\ell} \otimes n ] \; (x) \] $$ where $latex \circ$$ represents function composition, for $latex k = 0 , \ldots , K - 1$$, and $latex \ell = 0 , \ldots , L(k)$$, $latex I_{k,\ell}$$ and $latex J_{k,\ell}$$ are index vectors with $latex | J_{k,\ell} | = q(k)$$, $latex \| J_{k,\ell} \| < n$$, $latex | I_{k,\ell} | = p(k)$$, and $latex \| I_{k,\ell} \| \leq m$$. $head Simple Representation$$ In the simple representation, $latex r_0 (x) = fg(x)$$, $latex K = 1$$, $latex q(0) = n$$, $latex p(0) = m+1$$, $latex L(0) = 1$$, $latex I_{0,0} = (0 , \ldots , m)$$, and $latex J_{0,0} = (0 , \ldots , n-1)$$. $head SizeVector$$ The type $codei SizeVector$$ is defined by the $codei cppad_ipopt_nlp.hpp$$ include file to be a $cref SimpleVector$$ class with elements of type $code size_t$$. $head NumberVector$$ The type $codei NumberVector$$ is defined by the $codei cppad_ipopt_nlp.hpp$$ include file to be a $cref SimpleVector$$ class with elements of type $code Ipopt::Number$$. $head ADNumber$$ The type $codei ADNumber$$ is defined by the $codei cppad_ipopt_nlp.hpp$$ include file to be a an AD type that can be used to compute derivatives. $head ADVector$$ The type $codei ADVector$$ is defined by the $codei cppad_ipopt_nlp.hpp$$ include file to be a $cref SimpleVector$$ class with elements of type $code ADNumber$$. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ It specifies the dimension of the argument space; i.e., $latex x \in \B{R}^n$$. $head m$$ The argument $icode m$$ has prototype $codei% size_t %m% %$$ It specifies the dimension of the range space for $latex g$$; i.e., $latex g : \B{R}^n \rightarrow \B{R}^m$$. $head x_i$$ The argument $icode x_i$$ has prototype $codei% const NumberVector& %x_i% %$$ and its size is equal to $latex n$$. It specifies the initial point where Ipopt starts the optimization process. $head x_l$$ The argument $icode x_l$$ has prototype $codei% const NumberVector& %x_l% %$$ and its size is equal to $latex n$$. It specifies the lower limits for the argument in the optimization problem; i.e., $latex x^l$$. $head x_u$$ The argument $icode x_u$$ has prototype $codei% const NumberVector& %x_u% %$$ and its size is equal to $latex n$$. It specifies the upper limits for the argument in the optimization problem; i.e., $latex x^u$$. $head g_l$$ The argument $icode g_l$$ has prototype $codei% const NumberVector& %g_l% %$$ and its size is equal to $latex m$$. It specifies the lower limits for the constraints in the optimization problem; i.e., $latex g^l$$. $head g_u$$ The argument $icode g_u$$ has prototype $codei% const NumberVector& %g_u% %$$ and its size is equal to $latex n$$. It specifies the upper limits for the constraints in the optimization problem; i.e., $latex g^u$$. $head fg_info$$ The argument $icode fg_info$$ has prototype $codei% %FG_info fg_info% %$$ where the class $icode FG_info$$ is derived from the base class $code cppad_ipopt_fg_info$$. Certain virtual member functions of $icode fg_info$$ are used to compute the value of $latex fg(x)$$. The specifications for these member functions are given below: $subhead fg_info.number_functions$$ This member function has prototype $codei% virtual size_t cppad_ipopt_fg_info::number_functions(void) %$$ If $icode K$$ has type $code size_t$$, the syntax $codei% %K% = %fg_info%.number_functions() %$$ sets $icode K$$ to the number of functions used in the representation of $latex fg(x)$$; i.e., $latex K$$ in the $cref/representation/cppad_ipopt_nlp/fg(x)/Representation/$$ above. $pre $$ The $code cppad_ipopt_fg_info$$ implementation of this function corresponds to the simple representation mentioned above; i.e. $icode%K% = 1%$$. $subhead fg_info.eval_r$$ This member function has the prototype $codei% virtual ADVector cppad_ipopt_fg_info::eval_r(size_t %k%, const ADVector& %u%) = 0; %$$ Thus it is a pure virtual function and must be defined in the derived class $icode FG_info$$. $pre $$ This function computes the value of $latex r_k (u)$$ used in the $cref/representation/cppad_ipopt_nlp/fg(x)/Representation/$$ for $latex fg(x)$$. If $icode k$$ in $latex \{0 , \ldots , K-1 \}$$ has type $code size_t$$, $icode u$$ is an $code ADVector$$ of size $icode q(k)$$ and $icode r$$ is an $code ADVector$$ of size $icode p(k)$$ the syntax $codei% %r% = %fg_info%.eval_r(%k%, %u%) %$$ set $icode r$$ to the vector $latex r_k (u)$$. $subhead fg_info.retape$$ This member function has the prototype $codei% virtual bool cppad_ipopt_fg_info::retape(size_t %k%) %$$ If $icode k$$ in $latex \{0 , \ldots , K-1 \}$$ has type $code size_t$$, and $icode retape$$ has type $code bool$$, the syntax $codei% %retape% = %fg_info%.retape(%k%) %$$ sets $icode retape$$ to true or false. If $icode retape$$ is true, $code cppad_ipopt_nlp$$ will retape the operation sequence corresponding to $latex r_k (u)$$ for every value of $icode u$$. An $code cppad_ipopt_nlp$$ object should use much less memory and run faster if $icode retape$$ is false. You can test both the true and false cases to make sure the operation sequence does not depend on $icode u$$. $pre $$ The $code cppad_ipopt_fg_info$$ implementation of this function sets $icode retape$$ to true (while slower it is also safer to always retape). $subhead fg_info.domain_size$$ This member function has prototype $codei% virtual size_t cppad_ipopt_fg_info::domain_size(size_t %k%) %$$ If $icode k$$ in $latex \{0 , \ldots , K-1 \}$$ has type $code size_t$$, and $icode q$$ has type $code size_t$$, the syntax $codei% %q% = %fg_info%.domain_size(%k%) %$$ sets $icode q$$ to the dimension of the domain space for $latex r_k (u)$$; i.e., $latex q(k)$$ in the $cref/representation/cppad_ipopt_nlp/fg(x)/Representation/$$ above. $pre $$ The $code cppad_ipopt_h_base$$ implementation of this function corresponds to the simple representation mentioned above; i.e., $latex q = n$$. $subhead fg_info.range_size$$ This member function has prototype $codei% virtual size_t cppad_ipopt_fg_info::range_size(size_t %k%) %$$ If $icode k$$ in $latex \{0 , \ldots , K-1 \}$$ has type $code size_t$$, and $icode p$$ has type $code size_t$$, the syntax $codei% %p% = %fg_info%.range_size(%k%) %$$ sets $icode p$$ to the dimension of the range space for $latex r_k (u)$$; i.e., $latex p(k)$$ in the $cref/representation/cppad_ipopt_nlp/fg(x)/Representation/$$ above. $pre $$ The $code cppad_ipopt_h_base$$ implementation of this function corresponds to the simple representation mentioned above; i.e., $latex p = m+1$$. $subhead fg_info.number_terms$$ This member function has prototype $codei% virtual size_t cppad_ipopt_fg_info::number_terms(size_t %k%) %$$ If $icode k$$ in $latex \{0 , \ldots , K-1 \}$$ has type $code size_t$$, and $icode L$$ has type $code size_t$$, the syntax $codei% %L% = %fg_info%.number_terms(%k%) %$$ sets $icode L$$ to the number of terms in representation for this value of $icode k$$; i.e., $latex L(k)$$ in the $cref/representation/cppad_ipopt_nlp/fg(x)/Representation/$$ above. $pre $$ The $code cppad_ipopt_h_base$$ implementation of this function corresponds to the simple representation mentioned above; i.e., $latex L = 1$$. $subhead fg_info.index$$ This member function has prototype $codei% virtual void cppad_ipopt_fg_info::index( size_t %k%, size_t %ell%, SizeVector& %I%, SizeVector& %J% ) %$$ The argument $icode% k %$$ has type $codei size_t$$ and is a value between zero and $latex K-1$$ inclusive. The argument $icode% ell %$$ has type $codei size_t$$ and is a value between zero and $latex L(k)-1$$ inclusive. The argument $icode% I %$$ is a $cref SimpleVector$$ with elements of type $code size_t$$ and size greater than or equal to $latex p(k)$$. The input value of the elements of $icode I$$ does not matter. The output value of the first $latex p(k)$$ elements of $icode I$$ must be the corresponding elements of $latex I_{k,ell}$$ in the $cref/representation/cppad_ipopt_nlp/fg(x)/Representation/$$ above. The argument $icode% J %$$ is a $cref SimpleVector$$ with elements of type $code size_t$$ and size greater than or equal to $latex q(k)$$. The input value of the elements of $icode J$$ does not matter. The output value of the first $latex q(k)$$ elements of $icode J$$ must be the corresponding elements of $latex J_{k,ell}$$ in the $cref/representation/cppad_ipopt_nlp/fg(x)/Representation/$$ above. $pre $$ The $code cppad_ipopt_h_base$$ implementation of this function corresponds to the simple representation mentioned above; i.e., for $latex i = 0 , \ldots , m$$, $icode%I%[%i%] = %i%$$, and for $latex j = 0 , \ldots , n-1$$, $icode%J%[%j%] = %j%$$. $head solution$$ After the optimization process is completed, $icode solution$$ contains the following information: $subhead status$$ The $icode status$$ field of $icode solution$$ has prototype $codei% cppad_ipopt_solution::solution_status %solution%.status %$$ It is the final Ipopt status for the optimizer. Here is a list of the possible values for the status: $table $icode status$$ $cnext Meaning $rnext not_defined $cnext The optimizer did not return a final status to this $code cppad_ipopt_nlp$$ object. $rnext unknown $cnext The status returned by the optimizer is not defined in the Ipopt documentation for $code finalize_solution$$. $rnext success $cnext Algorithm terminated successfully at a point satisfying the convergence tolerances (see Ipopt options). $rnext maxiter_exceeded $cnext The maximum number of iterations was exceeded (see Ipopt options). $rnext stop_at_tiny_step $cnext Algorithm terminated because progress was very slow. $rnext stop_at_acceptable_point $cnext Algorithm stopped at a point that was converged, not to the 'desired' tolerances, but to 'acceptable' tolerances (see Ipopt options). $rnext local_infeasibility $cnext Algorithm converged to a non-feasible point (problem may have no solution). $rnext user_requested_stop $cnext This return value should not happen. $rnext diverging_iterates $cnext It the iterates are diverging. $rnext restoration_failure $cnext Restoration phase failed, algorithm doesn't know how to proceed. $rnext error_in_step_computation $cnext An unrecoverable error occurred while Ipopt tried to compute the search direction. $rnext invalid_number_detected $cnext Algorithm received an invalid number (such as $code nan$$ or $code inf$$) from the users function $icode%fg_info%.eval%$$ or from the CppAD evaluations of its derivatives (see the Ipopt option $code check_derivatives_for_naninf$$). $rnext internal_error $cnext An unknown Ipopt internal error occurred. Contact the Ipopt authors through the mailing list. $tend $subhead x$$ The $code x$$ field of $icode solution$$ has prototype $codei% NumberVector %solution%.x %$$ and its size is equal to $latex n$$. It is the final $latex x$$ value for the optimizer. $subhead z_l$$ The $code z_l$$ field of $icode solution$$ has prototype $codei% NumberVector %solution%.z_l %$$ and its size is equal to $latex n$$. It is the final Lagrange multipliers for the lower bounds on $latex x$$. $subhead z_u$$ The $code z_u$$ field of $icode solution$$ has prototype $codei% NumberVector %solution%.z_u %$$ and its size is equal to $latex n$$. It is the final Lagrange multipliers for the upper bounds on $latex x$$. $subhead g$$ The $code g$$ field of $icode solution$$ has prototype $codei% NumberVector %solution%.g %$$ and its size is equal to $latex m$$. It is the final value for the constraint function $latex g(x)$$. $subhead lambda$$ The $code lambda$$ field of $icode solution$$ has prototype $codei% NumberVector %solution%.lambda %$$ and its size is equal to $latex m$$. It is the final value for the Lagrange multipliers corresponding to the constraint function. $subhead obj_value$$ The $code obj_value$$ field of $icode solution$$ has prototype $codei% Number %solution%.obj_value %$$ It is the final value of the objective function $latex f(x)$$. $children% cppad_ipopt/example/get_started.cpp% cppad_ipopt/example/ode1.omh% cppad_ipopt/speed/ode_speed.cpp %$$ $head Example$$ The file $cref ipopt_nlp_get_started.cpp$$ is an example and test of $code cppad_ipopt_nlp$$ that uses the $cref/simple representation/cppad_ipopt_nlp/Simple Representation/$$. It returns true if it succeeds and false otherwise. The section $cref ipopt_nlp_ode$$ discusses an example that uses a more complex representation. $head Wish List$$ This is a list of possible future improvements to $code cppad_ipopt_nlp$$ that would require changed to the user interface: $list number$$ The routine $codei%fg_info.eval_r(%k%, %u%)%$$ should also support $codei NumberVector$$ for the type of the argument $code u$$ (this would certainly be more efficient when $codei%fg_info.retape(%k%)%$$ is true and $latex L(k) > 1$$). It could be an option for the user to provide this as well as the necessary $code ADVector$$ definition. $lnext There should a $cref Discrete$$ routine that the user can call to determine the value of $latex \ell$$ during the evaluation of $codei%fg_info.eval_r(%k%, %u%)%$$. This way data, which does not affect the derivative values, can be included in the function recording and evaluation. $lend $end ----------------------------------------------------------------------------- */ # include # include # include /*! \file cppad_ipopt_nlp.hpp \brief CppAD interface to Ipopt \ingroup cppad_ipopt_nlp_cpp */ // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /// A scalar value used to record operation sequence. typedef CppAD::AD ADNumber; /// A simple vector of values used to record operation sequence typedef CppAD::vector ADVector; /// A simple vector of size_t values. typedef CppAD::vector SizeVector; /// A simple vector of values used by Ipopt typedef CppAD::vector NumberVector; /*! Abstract base class user derives from to define the funcitons in the problem. */ class cppad_ipopt_fg_info { /// allow cppad_ipopt_nlp class complete access to this class friend class cppad_ipopt_nlp; private: /// domain space dimension for the functions f(x), g(x) size_t n_; /// range space dimension for the function g(x) size_t m_; /// the cppad_ipopt_nlp constructor uses this method to set n_ void set_n(size_t n) { n_ = n; } /// the cppad_ipopt_nlp constructor uses this method to set m_ void set_m(size_t m) { m_ = m; } public: /// destructor virtual so user derived class destructor gets called virtual ~cppad_ipopt_fg_info(void) { } /// number_functions; i.e. K (simple representation uses 1) virtual size_t number_functions(void) { return 1; } /// function that evaluates the users representation for f(x) and /// and g(x) is pure virtual so user must define it in derived class virtual ADVector eval_r(size_t k, const ADVector& u) = 0; /// should the function r_k (u) be retaped when ever the arguemnt /// u changes (default is true which is safe but slow) virtual bool retape(size_t k) { return true; } /// domain_size q[k] for r_k (u) (simple representation uses n) virtual size_t domain_size(size_t k) { return n_; } /// range_size p[k] for r_k (u) (simple representation uses m+1) virtual size_t range_size(size_t k) { return m_ + 1; } /// number_terms that use r_k (u) (simple represenation uses 1) virtual size_t number_terms(size_t k) { return 1; } /// return the index vectors I_{k,ell} and J_{k,ell} /// (simple representation uses I[i] = i and J[j] = j) virtual void index(size_t k, size_t ell, SizeVector& I, SizeVector& J) { assert( I.size() >= m_ + 1 ); assert( J.size() >= n_ ); for(size_t i = 0; i <= m_; i++) I[i] = i; for(size_t j = 0; j < n_; j++) J[j] = j; } }; /*! Class that contains information about the problem solution \section Nonlinear_Programming_Problem Nonlinear Programming Problem We are give smooth functions \f$ f : {\bf R}^n \rightarrow {\bf R} \f$ and \f$ g : {\bf R}^n \rightarrow {\bf R}^m \f$ and wish to solve the problem \f[ \begin{array}{rcl} {\rm minimize} & f(x) & {\rm w.r.t.} \; x \in {\bf R}^n \\ {\rm subject \; to} & g^l \leq g(x) \leq g^u \\ & x^l \leq x \leq x^u \end{array} \f] \section Users_Representation Users Representation The functions \f$ f : {\bf R}^n \rightarrow {\bf R} \f$ and \f$ g : {\bf R}^n \rightarrow {\bf R}^m \f$ are defined by \f[ \left( \begin{array}{c} f(x) \\ g(x) \end{array} \right) = \sum_{k=0}^{K-1} \; \sum_{\ell=0}^{L(k) - 1} [ (m+1) \otimes I_{k,\ell} ] \; \circ \; r_k \; \circ \; [ J_{k,\ell} \otimes n ] \; (x) \f] where for \f$ k = 0 , \ldots , K-1\f$, \f$ r_k : {\bf R}^{q(k)} \rightarrow {\bf R}^{p(k)} \f$. \section Deprecated_Evaluation_Methods Evaluation Methods The set of evaluation methods for this class is \verbatim { eval_f, eval_grad_f, eval_g, eval_jac_g, eval_h } \endverbatim Note that the \c bool return flag for the evaluations methods does not appear in the Ipopt documentation. Looking at the code, it seems to be a flag telling Ipopt to abort when the flag is false. */ class cppad_ipopt_solution { public: /// possible values for he solution status enum solution_status { not_defined, success, maxiter_exceeded, stop_at_tiny_step, stop_at_acceptable_point, local_infeasibility, user_requested_stop, feasible_point_found, diverging_iterates, restoration_failure, error_in_step_computation, invalid_number_detected, too_few_degrees_of_freedom, internal_error, unknown } status; /// the approximation solution NumberVector x; /// Lagrange multipliers corresponding to lower bounds on x NumberVector z_l; /// Lagrange multipliers corresponding to upper bounds on x NumberVector z_u; /// value of g(x) NumberVector g; /// Lagrange multipliers correspondiing constraints on g(x) NumberVector lambda; /// value of f(x) Ipopt::Number obj_value; /// constructor initializes solution status as not yet defined cppad_ipopt_solution(void) { status = not_defined; } }; /*! Class connects Ipopt to CppAD for derivative and sparsity pattern calculations. */ class cppad_ipopt_nlp : public Ipopt::TNLP { private: /// A Scalar value used by Ipopt typedef Ipopt::Number Number; /// An index value used by Ipopt typedef Ipopt::Index Index; /// Indexing style used in Ipopt sparsity structure typedef Ipopt::TNLP::IndexStyleEnum IndexStyleEnum; /// A simple vector of boolean values typedef CppAD::vectorBool BoolVector; /// A simple vector of AD function objects typedef CppAD::vector< CppAD::ADFun > ADFunVector; /// A simple vector of simple vectors of boolean values typedef CppAD::vector BoolVectorVector; /// A mapping that is dense in i, sparse in j, and maps (i, j) /// to the corresponding sparsity index in Ipopt. typedef CppAD::vector< std::map > IndexMap; // ------------------------------------------------------------------ // Values directly passed in to constuctor // ------------------------------------------------------------------ /// dimension of the domain space for f(x) and g(x) /// (passed to ctor) const size_t n_; /// dimension of the range space for g(x) /// (passed to ctor) const size_t m_; /// dimension of the range space for g(x) /// (passed to ctor) const NumberVector x_i_; /// lower limit for x /// (size n_), (passed to ctor) const NumberVector x_l_; /// upper limit for x /// (size n_) (passed to ctor) const NumberVector x_u_; /// lower limit for g(x) /// (size m_) (passed to ctor) const NumberVector g_l_; /// upper limit for g(x) /// (size m_) (passed to ctor) const NumberVector g_u_; /// pointer to base class version of derived class object used to get /// information about the user's representation for f(x) and g(x) /// (passed to ctor) cppad_ipopt_fg_info* const fg_info_; /// pointer to object where final results are stored /// (passed to ctor) cppad_ipopt_solution* const solution_; /// plus infinity as a value of type Number const Number infinity_; // ------------------------------------------------------------------ // Effectively const values determined during constructor using calls // to fg_info: // ------------------------------------------------------------------ /// The value of \f$ K \f$ in the representation. /// (effectively const) size_t K_; /// Does operation sequence for \f$ r_k (u) \f$ depend on \f$ u \f$. /// (size K_) (effectively const) BoolVector retape_; /// q_[k] is the domain space dimension for \f$ r_k (u) \f$ /// (size K_) (effectively const) SizeVector q_; /// p_[k] is the range space dimension for \f$ r_k (u) \f$ /// (size K_) (effectively const) SizeVector p_; /// L_[k] is number of times \f$ r_k (u) \f$ appears in /// the representation summation /// (size K_) (effectively const) SizeVector L_; // ------------------------------------------------------------------- // Other effectively const values determined by the constructor: // ------------------------------------------------------------------- /*! CppAD sparsity patterns for \f$ \{ r_k^{(1)} (u) \} \f$ (set by ctor). For k = 0 , ... , K_-1, pattern_jac_r_[k] is a CppAD sparsity pattern for the Jacobian of \f$ r_k (u) \f$ and as such it has size p_[k]*q_[k]. (effectively const) */ BoolVectorVector pattern_jac_r_; /*! CppAD sparsity patterns for \f$ \{ r_k^{(2)} (u) \} \f$ (set by ctor). For k = 0 , ... , K_-1, pattern_jac_r_[k] is a CppAD sparsity pattern for the Hessian of \f[ R(u) = \sum_{i=0}^{p[k]-1} r_k (u)_i \f] and as such it has size q_[k]*q_[k]. (effectively const) */ BoolVectorVector pattern_hes_r_; /// number non-zero is Ipopt sparsity structor for Jacobian of g(x) /// (effectively const) size_t nnz_jac_g_; /// row indices in Ipopt sparsity structor for Jacobian of g(x) /// (effectively const) SizeVector iRow_jac_g_; /// column indices in Ipopt sparsity structor for Jacobian of g(x) /// (effectively const) SizeVector jCol_jac_g_; /// number non-zero is Ipopt sparsity structor for Hessian of Lagragian /// (effectively const) size_t nnz_h_lag_; /// row indices in Ipopt sparsity structor for Hessian of Lagragian /// (effectively const) SizeVector iRow_h_lag_; /// column indices in Ipopt sparsity structor for Hessian of Lagragian /// (effectively const) SizeVector jCol_h_lag_; /*! Mapping from (i, j) in Jacobian of g(x) to Ipopt sparsity structure For i = 0 , ... , m_-1, index_jac_g_[i] is a standard map from column index values \c j to the corresponding index in the Ipopt sparsity structure for the Jacobian of g(x). */ IndexMap index_jac_g_; /*! Mapping from (i, j) in Hessian of fg(x) to Ipopt sparsity structure For i = 0 , ... , n_-1, index_hes_fg_[i] is a standard map from column index values \c j to the corresponding index in the Ipopt sparsity structure for the Hessian of the Lagragian. */ IndexMap index_hes_fg_; // ----------------------------------------------------------------- // Values that are changed by routine other than the constructor: // ----------------------------------------------------------------- /// For k = 0 , ... , K_-1, r_fun_[k] /// is a the CppAD function object corresponding to \f$ r_k (u) \f$. ADFunVector r_fun_; /*! Is r_fun[k] OK for current x. For k = 0 , ... , K_-1, tape_ok_[k] is true if current operations sequence in r_fun_[k] OK for this value of \f$ x \f$. Note that \f$ u = [ J_{k,\ell} \otimes n ] (x) \f$ may depend on the value of \f$ \ell \f$. */ BoolVector tape_ok_; /// work space of size equal maximum of q[k] w.r.t \c k. SizeVector J_; /// work space of size equal maximum of p[k] w.r.t \c k. SizeVector I_; // ------------------------------------------------------------ // Private Methods // ------------------------------------------------------------ /// block the default constructor from use cppad_ipopt_nlp(const cppad_ipopt_nlp&); /// blocks the assignment operator from use cppad_ipopt_nlp& operator=(const cppad_ipopt_nlp&); public: // ---------------------------------------------------------------- // See cppad_ipopt_nlp.cpp for doxygen documentation of these methods // ---------------------------------------------------------------- /// only constructor for cppad_ipopot_nlp cppad_ipopt_nlp( size_t n , size_t m , const NumberVector &x_i , const NumberVector &x_l , const NumberVector &x_u , const NumberVector &g_l , const NumberVector &g_u , cppad_ipopt_fg_info* fg_info , cppad_ipopt_solution* solution ); // use virtual so that derived class destructor gets called. virtual ~cppad_ipopt_nlp(); // return info about the nlp virtual bool get_nlp_info( Index& n , Index& m , Index& nnz_jac_g , Index& nnz_h_lag , IndexStyleEnum& index_style ); // return bounds for my problem virtual bool get_bounds_info( Index n , Number* x_l , Number* x_u , Index m , Number* g_l , Number* g_u ); // return the starting point for the algorithm virtual bool get_starting_point( Index n , bool init_x , Number* x , bool init_z , Number* z_L , Number* z_U , Index m , bool init_lambda , Number* lambda ); // return the objective value virtual bool eval_f( Index n , const Number* x , bool new_x , Number& obj_value ); // Method to return the gradient of the objective virtual bool eval_grad_f( Index n , const Number* x , bool new_x , Number* grad_f ); // return the constraint residuals virtual bool eval_g( Index n , const Number* x , bool new_x , Index m , Number* g ); // Method to return: // 1) The structure of the jacobian (if "values" is NULL) // 2) The values of the jacobian (if "values" is not NULL) virtual bool eval_jac_g( Index n , const Number* x , bool new_x , Index m , Index nele_jac , Index* iRow , Index* jCol , Number* values ); // Method to return: // 1) structure of hessian of the lagrangian (if "values" is NULL) // 2) values of hessian of the lagrangian (if "values" is not NULL) virtual bool eval_h( Index n , const Number* x , bool new_x , Number obj_factor , Index m , const Number* lambda , bool new_lambda , Index nele_hess , Index* iRow , Index* jCol , Number* values ); // called when the algorithm is completed so the TNLP can // store/write the solution virtual void finalize_solution( Ipopt::SolverReturn status , Index n , const Number* x , const Number* z_L , const Number* z_U , Index m , const Number* g , const Number* lambda , Number obj_value , const Ipopt::IpoptData* ip_data , Ipopt::IpoptCalculatedQuantities* ip_cq ); virtual bool intermediate_callback( Ipopt::AlgorithmMode mode, Index iter, Number obj_value, Number inf_pr, Number inf_du, Number mu, Number d_norm, Number regularization_size, Number alpha_du, Number alpha_pr, Index ls_trials, const Ipopt::IpoptData* ip_data, Ipopt::IpoptCalculatedQuantities* ip_cq ); }; // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- # endif cppad-20170000.3/cppad_ipopt/src/jac_g_map.cpp0000644000175200017650000001336013057470462020132 0ustar coincoin-web// $Id: jac_g_map.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "cppad_ipopt_nlp.hpp" # include "jac_g_map.hpp" // --------------------------------------------------------------------------- namespace cppad_ipopt { // --------------------------------------------------------------------------- /*! \{ \file jac_g_map.cpp \brief Creates a mapping between two representations for Jacobian of g. */ /*! Create mapping from CppAD to Ipopt sparse representations of Jacobian of g. The functions \f$ f : {\bf R}^n \rightarrow {\bf R} \f$ and \f$ g : {\bf R}^n \rightarrow {\bf R}^m \f$ are defined by the \ref Users_Representation. \param fg_info For k = 0 , ... , K-1, for ell = 0 , ... , L[k], the function call \verbatim fg_info->index(k, ell, I, J); \endverbatim is made by \c jac_g_map. The values \c k and \c ell are inputs. The input size of \c I ( \c J ) is greater than or equal p[k] ( q[k] ) and this size is not changed. The input values of the elements of \c I and \c J are not specified. The output value of the elements of \c I define \f[ I_{k, \ell} = ( {\rm I[0]} , \cdots , {\rm I[p[k]-1]} ) \f] The output value of the elements of \c J define \f[ J_{k, \ell} = ( {\rm J[0]} , \cdots , {\rm J[q[k]-1]} ) \f] \param m is the dimension of the range space for \f$ g(x) \f$; i.e., \f$ g(x) \in {\bf R}^m \f$. \param n is the dimension of the domain space for \f$ f(x) \f$ and \f$ g(x) \f$; i.e., \f$ x \in {\bf R}^n \f$. \param K is the number of functions \f$ r_k ( u ) \f$ used for the representation of \f$ f(x) \f$ and \f$ g(x) \f$. \param L is a vector with size \c K. For k = 0 , ... , K-1, L[k] is the number of terms that use \f$ r_k (u) \f$ in the representation of \f$ f(x) \f$ and \f$ g(x) \f$. \param p is a vector with size \c K. For k = 0 , ... , K-1, p[k] is dimension of the range space for \f$ r_k (u) \f$; i.e., \f$ r_k (u) \in {\bf R}^{p(k)} \f$. \param q is a vector with size \c K. For k = 0 , ... , K-1, q[k] is dimension of the domain space for \f$ r_k (u) \f$; i.e., \f$ u \in {\bf R}^{q(k)} \f$. \param pattern_jac_r is a vector with size \c K. For k = 0 , ... , K-1, pattern_jac_r[k] is a CppAD sparsity pattern for the Jacobian of the function \f$ r_k : {\bf R}^{q(k)} \rightarrow {\bf R}^{p(k)} \f$. As such, pattern_jac_r[k].size() == p[k] * q[k]. \param I is a work vector of length greater than or equal p[k] for all \c k. The input and output value of its elements are unspecified. The size of \c I is not changed. \param J is a work vector of length greater than or equal q[k] for all \c k. The input and output value of its elements are unspecified. The size of \c J is not changed. \param index_jac_g: On input, this is empty; i.e., index_jac_g.size() == 0. On output, it is the index mapping from \f$ (i, j) \f$ in the Jacobian of \f$ g(x) \f$ to the corresponding index value used by Ipopt to represent the Jacobian. Furthermore, if index_jac_g[i].find(j) == index_jac_g[i].end(), then the \f$ (i, j)\f$ entry in the Jacobian of \f$ g(x) \f$ is always zero. */ void jac_g_map( cppad_ipopt_fg_info* fg_info , size_t m , size_t n , size_t K , const CppAD::vector& L , const CppAD::vector& p , const CppAD::vector& q , const CppAD::vector& pattern_jac_r , CppAD::vector& I , CppAD::vector& J , CppAD::vector< std::map >& index_jac_g ) { using CppAD::vectorBool; size_t i, j, ij, k, ell; CPPAD_ASSERT_UNKNOWN( K == L.size() ); CPPAD_ASSERT_UNKNOWN( K == p.size() ); CPPAD_ASSERT_UNKNOWN( K == q.size() ); CPPAD_ASSERT_UNKNOWN( K == pattern_jac_r.size() ); # ifndef NDEBUG for(k = 0; k < K; k++) { CPPAD_ASSERT_UNKNOWN( p[k] <= I.size() ); CPPAD_ASSERT_UNKNOWN( q[k] <= J.size() ); CPPAD_ASSERT_UNKNOWN( p[k]*q[k] == pattern_jac_r[k].size() ); } # endif // Now compute pattern for g // (use standard set representation because can be huge). CppAD::vector< std::set > pattern_jac_g(m); for(k = 0; k < K; k++) for(ell = 0; ell < L[k]; ell++) { fg_info->index(k, ell, I, J); for(i = 0; i < p[k]; i++) if( I[i] != 0 ) { for(j = 0; j < q[k]; j++) { ij = i * q[k] + j; if( pattern_jac_r[k][ij] ) pattern_jac_g[I[i]-1].insert(J[j]); } } } // Now compute the mapping from (i, j) in the Jacobian of g to the // corresponding index value used by Ipopt to represent the Jacobian. CPPAD_ASSERT_UNKNOWN( index_jac_g.size() == 0 ); index_jac_g.resize(m); std::set::const_iterator itr; ell = 0; for(i = 0; i < m; i++) { for( itr = pattern_jac_g[i].begin(); itr != pattern_jac_g[i].end(); itr++) { index_jac_g[i][*itr] = ell++; } } return; } // --------------------------------------------------------------------------- } // end namespace cppad_ipopt // --------------------------------------------------------------------------- cppad-20170000.3/cppad_ipopt/src/makefile.in0000644000175200017650000005547713057470462017652 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; the Free Software Foundation # gives unlimited permission to copy and/or distribute it, # with or without modifications, as long as this notice is preserved. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY, to the extent permitted by law; without # even the implied warranty of MERCHANTABILITY or FITNESS FOR A # PARTICULAR PURPOSE. @SET_MAKE@ VPATH = @srcdir@ am__is_gnu_make = { \ if test -z '$(MAKELEVEL)'; then \ false; \ elif test -n '$(MAKE_HOST)'; then \ true; \ elif test -n '$(MAKE_VERSION)' && test -n '$(CURDIR)'; then \ true; \ else \ false; \ fi; \ } am__make_running_with_option = \ case $${target_option-} in \ ?) ;; \ *) echo "am__make_running_with_option: internal error: invalid" \ "target option '$${target_option-}' specified" >&2; \ exit 1;; \ esac; \ has_opt=no; \ sane_makeflags=$$MAKEFLAGS; \ if $(am__is_gnu_make); then \ sane_makeflags=$$MFLAGS; \ else \ case $$MAKEFLAGS in \ *\\[\ \ ]*) \ bs=\\; \ sane_makeflags=`printf '%s\n' "$$MAKEFLAGS" \ | sed "s/$$bs$$bs[$$bs $$bs ]*//g"`;; \ esac; \ fi; \ skip_next=no; \ strip_trailopt () \ { \ flg=`printf '%s\n' "$$flg" | sed "s/$$1.*$$//"`; \ }; \ for flg in $$sane_makeflags; do \ test $$skip_next = yes && { skip_next=no; continue; }; \ case $$flg in \ *=*|--*) continue;; \ -*I) strip_trailopt 'I'; skip_next=yes;; \ -*I?*) strip_trailopt 'I';; \ -*O) strip_trailopt 'O'; skip_next=yes;; \ -*O?*) strip_trailopt 'O';; \ -*l) strip_trailopt 'l'; skip_next=yes;; \ -*l?*) strip_trailopt 'l';; \ -[dEDm]) skip_next=yes;; \ -[JT]) skip_next=yes;; \ esac; \ case $$flg in \ *$$target_option*) has_opt=yes; break;; \ esac; \ done; \ test $$has_opt = yes am__make_dryrun = (target_option=n; $(am__make_running_with_option)) am__make_keepgoing = (target_option=k; $(am__make_running_with_option)) pkgdatadir = $(datadir)/@PACKAGE@ pkgincludedir = $(includedir)/@PACKAGE@ pkglibdir = $(libdir)/@PACKAGE@ pkglibexecdir = $(libexecdir)/@PACKAGE@ am__cd = CDPATH="$${ZSH_VERSION+.}$(PATH_SEPARATOR)" && cd install_sh_DATA = $(install_sh) -c -m 644 install_sh_PROGRAM = $(install_sh) -c install_sh_SCRIPT = $(install_sh) -c INSTALL_HEADER = $(INSTALL_DATA) transform = $(program_transform_name) NORMAL_INSTALL = : PRE_INSTALL = : POST_INSTALL = : NORMAL_UNINSTALL = : PRE_UNINSTALL = : POST_UNINSTALL = : build_triplet = @build@ host_triplet = @host@ subdir = cppad_ipopt/src ACLOCAL_M4 = $(top_srcdir)/aclocal.m4 am__aclocal_m4_deps = $(top_srcdir)/configure.ac am__configure_deps = $(am__aclocal_m4_deps) $(CONFIGURE_DEPENDENCIES) \ $(ACLOCAL_M4) DIST_COMMON = $(srcdir)/makefile.am $(am__DIST_COMMON) mkinstalldirs = $(install_sh) -d CONFIG_CLEAN_FILES = CONFIG_CLEAN_VPATH_FILES = am__vpath_adj_setup = srcdirstrip=`echo "$(srcdir)" | sed 's|.|.|g'`; am__vpath_adj = case $$p in \ $(srcdir)/*) f=`echo "$$p" | sed "s|^$$srcdirstrip/||"`;; \ *) f=$$p;; \ esac; am__strip_dir = f=`echo $$p | sed -e 's|^.*/||'`; am__install_max = 40 am__nobase_strip_setup = \ srcdirstrip=`echo "$(srcdir)" | sed 's/[].[^$$\\*|]/\\\\&/g'` am__nobase_strip = \ for p in $$list; do echo "$$p"; done | sed -e "s|$$srcdirstrip/||" am__nobase_list = $(am__nobase_strip_setup); \ for p in $$list; do echo "$$p $$p"; done | \ sed "s| $$srcdirstrip/| |;"' / .*\//!s/ .*/ ./; s,\( .*\)/[^/]*$$,\1,' | \ $(AWK) 'BEGIN { files["."] = "" } { files[$$2] = files[$$2] " " $$1; \ if (++n[$$2] == $(am__install_max)) \ { print $$2, files[$$2]; n[$$2] = 0; files[$$2] = "" } } \ END { for (dir in files) print dir, files[dir] }' am__base_list = \ sed '$$!N;$$!N;$$!N;$$!N;$$!N;$$!N;$$!N;s/\n/ /g' | \ sed '$$!N;$$!N;$$!N;$$!N;s/\n/ /g' am__uninstall_files_from_dir = { \ test -z "$$files" \ || { test ! 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Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- export LD_LIBRARY_PATH=@CPPAD_IPOPT_LD_PATH@ ./example cppad-20170000.3/cppad_ipopt/example/ode_simple_check.cpp0000644000175200017650000000204213057470462022346 0ustar coincoin-web// $Id: ode_simple_check.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "ode_run.hpp" # include "ode_simple.hpp" # include "ode_check.hpp" bool ode_simple_check(void) { bool ok = true; bool retape; size_t i; // solution vector NumberVector x; // number of time grid intervals between measurement values SizeVector N(Nz + 1); N[0] = 0; for(i = 1; i <= Nz; i++) N[i] = 4; for(i = 0; i < 2; i++) { retape = bool(i); ipopt_ode_case(retape, N, x); ok &= ode_check(N, x); } return ok; } cppad-20170000.3/cppad_ipopt/example/ode_fast_check.cpp0000644000175200017650000000203213057470462022011 0ustar coincoin-web// $Id: ode_fast_check.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include "ode_run.hpp" # include "ode_fast.hpp" # include "ode_check.hpp" bool ode_fast_check(void) { bool ok = true; bool retape; size_t i; // solution vector NumberVector x; // number of time grid intervals between measurement values SizeVector N(Nz + 1); N[0] = 0; for(i = 1; i <= Nz; i++) N[i] = 5; for(i = 0; i < 2; i++) { retape = bool(i); ipopt_ode_case(retape, N, x); ok &= ode_check(N, x); } return ok; } cppad-20170000.3/cppad_ipopt/example/ode_simple.hpp0000644000175200017650000000672213057470462021227 0ustar coincoin-web// $Id: ode_simple.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_SIMPLE_HPP # define CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_SIMPLE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_nlp_ode_simple.hpp$$ $spell cppad_ipopt_nlp Nz Ny Na $$ $section ODE Fitting Using Simple Representation$$ $mindex cppad_ipopt_nlp example source$$ $code $srcfile%cppad_ipopt/example/ode_simple.hpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include "ode_problem.hpp" // define in the empty namespace namespace { using namespace cppad_ipopt; class FG_simple : public cppad_ipopt_fg_info { private: bool retape_; SizeVector N_; SizeVector S_; public: // derived class part of constructor FG_simple(bool retape_in, const SizeVector& N) : retape_ (retape_in), N_(N) { assert( N_[0] == 0 ); S_.resize( N.size() ); S_[0] = 0; for(size_t i = 1; i < N_.size(); i++) S_[i] = S_[i-1] + N_[i]; } // Evaluation of the objective f(x), and constraints g(x) // using an Algorithmic Differentiation (AD) class. ADVector eval_r(size_t not_used, const ADVector& x) { count_eval_r(); // temporary indices size_t i, j, k; // # of components of x corresponding to values for y size_t ny_inx = (S_[Nz] + 1) * Ny; // # of constraints (range dimension of g) size_t m = ny_inx; // # of components in x (domain dimension for f and g) assert ( x.size() == ny_inx + Na ); // vector for return value ADVector fg(m + 1); // vector of parameters ADVector a(Na); for(j = 0; j < Na; j++) a[j] = x[ny_inx + j]; // vector for value of y(t) ADVector y(Ny); // objective function ------------------------------- fg[0] = 0.; for(k = 0; k < Nz; k++) { for(j = 0; j < Ny; j++) y[j] = x[Ny*S_[k+1] + j]; fg[0] += eval_H(k+1, y, a); } // initial condition --------------------------------- ADVector F = eval_F(a); for(j = 0; j < Ny; j++) { y[j] = x[j]; fg[1+j] = y[j] - F[j]; } // trapezoidal approximation -------------------------- ADVector ym(Ny), G(Ny), Gm(Ny); G = eval_G(y, a); ADNumber dy; for(k = 0; k < Nz; k++) { // interval between data points Number T = s[k+1] - s[k]; // integration step size Number dt = T / Number( N_[k+1] ); for(j = 0; j < N_[k+1]; j++) { size_t Index = (j + S_[k]) * Ny; // y(t) at end of last step ym = y; // G(y, a) at end of last step Gm = G; // value of y(t) at end of this step for(i = 0; i < Ny; i++) y[i] = x[Ny + Index + i]; // G(y, a) at end of this step G = eval_G(y, a); // trapezoidal approximation residual for(i = 0; i < Ny; i++) { dy = (G[i] + Gm[i]) * dt / 2; fg[1+Ny+Index+i] = y[i] - ym[i] - dy; } } } return fg; } // The operations sequence for r_eval does not depend on u, // hence retape = false should work and be faster. bool retape(size_t k) { return retape_; } }; } // END C++ # endif cppad-20170000.3/cppad_ipopt/example/makefile.am0000644000175200017650000000264713057470462020474 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # EXTRA_DIST = \ ode1.omh \ ode2.omh # check_PROGRAMS = example # AM_CXXFLAGS = -g $(CXX_FLAGS) # AM_CPPFLAGS = -I. \ -I$(top_srcdir) \ -I$(top_srcdir)/cppad_ipopt/src \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ -I$(IPOPT_DIR)/include # LDADD = \ -lcppad_ipopt \ $(CPPAD_IPOPT_LIBS) \ $(FCLIBS) \ $(PTHREAD_LIB) \ $(DL_LIB) AM_LDFLAGS = -L../src # example_SOURCES = \ example.cpp \ get_started.cpp \ ode_check.cpp \ ode_check.hpp \ ode_fast_check.cpp \ ode_fast.hpp \ ode_problem.hpp \ ode_run.hpp \ ode_simple_check.cpp \ ode_simple.hpp test: check ./test.sh cppad-20170000.3/cppad_ipopt/example/ode1.omh0000644000175200017650000000145113057470462017725 0ustar coincoin-web$Id: ode1.omh 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin ipopt_nlp_ode$$ $section Example Simultaneous Solution of Forward and Inverse Problem$$ $contents% cppad_ipopt/example/ode2.omh% cppad_ipopt/example/ode_run.hpp% cppad_ipopt/example/ode_check.cpp %$$ $end cppad-20170000.3/cppad_ipopt/example/ode_fast.hpp0000644000175200017650000001251413057470462020667 0ustar coincoin-web// $Id: ode_fast.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_FAST_HPP # define CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_FAST_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_nlp_ode_fast.hpp$$ $spell cppad_ipopt_nlp $$ $section ODE Fitting Using Fast Representation$$ $mindex cppad_ipopt_nlp example source$$ $code $srcfile%cppad_ipopt/example/ode_fast.hpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include "ode_problem.hpp" namespace { using namespace cppad_ipopt; class FG_fast : public cppad_ipopt_fg_info { private: bool retape_; SizeVector N_; SizeVector S_; public: // derived class part of constructor FG_fast(bool retape_in, const SizeVector& N) : retape_ (retape_in), N_(N) { assert( N_[0] == 0 ); S_.resize( N_.size() ); S_[0] = 0; for(size_t i = 1; i < N_.size(); i++) S_[i] = S_[i-1] + N_[i]; } // r^k for k = 0, 1, ..., Nz-1 used for measurements // r^k for k = Nz use for initial condition // r^k for k = Nz+1, ..., 2*Nz used for trapezoidal approx size_t number_functions(void) { return Nz + 1 + Nz; } ADVector eval_r(size_t k, const ADVector &u) { count_eval_r(); size_t j; ADVector y(Ny), a(Na); // objective function -------------------------------- if( k < Nz ) { // used for measurement with index k+1 ADVector r(1); // return value is a scalar // u is [y( s[k+1] ) , a] for(j = 0; j < Ny; j++) y[j] = u[j]; for(j = 0; j < Na; j++) a[j] = u[Ny + j]; r[0] = eval_H(k+1, y, a); return r; } // initial condition --------------------------------- if( k == Nz ) { ADVector r(Ny), F(Ny); // u is [y(t), a] at t = 0 for(j = 0; j < Ny; j++) y[j] = u[j]; for(j = 0; j < Na; j++) a[j] = u[Ny + j]; F = eval_F(a); for(j = 0; j < Ny; j++) r[j] = y[j] - F[j]; return r; } // trapezoidal approximation ------------------------- ADVector ym(Ny), G(Ny), Gm(Ny), r(Ny); // r^k for k = Nz+1, ... , 2*Nz // interval between data samples Number T = s[k-Nz] - s[k-Nz-1]; // integration step size Number dt = T / Number( N_[k-Nz] ); // u = [ y(t[i-1], a) , y(t[i], a), a ) for(j = 0; j < Ny; j++) { ym[j] = u[j]; y[j] = u[Ny + j]; } for(j = 0; j < Na; j++) a[j] = u[2 * Ny + j]; Gm = eval_G(ym, a); G = eval_G(y, a); for(j = 0; j < Ny; j++) r[j] = y[j] - ym[j] - (G[j] + Gm[j]) * dt / 2.; return r; } // The operations sequence for r_eval does not depend on u, // hence retape = false should work and be faster. bool retape(size_t k) { return retape_; } // size of the vector u in eval_r size_t domain_size(size_t k) { if( k < Nz ) return Ny + Na; // objective function if( k == Nz ) return Ny + Na; // initial value constraint return 2 * Ny + Na; // trapezodial constraints } // size of the return value from eval_r size_t range_size(size_t k) { if( k < Nz ) return 1; return Ny; } // number of terms that use this value of k size_t number_terms(size_t k) { if( k <= Nz ) return 1; // r^k used once for k <= Nz // r^k used N_[k-Nz] times for k > Nz return N_[k-Nz]; } void index(size_t k, size_t ell, SizeVector& I, SizeVector& J) { size_t i, j; // # of components of x corresponding to values for y size_t ny_inx = (S_[Nz] + 1) * Ny; // objective function ------------------------------- if( k < Nz ) { // index in fg corresponding to objective I[0] = 0; // u = [ y(t, a) , a ] // The first Ny components of u is y(t) at // t = s[k+1] = t[S_[k+1]] // x indices corresponding to this value of y for(j = 0; j < Ny; j++) J[j] = S_[k + 1] * Ny + j; // components of x correspondig to a for(j = 0; j < Na; j++) J[Ny + j] = ny_inx + j; return; } // initial conditions -------------------------------- if( k == Nz ) { // index in fg for inidial condition constraint for(j = 0; j < Ny; j++) I[j] = 1 + j; // u = [ y(t, a) , a ] where t = 0 // x indices corresponding to this value of y for(j = 0; j < Ny; j++) J[j] = j; // following that, u contains the vector a for(j = 0; j < Na; j++) J[Ny + j] = ny_inx + j; return; } // trapoziodal approximation ------------------------- // index of first grid point in this approximation i = S_[k - Nz - 1] + ell; // There are Ny difference equations for each time // point. Add one for the objective function, and Ny // for the initial value constraints. for(j = 0; j < Ny; j++) I[j] = 1 + Ny + i * Ny + j; // u = [ y(t, a) , y(t+dt, a) , a ] at t = t[i] for(j = 0; j < Ny; j++) { J[j] = i * Ny + j; // y^i indices J[Ny + j] = J[j] + Ny; // y^{i+1} indices } for(j = 0; j < Na; j++) J[2 * Ny + j] = ny_inx + j; // a indices } }; } // END C++ # endif cppad-20170000.3/cppad_ipopt/example/ode2.omh0000644000175200017650000003706613057470462017741 0ustar coincoin-web$Id: ode2.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin ipopt_nlp_ode_problem$$ $section An ODE Inverse Problem Example$$ $head Notation$$ The table below contains the name of a variable, the meaning of the variable value, and the value for this particular example. If the value is not specified in the table below, the corresponding value in $cref ipopt_nlp_ode_problem.hpp$$ can be changed and the example should still run (with no other changes). $table $bold Name$$ $cnext $bold Meaning$$ $cnext $bold Value$$ $rnext $latex Na$$ $cnext number of parameters to fit $cnext 3 $rnext $latex Ny$$ $cnext number components in ODE $cnext 2 $rnext $latex Nz$$ $cnext number of measurements $cnext 4 $rnext $latex N(i)$$ $cnext number of grid points between $th i-1$$ and $th i$$ measurement $rnext $latex S(i)$$ $cnext number of grid points up to an including the $th i$$ measurement $tend $head Forward Problem$$ We consider the following ordinary differential equation: $latex \[ \begin{array}{rcl} \partial_t y_0 ( t , a ) & = & - a_1 * y_0 (t, a ) \\ \partial_t y_1 (t , a ) & = & + a_1 * y_0 (t, a ) - a_2 * y_1 (t, a ) \end{array} \] $$ with the initial conditions $latex \[ y_0 (0 , a) = F(a) = \left( \begin{array}{c} a_0 \\ 0 \end{array} \right) \] $$ where $latex Na$$ is the number of parameters, $latex a \in \B{R}^{Na} $$ is an unknown parameter vector. The function and $latex F : \B{R}^{Na} \rightarrow \B{R}^{Ny} $$ is defined by the equation above where $latex Ny$$ is the number of components in $latex y(t, a)$$. Our forward problem is stated as follows: Given $latex a \in \B{R}^{Na}$$ determine the value of $latex y ( t , a ) $$, for $latex t \in R$$, that solves the initial value problem above. $head Measurements$$ We use $latex Nz$$ to denote the number of measurements. Suppose we are also given a measurement vector $latex z \in \B{R}^{Nz}$$ and for $latex i = 1, \ldots, Nz$$, we model $latex z_i$$ by $latex \[ z_i = y_1 ( s_i , a) + e_i \] $$ where $latex s_i \in \B{R}$$ is the time for the $th i$$ measurement, $latex e_i \sim {\bf N} (0 , \sigma^2 ) $$ is the corresponding noise, and $latex \sigma \in \B{R}_+$$ is the corresponding standard deviation. $subhead Simulation Analytic Solution$$ The following analytic solution to the forward problem is used to simulate a data set: $latex \[ \begin{array}{rcl} y_0 (t , a) & = & a_0 * \exp( - a_1 * t ) \\ y_1 (t , a) & = & a_0 * a_1 * \frac{\exp( - a_2 * t ) - \exp( -a_1 * t )}{ a_1 - a_2 } \end{array} \] $$ $subhead Simulation Parameter Values$$ $table $latex \bar{a}_0 = 1$$ $pre $$ $cnext initial value of $latex y_0 (t, a)$$ $rnext $latex \bar{a}_1 = 2$$ $pre $$ $cnext transfer rate from compartment zero to compartment one $rnext $latex \bar{a}_2 = 1$$ $pre $$ $cnext transfer rate from compartment one to outside world $rnext $latex \sigma = 0$$ $pre $$ $cnext standard deviation of measurement noise $rnext $latex e_i = 0$$ $pre $$ $cnext simulated measurement noise, $latex i = 1 , \ldots , Nz$$ $rnext $latex s_i = i * .5$$ $pre $$ $cnext time corresponding to the $th i$$ measurement, $latex i = 1 , \ldots , Nz$$ $tend $subhead Simulated Measurement Values$$ The simulated measurement values are given by the equation $latex \[ \begin{array}{rcl} z_i & = & e_i + y_1 ( s_i , \bar{a} ) \\ & = & e_i + \bar{a}_0 * \bar{a}_1 * \frac{\exp( - \bar{a}_2 * s_i ) - \exp( -\bar{a}_1 * s_i )} { \bar{a}_1 - \bar{a}_2 } \end{array} \] $$ for $latex k = 1, \ldots , Nz$$. $head Inverse Problem$$ The maximum likelihood estimate for $latex a$$ given $latex z$$ solves the following inverse problem $latex \[ \begin{array}{rcl} {\rm minimize} \; & \sum_{i=1}^{Nz} H_i [ y( s_i , a ) , a ] & \;{\rm w.r.t} \; a \in \B{R}^{Na} \end{array} \] $$ where the functions $latex H_i : \B{R}^{Ny} \times \B{R}^{Na} \rightarrow \B{R}$$ is defined by $latex \[ H_i (y, a) = ( z_i - y_1 )^2 \] $$ $head Trapezoidal Approximation$$ This example uses a trapezoidal approximation to solve the ODE. This approximation procedures starts with $latex \[ y^0 = y(0, a) = \left( \begin{array}{c} a_0 \\ 0 \end{array} \right) \] $$ Given a time grid $latex \{ t_i \}$$ and an approximate value $latex y^{i-1} $$ for $latex y ( t_{i-1} , a )$$, the a trapezoidal method approximates $latex y ( t_i , a )$$ (denoted by $latex y^i$$ ) by solving the equation $latex \[ y^i = y^{i-1} + \left[ G( y^i , a ) + G( y^{i-1} , a ) \right] * \frac{t_i - t_{i-1} }{ 2 } \] $$ where $latex G : \B{R}^{Ny} \times \B{R}^{Na} \rightarrow \B{R}^{Ny}$$ is the function representing this ODE; i.e. $latex \[ G(y, a) = \left( \begin{array}{c} - a_1 * y_0 \\ + a_1 * y_0 - a_2 * y_1 \end{array} \right) \] $$ This $latex G(y, a)$$ is linear with respect to $latex y$$, hence the implicit equation defining $latex y^i $$ can be solved inverting the a set of linear equations. In the general case, where $latex G(y, a)$$ is non-linear with respect to $latex y$$, an iterative procedure is used to calculate $latex y^i$$ from $latex y^{i-1}$$. $subhead Trapezoidal Time Grid$$ The discrete time grid, used for the trapezoidal approximation, is denoted by $latex \{ t_i \} $$ which is defined by: $latex t_0 = 0$$ and for $latex i = 1 , \ldots , Nz$$ and for $latex j = 1 , \ldots , N(i)$$, $latex \[ \begin{array}{rcl} \Delta t_i & = & ( s_i - s_{i-1} ) / N(i) \\ t_{S(i-1)+j} & = & s_{i-1} + \Delta t_i * j \end{array} \] $$ where $latex s_0 = 0$$, $latex N(i)$$ is the number of time grid points between $latex s_{i-1}$$ and $latex s_i$$, $latex S(0) = 0$$, and $latex S(i) = N(1) + \ldots + N(i)$$. Note that for $latex i = 0 , \ldots , S(Nz) $$, $latex y^i$$ denotes our approximation for $latex y( t_i , a )$$ and $latex t_{S(i)}$$ is equal to $latex s_i$$. $head Black Box Method$$ A common approach to an inverse problem is to treat the forward problem as a black box (that we do not look inside of or try to understand). In this approach, for each value of the parameter vector $latex a$$ one uses the $cref/trapezoidal approximation/ipopt_nlp_ode_problem/Trapezoidal Approximation/$$ (on a finer grid that $latex \{ s_i \}$$) to solve for $latex y_1 ( s_i , a )$$ for $latex i = 1 , \ldots , Nz$$. $subhead Two levels of Iteration$$ As noted above, the trapezoidal approximation often requires an iterative procedure. Thus, in this approach, there are two levels of iterations, one with respect to the parameter values during the minimization and the other for solving the trapezoidal approximation equation. $subhead Derivatives$$ In addition, in the black box approach, differentiating the ODE solution often involves differentiating an iterative procedure. Direct application of AD to compute these derivatives requires a huge amount of memory and calculations to differentiate the iterative procedure. (There are special techniques for applying AD to the solutions of iterative procedures, but that is outside the scope of this presentation). $head Simultaneous Method$$ The simultaneous forward and inverse method uses constraints to include the solution of the forward problem in the inverse problem. To be specific for our example, $latex \[ \begin{array}{rcl} {\rm minimize} & \sum_{i=1}^{Nz} H_i ( y^{N(i)} , a ) & \; {\rm w.r.t} \; y^1 \in \B{R}^{Ny} , \ldots , y^{S(Nz)} \in \B{R}^{Ny} , \; a \in \B{R}^{Na} \\ {\rm subject \; to} & y^j = y^{j-1} + \left[ G( y^{j-1} , a ) + G( y^j , a ) \right] * \frac{ t_j - t_{j-1} }{ 2 } & \; {\rm for} \; j = 1 , \ldots , S(Nz) \\ & y^0 = F(a) \end{array} \] $$ where for $latex i = 1, \ldots , Nz$$, $latex N(i)$$ is the number of time intervals between $latex s_{i-1}$$ and $latex s_i$$ (with $latex s_0 = 0$$) and $latex S(i) = N(1) + \ldots + N(i)$$. Note that, in this form, the iterations of the optimization procedure also solve the forward problem equations. In addition, the functions that need to be differentiated do not involve an iterative procedure. $children% cppad_ipopt/example/ode_problem.hpp %$$ $head Source$$ The file $cref ipopt_nlp_ode_problem.hpp$$ contains source code that defines the example values and functions defined above. $end ----------------------------------------------------------------------------- $begin ipopt_nlp_ode_simple$$ $spell cppad_ipopt_nlp $$ $section ODE Fitting Using Simple Representation$$ $mindex cppad_ipopt_nlp$$ $head Purpose$$ In this section we represent the objective and constraint functions, (in the simultaneous forward and reverse optimization problem) using the $cref/simple representation/cppad_ipopt_nlp/Simple Representation/$$ in the sense of $code cppad_ipopt_nlp$$. $head Argument Vector$$ The argument vector that we are optimizing with respect to ( $latex x$$ in $cref cppad_ipopt_nlp$$ ) has the following structure $latex \[ x = ( y^0 , \cdots , y^{S(Nz)} , a ) \] $$ Note that $latex x \in \B{R}^{S(Nz) + Na}$$ and $latex \[ \begin{array}{rcl} y^i & = & ( x_{Ny * i} , \ldots , x_{Ny * i + Ny - 1} ) \\ a & = & ( x_{Ny *S(Nz) + Ny} , \ldots , x_{Ny * S(Nz) + Na - 1} ) \end{array} \] $$ $head Objective Function$$ The objective function ( $latex fg_0 (x)$$ in $cref cppad_ipopt_nlp$$ ) has the following representation, $latex \[ fg_0 (x) = \sum_{i=1}^{Nz} H_i ( y^{S(i)} , a ) \] $$ $head Initial Condition Constraint$$ For $latex i = 1 , \ldots , Ny$$, we define the component functions $latex fg_i (x)$$, and corresponding constraint equations, by $latex \[ 0 = fg_i ( x ) = y_i^0 - F_i (a) \] $$ $head Trapezoidal Approximation Constraint$$ For $latex i = 1, \ldots , S(Nz)$$, and for $latex j = 1 , \ldots , Ny$$, we define the component functions $latex fg_{Ny*i + j} (x)$$, and corresponding constraint equations, by $latex \[ 0 = fg_{Ny*i + j } = y_j^{i} - y_j^{i-1} - \left[ G_j ( y^i , a ) + G_j ( y^{i-1} , a ) \right] * \frac{t_i - t_{i-1} }{ 2 } \] $$ $children% cppad_ipopt/example/ode_simple.hpp %$$ $head Source$$ The file $cref ipopt_nlp_ode_simple.hpp$$ contains source code for this representation of the objective and constraints. $end ----------------------------------------------------------------------------- $begin ipopt_nlp_ode_fast$$ $spell cppad_ipopt_nlp $$ $section ODE Fitting Using Fast Representation$$ $head Purpose$$ In this section we represent a more complex representation of the simultaneous forward and reverse ODE fitting problem (described above). The representation defines the problem using simpler functions that are faster to differentiate (either by hand coding or by using AD). $head Objective Function$$ We use the following representation for the $cref/objective function/ipopt_nlp_ode_simple/Objective Function/$$: For $latex k = 0 , \ldots , Nz - 1$$, we define the function $latex r^k : \B{R}^{Ny+Na} \rightarrow \B{R}$$ by $latex \[ \begin{array}{rcl} fg_0 (x) & = & \sum_{i=1}^{Nz} H_i ( y^{S(i)} , a ) \\ fg_0 (x) & = & \sum_{k=0}^{Nz-1} r^k ( u^{k,0} ) \end{array} \] $$ where for $latex k = 0 , \ldots , Nz-1$$, $latex u^{k,0} \in \B{R}^{Ny + Na}$$ is defined by $latex u^{k,0} = ( y^{S(k+1)} , a )$$ $subhead Range Indices I(k,0)$$ For $latex k = 0 , \ldots , Nz - 1$$, the range index in the vector $latex fg (x)$$ corresponding to $latex r^k ( u^{k,0} ) $$ is 0. Thus, the range indices are given by $latex I(k,0) = \{ 0 \}$$ for $latex k = 0 , \ldots , Nz-1$$. $subhead Domain Indices J(k,0)$$ For $latex k = 0 , \ldots , Nz - 1$$, the components of the vector $latex x$$ corresponding to the vector $latex u^{k,0}$$ are $latex \[ \begin{array}{rcl} u^{k,0} & = & ( y^{S(k+1} , a ) \\ & = & ( x_{Ny * S(k+1)} \; , \; \ldots \; , \; x_{Ny * S(k+1) + Ny - 1} \; , \; x_{Ny * S(Nz) + Ny } \; , \; \ldots \; , \; x_{Ny * S(Nz) + Ny + Na - 1} ) \end{array} \] $$ Thus, the domain indices are given by $latex \[ J(k,0) = \{ Ny * S(k+1) \; , \; \ldots \; , \; Ny * S(k+1) + Ny - 1 \; , \; Ny * S(Nz) + Ny \; , \; \ldots \; , \; Ny * S(Nz) + Ny + Na - 1 \} \] $$ $head Initial Condition$$ We use the following representation for the $cref/initial condition constraint/ ipopt_nlp_ode_simple/Initial Condition Constraint/$$: For $latex k = Nz$$ we define the function $latex r^k : \B{R}^{Ny} \times \B{R}^{Na + Ny}$$ by $latex \[ \begin{array}{rcl} 0 & = & fg_i ( x ) = y_i^0 - F_i (a) \\ 0 & = & r_{i-1}^k ( u^{k,0} ) = y_i^0 - F_i(a) \end{array} \] $$ where $latex i = 1 , \ldots , Ny$$ and where $latex u^{k,0} \in \B{R}^{Ny + Na}$$ is defined by $latex u^{k,0} = ( y^0 , a)$$. $subhead Range Indices I(k,0)$$ For $latex k = Nz$$, the range index in the vector $latex fg (x)$$ corresponding to $latex r^k ( u^{k,0} ) $$ are $latex I(k,0) = \{ 1 , \ldots , Ny \}$$. $subhead Domain Indices J(k,0)$$ For $latex k = Nz$$, the components of the vector $latex x$$ corresponding to the vector $latex u^{k,0}$$ are $latex \[ \begin{array}{rcl} u^{k,0} & = & ( y^0 , a) \\ & = & ( x_0 \; , \; \ldots \; , \; x_{Ny-1} \; , \; x_{Ny * S(Nz) + Ny } \; , \; \ldots \; , \; x_{Ny * S(Nz) + Ny + Na - 1} ) \end{array} \] $$ Thus, the domain indices are given by $latex \[ J(k,0) = \{ 0 \; , \; \ldots \; , \; Ny - 1 \; , \; Ny * S(Nz) + Ny \; , \; \ldots \; , \; Ny * S(Nz) + Ny + Na - 1 \} \] $$ $head Trapezoidal Approximation$$ We use the following representation for the $cref/trapezoidal approximation constraint/ ipopt_nlp_ode_simple/Trapezoidal Approximation Constraint/$$: For $latex k = 1 , \ldots , Nz$$, we define the function $latex r^{Nz+k} : \B{R}^{2*Ny+Na} \rightarrow \B{R}^{Ny}$$ by $latex \[ r^{Nz+k} ( y , w , a ) = y - w - [ G( y , a ) + G( w , a ) ] * \frac{ \Delta t_k }{ 2 } \] $$ For $latex \ell = 0 , \ldots , N(k)-1$$, using the notation $latex i = Ny * S(k-1) + \ell + 1$$, the corresponding trapezoidal approximation is represented by $latex \[ \begin{array}{rcl} 0 & = & fg_{Ny+i} (x) \\ & = & y^i - y^{i-1} - \left[ G( y^i , a ) + G( y^{i-1} , a ) \right] * \frac{\Delta t_k }{ 2 } \\ & = & r^{Nz+k} ( u^{Nz+k , \ell} ) \end{array} \] $$ where $latex u^{Nz+k,\ell} \in \B{R}^{2*Ny + Na}$$ is defined by $latex u^{Nz+k,\ell} = ( y^{i-1} , y^i , a)$$. $subhead Range Indices I(k,0)$$ For $latex k = Nz + 1, \ldots , 2*Nz$$, and $latex \ell = 0 , \ldots , N(k)-1$$, the range index in the vector $latex fg (x)$$ corresponding to $latex r^k ( u^{k,\ell} ) $$ are $latex I(k,\ell) = \{ Ny + i , \ldots , 2*Ny + i - 1 \}$$ where $latex i = Ny * S(k-1) + \ell + 1$$. $subhead Domain Indices J(k,0)$$ For $latex k = Nz + 1, \ldots , 2*Nz$$, and $latex \ell = 0 , \ldots , N(k)-1$$, define $latex i = Ny * S(k-1) + \ell + 1$$. The components of the vector $latex x$$ corresponding to the vector $latex u^{k,\ell}$$ are (and the function $latex fg (x) $$ in $cref cppad_ipopt_nlp$$ ) $latex \[ \begin{array}{rcl} u^{k, \ell} & = & ( y^{i-1} , y^i , a ) \\ & = & ( x_{Ny * (i-1)} \; , \; \ldots \; , \; x_{Ny * (i+1) - 1} \; , \; x_{Ny * S(Nz) + Ny } \; , \; \ldots \; , \; x_{Ny * S(Nz) + Ny + Na - 1} ) \end{array} \] $$ Thus, the domain indices are given by $latex \[ J(k,\ell) = \{ Ny * (i-1) \; , \; \ldots \; , \; Ny * (i+1) - 1 \; , \; Ny * S(Nz) + Ny \; , \; \ldots \; , \; Ny * S(Nz) + Ny + Na - 1 \} \] $$ $children% cppad_ipopt/example/ode_fast.hpp %$$ $head Source$$ The file $cref ipopt_nlp_ode_fast.hpp$$ contains source code for this representation of the objective and constraints. $end ------------------------------------------------------------------------------ cppad-20170000.3/cppad_ipopt/example/example.cpp0000644000175200017650000000405713057470462020534 0ustar coincoin-web// $Id: example.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // system include files used for I/O # include // C style asserts # include // CppAD include file # include // external complied tests extern bool ipopt_get_started(void); extern bool ode_simple_check(void); extern bool ode_fast_check(void); namespace { // function that runs one test static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), const char *name) { bool ok = true; ok &= TestOk(); if( ok ) { std::cout << "OK: " << name << std::endl; Run_ok_count++; } else { std::cout << "Error: " << name << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; // external compiled tests ok &= Run( ipopt_get_started, "ipopt_get_started" ); ok &= Run( ode_simple_check, "ode_simple_check" ); ok &= Run( ode_fast_check, "ode_fast_check" ); // check for errors using std::cout; using std::endl; assert( ok || (Run_error_count > 0) ); if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "OK: " << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Error: " << "memory leak detected" << endl; } // convert int(size_t) to avoid warning on _MSC_VER systems if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! ok ); } cppad-20170000.3/cppad_ipopt/example/CMakeLists.txt0000644000175200017650000000354713057470462021140 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Inherit build type from ../CMakeList.txt # Local include directories to search (not in package_prefix/include) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/../src ) # Local link directories to search (not in external packages) LINK_DIRECTORIES( ${CMAKE_CURRENT_BINARY_DIR}/../src ${ipopt_LIBRARY_DIRS} ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(cppad_ipopt_example EXCLUDE_FROM_ALL example.cpp get_started.cpp ode_check.cpp ode_check.hpp ode_fast_check.cpp ode_fast.hpp ode_problem.hpp ode_run.hpp ode_simple_check.cpp ode_simple.hpp ) # Extra compiler flags add_cppad_cxx_flags( cppad_ipopt_example ) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES(cppad_ipopt_example cppad_ipopt ${cppad_lib} ${ipopt_LIBRARIES} ${colpack_libs} ) # Add the check_cppad_ipopt_example target ADD_CUSTOM_TARGET(check_cppad_ipopt_example cppad_ipopt_example DEPENDS cppad_ipopt_example cppad_ipopt ) MESSAGE(STATUS "make check_cppad_ipopt_example: available") # Change check depends in parent environment add_to_list(check_cppad_ipopt_depends check_cppad_ipopt_example) SET(check_cppad_ipopt_depends "${check_cppad_ipopt_depends}" PARENT_SCOPE) cppad-20170000.3/cppad_ipopt/example/ode_problem.hpp0000644000175200017650000000606713057470462021400 0ustar coincoin-web// $Id: ode_problem.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_PROBLEM_HPP # define CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_PROBLEM_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_nlp_ode_problem.hpp$$ $spell cppad_ipopt_nlp Nz Ny Na $$ $section ODE Inverse Problem Definitions: Source Code$$ $mindex example$$ $code $srcfile%cppad_ipopt/example/ode_problem.hpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include "../src/cppad_ipopt_nlp.hpp" namespace { //------------------------------------------------------------------ typedef Ipopt::Number Number; Number a0 = 1.; // simulation value for a[0] Number a1 = 2.; // simulation value for a[1] Number a2 = 1.; // simulatioln value for a[2] // function used to simulate data Number y_one(Number t) { Number y_1 = a0*a1 * (exp(-a2*t) - exp(-a1*t)) / (a1 - a2); return y_1; } // time points were we have data (no data at first point) double s[] = { 0.0, 0.5, 1.0, 1.5, 2.0 }; // Simulated data for case with no noise (first point is not used) double z[] = { 0.0, y_one(0.5), y_one(1.0), y_one(1.5), y_one(2.0) }; // Number of measurement values size_t Nz = sizeof(z) / sizeof(z[0]) - 1; // Number of components in the function y(t, a) size_t Ny = 2; // Number of components in the vectro a size_t Na = 3; // Initial Condition function, F(a) = y(t, a) at t = 0 // (for this particular example) template Vector eval_F(const Vector &a) { Vector F(Ny); // y_0 (t) = a[0]*exp(-a[1] * t) F[0] = a[0]; // y_1 (t) = // a[0]*a[1]*(exp(-a[2] * t) - exp(-a[1] * t))/(a[1] - a[2]) F[1] = 0.; return F; } // G(y, a) = \partial_t y(t, a); i.e. the differential equation // (for this particular example) template Vector eval_G(const Vector &y , const Vector &a) { Vector G(Ny); // y_0 (t) = a[0]*exp(-a[1] * t) G[0] = -a[1] * y[0]; // y_1 (t) = // a[0]*a[1]*(exp(-a[2] * t) - exp(-a[1] * t))/(a[1] - a[2]) G[1] = +a[1] * y[0] - a[2] * y[1]; return G; } // H(i, y, a) = contribution to objective at i-th data point // (for this particular example) template Scalar eval_H(size_t i, const Vector &y, const Vector &a) { // This particular H is for a case where y_1 (t) is measured Scalar diff = z[i] - y[1]; return diff * diff; } // function used to count the number of calls to eval_r size_t count_eval_r(void) { static size_t count = 0; ++count; return count; } } // END C++ # endif cppad-20170000.3/cppad_ipopt/example/ode_run.hpp0000644000175200017650000000740113057470462020535 0ustar coincoin-web// $Id: ode_run.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_RUN_HPP # define CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_RUN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_nlp_ode_run.hpp$$ $spell Ipopt $$ $section Driver for Running the Ipopt ODE Example$$ $code $srcfile%cppad_ipopt/example/ode_run.hpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include "ode_problem.hpp" namespace { // BEGIN empty namespace ----------------------------------------- using namespace cppad_ipopt; template void ipopt_ode_case( bool retape , const SizeVector& N , NumberVector& x ) { bool ok = true; size_t i, j; // compute the partial sums of the number of grid points assert( N.size() == Nz + 1); assert( N[0] == 0 ); SizeVector S(Nz+1); S[0] = 0; for(i = 1; i <= Nz; i++) S[i] = S[i-1] + N[i]; // number of components of x corresponding to values for y size_t ny_inx = (S[Nz] + 1) * Ny; // number of constraints (range dimension of g) size_t m = ny_inx; // number of components in x (domain dimension for f and g) size_t n = ny_inx + Na; // the argument vector for the optimization is // y(t) at t[0] , ... , t[S[Nz]] , followed by a NumberVector x_i(n), x_l(n), x_u(n); for(j = 0; j < ny_inx; j++) { x_i[j] = 0.; // initial y(t) for optimization x_l[j] = -1.0e19; // no lower limit x_u[j] = +1.0e19; // no upper limit } for(j = 0; j < Na; j++) { x_i[ny_inx + j ] = .5; // initiali a for optimization x_l[ny_inx + j ] = -1.e19; // no lower limit x_u[ny_inx + j ] = +1.e19; // no upper } // all of the difference equations are constrained to the value zero NumberVector g_l(m), g_u(m); for(i = 0; i < m; i++) { g_l[i] = 0.; g_u[i] = 0.; } // object defining the objective f(x) and constraints g(x) FG_info fg_info(retape, N); // create the CppAD Ipopt interface cppad_ipopt_solution solution; Ipopt::SmartPtr cppad_nlp = new cppad_ipopt_nlp( n, m, x_i, x_l, x_u, g_l, g_u, &fg_info, &solution ); // Create an Ipopt application using Ipopt::IpoptApplication; Ipopt::SmartPtr app = new IpoptApplication(); // turn off any printing app->Options()->SetIntegerValue("print_level", 0); app->Options()->SetStringValue("sb", "yes"); // maximum number of iterations app->Options()->SetIntegerValue("max_iter", 30); // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) app->Options()->SetNumericValue("tol", 1e-9); // Derivative testing is very slow for large problems // so comment this out if you use a large value for N[]. app->Options()-> SetStringValue( "derivative_test", "second-order"); app->Options()-> SetNumericValue( "point_perturbation_radius", 0.); // Initialize the application and process the options Ipopt::ApplicationReturnStatus status = app->Initialize(); ok &= status == Ipopt::Solve_Succeeded; // Run the application status = app->OptimizeTNLP(cppad_nlp); ok &= status == Ipopt::Solve_Succeeded; // return the solution x.resize( solution.x.size() ); for(j = 0; j < x.size(); j++) x[j] = solution.x[j]; return; } } // END empty namespace ---------------------------------------------------- // END C++ # endif cppad-20170000.3/cppad_ipopt/example/makefile.in0000644000175200017650000005004613057470462020501 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; 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Bell # # CppAD is distributed under multiple licenses. 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_nlp_ode_check.cpp$$ $section Correctness Check for Both Simple and Fast Representations$$ $code $srcfile%cppad_ipopt/example/ode_check.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include "ode_run.hpp" bool ode_check(const SizeVector& N, const NumberVector& x) { bool ok = true; size_t i, j; // number of components of x corresponding to values for y size_t ny_inx = x.size() - Na; // compute the partial sums of the number of grid points // and the maximum step size for the trapezoidal approximation SizeVector S(Nz+1); S[0] = 0; double max_step = 0.; for(i = 1; i <= Nz; i++) { S[i] = S[i-1] + N[i]; max_step = std::max(max_step, (s[i] - s[i-1]) / N[i] ); } // split out return values NumberVector a(Na), y_0(Ny), y_1(Ny), y_2(Ny); for(j = 0; j < Na; j++) a[j] = x[ny_inx+j]; for(j = 0; j < Ny; j++) { y_0[j] = x[j]; y_1[j] = x[Ny + j]; y_2[j] = x[2 * Ny + j]; } // Check some of the optimal a value Number rel_tol = max_step * max_step; Number abs_tol = rel_tol; Number check_a[] = {a0, a1, a2}; // see the y_one function for(j = 0; j < Na; j++) { ok &= CppAD::NearEqual( check_a[j], a[j], rel_tol, abs_tol ); } // check accuarcy of constraint equations rel_tol = 1e-9; abs_tol = 1e-9; // check the initial value constraint NumberVector F = eval_F(a); for(j = 0; j < Ny; j++) ok &= CppAD::NearEqual(F[j], y_0[j], rel_tol, abs_tol); // check the first trapezoidal equation NumberVector G_0 = eval_G(y_0, a); NumberVector G_1 = eval_G(y_1, a); Number dt = (s[1] - s[0]) / Number(N[1]); Number check; for(j = 0; j < Ny; j++) { check = y_1[j] - y_0[j] - (G_1[j]+G_0[j])*dt/2; ok &= CppAD::NearEqual( check, 0., rel_tol, abs_tol); } // // check the second trapezoidal equation NumberVector G_2 = eval_G(y_2, a); if( N[1] == 1 ) dt = (s[2] - s[1]) / Number(N[2]); for(j = 0; j < Ny; j++) { check = y_2[j] - y_1[j] - (G_2[j]+G_1[j])*dt/2; ok &= CppAD::NearEqual( check, 0., rel_tol, abs_tol); } // // check the objective function (specialized to this case) check = 0.; NumberVector y_i(Ny); for(size_t k = 0; k < Nz; k++) { for(j = 0; j < Ny; j++) y_i[j] = x[S[k+1] * Ny + j]; check += eval_H(k + 1, y_i, a); } Number obj_value = 0.; // optimal object (no noise in simulation) ok &= CppAD::NearEqual(check, obj_value, rel_tol, abs_tol); // Use this empty namespace function to avoid warning that it is not used static size_t ode_check_count = 0; ode_check_count++; ok &= count_eval_r() == ode_check_count; return ok; } // END C++ cppad-20170000.3/cppad_ipopt/example/get_started.cpp0000644000175200017650000001210113057470462021373 0ustar coincoin-web// $Id: get_started.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_nlp_get_started.cpp$$ $spell cppad_nlp IpoptDir CppAD $$ $section Nonlinear Programming Using CppAD and Ipopt: Example and Test$$ $mindex ipopt AD$$ $head Purpose$$ This example program demonstrates how to use the class cppad_ipopt_nlp to solve the example problem in the Ipopt documentation; i.e., the problem $latex \[ \begin{array}{lc} {\rm minimize \; } & x_1 * x_4 * (x_1 + x_2 + x_3) + x_3 \\ {\rm subject \; to \; } & x_1 * x_2 * x_3 * x_4 \geq 25 \\ & x_1^2 + x_2^2 + x_3^2 + x_4^2 = 40 \\ & 1 \leq x_1, x_2, x_3, x_4 \leq 5 \end{array} \] $$ $head Configuration Requirement$$ This example will be compiled and tested provided that a value for $icode ipopt_prefix$$ is specified on the $cref cmake$$ command line. $code $srcfile%cppad_ipopt/example/get_started.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include namespace { using namespace cppad_ipopt; class FG_info : public cppad_ipopt_fg_info { private: bool retape_; public: // derived class part of constructor FG_info(bool retape_in) : retape_ (retape_in) { } // Evaluation of the objective f(x), and constraints g(x) // using an Algorithmic Differentiation (AD) class. ADVector eval_r(size_t k, const ADVector& x) { ADVector fg(3); // Fortran style indexing ADNumber x1 = x[0]; ADNumber x2 = x[1]; ADNumber x3 = x[2]; ADNumber x4 = x[3]; // f(x) fg[0] = x1 * x4 * (x1 + x2 + x3) + x3; // g_1 (x) fg[1] = x1 * x2 * x3 * x4; // g_2 (x) fg[2] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4; return fg; } bool retape(size_t k) { return retape_; } }; } bool ipopt_get_started(void) { bool ok = true; size_t j; // number of independent variables (domain dimension for f and g) size_t n = 4; // number of constraints (range dimension for g) size_t m = 2; // initial value of the independent variables NumberVector x_i(n); x_i[0] = 1.0; x_i[1] = 5.0; x_i[2] = 5.0; x_i[3] = 1.0; // lower and upper limits for x NumberVector x_l(n); NumberVector x_u(n); for(j = 0; j < n; j++) { x_l[j] = 1.0; x_u[j] = 5.0; } // lower and upper limits for g NumberVector g_l(m); NumberVector g_u(m); g_l[0] = 25.0; g_u[0] = 1.0e19; g_l[1] = 40.0; g_u[1] = 40.0; size_t icase; for(icase = 0; icase <= 1; icase++) { // Should cppad_ipopt_nlp retape the operation sequence for // every new x. Can test both true and false cases because // the operation sequence does not depend on x (for this case). bool retape = icase != 0; // object in derived class FG_info fg_info(retape); // create the Ipopt interface cppad_ipopt_solution solution; Ipopt::SmartPtr cppad_nlp = new cppad_ipopt_nlp( n, m, x_i, x_l, x_u, g_l, g_u, &fg_info, &solution ); // Create an instance of the IpoptApplication using Ipopt::IpoptApplication; Ipopt::SmartPtr app = new IpoptApplication(); // turn off any printing app->Options()->SetIntegerValue("print_level", 0); app->Options()->SetStringValue("sb", "yes"); // maximum number of iterations app->Options()->SetIntegerValue("max_iter", 10); // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) app->Options()->SetNumericValue("tol", 1e-9); // derivative testing app->Options()-> SetStringValue("derivative_test", "second-order"); app->Options()-> SetNumericValue( "point_perturbation_radius", 0. ); // Initialize the IpoptApplication and process the options Ipopt::ApplicationReturnStatus status = app->Initialize(); ok &= status == Ipopt::Solve_Succeeded; // Run the IpoptApplication status = app->OptimizeTNLP(cppad_nlp); ok &= status == Ipopt::Solve_Succeeded; /* Check some of the solution values */ ok &= solution.status == cppad_ipopt_solution::success; // double check_x[] = { 1.000000, 4.743000, 3.82115, 1.379408 }; double check_z_l[] = { 1.087871, 0., 0., 0. }; double check_z_u[] = { 0., 0., 0., 0. }; double rel_tol = 1e-6; // relative tolerance double abs_tol = 1e-6; // absolute tolerance for(j = 0; j < n; j++) { ok &= CppAD::NearEqual( check_x[j], solution.x[j], rel_tol, abs_tol ); ok &= CppAD::NearEqual( check_z_l[j], solution.z_l[j], rel_tol, abs_tol ); ok &= CppAD::NearEqual( check_z_u[j], solution.z_u[j], rel_tol, abs_tol ); } } return ok; } // END C++ cppad-20170000.3/cppad_ipopt/example/ode_check.hpp0000644000175200017650000000140513057470462021004 0ustar coincoin-web// $Id: ode_check.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_CHECK_HPP # define CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_CHECK_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ extern bool ode_check(const SizeVector& N, const NumberVector& x); # endif cppad-20170000.3/cppad_ipopt/CMakeLists.txt0000644000175200017650000000310313057470462017471 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Specify build type for this directory and all its subdirectories # (subdirectories do not specify build type). 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // system include files used for I/O # include // C style asserts # include // CppAD include file # include // external complied tests extern bool k_gt_one(void); extern bool multiple_solution(void); extern bool retape_k1_l1(void); extern bool retape_k1_l2(void); namespace { // function that runs one test static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), const char *name) { bool ok = true; ok &= TestOk(); if( ok ) { std::cout << "OK: " << name << std::endl; Run_ok_count++; } else { std::cout << "Error: " << name << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; // external compiled tests ok &= Run( k_gt_one, "k_get_one" ); ok &= Run( multiple_solution, "multiple_solution" ); ok &= Run( retape_k1_l1, "retape_k1_l1" ); ok &= Run( retape_k1_l2, "retape_k1_l2" ); // check for errors using std::cout; using std::endl; assert( ok || (Run_error_count > 0) ); if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "OK: " << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Error: " << "memory leak detected" << endl; } // convert int(size_t) to avoid warning on _MSC_VER systems if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! ok ); } cppad-20170000.3/cppad_ipopt/test/k_gt_one.cpp0000644000175200017650000001205113057470462020203 0ustar coincoin-web// $Id: k_gt_one.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // Begin empty namespace using namespace cppad_ipopt; // --------------------------------------------------------------------------- /* This solve the same problem as ../cppad_ipopt/cppad_ipopt_simple.cpp (repository revision 1276) in a convoluted way in order to test the representation code. */ class FG_K_gt_one : public cppad_ipopt_fg_info { private: bool retape_; public: // derived class part of constructor FG_K_gt_one(bool retape_in) : retape_ (retape_in) { } // Evaluation of the objective f(x), and constraints g(x) // using an Algorithmic Differentiation (AD) class. ADVector eval_r(size_t k, const ADVector& u) { // Fortran style indexing ADNumber x1 = u[3]; ADNumber x2 = u[2]; ADNumber x3 = u[1]; ADNumber x4 = u[0]; if( k == 0 ) { ADVector r(1); // f(x) r[0] = x1 * x4 * (x1 + x2 + x3) + x3; return r; } ADVector r(2); // g_1 (x) r[0] = x1 * x2 * x3 * x4; // g_2 (x) r[1] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4; return r; } bool retape(size_t k) { return retape_; } size_t number_functions(void) { return 2; } size_t domain_size(size_t k) { return 4; } size_t range_size(size_t k) { if( k == 0 ) return 1; return 2; } size_t number_terms(size_t k) { return 1; } void index(size_t k, size_t ell, SizeVector& I, SizeVector& J) { if( k == 0 ) I[0] = 0; else { I[0] = 1; I[1] = 2; } // reverse the order of the variables in u from that in x for(size_t j = 0; j < 4; j++) J[j] = 3-j; } }; } // end empty namespace bool k_gt_one(void) { bool ok = true; size_t j; // number of independent variables (domain dimension for f and g) size_t n = 4; // number of constraints (range dimension for g) size_t m = 2; // initial value of the independent variables NumberVector x_i(n); x_i[0] = 1.0; x_i[1] = 5.0; x_i[2] = 5.0; x_i[3] = 1.0; // lower and upper limits for x NumberVector x_l(n); NumberVector x_u(n); for(j = 0; j < n; j++) { x_l[j] = 1.0; x_u[j] = 5.0; } // lower and upper limits for g NumberVector g_l(m); NumberVector g_u(m); g_l[0] = 25.0; g_u[0] = 1.0e19; g_l[1] = 40.0; g_u[1] = 40.0; // known solution to check against double check_x[] = { 1.000000, 4.743000, 3.82115, 1.379408 }; size_t icase; for(icase = 0; icase <= 1; icase++) { // Should cppad_ipopt_nlp retape the operation sequence for // every new x. Can test both true and false cases because // the operation sequence does not depend on x (for this case). bool retape = bool(icase); // check case where upper and lower limits are equal if( icase == 1 ) { x_l[2] = check_x[2]; x_u[2] = check_x[2]; } // object in derived class FG_K_gt_one my_fg_info(retape); cppad_ipopt_fg_info *fg_info = &my_fg_info; // create the Ipopt interface cppad_ipopt_solution solution; Ipopt::SmartPtr cppad_nlp = new cppad_ipopt_nlp( n, m, x_i, x_l, x_u, g_l, g_u, fg_info, &solution ); // Create an instance of the IpoptApplication using Ipopt::IpoptApplication; Ipopt::SmartPtr app = new IpoptApplication(); // turn off any printing app->Options()->SetIntegerValue("print_level", 0); app->Options()->SetStringValue("sb", "yes"); // maximum number of iterations app->Options()->SetIntegerValue("max_iter", 10); // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) app->Options()->SetNumericValue("tol", 1e-9); // derivative testing app->Options()-> SetStringValue("derivative_test", "second-order"); // Initialize the IpoptApplication and process the options Ipopt::ApplicationReturnStatus status = app->Initialize(); ok &= status == Ipopt::Solve_Succeeded; // Run the IpoptApplication status = app->OptimizeTNLP(cppad_nlp); ok &= status == Ipopt::Solve_Succeeded; /* Check some of the solution values */ ok &= solution.status == cppad_ipopt_solution::success; // double check_z_l[] = { 1.087871, 0., 0., 0. }; double check_z_u[] = { 0., 0., 0., 0. }; double rel_tol = 1e-6; // relative tolerance double abs_tol = 1e-6; // absolute tolerance for(j = 0; j < n; j++) { ok &= CppAD::NearEqual( check_x[j], solution.x[j], rel_tol, abs_tol ); ok &= CppAD::NearEqual( check_z_l[j], solution.z_l[j], rel_tol, abs_tol ); ok &= CppAD::NearEqual( check_z_u[j], solution.z_u[j], rel_tol, abs_tol ); } } return ok; } cppad-20170000.3/cppad_ipopt/test/multiple_solution.cpp0000644000175200017650000000742413057470462022215 0ustar coincoin-web// $Id: multiple_solution.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // Begin empty namespace using namespace cppad_ipopt; // --------------------------------------------------------------------------- /* f(x) = x[1]; k=0, ell=0, I[0] = 0, J[0] = 1 g_0 (x) = x[0]; k=0, ell=1, I[0] = 1, J[0] = 0 g_1 (x) = x[1]; k=0, ell=2, I[0] = 2, J[0] = 1 minimize f(x) subject to -1 <= g_0(x) <= 0 0 <= g_1 (x) <= 1 The solution is x[1] = 0 and x[0] arbitrary. */ class FG_J_changes : public cppad_ipopt_fg_info { private: bool retape_; public: // constructor FG_J_changes(bool retape_in) : retape_ (retape_in) { } size_t number_functions(void) { return 1; } size_t domain_size(size_t k) { size_t q; switch(k) { case 0: q = 1; break; default: assert(0); } return q; } size_t range_size(size_t k) { size_t p; switch(k) { case 0: p = 1; break; default: assert(0); } return p; } size_t number_terms(size_t k) { size_t L; switch(k) { case 0: L = 3; break; default: assert(0); } return L; } void index(size_t k, size_t ell, SizeVector&I, SizeVector& J) { assert( I.size() >= 1 ); assert( J.size() >= 1 ); I[0] = ell; if( ell == 0 ) { J[0] = 1; return; } J[0] = ell - 1; return; } // retape function bool retape(size_t k) { return retape_; } ADVector eval_r(size_t k, const ADVector& u) { assert( u.size() == 1 ); ADVector r(1); r[0] = u[0] ; return r; } }; } // end empty namespace bool multiple_solution(void) { bool ok = true; // number of independent variables (domain dimension for f and g) size_t n = 2; // number of constraints (range dimension for g) size_t m = 2; // initial value of the independent variables NumberVector x_i(n); NumberVector x_l(n); NumberVector x_u(n); size_t i = 0; for(i = 0; i < n; i++) { x_i[i] = 0.; x_l[i] = -1.0; x_u[i] = +1.0; } // lower and upper limits for g NumberVector g_l(m); NumberVector g_u(m); g_l[0] = -1; g_u[0] = 0.; g_l[1] = 0.; g_u[1] = 1.; // object for evaluating function bool retape = false; FG_J_changes my_fg_info(retape); cppad_ipopt_fg_info *fg_info = &my_fg_info; cppad_ipopt_solution solution; Ipopt::SmartPtr cppad_nlp = new cppad_ipopt_nlp( n, m, x_i, x_l, x_u, g_l, g_u, fg_info, &solution ); // Create an instance of the IpoptApplication using Ipopt::IpoptApplication; Ipopt::SmartPtr app = new IpoptApplication(); // turn off any printing app->Options()->SetIntegerValue("print_level", 0); app->Options()->SetStringValue("sb", "yes"); // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) app->Options()->SetNumericValue("tol", 1e-9); app->Options()-> SetStringValue("derivative_test", "second-order"); // Initialize the IpoptApplication and process the options Ipopt::ApplicationReturnStatus status = app->Initialize(); ok &= status == Ipopt::Solve_Succeeded; // Run the IpoptApplication status = app->OptimizeTNLP(cppad_nlp); ok &= status == Ipopt::Solve_Succeeded; /* Check solution status */ ok &= solution.status == cppad_ipopt_solution::success; ok &= CppAD::NearEqual(solution.x[1], 0., 1e-6, 1e-6); return ok; } cppad-20170000.3/cppad_ipopt/test/retape_k1_l1.cpp0000644000175200017650000000654113057470462020674 0ustar coincoin-web// $Id: retape_k1_l1.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // Begin empty namespace using namespace cppad_ipopt; // --------------------------------------------------------------------------- class FG_retape : public cppad_ipopt_fg_info { public: // derived class part of constructor FG_retape(void) { } // Evaluation of the objective f(x), and constraints g(x) // using an Algorithmic Differentiation (AD) class. ADVector eval_r(size_t k, const ADVector& x) { ADVector fg(2); // f(x) if( x[0] >= 1. ) fg[0] = .5 * (x[0] * x[0] + x[1] * x[1]); else fg[0] = x[0] + .5 * x[1] * x[1]; // g (x) fg[1] = x[0]; return fg; } bool retape(size_t k) { return true; } }; } // end of empty namespace bool retape_k1_l1(void) { bool ok = true; size_t j; // number of independent variables (domain dimension for f and g) size_t n = 2; // number of constraints (range dimension for g) size_t m = 1; // initial value of the independent variables NumberVector x_i(n); x_i[0] = 2.0; x_i[1] = 2.0; // lower and upper limits for x NumberVector x_l(n); NumberVector x_u(n); for(j = 0; j < n; j++) { x_l[j] = -10.; x_u[j] = +10.; } // lower and upper limits for g NumberVector g_l(m); NumberVector g_u(m); g_l[0] = -1.; g_u[0] = 1.0e19; // object in derived class FG_retape fg_retape; cppad_ipopt_fg_info *fg_info = &fg_retape; // create the Ipopt interface cppad_ipopt_solution solution; Ipopt::SmartPtr cppad_nlp = new cppad_ipopt_nlp( n, m, x_i, x_l, x_u, g_l, g_u, fg_info, &solution ); // Create an instance of the IpoptApplication using Ipopt::IpoptApplication; Ipopt::SmartPtr app = new IpoptApplication(); // turn off any printing app->Options()->SetIntegerValue("print_level", 0); app->Options()->SetStringValue("sb", "yes"); // maximum number of iterations app->Options()->SetIntegerValue("max_iter", 10); // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) app->Options()->SetNumericValue("tol", 1e-9); // derivative testing app->Options()-> SetStringValue("derivative_test", "second-order"); // Initialize the IpoptApplication and process the options Ipopt::ApplicationReturnStatus status = app->Initialize(); ok &= status == Ipopt::Solve_Succeeded; // Run the IpoptApplication status = app->OptimizeTNLP(cppad_nlp); ok &= status == Ipopt::Solve_Succeeded; /* Check some of the solution values */ ok &= solution.status == cppad_ipopt_solution::success; // double check_x[] = { -1., 0. }; double rel_tol = 1e-6; // relative tolerance double abs_tol = 1e-6; // absolute tolerance for(j = 0; j < n; j++) { ok &= CppAD::NearEqual( check_x[j], solution.x[j], rel_tol, abs_tol ); } return ok; } cppad-20170000.3/cppad_ipopt/test/makefile.am0000644000175200017650000000250213057470462020006 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # EXTRA_DIST = test.sh.in # check_PROGRAMS = test_more # AM_CXXFLAGS = -g $(CXX_FLAGS) # AM_CPPFLAGS = -I. \ -I$(top_srcdir) \ -I$(top_srcdir)/cppad_ipopt/src \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ -I$(IPOPT_DIR)/include # LDADD = \ -lcppad_ipopt \ $(CPPAD_IPOPT_LIBS) \ $(FCLIBS) \ $(PTHREAD_LIB) \ $(DL_LIB) AM_LDFLAGS = -L../src # test_more_SOURCES = \ test_more.cpp \ k_gt_one.cpp \ multiple_solution.cpp \ retape_k1_l1.cpp \ retape_k1_l2.cpp test: check ./test.sh cppad-20170000.3/cppad_ipopt/test/retape_k1_l2.cpp0000644000175200017650000000735713057470462020703 0ustar coincoin-web// $Id: retape_k1_l2.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace { // Begin empty namespace using namespace cppad_ipopt; // --------------------------------------------------------------------------- /* A test case were retaping is required, no constraints, and L[0] > 1. */ class FG_info : public cppad_ipopt_fg_info { public: // derived class part of constructor FG_info (void) { } // r_0 (u) = u if u > 1 and u^2 otherwise. ADVector eval_r(size_t k, const ADVector& u) { ADVector r(1); if( u[0] > 1 ) r[0] = u[0]; else r[0] = u[0] * u[0]; return r; } // operation sequence depends on u bool retape(size_t k) { return true; } // K = 1 size_t number_functions(void) { return 1; } // q[k] = 1 size_t domain_size(size_t k) { return 1; } // p[k] = 1 size_t range_size(size_t k) { return 1; } // L[k] = 2 size_t number_terms(size_t k) { return 2; } // I_{k,ell} = 0 // objective function index // J_{k,ell} = ell // argument index void index(size_t k, size_t ell, SizeVector& I, SizeVector& J) { I[0] = 0; J[0] = ell; } }; } // end empty namespace bool retape_k1_l2(void) { bool ok = true; size_t j; // number of independent variables (domain dimension for f and g) size_t n = 2; // no constraints (range dimension for g) size_t m = 0; // initial value of the independent variables NumberVector x_i(n); x_i[0] = 0.0; // below break in eval_r definition x_i[1] = 2.0; // above break in eval_r definition // lower and upper limits for x NumberVector x_l(n); NumberVector x_u(n); for(j = 0; j < n; j++) { x_l[j] = -5.0; x_u[j] = +5.0; } // lower and upper limits for g NumberVector g_l; NumberVector g_u; // object in derived class FG_info my_fg_info; cppad_ipopt_fg_info *fg_info = &my_fg_info; // create the Ipopt interface cppad_ipopt_solution solution; Ipopt::SmartPtr cppad_nlp = new cppad_ipopt_nlp( n, m, x_i, x_l, x_u, g_l, g_u, fg_info, &solution ); // Create an instance of the IpoptApplication using Ipopt::IpoptApplication; Ipopt::SmartPtr app = new IpoptApplication(); // turn off any printing app->Options()->SetIntegerValue("print_level", 0); app->Options()->SetStringValue("sb", "yes"); // maximum number of iterations app->Options()->SetIntegerValue("max_iter", 10); // approximate accuracy in first order necessary conditions; // see Mathematical Programming, Volume 106, Number 1, // Pages 25-57, Equation (6) app->Options()->SetNumericValue("tol", 1e-9); // derivative testing app->Options()-> SetStringValue("derivative_test", "second-order"); app->Options()-> SetNumericValue("point_perturbation_radius", 0.); // Initialize the IpoptApplication and process the options Ipopt::ApplicationReturnStatus status = app->Initialize(); ok &= status == Ipopt::Solve_Succeeded; // Run the IpoptApplication status = app->OptimizeTNLP(cppad_nlp); ok &= status == Ipopt::Solve_Succeeded; /* Check the solution values */ ok &= solution.status == cppad_ipopt_solution::success; // double rel_tol = 1e-6; // relative tolerance double abs_tol = 1e-6; // absolute tolerance for(j = 0; j < n; j++) ok &= CppAD::NearEqual( 0., solution.x[j], rel_tol, abs_tol); return ok; } cppad-20170000.3/cppad_ipopt/test/CMakeLists.txt0000644000175200017650000000342513057470462020457 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the cppad_ipopt/test directory tests # Inherit build tyope from ../CMakeList.txt # Local include directories to search (not in package_prefix/include) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/../src ) # Local link directories to search (not in external packages) LINK_DIRECTORIES( ${CMAKE_CURRENT_BINARY_DIR}/../src ${ipopt_LIBRARY_DIRS} ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(cppad_ipopt_test EXCLUDE_FROM_ALL test_more.cpp k_gt_one.cpp multiple_solution.cpp retape_k1_l1.cpp retape_k1_l2.cpp ) add_cppad_cxx_flags(cppad_ipopt_test) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES(cppad_ipopt_test cppad_ipopt ${cppad_lib} ${ipopt_LIBRARIES} ${colpack_libs} ) # Add the check_cppad_ipopt_test target ADD_CUSTOM_TARGET(check_cppad_ipopt_test cppad_ipopt_test DEPENDS cppad_ipopt_test cppad_ipopt ) MESSAGE(STATUS "make check_cppad_ipopt_test: available") # Change check depends in parent environment add_to_list(check_cppad_ipopt_depends check_cppad_ipopt_test) SET(check_cppad_ipopt_depends "${check_cppad_ipopt_depends}" PARENT_SCOPE) cppad-20170000.3/cppad_ipopt/test/test.sh.in0000644000175200017650000000125613057470462017637 0ustar coincoin-web#! /bin/bash -e # $Id: test.sh.in 2506 2012-10-24 19:36:49Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- export LD_LIBRARY_PATH=@CPPAD_IPOPT_LD_PATH@ ./test_more cppad-20170000.3/print_for/0002755000175200017650000000000013057470462014436 5ustar coincoin-webcppad-20170000.3/print_for/CMakeLists.txt0000644000175200017650000000251613057470462017200 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the print_for directory tests # Inherit environment from ../CMakeList.txt # Specifies build type for this directory. 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin print_for_cout.cpp$$ $spell const var av num inuse omp_alloc bool makefile CppAD cppad.hpp std::cout endl namespace newline \nv VecAD $$ $section Printing During Forward Mode: Example and Test$$ $mindex mode print$$ $head Running$$ To build this program and run its correctness test see $cref cmake_check$$. $head Source Code$$ $srccode%cpp% */ # include namespace { using std::cout; using std::endl; using CppAD::AD; // use of PrintFor to check for invalid function arguments AD check_log(const AD& y) { // check during recording if( y <= 0. ) cout << "check_log: y = " << y << " is <= 0" << endl; // check during zero order forward calculation PrintFor(y, "check_log: y == ", y , " which is <= 0\n"); return log(y); } } void print_for(void) { using CppAD::PrintFor; // independent variable vector size_t n = 1; CPPAD_TESTVECTOR(AD) ax(n); ax[0] = 1.; Independent(ax); // print a VecAD::reference object that is a parameter CppAD::VecAD av(1); AD Zero(0); av[Zero] = 0.; PrintFor("v[0] = ", av[Zero]); // Print a newline to separate this from previous output, // then print an AD object that is a variable. PrintFor("\nv[0] + x[0] = ", av[0] + ax[0]); // A conditional print that will not generate output when x[0] = 2. PrintFor(ax[0], "\n 2. + x[0] = ", 2. + ax[0], "\n"); // A conditional print that will generate output when x[0] = 2. PrintFor(ax[0] - 2., "\n 3. + x[0] = ", 3. + ax[0], "\n"); // A log evaluations that will result in an error message when x[0] = 2. AD var = 2. - ax[0]; AD log_var = check_log(var); // dependent variable vector size_t m = 2; CPPAD_TESTVECTOR(AD) ay(m); ay[0] = av[Zero] + ax[0]; // define f: x -> y and stop tape recording CppAD::ADFun f(ax, ay); // zero order forward with x[0] = 2 CPPAD_TESTVECTOR(double) x(n); x[0] = 2.; cout << "v[0] = 0" << endl; cout << "v[0] + x[0] = 2" << endl; cout << " 3. + x[0] = 5" << endl; cout << "check_log: y == 0 which is <= 0" << endl; // ./makefile.am expects "Test passes" at beginning of next output line cout << "Test passes if four lines above repeat below:" << endl; f.Forward(0, x); return; } int main(void) { bool ok = true; print_for(); size_t thread; for(thread = 0; thread < 2; thread++) { ok &= CppAD::omp_alloc::inuse(thread) == 0; ok &= CppAD::omp_alloc::available(thread) == 0; } if( ! ok ) return 1; return 0; } /* %$$ $head Output$$ Executing the program above generates the following output: $codep v[0] = 0 v[0] + x[0] = 2 Test passes if two lines above repeat below: v[0] = 0 v[0] + x[0] = 2 $$ $end */ cppad-20170000.3/print_for/test.sh0000755000175200017650000000143213057470462015752 0ustar coincoin-web#! /bin/bash -e # $Id: test.sh 2506 2012-10-24 19:36:49Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- ./print_for | tee test.log sed -e '/^Test passes/,\$$d' < test.log > test.1 sed -e '1,/^Test passes/d' < test.log > test.2 if ! diff test.1 test.2 ; then exit 1 ; fi cppad-20170000.3/print_for/makefile.am0000644000175200017650000000233213057470462016530 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # # Make sure that ../cppad-uninstalled.pc works for determining cflags if CppAD_PKG_CONFIG CPPAD_INCLUDE = `( \ export PKG_CONFIG_PATH=$(top_builddir)/pkgconfig ; \ pkg-config --cflags cppad \ )` else CPPAD_INCLUDE = -I$(top_srcdir) endif # # Microsoft project files EXTRA_DIST = test.sh # check_PROGRAMS = print_for # AM_CPPFLAGS = -I. $(CPPAD_INCLUDE) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) # AM_CXXFLAGS = -g $(CXX_FLAGS) # print_for_SOURCES = print_for.cpp test: check $(srcdir)/test.sh cppad-20170000.3/configure.ac0000644000175200017650000006036413057470462014731 0ustar coincoin-webdnl --------------------------------------------------------------------------- dnl CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell dnl dnl CppAD is distributed under multiple licenses. This distribution is under dnl the terms of the dnl GNU General Public License Version 3. dnl dnl A copy of this license is included in the COPYING file of this distribution. dnl Please visit http://www.coin-or.org/CppAD/ for information on other licenses. dnl --------------------------------------------------------------------------- dnl dnl Process this file with autoconf to produce a configure script. dnl package version bug-report AC_INIT([cppad], [20170000.3], [cppad@list.coin-or.org]) AM_SILENT_RULES([yes]) dnl By defalut disable maintainer mode when running configure; dnl --enable-maintainer-mode will enable it. dnl This avoids the autoconf and automake tools being launched by make AM_MAINTAINER_MODE dnl Set the default install prefix to the installers home directory dnl cygwin begin delete: AC_PREFIX_DEFAULT(${HOME}) dnl cygwin end delete: dnl cygwin replace: AC_PREFIX_DEFAULT(/usr) dnl Run any macros required for proper operation of generated makefiles dnl nostdinc: Do not define standard include directories in generated makefiles dnl Note this must come before AC_PROG_CC; see dnl http://lists.gnu.org/archive/html/automake/2010-08/msg00113.html AM_INIT_AUTOMAKE([nostdinc subdir-objects -Wall]) # check if we have ar program have_ar='yes' AM_PROG_AR([have_ar='no']) AC_MSG_NOTICE([have_ar = $have_ar]) dnl ---------------------------------------------------------------------- AC_MSG_NOTICE([*** Check command line arguments that are longer used ****]) if test "$CPP_ERROR_WARN" != "" ; then AC_MSG_ERROR([The CPP_ERROR_WARN configure option is now CXX_FLAGS]) fi dnl AC_ARG_WITH(SpeedExample, AC_HELP_STRING( [--with-SpeedExample], [is not necessary, see install instructions.]), [SpeedExample="yes"], [SpeedExample="no"] ) if test "$SpeedExample" = "yes" ; then AC_MSG_ERROR([--with-SpeedExample not necessary, see install instructions.]) fi dnl AC_ARG_WITH(profiling, AC_HELP_STRING( [--with-profiling], [is not necessary, see install instructions.]), [profiling="yes"], [profiling="no"] ) if test "$profiling" = "yes" ; then AC_MSG_ERROR([--with-profiling not necessary, see install instructions.]) fi dnl AC_ARG_WITH(Speed, AC_HELP_STRING( [--with-Speed], [is not necessary, see install instructions.]), [Speed="yes"], [Speed="no"] ) if test "$Speed" = "yes" ; then AC_MSG_ERROR([--with-Speed not necessary, see install instructions.]) fi dnl AC_ARG_WITH(Introduction, AC_HELP_STRING( [--with-Introduction], [is not necessary, see install instructions.]), [Introduction="yes"], [Introduction="no"] ) if test "$Introduction" = "yes" ; then AC_MSG_ERROR([--with-Introduction not necessary, see install instructions.]) fi dnl AC_ARG_WITH(Example, AC_HELP_STRING( [--with-Example], [is not necessary, see install instructions.]), [Example="yes"], [Example="no"] ) if test "$Example" = "yes" ; then AC_MSG_ERROR([--with-Example not necessary, see install instructions.]) fi dnl AC_ARG_WITH(TestMore, AC_HELP_STRING( [--with-TestMore], [is not necessary, see install instructions.]), [TestMore="yes"], [TestMore="no"] ) if test "$TestMore" = "yes" ; then AC_MSG_ERROR([--with-TestMore not necessary, see install instructions.]) fi dnl AC_ARG_WITH(PrintFor, AC_HELP_STRING( [--with-PrintFor], [is not necessary, see install instructions.]), [PrintFor="yes"], [PrintFor="no"] ) if test "$PrintFor" = "yes" ; then AC_MSG_ERROR([--with-PrintFor not necessary, see install instructions.]) fi AC_ARG_WITH(sparse_set, AC_HELP_STRING([--with-sparse_set], [no longer available]), [sparse_set="yes"], [sparse_set="no"] ) if test "$sparse_set" = "yes" ; then AC_MSG_ERROR([--with-sparse_set is no longer available]) fi AC_ARG_WITH(sparse_list, AC_HELP_STRING([--with-sparse_list], [no longer necessary]), [sparse_set="yes"], [sparse_set="no"] ) if test "$sparse_set" = "yes" ; then AC_MSG_ERROR([--with-sparse_set is no longer necessary]) fi dnl -------------------------------------------------------------------------- AC_MSG_NOTICE([****** Check command line arguments that are used ***********]) dnl ----------------------------------------------------------------------- dnl The case where enable_msvc != no is defined and supported by Ted Ralphs AC_MSG_CHECKING([--enable-msvc]) AC_ARG_ENABLE([msvc], [AC_HELP_STRING([--enable-msvc], [Prefer (i)cl/ifort/link over GNU on MinGW/Cygwin.])], [enable_msvc=$enableval], [enable_msvc=no] ) AC_MSG_RESULT([$enable_msvc]) dnl the prefix directory corresponding to CppAD ------------------------- dnl The following seems to work but NONE is not in autoconf specifications AC_MSG_CHECKING([--prefix]) if test "$prefix" = "NONE" ; then AC_MSG_RESULT([$HOME]) else AC_MSG_RESULT([$prefix]) fi dnl Are we installing the documentation ----------------------------------- dnl cygwin begin delete: AC_MSG_CHECKING([--with-Documentation]) AC_ARG_WITH(Documentation, AC_HELP_STRING([--with-Documentation], [default is no]), [Documentation="yes"], [Documentation="no"] ) AM_CONDITIONAL(CppAD_DOCUMENTATION, test "$Documentation" = "yes") AC_MSG_RESULT([$Documentation]) dnl cygwin end delete: dnl cygwin replace: AM_CONDITIONAL(CppAD_DOCUMENTATION, test "yes" = "yes") dnl Are we using standard vectors ---------------------------------------- AC_MSG_CHECKING([--with-stdvector]) AC_ARG_WITH(stdvector, AC_HELP_STRING([--with-stdvector], [default is no]), [stdvector="yes"], [stdvector="no"] ) if test "$stdvector" = "yes" ; then AC_SUBST(cppad_stdvector, 1) else AC_SUBST(cppad_stdvector, 0) fi AC_MSG_RESULT([$stdvector]) dnl Are we using boost vectors ---------------------------------------- AC_MSG_CHECKING([--with-boostvector]) AC_ARG_WITH(boostvector, AC_HELP_STRING([--with-boostvector], [default is no]), [boostvector="yes"], [boostvector="no"] ) AC_MSG_RESULT([$boostvector]) if test "$boostvector" = "yes" ; then if test "$stdvector" != "no" ; then AC_MSG_ERROR([cannot --with both stdvector and boostvector]) fi AC_SUBST(cppad_boostvector, 1) else AC_SUBST(cppad_boostvector, 0) fi dnl Are we using eigen vectors ---------------------------------------- AC_MSG_CHECKING([--with-eigenvector]) AC_ARG_WITH(eigenvector, AC_HELP_STRING([--with-eigenvector], [default is no]), [eigenvector="yes"], [eigenvector="no"] ) AC_MSG_RESULT([$eigenvector]) if test "$eigenvector" = "yes" ; then if test "$stdvector" != "no" ; then AC_MSG_ERROR([cannot --with both stdvector and eigenvector]) fi if test "$boostvector" != "no" ; then AC_MSG_ERROR([cannot --with both boostvector and eigenvector]) fi AC_SUBST(cppad_eigenvector, 1) else AC_SUBST(cppad_eigenvector, 0) fi dnl Are we including deprecated features in the install----------- AC_MSG_CHECKING([--with-deprecated]) AC_ARG_WITH(deprecated, AC_HELP_STRING( [--with-deprecated], [include an implicit AD constructor from any type] ), [deprecated="yes"], [deprecated="no"] ) AC_MSG_RESULT([$deprecated]) AM_CONDITIONAL(CppAD_DEPRECATED, test "$deprecated" = 'yes' ) if test "$deprecated" = "yes" ; then AC_SUBST(cppad_deprecated, "1") else AC_SUBST(cppad_deprecated, "0") fi dnl The postfix directiory corresponding to CppAD ------------------------ AC_MSG_CHECKING([POSTFIX_DIR]) AC_ARG_VAR(POSTFIX_DIR, [postfix directory for CppAD installation] ) AM_CONDITIONAL(CppAD_POSTFIX, test "$POSTFIX_DIR" != "") if test "$POSTFIX_DIR" != "" ; then AC_MSG_RESULT([$POSTFIX_DIR]) else AC_MSG_RESULT([no]) fi dnl The prefix corresponding to the installation of Adolc --------------- AC_MSG_CHECKING([ADOLC_DIR]) AC_ARG_VAR(ADOLC_DIR, [value of configure prefix directory during Adolc install] ) AM_CONDITIONAL(CppAD_ADOLC, test "$ADOLC_DIR" != "") if test "$ADOLC_DIR" != "" ; then AC_MSG_RESULT([$ADOLC_DIR]) if test "$have_ar" = "no"; then AC_MSG_ERROR([ar is missing and ADOLC_DIR is present]) fi else AC_MSG_RESULT([no]) fi dnl The prefix corresponding to the installation of Eigen --------------- AC_MSG_CHECKING([EIGEN_DIR]) AC_ARG_VAR(EIGEN_DIR, [value of configure prefix directory during Eigen install] ) AM_CONDITIONAL(CppAD_EIGEN_DIR, test "$EIGEN_DIR" != "") if test "$EIGEN_DIR" != "" ; then AC_MSG_RESULT([$EIGEN_DIR]) AC_SUBST(EIGEN_INCLUDE, [-I$EIGEN_DIR/include]) else AC_MSG_RESULT([no]) AC_SUBST(EIGEN_INCLUDE, []) fi dnl The directory corresponding to the installation of FADBAD ----------- AC_MSG_CHECKING([FADBAD_DIR]) AC_ARG_VAR(FADBAD_DIR, [parent directory directly above FADBAD++ directory] ) AM_CONDITIONAL(CppAD_FADBAD, test "$FADBAD_DIR" != "") if test "$FADBAD_DIR" != "" ; then AC_MSG_RESULT([$FADBAD_DIR]) if test "$have_ar" = "no"; then AC_MSG_ERROR([ar is missing and FADBAD_DIR is present]) fi else AC_MSG_RESULT([no]) fi dnl The directory corresponding to the installation of SACADO ----------- AC_MSG_CHECKING([SACADO_DIR]) AC_ARG_VAR(SACADO_DIR, [value of the configure prefix directory during Sacado install] ) AM_CONDITIONAL(CppAD_SACADO, test "$SACADO_DIR" != "") if test "$SACADO_DIR" != "" ; then AC_MSG_RESULT([$SACADO_DIR]) if test "$have_ar" = "no"; then AC_MSG_ERROR([ar is missing and SACADO_DIR is present]) fi else AC_MSG_RESULT([no]) fi dnl The directory corresponding to the installation of IPOPT ----------- AC_MSG_CHECKING([IPOPT_DIR]) AC_ARG_VAR(IPOPT_DIR, [value of the configure prefix directory during Ipopt install] ) AM_CONDITIONAL(CppAD_IPOPT, test "$IPOPT_DIR" != "") if test "$IPOPT_DIR" != "" ; then AC_MSG_RESULT([$IPOPT_DIR]) if test "$have_ar" = "no"; then AC_MSG_ERROR([ar is missing and IPOPT_DIR is present]) fi else AC_MSG_RESULT([no]) fi dnl The directory corresponding to the installation of BOOST ------------ AC_MSG_CHECKING([BOOST_DIR]) AC_ARG_VAR(BOOST_DIR, [parent directory directly above boost directory] ) AM_CONDITIONAL(CppAD_BOOST_DIR, test "$BOOST_DIR" != "") if test "$BOOST_DIR" != "" ; then AC_MSG_RESULT([$BOOST_DIR]) AC_SUBST(BOOST_INCLUDE, [-I$BOOST_DIR/include]) else AC_MSG_RESULT([no]) AC_SUBST(BOOST_INCLUDE,[]) fi dnl The C++ compiler flags CXX_FLAGS ------------------------------------- dnl see AC_SUBST(CXXFLAGS, "") next to AC_PROG_CXX # AC_MSG_CHECKING([CXX_FLAGS]) AC_ARG_VAR(CXX_FLAGS, [ CXXFLAGS is ignored, use CXX_FLAGS for compiler flags] ) # cxx_flags for fadbad and eigen if test "$CXX_FLAGS" != "" ; then AC_MSG_RESULT([$CXX_FLAGS]) cxx_flags_fadbad=`echo "$CXX_FLAGS" | sed -e 's|-Wshadow||'` cxx_flags_eigen="$cxx_flags_fadbda -Wno-long-long" else AC_MSG_RESULT([no]) cxx_flags_fadbad="" cxx_flags_eigen="" fi AC_SUBST(CXX_FLAGS_FADBAD, "$cxx_flags_fadbad") AC_SUBST(CXX_FLAGS_EIGEN, "$cxx_flags_eigen") dnl The compiler OpenMP flags OPENMP_FLAGS ---------------------------------- AC_MSG_CHECKING([OPENMP_FLAGS]) AC_ARG_VAR(OPENMP_FLAGS, [ flags that instruct compiler to interpret OpenMP directrives ] ) if test "$OPENMP_FLAGS" != "" ; then AC_MSG_RESULT([$OPENMP_FLAGS]) else AC_MSG_RESULT([no]) fi AM_CONDITIONAL(CppAD_OPENMP, test "$OPENMP_FLAGS" != "") dnl The compiler OpenMP flags MAX_NUM_THREADS ------------------------------- AC_MSG_CHECKING([MAX_NUM_THREADS]) AC_ARG_VAR(MAX_NUM_THREADS, [ maximum number of threads that can be used with CppAD ] ) if test "$MAX_NUM_THREADS" != "" ; then AC_MSG_RESULT([$MAX_NUM_THREADS]) if test "$MAX_NUM_THREADS" -lt "4" ; then AC_MSG_ERROR( [ MAX_NUM_THREADS=$MAX_NUM_THREADS is less than 4 ] ) fi max_num_threads="$MAX_NUM_THREADS" else max_num_threads="48" AC_MSG_RESULT([no, using default value $max_num_threads]) fi AC_SUBST(cppad_max_num_threads, [$max_num_threads]) dnl type used for addresses in AD tapes [ default = unsigned int ] ----------- AC_MSG_CHECKING([TAPE_ADDR_TYPE]) AC_ARG_VAR(TAPE_ADDR_TYPE, [type used for addresses in AD tapes]) if test "$TAPE_ADDR_TYPE" == "" ; then addr_t="unsigned int" else addr_t="$TAPE_ADDR_TYPE" fi AC_SUBST(cppad_tape_addr_type, [$addr_t]) AC_MSG_RESULT([$addr_t]) ok="no" if test "$addr_t" == "size_t" ; then ok="yes" fi if test "$addr_t" == "int" ; then AC_MSG_WARN( [TAPE_ADDR_TYPE=int is for CppAD developers (not users)] ) ok="yes" fi if test "$addr_t" == "unsigned int" ; then ok="yes" fi if test "$addr_t" == "unsigned short int" ; then ok="yes" fi if test "$ok" == "no" ; then AC_MSG_ERROR( [$addr_t is not a valid choice for TAPE_ADDR_TYPE] ) fi dnl type used for tape identifier [ default = unsigned int ] ----------- AC_MSG_CHECKING([TAPE_ID_TYPE]) AC_ARG_VAR(TAPE_ID_TYPE, [type used for addresses in AD tapes]) if test "$TAPE_ID_TYPE" == "" ; then tape_id_t="unsigned int" else tape_id_t="$TAPE_ID_TYPE" fi AC_SUBST(cppad_tape_id_type, [$tape_id_t]) AC_MSG_RESULT([$tape_id_t]) ok="no" if test "$tape_id_t" == "size_t" ; then ok="yes" fi if test "$tape_id_t" == "int" ; then AC_MSG_WARN( [TAPE_ID_TYPE=int is for CppAD developers (not users)] ) ok="yes" fi if test "$tape_id_t" == "unsigned int" ; then ok="yes" fi if test "$tape_id_t" == "unsigned short int" ; then ok="yes" fi if test "$ok" == "no" ; then AC_MSG_ERROR( [$tape_id_t is not a valid choice for TAPE_ID_TYPE] ) fi AC_MSG_NOTICE([********** End Checking Command Line arguments ***************]) dnl -------------------------------------------------------------------------- if test "$enable_msvc" == "no" then cxx_list="g++ clang++ CC pgCC icpc gpp cxx cc++" cc_list="gcc clang cc pgcc icc" fc_list="gfortran ifort g95 fort77 f77 g77 pgf90 pgf77 ifc frt af77" else dnl This case defined and supported by Ted Ralphs cxx_list="icl cl g++" cc_list="icl cl gcc" fc_list="ifort gfortran" fi dnl -------------------------------------------------------------------------- dnl AC_PROG_CXX([compiler-search-list]) outputs CXX as C++ compiler to use AC_PROG_CXX([$cxx_list]) dnl erase any setting of CXXFLAGS, see CXX_FLAGS documentation AC_SUBST(CXXFLAGS, "") dnl AC_PROG_CC([compiler-search-list]) outputs CC as C++ compiler to use AC_PROG_CC([$cc_list]) dnl erase any setting of CFLAGS AC_SUBST(CFLAGS, "") dnl AC_PROG_FC ([compiler-search-list], [dialect]) AC_PROG_FC([$fc_list]) dnl not compiling any fortran so no need to touch flags dnl Check for pkgconfig AC_CHECK_PROG(have_pkg_config, [pkg-config], [yes], [no]) AM_CONDITIONAL(CppAD_PKG_CONFIG, test "$have_pkg_config" = "yes") dnl check if we can build libraries AM_CONDITIONAL(CppAD_HAVE_AR, test "$have_ar" = 'yes' ) if test "$have_ar" = 'no'; then AC_MSG_WARN( [cannot build any libraries because ar is missing; e.g,, speed/* not built] ) fi dnl test_one.sh.in settings for cppad_cxx_flags (no longer used ?) AC_SUBST(cppad_cxx_flags, "-g -O0") dnl auto-tools version does not colpack AC_SUBST(cppad_has_colpack, 0) dnl auto-tools version will assumes mkstemp is available. AC_SUBST(cppad_has_mkstemp, 1) AC_SUBST(cppad_has_tmpnam_s, 0) dnl auto-tools version cannot use c++11 compiler dnl so supress corresponding features AC_SUBST(cppad_has_nullptr, 0) AC_SUBST(cppad_has_rvalue, 0) AC_SUBST(cppad_has_cstdint_8_to_64, 0) AC_SUBST(cppad_cplusplus_201100_ok, 0) AC_SUBST(cppad_has_steady_clock, 0) dnl Determine if size_t has same size as unsigned int AC_CHECK_SIZEOF([size_t]) AC_CHECK_SIZEOF([unsigned int]) if test "$ac_cv_sizeof_size_t" != "$ac_cv_sizeof_unsigned_int" ; then AC_SUBST(cppad_size_t_not_unsigned_int, 1) else AC_SUBST(cppad_size_t_not_unsigned_int, 0) fi dnl Determine which definition we are using for CPPAD_TESTVECTOR if test "$stdvector$boostvector$eigenvector" = "nonono" ; then AC_SUBST(cppad_cppadvector, 1) else AC_SUBST(cppad_cppadvector, 0) fi dnl the gettimeofday check automatically generates a yes / no configure msg AC_CHECK_FUNC( gettimeofday, [gettimeofday="yes"], [gettimeofday="no"] ) if test "$gettimeofday" = "yes" ; then AC_SUBST(cppad_has_gettimeofday, 1) else AC_SUBST(cppad_has_gettimeofday, 0) fi dnl Use LIBTOOL for cppad_ipopt ? dnl AC_PROG_LIBTOOL dnl Determine if ranlib is present and where it is if present (set RANLIB) AC_PROG_RANLIB AC_MSG_CHECKING([whether using Microsoft C++ compiler]) AM_CONDITIONAL(CppAD_MS_COMPILER, test "$CXX" == "cl" || test "$CXX" == "icl") if test "$CXX" == "cl" || test "$CXX" == "icl"; then AC_MSG_RESULT([yes]) else AC_MSG_RESULT([no]) fi dnl Have configure check source directory to see if cppad/cppad.hpp is there AC_CONFIG_SRCDIR(cppad/cppad.hpp) dnl AC_PROG_CP outputs CPP as command to run C preprocessor AC_PROG_CPP dnl Do nothing if complier supports inline, otherwise try to find a subsitute dnl definition or, if cannot, define inline as empty AC_C_INLINE dnl determine FCLIBS, flags necessary for linking C++ with modern fortran AC_FC_LIBRARY_LDFLAGS dnl absolute path corresponding to top_builddig and top_srcdir in makefile.am dnl (used by cppad-uninstalled.pc.in). abs_top_builddir=`pwd` AC_SUBST(ABS_TOP_BUILDDIR, "$abs_top_builddir") abs_top_srcdir=`cd $srcdir ; pwd` AC_SUBST(ABS_TOP_SRCDIR, "$abs_top_srcdir") dnl -------------------------------------------------------------------------- dnl Check for C libraries dnl check for pthread library AC_CHECK_LIB( [pthread], [pthread_barrier_wait], [pthread="yes"], [pthread="no"] ) AM_CONDITIONAL(CppAD_PTHREAD, test "$pthread" = "yes") if test "$pthread" == "yes" ; then AC_SUBST(PTHREAD_LIB,"-lpthread") else AC_SUBST(PTHREAD_LIB,"") fi dnl check for dl library AC_SUBST(DL_LIB, "") AC_CHECK_LIB( [dl], [dlopen], [DL_LIB="-ldl"], [DL_LIB=""] ) dnl -------------------------------------------------------------------------- dnl check for boost thread library AC_LANG_PUSH([C++]) LDFLAGS_save=$LDFLAGS CXXFLAGS_save=$CXXFLAGS boost_thread_found='no' if test "$BOOST_DIR" != '' ; then CXXFLAGS="-I$BOOST_DIR/include $CXXFLAGS" fi if test "$BOOST_DIR" == '' && test "$boost_thread_found" == 'no' ; then bthread_lib='-lboost_thread-mt' LDFLAGS="$LDFLAGS_save $bthread_lib" AC_LINK_IFELSE( [AC_LANG_PROGRAM( [# include ], [boost::barrier wait(1);] )], [boost_thread_found='yes'], [boost_thread_found='no'] ) fi if test "$BOOST_DIR" != '' && test "$boost_thread_found" == 'no' ; then bthread_lib="$BOOST_DIR/lib/libboost_thread-mt.so" LDFLAGS="$LDFLAGS_save $bthread_lib" AC_LINK_IFELSE( [AC_LANG_PROGRAM( [# include ], [boost::barrier wait(1);] )], [boost_thread_found='yes'], [boost_thread_found='no'] ) fi if test "$BOOST_DIR" != '' && test "$boost_thread_found" == 'no' ; then bthread_lib="$BOOST_DIR/lib/libboost_thread-mt.a" LDFLAGS="$LDFLAGS_save $bthread_lib" AC_LINK_IFELSE( [AC_LANG_PROGRAM( [# include ], [boost::barrier wait(1);] )], [boost_thread_found='yes'], [boost_thread_found='no'] ) fi if test "$BOOST_DIR" == '' && test "$boost_thread_found" == 'no' ; then bthread_lib='-lboost_thread' LDFLAGS="$LDFLAGS_save $bthread_lib" AC_LINK_IFELSE( [AC_LANG_PROGRAM( [# include ], [boost::barrier wait(1);] )], [boost_thread_found='yes'], [boost_thread_found='no'] ) fi if test "$BOOST_DIR" != '' && test "$boost_thread_found" == 'no' ; then bthread_lib="$BOOST_DIR/lib/libboost_thread.so" LDFLAGS="$LDFLAGS_save $bthread_lib" AC_LINK_IFELSE( [AC_LANG_PROGRAM( [# include ], [boost::barrier wait(1);] )], [boost_thread_found='yes'], [boost_thread_found='no'] ) fi if test "$BOOST_DIR" != '' && test "$boost_thread_found" == 'no' ; then bthread_lib="$BOOST_DIR/lib/libboost_thread.a" LDFLAGS="$LDFLAGS_save $bthread_lib" AC_LINK_IFELSE( [AC_LANG_PROGRAM( [# include ], [boost::barrier wait(1);] )], [boost_thread_found='yes'], [boost_thread_found='no'] ) fi AM_CONDITIONAL(CppAD_BTHREAD, test "$boost_thread_found" = 'yes') if test "$boost_thread_found" == 'yes' ; then AC_SUBST(BTHREAD_LIB,"$bthread_lib") AC_MSG_RESULT([boost::thread library... yes]) else AC_SUBST(BTHREAD_LIB,'') AC_MSG_RESULT([boost::thread library... no]) fi LDFLAGS=$LDFLAGS_save CXXFLAGS=$CXXFLAGS_save AC_LANG_POP([C++]) # dnl -------------------------------------------------------------------------- dnl Library directories if test -e $IPOPT_DIR/lib/coin ; then IPOPT_LIBS="-L $IPOPT_DIR/lib/coin -L $IPOPT_DIR/lib/coin/ThirdParty" IPOPT_LD_PATH="$IPOPT_DIR/lib/coin:$IPOPT_DIR/lib/coin/ThirdParty" else IPOPT_LIBS="-L $IPOPT_DIR/lib" IPOPT_LD_PATH="$IPOPT_DIR/lib" fi AC_SUBST(CPPAD_IPOPT_LD_PATH, "$IPOPT_LD_PATH") # AC_SUBST(CPPAD_IPOPT_LIBS, "$IPOPT_LIBS -lipopt") if test "$have_pkg_config" == "yes"; then dnl set CPPAD_IPOPT_LIBS PKG_CONFIG_PATH="$IPOPT_DIR/lib/pkgconfig:$IPOPT_DIR/share/pkgconfig" PKG_CONFIG_PATH="$PKG_CONFIG_PATH:$IPOPT_DIR/lib64/pkgconfig" export PKG_CONFIG_PATH if pkg-config --libs ipopt >& /dev/null ; then CPPAD_IPOPT_LIBS=`pkg-config --libs ipopt` else dnl check for blas library AC_LANG_PUSH([Fortran]) AC_CHECK_LIB( [blas], [ddot], [CPPAD_IPOPT_LIBS="$CPPAD_IPOPT_LIBS -lblas"], ) dnl check for lapack library AC_CHECK_LIB( [lapack], [dgesv], [CPPAD_IPOPT_LIBS="$CPPAD_IPOPT_LIBS -llapack"], ) AC_LANG_POP([Fortran]) fi else dnl check for blas library AC_LANG_PUSH([Fortran]) AC_CHECK_LIB( [blas], [ddot], [CPPAD_IPOPT_LIBS="$CPPAD_IPOPT_LIBS -lblas"], ) dnl check for lapack library AC_CHECK_LIB( [lapack], [dgesv], [CPPAD_IPOPT_LIBS="$CPPAD_IPOPT_LIBS -llapack"], ) AC_LANG_POP([Fortran]) fi AC_MSG_RESULT([cppad_ipopt_nlp libraries: $CPPAD_IPOPT_LIBS]) dnl -------------------------------------------------------------------------- dnl Names set here so same cppad.pc.in works for both with cmake and autoconf. dnl (note that autoconf configuration does not allow for Colpack). dnl AC_SUBST(cppad_description, "Differentiation of C++ Algorithms") AC_SUBST(cppad_version, ${PACKAGE_VERSION} ) AC_SUBST(cppad_url, "http://www.coin-or.org/CppAD") if test "$prefix" == "NONE" ; then cppad_pkgconfig_cflags_value="-I$HOME/include" cppad_pkgconfig_libs_value="-L$HOME/lib" else cppad_pkgconfig_cflags_value="-I$prefix/include" cppad_pkgconfig_libs_value="-L$prefix/lib" fi if test "$POSTFIX_DIR" != "" ; then cppad_pkgconfig_cflags_value="$cppad_pkgconfig_cflags_value/$POSTFIX_DIR" cppad_pkgconfig_libs_value="$cppad_pkgconfig_libs_value/$POSTFIX_DIR" fi if test "$IPOPT_DIR" == "" ; then cppad_pkgconfig_libs_value="" cppad_pkgconfig_requires_value="" else cppad_pkgconfig_libs_value="$cppad_pkgconfig_libs_value -lcppad_ipopt" cppad_pkgconfig_requires_value="ipopt" fi AC_SUBST(cppad_pkgconfig_cflags, "$cppad_pkgconfig_cflags_value") AC_SUBST(cppad_pkgconfig_libs, "$cppad_pkgconfig_libs_value") AC_SUBST(cppad_pkgconfig_requires, "$cppad_pkgconfig_requires_value") AC_SUBST(cppad_prefix, "$prefix") AC_SUBST(cppad_abs_includedir, "$includedir") dnl dnl names set here so cppad.pc-uninstalled works both with cmake and autoconf AC_SUBST(cppad_SOURCE_DIR, ${ABS_TOP_SRCDIR} ) dnl dnl names set here so */test_one.sh.in works both with cmake and autoconf dnl (no longer used ?) AC_SUBST(adolc_prefix, ${ADOLC_DIR} ) AC_SUBST(eigen_prefix, ${EIGEN_DIR} ) AC_SUBST(ipopt_prefix, ${IPOPT_DIR} ) dnl dnl ----------------------------------------------------------------------- dnl AC_CONFIG_FILES(file-list) for each file in the list, configure will dnl read file.in, do its substitutions, and create file AC_CONFIG_FILES([ cppad/configure.hpp cppad_ipopt/example/test.sh cppad_ipopt/speed/test.sh cppad_ipopt/test/test.sh example/ipopt_solve/test.sh pkgconfig/cppad.pc pkgconfig/cppad-uninstalled.pc makefile compare_c/makefile cppad_ipopt/src/makefile cppad_ipopt/example/makefile cppad_ipopt/speed/makefile cppad_ipopt/test/makefile example/makefile example/atomic/makefile example/ipopt_solve/makefile example/optimize/makefile introduction/get_started/makefile introduction/exp_apx/makefile multi_thread/makefile multi_thread/test_multi/makefile print_for/makefile speed/adolc/makefile speed/cppad/makefile speed/double/makefile speed/example/makefile speed/fadbad/makefile speed/profile/makefile speed/profile/gprof.sed speed/sacado/makefile speed/src/makefile test_more/makefile ]) dnl END AC_CONFIG_FILES dnl the comment line above is used by ./new_stable.sh AC_CONFIG_COMMANDS( [example_ipopt_solve_test.sh], [chmod +x example/ipopt_solve/test.sh], ) [] AC_CONFIG_COMMANDS( [cppad_ipopt_example_test.sh], [chmod +x cppad_ipopt/example/test.sh], ) [] AC_CONFIG_COMMANDS( [cppad_ipopt_speed_test.sh], [chmod +x cppad_ipopt/speed/test.sh], [] ) AC_CONFIG_COMMANDS( [cppad_ipopt_test_test.sh], [chmod +x cppad_ipopt/test/test.sh], [] ) dnl create all the requested output files AC_OUTPUT cppad-20170000.3/INSTALL0000644000175200017650000000006112450414402013444 0ustar coincoin-webSee http://www.coin-or.org/CppAD/Doc/install.htm cppad-20170000.3/pkgconfig/0002755000175200017650000000000013057470462014403 5ustar coincoin-webcppad-20170000.3/pkgconfig/CMakeLists.txt0000644000175200017650000000512513057470462017144 0ustar coincoin-web# $Id: CMakeLists.txt 3859 2017-01-01 10:59:24Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Construct cppad.pc from cppad.pc.in; see # http://people.freedesktop.org/~dbn/pkg-config-guide.html # # Setting that are always included SET(cppad_pkgconfig_cflags "-I${cppad_abs_includedir}") SET(cppad_pkgconfig_libs "") SET(cppad_pkgconfig_requires "") # # Settings that are only included if cppad is configured with ipopt. # (Note that ipopt has a pkgconfig file.) IF( ipopt_prefix ) SET(cppad_pkgconfig_requires "ipopt") SET(cppad_pkgconfig_libs "-L${cppad_abs_libdir} -lcppad_ipopt") ENDIF( ipopt_prefix ) # # Settings that are only included if cppad is configured with colpack # (Note that colpack does not have a pkgconfig file.) IF( colpack_prefix ) SET(cppad_pkgconfig_libs "${cppad_pkgconfig_libs} -lColPack") FOREACH(dir ${cmake_install_libdirs}) IF(IS_DIRECTORY ${colpack_prefix}/${dir} ) SET(cppad_pkgconfig_libs "${cppad_pkgconfig_libs} -L${colpack_prefix}/${dir}" ) ENDIF(IS_DIRECTORY ${colpack_prefix}/${dir} ) ENDFOREACH(dir) FOREACH(dir ${cmake_install_includedirs}) IF(IS_DIRECTORY ${colpack_prefix}/${dir} ) SET(cppad_pkgconfig_cflags "${cppad_pkgconfig_cflags} -I${colpack_prefix}/${dir}" ) ENDIF(IS_DIRECTORY ${colpack_prefix}/${dir} ) ENDFOREACH(dir) ENDIF( colpack_prefix ) # print_variable(cppad_pkgconfig_cflags) print_variable(cppad_pkgconfig_libs) print_variable(cppad_pkgconfig_requires) # # Copy a file to another location and modify its contents. # configure_file(InputFile OutputFile [COPYONLY] [ESCAPE_QUOTES] [@ONLY]) CONFIGURE_FILE( ${CMAKE_CURRENT_SOURCE_DIR}/cppad.pc.in ${CMAKE_CURRENT_BINARY_DIR}/cppad.pc ) CONFIGURE_FILE( ${CMAKE_CURRENT_SOURCE_DIR}/cppad-uninstalled.pc.in ${CMAKE_CURRENT_BINARY_DIR}/cppad-uninstalled.pc ) # During install copy cppad.pc to CMAKE_INSTALL_PREFIX/ # install(FILES files... DESTINATION # [PERMISSIONS permissions...] # [CONFIGURATIONS [Debug|Release|...]] # [COMPONENT ] # [RENAME ] [OPTIONAL]) INSTALL(FILES ${CMAKE_CURRENT_BINARY_DIR}/cppad.pc DESTINATION ${cppad_abs_datadir}/pkgconfig ) cppad-20170000.3/pkgconfig/cppad-uninstalled.pc.in0000644000175200017650000000161513057470462020744 0ustar coincoin-web# $Id: cppad-uninstalled.pc.in 3754 2015-11-26 22:23:05Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # This file is used with pkg-config to include CppAD before it is installed. Name: cppad Description: @cppad_description@ Version: @cppad_version@ URL: @cppad_url@ Cflags: -I@cppad_SOURCE_DIR@ Libs: -L@cppad_BINARY_DIR@/lib -lcppad_lib Requires: cppad-20170000.3/pkgconfig/cppad.pc.in0000644000175200017650000000257613057470462016433 0ustar coincoin-web# $Id: cppad.pc.in 3760 2015-12-01 04:12:28Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # This file is used with pkg-config to include CppAD after it is installed # ------------------------------------------------------------------------- # HACK: With no specifications as to what will work in the future, set the # values 'includedir' and 'prefix' so cppad.pc works with the 2015-01-21 # verison of https://build.opensuse.org/package/view_file/ # windows:mingw:win32/mingw32-filesystem/mingw32-install-post.sh?expand=1 prefix=@cppad_prefix@ includedir=@cppad_abs_includedir@ # ------------------------------------------------------------------------- Name: cppad Description: @cppad_description@ Version: @cppad_version@ URL: @cppad_url@ Cflags: @cppad_pkgconfig_cflags@ Libs: @cppad_pkgconfig_libs@ Requires: @cppad_pkgconfig_requires@ cppad-20170000.3/build.sh0000755000175200017650000003530013057470462014071 0ustar coincoin-web#! /bin/bash -e # $Id: build.sh 3828 2016-08-27 22:19:01Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # build script for use with auto-tools install # ----------------------------------------------------------------------------- # prefix directories for the corresponding packages # # This test script no longer works with the current version of ADOLC # ADOLC_DIR=$HOME/prefix/adolc # BOOST_DIR=/usr CPPAD_DIR=$HOME/prefix/cppad EIGEN_DIR=$HOME/prefix/eigen FADBAD_DIR=$HOME/prefix/fadbad IPOPT_DIR=$HOME/prefix/ipopt SACADO_DIR=$HOME/prefix/sacado # version type is one of "trunk" or "stable" version_type="stable" # ----------------------------------------------------------------------------- if [ $0 != "./build.sh" ] then echo "./build.sh: must be executed in the directory that contians it" exit 1 fi if [ "$2" != "" ] then # when running multiple options, start by removing old log files touch junk.log list=`ls *.log` for log in $list do echo "rm $log" rm $log done # # run multiple options in order for option in $* do echo "==============================================================" echo "begin: ./build.sh $option" ./build.sh $option done echo "==============================================================" exit 0 fi # ----------------------------------------------------------------------------- if [ ! -e build ] then echo "mkdir build" mkdir build fi # ----------------------------------------------------------------------------- # Today's date in yyyy-mm-dd decimal digit format where # yy is year in century, mm is month in year, dd is day in month. yyyy_mm_dd=`date +%F` # # Version of cppad that corresponds to today. if [ "$version_type" == "trunk" ] then version=`bin/version.sh get` else version=`grep '^ *AC_INIT(' configure.ac | sed -e 's/[^,]*, *\([^ ,]*\).*/\1/' -e 's|\[||' -e 's|\]||'` yyyy_mm_dd=`echo $version | sed -e 's|\..*||' -e 's|\(....\)\(..\)|\1-\2-|'` fi # # Files are created by the configure command and copied to the source tree configure_file_list=" cppad/configure.hpp " # ----------------------------------------------------------------------------- # change version to current date if [ "$1" = "version" ] then echo 'bin/version.sh check' bin/version.sh check # echo "OK: ./build.sh version" exit 0 fi # ----------------------------------------------------------------------------- if [ "$1" = "automake" ] then # # check that autoconf and automake output are in original version makefile_in=`sed configure.ac \ -n \ -e '/END AC_CONFIG_FILES/,$d' \ -e '1,/AC_CONFIG_FILES/d' \ -e 's|/makefile$|&.in|' \ -e '/\/makefile.in/p'` auto_output=" depcomp install-sh missing configure config.guess config.sub $makefile_in " missing="" for name in $auto_output do if [ ! -e $name ] then if [ "$missing" != "" ] then missing="$missing, $name" else missing="$name" fi else # force remake of files rm "$name" fi done if [ "$missing" != "" ] then echo "The following files:" echo " $missing" echo "are not in subversion repository." echo "Check them in when this command is done completes." fi # echo "aclocal" aclocal # echo "skipping libtoolize" # echo "libtoolize -c -f -i" # if ! libtoolize -c -f -i # then # exit 1 # fi # echo "autoconf" autoconf # echo "automake --add-missing" automake --add-missing # link_list="missing install-sh depcomp config.sub config.guess" for name in $link_list do if [ -h "$name" ] then echo "Converting $name from a link to a regular file" # echo "cp $name $name.$$" cp $name $name.$$ # echo "mv $name.$$ $name" mv $name.$$ $name fi done # echo "OK: ./build.sh automake" exit 0 fi # ----------------------------------------------------------------------------- # configure if [ "$1" == "configure" ] then log_dir=`pwd` log_file="$1.log" # echo "cd build" cd build # dir_list=" --prefix=$CPPAD_DIR " if [ -e $BOOST_DIR/include/boost ] then dir_list="$dir_list BOOST_DIR=$BOOST_DIR" #_build_test_only: if [ ! -e $EIGEN_DIR/include/Eigen ] #_build_test_only: then #_build_test_only: dir_list="$dir_list --with-boostvector" #_build_test_only: fi fi if [ -e $EIGEN_DIR/include/Eigen ] then dir_list="$dir_list EIGEN_DIR=$EIGEN_DIR" #_build_test_only: dir_list="$dir_list --with-eigenvector" fi if [ -e $FADBAD_DIR/include/FADBAD++ ] then dir_list="$dir_list FADBAD_DIR=$FADBAD_DIR" fi if [ -e $IPOPT_DIR/include/coin/IpIpoptApplication.hpp ] then dir_list="$dir_list IPOPT_DIR=$IPOPT_DIR" fi if [ -e $SACADO_DIR/include/Sacado.hpp ] then dir_list="$dir_list SACADO_DIR=$SACADO_DIR" fi # Use =int (a signed type) to do more checking for # slicing from size_t to addr_t. special_types="" #_build_test_only: special_types="TAPE_ADDR_TYPE=int TAPE_ID_TYPE=int" # dir_list=`echo $dir_list | sed -e 's|\t\t*| |g'` cxx_flags="-Wall -ansi -pedantic-errors -std=c++98 -Wshadow" #_build_test_only: if [ -e $EIGEN_DIR/include/Eigen ] #_build_test_only: then #_build_test_only: cxx_flags="-Wall -ansi -pedantic-errors -std=c++98 -Wno-long-long -Wno-sign-compare" #_build_test_only: fi cat << EOF ../configure > $log_file \\ $dir_list \\ CXX_FLAGS=\"$cxx_flags\" \\ $special_types OPENMP_FLAGS=-fopenmp \\ --with-Documentation \\ --with-deprecated EOF # ../configure > $log_dir/$log_file \ $dir_list \ CXX_FLAGS="$cxx_flags" \ $special_types OPENMP_FLAGS=-fopenmp \ --with-Documentation \ --with-deprecated # for file in $configure_file_list do echo "cp $file ../$file" cp $file ../$file done # echo "OK: ./build.sh configure" exit 0 fi # ----------------------------------------------------------------------------- if [ "$1" = "dist" ] then # ---------------------------------------------------------------------- # Things to do in the original source directory # ---------------------------------------------------------------------- echo "Only include the *.xml version of the documentation in distribution" if ! grep < doc.omh > /dev/null \ 'This comment is used to remove the table below' then echo "Missing comment expected in doc.omh" exit 1 fi echo "sed -i.save doc.omh ..." sed -i.save doc.omh \ -e '/This comment is used to remove the table below/,/$tend/d' # if [ -e doc ] then echo "rm -r doc" rm -r doc fi # echo "bin/run_omhelp.sh xml" if ! bin/run_omhelp.sh xml then echo "mv doc.omh.save doc.omh" mv doc.omh.save doc.omh exit 1 fi # echo "mv doc.omh.save doc.omh" mv doc.omh.save doc.omh # No longer run these because tested when bin/package.sh is run. # Run automated checking of file names in original source directory # list=" # check_define.sh # check_example.sh # check_if.sh # check_include_def.sh # check_include_file.sh # check_include_omh.sh # check_makefile.sh # check_op_code.sh # check_replace.sh # check_svn_id.sh # check_verbatim.sh # " # for check in $list # do # echo "bin/$check" # bin/$check # done # ---------------------------------------------------------------------- # Things to do in the build directory # ---------------------------------------------------------------------- echo "cd build" cd build # if [ -e cppad-$version ] then echo "rm -rf cppad-$version" rm -rf cppad-$version fi for file in cppad-*.tgz do if [ -e $file ] then echo "rm $file" rm $file fi done # echo "make dist" make dist # if [ ! -e cppad-$version.tar.gz ] then echo "cppad-$version.tar.gz does not exist" echo "perhaps version is out of date" # exit 1 fi # change *.tgz to *.epl.tgz echo "mv cppad-$version.tar.gz cppad-$version.epl.tgz" mv cppad-$version.tar.gz cppad-$version.epl.tgz # echo "OK: ./build.sh dist" exit 0 fi # ----------------------------------------------------------------------------- # omhelp comes after dist because dist only includes one help output if [ "$1" = "omhelp" ] then if ! grep < doc.omh > /dev/null \ 'This comment is used to remove the table below' then echo "doc.omh is missing a table." echo "Try re-running build.sh configure." fi for flag in "printable" "" do # Run xml after htm so that index.htm points to cppad.xml # (see run_omhelp.sh). for ext in htm xml do echo "bin/run_omhelp.sh $ext $flag" bin/run_omhelp.sh $ext $flag done done # echo "OK: ./build.sh omhelp" exit 0 fi # ----------------------------------------------------------------------------- if [ "$1" = "doxygen" ] then echo "bin/run_doxygen.sh" bin/run_doxygen.sh # echo "OK: ./build.sh doxygen" exit 0 fi # ----------------------------------------------------------------------------- if [ "$1" = "gpl" ] then # create GPL licensed version echo "bin/gpl_license.sh cppad-$version build build" bin/gpl_license.sh cppad-$version build build # echo "OK: ./build.sh gpl" exit 0 fi # ----------------------------------------------------------------------------- if [ "$1" = "copy2doc" ] then for ext in epl gpl do echo "cp build/cppad-$version.$ext.tgz doc/cppad-$version.$ext.tgz" cp build/cppad-$version.$ext.tgz doc/cppad-$version.$ext.tgz done # echo "cp -r doxydoc doc/doxydoc" cp -r doxydoc doc/doxydoc # echo "cp *.log doc" cp *.log doc # echo "OK: ./build.sh copy2doc" exit 0 fi # ----------------------------------------------------------------------------- if [ "$1" == "all" ] then list=" version automake configure dist omhelp doxygen gpl copy2doc " if [ "$version_type" != "trunk" ] then # only use the help built during the build.sh dist command list=`echo $list | sed -e 's|omhelp||'` fi echo "./build.sh $list" ./build.sh $list echo "OK: ./build.sh all" exit 0 fi # ----------------------------------------------------------------------------- if [ "$1" = "test" ] then log_dir=`pwd` log_file="build_test.log" # -------------------------------------------------------------- # Things to do in the distribution directory # -------------------------------------------------------------- # # start log for this test echo "date > $log_file" date > $log_dir/$log_file # ---------------------------------------------------------------------- # Things to do in the build directory # ---------------------------------------------------------------------- echo "cd build" echo "cd build" >> $log_dir/$log_file cd build # # erase old distribution directory if [ -e cppad-$version ] then echo "rm -rf cppad-$version" echo "rm -rf cppad-$version" >> $log_dir/$log_file rm -rf cppad-$version fi # # create distribution directory echo "tar -xzf cppad-$version.epl.tgz" echo "tar -xzf cppad-$version.epl.tgz" >> $log_dir/$log_file tar -xzf cppad-$version.epl.tgz # # ---------------------------------------------------------------------- # Things to do in the build/disribution directory # ---------------------------------------------------------------------- echo "cd cppad-$version" echo "cd cppad-$version" >> $log_dir/$log_file cd cppad-$version # # build_test_only configuration echo "sed -i -e 's|^#_build_test_only:||' build.sh" sed -i -e 's|^#_build_test_only:||' build.sh # echo "./build.sh configure >> $log_file" ./build.sh configure >> $log_dir/$log_file # # test user documentation echo "bin/run_omhelp.sh xml >> $log_file" bin/run_omhelp.sh xml >> $log_dir/$log_file # # Developer documentation no longer works for auto-tools install # test developer documentation # echo "./build.sh doxygen >> $log_file" # ./build.sh doxygen >> $log_dir/$log_file # # ---------------------------------------------------------------------- # Things to do in the build/disribution/build directory # ---------------------------------------------------------------------- echo "cd build" echo "cd build" >> $log_dir/$log_file cd build # dir=`pwd` echo "To see progress in the 'make test' log file use" echo " ../temp.sh ( OK | All | tail | follow | file )" cat << EOF > $log_dir/../temp.sh #! /bin/bash -e case "\$1" in OK) grep OK $dir/make_test.log exit 0 ;; All) grep All $dir/make_test.log exit 0 ;; tail) tail $dir/make_test.log exit 0 ;; follow) tail -f $dir/make_test.log exit 0 ;; file) echo "$dir/make_test.log" exit 0 ;; *) echo "usage: ../temp.sh option" echo "where option is one of following: OK, All, tail, follow, file." exit 1 esac EOF chmod +x $log_dir/../temp.sh # # build and run all the tests echo "make test >& make_test.log" make test >& make_test.log # echo "rm ../temp.sh" rm $log_dir/../temp.sh # echo "cat make_test.log >> $log_file" cat make_test.log >> $log_dir/$log_file # # ignore warning in eigen (that has been reported) if grep ': *warning:' make_test.log then echo "There are warnings in $dir/make_test.log" exit 1 fi # -------------------------------------------------------------------- echo "cd ../../.." cd ../../.. # end the build_test.log file with the date and time echo "date >> $log_file" date >> $log_dir/$log_file # echo "No errors or warnings found; see build_test.log." # echo "OK: ./build.sh test" exit 0 fi # ----------------------------------------------------------------------------- # report build.sh usage error if [ "$1" != "" ] then echo "$1 is not a valid option" fi # if [ "$version_type" == "trunk" ] then all_cases="run all the options above in order" else all_cases="run all the options above in order with exception of omhelp" fi cat << EOF usage: ./build.sh option_1 option_2 ... options requires ------- -------- version: set version in AUTHORS, configure.ac, configure, ... omhelp: build all formats of user documentation in doc/*. automake: run the tools required by autoconf and automake. configure:run the configure script in the build directory. automake dist: create the distribution file build/cppad-version.epl.tgz. configure doxygen: build developer documentation in doxydoc/*. configure gpl: create build/*.gpl.zip and build/*.epl.zip. dist copy2doc: copy logs, tarballs & doxygen output into doc directory. dist,doxygen all: $all_cases test: use tarball to make test and put result in build_test.log. dist EOF # exit 1 cppad-20170000.3/COPYING0000644000175200017650000010554513057470467013504 0ustar coincoin-web/* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-09 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the Eclipse Public License Version 1.0. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. 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Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see . The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . cppad-20170000.3/bin/0002755000175200017650000000000013057470462013204 5ustar coincoin-webcppad-20170000.3/bin/new_release.sh0000755000175200017650000001634013057470462016036 0ustar coincoin-web#! /bin/bash -e # $Id: new_release.sh 3788 2016-02-09 15:50:06Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ "$0" != 'bin/new_release.sh' ] then echo "bin/new_release.sh: must be executed from its parent directory" exit 1 fi # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- svn_repo="https://projects.coin-or.org/svn/CppAD" stable_version="20160000" release='1' # ----------------------------------------------------------------------------- branch=`git branch | grep '^\*'` if [ "$branch" != '* master' ] then echo 'new_release.sh: must use master branch version of new_release.sh' exit 1 fi # ============================================================================= # master branch # ============================================================================= # Make sure local, remote and svn hash codes agree for this stable branch stable_branch=stable/$stable_version # # local hash code local_hash=`git show-ref $stable_branch | \ grep "refs/heads/$stable_branch" | \ sed -e "s| *refs/heads/$stable_branch||"` # # remote hash code remote_hash=`git show-ref $stable_branch | \ grep "refs/remotes/origin/$stable_branch" | \ sed -e "s| *refs/remotes/origin/$stable_branch||"` # # svn hash code svn_hash='' if svn info $svn_repo/$stable_branch >& /dev/null then svn_hash=`svn log $svn_repo/$stable_branch --limit 100 | \ grep 'end *hash *code:' | head -1 | sed -e 's|end *hash *code: *||'` fi # if [ "$local_hash" == '' ] && [ "$remote_hash" == '' ] then echo "new_release.sh: $stable_branch does not exist" echo "Check that master local and remote are the same and then ?" echo " git checkout master" echo " git checkout -b $stable_branch master" exit 1 fi if [ "$local_hash" == '' ] && [ "$remote_hash" != '' ] then echo "new_release.sh: local $stable_branch does not exist." echo " git checkout -b $stable_branch origin/$stable_branch" exit 1 fi # if [ "$remote_hash" == '' ] then echo "new_release.sh: $stable_branch does not exist ?" echo " git push origin $stable_branch" exit 1 fi if [ "$svn_hash" == '' ] then echo "new_release.sh: svn $stable_branch does not exist." echo "Make sure master and $stable_branch have same hash code," echo 'then follow instructions below for push and then svn copy ?' echo ' bin/push_git2svn.py trunk' echo " svn copy $svn_repo/trunk \\" echo " $svn_repo/$stable_branch" echo "log message: Create $stable_branch from trunk at revision ?" exit 1 fi # # check local == remote if [ "$local_hash" != "$remote_hash" ] then echo 'new_release.sh: local and remote differ for this branch' echo "local $stable_branch: $local_hash" echo "remote $stable_branch: $remote_hash" exit 1 fi # # check remote == svn if [ "$svn_hash" != "$remote_hash" ] then echo 'new_release.sh: remote and svn differ for this branch' echo "remote $stable_branch: $remote_hash" echo "svn $stable_branch: $svn_hash" echo 'Execute the following command ?' echo " bin/push_git2svn.py $stable_branch" exit 1 fi # ----------------------------------------------------------------------------- # Check that release version does not already exist # if svn list $svn_repo/releases | grep "$stable_version.$release" then echo "$svn_repo/releases/$stable_version.$release" echo 'already exists. Change the assignment' echo " release=$release" echo 'in bin/new_release.sh to a higher release number ?' exit 1 fi # if git tag --list | grep "$stable_version.$release" then echo 'This git reference tag already exists. Delete old version ?' echo " git tag -d $stable_version.$release" echo " git push --delete origin $stable_version.$release" exit 1 fi # ----------------------------------------------------------------------------- # Make sure master branch does not have uncomitted changes # before checking out stable branch list=`git status -s` if [ "$list" != '' ] then echo "new_release.sh: 'git status -s' is not empty (for master branch)" exit 1 fi # ============================================================================= # stable branch # ============================================================================= # checkout the stable branch branch=`git branch | grep '^\*' | sed -e 's|^\* *||'` if [ "$branch" != "$stable_branch" ] then echo_eval git checkout $stable_branch fi # ----------------------------------------------------------------------------- check_one=`bin/version.sh get` check_two=`grep "cppad-$stable_version\.$release" doc.omh \ | sed -e 's|cppad-\([0-9.]*\):.*|\1|'` if [ "$check_one" != "$check_two" ] then echo 'bin/new_release.sh: version number is not correct ?' echo " bin/version.sh set $stable_version.$release" echo ' bin/version.sh check' echo 'Then commit the changes.' exit 1 fi # ----------------------------------------------------------------------------- # make sure that autotools version of makfiles is up to current version echo_eval "./build.sh automake" list=`git status -s` if [ "$list" != '' ] then echo "new_release.sh: 'git status -s' is not empty" echo 'stable branch auto-tools install not up to current version' echo 'commit the local changes.' exit 1 fi # ----------------------------------------------------------------------------- read -p 'All checks have passed. More testing or commit release [t/c] ?' \ response if [ "$response" != 'c' ] then echo 'Exiting for more testing of stable branch' exit 1 fi # ----------------------------------------------------------------------------- # tag this release # echo_eval git tag -a \ -m \"corresponds $svn_repo/releases/$stable_version.$release\" \ $stable_version.$release # echo_eval git push origin $stable_version.$release # ----------------------------------------------------------------------------- msg="Creating releases/$stable_version.$release" rep_stable="$svn_repo/$stable_branch" rep_release="$svn_repo/releases/$stable_version.$release" echo_eval svn copy $rep_stable $rep_release -m \"$msg\" # ----------------------------------------------------------------------------- if [ ! -e build ] then echo_eval mkdir -p build fi echo_eval cd build echo_eval svn checkout $svn_repo/conf conf # echo_eval cd conf # msg="Update stable and release numbers in projDesc.xml" echo 'Settting stable and advance release in build/conf/projDesc.xml.' sed -i projDesc.xml \ -e "/^ * list_files.$$ for file in $list do if ! grep "$file" list_files.$$ > /dev/null then echo $file fi done rm list_files.$$ # ---------------------------------------------------------------------------- exit 0 cppad-20170000.3/bin/get_fadbad.sh0000755000175200017650000000613713057470462015610 0ustar coincoin-web#! /bin/bash -e # $Id: get_fadbad.sh 3730 2015-09-23 15:56:53Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # $begin get_fadbad.sh$$ $newlinech #$$ # $spell # Fadbad # CppAD # $$ # # $section Download and Install Fadbad in Build Directory$$ # $index fadbad, download and install$$ # $index download, install fadbad$$ # $index install, fadbad$$ # # $head Syntax$$ # $code bin/get_fadbad.sh$$ # # $head Purpose$$ # If you are using Unix, this command will download and install # $href%http://www.fadbad.com%Fadbad%$$ in the # CppAD $code build$$ directory. # # $head Distribution Directory$$ # This command must be executed in the # $cref/distribution directory/download/Distribution Directory/$$. # # $head External Directory$$ # The Fadbad source code is downloaded into the sub-directory # $code build/external$$ below the distribution directory. # # $head Prefix Directory$$ # The Fadbad include files are installed in the sub-directory # $code build/prefix/include/FADBAD++$$ below the distribution directory. # # $end # ----------------------------------------------------------------------------- if [ $0 != "bin/get_fadbad.sh" ] then echo "bin/get_fadbad.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- echo 'Download fadbad to build/external and install it to build/prefix' version='2.1' web_page='http://www.fadbad.com/download' cppad_dir=`pwd` prefix="$cppad_dir/build/prefix" installed_flag="build/external/fadbad-${version}.installed" if [ -e "$installed_flag" ] then echo "$installed_flag exists: Skipping get_fadbad.sh" exit 0 fi # ----------------------------------------------------------------------------- if [ ! -d build/external ] then echo_eval mkdir -p build/external fi echo_eval cd build/external # ----------------------------------------------------------------------------- if [ ! -e "FADBAD++-$version.tar.gz" ] then echo_eval wget --no-check-certificate $web_page/FADBAD++-$version.tar.gz fi if [ -e "FADBAD++" ] then echo_eval rm -r FADBAD++ fi echo_eval tar -xzf FADBAD++-$version.tar.gz if [ ! -e "$prefix/include" ] then echo_eval mkdir -p "$prefix/include" fi if [ -e "$prefix/include/FADBAD++" ] then echo_eval rm -r "$prefix/include/FADBAD++" fi echo_eval cp -r FADBAD++ "$prefix/include/FADBAD++" # ----------------------------------------------------------------------------- echo_eval touch $cppad_dir/$installed_flag echo "get_fadbad.sh: OK" cppad-20170000.3/bin/package.sh0000755000175200017650000001243413057470462015140 0ustar coincoin-web#! /bin/bash -e # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/package.sh" ] then echo "bin/package.sh: must be executed from its parent directory" exit 1 fi echo_log_eval() { echo $* echo $* >> $top_srcdir/package.log if ! eval $* >> $top_srcdir/package.log then echo "Error: check package.log" exit 1 fi } log_eval() { echo $* >> $top_srcdir/package.log if ! eval $* >> $top_srcdir/package.log then echo "Error: check package.log" exit 1 fi } if [ -e package.log ] then echo "rm package.log" rm package.log fi top_srcdir=`pwd` # ---------------------------------------------------------------------------- this_license=`\ grep '$verbatim%' omh/license.omh | sed -e 's|$verbatim%\(...\).*|\1|'` if [ "$this_license" == 'epl' ] then remove_list='gpl-3.0.txt bin/gpl_license.sh' elif [ "$this_license" == 'gpl' ] then remove_list='epl-v10.txt epl-v10.html bin/gpl_license.sh' else echo 'bin/package.sh: cannot find license in omh/license.omh' exit 1 fi # ---------------------------------------------------------------------------- # Make sure version is set correctly # # if this is the master, set version to today branch=`git branch | grep '^\*' | sed -e 's|^\* *||'` if [ "$branch" == 'master' ] then bin/version.sh set fi # make sure that version number is the same in all files echo_log_eval bin/version.sh check # # Get version number and make sure all copies agree version=`bin/version.sh get` echo_log_eval bin/version.sh get # ---------------------------------------------------------------------------- # Run automated checks for the form bin/check_*.sh with a few exceptions. # New version of doxygen yields errors in 20170000 source (so comment out) list=`ls bin/check_* | sed \ -e '/check_all.sh/d' \ -e '/check_jenkins.sh/d' \ -e '/check_doxygen.sh/d' \ -e '/check_svn_dist.sh/d'` for check in $list do echo_log_eval $check done # ---------------------------------------------------------------------------- # Check for doxygen errors # New version of doxygen yields errors in 20170000 source (so comment out) # echo_log_eval bin/run_doxygen.sh # ---------------------------------------------------------------------------- # Create the package directory package_dir="build/cppad-$version" if [ -e "$package_dir" ] then echo_log_eval rm -r $package_dir fi for lic in epl gpl do if [ -e "$package_dir.epl.tgz" ] then echo_log_eval rm $package_dir.$lic.tgz fi done echo_log_eval mkdir -p $package_dir # ----------------------------------------------------------------------------- # Source file that are coppied to the package directory file_list=`bin/ls_files.sh` # # Copy the files, creating sub-directories when necessary echo_log_eval echo "copy files to $package_dir" for file in $file_list $other_files do sub_dir=`echo $file | sed -e 's|\(.*\)/[^/]*$|\1|'` if [ "$sub_dir" != "$file" ] then if [ ! -e "$package_dir/$sub_dir" ] then log_eval mkdir -p $package_dir/$sub_dir fi fi log_eval cp $file $package_dir/$file done echo_log_eval echo "remove certain files from $package_dir" for file in $remove_list do if [ -e $package_dir/$file ] then echo_log_eval rm $package_dir/$file fi done # ---------------------------------------------------------------------------- # build the xml version of documentation for this distribution echo_log_eval cd $package_dir # # Only include the *.xml verison of the documentation in distribution # So remove the table at the top (but save the original doc.omh file). if ! grep < doc.omh > /dev/null \ 'This comment is used to remove the table below' then echo "Missing comment expected in doc.omh" exit 1 fi echo_log_eval echo "sed -i.save doc.omh ..." sed -i.save doc.omh \ -e '/This comment is used to remove the table below/,/$tend/d' # # This command creates omhelp.xml.log in current directory (and says so) echo_log_eval echo "bin/run_omhelp.sh xml" if ! bin/run_omhelp.sh xml then echo_log_eval cp omhelp.xml.log $top_srcdir/omhelp.xml.log exit 1 fi # Copy the log to the directory where the package.sh command was executed echo_log_eval cp omhelp.xml.log $top_srcdir/omhelp.xml.log # Restore the original doc.omh echo_log_eval mv doc.omh.save doc.omh # ---------------------------------------------------------------------------- # change back to the package parent directory and create the tarball echo_log_eval cd .. echo_log_eval tar -czf cppad-$version.$this_license.tgz cppad-$version # ---------------------------------------------------------------------------- # create gpl version of package echo_log_eval cd $top_srcdir if [ -e 'bin/gpl_license.sh' ] then if [ "$this_license" != 'epl' ] then echo 'package.sh: bin/gpl_license.sh found in gpl verison of source.' exit 1 fi echo_log_eval bin/gpl_license.sh cppad-$version build build fi # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/jenkins.sh0000755000175200017650000001340013057470462015200 0ustar coincoin-web#! /bin/bash -e # $Id: jenkins.sh 3842 2016-10-25 02:39:34Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/jenkins.sh" ] then echo "bin/jenkins.sh: must be executed from its parent directory" exit 1 fi if [ "$1" != '' ] then echo 'bin/jenkins.sh no longer has any arguments' exit 1 fi # ----------------------------------------------------------------------------- # distribution directory corresponding to this version of CppAD trunk_dir=`pwd` # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # Bash function that logs stdout, stderr, and executes a command. # In the special case where this is an echo command, # it just redirects the output to the log file. log_eval() { if [ "$1" == 'echo' ] then shift if ! echo $* >> $trunk_dir/jenkins.log then echo_eval cat $trunk_dir/jenkins.log echo_eval cat $trunk_dir/jenkins.err exit 1 fi else echo $* >> $trunk_dir/jenkins.log echo $* >> $trunk_dir/jenkins.err echo $* "1>> jenkins.log 2>> jenkins.err" if ! eval $* 1>> $trunk_dir/jenkins.log 2>> $trunk_dir/jenkins.err then echo_eval cat $trunk_dir/jenkins.log echo_eval cat $trunk_dir/jenkins.err exit 1 fi fi } for ext in log err do if [ -e "$trunk_dir/jenkins.$ext" ] then echo_eval rm $trunk_dir/jenkins.$ext fi done # -------------------------------------------------------------------------- if [ -e /usr/lib64 ] then libdir='lib64' else libdir='lib' fi # ----------------------------------------------------------------------- g++ --version # ----------------------------------------------------------------------- # Running bin/get_fadbad.sh ensures its include files are in # $trunk_dir/build/prefix/include/FADBAD++ log_eval bin/get_fadbad.sh # ------------------------------------------------------------------- # Running bin/get_eigen.sh ensures its include files are in # $trunk_dir/build/prefix/include/Eigen log_eval bin/get_eigen.sh # ------------------------------------------------------------------- # Running bin/get_ipopt.sh ensures its include files are in # $trunk_dir/build/prefix/include/coin # and library files in # $trunk_dir/build/prefix/$libdir # where $libdir is 'lib64' if /usr/lib64 exists and 'lib' otherwise. log_eval bin/get_ipopt.sh # ------------------------------------------------------------------- # Running bin/get_sacado.sh ensures its include files are in # $trunk_dir/build/prefix/include # and library files in # $trunk_dir/build/prefix/$libdir log_eval bin/get_sacado.sh # ------------------------------------------------------------------- # Running bin/get_colpack.sh ensures its library files are in # $trunk_dir/build/prefix/$libdir log_eval bin/get_colpack.sh # ------------------------------------------------------------------- # Running bin/get_acolc.sh ensures its include files are in # $trunk_dir/build/prefix/include/adolc # and library files in # $trunk_dir/build/prefix/$libdir log_eval bin/get_adolc.sh # ------------------------------------------------------------------- # something is wrong with the jenkins system or the autotools pushd build/prefix/$libdir for ver in 0 1 2 do for name in adolc ColPack do if [ -e "lib$name.so" ] && [ ! -e "lib$name.so.$ver" ] then log_eval ln -s lib$name.so lib$name.so.$ver fi done done popd # ------------------------------------------------------------------- system_name=`uname | sed -e 's|\(......\).*|\1|'` if [ "$system_name" == 'CYGWIN' ] then export PATH="$trunk_dir/build/prefix/bin:$PATH" else export LD_LIBRARY_PATH="$trunk_dir/build/prefix/$libdir" fi # ----------------------------------------------------------------------- # Use trunk_dir/build/auto_tools to build and test CppAD (no reuse) echo_eval cd build echo_eval rm -rf auto_tools echo_eval mkdir auto_tools echo_eval cd auto_tools # # configure cppad to use all the packages above if which rpm >& /dev/null then build_type=`rpm --eval %{_host}` build_type="--build=$build_type" else build_type='' fi # cat << EOF $trunk_dir/configure \\ $build_type \\ --disable-silent-rules \\ ADOLC_DIR="$trunk_dir/build/prefix" \\ SACADO_DIR="$trunk_dir/build/prefix" \\ EIGEN_DIR="$trunk_dir/build/prefix" \\ IPOPT_DIR="$trunk_dir/build/prefix" \\ FADBAD_DIR="$trunk_dir/build/prefix" \\ CXX_FLAGS='-Wall -std=c++11' \\ OPENMP_FLAGS=-fopenmp \\ 1>> jenkins.log 2>> jenkins.err EOF if ! $trunk_dir/configure $build_type \ --disable-silent-rules \ ADOLC_DIR="$trunk_dir/build/prefix" \ SACADO_DIR="$trunk_dir/build/prefix" \ EIGEN_DIR="$trunk_dir/build/prefix" \ IPOPT_DIR="$trunk_dir/build/prefix" \ FADBAD_DIR="$trunk_dir/build/prefix" \ CXX_FLAGS='-Wall -std=c++11' \ OPENMP_FLAGS=-fopenmp \ 1>> $trunk_dir/jenkins.log 2>> $trunk_dir/jenkins.err then echo "Error during configure command. Here is config.log file:" echo "--------------------------------------------------------" cat config.log exit 1 fi # # compile the tests log_eval make check # # run the tests log_eval echo "LD_LIBRARY_PATH=$LD_LIBRARY_PATH" log_eval ls -l "$trunk_dir/build/prefix/$libdir" log_eval make test # # print the test results on the console echo 'copy make test output to console' sed -n -e '/^make test$/,$p' $trunk_dir/jenkins.log # # make it here without an error exit echo "jenkins.sh: OK" cppad-20170000.3/bin/search.sh0000755000175200017650000000225213057470462015007 0ustar coincoin-web#! /bin/bash -e # $Id: search.sh 3781 2016-01-18 16:16:22Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/search.sh" ] then echo "bin/search.sh: must be executed from its parent directory" exit 1 fi if [ "$1" == "" ] then echo 'usage: bin/search.sh pattern' echo ' Search for pattern in the cppad source code' exit 1 fi pattern="$1" # ----------------------------------------------------------------------------- list=`bin/ls_files.sh | sed \ -e '/^configure$/d' \ -e '/^makefile.in$/d' \ -e '/\/makefile.in$/d' \ -e '/^compile/d'` grep -l "$pattern" $list # ---------------------------------------------------------------------------- exit 0 cppad-20170000.3/bin/dir_copy.sh0000755000175200017650000000437013057470462015355 0ustar coincoin-web#! /bin/bash -e # $Id: dir_copy.sh 3768 2015-12-28 18:58:35Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/dir_copy.sh" ] then echo "bin/dir_copy.sh: must be executed from its parent directory" exit 1 fi if [ "$3" == "" ] then echo "usage: bin/dir_copy.sh file_list direction dir" echo " file_list: a file containing a list of file names to copy," echo " direction: 'to' or 'from', and dir is a directory." exit 1 fi if [ "$2" != 'from' ] && [ "$2" != 'to' ] then echo "bin/dir_copy.sh: invalid direction=$2" exit 1 fi if [ "$2" == 'to' ] && [ ! -e "$1" ] then echo "bin/dir_copy.sh: can't find file_list=$1" exit 1 fi if [ "$2" == 'from' ] && [ ! -e "$3/$1" ] then echo "bin/dir_copy.sh: can't find file_list=$3/$1" exit 1 fi file_list="$1" direction="$2" directory="$3" # ----------------------------------------------------------------------------- # if [ "$direction" == 'to' ] then if [ -e "$directory" ] then echo "bin/dir_copy.sh $file_list $direction directory=$directory" echo "the directory already exists, remove it first." exit 1 fi echo "mkdir $directory" mkdir $directory # list=`cat $file_list` for path in $list do sub_dir=`echo $path | sed -e 's|[^/]*$||' -e 's|/$||'` file=`echo $path | sed -e 's|^.*/||'` if [ ! -d "$directory/$sub_dir" ] then echo "mkdir -p $directory/$sub_dir" mkdir -p $directory/$sub_dir fi echo "cp $path $directory/$path" cp $path $directory/$path done echo "cp $file_list $directory/$file_list" cp $file_list $directory/$file_list else list=`cat $directory/$file_list` for path in $list do echo "cp $directory/$path $path" cp $directory/$path $path done fi # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/check_makefile.sh0000755000175200017650000000720113057470462016453 0ustar coincoin-web#! /bin/bash -e # $Id: check_makefile.sh 3845 2016-11-19 01:50:47Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_makefile.sh" ] then echo "bin/check_makefile.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- echo "Checking include files listed in makefile.am" echo "-------------------------------------------------------" bin/ls_files.sh .h .hpp | sed -n \ -e '/^cppad\/deprecated\//d' \ -e '/cppad\/.*\.h$/p' \ -e '/cppad\/.*\.hpp$/p' \ > check_makefile.1.$$ echo 'cppad/configure.hpp' >> check_makefile.1.$$ sort -u check_makefile.1.$$ > check_makefile.2.$$ # sed < makefile.am -n \ -e '/^nobase_myinclude_HEADERS *=/,/^# End nobase_myinclude_HEADERS/p' | \ sed \ -e '/nobase_myinclude_HEADERS/d' \ -e 's/^\t//' \ -e 's/ *\\$//' \ -e 's/ *$//' \ -e '/^$/d' | sort > check_makefile.3.$$ # if diff check_makefile.2.$$ check_makefile.3.$$ then ok="yes" else ok="no" fi rm check_makefile.*.$$ echo "-------------------------------------------------------" if [ "$ok" = "no" ] then echo "Error: nothing should be between the two dashed lines above" exit 1 fi # ----------------------------------------------------------------------------- echo "Checking debugging flags in all makefile.am files." echo "-------------------------------------------------------" list=`bin/ls_files.sh | sed -n -e '/\/makefile.am$/p'` ok="yes" for file in $list do case $file in ( makefile.am | work/* | svn_dist/* ) ;; (multi_thread/makefile.am) ;; (speed/example/makefile.am) if grep '\-DNDEBUG' $file > /dev/null then echo "-DNDEBUG flag appears in $file" ok="no" fi if ! grep '\-g' $file > /dev/null then echo "-g flag does not appear in in $file" ok="no" fi ;; (test_more/makefile.am) sed -e '/ndebug/d' < $file > bin/check_makefile.$$ if grep '\-DNDEBUG' bin/check_makefile.$$ > /dev/null then echo "-DNDEBUG flag appears in $file" ok="no" fi if ! grep '\-g' $file > /dev/null then echo "-g flag does not appear in in $file" ok="no" fi rm bin/check_makefile.$$ ;; (speed/[^/]*/makefile.am | cppad_ipopt/speed/makefile.am) if ! grep '^[^#]*-DNDEBUG' $file > /dev/null then echo "Optimization flag is not defined in $file" ok="no" fi if ! grep '^#.*-g' $file > /dev/null then echo "Debug flag is not commented out in $file" ok="no" fi ;; (compare_c/makefile.am) if ! grep '^[^#]*-DNDEBUG' $file > /dev/null then echo "Optimization flag is not defined in $file" ok="no" fi if ! grep '^#.*-g' $file > /dev/null then echo "Debug flag is not commented out in $file" ok="no" fi ;; *) if grep '\-DNDEBUG' $file > /dev/null then echo "-DNDEBUG flag appears in $file" ok="no" fi if ! grep '\-g' $file > /dev/null then echo "-g flag does not appear in in $file" ok="no" fi ;; esac done echo "-------------------------------------------------------" if [ "$ok" = "yes" ] then echo "Ok: nothing is between the two dashed lines above" exit 0 else echo "Error: nothing should be between the two dashed lines above" exit 1 fi cppad-20170000.3/bin/cygwin_package.sh0000755000175200017650000003037213057470462016521 0ustar coincoin-web#! /bin/bash -e # $Id: cygwin_package.sh 3768 2015-12-28 18:58:35Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/cygwin_package.sh" ] then echo "bin/cygwin_package.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # experimental script for cygwin packaging of CppAD # # version and release number # # begin fresh cygwin_package directory # if [ -e cygwin_package ] then echo "rm -r cygwin_package" if ! rm -r cygwin_package then exit 1 fi fi # # determine the most recent version in the Download directory # version=`ls /cygdrive/c/Download/cppad-20*.gpl.tgz | sed -n -e 's|.*/||' -e 's|cppad-||' -e 's|.gpl.tgz||' -e '$,$p'` if [ "$version" == 20061208 ] then echo "change: f'(3) -> y'(3)" echo "change: introduction/get_started -> get_started" echo "change: get_started.cpp.htm -> getstarted.cpp.htm" echo "change: get_started.cpp.xml -> getstarted.cpp.xml" fi release="1" if [ ! -e "/cygdrive/c/Download/cppad-$version.gpl.tgz" ] then echo "Error determining the version number, cannot find" echo "/cygdrive/c/Download/cppad-$version.gpl.tgz" exit 1 fi # # extract the gpl version of the distribution # file="/cygdrive/c/Download/cppad-$version.gpl.tgz" if [ ! -e $file ] then exit 1 fi if [ -e cppad-$version ] then echo "rm -r cppad-$version" if ! rm -r cppad-$version then echo "Cannot remove old cppad-$version directory." fi fi echo "tar -xzf $file" if ! tar -xzf $file then echo "Cannot create new cppad-$version directory." exit 1 fi # # make a copy of the distribution in the cygwin_package sub-directory # echo "mkdir cygwin_package" mkdir cygwin_package echo "cp -r cppad-$version cygwin_package/cppad-$version-$release" if ! cp -r cppad-$version cygwin_package/cppad-$version-$release then exit 1 fi # # change into the cygwin_package sub-directory and stay there # echo "cd cygwin_package" if ! cd cygwin_package then exit 1 fi # # Create the setup.hint file ---------------------------------------------- # cat > setup.hint << EOF # To test the source or binary distribution, copy the source distribution file # cppad-$version-$release/introduction/get_started/get_started.cpp # to a temporary directory and execute the commands # g++ get_started.cpp -o get_started.exe # ./get_started # the resulting output should be # f'(3) computed by CppAD = 142 # # Requires a standard compliant C++ compiler; e.g., gcc-g++. requires: gcc-g++ # category: Math # sdesc: "C++ algorithmic differentiation by operator overloading" # ldesc: "C++ algorithmic differentiation by operator overloading. Forward and reverse mode as well as derivatives of arbitrary order are supported. See the documentation for this version ( /usr/share/doc/cppad-$version-$release/cppad.htm ) or the CppAD home page ( http://http://www.coin-or.org/CppAD/ ) for more details." EOF # # Create the source distribution ------------------------------------------ # # Create the cygwin README file # bin_doc="/usr/share/doc/cppad-$version-$release" src_doc="/usr/src/cppad-$version-$release/doc" web_doc="http://www.coin-or.org/CppAD/Doc" readme_file="cppad-$version-$release/README" # echo "create: $readme_file" # cat > $readme_file << EOF CppAD for cygwin version number $version release number $release. http://www.coin-or.org/CppAD This is the CppAD home page. cppad@list.coin-or.org This mailing list is used for CppAD discussion and bug reporting. You must first join the mailing list using its general information page http://list.coin-or.org/mailman/listinfo/CppAD (this avoids having spam on the mailing list). DOC We use DOC below for the directories that contains the CppAD documentation. Source distribution this version, DOC = cppad-$version-$release/doc Binary this version (post install), DOC = $bin_doc Source this version (post install), DOC = $src_doc The documentation of most recent version, DOC = $web_doc DOC/*.htm Files in the DOC directory with with the .htm extension represent mathematics using LaTex; for example see DOC/poly.htm. DOC/*.xml Files in the DOC directory with with the .xml extension represent mathematics using LaTex; for example see DOC/poly.xml. DOC/(cppad.xml or cppad.htm) Is the top (root) of the documentation tree for CppAD. DOC/(get_started.cpp.xml or get_started.cpp.htm) Contains an example for getting started using CppAD. DOC/(introduction.xml or introduction.htm) Contains an introduction by example to Algorithmic Differentiation. DOC/(whats_new.xml or whats_new.htm) Contains a list of changes and additions to CppAD in reverse order by date. DOC/(installunix.xml or installunix.htm) Contains documentation for the configure options which can be used to build the examples and tests for CppAD (using the source distribution). EOF # # change configure.ac # echo "Begin: modify configure.ac and files that depend on it." echo "sed < cppad-$version-$release/configure.ac > configure.ac \\" echo " -e '/dnl cygwin begin delete:/,/dnl cygwin end delete:/d' \\" echo " -e 's/dnl cygwin replace: *//'" # if ! sed < cppad-$version-$release/configure.ac > configure.ac \ -e '/dnl cygwin begin delete:/,/dnl cygwin end delete:/d' \ -e 's/dnl cygwin replace: *//' then exit 1 fi # if ! mv configure.ac cppad-$version-$release/configure.ac then exit 1 fi if ! cd cppad-$version-$release then exit 1 fi if ! aclocal then exit 1 fi if ! autoheader then exit 1 fi if ! autoconf then exit 1 fi if ! automake --add-missing then exit 1 fi # directory created by commands above and not in distribution echo "rm -r autom4te.cache" if ! rm -r autom4te.cache then exit 1 fi if ! cd .. then exit 1 fi echo "End: modify configure.ac and files that depend on it." # # create the cppad-$version.patch file # diff -N -r -u -p \ ../cppad-$version cppad-$version-$release > cppad-$version.patch # # create the cppad-$version-$release/CYGWIN-PATCHES sub-directory # echo "mkdir cppad-$version-$release/CYGWIN-PATCHES" if ! mkdir cppad-$version-$release/CYGWIN-PATCHES then exit 1 fi if ! cp $readme_file cppad-$version-$release/CYGWIN-PATCHES/cppad.README then exit 1 fi if ! cp setup.hint cppad-$version-$release/CYGWIN-PATCHES then exit 1 fi if ! cp cppad-$version.patch cppad-$version-$release/CYGWIN-PATCHES then exit 1 fi # # create cppad-$version-$release-src.tar.bz2 # echo "tar -cf cppad-$version-$release-src.tar cppad-$version-$release" if ! tar -cf cppad-$version-$release-src.tar cppad-$version-$release then exit 1 fi echo "bzip2 -z -f cppad-$version-$release-src.tar" if ! bzip2 -z -f cppad-$version-$release-src.tar then exit 1 fi # # Create the binary distribution ------------------------------------------ # # create the usr/include/cppad directory # echo "mkdir usr/include" mkdir usr mkdir usr/include # echo "cp -r cppad-$version-$release/cppad usr/include/cppad" if ! cp -r cppad-$version-$release/cppad usr/include/cppad then exit 1 fi chmod 644 usr/include/cppad/*.hpp chmod 644 usr/include/cppad/local/*.hpp chmod 755 usr/include/cppad chmod 755 usr/include/cppad/local # # create the usr/share/doc/cppad-$version directory # echo "mkdir usr/share/doc" mkdir usr/share mkdir usr/share/doc # echo "cp -r cppad-$version-$release/doc usr/share/doc/cppad-$version" if ! cp -r cppad-$version-$release/doc usr/share/doc/cppad-$version then exit 1 fi chmod 644 usr/share/doc/cppad-$version/* chmod 755 usr/share/doc/cppad-$version # # create the usr/share/doc/Cygwin/cppad-$version-$release.README # echo "mkdir usr/share/doc/Cygwin" if ! mkdir usr/share/doc/Cygwin then exit fi if ! cp $readme_file usr/share/doc/Cygwin/cppad-$version-$release.README then exit 1 fi # # create cppad-$version-$release.tar.bz2 # echo "tar -cf cppad-$version-$release.tar usr" if ! tar -cf cppad-$version-$release.tar usr then exit 1 fi echo "bzip2 -z -f cppad-$version-$release.tar" if ! bzip2 -z -f cppad-$version-$release.tar then exit 1 fi # # Test source install -------------------------------------------------------- # echo "Begin: test if source install" if [ -e /usr/include/cppad ] then echo "rm -r /usr/include/cppad" if ! rm -r /usr/include/cppad then exit 1 fi fi if [ -e /usr/share/doc/cppad-* ] then echo "rm -rf /usr/share/doc/cppad-*" if ! rm -rf /usr/share/doc/cppad-* then exit 1 fi fi mkdir test_src echo "cd test_src" if ! cd test_src then exit 1 fi echo "cp ../cppad-$version-$release-src.tar.bz2 ." if ! cp ../cppad-$version-$release-src.tar.bz2 . then exit 1 fi echo "bunzip2 cppad-$version-$release-src.tar.bz2" if ! bunzip2 cppad-$version-$release-src.tar.bz2 then exit 1 fi echo "tar -xf cppad-$version-$release-src.tar" if ! tar -xf cppad-$version-$release-src.tar then exit 1 fi echo "cd cppad-$version-$release" if ! cd cppad-$version-$release then exit 1 fi echo "./configure" if ! ./configure then exit 1 fi echo "make install" if ! make install then exit 1 fi echo "cd ../.." if ! cd ../.. then exit 1 fi dir="test_src/cppad-$version-$release/introduction/get_started" echo "cp $dir/get_started.cpp ." if ! cp $dir/get_started.cpp . then exit 1 fi if ! g++ get_started.cpp -o get_started.exe then exit 1 fi echo "./get_started > get_started.out" ./get_started > get_started.out echo "f'(3) computed by CppAD = 142" > get_started.chk if ! diff get_started.out get_started.chk then echo "error in get_started output" exit 1 fi file_list=" cppad get_started.cpp introduction whats_new installunix " ext_list=" htm xml " for file in $file_list do for ext in $ext_list do full_name=/usr/share/doc/cppad-$version/$file.$ext if [ ! -e "$full_name" ] then echo "cannot find $full_name" exit 1 fi done done echo "End: test if source install" # # Test binary install -------------------------------------------------------- # echo "Begin: test if binary install" if [ -e /usr/include/cppad ] then echo "rm -r /usr/include/cppad" if ! rm -r /usr/include/cppad then exit 1 fi fi if [ -e /usr/share/doc/cppad-* ] then echo "rm -rf /usr/share/doc/cppad-*" if ! rm -rf /usr/share/doc/cppad-* then exit 1 fi fi mkdir test_bin echo "cd test_bin" if ! cd test_bin then exit 1 fi echo "cp ../cppad-$version-$release.tar.bz2 ." if ! cp ../cppad-$version-$release.tar.bz2 . then exit 1 fi echo "bunzip2 cppad-$version-$release.tar.bz2" if ! bunzip2 cppad-$version-$release.tar.bz2 then exit 1 fi echo "tar -xf cppad-$version-$release.tar" if ! tar -xf cppad-$version-$release.tar then exit 1 fi echo "cp -r usr/include/cppad /usr/include/cppad" if ! cp -r usr/include/cppad /usr/include/cppad then exit 1 fi echo "cp -r usr/share/doc/cppad-$version /usr/share/doc/cppad-$version" if ! cp -r usr/share/doc/cppad-$version /usr/share/doc/cppad-$version then exit 1 fi echo "cd .." if ! cd .. then exit 1 fi if ! rm get_started.exe then exit 1 fi if ! g++ get_started.cpp -o get_started.exe then exit 1 fi echo "./get_started > get_started.out" ./get_started > get_started.out echo "f'(3) computed by CppAD = 142" > get_started.chk if ! diff get_started.out get_started.chk then echo "error in get_started output" exit 1 fi file_list=" cppad get_started.cpp introduction whats_new installunix " ext_list=" htm xml " for file in $file_list do for ext in $ext_list do full_name=/usr/share/doc/cppad-$version/$file.$ext if [ ! -e "$full_name" ] then echo "cannot find $full_name" exit 1 fi done done echo "End: test if binary install" # # Clean up ------------------------------------------------------------------ # echo "cd .." if ! cd .. then exit 1 fi list=" cppad-$version-$release usr cppad-$version.patch test_src test_bin " for dir in $list do echo "rm -r cygwin_package/$dir" if ! rm -r cygwin_package/$dir then exit 1 fi done echo "rm cygwin_package/get_started.*" if ! rm cygwin_package/get_started.* then exit 1 fi # # ---------------------------------------------------------------------------- # Done echo bin/"cygwin_package.sh: passed all its tests" exit 0 cppad-20170000.3/bin/get_colpack.sh0000755000175200017650000000762213057470462016023 0ustar coincoin-web#! /bin/bash -e # $Id: get_colpack.sh 3834 2016-09-30 03:42:56Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # $begin get_colpack.sh$$ $newlinech #$$ # $spell # colpack # gz # Col # CppAD # $$ # # $section Download and Install ColPack in Build Directory$$ # # $head Syntax$$ # $code bin/get_colpack.sh$$ # # $head Purpose$$ # If you are using Unix, this command will download and install # $href%http://cscapes.cs.purdue.edu/dox/ColPack/html/%ColPack%$$ in the # CppAD $code build$$ directory. # # $head Distribution Directory$$ # This command must be executed in the # $cref/distribution directory/download/Distribution Directory/$$. # # $head External Directory$$ # The ColPack source code is downloaded into the sub-directory # $code build/external$$ below the distribution directory. # # $head Prefix Directory$$ # The ColPack include files are installed in the sub-directory # $code build/prefix/include/ColPack$$ below the distribution directory. # # $head Reuse$$ # The file $codei%build/external/ColPack-%version%.tar.gz%$$ # and the directory $codei%build/external/ColPack-%version%$$ # will be reused if they exist. Delete this file and directory # to get a complete rebuild. # # $end # ----------------------------------------------------------------------------- if [ $0 != "bin/get_colpack.sh" ] then echo "bin/get_colpack.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- echo 'Download colpack to build/external and install it to build/prefix' version='1.0.10' web_page='https://codeload.github.com/CSCsw/ColPack/tar.gz' cppad_dir=`pwd` prefix="$cppad_dir/build/prefix" installed_flag="build/external/colpack-${version}.installed" if [ -e "$installed_flag" ] then echo "$installed_flag exists: Skipping get_colpack.sh" exit 0 fi # -------------------------------------------------------------------------- if [ -e /usr/lib64 ] then libdir='lib64' else libdir='lib' fi # ----------------------------------------------------------------------------- if [ ! -d build/external ] then echo_eval mkdir -p build/external fi echo_eval cd build/external # ----------------------------------------------------------------------------- if [ ! -e "ColPack-$version.tar.gz" ] then echo_eval curl $web_page/v$version -o ColPack-$version.tar.gz fi # ----------------------------------------------------------------------------- if [ ! -e ColPack-$version ] then echo_eval tar -xzf ColPack-$version.tar.gz fi echo_eval cd ColPack-$version # ----------------------------------------------------------------------------- if which autoconf >& /dev/null then echo_eval libtoolize echo_eval autoreconf --install --force fi # ----------------------------------------------------------------------------- # system_name=`uname | sed -e 's|\(......\).*|\1|'` if [ "$system_name" == 'CYGWIN' ] then lib_type='--enable-static --disable-shared' echo_eval ls -l ./configure echo_eval chmod +x ./configure else lib_type='--enable-static --enable-shared' fi echo_eval ./configure \ --prefix=$prefix \ --libdir=$prefix/$libdir \ $lib_type # echo_eval make install # ----------------------------------------------------------------------------- echo_eval touch $cppad_dir/$installed_flag echo "get_colpack: OK" cppad-20170000.3/bin/reduce_index.py0000755000175200017650000001216013057470462016215 0ustar coincoin-web#! /bin/python3 # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- import sys import os import re # ----------------------------------------------------------------------------- # list of words that should be excluded from mindex comamnds exclude_list = 'a an and as at by for in of or to'.split() # ----------------------------------------------------------------------------- def split_words(string) : pattern = '(\s|,)' replace = ' ' string = re.sub(pattern, replace, string) return string.split() # ----------------------------------------------------------------------------- if sys.argv[0] != 'bin/reduce_index.py' : msg = 'bin/reduce_index.py: must be executed from its parent directory' sys.exit(msg) # usage = 'usage: reduce_index.py file_name' narg = len(sys.argv) if narg != 2 : msg = '\n\tFound ' + str(narg-1) + ' command line arguments (expected 1).' sys.exit(usage + msg) file_name = sys.argv[1] # ----------------------------------------------------------------------------- if not os.path.exists(file_name) : msg = 'bin/reduce_index.py: cannot find file_name = ' + file_name sys.exit(msg) f_in = open(file_name, 'r') file_data = f_in.read() f_in.close() f_out = open(file_name, 'w') # ----------------------------------------------------------------------------- # some useful patterns begin_pattern = re.compile('[$]begin ([^$]*)[$][$]') end_pattern = re.compile('[$]end') section_pattern = re.compile('[$](section)\s([^$]*)[$][$]') index_pattern = re.compile('[$][mc]{0,1}(index) ([^$]*)[$][$]') cmd_pattern = re.compile('[$]([a-z]*) ([^$]*)[$][$]') # ----------------------------------------------------------------------------- def remove_index_cmd(string) : result = str() rest = string next_index = index_pattern.search(rest) while next_index != None : result += rest[ : next_index.start() ] rest = rest[ next_index.end() : ] if len(rest) > 0 : if rest[0] == '\n' : rest = rest[1 : ] next_index = index_pattern.search(rest) result += rest return result # # for each omhelp section in the file file_rest = file_data while len(file_rest) > 0 : # start of this section next_begin = begin_pattern.search(file_rest) if next_begin == None : f_out.write( file_rest ) file_rest = str() else : # end of this section next_end = end_pattern.search(file_rest) if next_end == None : sys.exit( 'No $end after' + next_begin(0) ) if next_end.end() < next_begin.end() : sys.exit( 'No $end after' + next_begin(0) ) # data for this section section_data = file_rest [ : next_end.end() ] file_rest = file_rest [ next_end.end() : ] # # get list of automatically generated index words for this section section_rest = section_data auto_list = list() while len(section_rest) > 0 : next_cmd = cmd_pattern.search(section_rest) if next_cmd == None : section_rest = str() else : section_rest = section_rest[ next_cmd.end() : ] cmd = next_cmd.group(1) if cmd in [ 'section', 'head', 'subhead' ] : for word in split_words( next_cmd.group(2) ) : auto_list.append( word.lower() ) # # list of index words not in automatically generated list section_rest = section_data index_list = list() exclude_list += auto_list for word in auto_list : if word.endswith('s') : exclude_list.append( word[: -1] ) else : exclude_list.append( word + 's' ) while len(section_rest) > 0 : next_index = index_pattern.search(section_rest) if next_index == None : section_rest = str() else : section_rest = section_rest[ next_index.end() : ] for word in split_words( next_index.group(2) ) : word_lower = word.lower() if not ( word_lower in exclude_list ) : index_list.append(word) exclude_list.append(word_lower) # keep words that are not in start of other words keep_index = list() for word_1 in index_list : ok_1 = True for word_2 in index_list : if word_2.startswith(word_1 + '_') : ok_1 = False if word_2.endswith('_' + word_1) : ok_1 = False if ok_1 : keep_index.append(word_1) # # write out data to the end of section command section_cmd = section_pattern.search(section_data) data = remove_index_cmd( section_data[ : section_cmd.end() ] ) f_out.write( data ) if len(keep_index) > 0 : index_cmd = '$mindex' for word in keep_index : index_cmd += ' ' + word index_cmd += '$$' f_out.write( '\n' + index_cmd ) data = remove_index_cmd( section_data[ section_cmd.end() : ] ) f_out.write( data ) # ----------------------------------------------------------------------------- f_out.close() print('reduce_index.py OK: ' + file_name ) sys.exit(0) cppad-20170000.3/bin/colpack.sh0000755000175200017650000001073213057470462015160 0ustar coincoin-web#! /bin/bash -e # $Id: colpack.sh 3768 2015-12-28 18:58:35Z bradbell $ if [ "$1" != 'forward' ] && [ "$1" != 'reverse' ] then echo 'usage: ./colpack.sh option' echo 'where option is "forward" or "reverse"' exit 1 fi if [ "$1" == 'forward' ] then color_variant="COLUMN_PARTIAL_DISTANCE_TWO" else color_variant="ROW_PARTIAL_DISTANCE_TWO" fi # ---------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------- if [ ! -e 'build/colpack' ] then echo_eval mkdir -p build/colpack fi echo 'create: build/colpack/colpack.cpp' cat<< EOF > build/colpack/colpack.cpp // Example using BipartiteGraphPartialColoringInterface // to generate the seed matrix for Jacobian #include "ColPackHeaders.h" int main() { size_t i, j, k; using std::cout; using std::endl; //* 32x9 matrix size_t i_RowCount = 32; size_t i_ColumnCount = 9; size_t i_MaxNonZerosInRows = 3; // JP[32][9] std::vector JP(i_RowCount); unsigned int n_data = i_RowCount * (i_MaxNonZerosInRows + 1); std::vector JP_memory(n_data); for(i = 0; i < i_RowCount; i++) JP[i] = JP_memory.data() + i * (i_MaxNonZerosInRows + 1); // JP[0][0] = 0; JP[1][0] = 1; JP[1][1] = 0; JP[2][0] = 1; JP[2][1] = 1; JP[3][0] = 1; JP[3][1] = 2; JP[4][0] = 1; JP[4][1] = 0; JP[5][0] = 3; JP[5][1] = 0; JP[5][2] = 1; JP[5][3] = 3; JP[6][0] = 3; JP[6][1] = 1; JP[6][2] = 2; JP[6][3] = 4; JP[7][0] = 2; JP[7][1] = 2; JP[7][2] = 5; JP[8][0] = 1; JP[8][1] = 3; JP[9][0] = 3; JP[9][1] = 3; JP[9][2] = 4; JP[9][3] = 6; JP[10][0] = 3; JP[10][1] = 4; JP[10][2] = 5; JP[10][3] = 7; JP[11][0] = 2; JP[11][1] = 5; JP[11][2] = 8; JP[12][0] = 1; JP[12][1] = 6; JP[13][0] = 2; JP[13][1] = 6; JP[13][2] = 7; JP[14][0] = 2; JP[14][1] = 7; JP[14][2] = 8; JP[15][0] = 1; JP[15][1] = 8; JP[16][0] = 1; JP[16][1] = 0; JP[17][0] = 2; JP[17][1] = 0; JP[17][2] = 1; JP[18][0] = 2; JP[18][1] = 1; JP[18][2] = 2; JP[19][0] = 1; JP[19][1] = 2; JP[20][0] = 2; JP[20][1] = 0; JP[20][2] = 3; JP[21][0] = 3; JP[21][1] = 1; JP[21][2] = 3; JP[21][3] = 4; JP[22][0] = 3; JP[22][1] = 2; JP[22][2] = 4; JP[22][3] = 5; JP[23][0] = 1; JP[23][1] = 5; JP[24][0] = 2; JP[24][1] = 3; JP[24][2] = 6; JP[25][0] = 3; JP[25][1] = 4; JP[25][2] = 6; JP[25][3] = 7; JP[26][0] = 3; JP[26][1] = 5; JP[26][2] = 7; JP[26][3] = 8; JP[27][0] = 1; JP[27][1] = 8; JP[28][0] = 1; JP[28][1] = 6; JP[29][0] = 1; JP[29][1] = 7; JP[30][0] = 1; JP[30][1] = 8; JP[31][0] = 0; cout << endl << "Sparsity pattern of Jacobian:" << endl; cout << " "; for(k = 0; k < 9; k++) cout << setw(3) << k; cout << endl; for(i = 0; i < i_RowCount; i++) { cout << setw(3) << i << ":"; k = 0; for (j = 1; j <= (int) JP[i][0]; j++) { while(k < JP[i][j]) { cout << setw(3) << 0; k++; } cout << setw(3) << 1; k++; } while(k < 9) { cout << setw(3) << 0; k++; } cout << endl; } // Step 1: Read the sparsity pattern of the given Jacobian matrix // (adolc format) and create the corresponding bipartite graph ColPack::BipartiteGraphPartialColoringInterface g( SRC_MEM_ADOLC, JP.data(), i_RowCount, i_ColumnCount ); g.PrintBipartiteGraph(); // Step 2: Do Partial-Distance-Two-Coloring // of the bipartite graph with the specified ordering g.PartialDistanceTwoColoring( "SMALLEST_LAST", "$color_variant" ); g.PrintColumnPartialColors(); g.PrintColumnPartialColoringMetrics(); // Step 3: From the coloring information, create and return seed matrix int ip1_SeedRowCount; int ip1_SeedColumnCount; double** RSeed = g.GetSeedMatrix(&ip1_SeedRowCount, &ip1_SeedColumnCount); int rows = ip1_SeedRowCount; int cols = ip1_SeedColumnCount; cout << "Seed matrix: (" << rows << "," << cols << ")" << endl; cout << " "; for(j = 0; j < cols; j++) cout << setw(3) << j; cout << endl; for(i = 0; i < rows; i++) { cout << setw(3) << i << ":"; for(j = 0; j < cols; j++) cout << setw(3) << int(RSeed[i][j]); cout << endl; } return 0; } EOF # ---------------------------------------------------------------------------- echo_eval cd build/colpack echo_eval g++ colpack.cpp \ -I$HOME/prefix/colpack/include/ColPack \ -L$HOME/prefix/colpack/lib64 \ -l ColPack \ -o colpack # echo_eval valgrind --leak-check=yes ./colpack # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/speed_branch.sh0000755000175200017650000000462313057470462016163 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/speed_branch.sh" ] then echo "bin/speed_branch.sh: must be executed from its parent directory" exit 1 fi if [ "$2" == '' ] then cat << EOF usage: bin/speed_branch.sh branch_one branch_two [option_1 [option_2 ...] ] where the possible options are: onetape, colpack, optimize, atomic, memory, boolsparsity, colpack EOF exit 1 fi branch_one="$1" branch_two="$2" # ---------------------------------------------------------------------------- shift shift option_list='none' for option in $* do if [ "$option_list" == 'none' ] then option_list="$option" else option_list="${option_list}_$option" fi done # ---------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- if [ ! -d '.git' ] then echo 'speed_branch.sh: only implemented for git repository' exit 1 fi # ----------------------------------------------------------------------------- dir='build/speed/cppad' for branch in $branch_one $branch_two do if [ -e "build/speed/cppad/$branch.$option_list.out" ] then echo "Using existing build/speed/cppad/$branch.$option_list.out" else echo_eval git checkout $branch # echo "bin/run_cmake.sh > $branch.log" bin/run_cmake.sh > $branch.log # cd $dir # echo "make check_speed_cppad >> $branch.log" make check_speed_cppad >> ../../../$branch.log # echo "./speed_cppad speed 123 $* > $branch.$option_list.out" ./speed_cppad speed 123 $* > $branch.$option_list.out # cd ../../.. fi done # compare the results echo " one=$branch_one , two=$branch_two" bin/speed_diff.sh \ $dir/$branch_one.$option_list.out $dir/$branch_two.$option_list.out # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/check_include_file.sh0000755000175200017650000000456513057470462017332 0ustar coincoin-web#! /bin/bash -e # $Id: check_include_file.sh 3847 2016-11-20 09:34:00Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_include_file.sh" ] then msg="must be executed from its parent directory" echo "bin/check_include_file.sh: $msg" exit 1 fi # ----------------------------------------------------------------------------- # echo "Checking difference between C++ include directives and file names." echo "-------------------------------------------------------------------" if [ -e check_include_file.1.$$ ] then echo "bin/check_include_file.sh: unexpected bin/check_include_file.1.$$" exit 1 fi list=`bin/ls_files.sh | sed -n \ -e '/\.cpp$/p' \ -e '/\.hpp$/p'` for file in $list do sed -n -e '/^# *include *> bin/check_include_file.1.$$ done # cat bin/check_include_file.1.$$ | \ sed -e 's%[^<]*<%%' -e 's%>.*$%%' | \ sort -u > bin/check_include_file.2.$$ # # The following files should never be included: # cppad/local/prototype_op.hpp # cppad/local/optimize/define_prototype.hpp # cppad/example/eigen_plugin.hpp # All other files should. # The file cppad/configure.hpp may not yet be created. bin/ls_files.sh | sed -n -e '/cppad\/.*\.hpp$/p' | \ sed \ -e '1,1s|^|cppad/configure.hpp\n|' \ -e '/cppad\/local\/prototype_op.hpp/d' \ -e '/cppad\/local\/optimize\/define_prototype.hpp/d' \ -e '/cppad\/example\/eigen_plugin.hpp/d' \ -e '/cppad\/deprecated\//d' | \ sort -u > bin/check_include_file.3.$$ # if diff bin/check_include_file.2.$$ bin/check_include_file.3.$$ then different="no" else different="yes" fi for index in 1 2 3 do rm bin/check_include_file.$index.$$ done # echo "-------------------------------------------------------------------" if [ $different = "yes" ] then echo "Error: nothing should be between the two dashed lines above" exit 1 else echo "Ok: nothing is between the two dashed lines above" exit 0 fi cppad-20170000.3/bin/add_copyright.sh0000755000175200017650000001106313057470462016362 0ustar coincoin-web#! /bin/bash -e # $Id: add_copyright.sh 3858 2016-12-26 16:17:59Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/add_copyright.sh" ] then echo "bin/add_copyright.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- if [ "$1" == "" ] then echo "bin/add_copyright.sh: file_name" exit 1 fi file_name="$1" if [ ! -e "$file_name" ] then echo "$file_name does not exist" exit 1 fi ext=`echo $file_name | sed -e 's/.*\.//'` if [ "$ext" == "" ] then echo "bin/add_copyright.sh: file_name does not have an extension" exit 1 fi # echo "write copyright message to bin/add_copyright.$$" case $ext in hpp) upper_name=`echo $file_name | tr [a-z./] [A-Z__]` cat << EOF > bin/add_copyright.$$ // \$Id\$ # ifndef CPPAD_$upper_name # define CPPAD_$upper_name /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ EOF ;; cpp | omh | i) cat << EOF > bin/add_copyright.$$ // \$Id\$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ EOF ;; cmake | txt) cat << EOF > bin/add_copyright.$$ # \$Id\$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- EOF ;; sh) cat << EOF > bin/add_copyright.$$ #! /bin/bash -e # \$Id\$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- EOF echo "chmod +x bin/add_copyright.$$" chmod +x bin/add_copyright.$$ ;; *) echo bin/"add_copyright.sh: extension $ext is not yet supported" exit 1 esac # # Add check for exection directory to scripts in bin/*.sh files if ( echo $file_name | grep 'bin/[^.]*\.sh$' > /dev/null ) then cat << EOF >> bin/add_copyright.$$ if [ \$0 != "$file_name" ] then echo "$file_name: must be executed from its parent directory" exit 1 fi EOF fi # echo "cat $file_name >> bin/add_copyright.$$" cat $file_name >> bin/add_copyright.$$ # echo "mv $file_name ~/trash" mv $file_name ~/trash # echo "mv bin/add_copyright.$$ $file_name" mv bin/add_copyright.$$ $file_name # # add endif at end of *.hpp files if [ "$ext" == 'hpp' ] then echo "# endif" >> $file_name fi # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/tag_month.sh0000755000175200017650000000702313057470462015523 0ustar coincoin-web#! /bin/bash -e # $Id:$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/tag_month.sh" ] then echo "bin/tag_month.sh: must be executed from its parent directory" exit 1 fi svn_repository="https://projects.coin-or.org/svn/CppAD" # -------------------------------------------------------------------------- # make sure that master is currently checked out git_branch=`git branch | sed -e '/^\*/! d' -e 's|^\* *||'` if [ "$git_branch" != 'master' ] then echo 'tag_month.sh: master is not currently checkout out' exit 1 fi # -------------------------------------------------------------------------- # make sure that version is consistent and all changes are checked in bin/version.sh check # -------------------------------------------------------------------------- # make sure repo is up to date git_status=`git status -s` if [ "$git_status" != '' ] then echo 'tag_month.sh: master has changes that are not checked in' exit 1 fi # -------------------------------------------------------------------------- # check that version corresponds to first of a month dd=`bin/version.sh get | sed -e 's|......\([0-9][0-9]\)|\1|' ` if [ "$dd" != '01' ] then echo 'tag_month.sh: verison does not correspond to first day of a month' exit 1 fi # -------------------------------------------------------------------------- # date of last change to svn repository svn_date=`svn log $svn_repository/trunk --limit 1 | grep '^r[0-9]* *|' | \ sed -e 's/^[^|]*|[^|]*| *\([0-9-]*\).*/\1/' -e 's|-||g'` # -------------------------------------------------------------------------- # get and check hash codes # local_hash=`git show-ref master | sed -e '/\/origin\//d' -e 's| refs.*||'` remote_hash=`git show-ref master | sed -e '/\/origin\//! d' -e 's| refs.*||'` svn_hash=`svn log $svn_repository/trunk --limit 1 | \ grep 'end *hash *code:' | sed -e 's|end *hash *code: *||'` # if [ "$local_hash" != "$remote_hash" ] then echo "tag_month.sh: master changes haven't been pushed to git repository" echo "local_hash = $local_hash" echo "remote_hash = $remote_hash" exit 1 fi if [ "$remote_hash" != "$svn_hash" ] then echo "tag_month.sh: master changes haven't been pushed to svn repository" echo "remote_hash = $remote_hash" echo "svn_hash = $svn_hash" exit 1 fi # ----------------------------------------------------------------------------- # If this version has already been tagged, delete the tag version=`bin/version.sh get` if git tag --list | grep "$version" then read -p "Delete preious tag for version $version [y/n] ?" response if [ "$response" != 'y' ] then echo 'tag_month.sh: aborting because tag already exists' exit 1 fi git tag -d $version git push --delete origin $version fi # echo "git tag -a \\" echo "-m \"Last changes copied to $svn_repository/trunk on $svn_date\" \\" echo "$version $svn_hash" git tag -a \ -m "Last changes copied to $svn_repository/trunk on $svn_date" \ $version $svn_hash # echo "git push origin $version" git push origin $version # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/doxyfile.sh0000755000175200017650000000607213057470462015371 0ustar coincoin-web#! /bin/bash -e # $Id: doxyfile.sh 3845 2016-11-19 01:50:47Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/doxyfile.sh" ] then echo "bin/doxyfile.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- if [ "$3" == "" ] then echo "usage: bin/doxyfile.sh version error_file output_directory" echo "creates the doxygen configuration file ./doxyfile" exit 1 fi version="$1" error_file="$2" output_directory="$3" # PREDEFINED:see http://www.stack.nl/~dimitri/doxygen/manual/preprocessing.html # 2DO: change EXTRACT_ALL to NO so get warnings for undocumented functions. echo "create bin/doxyfile.$$" cat << EOF > bin/doxyfile.$$ ALWAYS_DETAILED_SEC = YES BUILTIN_STL_SUPPORT = YES ENABLE_PREPROCESSING = YES MACRO_EXPANSION = YES EXTRACT_ALL = YES EXTRACT_LOCAL_CLASSES = YES EXTRACT_PRIVATE = YES EXTRACT_STATIC = YES EXTRACT_ANON_NSPACES = YES FILE_PATTERNS = *.hpp *.cpp FULL_PATH_NAMES = NO GENERATE_HTML = YES GENERATE_LATEX = NO GENERATE_TREEVIEW = YES INHERIT_DOCS = NO INLINE_INHERITED_MEMB = YES INPUT = \ ./cppad \ ./cppad/core \ ./cppad/local \ ./cppad/local/optimize \ ./cppad/ipopt \ ./cppad_ipopt/src \ ./cppad_lib \ ./cppad/utility \ ./speed/src LATEX_BATCHMODE = YES MACRO_EXPANSION = YES MULTILINE_CPP_IS_BRIEF = YES OUTPUT_DIRECTORY = $output_directory PREDEFINED = "__cplusplus=201103" "CPPAD_USE_CPLUSPLUS_2011=1" PROJECT_NAME = "CppAD: A C++ Algorithmic Differentiation Package" PROJECT_NUMBER = $version QT_AUTOBRIEF = YES REFERENCED_BY_RELATION = YES REFERENCES_LINK_SOURCE = NO SEPARATE_MEMBER_PAGES = YES SHOW_DIRECTORIES = YES SHOW_INCLUDE_FILES = NO SORT_GROUP_NAMES = YES SORT_MEMBER_DOCS = YES SORT_BRIEF_DOCS = YES SOURCE_BROWSER = YES STRIP_CODE_COMMENTS = NO SUBGROUPING = NO TAB_SIZE = 5 VERBATIM_HEADERS = NO WARN_LOGFILE = $error_file WARN_NO_PARAMDOC = YES EOF sed \ -e 's/\t/ /g' \ -e 's/^/s|^\\(/' \ -e 's/ *=/ *=\\).*|\\1/' \ -e 's/$/|/' \ -i bin/doxyfile.$$ # echo "doxygen -g doxyfile > /dev/null" doxygen -g doxyfile > /dev/null # echo "sed -f bin/doxyfile.$$ -i doxyfile" sed -f bin/doxyfile.$$ -i doxyfile # echo "rm bin/doxyfile.$$" rm bin/doxyfile.$$ # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/special_version.sh0000755000175200017650000000636213057470462016735 0ustar coincoin-web#! /bin/bash -e # $Id: special_version.sh 3768 2015-12-28 18:58:35Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/special_version.sh" ] then echo "bin/special_version.sh: must be executed from its parent directory" exit 1 fi # ---------------------------------------------------------------------------- version="$1" case "$version" in 2011 | 2012_0 | 2012_1 ) subversion_revision='2279' ;; 2012_2 ) subversion_revision='2347' ;; *) cat << EOF usage: bin/special_version.sh version where version is one of the following: 2011, 2012_0 2012_1 2012_2 EOF exit 1 ;; esac url='https://projects.coin-or.org/svn/CppAD/trunk' # ---------------------------------------------------------------------------- if [ -e "../special-$version" ] then echo "Using the existing directory ../special-$version" if [ -e ../special-$version/work ] then echo "rm -r ../special-$version/work" rm -r ../special-$version/work fi else echo "svn checkout -r $subversion_revision $url ../special-$version" svn checkout -r $subversion_revision $url ../special-$version fi echo "cd ../special-$version" cd ../special-$version # case "$1" in 2011) list="bthread openmp pthread" for threading in $list do file="multi_thread/$threading/team_$threading.cpp" svn revert $file # echo "sed -e 's|hold_memory(true)|hold_memory(false)|;' -i $file" sed -e 's|hold_memory(true)|hold_memory(false)|;' -i $file done ;; 2012_0) file='cppad/thread_alloc.hpp' thread_alloc_revision='2249' echo "svn cat $url/$file@$thread_alloc_revision > $file" svn cat $url/$file@$thread_alloc_revision > $file # # Always hold onto memory echo "sed -e 's/if( num_threads() == 1 )/if(false)/' -i $file" sed -e 's/if( num_threads() == 1 )/if(false)/' -i $file # # No hold_memory function echo "sed -e 's|^.*void parallel_|\tstatic void hold_memory(bool) {}\n&|'" echo " -i $file" sed -e 's|^.*void parallel_|\tstatic void hold_memory(bool) {}\n&|' \ -i $file ;; 2012_1 | 2012_2 ) ;; *) echo "bin/special_version.sh: program error" exit 1 ;; esac # file='cppad/configure.hpp' text="# define CPPAD_PACKAGE_STRING" svn revert $file echo "sed -i $file -e \"s|^$text.*|\1 \"cppad-$version\"|\"" sed -i $file -e "s|^\($text\) .*|\1 \"cppad-$version\"|" # echo "mkdir work ; cd work" mkdir work ; cd work # response='n' while [ "$response" != 'y' ] do dir=`pwd` echo "current working: $dir" echo "Enter configure options on next line (no options is default)" read -p "options: " options echo "../configure $options" read -p "Is this ok [y/n] ?" response done echo "../configure $options" ../configure $options # echo "cd multi_thread ; make test" cd multi_thread ; make test # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/get_eigen.sh0000755000175200017650000001061313057470462015470 0ustar coincoin-web#! /bin/bash -e # $Id: get_eigen.sh 3837 2016-10-09 23:45:56Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # $begin get_eigen.sh$$ $newlinech #$$ # $spell # gz # Eigen # CppAD # $$ # # $section Download and Install Eigen in Build Directory$$ # $index eigen, download and install$$ # $index download, install eigen$$ # $index install, eigen$$ # # $head Syntax$$ # $code bin/get_eigen.sh$$ # # $head Purpose$$ # If you are using Unix, this command will download and install # $href%http://eigen.tuxfamily.org%Eigen%$$ in the # CppAD $code build$$ directory. # # $head Distribution Directory$$ # This command must be executed in the # $cref/distribution directory/download/Distribution Directory/$$. # # $head External Directory$$ # The Eigen source code is downloaded into the sub-directory # $code build/external$$ below the distribution directory. # # $head Prefix Directory$$ # The Eigen include files are installed in the sub-directory # $code build/prefix/include/Eigen$$ below the distribution directory. # # $head Reuse$$ # The file $codei%build/external/eigen-%version%.tar.gz%$$ # and the directory $codei%build/external/eigen-%version%$$ # will be reused if they exist. Delete this file and directory # to get a complete rebuild. # # $end # ----------------------------------------------------------------------------- if [ $0 != "bin/get_eigen.sh" ] then echo "bin/get_eigen.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- echo 'Download eigen to build/external and install it to build/prefix' version='3.2.9' web_page='https://bitbucket.org/eigen/eigen/get' cppad_dir=`pwd` prefix="$cppad_dir/build/prefix" installed_flag="build/external/eigen-${version}.installed" if [ -e "$installed_flag" ] then echo "$installed_flag exists: Skipping get_eigen.sh" exit 0 fi # ----------------------------------------------------------------------------- # determine which version of cmake to use cmake --version | sed -n \ -e 's|[^0-9]*|.|g ' \ -e 's|\.\([0-9]*\)\.\([0-9]*\).*|\1 * 10 + \2|' \ -e '1,1p' \ | bc > get_ipopt.$$ cmake_version=`cat get_ipopt.$$` rm get_ipopt.$$ echo "cmake_version=$cmake_version" # cmake_program='' if [ "$cmake_version" -ge '28' ] then cmake_program='cmake' else for cmake_version in 28 29 do if which cmake$cmake_version >& /dev/null then cmake_program="cmake$cmake_version" fi done fi if [ "$cmake_program" == '' ] then echo 'cannot find a verison of cmake that is 2.8 or higher' exit 1 fi # ----------------------------------------------------------------------------- if [ ! -d build/external ] then echo_eval mkdir -p build/external fi echo_eval cd build/external # ----------------------------------------------------------------------------- if [ ! -e "eigen-$version.tar.gz" ] then echo_eval wget --no-check-certificate $web_page/$version.tar.gz echo_eval mv $version.tar.gz eigen-$version.tar.gz fi # ----------------------------------------------------------------------------- if [ -e eigen-eigen-* ] then echo_eval rm -r eigen-eigen-* fi if [ -e "$prefix/include/Eigen" ] then echo_eval rm "$prefix/include/Eigen" fi if [ ! -e eigen-$version ] then echo_eval tar -xzf eigen-$version.tar.gz git_name=`ls | grep eigen-eigen` echo_eval mv $git_name eigen-$version fi # ----------------------------------------------------------------------------- echo_eval cd eigen-$version if [ ! -e build ] then echo_eval mkdir build fi echo_eval cd build echo_eval $cmake_program .. -DCMAKE_INSTALL_PREFIX=$prefix echo_eval make install echo_eval ln -s $prefix/include/eigen3/Eigen $prefix/include/Eigen # ----------------------------------------------------------------------------- echo_eval touch $cppad_dir/$installed_flag echo "get_eigen.sh: OK" cppad-20170000.3/bin/batch_edit.sh0000755000175200017650000000506513057470462015635 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- revert_list=' ' move_list=' ' move_sed='s|/local/|/core/|' # cat << EOF > junk.sed s|taion|ation|g s|aation|ation|g EOF # ----------------------------------------------------------------------------- if [ $0 != "bin/batch_edit.sh" ] then echo "bin/batch_edit.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- cp bin/batch_edit.sh $HOME/trash/batch_edit.sh git reset --hard # --------------------------------------------------------------------------- list_all=`bin/ls_files.sh | sed \ -e '/^compile$/d' \ -e '/^config\.guess$/d' \ -e '/^config\.sub$/d' \ -e '/^configure$/d' \ -e '/^depcomp$/d' \ -e '/^epl-v10.txt$/d' \ -e '/^gpl-v10.txt$/d' \ -e '/^makefile.in$/d' \ -e '/\/makefile.in$/d' \ -e '/^missing$/d'` for file in $list_all do if [ "$file" != 'bin/batch_edit.sh' ] then sed -f junk.sed $file > junk.$$ if ! diff $file junk.$$ > /dev/null then echo_eval sed -f junk.sed -i $file fi fi done if [ -e junk.$$ ] then rm junk.$$ fi # ---------------------------------------------------------------------------- for old in $move_list do new=`echo $old | sed -e "$move_sed"` if [ -e "$new" ] then rm -r "$new" fi dir=`echo $new | sed -e 's|/[^/]*$||'` if [ "$dir" != "$new" ] && [ ! -e "$dir" ] then echo_eval mkdir $dir fi echo_eval git mv $old $new done # ---------------------------------------------------------------------------- # files that were hand edited and cached using 'git_new.sh to' if [ -e new ] then echo_eval git_new.sh from fi # ---------------------------------------------------------------------------- for file in $revert_list do echo_eval git checkout $file done # ---------------------------------------------------------------------------- cp $HOME/trash/batch_edit.sh bin/batch_edit.sh echo "$0: OK" exit 0 cppad-20170000.3/bin/check_define.sh0000755000175200017650000000377313057470462016142 0ustar coincoin-web#! /bin/bash -e # $Id: check_define.sh 3783 2016-01-21 20:14:22Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/check_define.sh" ] then echo "bin/check_define.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- echo "Check '# define' versus '# undef' names and check for addon names" echo '-----------------------------------------------------------------------' cmd_list='define undef' add_on_list='CG PY TMB MIXED' file_list=`bin/ls_files.sh | sed -n \ -e '/^cppad\/.*\.hpp$/p' \ -e '/^cppad\/.*\.hpp\.in$/p'` # add_on_error='false' for file in $file_list do for cmd in $cmd_list do if [ ! -e $file.in ] then sed -n -e "/^# *$cmd /p" $file | \ sed -e "s/^# *$cmd *\([A-Za-z0-9_]*\).*/\1/" >> tmp.$$ fi if [ "$cmd" == 'define' ] then sed -e '/_HPP$/d' -i tmp.$$ fi sort -u tmp.$$ > $cmd.$$ rm tmp.$$ done for add_on in $add_on_list do if grep "CPPAD_${add_on}_" $file then add_on_error='true' fi done done if [ "$add_on_error" == 'true' ] then echo '-----------------------------------------------------------------------' echo 'check_define.sh: Error: add_on preprocessor symbol found' rm undef.$$ rm define.$$ exit 1 fi if ! diff define.$$ undef.$$ then echo 'check_define.sh: Error: defines and undefs do not match' rm undef.$$ rm define.$$ exit 1 fi echo '-----------------------------------------------------------------------' rm undef.$$ rm define.$$ exit 0 cppad-20170000.3/bin/check_example.sh0000755000175200017650000000326113057470462016333 0ustar coincoin-web#! /bin/bash -e # $Id: check_example.sh 3781 2016-01-18 16:16:22Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_example.sh" ] then echo "bin/check_example.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- echo "Checking that all examples are in omh/example_list.omh" echo "-------------------------------------------------------" file_list=`bin/ls_files.sh | sed -n \ -e '/cppad_ipopt/d' \ -e '/example\//p' \ -e '/multi_thread\//p'` # sed < omh/example_list.omh > bin/check_example.$$ \ -n -e '/\$begin ListAllExamples\$\$/,/\$end/p' ok="yes" for file in $file_list do name=`grep '$begin' $file | sed -e 's/.*$begin *//' -e 's/ *$$.*//'` if [ "$name" != "" ] then if ! grep "$name" bin/check_example.$$ > /dev/null then echo "$name is missing from omh/example_list.omh" ok="no" fi fi done rm bin/check_example.$$ echo "-------------------------------------------------------" if [ "$ok" = "yes" ] then echo "Ok: nothing is between the two dashed lines above" exit 0 else echo "Error: nothing should be between the two dashed lines above" exit 1 fi cppad-20170000.3/bin/speed_diff.sh0000755000175200017650000000317413057470462015636 0ustar coincoin-web#! /bin/bash -e # $Id: speed_diff.sh 3768 2015-12-28 18:58:35Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ "$0" != 'bin/speed_diff.sh' ] then echo 'bin/speed_diff.sh: must be executed from its parent directory' exit 1 fi if [ "$2" == '' ] then cat << EOF usage: bin/speed_diff.sh speed_one.out speed_two.out where speed_one.out and speed_two.out are outputs from the speed_cppad program runing its 'speed' test. EOF exit 1 fi speed_one="$1" speed_two="$2" if [ ! -f "$speed_one" ] then echo "speed_diff.sh: the file $speed_one does not exist." exit 1 fi if [ ! -f "$speed_two" ] then echo "speed_diff.sh: the file $speed_two does not exist." exit 1 fi # sed -n \ -e 's|^[a-z]*_||' \ -e 's|_rate|_rate_one|' -e '/_rate_one/p' \ -e 's|available|available_one|' -e '/available_one/p' \ $speed_one > speed_diff.$$ # sed -n \ -e 's|^[a-z]*_||' \ -e 's|_rate|_rate_two|' -e '/_rate_two/p' \ -e 's|available|available_two|' -e '/available_two/p' \ $speed_two >> speed_diff.$$ # cat speed_diff.$$ | sort -u rm speed_diff.$$ # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/get_sacado.sh0000755000175200017650000001417413057470462015641 0ustar coincoin-web#! /bin/bash -e # $Id: get_sacado.sh 3730 2015-09-23 15:56:53Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # $begin get_sacado.sh$$ $newlinech #$$ # $spell # trilinos # gz # Sacado # CppAD # $$ # # $section Download and Install Sacado in Build Directory$$ # $index sacado, download and install$$ # $index download, install sacado$$ # $index install, sacado$$ # # $head Syntax$$ # $code bin/get_sacado.sh$$ # # $head Purpose$$ # If you are using Unix, this command will download and install # $href%http://trilinos.sandia.gov/packages/sacado%Sacado%$$ in the # CppAD $code build$$ directory. # # $head Distribution Directory$$ # This command must be executed in the # $cref/distribution directory/download/Distribution Directory/$$. # # $head External Directory$$ # The Sacado source code is downloaded into the sub-directory # $code build/external$$ below the distribution directory. # # $head Prefix Directory$$ # The Sacado libraries and include files are installed in the sub-directory # $code build/prefix$$ below the distribution directory. # # $head Reuse$$ # The file $codei%build/external/trilinos-%version%-Source.tar.gz%$$ # and the directory $codei%build/external/trilinos-%version%-Source%$$ # will be reused if they exist. Delete this file and directory # to get a complete rebuild. # # $end # ----------------------------------------------------------------------------- if [ $0 != "bin/get_sacado.sh" ] then echo "bin/get_sacado.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- echo 'Download sacado to build/external and install it to build/prefix' version="11.12.1" trilinos_dir="trilinos-$version-Source" web_page="http://trilinos.org/oldsite/download/files" cppad_dir=`pwd` prefix="$cppad_dir/build/prefix" installed_flag="build/external/trilinos-${version}.installed" if [ -e "$installed_flag" ] then echo "$installed_flag exists: Skipping get_sacado.sh" exit 0 fi # ----------------------------------------------------------------------------- # determine which version of cmake to use cmake --version | sed -n \ -e 's|[^0-9]*|.|g ' \ -e 's|\.\([0-9]*\)\.\([0-9]*\).*|\1 * 10 + \2|' \ -e '1,1p' \ | bc > get_sacado.$$ cmake_version=`cat get_sacado.$$` rm get_sacado.$$ echo "cmake_version=$cmake_version" # cmake_program='' if [ "$cmake_version" -ge '27' ] then cmake_program='cmake' else for cmake_version in 27 28 29 do if which cmake$cmake_version >& /dev/null then cmake_program="cmake$cmake_version" fi done fi if [ "$cmake_program" == '' ] then echo 'cannot find a verison of cmake that is 2.7 or higher' exit 1 fi # ----------------------------------------------------------------------------- # libdir if [ -e /usr/lib64 ] then libdir='lib64' else libdir='lib' fi # ----------------------------------------------------------------------------- # check if we have a local copy of coin lapack and blas libraries installed coin_lapack_blas='no' if [ -e build/prefix/$libdir/libcoinlapack.a ] then if [ -e build/prefix/$libdir/libcoinblas.a ] then coin_lapack_blas='yes' fi fi echo "coin_lapack_blas=$coin_lapack_blas" # ----------------------------------------------------------------------------- # change into build/external directory if [ ! -d build/external ] then echo_eval mkdir -p build/external fi echo_eval cd build/external # ----------------------------------------------------------------------------- # create the trilions source directory and change into it if [ ! -e "$trilinos_dir.tar.gz" ] then echo_eval wget --no-check-certificate $web_page/$trilinos_dir.tar.gz fi for package in Sacado Teuchos Trilinois do echo_eval rm -rf $prefix/include/$package* done if [ ! -e "$trilinos_dir" ] then echo_eval tar -xzf $trilinos_dir.tar.gz # ------------------------------------------------------------------------ # patch the cmake/tribits/modules/FindPythonInterp.cmake file file="$trilinos_dir/cmake/tribits/modules/FindPythonInterp.cmake" line='[HKEY_LOCAL_MACHINE\\\\SOFTWARE\\\\Python\\\\PythonCore\\\\2.8\\\\' line="${line}InstallPath]" if [ -e "$file" ] then echo "patch $file" sed \ -e 's|NAMES \(python2.7 python2.6\)|NAMES python2.8 \1|' \ -e "s|^\( *\)\[HKEY_LOCAL_MACHINE.*2\.7.*|\1$line\n&|" \ -i $file fi # ------------------------------------------------------------------------ fi echo_eval cd $trilinos_dir # ----------------------------------------------------------------------------- # change into build sub-directory if [ ! -e build ] then echo_eval mkdir build fi echo_eval cd build # ----------------------------------------------------------------------------- # cmake command and install if [ "$coin_lapack_blas" == 'yes' ] then echo_eval $cmake_program \ -D CMAKE_BUILD_TYPE:STRING=RELEASE \ -D Trilinos_ENABLE_Sacado:BOOL=ON \ -D Sacado_ENABLE_TESTS:BOOL=OFF \ -D CMAKE_INSTALL_PREFIX:PATH=$prefix \ -D Trilinos_INSTALL_LIB_DIR=$prefix/$libdir \ -D LAPACK_LIBRARY_NAMES:STRING=coinlapack \ -D BLAS_LIBRARY_NAMES:STRING=coinblas \ -D LAPACK_LIBRARY_DIRS:STRING=../prefix/$libdir \ -D BLAS_LIBRARY_DIRS:STRING=../prefix/$libdir \ ../ else echo_eval $cmake_program \ -D CMAKE_BUILD_TYPE:STRING=RELEASE \ -D Trilinos_ENABLE_Sacado:BOOL=ON \ -D Sacado_ENABLE_TESTS:BOOL=OFF \ -D CMAKE_INSTALL_PREFIX:PATH=$prefix \ -D Trilinos_INSTALL_LIB_DIR=$prefix/$libdir \ ../ fi echo_eval make install # ----------------------------------------------------------------------------- echo_eval touch $cppad_dir/$installed_flag echo "get_sacado.sh: OK" cppad-20170000.3/bin/check_if.sh0000755000175200017650000000327013057470462015276 0ustar coincoin-web#! /bin/bash -e # $Id: check_if.sh 3781 2016-01-18 16:16:22Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ "$0" != 'bin/check_if.sh' ] then echo "bin/check_if: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # CppAD uses preprocessor '# if 0' comment blocks for temporary changes # that will to be removed before testing for check in. echo "Checking for '# if 0' and '# if NDEBUG' commands in source code" echo "-------------------------------------------------------" ok="yes" list=`bin/ls_files.sh | sed -n \ -e '/\.cpp$/p' \ -e '/\.hpp$/p' \ -e '/\.hpp.in$/p'` for file in $list do if grep '^# *if *0 *$' $file > /dev/null then # CppAD uses /* comment */ for all its block commnets echo "$file has an '# if 0' preprocessor command" ok="no" fi if grep '^# *if *NDEBUG *$' $file > /dev/null then # This should probably be # ifndef NDEBUG ? echo "$file has an '# if NDEBUG' preprocessor command" ok="no" fi done echo "-------------------------------------------------------" if [ "$ok" = "no" ] then echo 'bin/check_if.sh: Error' exit 1 else echo 'bin/check_if.sh: OK' exit 0 fi cppad-20170000.3/bin/reduce_index.sh0000755000175200017650000000247013057470462016202 0ustar coincoin-web#! /bin/bash -e # $Id:$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/reduce_index.sh" ] then echo "bin/reduce_index.sh: must be executed from its parent directory" exit 1 fi if [ "$1" == '' ] then echo 'usage: bin/reduce_index.sh days' echo ' where days is an integer, runs bin/reduce_index.py' echo 'on all files checked in within the specified number of days.' fi days="$1" list=`git log --pretty=format: --name-only --since="$days days ago" | sed \ -e '/^ *$/d' \ -e '/^makefile\./d' -e '/\/makefile\./d' \ -e '/^CMakeLists.txt/d' -e '/\/CMakeLists.txt/d' \ -e '/^bin\/reduce_index.py/d'` for file in $list do if [ -e $file ] then git checkout $file bin/reduce_index.py $file fi done # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/trace.sh0000755000175200017650000000250313057470462014637 0ustar coincoin-web#! /bin/bash -e # $Id: trace.sh 3768 2015-12-28 18:58:35Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/trace.sh" ] then echo "bin/trace.sh: must be executed from its parent directory" exit 1 fi name="$1" option="$2" file="cppad/local/$name.hpp" # ok='yes' if [ "$option" != '0' ] && [ "$option" != '1' ] then ok='no' fi echo "grep '_TRACE [01]' $file" if ! grep '_TRACE [01]' $file > /dev/null then ok='no' fi if [ "$ok" == 'no' ] then echo 'usage: bin/trace.sh name (0|1)' echo ' where the file cppad/local/name.hpp has a defined TRACE option' exit 1 fi old=`grep '_TRACE [01]' $file` sed -e "s|TRACE [01]|TRACE $option|" -i $file new=`grep '_TRACE [01]' $file` # echo "old: $old" echo "new: $new" # # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/run_doxygen.sh0000755000175200017650000000416013057470462016103 0ustar coincoin-web#! /bin/bash -e # $Id: run_doxygen.sh 3853 2016-12-14 14:40:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != 'bin/run_doxygen.sh' ] then echo 'bin/run_doxygen.sh: must be executed from its parent directory' exit 1 fi echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- # run doxygen version=`bin/version.sh get` error_file='doxygen.err' output_directory='doxydoc' for name in doxyfile $error_file $output_directory do if [ -e $name ] then echo_eval rm -r $name fi done echo_eval mkdir doxydoc echo_eval bin/doxyfile.sh $version $error_file $output_directory # echo 'doxygen doxyfile > doxygen.log' doxygen doxyfile > doxygen.log # ----------------------------------------------------------------------------- # check for warnings and errors # doxygen_version=`doxygen --version | sed -e 's|\.|*100+|' -e 's|\.|*10+|' -e 's|\..*||'` let doxygen_version=$doxygen_version if (( $doxygen_version <= 155 )) then doxygen_version=`doxygen --version` echo "doxygen version $doxygen_version is <= 1.5.6" echo "Hence it is to old to check for warnings or errors." exit 0 fi if (( $doxygen_version == 163 )) then doxygen_version=`doxygen --version` echo "doxygen version $doxygen_version is == 1.6.3" echo "Hence it has a problem with warnings about missing # defines;" echo "see http://comments.gmane.org/gmane.text.doxygen.general/8594" exit 0 fi list=`head doxygen.err` if [ "$list" == "" ] then echo 'run_doxygen.sh OK' exit 0 fi echo 'bin/run_doxygen.sh: Doxygen errors or warnings; see doxygen.err' echo 'run_doxygen.sh: Error' exit 1 cppad-20170000.3/bin/epl_html2txt.py0000755000175200017650000000501113057470462016202 0ustar coincoin-web#! /usr/bin/python # $Id: epl_html2txt.py 2506 2012-10-24 19:36:49Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # import re # see http://docs.python.org/library/re.html # -------------------------------------------------------------------------- def remove_simple_cmd(cmd_start, cmd_end, text_in) : pattern = '(.*?)' + cmd_start + '(.*?)' + cmd_end pattern = re.compile(pattern, re.DOTALL) text_out = '' start = 0 while start < len(text_in): match = pattern.search(text_in, start) if match == None : text_out += text_in[start:-1] start = len(text_in) else : text_out += match.group(1) + match.group(2) start = match.end(0) return text_out # -------------------------------------------------------------------------- def remove_cmd_indent_text(cmd_start, cmd_end, text_in) : pattern = '(.*?)' + cmd_start + '(.*?)' + cmd_end pattern = re.compile(pattern, re.DOTALL) text_out = '' start = 0 while start < len(text_in): match = pattern.search(text_in, start) if match == None : text_out += text_in[start:-1] start = len(text_in) else : text_out += match.group(1) + '\t' text_out += re.sub('\n', '\n\t', match.group(2) ) start = match.end(0) return text_out # -------------------------------------------------------------------------- # file_in = open('epl-v10.html', 'rb') data_in = file_in.read() # -------------------------------------------------------------------------- # Extract body pattern = '(.*)' match = re.search(pattern, data_in, re.DOTALL) text = match.group(1) # -------------------------------------------------------------------------- text = remove_simple_cmd('', '', text) text = remove_simple_cmd('

', '

', text) text = remove_simple_cmd('

', '

', text) text = remove_cmd_indent_text('

', '

', text) # -------------------------------------------------------------------------- data_out = text file_out = open('epl-v10.txt', 'wb') file_out.write(data_out) file_out.close() cppad-20170000.3/bin/run_cmake.sh0000755000175200017650000001343713057470462015515 0ustar coincoin-web#! /bin/bash -e # $Id: run_cmake.sh 3839 2016-10-14 18:10:09Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/run_cmake.sh" ] then echo "bin/run_cmake.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------- verbose='no' standard='c++11' debug_speed='no' release_example='no' deprecated='no' profile_speed='no' clang='no' no_colpack='no' no_eigen='no' no_ipopt='no' no_documentation='no' testvector='boost' while [ "$1" != "" ] do if [ "$1" == '--help' ] then cat << EOF usage: bin/run_cmake.sh: \\ [--help] \\ [--verbose] \\ [--c++98] \\ [--debug_speed] \\ [--release_example] \\ [--deprecated] \\ [--profile_speed] \\ [--clang ] \\ [--no_colpack] \\ [--no_eigen] \\ [--no_ipopt] \\ [--no_documentation] \\ [--_vector] The --help option just prints this message and exits. The value above must be one of: cppad, boost, or eigen. EOF exit 0 elif [ "$1" == '--verbose' ] then verbose='yes' elif [ "$1" == '--c++98' ] then standard='c++98' elif [ "$1" == '--debug_speed' ] then debug_speed='yes' profile_speed='no' elif [ "$1" == '--release_example' ] then release_example='yes' elif [ "$1" == '--deprecated' ] then deprecated='yes' elif [ "$1" == '--profile_speed' ] then profile_speed='yes' debug_speed='no' elif [ "$1" == '--clang' ] then clang='yes' elif [ "$1" == '--no_colpack' ] then no_colpack='yes' elif [ "$1" == '--no_eigen' ] then no_eigen='yes' elif [ "$1" == '--no_ipopt' ] then no_ipopt='yes' elif [ "$1" == '--no_documentation' ] then no_documentation='yes' elif [ "$1" == '--cppad_vector' ] then testvector='cppad' elif [ "$1" == '--boost_vector' ] then testvector='boost' elif [ "$1" == '--eigen_vector' ] then testvector='eigen' else echo "$1 is an invalid option, try bin/run_cmake.sh --help" exit 1 fi shift done # --------------------------------------------------------------------------- if [ "$debug_speed" == 'yes' ] then sed -e 's|^SET(CMAKE_BUILD_TYPE .*|SET(CMAKE_BUILD_TYPE DEBUG)|' \ -i speed/CMakeLists.txt else sed -e 's|^SET(CMAKE_BUILD_TYPE .*|SET(CMAKE_BUILD_TYPE RELEASE)|' \ -i speed/CMakeLists.txt fi # --------------------------------------------------------------------------- if [ "$release_example" == 'yes' ] then sed -e 's|^SET(CMAKE_BUILD_TYPE .*|SET(CMAKE_BUILD_TYPE RELEASE)|' \ -i example/CMakeLists.txt else sed -e 's|^SET(CMAKE_BUILD_TYPE .*|SET(CMAKE_BUILD_TYPE DEBUG)|' \ -i example/CMakeLists.txt fi # --------------------------------------------------------------------------- if [ ! -e build ] then echo_eval mkdir build fi echo_eval cd build if [ -e CMakeCache.txt ] then echo_eval rm CMakeCache.txt fi if [ -e CMakeFiles ] then echo_eval rm -r CMakeFiles fi # --------------------------------------------------------------------------- # clean all variables in cmake cache cmake_args='-U .+' # if [ "$verbose" == 'yes' ] then # echo each command that make executes cmake_args="$cmake_args -D CMAKE_VERBOSE_MAKEFILE=YES" fi # ----------------------------------------------------------------------------- # cppad_prefix cmake_args="$cmake_args -D cppad_prefix=$HOME/prefix/cppad" # # cmake_install_includedirs if [ -d '/usr/include' ] then cmake_args="$cmake_args -D cmake_install_includedirs=include" fi # # cmake_install_datadir if [ -d '/usr/share' ] then cmake_args="$cmake_args -D cmake_install_datadir=share" fi # # cmake_install_docdir if [ -d '/usr/share' ] && [ "$no_documentation" == 'no' ] then cmake_args="$cmake_args -D cmake_install_docdir=share/doc" fi # # cmake_install_libdirs if [ -d '/usr/lib64' ] then cmake_args="$cmake_args -D cmake_install_libdirs='lib64;lib'" elif [ -d '/usr/lib' ] then cmake_args="$cmake_args -D cmake_install_libdirs='lib;lib64'" fi # # {package}_prefix package_list='fadbad adolc sacado' if [ "$no_colpack" == 'no' ] then package_list="$package_list colpack" fi if [ "$no_eigen" == 'no' ] then package_list="$package_list eigen" fi if [ "$no_ipopt" == 'no' ] then package_list="$package_list ipopt" fi for package in $package_list do dir=$HOME/prefix/$package if [ -d "$dir" ] then cmake_args="$cmake_args -D ${package}_prefix=$dir" fi done # # cppad_cxx_flags cppad_cxx_flags="-Wall -pedantic-errors -std=$standard" if [ "$testvector" != 'eigen' ] then cppad_cxx_flags="$cppad_cxx_flags -Wshadow" fi cmake_args="$cmake_args -D cppad_cxx_flags='$cppad_cxx_flags'" # # clang if [ "$clang" == 'yes' ] then cmake_args="$cmake_args -D CMAKE_C_COMPILER=clang" cmake_args="$cmake_args -D CMAKE_CXX_COMPILER=clang++" fi # # profile if [ "$profile_speed" == 'yes' ] then cmake_args="$cmake_args -D cppad_profile_flag=-pg" fi # # deprecated if [ "$deprecated" == 'yes' ] then cmake_args="$cmake_args -D cppad_deprecated=YES" else cmake_args="$cmake_args -D cppad_deprecated=NO" fi # # simple options cmake_args="$cmake_args -D cppad_testvector=$testvector" cmake_args="$cmake_args -D cppad_tape_id_type='int32_t'" cmake_args="$cmake_args -D cppad_tape_addr_type=int32_t" cmake_args="$cmake_args -D cppad_max_num_threads=48" # echo_eval cmake $cmake_args .. # # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/check_all.sh0000755000175200017650000001212413057470462015446 0ustar coincoin-web#! /bin/bash -e # $Id: check_all.sh 3781 2016-01-18 16:16:22Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_all.sh" ] then echo "bin/check_all.sh: must be executed from its parent directory" exit 1 fi echo_log_eval() { echo $* echo $* >> $top_srcdir/check_all.log if ! eval $* >> $top_srcdir/check_all.log 2> $top_srcdir/check_all.err then cat $top_srcdir/check_all.err echo 'Error: see check_all.log' exit 1 fi msg=`cat $top_srcdir/check_all.err` if [ "$msg" != '' ] then echo "$msg" echo 'Warning: see check_all.err' exit 1 fi rm $top_srcdir/check_all.err } log_eval() { echo $* >> $top_srcdir/check_all.log if ! eval $* >> $top_srcdir/check_all.log then echo "Error: check check_all.log" exit 1 fi } if [ -e check_all.log ] then echo "rm check_all.log" rm check_all.log fi top_srcdir=`pwd` echo "top_srcdir = $top_srcdir" # if ! random_zero_one=`expr $RANDOM % 2` then # expr exit status is 1 when the expression result is zero # supress shell exit in this case : fi echo "random_zero_one = $random_zero_one" # --------------------------------------------------------------------------- # circular shift program list and set program to first entry in list next_program() { program_list=`echo "$program_list" | sed -e 's| *\([^ ]*\) *\(.*\)|\2 \1|'` program=`echo "$program_list" | sed -e 's| *\([^ ]*\).*|\1|'` } # --------------------------------------------------------------------------- if [ -e "$HOME/prefix/cppad" ] then echo_log_eval rm -r $HOME/prefix/cppad fi # --------------------------------------------------------------------------- # Create package to run test in echo "bin/package.sh" bin/package.sh # ----------------------------------------------------------------------------- # choose which tarball to use for testing skip='' version=`bin/version.sh get` echo_log_eval cd build list=( `ls cppad-$version.*.tgz` ) if [ "${#list[@]}" == '1' ] then tarball="${list[0]}" skip="$skip other_tarball" else tarball="${list[$random_zero_one]}" fi echo_log_eval rm -rf cppad-$version echo_log_eval tar -xzf $tarball echo_log_eval cd cppad-$version # ----------------------------------------------------------------------------- if [ "$random_zero_one" == '0' ] then echo_log_eval bin/run_cmake.sh --boost_vector else echo_log_eval bin/run_cmake.sh --deprecated fi echo_log_eval cd build # ----------------------------------------------------------------------------- echo_log_eval make check # ----------------------------------------------------------------------------- for package in adolc eigen ipopt fadbad sacado do dir=$HOME/prefix/$package if [ ! -d "$dir" ] then skip="$skip $package" fi done # # extra speed tests not run with option specified for option in onetape colpack optimize atomic memory boolsparsity do echo_eval speed/cppad/speed_cppad correct 432 $option done echo_eval speed/adolc/speed_adolc correct 432 onetape echo_eval speed/adolc/speed_adolc sparse_jacobian 432 onetape colpack echo_eval speed/adolc/speed_adolc sparse_hessian 432 onetape colpack # # ---------------------------------------------------------------------------- # extra multi_thread tests program_list='' for threading in bthread openmp pthread do program="multi_thread/${threading}/multi_thread_${threading}" if [ ! -e $program ] then skip="$skip $program" else program_list="$program_list $program" # # fast cases, test for all programs echo_log_eval ./$program a11c echo_log_eval ./$program simple_ad echo_log_eval ./$program team_example fi done if [ "$program_list" != '' ] then # test_time=1,max_thread=4,mega_sum=1 next_program echo_log_eval ./$program harmonic 1 4 1 # # test_time=2,max_thread=4,num_zero=20,num_sub=30,num_sum=500,use_ad=true next_program echo_log_eval ./$program multi_newton 2 4 20 30 500 true # # case that failed in the past next_program echo_log_eval ./$program multi_newton 1 1 100 700 1 true # # case that failed in the past next_program echo_log_eval ./$program multi_newton 1 2 3 12 1 true fi # # print_for test if [ ! -e 'print_for/print_for' ] then skip="$skip print_for/print_for" else echo_log_eval print_for/print_for print_for/print_for | sed -e '/^Test passes/,$d' > junk.1.$$ print_for/print_for | sed -e '1,/^Test passes/d' > junk.2.$$ if diff junk.1.$$ junk.2.$$ then rm junk.1.$$ junk.2.$$ echo_log_eval echo "print_for: OK" else echo_log_eval echo "print_for: Error" exit 1 fi fi # echo_log_eval make install # if [ "$skip" != '' ] then echo_log_eval echo "check_all.sh: skip = $skip" exit 1 fi # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/check_copyright.sh0000755000175200017650000000464713057470462016721 0ustar coincoin-web#! /bin/bash -e # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/check_copyright.sh" ] then echo "bin/check_copyright.sh: must be executed from its parent directory" exit 1 fi if [ ! -e .git ] then echo 'This is not a git repository so cannot check copyright.' echo 'check_copyright.sh: skipped' exit 0 fi list=`git status | sed -n \ -e '/^[#\t ]*deleted:/p' \ -e '/^[#\t ]*modified:/p' \ -e '/^[#\t ]*both modified:/p' \ -e '/^[#\t ]*renamed:/p' \ -e '/^[#\t ]*new file:/p' | \ sed -e 's/^.*: *//' -e 's/ -> /\n/' | \ sed -e '/^makefile.in$/d' \ -e '/^.gitignore$/d' \ -e '/\/makefile.in$/d' \ -e '/\/check_copyright.sh$/d' \ -e '/AUTHORS/d' \ -e '/COPYING/d' | sort -u` cat << EOF > check_copyright.1.$$ # Change copyright second year to current year s/Copyright (C) \\([0-9]*\\)-[0-9][0-9] Bradley M. Bell/Copyright (C) \\1-17 Bradley M. Bell/ s/Copyright (C) \\([0-9]*\\)-20[0-9][0-9] Bradley M. Bell/Copyright (C) \\1-17 Bradley M. Bell/ EOF ok=true for file in $list do if [ -e $file ] then if ! grep 'Copyright (C) [0-9]*-[0-9][0-9]' $file > /dev/null then echo "Cannot find copyright message in $file" exit 1 fi sed -f check_copyright.1.$$ $file > check_copyright.2.$$ if ! diff $file check_copyright.2.$$ > /dev/null then echo '----------------------------------------------------' echo "check_copyright.sh: automatic changes to $file:" if diff $file check_copyright.2.$$ then echo 'bin/check_copyright.sh: program error' rm check_copyright.*.$$ exit 1 fi ok='no' if [ -x $file ] then mv check_copyright.2.$$ $file chmod +x $file else mv check_copyright.2.$$ $file fi fi fi done if [ "$ok" == 'no' ] then rm check_copyright.*.$$ exit 1 fi rm check_copyright.*.$$ # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/check_op_code.sh0000755000175200017650000000602413057470462016310 0ustar coincoin-web#! /bin/bash -e # $Id: check_op_code.sh 3768 2015-12-28 18:58:35Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_op_code.sh" ] then echo "bin/check_op_code.sh: must be executed from its parent directory" exit 1 fi echo "bin/check_op_code.sh: checking that op codes are in alphabetical order:" # --------------------------------------------------------------------------- # check enum list of codes are in alphabetical order sed -n -e '/^enum/,/^\tNumberOp /p' cppad/local/op_code.hpp | sed \ -e '/^enum/d' \ -e '/^\tNumberOp /d' \ -e 's/^[ ]*//' \ -e 's/Op[, ].*//' \ -e '/^\/\//d' > bin/op_code.1.$$ # sort --ignore-case bin/op_code.1.$$ > bin/op_code.2.$$ if ! diff bin/op_code.1.$$ bin/op_code.2.$$ then echo "check_op_code.sh: enum list is not in alphabetical order" rm bin/op_code.*.$$ exit 1 fi # ----------------------------------------------------------------------------- # check NumArgTable sed -n -e '/NumArgTable\[\]/,/^[ \t]*};/p' cppad/local/op_code.hpp | \ sed \ -e '/NumArgTable\[\]/d' \ -e '/NumberOp.*not used/d' \ -e '/^[ \t]*};/d' \ -e 's|^[ \t]*[0-9],* *// *||' \ -e 's|Op.*||' \ > bin/op_code.3.$$ # if ! diff bin/op_code.1.$$ bin/op_code.3.$$ then echo "check_op_code.sh: NumArgTable list is not in alphabetical order" rm bin/op_code.*.$$ exit 1 fi # ----------------------------------------------------------------------------- # check NumResTable (last line of NumResTable is not used) sed -n -e '/NumResTable\[\]/,/^[ \t]*};/p' cppad/local/op_code.hpp | \ sed \ -e '/NumResTable\[\]/d' \ -e '/^[ \t]*};/d' \ -e '/NumberOp.*not used/d' \ -e 's|^[ \t]*[0-9],* *// *||' \ -e 's|Op.*||' \ > bin/op_code.4.$$ # if ! diff bin/op_code.1.$$ bin/op_code.4.$$ then echo "check_op_code.sh: NumResTable list is not in alphabetical order" echo "(or missing last line)" rm bin/op_code.*.$$ exit 1 fi # ----------------------------------------------------------------------------- # check OpNameTable sed -n -e '/const char \*OpNameTable\[\]/,/^[ \t]*};/p' cppad/local/op_code.hpp | \ sed \ -e '/OpNameTable\[\]/d' \ -e '/"Number".*not used/d' \ -e '/^[ \t]*};/d' \ -e 's|^[ \t]*"||' \ -e 's|".*||' \ > bin/op_code.5.$$ # if ! diff bin/op_code.1.$$ bin/op_code.5.$$ then echo "check_op_code.sh: OpName list is not in alphabetical order" rm bin/op_code.*.$$ exit 1 fi # ----------------------------------------------------------------------------- # clean up rm bin/op_code.*.$$ # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/check_replace.sh0000755000175200017650000000325113057470462016312 0ustar coincoin-web#! /bin/bash -e # $Id: check_replace.sh 3853 2016-12-14 14:40:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/check_replace.sh" ] then echo "bin/check_replace.sh: must be executed from its parent directory" exit 1 fi check_replace() { define_file="cppad/local/$1" replace_file="cppad/local/$2" new_file="cppad/local/$2.$$" bin/replace_html.py $define_file $replace_file $new_file if ! diff $replace_file $new_file > /dev/null then cat << EOF check_replace.sh: Error: The replacement text in $replace_file does not match its definition in $define_file. Execute the following command to fix this: mv $new_file $replace_file EOF exit 1 fi rm $new_file } # ----------------------------------------------------------------------------- # files with definitions and replacemnet in same file check_replace cond_op.hpp cond_op.hpp check_replace load_op.hpp load_op.hpp check_replace store_op.hpp store_op.hpp check_replace forward0sweep.hpp forward1sweep.hpp # ----------------------------------------------------------------------------- echo "replace_html.sh: OK" exit 0 cppad-20170000.3/bin/run_omhelp.sh0000755000175200017650000000456113057470462015717 0ustar coincoin-web#! /bin/bash -e # $Id: run_omhelp.sh 3405 2014-11-26 14:20:55Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/run_omhelp.sh" ] then echo "bin/run_omhelp.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- # if [ "$1" != "htm" ] && [ "$1" != "xml" ] && [ "$1" != "clean" ] then echo "usage: bin/run_omhelp.sh (htm|xml|clean) [printable]" exit 1 fi if [ "$2" != "" ] && [ "$2" != "printable" ] then echo "usage: bin/run_omhelp.sh (htm|xml|clean) [printable]" exit 1 fi if [ "$1" == "clean" ] then echo_eval rm -rf doc exit 0 fi ext="$1" if [ "$2" == 'printable' ] then printable="yes" else printable='no' fi # echo "Building doc/*.$ext printable=$printable" if [ ! -e doc ] then echo_eval mkdir doc fi echo_eval cd doc cmd="omhelp ../doc.omh -noframe -debug -l http://www.coin-or.org/CppAD/" if [ "$ext" == "xml" ] then cmd="$cmd -xml" fi if [ $printable == 'yes' ] then cmd="$cmd -printable" fi echo "$cmd >& omhelp.$ext.log" if ! $cmd >& ../omhelp.$ext.log then cat ../omhelp.$ext.log echo "OMhelp could not build doc/*.$ext documentation." grep "^OMhelp Error:" ../omhelp.$ext.log exit 1 fi if grep "^OMhelp Warning:" ../omhelp.$ext.log then echo "See the complete warning messages in omhelp.$ext.log." exit 1 fi if [ "$printable" == 'yes' ] then root_name='_printable' else root_name='cppad' fi if [ ! -e "$root_name.$ext" ] then echo "run_omhelp.sh: Can't make $root_name.$ext the default page." exit 1 fi if [ -e 'index.htm' ] then echo_eval rm index.htm fi cat << EOF > index.html EOF # echo "OK: omhelp $*" exit 0 cppad-20170000.3/bin/push_git2svn.py0000755000175200017650000002567513057470462016231 0ustar coincoin-web#! /bin/python # $Id # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- from __future__ import print_function # ----------------------------------------------------------------------------- # list of svn commands to execute in the svn directory before make changes # indicated by git directory; some example commands are included below svn_commands = [ # 'svn mkdir cppad/utility', # 'svn move cppad/*.hpp cppad/utility', # 'svn move cppad/utility/cppad.hpp cppad/cppad.hpp', # 'svn move cppad/utility/base_require.hpp cppad/base_require.hpp', # 'svn move omh/library.omh omh/utility.omh' ] # ----------------------------------------------------------------------------- # imports import sys import os import re import subprocess import pdb # ----------------------------------------------------------------------------- # command line arguments usage = '\tbin/push_git2svn.py svn_branch_path\n' narg = len(sys.argv) if sys.argv[0] != 'bin/push_git2svn.py' : msg = 'bin/push_git2svn.py must be executed from its parent directory' sys.exit(usage + msg) if narg != 2 : msg = 'expected 1 but found ' + str(narg-1) + ' command line arguments' sys.exit(usage + msg) svn_branch_path = sys.argv[1] if svn_branch_path == 'master' : msg = 'trunk is the svn_branch_path for the master branch' sys.exit(usage + msg) # ----------------------------------------------------------------------------- # some settings svn_repository = 'https://projects.coin-or.org/svn/CppAD' git_repository = 'https://github.com/coin-or/CppAD' work_directory = 'build/work' # ----------------------------------------------------------------------------- # some simple functions def pause(question, choice_list) : response='' while not response in choice_list : print(question, end='') response = sys.stdin.readline() if response.endswith('\n') : response = response[:-1] return response # def system(cmd) : try : output = subprocess.check_output( cmd, stderr=subprocess.STDOUT, shell=True ) except subprocess.CalledProcessError as info : msg = info.output msg += '\nbin/push_git2svn.py exiting because command above failed' sys.exit(cmd + '\n\n' + msg) return output def print_system(cmd) : print(cmd) try : output = subprocess.check_output( cmd, stderr=subprocess.STDOUT, shell=True ) except subprocess.CalledProcessError as info : msg = info.output msg += '\nbin/push_git2svn.py exiting because command above failed' sys.exit(msg) return output id_pattern = re.compile(r'^.*\$Id.*$', re.MULTILINE) def ignore_data(data) : data = re.sub(id_pattern, '', data) return data # ----------------------------------------------------------------------------- # determine git_branch_name if svn_branch_path == 'trunk' : git_branch_name = 'master' git_branch_path = svn_branch_path elif svn_branch_path.startswith('branches/') : git_branch_name = svn_branch_path[len('branches/'):] git_branch_path = svn_branch_path else : git_branch_name = svn_branch_path git_branch_path = 'branches/' + svn_branch_path # ----------------------------------------------------------------------------- # hash code for the git branch cmd = 'git show-ref origin/' + git_branch_name git_hash_code = system(cmd) pattern = ' refs/remotes/origin/' + git_branch_name git_hash_code = git_hash_code.replace(pattern, '') # ----------------------------------------------------------------------------- # make sure work directory exists if not os.path.isdir(work_directory) : os.makedirs(work_directory) # ----------------------------------------------------------------------------- # checkout svn version of directory svn_directory = work_directory + '/svn' if os.path.isdir(svn_directory) : question = 'Use existing svn directory:\n\t' question += svn_directory + '\n' question += 'or remove it and check out a new copy ? [use/new] ' choice_list = [ 'use' , 'new' ] choice = pause(question, choice_list) if choice == 'new' : cmd = 'rm -rf ' + svn_directory print_system(cmd) else : choice = 'new' if choice == 'use' : cmd = 'svn revert --recursive ' + svn_directory print_system(cmd) cmd = 'svn update ' + svn_directory print_system(cmd) cmd = 'svn status ' + svn_directory svn_status = system(cmd) svn_status = svn_status.split('\n') for entry in svn_status : if entry.startswith('? ') : file_name = entry[8:] cmd = 'rm ' + file_name system(cmd) else : cmd = 'svn checkout ' cmd += svn_repository + '/' + svn_branch_path + ' ' + svn_directory print_system(cmd) # ---------------------------------------------------------------------------- tmp = os.getcwd() os.chdir( svn_directory ) for cmd in svn_commands : assert cmd.startswith('svn') print_system(cmd) os.chdir( tmp ) # ---------------------------------------------------------------------------- # git hash code corresponding to verison in svn directory cmd = 'svn info ' + svn_directory svn_info = system(cmd) rev_pattern = re.compile('Last Changed Rev: *([0-9]+)') match = re.search(rev_pattern, svn_info) svn_revision = match.group(1) cmd = 'svn log -r ' + svn_revision + ' ' + svn_directory svn_log = system(cmd) hash_pattern = re.compile('\nend hash code: *([0-9a-f]+)') match = re.search(hash_pattern, svn_log) if match : svn_hash_code = match.group(1) else : svn_hash_code = None # ----------------------------------------------------------------------------- # export the git verison of the directory git_directory = work_directory + '/git' if os.path.isdir(git_directory) : cmd = 'rm -rf ' + git_directory print_system(cmd) cmd = 'svn export ' cmd += git_repository + '/' + git_branch_path + ' ' + git_directory print_system(cmd) # ----------------------------------------------------------------------------- # list of files for the svn and git directories svn_pattern = re.compile(svn_directory + '/') svn_file_list = [] svn_dir_list = [] for directory, dir_list, file_list in os.walk(svn_directory) : ok = ( directory.find('/.svn/') == -1 ) ok = ok and ( not directory.endswith('/.svn') ) if ok : if directory != svn_directory : local_name = re.sub(svn_pattern, '', directory) svn_dir_list.append(local_name) for name in file_list : local_name = directory + '/' + name local_name = re.sub(svn_pattern, '', local_name) svn_file_list.append( local_name ) # git_pattern = re.compile(git_directory + '/') git_file_list = [] git_dir_list = [] for directory, dir_list, file_list in os.walk(git_directory) : index = directory.find('/.svn/') assert index == -1 if directory != git_directory : local_name = re.sub(git_pattern, '', directory) git_dir_list.append(local_name) for name in file_list : local_name = directory + '/' + name local_name = re.sub(git_pattern, '', local_name) git_file_list.append( local_name ) # ----------------------------------------------------------------------------- # list of files that have been created and deleted created_file_list=[] for name in git_file_list : if not name in svn_file_list : created_file_list.append(name) # deleted_file_list=[] for name in svn_file_list : if not name in git_file_list : deleted_file_list.append(name) # ----------------------------------------------------------------------------- # list of directories that have been created and deleted created_dir_list=[] for name in git_dir_list : if not name in svn_dir_list : created_dir_list.append(name) # deleted_dir_list=[] for name in svn_dir_list : if not name in git_dir_list : deleted_dir_list.append(name) # ----------------------------------------------------------------------------- # automated svn commands # for git_dir in created_dir_list : cmd = 'svn mkdir ' + svn_directory + '/' + git_dir print_system(cmd) # for git_file in created_file_list : git_f = open(git_directory + '/' + git_file, 'rb') git_data = git_f.read() git_f.close() git_data = ignore_data(git_data) # found = False for svn_file in deleted_file_list : svn_f = open(svn_directory + '/' + svn_file, 'rb') svn_data = svn_f.read() svn_f.close() svn_data = ignore_data(svn_data) # if svn_data == git_data : assert not found cmd = 'svn copy ' + svn_directory + '/' + svn_file + ' \\\n\t' cmd += svn_directory + '/' + git_file print_system(cmd) cmd = 'cp ' + git_directory + '/' + git_file + ' \\\n\t' cmd += svn_directory + '/' + git_file system(cmd) found = True if not found : cmd = 'cp ' + git_directory + '/' + git_file + ' \\\n\t' cmd += svn_directory + '/' + git_file system(cmd) cmd = 'svn add ' + svn_directory + '/' + git_file print_system(cmd) # for svn_file in deleted_file_list : svn_file_path = svn_directory + '/' + svn_file if os.path.isfile(svn_file_path) : cmd = 'svn delete --force ' + svn_file_path print_system(cmd) # for git_file in git_file_list : do_cp = True do_cp = do_cp and git_file not in created_file_list if git_file in svn_file_list : git_f = open(git_directory + '/' + git_file, 'rb') git_data = git_f.read() git_f.close() git_data = ignore_data(git_data) # svn_f = open(svn_directory + '/' + git_file, 'rb') svn_data = svn_f.read() svn_f.close() svn_data = ignore_data(svn_data) # do_cp = do_cp and git_data != svn_data if do_cp : cmd = 'cp ' + git_directory + '/' + git_file + ' \\\n\t' cmd += svn_directory + '/' + git_file system(cmd) # for svn_dir in deleted_dir_list : cmd = 'svn rm ' + svn_directory + '/' + svn_dir print_system(cmd) # ----------------------------------------------------------------------------- data = 'merge to branch: ' + svn_branch_path + '\n' data += 'from repository: ' + git_repository + '\n' if svn_hash_code != None : data += 'start hash code: ' + svn_hash_code + '\n' else : data += 'start hash code: missing\n' data += 'end hash code: ' + git_hash_code + '\n\n' if svn_hash_code != None : sed_cmd = "sed -e '/" + svn_hash_code + "/,$d'" cmd = 'git log origin/' + git_branch_name + ' | ' + sed_cmd output = system(cmd) data += output log_f = open( svn_directory + '/push_git2svn.log' , 'wb') log_f.write(data) log_f.close() # msg = '\nChange into svn directory with the command\n\t' msg += 'cd ' + svn_directory + '\n' msg += 'If these changes are OK, execute the command:\n\t' msg += 'svn commit --file push_git2svn.log\n' if svn_hash_code != None : msg += 'You should inspect and possibly edit push_git2svn.log' else : msg += 'The start hash code could not be automatically determined.\n' msg += 'You should edit push_git2svn.log to describe the changes.' print(msg) cppad-20170000.3/bin/speed_new.sh0000755000175200017650000000557413057470462015525 0ustar coincoin-web#! /bin/bash -e # $Id: speed_new.sh 3823 2016-07-01 12:30:50Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/speed_new.sh" ] then echo "bin/speed_new.sh: must be executed from its parent directory" exit 1 fi if [ "$1" == '' ] then cat << EOF usage: bin/speed_new.sh option_1 option_2 ... where the possible options are: onetape, colpack, optimize, atomic, memory, boolsparsity, colpack Use the special value 'none' for no options EOF exit 1 fi if [ "$1" == 'none' ] then shift fi if [ ! -d new ] then echo 'speed_new.sh: the directory ./new does not exist.' echo 'It should contain the new source code.' exit 1 fi # ------------------------------------------------------------------------- # if [ ! -e build/speed/cppad/cur_speed.out ] then # revert cppad source code to the current version git reset --hard # # compile and link the current version echo 'cd build; make check_speed_cppad; cd speed/cppad' cd build; make check_speed_cppad; cd speed/cppad # # run speed test for the current version echo './speed_cppad speed 123 $* > cur_speed.out' ./speed_cppad speed 123 $* > cur_speed.out # echo 'cd ../../..' cd ../../.. fi # # Convert cppad source to the new version echo 'git_new.sh from' git_new.sh from # if [ ! -e build/speed/cppad/new_speed.out ] then # compile and link the new version echo 'cd build; make check_speed_cppad; cd speed/cppad' cd build; make check_speed_cppad; cd speed/cppad # # run speed test for the new version echo './speed_cppad speed 123 $* > new_speed.out' ./speed_cppad speed 123 $* > new_speed.out # echo 'cd ../../..' cd ../../.. fi # compare versions echo 'cd build/speed/cppad' cd build/speed/cppad # echo "sed -n -e 's|_rate|_rate_cur|' -e '/_rate_/p' \\" echo " -e 's|available|available_cur|' -e '/available_cur/p' \\" echo " cur_speed.out > run.out" sed -n -e 's|_rate|_rate_cur|' -e '/_rate_/p' \ -e 's|available|available_cur|' -e '/available_cur/p' \ cur_speed.out > run.out # echo "sed -n -e 's|_rate|_rate_new|' -e '/_rate_/p' \\" echo " -e 's|available|available_new|' -e '/available_new/p' \\" echo " new_speed.out >> run.out" sed -n -e 's|_rate|_rate_new|' -e '/_rate_/p' \ -e 's|available|available_new|' -e '/available_new/p' \ new_speed.out >> run.out # echo "cat run.out | sort -u" cat run.out | sort -u # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/check_doxygen.sh0000755000175200017650000000166113057470462016357 0ustar coincoin-web#! /bin/bash -e # $Id: check_doxygen.sh 3853 2016-12-14 14:40:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_doxygen.sh" ] then echo "bin/check_doxygen.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- if ! bin/run_doxygen.sh then echo 'check_doxygen.sh: Error' exit 1 fi echo 'check_doxygen.sh: OK' exit 0 cppad-20170000.3/bin/check_cmake.sh0000755000175200017650000000562413057470462015765 0ustar coincoin-web#! /bin/bash -e # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_makefile.sh" ] then echo "bin/check_makefile.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- echo "Checking debugging flags in all CMakeLists.txt files." echo "-------------------------------------------------------" list=`bin/ls_files.sh | sed -n -e '/CMakeLists.txt$/p'` ok="yes" for file in $list do case $file in # no build type cases CMakeLists.txt | \ cppad/CMakeLists.txt | \ cppad_ipopt/example/CMakeLists.txt | \ cppad_ipopt/speed/CMakeLists.txt | \ cppad_ipopt/src/CMakeLists.txt | \ cppad_ipopt/test/CMakeLists.txt | \ cppad_lib/CMakeLists.txt | \ introduction/CMakeLists.txt | \ multi_thread/bthread/CMakeLists.txt | \ multi_thread/openmp/CMakeLists.txt | \ multi_thread/pthread/CMakeLists.txt | \ pkgconfig/CMakeLists.txt | \ speed/adolc/CMakeLists.txt | \ speed/cppad/CMakeLists.txt | \ speed/double/CMakeLists.txt | \ speed/example/CMakeLists.txt | \ speed/fadbad/CMakeLists.txt | \ speed/profile/CMakeLists.txt | \ speed/sacado/CMakeLists.txt | \ speed/src/CMakeLists.txt ) check="CMAKE_BUILD_TYPE" if grep -i "$check" $file > /dev/null then echo "'$check' appears in $file" ok='no' fi ;; # release build type cases compare_c/CMakeLists.txt | \ cppad_ipopt/CMakeLists.txt | \ speed/CMakeLists.txt ) check="CMAKE_BUILD_TYPE RELEASE" if ! grep "$check" $file > /dev/null then echo "'$check' does not appear in $file" ok='no' fi ;; # debug build type cases example/CMakeLists.txt | \ example/atomic/CMakeLists.txt | \ example/ipopt_solve/CMakeLists.txt | \ example/optimize/CMakeLists.txt | \ introduction/exp_apx/CMakeLists.txt | \ introduction/get_started/CMakeLists.txt | \ multi_thread/CMakeLists.txt | \ print_for/CMakeLists.txt | \ test_more/CMakeLists.txt ) check="CMAKE_BUILD_TYPE DEBUG" if ! grep "$check" $file > /dev/null then echo "'$check' does not appear in $file" ok='no' fi ;; # unknown CMakeLists.txt file *) echo "$file is not known to check_cmake.sh" ok='no' ;; esac done echo "-------------------------------------------------------" if [ "$ok" = "yes" ] then echo "Ok: nothing is between the two dashed lines above" exit 0 else echo "Error: nothing should be between the two dashed lines above" exit 1 fi cppad-20170000.3/bin/replace_html.py0000755000175200017650000001107713057470462016224 0ustar coincoin-web#! /bin/python # $Id: replace_html.py 3214 2014-03-18 20:50:38Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-14 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- import sys import os import re # ----------------------------------------------------------------------------- if sys.argv[0] != 'bin/replace_html.py' : msg = 'bin/replace_html.py: must be executed from its parent directory' sys.exit(msg) # usage = '''\nusage: replace_html.py define_file replace_file new_file where define_file: contains the define commands replace_file: contains the replace commands (many be same as define_file) new_file: is a copy of replace file with the replacements. The definitions are specified by: source where name is any unique name, with no spaces ' ', for the replacement text and source is the replacement text. The replacement positions are specified by: desination where name refers to a defined replacement text and destination is the text that is replaced. ''' narg = len(sys.argv) if narg != 4 : msg = '\nExpected 3 but found ' + str(narg-1) + ' command line arguments.' sys.exit(usage + msg) define_file = sys.argv[1] replace_file = sys.argv[2] new_file = sys.argv[3] # ----------------------------------------------------------------------------- if not os.path.exists(define_file) : msg = 'bin/replace_html.py: cannot find define_file = ' + define_file sys.exit(msg) if not os.path.exists(replace_file) : msg = 'bin/replace_html.py: cannot find replace_file = ' + replace_file sys.exit(msg) if os.path.exists(new_file) : msg = 'bin/replace_html.py: cannot overwrite new_file ' + new_file sys.exit(msg) f_in = open(define_file, 'rb') define_data = f_in.read() f_in.close() f_in = open(replace_file, 'rb') replace_data = f_in.read() f_in.close() # ----------------------------------------------------------------------------- # create define: a dictionary with replacement text definitions define = {} p_define = re.compile('') p_end = re.compile('') start = 0 while start < len(define_data) : rest = define_data[start : ] next_define = p_define.search(rest) if next_define == None : start = len(define_data) else : name = next_define.group(1) if name in define : msg = 'bin/replace_html.py: file = ' + define_file msg += '\ncontains two defintions for name = ' + name sys.exit(msg) rest = rest[ next_define.end() : ] # next_end = p_end.search(rest) source = rest [ 0 : next_end.start() ] define[name] = source start += next_define.end() + next_end.end() if name != next_end.group(1) : msg = 'bin/replace_html.py: file = ' + define_file msg += '\ndefine name = ' + name msg += ', end name = ' + next_end.group(1) sys.exit(msg) # ----------------------------------------------------------------------------- # create new_data: a string with the replacements made new_data = '' p_replace = re.compile('') start = 0 while start < len(replace_data) : rest = replace_data[start : ] next_replace = p_replace.search(rest) if next_replace == None : new_data += rest start = len(replace_data) else : name = next_replace.group(1) if name not in define : msg = 'bin/replace_html.py: file = ' + define_file msg += '\ncontains no defintions for name = ' + name sys.exit(msg) new_data += rest[0 : next_replace.end() ] new_data += define[name] # rest = rest[ next_replace.end() : ] next_end = p_end.search(rest) new_data += rest[ next_end.start() : next_end.end() ] start += next_replace.end() + next_end.end() if name != next_end.group(1) : msg = 'bin/replace_html.py: file = ' + replace_file msg += '\nreplace name = ' + name msg += ', end name = ' + next_end.group(1) sys.exit(msg) # ----------------------------------------------------------------------------- f_out = open(new_file, 'wb') f_out.write(new_data) f_out.close() # ----------------------------------------------------------------------------- sys.exit(0) cppad-20170000.3/bin/check_svn_id.sh0000755000175200017650000000364213057470462016165 0ustar coincoin-web#! /bin/bash -e # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_svn_id.sh" ] then echo "bin/check_svn_id.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- list=`git status | sed -n \ -e '/^[#\t ]*deleted:/p' \ -e '/^[#\t ]*modified:/p' \ -e '/^[#\t ]*both modified:/p' \ -e '/^[#\t ]*renamed:/p' \ -e '/^[#\t ]*new file:/p' | \ sed -e 's/^.*: *//' -e 's/ -> /\n/' | \ sed -e '/^makefile.in$/d' \ -e '/^.gitignore$/d' \ -e '/\/makefile.in$/d' \ -e '/bin\/check_svn_id.sh$/d' \ -e '/AUTHORS/d' \ -e '/COPYING/d' | sort -u` ok="yes" for file in $list do if [ -e $file ] then sed $file -e '/$Id.*\$/d' > check_svn_id.$$ if ! diff $file check_svn_id.$$ > /dev/null then echo '----------------------------------------------------' echo "check_svn_id.sh: automatic changes to $file:" if diff $file check_svn_id.$$ then echo 'bin/check_svn_id.sh: program error' rm check_svn_id.$$ exit 1 fi ok='no' if [ -x $file ] then mv check_svn_id.$$ $file chmod +x $file else mv check_svn_id.$$ $file fi fi fi done if [ -e check_svn_id.$$ ] then rm check_svn_id.$$ fi if [ "$ok" == 'no' ] then exit 1 fi # ---------------------------------------------------------------------------- echo "$0: OK" exit 0 cppad-20170000.3/bin/get_adolc.sh0000755000175200017650000001111713057470462015463 0ustar coincoin-web#! /bin/bash -e # $Id: get_adolc.sh 3730 2015-09-23 15:56:53Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # $begin get_adolc.sh$$ $newlinech #$$ # $spell # tgz # Adolc # gz # CppAD # $$ # # $section Download and Install Adolc in Build Directory$$ # # $head Syntax$$ # $code bin/get_adolc.sh$$ # # $head Purpose$$ # If you are using Unix, this command will download and install # $href%https://projects.coin-or.org/ADOL-C%ADOL-C%$$ in the # CppAD $code build$$ directory. # # $head Requirements$$ # You must first use $cref get_colpack.sh$$ to download and install # $code ColPack$$ (coloring algorithms used for sparse matrix derivatives). # # $head Distribution Directory$$ # This command must be executed in the # $cref/distribution directory/download/Distribution Directory/$$. # # $head External Directory$$ # The Adolc source code is downloaded into the sub-directory # $code build/external$$ below the distribution directory. # # $head Prefix Directory$$ # The Adolc include files are installed in the sub-directory # $code build/prefix/include/adolc$$ below the distribution directory. # # $head Reuse$$ # The files $codei%build/external/ADOL-C-%version%.tgz%$$ # and the directory $codei%build/external/ADOL-C-%version%$$ # will be reused if they exist. Delete this file and directory # to get a complete rebuild. # # $end # ----------------------------------------------------------------------------- if [ $0 != "bin/get_adolc.sh" ] then echo "bin/get_adolc.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- echo 'Download adolc to build/external and install it to build/prefix' # ADOL-C verison 2.5.2 results in: # adouble.h:74: error: 'badouble::badouble()' is protected # It apprears that newer versions of adolc assume some c++11 features; see # http://list.coin-or.org/pipermail/adol-c/2014-December/001023.html version='2.4.1' web_page="http://www.coin-or.org/download/source/ADOL-C" cppad_dir=`pwd` prefix="$cppad_dir/build/prefix" installed_flag="build/external/adolc-${version}.installed" if [ -e "$installed_flag" ] then echo "$installed_flag exists: Skipping get_adolc.sh" exit 0 fi # -------------------------------------------------------------------------- if [ -e /usr/lib64 ] then libdir='lib64' else libdir='lib' fi # ----------------------------------------------------------------------------- if [ ! -d build/external ] then echo_eval mkdir -p build/external fi echo_eval cd build/external # ----------------------------------------------------------------------------- if [ ! -e "ADOL-C-$version.tgz" ] then echo_eval wget --no-check-certificate $web_page/ADOL-C-$version.tgz fi # ----------------------------------------------------------------------------- if [ -e "$prefix/include/adolc" ] then echo_eval rm -r "$prefix/include/adolc" fi # ----------------------------------------------------------------------------- if [ ! -e ADOL-C-$version ] then echo_eval tar -xzf ADOL-C-$version.tgz fi echo_eval cd ADOL-C-$version # ----------------------------------------------------------------------------- system=`uname | tr [A-Z] [a-z] | sed -e 's|\([a-z][a-z]*\).*|\1|'` # ----------------------------------------------------------------------------- if which autoconf >& /dev/null then echo_eval autoreconf --install --force fi # ----------------------------------------------------------------------------- if [ ! -e build ] then echo_eval mkdir build fi echo_eval cd build # ----------------------------------------------------------------------------- flags="--prefix=$prefix --with-colpack=$prefix --libdir=$prefix/$libdir" if [ "$system" == 'cygwin' ] then flags="$flags --enable-static --disable-shared" else flags="$flags --enable-static --enable-shared" fi # echo_eval ../configure $flags echo_eval make install # ----------------------------------------------------------------------------- echo_eval touch $cppad_dir/$installed_flag echo "get_adolc: OK" cppad-20170000.3/bin/check_addon.sh0000755000175200017650000000263413057470462015770 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ "$0" != 'bin/check_addon.sh' ] then echo "bin/check_addon: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- addon_list=' CG PY TMB MIXED ' grep_cmd='' for addon in $addon_list do if [ "$grep_cmd" == '' ] then grep_cmd="CPPAD_${addon}_" else grep_cmd="$grep_cmd|CPPAD_${addon}_" fi done # echo "Checking soruce code for names reserved for addon packages" echo "-------------------------------------------------------" ok="yes" file_list=`bin/ls_files.sh` for file in $file_list do if grep -E $grep_cmd $file > /dev/null then echo "$file containts $grep_cmd" ok="no" fi done echo "-------------------------------------------------------" if [ "$ok" = "no" ] then echo 'bin/check_if.sh: Error' exit 1 else echo 'bin/check_if.sh: OK' exit 0 fi cppad-20170000.3/bin/check_srcfile.sh0000755000175200017650000000444713057470462016336 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_srcfile.sh" ] then echo "bin/check_srcfile.sh: must be executed from its parent directory" exit 1 fi cat << EOF > junk.sed /\$srcfile[^a-z]/! b skip N s/^#[ \\t]// s/^[ \\t]// s/\\n#[ \\t]// s/\\n[ \\t]// s/\$srcfile%// s/%.*// p : skip EOF special_case=' bin/check_srcfile.sh bin/package.sh cppad/core/cond_exp.hpp introduction/exp_apx/exp_2.omh introduction/exp_apx/exp_eps.omh omh/license.omh bin/batch_edit.sh ' # ----------------------------------------------------------------------------- # Make sure that OMhelp srcfile commands refer to same file as command echo "Checking that OMhelp srcfile commands include from file they appear in." echo "----------------------------------------------------------------------" list=`bin/ls_files.sh` different="no" for file in $list do ok='no' for name in $special_case do if [ "$file" == "$name" ] then ok='yes' fi done # reference=`sed -n -f junk.sed $file` if [ "$reference" == '' ] || [ "$reference" == "$file" ] then ok='yes' fi # ext=`echo $file | sed -e 's|.*\.||'` if [ "$ext" == 'omh' ] then file_root=`echo $file | sed -e 's|.*/||' -e 's|_hpp\.omh|.hpp|'` ref_root=`echo $reference | sed -e 's|.*/||'` if [ "$file_root" == "$ref_root" ] then ok='yes' fi file_root=`echo $file | sed -e 's|.*/||' -e 's|\.omh|.hpp|'` if [ "$file_root" == "$ref_root" ] then ok='yes' fi fi # if [ "$ok" == 'no' ] then echo "\$srcfile in $file references $reference" different="yes" fi done echo "-------------------------------------------------------------------" if [ $different = "yes" ] then echo "Error: nothing should be between the two dashed lines above" exit 1 else echo "OK: nothing is between the two dashed lines above" exit 0 fi cppad-20170000.3/bin/test_one.sh.in0000755000175200017650000000741513057470462015775 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Run one of the tests if [ "$0" != 'bin/test_one.sh' ] then cat << EOF usage: bin/test_one.sh dir/file [extra] dir: example, example/atomic, example/ipopt_solve, or test_more file: name of *.cpp file, with extension, that contains the test extra: extra options for the g++ command EOF exit 1 fi dir=`echo $1 | sed -e 's|/[^/]*$||'` file=`echo $1 | sed -e 's|.*/||'` extra="$2" if [ "$dir" == 'test_more/local' ] then dir='test_more' file="local/$file" fi # --------------------------------------------------------------------------- if [ "$dir" == '' ] then echo "test_one.sh: cannot find dir in front of file" exit 1 fi if [ ! -e "$dir/$file" ] then echo "test_one.sh: Cannot find the file $dir/$file" exit 1 fi if [ -e test_one.exe ] then rm test_one.exe fi if [ -e test_one.cpp ] then rm test_one.cpp fi original_dir=`pwd` # --------------------------------------------------------------------------- # include_flags include_flags="-I $original_dir" if [ -e @adolc_prefix@/include ] then include_flags="$include_flags -I @adolc_prefix@/include" fi if [ -e @colpack_prefix@/include ] then include_flags="$include_flags -I @colpack_prefix@/include" fi if [ -e @ipopt_prefix@/include ] then include_flags="$include_flags -I @ipopt_prefix@/include" fi if [ -e @eigen_prefix@/include ] then include_flags="$include_flags -isystem @eigen_prefix@/include" fi # -------------------------------------------------------------------------- # determine the function name fun=`grep "^bool *[a-zA-Z0-9_]* *( *void *)" $dir/$file | tail -1 | \ sed -e "s/^bool *\([a-zA-Z0-9_]*\) *( *void *)/\1/"` # # determine the main program main main=`echo *$dir | sed -e 's|.*/||' -e 's|$|.cpp|'` # # create test_one.cpp sed < $dir/$main > test_one.cpp \ -e '/ok *\&= *Run( /d' \ -e "s/.*This line is used by test_one.sh.*/ ok \&= Run( $fun, \"$fun\");/" # # compiler flags cxx_flags='@cppad_cxx_flags@' # # library flags library_flags=`pkg-config --libs ipopt` library_flags="$library_flags @PROJECT_BINARY_DIR@/cppad_lib/libcppad_lib.so" library_flags="$library_flags -lboost_thread -lpthread" for lib in lib lib64 do if [ -e @colpack_prefix@/$lib ] then library_flags="$library_flags -L@colpack_prefix@/$lib -lColPack" export LD_LIBRARY_PATH="$LD_LIBRARY_PATH:@colpack_prefix@/$lib" fi if [ -e @adolc_prefix@/$lib ] then library_flags="$library_flags -L@adolc_prefix@/$lib -ladolc" export LD_LIBRARY_PATH="$LD_LIBRARY_PATH:@adolc_prefix@/$lib" fi done # # compile command compile_command="g++ test_one.cpp -o test_one.exe $dir/$file $extra -g $cxx_flags $include_flags $library_flags " echo "$compile_command" $compile_command # -------------------------------------------------------------------------- new_library_path='@PROJECT_BINARY_DIR@/cppad_lib' has_library_path='yes' if ! echo $LD_LIBRARY_PATH | grep "$new_library_path" then has_library_path='no' export LD_LIBRARY_PATH="$new_library_path:$LD_LIBRARY_PATH" fi # -------------------------------------------------------------------------- # echo "./test_one.exe" if ! ./test_one.exe then if [ "$has_library_path" == 'no' ] then echo 'Must execute the following command before running in debugger' echo "export LD_LIBRARY_PATH=\"$new_library_path:\$LD_LIBRARY_PATH\"" fi exit 1 fi exit 0 cppad-20170000.3/bin/version.sh0000755000175200017650000000734713057470462015241 0ustar coincoin-web#! /bin/bash -e # $Id: version.sh 3788 2016-02-09 15:50:06Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != 'bin/version.sh' ] then echo 'bin/version.sh: must be executed from its parent directory' exit 1 fi if [ "$1" != 'get' ] && [ "$1" != 'set' ] && [ "$1" != 'check' ] then echo 'usage: bin/version.sh (get | set | check) [version]' echo 'get: Gets the current version number from CMakeLists.txt.' echo 'set: Sets CMakeLists.txt version number to version.' echo ' If version is not present, uses current yyyymmdd.' echo 'check: Checks that the version version number in CMakeLists.txt' echo ' is the same as in other files. If not, changes the other' echo ' files and exits with an error message' exit 1 fi echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- if [ "$1" == 'set' ] then if [ "$2" == '' ] then version=`date +%Y%m%d` else version="$2" fi echo 'sed -i.old CMakeLists.txt ...' sed \ -e "s/(\(cppad_version *\)\"[0-9.]\{8\}[0-9.]*\" *)/(\1\"$version\" )/" \ -i.old CMakeLists.txt if diff CMakeLists.txt.old CMakeLists.txt then echo 'No change in CMakeLists.txt' fi echo_eval rm CMakeLists.txt.old # echo 'version.sh set: OK' exit 0 fi # ----------------------------------------------------------------------------- # get the current version number version=`grep '^SET *( *cppad_version ' CMakeLists.txt | \ sed -e 's|^SET *( *cppad_version *"\([0-9.]\{8\}[0-9.]*\)" *)|\1|'` if ! (echo $version | grep '[0-9]\{8\}') > /dev/null then echo 'version.sh: Cannot find verison number in CMakeLists.txt' exit 1 fi if [ "$1" == 'get' ] then echo "$version" exit 0 fi # ----------------------------------------------------------------------------- # Make the version number in the relevant files is the same yyyy_mm_dd=`echo $version | sed \ -e 's|\([0-9]\{4\}\)0000|\10101|' \ -e 's|\(....\)\(..\)\(..\).*|\1-\2-\3|'` sed \ -e "s/, [0-9]\{4\}-[0-9]\{2\}-[0-9]\{2\} *,/, $yyyy_mm_dd,/" \ -i.old AUTHORS # sed \ -e "s/(\[cppad\], *\[[0-9]\{8\}[.0-9]*\] *,/([cppad], [$version],/" \ -i.old configure.ac # sed \ -e "s/cppad [0-9]\{8\}[.0-9]*/cppad $version/g" \ -e "s/VERSION='[0-9]\{8\}[.0-9]*'/VERSION='$version'/g" \ -e "s/configure [0-9]\{8\}[.0-9]*/configure $version/g" \ -e "s/config.status [0-9]\{8\}[.0-9]*/config.status $version/g" \ -e "s/\$as_me [0-9]\{8\}[.0-9]*/\$as_me $version/g" \ -e "s/Generated by GNU Autoconf.*$version/&./" \ -i.old configure list=' omh/install/auto_tools.omh omh/install/download.omh doc.omh ' for file in $list do sed -e "s/cppad-[0-9]\{8\}\(\.[eg]pl\)/cppad-$version\1/" \ -e "s/cppad-[0-9]\{8\}\.[0-9]*\(\.[eg]pl\)/cppad-$version\1/" \ -e "s/cppad-[0-9]\{8\}[0-9.]*\:/cppad-$version:/" \ -i.old $file done list=" $list AUTHORS configure.ac configure " ok='yes' for name in $list do if ! diff $name.old $name > /dev/null then echo '-------------------------------------------------------------' echo "diff $name.old $name" if diff $name.old $name then echo 'version.sh check: program error' exit 1 fi ok='no' fi rm $name.old done if [ "$ok" != 'yes' ] then echo 'version.sh check: Found and fixed differences' exit 1 fi echo 'version.sh check: OK' exit 0 cppad-20170000.3/bin/check_svn_dist.sh0000755000175200017650000000430613057470462016532 0ustar coincoin-web#! /bin/bash -e # $Id: check_svn_dist.sh 2506 2012-10-24 19:36:49Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-11 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e "bin/check_svn_dist.sh" ] then echo "bin/check_svn_dist.sh: must be executed from its parent directory" exit 1 fi # ----------------------------------------------------------------------------- log_dir=`pwd` script="bin/check_svn_dist.sh" repository="https://projects.coin-or.org/svn/CppAD" branch=`pwd | sed -e 's|.*/CppAD/||' -e 's|.*/cppad/||'` if [ -e "svn_dist" ] then echo "rm -rf svn_dist" rm -rf svn_dist fi # ---------------------------------------------------------------------------- echo "svn checkout $repository/$branch svn_dist" svn checkout $repository/$branch svn_dist # ---------------------------------------------------------------------------- # Things to do in the svn_dist directory # ---------------------------------------------------------------------- echo "cd svn_dist" cd svn_dist # echo "./build.sh configure" if ! ./build.sh configure then echo "$script: error durring ./build.sh configure in ./svn_dist" exit 1 fi # # ---------------------------------------------------------------------- # Things to do in the svn_dist/work directory # ---------------------------------------------------------------------- echo "cd work" cd work # echo "$script: make test >& svn_dist.log" echo "The following will give details of progress of command above" echo " tail -f svn_dist.log" make test >& $log_dir/svn_dist.log # if grep 'warning:' $log_dir/svn_dist.log then echo "$script: Stopping because there are warnings in svn_dist.log" exit 1 fi # echo "cat test.log >> svn_dist.log" cat test.log >> $log_dir/svn_dist.log # echo "OK: $script, results are in svn_dist.log" cppad-20170000.3/bin/proj_desc.py0000755000175200017650000001510113057470462015525 0ustar coincoin-web#! /bin/python3 # $Id # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # dictionary of replacements # import collections replace_dict = collections.OrderedDict() replace_dict['projectName'] = 'CppAD' replace_dict['projectRepo'] = 'CppAD' # replace_dict['projectDescription'] = ''' Given a C++ algorithm that computes function values, CppAD generates an algorithm that computes corresponding derivative values. ''' # replace_dict['projectShortDescription'] =''' A tool for differentiation of C++ functions. ''' # replace_dict['projectManager'] ='Brad Bell, http://www.seanet.com/~bradbell' replace_dict['projectHomePage'] = 'http://www.coin-or.org/CppAD' # replace_dict['projectLicense'] = ''' Eclipse Public License 1.0, or GNU General Public License 3.0 ''' replace_dict['projectLicenseURL'] = ''' http://www.opensource.org/licenses/alphabetica ''' replace_dict['coinLinkedProjects'] = '' replace_dict['projectLanguage'] = 'C++' replace_dict['activityStatus'] = 'Active' replace_dict['maturityLevel'] = '4' replace_dict['stableVersionNumber'] = '20150000' replace_dict['releaseNumber'] = '20150000.8' replace_dict['projectCategories'] = 'Optimization utility' replace_dict['documentation'] = 'http://www.coin-or.org/CppAD/Doc' replace_dict['sourceCodeDownload'] = ''' http://www.coin-or.org/download/source/CppAD ''' replace_dict['mailingList'] = ''' http://list.coin-or.org/mailman/listinfo/cppad ''' # ---------------------------------------------------------------------------- # # other_package = collections.OrderedDict( [ ('ADOL-C', 'http://www.coin-or.org/projects/ADOL-C.xml'), ('Boost uBlas vector', 'http://www.boost.org/doc/libs'), ('Boost Thread', 'http://www.boost.org/doc/libs'), ('ColPack', 'http://cscapes.cs.purdue.edu/dox/ColPack/html'), ('Eigen', 'http://eigen.tuxfamily.org'), ('FADBAD', 'http://www.fadbad.com/fadbad.htm'), ('Ipopt', 'http://www.coin-or.org/projects/Ipopt.xml'), ('OpenMP', 'http://openmp.org/wp'), ('Pthread', 'http,//pubs.opengroup.org/onlinepubs/009695399/basedefs/pthread.h.html'), ('Sacado', 'http://trilinos.org/packages/sacado') ] ) text='\n' for name in other_package : url = other_package[name] text += ' \n' text += ' ' + name + '\n' text += ' ' + url + '\n' text += ' Optional\n' text += ' \n' replace_dict['otherLinkedPackages'] = text # ----------------------------------------------------------------------------- # tested_platform = collections.OrderedDict( [ ('Linux', 'gcc'), ('Cygwin', 'gcc'), ('Microsoft Windows', 'MSVC++') ] ) text='\n' for system in tested_platform : compiler = tested_platform[system] text += ' \n' text += ' ' + system + '\n' text += ' ' + compiler + '\n' text += ' \n' replace_dict['testedPlatforms'] = text # ----------------------------------------------------------------------------- import sys import re import os import subprocess # ----------------------------------------------------------------------------- # command line arguments usage = '\tbin/proj_desc.py\n' narg = len(sys.argv) if sys.argv[0] != 'bin/proj_desc.py' : msg = 'bin/proj_desc.py must be executed from its parent directory' sys.exit(usage + msg) if narg != 1 : msg = 'expected 0 but found ' + str(narg-1) + ' command line arguments' sys.exit(usage + msg) # ----------------------------------------------------------------------------- def system_cmd(cmd) : try : output = subprocess.check_output( cmd, stderr=subprocess.STDOUT, shell=True ) except subprocess.CalledProcessError as info : msg = str( info.output , 'ascii' ) msg += '\nbin/proj_desc.py exiting because command above failed' sys.exit(msg) return str( output, 'ascii' ) # ----------------------------------------------------------------------------- # update cppad_conf_dir # cppad_conf_dir = os.environ['HOME'] + '/cppad.svn/conf' if os.path.exists(cppad_conf_dir ) : cmd = 'svn update ' + cppad_conf_dir print( cmd ) else : cmd = 'svn checkout https://projects.coin-or.org/svn/CppAD/conf ' cmd += cppad_conf_dir print( cmd ) # ----------------------------------------------------------------------------- # get the current verison of the file # file_name = cppad_conf_dir + '/projDesc.xml' file_ptr = open(file_name, 'r') file_data = file_ptr.read() file_ptr.close() # ----------------------------------------------------------------------------- # Do the replacemnets # # fix stableVersionNumber and releaseNumber (remove enclosing comment block) pattern = '' replace = '' file_data = re.sub(pattern, replace, file_data) # for key in replace_dict : value = replace_dict[key] start = '<' + key + '>' end = '' pattern = '[ \t]*' + start + '[a-zA-Z\s]*' + end replace = start + value + end file_data = re.sub(pattern, replace, file_data) # # projectCategories is a special case key = 'projectCategories' value = replace_dict[key] start = '<' + key + '>' end = '' pattern = '[ \t]*' + start + '[ \t]*' file_data = re.sub(pattern, replace, file_data) # pattern = '[ \t]*' + end + '[ \t]*' replace = start + '\n \n ' replace += value + '\n \n' + end file_data = re.sub(pattern, replace, file_data) # ----------------------------------------------------------------------------- # replace input file file_name = cppad_conf_dir + '/projDesc.xml' file_ptr = open(file_name, 'w') file_ptr.write(file_data) file_ptr.close() # ----------------------------------------------------------------------------- msg = 'check results in\n\t' + file_name + '\nand then execute' msg += '\n\tsvn commit -m "see bin/proj_desc.py" \\\n\t' + file_name print(msg) cppad-20170000.3/bin/check_user_def.sh0000755000175200017650000000414313057470462016474 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ $0 != "bin/check_user_def.sh" ] then echo "bin/check_user_def.sh: must be executed from its parent directory" exit 1 fi # --------------------------------------------------------------------------- echo 'Check user API preprocessor define symbols' echo '-----------------------------------------------------------------------' file_list=`bin/search.sh 'head CPPAD' | sed -e '/bin\/check_user_def.sh/d'` symbol_list='' for file in $file_list do symbol=`sed -n -e '/$head CPPAD/p' -e '/$subhead CPPAD/p' $file | sed \ -e 's/^.*head \(CPPAD[a-zA-Z0-9_]*\).*/\1/'` symbol_list="$symbol_list $symbol:$file" done for symbol_file in $symbol_list do symbol=`echo $symbol_file | sed -e 's|:.*||'` file=`echo $symbol_file | sed -e 's|.*:||'` if ! grep $symbol omh/preprocessor.omh > /dev/null then echo "The symbol $symbol" echo "appears in $file omhelp documentation" echo 'but does not appear in omh/preprocessor.omh' exit 1 fi done for symbol_file in $symbol_list do symbol=`echo $symbol_file | sed -e 's|:.*||'` file=`echo $symbol_file | sed -e 's|.*:||'` ok='false' if grep "$symbol *in user api" cppad/core/undef.hpp > /dev/null then ok='true' fi if grep "$symbol *in deprecated api" cppad/core/undef.hpp > /dev/null then ok='true' fi if [ "$ok" == 'false' ] then echo "The symbol $symbol" echo "appears in $file omhelp documentation" echo "but is not listed as in user api in cppad/core/undef.hpp" exit 1 fi done echo '-----------------------------------------------------------------------' echo "check_user_def.sh: OK" cppad-20170000.3/makefile.am0000644000175200017650000002764313057470467014547 0ustar coincoin-web# ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # BUILT_SOURCES = $(top_srcdir)/cppad/configure.hpp $(top_srcdir)/cppad/configure.hpp: cppad/configure.hpp cp cppad/configure.hpp $(top_srcdir)/cppad/configure.hpp # if CppAD_POSTFIX postfix_dir = $(POSTFIX_DIR) else postfix_dir = . endif # # Did user specify a value for ADOLC_DIR in configure command line if CppAD_ADOLC SPEED_ADOLC_TESTS = speed/adolc else SPEED_ADOLC_TESTS = endif # # Did user specify a value for FADBAD_DIR in configure command line if CppAD_FADBAD SPEED_FADBAD_TESTS = speed/fadbad else SPEED_FADBAD_TESTS = endif # # Did user specify a value for SACADO_DIR in configure command line if CppAD_SACADO SPEED_SACADO_TESTS = speed/sacado else SPEED_SACADO_TESTS = endif # # Did user specify a value for IPOPT_DIR in configure command line if CppAD_IPOPT IPOPT_TESTS = \ example/ipopt_solve \ cppad_ipopt/example \ cppad_ipopt/speed \ cppad_ipopt/test # IPOPT_DIRS = \ cppad_ipopt/src \ $(IPOPT_TESTS) # IPOPT_HEADER = \ cppad_ipopt/src/cppad_ipopt_nlp.hpp else IPOPT_TESTS = IPOPT_DIRS = IPOPT_HEADER = endif # # Is the library archiving program present if CppAD_HAVE_AR SPEED_TESTS = \ $(SPEED_ADOLC_TESTS) \ speed/cppad \ speed/double \ speed/example \ $(SPEED_FADBAD_TESTS) \ speed/profile \ $(SPEED_SACADO_TESTS) # SPEED_DIRS = \ speed/src \ $(SPEED_TESTS) else SPEED_TESTS = SPEED_DIRS = endif # --------------------------------------------------------------------------- myincludedir = $(includedir)/$(postfix_dir) # myinclude_HEADERS = \ $(IPOPT_HEADER) # nobase_myinclude_HEADERS = \ cppad/base_require.hpp \ cppad/configure.hpp \ cppad/core/abort_recording.hpp \ cppad/core/abs.hpp \ cppad/core/acosh.hpp \ cppad/core/ad_assign.hpp \ cppad/core/ad_binary.hpp \ cppad/core/ad_ctor.hpp \ cppad/core/add_eq.hpp \ cppad/core/add.hpp \ cppad/core/ad_fun.hpp \ cppad/core/ad.hpp \ cppad/core/ad_io.hpp \ cppad/core/ad_to_string.hpp \ cppad/core/ad_valued.hpp \ cppad/core/arithmetic.hpp \ cppad/core/asinh.hpp \ cppad/core/atan2.hpp \ cppad/core/atanh.hpp \ cppad/core/atomic_base.hpp \ cppad/core/azmul.hpp \ cppad/core/base_complex.hpp \ cppad/core/base_cond_exp.hpp \ cppad/core/base_double.hpp \ cppad/core/base_float.hpp \ cppad/core/base_hash.hpp \ cppad/core/base_limits.hpp \ cppad/core/base_std_math.hpp \ cppad/core/base_to_string.hpp \ cppad/core/bender_quad.hpp \ cppad/core/bool_fun.hpp \ cppad/core/bool_valued.hpp \ cppad/core/capacity_order.hpp \ cppad/core/check_for_nan.hpp \ cppad/core/checkpoint.hpp \ cppad/core/compare.hpp \ cppad/core/compute_assign.hpp \ cppad/core/cond_exp.hpp \ cppad/core/convert.hpp \ cppad/core/cppad_assert.hpp \ cppad/core/define.hpp \ cppad/core/dependent.hpp \ cppad/core/discrete.hpp \ cppad/core/div_eq.hpp \ cppad/core/div.hpp \ cppad/core/drivers.hpp \ cppad/core/epsilon.hpp \ cppad/core/equal_op_seq.hpp \ cppad/core/erf.hpp \ cppad/core/expm1.hpp \ cppad/core/for_one.hpp \ cppad/core/for_sparse_hes.hpp \ cppad/core/for_sparse_jac.hpp \ cppad/core/for_two.hpp \ cppad/core/forward.hpp \ cppad/core/fun_check.hpp \ cppad/core/fun_construct.hpp \ cppad/core/fun_eval.hpp \ cppad/core/hash_code.hpp \ cppad/core/hessian.hpp \ cppad/core/identical.hpp \ cppad/core/independent.hpp \ cppad/core/integer.hpp \ cppad/core/jacobian.hpp \ cppad/core/log1p.hpp \ cppad/core/lu_ratio.hpp \ cppad/core/mul_eq.hpp \ cppad/core/mul.hpp \ cppad/core/near_equal_ext.hpp \ cppad/core/numeric_limits.hpp \ cppad/core/num_skip.hpp \ cppad/core/old_atomic.hpp \ cppad/core/omp_max_thread.hpp \ cppad/core/optimize.hpp \ cppad/core/opt_val_hes.hpp \ cppad/core/ordered.hpp \ cppad/core/parallel_ad.hpp \ cppad/core/par_var.hpp \ cppad/core/pow.hpp \ cppad/core/print_for.hpp \ cppad/core/reverse.hpp \ cppad/core/rev_one.hpp \ cppad/core/rev_sparse_hes.hpp \ cppad/core/rev_sparse_jac.hpp \ cppad/core/rev_two.hpp \ cppad/core/sign.hpp \ cppad/core/sparse_hessian.hpp \ cppad/core/sparse.hpp \ cppad/core/sparse_jacobian.hpp \ cppad/core/standard_math.hpp \ cppad/core/std_math_98.hpp \ cppad/core/sub_eq.hpp \ cppad/core/sub.hpp \ cppad/core/tape_link.hpp \ cppad/core/test_vector.hpp \ cppad/core/testvector.hpp \ cppad/core/unary_minus.hpp \ cppad/core/unary_plus.hpp \ cppad/core/undef.hpp \ cppad/core/user_ad.hpp \ cppad/core/value.hpp \ cppad/core/var2par.hpp \ cppad/core/vec_ad.hpp \ cppad/core/zdouble.hpp \ cppad/cppad.hpp \ cppad/example/base_adolc.hpp \ cppad/example/cppad_eigen.hpp \ cppad/example/eigen_cholesky.hpp \ cppad/example/eigen_mat_inv.hpp \ cppad/example/eigen_mat_mul.hpp \ cppad/example/eigen_plugin.hpp \ cppad/example/mat_mul.hpp \ cppad/ipopt/solve_callback.hpp \ cppad/ipopt/solve.hpp \ cppad/ipopt/solve_result.hpp \ cppad/local/abs_op.hpp \ cppad/local/acosh_op.hpp \ cppad/local/acos_op.hpp \ cppad/local/add_op.hpp \ cppad/local/ad_tape.hpp \ cppad/local/asinh_op.hpp \ cppad/local/asin_op.hpp \ cppad/local/atanh_op.hpp \ cppad/local/atan_op.hpp \ cppad/local/color_general.hpp \ cppad/local/color_symmetric.hpp \ cppad/local/comp_op.hpp \ cppad/local/cond_op.hpp \ cppad/local/cosh_op.hpp \ cppad/local/cos_op.hpp \ cppad/local/cppad_colpack.hpp \ cppad/local/cskip_op.hpp \ cppad/local/csum_op.hpp \ cppad/local/declare_ad.hpp \ cppad/local/discrete_op.hpp \ cppad/local/div_op.hpp \ cppad/local/erf_op.hpp \ cppad/local/expm1_op.hpp \ cppad/local/exp_op.hpp \ cppad/local/for_hes_sweep.hpp \ cppad/local/for_jac_sweep.hpp \ cppad/local/forward0sweep.hpp \ cppad/local/forward1sweep.hpp \ cppad/local/forward2sweep.hpp \ cppad/local/hash_code.hpp \ cppad/local/independent.hpp \ cppad/local/load_op.hpp \ cppad/local/log1p_op.hpp \ cppad/local/log_op.hpp \ cppad/local/mul_op.hpp \ cppad/local/op_code.hpp \ cppad/local/op.hpp \ cppad/local/optimize/match_op.hpp \ cppad/local/optimize/cexp_info.hpp \ cppad/local/optimize/csum_stacks.hpp \ cppad/local/optimize/csum_variable.hpp \ cppad/local/optimize/get_op_info.hpp \ cppad/local/optimize/hash_code.hpp \ cppad/local/optimize/old2new.hpp \ cppad/local/optimize/op_info.hpp \ cppad/local/optimize/optimize_run.hpp \ cppad/local/optimize/record_csum.hpp \ cppad/local/optimize/record_pv.hpp \ cppad/local/optimize/record_vp.hpp \ cppad/local/optimize/record_vv.hpp \ cppad/local/optimize/size_pair.hpp \ cppad/local/optimize/usage.hpp \ cppad/local/parameter_op.hpp \ cppad/local/player.hpp \ cppad/local/pod_vector.hpp \ cppad/local/pow_op.hpp \ cppad/local/print_op.hpp \ cppad/local/prototype_op.hpp \ cppad/local/recorder.hpp \ cppad/local/reverse_sweep.hpp \ cppad/local/rev_hes_sweep.hpp \ cppad/local/rev_jac_sweep.hpp \ cppad/local/set_get_in_parallel.hpp \ cppad/local/sign_op.hpp \ cppad/local/sinh_op.hpp \ cppad/local/sin_op.hpp \ cppad/local/sparse_binary_op.hpp \ cppad/local/sparse_list.hpp \ cppad/local/sparse_pack.hpp \ cppad/local/sparse_pattern.hpp \ cppad/local/sparse_unary_op.hpp \ cppad/local/sqrt_op.hpp \ cppad/local/std_set.hpp \ cppad/local/store_op.hpp \ cppad/local/sub_op.hpp \ cppad/local/tanh_op.hpp \ cppad/local/tan_op.hpp \ cppad/local/user_state.hpp \ cppad/local/zmul_op.hpp \ cppad/speed/det_33.hpp \ cppad/speed/det_by_lu.hpp \ cppad/speed/det_by_minor.hpp \ cppad/speed/det_grad_33.hpp \ cppad/speed/det_of_minor.hpp \ cppad/speed/mat_sum_sq.hpp \ cppad/speed/ode_evaluate.hpp \ cppad/speed/sparse_hes_fun.hpp \ cppad/speed/sparse_jac_fun.hpp \ cppad/speed/uniform_01.hpp \ cppad/utility/check_numeric_type.hpp \ cppad/utility/check_simple_vector.hpp \ cppad/utility/elapsed_seconds.hpp \ cppad/utility/error_handler.hpp \ cppad/utility.hpp \ cppad/utility/index_sort.hpp \ cppad/utility/lu_factor.hpp \ cppad/utility/lu_invert.hpp \ cppad/utility/lu_solve.hpp \ cppad/utility/memory_leak.hpp \ cppad/utility/nan.hpp \ cppad/utility/near_equal.hpp \ cppad/utility/ode_err_control.hpp \ cppad/utility/ode_gear_control.hpp \ cppad/utility/ode_gear.hpp \ cppad/utility/omp_alloc.hpp \ cppad/utility/poly.hpp \ cppad/utility/pow_int.hpp \ cppad/utility/romberg_mul.hpp \ cppad/utility/romberg_one.hpp \ cppad/utility/rosen_34.hpp \ cppad/utility/runge_45.hpp \ cppad/utility/set_union.hpp \ cppad/utility/speed_test.hpp \ cppad/utility/thread_alloc.hpp \ cppad/utility/time_test.hpp \ cppad/utility/to_string.hpp \ cppad/utility/track_new_del.hpp \ cppad/utility/vector.hpp # End nobase_myinclude_HEADERS (check_makefile.sh uses this comment) # --------------------------------------------------------------- # # No objects or executables are required to install CppAD. # See 'make test' below for building the tests. SUBDIRS = \ $(IPOPT_DIRS) \ $(SPEED_DIRS) \ example \ example/atomic \ example/optimize \ compare_c \ introduction/get_started \ introduction/exp_apx \ print_for \ multi_thread \ multi_thread/test_multi \ test_more # # note that bin/gpl_license.sh is deleted by dist-hook EXTRA_DIST = \ bin \ build.sh \ doc.omh \ doc \ gpl-3.0.txt \ epl-v10.html \ omh \ uw_copy_040507.html \ \ compare_c/CMakeLists.txt \ cppad/CMakeLists.txt \ pkgconfig/CMakeLists.txt \ example/CMakeLists.txt \ example/atomic/CMakeLists.txt \ example/ipopt_solve/CMakeLists.txt \ example/optimize/CMakeLists.txt \ test_more/CMakeLists.txt \ CMakeLists.txt \ cppad_ipopt/src/CMakeLists.txt \ cppad_ipopt/example/CMakeLists.txt \ cppad_ipopt/test/CMakeLists.txt \ cppad_ipopt/CMakeLists.txt \ cppad_ipopt/speed/CMakeLists.txt \ speed/main.cpp \ speed/cppad/CMakeLists.txt \ speed/adolc/CMakeLists.txt \ speed/fadbad/CMakeLists.txt \ speed/src/CMakeLists.txt \ speed/example/CMakeLists.txt \ speed/CMakeLists.txt \ speed/double/CMakeLists.txt \ speed/profile/CMakeLists.txt \ speed/sacado/CMakeLists.txt \ multi_thread/bthread/CMakeLists.txt \ multi_thread/CMakeLists.txt \ multi_thread/openmp/CMakeLists.txt \ multi_thread/pthread/CMakeLists.txt \ print_for/CMakeLists.txt test_directory_list = \ $(IPOPT_TESTS) \ $(SPEED_TESTS) \ example \ example/atomic \ example/optimize \ compare_c \ introduction/get_started \ introduction/exp_apx \ multi_thread \ multi_thread/test_multi \ print_for \ test_more test: all rm -f test.log touch test.log echo "#! /bin/sh -e" > test.sh for dir in $(test_directory_list) ; do ( \ echo "#" >> test.sh ; \ echo "echo \"Running make test in $$dir\"" >> test.sh ; \ echo "cd $$dir " >> test.sh ; \ echo "make test" >> test.sh ; \ echo "cd $(ABS_TOP_BUILDDIR)" >> test.sh ; \ ) done echo "exit 0" >> test.sh chmod +x test.sh ./test.sh # dist-hook: rm -rf `find . -name .svn` rm $(distdir)/doc/error.wrd rm $(distdir)/bin/gpl_license.sh # doc_postfix = $(DESTDIR)$(datadir)/doc/$(postfix_dir) doc_package = $(DESTDIR)$(datadir)/doc/$(postfix_dir)/$(PACKAGE)-$(VERSION) inc_postfix = $(DESTDIR)/$(myincludedir) install-data-hook: if CppAD_DOCUMENTATION if [ ! -e $(doc_postfix) ] ; then mkdir -p $(doc_postfix) ; fi if [ -e $(doc_package) ] ; then rm -rf $(doc_package) ; fi cp -a $(top_srcdir)/doc $(doc_package) chmod -R a-w $(doc_package) chmod -R u+w $(doc_package) chmod -R a+r $(doc_package) endif if CppAD_DEPRECATED cp -a $(top_srcdir)/cppad/deprecated/* $(inc_postfix)/cppad chmod -R a-w $(inc_postfix)/cppad chmod -R u+w $(inc_postfix)/cppad chmod -R a+r $(inc_postfix)/cppad endif # pkgconfigdir = $(datadir)/pkgconfig pkgconfig_DATA = pkgconfig/cppad.pc cppad-20170000.3/NEWS0000644000175200017650000000033012450414402013111 0ustar coincoin-webThe HTML and XML summary of recent changes for the version of CppAD corresponding to the current date are in the files: http://www.coin-or.org/CppAD/Doc/whats_new.htm http://www.coin-or.org/CppAD/Doc/whats_new.xml cppad-20170000.3/CMakeLists.txt0000644000175200017650000003041713057470462015177 0ustar coincoin-web# ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # ============================================================================= # Some constants # ============================================================================= # Set the minimum required version of cmake for this project. # see http://www.cmake.org/pipermail/cmake/2013-January/053213.html CMAKE_MINIMUM_REQUIRED(VERSION 2.8) # cppad_version is used by set_version.sh to get the version number. SET(cppad_version "20170000.3" ) SET(cppad_url "http://www.coin-or.org/CppAD" ) SET(cppad_description "Differentiation of C++ Algorithms" ) # Set name of this project and create the variables # cppad_BINARY_DIR and cppad_SOURCE_DIR. # project(projectname [CXX] [C] [Java]) PROJECT(cppad) # Add this directory to the list of C++ preprocessor include directories # for the entire project. # include_directories([AFTER|BEFORE] [SYSTEM] dir1 dir2 ...) INCLUDE_DIRECTORIES( ${cppad_SOURCE_DIR} ) # ============================================================================= # Some system cmake language extensions # ============================================================================= # CHECK_CXX_SOURCE_COMPILES(source variable) # Checks whether the code given in source will compile, link and run and # return zero status. You can set # CMAKE_REQUIRED_LIBRARIES, CMAKE_REQUIRED_FLAGS and CMAKE_REQUIRED_INCLUDES # accordingly if additional libraries or compiler flags are required. INCLUDE(CheckCXXSourceRuns) # ============================================================================ # Some local cmake language # ============================================================================ # dos_path_to_unix(dos_path unix_path) INCLUDE(cmake/dos_path_to_unix.cmake) # # add_to_list(variable_list constant_value) INCLUDE(cmake/add_to_list.cmake) # # command_line_arg(variable default type description) INCLUDE(cmake/command_line_arg.cmake) # # optional_package(prefix_variable description) INCLUDE(cmake/optional_package.cmake) # # add_cppad_cxx_flags(target_name) INCLUDE(cmake/add_cppad_cxx_flags.cmake) # # sources_libs_define(prefix_name sources libs define) INCLUDE(cmake/sources_libs_define.cmake) # # check_source_runs(source variable) INCLUDE(cmake/check_source_runs.cmake) # # assert(variable) INCLUDE(cmake/assert.cmake) # # print_variable(variable) INCLUDE(cmake/print_variable.cmake) # ============================================================================= # command line arguments # ============================================================================= # cmake_install_datadir command_line_arg(cmake_install_datadir share STRING "directory, below prefix, where cmake installs cppad data files" ) # ----------------------------------------------------------------------------- # cmake_install_docdir command_line_arg(cmake_install_docdir NOTFOUND STRING "directory, below prefix, where cmake installs cppad documentation files" ) # ----------------------------------------------------------------------------- # cmake_install_includedirs command_line_arg(cmake_install_includedirs include STRING "directories, below prefix, where cmake installs include files" ) # ----------------------------------------------------------------------------- # cmake_install_libdirs command_line_arg(cmake_install_libdirs lib STRING "directories, below prefix, where cmake installs library files" ) # ----------------------------------------------------------------------------- # cppad_prefix command_line_arg(cppad_prefix /usr PATH "cppad install prefix" ) SET(CMAKE_INSTALL_PREFIX "${cppad_prefix}" CACHE PATH "value copied from cppad_prefix" FORCE ) IF( cmake_install_prefix ) MESSAGE(FATAL_ERROR "cmake_install_prefix has been changed to cppad_prefix" ) ENDIF( cmake_install_prefix ) # ----------------------------------------------------------------------------- # cppad_postfix command_line_arg(cppad_postfix NOTFOUND STRING "cppad install postfix" ) IF( cmake_install_postfix ) MESSAGE(FATAL_ERROR "cmake_install_postfix has been changed to cppad_postfix" ) ENDIF( cmake_install_postfix ) # ----------------------------------------------------------------------------- # cppad_cxx_flags command_line_arg(cppad_cxx_flags NOTFOUND STRING "compile flags used with cppad (besides debug, release, and profile flags)" ) # ----------------------------------------------------------------------------- # cppad_profile_flag command_line_arg(cppad_profile_flag NOTFOUND STRING "compile flag used to compile and link a profile version of a program" ) # ----------------------------------------------------------------------------- # External package prefixes with warnings SET(system_include FALSE) # # adolc_prefix optional_package(adolc_prefix ${system_include} "adolc install prefix") # # colpack_prefix optional_package(colpack_prefix ${system_include} "colpack install prefix") # # ipopt_prefix optional_package(ipopt_prefix ${system_include} "ipopt install prefix") # # sacado_prefix optional_package(sacado_prefix ${system_include} "sacado install prefix") # ----------------------------------------------------------------------------- # External package prefixes without warnings SET(system_include TRUE) # # eigen_prefix optional_package(eigen_prefix ${system_include} "eigen install prefix") # # fadbad_prefix optional_package(fadbad_prefix ${system_include} "fadbad install prefix") # ----------------------------------------------------------------------------- # cppad_has_colpack, colpack_libs, cppad_lib # IF( colpack_prefix ) SET(cppad_has_colpack 1) SET( colpack_libs "ColPack" ) SET( cppad_lib "cppad_lib" ) ELSE( colpack_prefix ) SET(cppad_has_colpack 0) SET( colpack_libs "" ) SET( cppad_lib "" ) ENDIF( colpack_prefix ) # ============================================================================= # automated system configuration # ============================================================================= # CMAKE_CXX_FLAGS # remove Visual Studio C++ warning level if specified in cppad_cxx_flags IF ( cppad_cxx_flags MATCHES "/W[0-9]" ) STRING( REGEX REPLACE "/W[0-9]" "" CMAKE_CXX_FLAGS ${CMAKE_CXX_FLAGS} ) ENDIF ( cppad_cxx_flags MATCHES "/W[0-9]" ) print_variable(CMAKE_CXX_FLAGS) # ----------------------------------------------------------------------------- # set cppad_abs_${middle_name} for middle_name equal to: # includedir, liddir, datadir, docdir FOREACH(middle_names includedirs libdirs datadir docdir) STRING(REGEX REPLACE "dirs" "dir" middle_name ${middle_names}) SET(middle_value NOTFOUND) FOREACH(dir ${cmake_install_${middle_names}}) IF( NOT middle_value ) SET(middle_value ${dir}) ENDIF( NOT middle_value ) ENDFOREACH(dir ${cmake_install_${middle_names}}) # SET(tmp "${cppad_prefix}/${middle_value}" ) IF ( cppad_postfix ) SET(cppad_abs_${middle_name} ${tmp}/${cppad_postfix}) ELSE ( cppad_postfix ) SET(cppad_abs_${middle_name} ${tmp}) ENDIF ( cppad_postfix ) ENDFOREACH(middle_names includedirs libdirs datadir docdir) # ----------------------------------------------------------------------------- # boost_prefix FIND_PACKAGE(Boost) IF ( Boost_FOUND ) # Extract the Boost prefix from Boost_INCLUDE_DIRS # # convert to using unix directory separator dos_path_to_unix("${Boost_INCLUDE_DIRS}" boost_include_dirs) # # convert to just one directory STRING(REGEX REPLACE "([^ ]+).*" "\\1" boost_include_dir "${boost_include_dirs}" ) # # extract part before last backslash STRING(REGEX REPLACE "([^ ]*)/[^/ ]*" "\\1" boost_prefix "${boost_include_dir}" ) print_variable(boost_prefix) # # add boost include directories FOREACH(dir ${cmake_install_includedirs}) IF( IS_DIRECTORY ${boost_prefix}/${dir} ) INCLUDE_DIRECTORIES( ${boost_prefix}/${dir} ) MESSAGE(STATUS "Found ${boost_prefix}/${dir}") ENDIF( IS_DIRECTORY ${boost_prefix}/${dir} ) ENDFOREACH( dir ) # # add boost link directories FOREACH(dir ${cmake_install_libdirs}) IF( IS_DIRECTORY ${boost_prefix}/${dir} ) LINK_DIRECTORIES( ${boost_prefix}/${dir} ) MESSAGE(STATUS "Found ${boost_prefix}/${dir}") ENDIF( IS_DIRECTORY ${boost_prefix}/${dir} ) ENDFOREACH( dir ) ENDIF ( Boost_FOUND ) # ----------------------------------------------------------------------------- # ipopt_LIBRARIES and ipopt_LIBRARY_DIRS IF( ipopt_prefix ) FIND_PACKAGE(PkgConfig) IF( NOT PKG_CONFIG_FOUND ) MESSAGE(FATAL_ERROR "Using ipopt_prefix but cannot find pkg-config") ENDIF( NOT PKG_CONFIG_FOUND ) # # Set the system environment variable PKG_CONFIG_PATH FOREACH(dir ${cmake_install_libdirs}) IF(EXISTS "${ipopt_prefix}/${dir}/pkgconfig/ipopt.pc") SET( ENV{PKG_CONFIG_PATH} ${ipopt_prefix}/${dir}/pkgconfig ) ENDIF(EXISTS "${ipopt_prefix}/${dir}/pkgconfig/ipopt.pc") ENDFOREACH(dir) # # pkg_check_modules( [REQUIRED] []*) # ipopt_LIBRARIES ... only the libraries (w/o the '-l') # ipopt_LIBRARY_DIRS ... the paths of the libraries (w/o the '-L') pkg_check_modules(ipopt ipopt) IF( NOT ipopt_FOUND ) MESSAGE(FATAL_ERROR "For all directories dir in cmake_install_libdirs, cannot find the file ipopt_prefix/dir/pkgconfig/ipopt.pc where ipopt_prefix = ${ipopt_prefix} cmake_install_libdirs = ${cmake_install_libdirs} " ) ENDIF( NOT ipopt_FOUND ) ENDIF( ipopt_prefix ) # ============================================================================= # Currently building tests as normal executables # ============================================================================= # The CMakeLists.txt file in the specified source directory is processed # before the current input file continues beyond this command. # add_subdirectory(source_dir [binary_dir] [EXCLUDE_FROM_ALL]) # # Initialize list of tests as empty SET(check_depends "") # # directories with no check depends entries ADD_SUBDIRECTORY(cppad) ADD_SUBDIRECTORY(pkgconfig) IF( colpack_prefix ) ADD_SUBDIRECTORY(cppad_lib) ENDIF( colpack_prefix) # IF( NOT ( "${check_depends}" STREQUAL "" ) ) MESSAGE(FATAL_ERROR "Error in CMakeLists.txt scripts") ENDIF( NOT ( "${check_depends}" STREQUAL "" ) ) # # directories with check depends entries ADD_SUBDIRECTORY(example) ADD_SUBDIRECTORY(compare_c) ADD_SUBDIRECTORY(introduction) ADD_SUBDIRECTORY(print_for) ADD_SUBDIRECTORY(test_more) ADD_SUBDIRECTORY(multi_thread) ADD_SUBDIRECTORY(speed) IF ( ipopt_prefix ) ADD_SUBDIRECTORY(cppad_ipopt) ENDIF( ipopt_prefix ) # ADD_CUSTOM_TARGET(check DEPENDS ${check_depends}) MESSAGE(STATUS "make check: avialable") # ============================================================================ # Copy a file to another location and modify its contents. # configure_file(InputFile OutputFile [COPYONLY] [ESCAPE_QUOTES] [@ONLY]) CONFIGURE_FILE( ${CMAKE_CURRENT_SOURCE_DIR}/bin/test_one.sh.in ${CMAKE_CURRENT_SOURCE_DIR}/bin/test_one.sh ) # ============================================================================= # install procedure # ============================================================================= # install(DIRECTORY dirs... DESTINATION # [FILE_PERMISSIONS permissions...] # [DIRECTORY_PERMISSIONS permissions...] # [USE_SOURCE_PERMISSIONS] [OPTIONAL] # [CONFIGURATIONS [Debug|Release|...]] # [COMPONENT ] [FILES_MATCHING] # [[PATTERN | REGEX ] # [EXCLUDE] [PERMISSIONS permissions...]] [...] # ) # Note a trailing / in the source directory name drops the source directory # name during the copy. # # During install copy all the cppad include files to # ${cppad_abs_includedir}/cppad INSTALL( DIRECTORY "${CMAKE_SOURCE_DIR}/cppad/" DESTINATION ${cppad_abs_includedir}/cppad FILES_MATCHING PATTERN "*.hpp" ) # # During install copy doc direcrory to cppad_abs_docdir/cppad IF ( cmake_install_docdir ) INSTALL( DIRECTORY "doc/" DESTINATION ${cppad_abs_docdir}/cppad ) ENDIF ( cmake_install_docdir ) # IF( ${cppad_deprecated} ) # During install copy deprecated include files INSTALL( DIRECTORY "${CMAKE_SOURCE_DIR}/cppad/deprecated/" DESTINATION ${cppad_abs_includedir}/cppad ) ENDIF( ${cppad_deprecated} ) cppad-20170000.3/bug/0002755000175200017650000000000013057470463013212 5ustar coincoin-webcppad-20170000.3/bug/alloc_global.sh0000755000175200017650000000631013057470462016160 0ustar coincoin-web#! /bin/bash -e # $Id: alloc_global.sh 2898 2013-09-18 13:07:32Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- #!/bin/bash -e # if [ ! -e build ] then mkdir build fi cd build if [ ! -e ../../cppad/configure.hpp ] then cmake ../.. fi # echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` echo "create $name.cpp" cat << EOF > $name.cpp // BEGIN PROGRAM # include # include # define NUMBER_THREADS 2 namespace { using CppAD::thread_alloc; // used to inform CppAD when we are in parallel execution mode bool in_parallel(void) { return static_cast( omp_in_parallel() ); } // used to inform CppAD of current thread number thread_number() size_t thread_number(void) { return static_cast( omp_get_thread_num() ); } // structure with information for one thread typedef struct { // function object (worker input) CppAD::vector x; } thread_one_t; // vector with information for all threads thread_one_t thread_all_[NUMBER_THREADS]; // -------------------------------------------------------------------- // function that does the work for one thread void worker(void) { size_t thread_num = thread_number(); thread_all_[thread_num].x.resize(1); thread_all_[thread_num].x[0]=static_cast(thread_num); std::stringstream stream; stream << "thread_num = " << thread_num << std::endl; std::cout << stream.str(); } } // Test routine called by the master thread (thread_num = 0). bool alloc_global(void) { bool ok = true; using std::cout; using std::endl; size_t num_threads = NUMBER_THREADS; if( omp_get_max_threads() < num_threads ) { cout << "can't set num_threads = " << num_threads << endl; ok = false; return ok; } // call setup for using thread_alloc in parallel mode. thread_alloc::parallel_setup(num_threads, in_parallel, thread_number); // Execute the worker function in parallel int thread_num; # pragma omp parallel for for(thread_num = 0; thread_num < num_threads; thread_num++) worker(); // end omp parallel for // now inform CppAD that there is only one thread thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL); for(thread_num = 0; thread_num < num_threads; thread_num++) { // check calculations by this thread in parallel model ok &= thread_all_[thread_num].x[0] == static_cast(thread_num); // free memory that was allocated by thread thread_num thread_all_[thread_num].x.resize(0); } return ok; } int main(void) { bool ok = alloc_global(); std::cout << "OK = " << ok << std::endl; return int(! ok); } EOF echo "g++ -g $name.cpp -I../.. -fopenmp -std=c++11 -o $name" g++ -g $name.cpp -I../.. -fopenmp -std=c++11 -o $name # echo "./$name" ./$name # echo "rm $name $name.cpp" rm $name $name.cpp cppad-20170000.3/bug/doxy_member.sh0000755000175200017650000000456213057470462016067 0ustar coincoin-web#! /bin/bash -e # $Id: doxy_member.sh 3237 2014-04-28 13:28:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-14 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Trying to figure out why ADFun::Forward appers twice where there is only # one implementation. # # ------------------------------------------------------------------------------ # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------- echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` # ----------------------------------------------- for dir in build doxy_member do if [ ! -e $dir ] then mkdir $dir fi cd $dir done # ------------------------------------------------------------------------- cat << EOF > $name.hpp template class my_class { private: T value_; public: void set_value(T value = 0); T get_value(void); }; EOF cat << EOF > implement.hpp /*! \\file implement.hpp Implementation of member functions */ /*! Member function that sets the value. \\param value [in] New value. */ template void my_class::set_value(T value) { value_ = value; } /*! Member function that gets the value. \\return Current value. */ template T my_class::get_value(void) { return value_; } EOF cat << EOF > $name.cpp # include # include "$name.hpp" # include "implement.hpp" int main(void) { my_class x; x.set_value(2); std::cout << "x.value = " << x.get_value() << std::endl; return 0; } EOF # ------------------------------------------------------------------------- # echo_eval doxygen -g doxyfile cp ../../../doxyfile . sed \ -e 's|^\(INPUT *=\)|& .|' \ -e 's|^\(FILE_PATTERNS *=\)|& *.hpp *.cpp|' \ -i doxyfile # ------------------------------------------------------------------------- echo_eval doxygen doxyfile # ------------------------------------------------------------------------- echo_eval g++ $name.cpp -o name echo_eval ./name cppad-20170000.3/bug/template.sh0000755000175200017650000000263013057470462015362 0ustar coincoin-web#! /bin/bash -e # $Id: template.sh 3719 2015-09-02 18:41:58Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- cat << EOF Description EOF cat << EOF > bug.$$ # include int main(void) { bool ok = true; using std::cout; // cout << "1. copy template.sh to .sh\n"; cout << "2. Edit .sh replacing description and C++ source code\n"; cout << "3. Run ./.sh\n"; cout << "where is a name that describes the bug\n"; // if( ok ) return 0; return 1; } EOF # ----------------------------------------------------------------------------- if [ ! -e build ] then mkdir build fi cd build echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` mv ../bug.$$ $name.cpp echo "g++ -I../.. --std=c++11 -g $name.cpp -o $name" g++ -I../.. --std=c++11 -g $name.cpp -o $name # echo "./$name" if ! ./$name then echo echo "$name.sh: Error" exit 1 fi echo echo "$name.sh: OK" exit 0 cppad-20170000.3/bug/eigen_shadow.sh0000755000175200017650000000334213057470462016204 0ustar coincoin-web#! /bin/bash -e # $Id: eigen_shadow.sh 3066 2013-12-29 17:27:20Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Eigen generates lots of warnings if -Wshadow is set of compile; e.g., # the first warning generated by this script is: # # warning: declaration of ‘value’ shadows a member of 'this' [-Wshadow] # explicit variable_if_dynamic(T value) : m_value(value) {} # ^ # ------------------------------------------------------------------------------ # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------- if [ ! -e build ] then mkdir build fi cd build echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` # cat << EOF > $name.cpp # include # include int main() { using Eigen::Matrix; using Eigen::Dynamic; Matrix A(1,1); A(0,0) = 6.0; if( A(0,0) != 6.0 ) { std::cout << "$name: Error" << std::endl; return 1; } std::cout << "$name: OK" << std::endl; return 0; } EOF if [ -e "$name" ] then echo_eval rm $name fi echo_eval g++ \ $name.cpp \ -I$HOME/prefix/eigen/include \ -g \ -O0 \ -std=c++11 \ -Wshadow \ -o $name echo_eval ./$name cppad-20170000.3/bug/std_vector.sh0000755000175200017650000000255413057470462015730 0ustar coincoin-web#! /bin/bash -e # $Id: std_vector.sh 2935 2013-10-12 19:40:01Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Using g++ 4.8.1 results in the following error message: # # std_vector.cpp:8:7: error: no match for ‘operator|=’ (operand types are # ‘std::vector::reference {aka std::_Bit_reference}’ and ‘bool’) # y[1] |= true; # ^ # ----------------------------------------------------------------------------- if [ ! -e build ] then mkdir build fi cd build echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` cat << EOF > $name.cpp # include int main(void) { int N = 1; std::vector y(N); for(int i = 0; i < N; i++ ) y[i] = false; y[0] = y[0] | true; y[1] |= true; return 0; } EOF echo "g++ -g $name.cpp -o $name" g++ -g $name.cpp -o $name # echo "./$name" ./$name # echo "rm $name $name.cpp" rm $name $name.cpp cppad-20170000.3/bug/sparsity.sh0000755000175200017650000000500713057470463015427 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- gigabytes='1.0' # memory limit in gigabytes # ----------------------------------------------------------------------------- kilobytes=`echo "($gigabytes * 10^9) / 1024" | bc` ulimit -Sv $kilobytes cat << EOF This is testing the idea that vector< std::set > sparsity; is inefficient compared to vector row, col; The results on one system for this script are: ./sparsity set 1e7 elapsed_seconds = 3.62206 ./sparsity set 2e7 std::bad_alloc ./sparsity vec 2e7 elapsed_seconds = 1.34243 ./sparsity vec 4e7 std::bad_alloc EOF cat << EOF > bug.$$ # include int main(int argc, char *argv[]) { using CppAD::elapsed_seconds; if( argc != 3 ) { std::cerr << "usage: $0 (set|vec) n" << std::endl; return 1; } bool set = std::strcmp(argv[1], "set") == 0; bool vec = std::strcmp(argv[1], "vec") == 0; bool ok = vec || set; if( ! ok ) { std::cerr << "usage: $0 (set|vec) n" << std::endl; return 1; } size_t n = size_t( std::atof( argv[2] ) ); const char* label; elapsed_seconds(); try { if( set ) { std::vector< std::set > my_set(n); for(size_t i = 0; i < n; i++) my_set[i].insert(i); } else { std::vector row; std::vector col; for(size_t i = 0; i < n; i++) { row.push_back(i); col.push_back(i); } } for(int i = 0; i < argc; i++) std::cout << argv[i] << " "; std::cout << "elapsed_seconds = " << elapsed_seconds() << std::endl; } catch( std::bad_alloc& ba ) { for(int i = 0; i < argc; i++) std::cout << argv[i] << " "; std::cout << ba.what() << std::endl; } return 0; } EOF # ----------------------------------------------------------------------------- if [ ! -e build ] then mkdir build fi cd build echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` mv ../bug.$$ $name.cpp echo "g++ -I../.. -DNDEBUG --std=c++11 $name.cpp -o $name" g++ -I../.. -DNDEBUG --std=c++11 $name.cpp -o $name # ./$name set 1e7 ./$name set 2e7 ./$name vec 2e7 ./$name vec 4e7 cppad-20170000.3/bug/cppad_cg.sh0000755000175200017650000001102713057470463015310 0ustar coincoin-web#! /bin/bash -e # $Id:$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- #! /bin/bash -e web_page='https://github.com/joaoleal/CppADCodeGen.git' # ----------------------------------------------------------------------------- # bash function that echos and executes a command echo_eval() { echo $* eval $* } # ----------------------------------------------------------------------------- cat << EOF This is not a bug but rather a demonstration of using conditional expressions with CppADCodeGen https://github.com/joaoleal/CppADCodeGen/ EOF # if [ ! -e build ] then echo_eval mkdir -p build fi echo_eval cd build cat << EOF > cppad_cg.cpp # include # include int main(void) { typedef CppAD::cg::CG cg_double; typedef CppAD::AD acg_double; // declare independent variables for f(x) size_t nx = 2; CppAD::vector ax(nx); ax[0] = 2.0; ax[1] = 3.0; CppAD::Independent(ax); // create dependent variables and values for f(x) // f(x) = x[0] / x[1] if (x[0] > 0 and x[1] >= x[0]) else 1.0 size_t nz = 1; CppAD::vector az(nz); acg_double acg_zero = acg_double(0.0); acg_double acg_one = acg_double(1.0); acg_double acg_temp_1 = CondExpGt(ax[1], ax[0], ax[0] / ax[1], acg_one); acg_double acg_temp_2 = CondExpGt(ax[0], acg_zero, acg_temp_1, acg_one); az[0] = acg_temp_2; // create AD function mapping independent to dependent variables CppAD::ADFun F(ax, az); // create the source code generator for function g(x) CppAD::cg::CodeHandler G; // declare the independent variables for g(x) CppAD::vector cg_x(nx); G.makeVariables(cg_x); // Compute the dependent variables and values for g(x) size_t ny = nz * nx; CppAD::vector cg_y(ny); cg_y = F.Jacobian(cg_x); // Mapping from variables in this program to variables in source_code // independent variable = x // dependent variable = y // temporary variable = v CppAD::cg::LanguageC langC("double"); CppAD::cg::LangCDefaultVariableNameGenerator nameGen; // generate the source code std::ostringstream source_code; G.generateCode(source_code, langC, cg_y, nameGen); // string corresponding to source code std::string source_str = source_code.str(); // C souce code corresponding to y = g(x) std::cout << source_str; return 0; } EOF # # Compile and run cppad_cg.cpp echo_eval g++ \ -g \ -std=c++11 \ -I$HOME/prefix/cppad_cg/include \ -I../.. \ cppad_cg.cpp -o cppad_cg # # Determine the maximum v index v_max_index=`./cppad_cg | sed \ -e '/^ *v\[[0-9]*\]/! d' \ -e 's|^ *v\[\([0-9]*\)\].*|\1|' | sort | tail -1` # # # Wrap y = g(x) in C++ function and test it cat << EOF > tst_cppad_cg.cpp # include namespace { using CppAD::zdouble; typedef CppAD::vector zvector; // // f(x) = x[0] / x[1] if (x[0] > 0 and x[1] >= x[0]) else 1.0 // g(x) = d/dx f(x) void g(const zvector& x, zvector& y) { zvector v($v_max_index + 1); EOF ./cppad_cg | sed -e 's|^ *|\t\t|' >> tst_cppad_cg.cpp cat << EOF >> tst_cppad_cg.cpp return; } } int main(void) { // initialize flag bool ok = true; // numerical precision for tests zdouble eps = 10. * std::numeric_limits::epsilon(); // number of components in vectors size_t nx = 2; size_t nz = 1; size_t ny = nz * nx; zdouble zero = 0.0; // // compute y = g(x) case where x[0] == 0.0 zvector x(nx), y(ny); x[0] = 0.0; x[1] = 0.0; g(x, y); // // check results ok &= CppAD::NearEqual(y[0], zero, eps, eps); ok &= CppAD::NearEqual(y[1], zero, eps, eps); // // compute y = g(x) case where g(x) = x[0] / x[1] x[0] = 2.0; x[1] = 3.0; g(x, y); // // check results ok &= CppAD::NearEqual(y[0], 1.0/x[1], eps, eps); ok &= CppAD::NearEqual(y[1], -x[0]/(x[1]*x[1]), eps, eps); // if( ! ok ) return 1; return 0; } EOF # # Compile test echo_eval g++ \ -g \ -std=c++11 \ -I../.. \ tst_cppad_cg.cpp -o tst_cppad_cg # if ! ./tst_cppad_cg then file="$HOME/install/cppad_cg/build/tst_cppad_cg.cpp" echo "install_cppad_cg.sh: Error" exit 1 fi # echo 'cppad_cg.sh: OK' exit 0 cppad-20170000.3/bug/numeric_limit.sh0000755000175200017650000001230313057470463016406 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- if [ ! -e ../cppad/configure.hpp ] then echo 'numeric_limits.sh: must first run bin/run_cmake.sh' echo 'from parent directory.' exit 1 fi cat << EOF This is not a bug, but rather a test of specialization of numeric_limits for AD types. EOF cat << EOF > bug.$$ # include /*! \\def CPPAD_STD_NUMERIC_LIMITS(Other, Base) This macro defines the specialization std::numeric_limits to have the same values and functions as the existing specialization std::numeric_limits. */ # define CPPAD_STD_NUMERIC_LIMITS(Other, Base) \\ namespace std {\\ template <> class numeric_limits\\ {\\ public:\\ static const bool is_specialized =\\ numeric_limits::is_specialized;\\ static const bool is_signed =\\ numeric_limits::is_signed;\\ static const bool is_integer =\\ numeric_limits::is_integer;\\ static const bool is_exact =\\ numeric_limits::is_exact;\\ static const bool has_infinity =\\ numeric_limits::has_infinity;\\ static const bool has_quiet_NaN =\\ numeric_limits::has_quiet_NaN;\\ static const bool has_signaling_NaN =\\ numeric_limits::has_signaling_NaN;\\ static const bool has_denorm_loss =\\ numeric_limits::has_denorm_loss;\\ static const bool is_iec559 =\\ numeric_limits::is_iec559;\\ static const bool is_bounded =\\ numeric_limits::is_bounded;\\ static const bool is_modulo =\\ numeric_limits::is_modulo;\\ static const bool traps =\\ numeric_limits::traps;\\ static const bool tinyness_before =\\ numeric_limits::tinyness_before;\\ static const int digits =\\ numeric_limits::digits;\\ static const int digits10 =\\ numeric_limits::digits10;\\ static const int radix =\\ numeric_limits::radix;\\ static const int min_exponent =\\ numeric_limits::min_exponent;\\ static const int min_exponent10 =\\ numeric_limits::min_exponent10;\\ static const int max_exponent =\\ numeric_limits::max_exponent;\\ static const int max_exponent10 =\\ numeric_limits::max_exponent10;\\ static const Base min(void)\\ { return static_cast( numeric_limits::min() ); }\\ static const Base max(void)\\ { return static_cast( numeric_limits::max() ); }\\ static const Base epsilon(void)\\ { return static_cast( numeric_limits::epsilon() ); }\\ static const Base round_error(void)\\ { return static_cast( numeric_limits::round_error() ); }\\ static const Base infinity(void)\\ { return static_cast( numeric_limits::infinity() ); }\\ static const Base quiet_NaN(void)\\ { return static_cast( numeric_limits::quiet_NaN() ); }\\ static const Base signaling_NaN(void)\\ { return static_cast( numeric_limits::signaling_NaN() ); }\\ static const Base denorm_min(void)\\ { return static_cast( numeric_limits::denorm_min() ); }\\ static const float_denorm_style has_denorm =\\ numeric_limits::has_denorm;\\ static const float_round_style round_style =\\ numeric_limits::round_style;\\ };\\ } CPPAD_STD_NUMERIC_LIMITS(double, CppAD::AD) # define PRINT_VAL(name) \\ std::cout << #name << " = " \\ << std::numeric_limits< CppAD::AD >::name << std::endl; # define PRINT_FUN(name) \\ std::cout << #name << " = " \\ << std::numeric_limits< CppAD::AD >::name() << std::endl; int main(void) { bool ok = true; // PRINT_VAL(is_specialized) PRINT_VAL(is_signed) PRINT_VAL(is_integer) PRINT_VAL(is_exact) PRINT_VAL(has_infinity) PRINT_VAL(has_quiet_NaN) PRINT_VAL(has_signaling_NaN) PRINT_VAL(has_denorm_loss) PRINT_VAL(is_iec559) PRINT_VAL(is_bounded) PRINT_VAL(is_modulo) PRINT_VAL(traps) PRINT_VAL(tinyness_before) // int PRINT_VAL(digits) PRINT_VAL(digits10) PRINT_VAL(radix) PRINT_VAL(min_exponent) PRINT_VAL(min_exponent10) PRINT_VAL(max_exponent) PRINT_VAL(max_exponent10) // function PRINT_FUN(min) PRINT_FUN(max) PRINT_FUN(epsilon) PRINT_FUN(round_error) PRINT_FUN(infinity) PRINT_FUN(quiet_NaN) PRINT_FUN(signaling_NaN) PRINT_FUN(denorm_min) // other PRINT_VAL(has_denorm) PRINT_VAL(round_style) // C++11 only // PRINT_VAL(max_digits10) // PRINT_FUN(lowest) // if( ok ) return 0; return 1; } EOF # ----------------------------------------------------------------------------- if [ ! -e build ] then mkdir build fi cd build echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` mv ../bug.$$ $name.cpp echo "g++ -I../.. --std=c++11 -g $name.cpp -o $name" g++ -I../.. --std=c++11 -g $name.cpp -o $name # echo "./$name" if ! ./$name then echo echo "$name.sh: Error" exit 1 fi echo echo "$name.sh: OK" exit 0 cppad-20170000.3/bug/gcc_complex.sh0000755000175200017650000000322513057470463016034 0ustar coincoin-web#! /bin/bash -e # $Id: gcc_complex.sh 2886 2013-08-06 15:54:58Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- echo_eval() { echo $* eval $* } # ----------------------------------------------- echo "create gcc_complex.cpp" cat << EOF > gcc_complex.cpp # include # include # include int main(void) { double inf = std::numeric_limits::infinity(); std::complex c_inf( inf ); std::complex c_1( 1. ); std::cout << "c_inf = " << c_inf << std::endl; std::cout << "c_1 = " << c_1 << std::endl; std::cout << "c_inf / c1 = " << c_inf / c_1 << std::endl; return 0; } EOF echo_eval g++ gcc_complex.cpp -o gcc_complex echo_eval ./gcc_complex cat << EOF Explination: (x + i*y) (x + i*y) * (a - i*b) (x*a - y*b) + i*(y*a - x*b) --------- = --------------------- = --------------------------- (a + i*b) (a + i*b) * (a - i*b) a*a + b*b In our case x = inf, y = 0, a = 1, b = 0, so we have (x + i*y) (inf*1 - 0*0) + i*(0*1 - inf*0) --------- = ------------------------------ = inf - i*nan (a + i*b) 1*1 + 0*0 EOF echo_eval rm gcc_complex.cpp gcc_complex cppad-20170000.3/bug/test_install.sh0000755000175200017650000000345513057470463016263 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- cat << EOF This is not a bug but rather a test of installing with cppad_prefix=$HOME/prefix EOF cat << EOF > bug.$$ # include int main(void) { bool ok = true; using std::cout; using CppAD::AD; // CPPAD_TESTVECTOR( AD ) ax(1), ay(1); ax[0] = 1.0; CppAD::Independent(ax); ay[0] = sin( ax[0] ); CppAD::ADFun f(ax, ay); // std::vector< std::set > p(1); p[0].insert(0); CppAD::vector< size_t > row(1), col(1); row[0] = 0; col[0] = 0; CppAD::sparse_jacobian_work work; work.color_method = "colpack"; CPPAD_TESTVECTOR(double) x(1), jac(1); x[0] = 2.0; f.SparseJacobianForward(x, p, row, col, jac, work); // ok &= jac[0] == std::cos( x[0] ); // if( ok ) return 0; return 1; } EOF # ----------------------------------------------------------------------------- if [ ! -e build ] then mkdir build fi cd build echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` mv ../bug.$$ $name.cpp cmd="g++ -I $HOME/prefix/cppad/include --std=c++11 -g $name.cpp -o $name" cmd="$cmd -L $HOME/prefix/cppad/lib64 -lcppad_lib" cmd="$cmd -L $HOME/prefix/colpack/lib64 -lColPack" echo "$cmd" eval $cmd # echo "./$name" if ! ./$name then echo echo "$name.sh: Error" exit 1 fi echo echo "$name.sh: OK" exit 0 cppad-20170000.3/bug/boost_lu.sh0000755000175200017650000001117013057470463015375 0ustar coincoin-web#! /bin/bash -e # $Id$ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- cat << EOF This test results in a very long error message with boost-1.55.0 and gcc-4.9.2. Here is the gist of the message: /usr/include/boost/numeric/ublas/detail/matrix_assign.hpp:33:35: error: no match for ‘operator<’ ... snip ... return norm_inf (e1 - e2) < epsilon * ^ The folowing change to /usr/include/boost/numeric/ublas/detail/matrix_assign.hpp seems to fix the problem: Old Text: return norm_inf (e1 - e2) < epsilon * std::max (std::max (norm_inf (e1), norm_inf (e2)), min_norm); New Text: S norm_1 = norm_inf(e1); S norm_2 = norm_inf(e2); S norm_diff = norm_inf(e1 - e2); return norm_diff < epsilon * std::max( std::max(norm_1, norm_2) , min_norm ); EOF cat << EOF > bug.$$ #include # define NUMERIC_LIMITS_FUN(name) \ static CppAD::AD name(void) \ { return static_cast< CppAD::AD > ( \ std::numeric_limits::name() \ ); \ } # define NUMERIC_LIMITS_BOOL(name) \ static const bool name = \ std::numeric_limits::name; # define NUMERIC_LIMITS_INT(name) \ static const int name = \ std::numeric_limits::name; namespace std { /// Specialization of numeric_limits< CppAD::AD > template <> class numeric_limits< CppAD::AD > { public: // has_denorm static const float_denorm_style has_denorm = std::numeric_limits::has_denorm; // round_style static const float_round_style round_style = std::numeric_limits::round_style; // bool NUMERIC_LIMITS_BOOL(is_specialized); NUMERIC_LIMITS_BOOL(is_signed); NUMERIC_LIMITS_BOOL(is_integer); NUMERIC_LIMITS_BOOL(is_exact); NUMERIC_LIMITS_BOOL(has_infinity); NUMERIC_LIMITS_BOOL(has_quiet_NaN); NUMERIC_LIMITS_BOOL(has_signaling_NaN); NUMERIC_LIMITS_BOOL(has_denorm_loss); NUMERIC_LIMITS_BOOL(is_iec559); NUMERIC_LIMITS_BOOL(is_bounded); NUMERIC_LIMITS_BOOL(is_modulo); NUMERIC_LIMITS_BOOL(traps); NUMERIC_LIMITS_BOOL(tinyness_before); // int NUMERIC_LIMITS_INT(digits); NUMERIC_LIMITS_INT(digits10); NUMERIC_LIMITS_INT(radix); NUMERIC_LIMITS_INT(min_exponent); NUMERIC_LIMITS_INT(min_exponent10); NUMERIC_LIMITS_INT(max_exponent); NUMERIC_LIMITS_INT(max_exponent10); /// functions NUMERIC_LIMITS_FUN( epsilon) NUMERIC_LIMITS_FUN( min ) NUMERIC_LIMITS_FUN( max ) }; } #include int main() { typedef CppAD::AD T; boost::numeric::ublas::matrix a(5,5); boost::numeric::ublas::permutation_matrix pert(5); // lu decomposition const std::size_t s = lu_factorize(a, pert); return 0; } EOF # ----------------------------------------------------------------------------- if [ ! -e build ] then mkdir build fi cd build echo "$0" name=`echo $0 | sed -e 's|.*/||' -e 's|\..*||'` mv ../bug.$$ $name.cpp echo "g++ -I../.. --std=c++11 -g $name.cpp -o $name >& $name.log" if ! g++ -I../.. --std=c++11 -g $name.cpp -o $name >& $name.log then cat << EOF > $name.sed s|\\[|&\\n|g s|\\]|&\\n|g s|[‘{}]|&\\n|g s|[a-zA-Z0-9_]* *=|\\n&|g # s|boost::numeric::ublas::||g s|/usr/include/boost/numeric/ublas/||g # s|CppAD::AD *|AD|g s|, basic_unit_lower<> >||g s|, basic_upper<> >||g s|scalar_minus|scalar_minus_AD|g s|triangular_adaptor<\\([^<>]*\\)>|triangular_\\1|g s|triangular_matrix_AD_ulower|AD_ulower|g s|triangular_matrix_AD_upper|AD_upper|g s|matrix_matrix_prod *|AD_prod_ulower_upper|g s| *||g s|matrix_matrix_binary|AD_prod_ulower_upper|g EOF echo "sed -f $name.sed $name.log > ../$name.log" sed -f $name.sed $name.log > ../$name.log echo "$name.sh: Compliation Error: see $name.log" exit 1 fi # echo "./$name" if ! ./$name then echo echo "$name.sh: Execution Error" exit 1 fi echo echo "$name.sh: OK" exit 0 cppad-20170000.3/bug/cmake_target.sh0000755000175200017650000000275613057470463016207 0ustar coincoin-web#! /bin/bash -e # $Id: cmake_target.sh 3090 2014-01-31 11:31:54Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-14 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- #! /bin/bash -e echo 'This script does not work properly on el6; see' echo 'https://bugzilla.redhat.com/show_bug.cgi?id=896116' echo # if [ -e build ] then rm -r build fi mkdir build cd build cat << EOF > hello_one.cpp # include int main(void) { std::cout << "hello_one" << std::endl << std::endl; return 0; } EOF cat << EOF > hello_two.cpp # include int main(void) { std::cout << "hello_two" << std::endl << std::endl; return 0; } EOF cat << EOF > CMakeLists.txt CMAKE_MINIMUM_REQUIRED(VERSION 2.6) # PROJECT(hello) # ADD_EXECUTABLE(hello_one EXCLUDE_FROM_ALL hello_one.cpp ) ADD_EXECUTABLE(hello_two EXCLUDE_FROM_ALL hello_two.cpp ) # ADD_CUSTOM_TARGET(check_one hello_one DEPENDS hello_one) ADD_CUSTOM_TARGET(check_two hello_two DEPENDS hello_two) # ADD_CUSTOM_TARGET(check DEPENDS check_one check_two) EOF # uname -a cmake --version cmake . make check cppad-20170000.3/introduction/0002755000175200017650000000000013057470463015156 5ustar coincoin-webcppad-20170000.3/introduction/exp_apx/0002755000175200017650000000000013057470463016622 5ustar coincoin-webcppad-20170000.3/introduction/exp_apx/exp_2_rev2.cpp0000644000175200017650000000532113057470463021300 0ustar coincoin-web// $Id: exp_2_rev2.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_2_rev2.cpp$$ $spell cstddef cmath exp_2_rev bool std fabs $$ $section exp_2: Verify Second Order Reverse Sweep$$ $mindex exp_2 mode$$ $srccode%cpp% */ # include // define size_t # include // prototype for fabs extern bool exp_2_for0(double *v0); // computes zero order forward sweep extern bool exp_2_for1(double *v1); // computes first order forward sweep bool exp_2_rev2(void) { bool ok = true; // set the value of v0[j], v1[j] for j = 1 , ... , 5 double v0[6], v1[6]; ok &= exp_2_for0(v0); ok &= exp_2_for1(v1); // initial all partial derivatives as zero double f_v0[6], f_v1[6]; size_t j; for(j = 0; j < 6; j++) { f_v0[j] = 0.; f_v1[j] = 0.; } // set partial derivative for f_5 f_v1[5] = 1.; ok &= std::fabs( f_v1[5] - 1. ) <= 1e-10; // partial f_5 w.r.t v_5^1 // f_4 = f_5( v_1^0 , ... , v_4^1 , v_2^0 + v_4^0 , v_2^1 + v_4^1 ) f_v0[2] += f_v0[5] * 1.; f_v0[4] += f_v0[5] * 1.; f_v1[2] += f_v1[5] * 1.; f_v1[4] += f_v1[5] * 1.; ok &= std::fabs( f_v0[2] - 0. ) <= 1e-10; // partial f_4 w.r.t. v_2^0 ok &= std::fabs( f_v0[4] - 0. ) <= 1e-10; // partial f_4 w.r.t. v_4^0 ok &= std::fabs( f_v1[2] - 1. ) <= 1e-10; // partial f_4 w.r.t. v_2^1 ok &= std::fabs( f_v1[4] - 1. ) <= 1e-10; // partial f_4 w.r.t. v_4^1 // f_3 = f_4( v_1^0 , ... , v_3^1, v_3^0 / 2 , v_3^1 / 2 ) f_v0[3] += f_v0[4] / 2.; f_v1[3] += f_v1[4] / 2.; ok &= std::fabs( f_v0[3] - 0. ) <= 1e-10; // partial f_3 w.r.t. v_3^0 ok &= std::fabs( f_v1[3] - 0.5 ) <= 1e-10; // partial f_3 w.r.t. v_3^1 // f_2 = f_3( v_1^0 , ... , v_2^1, v_1^0 * v_1^0 , 2 * v_1^0 * v_1^1 ) f_v0[1] += f_v0[3] * 2. * v0[1]; f_v0[1] += f_v1[3] * 2. * v1[1]; f_v1[1] += f_v1[3] * 2. * v0[1]; ok &= std::fabs( f_v0[1] - 1. ) <= 1e-10; // partial f_2 w.r.t. v_1^0 ok &= std::fabs( f_v1[1] - 0.5 ) <= 1e-10; // partial f_2 w.r.t. v_1^1 // f_1 = f_2( v_1^0 , v_1^1 , 1 + v_1^0 , v_1^1 ) f_v0[1] += f_v0[2] * 1.; f_v1[1] += f_v1[2] * 1.; ok &= std::fabs( f_v0[1] - 1. ) <= 1e-10; // partial f_1 w.r.t. v_1^0 ok &= std::fabs( f_v1[1] - 1.5) <= 1e-10; // partial f_1 w.r.t. v_1^1 return ok; } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/exp_2.cpp0000644000175200017650000000155313057470463020345 0ustar coincoin-web// $Id: exp_2.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN C++ # include // define fabs function # include "exp_2.hpp" // definition of exp_2 algorithm bool exp_2(void) { double x = .5; double check = 1 + x + x * x / 2.; bool ok = std::fabs( exp_2(x) - check ) <= 1e-10; return ok; } // END C++ cppad-20170000.3/introduction/exp_apx/exp_2.omh0000644000175200017650000006556113057470463020357 0ustar coincoin-web$Id: exp_2.omh 3788 2016-02-09 15:50:06Z bradbell $ ----------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. ----------------------------------------------------------------------------- $begin exp_2.hpp$$ $spell exp $$ $section exp_2: Implementation$$ $mindex exp_2$$ $code $srcfile%introduction/exp_apx/exp_2.hpp%0%// BEGIN C++%// END C++%$$ $$ $end ----------------------------------------------------------------------------- $begin exp_2.cpp$$ $spell exp $$ $section exp_2: Test$$ $code $srcfile%introduction/exp_apx/exp_2.cpp%0%// BEGIN C++%// END C++%$$ $$ $end ----------------------------------------------------------------------------- $begin exp_2_for0$$ $spell cpp exp_2_seq bool $$ $section exp_2: Operation Sequence and Zero Order Forward Mode$$ $mindex example$$ $head Mathematical Form$$ The operation sequence (see below) corresponding to the algorithm $cref exp_2.hpp$$ is the same for all values of $icode x$$. The mathematical form for the corresponding function is $latex \[ f(x) = 1 + x + x^2 / 2 \] $$ An algorithmic differentiation package does not operate on the mathematical function $latex f(x)$$ but rather on the particular algorithm used to compute the function (in this case $cref exp_2.hpp$$). $head Zero Order Expansion$$ In general, a zero order forward sweep is given a vector $latex x^{(0)} \in \B{R}^n$$ and it returns the corresponding vector $latex y^{(0)} \in \B{R}^m$$ given by $latex \[ y^{(0)} = f( x^{(0)} ) \]$$ The superscript $latex (0)$$ denotes zero order derivative; i.e., it is equal to the value of the corresponding variable. For the example we are considering here, both $latex n$$ and $latex m$$ are equal to one. $head Operation Sequence$$ An atomic $icode Type$$ operation is an operation that has a $icode Type$$ result and is not made up of other more basic operations. A sequence of atomic $icode Type$$ operations is called a $icode Type$$ operation sequence. Given an C++ algorithm and its inputs, there is a corresponding $icode Type$$ operation sequence for each type. If $icode Type$$ is clear from the context, we drop it and just refer to the operation sequence. $pre $$ We consider the case where $cref exp_2.hpp$$ is executed with $latex x^{(0)} = .5$$. The table below contains the corresponding operation sequence and the results of a zero order sweep. $subhead Index$$ The Index column contains the index in the operation sequence of the corresponding atomic operation and variable. A Forward sweep starts with the first operation and ends with the last. $subhead Code$$ The Code column contains the C++ source code corresponding to the corresponding atomic operation in the sequence. $subhead Operation$$ The Operation column contains the mathematical function corresponding to each atomic operation in the sequence. $subhead Zero Order$$ The Zero Order column contains the zero order derivative for the corresponding variable in the operation sequence. Forward mode refers to the fact that these coefficients are computed in the same order as the original algorithm; i.e, in order of increasing index in the operation sequence. $subhead Sweep$$ $center $table $bold Index$$ $cnext $pre $$ $cnext $bold Code$$ $cnext $pre $$ $cnext $bold Operation$$ $cnext $pre $$ $cnext $bold Zero Order$$ $rnext 1 $cnext $pre $$ $cnext $code Type v1 = x;$$ $cnext $cnext $latex v_1 = x $$ $cnext $cnext $latex v_1^{(0)} = 0.5$$ $rnext 2 $cnext $pre $$ $cnext $code Type v2 = Type(1) + v1;$$ $cnext $cnext $latex v_2 = 1 + v_1 $$ $cnext $cnext $latex v_2^{(0)} = 1.5$$ $rnext 3 $cnext $pre $$ $cnext $code Type v3 = v1 * v1;$$ $cnext $cnext $latex v_3 = v_1 * v_1 $$ $cnext $cnext $latex v_3^{(0)} = 0.25$$ $rnext 4 $cnext $pre $$ $cnext $code Type v4 = v3 / Type(2);$$ $cnext $cnext $latex v_4 = v_3 / 2$$ $cnext $cnext $latex v_4^{(0)} = 0.125$$ $rnext 5 $cnext $pre $$ $cnext $code Type v5 = v2 + v4;$$ $cnext $cnext $latex v_5 = v_2 + v_4 $$ $cnext $cnext $latex v_5^{(0)} = 1.625$$ $tend $$ $head Return Value$$ The return value for this case is $latex \[ 1.625 = v_5^{(0)} = f( x^{(0)} ) \] $$ $children% introduction/exp_apx/exp_2_for0.cpp %$$ $head Verification$$ The file $cref exp_2_for0.cpp$$ contains a routine that verifies the values computed above. It returns true for success and false for failure. $head Exercises$$ $list number$$ Suppose that $latex x^{(0)} = .2$$, what is the result of a zero order forward sweep for the operation sequence above; i.e., what are the corresponding values for $latex \[ v_1^{(0)} , v_2^{(0)} , \cdots , v_5^{(0)} \]$$ $lnext Create a modified version of $cref exp_2_for0.cpp$$ that verifies the values you obtained for the previous exercise. $lnext Create and run a main program that reports the result of calling the modified version of $cref exp_2_for0.cpp$$ in the previous exercise. $lend $end ------------------------------------------------------------------------------ $begin exp_2_for1$$ $spell exp_2_for $$ $section exp_2: First Order Forward Mode$$ $head First Order Expansion$$ We define $latex x(t)$$ near $latex t = 0$$ by the first order expansion $latex \[ x(t) = x^{(0)} + x^{(1)} * t \]$$ it follows that $latex x^{(0)}$$ is the zero, and $latex x^{(1)}$$ the first, order derivative of $latex x(t)$$ at $latex t = 0$$. $head Purpose$$ In general, a first order forward sweep is given the $cref/zero order derivative/exp_2_for0/Zero Order Expansion/$$ for all of the variables in an operation sequence, and the first order derivatives for the independent variables. It uses these to compute the first order derivatives, and thereby obtain the first order expansion, for all the other variables in the operation sequence. $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_2.hpp$$ to compute $latex \[ f(x) = 1 + x + x^2 / 2 \] $$ The corresponding derivative function is $latex \[ \partial_x f (x) = 1 + x \] $$ An algorithmic differentiation package does not operate on the mathematical form of the function, or its derivative, but rather on the $cref/operation sequence/exp_2_for0/Operation Sequence/$$ for the for the algorithm that is used to evaluate the function. $head Operation Sequence$$ We consider the case where $cref exp_2.hpp$$ is executed with $latex x = .5$$. The corresponding operation sequence and zero order forward mode values (see $cref/zero order sweep/exp_2_for0/Operation Sequence/Sweep/$$) are inputs and are used by a first order forward sweep. $subhead Index$$ The Index column contains the index in the operation sequence of the corresponding atomic operation. A Forward sweep starts with the first operation and ends with the last. $subhead Operation$$ The Operation column contains the mathematical function corresponding to each atomic operation in the sequence. $subhead Zero Order$$ The Zero Order column contains the zero order derivatives for the corresponding variable in the operation sequence (see $cref/zero order sweep/exp_2_for0/Operation Sequence/Sweep/$$). $subhead Derivative$$ The Derivative column contains the mathematical function corresponding to the derivative with respect to $latex t$$, at $latex t = 0$$, for each variable in the sequence. $subhead First Order$$ The First Order column contains the first order derivatives for the corresponding variable in the operation sequence; i.e., $latex \[ v_j (t) = v_j^{(0)} + v_j^{(1)} t \] $$ We use $latex x^{(1)} = 1$$ so that differentiation with respect to $latex t$$, at $latex t = 0$$, is the same as partial differentiation with respect to $latex x$$ at $latex x = x^{(0)}$$. $subhead Sweep$$ $center $table $bold Index$$ $cnext $pre $$ $cnext $bold Operation$$ $cnext $pre $$ $cnext $bold Zero Order$$ $cnext $pre $$ $cnext $bold Derivative$$ $cnext $pre $$ $cnext $bold First Order$$ $rnext 1 $cnext $pre $$ $cnext $latex v_1 = x $$ $cnext $cnext 0.5 $cnext $cnext $latex v_1^{(1)} = x^{(1)} $$ $cnext $cnext $latex v_1^{(1)} = 1$$ $rnext 2 $cnext $pre $$ $cnext $latex v_2 = 1 + v_1$$ $cnext $cnext 1.5 $cnext $cnext $latex v_2^{(1)} = v_1^{(1)}$$ $cnext $cnext $latex v_2^{(1)} = 1$$ $rnext 3 $cnext $pre $$ $cnext $latex v_3 = v_1 * v_1$$ $cnext $cnext 0.25 $cnext $cnext $latex v_3^{(1)} = 2 * v_1^{(0)} * v_1^{(1)}$$ $cnext $cnext $latex v_3^{(1)} = 1$$ $rnext 4 $cnext $pre $$ $cnext $latex v_4 = v_3 / 2$$ $cnext $cnext 0.125 $cnext $cnext $latex v_4^{(1)} = v_3^{(1)} / 2$$ $cnext $cnext $latex v_4^{(1)} = 0.5$$ $rnext 5 $cnext $pre $$ $cnext $latex v_5 = v_2 + v_4$$ $cnext $cnext 1.625 $cnext $cnext $latex v_5^{(1)} = v_2^{(1)} + v_4^{(1)}$$ $cnext $cnext $latex v_5^{(1)} = 1.5$$ $tend $$ $head Return Value$$ The derivative of the return value for this case is $latex \[ \begin{array}{rcl} 1.5 & = & v_5^{(1)} = \left[ \D{v_5}{t} \right]_{t=0} = \left[ \D{}{t} f ( x^{(0)} + x^{(1)} t ) \right]_{t=0} \\ & = & f^{(1)} ( x^{(0)} ) * x^{(1)} = f^{(1)} ( x^{(0)} ) \end{array} \] $$ (We have used the fact that $latex x^{(1)} = 1$$.) $children% introduction/exp_apx/exp_2_for1.cpp %$$ $head Verification$$ The file $cref exp_2_for1.cpp$$ contains a routine which verifies the values computed above. It returns true for success and false for failure. $head Exercises$$ $list number$$ Which statement in the routine defined by $cref exp_2_for1.cpp$$ uses the values that are calculated by the routine defined by $cref exp_2_for0.cpp$$ ? $lnext Suppose that $latex x = .1$$, what are the results of a zero and first order forward sweep for the operation sequence above; i.e., what are the corresponding values for $latex v_1^{(0)}, v_2^{(0)}, \cdots , v_5^{(0)}$$ and $latex v_1^{(1)}, v_2^{(1)}, \cdots , v_5^{(1)}$$ ? $lnext Create a modified version of $cref exp_2_for1.cpp$$ that verifies the derivative values from the previous exercise. Also create and run a main program that reports the result of calling the modified version of $cref exp_2_for1.cpp$$. $lend $end ------------------------------------------------------------------------------ $begin exp_2_rev1$$ $spell exp_2_rev $$ $section exp_2: First Order Reverse Mode$$ $head Purpose$$ First order reverse mode uses the $cref/operation sequence/exp_2_for0/Operation Sequence/$$, and zero order forward sweep values, to compute the first order derivative of one dependent variable with respect to all the independent variables. The computations are done in reverse of the order of the computations in the original algorithm. $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_2.hpp$$ to compute $latex \[ f(x) = 1 + x + x^2 / 2 \] $$ The corresponding derivative function is $latex \[ \partial_x f (x) = 1 + x \] $$ $head f_5$$ For our example, we chose to compute the derivative of the value returned by $cref exp_2.hpp$$ which is equal to the symbol $latex v_5$$ in the $cref/exp_2 operation sequence/exp_2_for0/Operation Sequence/$$. We begin with the function $latex f_5 $$ where $latex v_5$$ is both an argument and the value of the function; i.e., $latex \[ \begin{array}{rcl} f_5 ( v_1 , v_2 , v_3 , v_4 , v_5 ) & = & v_5 \\ \D{f_5}{v_5} & = & 1 \end{array} \] $$ All the other partial derivatives of $latex f_5 $$ are zero. $head Index 5: f_4$$ Reverse mode starts with the last operation in the sequence. For the case in question, this is the operation with index 5, $latex \[ v_5 = v_2 + v_4 \] $$ We define the function $latex f_4 ( v_1 , v_2 , v_3 , v_4 ) $$ as equal to $latex f_5 $$ except that $latex v_5 $$ is eliminated using this operation; i.e. $latex \[ f_4 = f_5 [ v_1 , v_2 , v_3 , v_4 , v_5 ( v_2 , v_4 ) ] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_4}{v_2} & = & \D{f_5}{v_2} + \D{f_5}{v_5} * \D{v_5}{v_2} & = 1 \\ \D{f_4}{v_4} & = & \D{f_5}{v_4} + \D{f_5}{v_5} * \D{v_5}{v_4} & = 1 \end{array} \] $$ All the other partial derivatives of $latex f_4$$ are zero. $head Index 4: f_3$$ The next operation has index 4, $latex \[ v_4 = v_3 / 2 \] $$ We define the function $latex f_3 ( v_1 , v_2 , v_3 ) $$ as equal to $latex f_4 $$ except that $latex v_4 $$ is eliminated using this operation; i.e., $latex \[ f_3 = f_4 [ v_1 , v_2 , v_3 , v_4 ( v_3 ) ] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_3}{v_1} & = & \D{f_4}{v_1} & = 0 \\ \D{f_3}{v_2} & = & \D{f_4}{v_2} & = 1 \\ \D{f_3}{v_3} & = & \D{f_4}{v_3} + \D{f_4}{v_4} * \D{v_4}{v_3} & = 0.5 \end{array} \] $$ $head Index 3: f_2$$ The next operation has index 3, $latex \[ v_3 = v_1 * v_1 \] $$ We define the function $latex f_2 ( v_1 , v_2 ) $$ as equal to $latex f_3 $$ except that $latex v_3 $$ is eliminated using this operation; i.e., $latex \[ f_2 = f_3 [ v_1 , v_2 , v_3 ( v_1 ) ] \] $$ Note that the value of $latex v_1$$ is equal to $latex x$$ which is .5 for this evaluation. It follows that $latex \[ \begin{array}{rcll} \D{f_2}{v_1} & = & \D{f_3}{v_1} + \D{f_3}{v_3} * \D{v_3}{v_1} & = 0.5 \\ \D{f_2}{v_2} & = & \D{f_3}{v_2} & = 1 \end{array} \] $$ $head Index 2: f_1$$ The next operation has index 2, $latex \[ v_2 = 1 + v_1 \] $$ We define the function $latex f_1 ( v_1 ) $$ as equal to $latex f_2 $$ except that $latex v_2 $$ is eliminated using this operation; i.e., $latex \[ f_1 = f_2 [ v_1 , v_2 ( v_1 ) ] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_1}{v_1} & = & \D{f_2}{v_1} + \D{f_2}{v_2} * \D{v_2}{v_1} & = 1.5 \end{array} \] $$ Note that $latex v_1$$ is equal to $latex x$$, so the derivative of this is the derivative of the function defined by $cref exp_2.hpp$$ at $latex x = .5$$. $children% introduction/exp_apx/exp_2_rev1.cpp %$$ $head Verification$$ The file $cref exp_2_rev1.cpp$$ contains a routine which verifies the values computed above. It returns true for success and false for failure. It only tests the partial derivatives of $latex f_j$$ that might not be equal to the corresponding partials of $latex f_{j+1}$$; i.e., the other partials of $latex f_j$$ must be equal to the corresponding partials of $latex f_{j+1}$$. $head Exercises$$ $list number$$ Which statement in the routine defined by $cref exp_2_rev1.cpp$$ uses the values that are calculated by the routine defined by $cref exp_2_for0.cpp$$ ? $lnext Consider the case where $latex x = .1$$ and we first preform a zero order forward sweep for the operation sequence used above. What are the results of a first order reverse sweep; i.e., what are the corresponding derivatives of $latex f_5 , f_4 , \ldots , f_1$$. $lnext Create a modified version of $cref exp_2_rev1.cpp$$ that verifies the values you obtained for the previous exercise. Also create and run a main program that reports the result of calling the modified version of $cref exp_2_rev1.cpp$$. $lend $end ------------------------------------------------------------------------------ $begin exp_2_for2$$ $spell exp_2_for $$ $section exp_2: Second Order Forward Mode$$ $head Second Order Expansion$$ We define $latex x(t)$$ near $latex t = 0$$ by the second order expansion $latex \[ x(t) = x^{(0)} + x^{(1)} * t + x^{(2)} * t^2 / 2 \]$$ It follows that for $latex k = 0 , 1 , 2$$, $latex \[ x^{(k)} = \dpow{k}{t} x (0) \] $$ $head Purpose$$ In general, a second order forward sweep is given the $cref/first order expansion/exp_2_for1/First Order Expansion/$$ for all of the variables in an operation sequence, and the second order derivatives for the independent variables. It uses these to compute the second order derivative, and thereby obtain the second order expansion, for all the variables in the operation sequence. $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_2.hpp$$ to compute $latex \[ f(x) = 1 + x + x^2 / 2 \] $$ The corresponding second derivative function is $latex \[ \Dpow{2}{x} f (x) = 1 \] $$ $head Operation Sequence$$ We consider the case where $cref exp_2.hpp$$ is executed with $latex x = .5$$. The corresponding operation sequence, zero order forward sweep values, and first order forward sweep values are inputs and are used by a second order forward sweep. $subhead Index$$ The Index column contains the index in the operation sequence of the corresponding atomic operation. A Forward sweep starts with the first operation and ends with the last. $subhead Zero$$ The Zero column contains the zero order sweep results for the corresponding variable in the operation sequence (see $cref/zero order sweep/exp_2_for0/Operation Sequence/Sweep/$$). $subhead Operation$$ The Operation column contains the first order sweep operation for this variable. $subhead First$$ The First column contains the first order sweep results for the corresponding variable in the operation sequence (see $cref/first order sweep/exp_2_for1/Operation Sequence/Sweep/$$). $subhead Derivative$$ The Derivative column contains the mathematical function corresponding to the second derivative with respect to $latex t$$, at $latex t = 0$$, for each variable in the sequence. $subhead Second$$ The Second column contains the second order derivatives for the corresponding variable in the operation sequence; i.e., the second order expansion for the $th i$$ variable is given by $latex \[ v_i (t) = v_i^{(0)} + v_i^{(1)} * t + v_i^{(2)} * t^2 / 2 \] $$ We use $latex x^{(0)} = 1$$, and $latex x^{(2)} = 0$$ so that second order differentiation with respect to $latex t$$, at $latex t = 0$$, is the same as the second partial differentiation with respect to $latex x$$ at $latex x = x^{(0)}$$. $subhead Sweep$$ $center $table $bold Index$$ $cnext $pre $$ $cnext $bold Zero$$ $cnext $pre $$ $cnext $bold Operation$$ $cnext $pre $$ $cnext $bold First$$ $cnext $pre $$ $cnext $bold Derivative$$ $cnext $pre $$ $cnext $bold Second$$ $rnext 1 $cnext $cnext 0.5 $cnext $pre $$ $cnext $latex v_1^{(1)} = x^{(1)} $$ $cnext $cnext 1 $cnext $cnext $latex v_1^{(2)} = x^{(2)}$$ $cnext $cnext $latex v_1^{(2)} = 0$$ $rnext 2 $cnext $cnext 1.5 $cnext $pre $$ $cnext $latex v_2^{(1)} = v_1^{(1)}$$ $cnext $cnext 1 $cnext $cnext $latex v_2^{(2)} = v_1^{(2)}$$ $cnext $cnext $latex v_2^{(2)} = 0$$ $rnext 3 $cnext $cnext 0.25 $cnext $pre $$ $cnext $latex v_3^{(1)} = 2 * v_1^{(0)} * v_1^{(1)}$$ $cnext $cnext 1 $cnext $cnext $latex v_3^{(2)} = 2 * (v_1^{(1)} * v_1^{(1)} + v_1^{(0)} * v_1^{(2)} )$$ $cnext $cnext $latex v_3^{(2)} = 2$$ $rnext 4 $cnext $cnext 0.125 $cnext $pre $$ $cnext $latex v_4^{(1)} = v_3^{(1)} / 2$$ $cnext $cnext .5 $cnext $cnext $latex v_4^{(2)} = v_3^{(2)} / 2$$ $cnext $cnext $latex v_4^{(2)} = 1$$ $rnext 5 $cnext $cnext 1.625 $cnext $pre $$ $cnext $latex v_5^{(1)} = v_2^{(1)} + v_4^{(1)}$$ $cnext $cnext 1.5 $cnext $cnext $latex v_5^{(2)} = v_2^{(2)} + v_4^{(2)}$$ $cnext $cnext $latex v_5^{(2)} = 1$$ $tend $$ $head Return Value$$ The second derivative of the return value for this case is $latex \[ \begin{array}{rcl} 1 & = & v_5^{(2)} = \left[ \Dpow{2}{t} v_5 \right]_{t=0} = \left[ \Dpow{2}{t} f( x^{(0)} + x^{(1)} * t ) \right]_{t=0} \\ & = & x^{(1)} * \Dpow{2}{x} f ( x^{(0)} ) * x^{(1)} = \Dpow{2}{x} f ( x^{(0)} ) \end{array} \] $$ (We have used the fact that $latex x^{(1)} = 1$$ and $latex x^{(2)} = 0$$.) $children% introduction/exp_apx/exp_2_for2.cpp %$$ $head Verification$$ The file $cref exp_2_for2.cpp$$ contains a routine which verifies the values computed above. It returns true for success and false for failure. $head Exercises$$ $list number$$ Which statement in the routine defined by $cref exp_2_for2.cpp$$ uses the values that are calculated by the routine defined by $cref exp_2_for1.cpp$$ ? $lnext Suppose that $latex x = .1$$, what are the results of a zero, first, and second order forward sweep for the operation sequence above; i.e., what are the corresponding values for $latex v_i^{(k)}$$ for $latex i = 1, \ldots , 5$$ and $latex k = 0, 1, 2$$. $lnext Create a modified version of $cref exp_2_for2.cpp$$ that verifies the derivative values from the previous exercise. Also create and run a main program that reports the result of calling the modified version of $cref exp_2_for2.cpp$$. $lend $end ------------------------------------------------------------------------------ $begin exp_2_rev2$$ $spell exp_2_rev $$ $section exp_2: Second Order Reverse Mode$$ $head Purpose$$ In general, a second order reverse sweep is given the $cref/first order expansion/exp_2_for1/First Order Expansion/$$ for all of the variables in an operation sequence. Given a choice of a particular variable, it computes the derivative, of that variables first order expansion coefficient, with respect to all of the independent variables. $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_2.hpp$$ to compute $latex \[ f(x) = 1 + x + x^2 / 2 \] $$ The corresponding second derivative is $latex \[ \Dpow{2}{x} f (x) = 1 \] $$ $head f_5$$ For our example, we chose to compute the derivative of $latex v_5^{(1)}$$ with respect to all the independent variable. For the case computed for the $cref/first order sweep/exp_2_for1/Operation Sequence/Sweep/$$, $latex v_5^{(1)}$$ is the derivative of the value returned by $cref exp_2.hpp$$. This the value computed will be the second derivative of the value returned by $cref exp_2.hpp$$. We begin with the function $latex f_5 $$ where $latex v_5^{(1)}$$ is both an argument and the value of the function; i.e., $latex \[ \begin{array}{rcl} f_5 \left( v_1^{(0)}, v_1^{(1)} , \ldots , v_5^{(0)} , v_5^{(1)} \right) & = & v_5^{(1)} \\ \D{f_5}{v_5^{(1)}} & = & 1 \end{array} \] $$ All the other partial derivatives of $latex f_5 $$ are zero. $head Index 5: f_4$$ Second order reverse mode starts with the last operation in the sequence. For the case in question, this is the operation with index 5. The zero and first order sweep representations of this operation are $latex \[ \begin{array}{rcl} v_5^{(0)} & = & v_2^{(0)} + v_4^{(0)} \\ v_5^{(1)} & = & v_2^{(1)} + v_4^{(1)} \end{array} \] $$ We define the function $latex f_4 \left( v_1^{(0)} , \ldots , v_4^{(1)} \right) $$ as equal to $latex f_5 $$ except that $latex v_5^{(0)} $$ and $latex v_5^{(1)}$$ are eliminated using this operation; i.e. $latex \[ f_4 = f_5 \left[ v_1^{(0)} , \ldots , v_4^{(1)} , v_5^{(0)} \left( v_2^{(0)} , v_4^{(0)} \right) , v_5^{(1)} \left( v_2^{(1)} , v_4^{(1)} \right) \right] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_4}{v_2^{(1)}} & = & \D{f_5}{v_2^{(1)}} + \D{f_5}{v_5^{(1)}} * \D{v_5^{(1)}}{v_2^{(1)}} & = 1 \\ \D{f_4}{v_4^{(1)}} & = & \D{f_5}{v_4^{(1)}} + \D{f_5}{v_5^{(1)}} * \D{v_5}{v_4^{(1)}} & = 1 \end{array} \] $$ All the other partial derivatives of $latex f_4$$ are zero. $head Index 4: f_3$$ The next operation has index 4, $latex \[ \begin{array}{rcl} v_4^{(0)} & = & v_3^{(0)} / 2 \\ v_4^{(1)} & = & v_3^{(1)} / 2 \end{array} \] $$ We define the function $latex f_3 \left( v_1^{(0)} , \ldots , v_3^{(1)} \right) $$ as equal to $latex f_4 $$ except that $latex v_4^{(0)}$$ and $latex v_4^{(1)}$$ are eliminated using this operation; i.e., $latex \[ f_3 = f_4 \left[ v_1^{(0)} , \ldots , v_3^{(1)} , v_4^{(0)} \left( v_3^{(0)} \right) , v_4^{(1)} \left( v_3^{(1)} \right) \right] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_3}{v_2^{(1)}} & = & \D{f_4}{v_2^{(1)}} & = 1 \\ \D{f_3}{v_3^{(1)}} & = & \D{f_4}{v_3^{(1)}} + \D{f_4}{v_4^{(1)}} * \D{v_4^{(1)}}{v_3^{(1)}} & = 0.5 \end{array} \] $$ All the other partial derivatives of $latex f_3$$ are zero. $head Index 3: f_2$$ The next operation has index 3, $latex \[ \begin{array}{rcl} v_3^{(0)} & = & v_1^{(0)} * v_1^{(0)} \\ v_3^{(1)} & = & 2 * v_1^{(0)} * v_1^{(1)} \end{array} \] $$ We define the function $latex f_2 \left( v_1^{(0)} , \ldots , v_2^{(1)} \right) $$ as equal to $latex f_3 $$ except that $latex v_3^{(0)} $$ and $latex v_3^{(1)}$$ are eliminated using this operation; i.e., $latex \[ f_2 = f_3 \left[ v_1^{(0)} , \ldots , v_2^{(1)} , v_3^{(0)} ( v_1^{(0)} ) , v_3^{(1)} ( v_1^{(0)} , v_1^{(1)} ) \right] \] $$ Note that, from the $cref/first order forward sweep/exp_2_for1/Operation Sequence/Sweep/$$, the value of $latex v_1^{(0)}$$ is equal to $latex .5$$ and $latex v_1^{(1)}$$ is equal 1. It follows that $latex \[ \begin{array}{rcll} \D{f_2}{v_1^{(0)}} & = & \D{f_3}{v_1^{(0)}} + \D{f_3}{v_3^{(0)}} * \D{v_3^{(0)}}{v_1^{(0)}} + \D{f_3}{v_3^{(1)}} * \D{v_3^{(1)}}{v_1^{(0)}} & = 1 \\ \D{f_2}{v_1^{(1)}} & = & \D{f_3}{v_1^{(1)}} + \D{f_3}{v_3^{(1)}} * \D{v_3^{(1)}}{v_1^{(1)}} & = 0.5 \\ \D{f_2}{v_2^{(0)}} & = & \D{f_3}{v_2^{(0)}} & = 0 \\ \D{f_2}{v_2^{(1)}} & = & \D{f_3}{v_2^{(1)}} & = 1 \end{array} \] $$ $head Index 2: f_1$$ The next operation has index 2, $latex \[ \begin{array}{rcl} v_2^{(0)} & = & 1 + v_1^{(0)} \\ v_2^{(1)} & = & v_1^{(1)} \end{array} \] $$ We define the function $latex f_1 ( v_1^{(0)} , v_1^{(1)} ) $$ as equal to $latex f_2 $$ except that $latex v_2^{(0)} $$ and $latex v_2^{(1)} $$ are eliminated using this operation; i.e., $latex \[ f_1 = f_2 \left[ v_1^{(0)} , v_1^{(1)} , v_2^{(0)} ( v_1^{(0)} ) , v_2^{(1)} ( v_1^{(1)} ) \right] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_1}{v_1^{(0)}} & = & \D{f_2}{v_1^{(0)}} + \D{f_2}{v_2^{(0)}} * \D{v_2^{(0)}}{v_1^{(0)}} & = 1 \\ \D{f_1}{v_1^{(1)}} & = & \D{f_2}{v_1^{(1)}} + \D{f_2}{v_2^{(1)}} * \D{v_2^{(1)}}{v_1^{(1)}} & = 1.5 \end{array} \] $$ Note that $latex v_1$$ is equal to $latex x$$, so the second derivative of the function defined by $cref exp_2.hpp$$ at $latex x = .5$$ is given by $latex \[ \Dpow{2}{x} v_5^{(0)} = \D{ v_5^{(1)} }{x} = \D{ v_5^{(1)} }{v_1^{(0)}} = \D{f_1}{v_1^{(0)}} = 1 \] $$ There is a theorem about Algorithmic Differentiation that explains why the other partial of $latex f_1$$ is equal to the first derivative of the function defined by $cref exp_2.hpp$$ at $latex x = .5$$. $children% introduction/exp_apx/exp_2_rev2.cpp %$$ $head Verification$$ The file $cref exp_2_rev2.cpp$$ contains a routine which verifies the values computed above. It returns true for success and false for failure. It only tests the partial derivatives of $latex f_j$$ that might not be equal to the corresponding partials of $latex f_{j+1}$$; i.e., the other partials of $latex f_j$$ must be equal to the corresponding partials of $latex f_{j+1}$$. $head Exercises$$ $list number$$ Which statement in the routine defined by $cref exp_2_rev2.cpp$$ uses the values that are calculated by the routine defined by $cref exp_2_for0.cpp$$ ? Which statements use values that are calculate by the routine defined in $cref exp_2_for1.cpp$$ ? $lnext Consider the case where $latex x = .1$$ and we first preform a zero order forward sweep, then a first order sweep, for the operation sequence used above. What are the results of a second order reverse sweep; i.e., what are the corresponding derivatives of $latex f_5 , f_4 , \ldots , f_1$$. $lnext Create a modified version of $cref exp_2_rev2.cpp$$ that verifies the values you obtained for the previous exercise. Also create and run a main program that reports the result of calling the modified version of $cref exp_2_rev2.cpp$$. $lend $end ------------------------------------------------------------------------------ cppad-20170000.3/introduction/exp_apx/exp_2.hpp0000644000175200017650000001007613057470463020352 0ustar coincoin-web// $Id: exp_2.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_INTRODUCTION_EXP_APX_EXP_2_HPP # define CPPAD_INTRODUCTION_EXP_APX_EXP_2_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_2$$ $spell cppad-%yyyymmdd% hpp Apx cpp const exp bool $$ $section Second Order Exponential Approximation$$ $mindex exp_2 example algorithm$$ $head Syntax$$ $codei%# include "exp_2.hpp"%$$ $pre $$ $icode%y% = exp_2(%x%)%$$ $head Purpose$$ This is a simple example algorithm that is used to demonstrate Algorithmic Differentiation (see $cref exp_eps$$ for a more complex example). $head Mathematical Form$$ The exponential function can be defined by $latex \[ \exp (x) = 1 + x^1 / 1 ! + x^2 / 2 ! + \cdots \] $$ The second order approximation for the exponential function is $latex \[ {\rm exp\_2} (x) = 1 + x + x^2 / 2 \] $$ $head include$$ The include command in the syntax is relative to $codei% cppad-%yyyymmdd%/introduction/exp_apx %$$ where $codei%cppad-%yyyymmdd%$$ is the distribution directory created during the beginning steps of the $cref%installation%Install%$$ of CppAD. $head x$$ The argument $icode x$$ has prototype $codei% const %Type% &%x% %$$ (see $icode Type$$ below). It specifies the point at which to evaluate the approximation for the second order exponential approximation. $head y$$ The result $icode y$$ has prototype $codei% %Type% %y% %$$ It is the value of the exponential function approximation defined above. $head Type$$ If $icode u$$ and $icode v$$ are $icode Type$$ objects and $icode i$$ is an $code int$$: $table $bold Operation$$ $cnext $bold Result Type$$ $cnext $bold Description$$ $rnext $icode%Type%(%i%)%$$ $cnext $icode Type$$ $cnext construct object with value equal to $icode i$$ $rnext $icode%Type u %=% v%$$ $cnext $icode Type$$ $cnext construct $icode u$$ with value equal to $icode v$$ $rnext $icode%u% * %v%$$ $cnext $icode Type$$ $cnext result is value of $latex u * v$$ $rnext $icode%u% / %v%$$ $cnext $icode Type$$ $cnext result is value of $latex u / v$$ $rnext $icode%u% + %v%$$ $cnext $icode Type$$ $cnext result is value of $latex u + v$$ $tend $childtable% introduction/exp_apx/exp_2.omh% introduction/exp_apx/exp_2_cppad.cpp %$$ $head Implementation$$ The file $cref exp_2.hpp$$ contains a C++ implementation of this function. $head Test$$ The file $cref exp_2.cpp$$ contains a test of this implementation. It returns true for success and false for failure. $head Exercises$$ $list number$$ Suppose that we make the call $codep double x = .1; double y = exp_2(x); $$ What is the value assigned to $code v1$$, $code v2$$, ... ,$code v5$$ in $cref exp_2.hpp$$ ? $lnext Extend the routine $code exp_2.hpp$$ to a routine $code exp_3.hpp$$ that computes $latex \[ 1 + x^2 / 2 ! + x^3 / 3 ! \] $$ Do this in a way that only assigns one value to each variable (as $code exp_2$$ does). $lnext Suppose that we make the call $codep double x = .5; double y = exp_3(x); $$ using $code exp_3$$ created in the previous problem. What is the value assigned to the new variables in $code exp_3$$ (variables that are in $code exp_3$$ and not in $code exp_2$$) ? $lend $end ------------------------------------------------------------------------------ */ // BEGIN C++ template Type exp_2(const Type &x) { Type v1 = x; // v1 = x Type v2 = Type(1) + v1; // v2 = 1 + x Type v3 = v1 * v1; // v3 = x^2 Type v4 = v3 / Type(2); // v4 = x^2 / 2 Type v5 = v2 + v4; // v5 = 1 + x + x^2 / 2 return v5; // exp_2(x) = 1 + x + x^2 / 2 } // END C++ # endif cppad-20170000.3/introduction/exp_apx/main.cpp0000644000175200017650000000573713057470463020264 0ustar coincoin-web// $Id: main.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_apx_main.cpp$$ $spell Cpp exp_eps apx $$ $section Correctness Tests For Exponential Approximation in Introduction$$ $mindex exp_apx main run$$ $head Running Tests$$ To build this program and run its correctness tests see $cref cmake_check$$. $head main.cpp$$ $code $srcfile%introduction/exp_apx/main.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ // system include files used for I/O # include // external complied tests extern bool exp_2(void); extern bool exp_2_cppad(void); extern bool exp_2_for1(void); extern bool exp_2_for2(void); extern bool exp_2_rev1(void); extern bool exp_2_rev2(void); extern bool exp_2_for0(void); extern bool exp_eps(void); extern bool exp_eps_cppad(void); extern bool exp_eps_for1(void); extern bool exp_eps_for2(void); extern bool exp_eps_for0(void); extern bool exp_eps_rev1(void); extern bool exp_eps_rev2(void); namespace { static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), std::string name) { bool ok = true; std::streamsize width = 20; std::cout.width( width ); std::cout.setf( std::ios_base::left ); std::cout << name.c_str(); // ok &= name.size() < size_t(width); ok &= TestOk(); if( ok ) { std::cout << "OK" << std::endl; Run_ok_count++; } else { std::cout << "Error" << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; using namespace std; // This comment is used by OneTest // external compiled tests ok &= Run( exp_2, "exp_2" ); ok &= Run( exp_2_cppad, "exp_2_cppad" ); ok &= Run( exp_2_for0, "exp_2_for0" ); ok &= Run( exp_2_for1, "exp_2_for1" ); ok &= Run( exp_2_for2, "exp_2_for2" ); ok &= Run( exp_2_rev1, "exp_2_rev1" ); ok &= Run( exp_2_rev2, "exp_2_rev2" ); ok &= Run( exp_eps, "exp_eps" ); ok &= Run( exp_eps_cppad, "exp_eps_cppad" ); ok &= Run( exp_eps_for0, "exp_eps_for0" ); ok &= Run( exp_eps_for1, "exp_eps_for1" ); ok &= Run( exp_eps_for2, "exp_eps_for2" ); ok &= Run( exp_eps_rev1, "exp_eps_rev1" ); ok &= Run( exp_eps_rev2, "exp_eps_rev2" ); if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! ok ); } // END C++ cppad-20170000.3/introduction/exp_apx/exp_2_cppad.cpp0000644000175200017650000000775213057470463021523 0ustar coincoin-web// $Id: exp_2_cppad.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_2_cppad$$ $spell Taylor coef resize cppad.hpp cmath fabs bool exp_2_cppad dx dy dw endl hpp http org std www CppAD apx $$ $section exp_2: CppAD Forward and Reverse Sweeps$$. $head Purpose$$ Use CppAD forward and reverse modes to compute the partial derivative with respect to $latex x$$, at the point $latex x = .5$$, of the function $codei% exp_2(%x%) %$$ as defined by the $cref exp_2.hpp$$ include file. $head Exercises$$ $list number$$ Create and test a modified version of the routine below that computes the same order derivatives with respect to $latex x$$, at the point $latex x = .1$$ of the function $codei% exp_2(%x%) %$$ $lnext Create a routine called $codei% exp_3(%x%) %$$ that evaluates the function $latex \[ f(x) = 1 + x^2 / 2 + x^3 / 6 \] $$ Test a modified version of the routine below that computes the derivative of $latex f(x)$$ at the point $latex x = .5$$. $lend $srccode%cpp% */ # include // http://www.coin-or.org/CppAD/ # include "exp_2.hpp" // second order exponential approximation bool exp_2_cppad(void) { bool ok = true; using CppAD::AD; using CppAD::vector; // can use any simple vector template class using CppAD::NearEqual; // checks if values are nearly equal // domain space vector size_t n = 1; // dimension of the domain space vector< AD > X(n); X[0] = .5; // value of x for this operation sequence // declare independent variables and start recording operation sequence CppAD::Independent(X); // evaluate our exponential approximation AD x = X[0]; AD apx = exp_2(x); // range space vector size_t m = 1; // dimension of the range space vector< AD > Y(m); Y[0] = apx; // variable that represents only range space component // Create f: X -> Y corresponding to this operation sequence // and stop recording. This also executes a zero order forward // sweep using values in X for x. CppAD::ADFun f(X, Y); // first order forward sweep that computes // partial of exp_2(x) with respect to x vector dx(n); // differential in domain space vector dy(m); // differential in range space dx[0] = 1.; // direction for partial derivative dy = f.Forward(1, dx); double check = 1.5; ok &= NearEqual(dy[0], check, 1e-10, 1e-10); // first order reverse sweep that computes the derivative vector w(m); // weights for components of the range vector dw(n); // derivative of the weighted function w[0] = 1.; // there is only one weight dw = f.Reverse(1, w); // derivative of w[0] * exp_2(x) check = 1.5; // partial of exp_2(x) with respect to x ok &= NearEqual(dw[0], check, 1e-10, 1e-10); // second order forward sweep that computes // second partial of exp_2(x) with respect to x vector x2(n); // second order Taylor coefficients vector y2(m); x2[0] = 0.; // evaluate second partial .w.r.t. x y2 = f.Forward(2, x2); check = 0.5 * 1.; // Taylor coef is 1/2 second derivative ok &= NearEqual(y2[0], check, 1e-10, 1e-10); // second order reverse sweep that computes // derivative of partial of exp_2(x) w.r.t. x dw.resize(2 * n); // space for first and second derivatives dw = f.Reverse(2, w); check = 1.; // result should be second derivative ok &= NearEqual(dw[0*2+1], check, 1e-10, 1e-10); return ok; } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/makefile.am0000644000175200017650000000241413057470463020715 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # # Microsoft project files EXTRA_DIST = \ exp_2.omh \ exp_eps.omh # check_PROGRAMS = exp_apx # AM_CPPFLAGS = -I. -I$(top_srcdir) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) AM_CXXFLAGS = -g $(CXX_FLAGS) # exp_apx_SOURCES = \ main.cpp \ exp_2.cpp \ exp_2.hpp \ exp_2_cppad.cpp \ exp_2_for1.cpp \ exp_2_for2.cpp \ exp_2_rev1.cpp \ exp_2_rev2.cpp \ exp_2_for0.cpp \ exp_eps.cpp \ exp_eps.hpp \ exp_eps_cppad.cpp \ exp_eps_for1.cpp \ exp_eps_for2.cpp \ exp_eps_for0.cpp \ exp_eps_rev1.cpp \ exp_eps_rev2.cpp test: check ./exp_apx cppad-20170000.3/introduction/exp_apx/exp_eps_for0.cpp0000644000175200017650000000335613057470463021724 0ustar coincoin-web// $Id: exp_eps_for0.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_eps_for0.cpp$$ $spell std exp_eps_seq cmath bool fabs $$ $section exp_eps: Verify Zero Order Forward Sweep$$ $mindex exp_eps$$ $srccode%cpp% */ # include // for fabs function bool exp_eps_for0(double *v0) // double v0[8] { bool ok = true; double x = .5; v0[1] = x; // abs_x = x; ok &= std::fabs( v0[1] - 0.5) < 1e-10; v0[2] = 1. * v0[1]; // temp = term * abs_x; ok &= std::fabs( v0[2] - 0.5) < 1e-10; v0[3] = v0[2] / 1.; // term = temp / Type(k); ok &= std::fabs( v0[3] - 0.5) < 1e-10; v0[4] = 1. + v0[3]; // sum = sum + term; ok &= std::fabs( v0[4] - 1.5) < 1e-10; v0[5] = v0[3] * v0[1]; // temp = term * abs_x; ok &= std::fabs( v0[5] - 0.25) < 1e-10; v0[6] = v0[5] / 2.; // term = temp / Type(k); ok &= std::fabs( v0[6] - 0.125) < 1e-10; v0[7] = v0[4] + v0[6]; // sum = sum + term; ok &= std::fabs( v0[7] - 1.625) < 1e-10; return ok; } bool exp_eps_for0(void) { double v0[8]; return exp_eps_for0(v0); } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/exp_eps_for1.cpp0000644000175200017650000000361413057470463021722 0ustar coincoin-web// $Id: exp_eps_for1.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_eps_for1.cpp$$ $spell std vars exp_eps_for cmath fabs bool $$ $section exp_eps: Verify First Order Forward Sweep$$ $mindex exp_2$$ $srccode%cpp% */ # include // for fabs function extern bool exp_eps_for0(double *v0); // computes zero order forward sweep bool exp_eps_for1(double *v1) // double v[8] { bool ok = true; double v0[8]; // set the value of v0[j] for j = 1 , ... , 7 ok &= exp_eps_for0(v0); v1[1] = 1.; // v1 = x ok &= std::fabs( v1[1] - 1. ) <= 1e-10; v1[2] = 1. * v1[1]; // v2 = 1 * v1 ok &= std::fabs( v1[2] - 1. ) <= 1e-10; v1[3] = v1[2] / 1.; // v3 = v2 / 1 ok &= std::fabs( v1[3] - 1. ) <= 1e-10; v1[4] = v1[3]; // v4 = 1 + v3 ok &= std::fabs( v1[4] - 1. ) <= 1e-10; v1[5] = v1[3] * v0[1] + v0[3] * v1[1]; // v5 = v3 * v1 ok &= std::fabs( v1[5] - 1. ) <= 1e-10; v1[6] = v1[5] / 2.; // v6 = v5 / 2 ok &= std::fabs( v1[6] - 0.5 ) <= 1e-10; v1[7] = v1[4] + v1[6]; // v7 = v4 + v6 ok &= std::fabs( v1[7] - 1.5 ) <= 1e-10; return ok; } bool exp_eps_for1(void) { double v1[8]; return exp_eps_for1(v1); } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/exp_eps_for2.cpp0000644000175200017650000000370213057470463021721 0ustar coincoin-web// $Id: exp_eps_for2.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_eps_for2.cpp$$ $spell std vars exp_eps_for cmath fabs bool $$ $section exp_eps: Verify Second Order Forward Sweep$$ $mindex first exp_2$$ $srccode%cpp% */ # include // for fabs function extern bool exp_eps_for0(double *v0); // computes zero order forward sweep extern bool exp_eps_for1(double *v1); // computes first order forward sweep bool exp_eps_for2(void) { bool ok = true; double v0[8], v1[8], v2[8]; // set the value of v0[j], v1[j] for j = 1 , ... , 7 ok &= exp_eps_for0(v0); ok &= exp_eps_for1(v1); v2[1] = 0.; // v1 = x ok &= std::fabs( v2[1] - 0. ) <= 1e-10; v2[2] = 1. * v2[1]; // v2 = 1 * v1 ok &= std::fabs( v2[2] - 0. ) <= 1e-10; v2[3] = v2[2] / 1.; // v3 = v2 / 1 ok &= std::fabs( v2[3] - 0. ) <= 1e-10; v2[4] = v2[3]; // v4 = 1 + v3 ok &= std::fabs( v2[4] - 0. ) <= 1e-10; v2[5] = v2[3] * v0[1] + 2. * v1[3] * v1[1] // v5 = v3 * v1 + v0[3] * v2[1]; ok &= std::fabs( v2[5] - 2. ) <= 1e-10; v2[6] = v2[5] / 2.; // v6 = v5 / 2 ok &= std::fabs( v2[6] - 1. ) <= 1e-10; v2[7] = v2[4] + v2[6]; // v7 = v4 + v6 ok &= std::fabs( v2[7] - 1. ) <= 1e-10; return ok; } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/CMakeLists.txt0000644000175200017650000000306213057470463021361 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the introduction/exp_apx directory tests # Specifies build type for this directory. Possible values are # empty, Debug, Release, RelWithDebInfo and MinSizeRel SET(CMAKE_BUILD_TYPE DEBUG) # ADD_EXECUTABLE(introduction_exp_apx EXCLUDE_FROM_ALL main.cpp exp_2.cpp exp_2.hpp exp_2_cppad.cpp exp_2_for1.cpp exp_2_for2.cpp exp_2_rev1.cpp exp_2_rev2.cpp exp_2_for0.cpp exp_eps.cpp exp_eps.hpp exp_eps_cppad.cpp exp_eps_for1.cpp exp_eps_for2.cpp exp_eps_for0.cpp exp_eps_rev1.cpp exp_eps_rev2.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( introduction_exp_apx ) # Add this check target ADD_CUSTOM_TARGET(check_introduction_exp_apx introduction_exp_apx DEPENDS introduction_exp_apx ) MESSAGE(STATUS "make check_introduction_exp_apx: available") # Change check depends in parent environment add_to_list(check_introduction_depends check_introduction_exp_apx) SET(check_introduction_depends "${check_introduction_depends}" PARENT_SCOPE) cppad-20170000.3/introduction/exp_apx/exp_eps_rev1.cpp0000644000175200017650000000422513057470463021727 0ustar coincoin-web// $Id: exp_eps_rev1.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_eps_rev1.cpp$$ $spell cstddef cmath vars ir iq ir ia df exp_eps_rev bool std fabs $$ $section exp_eps: Verify First Order Reverse Sweep$$ $mindex exp_eps$$ $srccode%cpp% */ # include // define size_t # include // for fabs function extern bool exp_eps_for0(double *v0); // computes zero order forward sweep bool exp_eps_rev1(void) { bool ok = true; // set the value of v0[j] for j = 1 , ... , 7 double v0[8]; ok &= exp_eps_for0(v0); // initial all partial derivatives as zero double f_v[8]; size_t j; for(j = 0; j < 8; j++) f_v[j] = 0.; // set partial derivative for f7 f_v[7] = 1.; ok &= std::fabs( f_v[7] - 1. ) <= 1e-10; // f7_v7 // f6( v1 , v2 , v3 , v4 , v5 , v6 ) f_v[4] += f_v[7] * 1.; f_v[6] += f_v[7] * 1.; ok &= std::fabs( f_v[4] - 1. ) <= 1e-10; // f6_v4 ok &= std::fabs( f_v[6] - 1. ) <= 1e-10; // f6_v6 // f5( v1 , v2 , v3 , v4 , v5 ) f_v[5] += f_v[6] / 2.; ok &= std::fabs( f_v[5] - 0.5 ) <= 1e-10; // f5_v5 // f4( v1 , v2 , v3 , v4 ) f_v[1] += f_v[5] * v0[3]; f_v[3] += f_v[5] * v0[1]; ok &= std::fabs( f_v[1] - 0.25) <= 1e-10; // f4_v1 ok &= std::fabs( f_v[3] - 0.25) <= 1e-10; // f4_v3 // f3( v1 , v2 , v3 ) f_v[3] += f_v[4] * 1.; ok &= std::fabs( f_v[3] - 1.25) <= 1e-10; // f3_v3 // f2( v1 , v2 ) f_v[2] += f_v[3] / 1.; ok &= std::fabs( f_v[2] - 1.25) <= 1e-10; // f2_v2 // f1( v1 ) f_v[1] += f_v[2] * 1.; ok &= std::fabs( f_v[1] - 1.5 ) <= 1e-10; // f1_v2 return ok; } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/makefile.in0000644000175200017650000005106313057470463020732 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; the Free Software Foundation # gives unlimited permission to copy and/or distribute it, # with or without modifications, as long as this notice is preserved. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY, to the extent permitted by law; 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_eps_rev2.cpp$$ $spell cstddef cmath vars ir iq ir ia df exp_eps_rev bool std fabs $$ $section exp_eps: Verify Second Order Reverse Sweep$$ $mindex exp_eps$$ $srccode%cpp% */ # include // define size_t # include // for fabs function extern bool exp_eps_for0(double *v0); // computes zero order forward sweep extern bool exp_eps_for1(double *v1); // computes first order forward sweep bool exp_eps_rev2(void) { bool ok = true; // set the value of v0[j], v1[j] for j = 1 , ... , 7 double v0[8], v1[8]; ok &= exp_eps_for0(v0); ok &= exp_eps_for1(v1); // initial all partial derivatives as zero double f_v0[8], f_v1[8]; size_t j; for(j = 0; j < 8; j++) { f_v0[j] = 0.; f_v1[j] = 0.; } // set partial derivative for f_7 f_v1[7] = 1.; ok &= std::fabs( f_v1[7] - 1. ) <= 1e-10; // partial f_7 w.r.t. v_7^1 // f_6 = f_7( v_1^0 , ... , v_6^1 , v_4^0 + v_6^0, v_4^1 , v_6^1 ) f_v0[4] += f_v0[7]; f_v0[6] += f_v0[7]; f_v1[4] += f_v1[7]; f_v1[6] += f_v1[7]; ok &= std::fabs( f_v0[4] - 0. ) <= 1e-10; // partial f_6 w.r.t. v_4^0 ok &= std::fabs( f_v0[6] - 0. ) <= 1e-10; // partial f_6 w.r.t. v_6^0 ok &= std::fabs( f_v1[4] - 1. ) <= 1e-10; // partial f_6 w.r.t. v_4^1 ok &= std::fabs( f_v1[6] - 1. ) <= 1e-10; // partial f_6 w.r.t. v_6^1 // f_5 = f_6( v_1^0 , ... , v_5^1 , v_5^0 / 2 , v_5^1 / 2 ) f_v0[5] += f_v0[6] / 2.; f_v1[5] += f_v1[6] / 2.; ok &= std::fabs( f_v0[5] - 0. ) <= 1e-10; // partial f_5 w.r.t. v_5^0 ok &= std::fabs( f_v1[5] - 0.5 ) <= 1e-10; // partial f_5 w.r.t. v_5^1 // f_4 = f_5( v_1^0 , ... , v_4^1 , v_3^0 * v_1^0 , // v_3^1 * v_1^0 + v_3^0 * v_1^1 ) f_v0[1] += f_v0[5] * v0[3] + f_v1[5] * v1[3]; f_v0[3] += f_v0[5] * v0[1] + f_v1[5] * v1[1]; f_v1[1] += f_v1[5] * v0[3]; f_v1[3] += f_v1[5] * v0[1]; ok &= std::fabs( f_v0[1] - 0.5 ) <= 1e-10; // partial f_4 w.r.t. v_1^0 ok &= std::fabs( f_v0[3] - 0.5 ) <= 1e-10; // partial f_4 w.r.t. v_3^0 ok &= std::fabs( f_v1[1] - 0.25 ) <= 1e-10; // partial f_4 w.r.t. v_1^1 ok &= std::fabs( f_v1[3] - 0.25 ) <= 1e-10; // partial f_4 w.r.t. v_3^1 // f_3 = f_4( v_1^0 , ... , v_3^1 , 1 + v_3^0 , v_3^1 ) f_v0[3] += f_v0[4]; f_v1[3] += f_v1[4]; ok &= std::fabs( f_v0[3] - 0.5 ) <= 1e-10; // partial f_3 w.r.t. v_3^0 ok &= std::fabs( f_v1[3] - 1.25) <= 1e-10; // partial f_3 w.r.t. v_3^1 // f_2 = f_3( v_1^0 , ... , v_2^1 , v_2^0 , v_2^1 ) f_v0[2] += f_v0[3]; f_v1[2] += f_v1[3]; ok &= std::fabs( f_v0[2] - 0.5 ) <= 1e-10; // partial f_2 w.r.t. v_2^0 ok &= std::fabs( f_v1[2] - 1.25) <= 1e-10; // partial f_2 w.r.t. v_2^1 // f_1 = f_2 ( v_1^0 , v_2^0 , v_1^0 , v_2^0 ) f_v0[1] += f_v0[2]; f_v1[1] += f_v1[2]; ok &= std::fabs( f_v0[1] - 1. ) <= 1e-10; // partial f_1 w.r.t. v_1^0 ok &= std::fabs( f_v1[1] - 1.5 ) <= 1e-10; // partial f_1 w.r.t. v_1^1 return ok; } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/exp_2_for0.cpp0000644000175200017650000000272713057470463021277 0ustar coincoin-web// $Id: exp_2_for0.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_2_for0.cpp$$ $spell std exp_2_seq cmath bool fabs $$ $section exp_2: Verify Zero Order Forward Sweep$$ $mindex exp_2$$ $srccode%cpp% */ # include // for fabs function bool exp_2_for0(double *v0) // double v0[6] { bool ok = true; double x = .5; v0[1] = x; // v1 = x ok &= std::fabs( v0[1] - 0.5) < 1e-10; v0[2] = 1. + v0[1]; // v2 = 1 + v1 ok &= std::fabs( v0[2] - 1.5) < 1e-10; v0[3] = v0[1] * v0[1]; // v3 = v1 * v1 ok &= std::fabs( v0[3] - 0.25) < 1e-10; v0[4] = v0[3] / 2.; // v4 = v3 / 2 ok &= std::fabs( v0[4] - 0.125) < 1e-10; v0[5] = v0[2] + v0[4]; // v5 = v2 + v4 ok &= std::fabs( v0[5] - 1.625) < 1e-10; return ok; } bool exp_2_for0(void) { double v0[6]; return exp_2_for0(v0); } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/exp_eps.cpp0000644000175200017650000000167013057470463020773 0ustar coincoin-web// $Id: exp_eps.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN C++ # include // for fabs function # include "exp_eps.hpp" // definition of exp_eps algorithm bool exp_eps(void) { double x = .5; double epsilon = .2; double check = 1 + .5 + .125; // include 1 term less than epsilon bool ok = std::fabs( exp_eps(x, epsilon) - check ) <= 1e-10; return ok; } // END C++ cppad-20170000.3/introduction/exp_apx/exp_eps.omh0000644000175200017650000010077713057470463021004 0ustar coincoin-web$Id: exp_eps.omh 3788 2016-02-09 15:50:06Z bradbell $ ---------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. ----------------------------------------------------------------------------- $begin exp_eps.hpp$$ $spell exp_eps $$ $section exp_eps: Implementation$$ $mindex exp_eps$$ $code $srcfile%introduction/exp_apx/exp_eps.hpp%0%// BEGIN C++%// END C++%$$ $$ $end ----------------------------------------------------------------------------- $begin exp_eps.cpp$$ $spell exp_eps $$ $section exp_eps: Test of exp_eps$$ $code $srcfile%introduction/exp_apx/exp_eps.cpp%0%// BEGIN C++%// END C++%$$ $$ $end ----------------------------------------------------------------------------- $begin exp_eps_for0$$ $spell cpp exp_eps_seq bool $$ $section exp_eps: Operation Sequence and Zero Order Forward Sweep$$ $mindex example$$ $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_eps.hpp$$ to compute $codei%exp_eps(%x%, %epsilon%)%$$ with $icode x$$ is equal to .5 and $icode epsilon$$ is equal to .2. For this case, the mathematical form for the operation sequence corresponding to the $code exp_eps$$ is $latex \[ f( x , \varepsilon ) = 1 + x + x^2 / 2 \] $$ Note that, for these particular values of $icode x$$ and $icode epsilon$$, this is the same as the mathematical form for $cref/exp_2/exp_2_for0/Mathematical Form/$$. $head Operation Sequence$$ We consider the $cref/operation sequence/glossary/Operation/Sequence/$$ corresponding to the algorithm $cref exp_eps.hpp$$ with the argument $icode x$$ is equal to .5 and $icode epsilon$$ is equal to .2. $subhead Variable$$ We refer to values that depend on the input variables $icode x$$ and $icode epsilon$$ as variables. $subhead Parameter$$ We refer to values that do not depend on the input variables $icode x$$ or $icode epsilon$$ as parameters. Operations where the result is a parameter are not included in the zero order sweep below. $subhead Index$$ The Index column contains the index in the operation sequence of the corresponding atomic operation and variable. A Forward sweep starts with the first operation and ends with the last. $subhead Code$$ The Code column contains the C++ source code corresponding to the corresponding atomic operation in the sequence. $subhead Operation$$ The Operation column contains the mathematical function corresponding to each atomic operation in the sequence. $subhead Zero Order$$ The Zero Order column contains the $cref/zero order derivative/exp_2_for0/Zero Order Expansion/$$ for the corresponding variable in the operation sequence. Forward mode refers to the fact that these coefficients are computed in the same order as the original algorithm; i.e., in order of increasing index. $subhead Sweep$$ $center $table $bold Index$$ $cnext $pre $$ $cnext $bold Code$$ $cnext $pre $$ $cnext $bold Operation$$ $cnext $pre $$ $cnext $bold Zero Order$$ $rnext 1 $cnext $pre $$ $cnext $code abs_x = x;$$ $cnext $cnext $latex v_1 = x $$ $cnext $cnext $latex v_1^{(0)} = 0.5$$ $rnext 2 $cnext $pre $$ $cnext $code temp = term * abs_x;$$ $cnext $cnext $latex v_2 = 1 * v_1 $$ $cnext $cnext $latex v_2^{(0)} = 0.5$$ $rnext 3 $cnext $pre $$ $cnext $code term = temp / Type(k);$$ $cnext $cnext $latex v_3 = v_2 / 1$$ $cnext $cnext $latex v_3^{(0)} = 0.5$$ $rnext 4 $cnext $pre $$ $cnext $code sum = sum + term;$$ $cnext $cnext $latex v_4 = 1 + v_3 $$ $cnext $cnext $latex v_4^{(0)} = 1.5$$ $rnext 5 $cnext $pre $$ $cnext $code temp = term * abs_x;$$ $cnext $cnext $latex v_5 = v_3 * v_1 $$ $cnext $cnext $latex v_5^{(0)} = 0.25$$ $rnext 6 $cnext $pre $$ $cnext $code term = temp / Type(k);$$ $cnext $cnext $latex v_6 = v_5 / 2$$ $cnext $cnext $latex v_6^{(0)} = 0.125$$ $rnext 7 $cnext $pre $$ $cnext $code sum = sum + term;$$ $cnext $cnext $latex v_7 = v_4 + v_6 $$ $cnext $cnext $latex v_7^{(0)} = 1.625$$ $tend $$ $head Return Value$$ The return value for this case is $latex \[ 1.625 = v_7^{(0)} = f ( x^{(0)} , \varepsilon^{(0)} ) \] $$ $head Comparisons$$ If $icode x$$ were negative, or if $icode epsilon$$ were a much smaller or much larger value, the results of the following comparisons could be different: $codep if( Type(0) > x ) while(term > epsilon) $$ This in turn would result in a different operation sequence. Thus the operation sequence above only corresponds to $cref exp_eps.hpp$$ for values of $icode x$$ and $icode epsilon$$ within a certain range. Note that there is a neighborhood of $latex x = 0.5$$ for which the comparisons would have the same result and hence the operation sequence would be the same. $children% introduction/exp_apx/exp_eps_for0.cpp %$$ $head Verification$$ The file $cref exp_eps_for0.cpp$$ contains a routine that verifies the values computed above. It returns true for success and false for failure. $head Exercises$$ $list number$$ Suppose that $latex x^{(0)} = .1$$, what is the result of a zero order forward sweep for the operation sequence above; i.e., what are the corresponding values for $latex v_1^{(0)} , v_2^{(0)} , \ldots , v_7^{(0)}$$. $lnext Create a modified version of $cref exp_eps_for0.cpp$$ that verifies the values you obtained for the previous exercise. $lnext Create and run a main program that reports the result of calling the modified version of $cref exp_eps_for0.cpp$$ in the previous exercise. $lend $end ----------------------------------------------------------------------------- $begin exp_eps_for1$$ $spell exp_eps_for $$ $section exp_eps: First Order Forward Sweep$$ $head First Order Expansion$$ We define $latex x(t)$$ and $latex \varepsilon(t) ]$$ near $latex t = 0$$ by the first order expansions $latex \[ \begin{array}{rcl} x(t) & = & x^{(0)} + x^{(1)} * t \\ \varepsilon(t) & = & \varepsilon^{(0)} + \varepsilon^{(1)} * t \end{array} \]$$ It follows that $latex x^{(0)}$$ ($latex \varepsilon^{(0)}$$) is the zero, and $latex x^{(1)}$$ ($latex \varepsilon^{(1)}$$) the first, order derivative of $latex x(t)$$ at $latex t = 0$$ ($latex \varepsilon (t)$$) at $latex t = 0$$. $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_eps.hpp$$ to compute $codei%exp_eps(%x%, %epsilon%)%$$ with $icode x$$ is equal to .5 and $icode epsilon$$ is equal to .2. For this case, the mathematical function for the operation sequence corresponding to $code exp_eps$$ is $latex \[ f ( x , \varepsilon ) = 1 + x + x^2 / 2 \] $$ The corresponding partial derivative with respect to $latex x$$, and the value of the derivative, are $latex \[ \partial_x f ( x , \varepsilon ) = 1 + x = 1.5 \] $$ $head Operation Sequence$$ $subhead Index$$ The Index column contains the index in the operation sequence of the corresponding atomic operation. A Forward sweep starts with the first operation and ends with the last. $subhead Operation$$ The Operation column contains the mathematical function corresponding to each atomic operation in the sequence. $subhead Zero Order$$ The Zero Order column contains the zero order derivatives for the corresponding variable in the operation sequence (see $cref/zero order sweep/exp_2_for1/Operation Sequence/Sweep/$$). $subhead Derivative$$ The Derivative column contains the mathematical function corresponding to the derivative with respect to $latex t$$, at $latex t = 0$$, for each variable in the sequence. $subhead First Order$$ The First Order column contains the first order derivatives for the corresponding variable in the operation sequence; i.e., $latex \[ v_j (t) = v_j^{(0)} + v_j^{(1)} t \] $$ We use $latex x^{(1)} = 1$$ and $latex \varepsilon^{(1)} = 0$$, so that differentiation with respect to $latex t$$, at $latex t = 0$$, is the same partial differentiation with respect to $latex x$$ at $latex x = x^{(0)}$$. $subhead Sweep$$ $center $table $bold Index$$ $cnext $pre $$ $cnext $bold Operation$$ $cnext $pre $$ $cnext $bold Zero Order$$ $cnext $pre $$ $cnext $bold Derivative$$ $cnext $pre $$ $cnext $bold First Order$$ $rnext 1 $cnext $pre $$ $cnext $latex v_1 = x $$ $cnext $cnext 0.5 $cnext $cnext $latex v_1^{(1)} = x^{(1)} $$ $cnext $cnext $latex v_1^{(1)} = 1$$ $rnext 2 $cnext $pre $$ $cnext $latex v_2 = 1 * v_1$$ $cnext $cnext 0.5 $cnext $cnext $latex v_2^{(1)} = 1 * v_1^{(1)}$$ $cnext $cnext $latex v_2^{(1)} = 1$$ $rnext 3 $cnext $pre $$ $cnext $latex v_3 = v_2 / 1$$ $cnext $cnext 0.5 $cnext $cnext $latex v_3^{(1)} = v_2^{(1)} / 1$$ $cnext $cnext $latex v_3^{(1)} = 1$$ $rnext 4 $cnext $pre $$ $cnext $latex v_4 = 1 + v_3$$ $cnext $cnext 1.5 $cnext $cnext $latex v_4^{(1)} = v_3^{(1)} $$ $cnext $cnext $latex v_4^{(1)} = 1$$ $rnext 5 $cnext $pre $$ $cnext $latex v_5 = v_3 * v_1$$ $cnext $cnext 0.25 $cnext $cnext $latex v_5^{(1)} = v_3^{(1)} * v_1^{(0)} + v_3^{(0)} * v_1^{(1)}$$ $cnext $cnext $latex v_5^{(1)} = 1$$ $rnext 6 $cnext $pre $$ $cnext $latex v_6 = v_5 / 2$$ $cnext $cnext 0.125 $cnext $cnext $latex v_6^{(1)} = v_5^{(1)} / 2$$ $cnext $cnext $latex v_6^{(1)} = 0.5$$ $rnext 7 $cnext $pre $$ $cnext $latex v_7 = v_4 + v_6$$ $cnext $cnext 1.625 $cnext $cnext $latex v_7^{(1)} = v_4^{(1)} + v_6^{(1)}$$ $cnext $cnext $latex v_7^{(1)} = 1.5$$ $tend $$ $head Return Value$$ The derivative of the return value for this case is $latex \[ \begin{array}{rcl} 1.5 & = & v_7^{(1)} = \left[ \D{v_7}{t} \right]_{t=0} = \left[ \D{}{t} f( x^{(0)} + x^{(1)} * t , \varepsilon^{(0)} ) \right]_{t=0} \\ & = & \partial_x f ( x^{(0)} , \varepsilon^{(0)} ) * x^{(1)} = \partial_x f ( x^{(0)} , \varepsilon^{(0)} ) \end{array} \] $$ (We have used the fact that $latex x^{(1)} = 1$$ and $latex \varepsilon^{(1)} = 0$$.) $children% introduction/exp_apx/exp_eps_for1.cpp %$$ $head Verification$$ The file $cref exp_eps_for1.cpp$$ contains a routine that verifies the values computed above. It returns true for success and false for failure. $head Exercises$$ $list number$$ Suppose that $latex x = .1$$, what are the results of a zero and first order forward mode sweep for the operation sequence above; i.e., what are the corresponding values for $latex v_1^{(0)}, v_2^{(0)}, \cdots , v_7^{(0)}$$ and $latex v_1^{(1)}, v_2^{(1)}, \cdots , v_7^{(1)}$$ ? $lnext Create a modified version of $cref exp_eps_for1.cpp$$ that verifies the derivative values from the previous exercise. Also create and run a main program that reports the result of calling the modified version of $cref exp_eps_for1.cpp$$. $lnext Suppose that $latex x = .1$$ and $latex \epsilon = .2$$, what is the operation sequence corresponding to $codei% exp_eps(%x%, %epsilon%) %$$ $lend $end ----------------------------------------------------------------------------- $begin exp_eps_rev1$$ $spell exp_eps_rev $$ $section exp_eps: First Order Reverse Sweep$$ $mindex mode$$ $head Purpose$$ First order reverse mode uses the $cref/operation sequence/exp_eps_for0/Operation Sequence/$$, and zero order forward sweep values, to compute the first order derivative of one dependent variable with respect to all the independent variables. The computations are done in reverse of the order of the computations in the original algorithm. $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_eps.hpp$$ to compute $codei%exp_eps(%x%, %epsilon%)%$$ with $icode x$$ is equal to .5 and $icode epsilon$$ is equal to .2. For this case, the mathematical function for the operation sequence corresponding to $code exp_eps$$ is $latex \[ f ( x , \varepsilon ) = 1 + x + x^2 / 2 \] $$ The corresponding partial derivatives, and the value of the derivatives, are $latex \[ \begin{array}{rcl} \partial_x f ( x , \varepsilon ) & = & 1 + x = 1.5 \\ \partial_\varepsilon f ( x , \varepsilon ) & = & 0 \end{array} \] $$ $head epsilon$$ Since $latex \varepsilon$$ is an independent variable, it could included as an argument to all of the $latex f_j$$ functions below. The result would be that all the partials with respect to $latex \varepsilon$$ would be zero and hence we drop it to simplify the presentation. $head f_7$$ In reverse mode we choose one dependent variable and compute its derivative with respect to all the independent variables. For our example, we chose the value returned by $cref exp_eps.hpp$$ which is $latex v_7$$. We begin with the function $latex f_7$$ where $latex v_7$$ is both an argument and the value of the function; i.e., $latex \[ \begin{array}{rcl} f_7 ( v_1 , v_2 , v_3 , v_4 , v_5 , v_6 , v_7 ) & = & v_7 \\ \D{f_7}{v_7} & = & 1 \end{array} \] $$ All the other partial derivatives of $latex f_7$$ are zero. $head Index 7: f_6$$ The last operation has index 7, $latex \[ v_7 = v_4 + v_6 \] $$ We define the function $latex f_6 ( v_1 , v_2 , v_3 , v_4 , v_5 , v_6 ) $$ as equal to $latex f_7$$ except that $latex v_7$$ is eliminated using this operation; i.e. $latex \[ f_6 = f_7 [ v_1 , v_2 , v_3 , v_4 , v_5 , v_6 , v_7 ( v_4 , v_6 ) ] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_6}{v_4} & = & \D{f_7}{v_4} + \D{f_7}{v_7} * \D{v_7}{v_4} & = 1 \\ \D{f_6}{v_6} & = & \D{f_7}{v_6} + \D{f_7}{v_7} * \D{v_7}{v_6} & = 1 \end{array} \] $$ All the other partial derivatives of $latex f_6$$ are zero. $head Index 6: f_5$$ The previous operation has index 6, $latex \[ v_6 = v_5 / 2 \] $$ We define the function $latex f_5 ( v_1 , v_2 , v_3 , v_4 , v_5 ) $$ as equal to $latex f_6 $$ except that $latex v_6 $$ is eliminated using this operation; i.e., $latex \[ f_5 = f_6 [ v_1 , v_2 , v_3 , v_4 , v_5 , v_6 ( v_5 ) ] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_5}{v_4} & = & \D{f_6}{v_4} & = 1 \\ \D{f_5}{v_5} & = & \D{f_6}{v_5} + \D{f_6}{v_6} * \D{v_6}{v_5} & = 0.5 \end{array} \] $$ All the other partial derivatives of $latex f_5$$ are zero. $head Index 5: f_4$$ The previous operation has index 5, $latex \[ v_5 = v_3 * v_1 \] $$ We define the function $latex f_4 ( v_1 , v_2 , v_3 , v_4 ) $$ as equal to $latex f_5 $$ except that $latex v_5 $$ is eliminated using this operation; i.e., $latex \[ f_4 = f_5 [ v_1 , v_2 , v_3 , v_4 , v_5 ( v_3 , v_1 ) ] \] $$ Given the information from the forward sweep, we have $latex v_3 = 0.5 $$ and $latex v_1 = 0.5 $$. It follows that $latex \[ \begin{array}{rcll} \D{f_4}{v_1} & = & \D{f_5}{v_1} + \D{f_5}{v_5} * \D{v_5}{v_1} & = 0.25 \\ \D{f_4}{v_2} & = & \D{f_5}{v_2} & = 0 \\ \D{f_4}{v_3} & = & \D{f_5}{v_3} + \D{f_5}{v_5} * \D{v_5}{v_3} & = 0.25 \\ \D{f_4}{v_4} & = & \D{f_5}{v_4} & = 1 \end{array} \] $$ $head Index 4: f_3$$ The previous operation has index 4, $latex \[ v_4 = 1 + v_3 \] $$ We define the function $latex f_3 ( v_1 , v_2 , v_3 ) $$ as equal to $latex f_4 $$ except that $latex v_4 $$ is eliminated using this operation; i.e., $latex \[ f_3 = f_4 [ v_1 , v_2 , v_3 , v_4 ( v_3 ) ] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_3}{v_1} & = & \D{f_4}{v_1} & = 0.25 \\ \D{f_3}{v_2} & = & \D{f_4}{v_2} & = 0 \\ \D{f_3}{v_3} & = & \D{f_4}{v_3} + \D{f_4}{v_4} * \D{v_4}{v_3} & = 1.25 \end{array} \] $$ $head Index 3: f_2$$ The previous operation has index 3, $latex \[ v_3 = v_2 / 1 \] $$ We define the function $latex f_2 ( v_1 , v_2 ) $$ as equal to $latex f_3 $$ except that $latex v_3 $$ is eliminated using this operation; i.e., $latex \[ f_2 = f_4 [ v_1 , v_2 , v_3 ( v_2 ) ] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_2}{v_1} & = & \D{f_3}{v_1} & = 0.25 \\ \D{f_2}{v_2} & = & \D{f_3}{v_2} + \D{f_3}{v_3} * \D{v_3}{v_2} & = 1.25 \end{array} \] $$ $head Index 2: f_1$$ The previous operation has index 1, $latex \[ v_2 = 1 * v_1 \] $$ We define the function $latex f_1 ( v_1 ) $$ as equal to $latex f_2 $$ except that $latex v_2 $$ is eliminated using this operation; i.e., $latex \[ f_1 = f_2 [ v_1 , v_2 ( v_1 ) ] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_1}{v_1} & = & \D{f_2}{v_1} + \D{f_2}{v_2} * \D{v_2}{v_1} & = 1.5 \end{array} \] $$ Note that $latex v_1$$ is equal to $latex x$$, so the derivative of $codei%exp_eps(%x%, %epsilon%)%$$ at $icode x$$ equal to .5 and $icode epsilon$$ equal .2 is 1.5 in the $icode x$$ direction and zero in the $icode epsilon$$ direction. We also note that $cref/forward/exp_eps_for1/$$ forward mode gave the same result for the partial in the $icode x$$ direction. $children% introduction/exp_apx/exp_eps_rev1.cpp %$$ $head Verification$$ The file $cref exp_eps_rev1.cpp$$ contains a routine that verifies the values computed above. It returns true for success and false for failure. It only tests the partial derivatives of $latex f_j$$ that might not be equal to the corresponding partials of $latex f_{j+1}$$; i.e., the other partials of $latex f_j$$ must be equal to the corresponding partials of $latex f_{j+1}$$. $head Exercises$$ $list number$$ Consider the case where $latex x = .1$$ and we first preform a zero order forward mode sweep for the operation sequence used above (in reverse order). What are the results of a first order reverse mode sweep; i.e., what are the corresponding values for $latex \D{f_j}{v_k}$$ for all $latex j, k$$ such that $latex \D{f_j}{v_k} \neq 0$$. $lnext Create a modified version of $cref exp_eps_rev1.cpp$$ that verifies the values you obtained for the previous exercise. Also create and run a main program that reports the result of calling the modified version of $cref exp_eps_rev1.cpp$$. $lend $end ----------------------------------------------------------------------------- $begin exp_eps_for2$$ $spell exp_eps_for $$ $section exp_eps: Second Order Forward Mode$$ $head Second Order Expansion$$ We define $latex x(t)$$ and $latex \varepsilon(t) ]$$ near $latex t = 0$$ by the second order expansions $latex \[ \begin{array}{rcl} x(t) & = & x^{(0)} + x^{(1)} * t + x^{(2)} * t^2 / 2 \\ \varepsilon(t) & = & \varepsilon^{(0)} + \varepsilon^{(1)} * t + \varepsilon^{(2)} * t^2 / 2 \end{array} \]$$ It follows that for $latex k = 0 , 1 , 2$$, $latex \[ \begin{array}{rcl} x^{(k)} & = & \dpow{k}{t} x (0) \\ \varepsilon^{(k)} & = & \dpow{k}{t} \varepsilon (0) \end{array} \] $$ $head Purpose$$ In general, a second order forward sweep is given the $cref/first order expansion/exp_2_for1/First Order Expansion/$$ for all of the variables in an operation sequence, and the second order derivatives for the independent variables. It uses these to compute the second order derivative, and thereby obtain the second order expansion, for all the variables in the operation sequence. $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_eps.hpp$$ to compute $codei%exp_eps(%x%, %epsilon%)%$$ with $icode x$$ is equal to .5 and $icode epsilon$$ is equal to .2. For this case, the mathematical function for the operation sequence corresponding to $code exp_eps$$ is $latex \[ f ( x , \varepsilon ) = 1 + x + x^2 / 2 \] $$ The corresponding second partial derivative with respect to $latex x$$, and the value of the derivative, are $latex \[ \Dpow{2}{x} f ( x , \varepsilon ) = 1. \] $$ $head Operation Sequence$$ $subhead Index$$ The Index column contains the index in the operation sequence of the corresponding atomic operation. A Forward sweep starts with the first operation and ends with the last. $subhead Zero$$ The Zero column contains the zero order sweep results for the corresponding variable in the operation sequence (see $cref/zero order sweep/exp_2_for0/Operation Sequence/Sweep/$$). $subhead Operation$$ The Operation column contains the first order sweep operation for this variable. $subhead First$$ The First column contains the first order sweep results for the corresponding variable in the operation sequence (see $cref/first order sweep/exp_2_for1/Operation Sequence/Sweep/$$). $subhead Derivative$$ The Derivative column contains the mathematical function corresponding to the second derivative with respect to $latex t$$, at $latex t = 0$$, for each variable in the sequence. $subhead Second$$ The Second column contains the second order derivatives for the corresponding variable in the operation sequence; i.e., the second order expansion for the $th i$$ variable is given by $latex \[ v_i (t) = v_i^{(0)} + v_i^{(1)} * t + v_i^{(2)} * t^2 / 2 \] $$ We use $latex x^{(1)} = 1$$, $latex x^{(2)} = 0$$, use $latex \varepsilon^{(1)} = 1$$, and $latex \varepsilon^{(2)} = 0$$ so that second order differentiation with respect to $latex t$$, at $latex t = 0$$, is the same as the second partial differentiation with respect to $latex x$$ at $latex x = x^{(0)}$$. $subhead Sweep$$ $center $table $bold Index$$ $cnext $pre $$ $cnext $bold Zero$$ $cnext $pre $$ $cnext $bold Operation$$ $cnext $pre $$ $cnext $bold First$$ $cnext $pre $$ $cnext $bold Derivative$$ $cnext $pre $$ $cnext $bold Second$$ $rnext 1 $cnext $cnext 0.5 $cnext $cnext $latex v_1^{(1)} = x^{(1)} $$ $cnext $cnext 1 $cnext $cnext $latex v_2^{(2)} = x^{(2)} $$ $cnext $cnext 0 $rnext 2 $cnext $cnext 0.5 $cnext $cnext $latex v_2^{(1)} = 1 * v_1^{(1)}$$ $cnext $cnext 1 $cnext $cnext $latex v_2^{(2)} = 1 * v_1^{(2)}$$ $cnext $cnext 0 $rnext 3 $cnext $cnext 0.5 $cnext $cnext $latex v_3^{(1)} = v_2^{(1)} / 1$$ $cnext $cnext 1 $cnext $cnext $latex v_3^{(2)} = v_2^{(2)} / 1$$ $cnext $cnext 0 $rnext 4 $cnext $cnext 1.5 $cnext $cnext $latex v_4^{(1)} = v_3^{(1)} $$ $cnext $cnext 1 $cnext $cnext $latex v_4^{(2)} = v_3^{(2)} $$ $cnext $cnext 0 $rnext 5 $cnext $cnext 0.25 $cnext $cnext $latex v_5^{(1)} = v_3^{(1)} * v_1^{(0)} + v_3^{(0)} * v_1^{(1)}$$ $cnext $cnext 1 $cnext $cnext $latex v_5^{(2)} = v_3^{(2)} * v_1^{(0)} + 2 * v_3^{(1)} * v_1^{(1)} + v_3^{(0)} * v_1^{(2)}$$ $cnext $cnext 2 $rnext 6 $cnext $cnext 0.125 $cnext $cnext $latex v_6^{(1)} = v_5^{(1)} / 2$$ $cnext $cnext 0.5 $cnext $cnext $latex v_6^{(2)} = v_5^{(2)} / 2$$ $cnext $cnext 1 $rnext 7 $cnext $cnext 1.625 $cnext $cnext $latex v_7^{(1)} = v_4^{(1)} + v_6^{(1)}$$ $cnext $cnext 1.5 $cnext $cnext $latex v_7^{(2)} = v_4^{(2)} + v_6^{(2)}$$ $cnext $cnext 1 $tend $$ $head Return Value$$ The second derivative of the return value for this case is $latex \[ \begin{array}{rcl} 1 & = & v_7^{(2)} = \left[ \Dpow{2}{t} v_7 \right]_{t=0} = \left[ \Dpow{2}{t} f( x^{(0)} + x^{(1)} * t , \varepsilon^{(0)} ) \right]_{t=0} \\ & = & x^{(1)} * \Dpow{2}{x} f ( x^{(0)} , \varepsilon^{(0)} ) * x^{(1)} = \Dpow{2}{x} f ( x^{(0)} , \varepsilon^{(0)} ) \end{array} \] $$ (We have used the fact that $latex x^{(1)} = 1$$, $latex x^{(2)} = 0$$, $latex \varepsilon^{(1)} = 1$$, and $latex \varepsilon^{(2)} = 0$$.) $children% introduction/exp_apx/exp_eps_for2.cpp %$$ $head Verification$$ The file $cref exp_eps_for2.cpp$$ contains a routine which verifies the values computed above. It returns true for success and false for failure. $head Exercises$$ $list number$$ Which statement in the routine defined by $cref exp_eps_for2.cpp$$ uses the values that are calculated by the routine defined by $cref exp_eps_for1.cpp$$ ? $lnext Suppose that $latex x = .1$$, what are the results of a zero, first, and second order forward sweep for the operation sequence above; i.e., what are the corresponding values for $latex v_i^{(k)}$$ for $latex i = 1, \ldots , 7$$ and $latex k = 0, 1, 2$$. $lnext Create a modified version of $cref exp_eps_for2.cpp$$ that verifies the derivative values from the previous exercise. Also create and run a main program that reports the result of calling the modified version of $cref exp_eps_for2.cpp$$. $lend $end ----------------------------------------------------------------------------- $begin exp_eps_rev2$$ $spell exp_eps_rev $$ $section exp_eps: Second Order Reverse Sweep$$ $head Purpose$$ In general, a second order reverse sweep is given the $cref/first order expansion/exp_eps_for1/First Order Expansion/$$ for all of the variables in an operation sequence. Given a choice of a particular variable, it computes the derivative, of that variables first order expansion coefficient, with respect to all of the independent variables. $head Mathematical Form$$ Suppose that we use the algorithm $cref exp_eps.hpp$$ to compute $codei%exp_eps(%x%, %epsilon%)%$$ with $icode x$$ is equal to .5 and $icode epsilon$$ is equal to .2. For this case, the mathematical function for the operation sequence corresponding to $code exp_eps$$ is $latex \[ f ( x , \varepsilon ) = 1 + x + x^2 / 2 \] $$ The corresponding derivative of the partial derivative with respect to $latex x$$ is $latex \[ \begin{array}{rcl} \Dpow{2}{x} f ( x , \varepsilon ) & = & 1 \\ \partial_\varepsilon \partial_x f ( x , \varepsilon ) & = & 0 \end{array} \] $$ $head epsilon$$ Since $latex \varepsilon$$ is an independent variable, it could included as an argument to all of the $latex f_j$$ functions below. The result would be that all the partials with respect to $latex \varepsilon$$ would be zero and hence we drop it to simplify the presentation. $head f_7$$ In reverse mode we choose one dependent variable and compute its derivative with respect to all the independent variables. For our example, we chose the value returned by $cref exp_eps.hpp$$ which is $latex v_7$$. We begin with the function $latex f_7$$ where $latex v_7$$ is both an argument and the value of the function; i.e., $latex \[ \begin{array}{rcl} f_7 \left( v_1^{(0)} , v_1^{(1)} , \ldots , v_7^{(0)} , v_7^{(1)} \right) & = & v_7^{(1)} \\ \D{f_7}{v_7^{(1)}} & = & 1 \end{array} \] $$ All the other partial derivatives of $latex f_7$$ are zero. $head Index 7: f_6$$ The last operation has index 7, $latex \[ \begin{array}{rcl} v_7^{(0)} & = & v_4^{(0)} + v_6^{(0)} \\ v_7^{(1)} & = & v_4^{(1)} + v_6^{(1)} \end{array} \] $$ We define the function $latex f_6 \left( v_1^{(0)} , \ldots , v_6^{(1)} \right) $$ as equal to $latex f_7$$ except that $latex v_7^{(0)}$$ and $latex v_7^{(1)}$$ are eliminated using this operation; i.e. $latex \[ f_6 = f_7 \left[ v_1^{(0)} , \ldots , v_6^{(1)} , v_7^{(0)} \left( v_4^{(0)} , v_6^{(0)} \right) , v_7^{(1)} \left( v_4^{(1)} , v_6^{(1)} \right) \right] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_6}{v_4^{(1)}} & = & \D{f_7}{v_4^{(1)}} + \D{f_7}{v_7^{(1)}} * \D{v_7^{(1)}}{v_4^{(1)}} & = 1 \\ \D{f_6}{v_6^{(1)}} & = & \D{f_7}{v_6^{(1)}} + \D{f_7}{v_7^{(1)}} * \D{v_7^{(1)}}{v_6^{(1)}} & = 1 \end{array} \] $$ All the other partial derivatives of $latex f_6$$ are zero. $head Index 6: f_5$$ The previous operation has index 6, $latex \[ \begin{array}{rcl} v_6^{(0)} & = & v_5^{(0)} / 2 \\ v_6^{(1)} & = & v_5^{(1)} / 2 \end{array} \] $$ We define the function $latex f_5 \left( v_1^{(0)} , \ldots , v_5^{(1)} \right) $$ as equal to $latex f_6 $$ except that $latex v_6^{(0)}$$ and $latex v_6^{(1)}$$ are eliminated using this operation; i.e. $latex \[ f_5 = f_6 \left[ v_1^{(0)} , \ldots , v_5^{(1)} , v_6^{(0)} \left( v_5^{(0)} \right) , v_6^{(1)} \left( v_5^{(1)} \right) \right] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_5}{v_4^{(1)}} & = & \D{f_6}{v_4^{(1)}} & = 1 \\ \D{f_5}{v_5^{(1)}} & = & \D{f_6}{v_5} + \D{f_6}{v_6^{(1)}} * \D{v_6^{(1)}}{v_5^{(1)}} & = 0.5 \end{array} \] $$ All the other partial derivatives of $latex f_5$$ are zero. $head Index 5: f_4$$ The previous operation has index 5, $latex \[ \begin{array}{rcl} v_5^{(0)} & = & v_3^{(0)} * v_1^{(0)} \\ v_5^{(1)} & = & v_3^{(1)} * v_1^{(0)} + v_3^{(0)} * v_1^{(1)} \end{array} \] $$ We define the function $latex f_4 \left( v_1^{(0)} , \ldots , v_4^{(1)} \right) $$ as equal to $latex f_5 $$ except that $latex v_5^{(0)}$$ and $latex v_5^{(1)}$$ are eliminated using this operation; i.e. $latex \[ f_4 = f_5 \left[ v_1^{(0)} , \ldots , v_4^{(1)} , v_5^{(0)} \left( v_1^{(0)}, v_3^{(0)} \right) , v_5^{(1)} \left( v_1^{(0)}, v_1^{(1)}, v_3^{(0)} , v_3^{(1)} \right) , \right] \] $$ Given the information from the forward sweep, we have $latex v_1^{(0)} = 0.5$$, $latex v_3^{(0)} = 0.5$$, $latex v_1^{(1)} = 1$$, $latex v_3^{(1)} = 1$$, and the fact that the partial of $latex f_5$$ with respect to $latex v_5^{(0)}$$ is zero, we have $latex \[ \begin{array}{rcll} \D{f_4}{v_1^{(0)}} & = & \D{f_5}{v_1^{(0)}} + \D{f_5}{v_5^{(1)}} * \D{v_5^{(1)}}{v_1^{(0)}} & = 0.5 \\ \D{f_4}{v_1^{(1)}} & = & \D{f_5}{v_1^{(1)}} + \D{f_5}{v_5^{(1)}} * \D{v_5^{(1)}}{v_1^{(1)}} & = 0.25 \\ \D{f_4}{v_3^{(0)}} & = & \D{f_5}{v_3^{(0)}} + \D{f_5}{v_5^{(1)}} * \D{v_5^{(1)}}{v_3^{(0)}} & = 0.5 \\ \D{f_4}{v_3^{(1)}} & = & \D{f_3}{v_1^{(1)}} + \D{f_5}{v_5^{(1)}} * \D{v_5^{(1)}}{v_3^{(1)}} & = 0.25 \\ \D{f_4}{v_4^{(1)}} & = & \D{f_5}{v_4^{(1)}} & = 1 \end{array} \] $$ All the other partial derivatives of $latex f_5$$ are zero. $head Index 4: f_3$$ The previous operation has index 4, $latex \[ \begin{array}{rcl} v_4^{(0)} = 1 + v_3^{(0)} \\ v_4^{(1)} = v_3^{(1)} \end{array} \] $$ We define the function $latex f_3 \left( v_1^{(0)} , \ldots , v_3^{(1)} \right) $$ as equal to $latex f_4 $$ except that $latex v_4^{(0)}$$ and $latex v_4^{(1)}$$ are eliminated using this operation; i.e. $latex \[ f_3 = f_4 \left[ v_1^{(0)} , \ldots , v_3^{(1)} , v_4^{(0)} \left( v_3^{(0)} \right) , v_4^{(1)} \left( v_3^{(1)} \right) \right] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_3}{v_1^{(0)}} & = & \D{f_4}{v_1^{(0)}} & = 0.5 \\ \D{f_3}{v_1^{(1)}} & = & \D{f_4}{v_1^{(1)}} & = 0.25 \\ \D{f_3}{v_2^{(0)}} & = & \D{f_4}{v_2^{(0)}} & = 0 \\ \D{f_3}{v_2^{(1)}} & = & \D{f_4}{v_2^{(1)}} & = 0 \\ \D{f_3}{v_3^{(0)}} & = & \D{f_4}{v_3^{(0)}} + \D{f_4}{v_4^{(0)}} * \D{v_4^{(0)}}{v_3^{(0)}} & = 0.5 \\ \D{f_3}{v_3^{(1)}} & = & \D{f_4}{v_3^{(1)}} + \D{f_4}{v_4^{(1)}} * \D{v_4^{(1)}}{v_3^{(1)}} & = 1.25 \end{array} \] $$ $head Index 3: f_2$$ The previous operation has index 3, $latex \[ \begin{array}{rcl} v_3^{(0)} & = & v_2^{(0)} / 1 \\ v_3^{(1)} & = & v_2^{(1)} / 1 \end{array} \] $$ We define the function $latex f_2 \left( v_1^{(0)} , \ldots , v_2^{(1)} \right) $$ as equal to $latex f_3 $$ except that $latex v_3^{(0)}$$ and $latex v_3^{(1)}$$ are eliminated using this operation; i.e. $latex \[ f_2 = f_3 \left[ v_1^{(0)} , \ldots , v_2^{(1)} , v_3^{(0)} \left( v_2^{(0)} \right) , v_3^{(1)} \left( v_2^{(1)} \right) \right] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_2}{v_1^{(0)}} & = & \D{f_3}{v_1^{(0)}} & = 0.5 \\ \D{f_2}{v_1^{(1)}} & = & \D{f_3}{v_1^{(1)}} & = 0.25 \\ \D{f_2}{v_2^{(0)}} & = & \D{f_3}{v_2^{(0)}} + \D{f_3}{v_3^{(0)}} * \D{v_3^{(0)}}{v_2^{(0)}} & = 0.5 \\ \D{f_2}{v_2^{(1)}} & = & \D{f_3}{v_2^{(1)}} + \D{f_3}{v_3^{(1)}} * \D{v_3^{(1)}}{v_2^{(0)}} & = 1.25 \end{array} \] $$ $head Index 2: f_1$$ The previous operation has index 1, $latex \[ \begin{array}{rcl} v_2^{(0)} & = & 1 * v_1^{(0)} \\ v_2^{(1)} & = & 1 * v_1^{(1)} \end{array} \] $$ We define the function $latex f_1 \left( v_1^{(0)} , v_1^{(1)} \right) $$ as equal to $latex f_2 $$ except that $latex v_2^{(0)}$$ and $latex v_2^{(1)}$$ are eliminated using this operation; i.e. $latex \[ f_1 = f_2 \left[ v_1^{(0)} , v_1^{(1)} , v_2^{(0)} \left( v_1^{(0)} \right) , v_2^{(1)} \left( v_1^{(1)} \right) \right] \] $$ It follows that $latex \[ \begin{array}{rcll} \D{f_1}{v_1^{(0)}} & = & \D{f_2}{v_1^{(0)}} + \D{f_2}{v_2^{(0)}} * \D{v_2^{(0)}}{v_1^{(0)}} & = 1 \\ \D{f_1}{v_1^{(1)}} & = & \D{f_2}{v_1^{(1)}} + \D{f_2}{v_2^{(1)}} * \D{v_2^{(1)}}{v_1^{(1)}} & = 1.5 \end{array} \] $$ Note that $latex v_1$$ is equal to $latex x$$, so the second partial derivative of $codei%exp_eps(%x%, %epsilon%)%$$ at $icode x$$ equal to .5 and $icode epsilon$$ equal .2 is $latex \[ \Dpow{2}{x} v_7^{(0)} = \D{v_7^{(1)}}{x} = \D{f_1}{v_1^{(0)}} = 1 \] $$ There is a theorem about algorithmic differentiation that explains why the other partial of $latex f_1$$ is equal to the first partial of $codei%exp_eps(%x%, %epsilon%)%$$ with respect to $latex x$$. $children% introduction/exp_apx/exp_eps_rev2.cpp %$$ $head Verification$$ The file $cref exp_eps_rev2.cpp$$ contains a routine that verifies the values computed above. It returns true for success and false for failure. It only tests the partial derivatives of $latex f_j$$ that might not be equal to the corresponding partials of $latex f_{j+1}$$; i.e., the other partials of $latex f_j$$ must be equal to the corresponding partials of $latex f_{j+1}$$. $head Exercises$$ $list number$$ Consider the case where $latex x = .1$$ and we first preform a zero order forward mode sweep for the operation sequence used above (in reverse order). What are the results of a first order reverse mode sweep; i.e., what are the corresponding values for $latex \D{f_j}{v_k}$$ for all $latex j, k$$ such that $latex \D{f_j}{v_k} \neq 0$$. $lnext Create a modified version of $cref exp_eps_rev2.cpp$$ that verifies the values you obtained for the previous exercise. Also create and run a main program that reports the result of calling the modified version of $cref exp_eps_rev2.cpp$$. $lend $end ----------------------------------------------------------------------------- cppad-20170000.3/introduction/exp_apx/exp_2_for1.cpp0000644000175200017650000000322113057470463021266 0ustar coincoin-web// $Id: exp_2_for1.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_2_for1.cpp$$ $spell std exp_2_for cmath fabs bool $$ $section exp_2: Verify First Order Forward Sweep$$ $mindex exp_2$$ $srccode%cpp% */ # include // prototype for fabs extern bool exp_2_for0(double *v0); // computes zero order forward sweep bool exp_2_for1(double *v1) // double v1[6] { bool ok = true; double v0[6]; // set the value of v0[j] for j = 1 , ... , 5 ok &= exp_2_for0(v0); v1[1] = 1.; // v1 = x ok &= std::fabs( v1[1] - 1. ) <= 1e-10; v1[2] = v1[1]; // v2 = 1 + v1 ok &= std::fabs( v1[2] - 1. ) <= 1e-10; v1[3] = v1[1] * v0[1] + v0[1] * v1[1]; // v3 = v1 * v1 ok &= std::fabs( v1[3] - 1. ) <= 1e-10; v1[4] = v1[3] / 2.; // v4 = v3 / 2 ok &= std::fabs( v1[4] - 0.5) <= 1e-10; v1[5] = v1[2] + v1[4]; // v5 = v2 + v4 ok &= std::fabs( v1[5] - 1.5) <= 1e-10; return ok; } bool exp_2_for1(void) { double v1[6]; return exp_2_for1(v1); } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/exp_2_for2.cpp0000644000175200017650000000325313057470463021274 0ustar coincoin-web// $Id: exp_2_for2.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_2_for2.cpp$$ $spell std exp_2_for cmath fabs bool $$ $section exp_2: Verify Second Order Forward Sweep$$ $mindex exp_2$$ $srccode%cpp% */ # include // prototype for fabs extern bool exp_2_for0(double *v0); // computes zero order forward sweep extern bool exp_2_for1(double *v1); // computes first order forward sweep bool exp_2_for2(void) { bool ok = true; double v0[6], v1[6], v2[6]; // set the value of v0[j], v1[j], for j = 1 , ... , 5 ok &= exp_2_for0(v0); ok &= exp_2_for1(v1); v2[1] = 0.; // v1 = x ok &= std::fabs( v2[1] - 0. ) <= 1e-10; v2[2] = v2[1]; // v2 = 1 + v1 ok &= std::fabs( v2[2] - 0. ) <= 1e-10; v2[3] = 2.*(v0[1]*v2[1] + v1[1]*v1[1]); // v3 = v1 * v1 ok &= std::fabs( v2[3] - 2. ) <= 1e-10; v2[4] = v2[3] / 2.; // v4 = v3 / 2 ok &= std::fabs( v2[4] - 1. ) <= 1e-10; v2[5] = v2[2] + v2[4]; // v5 = v2 + v4 ok &= std::fabs( v2[5] - 1. ) <= 1e-10; return ok; } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/exp_eps.hpp0000644000175200017650000001270013057470463020774 0ustar coincoin-web// $Id: exp_eps.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_INTRODUCTION_EXP_APX_EXP_EPS_HPP # define CPPAD_INTRODUCTION_EXP_APX_EXP_EPS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_eps$$ $spell cppad-%yyyymmdd% hpp Apx cpp const exp_eps bool $$ $section An Epsilon Accurate Exponential Approximation$$ $mindex exp_eps example algorithm$$ $head Syntax$$ $codei%# include "exp_eps.hpp"%$$ $pre $$ $icode%y% = exp_eps(%x%, %epsilon%)%$$ $head Purpose$$ This is a an example algorithm that is used to demonstrate how Algorithmic Differentiation works with loops and boolean decision variables (see $cref exp_2$$ for a simpler example). $head Mathematical Function$$ The exponential function can be defined by $latex \[ \exp (x) = 1 + x^1 / 1 ! + x^2 / 2 ! + \cdots \] $$ We define $latex k ( x, \varepsilon ) $$ as the smallest non-negative integer such that $latex \varepsilon \geq x^k / k !$$; i.e., $latex \[ k( x, \varepsilon ) = \min \{ k \in {\rm Z}_+ \; | \; \varepsilon \geq x^k / k ! \} \] $$ The mathematical form for our approximation of the exponential function is $latex \[ \begin{array}{rcl} {\rm exp\_eps} (x , \varepsilon ) & = & \left\{ \begin{array}{ll} \frac{1}{ {\rm exp\_eps} (-x , \varepsilon ) } & {\rm if} \; x < 0 \\ 1 + x^1 / 1 ! + \cdots + x^{k( x, \varepsilon)} / k( x, \varepsilon ) ! & {\rm otherwise} \end{array} \right. \end{array} \] $$ $head include$$ The include command in the syntax is relative to $codei% cppad-%yyyymmdd%/introduction/exp_apx %$$ where $codei%cppad-%yyyymmdd%$$ is the distribution directory created during the beginning steps of the $cref%installation%Install%$$ of CppAD. $head x$$ The argument $icode x$$ has prototype $codei% const %Type% &%x% %$$ (see $icode Type$$ below). It specifies the point at which to evaluate the approximation for the exponential function. $head epsilon$$ The argument $icode epsilon$$ has prototype $codei% const %Type% &%epsilon% %$$ It specifies the accuracy with which to approximate the exponential function value; i.e., it is the value of $latex \varepsilon$$ in the exponential function approximation defined above. $head y$$ The result $icode y$$ has prototype $codei% %Type% %y% %$$ It is the value of the exponential function approximation defined above. $head Type$$ If $icode u$$ and $icode v$$ are $icode Type$$ objects and $icode i$$ is an $code int$$: $table $bold Operation$$ $cnext $bold Result Type$$ $cnext $bold Description$$ $rnext $icode%Type%(%i%)%$$ $cnext $icode Type$$ $cnext object with value equal to $icode i$$ $rnext $icode%Type u %=% v%$$ $cnext $icode Type$$ $cnext construct $icode u$$ with value equal to $icode v$$ $rnext $icode%u% > %v%$$ $cnext $code bool$$ $cnext true, if $icode u$$ greater than $icode v$$, an false otherwise $rnext $icode%u% = %v%$$ $cnext $icode Type$$ $cnext new $icode u$$ (and result) is value of $icode v$$ $rnext $icode%u% * %v%$$ $cnext $icode Type$$ $cnext result is value of $latex u * v$$ $rnext $icode%u% / %v%$$ $cnext $icode Type$$ $cnext result is value of $latex u / v$$ $rnext $icode%u% + %v%$$ $cnext $icode Type$$ $cnext result is value of $latex u + v$$ $rnext $codei%-%u%$$ $cnext $icode Type$$ $cnext result is value of $latex - u$$ $tend $children% introduction/exp_apx/exp_eps.omh% introduction/exp_apx/exp_eps_cppad.cpp %$$ $head Implementation$$ The file $cref exp_eps.hpp$$ contains a C++ implementation of this function. $head Test$$ The file $cref exp_eps.cpp$$ contains a test of this implementation. It returns true for success and false for failure. $head Exercises$$ $list number$$ Using the definition of $latex k( x, \varepsilon )$$ above, what is the value of $latex k(.5, 1)$$, $latex k(.5, .1)$$, and $latex k(.5, .01)$$ ? $lnext Suppose that we make the following call to $code exp_eps$$: $codep double x = 1.; double epsilon = .01; double y = exp_eps(x, epsilon); $$ What is the value assigned to $code k$$, $code temp$$, $code term$$, and $code sum$$ the first time through the $code while$$ loop in $cref exp_eps.hpp$$ ? $lnext Continuing the previous exercise, what is the value assigned to $code k$$, $code temp$$, $code term$$, and $code sum$$ the second time through the $code while$$ loop in $cref exp_eps.hpp$$ ? $lend $end ----------------------------------------------------------------------------- */ // BEGIN C++ template Type exp_eps(const Type &x, const Type &epsilon) { // abs_x = |x| Type abs_x = x; if( Type(0) > x ) abs_x = - x; // initialize int k = 0; // initial order Type term = 1.; // term = |x|^k / k ! Type sum = term; // initial sum while(term > epsilon) { k = k + 1; // order for next term Type temp = term * abs_x; // term = |x|^k / (k-1)! term = temp / Type(k); // term = |x|^k / k ! sum = sum + term; // sum = 1 + ... + |x|^k / k ! } // In the case where x is negative, use exp(x) = 1 / exp(-|x|) if( Type(0) > x ) sum = Type(1) / sum; return sum; } // END C++ # endif cppad-20170000.3/introduction/exp_apx/exp_eps_cppad.cpp0000644000175200017650000001114613057470463022141 0ustar coincoin-web// $Id: exp_eps_cppad.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_eps_cppad$$ $spell Taylor dy coef resize cppad.hpp cmath fabs bool exp_eps_cppad du dv dw endl hpp http org std www CppAD apx $$ $section exp_eps: CppAD Forward and Reverse Sweeps$$. $head Purpose$$ Use CppAD forward and reverse modes to compute the partial derivative with respect to $latex x$$, at the point $latex x = .5$$ and $latex \varepsilon = .2$$, of the function $codei% exp_eps(%x%, %epsilon%) %$$ as defined by the $cref exp_eps.hpp$$ include file. $head Exercises$$ $list number$$ Create and test a modified version of the routine below that computes the same order derivatives with respect to $latex x$$, at the point $latex x = .1$$ and $latex \varepsilon = .2$$, of the function $codei% exp_eps(%x%, %epsilon%) %$$ $lnext Create and test a modified version of the routine below that computes partial derivative with respect to $latex x$$, at the point $latex x = .1$$ and $latex \varepsilon = .2$$, of the function corresponding to the operation sequence for $latex x = .5$$ and $latex \varepsilon = .2$$. Hint: you could define a vector u with two components and use $codei% %f%.Forward(0, %u%) %$$ to run zero order forward mode at a point different form the point where the operation sequence corresponding to $icode f$$ was recorded. $lend $srccode%cpp% */ # include // http://www.coin-or.org/CppAD/ # include "exp_eps.hpp" // our example exponential function approximation bool exp_eps_cppad(void) { bool ok = true; using CppAD::AD; using CppAD::vector; // can use any simple vector template class using CppAD::NearEqual; // checks if values are nearly equal // domain space vector size_t n = 2; // dimension of the domain space vector< AD > U(n); U[0] = .5; // value of x for this operation sequence U[1] = .2; // value of e for this operation sequence // declare independent variables and start recording operation sequence CppAD::Independent(U); // evaluate our exponential approximation AD x = U[0]; AD epsilon = U[1]; AD apx = exp_eps(x, epsilon); // range space vector size_t m = 1; // dimension of the range space vector< AD > Y(m); Y[0] = apx; // variable that represents only range space component // Create f: U -> Y corresponding to this operation sequence // and stop recording. This also executes a zero order forward // mode sweep using values in U for x and e. CppAD::ADFun f(U, Y); // first order forward mode sweep that computes partial w.r.t x vector du(n); // differential in domain space vector dy(m); // differential in range space du[0] = 1.; // x direction in domain space du[1] = 0.; dy = f.Forward(1, du); // partial w.r.t. x double check = 1.5; ok &= NearEqual(dy[0], check, 1e-10, 1e-10); // first order reverse mode sweep that computes the derivative vector w(m); // weights for components of the range vector dw(n); // derivative of the weighted function w[0] = 1.; // there is only one weight dw = f.Reverse(1, w); // derivative of w[0] * exp_eps(x, epsilon) check = 1.5; // partial w.r.t. x ok &= NearEqual(dw[0], check, 1e-10, 1e-10); check = 0.; // partial w.r.t. epsilon ok &= NearEqual(dw[1], check, 1e-10, 1e-10); // second order forward sweep that computes // second partial of exp_eps(x, epsilon) w.r.t. x vector x2(n); // second order Taylor coefficients vector y2(m); x2[0] = 0.; // evaluate partial w.r.t x x2[1] = 0.; y2 = f.Forward(2, x2); check = 0.5 * 1.; // Taylor coef is 1/2 second derivative ok &= NearEqual(y2[0], check, 1e-10, 1e-10); // second order reverse sweep that computes // derivative of partial of exp_eps(x, epsilon) w.r.t. x dw.resize(2 * n); // space for first and second derivative dw = f.Reverse(2, w); check = 1.; // result should be second derivative ok &= NearEqual(dw[0*2+1], check, 1e-10, 1e-10); return ok; } /* %$$ $end */ cppad-20170000.3/introduction/exp_apx/exp_2_rev1.cpp0000644000175200017650000000347313057470463021305 0ustar coincoin-web// $Id: exp_2_rev1.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin exp_2_rev1.cpp$$ $spell cstddef cmath exp_2_rev bool std fabs $$ $section exp_2: Verify First Order Reverse Sweep$$ $mindex exp_2 mode$$ $srccode%cpp% */ # include // define size_t # include // prototype for fabs extern bool exp_2_for0(double *v0); // computes zero order forward sweep bool exp_2_rev1(void) { bool ok = true; // set the value of v0[j] for j = 1 , ... , 5 double v0[6]; ok &= exp_2_for0(v0); // initial all partial derivatives as zero double f_v[6]; size_t j; for(j = 0; j < 6; j++) f_v[j] = 0.; // set partial derivative for f5 f_v[5] = 1.; ok &= std::fabs( f_v[5] - 1. ) <= 1e-10; // f5_v5 // f4 = f5( v1 , v2 , v3 , v4 , v2 + v4 ) f_v[2] += f_v[5] * 1.; f_v[4] += f_v[5] * 1.; ok &= std::fabs( f_v[2] - 1. ) <= 1e-10; // f4_v2 ok &= std::fabs( f_v[4] - 1. ) <= 1e-10; // f4_v4 // f3 = f4( v1 , v2 , v3 , v3 / 2 ) f_v[3] += f_v[4] / 2.; ok &= std::fabs( f_v[3] - 0.5) <= 1e-10; // f3_v3 // f2 = f3( v1 , v2 , v1 * v1 ) f_v[1] += f_v[3] * 2. * v0[1]; ok &= std::fabs( f_v[1] - 0.5) <= 1e-10; // f2_v1 // f1 = f2( v1 , 1 + v1 ) f_v[1] += f_v[2] * 1.; ok &= std::fabs( f_v[1] - 1.5) <= 1e-10; // f1_v1 return ok; } /* %$$ $end */ cppad-20170000.3/introduction/get_started/0002755000175200017650000000000013057470463017463 5ustar coincoin-webcppad-20170000.3/introduction/get_started/makefile.am0000644000175200017650000000166713057470463021567 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # check_PROGRAMS = get_started # AM_CPPFLAGS = -I. -I$(top_srcdir) $(BOOST_INCLUDE) $(EIGEN_INCLUDE) AM_CXXFLAGS = -g $(CXX_FLAGS) # get_started_SOURCES = get_started.cpp # test: check ./get_started cppad-20170000.3/introduction/get_started/CMakeLists.txt0000644000175200017650000000254313057470463022225 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin get_started.cpp$$ $spell cppad.hpp http://www.coin-or.org/CppAD/ getstarted namespace iostream const std powx Jacobian jac endl da cout $$ $section Getting Started Using CppAD to Compute Derivatives$$ $mindex simple example start$$ $head Purpose$$ Demonstrate the use of CppAD by computing the derivative of a simple example function. $head Function$$ The example function $latex f : \B{R} \rightarrow \B{R}$$ is defined by $latex \[ f(x) = a_0 + a_1 * x^1 + \cdots + a_{k-1} * x^{k-1} \] $$ where $icode a$$ is a fixed vector of length $icode k$$. $head Derivative$$ The derivative of $latex f(x)$$ is given by $latex \[ f' (x) = a_1 + 2 * a_2 * x + \cdots + (k-1) * a_{k-1} * x^{k-2} \] $$ $head Value$$ For the particular case in this example, $latex k$$ is equal to 5, $latex a = (1, 1, 1, 1, 1)$$, and $latex x = 3$$. If follows that $latex \[ f' ( 3 ) = 1 + 2 * 3 + 3 * 3^2 + 4 * 3^3 = 142 \] $$ $head Poly$$ The routine $code Poly$$ is defined below for this particular application. A general purpose polynomial evaluation routine is documented and distributed with CppAD (see $cref Poly$$). $head Exercises$$ Modify the program below to accomplish the following tasks using CppAD: $list number$$ Compute and print the derivative of $latex f(x) = 1 + x + x^2 + x^3 + x^4$$ at the point $latex x = 2$$. $lnext Compute and print the derivative of $latex f(x) = 1 + x + x^2 / 2$$ at the point $latex x = .5$$. $lnext Compute and print the derivative of $latex f(x) = \exp (x) - 1 - x - x^2 / 2$$ at the point $latex x = .5$$. $lend $head Program$$ $srccode%cpp% */ #include // standard input/output #include // standard vector #include // the CppAD package http://www.coin-or.org/CppAD/ namespace { // define y(x) = Poly(a, x) in the empty namespace template Type Poly(const std::vector &a, const Type &x) { size_t k = a.size(); Type y = 0.; // initialize summation Type x_i = 1.; // initialize x^i size_t i; for(i = 0; i < k; i++) { y += a[i] * x_i; // y = y + a_i * x^i x_i *= x; // x_i = x_i * x } return y; } } // main program int main(void) { using CppAD::AD; // use AD as abbreviation for CppAD::AD using std::vector; // use vector as abbreviation for std::vector size_t i; // a temporary index // vector of polynomial coefficients size_t k = 5; // number of polynomial coefficients vector a(k); // vector of polynomial coefficients for(i = 0; i < k; i++) a[i] = 1.; // value of polynomial coefficients // domain space vector size_t n = 1; // number of domain space variables vector< AD > X(n); // vector of domain space variables X[0] = 3.; // value corresponding to operation sequence // declare independent variables and start recording operation sequence CppAD::Independent(X); // range space vector size_t m = 1; // number of ranges space variables vector< AD > Y(m); // vector of ranges space variables Y[0] = Poly(a, X[0]); // value during recording of operations // store operation sequence in f: X -> Y and stop recording CppAD::ADFun f(X, Y); // compute derivative using operation sequence stored in f vector jac(m * n); // Jacobian of f (m by n matrix) vector x(n); // domain space vector x[0] = 3.; // argument value for derivative jac = f.Jacobian(x); // Jacobian for operation sequence // print the results std::cout << "f'(3) computed by CppAD = " << jac[0] << std::endl; // check if the derivative is correct int error_code; if( jac[0] == 142. ) error_code = 0; // return code for correct case else error_code = 1; // return code for incorrect case return error_code; } /* %$$ $head Output$$ Executing the program above will generate the following output: $codep f'(3) computed by CppAD = 142 $$ $head Running$$ To build and run this program see $cref cmake_check$$. $end */ cppad-20170000.3/introduction/CMakeLists.txt0000644000175200017650000000204613057470463017716 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the introduction/* directory tests # SET(check_introduction_depends "") ADD_SUBDIRECTORY(exp_apx) ADD_SUBDIRECTORY(get_started) # Add the check_introduction target ADD_CUSTOM_TARGET(check_introduction DEPENDS ${check_introduction_depends}) MESSAGE(STATUS "make check_introduction: available") # Change check depends in parent environment add_to_list(check_depends check_introduction) SET(check_depends "${check_depends}" PARENT_SCOPE) cppad-20170000.3/multi_thread/0002755000175200017650000000000013057470463015116 5ustar coincoin-webcppad-20170000.3/multi_thread/bthread/0002755000175200017650000000000013057470463016527 5ustar coincoin-webcppad-20170000.3/multi_thread/bthread/team_bthread.cpp0000644000175200017650000002027613057470463021657 0ustar coincoin-web// $Id: team_bthread.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin team_bthread.cpp$$ $spell bthread $$ $section Boost Thread Implementation of a Team of AD Threads$$ $mindex bthread$$ See $cref team_thread.hpp$$ for this routines specifications. $code $srcfile%multi_thread/bthread/team_bthread.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include "../team_thread.hpp" # define MAX_NUMBER_THREADS 48 namespace { using CppAD::thread_alloc; // number of threads in the team size_t num_threads_ = 1; // no need to cleanup up thread specific data void cleanup(size_t*) { return; } // thread specific pointer the thread number (initialize as null) boost::thread_specific_ptr thread_num_ptr_(cleanup); // type of the job currently being done by each thread enum thread_job_t { init_enum, work_enum, join_enum } thread_job_; // barrier used to wait for other threads to finish work boost::barrier* wait_for_work_ = CPPAD_NULL; // barrier used to wait for master thread to set next job boost::barrier* wait_for_job_ = CPPAD_NULL; // Are we in sequential mode; i.e., other threads are waiting for // master thread to set up next job ? bool sequential_execution_ = true; // structure with information for one thread typedef struct { // The thread boost::thread* bthread; // CppAD thread number as global (pointed to by thread_num_ptr_) size_t thread_num; // true if no error for this thread, false otherwise. bool ok; } thread_one_t; // vector with information for all threads thread_one_t thread_all_[MAX_NUMBER_THREADS]; // pointer to function that does the work for one thread void (* worker_)(void) = CPPAD_NULL; // --------------------------------------------------------------------- // in_parallel() bool in_parallel(void) { return ! sequential_execution_; } // --------------------------------------------------------------------- // thread_number() size_t thread_number(void) { // return thread_all_[thread_num].thread_num return *thread_num_ptr_.get(); } // -------------------------------------------------------------------- // function that gets called by boost thread constructor void thread_work(size_t thread_num) { bool ok = wait_for_work_ != CPPAD_NULL; ok &= wait_for_job_ != CPPAD_NULL; ok &= thread_num != 0; // thread specific storage of thread number for this thread thread_num_ptr_.reset(& thread_all_[thread_num].thread_num ); while( true ) { // Use wait_for_jog_ to give master time in sequential mode // (so it can change global information like thread_job_) wait_for_job_->wait(); // case where we are terminating this thread (no more work) if( thread_job_ == join_enum) break; // only other case once wait_for_job_ has been completed (so far) ok &= thread_job_ == work_enum; worker_(); // Use wait_for_work_ to inform master that our work is done and // that this thread will not use global infromation until // passing its barrier wait_for_job_ above. wait_for_work_->wait(); } thread_all_[thread_num].ok &= ok; return; } } bool team_create(size_t num_threads) { bool ok = true;; if( num_threads > MAX_NUMBER_THREADS ) { std::cerr << "team_create: num_threads greater than "; std::cerr << MAX_NUMBER_THREADS << std::endl; exit(1); } // check that we currently do not have multiple threads running ok = num_threads_ == 1; ok &= wait_for_work_ == CPPAD_NULL; ok &= wait_for_job_ == CPPAD_NULL; ok &= sequential_execution_; size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { // Each thread gets a pointer to its version of this thread_num // so it knows which section of thread_all it is working with thread_all_[thread_num].thread_num = thread_num; // initialize thread_all_[thread_num].ok = true; thread_all_[0].bthread = CPPAD_NULL; } // Finish setup of thread_all_ for this thread thread_num_ptr_.reset(& thread_all_[0].thread_num); // Now that thread_number() has necessary information for the case // num_threads_ == 1, and while still in sequential mode, // call setup for using CppAD::AD in parallel mode. thread_alloc::parallel_setup(num_threads, in_parallel, thread_number); thread_alloc::hold_memory(true); CppAD::parallel_ad(); // now change num_threads_ to its final value. num_threads_ = num_threads; // initialize two barriers, one for work done, one for new job ready wait_for_work_ = new boost::barrier(num_threads); wait_for_job_ = new boost::barrier(num_threads); // initial job for the threads thread_job_ = init_enum; if( num_threads > 1 ) sequential_execution_ = false; // This master thread is already running, we need to create // num_threads - 1 more threads for(thread_num = 1; thread_num < num_threads; thread_num++) { // Create the thread with thread number equal to thread_num thread_all_[thread_num].bthread = new boost::thread(thread_work, thread_num); } // Current state is other threads are at wait_for_job_. // This master thread (thread zero) has not completed wait_for_job_ sequential_execution_ = true; return ok; } bool team_work(void worker(void)) { // Current state is other threads are at wait_for_job_. // This master thread (thread zero) has not completed wait_for_job_ bool ok = sequential_execution_; ok &= thread_number() == 0; ok &= wait_for_work_ != CPPAD_NULL; ok &= wait_for_job_ != CPPAD_NULL; // set global version of this work routine worker_ = worker; // set the new job that other threads are waiting for thread_job_ = work_enum; // Enter parallel exectuion when master thread calls wait_for_job_ if( num_threads_ > 1 ) sequential_execution_ = false; wait_for_job_->wait(); // Now do the work in this thread and then wait // until all threads have completed wait_for_work_ worker(); wait_for_work_->wait(); // Current state is other threads are at wait_for_job_. // This master thread (thread zero) has not completed wait_for_job_ sequential_execution_ = true; size_t thread_num; for(thread_num = 0; thread_num < num_threads_; thread_num++) ok &= thread_all_[thread_num].ok; return ok; } bool team_destroy(void) { // Current state is other threads are at wait_for_job_. // This master thread (thread zero) has not completed wait_for_job_ bool ok = sequential_execution_; ok &= thread_number() == 0; ok &= wait_for_work_ != CPPAD_NULL; ok &= wait_for_job_ != CPPAD_NULL; // set the new job that other threads are waiting for thread_job_ = join_enum; // enter parallel exectuion soon as master thread completes wait_for_job_ if( num_threads_ > 1 ) sequential_execution_ = false; wait_for_job_->wait(); // now wait for the other threads to be destroyed size_t thread_num; ok &= thread_all_[0].bthread == CPPAD_NULL; for(thread_num = 1; thread_num < num_threads_; thread_num++) { thread_all_[thread_num].bthread->join(); delete thread_all_[thread_num].bthread; thread_all_[thread_num].bthread = CPPAD_NULL; } // now we are down to just the master thread (thread zero) sequential_execution_ = true; // destroy wait_for_work_ delete wait_for_work_; wait_for_work_ = CPPAD_NULL; // destroy wait_for_job_ delete wait_for_job_; wait_for_job_ = CPPAD_NULL; // check ok before changing num_threads_ for(thread_num = 0; thread_num < num_threads_; thread_num++) ok &= thread_all_[thread_num].ok; // now inform CppAD that there is only one thread num_threads_ = 1; thread_alloc::parallel_setup(num_threads_, CPPAD_NULL, CPPAD_NULL); thread_alloc::hold_memory(false); CppAD::parallel_ad(); return ok; } const char* team_name(void) { return "bthread"; } // END C++ cppad-20170000.3/multi_thread/bthread/simple_ad_bthread.cpp0000644000175200017650000002052213057470463022660 0ustar coincoin-web// $Id: simple_ad_bthread.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin simple_ad_bthread.cpp$$ $spell bthread CppAD $$ $section A Simple Boost Threading AD: Example and Test$$ $mindex thread AD$$ $head Purpose$$ This example demonstrates how CppAD can be used in a boost multi-threading environment. $head Source Code$$ $code $srcfile%multi_thread/bthread/simple_ad_bthread.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include # include # define NUMBER_THREADS 4 namespace { // structure with problem specific information typedef struct { // function argument (worker input) double x; // This structure would also have return information in it, // but this example only returns the ok flag } problem_specific; // ===================================================================== // General purpose code you can copy to your application // ===================================================================== using CppAD::thread_alloc; // ------------------------------------------------------------------ // thread specific point to the thread number (initialize as null) void cleanup(size_t*) { return; } boost::thread_specific_ptr thread_num_ptr_(cleanup); // Are we in sequential mode; i.e., other threads are waiting for // master thread to set up next job ? bool sequential_execution_ = true; // used to inform CppAD when we are in parallel execution mode bool in_parallel(void) { return ! sequential_execution_; } // used to inform CppAD of current thread number thread_number() size_t thread_number(void) { // return thread_all_[thread_num].thread_num return *thread_num_ptr_.get(); } // --------------------------------------------------------------------- // structure with information for one thread typedef struct { // number for this thread (thread specific points here) size_t thread_num; // pointer to this boost thread boost::thread* bthread; // false if an error occurs, true otherwise bool ok; // pointer to problem specific information problem_specific* info; } thread_one_t; // vector with information for all threads thread_one_t thread_all_[NUMBER_THREADS]; // -------------------------------------------------------------------- // function that initializes the thread and then calls actual worker bool worker(size_t thread_num, problem_specific* info); void run_one_worker(size_t thread_num) { bool ok = true; // The master thread should call worker directly ok &= thread_num != 0; // This is not the master thread, so thread specific infromation // has not yet been set. We use it to inform other routines // of this threads number. // We must do this before calling thread_alloc::thread_num(). thread_num_ptr_.reset(& thread_all_[thread_num].thread_num); // Check the value of thread_alloc::thread_num(). ok = thread_num == thread_alloc::thread_num(); // Now do the work ok &= worker(thread_num, thread_all_[thread_num].info); // pass back ok information for this thread thread_all_[thread_num].ok = ok; // no return value return; } // ---------------------------------------------------------------------- // function that calls all the workers bool run_all_workers(size_t num_threads, problem_specific* info_all[]) { bool ok = true; // initialize thread_all_ (execpt for pthread_id) size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { // pointed to by thread specific info for this thread thread_all_[thread_num].thread_num = thread_num; // initialize as false to make sure worker gets called by other // threads. Note that thread_all_[0].ok does not get used thread_all_[thread_num].ok = false; // problem specific information thread_all_[thread_num].info = info_all[thread_num]; } // master bthread number thread_num_ptr_.reset(& thread_all_[0].thread_num); // Now thread_number() has necessary information for this thread // (number zero), and while still in sequential mode, // call setup for using CppAD::AD in parallel mode. thread_alloc::parallel_setup( num_threads, in_parallel, thread_number ); thread_alloc::hold_memory(true); CppAD::parallel_ad(); // inform CppAD that we now may be in parallel execution mode sequential_execution_ = false; // This master thread is already running, we need to create // num_threads - 1 more threads thread_all_[0].bthread = CPPAD_NULL; for(thread_num = 1; thread_num < num_threads; thread_num++) { // Create the thread with thread number equal to thread_num thread_all_[thread_num].bthread = new boost::thread(run_one_worker, thread_num); } // now call worker for the master thread thread_num = thread_alloc::thread_num(); ok &= thread_num == 0; ok &= worker(thread_num, thread_all_[thread_num].info); // now wait for the other threads to finish for(thread_num = 1; thread_num < num_threads; thread_num++) { thread_all_[thread_num].bthread->join(); delete thread_all_[thread_num].bthread; thread_all_[thread_num].bthread = CPPAD_NULL; } // Inform CppAD that we now are definately back to sequential mode sequential_execution_ = true; // now inform CppAD that there is only one thread thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL); thread_alloc::hold_memory(false); CppAD::parallel_ad(); // check to ok flag returned by during calls to work by other threads for(thread_num = 1; thread_num < num_threads; thread_num++) ok &= thread_all_[thread_num].ok; return ok; } // ===================================================================== // End of General purpose code // ===================================================================== // function that does the work for one thread bool worker(size_t thread_num, problem_specific* info) { bool ok = true; // CppAD::vector uses the CppAD fast multi-threading allocator CppAD::vector< CppAD::AD > ax(1), ay(1); ax[0] = info->x; Independent(ax); ay[0] = sqrt( ax[0] * ax[0] ); CppAD::ADFun f(ax, ay); // Check function value corresponds to the identity double eps = 10. * CppAD::numeric_limits::epsilon(); ok &= CppAD::NearEqual(ay[0], ax[0], eps, eps); // Check derivative value corresponds to the identity. CppAD::vector d_x(1), d_y(1); d_x[0] = 1.; d_y = f.Forward(1, d_x); ok &= CppAD::NearEqual(d_x[0], 1., eps, eps); return ok; } } bool simple_ad(void) { bool ok = true; size_t num_threads = NUMBER_THREADS; // Check that no memory is in use or avialable at start // (using thread_alloc in sequential mode) size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { ok &= thread_alloc::inuse(thread_num) == 0; ok &= thread_alloc::available(thread_num) == 0; } // initialize info_all problem_specific *info, *info_all[NUMBER_THREADS]; for(thread_num = 0; thread_num < num_threads; thread_num++) { // problem specific information size_t min_bytes(sizeof(info)), cap_bytes; void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes); info = static_cast(v_ptr); info->x = double(thread_num) + 1.; info_all[thread_num] = info; } ok &= run_all_workers(num_threads, info_all); // go down so that free memory for other threads before memory for master thread_num = num_threads; while(thread_num--) { // delete problem specific information void* v_ptr = static_cast( info_all[thread_num] ); thread_alloc::return_memory( v_ptr ); // check that there is no longer any memory inuse by this thread ok &= thread_alloc::inuse(thread_num) == 0; // return all memory being held for future use by this thread thread_alloc::free_available(thread_num); } return ok; } // END C++ cppad-20170000.3/multi_thread/bthread/CMakeLists.txt0000644000175200017650000000375413057470463021276 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the multi_thread/bthread directory tests # Inherit build type from ../CMakeList.txt # Local include directories to search (not in package_prefix/include) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/.. ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(multi_thread_bthread EXCLUDE_FROM_ALL ../thread_test.cpp ../../speed/src/microsoft_timer.cpp ../multi_newton_time.cpp ../multi_newton.cpp ../multi_newton_work.cpp ../team_example.cpp ../harmonic_time.cpp ../harmonic.cpp ../harmonic_work.cpp a11c_bthread.cpp simple_ad_bthread.cpp team_bthread.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( multi_thread_bthread ) # Paths in which the linker will search for libraries, # only applies to targets created after it is called LINK_DIRECTORIES( ${bthread_lib_path} ) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES(multi_thread_bthread ${bthread_lib}) # Add the check_multi_thread_bthread target ADD_CUSTOM_TARGET(check_multi_thread_bthread multi_thread_bthread simple_ad DEPENDS multi_thread_bthread ) MESSAGE(STATUS "make check_multi_thread_bthread: available") # Change check depends in parent environment add_to_list(check_multi_thread_depends check_multi_thread_bthread) SET(check_multi_thread_depends "${check_multi_thread_depends}" PARENT_SCOPE) cppad-20170000.3/multi_thread/bthread/a11c_bthread.cpp0000644000175200017650000000574113057470463021456 0ustar coincoin-web// $Id: a11c_bthread.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin a11c_bthread.cpp$$ $spell bthread bthreads CppAD const $$ $section A Simple Boost Thread Example and Test$$ $mindex A.1.1c$$ $head Purpose$$ This example just demonstrates Boost threads and does not use CppAD at all. $head Source Code$$ $code $srcfile%multi_thread/bthread/a11c_bthread.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ---------------------------------------------------------------------------- */ // BEGIN C++ # include # include # include # include # define NUMBER_THREADS 4 namespace { // Begin empty namespace class worker_t { private: int n_; float* a_; float* b_; public: void setup(size_t n, float* a, float* b) { n_ = static_cast(n); a_ = a; b_ = b; } // Beginning of Example A.1.1.1c of OpenMP 2.5 standard document void a1(int n, float *a, float *b) { int i; // for some reason this function is missing on some systems // assert( bthread_is_multithreaded_np() > 0 ); for(i = 1; i < n; i++) b[i] = (a[i] + a[i-1]) / 2.0; return; } // End of Example A.1.1.1c of OpenMP 2.5 standard document void operator()() { a1(n_, a_, b_); } }; } bool a11c(void) { bool ok = true; // Test setup size_t i, j, n_total = 10; float *a = new float[n_total]; float *b = new float[n_total]; for(i = 0; i < n_total; i++) a[i] = float(i); // number of threads size_t number_threads = NUMBER_THREADS; // set of workers worker_t worker[NUMBER_THREADS]; // threads for each worker boost::thread* bthread[NUMBER_THREADS]; // Break the work up into sub work for each thread size_t n = n_total / number_threads; size_t n_tmp = n; float* a_tmp = a; float* b_tmp = b; worker[0].setup(n_tmp, a_tmp, b_tmp); for(j = 1; j < number_threads; j++) { n_tmp = n + 1; a_tmp = a_tmp + n - 1; b_tmp = b_tmp + n - 1; if( j == (number_threads - 1) ) n_tmp = n_total - j * n + 1; worker[j].setup(n_tmp, a_tmp, b_tmp); // create this thread bthread[j] = new boost::thread(worker[j]); } // do this threads protion of the work worker[0](); // wait for other threads to finish for(j = 1; j < number_threads; j++) { bthread[j]->join(); delete bthread[j]; } // check the result float eps = 100. * std::numeric_limits::epsilon(); for(i = 1; i < n ; i++) ok &= std::fabs( (2. * b[i] - a[i] - a[i-1]) / b[i] ) <= eps; delete [] a; delete [] b; return ok; } // END C++ cppad-20170000.3/multi_thread/makefile.am0000644000175200017650000000455013057470463017214 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD puts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # if CppAD_OPENMP OPENMP_TEST = openmp_test else OPENMP_TEST = endif # if CppAD_BTHREAD # BTHREAD_LIB set to proper value in this case BTHREAD_TEST = bthread_test if CppAD_BOOST_DIR BOOST_LIB = -L$(BOOST_DIR)/lib endif else # BTHREAD_LIB empty in this case BTHREAD_TEST = BOOST_LIB = endif # if CppAD_PTHREAD PTHREAD_TEST = pthread_test else PTHREAD_TEST = endif # check_PROGRAMS = $(OPENMP_TEST) $(BTHREAD_TEST) $(PTHREAD_TEST) # if CppAD_MS_COMPILER # AM_CXXFLAGS = -EHsc -g $(CXX_FLAGS) AM_CXXFLAGS = -EHsc -DNDEBUG -O2 $(CXX_FLAGS) else # AM_CXXFLAGS = -g $(CXX_FLAGS) AM_CXXFLAGS = -DNDEBUG -O2 $(CXX_FLAGS) endif # AM_CPPFLAGS = \ -I. \ -I$(top_srcdir) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ $(OPENMP_FLAGS) # AM_LDFLAGS = $(OPENMP_FLAGS) LDADD = $(BOOST_LIB) $(BTHREAD_LIB) $(PTHREAD_LIB) # SHARED_SRC = \ thread_test.cpp \ team_thread.hpp \ \ multi_newton_time.cpp multi_newton_time.hpp \ multi_newton.cpp multi_newton.hpp \ multi_newton_work.cpp multi_newton_work.hpp \ team_example.cpp team_example.hpp \ harmonic_time.cpp harmonic_time.hpp \ harmonic.cpp harmonic.hpp \ harmonic_work.cpp harmonic_work.hpp # bthread_test_SOURCES = \ $(SHARED_SRC) \ bthread/team_bthread.cpp \ bthread/a11c_bthread.cpp \ bthread/simple_ad_bthread.cpp # openmp_test_SOURCES = \ $(SHARED_SRC) \ openmp/team_openmp.cpp \ openmp/a11c_openmp.cpp \ openmp/simple_ad_openmp.cpp # pthread_test_SOURCES = \ $(SHARED_SRC) \ pthread/team_pthread.cpp \ pthread/a11c_pthread.cpp \ pthread/simple_ad_pthread.cpp # dist_noinst_SCRIPTS = test.sh # test: check $(srcdir)/test.sh cppad-20170000.3/multi_thread/multi_newton.hpp0000644000175200017650000000206013057470463020347 0ustar coincoin-web// $Id: multi_newton.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_MULTI_THREAD_MULTI_NEWTON_HPP # define CPPAD_MULTI_THREAD_MULTI_NEWTON_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ extern bool multi_newton( CppAD::vector &xout , void fun(double x, double& f, double& df) , size_t num_sub , double xlow , double xup , double epsilon , size_t max_itr , size_t num_threads ); # endif cppad-20170000.3/multi_thread/multi_newton_work.hpp0000644000175200017650000000224013057470463021411 0ustar coincoin-web// $Id: multi_newton_work.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_MULTI_THREAD_MULTI_NEWTON_WORK_HPP # define CPPAD_MULTI_THREAD_MULTI_NEWTON_WORK_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include extern bool multi_newton_setup( void (fun)(double x, double& f, double& df) , size_t num_sub , double xlow , double xup , double epsilon , size_t max_itr , size_t num_threads ); extern void multi_newton_worker(void); extern bool multi_newton_combine(CppAD::vector& xout); # endif cppad-20170000.3/multi_thread/CMakeLists.txt0000644000175200017650000000723413057470463017662 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Specifies build type for this directory and all its subdirecgtories # (subdirectories do not specify build type). # Possible values are , Debug, Release, RelWithDebInfo and MinSizeRel SET(CMAKE_BUILD_TYPE DEBUG) # initialize list as empty SET(check_multi_thread_depends "") # Define the operation # CHECK_LIBRARY_EXISTS (LIBRARY FUNCTION LOCATION VARIABLE) # LIBRARY - the name of the library you are looking for # FUNCTION - the name of the function # LOCATION - location where the library should be found # VARIABLE - variable to store the result INCLUDE(CheckLibraryExists) # If openmp found, set OpenMP_CXX_FLAGS and process its subdirectory # FIND_PACKAGE(OpenMP) IF ( OPENMP_FOUND ) # OpenMP_CXX_FLAGS - flags to add to the CXX compiler for OpenMP support ADD_SUBDIRECTORY(openmp) ENDIF ( OPENMP_FOUND ) # If pthreads found, set pthread_lib and pthread_lib_path and process subdir # # find_library( name1 [path1 path2 ...]) SET(pthread_lib "pthread") FIND_LIBRARY(pthread_lib_path pthread) MESSAGE(STATUS "pthread library path = ${pthread_lib_path}") IF ( pthread_lib_path ) CHECK_LIBRARY_EXISTS( pthread pthread_barrier_wait ${pthread_lib_path} pthread_ok ) IF ( pthread_ok ) ADD_SUBDIRECTORY(pthread) ENDIF ( pthread_ok ) ENDIF ( pthread_lib_path ) # IF we find a boost multi-threadding library, define the corresponding # bthread_lib, bthread_lib_path, and process the bthread subdirectory. IF ( Boost_FOUND ) SET(bthread_lib NOTFOUND) FOREACH(idir ${cmake_install_includedirs}) FOREACH(ldir ${cmake_install_libdirs}) FOREACH(lname boost_thread-mt boost_thread ) # abort this search when find a match IF( NOT bthread_lib ) # SET(CMAKE_REQUIRED_INCLUDES "${boost_prefix}/${idir}") SET(CMAKE_REQUIRED_LIBRARIES "${lname}" ) SET(lpath "${boost_prefix}/${ldir}" ) SET(CMAKE_REQUIRED_FLAGS "-L${lpath}" ) # CHECK_CXX_SOURCE_RUNS(source variable) SET(source " # include int main(void) { boost::barrier wait(1); return 0; }" ) SET(flag ${idir}_${ldir}_${lname}_ok ) CHECK_CXX_SOURCE_RUNS("${source}" ${flag} ) IF ( ${flag} ) SET(bthread_lib ${lname} ) SET(bthread_lib_path ${lpath} ) ENDIF ( ${flag} ) ENDIF( NOT bthread_lib ) ENDFOREACH(lname boost_thread boost_thread-mt) ENDFOREACH(ldir ${cmake_install_liddirs}) ENDFOREACH(idir ${cmake_install_includedirs}) # IF( bthread_lib ) ADD_SUBDIRECTORY(bthread) MESSAGE(STATUS "boost multi-threading library = ${bthread_lib_path}/${bthread_lib}" ) ELSE( bthread_lib ) MESSAGE(STATUS "Could not find boost multi-threading library") ENDIF( bthread_lib ) ENDIF ( Boost_FOUND ) IF( NOT( "${check_multi_threads_depends}" STREQUAL "" ) ) # check_multi_thread ADD_CUSTOM_TARGET(check_multi_thread DEPENDS ${check_multi_thread_depends}) MESSAGE(STATUS "make check_multi_thread: available") # Change check depends in parent environment add_to_list(check_depends check_multi_thread) SET(check_depends "${check_depends}" PARENT_SCOPE) ENDIF( NOT( "${check_multi_threads_depends}" STREQUAL "" ) ) cppad-20170000.3/multi_thread/harmonic.cpp0000644000175200017650000000457713057470463017435 0ustar coincoin-web// $Id: harmonic.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin harmonic.cpp$$ $spell inv num bool $$ $section Multi-Threaded Implementation of Summation of 1/i$$ $mindex harmonic multi_thread$$ $head Syntax$$ $icode%ok% = harmonic(%sum%, %num_sum%, %num_threads%)%$$ $head Summation$$ Multi-threaded computation of the summation that defines the harmonic series $latex \[ s = 1 + 1/2 + 1/3 + ... + 1/n \] $$ $head ok$$ This return value has prototype $codei% bool %ok% %$$ If this return value is false, an error occurred during $code harmonic$$. $head sum$$ This argument has prototype $codei% double& %sum% %$$ The input value of the argument does not matter. Upon return it is the value of the summation; i.e. $latex s$$. $head num_sum$$ This argument has prototype $codei% size_t %num_sum% %$$ It specifies the number of terms in the summation; i.e. $latex n$$. $head num_threads$$ This argument has prototype $codei% size_t %num_threads% %$$ It specifies the number of threads that are available for this test. If it is zero, the test is run without a multi-threading environment. $childtable% multi_thread/harmonic_time.cpp% multi_thread/harmonic_work.cpp %$$ $head Source$$ $code $srcfile%multi_thread/harmonic.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ // general purpose multi-threading interface # include "team_thread.hpp" // special utilities for the harmonic problem # include "harmonic_work.hpp" bool harmonic(double& sum, size_t num_sum, size_t num_threads) { // sum = 1/num_sum + 1/(num_sum-1) + ... + 1 bool ok = true; // setup the work for num_threads_ threads ok &= harmonic_setup(num_sum, num_threads); // now do the work for each thread if( num_threads > 0 ) team_work( harmonic_worker ); else harmonic_worker(); // now combine the result for all the threads ok &= harmonic_combine(sum); return ok; } // END C++ cppad-20170000.3/multi_thread/team_example.cpp0000644000175200017650000001041313057470463020260 0ustar coincoin-web// $Id: team_example.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin team_example.cpp$$ $spell CppAD $$ $section Using a Team of AD Threads: Example and Test$$ $mindex thread$$ $head Purpose$$ This example demonstrates how use a team threads with CppAD. $head thread_team$$ The following three implementations of the $cref team_thread.hpp$$ specifications are included: $table $rref team_openmp.cpp$$ $rref team_bthread.cpp$$ $rref team_pthread.cpp$$ $tend $head Source Code$$ $code $srcfile%multi_thread/team_example.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include # include "team_thread.hpp" # define NUMBER_THREADS 4 namespace { using CppAD::thread_alloc; // structure with information for one thread typedef struct { // function argument (worker input) double x; // false if an error occurs, true otherwise (worker output) bool ok; } work_one_t; // vector with information for all threads // (use pointers instead of values to avoid false sharing) work_one_t* work_all_[NUMBER_THREADS]; // -------------------------------------------------------------------- // function that does the work for one thread void worker(void) { using CppAD::NearEqual; using CppAD::AD; bool ok = true; size_t thread_num = thread_alloc::thread_num(); // CppAD::vector uses the CppAD fast multi-threading allocator CppAD::vector< AD > ax(1), ay(1); ax[0] = work_all_[thread_num]->x; Independent(ax); ay[0] = sqrt( ax[0] * ax[0] ); CppAD::ADFun f(ax, ay); // Check function value corresponds to the identity double eps = 10. * CppAD::numeric_limits::epsilon(); ok &= NearEqual(ay[0], ax[0], eps, eps); // Check derivative value corresponds to the identity. CppAD::vector d_x(1), d_y(1); d_x[0] = 1.; d_y = f.Forward(1, d_x); ok &= NearEqual(d_x[0], 1., eps, eps); // pass back ok information for this thread work_all_[thread_num]->ok = ok; } } // This test routine is only called by the master thread (thread_num = 0). bool team_example(void) { bool ok = true; size_t num_threads = NUMBER_THREADS; // Check that no memory is in use or avialable at start // (using thread_alloc in sequential mode) size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { ok &= thread_alloc::inuse(thread_num) == 0; ok &= thread_alloc::available(thread_num) == 0; } // initialize work_all_ for(thread_num = 0; thread_num < num_threads; thread_num++) { // allocate separate memory for this thread to avoid false sharing size_t min_bytes(sizeof(work_one_t)), cap_bytes; void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes); work_all_[thread_num] = static_cast(v_ptr); // incase this thread's worker does not get called work_all_[thread_num]->ok = false; // parameter that defines the work for this thread work_all_[thread_num]->x = double(thread_num) + 1.; } ok &= team_create(num_threads); ok &= team_work(worker); ok &= team_destroy(); // go down so that free memrory for other threads before memory for master thread_num = num_threads; while(thread_num--) { // check that this thread was ok with the work it did ok &= work_all_[thread_num]->ok; // delete problem specific information void* v_ptr = static_cast( work_all_[thread_num] ); thread_alloc::return_memory( v_ptr ); // check that there is no longer any memory inuse by this thread // (for general applications, the master might still be using memory) ok &= thread_alloc::inuse(thread_num) == 0; // return all memory being held for future use by this thread thread_alloc::free_available(thread_num); } return ok; } // END C++ cppad-20170000.3/multi_thread/makefile.in0000644000175200017650000006243513057470463017233 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; 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maintainer-clean maintainer-clean-generic mostlyclean \ mostlyclean-compile mostlyclean-generic pdf pdf-am ps ps-am \ tags tags-am uninstall uninstall-am .PRECIOUS: makefile # test: check $(srcdir)/test.sh # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: cppad-20170000.3/multi_thread/harmonic_work.cpp0000644000175200017650000001320113057470463020457 0ustar coincoin-web// $Id: harmonic_work.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin harmonic_work.cpp$$ $spell inv num $$ $section Multi-threading Sum of 1/i Utility Routines$$ $mindex harmonic_work setup worker combine$$ $head Syntax$$ $icode%ok% = harmonic_setup(%num_sum%, %num_threads%) %$$ $codei%harmonic_worker() %$$ $icode%ok% = harmonic_combine(%sum%) %$$ $head Purpose$$ These routines aid in the multi-threading computation of the summation that defines the harmonic series $latex \[ 1 + 1/2 + 1/3 + ... + 1/n \] $$ $head harmonic_setup$$ Calling this function splits up the computation of the summation into different parts for each thread. $subhead num_sum$$ The argument $icode num_sum$$ has prototype $codei% size_t %num_sum% %$$ It specifies the value of $latex n$$ in the summation. $subhead num_threads$$ The argument $icode num_threads$$ has prototype $codei% size_t %num_threads% %$$ It specifies the number of threads that will be used for the summation. In the special case where $icode num_thread$$ is zero, the summation should be done by one thread, but without the overhead of the multi_threading system. $head harmonic_worker$$ Calling this function does the computation for one thread. Following a call to $code harmonic_setup$$, this function should be called by each of the $icode num_threads$$ threads. $head harmonic_combine$$ After the $icode num_threads$$ threads have completed their calls to $code harmonic_worker$$, this function call will combine the results and return the final summation. $head Source$$ $code $srcfile%multi_thread/harmonic_work.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include "harmonic_work.hpp" # define MAX_NUMBER_THREADS 48 namespace { using CppAD::thread_alloc; // number of threads specified by previous call to harmonic_setup size_t num_threads_ = 0; // structure with information for one thread typedef struct { // index to start summation at (worker input) size_t start; // index to end summation at (worker input) size_t stop; // summation for this thread (worker output) double sum; // false if an error occurs, true otherwise (worker output) bool ok; } work_one_t; // vector with information for all threads // (use pointers instead of values to avoid false sharing) work_one_t* work_all_[MAX_NUMBER_THREADS]; } // ----------------------------------------------------------------------- // do the work for one thread void harmonic_worker(void) { // sum = 1/(stop-1) + 1/(stop-2) + ... + 1/start size_t thread_num = thread_alloc::thread_num(); size_t num_threads = std::max(num_threads_, size_t(1)); bool ok = thread_num < num_threads; size_t start = work_all_[thread_num]->start; size_t stop = work_all_[thread_num]->stop; double sum = 0.; ok &= stop > start; size_t i = stop; while( i > start ) { i--; sum += 1. / double(i); } work_all_[thread_num]->sum = sum; work_all_[thread_num]->ok = ok; } // ----------------------------------------------------------------------- // setup the work up for multiple threads bool harmonic_setup(size_t num_sum, size_t num_threads) { // sum = 1/num_sum + 1/(num_sum-1) + ... + 1 num_threads_ = num_threads; num_threads = std::max(num_threads_, size_t(1)); bool ok = num_threads == thread_alloc::num_threads(); ok &= num_sum >= num_threads; size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { // allocate separate memory for this thread to avoid false sharing size_t min_bytes(sizeof(work_one_t)), cap_bytes; void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes); work_all_[thread_num] = static_cast(v_ptr); // in case this thread's worker does not get called work_all_[thread_num]->ok = false; // parameters that define the work for this and previous thread if( thread_num == 0 ) work_all_[0]->start = 1; else { size_t index = (num_sum * thread_num) / num_threads; work_all_[thread_num-1]->stop = index; work_all_[thread_num]->start = index; } } work_all_[num_threads-1]->stop = num_sum + 1; return ok; } // ----------------------------------------------------------------------- // get the result of the work bool harmonic_combine(double& sum) { // sum = 1/num_sum + 1/(num_sum-1) + ... + 1 bool ok = true; size_t num_threads = std::max(num_threads_, size_t(1)); sum = 0.; // go down so that free memory for other threads before memory for master size_t thread_num = num_threads; while(thread_num--) { // check that this tread was ok with the work it did ok &= work_all_[thread_num]->ok; // add this threads contribution to the sum sum += work_all_[thread_num]->sum; // delete problem specific information void* v_ptr = static_cast( work_all_[thread_num] ); thread_alloc::return_memory( v_ptr ); // check that there is no longer any memory inuse by this thread // (for general applications, the master might still be using memory) ok &= thread_alloc::inuse(thread_num) == 0; // return all memory being held for future use by this thread thread_alloc::free_available(thread_num); } return ok; } // END C++ cppad-20170000.3/multi_thread/multi_newton_time.cpp0000644000175200017650000001731713057470463021373 0ustar coincoin-web// $Id: multi_newton_time.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin multi_newton_time.cpp$$ $spell num Cpp bool alloc openmp $$ . $section Timing Test of Multi-Threaded Newton Method$$ $mindex multi_newton_time multi_thread AD speed$$ $head Syntax$$ $icode%ok% = multi_newton_time(%time_out%, %num_threads%, %num_zero%, %num_sub%, %num_sum%, %use_ad% )%$$ $head Purpose$$ Runs correctness and timing test for a multi-threaded Newton method. This test uses Newton's method to determine all the zeros of the sine function on an interval. CppAD, or hand coded derivatives, can be used to calculate the derivatives used by Newton's method. The calculation can be done in parallel on the different sub-intervals. In addition, the calculation can be done without multi-threading. $head ok$$ This return value has prototype $codei% bool %ok% %$$ If it is true, $code multi_newton_time$$ passed the correctness test. Otherwise it is false. $head time_out$$ This argument has prototype $codei% double& %time_out% %$$ The input value of the argument does not matter. Upon return it is the number of wall clock seconds required for the multi-threaded Newton method can compute all the zeros. $head test_time$$ Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported $icode time_out$$ is the total wall clock time divided by the number of repeats. $head num_threads$$ This argument has prototype $codei% size_t %num_threads% %$$ It specifies the number of threads that are available for this test. If it is zero, the test is run without multi-threading and $codei% 1 == CppAD::thread_alloc::num_threads() %$$ when $code multi_newton_time$$ is called. If it is non-zero, the test is run with multi-threading and $codei% %num_threads% == CppAD::thread_alloc::num_threads() %$$ when $code multi_newton_time$$ is called. $head num_zero$$ This argument has prototype $codei% size_t %num_zero% %$$ and it must be greater than one. It specifies the actual number of zeros in the test function $latex \sin(x)$$. To be specific, $code multi_newton_time$$ will attempt to determine all of the values of $latex x$$ for which $latex \sin(x) = 0 $$ and $latex x$$ is in the interval $codei% [ 0 , (%num_zero% - 1) * %pi% ] %$$. $head num_sub$$ This argument has prototype $codei% size_t %num_sub% %$$ It specifies the number of sub-intervals to divide the total interval into. It must be greater than zero and should probably be greater than two times $icode num_zero$$. $head num_sum$$ This argument has prototype $codei% size_t %num_sum% %$$ and must be greater than zero. The actual function used by the Newton method is $latex \[ f(x) = \frac{1}{n} \sum_{i=1}^{n} \sin (x) \] $$ where $latex n$$ is equal to $icode num_sum$$. Larger values of $icode num_sum$$ simulate a case where the evaluation of the function $latex f(x)$$ takes more time. $head use_ad$$ This argument has prototype $codei% bool %user_ad% %$$ If $icode use_ad$$ is $code true$$, then derivatives will be computed using CppAD. Note that this derivative computation includes re-taping the function for each value of $latex x$$ (even though re-taping is not necessary). $pre $$ If $icode use_ad$$ is $code false$$, derivatives will be computed using a hand coded routine. $head Source$$ $code $srcfile%multi_thread/multi_newton_time.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include # include # include "multi_newton.hpp" namespace { // empty namespace // values correspond to arguments in previous call to multi_newton_time size_t num_threads_;// value passed to multi_newton_time size_t num_zero_; // number of zeros of f(x) in the total interval size_t num_sub_; // number of sub-intervals to split calculation into size_t num_sum_; // larger values make f(x) take longer to calculate // value of xout corresponding to most recent call to test_once CppAD::vector xout_; // either fun_ad or fun_no depending on value of use_ad void (*fun_)(double x, double& f, double& df) = 0; // A version of the sine function that can be made as slow as we like template Float f_eval(Float x) { Float sum = 0.; size_t i; for(i = 0; i < num_sum_; i++) sum += sin(x); return sum / Float(num_sum_); } // Direct calculation of derivative with same number of floating point // operations as for f_eval. double df_direct(double x) { double sum = 0.; size_t i; for(i = 0; i < num_sum_; i++) sum += cos(x); return sum / double(num_sum_); } // AD calculation of detivative void fun_ad(double x, double& f, double& df) { // use CppAD::vector because it uses fast multi-threaded memory alloc using CppAD::vector; using CppAD::AD; vector< AD > X(1), Y(1); X[0] = x; CppAD::Independent(X); Y[0] = f_eval(X[0]); CppAD::ADFun F(X, Y); vector dx(1), dy(1); dx[0] = 1.; dy = F.Forward(1, dx); f = Value( Y[0] ); df = dy[0]; return; } // evaulate the function and its derivative void fun_no(double x, double& f, double& df) { f = f_eval(x); df = df_direct(x); return; } // Run computation of all the zeros once void test_once(void) { if( num_zero_ == 0 ) { std::cerr << "multi_newton_time: num_zero == 0" << std::endl; exit(1); } double pi = 4. * std::atan(1.); double xlow = 0.; double xup = (num_zero_ - 1) * pi; double eps = xup * 100. * CppAD::numeric_limits::epsilon(); size_t max_itr = 20; bool ok = multi_newton( xout_ , fun_ , num_sub_ , xlow , xup , eps , max_itr , num_threads_ ); if( ! ok ) { std::cerr << "multi_newton: error" << std::endl; exit(1); } return; } // Repeat computation of all the zeros a specied number of times void test_repeat(size_t repeat) { size_t i; for(i = 0; i < repeat; i++) test_once(); return; } } // end empty namespace bool multi_newton_time( double& time_out , double test_time , size_t num_threads , size_t num_zero , size_t num_sub , size_t num_sum , bool use_ad ) { bool ok = true; using CppAD::thread_alloc; // Set local namespace environment variables num_threads_ = num_threads; num_zero_ = num_zero; num_sub_ = num_sub; num_sum_ = num_sum; if( use_ad ) fun_ = fun_ad; else fun_ = fun_no; // expect number of threads to already be set up if( num_threads > 0 ) ok &= num_threads == CppAD::thread_alloc::num_threads(); else ok &= 1 == CppAD::thread_alloc::num_threads(); // run the test case and set time return value time_out = CppAD::time_test(test_repeat, test_time); // Call test_once for a correctness check double pi = 4. * std::atan(1.); double xup = (num_zero_ - 1) * pi; double eps = xup * 100. * CppAD::numeric_limits::epsilon(); ok &= (xout_.size() == num_zero); size_t i = 0; for(i = 0; i < num_zero; i++) ok &= std::fabs( xout_[i] - pi * i) <= 2 * eps; // xout_ is a static variable, so clear it to free its memory xout_.clear(); // return correctness check result return ok; } // END C++ cppad-20170000.3/multi_thread/harmonic.hpp0000644000175200017650000000137013057470463017426 0ustar coincoin-web// $Id: harmonic.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_MULTI_THREAD_HARMONIC_HPP # define CPPAD_MULTI_THREAD_HARMONIC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ extern bool harmonic(double& sum, size_t num_sum, size_t num_threads); # endif cppad-20170000.3/multi_thread/pthread/0002755000175200017650000000000013057470463016545 5ustar coincoin-webcppad-20170000.3/multi_thread/pthread/simple_ad_pthread.cpp0000644000175200017650000002300113057470463022707 0ustar coincoin-web// $Id: simple_ad_pthread.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin simple_ad_pthread.cpp$$ $spell pthread CppAD $$ $section A Simple pthread AD: Example and Test$$ $mindex AD$$ $head Purpose$$ This example demonstrates how CppAD can be used in a pthread multi-threading environment. $head Source Code$$ $code $srcfile%multi_thread/pthread/simple_ad_pthread.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include # include # define NUMBER_THREADS 4 namespace { // structure with problem specific information typedef struct { // function argument (worker input) double x; // This structure would also have return information in it, // but this example only returns the ok flag } problem_specific; // ===================================================================== // General purpose code you can copy to your application // ===================================================================== using CppAD::thread_alloc; // ------------------------------------------------------------------ // key for accessing thread specific information pthread_key_t thread_specific_key_; // no need to destroy thread specific information void thread_specific_destructor(void* thread_num_vptr) { return; } // Are we in sequential mode; i.e., other threads are waiting for // master thread to set up next job ? bool sequential_execution_ = true; // used to inform CppAD when we are in parallel execution mode bool in_parallel(void) { return ! sequential_execution_; } // used to inform CppAD of current thread number thread_number() size_t thread_number(void) { // get thread specific information void* thread_num_vptr = pthread_getspecific(thread_specific_key_); size_t* thread_num_ptr = static_cast(thread_num_vptr); size_t thread_num = *thread_num_ptr; return thread_num; } // --------------------------------------------------------------------- // structure with information for one thread typedef struct { // number for this thread (thread specific points here) size_t thread_num; // pthread unique identifier for this thread pthread_t pthread_id; // false if an error occurs, true otherwise bool ok; // pointer to problem specific information problem_specific* info; } thread_one_t; // vector with information for all threads thread_one_t thread_all_[NUMBER_THREADS]; // -------------------------------------------------------------------- // function that initializes the thread and then calls the actual worker bool worker(size_t thread_num, problem_specific* info); void* run_one_worker(void* thread_num_vptr) { bool ok = true; // thread_num for this thread size_t thread_num = *static_cast(thread_num_vptr); // The master thread should call worker directly ok &= thread_num != 0; // This is not the master thread, so thread specific infromation // has not yet been set. We use it to inform other routines // of this threads number. // We must do this before calling thread_alloc::thread_num(). int rc = pthread_setspecific( thread_specific_key_, thread_num_vptr ); ok &= rc == 0; // check the value of thread_alloc::thread_num(). ok = thread_num == thread_alloc::thread_num(); // Now do the work ok &= worker(thread_num, thread_all_[thread_num].info); // pass back ok information for this thread thread_all_[thread_num].ok = ok; // no return value return CPPAD_NULL; } // -------------------------------------------------------------------- // function that calls all the workers bool run_all_workers(size_t num_threads, problem_specific* info_all[]) { bool ok = true; // initialize thread_all_ (execpt for pthread_id) size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { // pointed to by thread specific info for this thread thread_all_[thread_num].thread_num = thread_num; // initialize as false to make sure worker gets called by other // threads. Note that thread_all_[0].ok does not get used thread_all_[thread_num].ok = false; // problem specific information thread_all_[thread_num].info = info_all[thread_num]; } // master pthread_id thread_all_[0].pthread_id = pthread_self(); // error flag for calls to pthread library int rc; // create a key for thread specific information rc = pthread_key_create( &thread_specific_key_, thread_specific_destructor ); ok &= (rc == 0); // set thread specific information for this (master thread) void* thread_num_vptr = static_cast( &(thread_all_[0].thread_num) ); rc = pthread_setspecific(thread_specific_key_, thread_num_vptr); ok &= (rc == 0); // Now thread_number() has necessary information for this thread // (number zero), and while still in sequential mode, // call setup for using CppAD::AD in parallel mode. thread_alloc::parallel_setup( num_threads, in_parallel, thread_number ); thread_alloc::hold_memory(true); CppAD::parallel_ad(); // inform CppAD that we now may be in parallel execution mode sequential_execution_ = false; // structure used to create the threads pthread_t pthread_id; // default for pthread_attr_setdetachstate is PTHREAD_CREATE_JOINABLE pthread_attr_t* no_attr= CPPAD_NULL; // This master thread is already running, we need to create // num_threads - 1 more threads for(thread_num = 1; thread_num < num_threads; thread_num++) { // Create the thread with thread number equal to thread_num thread_num_vptr = static_cast ( &(thread_all_[thread_num].thread_num) ); rc = pthread_create( &pthread_id , no_attr , run_one_worker, thread_num_vptr ); thread_all_[thread_num].pthread_id = pthread_id; ok &= (rc == 0); } // now call worker for the master thread thread_num = thread_alloc::thread_num(); ok &= thread_num == 0; ok &= worker(thread_num, thread_all_[thread_num].info); // now wait for the other threads to finish for(thread_num = 1; thread_num < num_threads; thread_num++) { void* no_status = CPPAD_NULL; rc = pthread_join( thread_all_[thread_num].pthread_id, &no_status ); ok &= (rc == 0); } // Inform CppAD that we now are definately back to sequential mode sequential_execution_ = true; // now inform CppAD that there is only one thread thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL); thread_alloc::hold_memory(false); CppAD::parallel_ad(); // destroy the key for thread specific data pthread_key_delete(thread_specific_key_); // check to ok flag returned by during calls to work by other threads for(thread_num = 1; thread_num < num_threads; thread_num++) ok &= thread_all_[thread_num].ok; return ok; } // ===================================================================== // End of General purpose code // ===================================================================== // function that does the work for one thread bool worker(size_t thread_num, problem_specific* info) { bool ok = true; // CppAD::vector uses the CppAD fast multi-threading allocator CppAD::vector< CppAD::AD > ax(1), ay(1); ax[0] = info->x; Independent(ax); ay[0] = sqrt( ax[0] * ax[0] ); CppAD::ADFun f(ax, ay); // Check function value corresponds to the identity double eps = 10. * CppAD::numeric_limits::epsilon(); ok &= CppAD::NearEqual(ay[0], ax[0], eps, eps); // Check derivative value corresponds to the identity. CppAD::vector d_x(1), d_y(1); d_x[0] = 1.; d_y = f.Forward(1, d_x); ok &= CppAD::NearEqual(d_x[0], 1., eps, eps); return ok; } } bool simple_ad(void) { bool ok = true; size_t num_threads = NUMBER_THREADS; // Check that no memory is in use or avialable at start // (using thread_alloc in sequential mode) size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { ok &= thread_alloc::inuse(thread_num) == 0; ok &= thread_alloc::available(thread_num) == 0; } // initialize info_all problem_specific *info, *info_all[NUMBER_THREADS]; for(thread_num = 0; thread_num < num_threads; thread_num++) { // problem specific information size_t min_bytes(sizeof(info)), cap_bytes; void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes); info = static_cast(v_ptr); info->x = double(thread_num) + 1.; info_all[thread_num] = info; } ok &= run_all_workers(num_threads, info_all); // go down so that free memory for other threads before memory for master thread_num = num_threads; while(thread_num--) { // delete problem specific information void* v_ptr = static_cast( info_all[thread_num] ); thread_alloc::return_memory( v_ptr ); // check that there is no longer any memory inuse by this thread ok &= thread_alloc::inuse(thread_num) == 0; // return all memory being held for future use by this thread thread_alloc::free_available(thread_num); } return ok; } // END C++ cppad-20170000.3/multi_thread/pthread/CMakeLists.txt0000644000175200017650000000375413057470463021314 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the multi_thread/pthread directory tests # Inherit build type from ../CMakeList.txt # Local include directories to search (not in package_prefix/include) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/.. ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(multi_thread_pthread EXCLUDE_FROM_ALL ../thread_test.cpp ../../speed/src/microsoft_timer.cpp ../multi_newton_time.cpp ../multi_newton.cpp ../multi_newton_work.cpp ../team_example.cpp ../harmonic_time.cpp ../harmonic.cpp ../harmonic_work.cpp a11c_pthread.cpp simple_ad_pthread.cpp team_pthread.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( multi_thread_pthread ) # Paths in which the linker will search for libraries, # only applies to targets created after it is called LINK_DIRECTORIES( ${pthread_lib_path} ) # List of libraries to be linked into the specified target TARGET_LINK_LIBRARIES(multi_thread_pthread ${pthread_lib}) # Add the check_multi_thread_pthread target ADD_CUSTOM_TARGET(check_multi_thread_pthread multi_thread_pthread simple_ad DEPENDS multi_thread_pthread ) MESSAGE(STATUS "make check_multi_thread_pthread: available") # Change check depends in parent environment add_to_list(check_multi_thread_depends check_multi_thread_pthread) SET(check_multi_thread_depends "${check_multi_thread_depends}" PARENT_SCOPE) cppad-20170000.3/multi_thread/pthread/a11c_pthread.cpp0000644000175200017650000000665213057470463021514 0ustar coincoin-web// $Id: a11c_pthread.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin a11c_pthread.cpp$$ $spell pthread pthreads CppAD const $$ $section A Simple Parallel Pthread Example and Test$$ $mindex OpenMP A.1.1c thread$$ $head Purpose$$ This example just demonstrates pthreads and does not use CppAD at all. $head Source Code$$ $code $srcfile%multi_thread/pthread/a11c_pthread.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ---------------------------------------------------------------------------- */ // BEGIN C++ # include # include # include # include // define CPPAD_NULPTR # include # if CPPAD_USE_CPLUSPLUS_2011 # define CPPAD_NULL nullptr # else # define CPPAD_NULL 0 # endif // # define NUMBER_THREADS 4 # ifdef NDEBUG # define CHECK_ZERO(expression) expression # else # define CHECK_ZERO(expression) assert( expression == 0 ); # endif namespace { // Beginning of Example A.1.1.1c of OpenMP 2.5 standard document --------- void a1(int n, float *a, float *b) { int i; // for some reason this function is missing on some systems // assert( pthread_is_multithreaded_np() > 0 ); for(i = 1; i < n; i++) b[i] = (a[i] + a[i-1]) / 2.0; return; } // End of Example A.1.1.1c of OpenMP 2.5 standard document --------------- struct start_arg { int n; float* a; float* b; }; void* start_routine(void* arg_vptr) { start_arg* arg = static_cast( arg_vptr ); a1(arg->n, arg->a, arg->b); void* no_status = CPPAD_NULL; pthread_exit(no_status); return no_status; } } bool a11c(void) { bool ok = true; // Test setup int i, j, n_total = 10; float *a = new float[n_total]; float *b = new float[n_total]; for(i = 0; i < n_total; i++) a[i] = float(i); // number of threads int n_thread = NUMBER_THREADS; // the threads pthread_t thread[NUMBER_THREADS]; // arguments to start_routine struct start_arg arg[NUMBER_THREADS]; // attr pthread_attr_t attr; CHECK_ZERO( pthread_attr_init( &attr ) ); CHECK_ZERO( pthread_attr_setdetachstate(&attr, PTHREAD_CREATE_JOINABLE) ); // // Break the work up into sub work for each thread int n = n_total / n_thread; arg[0].n = n; arg[0].a = a; arg[0].b = b; for(j = 1; j < n_thread; j++) { arg[j].n = n + 1; arg[j].a = arg[j-1].a + n - 1; arg[j].b = arg[j-1].b + n - 1; if( j == (n_thread - 1) ) arg[j].n = n_total - j * n + 1; } for(j = 0; j < n_thread; j++) { // inform each thread of which block it is working on void* arg_vptr = static_cast( &arg[j] ); CHECK_ZERO( pthread_create( &thread[j], &attr, start_routine, arg_vptr ) ); } for(j = 0; j < n_thread; j++) { void* no_status = CPPAD_NULL; CHECK_ZERO( pthread_join(thread[j], &no_status) ); } // check the result float eps = 100. * std::numeric_limits::epsilon(); for(i = 1; i < n ; i++) ok &= std::fabs( (2. * b[i] - a[i] - a[i-1]) / b[i] ) <= eps; delete [] a; delete [] b; return ok; } // END C++ cppad-20170000.3/multi_thread/pthread/team_pthread.cpp0000644000175200017650000002500613057470463021707 0ustar coincoin-web// $Id: team_pthread.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin team_pthread.cpp$$ $spell Cygwin pthread $$ $section Pthread Implementation of a Team of AD Threads$$ $mindex pthread_exit$$ See $cref team_thread.hpp$$ for this routines specifications. $head Bug in Cygwin$$ There is a bug in $code pthread_exit$$, using cygwin 5.1 and g++ version 4.3.4, whereby calling $code pthread_exit$$ is not the same as returning from the corresponding routine. To be specific, destructors for the vectors are not called and a memory leaks result. Set the following preprocessor symbol to 1 to demonstrate this bug: $srccode%cpp% */ # define DEMONSTRATE_BUG_IN_CYGWIN 0 /* %$$ $code $srcfile%multi_thread/pthread/team_pthread.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include "../team_thread.hpp" # define MAX_NUMBER_THREADS 48 // It seems that when a barrier is passed, its counter is automatically reset // to its original value and it can be used again, but where is this // stated in the pthreads speicifcations ? namespace { using CppAD::thread_alloc; // number of threads in the team size_t num_threads_ = 1; // key for accessing thread specific information pthread_key_t thread_specific_key_; // no need to destroy thread specific information void thread_specific_destructor(void* thread_num_vptr) { return; } // type of the job currently being done by each thread enum thread_job_t { init_enum, work_enum, join_enum } thread_job_; // barrier used to wait for other threads to finish work pthread_barrier_t wait_for_work_; // barrier used to wait for master thread to set next job pthread_barrier_t wait_for_job_; // Are we in sequential mode; i.e., other threads are waiting for // master thread to set up next job ? bool sequential_execution_ = true; // structure with information for one thread typedef struct { // cppad unique identifier for thread that uses this struct size_t thread_num; // pthread unique identifier for thread that uses this struct pthread_t pthread_id; // true if no error for this thread, false otherwise. bool ok; } thread_one_t; // vector with information for all threads thread_one_t thread_all_[MAX_NUMBER_THREADS]; // pointer to function that does the work for one thread void (* worker_)(void) = CPPAD_NULL; // --------------------------------------------------------------------- // in_parallel() bool in_parallel(void) { return ! sequential_execution_; } // --------------------------------------------------------------------- // thread_number() size_t thread_number(void) { // get thread specific information void* thread_num_vptr = pthread_getspecific(thread_specific_key_); size_t* thread_num_ptr = static_cast(thread_num_vptr); size_t thread_num = *thread_num_ptr; if( thread_num >= num_threads_ ) { std::cerr << "thread_number: program error" << std::endl; exit(1); } return thread_num; } // -------------------------------------------------------------------- // function that gets called by pthread_create void* thread_work(void* thread_num_vptr) { int rc; bool ok = true; // Set thread specific data where other routines can access it rc = pthread_setspecific(thread_specific_key_, thread_num_vptr); ok &= rc == 0; // thread_num to problem specific information for this thread size_t thread_num = *static_cast(thread_num_vptr); // master thread does not use this routine ok &= thread_num > 0; while( true ) { // Use wait_for_job_ to give master time in sequential mode // (so it can change global infromation like thread_job_) rc = pthread_barrier_wait(&wait_for_job_); ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD); // case where we are terminating this thread (no more work) if( thread_job_ == join_enum ) break; // only other case once wait_for_job_ barrier is passed (so far) ok &= thread_job_ == work_enum; worker_(); // Use wait_for_work_ to inform master that our work is done and // that this thread will not use global information until // passing its barrier wait_for_job_ above. rc = pthread_barrier_wait(&wait_for_work_); ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD); } thread_all_[thread_num].ok = ok; # if DEMONSTRATE_BUG_IN_CYGWIN // Terminate this thread void* no_status = CPPAD_NULL; pthread_exit(no_status); # endif return CPPAD_NULL; } } bool team_create(size_t num_threads) { bool ok = true;; int rc; if( num_threads > MAX_NUMBER_THREADS ) { std::cerr << "team_create: num_threads greater than "; std::cerr << MAX_NUMBER_THREADS << std::endl; exit(1); } // check that we currently do not have multiple threads running ok = num_threads_ == 1; ok &= sequential_execution_; size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { // Each thread gets a pointer to its version of this thread_num // so it knows which section of thread_all_ it is working with thread_all_[thread_num].thread_num = thread_num; // initialize thread_all_[thread_num].ok = true; } // Finish setup of thread_all_ for this thread thread_all_[0].pthread_id = pthread_self(); // create a key for thread specific information rc = pthread_key_create(&thread_specific_key_,thread_specific_destructor); ok &= (rc == 0); // set thread specific information for this (master thread) void* thread_num_vptr = static_cast(&(thread_all_[0].thread_num)); rc = pthread_setspecific(thread_specific_key_, thread_num_vptr); ok &= (rc == 0); // Now that thread_number() has necessary information for this thread // (number zero), and while still in sequential mode, // call setup for using CppAD::AD in parallel mode. thread_alloc::parallel_setup(num_threads, in_parallel, thread_number); thread_alloc::hold_memory(true); CppAD::parallel_ad(); // Now change num_threads_ to its final value. Waiting till now allows // calls to thread_number during parallel_setup to check thread_num == 0. num_threads_ = num_threads; // initialize two barriers, one for work done, one for new job ready pthread_barrierattr_t* no_barrierattr = CPPAD_NULL; rc = pthread_barrier_init( &wait_for_work_, no_barrierattr, num_threads ); ok &= (rc == 0); rc = pthread_barrier_init( &wait_for_job_, no_barrierattr, num_threads ); ok &= (rc == 0); // structure used to create the threads pthread_t pthread_id; // default for pthread_attr_setdetachstate is PTHREAD_CREATE_JOINABLE pthread_attr_t* no_attr= CPPAD_NULL; // initial job for the threads thread_job_ = init_enum; if( num_threads > 1 ) sequential_execution_ = false; // This master thread is already running, we need to create // num_threads - 1 more threads for(thread_num = 1; thread_num < num_threads; thread_num++) { // Create the thread with thread number equal to thread_num thread_num_vptr = static_cast ( &(thread_all_[thread_num].thread_num) ); rc = pthread_create( &pthread_id , no_attr , thread_work , thread_num_vptr ); thread_all_[thread_num].pthread_id = pthread_id; ok &= (rc == 0); } // Current state is other threads are at wait_for_job_. // This master thread (thread zero) has not completed wait_for_job_ sequential_execution_ = true; return ok; } bool team_work(void worker(void)) { int rc; // Current state is other threads are at wait_for_job_. // This master thread (thread zero) has not completed wait_for_job_ bool ok = sequential_execution_; ok &= thread_number() == 0; // set global version of this work routine worker_ = worker; // set the new job that other threads are waiting for thread_job_ = work_enum; // enter parallel execution soon as master thread completes wait_for_job_ if( num_threads_ > 1 ) sequential_execution_ = false; // wait until all threads have completed wait_for_job_ rc = pthread_barrier_wait(&wait_for_job_); ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD); // Now do the work in this thread and then wait // until all threads have completed wait_for_work_ worker(); rc = pthread_barrier_wait(&wait_for_work_); ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD); // Current state is other threads are at wait_for_job_. // This master thread (thread zero) has not completed wait_for_job_ sequential_execution_ = true; size_t thread_num; for(thread_num = 0; thread_num < num_threads_; thread_num++) ok &= thread_all_[thread_num].ok; return ok; } bool team_destroy(void) { int rc; // Current state is other threads are at wait_for_job_. // This master thread (thread zero) has not completed wait_for_job_ bool ok = sequential_execution_; ok &= thread_number() == 0; // set the new job that other threads are waiting for thread_job_ = join_enum; // Enter parallel exectuion soon as master thread completes wait_for_job_ if( num_threads_ > 1 ) sequential_execution_ = false; rc = pthread_barrier_wait(&wait_for_job_); ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD); // now wait for the other threads to exit size_t thread_num; for(thread_num = 1; thread_num < num_threads_; thread_num++) { void* no_status = CPPAD_NULL; rc = pthread_join( thread_all_[thread_num].pthread_id, &no_status ); ok &= (rc == 0); } // now we are down to just the master thread (thread zero) sequential_execution_ = true; // destroy the key for thread specific data pthread_key_delete(thread_specific_key_); // destroy wait_for_work_ rc = pthread_barrier_destroy(&wait_for_work_); ok &= (rc == 0); // destroy wait_for_job_ rc = pthread_barrier_destroy(&wait_for_job_); ok &= (rc == 0); // check ok before changing num_threads_ for(thread_num = 0; thread_num < num_threads_; thread_num++) ok &= thread_all_[thread_num].ok; // now inform CppAD that there is only one thread num_threads_ = 1; thread_alloc::parallel_setup(num_threads_, CPPAD_NULL, CPPAD_NULL); thread_alloc::hold_memory(false); CppAD::parallel_ad(); return ok; } const char* team_name(void) { return "pthread"; } // END C++ cppad-20170000.3/multi_thread/team_example.hpp0000644000175200017650000000133513057470463020270 0ustar coincoin-web// $Id: team_example.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_MULTI_THREAD_TEAM_EXAMPLE_HPP # define CPPAD_MULTI_THREAD_TEAM_EXAMPLE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ extern bool team_example(void); # endif cppad-20170000.3/multi_thread/thread_test.cpp0000644000175200017650000002713613057470463020137 0ustar coincoin-web// $Id: thread_test.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin thread_test.cpp$$ $escape $$ $spell inv mega cpp num pthread pthreads openmp bthread $$ $section Run Multi-Threading Examples and Speed Tests$$ $mindex thread_test multi openmp pthread bthread$$ $head Syntax$$ $codei%./multi_thread_%threading% a11c ./multi_thread_%threading% simple_ad ./multi_thread_%threading% team_example ./multi_thread_%threading% harmonic %test_time% %max_threads% %mega_sum% ./multi_thread_%threading% multi_newton %test_time% %max_threads% \ %num_zero% %num_sub% %num_sum% %use_ad% %$$ $head Running Tests$$ You can build this program and run the default version of its test parameters by executing the following commands: $codei% cd multi_thread make test %$$ After this operation you can run the syntax above for the different valid values of $icode threading$$: $subhead threading$$ If the $cref cmake$$ command output indicates that $code openmp$$ is supported by your system, you can execute the syntax above with $icode threading$$ equal to $code openmp$$. $pre $$ If the $cref cmake$$ command output indicates that $code pthreads$$ with barriers is supported by your system, you can execute the syntax above with $icode threading$$ equal to $code pthread$$. $pre $$ If the $cref cmake$$ command output indicates that $code boost$$ threads is supported is by your system, you can execute the syntax above with $icode threading$$ equal to $code bthread$$. $head Purpose$$ Runs the CppAD multi-threading examples and timing tests: $children% multi_thread/openmp/a11c_openmp.cpp% multi_thread/bthread/a11c_bthread.cpp% multi_thread/pthread/a11c_pthread.cpp% multi_thread/openmp/simple_ad_openmp.cpp% multi_thread/bthread/simple_ad_bthread.cpp% multi_thread/pthread/simple_ad_pthread.cpp% multi_thread/team_example.cpp% multi_thread/harmonic.cpp% multi_thread/multi_newton.cpp% multi_thread/team_thread.hpp %$$ $head a11c$$ The examples $cref a11c_openmp.cpp$$, $cref a11c_bthread.cpp$$, and $cref a11c_pthread.cpp$$ demonstrate simple multi-threading, without algorithmic differentiation. $head simple_ad$$ The examples $cref simple_ad_openmp.cpp$$, $cref simple_ad_bthread.cpp$$, and $cref simple_ad_pthread.cpp$$ demonstrate simple multi-threading, with algorithmic differentiation, using OpenMP, boost threads and pthreads respectively. $head team_example$$ The $cref team_example.cpp$$ routine demonstrates simple multi-threading with algorithmic differentiation and using a $cref/team of threads/team_thread.hpp/$$. $head harmonic$$ The $cref harmonic_time.cpp$$ routine preforms a timing test for a multi-threading example without algorithmic differentiation using a team of threads. $subhead test_time$$ Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported time is the total wall clock time divided by the number of repeats. $subhead max_threads$$ If the argument $icode max_threads$$ is a non-negative integer specifying the maximum number of threads to use for the test. The specified test is run with the following number of threads: $codei% %num_threads% = 0 , %...% , %max_threads% %$$ The value of zero corresponds to not using the multi-threading system. $subhead mega_sum$$ The command line argument $icode mega_sum$$ is an integer greater than or equal one and has the same meaning as in $cref/harmonic_time.cpp/harmonic_time.cpp/mega_sum/$$. $head multi_newton$$ The $cref multi_newton_time.cpp$$ routine preforms a timing test for a multi-threading example with algorithmic differentiation using a team of threads. $subhead test_time$$ Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported time is the total wall clock time divided by the number of repeats. $subhead max_threads$$ If the argument $icode max_threads$$ is a non-negative integer specifying the maximum number of threads to use for the test. The specified test is run with the following number of threads: $codei% %num_threads% = 0 , %...% , %max_threads% %$$ The value of zero corresponds to not using the multi-threading system. $subhead num_zero$$ The command line argument $icode num_zero$$ is an integer greater than or equal two and has the same meaning as in $cref/multi_newton_time.cpp/multi_newton_time.cpp/num_zero/$$. $subhead num_sub$$ The command line argument $icode num_sub$$ is an integer greater than or equal one and has the same meaning as in $cref/multi_newton_time.cpp/multi_newton_time.cpp/num_sub/$$. $subhead num_sum$$ The command line argument $icode num_sum$$ is an integer greater than or equal one and has the same meaning as in $cref/multi_newton_time.cpp/multi_newton_time.cpp/num_sum/$$. $subhead use_ad$$ The command line argument $icode use_ad$$ is either $code true$$ or $code false$$ and has the same meaning as in $cref/multi_newton_time.cpp/multi_newton_time.cpp/use_ad/$$. $head Team Implementations$$ The following routines are used to implement the specific threading systems through the common interface $cref team_thread.hpp$$: $table $rref team_openmp.cpp$$ $rref team_bthread.cpp$$ $rref team_pthread.cpp$$ $tend $head Source$$ $code $srcfile%multi_thread/thread_test.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include # include # include "team_thread.hpp" # include "team_example.hpp" # include "harmonic_time.hpp" # include "multi_newton_time.hpp" extern bool a11c(void); extern bool simple_ad(void); namespace { size_t arg2size_t( const char* arg , int limit , const char* error_msg ) { int i = std::atoi(arg); if( i >= limit ) return size_t(i); std::cerr << "value = " << i << std::endl; std::cerr << error_msg << std::endl; exit(1); } double arg2double( const char* arg , double limit , const char* error_msg ) { double d = std::atof(arg); if( d >= limit ) return d; std::cerr << "value = " << d << std::endl; std::cerr << error_msg << std::endl; exit(1); } } int main(int argc, char *argv[]) { using CppAD::thread_alloc; bool ok = true; using std::cout; using std::endl; // commnd line usage message const char* usage = "./_test a11c\n" "./_test simple_ad\n" "./_test team_example\n" "./_test harmonic test_time max_threads mega_sum\n" "./_test multi_newton test_time max_threads\\\n" " num_zero num_sub num_sum use_ad\\\n" "where is bthread, openmp, or pthread"; // command line argument values (assign values to avoid compiler warnings) size_t num_zero=0, num_sub=0, num_sum=0; bool use_ad=true; // put the date and time in the output file std::time_t rawtime; std::time( &rawtime ); const char* gmt = std::asctime( std::gmtime( &rawtime ) ); size_t len = size_t( std::strlen(gmt) ); cout << "gmtime = '"; for(size_t i = 0; i < len; i++) if( gmt[i] != '\n' ) cout << gmt[i]; cout << "';" << endl; // CppAD version number cout << "cppad_version = '" << CPPAD_PACKAGE_STRING << "';" << endl; // put the team name in the output file cout << "team_name = '" << team_name() << "';" << endl; // print command line as valid matlab/octave cout << "command = '" << argv[0]; for(int i = 1; i < argc; i++) cout << " " << argv[i]; cout << "';" << endl; ok = false; const char* test_name = ""; if( argc > 1 ) test_name = *++argv; bool run_a11c = std::strcmp(test_name, "a11c") == 0; bool run_simple_ad = std::strcmp(test_name, "simple_ad") == 0; bool run_team_example = std::strcmp(test_name, "team_example") == 0; bool run_harmonic = std::strcmp(test_name, "harmonic") == 0; bool run_multi_newton = std::strcmp(test_name, "multi_newton") == 0; if( run_a11c || run_simple_ad || run_team_example ) ok = (argc == 2); else if( run_harmonic ) ok = (argc == 5); else if( run_multi_newton ) ok = (argc == 8); if( ! ok ) { std::cerr << "test_name = " << test_name << endl; std::cerr << "argc = " << argc << endl; std::cerr << usage << endl; exit(1); } if( run_a11c || run_simple_ad || run_team_example ) { if( run_a11c ) ok = a11c(); else if( run_simple_ad ) ok = simple_ad(); else ok = team_example(); if( thread_alloc::free_all() ) cout << "free_all = true;" << endl; else { ok = false; cout << "free_all = false;" << endl; } if( ok ) cout << "OK = true;" << endl; else cout << "OK = false;" << endl; return ! ok; } // test_time double test_time = arg2double( *++argv, 0., "run: test_time is less than zero" ); // max_threads size_t max_threads = arg2size_t( *++argv, 0, "run: max_threads is less than zero" ); size_t mega_sum = 0; // assignment to avoid compiler warning if( run_harmonic ) { // mega_sum mega_sum = arg2size_t( *++argv, 1, "run: mega_sum is less than one" ); } else { ok &= run_multi_newton; // num_zero num_zero = arg2size_t( *++argv, 2, "run: num_zero is less than two" ); // num_sub num_sub = arg2size_t( *++argv, 1, "run: num_sub is less than one" ); // num_sum num_sum = arg2size_t( *++argv, 1, "run: num_sum is less than one" ); // use_ad ++argv; if( std::strcmp(*argv, "true") == 0 ) use_ad = true; else if( std::strcmp(*argv, "false") == 0 ) use_ad = false; else { std::cerr << "run: use_ad = '" << *argv; std::cerr << "' is not true or false" << endl; exit(1); } } // run the test for each number of threads size_t num_threads, inuse_this_thread = 0; cout << "time_all = [" << endl; for(num_threads = 0; num_threads <= max_threads; num_threads++) { double time_out; // set the number of threads if( num_threads > 0 ) ok &= team_create(num_threads); // ammount of memory initialy inuse by thread zero ok &= 0 == thread_alloc::thread_num(); inuse_this_thread = thread_alloc::inuse(0); // run the requested test if( run_harmonic ) ok &= harmonic_time(time_out, test_time, num_threads, mega_sum); else { ok &= run_multi_newton; ok &= multi_newton_time( time_out , test_time , num_threads , num_zero , num_sub , num_sum , use_ad ); } // set back to one thread and fee all avaialable memory if( num_threads > 0 ) ok &= team_destroy(); size_t thread; for(thread = 0; thread < num_threads; thread++) { thread_alloc::free_available(thread); if( thread == 0 ) ok &= thread_alloc::inuse(thread) == inuse_this_thread; else ok &= thread_alloc::inuse(thread) == 0; } cout << "\t" << time_out << " % "; if( num_threads == 0 ) cout << "no threading" << endl; else cout << num_threads << " threads" << endl; } cout << "];" << endl; // if( thread_alloc::free_all() ) cout << "free_all = true;" << endl; else { ok = false; cout << "free_all = false;" << endl; } if( ok ) cout << "OK = true;" << endl; else cout << "OK = false;" << endl; return ! ok; } // END C++ cppad-20170000.3/multi_thread/multi_newton_time.hpp0000644000175200017650000000161513057470463021372 0ustar coincoin-web// $Id: multi_newton_time.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_MULTI_THREAD_MULTI_NEWTON_TIME_HPP # define CPPAD_MULTI_THREAD_MULTI_NEWTON_TIME_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ bool multi_newton_time( double& time_out , double test_time , size_t num_thread , size_t num_zero , size_t num_sub , size_t num_sum , bool use_ad ); # endif cppad-20170000.3/multi_thread/harmonic_work.hpp0000644000175200017650000000155313057470463020473 0ustar coincoin-web// $Id: harmonic_work.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_MULTI_THREAD_HARMONIC_WORK_HPP # define CPPAD_MULTI_THREAD_HARMONIC_WORK_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include extern void harmonic_worker(void); extern bool harmonic_setup(size_t num_sum, size_t num_threads); extern bool harmonic_combine(double& sum); # endif cppad-20170000.3/multi_thread/test.sh0000755000175200017650000000424713057470463016441 0ustar coincoin-web#! /bin/sh -e # $Id: test.sh 2506 2012-10-24 19:36:49Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # script used by */makefile.am to run a default case for all the the tests # -------------------------------------------------------------------------- # setup next_program() { i_program=`expr $i_program + 1` if [ $i_program -ge $n_program ] then i_program='0' fi case $i_program in 0) program=`echo "$program_list" | sed -e 's| \([^ ]*\).*|\1|'` ;; 1) program=`echo "$program_list" | sed -e 's| [^ ]* \([^ ]*\).*|\1|'` ;; 2) program=`echo "$program_list" | sed -e 's| [^ ]* [^ ]* ||'` ;; esac } n_program='3' program_list=' openmp_test pthread_test bthread_test' for program in openmp_test pthread_test bthread_test do if [ ! -e "$program" ] then program_list=`echo "$program_list" | sed -e "s| $program||"` n_program=`expr $n_program - 1` fi done if [ "$n_program" = '0' ] then echo "multi_thread/test.sh: nothing to test" exit 0 fi i_program='0' next_program # -------------------------------------------------------------------------- # test_time=1 max_thread=4, mega_sum=1 ./$program harmonic 1 4 1 next_program echo # test_time= 2 max_thread=4, num_zero=20, num_sub=30, num_sum=500, use_ad=true ./$program multi_newton 2 4 20 30 500 true next_program echo # case that failed in the past ./$program multi_newton 1 1 100 700 1 true next_program echo # case that failed in the past ./$program multi_newton 1 2 3 12 1 true next_program echo # fast cases, do all programs for program in openmp_test pthread_test bthread_test do if [ -e "$program" ] then ./$program a11c echo ./$program simple_ad echo ./$program team_example echo fi done cppad-20170000.3/multi_thread/test_multi/0002755000175200017650000000000013057470463017307 5ustar coincoin-webcppad-20170000.3/multi_thread/test_multi/makefile.am0000644000175200017650000000222313057470463021400 0ustar coincoin-web# $Id: makefile.am 3779 2016-01-01 11:26:11Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # # CppAD pusts all it's preprocessor definitions in the cppad/configure.hpp DEFS = # if CppAD_OPENMP TEST_OPENMP_FLAG = -DCPPAD_TEST_OPENMP else TEST_OPENMP_FLAG = endif # check_PROGRAMS = test_multi # AM_CPPFLAGS = -I. \ -I$(top_srcdir) \ $(OPENMP_FLAGS) \ $(BOOST_INCLUDE) \ $(EIGEN_INCLUDE) \ $(TEST_OPENMP_FLAG) # AM_CXXFLAGS = -g $(ADOLC_FLAGS) $(CXX_FLAGS) # AM_LDFLAGS = $(ADOLC_LIB) $(OPENMP_FLAGS) # test_multi_SOURCES = \ test_multi.cpp \ user_atomic.cpp test: check ./test_multi cppad-20170000.3/multi_thread/test_multi/test_multi.cpp0000644000175200017650000000405713057470463022210 0ustar coincoin-web// $Id: test_multi.cpp 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // system include files used for I/O # include // memory leak checker # include // various examples / tests extern bool user_atomic_openmp(void); namespace { // function that runs one test static size_t Run_ok_count = 0; static size_t Run_error_count = 0; bool Run(bool TestOk(void), std::string name) { bool ok = true; std::streamsize width = 20; std::cout.width( width ); std::cout.setf( std::ios_base::left ); std::cout << name; // ok &= name.size() < size_t(width); ok &= TestOk(); if( ok ) { std::cout << "OK" << std::endl; Run_ok_count++; } else { std::cout << "Error" << std::endl; Run_error_count++; } return ok; } } // main program that runs all the tests int main(void) { bool ok = true; using namespace std; # ifdef CPPAD_TEST_OPENMP ok &= Run( user_atomic_openmp, "user_atomic_openmp" ); # endif // check for errors using std::cout; using std::endl; assert( ok || (Run_error_count > 0) ); if( CppAD::thread_alloc::free_all() ) { Run_ok_count++; cout << "OK: " << "No memory leak detected" << endl; } else { ok = false; Run_error_count++; cout << "Error: " << "memory leak detected" << endl; } // convert int(size_t) to avoid warning on _MSC_VER systems if( ok ) cout << "All " << int(Run_ok_count) << " tests passed." << endl; else cout << int(Run_error_count) << " tests failed." << endl; return static_cast( ! ok ); } // END PROGRAM cppad-20170000.3/multi_thread/test_multi/user_atomic.cpp0000644000175200017650000001277013057470463022332 0ustar coincoin-web// $Id: user_atomic.cpp 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # define NUMBER_THREADS 4 # define NUMBER_CALLS 40 // y[0] = x[0] + x[1] // y[1] = x[1] + x[2] namespace { # ifdef CPPAD_TEST_OPENMP // ------------------------------------------------------------------ // used to inform CppAD when we are in parallel execution mode bool in_parallel(void) { return static_cast( omp_in_parallel() ); } // ------------------------------------------------------------------ // used to inform CppAD of the current thread number size_t thread_number(void) { return static_cast( omp_get_thread_num() ); } # endif // y[0] = x[0] + x[1] bool user_atomic_forward( size_t id , size_t k , size_t n , size_t m , const CppAD::vector& vx , CppAD::vector& vy , const CppAD::vector& tx , CppAD::vector& ty ) { assert(n >= 3 && m == 2); if( k > 0 ) return false; ty[0] = tx[0] + tx[1]; ty[1] = tx[1] + tx[2]; if( vy.size() > 0 ) { vy[0] = (vx[0] | vx[1]); vy[1] = (vx[1] | vx[2]); } return true; } bool user_atomic_reverse( size_t id , size_t k , size_t n , size_t m , const CppAD::vector& tx , const CppAD::vector& ty , CppAD::vector& px , const CppAD::vector& py ) { return false; } bool user_atomic_for_jac_sparse( size_t id , size_t n , size_t m , size_t q , const CppAD::vector< std::set >& r , CppAD::vector< std::set >& s ) { return false; } bool user_atomic_rev_jac_sparse( size_t id , size_t n , size_t m , size_t q , CppAD::vector< std::set >& r , const CppAD::vector< std::set >& s ) { return false; } bool user_atomic_rev_hes_sparse( size_t id , size_t n , size_t m , size_t q , const CppAD::vector< std::set >& r , const CppAD::vector& s , CppAD::vector& t , const CppAD::vector< std::set >& u , CppAD::vector< std::set >& v ) { return false; } CPPAD_USER_ATOMIC( my_user_atomic , CppAD::vector , double , user_atomic_forward , user_atomic_reverse , user_atomic_for_jac_sparse , user_atomic_rev_jac_sparse , user_atomic_rev_hes_sparse ) bool user_atomic(int call_index) { bool ok = true; using CppAD::AD; using CppAD::vector; size_t j; size_t m = 2; size_t n = size_t(call_index + 3); vector< AD > ax(n), ay(m); for(j = 0; j < n; j++) ax[j] = AD(j + 1); CppAD::Independent(ax); // use user atomic function size_t id = 0; my_user_atomic(id, ax, ay); // create function CppAD::ADFun g(ax, ay); // now use the tape with the user atomic function vector x(n), y(m); for(j = 0; j < n; j++) x[j] = (j + 1) * (j + 1); y = g.Forward(0, x); // y[0] = x[0] + x[1] ok &= (y[0] == x[0] + x[1]); // y[1] = x[1] + x[2] ok &= (y[0] == x[0] + x[1]); return ok; } } # ifdef CPPAD_TEST_OPENMP # include bool user_atomic_openmp(void) { using CppAD::thread_alloc; bool ok = true; bool ok_all[NUMBER_CALLS]; size_t num_threads = NUMBER_THREADS; int int_num_threads = int(num_threads); // make first call in sequential mode int call_index = 0; ok &= user_atomic(call_index); // turn off dynamic thread adjustment omp_set_num_threads( int_num_threads ); // setup for using CppAD::AD in parallel thread_alloc::parallel_setup( num_threads, in_parallel, thread_number ); thread_alloc::hold_memory(true); CppAD::parallel_ad(); # pragma omp parallel for for(call_index = 0; call_index < NUMBER_CALLS; call_index++) ok_all[call_index] = user_atomic(call_index); // end omp parallel for // tear down parallel mode omp_set_num_threads(1); thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL); thread_alloc::hold_memory(false); CppAD::parallel_ad(); // combine all the ok flags into one for(call_index = 0; call_index < int_num_threads; call_index++) ok &= ok_all[call_index]; // -------------------------------------------------------------------- // Free all temporary work space associated with user_atomic objects. // (If there are future calls to user atomic functions, they will // create new temporary work space.) 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Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin simple_ad_openmp.cpp$$ $spell openmp CppAD $$ $section A Simple OpenMP AD: Example and Test$$ $mindex AD$$ $head Purpose$$ This example demonstrates how CppAD can be used in a OpenMP multi-threading environment. $head Source Code$$ $code $srcfile%multi_thread/openmp/simple_ad_openmp.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include # include # define NUMBER_THREADS 4 namespace { // structure with problem specific information typedef struct { // function argument (worker input) double x; // This structure would also have return information in it, // but this example only returns the ok flag } problem_specific; // ===================================================================== // General purpose code you can copy to your application // ===================================================================== using CppAD::thread_alloc; // ------------------------------------------------------------------ // used to inform CppAD when we are in parallel execution mode bool in_parallel(void) { return omp_in_parallel() != 0; } // ------------------------------------------------------------------ // used to inform CppAD of the current thread number size_t thread_number(void) { return static_cast( omp_get_thread_num() ); } // ------------------------------------------------------------------ // structure with information for one thread typedef struct { // false if an error occurs, true otherwise (worker output) bool ok; } thread_one_t; // vector with information for all threads thread_one_t thread_all_[NUMBER_THREADS]; // ------------------------------------------------------------------ // function that calls all the workers bool worker(problem_specific* info); bool run_all_workers(size_t num_threads, problem_specific* info_all[]) { bool ok = true; // initialize thread_all_ int thread_num, int_num_threads = int(num_threads); for(thread_num = 0; thread_num < int_num_threads; thread_num++) { // initialize as false to make sure gets called for all threads thread_all_[thread_num].ok = false; } // turn off dynamic thread adjustment omp_set_dynamic(0); // set the number of OpenMP threads omp_set_num_threads( int_num_threads ); // setup for using CppAD::AD in parallel thread_alloc::parallel_setup( num_threads, in_parallel, thread_number ); thread_alloc::hold_memory(true); CppAD::parallel_ad(); // execute worker in parallel # pragma omp parallel for for(thread_num = 0; thread_num < int_num_threads; thread_num++) thread_all_[thread_num].ok = worker(info_all[thread_num]); // end omp parallel for // set the number of OpenMP threads to one omp_set_num_threads(1); // now inform CppAD that there is only one thread thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL); thread_alloc::hold_memory(false); CppAD::parallel_ad(); // check to ok flag returned by during calls to work by other threads for(thread_num = 1; thread_num < int_num_threads; thread_num++) ok &= thread_all_[thread_num].ok; return ok; } // ===================================================================== // End of General purpose code // ===================================================================== // function that does the work for one thread bool worker(problem_specific* info) { using CppAD::NearEqual; using CppAD::AD; bool ok = true; // CppAD::vector uses the CppAD fast multi-threading allocator CppAD::vector< AD > ax(1), ay(1); ax[0] = info->x; Independent(ax); ay[0] = sqrt( ax[0] * ax[0] ); CppAD::ADFun f(ax, ay); // Check function value corresponds to the identity double eps = 10. * CppAD::numeric_limits::epsilon(); ok &= NearEqual(ay[0], ax[0], eps, eps); // Check derivative value corresponds to the identity. CppAD::vector d_x(1), d_y(1); d_x[0] = 1.; d_y = f.Forward(1, d_x); ok &= NearEqual(d_x[0], 1., eps, eps); return ok; } } bool simple_ad(void) { bool ok = true; size_t num_threads = NUMBER_THREADS; // Check that no memory is in use or avialable at start // (using thread_alloc in sequential mode) size_t thread_num; for(thread_num = 0; thread_num < num_threads; thread_num++) { ok &= thread_alloc::inuse(thread_num) == 0; ok &= thread_alloc::available(thread_num) == 0; } // initialize info_all problem_specific *info, *info_all[NUMBER_THREADS]; for(thread_num = 0; thread_num < num_threads; thread_num++) { // problem specific information size_t min_bytes(sizeof(info)), cap_bytes; void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes); info = static_cast(v_ptr); info->x = double(thread_num) + 1.; info_all[thread_num] = info; } ok &= run_all_workers(num_threads, info_all); // go down so that free memory for other threads before memory for master thread_num = num_threads; while(thread_num--) { // delete problem specific information void* v_ptr = static_cast( info_all[thread_num] ); thread_alloc::return_memory( v_ptr ); // check that there is no longer any memory inuse by this thread ok &= thread_alloc::inuse(thread_num) == 0; // return all memory being held for future use by this thread thread_alloc::free_available(thread_num); } return ok; } // END C++ cppad-20170000.3/multi_thread/openmp/CMakeLists.txt0000644000175200017650000000372113057470463021155 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the multi_thread/openmp directory tests # Inherit build type from ../CMakeList.txt # Local include directories to search (not in package_prefix/include) INCLUDE_DIRECTORIES( ${CMAKE_CURRENT_SOURCE_DIR}/.. ) # Cannot find specifications for CMAKE_CXX_FLAGS in version 2.6 documentation # so using ADD_DEFINITIONS instead. ADD_DEFINITIONS( ${OpenMP_CXX_FLAGS} ) # add_executable( [WIN32] [MACOSX_BUNDLE] [EXCLUDE_FROM_ALL] # source1 source2 ... sourceN # ) ADD_EXECUTABLE(multi_thread_openmp EXCLUDE_FROM_ALL ../thread_test.cpp ../../speed/src/microsoft_timer.cpp ../multi_newton_time.cpp ../multi_newton.cpp ../multi_newton_work.cpp ../team_example.cpp ../harmonic_time.cpp ../harmonic.cpp ../harmonic_work.cpp a11c_openmp.cpp simple_ad_openmp.cpp team_openmp.cpp ) # Compiler flags for cppad source add_cppad_cxx_flags( multi_thread_openmp ) # Extra flags used by linker for openmp support SET(CMAKE_EXE_LINKER_FLAGS ${OpenMP_CXX_FLAGS} ) # Add the check_multi_thread_openmp target ADD_CUSTOM_TARGET(check_multi_thread_openmp multi_thread_openmp simple_ad DEPENDS multi_thread_openmp ) MESSAGE(STATUS "make check_multi_thread_openmp: available") # Change check depends in parent environment add_to_list(check_multi_thread_depends check_multi_thread_openmp) SET(check_multi_thread_depends "${check_multi_thread_depends}" PARENT_SCOPE) cppad-20170000.3/multi_thread/openmp/a11c_openmp.cpp0000644000175200017650000000411513057470463021222 0ustar coincoin-web// $Id: a11c_openmp.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin a11c_openmp.cpp$$ $spell CppAD const $$ $section A Simple OpenMP Example and Test$$ $mindex A.1.1c thread$$ $head Purpose$$ This example just demonstrates OpenMP and does not use CppAD at all. $head Source Code$$ $code $srcfile%multi_thread/openmp/a11c_openmp.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end ---------------------------------------------------------------------------- */ // BEGIN C++ # include # include # include # include # define NUMBER_THREADS 4 namespace { // Beginning of Example A.1.1.1c of OpenMP 2.5 standard document --------- void a1(int n, float *a, float *b) { int i; # pragma omp parallel for for(i = 1; i < n; i++) /* i is private by default */ { assert( omp_get_num_threads() == NUMBER_THREADS ); b[i] = (a[i] + a[i-1]) / float(2); } } // End of Example A.1.1.1c of OpenMP 2.5 standard document --------------- } bool a11c(void) { bool ok = true; // Test setup int i, n = 1000; float *a = new float[n]; float *b = new float[n]; for(i = 0; i < n; i++) a[i] = float(i); int n_thread = NUMBER_THREADS; // number of threads in parallel regions omp_set_dynamic(0); // off dynamic thread adjust omp_set_num_threads(n_thread); // set the number of threads a1(n, a, b); // check the result float eps = float(100) * std::numeric_limits::epsilon(); for(i = 1; i < n ; i++) ok &= std::fabs( (float(2) * b[i] - a[i] - a[i-1]) / b[i] ) <= eps; delete [] a; delete [] b; return ok; } // END C++ cppad-20170000.3/multi_thread/openmp/team_openmp.cpp0000644000175200017650000000521313057470463021423 0ustar coincoin-web// $Id: team_openmp.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin team_openmp.cpp$$ $spell openmp $$ $section OpenMP Implementation of a Team of AD Threads$$ See $cref team_thread.hpp$$ for this routines specifications. $code $srcfile%multi_thread/openmp/team_openmp.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include "../team_thread.hpp" namespace { using CppAD::thread_alloc; // number of threads in this team size_t num_threads_; // used to inform CppAD when we are in parallel execution mode bool in_parallel(void) { return omp_in_parallel() != 0; } // used to inform CppAD of the current thread number size_t thread_num(void) { return static_cast( omp_get_thread_num() ); } } bool team_create(size_t num_threads) { bool ok = ! in_parallel(); ok &= thread_num() == 0;; ok &= num_threads > 0; // Turn off dynamic thread adjustment omp_set_dynamic(0); // Set the number of OpenMP threads omp_set_num_threads( int(num_threads) ); // setup for using CppAD::AD in parallel thread_alloc::parallel_setup(num_threads, in_parallel, thread_num); thread_alloc::hold_memory(true); CppAD::parallel_ad(); // inform team_work of number of threads num_threads_ = num_threads; return ok; } bool team_work(void worker(void)) { bool ok = ! in_parallel(); ok &= thread_num() == 0;; ok &= num_threads_ > 0; int number_threads = int(num_threads_); int thread_num; # pragma omp parallel for for(thread_num = 0; thread_num < number_threads; thread_num++) worker(); // end omp parallel for return ok; } bool team_destroy(void) { bool ok = ! in_parallel(); ok &= thread_num() == 0;; ok &= num_threads_ > 0; // inform team_work of number of threads num_threads_ = 1; // Set the number of OpenMP threads to one omp_set_num_threads(num_threads_); // inform CppAD no longer in multi-threading mode thread_alloc::parallel_setup(num_threads_, CPPAD_NULL, CPPAD_NULL); thread_alloc::hold_memory(false); CppAD::parallel_ad(); return ok; } const char* team_name(void) { return "openmp"; } // END C++ cppad-20170000.3/multi_thread/harmonic_time.cpp0000644000175200017650000001071113057470463020436 0ustar coincoin-web// $Id: harmonic_time.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin harmonic_time.cpp$$ $spell openmp pthreads alloc num bool mega inv CppAD parallelize $$ $section Timing Test of Multi-Threaded Summation of 1/i$$ $mindex harmonic_time multi_thread speed$$ $head Syntax$$ $icode%ok% = harmonic_time(%time_out%, %num_threads%, %mega_sum%)%$$ $head Purpose$$ Runs a correctness and timing test for a multi-threaded computation of the summation that defines the harmonic series $latex \[ 1 + 1/2 + 1/3 + ... + 1/n \] $$ This routine must be called in sequential execution mode, even though $cref/in_parallel/ta_in_parallel/$$ may return true. $head ok$$ This return value has prototype $codei% bool %ok% %$$ If it is true, $code harmonic_time$$ passed the correctness test. Otherwise it is false. $head time_out$$ This argument has prototype $codei% double& %time_out% %$$ The input value of the argument does not matter. Upon return it is the number of wall clock seconds required for to compute the $cref/summation/harmonic_time.cpp/Purpose/$$. $head test_time$$ Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported $icode time_out$$ is the total wall clock time divided by the number of repeats. $head num_threads$$ This argument has prototype $codei% size_t %num_threads% %$$ It specifies the number of threads that are available for this test. If it is zero, the test is run without the multi-threading environment and $codei% 1 == CppAD::thread_alloc::num_threads() %$$ when $code harmonic_time$$ is called. If it is non-zero, the test is run with the multi-threading and $codei% %num_threads% = CppAD::thread_alloc::num_threads() %$$ when $code harmonic_time$$ is called. $head mega_sum$$ This argument has prototype $codei% size_t& %mega_sum% %$$ and is greater than zero. The value $latex n$$ in the $cref/summation/harmonic_time.cpp/Purpose/$$. is equal to $latex 10^6$$ times $icode mega_sum$$. $head Source$$ $code $srcfile%multi_thread/harmonic_time.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include # include # include # include # include # include // Note there is no mention of parallel mode in the documentation for // speed_test (so it is safe to use without special consideration). # include # include "harmonic.hpp" namespace { // empty namespace // value of num_threads in previous call to harmonic_time. size_t num_threads_; // value of mega_sum in previous call to harmonic_time. size_t mega_sum_; // value of sum resulting from most recent call to test_once double sum_ = 0.; void test_once(void) { if( mega_sum_ < 1 ) { std::cerr << "harmonic_time: mega_sum < 1" << std::endl; exit(1); } size_t num_sum = mega_sum_ * 1000000; bool ok = harmonic(sum_, num_sum, num_threads_); if( ! ok ) { std::cerr << "harmonic: error" << std::endl; exit(1); } return; } void test_repeat(size_t repeat) { size_t i; for(i = 0; i < repeat; i++) test_once(); return; } } // end empty namespace bool harmonic_time( double& time_out, double test_time, size_t num_threads, size_t mega_sum) { bool ok = true; using std::vector; // arguments passed to harmonic_time num_threads_ = num_threads; mega_sum_ = mega_sum; // convert zero to actual number of threads num_threads = std::max(num_threads_, size_t(1)); // expect number of threads to already be set up ok &= num_threads == CppAD::thread_alloc::num_threads(); // run the test case and set the time return value time_out = CppAD::time_test(test_repeat, test_time); // Correctness check double eps = mega_sum_ * 1e3 * std::numeric_limits::epsilon(); size_t i = mega_sum_ * 1000000; double check = 0.; while(i) check += 1. / double(i--); ok &= std::fabs(sum_ - check) <= eps; return ok; } // END C++ cppad-20170000.3/multi_thread/team_thread.hpp0000644000175200017650000000742313057470463020110 0ustar coincoin-web// $Id: team_thread.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_MULTI_THREAD_TEAM_THREAD_HPP # define CPPAD_MULTI_THREAD_TEAM_THREAD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin team_thread.hpp$$ $spell pthreads const cstddef bool pthread initializes hpp num CppAD ta $$ $section Specifications for A Team of AD Threads$$ $head Syntax$$ $codei%include "team_thread.hpp" %ok% = team_create(%num_threads%) %ok% = team_work(%worker%) %ok% = team_destroy() %name% = team_name() %$$ $head Purpose$$ These routines start, use, and stop a team of threads that can be used with the CppAD type $code AD$$. For example, these could be OpenMP threads, pthreads, or Boost threads to name a few. $head Restrictions$$ Calls to the routines $code team_create$$, $code team_work$$, and $code team_destroy$$, must all be done by the master thread; i.e., $cref/thread_num/ta_thread_num/$$ must be zero. In addition, they must all be done in sequential execution mode; i.e., when the master thread is the only thread that is running ($cref/in_parallel/ta_in_parallel/$$ must be false). $head team_create$$ The argument $icode%num_threads% > 0%$$ has type $code size_t$$ and specifies the number of threads in this team. This initializes both $code AD$$ and $code team_work$$ to be used with $icode num_threads$$. If $icode%num_threads% > 1%$$, $icode%num_threads% - 1%$$ new threads are created and put in a waiting state until $code team_work$$ is called. $head team_work$$ This routine may be called one or more times between the call to $code team_create$$ and $code team_destroy$$. The argument $icode worker$$ has type $codei%bool %worker%(void)%$$. Each call to $code team_work$$ runs $icode num_threads$$ versions of $icode worker$$ with the corresponding value of $cref/thread_num/ta_thread_num/$$ between zero and $icode%num_threads% - 1%$$ and different for each thread, $head team_destroy$$ This routine terminates all the other threads except for thread number zero; i.e., it terminates the threads corresponding to $codei% %thread_num% = 1 , ... , %num_threads%-1 %$$ $head team_name$$ This routines returns a name that identifies this thread_team. The return value has prototype $codei% const char* %name% %$$ and is a statically allocated $code '\0'$$ terminated C string. $head ok$$ The return value $icode ok$$ has type $code bool$$. It is $code false$$ if an error is detected during the corresponding call. Otherwise it is $code true$$. $children% multi_thread/openmp/team_openmp.cpp% multi_thread/bthread/team_bthread.cpp% multi_thread/pthread/team_pthread.cpp %$$ $head Example Use$$ Example use of these specifications can be found in the file $cref team_example.cpp$$. $head Example Implementation$$ Example implementations of these specifications can be found in the files: $table $rref team_openmp.cpp$$ $rref team_bthread.cpp$$ $rref team_pthread.cpp$$ $tend $head Speed Test of Implementation$$ Speed tests of using CppAD with the team implementations above can be found in: $table $rref harmonic.cpp$$ $rref multi_newton.cpp$$ $tend $head Source$$ $srccode%cpp% */ # include // for size_t extern bool team_create(size_t num_threads); extern bool team_work(void worker(void)); extern bool team_destroy(void); extern const char* team_name(void); /* %$$ $end */ # endif cppad-20170000.3/multi_thread/harmonic_time.hpp0000644000175200017650000000143413057470463020445 0ustar coincoin-web// $Id: harmonic_time.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_MULTI_THREAD_HARMONIC_TIME_HPP # define CPPAD_MULTI_THREAD_HARMONIC_TIME_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ bool harmonic_time( double& time_out, double test_time, size_t n_thread, size_t mega_sum); # endif cppad-20170000.3/multi_thread/multi_newton.cpp0000644000175200017650000001176613057470463020357 0ustar coincoin-web// $Id: multi_newton.cpp 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin multi_newton.cpp$$ $spell CppAD xout num xlow xup itr bool df $$ $section A Multi-Threaded Newton's Method$$ $mindex multi_newton threading thread multi-threading$$ $head Syntax$$ $icode%ok% = %multi_newton(%xout%, %fun%, %num_sub%, %xlow%, %xup%, %epsilon%, %max_itr%, %num_threads% )%$$ $head Purpose$$ Multi-threaded determination of the argument values $latex x$$, in the interval $latex [a, b]$$ (where $latex a < b$$), such that $latex f(x) = 0$$. $head Method$$ For $latex i = 0 , \ldots , n$$, we define the $th i$$ grid point $latex g_i$$ by $latex \[ g_i = a \frac{n - i}{n} + b \frac{i}{n} \] $$ For $latex i = 0 , \ldots , n-1$$, we define the $th i$$ sub-interval of $latex [a, b]$$ by $latex \[ I_i = [ g_i , g_{i+1} ] \] $$ Newton's method is applied starting at the center of each of the sub-intervals $latex I_i$$ for $latex i = 0 , \ldots , n-1$$ and at most one zero is found for each sub-interval. $head ok$$ The return value $icode ok$$ has prototype $codei% bool %ok% %$$ If an error occurs, it is false, otherwise it is true. $head xout$$ The argument $icode xout$$ has the prototype $codei% CppAD::vector& %xout% %$$ The input size and value of the elements of $icode xout$$ do not matter. Upon return from $code multi_newton$$, the size of $icode xout$$ is less than or equal the number of sub-intervals $latex n$$ and $latex \[ | f( xout[i] ) | \leq epsilon \] $$ for each valid index $codei%0% <= %i% < %xout%.size()%$$. Two $latex x$$ solutions are considered equal (and joined as one) if the absolute difference between the solutions is less than $latex (b - a) / n$$. $head fun$$ The argument $icode fun$$ has prototype $codei% void %fun% (double %x%, double& %f%, double& %df%) %$$ This function must evaluate $latex f(x)$$, and its derivative $latex f^{(1)} (x)$$, using the syntax $codei% %fun%(%x%, %f%, %df%) %$$ where the arguments to $icode fun$$ have the prototypes $codei% double %x% double& %f% double& %df% %$$. The input values of $icode f$$ and $icode df$$ do not matter. Upon return they are $latex f(x)$$ and $latex f^{(1)} (x)$$ respectively. $head num_sub$$ The argument $icode num_sub$$ has prototype $codei% size_t %num_sub% %$$ It specifies the number of sub-intervals; i.e., $latex n$$. $head xlow$$ The argument $icode xlow$$ has prototype $codei% double %xlow% %$$ It specifies the lower limit for the entire search interval; i.e., $latex a$$. $head xup$$ The argument $icode xup$$ has prototype $codei% double %xup% %$$ It specifies the upper limit for the entire search interval; i.e., $latex b$$. $head epsilon$$ The argument $icode epsilon$$ has prototype $codei% double %epsilon% %$$ It specifies the convergence criteria for Newton's method in terms of how small the function value must be. $head max_itr$$ The argument $icode max_itr$$ has prototype $codei% size_t %max_itr% %$$ It specifies the maximum number of iterations of Newton's method to try before giving up on convergence (on each sub-interval). $head num_threads$$ This argument has prototype $codei% size_t %num_threads% %$$ It specifies the number of threads that are available for this test. If it is zero, the test is run without the multi-threading environment. $childtable% multi_thread/multi_newton_time.cpp% multi_thread/multi_newton_work.cpp %$$ $head Source$$ $code $srcfile%multi_thread/multi_newton.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end --------------------------------------------------------------------------- */ // BEGIN C++ // general purpose multi-threading interface # include "team_thread.hpp" // special utilities for the multi_newton problem # include "multi_newton_work.hpp" bool multi_newton( CppAD::vector &xout , void fun(double x, double& f, double& df) , size_t num_sub , double xlow , double xup , double epsilon , size_t max_itr , size_t num_threads ) { bool ok = true; using CppAD::AD; using CppAD::vector; // setup the work for num_threads threads ok &= multi_newton_setup( fun, num_sub, xlow, xup, epsilon, max_itr, num_threads ); // now do the work for each thread if( num_threads > 0 ) team_work( multi_newton_worker ); else multi_newton_worker(); // now combine the result for all the threads ok &= multi_newton_combine(xout); return ok; } // END C++ cppad-20170000.3/multi_thread/multi_newton_work.cpp0000644000175200017650000003113413057470463021410 0ustar coincoin-web// $Id: multi_newton_work.cpp 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin multi_newton_work.cpp$$ $spell num $$ $section Multi-threading Newton Method Utility Routines$$ $mindex multi_newton_work setup worker combine$$ $spell Cpp xlow xup itr df xout df $$ $head Syntax$$ $icode%ok% = multi_newton_setup( %fun%, %num_sub%, %xlow%, %xup%, %epsilon%, %max_itr%, %num_threads% )%$$ $codei%multi_newton_worker() %$$ $icode%ok% = multi_newton_combine(%xout%) %$$ $head Purpose$$ These routines aid in the computation of multiple zeros of a function $latex f: [ a, b] \rightarrow {\bf R}$$. $head multi_newton_setup$$ Calling this functions splits up the computation of the zeros into different sub-intervals for each thread. $subhead fun$$ The argument $icode fun$$ has prototype $codei% void %fun% (double %x%, double& %f%, double& %df%) %$$ This argument must evaluate the function $latex f(x)$$, and its derivative $latex f^{(1)} (x)$$, using the syntax $codei% %fun%(%x%, %f%, %df%) %$$ where the arguments have the prototypes $codei% double %x% double& %f% double& %df% %$$. The input values of $icode f$$ and $icode df$$ do not matter. Upon return they are $latex f(x)$$ and $latex f^{(1)} (x)$$ respectively. $subhead num_sub$$ The argument $icode num_sub$$ has prototype $codei% size_t %num_sub% %$$ It specifies the number of sub-intervals; i.e., $latex n$$ in to split the calculation into. $head xlow$$ The argument $icode xlow$$ has prototype $codei% double %xlow% %$$ It specifies the lower limit for the entire search; i.e., $latex a$$. $subhead xup$$ The argument $icode xup$$ has prototype $codei% double %xup% %$$ It specifies the upper limit for the entire search; i.e., $latex b$$. $subhead epsilon$$ The argument $icode epsilon$$ has prototype $codei% double %epsilon% %$$ It specifies the convergence criteria for Newton's method in terms of how small the function value $latex | f(x) | \leq \varepsilon$$. $head max_itr$$ The argument $icode max_itr$$ has prototype $codei% size_t %max_itr% %$$ It specifies the maximum number of iterations of Newton's method to try before giving up on convergence. $subhead num_threads$$ This argument has prototype $codei% size_t %num_threads% %$$ It specifies the number of threads that are available for this test. If it is zero, the test is run without multi-threading. $head multi_newton_worker$$ Calling this function does the computation for one thread. Following a call to $code multi_newton_setup$$, this function should be called by each of the $icode num_threads$$ threads. $head multi_newton_combine$$ After the $icode num_threads$$ threads have completed their calls to $code multi_newton_worker$$, this function call will combine the results and return the final set of approximate zeros for $latex f(x)$$. $subhead xout$$ The argument $icode xout$$ has the prototype $codei% CppAD::vector& %xout% %$$ The input size and value of the elements of $icode xout$$ do not matter. Upon return from $code multi_newton_combine$$, the size of $icode xout$$ is less than or equal $latex n$$ and $codei% | %f%( %xout%[%i%] ) | <= %epsilon% %$$ for each valid index $icode i$$. In addition, the elements of $icode xout$$ are in ascending order and $codei% %xout%[i+1] - %xout%[%i%] >= 0.5 * (%xup% - %xlow%) / %num_sub% %$$ $head Source$$ $code $srcfile%multi_thread/multi_newton_work.cpp%0%// BEGIN C++%// END C++%1%$$ $$ $end */ // BEGIN C++ # include # include "multi_newton_work.hpp" # define USE_THREAD_ALLOC_FOR_WORK_ALL 1 namespace { using CppAD::thread_alloc; // This vector template class frees all memory when resized to zero. // In addition, its memory allocation works well during multi-threading. using CppAD::vector; // number of threads in previous call to multi_newton_setup size_t num_threads_ = 0; // convergence criteria in previous call to multi_newton_setup double epsilon_ = 0.; // maximum number of iterations in previous call to multi_newton_setup size_t max_itr_ = 0; // length for all sub-intervals double sub_length_ = 0.; // function we are finding zeros of in previous call to multi_newton_setup void (*fun_)(double x, double& f, double& df) = 0; // structure with information for one thread typedef struct { // number of sub intervals (worker input) size_t num_sub; // beginning of interval (worker input) double xlow; // end of interval (worker input) double xup; // vector of zero candidates (worker output) // after call to multi_newton_setup: x.size() == 0 // after call to multi_newton_work: x.size() is number of zeros // after call to multi_newton_combine: x.size() == 0 vector x; // false if an error occurs, true otherwise (worker output) bool ok; } work_one_t; // vector with information for all threads // after call to multi_newton_setup: work_all.size() == num_threads // after call to multi_newton_combine: work_all.size() == 0 // (use pointers instead of values to avoid false sharing) vector work_all_; } // ----------------------------------------------------------------------- // do the work for one thread void multi_newton_worker(void) { using CppAD::vector; // Split [xlow, xup] into num_sub intervales and // look for one zero in each sub-interval. size_t thread_num = thread_alloc::thread_num(); size_t num_threads = std::max(num_threads_, size_t(1)); bool ok = thread_num < num_threads; size_t num_sub = work_all_[thread_num]->num_sub; double xlow = work_all_[thread_num]->xlow; double xup = work_all_[thread_num]->xup; vector& x = work_all_[thread_num]->x; // check arguments ok &= max_itr_ > 0; ok &= num_sub > 0; ok &= xlow < xup; ok &= x.size() == 0; // check for special case where there is nothing for this thread to do if( num_sub == 0 ) { work_all_[thread_num]->ok = ok; return; } // check for a zero on each sub-interval size_t i; double xlast = xlow - 2 * sub_length_; // over sub_length_ away from x_low double flast = 2 * epsilon_; // any value > epsilon_ would do for(i = 0; i < num_sub; i++) { // note that when i == 0, xlow_i == xlow (exactly) double xlow_i = xlow + i * sub_length_; // note that when i == num_sub - 1, xup_i = xup (exactly) double xup_i = xup - (num_sub - i - 1) * sub_length_; // initial point for Newton iterations double xcur = (xup_i + xlow_i) / 2.; // Newton iterations bool more_itr = true; size_t itr = 0; // initialize these values to avoid MSC C++ warning double fcur=0.0, dfcur=0.0; while( more_itr ) { fun_(xcur, fcur, dfcur); // check end of iterations if( fabs(fcur) <= epsilon_ ) more_itr = false; if( (xcur == xlow_i ) & (fcur * dfcur > 0.) ) more_itr = false; if( (xcur == xup_i) & (fcur * dfcur < 0.) ) more_itr = false; // next Newton iterate if( more_itr ) { xcur = xcur - fcur / dfcur; // keep in bounds xcur = std::max(xcur, xlow_i); xcur = std::min(xcur, xup_i); more_itr = ++itr < max_itr_; } } if( fabs( fcur ) <= epsilon_ ) { // check for case where xcur is lower bound for this // sub-interval and upper bound for previous sub-interval if( fabs(xcur - xlast) >= sub_length_ ) { x.push_back( xcur ); xlast = xcur; flast = fcur; } else if( fabs(fcur) < fabs(flast) ) { x[ x.size() - 1] = xcur; xlast = xcur; flast = fcur; } } } work_all_[thread_num]->ok = ok; } // ----------------------------------------------------------------------- // setup the work up for multiple threads bool multi_newton_setup( void (fun)(double x, double& f, double& df) , size_t num_sub , double xlow , double xup , double epsilon , size_t max_itr , size_t num_threads ) { num_threads_ = num_threads; num_threads = std::max(num_threads_, size_t(1)); bool ok = num_threads == thread_alloc::num_threads(); // inputs that are same for all threads epsilon_ = epsilon; max_itr_ = max_itr; fun_ = fun; // resize the work vector to accomidate the number of threads ok &= work_all_.size() == 0; work_all_.resize(num_threads); // length of each sub interval sub_length_ = (xup - xlow) / double(num_sub); // determine values that are specific to each thread size_t num_min = num_sub / num_threads; // minimum num_sub size_t num_more = num_sub % num_threads; // number that have one more size_t sum_num = 0; // sum with respect to thread of num_sub size_t thread_num, num_sub_thread; for(thread_num = 0; thread_num < num_threads; thread_num++) { # if USE_THREAD_ALLOC_FOR_WORK_ALL // allocate separate memory for this thread to avoid false sharing size_t min_bytes(sizeof(work_one_t)), cap_bytes; void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes); work_all_[thread_num] = static_cast(v_ptr); // thread_alloc is a raw memory allocator; i.e., it does not call // the constructor for the objects it creates. The CppAD::vector // class requires it's constructor to be called so we do it here new(& (work_all_[thread_num]->x) ) vector(); # else work_all_[thread_num] = new work_one_t; # endif // number of sub-intervalse for this thread if( thread_num < num_more ) num_sub_thread = num_min + 1; else num_sub_thread = num_min; // when thread_num == 0, xlow_thread == xlow double xlow_thread = xlow + sum_num * sub_length_; // when thread_num == num_threads - 1, xup_thread = xup double xup_thread = xlow + (sum_num + num_sub_thread) * sub_length_; if( thread_num == num_threads - 1 ) xup_thread = xup; // update sum_num for next time through loop sum_num += num_sub_thread; // input information specific to this thread work_all_[thread_num]->num_sub = num_sub_thread; work_all_[thread_num]->xlow = xlow_thread; work_all_[thread_num]->xup = xup_thread; ok &= work_all_[thread_num]->x.size() == 0; // in case this thread does not get called work_all_[thread_num]->ok = false; } ok &= sum_num == num_sub; return ok; } // ----------------------------------------------------------------------- // get the result of the work bool multi_newton_combine(CppAD::vector& xout) { // number of threads in the calculation size_t num_threads = std::max(num_threads_, size_t(1)); // remove duplicates and points that are not solutions xout.resize(0); bool ok = true; size_t thread_num; // initialize as more that sub_lenght_ / 2 from any possible solution double xlast = - sub_length_; for(thread_num = 0; thread_num < num_threads; thread_num++) { vector& x = work_all_[thread_num]->x; size_t i; for(i = 0; i < x.size(); i++) { // check for case where this point is lower limit for this // thread and upper limit for previous thread if( fabs(x[i] - xlast) >= sub_length_ ) { xout.push_back( x[i] ); xlast = x[i]; } else { double fcur, flast, df; fun_(x[i], fcur, df); fun_(xlast, flast, df); if( fabs(fcur) < fabs(flast) ) { xout[ xout.size() - 1] = x[i]; xlast = x[i]; } } } ok &= work_all_[thread_num]->ok; } // go down so free memory for other threads before memory for master thread_num = num_threads; while(thread_num--) { # if USE_THREAD_ALLOC_FOR_WORK_ALL // call the destructor for CppAD::vector destructor work_all_[thread_num]->x.~vector(); // delete the raw memory allocation void* v_ptr = static_cast( work_all_[thread_num] ); thread_alloc::return_memory( v_ptr ); # else delete work_all_[thread_num]; # endif // Note that xout corresponds to memroy that is inuse by master // (so we can only chech have freed all their memory). if( thread_num > 0 ) { // check that there is no longer any memory inuse by this thread ok &= thread_alloc::inuse(thread_num) == 0; // return all memory being held for future use by this thread thread_alloc::free_available(thread_num); } } // now we are done with the work_all_ vector so free its memory // (because it is a static variable) work_all_.clear(); return ok; } // END C++ cppad-20170000.3/makefile.in0000644000175200017650000013041213057470467014545 0ustar coincoin-web# makefile.in generated by automake 1.15 from makefile.am. # @configure_input@ # Copyright (C) 1994-2014 Free Software Foundation, Inc. # This Makefile.in is free software; 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cppad_url = @cppad_url@ cppad_version = @cppad_version@ datadir = @datadir@ datarootdir = @datarootdir@ docdir = @docdir@ dvidir = @dvidir@ eigen_prefix = @eigen_prefix@ exec_prefix = @exec_prefix@ have_pkg_config = @have_pkg_config@ host = @host@ host_alias = @host_alias@ host_cpu = @host_cpu@ host_os = @host_os@ host_vendor = @host_vendor@ htmldir = @htmldir@ includedir = @includedir@ infodir = @infodir@ install_sh = @install_sh@ ipopt_prefix = @ipopt_prefix@ libdir = @libdir@ libexecdir = @libexecdir@ localedir = @localedir@ localstatedir = @localstatedir@ mandir = @mandir@ mkdir_p = @mkdir_p@ oldincludedir = @oldincludedir@ pdfdir = @pdfdir@ prefix = @prefix@ program_transform_name = @program_transform_name@ psdir = @psdir@ sbindir = @sbindir@ sharedstatedir = @sharedstatedir@ srcdir = @srcdir@ sysconfdir = @sysconfdir@ target_alias = @target_alias@ top_build_prefix = @top_build_prefix@ top_builddir = @top_builddir@ top_srcdir = @top_srcdir@ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # BUILT_SOURCES = $(top_srcdir)/cppad/configure.hpp @CppAD_POSTFIX_FALSE@postfix_dir = . # @CppAD_POSTFIX_TRUE@postfix_dir = $(POSTFIX_DIR) @CppAD_ADOLC_FALSE@SPEED_ADOLC_TESTS = # # Did user specify a value for ADOLC_DIR in configure command line @CppAD_ADOLC_TRUE@SPEED_ADOLC_TESTS = speed/adolc @CppAD_FADBAD_FALSE@SPEED_FADBAD_TESTS = # # Did user specify a value for FADBAD_DIR in configure command line @CppAD_FADBAD_TRUE@SPEED_FADBAD_TESTS = speed/fadbad @CppAD_SACADO_FALSE@SPEED_SACADO_TESTS = # # Did user specify a value for SACADO_DIR in configure command line @CppAD_SACADO_TRUE@SPEED_SACADO_TESTS = speed/sacado @CppAD_IPOPT_FALSE@IPOPT_TESTS = # # Did user 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cppad/cppad.hpp \ cppad/example/base_adolc.hpp \ cppad/example/cppad_eigen.hpp \ cppad/example/eigen_cholesky.hpp \ cppad/example/eigen_mat_inv.hpp \ cppad/example/eigen_mat_mul.hpp \ cppad/example/eigen_plugin.hpp \ cppad/example/mat_mul.hpp \ cppad/ipopt/solve_callback.hpp \ cppad/ipopt/solve.hpp \ cppad/ipopt/solve_result.hpp \ cppad/local/abs_op.hpp \ cppad/local/acosh_op.hpp \ cppad/local/acos_op.hpp \ cppad/local/add_op.hpp \ cppad/local/ad_tape.hpp \ cppad/local/asinh_op.hpp \ cppad/local/asin_op.hpp \ cppad/local/atanh_op.hpp \ cppad/local/atan_op.hpp \ cppad/local/color_general.hpp \ cppad/local/color_symmetric.hpp \ cppad/local/comp_op.hpp \ cppad/local/cond_op.hpp \ cppad/local/cosh_op.hpp \ cppad/local/cos_op.hpp \ cppad/local/cppad_colpack.hpp \ cppad/local/cskip_op.hpp \ cppad/local/csum_op.hpp \ cppad/local/declare_ad.hpp \ cppad/local/discrete_op.hpp \ cppad/local/div_op.hpp \ cppad/local/erf_op.hpp \ cppad/local/expm1_op.hpp \ cppad/local/exp_op.hpp \ cppad/local/for_hes_sweep.hpp \ cppad/local/for_jac_sweep.hpp \ cppad/local/forward0sweep.hpp \ cppad/local/forward1sweep.hpp \ cppad/local/forward2sweep.hpp \ cppad/local/hash_code.hpp \ cppad/local/independent.hpp \ cppad/local/load_op.hpp \ cppad/local/log1p_op.hpp \ cppad/local/log_op.hpp \ cppad/local/mul_op.hpp \ cppad/local/op_code.hpp \ cppad/local/op.hpp \ cppad/local/optimize/match_op.hpp \ cppad/local/optimize/cexp_info.hpp \ cppad/local/optimize/csum_stacks.hpp \ cppad/local/optimize/csum_variable.hpp \ cppad/local/optimize/get_op_info.hpp \ cppad/local/optimize/hash_code.hpp \ cppad/local/optimize/old2new.hpp \ cppad/local/optimize/op_info.hpp \ cppad/local/optimize/optimize_run.hpp \ cppad/local/optimize/record_csum.hpp \ cppad/local/optimize/record_pv.hpp \ cppad/local/optimize/record_vp.hpp \ cppad/local/optimize/record_vv.hpp \ cppad/local/optimize/size_pair.hpp \ cppad/local/optimize/usage.hpp \ cppad/local/parameter_op.hpp \ cppad/local/player.hpp \ cppad/local/pod_vector.hpp \ cppad/local/pow_op.hpp \ cppad/local/print_op.hpp \ cppad/local/prototype_op.hpp \ cppad/local/recorder.hpp \ cppad/local/reverse_sweep.hpp \ cppad/local/rev_hes_sweep.hpp \ cppad/local/rev_jac_sweep.hpp \ cppad/local/set_get_in_parallel.hpp \ cppad/local/sign_op.hpp \ cppad/local/sinh_op.hpp \ cppad/local/sin_op.hpp \ cppad/local/sparse_binary_op.hpp \ cppad/local/sparse_list.hpp \ cppad/local/sparse_pack.hpp \ cppad/local/sparse_pattern.hpp \ cppad/local/sparse_unary_op.hpp \ cppad/local/sqrt_op.hpp \ cppad/local/std_set.hpp \ cppad/local/store_op.hpp \ cppad/local/sub_op.hpp \ cppad/local/tanh_op.hpp \ cppad/local/tan_op.hpp \ cppad/local/user_state.hpp \ cppad/local/zmul_op.hpp \ cppad/speed/det_33.hpp \ cppad/speed/det_by_lu.hpp \ cppad/speed/det_by_minor.hpp \ cppad/speed/det_grad_33.hpp \ cppad/speed/det_of_minor.hpp \ cppad/speed/mat_sum_sq.hpp \ cppad/speed/ode_evaluate.hpp \ cppad/speed/sparse_hes_fun.hpp \ cppad/speed/sparse_jac_fun.hpp \ cppad/speed/uniform_01.hpp \ cppad/utility/check_numeric_type.hpp \ cppad/utility/check_simple_vector.hpp \ cppad/utility/elapsed_seconds.hpp \ cppad/utility/error_handler.hpp \ cppad/utility.hpp \ cppad/utility/index_sort.hpp \ cppad/utility/lu_factor.hpp \ cppad/utility/lu_invert.hpp \ cppad/utility/lu_solve.hpp \ cppad/utility/memory_leak.hpp \ cppad/utility/nan.hpp \ cppad/utility/near_equal.hpp \ cppad/utility/ode_err_control.hpp \ cppad/utility/ode_gear_control.hpp \ cppad/utility/ode_gear.hpp \ cppad/utility/omp_alloc.hpp \ cppad/utility/poly.hpp \ cppad/utility/pow_int.hpp \ cppad/utility/romberg_mul.hpp \ cppad/utility/romberg_one.hpp \ cppad/utility/rosen_34.hpp \ cppad/utility/runge_45.hpp \ cppad/utility/set_union.hpp \ cppad/utility/speed_test.hpp \ cppad/utility/thread_alloc.hpp \ cppad/utility/time_test.hpp \ cppad/utility/to_string.hpp \ cppad/utility/track_new_del.hpp \ cppad/utility/vector.hpp # End nobase_myinclude_HEADERS (check_makefile.sh uses this comment) # 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do ( \ echo "#" >> test.sh ; \ echo "echo \"Running make test in $$dir\"" >> test.sh ; \ echo "cd $$dir " >> test.sh ; \ echo "make test" >> test.sh ; \ echo "cd $(ABS_TOP_BUILDDIR)" >> test.sh ; \ ) done echo "exit 0" >> test.sh chmod +x test.sh ./test.sh # dist-hook: rm -rf `find . -name .svn` rm $(distdir)/doc/error.wrd rm $(distdir)/bin/gpl_license.sh install-data-hook: @CppAD_DOCUMENTATION_TRUE@ if [ ! -e $(doc_postfix) ] ; then mkdir -p $(doc_postfix) ; fi @CppAD_DOCUMENTATION_TRUE@ if [ -e $(doc_package) ] ; then rm -rf $(doc_package) ; fi @CppAD_DOCUMENTATION_TRUE@ cp -a $(top_srcdir)/doc $(doc_package) @CppAD_DOCUMENTATION_TRUE@ chmod -R a-w $(doc_package) @CppAD_DOCUMENTATION_TRUE@ chmod -R u+w $(doc_package) @CppAD_DOCUMENTATION_TRUE@ chmod -R a+r $(doc_package) @CppAD_DEPRECATED_TRUE@ cp -a $(top_srcdir)/cppad/deprecated/* $(inc_postfix)/cppad @CppAD_DEPRECATED_TRUE@ chmod -R a-w $(inc_postfix)/cppad @CppAD_DEPRECATED_TRUE@ chmod -R u+w $(inc_postfix)/cppad @CppAD_DEPRECATED_TRUE@ chmod -R a+r $(inc_postfix)/cppad # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: cppad-20170000.3/omh/0002755000175200017650000000000013057470467013224 5ustar coincoin-webcppad-20170000.3/omh/new_feature.omh0000644000175200017650000000360313057470463016231 0ustar coincoin-web$Id: new_feature.omh 3779 2016-01-01 11:26:11Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin NewFeature$$ $spell cppad.hpp CppAD Makefile Microsoft OMhelp cvs dsp nobase $$ $section Adding a New Feature to the CppAD Distribution$$ $head Overview$$ Suppose that you add a new feature to CppAD and the corresponding include file is $icode%Name%.h%$$. You should check each of the following steps: $list number$$ Add the new file $icode%Name%.h%$$ to the cvs repository. $lnext Add a test file called $codei%example/%Name%.cpp%$$ that check for correct results (and run the test to make sure it works). $lnext Add the new file $codei%example/%Name%.cpp%$$ to the cvs repository. $lnext Add a call to the new test in the file $code example/example.cpp$$. $lnext Add the file $icode%Name%.cpp%$$ to the list of $code Example_SOURCES$$ in the file $code example/Makefile.am$$. $lnext Add the file $icode%Name%.cpp%$$ to the list of source files corresponding to the Microsoft C++ project file $code example/Example.dsp$$. $lnext Add the file $icode%Name%.h%$$ to the list of $code nobase_include_HEADERS$$ in the file $code Makefile.am$$. $lnext Add the new feature to the OMhelp documentation tree. $lnext Add the new feature the cppad/cppad.hpp include tree. $lnext Mention the new feature in the WhatsNew file for the current year. $lend $end cppad-20170000.3/omh/appendix.omh0000644000175200017650000000160713057470463015537 0ustar coincoin-web$Id: appendix.omh 3759 2015-11-30 19:54:58Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin Appendix$$ $spell $$ $section Appendix$$ $childtable% omh/faq.omh% omh/theory/theory.omh% omh/glossary.omh% omh/bib.omh% omh/wish_list.omh% omh/whats_new/whats_new.omh% omh/deprecated/deprecated.omh% compare_c/CMakeLists.txt% omh/numeric_ad.omh% omh/addon.omh% omh/license.omh %$$ $end cppad-20170000.3/omh/simple_vector.omh0000644000175200017650000001515213057470463016602 0ustar coincoin-web$Id: simple_vector.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin SimpleVector$$ $spell std valarray Cpp const Resize $$ $section Definition of a Simple Vector$$ $mindex value_type [] NDEBUG$$ $head Template Class Requirements$$ A simple vector template class $icode SimpleVector$$, is any template class that satisfies the requirements below. The following is a list of some simple vector template classes: $table $bold Name$$ $cnext $bold Documentation$$ $rnext $code std::vector$$ $cnext Section 16.3 of $cref/The C++ Programming Language/Bib/The C++ Programming Language/$$ $rnext $code std::valarray$$ $cnext Section 22.4 of $cref/The C++ Programming Language/Bib/The C++ Programming Language/$$ $rnext $code CppAD::vector$$ $cnext $tref CppAD_vector$$ $tend $head Elements of Specified Type$$ A simple vector class with elements of type $icode Scalar$$, is any class that satisfies the requirements for a class of the form $codei% %SimpleVector%<%Scalar%> %$$ The routine $cref CheckSimpleVector$$ can be used to check that a class is a simple vector class with a specified element type. $head Default Constructor$$ The syntax $codei% %SimpleVector%<%Scalar%> %x%; %$$ creates an empty vector $icode x$$ ($icode%x%.size()%$$ is zero) that can later contain elements of the specified type (see $cref/resize/SimpleVector/Resize/$$ below). $head Sizing Constructor$$ If $icode n$$ has type $code size_t$$, $codei% %SimpleVector%<%Scalar%> %x%(%n%) %$$ creates a vector $icode x$$ with $icode n$$ elements each of the specified type. $head Copy Constructor$$ If $icode x$$ is a $icode%SimpleVector%<%Scalar%>%$$ object, $codei% %SimpleVector%<%Scalar%> %y%(%x%) %$$ creates a vector with the same type and number of elements as $icode x$$. The $icode Scalar$$ assignment operator ( $code =$$ ) is used to set each element of $icode y$$ equal to the corresponding element of $icode x$$. This is a `deep copy' in that the values of the elements of $icode x$$ and $icode y$$ can be set independently after the copy. The argument $icode x$$ is passed by reference and may be $code const$$. $head Element Constructor and Destructor$$ The default constructor for type $icode Scalar$$ is called for every element in a vector when the vector element is created. The $icode Scalar$$ destructor is called when it is removed from the vector (this includes when the vector is destroyed). $head Assignment$$ If $icode x$$ and $icode y$$ are $icode%SimpleVector%<%Scalar%>%$$ objects, $codei% %y% = %x% %$$ uses the $icode Scalar$$ assignment operator ( $code =$$ ) to set each element of $icode y$$ equal to the corresponding element of $icode x$$. This is a `deep assignment' in that the values of the elements of $icode x$$ and $icode y$$ can be set independently after the assignment. The vectors $icode x$$ and $icode y$$ must have the same number of elements. The argument $icode x$$ is passed by reference and may be $code const$$. $pre $$ The type returned by this assignment is unspecified; for example, it might be void in which case the syntax $codei% %z% = %y% = %x% %$$ would not be valid. $head Size$$ If $icode x$$ is a $icode%SimpleVector%<%Scalar%>%$$ object and $code n$$ has type $code size_t$$, $codei% %n% = size_t( %x%.size() ) %$$ sets $icode n$$ to the number of elements in the vector $icode x$$. The object $icode x$$ may be $code const$$. $head Resize$$ If $icode x$$ is a $icode%SimpleVector%<%Scalar%>%$$ object and $code n$$ has type $code size_t$$, $codei% %x%.resize(%n%) %$$ changes the number of elements contained in the vector $icode x$$ to be $icode n$$. The value of the elements of $icode x$$ are not specified after this operation; i.e., any values previously stored in $icode x$$ are lost. (The object $icode x$$ can not be $code const$$.) $head Value Type$$ If $icode Vector$$ is any simple vector class, the syntax $codei% %Vector%::value_type %$$ is the type of the elements corresponding to the vector class; i.e., $codei% %SimpleVector%<%Scalar%>::value_type %$$ is equal to $icode Scalar$$. $head Element Access$$ If $icode x$$ is a $icode%SimpleVector%<%Scalar%>%$$ object and $icode i$$ has type $code size_t$$, $codei% %x%[%i%] %$$ returns an object of an unspecified type, referred to here as $icode elementType$$. $subhead Using Value$$ If $icode elementType$$ is not the same as $icode Scalar$$, the conversion operator $codei% static_cast<%Scalar%>(%x%[%i%]) %$$ is used implicitly when $icode%x%[%i%]%$$ is used in an expression with values of type $icode Scalar$$. For this type of usage, the object $icode x$$ may be $code const$$. $subhead Assignment$$ If $icode y$$ is an object of type $icode Scalar$$, $codei% %x%[%i%] = %y% %$$ assigns the $th i$$ element of $icode x$$ to have value $icode y$$. For this type of usage, the object $icode x$$ can not be $code const$$. The type returned by this assignment is unspecified; for example, it might be void in which case the syntax $codei% %z% = %x%[%i%] = %y% %$$ would not be valid. $head Example$$ $children% example/simple_vector.cpp %$$ The file $cref simple_vector.cpp$$ contains an example and test of a Simple template class. It returns true if it succeeds and false otherwise. (It is easy to modify to test additional simple vector template classes.) $head Exercise$$ $list number$$ If $icode Vector$$ is a simple vector template class, the following code may not be valid: $codei% %Vector% x(2); x[2] = 1.; %$$ Create and run a program that executes the code segment above where $icode Vector$$ is each of the following cases: $code std::vector$$, $code CppAD::vector$$. Do this both where the compiler option $code -DNDEBUG$$ is and is not present on the compilation command line. $lnext If $icode Vector$$ is a simple vector template class, the following code may not be valid: $codei% %Vector% x(2); %Vector% y(1); x[0] = 0; x[1] = 1; y = x; %$$ Create and run a program that executes the code segment above where $icode Vector$$ is each of the following cases: $code std::valarray$$, $code CppAD::vector$$. Do this both where the compiler option $code -DNDEBUG$$ is and is not present on the compilation command line. $lend $end cppad-20170000.3/omh/atomic.omh0000644000175200017650000000134013057470463015175 0ustar coincoin-web// $Id: atomic.omh 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin atomic$$ $section Atomic AD Functions$$ $mindex operation$$ $childtable% cppad/core/checkpoint.hpp% omh/atomic_base.omh %$$ $end cppad-20170000.3/omh/whats_new/0002755000175200017650000000000013057470463015217 5ustar coincoin-webcppad-20170000.3/omh/whats_new/whats_new_09.omh0000644000175200017650000004214613057470463020240 0ustar coincoin-web$Id: whats_new_09.omh 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_09$$ $spell openmp arg std bool Microsoft retape isnan atan asin acos sqrt OMhelp doxygen exp_eps_apx cos tarball IpIpoptApplication IpoptDir autoconf automake config jacobian valgrind svn Prev CppAD Adolc cppad hpp op pycppad cond_exp VecAD Jacobians Jac Taylor $$ $section Changes and Additions to CppAD During 2009$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2009 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. (Comments about developer documentation are only important if you are trying to read and understand the CppAD source code.) $head 12-23$$ The $code ADFun$$ $cref/assignment operator/FunConstruct/Assignment Operator/$$ was changed so that it now copies forward mode Taylor coefficients and sparsity pattern information. (This assignment operator was added on $cref/10-24/whats_new_09/10-24/$$.) You can use $cref capacity_order$$ to delete the Taylor coefficients before copying them. Two new functions were added so that you can query and delete the forward mode sparsity information; see $cref/size_forward_bool/ForSparseJac/f/size_forward_bool/$$ and $cref/size_forward_set/ForSparseJac/f/size_forward_set/$$. $head 12-22$$ Convert the optimization of a sequence of additions from multiple operators to one operator with a varying number of arguments. This improved the speed for forward and reverse mode computations of an optimized tape. $head 12-18$$ It turns out that detection of a sequence of additions makes the optimization longer. This was simplified and makes slightly faster by converting two jointly recursive routines to one non-recursive routine that uses a stack for the necessary information. More work is planned to make this optimization faster. $head 12-12$$ Detection of a sequence of additions that can be converted to one variable during the $cref optimize$$ process. This leads to a significant improvement in the tape size and speed. $head 12-04$$ Change hash coding of parameter values as part of operators during the $cref optimize$$ process. This should leads to more detection and removal of duplicate operations. $head 12-02$$ Fix minor grammatical error in the Purpose heading for $cref/conditional expressions/CondExp/Purpose/$$. $pre $$ Add the following functions: $cref/size_op/seq_property/size_op/$$, $cref/size_op_arg/seq_property/size_op_arg/$$, and $cref/size_op_seq/seq_property/size_op_seq/$$. In addition, improve and extend the $cref seq_property.cpp$$ example. $head 11-28$$ Fix bug in tape optimization with $cref VecAD$$ objects. $head 11-27$$ Remove duplicate expressions for the commutative binary operators; i.e., addition and multiplication. $head 11-26$$ Improve $cref optimize$$ command so that it removes some duplicate expressions from the tape (more of this is planned). $head 10-30$$ Make program that check Ipopt ODE example correctness a separate file $cref ipopt_nlp_ode_check.cpp$$ Split out Ipopt driver for ODE example $cref ipopt_nlp_ode_run.hpp$$. Add the speed testing problem $code ipopt_cppad/ipopt_ode_speed.cpp$$. $head 10-29$$ Split out the $cref/ode inverse problem/ipopt_nlp_ode_problem/$$, $cref/its simple representation/ipopt_nlp_ode_simple/$$, and $cref/its fast representation/ipopt_nlp_ode_fast/$$, as a separate files; to be specific, $cref ipopt_nlp_ode_problem.hpp$$, $cref ipopt_nlp_ode_simple.hpp$$, $cref ipopt_nlp_ode_fast.hpp$$, and $cref ipopt_nlp_ode_check.cpp$$. $head 10-28$$ Improve the documentation for $cref ipopt_nlp_ode_simple$$ and $cref ipopt_nlp_ode_fast$$. $head 10-27$$ Moved old $code ipopt_cppad_simple.cpp$$ to $cref ipopt_nlp_get_started.cpp$$, created the example $cref ipopt_nlp_ode_simple.hpp$$, and split and $code ipopt_cppad_ode.cpp$$ into $cref ipopt_nlp_ode_fast.hpp$$ and $cref ipopt_nlp_ode_check.cpp$$. $head 10-24$$ Added the $cref/assignment operator/FunConstruct/Assignment Operator/$$ to the $code ADFun$$ object class. This makes a copy of the entire operation sequence in another function object. The intention is that the two functions objects can do calculations in parallel. In addition, CppAD now check for the $code ADFun$$ $cref/copy constructor/FunConstruct/Copy Constructor/$$ and generates an error message if it is used. $head 10-23$$ The $cref sparse_hessian$$ routine was extended so the user can now choose between vectors of sets and boolean vectors for representing $cref/sparsity patterns/glossary/Sparsity Pattern/$$. $head 10-21$$ The $cref CheckSimpleVector$$ function was extended so that it can check simple vectors where the elements of the vector can not be assigned to integer values. This was done by adding the $cref/x, y/CheckSimpleVector/x, y/$$ arguments to $code CheckSimpleVector$$. $head 10-16$$ The $cref sparse_jacobian$$ routine was extended so the user can now choose between vectors of sets and boolean vectors for representing $cref/sparsity patterns/glossary/Sparsity Pattern/$$. $head 10-14$$ The $icode packed$$ parameter for the sparsity routines $cref ForSparseJac$$, $cref RevSparseJac$$, and $cref RevSparseHes$$ (introduced on $cref/09-26/whats_new_09/09-26/$$) has been removed. It has been replaced by changing the argument and return values to be more versatile. To be specific, they can now represent sparsity using vectors of $code std::set$$ instead of just as vectors of $code bool$$ (see $cref/sparsity patterns/glossary/Sparsity Pattern/$$). $head 10-03$$ The Microsoft Visual Studio project files for examples and testing and for more correctness testing were not including some new tests in their builds. This has been fixed. $head 09-30$$ Added the $cref cppad_sparse_jacobian.cpp$$ speed test and increased the sizes used by $cref link_sparse_hessian$$. Some mistakes were fixed in the documentation for speed tests $cref link_sparse_hessian$$ and $cref sparse_hes_fun$$. $head 09-29$$ The documentation definition of the function $latex H(x)$$ in $cref RevSparseHes$$ was missing a factor of $latex R$$. This has been fixed. $head 09-28$$ Changed $cref RevSparseHes$$ so that it uses a sparse representation when the corresponding call to $cref ForSparseJac$$ used a sparse representation. This should have been included with the change on 09-26 because Hessian sparsity patters after $code ForSparseJac$$ with $icode packed$$ did not work. Thus, this could be considered a bug fix. $head 09-26$$ Added the $code packed$$ parameter to $cref ForSparseJac$$ and $cref RevSparseJac$$. If $icode packed$$ is false, a sparse instead of packed representation is used during the calculations of sparsity patterns. The sparse representation should be faster, and use less memory, for very large sparse Jacobians. The functions $code ForSparseJac$$ and $code RevSparseJac$$ return packed representations. The plan is to eventually provide new member functions that return sparse representations. $head 09-20$$ Fixed a bug in the $cref/Hessian Sparsity/RevSparseHes/$$ calculations that included use of $cref VecAD$$ objects. $head 09-19$$ Some more memory allocation improvements (related to those on 09-18) were made. $head 09-18$$ A bug was found in all the $cref/Sparsity/Sparse/$$ calculations. The result was that eight times the necessary memory was being used during these calculations. This has been fixed. $head 08-25$$ Add $cref ad_fun.cpp$$ an example of how to create your own interface to an $cref ADFun$$ object. $head 08-14$$ Add $cref ad_in_c.cpp$$ an example of how to link CppAD to other languages. $head 08_13$$ Add an option to $cref optimize$$ an operation sequence. $pre $$ $bold Begin Merge$$ $pre $$ of changes from the directory $code branches/optimize$$ in the CppAD subversion repository. The subheading dates below represent when the correspond change was made in $code branches/optimize$$. $subhead 08-13$$ An automatic check of the $cref forward_zero$$ results was added after each call to $cref/f.optimize()/optimize/$$ (this $cref/check/optimize/Checking Optimization/$$ is skipped when $code NDEBUG$$ is defined). In addition, all of the $codei%speed/cppad/%*%.cpp%$$ tests now check and use the speed test $cref/optimize/speed_main/Global Options/optimize/$$ flag. $subhead 08-11$$ Change the speed test $cref/main program/speed_main/$$ so that it uses a list of options instead of a boolean flag for each option. This will make it possible to add options in the future with out having to change all the existing tests because the options are now global variables instead of arguments to the speed test routines; for example, see $code retape$$ speed test option. $subhead 08-10$$ The routine for $cref/optimizing/optimize/$$ the operation sequence has been added has been further tested using $code test_more/optimize.cpp$$. Some bugs have been fix and the routine can now be trusted to work correctly. $pre $$ The function $cref/size_VecAD/seq_property/size_VecAD/$$ function was added so that the user could see the $code VecAD$$ vectors and elements corresponding to an operation sequence. $subhead 08-09$$ A routine for $cref/optimizing/optimize/$$ the operation sequence has been added. This is a preliminary version and needs more testing before it can be trusted to work correctly. $pre $$ $bold End Merge$$ $head 08-06$$ Add hash table coding to reduce the number of copies of the same parameter value necessary in a tape recording. In addition, add the function $cref/size_par/seq_property/size_par/$$ was added so that the user could see the number of parameters corresponding to an operation sequence. $head 08-02$$ Fix bug in new version of how $cref ForSparseJac$$ handles $cref VecAD$$ objects. $pre $$ Fix bug in overnight build where HTML version and entire documentation as one page versions of documentation were not being built. $pre $$ Fix missing new line under $cref/Using Value/SimpleVector/Element Access/Using Value/$$ heading for simple vector documentation. $head 08-01$$ Fix bug in reverse mode Jacobian $cref/sparsity/RevSparseJac/$$ for $cref VecAD$$ objects. $head 07-31$$ The $cref/forward/ForSparseJac/$$ and $cref/reverse/RevSparseJac/$$ sparse Jacobian routines have been improved so the resulting sparsity patterns are valid for all values of the independent variables (even if you use $cref CondExp$$ or $cref VecAD$$). $head 07-26$$ Convert developer documentation from forward and reverse mode sweep routines from OMhelp to doxygen. $head 07-25$$ Add developer documentation for $cref PrintFor$$ operations. $head 07-24$$ Add developer documentation for $cref Discrete$$ operations. $head 07-23$$ Add developer documentation for tape evaluation of $cref VecAD$$ store operations. (a store operation changes the value of a VecAD element). $pre $$ Improve the $cref vec_ad.cpp$$ user example. $subhead 07-06$$ Fixed a bug in second or higher order reverse mode calculations that used $cref VecAD$$. This bug was demonstrated by the test case $code SecondOrderReverse$$ in the file $code test_more/vec_ad.cpp$$. $pre $$ Add developer documentation for tape evaluation of the VecAD load operations (a load operation accesses an element of the vector but does not change it.) $pre $$ Fix $code isnan$$ undefined in $code example/cond_exp.cpp$$ error introduced on 07-04 change. $head 07-04$$ Add developer documentation for the $cref CompareChange$$ operations during tape evaluation. $pre $$ $bold Begin Merge$$ $pre $$ of changes from the directory $code branches/sweep$$ in the CppAD subversion repository. The subheading dates below represent when the correspond change was made in $code branches/sweep$$. $subhead 07-04$$ Fixed a bug in second or higher order reverse mode calculations that included $cref/conditional expressions/CondExp/$$. This bug was demonstrated by the test case $code SecondOrderReverse$$ in the file $code test_more/cond_exp.cpp$$. $pre $$ A simpler and useful example was provided for $cref/conditional expressions/CondExp/$$; see $cref cond_exp.cpp$$. $subhead 07-03$$ Some minor improvements were made to the documentation for $cref CondExp$$. To be specific, a newer OMhelp option was used to change the formatting of the syntax, some of the argument names were changed to be more descriptive. $subhead 07-02$$ Add developer doxygen documentation of tape evaluation for power (exponentiation) operators. $subhead 07-01$$ Fix an example indexing error in $code introduction/exp_apx/exp_eps_for2.cpp$$ (found by valgrind). $pre $$ Add developer doxygen documentation of tape evaluation for multiplication and division operators. $subhead 06-30$$ Add developer doxygen documentation of tape evaluation for addition and subtraction operators. $subhead 06-29$$ Add developer doxygen documentation of tape evaluation for sin, sinh, cos, and cosh. $subhead 06-28$$ Add developer doxygen documentation of tape evaluation for atan, asin, acos, sqrt, log. $pre $$ $bold End Merge$$ $head 06-25$$ The tarball for most recent release (of the subversion trunk for CppAD) was not being placed in the $href%http://www.coin-or.org/download/source/CppAD/%download%$$ directory. This has been fixed. $head 06-22$$ Fix compiler warnings during the $code openmp/run.sh$$ test. $pre $$ Changed $cref speed_example.cpp$$ to omit the $code speed_test$$ from the correctness result. In stead, a message is printed explaining that timing tests need to be run without a lot of other demands on the system. $head 06-21$$ The configure instructions for $cref/ipopt_dir/auto_tools/ipopt_dir/$$ had the wrong path for $code IpIpoptApplication.hpp$$. This has been fixed. $head 06-20$$ Upgrade to from autoconf 2.61 to 2.63, and from automake 1.10.1 to 1.11. $pre $$ Fix conflict between CppAD's use of config.h preprocessor symbols and other packages use of the same symbol names. $head 06-06$$ $list number$$ Using complex of an AD type (instead of AD of complex) was not working correctly in $code not_complex_ad.cpp$$ because the $cref/default constructor/ad_ctor/$$ for an AD object has an unspecified value. This has been fixed for the complex type by changing the default constructor to use value zero. (The $code not_complex_ad.cpp$$ example has been removed; see $cref/complex FAQ/Faq/Complex Types/$$.) $lnext Fixing the $code not_complex_ad.cpp$$ problem above also fixed a warning generated by $href%http://valgrind.org/%valgrind%$$. Now $code valgrind$$ runs the CppAD $code example/example$$ program with out any warning or error messages. In addition, a minor initialization error was fixed in the $code test_more/jacobian.cpp$$ routine so now $code valgrind$$ also runs the CppAD $code test_more/test_more$$ program with out any warnings or error messages. $lend $head 05-20$$ A change was make to the trunk on 05-19 (svn revision 1361) that broke the $cref/Unix install/auto_tools/$$ procedure. This was has been fixed (revision 1362). $head 03-24$$ Added cross references in the $cref/examples/ListAllExamples/$$ to occurrence of the following tokens: $cref AD$$, $cref/ADFun/FunConstruct/$$, $cref/CPPAD_TEST_VECTOR/test_vector/$$, $cref Forward$$, $cref Independent$$, $cref Jacobian$$ $cref NearEqual$$, $cref Reverse$$. $head 02-20$$ Demonstrate using AD to compute the derivative of the solution of an ODE with respect to a parameter (in the $cref runge45_2.cpp$$ example). $head 02-15$$ Change the distribution $cref/compressed tar file/download/Compressed Archives/$$ to only contain one copy of the documentation. Link to the current Internet documentation for the other three copies. $head 02-01$$ Move the $code Prev$$ and $code Next$$ buttons at the top of the documentation to the beginning so that their position does not change between sections. This makes it easier to repeatedly select this links. $head 01-31$$ Modify $code cppad/local/op_code.hpp$$ to avoid incorrect warning by g++ version 4.3.2 when building $code pycppad$$ (a python interface to CppAD). $head 01-18$$ Sometimes an error occurs while taping AD operations. The $cref abort_recording$$ function has been added to make it easier to recover in such cases. $pre $$ Previously, CppAD speed and comparison tests used Adolc-1.10.2. The version used in the tests has been upgraded to $href% https://projects.coin-or.org/ADOL-C% Adolc-2.0.0. %$$ $pre $$ A discussion has been added to the documentation for $cref Jacobian$$ about its use of $cref/forward or reverse/Jacobian/Forward or Reverse/$$ mode depending on which it estimates is more efficient. $pre $$ A minor typo has been fixed in the description of $code W(t, u)$$ in $cref reverse_any$$. To be specific, $latex o ( t^{p-1} ) * t^{1-p} \rightarrow 0$$ has been replaced by $latex o ( t^{p-1} ) / t^{1-p} \rightarrow 0$$. $head 01-06$$ Made some minor improvements to the documentation in $cref FunConstruct$$. $end cppad-20170000.3/omh/whats_new/whats_new.omh0000644000175200017650000000332413057470463017723 0ustar coincoin-web$Id: whats_new.omh 3782 2016-01-19 12:05:43Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new$$ $spell CppAD Eigen std namespace $$ $section Changes and Additions to CppAD$$ $head Introduction$$ The sections listed below contain a list of the changes to CppAD in reverse order by date. The purpose of these sections is to assist you in learning about changes between various versions of CppAD. $children% omh/whats_new/whats_new_16.omh% omh/whats_new/whats_new_15.omh% omh/whats_new/whats_new_14.omh% omh/whats_new/whats_new_13.omh% omh/whats_new/whats_new_12.omh% omh/whats_new/whats_new_11.omh% omh/whats_new/whats_new_10.omh% omh/whats_new/whats_new_09.omh% omh/whats_new/whats_new_08.omh% omh/whats_new/whats_new_07.omh% omh/whats_new/whats_new_06.omh% omh/whats_new/whats_new_05.omh% omh/whats_new/whats_new_04.omh% omh/whats_new/whats_new_03.omh %$$ $head This Year$$ $cref whats_new_16$$ $head Previous Years$$ $cref whats_new_15$$ $cref whats_new_14$$ $cref whats_new_13$$ $cref whats_new_12$$ $cref whats_new_11$$, $cref whats_new_10$$, $cref whats_new_09$$, $cref whats_new_08$$, $cref whats_new_07$$, $cref whats_new_06$$, $cref whats_new_05$$, $cref whats_new_04$$, $cref whats_new_03$$. $end cppad-20170000.3/omh/whats_new/whats_new_10.omh0000644000175200017650000002312413057470463020223 0ustar coincoin-web$Id: whats_new_10.omh 3768 2015-12-28 18:58:35Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_10$$ $spell Wshadow pkg-config Dir libipopt const Linpack Blas makefile op arg checkpointing sizeof libcppad_ipopt.a Microsoft Lagragian iostream obj_value std::cout endl gcc retape hpp ifdef nlp ipopt_cppad/src CppAD $$ $section Changes and Additions to CppAD During 2010$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2010 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-31$$ $list number$$ Add specifications for the CppAD $cref pkgconfig$$ files. $lnext Update the CppAD README file. $lnext Move most all CppAD development shell scripts to the $code bin$$ subdirectory of the distribution directory. $lnext Fix warnings generated by the $code g++$$ compiler option $code -Wshadow$$; for example, $code sparse_pack.hpp:101:2: warning: declaration of 'end' shadows a member of 'this' $$ $lend $head 11-27$$ If $code NDEBUB$$ was defined, the default CppAD $cref/error handler/ErrorHandler/$$ would return because its $code assert$$ had no effect in this case. This has been fixed by placing a call to $code std::exit(1)$$ after its assert. $head 09-26$$ There was a bug (introduced on 09-22) in $code make test$$ when the $code configure$$ command was executed from a directory other than the distribution directory (the $cref cppad_ipopt_nlp$$ did not build). This has been fixed. $head 09-22$$ Promote $cref cppad_ipopt_nlp$$ from an example to a library that gets installed (provided that the $cref/ipopt_dir/auto_tools/ipopt_dir/$$ is specified on the $code configure$$ command line). $head 08-21$$ Fix problems with linking of $cref cppad_ipopt_nlp$$ test with both older and newer versions of $code ipopt$$. $head 07-14$$ The new versions of ipopt use $code pkg-config$$ to record the location where its necessary libraries are stored on the system. The cppad $cref/configure/auto_tools/Configure/$$ command has been improved so that it can work both with versions of ipopt that use $code pkg-config$$ and ones that don't. $head 07-11$$ Old versions of the ipopt library were located in $icode%ipopt_dir%/lib/libipopt.%*%$$ (see $cref/ipopt_dir/auto_tools/ipopt_dir/$$), but newer versions will be located in $icode%ipopt_dir%/lib/coin/libipopt.%*%$$. The directory $icode%ipopt_dir%/lib/coin%$$ has been added to the library search path so that the $cref/cppad_ipopt_nlp examples/cppad_ipopt_nlp/Example/$$ work with both old and new versions of ipopt. $head 06-01$$ In the case where the preprocessor symbol $code NDEBUG$$ was defined (see $cref/speed/Faq/Speed/$$), the function $codei% CheckSimpleVector(const %Scalar%& %x%, const %Scalar%& %y%) %$$ was not defined; see $href%http://list.coin-or.org/pipermail/cppad/2010q2/000166.html%bug report%$$. This has been fixed. $head 04-28$$ Change the multi-level taping examples $cref mul_level.cpp$$ and $cref mul_level_adolc.cpp$$ to be more efficient. $head 04-26$$ Include Blas and Linpack libraries in makefile links for $cref cppad_ipopt_nlp$$ examples. This removes the need to use get.Blas when building Ipopt. $pre $$ The speed test in $code cppad_ipopt/speed$$ was missing a link to the library $code ../src/libcppad_ipopt.a$$. This has been fixed. $head 04-24$$ There was a bug in the error checking done by $code cppad/local/sub_op.hpp$$ that caused the following improper abort: $codei% Error detected by false result for arg[1] < i_z at line 337 in the file %...%/include/cppad/local/sub_op.hpp %$$ This was fixed in the trunk. It was also fixed in the release with version number $code 20100101.3$$ which can be downloaded from the CppAD $href%http://www.coin-or.org/download/source/CppAD/%download directory%$$. $head 04-01$$ Some of the $cref speed_utility$$ library (in $code speed/src$$) was being compiled for debugging. This has been changed and they are now compiled with debugging off and optimization on. $head 03-11$$ The old $cref reverse_any$$ example was moved to $cref reverse_three.cpp$$, the old checkpoint example is now the general case reverse example, and a better $code checkpoint.cpp/$$ example was created. $head 03-10$$ The $cref optimize$$ routine would mistakenly remove some expressions that depended on the independent variables and that affected the result of certain $cref CondExp$$ operations. This has been fixed. $head 03-09$$ Extend $cref reverse_any$$ so that it can be used for $cref/checkpointing/checkpoint/$$; i.e., splitting reverse mode calculations at function composition points. $head 03-03$$ Fixed a bug in handling $cref/vector of boolean/glossary/Sparsity Pattern/Vector of Boolean/$$ sparsity patterns. (when the number of elements per set was a multiple of $code sizeof(size_t))$$. $head 02-11$$ The $code speed$$ directory has been reorganized and the common part of the $cref/link functions/speed_main/Link Functions/$$, as well as the $cref microsoft_timer$$, have been moved to the subdirectory $code speed/src$$ where a library is built. $head 02-08$$ A bug was introduced in the $cref/02-05/whats_new_10/02-05/$$ change whereby the $code make$$ command tried to build the $code libcppad_ipopt.a$$ library even if $code IPOPT_DIR$$ was not specified on the $cref/configure/auto_tools/Configure/$$ command line. This has been fixed. $head 02-06$$ The Microsoft project files for the speed tests were extended so that the worked properly for the Release (as well as the Debug) configuration. (This required conversion from Visual Studio Version 7 to Visual Studio 2008 format.) $pre $$ Add an automated check for $cref optimize$$ bug fixed on $code 02-05$$. (Automatic checking for $cref PrintFor$$ bug was added on $code 02-05$$.) $head 02-05$$ $list number$$ Simplify running all the tests by adding the $code make test$$ command. $lnext Simplify the $cref/configure/auto_tools/Configure/$$ command by removing need for: $code --with-Speed$$, $code --with-Introduction$$, $code --with-Example$$, $code --with-TestMore$$, and $code --with-PrintFor$$. $lnext Add files that were missing in the Microsoft Visual Studio projects. $lnext Fix two significant bugs. One in the $cref optimize$$ command and the other in the $cref PrintFor$$ command. $lend $head 02-03$$ Fix a mistakes in the test $cref bender_quad.cpp$$. In addition, the $cref optimize$$ routine was used to reduce the tape before doing the calculations. $pre $$ The routine $cref opt_val_hes$$ was added as an alternative to $cref BenderQuad$$. $head 01-26$$ Another speed improvement was made to $cref cppad_ipopt_nlp$$. To be specific, the Lagragian multipliers where checked and components that were zero were excluded form the Hessian evaluation. $head 01-24$$ It appears that in $cref cppad_ipopt_nlp$$, when $code retape[k]$$ was true, and $code L[k] > 1$$, it was possible to use the wrong operation sequence in the calculations (though a test case that demonstrated this could not be produced). This is because the argument value to $latex r_k (u)$$ depends on the value of $latex \ell$$ in the expression $latex \[ r_k \circ [ J_{k, \ell} \otimes n ] (x) \] $$ (even when the value of $latex x$$ does not change). $pre $$ There was a bug in the $cref ipopt_nlp_ode_check.cpp$$ program, for a long time, that did not show up until now. Basically, the check had code of the was using an undefined value. This has been fixed. $head 01-23$$ Improve the sparsity patterns and reduce the amount of memory required for large sparse problems using $cref cppad_ipopt_nlp$$. The speed test $code cppad_ipopt/speed$$ showed significant improvement. $head 01-20$$ We plan to split up the $code ipopt_cppad/src/ipopt_cppad_nlp.hpp$$ include file. In preparation, the example $code ipopt_cppad$$ has been changed to $code cppad_ipopt$$. This will facilitate using $code CPPAD_IPOPT_*$$ for the $code # ifdef$$ commands in the new include files (note that they must begin with $code CPPAD$$). $head 01-18$$ The $code ipopt_cppad$$ subdirectory of the distribution has been split into an $code src$$, $code example$$, and $code speed$$ subdirectories. The $code example$$ ($code speed$$) subdirectory is where one builds the $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ examples ($cref%speed tests%ipopt_ode_speed.cpp%$$). $head 01-04$$ The following items have been fulfilled and hence were removed for the $cref wish_list$$: $list number$$ If an exception occurs before the call to the corresponding $cref ADFun$$ constructor or $cref Dependent$$, the tape recording can be stopped using $cref abort_recording$$. $lnext A speed test for $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ was added; see $cref ipopt_ode_speed.cpp$$. $lnext The $cref optimize$$ command uses hash coding to check when an expression is already in the tape and can be reused. $lnext The $cref optimize$$ command removes operations that are not used by any of the dependent variables. $lnext The $cref ad_in_c.cpp$$ example demonstrates how to connect CppAD to an arbitrary scripting language. $lnext The vector of sets option has been added to sparsity calculations; see $cref/sparsity pattern/glossary/Sparsity Pattern/$$. $lend $end cppad-20170000.3/omh/whats_new/whats_new_11.omh0000644000175200017650000007457213057470463020241 0ustar coincoin-web$Id: whats_new_11.omh 3794 2016-02-29 20:42:44Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_11$$ $spell eps cxx namespace boostvector mega inv bthread pthread pthreads Std retape cygwin vcproj pthread https abs_geq CondExpRel num Taylor Tanh Rosen Runge executables matlab Addr sizeof undefine config adolc initializer vec Bool op omp_alloc isnan gcc hasnan instantiation Microsoft svn hes openmp prefixdir pkgconfig Fadbad Wshadow omh dir libspeed cppad_ipopt_nlp.hpp automake makefile builddir gpl http://www.coin-or.org/download/source/CppAD/cppad-20110101.0.cpl.tgz $$ $section Changes and Additions to CppAD During 2011$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2011 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-30$$ $list number$$ There was a bug when using $cref abs$$ with an $code AD< AD >$$ argument, whereby the corresponding $code AD$$ operation sequence depended on the value of the argument to the $code abs$$ function. $lnext Change the specifications for the derivative of the $cref abs$$ function to be the $cref sign$$ function instead of a directional derivative. $lnext Add the $cref sign$$ function to the $codei%AD<%Base%>%$$ list of available functions. In addition, add the $cref%sign%base_std_math%sign%$$ function to the list of $cref%base type requirements%base_require%$$. $lend $head 12-28$$ The file $cref/time_test.hpp/time_test/Include/$$ was not being included by $code cppad/cppad.hpp$$. This has been fixed. $head 12-21$$ The types $code SizeVector$$, $code NumberVector$$, $code ADNumber$$, and $code ADVector$$, were in the global namespace and this was causing warnings about the shadowing of these declarations. The $cref/cppad_ipopt namespace/cppad_ipopt_nlp/cppad_ipopt namespace/$$ was created to avoid these problems. The simplest way to make old $cref cppad_ipopt_nlp$$ code work with this change is to use the command $codep using namespace cppad_ipopt; $$ $head 12-20$$ $list number$$ Change $code team_start$$ to $cref/team_create/team_thread.hpp/team_create/$$ and $code team_stop$$ to $cref/team_destroy/team_thread.hpp/team_destroy/$$. $lnext Change $code NDEBUG$$ mentions to include link to $cref/NDEBUG/Faq/Speed/NDEBUG/$$. $lnext Improve $cref memory_leak$$ documentation. $lend $head 11-29$$ THe $cref time_test$$ routine was still executing the test at least twice, even if that was not necessary for the specified minimum time. This has been fixed. $head 11-27$$ Move $code multi_thread.cpp$$ to $cref thread_test.cpp$$ and fix its $cref/running/thread_test.cpp/Running Tests/$$ instructions. $head 11-24$$ Create $cref preprocessor$$ section with pointers to all the preprocessor symbols that are in the CppAD API. $head 11-21$$ Separate $cref/--with-boostvector/auto_tools/--with-testvector/$$ for $cref/boost_dir/auto_tools/boost_dir/$$. This enables one to specify $icode boost_dir$$ for $cref team_bthread.cpp$$ with out using boost vectors. $head 11-20$$ $list number$$ Move $code sum_i_inv.cpp$$ to $cref harmonic.cpp$$. $lnext Include the date, time, CppAD version, and $cref/team_name/team_thread.hpp/team_name/$$ in the $cref thread_test.cpp$$ output. $lend $head 11-18$$ $list number$$ The $cref thread_test.cpp$$ program was truncating $icode test_time$$ to the nearest integer. This has been fixed. $lnext The $cref time_test$$ routine has been made more efficient and now check for the case where only one execution of the test is necessary to achieve the desired $icode test_time$$ (it used to always run at least two). $lnext The $code sum_i_inv_time.cpp$$ and $cref multi_newton.cpp$$ routines were calling the test an extra time at the end to check for correctness. The results of the last test are now cached and used for the correctness test so that an extra call is not necessary (to make the tests run faster when only a few repetitions are necessary). $lend $head 11-17$$ $list number$$ Create another speed testing routine $cref time_test$$ which is like $cref speed_test$$ but it returns the time instead of rate and as a $code double$$ instead of a $code size_t$$. The use it for the timing tests in $code sum_i_inv_time.cpp$$ and $cref multi_newton_time.cpp$$. $lnext Add $icode test_time$$ as a command line argument to the multi-threading $code sum_i_inv$$ and $cref/multi_newton/thread_test.cpp/multi_newton/$$ timing tests. $lend $head 11-09$$ Change $code thread_team.hpp$$ to $cref team_thread.hpp$$ and do the same for all other names that ended in $code _team$$; e.g., $cref team_openmp.cpp$$. $head 11-07$$ The users choice for $cref test_vector$$ was not actually changing the tests that the user ran. This have been fixed. $head 11-06$$ Make all the output generated by $cref multi_newton.cpp$$ valid matlab and octave input so it is easy to plot the results. $head 11-04$$ Use thread specific data to simplify $cref team_openmp.cpp$$. $head 11-01$$ Make $cref team_bthread.cpp$$ more similar to $cref team_pthread.cpp$$. $head 10-30$$ $list number$$ Reorganize and improve the $cref multi_thread$$ section and its subsections. $lnext There was a bug in $cref multi_newton_work.cpp$$ that only showed up when the number of threads was greater than or equal 4. This has been fixed. In addition, $cref/CPPAD_MAX_NUM_THREADS/multi_thread/CPPAD_MAX_NUM_THREADS/$$ was increased from 2 to 4 (to enable testing for this bug). $lnext The accuracy expected in the $code sum_i_inv.cpp$$ results were failing when $code mega_sum$$ was large. This check has been modified to include a correction for $icode mega_sum$$. $lend $head 10-29$$ The following changes were merged in from $code branches/thread$$: $list number$$ Move $code openmp$$ to $code multi_thread/openmp$$. and create $code multi_thread/bthread$$, $code multi_thread/pthread$$ with similar tests. $lnext Put multi-threading common code in $code multi_thread$$ directory and threading system specific code in $codei%multi_thread/%threading%$$ for $icode threading$$ equal to $code openmp$$, $code bthread$$, and $code pthread$$. $lnext Update the README file. $lnext Remove the $code bug/optimize.sh$$ file (no longer a bug). $lnext Make $code arc_tan.cpp$$ utility that can be used by multiple multi-threading tests. $lnext Create $cref team_thread.hpp$$ specifications, move OpenMP management to $cref team_openmp.cpp$$, Boost thread management to $cref team_bthread.cpp$$, and pthread management to $cref team_pthread.cpp$$. $lnext All of the make files were modified so that the command $codep make test $$ would run the tests for the current directory. $lnext Extend the multi-threading speed tests $code sum_i_inv.cpp$$ and $cref multi_newton.cpp$$ so they run using Boost threads and pthreads (as well as OpenMP threads). $lend $head 10-14$$ Fix some compiler warnings about shadowed variables that were detected by $code g++$$ version $code 4.6.1 20110908$$. $head 10-12$$ $list number$$ The MAC version of the $code pthread$$ library does not include the $code pthread_barrier_wait$$ function; i.e., is not compliant with the IEEE Std 1003.1, 2004 Edition for $code pthread$$. This caused the $code pthread_simple_ad.cpp$$ to fail to compile on the MAC. This has been fixed by not compiling the $code pthread$$ examples unless $code pthread_barrier_wait$$ is present. $lnext The $cref cppad_ipopt_nlp$$ routine has been changed to $cref optimize$$ the functions $latex r_k (u)$$ such that $codei%retape(%k%)%$$ is false. $lend $head 09-06$$ $list number$$ Add the $href% http://www.boost.org/doc/libs/1_47_0/doc/html/thread.html% boost multi-threading %$$ examples $cref a11c_bthread.cpp$$ and $code bthread_simple_ad.cpp$$. $lnext Improve documentation for $cref/thread_num/ta_parallel_setup/thread_num/$$ argument to $code parallel_setup$$. $lnext More simplification of $code bthread_simple_ad.cpp$$ example. $lend $head 09-05$$ Simply and fix some problems with $code pthread_simple_ad.cpp$$, including avoiding a $cref/Bug in Cygwin/team_pthread.cpp/Bug in Cygwin/$$. $head 09-02$$ $list number$$ The OpenMP speed test program $code openmp/run.cpp$$ was not setting the number of threads for the one thread case (so dynamic thread adjustment was used). This has been fixed. $lnext The $cref thread_alloc.cpp$$ example was missing from the Microsoft $code example/example.vcproj$$ file and a attempt was made to link to missing OpenMP routines (this has been fixed). In addition, some Microsoft compiler warning have been fixed; see the examples and tests in the Windows install instructions. $lnext There was an oversight, and $code CPPAD_MAX_NUM_THREAD$$ was being set to 2 when $code _OPENMP$$ was not defined. This has been fixed and $cref/CPPAD_MAX_NUM_THREADS/multi_thread/CPPAD_MAX_NUM_THREADS/$$ has been documented and is now part of the CppAD API. $lnext The $code pthread_simple_ad.cpp$$ test failed under cygwin. This was because the previous test $code openmp_ad.cpp$$ was set up calls to OpenMP routines that were still in effect when $code pthread/simple_ad$$ ran. This has been fixed by making $icode%num_threads% == 1%$$ a special case in $cref/parallel_setup/ta_parallel_setup/$$. $lend $head 09-01$$ $list number$$ Modify the CppAD trunk using the changes from svn revision 2060 to revision 2081 in the branch $codep https://projects.coin-or.org/svn/CppAD/branches/pthread $$ These changes are described below under the headings $cref/08-21/whats_new_11/09-01/08-21/$$ through $cref/08-31/whats_new_11/09-01/08-31/$$. $lnext There was a bug in the $cref old_atomic$$ functions in the case where none of the elements of the argument to the function was a $cref/variable/glossary/Variable/$$. This has been fixed. In addition, $cref old_tan.cpp$$ generated an assert for this case and this has also been fixed (in addition to including an example for this case). $lend $subhead 08-31$$ $list number$$ Move the $code sum_i_inv_time.cpp$$ test from $code openmp/run.sh$$ to $code openmp/run.cpp$$. $lnext Change $code --with-openmp$$ to $cref/OPENMP_FLAGS=openmp_flags/auto_tools/openmp_flags/$$ configure command line argument. $lend $subhead 08-30$$ $list number$$ Create the $code openmp/run.cpp$$ program and move the $code openmp_multi_newton.cpp$$ test from $code openmp/run.sh$$ to $code openmp/run.cpp$$. This uses $cref/configure/auto_tools/Configure/$$ information for building the tests. $lnext Document the $code --with-openmp$$ configure command line argument. $lnext Move $code openmp/multi_newton.hpp$$ to $code openmp/newton_method.hpp$$ and $code openmp/multi_newton.cpp$$ to $code openmp/newton_example.cpp$$. $lend $subhead 08-25$$ $list number$$ Replace $cref omp_alloc$$ by $cref thread_alloc$$ in $cref multi_thread$$, the section on how to use CppAD in parallel. $lnext Implement $cref omp_alloc$$ as links to corresponding $cref thread_alloc$$ sections. $lnext Create the $code pthread_simple_ad.cpp$$ example that does AD using the pthread library. In addition, fix some problems in $code openmp_simple_ad.cpp$$ $lnext Move $code openmp/example_a11c.cpp$$ to $cref|example/a11c_openmp.cpp|a11c_openmp.cpp|$$. $lnext Move $code openmp/parallel_ad.cpp$$ to $code openmp_simple_ad.cpp$$. $lend $subhead 08-23$$ Beginning steps in replacing $cref omp_alloc$$ by $cref thread_alloc$$: $list number$$ Replace $cref omp_alloc$$ by $cref thread_alloc$$ in the $cref/utilities/utility/$$. $lnext move $cref omp_alloc$$ to the deprecated section of the documentation. $lnext Change all $cref omp_alloc$$ section names to begin with $code omp_$$, and change all $cref thread_alloc$$ section names to begin with $code new_$$. $lnext Convert $cref CppAD_vector$$ from using $cref omp_alloc$$ to using $cref thread_alloc$$ for memory allocation. $lnext Extend the $cref memory_leak$$ routine to also check the $cref thread_alloc$$ allocator. $lend $subhead 08-21$$ Create the OpenMP and pthread examples $cref a11c_openmp.cpp$$, $cref a11c_pthread.cpp$$, and $code openmp_simple_ad.cpp$$. These OpenMP examples were originally in the $code openmp$$ directory, and have been moved, and modified to conform, to the normal example directory. $head 08-11$$ Modify the CppAD trunk using the changes from svn revision 2044 to revision 2056 in the branch $codep https://projects.coin-or.org/svn/CppAD/branches/base_require $$ These changes are described below under the headings $cref/08-04/whats_new_11/08-11/08-04/$$ through $cref/08-10/whats_new_11/08-11/08-10/$$. $subhead 08-10$$ $list number$$ Add the output stream optional argument $icode s$$ in $codei% %f%.Forward(0, %x%, %s%) %$$ See $cref/zero order forward mode/forward_zero/$$ and $cref PrintFor$$. $lnext Improve $cref omp_alloc.cpp$$ example. $lend $subhead 08-09$$ $list number$$ $cref base_require$$: Add $cref/epsilon/numeric_limits/epsilon/$$ to the $icode Base$$ type requirements. $lnext Extend $code epsilon$$ to AD types. $lend $subhead 08-08$$ $list number$$ Improve the $cref base_require$$ documentation for $cref/standard math functions/base_std_math/$$. $lnext $cref base_require$$: Add $code abs_geq$$ to the $cref/requirements/base_require/$$ for a user defined $icode Base$$ type. $lnext Check that zero order forward mode results are approximately equal, instead of exactly equal, after an $cref optimize$$ operation. This fixes a bug in the optimize correctness check (The order of operations can be changed by $code optimize$$ and hence the zero order forward mode results may not be exactly the same.) $lend $subhead 08-07$$ Improve the $cref base_require$$ documentation for $cref/EqualOpSeq/base_identical/EqualOpSeq/$$, $cref/Identical/base_identical/Identical/$$ $cref/Integer/base_require/Integer/$$, and $cref/Ordered/base_ordered/$$ operations. $subhead 08-06$$ Add the $cref/CondExpRel/base_cond_exp/CondExpRel/$$ paragraph to the base requirements documentation. This was missing and are required for $cref CondExp$$ to work with $codei%AD<%Base%>%$$ arguments and a non-standard $icode Base$$ type. $subhead 08-04$$ $list number$$ $cref base_require$$: Change the $cref/include/base_require/Include Order/$$ file name to $cref/base_require.hpp/base_require/$$. $lnext Use $cref base_float.hpp$$ and $cref base_double.hpp$$ as additional examples for the $cref/CondExp Base requirements/base_cond_exp/$$ requirements. $lend $head 08-03$$ Change $cref PrintFor$$ condition from less than or equal zero to not greater than zero;i.e., not positive. This makes $code nan$$ print because it results in false for all comparisons. $head 08-02$$ $list number$$ Change $cref PrintFor$$ so it no longer aborts execution when there is no operation sequence being recording; see $cref/start recording/Independent/Start Recording/$$. $lnext Improve the $cref print_for_cout.cpp$$ example. $lend $head 07-31$$ Add a conditional version of the $cref PrintFor$$ command $codei% PrintFor(%text%, %y%, %z%) %$$ which only prints when $icode%z% <= 0%$$. This is useful for error reporting during forward mode; i.e., reporting when the argument to the $code log$$ function is not valid. $head 07-29$$ $list number$$ The routines $cref/set_max_num_threads/omp_max_num_threads/$$ and $code get_max_num_threads$$ were created. User's will need to replace calls to $cref/max_num_threads/old_max_num_threads/$$ by calls to $code set_max_num_threads$$. $lnext The functions $cref omp_efficient$$ was deprecated because it has not been shown to be useful. $lend $head 07-28$$ $list number$$ Change $cref omp_return_memory$$ so that if $cref omp_max_num_threads$$ is one (the default), $cref omp_alloc$$ does not hold onto memory (keep it available for the corresponding thread). $lnext Add files that were missing from the Microsoft Visual Studio $code example$$ and $code test_more$$ subdirectory project files. $lnext Fix some warnings generated by Microsoft Visual Studio 2010 build. $lend $head 07-27$$ Make $code tan$$ and $code tanh$$ $cref/atomic/glossary/Operation/Atomic/$$ operations; see $cref tan_forward$$ and $cref tan_reverse$$. $head 07-25$$ Finish the $cref old_atomic$$ example $cref old_tan.cpp$$. This is also a design and implementation of the routines necessary to make $code tan$$ and $code tanh$$ CppAD atomic operations. $head 07-18$$ The reverse mode formulas for $latex Z(t)$$ need to involve the lower order Taylor coefficients for $latex Y(t)$$. This has been fixed in $cref tan_reverse$$. $head 07-17$$ $list number$$ Fix bug in $cref old_atomic$$ functions. To be specific, the Taylor coefficients for $latex y$$, of order less than $icode k$$, were not passed into the $code old_atomic$$ $cref/forward/old_atomic/forward/$$ callback function. $lnext Derive the theory for including the tangent and hyperbolic tangent as CppAD atomic operations $cref tan_forward$$ and $cref tan_reverse$$; see the wish list item $code Tan and Tanh$$. $lnext Implement and test forward mode calculation of derivative for the tangent and hyperbolic tangent functions; see the new $cref old_atomic$$ example $cref old_tan.cpp$$. $lend $head 07-14$$ $list number$$ The $cref auto_tools$$ instructions for running the individual correctness and speed tests were out of date. This has been fixed; see $cref/example and tests/auto_tools/make/Examples and Tests/$$. $lnext Move $code parallel_ad.cpp$$ from $code example$$ directory to $code openmp$$ directory (and convert it from a function to a program). $lnext Simplify $code example_a11c.cpp$$ by making it just a correctness test. $lnext Change $code openmp/run.sh$$ so that it runs correctness tests with the compiler debugging flags. $lend $head 07-13$$ $list number$$ static hash code data that was begin used by multiple threads when recording $codei%AD<%Base%>%$$ operations $cref omp_in_parallel$$ execution mode. This has been fixed. $lnext Make the $cref/sparsity/Sparse/$$ calculations safe for use during $cref omp_in_parallel$$ execution mode. $lnext Add the $code parallel_ad.cpp$$ example. $lnext Change $code example_a11c.cpp$$ example so that is just a correctness (not speed) test. $lend $head 07-11$$ $list number$$ Change the upper limit for $cref omp_max_num_threads$$ from 32 to 48. $lnext Add $cref/parallel/ta_in_parallel/$$ documentation for, $code nan$$, $cref/Rosen34/Rosen34/Parallel Mode/$$, and $cref/Runge45/Runge45/Parallel Mode/$$. $lnext Fix $cref CheckNumericType$$ and $cref CheckSimpleVector$$ so they work properly when used in parallel mode. $lend $subhead openmp/run.sh$$ The following changes were made to $code openmp/run.sh$$: $list number$$ $lnext Change to $code openmp/run.sh$$ maximum number of threads instead of specifying the entire set of values to be tested. $lnext Change settings for $code newton_example$$ so that $code n_gird$$ is a multiple of the maximum number of threads. $lnext Report dynamic number of thread results as a separate result in the summary output line. $lnext Fix automatic removal of executables from $code openmp$$ directory (was commented out). $lnext The documentation for $code openmp/run.sh$$ was moved to the $code multi_thread$$ section. $lend $head 07-10$$ $list number$$ Add link to $tref Discrete$$ in $cref multi_thread$$. $lnext Make use of the $cref TrackNewDel$$ routines $cref omp_in_parallel$$ execution mode an error (it never worked properly); see $cref/TrackNewDel multi-threading/TrackNewDel/Multi-Threading/$$. $lnext Change $cref memory_leak$$ so that it checks for a leak in all threads. This is what $code openmp_newton_example.cpp$$ and $code sum_i_inv_time.cpp$$ assumed was being done. $lend $head 07-09$$ All the OpenMP parallel execution requirements have been grouped in the section $cref multi_thread$$. $head 07-07$$ Add the routine $cref parallel_ad$$ to fix bug when using $codei%AD<%Base%>%$$ in $cref/parallel/omp_in_parallel/$$ execution mode. $head 06-23$$ $list number$$ Fix a bug whereby the assert $codei% Error detected by false result for ! omp_in_parallel() at line %n% in the file %prefix%/include/cppad/omp_alloc.hpp %$$ sometimes occurred. $lnext The routine $cref omp_max_thread$$ was deprecated, use the routine $cref omp_max_num_threads$$ instead. $lnext The deprecated routines have been grouped together in the $cref deprecated$$ section of the CppAD manual. $lend $head 06-21$$ $list number$$ The $code openmp/run.sh$$ routine was changed to use zero, instead of $code automatic$$, for automatic choice of $code openmp/run.sh$$ number of repeats and maximum number of threads. $lnext The output of each of the OpenMP examples / speed tests (run by $code openmp/run.sh$$) was changed to be valid matlab / octave assignment statements. $lnext In the case where OpenMP is enabled during compilation, a summary for the different number of threads as added at the end of the $code openmp/run.sh$$ output. $lend $head 06-18$$ $list number$$ The $cref/tape_addr_type/auto_tools/tape_addr_type/$$ option was added to the $cref/configure/auto_tools/Configure/$$ command line. $lnext The function $cref/size_op_seq/seq_property/size_op_seq/$$ results uses $code sizeof(CppAD_TAPE_ADDR_TYPE)$$ where it used to use $code sizeof(size_t)$$. $lnext Remove $code cppad/config.h$$ from CppAD distribution, (put the information in $code cppad/configure.hpp$$.) This removes the need to undefine symbols that were defined by $code cppad/config.h$$ and that did not begin with $code CPPAD_$$. $lnext Change $cref/adolc/auto_tools/adolc_dir/$$ library linkage so it works with version $code ADOL-C-2.2.0$$. $lend $head 05-29$$ Fix bug (introduced on $cref/05-22/whats_new_11/05-22/$$) whereby constructor might not be called (but required) when the $cref/base type/base_require/$$ is not plain old data. $head 05-28$$ $list number$$ Add the $cref omp_efficient$$ routine to the $cref omp_alloc$$ system. $lnext Improve the $code omp_alloc$$ tracing so it prints the same pointer as returned to the user (not an offset version of that pointer). $lend $head 05-26$$ Fix Visual Studio project files that were broken during the change on 05-22. In addition, in the file $code cppad/omp_alloc.hpp$$, suppress the following Microsoft Visual Studio warning $codep warning C4345: behavior change: an object of POD type constructed with an initializer of the form () will be default-initialized $$ $head 05-22$$ $list number$$ The old memory tracking routines $cref TrackNewDel$$ have been deprecated. Their use should be replaced using the $cref omp_alloc$$ a memory allocator which is designed to work well in a multi-threading OpenMP environment; see $cref/purpose/omp_alloc/Purpose/$$. $lnext The replacement of $code TrackNewDel$$ by $code omp_alloc$$ has been throughout the CppAD source code, including the examples that used $code TrackNewDel$$; namely, $cref mul_level_adolc.cpp$$, $cref mul_level_adolc_ode.cpp$$. $lnext The CppAD vector template class and the $cref/vectorBool/CppAD_vector/vectorBool/$$ class were modified to use the $code omp_alloc$$ $cref/memory/CppAD_vector/Memory and Parallel Mode/$$ manager. This should improves its speed of memory allocation $cref omp_in_parallel$$ sections of a program. $lnext The $cref speed_test$$ argument $cref/size_vec/speed_test/size_vec/$$ call was by value, instead of by reference (as documented). This has been fixed and the call is now by reference. $lnext The $cref/capacity/CppAD_vector/capacity/$$ function has been added to the CppAD vector class. $lnext The simple vector $cref/ element constructor and destructor/ SimpleVector/ Element Constructor and Destructor /$$ description has been changed to explicitly specify that the default constructor is used to initialize elements of the array. $lnext The $cref/size_op_seq/seq_property/size_op_seq/$$ documentation has been improved to mention that the allocated memory may be larger. $lend $head 05-11$$ $list number$$ Avoid ambiguity in the definition of the $cref/complex isnan/base_complex.hpp/isnan/$$ function. $lnext Errors during $code make test$$ were not being detected. This has been fixed. $lend $head 05-03$$ $list number$$ If $code NDEBUG$$ is not defined, the $cref/hasnan/nan/$$ function is used to make sure that the results of any $cref Forward$$ operation does not contain a nan (not a number). If so, an error message is generated and the program terminates. This error message and termination can be caught; see $cref ErrorHandler$$. $lnext In the event that the $cref cppad_ipopt_nlp$$ objective function, the constraints, or their derivatives are infinite, an error message is generated and the program terminates (proved that $code NDEBUG$$ is not defined and the default error handler has not been replaced). $lend $head 04-29$$ $list number$$ The Microsoft Visual Studio 2003 project files for the Windows examples and tests no longer worked because the current version of CppAD uses local types in template instantiation; see $href% http://msdn.microsoft.com/en-us/library/bh44f2cb(v=vs.71).aspx% Compiler Error C2918 %$$. These project files were converted to Visual Studio 2008 where they do work (if you use a later version, Visual Studio should automatically convert them for you). $lnext The old speed test directory was moved to $code speed_cppad$$ before the new $cref speed$$ test organization was created on 2006-12-11 (revision 715 of the repository). The old speed tests have not been used for years and so have been deleted. $lend $head 04-20$$ The $code openmp/run.sh$$ script what changed to take an argument that specifies which tests is run (it no longer runs all the tests). Also improve the openmp test program output formatting. $head 04-19$$ The $icode use_ad$$ option was added to the $code openmp_newton_example.cpp$$ test case. $head 03-19$$ The subversion write protected directory $code bin/.svn$$ was mistakenly part of the $cref/compressed tar file/download/Compressed Archives/$$. It has been removed. $head 03-11$$ The vector of sets argument $cref/r/old_atomic/rev_hes_sparse/r/$$ to the $code old_atomic$$ function $icode rev_hes_sparse$$ must have size greater than or equal to $icode n$$. There was a check that its size was greater than or equal $icode q$$. This was incorrect and has been fixed. $head 03-05$$ Add the $cref/conjugate gradient/conj_grad.cpp/$$ example. $head 02-22$$ Add the $cref/atomic/speed_main/Global Options/atomic/$$ option to the speed test program and use $cref old_mat_mul.hpp$$ during the $cref cppad_mat_mul.cpp$$ speed test when the atomic option is specified. $head 02-19$$ There was a bug when $cref omp_max_thread$$ was set to one, and $code NDEBUG$$ was not defined, the thread corresponding to parameters was one, but the only valid thread number was zero (only one thread) and an CPPAD stopped with an assertion error. This has been fixed. $head 02-17$$ There was a mistake in $code openmp/run.sh$$ where it attempted to remove a non-existent file in the case where $code openmp/run.sh$$ openmp_flag was not $code ""$$. This has been fixed. $head 02-15$$ A matrix multiply speed test has been added. So far, this has only implemented for the $cref/cppad/cppad_mat_mul.cpp/$$ and $cref/double/double_mat_mul.cpp/$$ cases. (For the time being this test is not available for the other speed comparison cases.) $head 02-09$$ A variable in $code old_atomic.hpp$$ was declare of type $icode Base$$ when it should have been declared of type $code size_t$$. It caused the $cref old_atomic$$ feature to fail with some base types. This has been fixed. $pre $$ The $cref old_mat_mul.hpp$$ example has been improved by caching the $latex x$$ variable information and using it during $cref/reverse Hessian sparsity/old_atomic/rev_hes_sparse/$$ calculations. $pre $$ Some of the $cref old_atomic$$ documentation was extended to include more explanation. $head 02-06$$ The use can now define complex $cref/atomic/old_atomic/$$ operations and store them in a CppAD $cref ADFun$$ object. This item has been remove from the $cref/wish list/wish_list/$$. $pre $$ The documentation for $cref RevSparseHes$$ had a dimension error. This has been fixed. $pre $$ A faster set operations item was added to the wish list. This has since been satisfied by $code cppad_sparse_list$$ choice during the install process (since removed). $head 02-02$$ The documentation for $cref ForSparseJac$$ had some formatting errors. The errors have been fix and the documentation has been improved. $head 02-01$$ The subversion install instructions were brought up to date. They have since been replaced by just separate $code subversion$$ instructions. $head 01-19$$ The directory where the $cref pkgconfig$$ file $code cppad.pc$$ is stored has been moved from $icode%prefixdir%/lib/pkgconfig/cppad.pc%$$ to $icode%prefixdir%/share/pkgconfig/cppad.pc%$$; see $href%http://lists.fedoraproject.org/pipermail/devel/2011-January/147915.html% devel@lists.fedoraproject.org%$$. $head 01-16$$ The following have been fixed: $list number$$ The install of the documentation failed when it was done from a directory other than the top source directory. $lnext The GPL distribution had the output of the $cref/configure/auto_tools/Configure/$$ command in it. $lnext Since the change on 01-09, the file $code omh/whats_new_11.omh$$ has been required to build the documentation (and it has been missing from the distribution). $lnext Fadbad was generating warnings due to the $code -Wshadow$$ flag with the $code g++$$ compiler. The Fadbad $cref/speed/speed_fadbad/$$ tests have a special flag with this warning removed from the $cref/cxx_flags/auto_tools/cxx_flags/$$. $lend $head 01-09$$ There were some problems running $code make test$$ in the releases $codei% http://www.coin-or.org/download/source/CppAD/cppad-20110101.0.%license%.tgz %$$ where $icode license$$ is $code gpl$$ or $code cpl$$. $list number$$ The version of automake used to build the corresponding $code makefile.in$$ files did not define $code abs_top_builddir$$. $lnext The include file $code cppad_ipopt_nlp.hpp$$ was always installed, even if $cref/ipopt_dir/auto_tools/ipopt_dir/$$ was not defined on the $code configure$$ command line. $lnext The speed test library $code libspeed.a$$ was being installed (it is only intended for testing). $lend These problems are fixed in the trunk and these fixes will be copied to the corresponding stable and release versions; i.e., $codei% http://www.coin-or.org/download/source/CppAD/cppad-20110101.1.%license%.tgz %$$ will not have this problem. $end cppad-20170000.3/omh/whats_new/whats_new_03.omh0000644000175200017650000005150313057470463020227 0ustar coincoin-web$Id: whats_new_03.omh 3686 2015-05-11 16:14:25Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_03$$ $spell dir Eq.cpp cppad.hpp Hess Taylor Def indvar bool CppADvector ADdouble sqrt atan exp valarray Faq Lu Det Cpp Microsoft mak std Cygwin Var const namespace Geq Leq ini $$ $section Changes and Additions to CppAD During 2003$$ $head Introduction$$ This section contains a list of the changes plus for (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions. $head 12-24$$ Some references to $code double$$ should have been references to the $cref/base type/glossary/Base Type/$$ (in reverse mode and in the $code Grad/$$ and $code Hess$$ functions). This has been fixed. $head 12-22$$ The preprocessor symbol $code WIN32$$ was being used to determine if one was using Microsoft's C++ compiler. This symbol is predefined by the $href%http://www.mingw.org%MinGW%$$ version of the GNU C++ compiler and hence CppAD had errors during installation using MinGW. This has been fixed by using the preprocessor symbol $code _MSC_VER$$ to determine if one is using the Microsoft C++ compiler. $head 12-14$$ The extended system solvers $code OdeOne$$ and $code OdeTwo$$ have been removed from the distribution. In addition, the interface to the ODE solvers have been simplified. $head 12-13$$ Remove the $code CppADCreateTape$$ macro and have the tapes created and grow automatically. $head 12-12$$ The old method where one directly accesses the tape has been removed and the following functions are no longer available: $codei% size_t %TapeName%.Independent(AD<%Base%> &%indvar%) size_t %TapeName%.Record(size_t %order%) size_t %TapeName%.Stop(void) bool Dependent(const AD<%Base%> &%var%) const bool %TapeName%.Dependent(const AD<%Base%> &%var%) const size_t %TapeName%.Total(void) const size_t %TapeName%.Required(void) const size_t %TapeName%.Erase(void) TapeState %TapeName%.State(void) const size_t %TapeName%.Order(void) const size_t %TapeName%.Required(void) const bool Parameter(CppADvector< AD<%Base%> > &%u%) %TapeName%.Forward(%indvar%) %TapeName%.Reverse(%var%) %TapeName%.Partial(%var%) %TapeName%.ForwardTwo(%indvar%) %TapeName%.ReverseTwo(%var%) %TapeName%.PartialTwo(%var%) %$$ $head 12-10$$ The change on $cref/12-01/whats_new_03/12-01/$$ make the taping process simpler if one does not directly access $code CppADCreateTape$$. The $cref/examples/example/$$ were changed to not use $icode TapeName$$. The following examples were skipped because they document the functions that access $icode TapeName$$: $code DefFun.cpp$$, $code For.cpp$$, $code for_two.cpp$$, $code Rev.cpp$$, and $code rev_two.cpp$$. $head 12-05$$ There was a bug in $icode%f%.Rev%$$ and $icode%f%.RevTwo%$$ and when two dependent variables were always equal and shared the same location in the tape. This has been fixed. $pre $$ The ODE Example was changed to tape the solution (and not use $code OdeOne$$ or $code OdeTwo$$). This is simpler to use and the resulting speed tests gave much faster results. $head 12-01$$ The following function has been added: $codei% void Independent(const CppADvector<%Base%> &%x%) %$$ which will declare the independent variables and begin recording $codei%AD<%Base%>%$$ operations (see $cref Independent$$). The $cref ADFun$$ constructor was modified so that it stops the recording and erases that tape as well as creates the $cref ADFun$$ object. In addition, the tape no longer needs to be specified in the constructor. $head 11-21$$ Add $code StiffZero$$ to set of ODE solvers. $head 11-20$$ The $code AbsGeq$$ and $code LeqZero$$ in $cref LuSolve$$ were changed to template functions so they could have default definitions in the case where the $code <=$$ and $code >=$$ operators are defined. This made the $code double$$ and $code AD$$ use of $code LuSolve$$ simpler because the user need not worry about these functions. On the other hand, it made the $code std::complex$$ and $code AD$$ use of $code LuSolve$$ more complex. $pre $$ The member function names for the $icode fun$$ argument to ODE were changed from $icode%fun%.f%$$ to $icode%fun%.Ode%$$ and from $icode%fun%.g%$$ to $icode%fun%.Ode_ini%$$. $head 11-16$$ The $cref/table of contents/_contents/$$ was reorganized to provide a better grouping of the documentation. $pre $$ The $cref LuSolve$$ utility is now part of the distribution and not just an example; i.e., it is automatically included by $code cppad.hpp$$. $head 11-15$$ The ODE solver was modified so that it can be used with any type (not just an AD type. This was useful for the speed testing. It is also useful for determining how the integrator steps should be before starting the tape. $pre $$ The template argument $icode Type$$ was changed to $icode Base$$ where ever it was the $cref/base type/glossary/Base Type/$$ of an AD class. $head 11-14$$ An $code speed_cppad/OdeSpeed.cpp/$$ test was added and some changes were made to the ODE interface in order to make it faster. The most significant change was in the specifications for the ODE function object $icode fun$$. $head 11-12$$ The user defined unary function example $code example/UnaryFun.cpp$$ was incorrect. It has been corrected and extended. $head 11-11$$ The $cref/CppAD::vector/CppAD_vector/$$ template class is now used where the $code std::vector$$ template class was previously used. You can replace the $code CppAD::vector$$ class with a vector template class of your choosing during the $cref Install$$ procedure. $head 11-06$$ The documentation for $cref/taping derivative calculations/mul_level/$$ was improved as well as the corresponding example. In order to make this simpler, the example tape name $code DoubleTape$$ was changed to $code ADdoubleTape$$ (and the other example tape names were also changed). $head 11-04$$ The ODE utility was changed from an example to part of the distribution. In addition, it was extended so that it now supports taping the solution of the differential equations (case $icode order$$ equal zero) or solving the extended set of differential equations for both first and second derivatives (cases $icode order$$ equal one and two). In addition, an initial condition that depends on the parameter values is also allowed. $head 11-02$$ It is now legal to differentiate a $cref/parameter/glossary/Parameter/$$ with respect to an $cref/independent variable/glossary/Tape/Independent Variable/$$ (parameter derivatives are always equal to zero). This is an extension of the $code Reverse$$, $code Partial$$, $code ReverseTwo$$, and $code PartialTwo$$ functions. $head 10-21$$ All the $code CppAD$$ include files, except $code cppad.hpp$$ were moved into an $code include$$ subdirectory. $head 10-16$$ The $cref ADFun$$ template class was added so that one can save a tape recording and use it as a differentiable function. The $code ADFun$$ functions supports directional derivatives in both $cref Forward$$ and $cref Reverse$$ mode where as the tape only supports partial derivatives. $head 10-14$$ The $code sqrt$$ function was added to the $cref unary_standard_math$$ functions. In addition, a definition of the power function for the types $code float$$ and $code double$$ was automatically included in the $code CppAD$$ namespace. $pre $$ The $cref Value$$ function was changed so that it can be called when the tape is in the Empty state. $head 10-10$$ The $code atan$$ function was added to the $cref unary_standard_math$$ functions. $head 10-06$$ In the notation below, $icode zero$$ and $icode one$$ are parameters that are exactly equal to zero and one. If the variables $icode z$$ and $icode x$$ were related in any of the following ways, they share can share the same record on the tape because they will have the same derivatives. $codei% %z% = %x% + %zero% %z% = %x% * %one% %z% = %zero% + %x% %z% = %one% * %x% %z% = %x% - %zero% %z% = %x% / %one% %$$ Furthermore, in the following cases, the result $icode z$$ is a parameter (equal to zero) and need not be recorded in the tape: $codei% %z% = %x% * %zero% %z% = %zero% / %x% %z% = %zero% * %x% %$$ The $cref/arithmetic operators/Arithmetic/$$ were all checked to make sure they did not add to the tape in these special cases. The total record count for the program in the Example directory was 552 before this change and 458 after. $head 10-05$$ The process of converting the tape to operators was completed. In order to make this conversion, the binary user defined functions were removed. (Bob Goddard suggested a very nice way to keep the unary functions.) Another significant change was made to the user interface during this procedure, the standard math library functions are now part of the CppAD distribution and not defined by the user. $pre $$ The function $icode%TapeName%.Total%$$ was added to make it easy to track how many tape records are used by the test suite. This will help with future optimization of the CppAD recording process. $pre $$ There was a bug (found by $href%mailto:magister@u.washington.edu%Mike Dodds%$$) in the error checking of the $icode/TapeName/.Erase/$$ function. If $code Erase$$ was called twice in a row, and $code NDEBUG$$ was false during compilation, the program would abort. This has been fixed. $head 09-30$$ A process of changing the tape from storing partial derivatives to storing operators has been started. This will make the tape smaller and it will enable the computation of higher derivatives with out having to tape the tape (see $cref mul_level$$). The Add, Subtract, Multiply and Divide operators have been converted. The user defined functions are presenting some difficulties, so this process has not yet been completed. $pre $$ There was a bug in reverse mode when an dependent variable was exactly equal to an independent variable. In this case, it was possible for it to be located before other of the independent variables on the tape. These other independent variable partials were not initialized to zero before the reverse calculation and hence had what ever value was left by the previous mode calculation. This has been fixed and the $code Eq.cpp$$ example has been changed to test for this case. $pre $$ The following tape functions were changed to be declared $code const$$ because they do not modify the tape in any way: $code State$$, $code Order$$, $code Required$$, $code Dependent$$, and $cref/Parameter/ParVar/$$. $head 09-20$$ The functions $code Grad$$ and $code Hess$$ were changed to use function objects instead of function pointers. $head 09-19$$ The higher order constructors (in standard valarray) were removed from the ODE example in order to avoid memory allocation of temporaries (and hence increase speed). In addition, the function objects in the ODE examples were changed to be $code const$$. $head 09-18$$ An ordinary differential equation solver was added. In addition, the extended system to differentiate the solution was included. $head 09-15$$ The linked list of AD variables was not being maintained correctly by the AD destructor. This was fixed by have the destructor use $code RemoveFromVarList$$ to remove variables from the list. ($code RemoveFromVarList$$ is a private AD member function not visible to the user.) $head 09-14$$ There is a new Faq question about evaluating derivatives at multiple values for the $cref/independent variables/Faq/Independent Variables/$$. $head 09-13$$ An example that uses $code AD< AD >$$ to compute higher derivatives was added. $pre $$ The name $code GaussEliminate$$ was changed to $cref LuSolve$$ to better reflect the solution method. $head 09-06$$ Changed the $cref get_started.cpp$$ and $cref complex_poly.cpp$$ examples so they use a template function with both base type and AD type arguments. (The resulting code is simpler and a good use of templates.) $head 09-05$$ A $cref/getting started/get_started.cpp/$$ example was added and the organization of the $cref/Examples/example/$$ was changed. $head 09-04$$ The $code AbsOfDoubleNotDefine$$ flag is no longer used and it was removed from the Windows $cref/install/Install/$$ instructions. $pre $$ The 03-09-03 distribution did not have the proper date attached to it. The distribution script has been changed so that attaching the proper date is automated (i.e., this should not happen again). $pre $$ A $tref faq$$ section was started. $head 09-03$$ Added the $cref Value$$ function which returns the $cref/base type/glossary/Base Type/$$ value corresponding to an AD object. $head 08-23$$ A new version of Cygwin was installed on the development system (this may affect the timing tests reported in this document). In addition, $cref LuSolve$$ was changed to use back substitution instead of reduction to an identity matrix. This reduced the number of floating point operations corresponding to evaluation of the determinant. The following results correspond to the speed test of DetLu on a 9 by 9 matrix: $table $bold Version$$ $cnext $bold double Rate$$ $cnext $bold AD Rate$$ $cnext $bold Gradient Rate$$ $cnext $bold Hessian Rate$$ $cnext $bold Tape Length$$ $rnext 03-08-20 $cnext 8,524 $cnext 5,278 $cnext 4,260 $cnext 2,450 $cnext 532 $rnext 03-08-23 $cnext 7,869 $cnext 4,989 $cnext 4,870 $cnext 2,637 $cnext 464 $tend $head 08-22$$ The $cref/unary minus/UnaryMinus/$$ operator was added to the AD operations. $head 08-19$$ The standard math function examples were extended to include the complex case. $pre $$ The $cref LuSolve$$ routine what changed to use $codei%std::vector<%Base%> &%$$ arguments in place of $icode%Base% *%$$ arguments. This removes the need to use $code new$$ and $code delete$$ with $code LuSolve$$. $pre $$ When testing the speed of the change to using standard vector, it was noticed that the LuSolve routine was much slower. (see times for 03-08-16 below). This was do to computing the determinant instead of the log of the determinant. Converting back to the log of the determinant regained the high speeds. The following results correspond to the speed test of DetLu on a 9 by 9 matrix: $table $bold Version$$ $cnext $bold double Rate$$ $cnext $bold AD Rate$$ $cnext $bold Gradient Rate$$ $cnext $bold Hessian Rate$$ $cnext $bold Tape Length$$ $rnext 03-08-16 $cnext 9,509 $cnext 5,565 $cnext 3,587 $cnext 54 $cnext 537 $rnext 03-08-19 $cnext 8,655 $cnext 5,313 $cnext 4,307 $cnext 2,495 $cnext 532 $tend $head 08-17$$ The macro $code CppADTapeOverflow$$ was added so that CppAD can check for tape overflow even in the $code NDEBUG$$ preprocessor flag is defined. $head 08-16$$ The $cref LuSolve$$ routine was extended to handle complex arguments. Because the complex absolute value function is nowhere differentiable, this required the allowing for user defined $cref/boolean valued functions with AD arguments/BoolFun/$$. The examples $cref lu_solve.cpp$$ and $code GradLu.cpp$$ were converted to a complex case. $head 08-11$$ The routine $cref LuSolve$$ was made more efficient so that it is more useful as a tool for differentiating linear algebra calculations. The following results correspond to the speed test of DetLu on a 9 by 9 matrix: $table $bold Version$$ $cnext $bold double Rate$$ $cnext $bold AD Rate$$ $cnext $bold Gradient Rate$$ $cnext $bold Hessian Rate$$ $cnext $bold Tape Length$$ $rnext 03-08-10 $cnext 49,201 $cnext 7,787 $cnext 2,655 $cnext 1,809 $cnext 824 $rnext 03-08-11 $cnext 35,178 $cnext 12,681 $cnext 4,521 $cnext 2,541 $cnext 540 $tend In addition the corresponding test case $cref lu_solve.cpp$$ was changed to a Hilbert matrix case. $head 08-10$$ A $cref/complex polynomial/complex_poly.cpp/$$ example was added. $pre $$ The documentation and type conversion in $cref LuSolve$$ was improved. $pre $$ The absolute value function was removed from the examples because some systems do not yet properly support $codei%double abs(double %x%)%$$, $head 08-07$$ Because the change to the multiplication operator had such a large positive effect, all of the $cref/arithmetic operators/Arithmetic/$$ were modified to reduce the amount of information in the tape (where possible). $head 08-06$$ During Lu factorization, certain elements of the matrix are know to be zero or one and do not depend on the variables. The $cref/multiplication/ad_binary/$$ operator was modified to take advantage of this fact. This reduced the size of the tape and increased the speed for the calculation of the gradient and Hessian for the Lu determinant test of a 5 by 5 matrix as follows: $table $bold Version$$ $cnext $bold Tape Length$$ $cnext $bold Gradient Rate$$ $cnext $bold Hessian Rate$$ $rnext 03-08-05 $cnext 176 $cnext 11,362 $cnext 1,149 $rnext 03-08-06 $cnext 167 $cnext 12,780 $cnext 10,625 $tend $head 08-05$$ Fixed a mistake in the calculation of the sign of the determinant in the $cref LuSolve$$ example. $head 08-04$$ Added a the compiler flag $codep AbsOfDoubleNotDefined $$ to the make files so that it could be removed on systems where the function $codei% double abs(double %x%) %$$ was defined in $code math.h$$. $head 08-03$$ The $code Grad$$ and $code Hess$$ functions were modified to handel the case where the function does not depend on the independent variables. $pre $$ The $cref LuSolve$$ example was added to show how on can differentiate linear algebra calculations. In addition, it was used to add another set of $cref/speed tests/speed_cppad/$$. $pre $$ The standard Math functions were added both as examples of defining atomic operations and to support mathematical operations for the $code AD$$ case. $pre $$ The $cref/<%$$ data structure was changed to include a doubly linked list of variables. This enabled the $cref/AD copy constructor/ad_ctor/$$ constructor and $cref/assignment/ad_assign/$$ operator to create multiple references to the same place in the tape. This reduced the size of the tape and increased the speed for the calculation of the gradient and Hessian for the determinant of a 5 by 5 matrix as follows: $table $bold Version$$ $cnext $bold Tape Length$$ $cnext $bold Gradient Rate$$ $cnext $bold Hessian Rate$$ $rnext 03-07-22 $cnext 1668 $cnext 1,363 $cnext 53 $rnext 03-07-26 $cnext 436 $cnext 3,436 $cnext 213 $tend $head 07-22$$ The facility was added so that the user can define binary functions together with their derivatives. (This facility has been removed because it is better to define binary functions using AD variables.) $pre $$ The Windows version make file directive $code /I ..\..$$ in $code example\Example.mak$$ and $code Speed\Speed.mak$$ was changed to $code /I ..$$ (as it should have been). $head 07-20$$ The facility was added so that the user can define unary functions, together with their derivatives. For example, the standard math functions such as $cref/exp/exp.cpp/$$ are good candidates for such definitions. (This feature has been replaced by and the standard math functions are now part of the AD types, see $cref AD$$.) $pre $$ The first Alpha for the Windows $cref/installation/Install/$$ was released. $head 07-18$$ Computing the determinant of a minor of a matrix $cref det_of_minor$$ was documented as a realistic example using CppAD. $head 07-16$$ Fixed some non-standard constructions that caused problems with the installation on other machines. $pre $$ Compiled and ran the tests under Microsoft Windows. (The Windows release should not take much more work.) $head 07-14$$ First Alpha release of CppAD and is being released under the $cref/Gnu Public License/License/$$. It is intended for use by a Unix system. A Microsoft release is intended in the near future. $end cppad-20170000.3/omh/whats_new/whats_new_12.omh0000644000175200017650000007727613057470463020246 0ustar coincoin-web$Id: whats_new_12.omh 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_12$$ $dollar @$$ $spell checkpointing Jacobians doxygen txt sys stdbool datadir pkgconfig cppad_ipopt_nlp includedir includedirs libdir libdirs Ubuntu Microsoft cmake CondExpOp src std hes dw uninitialised resize bool taddr eigen fabs mul det_lu adolc fadbad sacado CppADvector retape Jacobian dir -lteuchos trilinos inorder pthread helgrind Taylor Debian valgrind num alloc makefile hpp gcc cppad-%yyyymmdd% lpthread xout fabs fcur CppAD openmp $$ $section CppAD Changes and Additions During 2012$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2012 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-30$$ $list number$$ Merge changes in $code branches/ipopt_solve$$ to $code trunk$$, delete that branch, and advance version number to $code cppad-20121230$$. $lnext Remove $code cppad/configure.hpp$$ from repository because it is built by the configuration process (even for MS Visual Studio, now that we are using $cref cmake$$). $lnext Add the $codei%AD<%Base%>%$$ input stream operator $cref/>>/ad_input/$$. $lend $head 12-29$$ In $code branches/ipopt_solve$$: $list number$$ Complete implementation of sparse Jacobian and Hessian calculations and add options that allow to user to choose between forward and reverse sparse Jacobians. $lnext The $cref ipopt_solve$$ routine seems to be faster and simpler than $cref cppad_ipopt_nlp$$. More speed comparisons would be good to have. $lnext All of the $cref/ADFun Drivers/Drivers/$$ have added specifications for the zero order Taylor coefficients after the routine is called. For example, see $cref/Hessian uses forward/Hessian/Hessian Uses Forward/$$. $lend $head 12-28$$ In $code branches/ipopt_solve$$: $list number$$ Add the $cref ipopt_solve_retape.cpp$$ and $cref ipopt_solve_ode_inverse.cpp$$ examples. $lnext Use $code ipopt::solve$$ $cref/options/ipopt_solve/options/$$ argument (and not a file) for all the Ipopt options. As well as allowing for adding $code ipopt::solve$$ special options; e.g., $cref/retape/ipopt_solve/options/Retape/$$. $lend $head 12-27$$ In $code branches/ipopt_solve$$: Change documentation section names that begin with $code cppad_ipopt$$ to begin with $cref/ipopt_nlp/cppad_ipopt_nlp/$$ to distinguish them from $cref/CppAD::ipopt::solve/ipopt_solve/$$. $head 12-26$$ In $code branches/ipopt_solve$$: $list number$$ Convert documentation most all documentation references from the deprecated $cref auto_tools$$ instructions to the new $cref cmake$$ instructions. $lnext Include the $cref Introduction$$ programs in the $cref cmake_check$$ built using $cref cmake$$. $lnext Deprecate $cref cppad_ipopt_nlp$$ and replace it by $cref ipopt_solve$$ which is easier to use. This is a first version of $code ipopt_solve$$ and its speed and memory use needs to be improved. $lend $head 12-23$$ Copy development $code trunk$$ to $code branches/ipopt_solve$$. $head 12-22$$ Define a doxygen module (group) for each file that has doxygen documentation. $head 12-20$$ $list number$$ The $cref/install instructions/install/Instructions/$$ were installing $code cppad/CMakeLists.txt$$ and $code cppad/configure.hpp.in$$ in the $code cppad$$ include directory. This has been fixed so that only $icode%*%.h%$$ and $icode%*%.hpp%$$ files get installed in the $code cppad$$ include directory. $lnext Advance the version number to $code cppad-20121220$$. $lend $head 12-19$$ The files $code $$ and $code $$ do not exist for all C compilers, and this caused a problem when using the Windows compiler. This has been fixed by defining the type bool inside the $code compare_c/det_by_minor.c$$ source code. $head 12-17$$ There was a mistake in a check for a valid op code in the file $code hash_code.hpp$$. This mistake could generate a C++ assertion with an unknown error source. It has been fixed. $head 12-15$$ $list number$$ Advance version number from $code 20121120$$ to $code 20121215$$. Note that the CppAD version number no longer automatically advances with the date and is rather chosen to advance to the current date. $lnext The $cref cmake$$ installation was putting the $code cppad.pc$$ $cref pkgconfig$$ file in $codei% cppad_prefix%/cmake_install_datadir%/cppad.pc %$$ This has been fixed and is now $codei% cppad_prefix%/cmake_install_datadir%/pkgconfig/cppad.pc %$$ $lnext The $cref pkgconfig$$ documentation has been improved. $lnext The command for running the $cref/adolc examples/adolc_prefix/Examples/$$ and $cref/eigen examples/eigen_prefix/Examples/$$ was fixed (changed from $code make check$$ to $code make check_example$$). $lend $head 12-14$$ $list number$$ Fix the old $cref auto_tools$$ so that it works with the new $code cppad.pc$$. $lnext Fix the old installation $cref/--with-Documentation/auto_tools/--with-Documentation/$$ option (it was attempting to copy from the wrong directory). $lend $head 12-13$$ $list number$$ Include documentation for $cref ipopt_prefix$$ $lnext Fix the $code cppad.pc$$ $cref pkgconfig$$ file so that it includes the necessary libraries and include commands when $cref ipopt_prefix$$ is specified; see $cref/pkgconfig usage/pkgconfig/Usage/$$. $lend $head 11-28$$ Update the $cref wish_list$$: $list number$$ Remove Microsoft compiler warning item that has been fixed. $lnext Remove faster sparse set operations item that was completed using $code cppad_sparse_list$$ (not part of user API). $lnext Remove $cref cmake$$ items that have been completed. $lnext Remove $cref CondExp$$ items related to using $code AD< std::complex >$$ types because it is better to use $code std::complex< AD >$$. $lnext Remove $cref thread_alloc$$ memory chunk item that has been completed. $lnext Remove $cref VecAD$$ item about slicing from floating point type to $code int$$ (not important). $lnext Change an Ipopt item to a $cref cppad_ipopt_nlp$$ (which was removed because $code cppad_ipopt_nlp$$ is now deprecated). Add new $code cppad_ipopt_sum$$ item to the wish list. (This has been removed because $cref/checkpointing/checkpoint/$$ can now be used for this purpose.) $lnext Add new $code old_atomic$$ $cref wish_list$$ item (since removed). $lend $head 11-21$$ $list number$$ Fix the version number in link to the $cref/current download files/download/Current Version/$$. $lnext Change the $code subversion$$ download instructions to use the $code export$$ instead of $code checkout$$ command. This avoids downloading the source code control files. $lend $head 11-20$$ $list number$$ The $code cmake$$ variables $code cmake_install_includedir$$ and $code cmake_install_libdir$$ were changed to $cref/cmake_install_includedirs/cmake/cmake_install_includedirs/$$ and $cref/cmake_install_libdirs/cmake/cmake_install_libdirs/$$ to signify the fact that they can now be a list of directories. $lnext Advance version number to $code cppad-20121120$$. $lend $head 11-17$$ $list number$$ Finish documenting the new $cref cmake$$ configuration instructions and deprecate the old $cref/unix/auto_tools/$$ instructions. $lnext Change the specifications for $cref/CPPAD_MAX_NUM_THREADS/multi_thread/CPPAD_MAX_NUM_THREADS/$$ to allow for a value of one. This enables one to have more tapes during a program execution. $lnext Include the $cref/C versus C++/compare_c/$$ speed comparison in the $cref cmake$$ build. $lend $head 11-16$$ Fix a warning that occurred in $cref Rosen34$$ when it was compiled with the preprocessor symbol $code NDEBUG$$ defined. $head 11-14$$ Advanced the CppAD version to $code cppad-20121114$$. $list number$$ Started documenting the $cref cmake$$ configuration procedure during installation. This included factoring out the $cref download$$ procedure as a separate section so that the same download instruction also apply to the $cref/unix/auto_tools/$$ install procedure. $lnext Changed $cref%example/compare_change.cpp%compare_change.cpp%$$ to just return true when $code NDEBUG$$ is defined. This enabled all the tests in the $code example$$ directory to be compiled with $code NDEBUG$$ is defined and to pass. $lnext In the case where $code NDEBUG$$ is defined, removed detection of $code nan$$ during forward mode from $code test_more/forward.cpp%$$. This enables all the tests in the $code test_more$$ directory to be compiled with $code NDEBUG$$ is defined and to pass. $lnext Started a wish list for CppAD's use of $cref cmake$$. The wish list items were completed and removed. $lend $head 11-09$$ The $cref team_pthread.cpp$$ was failing to link on Ubuntu 12.04 because the libraries were not at the end of the link line. This has been fixed. $head 11-06$$ $list number$$ Remove some remaining references to the old licenses CPL-1.0 and GPL-2.0; see $cref/10-24/whats_new_12/10-24/$$. $lnext Remove out of date Microsoft project files from the distribution. The build system is being converted to use $href%http://www.cmake.org%cmake%$$ which builds these files automatically and thereby keeps them up to date. This feature is not yet documented, but one can inspect the file $code bin/run_cmake.sh$$ to see how to use $code cmake$$ with CppAD. $lend $head 11-04$$ Add missing return value to the example $code base_alloc$$ $cref/CondExpOp/base_alloc.hpp/CondExpOp/$$ function. This has been fixed and the comments for this example have been improved. $head 10-31$$ The CppAD $cref/profiling/auto_tools/Profiling CppAD/$$ was not compiling the $code speed/src/*.cpp$$ files with the profiling flag. This has been changes (only for the profiling speed test). $head 10-30$$ The $cref/fadbad_dir/auto_tools/fadbad_dir/$$ directory install instructions were changed. To be specific, $code FADBAD++$$ was changed to $code include/FADBAD++$$. This makes it more like the other optional packages. $head 10-25$$ The test $cref runge45_1.cpp$$ was failing when using gcc-4.5.2. This has been fixed by properly defining $codei%fabs(%x%)%$$ where $icode x$$ is a double (without the $code std$$ in front). $head 10-24$$ Change the CppAD licenses from CPL-1.0 and GPL-2.0 to EPL-1.0 and GPL-3.0. $head 10-12$$ $list number$$ Change all the multiple levels of AD examples to start with $cref mul_level$$. To be specific, move $code ode_taylor.cpp$$ to $cref mul_level_ode.cpp$$ and $code ode_taylor_adolc.cpp$$ to $cref mul_level_adolc_ode.cpp$$. $lnext Add $cref ode_taylor.cpp$$ as a example of Taylor's method for solving ODEs, ($cref mul_level_ode.cpp$$ is an application of this method to multi-level AD.) $lend $head 10-04$$ $list number$$ Change $cref speed_main$$ so that it outputs small rates (less than 1000) with two decimal points of precision (instead of as integers). In addition, flush result for each size when it finishes to give user more feedback about how things are progressing. $lnext Add the optional $cref/test_size/time_test/test_size/$$ argument to the $code time_test$$ routine. $lend $head 10-03$$ Change the $code hold_memory$$ speed to option to just $cref/memory/speed_main/Global Options/memory/$$. In addition, in the speed test output, include all of the options that are present in the output variable name; see $cref/speed results/speed_main/Speed Results/$$. $head 10-02$$ Fix another problem with Debian's $code /bin/sh$$ shell executing $code multi_thread/test.sh$$; see $cref/03-17/whats_new_12/03-17/$$ $head 09-24$$ Improve documentation for the $cref old_atomic$$ $cref/rev_hes_sparse/old_atomic/rev_hes_sparse/$$ argument $cref/v/old_atomic/rev_hes_sparse/v/$$. In addition, add sparsity calculations to the $cref old_reciprocal.cpp$$ example. $head 09-11$$ Add $code user_simple.cpp$$, a simpler $cref old_atomic$$ example. $head 08-05$$ $list number$$ A new type was added for the internal representation of $cref/vector of sets/glossary/Sparsity Pattern/Vector of Sets/$$ sparsity patterns; see the configure $code --with-sparse_option$$ (since removed). $lnext A new speed test, $cref compare_c$$, compares the speed of the same source code compiled with C and C++. $lend $head 07-30$$ $list number$$ The $cref/clear/CppAD_vector/clear/$$ function was added to $code CppAD::vector$$. $lnext Warning !!: The $code CppAD::vector$$ $cref/resize/CppAD_vector/resize/$$ specifications were changed so that $icode%x%.resize(0)%$$ no longer frees the corresponding memory (use $icode%x%.clear()%$$ instead). $lnext Fix a bug in error checking during $cref optimize$$ procedure had the following $code valgrind$$ symptom during the $code optimize.cpp$$ example: $codep ==6344== Conditional jump or move depends on uninitialised value(s) $$ $lnext Fix mistake in $cref old_tan.cpp$$ where $code w[2] = 0$$ was missing before the call $codep dw = F.Reverse(1, w); $$ $lend $head 07-08$$ $list number$$ Improve the documentation for $cref pow$$ and $cref pow_int$$. $lnext Change all the example section names to be same as corresponding file names; e.g. change $code vectorBool.cpp$$ to $cref vector_bool.cpp$$ for the example $code example/vector_bool.cpp$$. $lend $head 07-07$$ Add the $code CPPAD_TAPE_ID_TYPE$$ argument to the $cref/configure/auto_tools/Configure/$$ command line. $head 07-05$$ Deprecate $cref/CPPAD_TEST_VECTOR/test_vector/$$ and use $cref/CPPAD_TESTVECTOR/testvector/$$ in its place. This fixes a problem introduced by changes on 07-03 whereby code that used $code CPPAD_TEST_VECTOR$$ would no longer work. $head 07-04$$ $list number$$ Replace the requirement that the $cref SimpleVector$$ $cref/size/SimpleVector/Size/$$ function return a $code size_t$$ value to the requirement that it can be converted to a $code size_t$$ value. $lnext The $cref/--with-eigenvector/auto_tools/Configure/$$ option was added to the $code configure$$ command line. $lend $head 07-03$$ Fix bug in $cref old_atomic$$ functions identification of variables that caused $cref old_tan.cpp$$ to fail with error message $codep Error detected by false result for y_taddr > 0 at line 262 in the file cppad/local/dependent.hpp $$ $head 07-02$$ Add $cref eigen_plugin.hpp$$ so that an Eigen vector can be used as a $cref/SimpleVector/$$. $head 07-01$$ $list number$$ Change $cref cppad_eigen.hpp$$ to match new specifications and example in eigen help files on $href% http://eigen.tuxfamily.org/dox/TopicCustomizingEigen.html% customizing and extending eigen. %$$ $lnext Fix bug whereby a newly constructed $cref VecAD$$ object was a $cref/variable/ParVar/$$ (instead of a parameter) directly after construction (when no previous $cref/ADFun/FunConstruct/$$ object had been created). $lnext Change a $code ok != a == 0.$$ to $code ok &= a == 0.$$ in the example $cref ad_ctor.cpp$$. $lnext Add the $cref eigen_array.cpp$$ example. $lend $head 06-17$$ $list number$$ Move $cref epsilon$$ to $cref numeric_limits$$ and add the functions $code min$$ and $code max$$ in $icode%CppAD::numeric_limits<%Type%>%$$. $lnext Convert use of the deprecated $cref epsilon$$ in examples to use of $code numeric_limits$$ $cref/epsilon/numeric_limits/epsilon/$$. $lnext Complete $cref cppad_eigen.hpp$$ interface to $code lowest$$ and $code highest$$ functions for all non-complex AD types. $lend $head 06-16$$ Add the example $cref eigen_det.cpp$$ that uses the $href%http://eigen.tuxfamily.org%Eigen%$$ linear algebra package. $head 06-15$$ Include the $cref base_adolc.hpp$$ as $code $$ under the $cref/prefix_dir/auto_tools/prefix_dir/$$ directory. $head 06-12$$ Increase the size and of the $cref/sparse Jacobian speed tests/link_sparse_jacobian/$$. $head 06-10$$ $list number$$ Add the $cref/hold_memory/speed_main/Global Options/memory/$$ option to the speed test main program. This was changed to just $code memory$$; see $cref/10-03/whats_new_12/10-03/$$. $lnext In $cref cppad_sparse_jacobian.cpp$$, change $code USE_BOOL_SPARSITY$$ from true to false. In addition, change the number of non-zeros per row from about approximately three to approximately ten. $lend $head 06-09$$ Change $cref adolc_sparse_jacobian.cpp$$ to use the sparse adolc Jacobian (instead of the full Jacobian) driver. This was also done for $cref adolc_sparse_hessian.cpp$$, but there is a problem with the test that is being investigated. $head 06-08$$ Implement the matrix multiply speed test $cref link_mat_mul$$ for all packages (there is a problem with the $cref fadbad_mat_mul.cpp$$ implementation and it is being looked into). $head 06-07$$ Make all the speed tests implementations (for the specific packages) uniform by having a Specification and Implementation heading and similar indexing. For example, see $cref adolc_det_minor.cpp$$, $cref cppad_det_minor.cpp$$, $cref double_det_minor.cpp$$, $cref fadbad_det_minor.cpp$$, and $cref sacado_det_minor.cpp$$. $head 06-05$$ Add the $cref sacado_ode.cpp$$ speed test. $head 06-04$$ $list number$$ The specifications for $cref Runge45$$ where changes so that it uses the $code fabs$$ function instead of the $code <$$ operation. This enabled the a more precise statement about its $cref/operation sequence/Runge45/Operation Sequence/$$. $lnext The $code fabs$$ function as added to the CppAD standard math library (see $cref abs$$) and the $cref/base type requirements/base_std_math/$$. This enables one to write code that works with $code AD$$ as well as $code double$$ without having to define $code abs$$ for $code double$$ arguments (and similarly for $code float$$). $lnext Add the $cref adolc_ode.cpp$$ and $cref fadbad_ode.cpp$$ speed tests (and edit the $cref cppad_ode.cpp$$ test). $lend $head 06-03$$ $list number$$ The $code CppAD::vector$$ class was extended to allow assignment with the target of size zero and the source of non-zero size; see $cref/check size/CppAD_vector/Assignment/Check Size/$$. $lnext A memory leak and a bug in $code cppad_mat_mul.cpp$$ were fixed (the bug was related to the change to $code CppAD::vector$$ above). $lend $head 06-02$$ $list number$$ Remove the deprecated symbol $cref/CppADvector/test_vector/Deprecated 2012-07-03/$$ from the $cref det_by_lu$$ speed test source code $cref det_by_lu.hpp$$. $lnext Include $cref memory_leak$$ in the list of $cref deprecated$$ features. $lnext Change the $cref ode_evaluate$$ speed test utility so that its $cref/operation sequence/glossary/Operation/Sequence/$$ does not depend on the repetition; see $cref/p == 0/ode_evaluate/p/p == 0/$$ in its documentation. $lnext Use same argument for taping and derivative evaluation when $code retape$$ speed test option is true. $lnext Implement the $icode%retape% == false%$$ option in $cref cppad_ode.cpp$$. $lnext Have $cref cppad_det_lu.cpp$$, $cref cppad_det_minor.cpp$$, and $cref cppad_poly.cpp$$, return false when one of the specified options is not supported. Do the same for $icode%package%_%test%.cpp%$$ for $icode package$$ equal to $code adolc$$, $code fadbad$$, and $code sacado$$ and for $icode test$$ equal to $code det_lu$$, $code det_minor$$, $code poly$$. $lend $head 06-01$$ Change $cref cppad_sparse_hessian.cpp$$ and $cref cppad_sparse_jacobian.cpp$$ to use the $icode row$$, $icode col$$ interface to $cref sparse_hessian$$. In addition, implement the speed test $code retape$$ speed test option for these tests. $head 05-31$$ Add the $code cppad_print_optimize$$ routine to so that the corresponding code does not need to be reproduced for all the $cref speed_cppad$$ tests. In addition, during CppAD speed tests, print out the optimization results for each test size. $head 05-30$$ Change specifications for $cref link_sparse_hessian$$ so that the row and column indices are inputs (instead of being chosen randomly by the test for each repetition). This enables use of the $code retape$$ speed test option during sparse Hessian speed tests. $head 05-29$$ Add $cref index_sort$$ to the general purpose template $cref/utilities/utility/$$ so that it can be used by the implementations of $cref link_sparse_jacobian$$ and $cref link_sparse_hessian$$. $head 05-27$$ Split the sparse Jacobian and Hessian test function the separate function $cref sparse_jac_fun$$ and $cref sparse_hes_fun$$ (do not use sparse Hessian for both). In addition, change row and column indices from $icode i$$ and $icode j$$ to $icode row$$ and $icode col$$. $head 05-24$$ Merged in changes from $code branches/sparse$$: $list number$$ A new interface was added to $cref sparse_jacobian$$ and $cref sparse_hessian$$. This interface returns a sparse representation of the corresponding matrices using row and column index vectors. $lnext The examples $cref sparse_jacobian.cpp$$ and $cref sparse_hessian.cpp$$ were improved and extended to include the new interface. $lnext The definition of an $cref/AD function/glossary/AD Function/$$ was improved to include definition of the corresponding $icode n$$ and $icode m$$. $lend $head 04-19$$ The $cref/BOOST_DIR/auto_tools/boost_dir/$$ configure command line value has been changed to be the corresponding prefix during the installation of boost. To be specific, it used to be that $codei%boost_dir%/boost%$$ was the boost include directory, now $codei%boost_dir%/include%$$ is the boost include directory. This make it the same as the other directory arguments on the configure command line. In addition, it fixes some bugs in the detection of the boost multi-threading library. $head 04-18$$ Add documentation and testing for not using $cref/free_all/ta_free_all/$$ and $cref/old_atomic clear/old_atomic/clear/$$ while in $cref/parallel/ta_in_parallel/$$ mode. $head 04-17$$ Fix bug when using $cref old_atomic$$ functions with $cref/multi_threading/multi_thread/$$. $head 04-10$$ Add control of the $cref/max_num_threads/auto_tools/max_num_threads/$$ argument to the unix $cref/configure/auto_tools/Configure/$$ command. $head 04-06$$ $list number$$ A change was made to the way that the tapes were managed to reduce false sharing during $cref/multi-threading/multi_thread/$$. Because of this change, it is now suggest that the user call $cref parallel_ad$$ after the multi-threading section of the program. $lnext The routine $cref ta_free_all$$ was created to make it easier to manage memory and the routine $cref memory_leak$$ was deprecated. $lnext Add the $code -lteuchos$$ flag to the link line for the $cref speed_sacado$$ tests. (This was not necessary for $code trilinos-10.8.3$$ but is necessary for $code trilinos-10.10.1$$) $lend $head 04-05$$ The restriction was added that $cref parallel_ad$$ cannot be called while a tape is being recorded. This was necessary inorder to initialize some new statics in the tape. $head 04-01$$ Fixed a race condition when using CppAD with $cref/multi-threading/multi_thread/$$. This has been fixed and the error message below no longer occurs. Suppose that you ran the CppAD $cref/configure/auto_tools/Configure/$$ command in the $code work$$ directory. If you then edited the file $code work/multi_thread/makefile$$ and changed $codep # AM_CXXFLAGS = -g @(CXX_FLAGS) AM_CXXFLAGS = -DNDEBUG -O2 @(CXX_FLAGS) $$ to $codep AM_CXXFLAGS = -g @(CXX_FLAGS) # AM_CXXFLAGS = -DNDEBUG -O2 @(CXX_FLAGS) $$ and then executed the commands $codep make clean make pthread_test valgrind --tool=helgrind ./pthread_test simple_ad $$ The following error message would result: $icode% ... snip ...% ==7041== Possible data race during write of size 4 at 0x8077460 by thread #1 ==7041== at 0x804FE23: CppAD::AD::tape_new() (tape_link.hpp:221) % ... snip ... %$$ $head 03-27$$ Reduce the amount of memory allocation and copying of information during a $cref Dependent$$ operation or an $code ADFun$$ $cref/sequence constructor/FunConstruct/Sequence Constructor/$$. $head 03-26$$ Calling $code taylor_capacity$$, with to with capacity equal to zero, was not $cref/freeing memory/capacity_order/c/Freeing Memory/$$. This has been fixed. $head 03-23$$ $list number$$ Improve, the multi-threading examples $cref simple_ad_openmp.cpp$$, $cref simple_ad_bthread.cpp$$, and $cref simple_ad_pthread.cpp$$. This includes separating generic code that can be used for all applications from problem specific code. $lnext Add initialization of statics in $cref/CheckSimpleVector/parallel_ad/CheckSimpleVector/$$ during $code parallel_ad$$ call. These statics are required to use $cref/CppAD::vector/CppAD_vector/$$. $lnext Add a debugging check to make sure $cref CheckSimpleVector$$ is initialized in sequential mode. $lend $head 03-21$$ Fix an incorrect error check in $code thread_alloc$$ that did not allow $cref ta_return_memory$$ to return memory in sequential execution mode that was allocated by a different thread during parallel execution. $head 03-17$$ Debian recently converted the default shell corresponding to $code /bin/sh$$ to $code dash$$ (which caused $code multi_thread/test.sh$$ to fail). This has been fixed. In general, Debian's policy is that $code bin/sh$$ will be a $href% http://pubs.opengroup.org/onlinepubs/009695399/utilities/xcu_chap02.html% Posix Shell %$$. $head 03-11$$ There was a bug in $cref thread_alloc$$ where extra memory was held onto even if $cref/hold_memory/ta_hold_memory/$$ was never called and only one thread was used by the program. This caused $codei% valgrind --leak-check=full --show-reachable=yes %$$ to generate an error message. If $cref/multiple threads/multi_thread/$$ are used, one should free this $cref/extra memory/ta_free_available/Purpose/Extra Memory/$$ for threads other than thread zero. If $code hold_memory$$ is used, one should call $cref/free_available/ta_free_available/$$ for all threads. $head 03-03$$ $list number$$ Add the examples $cref simple_ad_openmp.cpp$$, $cref simple_ad_bthread.cpp$$ and $cref simple_ad_pthread.cpp$$. $lnext Fix bug in finding boost multi-threading library (due to fact that $cref/boost_dir/auto_tools/boost_dir/$$ is not the prefix during the boost installation). $lend $head 03-02$$ $list number$$ Change the name $code simple_ad.cpp$$ to $cref team_example.cpp$$ $lnext The multi-threading $code team_example.cpp$$ example was changed to use $latex f(x) = \sqrt{ x^2 }$$ instead of the function $latex {\rm atan2} [ \sin(x) , \cos (x) ]$$ (both functions should behave like the identity function $latex f(x) = x$$). This enabled the removal of $code multi_thread/arc_tan.cpp$$. $lnext In $cref team_example.cpp$$ check that all of the threads pass their individual test; i.e. $codei%work_all_[%thread_num%]%.ok%$$ is true for all $icode thread_num$$. $lend $head 02-11$$ $list number$$ The requirements in $cref base_member$$ were missing from the $cref base_require$$ documentation. In addition, the $cref base_require.cpp$$ example has been added. $lend The specifications for $cref memory_leak$$ where changes so that calling routine specifies the amount of static memory to add. In addition, it is now possible to call $code memory_leak$$ when $cref/num_threads/ta_num_threads/$$ is greater than one (still can't be in parallel mode). $head 02-10$$ $list number$$ Add the missing Base class requirements in the entire $cref base_member$$ section and under the $cref/Output Operator/base_require/Output Operator/$$ in the $cref base_require$$ section. $lnext Add the $cref base_alloc.hpp$$ example. $lend $head 02-09$$ $list number$$ Add the $icode set_static$$ to $cref memory_leak$$. This is necessary for testing base types that allocate memory for each element. $lnext Fix memory allocation bug in $code cppad/local/pod_vector.hpp$$ when each element of the $cref/Base/base_require/$$ type allocated memory. $lend $head 01-30$$ Make another attempt to fix linking with boost threads where the wrong version of the library is in the system include directory; i.e., to have $cref/boost_dir/auto_tools/boost_dir/$$ override the default library. $head 01-27$$ There were some problems with $cref/configure's/auto_tools/Configure/$$ automatic detection of the boost multi-threading library. These have been fixed. $head 01-24$$ It used to be that $cref thread_alloc$$ did not hold onto memory when $icode num_threads$$ was one in the previous call to $cref/parallel_setup/ta_parallel_setup/$$. Holding onto memory is now controlled by the separate routine $cref/hold_memory/ta_hold_memory/$$. This give the user more control over the memory allocator and the ability to obtain a speed up even when there is only one thread. To convert old code to the new interface, after each call to $codei% thread_alloc::parallel_setup(%num_threads%, %in_parallel%, %thread_num%); %$$ put the following call $codei% thread_alloc::hold_memory(%num_threads% > 1); %$$ $head 01-23$$ Change variable notation and use $cref optimize$$ in $cref mul_level.cpp$$. $head 01-20$$ $list number$$ Add the example $cref change_param.cpp$$ which shows how to compute derivatives of functions that have parameters that change, but derivatives are not computed with respect to these parameters. $lnext The documentation for machine $cref epsilon$$ has been improved. (The fact that it can be used for $icode Base$$ types was missing.) $lend $head 01-19$$ $list number$$ In cases where $code test.sh$$ is trivial, put its operations in corresponding makefile. $lnext Fix problem compiling $code cppad/speed/sparse_evaluate.hpp$$ under gcc on Fedora 17. $lnext Run $code multi_thread/test.sh$$ from source directory (no need to copy to build directory). $lend $head 01-16$$ The test program $code multi_thread/test.sh$$ failed if the $cref/openmp_flags/auto_tools/openmp_flags/$$ not present in the $code configure$$ command. This has been fixed. In addition, this $code test.sh$$ has been made faster by cycling through the available threading systems instead of doing every system for every test. $head 01-15$$ Fix $code make test$$ so it works when $cref/configure/auto_tools/Configure/$$ is run in the distribution directory $codei%cppad-%yyyymmdd%$$ (not just when it is run in a different directory). $head 01-12$$ The $code -lpthread$$ library was missing from the $cref multi_thread$$ test program linker command. This has been fixed. $head 01-07$$ $list number$$ A duplicated code block beginning with $codep if( fabs( fcur ) <= epsilon_ ) $$ was removed from the routine $code multi_newton_worker$$, in the file $cref multi_newton_work.cpp$$. $lnext The distance between solutions that are joined to one solution has been corrected from $latex (b - a) / (2 n )$$ to $latex (b - a) / n $$; see $cref/xout/multi_newton.cpp/xout/$$. The correction was in the file $cref multi_newton_work.cpp$$ where $code sub_length_ / 2$$ was change to $code sub_length_$$. $lend $head 01-02$$ $list number$$ The $cref thread_alloc$$ memory allocator was changed to avoid certain false sharing situations (cases where two different thread were changing and using memory that is on the same page of cache). On one tests machine, the execution time for the 32 thread case for the test $codep ./openmp_test multi_newton 1 32 1000 4800 10 true $$ improved from 0.0302 seconds to 0.0135 seconds. $lnext There was a problem with the correctness test section of the $cref multi_newton_time.cpp$$ test. The convergence criteria, and correctness criteria, needed to be scaled by the largest argument values. This was a problem with over a hundred zeros were included in the test (and the largest argument value was $latex 100 \pi$$ or more). $lnext There was a problem with the way that $cref/multi_newton_combine/multi_newton_work.cpp/multi_newton_combine/$$ joined two solutions into one. It is possible that one of the solutions that needs to be joined is on the boundary and very close to a solution in the next (or previous interval) that is not on the boundary. In this case, the one with the smaller function value is chosen. $lend for the previous $end cppad-20170000.3/omh/whats_new/whats_new_04.omh0000644000175200017650000007170013057470463020231 0ustar coincoin-web$Id: whats_new_04.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_04$$ $spell cppad.hpp deps executables Runge Rhs aclocal config Makefile ublas Autoconf Automake cppad yy mm dd Faq acos asin sqrt exp usr nmake mak namespace CppADvector atan cos retape Vec const std Hess depricated Det Lu dsp Arg Cpp Microsoft Taylor dep ind $$ $section Changes and Additions to CppAD During 2004$$ $head Introduction$$ This section contains a list of the changes plus future plans for CppAD during 2004 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions. $head 12-11$$ The documentation for the CppAD error macros was improved. The package title in $cref cppad$$ was changed. The documentation for $cref/CppAD::vector/CppAD_vector/$$ was improved and the corresponding source code $code cppad/vector.hpp$$ was included. $head 12-09$$ The $cref LuSolve$$ and $code OdeRunge$$ source code was modified to make the more in line with the introduction to C++ AD book ($code OdeRunge$$ has been replaced by $cref Runge45$$). In addition, the examples $code OdeRunge.cpp$$ and $cref lu_solve.cpp$$ were modified to make the simpler. (The more complex version of $code OdeRunge.cpp$$ was moved to the $code TestMore$$ directory.) $head 12-03$$ The $cref Poly$$ documentation and source code were modified to make them more in line with the introduction to C++ AD book. $head 11-17$$ Changing to Autoconf and Automake on $cref/08-24/whats_new_04/08-24/$$ mistakenly forgot the $code -Wall$$ compiler switch (all warnings). This has been added and the corresponding warnings have been fixed. $head 11-16$$ The 11-15 Debug version would not compile under Visual C++ version 7.0 because a declaration of $code LessThanOrZero$$ was missing. This has been fixed. $head 11-15$$ The $cref ForOne$$ and $cref RevOne$$ easy to use $cref/drivers/Drivers/$$ were added. $head 11-14$$ The notation in the $cref ADFun$$ sections was changed to make the $cref Forward$$ and $cref Reverse$$ routines easier to use. $head 11-13$$ The Taylor coefficient vector and matrix notation was folded into just $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. $head 11-12$$ If $code NDEBUG$$ is not defined during compile time, all $codei%AD<%Base%>%$$ $cref/comparison/Compare/$$ operations are checked during $cref/zero order/forward_zero/$$ forward mode calculations. The $cref CompareChange$$ function returns the number of comparison operations that have changed. $head 11-10$$ The $cref get_started.cpp$$ example was changed to use the $cref Jacobian$$ driver. In addition, more $cref/index/_index/$$ entries, that point to the $cref/easy to use drivers/Drivers/$$, were added. $head 11-04$$ The Microsoft Visual Studio project file $code example/Example.dsp/$$ was missing some new examples that needed to be linked in the install windows procedure. This has been fixed. $head 11-02$$ The $cref/unix installation/auto_tools/$$ required the user to touch the files to get the dates in proper order. This is no longer necessary. $head 11-01$$ Some of the dependency directories and files, for example $code PrintFor/.deps$$ and $code PrintFor/.deps/PrintFor.Po$$ had an extra $code ?$$ at the end of their names. This seems to have been fixed by using a newer version of the autoconf and automake tools. $head 10-29$$ Add the example and test $cref simple_vector.cpp$$ to the $cref SimpleVector$$ documentation. $pre $$ The specifications for $cref/preprocessor symbols/preprocessor/$$ state that all the CppAD preprocessor symbols begin with $code CppAD$$ (so they do not conflict with other packages). Some preprocessor symbols in the file $code cppad/config.h$$ did began with $code WITH_$$. This has been fixed. $head 10-28$$ The examples $cref hes_lu_det.cpp$$, $cref hes_minor_det.cpp$$, $cref jac_lu_det.cpp$$, and $cref jac_minor_det.cpp$$ used the negative of a $code size_t$$ value. The value has been changed to an $code int$$. $pre $$ The $cref/CppAD::vector/CppAD_vector/$$ template class was converted into a library routine so it can be used separately from the rest of CppAD. $head 10-27$$ The $cref PrintFor$$ example was moved to its own directory because the conversion from VC 6.0 to VC 7.0 projects did not work when there were multiple executables in one project file. The $cref install$$ instructions were modified to reflect this change. $head 10-21$$ One declaration (for the $cref Value$$ function) was missing from the file $code cppad/local/Declare.h$$. This has been added and CppAD should now compile and run under both Microsoft VC 6.0 and 7.0. $head 10-19$$ The current version of CppAD has a problem compiling under Microsoft Visual C++ version 7.0 (it compiles and works under version 6.0). The problem appears to be due to a closer agreement between VC 7.0 and the C++ standard for declaring templates functions as friends. Some friend declarations were removed and others were made more specific in order to migrate the a version that will compile and run using VC 7.0. $head 10-16$$ The example $cref compare.cpp$$ displayed the text from $cref bool_fun.cpp$$ by mistake. This has been fixed. $pre $$ The $cref Compare$$ operators have been extended to work with $code int$$ operands. $head 10-06$$ The test $code TapeDetLu$$ was added to $code speed_cppad/DetLuSpeed.cpp$$ and $code TapeDetMinor$$ was added to $code speed_cppad/DetMinorSpeed.cpp$$. These tests just tape the calculations without computing any derivatives. Using this, and the other tests, one can to separate the taping time from the derivative calculation time. $pre $$ The windows installation steps do not build a $code config.h$$ file. Hence a default $code config.h$$ file was added to the distribution for use with Microsoft Visual Studio. $pre $$ The $code Distribute$$ section of the developer documentation was brought up to date. $pre $$ Links to the ADOLC and FADBAD download pages were added to the $cref/unix installation/auto_tools/$$ instructions. $head 09-29$$ The include files for the $cref/utilities/utility/$$ are now included by the root file $code cppad/cppad.hpp$$. They can still be included individually with out the rest of the CppAD package. $head 09-26$$ The routine $code OdeRunge$$ was modified so that it will now integrate functions of a complex arguments. This was done by removing all uses of greater than and less than comparisons were removed. ($code OdeRunge$$ has been replaced by $cref Runge45$$). $pre $$ The changes on $cref/09-21/whats_new_04/09-21/$$ did not fix all the file date and time problems; i.e., automake was still running in response to the $cref/unix installation/auto_tools/$$ $code make$$ command. $head 09-23$$ There was a reference to $icode B$$ that should have been $icode X$$ in the description of the $cref/X/LuSolve/X/$$ argument of $code LuSolve$$. This has been fixed. $head 09-21$$ The $cref CondExp$$ function has been modified so that it works properly for $codei%AD< AD<%Base%> >%$$ types; i.e., it now works for multiple levels of taping. $pre $$ The date of the files $code aclocal.m4$$ and $code config.h.in$$ were later than the date of top level $code Makefile.am$$. This caused the $code make$$ command during the $cref/unix installation/auto_tools/$$ to try to run $code autoconf$$ and this did not work on systems with very old versions of $code autoconf$$. This has been fixed. $head 09-13$$ The examples that are specific to an operation were moved to be below that operation in the documentation tree. For example $cref add.cpp$$ is below $cref ad_binary$$ in the documentation tree. $head 09-10$$ The version released on 04-09-09 did not have the new file $code PrintFor.h$$ in $code cppad/local$$. This has been fixed. $pre $$ The $icode Base$$ type requirements were simplified. $pre $$ The $cref/Unix installation/auto_tools/$$ instructions were modified so just one make command was executed at the top level. This was necessary because the order of the makes is now important (as previously suggested, the makes did not work properly). $head 09-09$$ The $cref PrintFor$$ function was added so that users can debug the computation of function values at arguments that are different from those used when taping. $head 09-07$$ In the $cref/Unix installation/auto_tools/$$ instructions place $code ./$$ in front of current directory program names; for example, $code ./GetStarted$$ instead of $code GetStarted$$ (because some unix systems do not have the current directory in the default executable path). $head 09-04$$ A library containing the $cref SpeedTest$$ and $cref NearEqual$$ object files was added to the distribution. $pre $$ All of the include files of the form $codei%%$$ were moved to $codei%%$$. $head 09-02$$ Some more messages were added to the output of $code configure$$ during the $cref/Unix installation/auto_tools/$$. $pre $$ The suggested compression program during Windows installation was changed from $href% http://www.7-zip.org% 7-zip %$$ to $href% http://www.winzip.com% WinZip %$$. $head 08-27$$ The error messages printed by the default version of the CppAD error macros had $code YY-MM-DD$$ in place of the date for the current version. This has been fixed. $pre $$ All the correctness tests are now compiled with the $code -g$$ command line option (the speed tests are still compiled with $code -O2 -DNDEBUG$$). $pre $$ The $cref/installation instructions/Install/$$ for Unix and Windows were split into separate pages. $head 08-25$$ The $cref/installation/Install/$$ now automates the replacement of $cref/CppAD::vector/CppAD_vector/$$ by either the $code std::vector$$ or $code boost::numeric::ublas::vector$$. $head 08-24$$ This date marks the first release that uses the Gnu tools Autoconf and Automake. This automates the building of the make files for the $cref/installation/Install/$$ and is the standard way to distribute open source software. This caused some organizational changes, for example, the $cref/GetStarted/get_started.cpp/$$ example now has its own directory and the distribution directory is named $codei% cppad-%yy%-%mm%-%dd% %$$ where $icode%yy%-%mm%-%dd%$$ is the year, month and date of the distribution. (Note the distribution directory is different from the directory where CppAD is finally installed.) $head 08-12$$ Move $code OdeExplicit$$ into the $code cppad/library/$$ directory. In addition, change it so that the vector type was a template argument; i.e., works for any type of vector (not just $code CppADvector$$). $head 07-31$$ Move $cref LuSolve$$ into the $code cppad/library/$$ directory. In addition, change it so that the vector type was a template argument; i.e., works for any type of vector (not just $code CppADvector$$). $head 07-08$$ The file $code cppad/example/NearEqual.h$$ has been moved to $code cppad/example/NearEqualExt.h$$ because it contains extensions of the $cref NearEqual$$ routine to $code AD$$ types. $head 07-07$$ The $code double$$ and $code std::complex$$ cases for the $cref NearEqual$$ routine arguments has been moved to the general purpose $cref/utilities/utility/$$. $head 07-03$$ The CppAD error macros names $code CppADExternalAssert$$ and $code CppADInternalAssert$$ were changed to $code CppADUsageError$$ and $code CppADUnknownError$$. The $cref SpeedTest$$ routine was changed to use $code CppADUsageError$$ instead of a C assert. $head 07-02$$ The $cref SpeedTest$$ output was improved so that the columns of values line up. Previously, this was not the case when the number of digits in the size changed. $head 06-29$$ Added code to trap and report memory allocation errors during $code new$$ operations. $head 06-25$$ A discussion of the order dependence of the $cref/assignment/ad_assign/$$ operator and the $cref/independent function/Independent/$$ was added to the $cref/Faq/Faq/Assignment and Independent/$$. In addition, a similar discussion was added to the documentation for the $cref Independent$$ function. $pre $$ The definition of a $cref/parameter/glossary/Parameter/$$ and $cref/variable/glossary/Variable/$$ were changed to reflect that fact that these are time dependent (current) properties of an $codei%AD<%Base%>%$$ object. $head 06-12$$ All of the $cref/arithmetic operators/Arithmetic/$$ (except for the unary operators) can now accept $code int$$ arguments. The documentation for these arguments has been changed to reflect this. In addition, the corresponding test cases have been changed to test this and to test high order derivative cases. The old versions of these tests were moved into the $code cppad/Test$$ directory. $head 06-04$$ The $cref/atan2/atan2/$$ function was added. $head 06-03$$ The $code asin$$ and $code acos$$ $cref unary_standard_math$$ functions were added. $pre $$ There was a bug the reverse mode theory and calculation of derivatives of $cref sqrt$$ for fourth and higher orders. This has been fixed. In addition, the following examples have been changed so that they test derivative up to fifth order: $cref/asin/Asin.cpp/$$, $cref/atan/atan.cpp/$$, $cref/cos/cos.cpp/$$, $cref/exp/exp.cpp/$$, $cref/log/log.cpp/$$, $cref/sin/sin.cpp/$$, $cref/sqrt/sqrt.cpp/$$. $head 06-01$$ There was a bug in the $cref atan$$ function $cref/forward mode/Forward/$$ calculations for Taylor coefficient orders greater than two. This has been fixed. $head 05-30$$ The $cref/sin/sin.cpp/$$ and $cref/cos/cos.cpp/$$ examples were changed so that they tested higher order derivatives. $head 05-29$$ The forward mode recursion formulas for each of the $xref/ ForwardTheory/ Standard Math Functions/ Cases that Apply Recursion Above/ standard math functions/ 1 /$$ has been split into separate sections. $pre $$ A roman (instead of italic) font was used for the name of for the name of each of the standard math functions in the assumption statements below the section for the standard math functions. For example, $latex \sin(x)$$ instead of $latex sin(x)$$. $head 05-26$$ In the documentation for $cref Poly$$, the reference to $code example/Poly.h$$ was corrected to $code cppad/library/Poly.h$$. $pre $$ In the documentation for $cref SpeedTest$$, the reference to $code Lib/SpeedTest.h$$ was corrected to $code cppad/library/SpeedTest.h$$. In addition, the example case was corrected. $pre $$ In $cref Reverse$$, the definition for $latex U(t, u)$$ had $latex t^p-1$$ where it should have had $latex t^{p-1}$$. This has been fixed. $head 05-25$$ The special case where the second argument to the $cref pow$$ function is an $code int$$ has been added. $head 05-14$$ Change all of the include syntax $codei% # include "%filename%" %$$ to the syntax $codei% # include <%filename%> %$$ so that examples and other use better reflect how one would use CppAD after it was installed in a standard include directory; for example $code /usr/local/include/cppad$$. $pre $$ The user documentation was moved from the directory $code cppad/User$$ to the directory $code cppad/Doc$$. $pre $$ The directory $code cppad/Lib$$ was moved to $code cppad/library$$ to reflect that fact that it is not what one expects in a standard $code lib$$ directory or a standard $code include$$ directory. $head 05-12$$ The string $code YY-MM-DD$$ in the preprocessor symbol $code CppADVersion$$ was not being replaced by the current date during distribution. This resulted in the $code CppADExternalAssert$$ macro printing $code YY-MM-DD$$ where is should have printed the date of distribution. This has been fixed. $pre $$ All of the include commands of the form $codei% # include "include/%name%.h" # include "lib/%name%.h" %$$ have been changed to the form $codei% # include "cppad/include/%name%.h" # include "cppad/lib/%name%.h" %$$ This will avoid mistakenly loading a file from another package that is in the set of directories being searched by the compiler. It is therefore necessary to specify that the directory above the $code CppAD$$ directory be searched by the compiler. For example, if $code CppAD$$ is in $code /usr/local/cppad$$, you must specify that $code /usr/local$$ be searched by the compiler. Note that if $code /usr/local/cppad/$$ is no longer searched, you will have to change $codep # include "cppad.hpp" $$ to $codep # include "cppad/cppad.hpp" $$. $pre $$ The window $code nmake$$ file $code Speed/Speed.mak$$ was out of date. This has been fixed. $head 05-09$$ Move $cref Poly$$ and $cref SpeedTest$$ into the $code cppad/Lib$$ directory and the $code CppAD$$ namespace. $head 05-07$$ The $cref/divide operator tests/div.cpp/$$ were extended to include a second order derivative calculation using reverse mode. $pre $$ The $cref Poly$$ routine was modified to be more efficient in the derivative case. In addition, it was changed to use an arbitrary vector for the coefficients (not just a $code CppADvector$$). $head 05-04$$ A reloading of the data base caused the files $code include/atan.h$$ and $code include/cos.h$$ to be mistakenly started with lower case letters. These have been moved to $code include/Atan.h$$ and $code include/Cos.h$$ respectively. $head 05-03$$ The $cref Reverse$$ mode calculations for $cref/conditional expressions/CondExp/$$ were mistakenly left out. This has been fixed. $head 04-29$$ The unary functions, such as $cref sin$$ and $cref cos$$, were not defined for elements of an $cref VecAD$$ vector. This has been fixed. $head 04-28$$ The operator $cref/< >%$$ class had values that were variables in the $codei%AD<%Base%>%$$ class. This has been fixed. $head 04-01$$ The name of the class that tapes indexing operations was changed from $code ADVec$$ to $cref VecAD$$. This class was extended so that the value of elements in these vectors can be variables (need not be $cref/parameters/glossary/Parameter/$$). $head 03-30$$ Do some simple searching of the parameter table during taping avoid multiple copies of parameters on tape (use less tape memory). $head 03-28$$ The version $cref/ADVec/VecAD/$$, a vector class that tapes indexing operations, is now available. It is currently restricted by the fact that all the values in the vector must be $cref/parameters/Glossary/Parameter/$$. $head 03-25$$ The internal taping structure has been changed to have variable length instructions. This is to save memory on the tape. In addition, it may help in the implementation of the vector class that tracks indexing. (A now functioning version of this class is described in $cref VecAD$$.) $head 03-18$$ A change was made to the way parameter values are stored on the tape. This resulted in a significant savings in the amount of memory required. $head 03-17$$ Change the return type for $cref SpeedTest$$ from $code const char *$$ to $code std::string$$. The memory required for the largest test cases was added to the $cref speed_cppad$$ tests output. $head 03-15$$ The comparison between ADOLC and CppAD for the $code DetLuADOLC.cpp/$$ example was returning an error (because it was checking for exact equality of calculated derivatives instead of nearly equal). This has been fixed. $head 03-12$$ The user defined unary functions were removed and the user defined $cref/discrete functions/Discrete/$$ were added. These discrete functions add the capability of conditional expressions (alternate calculations) being included in an $cref ADFun$$ object. $head 03-11$$ The classes $cref det_by_minor$$ and $cref det_by_lu$$ were added and used these to simplify the examples that compute determinants. $head 03-09$$ The routines $code Grad$$ and $code Hess$$ have been removed. You should use $cref Jacobian$$ and $cref Hessian$$ instead. $head 03-07$$ The driver routines $cref Hessian$$ and $cref RevTwo$$ has been added. These to compute specialized subsets of the second order partials. $pre $$ Documentation errors in $cref ForTwo$$ and $cref Reverse$$ were fixed. The $cref example$$ documentation was reorganized. $head 03-06$$ The driver $cref ForTwo$$ has been added. It uses forward mode to compute a subset of the second order partials. $pre $$ Split all of the "example" and "test" index entries that come from $codei%cppad/example/%*%.cpp%$$ into sorted subheadings. $head 03-05$$ The $code Grad$$ routine, which only computed first derivatives of scalar valued functions, has been replaced by the $cref Jacobian$$ routine which computes the derivative of vector valued functions. $head 03-04$$ The bug reported on $cref/02-17/whats_new_04/02-17/$$ was present in all the operators. These have all been fixed and tests for all the operators have been added to the $code cppad/Test$$ directory. $pre $$ The $cref/f.Parameter()/seq_property/Parameter/$$ function was added so that one can count how many components of the range space depend on the value of the domain space components. This helps when deciding whether to use forward or reverse mode. $head 03-03$$ Special operators were added to distinguish the cases where one of the operands is a $cref/parameter/glossary/Parameter/$$. This reduced the amount of branching that is necessary when executing $cref Forward$$ and $cref Reverse$$ calculations. $pre $$ The $cref Independent$$ and $cref/Parameter/seq_property/Parameter/$$ functions were moved below $cref ADFun$$ in the documentation. $head 03-01$$ The DetLuADOLC.cpp, DetLu case was added to the ADOLC comparison tests. $head 02-29$$ Under certain optimization flag values, and on certain systems, an error was reported by the ADOLC correctness comparison. It turned out that CppAD was not initializing a particular index when debugging was turned off. This has been fixed. $head 02-28$$ A set of routines for comparing CppAD with ADOLC has been added to the distribution. In addition, documentation for compiling and linking the $cref/Examples/example/$$ and $cref/Speed Tests/speed_cppad/$$ has been added. $head 02-21$$ If you use the user defined unary atomic functions there is a restriction on the order of the derivatives that can be calculated. This restriction was documented in the user defined unary function $cref Forward$$ and $cref Reverse$$. (These unary functions were removed on $cref/03-12/whats_new_04/03-12/$$.) $head 02-20$$ A user interface to arbitrary order $cref/reverse mode/Reverse/$$ calculations was implemented. In addition, the $cref ADFun$$ member functions $code Rev$$ and $code RevTwo$$ were removed because it is easier to use the uniform syntax below: $table $bold Old Syntax$$ $cnext $bold Uniform Syntax$$ $rnext $icode%r1% = %f%.Rev(%v%)%$$ $cnext $icode%r1% = %f%.Reverse(1, %v%)%$$ $rnext $icode%q1% = %f%.RevTwo(%v%)%$$ $cnext $icode%r2% = %f%.Reverse(2, %v%)%$$ $rnext $cnext $icode%q1%[%i%] == %r2%[2 * %i% + 1]%$$ $tend $pre $$ The $cref Theory$$ section has been completely changed so that it corresponds to the arbitrary order calculations. (Some of this change was made when the arbitrary forward mode interface was added on $cref/04-02-15/whats_new_04/02-15/$$. $pre $$ The directory $code cppad/Test$$ has been added. It contains tests cases that are not intended as examples. $head 02-17$$ There was a bug in the way CppAD handled the parameters zero and one when they were variables on a lower level tape; i.e. x might be a parameter on an $codei%AD< AD<%Base%> >%$$ tape and a its value might be a variable on the $codei%AD<%Base%>%$$ tape. This bug in the multiply and divide routines has been fixed. $pre $$ There was a bug that is some cases reported a divide by zero error when the numerator was zero. This has been fixed. $head 02-16$$ A bug in $cref Forward$$ prevented the calculation of derivatives with higher order than two. In addition, this checking for user errors in the use of $code Forward$$ was also faulty. This has been fixed. $pre $$ The Microsoft project file $code example\Example.dsp$$ was out of date. This has been fixed. $pre $$ The example that $cref/tapes derivative calculations/mul_level/$$ has been changed to an application of $cref/Taylor's method/mul_level_ode.cpp/$$ for solving ordinary differential equations. $head 02-15$$ A user interface to arbitrary order $cref/ forward mode/Forward/$$ calculations was implemented. In addition, the $cref ADFun$$ member functions $code Arg$$, $code For$$ and $code ForTwo$$ were removed because it is easier to use the uniform syntax below: $table $bold Old Syntax$$ $cnext $bold Uniform Syntax$$ $rnext $icode%v0% = %f%.Arg(%u0%)%$$ $cnext $icode%v0% = %f%.Forward(0, %u0%)%$$ $rnext $icode%v1% = %f%.For(%u1%)%$$ $cnext $icode%v1% = %f%.Forward(1, %u1%)%$$ $rnext $icode%v2% = %f%.For(%u2%)%$$ $cnext $icode%v2% = %f%.Forward(1, %u2%)%$$ $tend $head 02-12$$ All of the derivative calculations are now done using arbitrary order Taylor arithmetic routines. The $cref Theory$$ section was changed to document this method of calculation. $head 02-01$$ The definition of a $cref/Taylor coefficient/glossary/Taylor Coefficient/$$ was changed to include the factorial factor. This change was also made to the output specifications for the $code FunForTwo$$ routine. $head 01-29$$ There were some bugs in the $code FunArg$$ function that were fixed. $list number$$ If one of the dependent variables was a $cref/parameter/glossary/Parameter/$$ $code FunArg$$ did not set it's value properly. (All its derivatives are zero and this was handled properly.) $lnext The user defined unary functions were not computed correctly. $lend The specifications for the usage and unknown CppAD error macros were modified so that they could be used with out side effects. $head 01-28$$ Some corrections and improvements were made to the documentation including: $code CppADvector$$ was placed before its use, a reference to $code Ode_ind$$ and $code Ode_dep$$ was fixed in $code OdeImplicit$$. $head 01-22$$ The specifications for the routine $code FunForTwo$$ was changed to use $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. This makes the interface to CppAD closer to the interface for $href%https://projects.coin-or.org/ADOL-C%ADOLC%$$. $end cppad-20170000.3/omh/whats_new/whats_new_13.omh0000644000175200017650000004174613057470463020240 0ustar coincoin-web$Id: whats_new_13.omh 3855 2016-12-19 00:30:54Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_13$$ $dollar @$$ $spell ctor Num autotools nz Jacobian CondExp Lt Gt Eq op_arg Adolc aka sacado resize sb IpIpoptAlg.cpp inf const algo afun cxx checkpointing cout typename bool struct impl std alloc ptr isnan cmake namespace testvector eigen microsoft src jac hpp Wunused Cpp cppad $$ $section CppAD Changes and Additions During 2013$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2013 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-29$$ $list number$$ The include file $cref cppad_eigen.hpp$$ now automatically includes $code cppad.hpp$$. $lnext There was a problem with this automation when $code eigen$$ was used for the cppad $cref testvector$$. This has been fixed. $lnext There was a problem with deprecated $cref auto_tools$$ (created when optional implicit constructor from any type was added). This has been fixed by adding the $code --with-implicit_ctor$$ option (later changed to $cref/--with-deprecated/auto_tools/--with-deprecated/$$). $lend $head 12-27$$ The constructor from an arbitrary type to $codei%AD<%Base%>%$$ was implicit, but there was no specification to this effect. The caused problems when using CppAD with $cref/eigen 3.2/eigen_prefix/$$ (scheduled to be fixed in 3.3). The default for this constructor has been changed to be $cref/explicit/ad_ctor/x/explicit/$$. In addition, other $cref/implicit/ad_ctor/x/implicit/$$ constructors are now listed in the documentation. $pre $$ If you get a compiler error on an constructor / assignment of the form $codei% AD<%Base%> x = %y% %$$ (that used to work) try changing the constructor call to $codei% AD<%Base%>( %y% ) %$$ A deprecated alternative is to make this constructor implicit using the $cref/cppad_deprecated/cmake/cppad_deprecated/$$ option during the install procedure. $head 12-26$$ Document fact that $cref/monthly versions/download/Monthly Versions/$$ of the CppAD compressed tar file last till the end of the year. $head 12-24$$ The interface to $cref/eigen/cppad_eigen.hpp/$$ defined a function $codei% NumTraits< CppAD::AD<%Base%> >::dummy_epsilon() %$$ that should have been named $code dummy_precision()$$. This has been fixed. $head 11-27$$ $list number$$ Fix bug when using $cref optimize$$ with an $cref ADFun$$ object containing the $cref sign$$ function. $lnext Add $cref atomic_norm_sq.cpp$$, an atomic function example with domain dimension two and range dimension one. $lend $head 11-13$$ It used to be that one had to define the $code std::set$$ version of $cref atomic_rev_sparse_jac$$ for each atomic function that was part of an $cref ADFun$$ object that was $cref/optimized/optimize/$$. Now the current $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ setting is used to determine if the $code bool$$ or $code std::set$$ version of $code rev_sparse_jac$$ is used by the optimization process. $head 11-12$$ Error detection and reporting (when $code NDEBUG$$ is not defined) has been added for the following case: Using $cref optimize$$ with $cref atomic_base$$ functions that have not defined $cref/rev_sparse_jac/optimize/Atomic Functions/rev_sparse_jac/$$. $head 10-29$$ The $cref/optimization/CondExp/Optimize/$$ now handles nested conditional expressions. For example, give the code $codep x = CondExpLt(left_x, right_x, true_x, false_x) y = CondExpGt(left_y, right_y, true_y, false_y) z = CondExpEq(left_z, right_z, x, y) $$ only two of the conditional expressions will be evaluated (one will be skipped depending on the result of $code left_z == right_z$$). For more details, see $cref optimize_nest_conditional.cpp$$. $head 10-23$$ $list number$$ Fix a bug in the optimization of calls to $cref atomic$$ functions. This bug existed before recent change to optimizing conditional expressions. This required adding the $cref/dependency/RevSparseJac/dependency/$$ argument to the reverse Jacobian sparsity pattern calculation. $lnext Fix the deprecated autotools install (see $cref auto_tools$$) which was broken by the changes on 10-22. To be specific, the example for $cref number_skip$$ was not being included. $lend $head 10-22$$ $list number$$ Add $cref/optimization/optimize/$$ of conditional expressions; see $cref/CondExp/CondExp/Optimize/$$. $lnext Add a phantom argument at the beginning of the operations sequence; $cref/size_op_arg/seq_property/size_op_arg/$$ and $cref seq_property.cpp$$. (This helps with the optimization mentioned above.) $lnext Add the function $cref number_skip$$ to measure how much optimization of the conditional expressions there is. $lend $head 10-16$$ Fix bug in $cref/Tracing/wish_list/Tracing/$$ $cref atomic$$ functions. $head 10-15$$ The documentation for the class $cref/vectorBool/CppAD_vector/vectorBool/$$ was improved. $head 10-14$$ The script $cref get_adolc.sh$$ was added (for downloading and installing $href%https://projects.coin-or.org/ADOL-C%ADOL-C%$$) in the $code build$$ directory. Note that this local install of Adolc requires ColPack; see $cref get_colpack.sh$$. In addition, the requirement that ColPack and Adolc are installed with the same prefix was added. $head 10-13$$ Make sure that all of the $cref/preprocessor symbols/cppad/Preprocessor Symbols/$$, that are not part of the CppAD API, are undefined when the $code $$ file concludes. $head 10-12$$ $list number$$ Change $cref get_eigen.sh$$ so that it will reuse install information when it is present. In addition document reuse for $cref/get_eigen.sh/get_eigen.sh/Reuse/$$, $cref/get_ipopt.sh/get_ipopt.sh/Reuse/$$, and $cref/get_sacado.sh/get_sacado.sh/Reuse/$$. $lnext Fix following $code g++$$ error on OSX system: $codep error: no match for 'operator|=' (operand types are 'std::vector::reference {aka std::_Bit_reference}' and 'bool') Check[i * n + j] |= F2[i * n + k] & r[ k * n + j]; ^ $$ $lend $head 09-20$$ $list number$$ Add lines for $cref atomic_base$$ function documentation to both the definition and use of each operation. This required adding sub-headings in the example usages corresponding to the function documentation sections. For example; see $cref/atomic forward examples/atomic_forward/Examples/$$. $lnext Improve the documentation for $cref atomic_base_clear$$ and remove its use from the $cref/atomic_base examples/atomic_base/Examples/$$ (because it is not needed). $lend $head 09-19$$ Add links from the $cref atomic_base$$ functions documentation to the corresponding examples. This required adding headings in the examples that correspond to the function documentation sections. For example; see $cref/atomic forward examples/atomic_forward/Examples/$$. $head 09-18$$ $list number$$ A segmentation fault would occur if an $cref ADFun$$ object used an $cref atomic$$ function that had been deleted. This has been fixed so that when $code NDEBUG$$ is not defined, an error message is generated. $lnext A mistake in the documentation for $cref/Memory and Parallel Mode/CppAD_vector/Memory and Parallel Mode/$$ has been fixed. This corresponds to the change in the specifications for $cref/CppAD::vector::resize/CppAD_vector/resize/$$ made on $cref/2012-07-30/whats_new_12/07-30/$$ $lnext There was a bug during the $cref/checking for nan/check_for_nan/$$ during $cref reverse$$ mode. This has been fixed. $lnext It appears, from inspecting the Ipopt source file $code Ipopt/src/Algorithm/IpIpoptAlg.cpp$$ that the option $code sb$$ to $code yes$$ suppress the printing of the Ipopt banner. The Ipopt examples and tests have been changed to use this option (although it is not in the ipopt documentation). $lnext Fix the a typo in the documentation for $code ipopt_solve$$ $cref/Integer/ipopt_solve/options/Integer/$$ options ($code Numeric$$ was changed to $code Integer$$). $lend $head 09-07$$ There was a bug in the cumulative sum operator (which is used by $cref optimize$$ ) for $cref Forward$$ orders greater than zero. This was detected by the $cref checkpoint$$ tests when $code optimize$$ was used to make the checkpoint functions faster. The bug has been fixed and the checkpoint functions now use optimize (and hence should be faster). $head 08-12$$ $list number$$ The ability to turn on and off checking for $cref nan$$ in $cref Forward$$ mode results has been added; see $cref check_for_nan$$. $lnext Use this option to remove the need to handel $code nan$$ as a special case in $cref checkpoint$$ functions that $cref/atomic functions/optimize/Atomic Functions/$$ in within another function is optimized. $lnext Check $cref/reverse/reverse_any/$$ mode results when $cref check_for_nan$$ is true. (It used to be the case that only $cref/forward/forward_order/$$ results were checked for $code nan$$.) $lend $head 08-11$$ If an $cref atomic$$ function had arguments that did not affect the final dependent variables in $icode f$$, $cref/f.optimize()/optimize/$$ would fail. This has been fixed. In addition, documentation about using $code optimize$$ with $cref/atomic functions/optimize/Atomic Functions/$$ has been added. $head 08-06$$ Fix a case where the test $code test_more/num_limits.cpp$$ failed because $codep double inf = std::numeric_limits::infinity(); double check = std::complex(inf) / std::complex(1.) $$ can result in the imaginary part of $code check$$ being $code - nan$$. $head 07-26$$ Allow for use of $code const::string&$$ as a possible type for $cref/name/atomic_ctor/atomic_base/name/$$ in the $code atomic_base$$ constructor. $head 05-28$$ Remove $icode ok$$ return flag from $cref/checkpoint algo/checkpoint/algo/$$ and $cref/checkpoint atom_fun/checkpoint/atom_fun/$$. $head 05-21$$ $list number$$ Deprecate the $cref old_atomic$$ interface and replace it by the $cref atomic_base$$ and $cref checkpoint$$ interfaces. $lnext There was a problem with the $cref cmake$$ command if the $cref/cppad_cxx_flags/cmake/cppad_cxx_flags/$$ was not specified. This has been fixed. $lend $head 05-17$$ $list number$$ Add the $cref/transpose/ForSparseJac/transpose/$$ option to $cref/ForSparseJac/$$. $lnext Add the $cref/transpose/RevSparseHes/transpose/$$ option to $cref/RevSparseHes/$$. $lend $head 05-15$$ Change $cref RevSparseJac$$ parameter names to be closer to the $cref ForSparseJac$$ names so the difference is clearer. $head 05-14$$ $list number$$ The $cref checkpoint$$ class has been added. This is a much easier way to do checkpointing than the old checkpoint example. The old checkpointing example is now the $cref reverse_checkpoint.cpp$$ example. $lnext Fix bug in $cref RevSparseJac$$ for case when $cref/q/RevSparseJac/q/$$ was not equal to $icode m$$ (range dimension) and sparsity pattern was a vector of $code bool$$. $lnext Add the $cref/transpose/RevSparseJac/transpose/$$ option to $cref/RevSparseJac/$$. $lend $head 05-12$$ The sparse hessian example in $cref old_reciprocal.cpp$$ was not being run. This has been fixed. $head 05-11$$ The $cref/old_atomic examples/old_atomic/Example/$$ names were all changed to begin with $code user$$. $head 05-04$$ The option to compute $cref/multiple orders/forward_order/xq/Multiple Orders/$$ was added. The $cref old_usead_2.cpp$$ example shows the need for this. The problem is that a new atomic function interface needs to be designed with checkpointing as a particular application. Multiple order forward mode is the first step in this direction. $head 04-28$$ $list number$$ The scripts $cref get_eigen.sh$$ and $cref get_sacado.sh$$ were added. If you are using Unix, and you do not have $href%http://eigen.tuxfamily.org%Eigen%$$ or $href%http://trilinos.sandia.gov/packages/sacado%Sacado%$$ installed on your system, you can use the corresponding script to download and install a local copy for use when testing CppAD. $lnext The code $codei%std::cout << %X%$$, would generate a compile error when $icode X$$ was an Eigen matrix with $codei%CppAD::AD<%Base%>%$$ elements. This has been fixed. $lend $head 04-27$$ There was a problem using the output operator $code <<$$ with and $cref/eigen/cppad_eigen.hpp/$$ matrix of $code AD$$ elements. This has been fixed using a template partial specialization of $codep template struct significant_decimals_default_impl $$ because the original template requires definition of a implicit conversion from the scalar type to an $code int$$ and this is dangerous for AD types (note that $cref Integer$$ is used for explicit conversions). $head 04-26$$ $list number$$ The example $cref old_usead_2.cpp$$ was completed. This is a more realistic, but also more complicated, example of using AD to computed derivatives inside an atomic function. $lnext The script $cref get_fadbad.sh$$ has been added. If you are using Unix, and you do not have $href%http://www.fadbad.com%FADBAD%$$ installed on your system, you can use this script to download and install a local copy for use when testing CppAD. $lend $end $head 04-20$$ The example $cref old_usead_1.cpp$$ was added. $head 04-16$$ The script $cref get_ipopt.sh$$ has been added. If you are using Unix, and you do not have $href%http://www.coin-or.org/projects/Ipopt.xml%Ipopt%$$ installed on your system, you can use this script to download and install a local copy for use when testing CppAD. $head 04-14$$ The following program, when executed, would cause a CppAD assertion with an unknown source: $codep # include int main(void) { size_t min_bytes = static_cast(-1); size_t cap_bytes; void *v_ptr = CppAD::thread_alloc::get_memory(min_bytes, cap_bytes); return 0; } $$ It now generates the following message, (when compiled without $cref/NDEBUG/faq/Speed/NDEBUG/$$)" $codep get_memory(min_bytes, cap_bytes): min_bytes is too large Error detected by false result for min_bytes < std::numeric_limits::max() / 2 $$ $head 03-02$$ The function $cref/isnan/nan/$$ no longer allows for systems that return false for $icode%x% != %x%$$ when $icode x$$ is $code NaN$$. This makes the $code isnan$$ function faster. In addition, it removes the need to store a static value which causes complications for parallel execution (as well as other problems). Thus, it is no longer necessary for the first call to $code isnan$$ to be during sequential execution and it has been removed from the multi-threading $cref/initialization/multi_thread/Initialization/$$ list. $head 03-01$$ Remove the $cref cmake$$ $code cppad_c11_flag$$ and instead automatically detect if the compiler supports specific c++11 features. $head 02-27$$ The test $cref num_limits.cpp$$ was failing during testing of Fedora-19; see $href%https://bugzilla.redhat.com/show_bug.cgi?id=913929% Bug 913929%$$. This has been fixed. $head 02-20$$ $list number$$ The documentation for the $cref cmake$$ install option $code cppad_test_vector_namespace$$ was fixed to be $cref/cppad_testvector/cmake/cppad_testvector/$$. This was also fixed for the $cref/eigen test vector/eigen_prefix/Test Vector/$$ documentation. $lnext An option to specify that the compiler supports c++11 constructs, $code cppad_c11_flag$$, was added to the $code cmake$$ command line. $lend $head 01-07$$ Fix undefined $code microsoft_timer$$ when building the $cref speed_example.cpp$$ program. $head 01-06$$ $list number$$ The $cref limits$$ documentation was corrected an improved. $lnext The $cref num_limits.cpp$$ example was simplified and restricted to just testing for $code AD$$. $lnext Testing for types other than $code AD$$ was moved to $code test_more/num_limits.cpp$$. In addition, $code test_more/num_limits.cpp$$ was modified to avoid the use of guard digits (and hence test failure) on more machines. $lend $head 01-05$$ $list number$$ The $cref num_limits.cpp$$ example was failing on some machines because they were using guard digits during calculations. This has been fixed by using vectors instead of scalars for storing values. $lnext The $cref speed_example.cpp$$ was not linking when using a shared object library for the code in $code speed/src$$. This has been fixed by not including the library when linking the speed examples. $lend $head 01-02$$ $list number$$ A new stable version of CppAD, for 2013, was created and its first release $code cppad-20130000.0$$ is available for download at $pre $$ $href%http://www.coin-or.org/download/source/CppAD/%$$ $lnext Advance version number for trunk to $code 20130102$$. $lend $head 01-01$$ When compiling with $cref/NDEBUG/Faq/Speed/NDEBUG/$$ defined, the following warning could be generated: $codei% %...%rev_sparse_jac.hpp:315:9: warning: unused variable 'm' [-Wunused-variable] %$$ This has been fixed. $end cppad-20170000.3/omh/whats_new/whats_new_05.omh0000644000175200017650000006603213057470463020234 0ustar coincoin-web$Id: whats_new_05.omh 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_05$$ $spell html Dir cppad.hpp acos asin autoconf ptr Erf CppADlib logdet valarray Jacobian bool yy mm dd pkzip gz Neg maxabs Romberg cos Le Lt Eq Ge Gt op gcc Cygwin std Lu CppADvector Jon Pearce namespace dsw dsp sln vcproj CondExp Microsoft inline scur Vec Rosen Runge-Kutta Linux typedef Cpp atan $$ $section Changes and Additions to CppAD During 2005$$ $head 12-24$$ Fix a memory leak that could occur during the $cref ForSparseJac$$ calculations. $head 12-23$$ The buffers that are used to do $cref RevSparseJac$$ and $cref RevSparseHes$$ calculations are now freed directly after use. $pre $$ The $cref TrackNewDel.cpp$$ example was missing from the Windows install examples and testing project file. This has been fixed. $head 12-22$$ The buffer that is are used to do $cref Reverse$$ mode calculations is now freed directly after use. This reduces the memory requirements attached to an $cref ADFun$$ object. $head 12-20$$ Buffers that are used to store the tape information corresponding to the $codei%AD<%Base%>%$$ type are now freed when the corresponding $cref ADFun$$ object is constructed. This reduces memory requirements and actually had better results with the $cref speed_cppad$$ tests. $pre $$ The $cref speed_cppad$$ test program now outputs the version of CppAD at the top (to help when comparing output between different versions). $head 12-19$$ The $cref TrackNewDel$$ routines were added for track memory allocation and deletion with $code new[]$$ and $code delete[]$$. This is in preparation for making CppAD more efficient in it's use of memory. The bug mentioned on $cref/12-01/whats_new_05/12-01/$$ resurfaced and the corresponding routine was changed as follows: $codep static local::ADTape *Tape(void) { // If we return &tape, instead of creating and returning ptr, // there seems to be a bug in g++ with -O2 option. static local::ADTape tape; static local::ADTape *ptr = &tape; return ptr; } $$ $head 12-16$$ The $cref NearEqual$$ function documentation for the relative error case was changed to $codei% | %x% - %y% | <= %r% * ( |%x%| + |%y%| ) %$$ so that there is no problem with division by zero when $icode x$$ and $icode y$$ are zero (the code was changed to that form also). The $code std::abs$$ function replaced the direct computation of the complex norms (for the complex case in $code NearEqual$$). In addition, more extensive testing was done in $cref near_equal.cpp$$. $head 12-15$$ Extend $cref NearEqual$$ and $cref NearEqualExt$$ to cover more cases while converting them from, a library function in $code lib/CppADlib.a$$ and an utility in $code example/NearEqualExt.h$$, to a template functions in $code cppad/near_equal.hpp$$ and $code cppad/local/NearEqualExt.h$$. This is another step along the way of removing the entire $code CppADlib.a$$ library. $pre $$ The change on $cref/12-14/whats_new_05/12-14/$$ broke the Microsoft project files $code example/Example.sln$$ and $code TestMore/TestMore.sln$$ used during CppAD installation on Windows. This has been fixed. $pre $$ Move $code lib/SpeedTest.cpp$$ to $code cppad/speed_test.hpp$$. This was the last change necessary in order to remove the CppAD library, so remove all commands related to building and linking $code CppADlib.a$$. The corresponding entry has been removed from the $cref wish_list$$. $pre $$ One of the entries in the $cref wish_list$$ corresponded to the $cref Integer$$ function. It has also been removed (because it is already implemented). $head 12-14$$ Extend $cref erf$$ to cover more cases while converting it from a function in $code lib/CppADlib.a$$ to a template function in $code cppad/local/Erf.h$$. This is one step along the way of removing the entire $code CppADlib.a$$ library. $head 12-11$$ Group routines that extend the domain for which an $cref ADFun$$ object is useful into the ExtendDomain section. $pre $$ Add an example of a C callable routine that computes derivatives using CppAD (see $cref interface2c.cpp$$). $head 12-08$$ Split out $cref LuFactor$$ with the $icode ratio$$ argument to a separate function called $cref LuRatio$$. This needed to be done because $cref LuRatio$$ is more restrictive and should not be part of the general template $cref/utilities/utility/$$. $head 12-07$$ Improve $cref CheckSimpleVector$$ so that it tests element assignment. Change $cref check_simple_vector.cpp$$ so that it provides and example and test of a case where a simple vector returns a type different from the element type and the element assignment returns $code void$$. $head 12-06$$ The specifications for a $cref SimpleVector$$ template class were extended so that the return type of an element access is not necessarily the same as the type of the elements. This enables us to include $code std::vector$$ which packs multiple elements into a single storage location and returns a special type on element access (not the same as $code bool$$). To be more specific, if $icode x$$ is a $code std::vector$$ object and $icode i$$ has type $code size_t$$, $icode%x%[%i%]%$$ does not have type $code bool$$. $pre $$ Add a Home icon, that links to the $href% http://www.coin-or.org/CppAD/% CppAD home page %$$, to the top left of the navigation frame (left frame) for each documentation section. $head 12-05$$ The $cref RevSparseHes$$ reverse mode Hessian sparsity calculation has been added. $pre $$ The definition of a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ has been corrected to properly correspond to the more efficient form mentioned under $cref/whats_new_05/whats_new_05/11-20/$$ below. $pre $$ The dates in this file used to correspond to local time for when the change was checked into the $href% http://projects.coin-or.org/CppAD/browser% subversion repository %$$. From now on the dates in this file will correspond to the first version of CppAD where the change appears; i.e., the date in the unix and windows download file names $codei%CppAD-%yy%-%mm%-%dd%$$. $head 12-03$$ There was a bug in the $cref RevSparseJac$$ reverse mode sparsity patterns when used with $cref VecAD$$ calculations. This bug was fixed and the calculations were made more efficient (fewer true entries). $head 12-02$$ There was a bug in the $cref ForSparseJac$$ forward mode sparsity patterns when used with $cref VecAD$$ calculations. This bug was fixed and the calculations were made more efficient (fewer true entries). $head 12-01$$ The speed test of $cref lu_vec_ad.cpp$$ has been reinstated. It appears that there is some sort of bug in the gcc compiler with the -O2 option whereby the following member function $codep static local::ADTape *Tape(void) { static local::ADTape tape; return &tape; } $$ (in $code cppad/local/AD.h$$) would sometimes return a null value (during $cref VecAD$$ operations). A speed improvement in $code cppad/local/ExtendBuffer.h$$ seems to prevent this problem. This fix is not well understood; i.e., we should watch to see if this problem reoccurs. $pre $$ The source code for $cref lu_vec_ad_ok.cpp$$ was mistakenly used for $code speed_cppad/LuSolveSpeed.cpp$$. This has been fixed. $head 11-23$$ The speed test of $cref lu_vec_ad.cpp$$ has been commented out because it sometimes generates a segmentation fault. Here is an explanation: $pre $$ If $icode X$$ is a $codei%AD<%Base%>%$$ object, $icode y$$ is a $icode Base$$ object, $icode%X%[%y%]%$$ uses pointer from the element back to the original vector. Optimizing compilers might reorder operations so that the vector is destroyed before the object is used. This can be avoided by changing the syntax for $cref VecAD$$ objects to use $code set$$ and $code get$$ member functions. $head 11-22$$ A much better $cref/example/vec_ad.cpp/$$ for using $cref VecAD$$ vectors has been provided. In addition, a bug in the computation of derivatives using $code VecAD$$ vectors has been fixed. $pre $$ CppAD now checks that the domain dimension during $cref Independent$$ and the range dimension during $cref ADFun$$ (provided that $code -DNDEBUG$$ is not defined). If either of these is zero, the $code CppADUsageError$$ macro is invoked. $head 11-20$$ The sparsity pattern routines $cref ForSparseJac$$ and $cref RevSparseJac$$ have been modified so that they are relative to the Jacobian at a single argument value. This enables us to return more efficient $cref/sparsity patterns/glossary/Sparsity Pattern/$$. $pre $$ An extra $cref/exception/VecAD/VecAD::reference/Exceptions/$$ has been added to the use of $cref VecAD$$ elements. This makes $code VecAD$$ some what more efficient. $head 11-19$$ Improve the output messages generated during execution of the $cref/configure/auto_tools/Configure/$$ command. $pre $$ Put a try and catch block around all of the uses of $code new$$ so that if a memory allocation error occurs, it will generate a $code CppADUsageError/$$ message. $pre $$ The $cref get_started.cpp$$ example has been simplified so that it is easier to understand. $head 11-15$$ Fix a memory leak in both the $cref ForSparseJac$$ and $cref RevSparseJac$$ calculations. $head 11-12$$ Add reverse mode $cref/Jacobian sparsity/RevSparseJac/$$ calculation. $head 11-09$$ Add prototype documentation for $cref/logdet/LuSolve/logdet/$$ in the $cref LuSolve$$ function. $pre $$ Add the optional $icode ratio$$ argument to the $cref LuFactor$$ routine. (This has since been moved to a separate routine called $cref LuRatio$$.) $head 11-07$$ Remove some blank lines from the example files listed directly below (under 11-06). Comments for computing the entire Jacobian $cref/entire sparsity pattern/ForSparseJac/Entire Sparsity Pattern/$$ was added. $head 11-06$$ The cases of $code std::vector$$, $code std::valarray$$, and $code CppAD::vector$$ were folded into the standard example and tests format for the following cases: $cref rev_two.cpp$$, $cref rev_one.cpp$$, $code Reverse.cpp$$, $cref hessian.cpp$$, $cref jacobian.cpp$$, $cref forward.cpp$$, $cref for_two.cpp$$, $cref for_one.cpp$$, $code Fun.cpp$$ ($code Fun.cpp$$ has since been replaced by $cref independent.cpp$$, $code Reverse.cpp$$ has since been replaced by $cref reverse_one.cpp$$ and $code reverse_checkpoint.cpp$$). $head 11-01$$ Add forward mode $cref/Jacobian sparsity/ForSparseJac/$$ calculation. $head 10-20$$ Add $cref/sparsity patterns/glossary/Sparsity Pattern/$$ to the whish list. $head 10-18$$ The Unix install $cref/configure/auto_tools/Configure/$$ command was missing the $code --$$ before of the $code prefix$$ command line argument. $head 10-14$$ The template class $cref CppAD_vector$$ uses a try/catch block during the allocation of memory (for error reporting). This may be slow down memory allocation and hence it is now replaced by simple memory allocation when the preprocessor variable $code NDEBUG$$ is defined. $pre $$ The specialization of $code CppAD::vector$$ was moved to $cref/vectorBool/CppAD_vector/vectorBool/$$ so that $code CppAD::vector$$ does not pack one bit per value (which can be slow to access). $head 10-12$$ Change the $cref/configure/auto_tools/Configure/$$ script so that compilation of the $cref get_started.cpp$$ and $cref print_for_cout.cpp$$ examples are optional. $pre $$ One of the dates in the Unix installation extraction discussion was out of date. This has been fixed. $head 10-06$$ Change the Unix install $code configure$$ script so that is reports information using the same order and notation as its $cref/documentation/auto_tools/Configure/$$. $pre $$ Some compiler errors in the $cref ode_gear_control.cpp$$ and $cref ode_stiff.cpp$$ examples were fixed. $head 09-29$$ Add a specialization to $cref CppAD_vector$$ for the $code CppAD::vector$$ case. A test for the $code push_back$$ member function as well as a $cref CheckSimpleVector$$ test has been added to $cref cppad_vector.cpp$$. The source code for this template vector class, $code cppad/vector.hpp$$, has been removed from the documentation. $head 09-27$$ Add the $cref/prefix_dir/auto_tools/prefix_dir/$$ and $icode postfix_dir$$ ($icode postfix_dir$$ has since been removed) options to the $code configure$$ command line. This gives the user more control over the location where CppAD is installed. $head 09-24$$ The stiff Ode routines, $cref OdeGear$$ and $cref OdeGearControl$$, were added to the $cref/utilities/utility/$$. A comparison various Ode solvers on a stiff problem $cref ode_stiff.cpp$$ was added. In addition, $code OdeGear$$ and $code OdeGearControl$$ were added to the $cref/utilities/utility/$$ and the library was reorganized. $head 09-20$$ The Microsoft compiler project files $code example/Example.vcproj$$ and $code TestMore/TestMore.vcproj$$ were not up to date. This has been fixed. In addition, the example $cref numeric_type.cpp$$ has been added. $pre $$ Make the building of the $code Example$$, $code TestMore$$, and $code Speed$$, directories optional during the $cref/configure/auto_tools/Configure/$$ command. The $cref/Unix installation instructions/auto_tools/$$ were overhauled to make the larger set of options easy to understand. $head 09-14$$ Added the $cref NumericType$$ concept and made the following library routines require this concept for their floating point template parameter type: $cref LuSolve$$, $cref LuFactor$$, $cref RombergOne$$, $cref RombergMul$$, $cref Runge45$$, $cref Rosen34$$, and $cref OdeErrControl$$. This is more restrictive than the previous requirements for these routines but it enables future changes to the implementation of these routines (for optimization purposes) with out affecting their specifications. $head 09-09$$ Add the $cref UnaryPlus$$ operator and move the $code Neg$$ examples and tests to $cref UnaryMinus$$. $head 09-07$$ Change name of distribution files from $code CppAD.unix.tar.gz$$ and $code CppAD.dos.tar.gz$$ to $codei%CppAD-%yy%-%mm%-%dd%.tar.gz%$$ and $codei%CppAD-%yy%-%mm%-%dd%.zip%$$ (the $icode%*%.zip%$$ file uses pkzip compression). $head 08-30$$ The $icode maxabs$$ argument has been added to the $cref OdeErrControl$$ function so that it can be used with relative errors where components of the ODE solution may be zero (some of the time). In addition, some of the rest of the OdeErrControl documentation has been improved. $pre $$ The documentation for replacing defaults in CppAD error macros has been improved. $head 08-24$$ Changed $code Romberg$$ to $cref RombergOne$$ and added $cref RombergMul$$. In addition, added missing entries to $cref ListAllExamples$$ and reorganized $cref/utilities/utility/$$. $head 08-20$$ Backed out addition of $code Romberg$$ integration routine (at this point uncertain of the interface that is most useful in the context of AD.) $head 08-19$$ Added a $code Romberg$$ integration routine for where the argument types are template parameters (for use with AD types). $head 08-15$$ The Microsoft project files $code example/Example.vcproj$$ and $code TestMore/TestMore.vcproj$$ were missing some necessary routines. In addition, $code Speed/Speed.vcproj$$ was generating a warning. This has been fixed. $head 08-14$$ An $cref Integer$$ conversion function as been added. $pre $$ The $cref value.cpp$$ example has been improved and the old example has been moved into the $code TestMore$$ directory. $head 08-13$$ The $cref unary_standard_math$$ functions $code sinh$$, and $code cosh$$ have been added. In addition, more correctness testing has been added for the $code sin$$ and $code cos$$ functions. $pre $$ The $cref OdeErrControl$$ routine could lock in an infinite loop. This has been fixed and a test case has been added to check for this problem. $head 08-07$$ The $cref/conditional expression/CondExp/$$ function has been changed from just $code CondExp$$ to $code CondExpLt$$, $code CondExpLe$$, $code CondExpEq$$, $code CondExpGe$$, $code CondExpGt$$. This should make code with conditional expressions easier to understand. In addition, it should reduce the number of tape operations because one need not create as many temporaries to do comparisons with. The old $code CondExp$$ function has been deprecated. $head 07-21$$ Remove unnecessary no-op that was left in tape for the $cref unary_standard_math$$ functions $code acos$$, $code asin$$, $code atan$$, $code cos$$. $pre $$ Improve the index entries in the documentation that corresponds to the $code cppad/local$$ directory source code. $head 07-19$$ The $cref wish_list$$ and $code Bugs$$ information were moved out of this section and into their own separate sections (the Bugs section has been removed; see the $code bug$$ subdirectory instead). $pre $$ A discussion of $cref/VecAD speed and memory/VecAD/Speed and Memory/$$ was added as well as an entry in the $cref wish_list$$ to make it more efficient. $head 07-15$$ The $code BOOST_DIR$$ and $code CPP_ERROR_WARN$$ $cref/configure/auto_tools/Configure/$$ options were not properly implemented for compiling the $code lib$$ sub-directory. This has been fixed. $pre $$ Some compiler warnings in the file $code lib/ErrFun.cpp$$, which computes the $cref erf$$ function, have been fixed. $head 07-11$$ The $cref/push_back/CppAD_vector/push_back/$$ function has been added to the $code CppAD::vector$$ template class. $pre $$ It appears that the $code TestMore/Runge45.cpp$$ file was missing an include of $code example/NearEqualExt.h$$. This has been fixed. $head 07-08$$ The documentation for $cref Forward$$ and $cref Reverse$$ has been improved. $head 07-05$$ The $cref rosen_34.cpp$$ example mixed the $cref/CppAD::vector/CppAD_vector/$$ and $code CppADvector$$ vector types. This caused the compilation of the examples to fail when $code CppADvector$$ was defined as something other than $code CppAD::vector$$ (found by Jon Pearce). This has been fixed. $pre $$ The $cref CheckSimpleVector$$ run time code has been improved so that it is only run once per case that is being checked. $pre $$ Simple Vector concept checking ($cref CheckSimpleVector$$) was added to the routines: $cref ForOne$$, $cref ForTwo$$, $cref Forward$$, $cref ADFun$$, $cref Hessian$$, $cref Independent$$, $cref Jacobian$$, $cref RevOne$$, $cref RevTwo$$, and $cref Reverse$$. $head 07-04$$ Simple Vector concept checking ($cref CheckSimpleVector$$) was added to the routines: $cref LuFactor$$, $cref LuSolve$$, $cref LuInvert$$, $cref OdeErrControl$$, $cref Runge45$$, and $cref Rosen34$$. $pre $$ The previous version of the routine $cref OdeErrControl$$ was mistakenly in the global namespace. It has been moved to the $code CppAD$$ namespace (where all the other $cref/utilities/utility/$$ routines are). $pre $$ The previous distribution (version 05-07-02) was missing the file $code cppad/local/Default.h$$. This has been fixed. $head 07-03$$ Added $cref CheckSimpleVector$$, a C++ concept checking utility that checks if a vector type has all the necessary conditions to be a $cref SimpleVector$$ class with a specific element type. $head 07-02$$ Version 7 of Microsoft's C++ compiler supports the standard declaration for a friend template function. Version 6 did not and CppAD used macros to substitute the empty string for $code $$, $code < AD >$$, and $code < VecAD >$$ in these declarations. These macro substitutions have been removed because Version 6 of Microsoft's C++ compiler is no longer supported by CppAD. $pre $$ The copy base section was split into the default constructor and the construction for the base type. The construction from base type has been extended to include any type that is convertible to the base type. As a special case, this provides the previous wish list item of a constructor from an arbitrary $icode Base$$ to a $codei%AD< AD<%Base%> >%$$, $codei%AD< AD< AD<%Base%> > >%$$ etc. $head 07-01$$ The permissions were set as executable for many of the no-executable files in the distribution; for example, the $code README$$, file. This has been fixed. $head 06-25$$ Some improvements were made to the README, AUTHORS, COPYING, and INSTALL files. In addition, the file $code UWCopy040507.html$$ which contains the University of Washington's copyright policy (see Section 2) was added to the distribution. $head 06-24$$ The $code List2Vector$$ $cref/example utility/ExampleUtility/$$ is no longer used and has been removed. $head 06-18$$ CppAD is now supported by Microsoft Visual C++ version 7 or higher. The version 6 project files $icode%*%.dsw%$$ and $icode%*%.dsp%$$ have been replaced by the version 7 project files $icode%*%.sln%$$ and $icode%*%.vcproj%$$. $head 06-14$$ A new $cref/CondExp example/cond_exp.cpp/$$ has been added and the old $cref CondExp$$ example has been moved to the $code TestMore$$ directory (it is now only a test). $head 06-13$$ The changes made on 06-06 do not run under Microsoft Visual C++ version 6.0 (even though they are within the C++ standard). Preliminary testing under version 7 indicates that Microsoft has fixed this problem in later versions of their C++ compiler. $head 06-06$$ Converted the routines $cref Forward$$ and $cref Reverse$$ to allow for any $cref SimpleVector$$ instead of just $code CppADvector$$. In addition, separated the syntax of the function call from the prototype for each of the arguments. This was also done for all the easy to use $cref Drivers$$ as well as the $cref Independent$$ function and the $cref ADFun$$ constructor. $pre $$ Add a section containing a list of $cref/all the examples/ListAllExamples/$$. $head 05-19$$ A significant improvement in speed was obtained by moving the buffer extension to a separate function and then inline the rest of putting operators in the tape. For example, here is part of the speed test output before this change: $codep Tape of Expansion by Minors Determinant: Length = 350, Memory = 6792 size = 5 rate = 230 size = 4 rate = 1,055 size = 3 rate = 3,408 size = 2 rate = 7,571 size = 1 rate = 13,642 $$ and here is the same output after this change: $codep Tape of Expansion by Minors Determinant: Length = 350, Memory = 6792 size = 5 rate = 448 size = 4 rate = 2,004 size = 3 rate = 5,761 size = 2 rate = 10,221 size = 1 rate = 14,734 $$ Note that your results will vary depending on operating system and machine. $head 05-18$$ Change name of $code OdeControl$$ to $cref OdeErrControl$$ and improve its documentation. $pre $$ Correct the syntax for the $cref/Parameter and Variable/ParVar/$$ functions. $head 05-16$$ Change $cref OdeErrControl$$ to have method return its order instead of having a separate argument to $code OdeErrControl$$. $pre $$ Add the argument $icode scur$$ to $code OdeErrControl$$, improve $code OdeErrControl$$ choice of step size and documentation. $head 05-12$$ Using profiling, the $cref/multiplication operator/ad_binary/$$ was show to take a significant amount of time. It was reorganized in order to make it faster. The profiling indicated an improvement so that same change was made to the $cref ad_binary$$ and $cref compute_assign$$ operators. $head 05-06$$ The documentation for $cref SimpleVector$$ and $cref NearEqual$$ were changed to use more syntax (what the user enters) and simpler prototypes (the compiler oriented description of the arguments). In addition, exercises were added at the end of the $cref SimpleVector$$, $cref CppAD_vector$$, and $cref NearEqual$$ documentation. $pre $$ There was a undesired divide by zero case in the file $code TestMore/VecUnary.cpp$$ that just happened to work in corresponding $cref NearEqual$$ check. The $code NearEqual$$ routine has been changed to return false if either of the values being compared is infinite or not a number. In addition, the divide by zero has been removed from the $code TestMore/VecUnary.cpp$$ test. $head 05-01$$ The doubly linked list was also removed from the $cref VecAD$$ internal data structure because this method of coding is simpler and it makes it more like the rest of CppAD. $head 04-21$$ The profiling indicated that the destructor for an AD object was using a significant amount of time. The internal data structure of an AD object had a doubly linked list that pointed to the current variables and this was modified when an AD object was destroyed. In order to speed AD operations in general, the internal data structure of an AD object has been changed so that this list is no longer necessary (a tape id number is used in its place) $pre $$ During the process above, the function $cref/Variable/ParVar/$$ was added. $head 04-20$$ Add $cref/profiling/auto_tools/Profiling CppAD/$$ to the speed tests. $head 04-19$$ Remove an extra (not necessary) semi-colon from the file $code cppad/local/Operator.h$$. $head 03-26$$ The new routine $cref OdeErrControl$$ does automatic step size control for the ODE solvers. $head 03-23$$ The routine $cref Rosen34$$ is an improved stiff integration method that has an optional error estimate in the calling sequence. You must change all your calls to $code OdeImplicit$$ to use $code Rosen34$$ (but do not need to change other arguments because error estimate is optional). $head 03-22$$ The routine $cref Runge45$$ is an improved Runge-Kutta method that has an optional error estimate in the calling sequence. You must change all your calls to $code OdeRunge$$ to use $code Runge45$$ (but do not need to change other arguments because error estimate is optional). $head 03-09$$ Some extra semi-colons (empty statements) were generating warnings on some compilers. The ones that occurred after the macros $code CppADStandardMathBinaryFun$$, $code CppADCompareMember$$, $code CppADBinaryMember$$, and $code CppADFoldBinaryOperator$$ have been removed. $head 03-04$$ An new multiple level of AD example $cref mul_level$$ was added. $head 03-01$$ An option that specifies error and warning $cref/flags/auto_tools/cxx_flags/$$ for all the C++ compile commands, was added to the $cref/Unix installation instructions/auto_tools/$$. $head 02-24$$ The routine $cref LuSolve$$ was split into $cref LuFactor$$ and $cref LuInvert$$. This enables one to efficiently solve equations where the matrix does not change and the right hand side for one equation depends on the left hand side for a previous equation. $pre $$ An extra requirement was added to the $cref SimpleVector$$ template class. There must be a typedef for $code value_type$$ which is the type of elements in the vector $pre $$ Under Mandrake Linux 10.1, some template friend declarations were failing because the corresponding operations were not declared before being indicated as friends (found by $href%mailto:Jean-Pierre.Dussault@Usherbrooke.ca%Jean-Pierre Dussault%$$). This has been fixed. $head 01-08$$ The $cref erf$$ function was added. The implementation of this function used conditional expressions ($cref CondExp$$) and some times the expression that was not valid in a region caused division by zero. For this reason, the check and abort on division by zero has been removed. $end cppad-20170000.3/omh/whats_new/whats_new_14.omh0000644000175200017650000003402213057470463020226 0ustar coincoin-web$Id: whats_new_14.omh 3796 2016-03-02 05:55:58Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_14$$ $dollar @$$ $spell cstdint addr omhelp autoconf automake alloc ifndef asin acos uj op hpp taylor forwardzero forwardone forwardany const doxygen ipopt adolc colpack Jacobian openmp pthread bthread isnan onetape retape fadbad sacado boolsparsity cmake docdir CppAD cppad datadir erf cmath ctor std num $$ $section CppAD Changes and Additions During 2014$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2014 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-30$$ There was a bug in the $cref cmake$$ whereby it would sometimes mistakenly exit with the error message $codep cppad_max_num_threads is not an integer greater than or equal 4 $$ This has been fixed. $head 12-29$$ The example $code not_complex_ad.cpp$$ was using the type $codei% std::complex< CppAD::AD > %$$ and was failing to compile with the $code clang$$ complier. This example has been removed because it is not consistent with the C++ standard; see $cref/complex FAQ/faq/Complex Types/$$. $head 12-28$$ $list number$$ Fix some warnings generated by clang 3.5 about local functions that were not being used; e.g., sub-tests that were not being executed. $lnext Fix $code cmake$$ setting $code cppad_implicit_ctor_from_any_type$$ Note that this cmake option has since been replaced by $cref/cppad_deprecated/cmake/cppad_deprecated/$$. $lnext The $code clang++$$ compiler was optimizing out the calculations in the $cref time_test.cpp$$ and $cref speed_test.cpp$$ examples. This caused these tests to hang while trying to determine how many times to repeat the test. This has been fixed. $lend $head 12-27$$ More work on the bug in $cref/optimizing/CondExp/Optimize/$$ conditional expressions. $head 12-26$$ A minimal example for computing cross terms in atomic operation Hessian sparsity patterns $cref atomic_rev_sparse_hes.cpp$$ was added. $head 12-25$$ More work on the bug in $cref/optimizing/CondExp/Optimize/$$ conditional expressions. $head 12-23$$ The c++11 standard includes the error function $cref erf$$ in $code cmath$$. If the c++ compiler has the error function defined in $code cmath$$, the complier version of the error function is used and it corresponds to an atomic operation. $pre $$ Fix typo in tangent reverse mode theory for $cref/Positive Orders/tan_reverse/Positive Orders Z(t)/$$. $head 12-22$$ There was a bug related to $cref/optimizing/CondExp/Optimize/$$ conditional expressions. This has been fixed. $head 12-17$$ Fix some compiler warnings and $cref speed$$ program names when using the deprecated $cref/auto-tools/auto_tools/$$ install procedure. $head 12-16$$ If the $code c++11$$ include file $code $$ defines all the standard types, they can be used by to specify $cref/cppad_tape_addr_type/cmake/cppad_tape_addr_type/cstdint/$$ and $cref/cppad_tape_id_type/cmake/cppad_tape_id_type/cstdint/$$. $head 12-15$$ Correct the title and $cref _index$$ entries for $cref forward_two$$ from first to second order. $head 11-28$$ Improve the $cref/index/_index/$$ and $code search$$ using a new version of the $code omhelp$$ documentation tool. $head 11-27$$ $list number$$ Add alignment to the $cref/get_memory/ta_get_memory/Alignment/$$ and $cref/create_array/ta_create_array/Alignment/$$ specifications and $cref/thread_alloc example/thread_alloc.cpp/$$. $lnext Advance the deprecated $cref/unix install/auto_tools/$$ utilities to autoconf-2.69 and automake-1.13.4. $lend $head 09-28$$ Fix more bugs related to optimizing condition conditional expressions. $list number$$ Using old instead of new operator indices. $lnext Not properly following dependence back through atomic operations. $lnext Aborting during forward order zero, when skipping computation for a variable that was already completed (the skip is still useful for higher orders and for reverse mode). $lnext Reverse mode not properly handling the variable number of arguments in the conditional skip operation. $lnext Reverse mode tracing not properly handling the variable number of argument operations; i.e., conditional skip and cumulative summation. $lend $head 09-27$$ Fix a bug that occurred when $cref/f.optimize/optimize/$$ was used with a function $icode f$$ that contained calls to user defined $cref atomic$$ operations and $cref/conditional expressions/CondExp/$$. $head 09-25$$ Fix a bug that occurred when $cref/f.optimize/optimize/$$ was used with a function $icode f$$ that contained $cref discrete$$ functions. $head 09-21$$ Fix a typo in documentation for $cref/any order reverse/reverse_any/$$. To be specific, $latex x^{(k)}$$ was changed to be $latex u^{(k)}$$. $head 05-28$$ $list number$$ Change the $cref/boolsparsity/speed_main/Sparsity Options/boolsparsity/$$ so that it only affects the sparsity speed tests $cref/sparse_jacobian/link_sparse_jacobian/$$ and $cref/sparse_hessian/link_sparse_hessian/$$; i.e., it is now ignored by the other tests. $lnext Improve the $cref speed$$ documentation page. $lend $head 05-27$$ $list number$$ The $code cppad_colpack.cpp$$ file was not being copied to the specified directory. In addition, the specified directory was changed from an include directory to data directory because $code cppad_colpack.cpp$$ is not an include file. $lnext If $cref colpack_prefix$$ was specified, the CppAD $cref pkgconfig$$ file was missing some information. This has been fixed. $lend $head 05-23$$ The $cref speed$$ test instructions were converted from using the old auto-tools $cref/unix install/auto_tools/$$ instructions to use the $cref cmake$$ install instructions. These instructions should work on any system, not just unix. $head 05-22$$ $list number$$ Add multiple direction for mode $cref forward_dir$$ and use it to speed up the forward version of $cref sparse_jacobian$$. Below is an example run of $cref cppad_sparse_jacobian.cpp$$ results before this change: $codep cppad_sparse_jacobian_size = [ 100, 400, 900, 1600, 2500 ] cppad_sparse_jacobian_rate = [ 2973, 431.94, 142.25, 78.64, 26.87 ] $$ and after this change: $codep cppad_sparse_jacobian_size = [ 100, 400, 900, 1600, 2500 ] cppad_sparse_jacobian_rate = [ 6389, 954.26, 314.04, 180.06, 56.95 ] $$ Due to the success of this change, $code multiple direction$$ items were added to the wish list (they were later removed). $lnext Improve the forward mode tracing of arguments to, and results from, user defined $cref atomic$$ operations. $lend $head 05-20$$ $list number$$ Move $code speed/adolc/alloc_mat.hpp$$ to $code speed/adolc/adolc_alloc_mat.hpp$$ so it has the same name is its $code # ifndef$$ command. $lnext Fix $code # ifndef$$ command in $code cppad/ipopt/solve_callback.hpp$$. $lnext Add $code # ifndef$$ command to $code test_more/extern_value.hpp$$. $lend $head 05-19$$ In the files $code cppad/local/asin_op.hpp$$ and $code cppad/local/acos_op.hpp$$ there were assignments of the form $code uj = 0.$$ where $code u_j$$ has type $cref/Base/glossary/Base Type/$$. These may have not be defined operations in certain cases and have been converted to $code uj = Base(0)$$. $head 05-16$$ There was a mistake in printing the arguments for $code CSumOp$$ and $code CSkipOp$$ when using the undocumented $code TRACE$$ option during forward mode (available in files of the form $codei%cppad/local/%*%sweep.hpp/%$$). This has been fixed. $head 05-14$$ $list number$$ There were some global variables in the file $code cppad/local/op_code.hpp$$ that might have caused multiple definitions during link time for CppAD applications. These variables have been changed to be local so that this cannot happen. $lnext There was a mistaken assert that the number of arguments for the $code BeginOp$$ was zero that caused an abort when using the undocumented $code TRACE$$ option available in files of the form $codei%cppad/local/%*%sweep.hpp/%$$. This has been fixed. $lend $head 03-18$$ $list number$$ The $cref/size_taylor/FunDeprecated/size_taylor/$$ and $cref/capacity_taylor/FunDeprecated/capacity_taylor/$$ functions were deprecated; use $cref size_order$$ and $cref capacity_order$$ instead. $lnext The documentation for $cref forward$$ and the examples $cref forward.cpp$$, $cref forward_order.cpp$$, have been improved. To be more specific, $cref forward_order$$ now references the special cases $cref forward_zero$$, $cref forward_one$$ and the new case $cref forward_two$$. $lend $head 03-17$$ The $cref/move semantics/CppAD_vector/Assignment/Move Semantics/$$ version of the $code CppAD::vector$$ assignment statement was not checking vector sizes. This has been fixed so that things work the same with compilers that do not have move semantics. (Note that with move semantics, no extra memory allocation is done even if the target vector has a different size.) $head 03-09$$ The documentation links $code forwardzero$$, $code forwardone$$, and $code forwardany$$ have been changed to $cref forward_zero$$, $cref forward_one$$, and $cref forward_order$$ respectively. This may affect links from other web pages to the CppAD documentation. $head 03-05$$ The names $icode p$$ and $icode q$$ in the $cref/forward/forward_order/$$, $cref/reverse/reverse_any/$$, $cref atomic_forward$$, and $cref atomic_reverse$$ functions were reverse so that $icode%p% <= %q%$$. This is only a notational change to make the arguments easier to remember. $head 03-02$$ $list number$$ In the output for the speed $cref/correct/speed_main/test/correct/$$ test, mention which tests are not available. Note that the set of available tests can depend on the $cref/list of options/speed_main/Global Options/$$. $lnext In the documentation for $cref/n_sweep/sparse_jacobian/n_sweep/$$, mention that it is equal to the number of colors determined by the $cref/color_method/sparse_jacobian/work/color_method/$$. $lnext The $cref speed_cppad$$ tests were simplified by removing the printing of auxillary information related to the $cref/optimize/speed_main/Global Options/optimize/$$ option. Future auxillary information will be passed back in a manner similar to $cref/n_sweep/link_sparse_jacobian/n_sweep/$$ for the sparse jacobian test. $lnext $cref/Move semantics/CppAD_vector/Assignment/Move Semantics/$$ were added to the $code CppAD::vector$$ assignment operator. $lend $head 03-01$$ $list number$$ Change the prototype for $icode row$$ and $icode col$$ in the $cref link_sparse_jacobian$$ speed test to be $code const$$; i.e., they are not changed. $lnext Move $icode x$$ near end of $cref link_sparse_hessian$$ speed test parameter list, (as is the case for $cref link_sparse_jacobian$$). $lend $head 02-28$$ The $cref/data/CppAD_vector/data/$$ function was added to the $code CppAD::vector$$ template class. $head 02-27$$ The CppAD developer documentation for the subdirectory $code cppad/ipopt$$ was not being built by the command $code bin/run_doxygen.sh$$. This has been fixed. $head 02-26$$ $list number$$ The $cref/adolc/speed_adolc/$$ and $cref/cppad/speed_cppad/$$ sparse jacobian speed tests now print out $cref/n_sweep/sparse_jacobian/n_sweep/$$. $lnext The size of some of the $cref speed$$ test cases has been increased to test behavior for larger problems. $lnext A link to $cref ode_evaluate$$ was missing in the $cref/Speed Utility Routines/speed_utility/Speed Utility Routines/$$ table. This has been fixed. $lend $head 02-23$$ The $cref/color_method/sparse_jacobian/work/color_method/$$ option was added to the sparse Jacobian calculations. This enables one to use $cref/ColPack/colpack_prefix/$$ do color the rows or columns. The speed test $cref/colpack/speed_main/Sparsity Options/colpack/$$ option was also added (but not yet implemented for $cref/sparse_hessian/link_sparse_hessian/$$ speed tests). $head 02-22$$ The program names in $cref thread_test.cpp$$ where changes from $icode%threading%_test%$$ to $codei%multi_thread_%threading%$$ where $icode threading$$ is $code openmp$$, $code pthread$$ or $code bthread$$. $head 02-17$$ Fix ambiguous call to $cref/isnan/nan/isnan/$$ during MS Visual Studio 2012 compilation. $head 02-15$$ $list number$$ The $cref/boolsparsity/speed_main/Sparsity Options/boolsparsity/$$ option was added to the $cref speed_main$$ program. $lnext The $code retape$$ option what changed to $cref/onetape/speed_main/Global Options/onetape/$$ so that the default is to retape (option not present). This was done because $cref/fadbad/fadbad_prefix/$$ and $cref/sacado/sacado_prefix/$$ always retape. $lnext The documentation, and example source code, for all the speed $cref/options/speed_main/Global Options/$$ was improved (made clearer). $lnext Improve the success rate for $cref speed_test.cpp$$ and $cref time_test.cpp$$. $lend $head 01-26$$ The destination directory for the $cref/cppad documentation/cmake/cmake_install_docdir/$$ is now set separately from the data directory using the $code cmake$$ option $codei% -D cmake_install_docdir=%cmake_install_docdir% %$$ This has increased the flexibility of the documentation installation and removed the need for the option $codei% -D cppad_documentation=%yes_or_no% %$$ which has been removed. $head 01-21$$ The destination directory for the cppad documentation used to be one of the following: $codei% %prefix%/%datadir%/doc/cppad-%version% %prefix%/%datadir%/doc/%postfix%cppad-%version% %$$ This has been changed by dropping the $icode version$$ number at the end of the directory name. $head 01-10$$ The change on $cref/2013-12-27/whats_new_13/12-27/$$ caused a conversion error in $cref atan2$$ when it was used with $code AD< AD >$$ arguments (and other similar cases). This has been fixed. $end cppad-20170000.3/omh/whats_new/whats_new_06.omh0000644000175200017650000010204013057470463020223 0ustar coincoin-web$Id: whats_new_06.omh 3768 2015-12-28 18:58:35Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_06$$ $spell speedtest apx exp_eps Alloc fadbad exp Dir Romberg yyyymmdd yy-mm-dd Det cppad Adolc Makefile omh config.h Microsoft hpp valgrind memcheck Kasper Kristensen taylor BAvector fy uninitialized Tautschnig resize gcc var const dw VecADelem atan namespace Cygwin messaging usr aclocal automake autoconf user underquoted Hes Jac CppAD sed gprof Mul.h Div.h det_lu $$ $section Changes and Additions to CppAD During 2006$$ $mindex aclocal$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2006 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-24$$ Move $code exp_eps_ad$$ to $code exp_eps_cppad$$ and add exercises to the following sections: $cref exp_eps_rev1$$, $cref exp_eps_cppad$$. $pre $$ Add operation sequence indices to help track operations in $cref exp_eps_for0$$, $cref exp_eps_for1$$, $cref exp_eps_rev1$$. $head 12-23$$ Add exercises to the following sections: $cref get_started.cpp$$, $cref exp_eps$$, $cref exp_eps_for0$$, and $cref exp_eps_for1$$. $head 12-22$$ Move $cref get_started.cpp$$ below the $cref introduction$$ directory. $pre $$ Move the exponential example to the subdirectory $code introduction/exp_apx$$ and change the $code --with-Introduction$$ unix configure option to build both the $cref get_started.cpp$$ and $cref exp_apx_main.cpp$$ example programs. (The $code --with-GetStarted$$ configure command line option has been removed.) $head 12-21$$ Add the $cref/source code for Poly/poly.hpp/$$ to the documentation and include $cref Poly$$ in the in the $cref speed_utility$$ section. $pre $$ The $cref get_started.cpp$$ section has been moved into the $cref Introduction$$ and $cref/exercises/get_started.cpp/Exercises/$$ were added to that section. In addition some sections has switched position between the top level $cref CppAD$$ and the $cref Appendix$$. $head 12-19$$ Reorganize so that the source code is below the corresponding routine in the documentation tree (instead of at the same level) for the following routines: $cref det_by_minor$$, $cref det_grad_33$$, $cref uniform_01$$, $cref det_of_minor$$, $cref det_by_lu$$, $cref LuInvert$$, $cref LuFactor$$, $cref LuSolve$$. $pre $$ Separate the specifications for the source in $cref speed_utility$$ and add cross reference to the following routine specification and implementations: $cref det_by_minor$$, $cref det_grad_33$$, $cref uniform_01$$, $cref det_of_minor$$, $cref det_by_lu$$, $cref LuInvert$$, $cref LuFactor$$, $cref LuSolve$$. $head 12-18$$ Make the $cref speed$$ source code easier to read. $pre $$ Change the speed test output name $code det_poly$$ to $code poly$$ (as it should have been). $head 12-17$$ The speed test $cref det_grad_33$$ was missing its documentation (this has been fixed). In addition, the titles and indexing for the speed test documentation has been improved. $pre $$ Add to the specifications that each repeated test corresponds to a different matrix in $cref/det_lu/link_det_lu/$$ and $cref/det_minor/link_det_minor/$$. In addition, modify all the speed tests so that they abide by this rule. $pre $$ Change some references from the deprecated name $code CppAD.h$$ to new name $code cppad.hpp$$. $pre $$ Change $cref adolc_det_minor.cpp$$ and $cref cppad_det_minor.cpp$$ to tape once and reuse operation sequence for each repeated matrix in the test. $pre $$ Add the $cref/poly/link_poly/$$ speed test for all three packages. In addition, correct a missing include in $cref poly$$ routine. $head 12-15$$ The wish list item to simplify and better organize the speed tests been completed: $table $cref|speed/|speed|$$ $cnext template functions that are speed tested $rnext $code speed/example$$ $cnext example usage of speed template functions $rnext $cref|speed/adolc|speed_adolc|$$ $cnext Adolc drivers for the template functions $rnext $cref|speed/cppad|speed_cppad|$$ $cnext CppAD drivers for the template functions $rnext $cref|speed/fadbad|speed_fadbad|$$ $cnext Fadbad drivers for the template functions $rnext $cref|speed/profile|auto_tools|Profiling CppAD|$$ $cnext profiling version of CppAD drivers $tend $head 12-13$$ Next step for the speed wish list item: remove $code speed_cppad$$ from the documentation and replace it by $code speed/cppad$$, see $cref speed_cppad$$ for the new CppAD speed test routines. $head 12-12$$ Started the speed wish list item by move the $code adolc$$ director to $code speed/adolc$$ and $code fadbad$$ to $code speed/fadbad$$. $head 12-11$$ Started the speed wish list item by creating the $code speed/example$$ directory and moving the relevant examples from $codei%example/%*%.cpp%$$ and $codei%speed_example/%*%.cpp%$$ to $codei%speed/example/%*%.cpp%$$. In addition, the relevant include files have been moved from $codei%example/%*%.hpp%$$ to $codei%speed/%*%.hpp%$$. $pre $$ A new $cref speed_test$$ routine was added to the library. $head 12-10$$ The $cref pow$$ function was changed to be a an $codei%AD<%Base%>%$$ $cref/atomic/glossary/Operation/Atomic/$$ operation. This function used to return a $code nan$$ if $icode x$$ is negative because it was implemented as $codei% pow(%x%, %y%) = exp( log(%x%) * %y% ) %$$ This has been fixed so that the function and its derivatives are now calculated properly when $icode x$$ is less than zero. The $cref pow$$ documentation was improved and the $cref pow.cpp$$ example was changed to test more cases and to use the same variable names as in the documentation. $head 12-09$$ A speed wish list item was added to the wish list. $pre $$ The prototype for $code int$$ arguments in binary operations (for example $cref/addition/ad_binary/$$) was documented as $syntax const int &$$ but was actually just plain $code int$$. This has been fixed. (Later changed to $code double$$.) $head 12-07$$ Fix bug in the subversion installation instructions; see $href%http://list.coin-or.org/pipermail/cppad/2006q4/000076.html%bug report%$$. $pre $$ The some of the automatically generated $code makefile.in$$ files had an improper license statement in the GPL license version. This has been fixed. $head 12-05$$ Add the unix installation $cref/--with-Documentation/auto_tools/--with-Documentation/$$ option and remove the $icode postfix_dir$$ option. $pre $$ Create a fixed $cref whats_new$$ section above the section for each particular year. Also improve the CppAD distribution $code README$$ file. $head 12-03$$ The include file directory $code CppAD$$ was changed to be all lower case; i.e., $code cppad$$. If you are using a Unix system, see $cref include_deprecated$$. This completes the following $cref wish_list$$ items (which were removed): $list number$$ File and directory names should only contain lowercase letters, numbers underscores and possibly one period. The leading character must be alphabetic. $lnext C++ header files should have the $code .hpp$$ extension. $lend $head 12-02$$ Put explanation of version numbering in the download instructions. $pre $$ Correct some file name references under the Windows heading in $cref speed_cppad$$. $head 12-01$$ All of the $code Makefile.am$$ and $code Makefile$$ files were changed to lower case; i.e., $code makefile.am$$ and $code makefile$$. $pre $$ Fix compiler warning while compiling $code cppad/RombergOne/$$ (mistake occurred during $cref/11-20/whats_new_06/11-29/$$ change). $head 11-30$$ Cygwin packages, and other system packages, should not have a dash in the version number. See $href% http://cygwin.com/setup.html#naming% cygwin package file naming %$$ or, to quote the $href% http://www.rpm.org/max-rpm/ch-rpm-file-format.html% rpm file naming convention %$$ $italic The only restriction placed on the version is that it cannot contain a dash "-". $$ As per the acceptable package naming conventions for cygwin, CppAD version numbering has be changed from $icode%yy%-%mm%-%dd%$$ format to $icode yyyymmdd$$; i.e. $code cppad-06-11-30$$ was changed to $code cppad-20061130$$. $head 11-29$$ There was a problem using $cref RombergOne$$ with floating point types other than $code double$$. This has been fixed. $head 11-28$$ The $cref/installation/Install/$$ download files were not being built because $code Makefile.am$$ referenced $code Doc$$ when it should have referenced $code doc$$. This has been fixed. $head 11-23$$ A Version Numbering entry was added to the $cref wish_list$$ (this was completed on $cref/11-30/whats_new_06/11-30/$$). $head 11-18$$ The example routine that computes determinants using expansion by minors $code DetOfMinor$$ was changed to $cref det_of_minor$$, in preparation for more formal speed comparisons with other packages. To be specific, its documentation was improved, its dependence on the rest of CppAD was removed (it no longer includes $cref/CppAD.h/cppad/$$). $head 11-12$$ The $cref example.cpp$$ and $code test_more/test_more.cpp$$ programs were changed to print out the number of tests that passed or failed instead of just "All the tests passed" or "At least one of the tests failed". $pre $$ The windows project files for examples and testing should have been changes to use lower case file names on as part of the 11-08 change below. This has been fixed. $head 11-08$$ Move the $code Example$$ directory to $code example$$ and change all its files to use lower case names. $head 11-06$$ Move the $code TestMore$$ directory to $code test_more$$ and change all its files to use lower case names. $head 11-05$$ Remove references in the $cref speed_cppad$$ tests to the $code Memory$$ and $code Size$$ functions because they have been $cref/deprecated/FunDeprecated/$$. $pre $$ Correct some references to $code var_size$$ that should have been $cref/size_var/seq_property/size_var/$$. $head 11-04$$ Put text written to standard output in the documentation for the $cref/get_started.cpp/get_started.cpp/Output/$$ and $code print_for.cpp$$ examples. (Now documentation can be built from a subversion checkout with out needing to execute automake.) The $code PrintFor.cpp$$ and $code speedtest.cpp$$ examples were missing in $cref ListAllExamples$$ (which has been fixed). $pre $$ Move the $code Speed$$ directory to $code speed$$ and change all its files to use lower case names. $head 11-02$$ The $code print_for$$ directory was referenced as $code PrintFor$$ in the root CppAD $code Makefile.am$$ this has been fixed. $pre $$ The documentation for the Adolc helper routines $code AllocVec$$ and $code AllocMat$$ were not being included. This has been fixed. $pre $$ Move the $code GetStarted$$ directory to $code get_started$$ and change all its files to use lower case names. $head 11-01$$ Move the $code PrintFor$$ directory to $code print_for$$ and change all its files to use lower case names. $head 10-31$$ Move the $code SpeedExample$$ directory to $code speed_cppad_example$$ and change all its files to use lower case names. $head 10-29$$ Move the $code Adolc$$ directory to $code adolc$$ and change all its files to use lower case names. $pre $$ Change all the file in the $code omh$$ directory to use lower case names. $pre $$ The file $code Makefile.am$$ in the distribution directory had the CPL copyright message in the GPL version. This has been fixed. $head 10-28$$ The copyright message in the script files $code example/OneTest$$ and $code TestMore/OneTest$$ were GPL (in the CPL distribution). This has been fixed by moving them to $code example/OneTest.sh$$ and $code TestMore/OneTest.sh$$ so that the distribution automatically edits the copyright message. $head 10-27$$ Change $cref hes_lagrangian.cpp$$ example so that it computes the Lagrangian two ways. One is simpler and the other can be used to avoid re-taping operation sequence. $head 10-26$$ Change $cref hes_lagrangian.cpp$$ example so that it modifies the independent variable vector between the call to $cref Independent$$ and the $codei%ADFun<%Base%>%$$ $cref/constructor/FunConstruct/$$. $head 10-25$$ A subversion install procedure was added to the documentation. $pre $$ Fix definition of preprocessor symbol $code PACKAGE_STRING$$ in $code Speed/Speed.cpp$$ (broken by change on 10-18). $pre $$ Added the example $cref hes_lagrangian.cpp$$ which computes the Hessian of a Lagrangian. $head 10-18$$ Document and fix possible conflicts for $cref/preprocessor symbols/preprocessor/$$ that do not begin with $code CppAD$$ or $code CPPAD_$$. $pre $$ Include a default value for the file $code cppad/config.h$$ in the subversion repository. $head 10-16$$ Fix bug when using $cref OdeErrControl$$ with the type $code AD< AD >$$. $head 10-10$$ Add the $cref Var2Par$$ function so it is possible to obtain the $cref Value$$ of a variable. Move the $code Discrete.cpp$$ example to $cref tape_index.cpp$$. Fix the Microsoft project file so that the Windows install examples and testing works properly (it was missing the $cref stack_machine.cpp$$ example). $head 09-30$$ These changes were grouped together because it took a while for Coin-Or to review the dual licensing version and because it was not possible to get the nightly build changed: $list number$$ Change shell scripts to use *.sh extension. $lnext Two versions, one with CPL and other with GPL license. $lnext Change subversion version of CppAD from GPL to CPL copyright. $lnext Change all files in cppad/local to use lower case and *.hpp extension. $lnext CppAD_vector.h was generating a warning on version 4 of gcc. This have been fixed. $lnext Change the preprocessor $code # define$$ commands in $code cppad/local/*.hpp$$ to use upper case names. $lnext Add the $cref stack_machine.cpp$$ example. $lend $head 08-17$$ Some error message occurred while executing $codep valgrind --tool=memcheck example/example valgrind --tool=memcheck TestMore/TestMore $$ These were not really bugs, but they have been fixed to avoid this conflict between CppAD and $href%http://valgrind.org/%valgrind%$$. $head 07-14$$ Make some improvements were made to the $cref Introduction$$, $cref exp_eps.hpp$$ and $cref exp_eps_rev1$$ sections. $head 07-12$$ Use a drop down menu for the navigation links, instead of a separate frame for the navigation links, for each section in the documentation. $head 06-29$$ Newer versions of the gcc compiler generated an error because $cref erf$$ was using $cref CondExp$$ before it was defined. This was found by Kasper Kristensen and his fix has been included in the CppAD distribution. $head 06-22$$ The $cref ADFun$$ operation $icode%f%(%x%, %y%)%$$ no longer executes a zero order $cref Forward$$ operation when a new operation sequence is stored in $icode f$$. In addition, the syntax for this operation was changed to $icode%f%.Dependent(%y%)%$$ (see $cref Dependent$$). $comment ----------------------------------------------------------- $$ $head 06-19$$ The changes listed under 06-17 and 06-18 were made in the branches/ADFun branch of the CppAD subversion repository. They did not get merged into the trunk and become part of the distribution until 06-19. This accomplished the following goal, which was removed from the $cref wish_list$$: $pre $$ "We would like to be able to erase the function values so that $cref ADFun$$ objects use less memory. We may even want to erase the AD operation sequence so that $cref ADFun$$ objects use even less memory and can be used for a subsequent AD operation sequence." $subhead 06-17$$ Added $cref capacity_order$$ which can be used to control the amount of memory used to store $cref Forward$$ results. Also $cref/deprecated/FunDeprecated/$$ $code taylor_size$$, and defined $cref size_order$$ in its place. $subhead 06-18$$ Added the $cref/ADFun default constructor/FunConstruct/$$ and the ability to $cref/store a new operation sequence/Dependent/$$ in an $code ADFun$$ object with out having to use $code ADFun$$ pointers together with $code new$$ and $code delete$$. $comment ----------------------------------------------------------- $$ $head 06-17$$ The location where the distribution files are stored has changed and this broke the Download Current Version links for the unix and windows installation. This has been fixed. $pre $$ The compiling instructions for the $cref speed_cppad$$ routines have been improved. $pre $$ The $cref Value$$ function has been extended to allow for $cref/parameter/glossary/Parameter/$$ arguments even if the corresponding tape is in the Recording state. $pre $$ The $cref BenderQuad$$ documentation and example have been improved by changing $icode Vector$$ to $icode BAvector$$ to emphasize that it corresponds to a vector of $icode Base$$ objects. $head 06-15$$ Change $cref BenderQuad$$ to use $icode%Base%$$ instead of $codei%AD<%Base%>%$$ where every possible. This allows for more calculations to be done in the base type; i.e., is more efficient. $head 06-09$$ Add a size check (size one) for the $cref/function value argument, g/BenderQuad/g/$$ in $code BenderQuad$$. $head 06-07$$ Some major changes were made to the notation in $cref get_started.cpp$$ (to make it easier to start using CppAD). $pre $$ In the $cref Introduction$$ example, $latex exp_eps$$ was changed to $latex {\rm exp\_eps}$$. $head 06-05$$ Change $cref BenderQuad$$ $latex F_y (x, y)$$ to $latex H(x,y)$$ so applies in a more general setting. This was another change to the $code BenderQuad$$ interface, $icode%fun%.fy%$$ was changed to $icode%fun%.h%$$. $head 06-02$$ Newer versions of the gcc compiler generated a warning for possible use of an uninitialized pointer. This was found by Michael Tautschnig and his fix has been included in the CppAD distribution. $head 05-31$$ The interface to $cref BenderQuad$$ has been changed. Now all the function evaluation routines are member functions of one class object. This makes it easy for them to share common data. $head 05-29$$ Change statement of command syntax to be in the same browser frame as the command documentation (for all the commands with a syntax statement). Now when a user links to a specific heading in a command's documentation, the syntax for that command is automatically included. Before the user needed to follow another link to see to the command syntax. $head 05-27$$ Added $cref BenderQuad$$ for computing the Hessian of Bender's reduced objective function. $pre $$ Added special specifications for $code resize(0)$$ to $cref CppAD_vector$$. $head 05-03$$ The g++ (GCC) 4.1.0 (Red Hat 4.1.0-3) compiler reported an error because certain functions were used before being defined (version 3.4.4 did not complain about this). This has been fixed. $head 04-29$$ Change all of the example and test driver programs so that they return error codes; i.e., zero for no error and one for an error. $pre $$ Add more discussion and a reference for a $code gcc 3.4.4 -O2$$ bug (since been removed). $head 04-28$$ Improve the $cref get_started.cpp$$ example and move it so that it is visible at the too level of the documentation. $head 04-26$$ The programs in $cref Introduction$$ have been converted to automated test that return true or false with the driver program $cref/Introduction/exp_apx_main.cpp/$$. $head 04-25$$ Add an $cref Introduction$$ section to the documentation (replaces old example that was part of the $cref Theory$$ section). $head 04-19$$ A discussion was added near the end of the $cref FunCheck$$ documentation. And the cross references to the $cref CompareChange$$ discussion were changed to the FunCheck discussion. $pre $$ An operation sequence entry was added to the $cref wish_list$$. $head 04-18$$ The new definitions for $cref/AD of Base/glossary/AD of Base/$$ and $cref/operation sequence/glossary/Operation/Sequence/$$ have been used throughout the documentation. $pre $$ Add the $cref FunCheck$$ section for checking that a sequence of operations is as intended. $head 04-17$$ The documentation for $cref SpeedTest$$ and $cref Poly$$ was improved. $pre $$ Definitions were added for an atomic $cref/operation/glossary/Operation/$$ and for an operation sequence being dependent and independent of the values of specific operands. $pre $$ The definition of AD sequence of operations was made abstract and moved to the glossary as $cref/Type operation sequence/glossary/Operation/Sequence/$$. $head 04-15$$ The $cref mul_level$$ example was moved from $cref ADFun$$ to $cref General$$. The documentation for $cref SpeedTest$$ was improved. $head 04-14$$ Documentation and examples were improved for the following routines: $cref ForTwo$$, $cref RevTwo$$. In addition, the computation in $code RevTwo$$ was made more efficient (it used to possibly calculate some first order partials that were not used). $head 04-13$$ Documentation and examples were improved for the following routines: $cref Jacobian$$, $cref ForOne$$, $cref RevOne$$, and $cref Hessian$$. $head 04-08$$ In the case where $cref/use_VecAD/FunDeprecated/use_VecAD/$$ is true, the $cref ForSparseJac$$ calculation in only for the current independent variable values. In this case, the sparsity pattern can be (and has been) made more efficient; i.e., fewer true values (because it only applies to the current $cref forward_zero$$). $pre $$ The conversion from $cref/VecAD::reference/VecAD/VecAD::reference/$$ to $cref AD$$ gave a compile error (this has been fixed). Code example for this fix $codep VecAD V(1); AD zero = 0; V[zero] = 1.; static_cast< AD > ( V[zero] ); $$ $head 04-06$$ The $cref ForSparseJac$$, $cref RevSparseJac$$, $cref RevSparseHes$$ sparsity results are now valid for all independent variable values (if the AD operation sequence does no use any $codei%VecAD<%Base%>%$$ operands). In addition, the $code ForSparseJac$$, $cref RevSparseJac$$ and $cref RevSparseHes$$ documentation and examples were improved. $pre $$ The $cref/useVecAD/FunDeprecated/use_VecAD/$$ member function was added to $cref ADFun$$ objects. $pre $$ The $code var_size$$ member function was changed to $cref/size_var/seq_property/size_var/$$ (this is not backward compatible, but $code var_size$$ was just added on $cref/04-03/whats_new_06/04-03/$$). $head 04-05$$ The documentation and example for $cref CompareChange$$ were improved and moved to be part of the $cref Forward$$ section. $head 04-04$$ The documentation and examples for $cref Reverse$$ were improved and split into $cref reverse_one$$ and $cref reverse_any$$. $head 04-03$$ Create separate sections for the $cref/zero/forward_zero/$$ and $cref forward_one$$ first order case of $cref Forward$$ mode. $pre $$ The ADFun $cref/Size/FunDeprecated/Size/$$ member function has been deprecated (use $cref size_order$$ instead). $pre $$ The $cref Reverse$$ member function is now declared, and documented as, $code const$$; i.e., it does not effect the state of the ADFun object. $pre $$ Change the examples that use $cref Reverse$$ to use the same return value notation as the documentation; i.e., $code dw$$. $head 04-02$$ The member functions of $cref ADFun$$ that return properties of AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ have been grouped into the $cref seq_property$$ section. In addition, the $cref seq_property.cpp$$ example has been added. $pre $$ The $cref CompareChange$$ function documentation was improved and moved to a separate section. $pre $$ Group the documentation for the $cref ADFun$$ member functions that $cref/evaluate functions and derivative values/FunEval/$$. $pre $$ Remove the old $code Fun.cpp$$ example and extend $cref independent.cpp$$ so that it demonstrates using different choices for the $cref SimpleVector$$ type. $head 04-01$$ Move the $cref/ADFun Constructor/FunConstruct/$$ to its own separate section, improve its documentation, and use $cref independent.cpp$$ for its example. $pre $$ The following member functions of $cref ADFun$$ have been $cref/deprecated/FunDeprecated/$$: $code Order$$, $code Memory$$. $pre $$ The wish list entry for Memory usage was updated on 04-01. The request was implemented on $cref/06-19/whats_new_06/06-19/$$ and the entry was removed from the wish list. $head 03-31$$ Add examples for the $cref/Parameter, Variable/ParVar/$$ and $cref Independent$$ functions. $pre $$ Move the $cref/Parameter and Variable/ParVar/$$ functions from the $cref ADFun$$ section to the $cref AD$$ section. $pre $$ In the examples for the $cref AD$$ sections, refer to the range space vector instead of the dependent variable vector because some of the components may not be $cref/variables/glossary/Variable/$$. $head 03-30$$ Move the $cref LuRatio$$ section below $cref LuDetAndSolve$$. $pre $$ Move the definition of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ from the glossary to the $cref AD$$ section. $pre $$ Improve the definition of tape state. $pre $$ Add mention of taping to $cref Erf$$, $cref BoolFun$$, $cref NearEqualExt$$,and $cref Pow$$. $pre $$ Change the definition for $cref/VecAD::reference/VecAD/VecAD::reference/$$ so that it stands out of the text better. $head 03-29$$ Mention the $cref/VecAD::reference/VecAD/VecAD::reference/$$ case in documentation and examples for $cref abs$$, $cref atan2$$, $cref erf$$, and $cref pow$$. $pre $$ Fix a bug derivative computation for $codei%abs(%x%)%$$ when $icode x$$ had type $codei%AD< AD >%$$ and $icode x$$ had value zero. $pre $$ Fix a bug using non-zero AD indices for $cref VecAD$$ vectors while the tape is in the empty state. $pre $$ Extend $cref erf$$ to include $code float$$, $code double$$, and $codei%VecAD<%Base%>::reference%$$. $head 03-28$$ Mention the $cref/VecAD::reference/VecAD/VecAD::reference/$$ case in documentation and examples for $cref UnaryPlus$$, $cref UnaryMinus$$, $cref ad_binary$$, $cref compute_assign$$, and $cref unary_standard_math$$ $head 03-27$$ Extend and improve the $cref/VecAD exceptions/VecAD/VecAD::reference/Exceptions/$$. $pre $$ Mention the $cref/VecAD::reference/VecAD/VecAD::reference/$$ case and generally improve $cref/addition/ad_binary/$$ documentation and examples. $head 03-26$$ Improve documentation and examples for $cref VecAD$$ and change its element type from $codei%VecADelem<%Base%>%$$ to $codei%VecAD_reference<%Base%>%$$ (so that it looks more like $cref/VecAD::reference/VecAD/VecAD::reference/$$). $pre $$ Mention the $cref/VecAD::reference/VecAD/VecAD::reference/$$ case and generally improve $cref Value$$, $cref ad_output$$ and $cref/assignment/ad_assign/$$ documentation and examples. $pre $$ Extend $cref Integer$$ and $cref PrintFor$$ to include the $cref/VecAD::reference/VecAD/VecAD::reference/$$ case (and mention in documentation and examples). $head 03-24$$ Move $cref VecAD$$ and $cref LuRatio$$ from the old ExtendDomain section to $cref AD$$. $head 03-23$$ Improve documentation and examples for $cref CondExp$$ and $cref Discrete$$. Move both of these sections from ExtendDomain to $cref ADValued$$. $head 03-22$$ The documentation sections under $cref AD$$ have been organized into a new set of sub-groups. $head 03-18$$ The documentation and example for $cref PrintFor$$ have been improved. The sections below $cref AD$$ in the documentation have been organized into subgroups. $head 03-17$$ The documentation and examples have been improved for the following functions: $cref BoolFun$$, and $cref NearEqualExt$$. $head 03-16$$ Improve the documentation and example for the $cref pow$$ function. This includes splitting out and generalizing the integer case $cref pow_int$$. $pre $$ The copies of the $code atan2$$ function were included in the CppAD namespace for the $code float$$ and $code double$$ types. $head 03-15$$ Improve the $cref/introduction/cppad/Introduction/$$ to CppAD. $head 03-11$$ The file $code cppad/local/MathOther.h$$ had a file name case error that prevented the documentation from building and tests from running (except under Cygwin which is not really case sensitive). This has been fixed. $pre $$ The term AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ has been defined. It will be used to improve the user's understanding of exactly how an $cref ADFun$$ object is related to the C++ algorithm. $head 03-10$$ The math functions that are not under $cref unary_standard_math$$ have been grouped under $code MathOther$$. $pre $$ The documentation and examples have been improved for the following functions: $cref abs$$, $cref atan2$$. $head 03-09$$ The examples $cref cos.cpp$$, $cref cosh.cpp$$, $cref exp.cpp$$, $cref log.cpp$$, $cref log10.cpp$$, $cref sin.cpp$$, $cref sinh.cpp$$, $cref sqrt.cpp$$ have been improved. $head 03-07$$ The $code tan$$ function has been added to CppAD. $pre $$ The examples $cref Acos.cpp$$, $cref Asin.cpp$$ and $cref atan.cpp$$ have been improved. $head 03-05$$ The AD standard math unary functions documentation has been grouped together with improved documentation in $cref unary_standard_math$$. $head 02-28$$ The $cref ad_output$$ and $cref Abs$$ documentation and example have been improved. Minor improvements were also made to the $cref lu_vec_ad.cpp$$ documentation. $head 02-25$$ The $cref Compare$$ documentation and example have been improved. $head 02-24$$ The documentation and examples have been improved for the following sections: $cref/division/ad_binary/$$, $cref/-=/compute_assign/$$, $cref/*=/compute_assign/$$, and $cref%/=%compute_assign%$$. $head 02-23$$ The $cref/multiplication/ad_binary/$$ documentation and example have been improved. $head 02-21$$ The $cref/subtraction/ad_binary/$$ documentation and example have been improved. $pre $$ There was a bug $cref RevTwo$$ that was not detected by the $cref rev_two.cpp$$ test. This bug was reported by $href% http://list.coin-or.org/pipermail/cppad/2006-February/000020.html% Kasper Kristensen %$$ A test was added $code TestMore/rev_two.cpp$$ that detects this problem and the problem has been fixed. $head 02-15$$ The $cref/+=/compute_assign/$$ documentation and example have been improved. $head 02-14$$ The $cref/addition/ad_binary/$$ documentation and example have been improved. $head 02-13$$ Combine the old binary operator and computed assignment documentation into $cref Arithmetic$$ documentation. $pre $$ The documentation and examples have been improved for the following sections: $cref/assignment/ad_assign/$$, $cref UnaryPlus$$, $xref UnaryMinus$$. $head 02-11$$ The documentation and examples have been improved for the following sections: $cref ad_ctor$$, $cref ad_ctor$$ and $cref ad_assign$$, and $cref Value$$. $head 02-10$$ This is the beginning of a pass to improve the documentation: The documentation sections The CopyBase (formerly FromBase and now part of $cref ad_ctor$$ and $cref ad_assign$$) and $cref/AD copy constructor/ad_ctor/$$ (formerly Copy) documentation has been modified. $pre $$ Some of the error messaging during $cref ADFun$$ construction has been improved. $head 02-04$$ There was a read memory access past the end of an array in $cref/CppAD::vector::push_back/CppAD_vector/push_back/$$. This has been fixed and in addition $cref TrackNewDel$$ is now used to do and check the allocation in $code CppAD::vector$$. $pre $$ The routines $cref Runge45$$ and $cref Rosen34$$ had static vectors to avoid recalculation on each call. These have been changed to be plain vectors to avoid memory leak detection by $cref/TrackCount/TrackNewDel/TrackCount/$$. $head 01-20$$ Add $cref/software guidelines/wish_list/Software Guidelines/$$ to the wish list. $head 01-18$$ Improve the definition for $cref/parameters/glossary/Parameter/$$ and $cref/variables/glossary/Variable/$$. Remove unnecessary reference to parameter and variable in documentation for $cref Independent$$. $head 01-08$$ The aclocal program is part of the automake and autoconf system. It often generates warnings of the form: $codei% /usr/share/aclocal/%...%: warning: underquoted definition of %...% %$$ The shell script file $code FixAclocal$$, which attempts to fix these warnings, was added to the distribution. $head 01-07$$ Change CppAD error handler from using the macros defined in $code cppad/CppADError.h$$ to using a class defined in $cref%cppad/utility/error_handler.hpp%ErrorHandler%$$. The macros $code CppADUnknownError$$ and $code CppADUsageError$$ have been deprecated (they are temporarily still available in the file $code cppad/local/CppADError.h$$). $head 01-02$$ Add the sed script $code Speed/gprof.sed$$ to aid in the display of the $cref/profiling/auto_tools/Profiling CppAD/$$ output. $pre $$ Make the following source code files easier to understand: $code Add.h$$, $code Sub.h$$, $code Mul.h$$, $code Div.h$$ (in the directory $code cppad/local$$). $head 01-05$$ Make the following source code files easier to understand: $code RevSparseHes.h$$, $code Reverse.h$$, $code Fun.h$$, $code Forward.h$$, $code ForSparseJac.h$$, $code RevSparseJac.h$$ (in the directory $code cppad/local$$). $end cppad-20170000.3/omh/whats_new/whats_new_15.omh0000644000175200017650000007301313057470463020232 0ustar coincoin-web$Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_15$$ $dollar @$$ $spell addon runge lcppad ind const enum ctor dimensioned cskip_op adolc zdouble expm1 eigen expm1 atanh acosh asinh src op onetape CppAD colpack hes cppad Jacobian gettimeofday cmake hpp dir includedirs libdirs datadir docdir std cxx erf var NumRes chrono aeps CondExpGt hasnan Adolc resize bool alloc adouble gmtime asctime ipopt fadbad sacado unreferenced azmul retape $$ $section CppAD Changes and Additions During 2015$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2015 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-31$$ The $cref download$$ instructions were modified to have more mention of using $cref/git/download/Current Version/Git/$$ and less mention of $cref/subversion/download/Current Version/Subversion/$$. $head 12-29$$ Separate $cref to_string$$ from $cref ad_to_string$$ so that it can be used without the rest of CppAD; i.e., by including $codei% # include %$$ $head 12-28$$ $list number$$ Add the $cref to_string$$ utility. $lnext Add $cref base_to_string$$ to the Base type requirements. $lnext A $cref/Base requirements/wish_list/Base Requirements/$$ item was added to the wish list. $lnext The $cref wish_list$$ item to reorganize the include directory has been removed. It was completed when the utilities was moved to $code cppad/utility$$; see $cref/11-30/whats_new_15/11-30/$$. $lend $head 12-08$$ $list number$$ A convention was included for addon $cref/library files/addon/Library Files/$$. $lnext Change new $cref utility$$ specifications to allow for individual file includes; e.g., $code $$. $lend $head 12-01$$ Fix problem with $cref auto_tools$$ install handling of the deprecated files. This included changing the auto-tools $code --with-implicit_ctor$$ option to $cref/--with-deprecated/auto_tools/--with-deprecated/$$. $head 11-30$$ $list number$$ The $code library$$ section has been moved to the $cref/utilities/utility/$$ section. In addition, the corresponding source code files in $code cppad$$ have been moved to $code cppad/utility$$. $lnext The individual $cref utility$$ include files have been deprecated; see $cref include_deprecated$$. For example, $codep # include $$ You should us the utility include instead; i.e., $codep # include $$ $lnext The $cref numeric_ad$$ routines where moved from the $code library$$ the a separate documentation section. $lnext Change $code cmake_install_prefix$$ to $cref/cppad_prefix/cmake/cppad_prefix/$$ and Change $code cmake_install_postfix$$ to $cref/cppad_postfix/cmake/cppad_postfix/$$. $lnext Change $code cppad_implicit_ctor_from_any_type$$ to $cref/cppad_deprecated/cmake/cppad_deprecated/$$ and change its specifications to refer to all deprecated features. $lend $head 11-25$$ $list number$$ CppAD now installs the object library $codep -lcppad_lib $$ to be included when linking. Currently, it is only required when $cref colpack_prefix$$ is specified on the $cref/cmake command/cmake/CMake Command/$$. $lnext It is no longer necessary to compile and link the file $codep cppad_colpack.cpp $$ when $cref colpack_prefix$$ is specified during the install process; see $cref/cmake command/cmake/CMake Command/$$. (It is included in $code cppad_lib$$). $lend $head 11-24$$ $list number$$ The $code check_for_nan$$ output now includes the first dependent variable $cref/index/check_for_nan/Error Message/index/$$ that is $code nan$$ in its error message. $lnext Change the $cref/deprecated include/include_deprecated/$$ reference $code pow_int.h$$ to $code pow_int.hpp$$ in $cref pow_int$$. $lend $head 11-14$$ There was a bug in the new $cref/get_check_for_nan/check_for_nan/get_check_for_nan/$$ feature that writes independent variable values to a temporary file; see $cref/11-06/whats_new_15/11-06/$$ below. This has been fixed. $head 11-08$$ $list number$$ Fixed a bug in the $cref RevSparseJac$$ routine. To be specific, the argument $cref/r/RevSparseJac/r/$$ was transposed from what the documentation said. (This has no effect in the usual case where $icode r$$ is the identity.) $lnext Added the $cref bool_sparsity.cpp$$ examples which show how to conserve memory when computing sparsity patterns. $lnext Modified the $cref ipopt_solve$$ procedure to take advantage of the memory conserving sparsity pattern calculations when $cref/retape/ipopt_solve/options/Retape/$$ is false. $lnext Added the $cref/bit_per_unit/CppAD_vector/vectorBool/bit_per_unit/$$ function to the $code vectorBool$$ class. (This aids the memory conservation mentioned above.) $lend $head 11-06$$ It is often difficult to determine what cause a $code nan$$ result during an operation with an $cref ADFun$$ object. The new feature $cref/get_check_for_nan/check_for_nan/get_check_for_nan/$$ was added to make this easier. $head 10-21$$ There was a mistake in the documentation for $cref index_sort$$, the argument $cref/ind/index_sort/ind/$$ is not $code const$$. $head 10-16$$ Add a $cref PrintFor$$ optimization wish list item. This has been done, see $cref/no_print_for_op/optimize/options/no_print_for_op/$$. $head 10-06$$ $list number$$ Add $cref/CPPAD_USE_CPLUSPLUS_2011 /preprocessor /Documented Here /CPPAD_USE_CPLUSPLUS_2011 /$$, $code CPPAD_NUMERIC_LIMITS$$, and $code CPPAD_STANDARD_MATH_UNARY$$, to the $cref preprocessor$$ section. In addition, remove checking that all user API preprocessor symbols are in this section form the $cref wish_list$$. $lnext Alphabetize and make some corrections to $cref/list of examples/ListAllExamples/$$. $lnext The documentation for some of the $cref deprecated$$ features was missing the date when they were deprecated. This has been fixed; e.g., see $cref/Deprecated 2012-12-26/auto_tools/Deprecated 2012-12-26/$$. $lend $head 10-04$$ $list number$$ $cref base_require$$: Add the macro $cref/CPPAD_NUMERIC_LIMITS/base_limits/CPPAD_NUMERIC_LIMITS/$$ to aid in setting the numeric limits for a user defined $icode Base$$ class. $lnext $cref base_require$$: The $cref/quiet_NaN/numeric_limits/quiet_NaN/$$ function has been added to the CppAD $code numeric_limits$$. Note the reason for not using $cref/std::numeric_limits/numeric_limits/std::numeric_limits/$$. $lnext The $cref/nan(zero)/nan/nan(zero)/$$ function computes a $code nan$$ by dividing zero by zero which results in a warning when using some compilers. This function has been deprecated and the corresponding $cref wish_list$$ item has been removed. $lnext Move documentation for $cref zdouble$$ to $cref deprecated$$ section and documentation for $cref numeric_limits$$ to $cref ADValued$$. $lnext Remove all uses of, and references to, $cref zdouble$$ from the $cref/examples/Example/$$. $lend $head 10-03$$ $cref base_require$$: It is no longer necessary to define the specialization for $codei%CppAD::epsilon<%Base>()%$$ for each $icode Base$$ type. $head 10-02$$ There was a bug in $code test_more/azmul.cpp$$ whereby the vector $code z$$ had the wrong dimension (in two places). This has been fixed. $head 09-28$$ $list number$$ Use the current $cref atomic_option$$ setting to determine which type of sparsity patterns to use for $cref/dependency/dependency.cpp/$$ calculations during $cref optimize$$ procedure. It used to be that the $cref/bool_sparsity_enum/atomic_option/atomic_sparsity/bool_sparsity_enum/$$ was used when $cref/pack_sparsity_enum/atomic_option/atomic_sparsity/pack_sparsity_enum/$$ was specified. $lnext It is not longer an error to take the derivative of the square root function, because the result may be the part of a $cref/conditional expression/CondExp/$$ that is not used. $lnext Update the $cref wish_list$$ section. $lend $head 09-27$$ $list number$$ It is no longer necessary to use the $cref zdouble$$ class when computing with $cref/multiple levels of AD/mul_level/$$ $cref/conditional expressions/CondExp/$$ and $cref/reverse mode/reverse/$$. $lnext The $code zdouble$$ class has been deprecated. Use the $cref azmul$$ function for absolute zero (when it is needed). $lend $head 09-25$$ $cref base_require$$: $cref/absolute zero multiplication/base_require/Absolute Zero, azmul/$$ is now required for user defined base types. This makes it possible to combine $cref/conditional expression/CondExp/$$, $cref/multiple levels/mul_level/$$, $cref/reverse/Reverse/$$, and a base type that has standard ieee multiplication; e.g., $code double$$. In other words, not all multiplications will need to have an absolute zero (as is the case with the $cref zdouble$$ base class. $head 09-24$$ Fix some Visual Studio 2013 C++ level four $code /W4$$ warnings (previous warnings were are level 3). In addition, disable warning $code 4100$$ unreferenced formal parameter, and warning $code 4127$$ conditional expression is constant. $head 09-23$$ CppAD can optionally test its use with the external packages $cref/eigen/get_eigen.sh/$$, $cref/ipopt/get_ipopt.sh/$$, and $cref/colpack/get_colpack.sh/$$. In addition, it can compare its $cref speed$$ with the external AD packages $cref/adolc/get_adolc.sh/$$, $cref/fadbad/get_fadbad.sh/$$, and $cref/sacado/get_sacado.sh/$$. The scripts that download and install a local copy of these external packages have been modified to automatically skip installation when it has already been done. $head 09-21$$ Improve discussion of $cref/windows download and testing /download /Windows File Extraction and Testing /$$. $head 09-20$$ $list number$$ Add the $cref/cppad_profile_flag/cmake/cppad_profile_flag/$$ to the list of possible $code cmake$$ command arguments. $lnext More of the warnings generated by Visual Studio 2013 have been fixed. One remaining warning is about $code asctime$$ and $code gmtime$$ not being thread safe. $lend $head 09-19$$ $list number$$ There was a bug in the $cref/numeric_limits/base_alloc.hpp/numeric_limits/$$ section of the example user defined base type. This has been fixed. $lnext There were some compile and link errors when running the tests using Visual Studio 2013. These have been fixed. $lnext Many of the warnings generated by Visual Studio 2013 have been fixed. $lend $head 09-16$$ The conditional expressions, $cref CondExp$$, were not working for the type $code< CppAD::AD >$$ where $code adouble$$ is the ADOL-C AD type. This has been fixed by adding a call to $cref/CPPAD_COND_EXP_REL/base_adolc.hpp/CondExpRel/$$ in $code base_adolc.hpp$$. $head 09-03$$ $list number$$ There was a bug in the $cref/vectorBool/CppAD_vector/vectorBool/$$ $cref/assignment/CppAD_vector/Assignment/$$. To be specific, it not allow a size zero vector to be assigned using a vector any other size. This has been fixed. $lnext The addition of the $cref/pack/atomic_option/atomic_sparsity/pack_sparsity_enum/$$ option on 08-31 introduced a bug in the calculation of $cref RevSparseHes$$. The $cref checkpoint.cpp$$ example was changed to demonstrate this problem and the bug was fixed. $lend $head 09-02$$ The $cref/dependency pattern/dependency.cpp/Dependency Pattern/$$ was not being computed correctly for the $cref sign$$, $cref Discrete$$, and $cref VecAD$$ operations. This has been fixed. This could have caused problems using $cref checkpoint$$ functions that used any of these operations. $head 08-31$$ $list number$$ Mention the fact that using checkpoint functions can make $cref/recordings faster/checkpoint/Purpose/Faster Recording/$$. $lnext Add the $cref/pack/atomic_option/atomic_sparsity/pack_sparsity_enum/$$ sparsity option for $cref atomic_base$$ operations. $lnext Add the pack sparsity option to $cref/checkpoint/checkpoint/sparsity/$$ functions. $lnext Added the $code example/atomic/sparsity.cpp$$ example. $lnext Remove mention of OpenMP from $cref/thread_alloc::thread_num/ta_thread_num/$$ ($cref thread_alloc$$ never was OpenMP specific). $lend $head 08-30$$ $list number$$ The $cref/sparsity/atomic_ctor/atomic_base/sparsity/$$ argument was added to the $code atomic_base$$ constructor and the $cref/checkpoint/checkpoint/sparsity/$$ constructor. $lnext Make $cref atomic_norm_sq.cpp$$ an example with no set sparsity and $cref atomic_reciprocal.cpp$$ an example with no bool sparsity. $lnext Improve discussion of $code Independent$$ and $cref/parallel mode/Independent/Parallel Mode/$$. $lend $head 08-29$$ Some asserts in the $cref checkpoint$$ implementation were not using the CppAD $cref ErrorHandler$$. This has been fixed. $head 08-28$$ Free $cref checkpoint$$ function sparsity patters during $cref forward$$ operations that use its atomic operation. (They kept between sparsity calculations because they do not change.) $head 08-26$$ Fix a bug in $cref RevSparseJac$$ when used to compute sparsity pattern for a subset of the rows in a $cref checkpoint$$ function. $head 08-25$$ Reduce the amount of memory required for $cref checkpoint$$ functions (since sparsity patterns are now being held so they do not need to be recalculated). $head 08-20$$ Added an example that computes the sparsity pattern for a subset of the $cref/Jacobian/sparsity_sub.cpp/ForSparseJac/$$ and a subset of the $cref/Hessian/sparsity_sub.cpp/RevSparseHes/$$. $head 08-17$$ $list number$$ Do some optimization of the $cref checkpoint$$ feature so that sparsity patterns are stored and not recalculated. $lnext Fix a warning (introduced on 08-11) where the $code CppAD::vector$$ $cref/data/CppAD_vector/data/$$ function was being shadowed by a local variable. $lnext The source code control for CppAD has a link to $code compile$$, instead of real file. This sometimes caused problems with the deprecated $cref auto_tools$$ install procedure and has been fixed. $lend $head 08-16$$ $list number$$ Improve the documentation for checkpoint functions. To be specific, change the $cref/syntax/checkpoint/Syntax/$$ to use the name $icode atom_fun$$. In addition, include the fact that $icode atom_fun$$ must not be destructed for as along as the corresponding atomic operations are used. $lnext Add the $cref/size_var/checkpoint/size_var/$$ function to the checkpoint objects. $lend $head 08-09$$ Add the preservation of data to the specifications of a $code CppAD::vector$$ during a $cref/resize/CppAD_vector/resize/$$ when the capacity of the vector does not change. In addition, added and example of this to $cref cppad_vector.cpp$$. $head 08-06$$ The $cref zdouble$$ $cref/numeric_limits/base_limits/$$ were not being computed properly. This has been fixed. $head 07-31$$ Added the $cref sparse_sub_hes.cpp$$ example, a way to compute the sparsity for a subset of variables without using $cref/multiple levels of AD/mul_level/$$. $head 06-16$$ $list number$$ There were some $cref/unknown/cppad_assert/Unknown/$$ asserts when the sparsity pattern $icode p$$ in $cref/sparse_jacobian/sparse_jacobian/p/$$ and $cref/sparse_hessian/sparse_hessian/p/$$ was not properly dimensioned. These have been changed to $cref/known/cppad_assert/Known/$$ asserts to give better error reporting. $lnext In the special case where sparse Hessian $cref/work/sparse_hessian/work/$$ or sparse Jacobian $cref/work/sparse_hessian/work/$$ was specified and the set of elements to be computed was empty, the work vector is empty after the call (and it appears to need to be calculated on subsequent calls). This resulted in a bug when the sparsity pattern was not provided on subsequent calls (and has been fixed). $lend $head 06-11$$ $list number$$ Some C++11 features were not being taken advantage of after the change on $cref/05-10/whats_new_15/05-10/$$. To be specific, move semantics, the high resolution clock, and null pointers. This has been fixed. $lnext In the example $cref zdouble.cpp$$, the vector $code a1z$$ was not properly dimensioned. This has been fixed and the dimensions of all the variables have been clarified. $lend $head 06-09$$ Add an $cref/abort_op_index/Independent/abort_op_index/$$ item to the wish list. It has since been removed (domain errors may not affect the results due to $cref/conditional expressions/CondExp/$$). $head 06-07$$ Add a $cref/absolute zero/base_require/Absolute Zero, azmul/$$ item and a $cref numeric_limits$$ item to the wish list. The absolute zero item has been completed and the numeric limit item was modified on implementation. Remove the multiple directions with list item. $head 05-26$$ $subhead cond_exp_1$$ There was a problem using $cref/conditional expressions/CondExp/$$ with $cref/multiple levels of AD/mul_level/$$ where the result of the conditional expression might not be determined during forward mode. This would generate an assert of the form: $codei% Error detected by false result for IdenticalPar(%side%) at line %number% in the file %...%/cppad/local/cskip_op.hpp %$$ where $icode side$$ was $code left$$ or $code right$$ and $icode number$$ was the line number of an assert in $code cskip_op.hpp$$. This has been fixed. $subhead cond_exp_2$$ There was a problem with using $cref/conditional expressions/CondExp/$$ and $cref/reverse mode/reverse/$$ with $cref/multiple levels of AD/mul_level/$$. This was problem was represented by the file $code bug/cond_exp_2.sh$$. $list number$$ The problem above has been fixed by adding the base type $code zdouble$$, see $cref/CppAD motivation/zdouble/Motivation/CppAD/$$ for this new type. (It is no longer necessary to use $code zdouble$$ to get an absolute zero because CppAD now uses $cref azmul$$ where an absolute zero is required.) $lnext The sections $cref mul_level$$, $cref change_param.cpp$$, $cref mul_level.cpp$$, and $cref mul_level_ode.cpp$$ were changed to use $cref zdouble$$. $lnext The $cref/adolc/adolc_prefix/$$ multi-level examples $cref mul_level_adolc.cpp$$ and $cref mul_level_adolc_ode.cpp$$ were changed to mention the limitations because Adolc does not have an $cref/absolute zero/zdouble/Absolute Zero/$$. $lnext The example above were also changed so that AD variable names that indicated the level of AD for the variable. $lnext $cref base_require$$: The base type requirements were modified to include mention of $cref/absolute zero/base_require/Absolute Zero, azmul/$$. In addition, the base type requirements $cref/API warning/base_require/API Warning/$$ is now more informative. $lend $head 05-11$$ Reorganize the $cref unary_standard_math$$ documentation. $head 05-10$$ $list number$$ Add the exponential minus one function $cref log1p$$. $lnext $cref base_require$$: If you are defining your own base type, note that $cref/log1p/base_std_math/erf, asinh, acosh, atanh, expm1, log1p/$$ was added to the base type requirements. $lnext Use the single preprocessor flag $code CPPAD_USE_CPLUSPLUS_2011$$ to signal that the functions $cref/erf, asinh, acosh, atanh, expm1, log1p /base_std_math /erf, asinh, acosh, atanh, expm1, log1p /$$ are part of the base type requirements. $lend $head 05-09$$ $list number$$ Add the exponential minus one function $cref expm1$$. If you are defining your own base type, note that $cref/expm1/base_std_math/erf, asinh, acosh, atanh, expm1, log1p/$$ was added to the base type requirements. $lnext Fix some warnings about comparing signed and unsigned integers when using $cref/eigen/cppad_testvector/eigen/$$ for the CppAD test vector. (The eigen vector $code size()$$ function returns an $code int$$ instead of a $code size_t$$.) $lend $head 05-08$$ $list number$$ Add the inverse hyperbolic sine function $cref atanh$$. If you are defining your own base type, note that $cref/atanh/base_std_math/erf, asinh, acosh, atanh, expm1, log1p/$$ was added to the base type requirements. $lnext Fix a bug in the implementation of the $code acosh$$ multiple direction forward mode $cref forward_dir$$ (when compiler has $cref/acosh/acosh/CPPAD_USE_CPLUSPLUS_2011/$$). $lend $head 05-07$$ Add the inverse hyperbolic sine function $cref acosh$$. If you are defining your own base type, note that $cref/acosh/base_std_math/erf, asinh, acosh, atanh, expm1, log1p/$$ was added to the base type requirements. $head 05-05$$ Add the inverse hyperbolic sine function $cref asinh$$. If you are defining your own base type, note that $cref/asinh/base_std_math/erf, asinh, acosh, atanh, expm1, log1p/$$ was added to the base type requirements. $head 04-18$$ In the sparse jacobian and sparse hessian calculations, If $icode work$$ is present, and has already been computed, the sparsity pattern $icode p$$ is not used. This has been added to the documentation; see $cref/sparse jacobian/sparse_jacobian/work/p/$$ and $cref/sparse hessian/sparse_hessian/work/p/$$ documentation for $icode work$$ and $icode p$$. $head 03-13$$ Remove the syntax $codei% AD<%Base%> %y% = %x% %$$ for the $cref/AD constructor/ad_ctor/$$ documentation because it does not work when the constructor is $cref/explicit/ad_ctor/x/explicit/$$. Also document the restriction that the constructor in the $cref/assignment/ad_assign/$$ must be implicit. $head 03-06$$ The developers of the $href%https://github.com/kaskr/adcomp%TMB%$$ package reported that for large $cref ADFun$$ tapes, the $cref optimize$$ routine uses a large amount of memory because it allocates a standard set for each variable on the tape. These sets are only necessary for variables in $cref/conditional expressions/condexp/$$ that can be skipped once the independent variables have a set value. The problem has been reduced by using a NULL pointer for the empty set and similar changes. It still needs more work. $head 02-28$$ It used to be the case that the $cref/Reverse mode/reverse/$$ would propagate $cref nan$$ through the $cref/conditional expression/condexp/$$ case that is not used. For example, if $codep Independent(ax); AD aeps = 1e-10; ay[0] = CondExpGt( ax[0], aeps, 1.0/ax[0], 1.0/aeps ); ADFun f(ax, ay); $$ The corresponding reverse mode calculation, at $code x[0] = 0.0$$, would result in $codep Error detected by false result for ! ( hasnan(value) && check_for_nan_ ) $$ This has been fixed so that only the conditional expression case that is used affects the reverse mode results. The example $cref cond_exp.cpp$$ was changed to reflect this (a check for $code nan$$ was changed to a check for zero). Note that this fix only works when $cref/IdenticalPar/base_identical/Identical/IdenticalPar/$$ is true for the base type of the result in the conditional expression; e.g., one can still get a $code nan$$ effect from the case that is not selected when using $code AD< AD >$$ conditional expressions. $head 02-18$$ If the compiler supports the c++11 feature $code std::chrono:high_resolution_clock$$ then use it for the $cref elapsed_seconds$$ function. $head 02-16$$ The new example $cref sub_sparse_hes.cpp$$ shows one way to compute a Hessian for a subset of variables without having to compute the sparsity pattern for the entire functions. $head 02-14$$ Fix another bug in the derivative calculations for the c++11 version of the error function; see $cref/CPPAD_USE_CPLUSPLUS_2011/erf/CPPAD_USE_CPLUSPLUS_2011/$$. $head 02-11$$ Fix a bug in the optimization of conditional expressions. To be specific, if $cref/NDEBUG/faq/Speed/NDEBUG/$$ is not defined, one could get an assert with the message: $codep Error detected by false result for var_index_ >= NumRes(op_) $$ $head 02-10$$ The change on $cref/2014-12-23/whats_new_14/12-23/$$ introduced a bug when the c++11 version of the error function was used with an $cref/optimized/optimize/$$ function. see $cref/CPPAD_USE_CPLUSPLUS_2011/erf/CPPAD_USE_CPLUSPLUS_2011/$$. There was also a bug in the sparsity calculations for when this erf function was included. These bugs have been fixed. $head 02-09$$ The test $code test_more/optimize.cpp$$ was failing on some systems because an exactly equality check should have been a near equal check. This has been fixed. $head 02-07$$ On some systems, the library corresponding to $code speed/src$$ could not be found. This library is only used for testing and so has been changed to always be static (hence does not need to be found at run time). $head 02-06$$ There was a bug in the coloring method change on $cref/2015-01-07/whats_new_15/01-07/$$. To be specific, $icode%work%.color_method%$$ was not being set to $code "cppad.symmetric"$$ after $icode%work%.color_method.clear()%$$. This has been fixed. $head 02-04$$ $list number$$ Enable the same install of CppAD to be used both with and without C++11 features; e.g., with both $code g++ --std=c++11$$ and with $code g++ --std=c++98$$. Previously if the $cref/cppad_cxx_flags/cmake/cppad_cxx_flags/$$ specified C++11, then it could only be used in that way. $lnext The $cref/cmake command/cmake/CMake Command/$$ now requires the version of $code cmake$$ to be greater than or equal 2.8 (due a bug in $code cmake$$ version 2.6). $lend $head 02-03$$ Improved the searching for the boost multi-threading library which is used for by the $cref team_bthread.cpp$$ case of the $cref thread_test.cpp$$ example and test. $head 02-02$$ Improve the documentation for the $cref/cmake command/cmake/CMake Command/$$ line options $codei% cmake_install_%dir% %$$ for $icode dir$$ equal to $code prefix$$, $code postfix$$, $code includedirs$$, $code libdirs$$, $code datadir$$, and $code docdir$$. $head 01-30$$ Fix bug in $cref link_sparse_hessian$$ speed test introduced on $cref/01-09/whats_new_15/01-09/$$ below. $head 01-29$$ Fix some warnings generated by $code g++ 4.9.2$$. $head 01-26$$ The change of global variables to local in $code cppad/local/op_code.hpp$$ on $cref/2014-50-14/whats_new_14/05-14/$$ created a bug in $cref parallel_ad$$ (some local statics needed to be initialized). This has been fixed. $head 01-23$$ There was a bug in the $cref cmake$$ install detection of compiler features. One symptom of this bug was that on systems that had the $code gettimeofday$$ function, the cmake install would sometimes report $codei% cppad_has_gettimeofday = 0 %$$ This has been fixed. $head 01-21$$ The deprecated $cref auto_tools$$ procedure had a bug in the detection of when the size of an $code unsigned int$$ was the same as the size of a $code size_t$$. This has been fixed. $head 01-20$$ $list number$$ The new $cref compare_change$$ interface has been created and the old $cref CompareChange$$ function has been deprecated; see the $cref compare_change.cpp$$ example. This enables one to determine the source code during taping that corresponds to changes in the comparisons during $cref/zero order forward/forward_zero/$$ operations; see $cref/abort_op_index/Independent/abort_op_index/$$. $lnext This new $cref compare_change$$ interface can detect comparison changes even if $cref/NDEBUG/Faq/Speed/NDEBUG/$$ is defined and even if $cref/f.optimize()/optimize/$$ has been called. The deprecated function $code CompareChange$$ used to always return zero after $codei% %f%.optimize() %$$ and was not even defined when $code NDEBUG$$ was defined. There was a resulting speed effect for this; see $cref/no_compare_op/optimize/options/no_compare_op/$$. $lnext The date when some features where deprecated has been added to the documentation. For example, see $cref/Deprecated 2006-12-17/include_deprecated/Deprecated 2006-12-17/$$. $lend $head 01-09$$ $list number$$ The change 01-07 below included (but did not mention) using a sparse, instead of full, structure for the Hessian in the test. This has also been done for the $cref/sparse Jacobian/link_sparse_jacobian/$$ test. $lnext For both the $cref/sparse_jacobian/link_sparse_jacobian/$$ and $cref/sparse_hessian/link_sparse_hessian/$$ tests, the sparse function is only chosen once (it used to be different for every repeat). This reduced the amount of computation not connected what is being tested. It also make the $cref/onetape/speed_main/Global Options/onetape/$$ a valid option for these tests. $lnext There was a bug in the $cref/multiple direction forward/forward_dir/$$ routine. Results for function values that are $cref/parameter/parvar/$$ were not being computed properly (all the derivatives are zero in this case). This has been fixed. $lend $head 01-07$$ The following changes were merged in from the $code color_hes$$ branch: $list number$$ Specify the type of $cref/coloring/sparse_hessian/work/color_method/$$ for the sparse hessian calculations. To be specific, instead of $code "cppad"$$ and $code "colpack"$$, the choices are $code "cppad.symmetric"$$, $code "cppad.general"$$, and $code "colpack.star"$$. This is not compatible with the change on $cref/01-02/whats_new_15/01-02/$$, which was so recent that this should not be a problem. $lnext The $cref/n_sweep/link_sparse_hessian/n_sweep/$$ values were not being returned properly by $cref cppad_sparse_hessian.cpp$$ and $cref adolc_sparse_hessian.cpp$$. The CppAD version has been fixed and the ADOL-C version has been set to zero. $lnext The $cref link_sparse_hessian$$ example case was to sparse for good testing (by mistake). This has been fixed. $lnext Add $icode n_sweep$$ to $cref/link_sparse_hessian/link_sparse_hessian/n_sweep/$$ and $cref/speed_main/speed_main/Speed Results/n_sweep/$$. $lnext Change the $code cppad$$ sparse Hessian $cref/color_method/sparse_hessian/work/color_method/$$ to take advantage of the symmetry of the Hessian (in a similar fashion to the $code colpack$$ coloring method). $lend $head 01-02$$ Added to option to uses $cref/colpack/colpack_prefix/$$ for the sparse Hessian $cref/coloring method/sparse_hessian/work/color_method/$$; see the example $cref colpack_hes.cpp$$. $end cppad-20170000.3/omh/whats_new/whats_new_07.omh0000644000175200017650000006731613057470463020244 0ustar coincoin-web$Id: whats_new_07.omh 3799 2016-03-12 12:33:53Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_07$$ $spell mul cxx omh tgz yyyymmdd isnan gcc executables makefiles tarballs autoconf Fadbad Sacado::Tay Dir Ginac xi Bool CppADvector inv namespace det_lu adouble Adolc op sqrt eps mega Kipp vcproj exp_apx Microsoft threadprivate gettimeofday ifndef Vec openmp dy automake makefile CppAD cygwin cppad.hpp config.h dd Adolc Taylor $$ $section Changes and Additions to CppAD During 2007$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2007 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-29$$ License conversions missed the copyright message at the top in the following special cases: $code makefile.am$$, $code makefile.in$$, and $code omh/license.omh$$. $head 12-25$$ The $cref install$$ instructions have been improved. $head 12-21$$ The $cref/--with-Documentation/auto_tools/--with-Documentation/$$ option on the $code configure$$ command line caused an error on some systems because it attempted to copy to many files. This has been fixed by copying the directory instead of the individual files. $head 12-08$$ By mistake, the documentation $cref License$$ statement for the GPL distribution was the same as for the CPL distribution. This has been fixed. $head 12-05$$ Change the name of the spec file from $codei%cppad-%yyyymmdd%.spec%$$ to $code cppad.spec$$. $head 12-04$$ Add the capability for the RPM spec file to use a different prefix directory. $head 12-03$$ This is the first version with the rpm spec file $code cppad.spec$$. $head 12-02$$ Add the $codei%DESTDIR=%directory%$$ option on the $cref/make install/auto_tools/make install/$$ command line. $head 11-29$$ The $cref unary_standard_math$$ function $code sqrt$$ did not link properly when $icode Base$$ was $code AD$$. This has been fixed. $head 11-23$$ The routines $code nan$$ and $code isnan$$ were failing for some systems because they use $code nan$$ and or $code isnan$$ as preprocessor symbols. This has been fixed; see $cref/macros/nan/Include/Macros/$$. In addition, the example and test $cref nan.cpp$$ has been added. $head 11-18$$ Speed tests for $code tape_values$$ branch were not better than trunk, so the good parts of that branch (but not all) were merged into the trunk. $pre $$ The interface specifications for $cref/base type requirements/base_require/$$ have been changed so that CppAD would compile with $code gcc 4.1.1$$ (which requires more definitions before use in template functions). This changed of requirements is demonstrated by the $cref base_complex.hpp$$ and $cref base_adolc.hpp$$ examples. $pre $$ The problem with newer C++ compilers requiring more definitions before use also required the user to know about $code float$$ and $code double$$ definitions for the standard math functions in the CppAD namespace; see $cref base_std_math$$. $pre $$ The $code example/test_one.sh$$ and $code test_more/test_one.sh$$ scripts were modified so that one only need specify the test file name (does not also need the test routine name). Some of the test routine declarations were changed from $icode/name/()/$$ to $icode/name/(void)/$$ to make this possible. $pre $$ The program $code test_more/test_more$$ was changed to always report the memory leak test results (same as $code example/example$$). $pre $$ The $cref PrintFor$$ function was putting an unused variable in the tape. This has been fixed. $head 11-06$$ Added the $code -DRAD_EQ_ALIAS$$ compiler flag to the $cref/Sacado speed tests/speed_sacado/$$. In addition, compiler flag documentation was included for Sacado and all the other speed tests. $head 11-05$$ MS project files have been added for running the $cref/cppad/speed_cppad/$$ and $cref/double/speed_double/$$ speed tests. $head 11-04$$ The $code cppad/config.h$$ file was not compatible with the Windows install procedure and the Windows project's could not find a certain include file. This has been fixed. $pre $$ The $cref/unix install/auto_tools/$$ procedure has been modified so that the one configure flag $code --with-Speed$$ builds all the possible executables related to the speed testing. $head 11-03$$ Improve the $cref speed_main$$ documentation and output (as well as the title for other sections under $cref speed$$). $pre $$ The subversion copy of the $cref/configure/auto_tools/Configure/$$ script was not executable. This has been fixed. $head 11-02$$ The instructions for downloading the current version using $code subversion$$ have changed. The user should now directly edit the file $codep trunk/configure $$ in order to set the correct date for the installation and to build the corresponding documentation. $pre $$ The $cref speed$$ section has been slightly reorganized (the main program and utilities have been separated). $pre $$ Add $cref speed_double$$ for testing the speed of evaluating functions in $code double$$ as apposed to gradients using AD types. $head 11-01$$ The instructions for downloading the current version using subversion have changed. The user must now execute the command $codep ./build.sh version $$ in order to set the correct version number for her (or his) installation. $pre $$ Add the return status for all the correctness tests to the documentation; see $code make test$$. $head 10-30$$ The download instructions did not update current version number and this broke the links to the current tarballs. This has been fixed. $pre $$ The documentation for $cref det_by_minor$$ and $cref det_by_lu$$ has been improved. The order of the elements in $cref det_of_minor$$ has been corrected (they were transposed but this did not really matter because determinants of transposes are equal). $pre $$ The makefiles in the distribution have been changed so that one can run configure from a directory other than the distribution directory. $head 10-27$$ A $code subversion$$ method for downloading CppAD has been added. $pre $$ The installation was broken on some systems because the $cref/configure/auto_tools/Configure/$$ command tried to run the $code autoconf$$ and $code automake$$ programs. This has been fixed by adding $code AM_MAINTAINER_MODE$$ to the $code autoconf$$ input file. $pre $$ Extend the $code subversion$$ methods to include a full installation and old versions. $head 10-23$$ The $cref/cxx_flags/auto_tools/cxx_flags/$$ environment variable has been changed from $code CPP_ERROR_WARN$$ to $code CXX_FLAGS$$. $pre $$ The command $code configure --help$$ now prints a description of the environment variables $code ADOLC_DIR$$, $code FADBAD_DIR$$, $code SACADO_DIR$$, $code BOOST_DIR$$, and $code CXX_FLAGS$$. In addition, if the environment variables $code POSTFIX_DIR$$ or $code CPP_ERROR_WARN$$ are used, an message is printed saying that are not longer valid. $head 10-22$$ The correctness checks and speed test wrappers were moved from the individual package directories to $cref speed_main$$. This way they do not have to be reproduced for each package. This makes it easier to add a new package, but it requires the prototype for $codei%compute_%test_name%$$ to be the same for all packages. $pre $$ The $href%http://trilinos.sandia.gov/packages/sacado/%Sacado%$$ package was added to the list of $cref speed$$ tests. In addition, the discussion about how to run each of the speed tests was corrected to include the $icode seed$$ argument. $pre $$ The $icode postfix_dir$$ option was removed on $cref/2006-12-05/whats_new_06/12-05/$$ but it was not removed from the $cref/configure/auto_tools/Configure/$$ documentation. This has been fixed. $pre $$ The routine $cref CheckSimpleVector$$ was changed. It used to require conversion of the form $codei% %Scalar%(%i%) %$$ where $icode i$$ was $code 0$$ or $code 1$$. This does not work with when $icode Scalar$$ is $code Sacado::Tay::Taylor$$. This requirement has been changed (see $cref/restrictions/CheckSimpleVector/Restrictions/$$) to support of $codei% %x% = %i% %$$ where $icode x$$ has type $icode Scalar$$ and $icode i$$ has type $code int$$. $pre $$ Fix include directives in $cref speed_fadbad$$ programs $code det_lu$$, $code det_minor$$, and $code poly$$, to use $code FADBAD++$$ instead of $code Fadbad++$$ directory. $pre $$ Add $code ADOLC_DIR$$, $code FADBAD_DIR$$, $code SACADO_DIR$$, and $code BOOST_DIR$$ to the $cref/configure/auto_tools/Configure/$$ help string. $head 10-16$$ Add $icode seed$$ argument and improve $cref speed_main$$ documentation. $head 10-13$$ Fix the title in $cref adolc_det_lu.cpp$$. Add the package name to each test case result printed by $cref speed_main$$. $head 10-05$$ Added and example using complex calculations for a function that is not complex differentiable $code not_complex_ad.cpp$$. (This example has been removed; see $cref/complex FAQ/Faq/Complex Types/$$.) $head 10-02$$ Extend the $cref pow$$ function to work for any case where one argument is $codei%AD<%Base%>%$$ and the other is $code double$$ (as do the binary operators). $head 09-06$$ If the $cref/method.step/OdeErrControl/Method/step/$$ function returned $code nan$$ (not a number), it was possible for $cref OdeErrControl$$ to drop into an infinite loop. This has been fixed. $head 08-09$$ Let user detect and handel the case where an ODE initial vector $icode xi$$ contains not a number $code nan$$ (see $cref Runge45$$, $cref Rosen34$$, and $cref OdeErrControl$$). $pre $$ Use the $code ||$$ operation instead of $code |$$ operator in the $code nan$$ function (The Ginac library seems to use an alias for the type $code bool$$ and does not have $code |$$ defined for this alias). $pre $$ The file $code test_more/ode_err_control.cpp$$ was using the wrong include file name since the change on 08/07. This has been fixed. $head 08-07$$ Sometimes an ODE solver takes to large a step and this results in invalid values for the variables being integrated. The ODE solvers $cref Runge45$$ and $cref Rosen34$$ have been modified to abort and return $cref nan$$ when it is returned by the differential equation evaluation. The solver $cref OdeErrControl$$ have been modified to try smaller steps when this happens. $pre $$ Fix an $cref/Sequence Constructor/FunConstruct/Sequence Constructor/$$ referenced to $code Dependent$$ in documentation (was using the $cref FunDeprecated$$ one argument syntax). $pre $$ Add comment about mixing debug and non-debug versions of CppAD in $cref/TrackDelVec/TrackNewDel/TrackDelVec/$$ error message. $head 07-30$$ $code CppADCreateBinaryBool$$ and $code CppADCreateUnaryBool$$ have been replaced by $code CPPAD_BOOL_BINARY$$ and $code CPPAD_BOOL_UNARY$$ respectively. In addition, the $cref wish_list$$ item for conversion of all preprocessor macros to upper case been completed and removed. $head 07-29$$ The preprocessor macros $code CppADUsageError$$ and $code CppADUnknownError$$ have been replaced by $code CPPAD_ASSERT_KNOWN$$ and $code CPPAD_ASSERT_UNKNOWN$$ respectively. The meaning for these macros has been included in the $cref cppad_assert$$ section. In addition, the $icode known$$ argument to $cref ErrorHandler$$ was wrong for the unknown case. $pre $$ The $cref wish_list$$ item for conversion of all preprocessor macros to upper case has been changes (to an item that was previous missing). $head 07-28$$ The preprocessor macro $code CPPAD_DISCRETE_FUNCTIOIN$$ was defined as a replacement for $code CppADCreateDiscrete$$ which has been deprecated. $head 07-26$$ Merge in changes made in $code branches/test_vector$$. $subhead 07-26$$ Change all occurrences of $code CppADvector$$, in the files $codei%test_more/%*%.cpp%$$ and $codei%speed/%*%/%*%.cpp%$$, where changed to $code CPPAD_TEST_VECTOR$$. All occurrences of the $code CppADvector$$ in the documentation were edited to reflect that fact that it has been deprecated. The documentation index and search for deprecated items has been improved. $subhead 07-25$$ Deprecate the preprocessor symbol $code CppADvector$$ and start changing it to $small $cref/CPPAD_TEST_VECTOR/test_vector/$$ $$. $pre $$ Change all occurrences of $code CppADvector$$, in the $codei%example/%*%.cpp%$$ files, to $code CPPAD_TEST_VECTOR$$. $head 07-23$$ The $cref TrackNewDel$$ macros $code CppADTrackNewVec$$, $code CppADTrackDelVec$$, and $code CppADTrackExtend$$ have been deprecated. The new macros names to use are $code CPPAD_TRACK_NEW_VEC$$, $code CPPAD_TRACK_DEL_VEC$$, and $code CPPAD_TRACK_EXTEND$$ respectively. This item has been removed from the $cref/software guidelines/wish_list/Software Guidelines/$$ section of the wish list. $pre $$ The member variable $cref/software guideline/wish_list/Software Guidelines/$$ wish list item has be brought up to date. $head 07-22$$ Minor improvements to the $cref mul_level_adolc_ode.cpp$$ example. $head 07-21$$ $list number$$ The $code openmp/run.sh$$ example programs $code example_a11c.cpp$$, $code openmp_newton_example.cpp$$, and $code sum_i_inv.cpp$$ have been changed so that they run on more systems (are C++ standard compliant). $lnext $cref base_require$$: The $code IdenticalEqual$$ function, in the $cref base_require$$ specification, was changed to $code IdenticalEqualPar$$ (note the $cref/API warning/base_require/API Warning/$$ in the $icode Base$$ requirement specifications). $lnext Implementation of the $cref/base requirements/base_require/$$ for complex types were moved into the $cref base_complex.hpp$$ example. $lend $head 07-20$$ The download for CppAD was still broken. It turned out that the copyright message was missing from the file $cref base_adolc.hpp$$ and this stopped the creation of the download files. This has been fixed. In addition, the automated testing procedure has been modified so that missing copyright messages and test program failures will be more obvious in the test log. $head 07-19$$ The download for CppAD has been broken since the example $code mul_level_adolc_ode.cpp$$ was added because the $code example/example$$ program was failing. This has been fixed. $head 07-18$$ A realistic example using Adolc with CppAD $cref mul_level_adolc_ode.cpp$$ was added. The documentation for $cref TrackNewDel$$ was improved. $head 07-14$$ Add a discussion at the beginning of $cref mul_level_ode.cpp$$ example (and improve the notation used in the example). $head 07-13$$ Separate the include file $cref base_adolc.hpp$$ from the $cref mul_level_adolc.cpp$$ example so that it can be used by other examples. $head 06-22$$ Add $cref mul_level_adolc.cpp$$, an example that demonstrates using $code adouble$$ and for the $cref/Base/base_require/$$ type. $pre $$ The $cref get_started.cpp$$ example did not build when the $code --with-Introduction$$ and $code BOOST_DIR$$ options were included on the $cref/configure/auto_tools/Configure/$$ command line. In fact, some of the $cref speed$$ tests also had compilation errors when $code BOOST_DIR$$ was include in the configure command. This has been fixed. $pre $$ There was a namespace reference missing in the files that could have caused compilation errors in the files $code speed/cppad/det_minor.cpp$$ and $code speed/cppad/det_lu.cpp$$. This has been fixed. $head 06-20$$ The MS project $code test_more/test_more.vcproj$$ would not build because the file $code test_more/fun_check.cpp$$ was missing; this has been fixed. In addition, fix warnings generated by the MS compiler when compiling the $code test_more/test_more.cpp$$ file. $pre $$ Add a section defining the $cref/Base type requirements/base_require/$$. Remove the $icode Base$$ type restrictions from the $cref Faq$$. Make all the prototype for the default Base types agree with the specifications in the Base type requirements. $pre $$ Fix the description of the $code tan$$ function in $cref unary_standard_math$$. $head 06-14$$ The routine $cref Rosen34$$ ( $cref Runge45$$ ) had a division of a $code size_t$$ ( $code int$$ ) by a $icode Scalar$$, where $icode Scalar$$ was any $cref NumericType$$. Such an operation may not be valid for a particular numeric type. This has been fixed by explicitly converting the $code size_t$$ to an $code int$$, then converting the $code int$$ to a $icode Scalar$$, and then preforming the division. (The conversion of an $code int$$ to any numeric type must be valid.) $head 05-26$$ If the $icode Base$$ type is not $code double$$, the $cref/computed assignment/compute_assign/$$ operators did not always allow for $code double$$ operands. For example, if $icode x$$ had type $code AD< AD >$$ $codei% %x% += .5; %$$ would slice the value $code .5$$ to an $code int$$ and then convert it to an $code AD< AD >$$. This has been fixed. $pre $$ This slicing has also been fixed in the $cref/assignment/ad_assign/$$ operation. In addition, the assignment and copy operations have been grouped together in the documentation; see $cref ad_ctor$$ and $cref ad_assign$$. $head 05-25$$ Document usage of $code double$$ with binary arithmetic operators, and combine all those operators into one section ($cref ad_binary$$). $pre $$ The documentation for all the $cref/computed assignment/compute_assign/$$ operators has been grouped together. In addition, a computed assignment wish list item has been added (it was completed and removed with the $cref/05-26/whats_new_07/05-26/$$ update.) $head 05-24$$ Suppose that $icode op$$ is a binary operation and we have $codei% %left% %op% %right% %$$ where one of the operands was $code AD< AD >$$ and the other operand was $code double$$. There was a bug in this case that caused the $code double$$ operand to be converted to $code int$$ before being converted to $code AD< AD >$$. This has been fixed. $head 05-22$$ The Microsoft examples and testing project file $code example/example.vcproj$$ was missing a reference to the source code file $code example/reverse_two.cpp$$. This has been fixed. $head 05-08$$ Reverse mode does not work with the $cref pow$$ function when the base is less than or equal zero and the exponent is an integer. For this reason, the $cref pow_int$$ function is no longer deprecated (and is used by CppAD when the exponent has type $code int$$). $head 05-05$$ Third and fourth order derivatives were included in the routine $code test_more/sqrt.cpp$$ that tests square roots. $pre $$ The return value descriptions were improved for the introduction examples: $cref/exp_2_for1/exp_2_for1/Return Value/$$, $cref/exp_2_for2/exp_2_for2/Return Value/$$, $cref/exp_eps_for1/exp_eps_for1/Return Value/$$, and $cref/exp_eps_for2/exp_eps_for2/Return Value/$$. $pre $$ The summation index in $cref sqrt_reverse$$ was changed from $latex k$$ to $latex \ell$$ to make partial differentiation with respect to $latex z^{(k)}$$ easier to understand. In addition, a sign error was corrected near the end of $cref sqrt_reverse$$. $pre $$ The dimension for the notation $latex X$$ in $cref reverse_identity$$ was corrected. $pre $$ The word mega was added to the spelling exception list for $code openmp/run.sh$$. $head 04-19$$ Improve connection from $cref reverse_identity$$ theorem to $cref reverse_any$$ calculations. $pre $$ Improve the $code openmp/run.sh$$ script. It now runs all the test cases at once in addition to including multiple number of thread cases for each test. $pre $$ Add the $code sum_i_inv_time.cpp$$ OpenMP example case. $pre $$ There was a typo in the $cref/second order/forward_order/Second Order/$$ discussion (found by Kipp Martin). It has been fixed. $head 04-17$$ Add a paragraph to $cref reverse_identity$$ explaining how it relates to $cref reverse_any$$ calculations. Add description of $cref/first/reverse_any/First Order/$$ and $cref/second order/reverse_any/Second Order/$$ results in $cref reverse_any$$. $head 04-14$$ Simplify the $cref Reverse$$ mode documentation by creating a separate $cref reverse_two$$ section for second order reverse, making major changes to the description in $cref reverse_any$$, and creating a third order example $cref reverse_checkpoint.cpp$$ for reverse mode calculations. $pre $$ Improve the $cref reverse_identity$$ proof. $head 04-11$$ Merge in changes made in $code branches/intro$$. $subhead 04-11$$ Add $cref exp_eps_rev2$$ and its verification routine $cref exp_eps_rev2.cpp$$. $subhead 04-10$$ Finished off $cref exp_2_rev2$$ and added $cref exp_2_rev2.cpp$$ which verifies its calculations. Added second order calculations to $cref exp_2_cppad$$. Added $cref exp_eps_for2$$ and its verification routine. $subhead 04-07$$ Added a preliminary version of $cref exp_2_rev2$$ (does not yet have verification or exercises). $subhead 04-06$$ Fixed a problem with the Microsoft Visual Studio project file $code introduction/exp_apx/exp_apx.vcproj$$ (it did not track the file name changes of the form $code exp_apx/exp_2_for$$ to $code exp_apx/exp_2_for1$$ on 04-05). $pre $$ Added $cref exp_2_for2$$ to introduction. $subhead 04-05$$ Use order expansions in introduction; e.g., the $cref/second order expansion/exp_2_for2/Second Order Expansion/$$ for the $cref exp_2$$ example. $head 03-31$$ Merge in changes made in $code branches/intro$$ and remove the corresponding Introduction item from the wish list: $subhead 03-31$$ Create the a simpler exponential approximation in the $cref introduction$$ called $cref exp_2$$ which has a different program variable for each variable in the operation sequence. $pre $$ Simplify the $cref exp_eps$$ approximation using the $latex v_1 , \ldots , v_7$$ notation so that variables directly correspond to index in operation sequence (as with the $cref exp_2$$ example). $subhead 03-30$$ The Microsoft project file $code introduction/exp_apx/exp_apx.vcproj$$ was referencing $code exp_apx_ad.cpp$$ which no longer exists. It has been changed to reference $code exp_apx_cppad.cpp$$ which is the new name for that file. $head 03-29$$ Fixed entries in this file where the year was mistakenly used for the month. To be more specific, $codei%07-%dd%$$ was changed to $codei%03-%dd%$$ for some of the entries directly below. $pre $$ Corrected some places where $code CppAD$$ was used in stead of $code Adolc$$ in the $cref adolc_poly.cpp$$ documentation. $pre $$ Added an Introduction and $cref/Tracing/wish_list/Tracing/$$ entry to the wish list. (The Introduction item was completed on $cref/03-31/whats_new_07/03-31/$$.) $head 03-20$$ Example A.1.1c, $code example_a11c.cpp$$, from the OpenMP 2.5 standards document, was added to the tests that can be run using $code openmp/run.sh$$. $head 03-15$$ Included the changes from openmp branch so that so CppAD does not use the OpenMP $code threadprivate$$ command (some systems do not support this command). $subhead 03-15$$ Add command line arguments to $code openmp_newton_example.cpp$$, and modified $code openmp/run.sh$$ to allow for more flexible testing. $subhead 03-14$$ Fixed some Microsoft compiler warnings by explicitly converting from $code size_t$$ to $code int$$. $pre $$ In the Microsoft compiler case, the $code cppad/config.h$$ file had the wrong setting of $code GETTIMEOFDAY$$. The setting is now overridden (and always false) when the $code _MSC_VER$$ preprocessor symbol is defined. $pre $$ Some minor changes were made in an effort to speed up the multi-threading case. $subhead 03-13$$ Started a new openmp branch and created a version of CppAD that does not use the OpenMP $code threadprivate$$ command (not supported on some systems). $head 03-09$$ Included the changes from openmp branch so that OpenMP can be used with CppAD, see $cref omp_max_thread$$. The changes dated between $cref/02-15/whats_new_07/03-09/02-15/$$ and 03-28 below were made in the openmp branch and transferred to the trunk on 03-09. $subhead 03-28$$ The conditional include commands were missing on some include files; for example $codep # ifndef CPPAD_BENDER_QUAD_HPP # define CPPAD_BENDER_QUAD_HPP $$ was missing at the beginning of the $cref BenderQuad$$ include file. This has been fixed. $pre $$ The $code speed_test$$ routines $cref/timing/speed_test/Timing/$$ was changed to use $code gettimeofday$$ if it is available. ($code gettimeofday$$ measures wall clock time which is better in a multi-threading environment). $pre $$ Added the user multi-threading interface $cref omp_max_thread$$ along with its examples which are distributed in the directory $code openmp$$. $pre $$ The $codei%speed/%*%.hpp%$$ files have been moved to $codei%cppad/speed/%*%.hpp%$$ and the corresponding wish list item has been removed. $pre $$ The multiple tapes with the same base type wish list item have been removed (it's purpose was multi-threading which has been implemented). $subhead 02-27$$ The $cref speed$$ include files are currently being distributed above the $code cppad$$ include directory. A fix this wish list item has been added. $pre $$ Multiple active tapes required a lot of multi-threading access management for the tapes. This was made simpler (and faster) by having at most one tape per thread. $subhead 02-22$$ The include command in the $cref speed_test$$ documentation was $codep # include $$ but it should have been $codep # include $$ This has been fixed. $subhead 02-17$$ An entry about optimizing the operation sequence in an $cref/ADFun/FunConstruct/$$ object was added to the $cref wish_list$$. $pre $$ Change the argument syntax for $cref Dependent$$ and deprecate the $cref/old Dependent syntax/FunDeprecated/Dependent/$$. $subhead 02-16$$ Added $codei%VecAD<%Base%>%$$ as a valid argument type for the $cref/Parameter and Variable/ParVar/$$ functions. In addition, $cref/size_t indexing/VecAD/size_t Indexing/$$ is was extended to be allowed during taping so long as the VecAD object is a parameter. $subhead 02-15$$ Fixed the $code example/test_one.sh$$ script (it was using its old name $code one_test$$). $head 02-06$$ The $cref BenderQuad$$ documentation was improved by adding the fact that the $icode x$$ and $icode y$$ arguments to the $codei%f%.dy%$$ member function are equal to the $icode x$$ and $icode y$$ arguments to $code BenderQuad$$. Hence values depending on them can be stored as private objects in $icode f$$ and need not be recalculated. $head 02-04$$ The method for distributing the documentation needed to be changed in the top level $code makefile.am$$ in order to be compatible with automake version 1.10. $head 02-03$$ The change on $cref/02-01/whats_new_07/02-01/$$ had a new, saved as a static pointer, with no corresponding delete. This was not a bug, but it has been changed to avoid an error message when using CppAD with $href%http://valgrind.org/%valgrind%$$. $pre $$ The change to the $code pow$$ function on $cref/06-12-10/whats_new_06/12-10/$$ did not include the necessary changes to the $cref/Sparsity/Sparse/$$ calculations. This has been fixed. $head 02-02$$ Fix minor errors and improve $cref/profiling/auto_tools/Profiling CppAD/$$ documentation. Also change the problem sizes used for the $cref speed$$ tests. $head 02-01$$ There seems to be a bug in the cygwin version of g++ version 3.4.4 with the -O2 flag whereby some static variables in static member functions sometimes do not get constructed before being used. This has been avoided by using a static pointer and the new operator in cppad/local/ad.hpp. $head 01-29$$ The copyright message was missing from some of the distribution files for some new files added on $cref%06-12-15%whats_new_06%12-15%$$. This resulted in the tarballs $icode%*%.tgz%$$ and $icode%*%.zip%$$ not existing for a period of time. The automated tests have been extended so that this should not happen again. $end cppad-20170000.3/omh/whats_new/whats_new_16.omh0000644000175200017650000003561713057470463020243 0ustar coincoin-web$Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_16$$ $spell alloc hpp valgrind uninitialized adouble CppAD Eigen std namespace cppad Hes Jac mul ifndef xam makefile vy inv atanh colpack Wmisleading gcc sacado chrono const_iterator op mingw $$ $section Changes and Additions to CppAD During 2016$$ $head Introduction$$ The sections listed below contain a list of the changes to CppAD in reverse order by date. The purpose of these sections is to assist you in learning about changes between various versions of CppAD. $head 12-23$$ Added a way for the user to determine what tests options are available; see $cref/make check/cmake/make check/$$. $head 12-20$$ Change the optimize $cref/examples/optimize/Examples/$$ to use $cref NearEqual$$ for floating point tests (instead of exactly equal). There were some other exactly equal floating point tests that were failing on a $code mingw$$ system. Theses have also been fixed. $head 12-18$$ Add the $cref/no_print_for_op/optimize/options/no_print_for_op/$$ to the optimize routine. $head 12-13$$ $list number$$ Fix a bug in $cref ForSparseHes$$. To be more specific, there was a bug in handling the cumulative summations operator in this routine. This could only come up when used an $cref/optimized/optimize/$$ $cref/f/ForSparseHes/f/$$, $lnext Add the $cref/nest_conditional.cpp/optimize_nest_conditional.cpp/$$ example. $lend $head 12-11$$ Improve the $cref optimize$$ documentation. This includes making examples that demonstrate specific aspects of the optimization; see $cref/forward_active.cpp/optimize_forward_active.cpp/$$, $cref/reverse_active.cpp/optimize_reverse_active.cpp/$$, $cref/compare_op.cpp/optimize_compare_op.cpp/$$, $cref/conditional_skip.cpp/optimize_conditional_skip.cpp/$$, $cref/cumulative_sum.cpp/optimize_cumulative_sum.cpp/$$. $head 12-09$$ The $cref/options/optimize/options/$$ argument was added to the optimize routine. $head 11-18$$ Move classes and functions that are part of the user API from the $code cppad/local$$ directory to the $code cppad/core$$ directory. The remaining symbols, in the $code cppad/local$$ directory, are now in the $code CppAD::local$$ namespace. Note that a class in the $code CppAD$$ name space, may have a member function that is not part of the user API. $head 11-14$$ Increase the speed of the $code sparse_pack$$ class. This improves the speed for $cref/vector of boolean/glossary/Sparsity Pattern/Vector of Boolean/$$ sparsity pattern calculations. $head 11-13$$ Merged in the $code sparse$$ branch which has $code const_iterator$$, instead of $code next_element$$ for the $code sparse_list$$ and $code sparse_pack$$ classes. These classes are not part of the CppAD API and hence their specifications can change (as in this case). They can be used to get more efficient representations of $cref/sparsity patterns/glossary/Sparsity Pattern/$$. $head 10-27$$ The optional $cref/optimize/checkpoint/optimize/$$ option was added to the checkpoint functions. $head 10-12$$ $list number$$ Change $cref elapsed_seconds$$ to use $code std::chrono::steady_clock$$ instead of $code std::chrono::high_resolution_clock$$. $lnext The test for C++11 features was failing on a Mac system because the elapsed time was returning as zero (between two events). This test has been made more robust by add a one millisecond sleep between the two clock accesses. $lend $head 09-29$$ The multiple directions version of $cref/forward/forward_dir/$$ was missing $cref erf$$ function in the case where C++ 2011 was supported; see $href%https://github.com/coin-or/CppAD/issues/16%issue 16%$$. This has been fixed. $head 09-27$$ Change the implementation of $cref atomic_eigen_cholesky.hpp$$ so that the computation of $latex M_k$$ exactly agrees with the corresponding $cref/theory/cholesky_theory/$$. $head 09-26$$ $list number$$ A possible bug in the $cref optimize$$ command was fixed. To be specific, a warning of the form indentations; $codei% warning: this 'if' clause does not guard... [-Wmisleading-indentation] %$$ using the gcc-6.2.1 compiler, was fixed and it may have fixed a bug. $lnext There was a problem with the $cref/sacado/speed_sacado/$$ where the symbol $code HAS_C99_TR1_CMATH$$ was being defined twice. This has been fixed by leaving it up to the sacado install to determine if this symbol should be defined. $lend $head 09-16$$ Fix a problem using the $cref/colpack/speed_main/Sparsity Options/colpack/$$ option to the $code speed_cppad$$ program. (There was a problem whereby the $code speed_cppad$$ program did not properly detect when $code colpack$$ was available.) $head 09-13$$ Test third order and fix bug in $cref atomic_eigen_cholesky.hpp$$ for orders greater than or equal to three. $head 08-30$$ Add the $cref atomic_eigen_cholesky.cpp$$ example. $head 08-25$$ $list number$$ Fix some missing include files in $code optimize.hpp$$ and $code set_union.hpp$$ (when compiling with MS Visual Studio 2015). $lnext Fix a warning in $code atanh.hpp$$ (when compiling with MS Visual Studio 14). $lnext Fix a typo in the $cref/Reverse/atomic_eigen_mat_inv.hpp/Theory/Reverse/$$ section of the $code eigen_mat_inv.hpp$$ example. $lend $head 07-17$$ Add documentation for only needing to compute a $cref/column subset/sparse_hessian/p/Column Subset/$$ of the sparsity pattern when computing a subset of a sparse Hessians. In addition, improve the corresponding example $cref sparse_sub_hes.cpp$$. $head 07-14$$ Correct title in $cref ForSparseHes$$ (change Reverse to Forward). $head 06-30$$ Change the $cref atomic_mat_mul.cpp$$ example so that on atomic object works for matrices of any size. $head 06-29$$ Change the $cref atomic_base$$ examples so they do no longer use the deprecated $cref/atomic function/deprecated/Atomic Functions/$$ interfaces to $code for_sparse_jac$$, $code rev_sparse_jac$$, $code for_sparse_hes$$, and $code rev_sparse_hes$$. $head 06-27$$ $list number$$ Improve the $cref atomic_eigen_mat_mul.hpp$$ and $cref atomic_eigen_mat_inv.hpp$$ examples. Most importantly, one atomic object now works for matrices of any size. $lnext Add the vector $icode x$$, that contains the parameters in an atomic function call to the user following atomic functions: $cref/for_sparse_jac/atomic_rev_sparse_jac/Implementation/x/$$, $cref/rev_sparse_jac/atomic_rev_sparse_jac/Implementation/x/$$, $cref/for_sparse_hes/atomic_rev_sparse_jac/Implementation/x/$$, $cref/rev_sparse_hes/atomic_rev_sparse_jac/Implementation/x/$$. This enables one to pass parameter information to these functions; e.g., the dimensions of matrices that the function operates on. $lend $head 06-25$$ Add more entries to the optimization $cref/wish_list/wish_list/Optimization/$$. $head 06-10$$ Add a $cref/check_finite/wish_list/check_finite/$$ wish list item. $head 05-05$$ $list number$$ Add documentation for $cref/redirecting output/PrintFor/Redirecting Output/$$ for the $code PrintFor$$ function. $lnext Change distributed version to build examples as debug instead of release version. (Was changed to release version while checking for compiler warnings; see $code 04-17$$ below). $lend $head 04-17$$ Fix all some compiler warnings that occurred when compiling the $cref/examples/Example/$$ with $cref/NDEBUG/faq/Speed/NDEBUG/$$ defined. $head 03-27$$ $list number$$ Fix a bug in the calculation of the $cref atomic_eigen_mat_inv.hpp$$ $cref/reverse/atomic_eigen_mat_inv.hpp/Private/reverse/$$ example. $lnext Use a very simple method (that over estimates variables) for calculating $cref/vy/atomic_forward/vy/$$ in the $cref atomic_eigen_mat_inv.hpp$$ $cref/forward/atomic_eigen_mat_inv.hpp/Private/forward/$$ example. $lend $head 03-26$$ $list number$$ Implement and test the $cref atomic_eigen_mat_inv.cpp$$ $cref/reverse/atomic_eigen_mat_inv.hpp/Private/reverse/$$ is implemented. $lnext Fix a bug in the calculation of $cref/vy/atomic_forward/vy/$$ in the $cref atomic_eigen_mat_inv.hpp$$ $cref/forward/atomic_eigen_mat_inv.hpp/Private/forward/$$ example. $lend $head 03-25$$ $list number$$ Start construction of the $cref atomic_eigen_mat_inv.cpp$$ example, currently only $cref/forward/atomic_eigen_mat_inv.hpp/Private/forward/$$ is implemented and tested. $lnext More improvements to $cref atomic_eigen_mat_mul.cpp$$ example. $lend $head 03-24$$ $list number$$ Fix build of $code example/atomic.cpp$$ when $cref eigen_prefix$$ is not available (bug introduced when $cref atomic_eigen_mat_mul.cpp$$ was added). $lnext Extend $cref atomic_eigen_mat_mul.cpp$$ example to include $cref/for_sparse_jac/atomic_eigen_mat_mul.hpp/Private/for_sparse_jac/$$, $cref/rev_sparse_jac/atomic_eigen_mat_mul.hpp/Private/rev_sparse_jac/$$, $cref/for_sparse_hes/atomic_eigen_mat_mul.hpp/Private/for_sparse_hes/$$, $cref/rev_sparse_hes/atomic_eigen_mat_mul.hpp/Private/rev_sparse_hes/$$. $lnext Fix a bug in the $cref ForSparseHes$$ routine. $lnext Edit $cref atomic_rev_sparse_hes$$ documentation. $lend $head 03-23$$ $list number$$ Fix bug in auto-tools file $code example/atomic/makefile.am$$ (introduced on 03-22). $lnext Improve the $cref atomic_eigen_mat_mul.cpp$$ example and extend it to include reverse mode. $lend $head 03-22$$ $list number$$ Start construction of the $cref atomic_eigen_mat_mul.cpp$$ example. $lnext change $code atomic_ode.cpp$$ to $cref checkpoint_ode.cpp$$ and $code atomic_extended_ode.cpp$$ to $cref checkpoint_extended_ode.cpp$$. $lend $head 03-21$$ Change the $cref atomic_mat_mul.hpp$$ class name from $code mat_mul$$ to $code atomic_mat_mul$$. This example use of the name $code mat_mul$$ in the $cref atomic_mat_mul.cpp$$ example / test. $head 03-20$$ $list number$$ Include the sub-directory name to the include guards in $icode%*%.hpp%$$ files. For example, $codep # ifndef CPPAD_UTILITY_VECTOR_HPP # define CPPAD_UTILITY_VECTOR_HPP $$ appears in the file $code cppad/utility/vector.hpp$$. This makes it easier to avoid conflicts when choosing $cref addon$$ names. $lnext Add the $cref set_union$$ utility and use it to simplify the $cref atomic$$ examples that use $cref/vector of sets/glossary/Sparsity Pattern/Vector of Sets/$$ sparsity patterns. $lend $head 03-19$$ $list number$$ Move $cref atomic_mat_mul.cpp$$ to $code atomic_mat_mul_xam.cpp$$ (moved back on $cref/03-21/whats_new_16/03-21/$$. $lnext Move $code atomic_matrix_mul.hpp$$ to $cref atomic_mat_mul.hpp$$. $lend $head 03-17$$ Add the $code atomic_ode.cpp$$ and $code atomic_extended_ode.cpp$$ examples. $head 03-12$$ $list number$$ Move the example $code reverse_any.cpp$$ to $cref reverse_checkpoint.cpp$$. $lnext Add the $cref atomic_mul_level.cpp$$ example. $lend $head 03-05$$ The following atomic function examples were added These examples are for a specific atomic operation. In addition, the domain and range dimensions for these examples are not one and not equal to each other: $cref atomic_forward.cpp$$, $cref atomic_reverse.cpp$$, $cref atomic_for_sparse_jac.cpp$$, $cref atomic_rev_sparse_jac.cpp$$, $cref atomic_for_sparse_hes.cpp$$, $cref atomic_rev_sparse_hes.cpp$$. $head 03-01$$ $list number$$ Improve documentation of implementation requirements for the atomic $cref/rev_sparse_jac/atomic_rev_sparse_jac/Implementation/$$. $lnext Make some corrections to the $cref atomic_for_sparse_hes$$ documentation. and fix a bug in how CppAD used these functions. $lend $head 02-29$$ $list number$$ Merged sparse into master branch. This makes the $cref ForSparseHes$$ routine available for use. $lnext Changed the $cref/global options/speed_main/Global Options/$$ in the speed test main program to use one global variable with prototype $srccode%cpp% extern std::map global_option; %$$ $lend $head 02-28$$ Fix a mistake in the old atomic $code example/sparsity/sparsity.cpp$$ example. This example has since been changed to $cref atomic_set_sparsity.cpp$$. $head 02-27$$ The $code --with-sparse_set$$ and $code --with-sparse_set$$ options were removed from the $cref auto_tools$$ install procedure. $head 02-26$$ The condition that the operation sequence in $icode f$$ is $cref/independent/glossary/Operation/Independent/$$ of the independent variables was added to the statement about the validity of the sparsity patterns; see $icode x$$ in $cref/ForSparseJac/ForSparseJac/x/$$, $cref/RevSparseJac/RevSparseJac/x/$$, and $cref/RevSparseHes/RevSparseHes/x/$$. $head 02-25$$ The $cref cmake$$ command line argument $code cppad_sparse_list$$ has been removed (because it is so much better than the other option). $head 02-23$$ A new version of the $code cppad_sparse_list$$ class (not part of user API) uses reference counters to reduce the number of copies of sets that are equal. This improved the speed of sparsity pattern computations that use the $cref/vector of sets/glossary/Sparsity Pattern/Vector of Sets/$$ representation. For example, the results for the $cref cppad_sparse_hessian.cpp$$ test compare as follows: $codep sparse_hessian_size = [ 100, 400, 900, 1600, 2500 ] sparse_hessian_rate_old = [ 1480, 265.21, 93.33, 41.93, 0.86 ] sparse_hessian_rate_new = [ 1328, 241.61, 92.99, 40.51, 3.80 ] $$ Note that the improvement is only for large problems. In fact, for large problems, preliminary testing indicates that the new vector of sets representation preforms better than the $cref/vector of boolean/glossary/Sparsity Pattern/Vector of Boolean/$$ representation. $head 01-21$$ Fix a $code valgrind$$ warning about use of uninitialized memory in the test $code test_more/checkpoint.cpp$$ (the problem was in the test). $head 01-20$$ $list number$$ Fix a $code valgrind$$ warning about use of uninitialized memory when using the $cref/adouble/base_adolc.hpp/$$ base type. This required an optional $cref base_hash$$ function and the special $cref/adouble hash_code/base_adolc.hpp/hash_code/$$ implementation. $lnext The $code adouble$$ $cref to_string$$ functions required a special implementation; see $cref/adouble to_string/base_adolc.hpp/to_string/$$. $lnext Add the $cref/to_string/base_alloc.hpp/to_string/$$ and $cref/hash_code/base_alloc.hpp/hash_code/$$ examples to the $code base_alloc.hpp$$ example. $lend $head 01-18$$ $list number$$ Fix ambiguity between $code CppAD::sin$$ and $code std::sin$$, and other standard math functions, when using $codep using namespace std; using namespace CppAD; $$ This is OK for simple programs, but not generally recommended. See $code double$$ version of base class definitions for $cref/Unary Standard Math/base_double.hpp/Unary Standard Math/$$ for more details. $lnext Change Eigen array example $cref eigen_array.cpp$$ to use member function version of $code sin$$ function (as per Eigen's array class documentation). $lend $end cppad-20170000.3/omh/whats_new/whats_new_08.omh0000644000175200017650000003344013057470463020234 0ustar coincoin-web$Id: whats_new_08.omh 3768 2015-12-28 18:58:35Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_08$$ $spell dir inline tanh erf nlp fg_vector Bool Ipopt Jacobians Jacobian cygwin retape det Adolc gcc speedtest tarballs cppad cpl gpl tgz Microsoft op CppAD yum vec eval const $$ $section Changes and Additions to CppAD During 2008$$ $mindex erf ipopt_cppad_nlp$$ $head Introduction$$ This section contains a list of the changes to CppAD during 2008 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. $head 12-19$$ In the documentation for $cref pow_int$$ change the integer exponent from $codei%int %y%$$ to $codei%const int &%y%$$. In the implementation for $cref pow$$ make the integer base case agree with the documentation; i.e., change from $codei%int %x%$$ to $codei%const int &%x%$$. $head 12-14$$ Added another test of $cref mul_level$$ calculations (in the $code test_more$$ directory). $head 12-04$$ Extensive explanation for the $code ipopt_cppad/ipopt_cppad_ode$$ example was provided in the section $cref/ipopt_cppad_ode/ipopt_nlp_ode/$$. $head 11-22$$ The CppAD interface to the Ipopt nonlinear programming solver $cref cppad_ipopt_nlp$$ has been moved from $code example/ipopt_cppad_nlp$$ to $code ipopt_cppad/ipopt_cppad_nlp$$. $head 11-21$$ The Microsoft's Visual C++ Version 9.0 generates a warning of the form $codei warning C4396:%...%$$ for every template function that is declared as a both a friend and inline (it thinks it is only doing this for specializations of template functions). The warnings are no longer generated because these $code inline$$ directives are converted to empty code when a Microsoft Visual C++ is used. $head 11-20$$ The function $codei%tanh(%x%)%$$ was added to the $cref unary_standard_math$$ functions. The $code abs$$ and $code erf$$ functions were removed from the $cref/Base requirements/base_require/$$. The restrictions about the Base class were removed from $cref abs$$, $cref atan2$$, $cref LuRatio$$, $cref erf$$. $pre $$ Visual Studio Version 9.0 could not handle the large number of static constants in the CppAD $cref erf$$ function. This function was changed to a simpler representation that is much faster and that is differentiable at all points (not defined differently on subregions). The down side to this is that the new version is not as accurate. $head 10-27$$ Change prototypes for $code ipopt_cppad/ipopt_cppad_ode$$ helper routines to use $code const$$ (where appropriate). $head 10-17$$ Major improvements to the $code ipopt_cppad/ipopt_cppad_ode$$ example. $head 10-16$$ Minor improvement to description of optimization argument in $code ipopt_cppad/ipopt_cppad_ode$$. $head 09-30$$ Add or modify some wish list entries; see $code cppad_ipopt_nlp$$ (since removed), multiple argument forward (completed with $cref forward_dir$$), and sparsity patterns ($cref/sparsity patterns/glossary/Sparsity Pattern/$$ has been fulfilled). $head 09-26$$ Use parenthesis and brackets to group terms of the form $latex m \times I$$ to make the documentation of $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ easier to read. Changed $code ipopt_cppad/ipopt_cppad_ode$$ to use $latex y(t)$$ for the solution of the ODE to distinguish it for $latex x$$, the vector we are optimizing with respect to. $head 09-18$$ Changed $code ipopt_cppad/ipopt_cppad_ode$$ to a case where $latex x(t)$$ is a pair of exponential functions instead of a linear and quadratic. Fixed some of the comments in this example and included the source code in the documentation (which was missing by mistake). $head 09-17$$ Changed $code ipopt_cppad/ipopt_cppad_ode$$ to a case where there are two components in the ODE (instead of one). Also removed an initialization section that was only intended for tests with a specific initial value. $head 09-16$$ Add $code ipopt_cppad/ipopt_cppad_ode$$, an example and test that optimizes the solution of an ODE. Change $code r_eval$$ to $code eval_r$$ in $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$. Fix a dimension of $code u_ad$$ error in $code ipopt_cppad_nlp$$. $head 09-12$$ Converted from storing full Hessian and Jacobian to a sparse data structure in $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$. This greatly reduced the memory requirements (and increased the speed) for sparse problems. $head 09-10$$ Fixed more indexing bugs in $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ that effected cases where the domain index vector $latex J_{k, \ell}$$ was different for different values of $latex k$$ and $latex \ell$$. $pre $$ In $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$, combined $icode%fg_info%->domain_index()%$$ and $icode%fg_info%->range_index()%$$ into a single function called $icode%fg_info%->index()%$$. Also added more error checking (if $code NDEBUG$$ is not defined). $head 09-09$$ Fixed an indexing bug in $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$. (This effected cases where the domain index vector $latex J_{k, \ell}$$ was different for different values of $latex k$$ and $latex \ell$$.) $head 09-07$$ Change $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ so that object and constraints are expressed as the double summation of simpler functions. This is more versatile that the single summation representation. $head 09-06$$ Checked in a major change to $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ whereby the object and constraints can be expressed as the sum of simpler functions. This is the first step in what will eventually be a more versatile representation. $head 09-05$$ Fix bug in $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ (not recording the function at the proper location. Here is the difference that occurred multiple places in the $code ipopt_cppad/ipopt_cppad_nlp.cpp$$ source: $codep for(j = 0; j < n_; j++) - x_ad_vec[0] = x[j]; + x_ad_vec[j] = x[j]; $$ This did not show up in testing because there currently is no test of $code ipopt_cppad_nlp$$ where the operation sequence depends on the value of $latex x$$. $pre $$ Changed $code eval_grad_f$$ in $code ipopt_cppad_nlp.cpp$$ to be more efficient. $head 09-04$$ The $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ interface has been changed to use a derived class object instead of a pointer to a function. $head 09-03$$ The $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ interface has been changed to use $code size_t$$ instead of $code Ipopt::Index$$. $head 09-01$$ Back out the changes made to $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ on 08-29 (because testing proved the change to be less efficient in the case that motivated the change). $head 08-29$$ The $code push_vector$$ member function was missing from the $cref/vectorBool/Cppad_vector/vectorBool/$$ class. This has been fixed. In addition, it seems that for some cases (or compilers) the assignment $codei% %x%[%i%] = %y%[%j%] %$$ did not work properly when both $icode x$$ and $icode y$$ had type $code vectorBool$$. This has been fixed. $pre $$ The $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ example has been extended so that it allows for both scalar and vector evaluation of the objective and constraints; see the argument $icode fg_vector$$ in $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$. In the case where there is not a lot of common terms between the functions, the scalar evaluation may be more efficient. $head 08-19$$ Add $cref/push of a vector/CppAD_vector/push_vector/$$ to the $code CppAD::vector$$ template class. This makes it easy to accumulate multiple scalars and $cref/simple vectors/SimpleVector/$$ into one large $code CppAD::vector$$. $head 08-08$$ There was an indexing bug in the $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$ example that affected the $icode retape$$ equal to $code false$$ case. This has been fixed. In addition, the missing $icode retape$$ documentation was added. $head 07-02$$ Extend $cref/configure/auto_tools/Configure/$$ command to check for extras libraries that are necessary for linking the ipopt example. $head 06-18$$ Add specifications for the Ipopt class $cref/ipopt_cppad_nlp/cppad_ipopt_nlp/$$. This is only an example class it may change with future versions of CppAD. $head 06-15$$ The nonlinear programming example $cref ipopt_nlp_get_started.cpp$$ was added. This is a preliminary version of this example. $head 06-11$$ The sparsity pattern for the Hessian was being calculated each time by $cref/SparseHessian/sparse_hessian/$$. This is not efficient when the pattern does not change between calls to $code SparseHessian$$. An optional sparsity pattern argument was added to $code SparseHessian$$ so that it need not be recalculated each time. $head 06-10$$ The sparsity pattern for the Jacobian was being calculated each time by $cref/SparseJacobian/sparse_jacobian/$$. This is not efficient when the pattern does not change between calls to $code SparseJacobian$$. An optional sparsity pattern argument was added to $code SparseJacobian$$ so that it need not be recalculated each time. $head 05-08$$ The $cref sparse_jacobian$$ routine has been added. $pre $$ The example in $cref sparse_hessian$$ pointed to $cref hessian.cpp$$ instead of $cref sparse_hessian.cpp$$. This has been fixed. $head 05-03$$ The $code retape$$ flag has been added to $cref speed_main$$. In addition the routines $cref link_det_minor$$, $cref link_poly$$, and $cref link_ode$$ pass this flag along to the speed test implementations (because the corresponding tests have a fixed operation sequence). If this flag is false, a test implementation is allowed to just tape the operation sequence once and reuse it. The following tests use this flag: $cref adolc_det_minor.cpp$$, $cref cppad_det_minor.cpp$$, $cref cppad_ode.cpp$$, $cref adolc_poly.cpp$$, $cref cppad_poly.cpp$$. $pre $$ Create specialized zero order forward mode routine that should be faster, but does not test out as faster under cygwin g++ (GCC) 3.4.4. $head 04-20$$ Added the $cref ode_evaluate$$ speed test utility in preparation for having ode speed tests. Created ode speed test for the $code cppad$$ and $code double$$ cases; see $cref speed_main$$. In addition, added the examples $cref ode_evaluate.cpp$$ and $cref sparse_hessian.cpp$$. $pre $$ Changed the $cref speed_main$$ routines defined for each package from $codei%compute_%name%$$ to $codei%link_%name%$$. For example, in $code speed/cppad/det_minor.cpp$$, the function name $code compute_det_minor$$ was changed to $code link_det_minor$$. $head 04-18$$ Fix a problem in the $cref link_poly$$ correctness test. Also add $cref double_sparse_hessian.cpp$$ to the set speed and correctness tests (now available). $head 04-10$$ Change all the $cref/Adolc speed/speed_adolc/$$ examples to use $cref TrackNewDel$$ instead of using $code new$$ and $code delete$$ directly. This makes it easy to check for memory allocation errors and leaks (when $code NDEBUG$$ is not defined). Also include in documentation sub functions that indicate the $code sparse_hessian$$ speed test is not available for $cref double_sparse_hessian.cpp$$, $cref fadbad_sparse_hessian.cpp$$, and $cref sacado_sparse_hessian.cpp$$. $head 04-06$$ The following $cref/wish list/wish_list/$$ entry has been completed and removed from the list: "Change private member variables names (not part of the user interface) so that they all end with an underscore." $head 04-04$$ Fix a problem compiling the speed test $cref/main/speed_main/$$ program with gcc 4.3. $head 03-27$$ Corrected $cref cppad_sparse_hessian.cpp$$ so that it uses the sparse case when $code USE_CPPAD_SPARSE_HESSIAN$$ is $code 1$$. Also added a wish list sparsity pattern entry (the $cref/sparsity pattern/glossary/Sparsity Pattern/$$ entry has been fulfilled). $pre $$ Change the name of $code speedtest.cpp$$ to $cref speed_program.cpp$$. $head 02-05$$ Change windows install instructions to use Unix formatted files (so only two instead of four tarballs are necessary for each version). The Microsoft project files for $code speed/cppad$$, $code speed/double$$, and $code speed/example$$ were missing. This has also been fixed. $head 02-03$$ There was an ambiguity problem (detected by g++ 4.3) with the following operations $codei% %x% %op% %y% %$$ where $icode x$$ and $icode y$$ were $code AD$$ and $icode op$$ was a member operator of that class. This has been fixed by making all such member functions friends instead of members of $code AD$$. $pre $$ Remove computed assignment entry from wish list (it was fixed on $cref/2007-05-26/whats_new_07/05-26/$$). Add an expression hashing entry to the $cref wish_list$$ (it has since been removed). Add Library and Scripting Languages to the wish list (this has since been fulfilled by the example $cref ad_in_c.cpp$$). $head 01-26$$ The $cref LuFactor$$ routine gave a misleading error message when the input matrix had not a number or infinity in it. This has been fixed. $head 01-24$$ The $cref/postfix_dir/auto_tools/postfix_dir/$$ has been added to the $code configure$$ command line options. $head 01-21$$ A sparse Hessian case was added to the $cref speed$$ tests; see $cref/sparse_hessian/link_sparse_hessian/$$. $head 01-20$$ CppAD can now be installed using $code yum$$ on $code Fedora$$ operating systems. $head 01-11$$ The CppAD correctness tests assume that machine epsilon is less than $code 1e-13$$. A test for this has been added to the $code test_more/test_more$$ program. $head 01-08$$ Added a $cref sparse_hessian$$ routine and extended $cref Hessian$$ to allow for a weight vector $icode w$$ instead of just one component $icode l$$. $end cppad-20170000.3/omh/deprecated/0002755000175200017650000000000013057470463015320 5ustar coincoin-webcppad-20170000.3/omh/deprecated/include_deprecated.omh0000644000175200017650000001007113057470463021625 0ustar coincoin-web$Id: include_deprecated.omh 3762 2015-12-01 14:35:37Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin include_deprecated$$ $spell sudo mv Rosen cppad.hpp CppAD Runge cp dir ln lu Romberg Mul $$ $section Deprecated Include Files$$ $head Deprecated 2015-11-30$$ The $cref utility$$ individual include files have been deprecated; e.g., $codep # include $$ You should instead use $codep # include $$ $head Deprecated 2006-12-17$$ The following is a list of deprecated include file names and the corresponding names that should be used. For example, if your program uses the deprecated preprocessor command $codep # include $$ you should change it to the command $codep # include $$ $head Linking New Files to Deprecated Commands$$ On Unix systems, references in your source code of the from $codei% # include %$$ will refer to the older versions of CppAD unless you preform the following steps (this only needs to be done once, not for every install): $codei% cp %prefix_dir%/include sudo mv CppAD CppAD.old sudo ln -s cppad CppAD %$$ where $cref/prefix_dir/auto_tools/prefix_dir/$$ is the prefix directory corresponding to your $cref/Unix installation/auto_tools/$$. This will link form the deprecated commands to the commands that should be used: $table $bold Deprecated$$ $pre $$ $cnext $bold Should Use$$ $pre $$ $cnext $bold Documentation$$ $rnext CppAD/CheckNumericType.h $pre $$ $cnext cppad/check_numeric_type.hpp $pre $$ $cnext $cref CheckNumericType$$ $rnext CppAD/CheckSimpleVector.h $pre $$ $cnext cppad/check_simple_vector.hpp $pre $$ $cnext $cref CheckSimpleVector$$ $rnext CppAD/CppAD.h $pre $$ $cnext cppad/cppad.hpp $pre $$ $cnext $cref CppAD$$ $rnext CppAD/CppAD_vector.h $pre $$ $cnext cppad/vector.hpp $pre $$ $cnext $cref CppAD_vector$$ $rnext CppAD/ErrorHandler.h $pre $$ $cnext cppad/error_handler.hpp $pre $$ $cnext $cref ErrorHandler$$ $rnext CppAD/LuFactor.h $pre $$ $cnext cppad/lu_factor.hpp $pre $$ $cnext $cref LuFactor$$ $rnext CppAD/LuInvert.h $pre $$ $cnext cppad/lu_invert.hpp $pre $$ $cnext $cref LuInvert$$ $rnext CppAD/LuSolve.h $pre $$ $cnext cppad/lu_solve.hpp $pre $$ $cnext $cref LuSolve$$ $rnext CppAD/NearEqual.h $pre $$ $cnext cppad/near_equal.hpp $pre $$ $cnext $cref NearEqual$$ $rnext CppAD/OdeErrControl.h $pre $$ $cnext cppad/ode_err_control.hpp $pre $$ $cnext $cref OdeErrControl$$ $rnext CppAD/OdeGear.h $pre $$ $cnext cppad/ode_gear.hpp $pre $$ $cnext $cref OdeGear$$ $rnext CppAD/OdeGearControl.h $pre $$ $cnext cppad/ode_gear_control.hpp $pre $$ $cnext $cref OdeGearControl$$ $rnext CppAD/Poly.h $pre $$ $cnext cppad/poly.hpp $pre $$ $cnext $cref Poly$$ $rnext CppAD/PowInt.h $pre $$ $cnext cppad/pow_int.hpp $pre $$ $cnext $cref pow_int$$ $rnext CppAD/RombergMul.h $pre $$ $cnext cppad/romberg_mul.hpp $pre $$ $cnext $cref RombergMul$$ $rnext CppAD/RombergOne.h $pre $$ $cnext cppad/romberg_one.hpp $pre $$ $cnext $cref RombergOne$$ $rnext CppAD/Rosen34.h $pre $$ $cnext cppad/rosen_34.hpp $pre $$ $cnext $cref Rosen34$$ $rnext CppAD/Runge45.h $pre $$ $cnext cppad/runge_45.hpp $pre $$ $cnext $cref Runge45$$ $rnext CppAD/SpeedTest.h $pre $$ $cnext cppad/speed_test.hpp $pre $$ $cnext $cref SpeedTest$$ $rnext CppAD/TrackNewDel.h $pre $$ $cnext cppad/track_new_del.hpp $pre $$ $cnext $cref TrackNewDel$$ $tend $end cppad-20170000.3/omh/deprecated/omp_alloc.omh0000644000175200017650000000327013057470463017772 0ustar coincoin-web// $Id: omp_alloc.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin omp_alloc$$ $spell openmp cppad/utility/omp_alloc.hpp CppAD $$ $section A Quick OpenMP Memory Allocator Used by CppAD$$ $mindex multi-threading allocation$$ $head Syntax$$ $code # include $$ $head Purpose$$ The C++ $code new$$ and $code delete$$ operators are thread safe, but this means that a thread may have to wait for a lock on these operations. Once memory is obtained for a thread, the $code omp_alloc$$ memory allocator keeps that memory $cref omp_available$$ for the thread so that it can be re-used without waiting for a lock. All the CppAD memory allocations use this utility. The $cref omp_free_available$$ function should be used to return memory to the system (once it is no longer required by a thread). $head Include$$ The routines in sections below are defined by $code cppad/omp_alloc.hpp$$. This file is included by $code cppad/cppad.hpp$$, but it can also be included separately with out the rest of the $code CppAD$$. $head Deprecated 2011-08-23$$ Use $cref thread_alloc$$ instead. $childtable% cppad/utility/omp_alloc.hpp% test_more/omp_alloc.cpp %$$ $end */ cppad-20170000.3/omh/deprecated/fun_deprecated.omh0000644000175200017650000001200113057470463020765 0ustar coincoin-web$Id: fun_deprecated.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin FunDeprecated$$ $spell bool VecAD CppAD const Taylor sizeof var $$ $section ADFun Object Deprecated Member Functions$$ $head Syntax$$ $icode%f%.Dependent(%y%) %$$ $icode%o% = %f%.Order() %$$ $icode%m% = %f%.Memory() %$$ $icode%s% = %f%.Size() %$$ $icode%t% = %f%.taylor_size() %$$ $icode%u% = %f%.use_VecAD() %$$ $icode%v% = %f%.size_taylor() %$$ $icode%w% = %f%.capacity_taylor() %$$ $head Purpose$$ The $codei%ADFun<%Base%>%$$ functions documented here have been deprecated; i.e., they are no longer approved of and may be removed from some future version of CppAD. $head Dependent$$ A recording of and AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ is started by a call of the form $codei% Independent(%x%) %$$ If there is only one such recording at the current time, you can use $icode%f%.Dependent(%y%)%$$ in place of $codei% %f%.Dependent(%x%, %y%) %$$ See $cref Dependent$$ for a description of this operation. $subhead Deprecated 2007-08-07$$ This syntax was deprecated when CppAD was extended to allow for more than one $codei%AD<%Base%>%$$ recording to be active at one time. This was necessary to allow for multiple threading applications. $head Order$$ The result $icode o$$ has prototype $codei% size_t %o% %$$ and is the order of the previous forward operation using the function $icode f$$. This is the highest order of the $cref/Taylor coefficients/glossary/Taylor Coefficient/$$ that are currently stored in $icode f$$. $subhead Deprecated 2006-03-31$$ Zero order corresponds to function values being stored in $icode f$$. In the future, we would like to be able to erase the function values so that $icode f$$ uses less memory. In this case, the return value of $code Order$$ would not make sense. Use $cref size_order$$ to obtain the number of Taylor coefficients currently stored in the ADFun object $icode f$$ (which is equal to the order plus one). $head Memory$$ The result $codei% size_t %m% %$$ and is the number of memory units ($code sizeof$$) required for the information currently stored in $icode f$$. This memory is returned to the system when the destructor for $icode f$$ is called. $subhead Deprecated 2006-03-31$$ It used to be the case that an ADFun object just kept increasing its buffers to the maximum size necessary during its lifetime. It would then return the buffers to the system when its destructor was called. This is no longer the case, an ADFun object now returns memory when it no longer needs the values stored in that memory. Thus the $code Memory$$ function is no longer well defined. $head Size$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the number of variables in the operation sequence plus the following: one for a phantom variable with tape address zero, one for each component of the domain that is a parameter. The amount of work and memory necessary for computing function values and derivatives using $icode f$$ is roughly proportional to $icode s$$. $subhead Deprecated 2006-04-03$$ There are other sizes attached to an ADFun object, for example, the number of operations in the sequence. In order to avoid confusion with these other sizes, use $cref/size_var/seq_property/size_var/$$ to obtain the number of variables in the operation sequence. $head taylor_size$$ The result $icode t$$ has prototype $codei% size_t %t% %$$ and is the number of Taylor coefficient orders currently calculated and stored in the ADFun object $icode f$$. $subhead Deprecated 2006-06-17$$ This function has been replaced by $cref size_order$$. $head use_VecAD$$ The result $icode u$$ has prototype $codei% bool %u% %$$ If it is true, the AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ stored in $icode f$$ contains $cref/VecAD/VecAD/VecAD::reference/$$ operands. Otherwise $icode u$$ is false. $subhead Deprecated 2006-04-08$$ You can instead use $codei% %u% = %f%.size_VecAD() > 0 %$$ $head size_taylor$$ The result $icode v$$ has prototype $codei% size_t %v% %$$ and is the number of Taylor coefficient orders currently calculated and stored in the ADFun object $icode f$$. $subhead Deprecated 2014-03-18$$ This function has been replaced by $cref size_order$$. $head capacity_taylor$$ The result $icode w$$ has prototype $codei% size_t %w% %$$ and is the number of Taylor coefficient orders currently allocated in the ADFun object $icode f$$. $subhead Deprecated 2014-03-18$$ This function has been replaced by $cref capacity_order$$. $end cppad-20170000.3/omh/deprecated/compare_change.omh0000644000175200017650000000475113057470463020765 0ustar coincoin-web/* $Id$ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin CompareChange$$ $spell const $$ $section Comparison Changes During Zero Order Forward Mode$$ $mindex ADFun CompareChange$$ $head Syntax$$ $icode%c% = %f%.CompareChange()%$$ $pre $$ $bold See Also$$ $cref FunCheck$$ $head Deprecated 2015-01-20$$ This routine has been deprecated, use $cref compare_change$$ instead. $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. This function may be not agree with the algorithm that was used to create the corresponding AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ because of changes in AD $cref/comparison/Compare/$$ results. The $code CompareChange$$ function can be used to detect these changes. $head f$$ The object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ $head c$$ The result $icode c$$ has prototype $codei% size_t %c% %$$ It is the number of $codei%AD<%Base%>%$$ $cref/comparison/Compare/$$ operations, corresponding to the previous call to $cref Forward$$ $codei% %f%.Forward(0, %x%) %$$ that have a different result from when $icode F$$ was created by taping an algorithm. $head Discussion$$ If $icode c$$ is not zero, the boolean values resulting from some of the $cref/comparison operations/Compare/$$ corresponding to $icode x$$ are different from when the AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ was created. In this case, you may want to re-tape the algorithm with the $cref/independent variables/glossary/Tape/Independent Variable/$$ equal to the values in $icode x$$ (so AD operation sequence properly represents the algorithm for this value of independent variables). On the other hand, re-taping the AD operation sequence usually takes significantly more time than evaluation using $cref forward_zero$$. If the functions values have not changed (see $cref FunCheck$$) it may not be worth re-taping a new AD operation sequence. $end cppad-20170000.3/omh/deprecated/deprecated.omh0000644000175200017650000000342613057470463020130 0ustar coincoin-web// $Id: deprecated.omh 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin deprecated$$ $spell CppAD Bool jac hes $$ $section CppAD Deprecated API Features$$ $childtable% omh/deprecated/include_deprecated.omh% omh/deprecated/fun_deprecated.omh% omh/deprecated/compare_change.omh% cppad/core/omp_max_thread.hpp% cppad/utility/track_new_del.hpp% omh/deprecated/omp_alloc.omh% cppad/utility/memory_leak.hpp% cppad/core/epsilon.hpp% cppad/core/test_vector.hpp% cppad_ipopt/src/cppad_ipopt_nlp.hpp% cppad/core/old_atomic.hpp% cppad/core/zdouble.hpp %$$ $table $cref/CppADCreateUnaryBool/BoolFun/Deprecated 2007-07-31/$$ $cnext $title BoolFun$$ $rnext $cref/CppADCreateDiscrete/Discrete/CppADCreateDiscrete Deprecated 2007-07-28/$$ $cnext $title Discrete$$ $rnext $cref auto_tools$$ $cnext $title auto_tools$$ $rnext $cref/nan(zero)/nan/nan(zero)/$$ $cnext $codei%nan(%zero%)%$$ $tend $head Atomic Functions$$ The following are links to deprecated $cref atomic_base$$ interfaces: $cref/for_sparse_jac/atomic_for_sparse_jac/Deprecated 2016-06-27/$$, $cref/rev_sparse_jac/atomic_rev_sparse_jac/Deprecated 2016-06-27/$$, $cref/for_sparse_hes/atomic_for_sparse_hes/Deprecated 2016-06-27/$$, $cref/rev_sparse_hes/atomic_rev_sparse_hes/Deprecated 2016-06-27/$$. $end cppad-20170000.3/omh/det_by_minor_hpp.omh0000644000175200017650000000156413057470463017252 0ustar coincoin-web$Id: det_by_minor_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin det_by_minor.hpp$$ $spell det_by_minor ifndef endif $$ $section Source: det_by_minor$$ $mindex source$$ $code # ifndef CPPAD_DET_BY_MINOR_HPP $pre $$ # define CPPAD_DET_BY_MINOR_HPP $srcfile%cppad/speed/det_by_minor.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/introduction.omh0000644000175200017650000001007513057470463016447 0ustar coincoin-web$Id: introduction.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin Introduction$$ $spell exp_eps Griewank Andreas CppAD $$ $section An Introduction by Example to Algorithmic Differentiation$$ $mindex AD Automatic$$ $head Purpose$$ This is an introduction by example to Algorithmic Differentiation. Its purpose is to aid in understand what AD calculates, how the calculations are preformed, and the amount of computation and memory required for a forward or reverse sweep. $head Preface$$ $subhead Algorithmic Differentiation$$ Algorithmic Differentiation (often referred to as Automatic Differentiation or just AD) uses the software representation of a function to obtain an efficient method for calculating its derivatives. These derivatives can be of arbitrary order and are analytic in nature (do not have any truncation error). $subhead Forward Mode$$ A forward mode sweep computes the partial derivative of all the dependent variables with respect to one independent variable (or independent variable direction). $subhead Reverse Mode$$ A reverse mode sweep computes the derivative of one dependent variable (or one dependent variable direction) with respect to all the independent variables. $subhead Operation Count$$ The number of floating point operations for either a forward or reverse mode sweep is a small multiple of the number required to evaluate the original function. Thus, using reverse mode, you can evaluate the derivative of a scalar valued function with respect to thousands of variables in a small multiple of the work to evaluate the original function. $subhead Efficiency$$ AD automatically takes advantage of the speed of your algorithmic representation of a function. For example, if you calculate a determinant using LU factorization, AD will use the LU representation for the derivative of the determinant (which is faster than using the definition of the determinant). $head Outline$$ $list Alpha$$ Demonstrate the use of CppAD to calculate derivatives of a polynomial: $cref get_started.cpp$$. $lnext Present two algorithms that approximate the exponential function. The first algorithm $cref exp_2.hpp$$ is simpler and does not include any logical variables or loops. The second algorithm $cref exp_eps.hpp$$ includes logical operations and a $code while$$ loop. For each of these algorithms, do the following: $list number$$ Define the mathematical function corresponding to the algorithm ($cref exp_2$$ and $cref exp_eps$$). $lnext Write out the floating point operation sequence, and corresponding values, that correspond to executing the algorithm for a specific input ($cref exp_2_for0$$ and $cref exp_eps_for0$$). $lnext Compute a forward sweep derivative of the operation sequence ($cref exp_2_for1$$ and $cref exp_eps_for1$$). $lnext Compute a reverse sweep derivative of the operation sequence ($cref exp_2_rev1$$ and $cref exp_eps_rev1$$). $lnext Use CppAD to compute both a forward and reverse sweep of the operation sequence ($cref exp_2_cppad$$ and $cref exp_eps_cppad$$). $lend $lnext The program $cref exp_apx_main.cpp$$ runs all of the test routines that validate the calculations in the $cref exp_2$$ and $cref exp_eps$$ presentation. $lend $head Reference$$ An in-depth review of AD theory and methods can be found in the book $icode Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation $$, Andreas Griewank, SIAM Frontiers in Applied Mathematics, 2000. $childtable% introduction/get_started/get_started.cpp% introduction/exp_apx/exp_2.hpp% introduction/exp_apx/exp_eps.hpp% introduction/exp_apx/main.cpp %$$ $end cppad-20170000.3/omh/multi_thread.omh0000644000175200017650000000605213057470463016407 0ustar coincoin-web// $Id: multi_thread.omh 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin multi_thread$$ $spell cppad_max_num_threads alloc CppAD Rosen Runge $$ $section Using CppAD in a Multi-Threading Environment$$ $mindex mode execution maximum number$$ $head Purpose$$ Extra steps and care must be taken to use CppAD in $cref/parallel/ta_in_parallel/$$ execution mode. This section collects this information in one place. $head CPPAD_MAX_NUM_THREADS$$ The value $code CPPAD_MAX_NUM_THREADS$$ is an absolute maximum for the number of threads that CppAD should support. If this preprocessor symbol is defined before including any CppAD header files, it must be an integer greater than or equal to one. Otherwise, $cref/cppad_max_num_threads/cmake/cppad_max_num_threads/$$ is used to define this preprocessor symbol. Note that the minimum allowable value for $icode cppad_max_num_threads$$ is 4; i.e., you can only get smaller values for $code CPPAD_MAX_NUM_THREADS$$ by defining it before including the CppAD header files. $head parallel_setup$$ Using any of the following routines in a multi-threading environment requires that $cref/thread_alloc::parallel_setup/ta_parallel_setup/$$ has been completed: $cref/CppAD::vector/CppAD_vector/Memory and Parallel Mode/$$, $cref/CheckSimpleVector/CheckSimpleVector/Parallel Mode/$$, $cref/CheckNumericType/CheckNumericType/Parallel Mode/$$, $cref parallel_ad$$. $head hold_memory$$ Memory allocation should be much faster after calling $code hold_memory$$ with $cref/value/ta_hold_memory/value/$$ equal to true. This may even be true if there is only one thread. $head Parallel AD$$ One must first call $cref/thread_alloc::parallel_setup/ta_parallel_setup/$$ and then call $cref parallel_ad$$ before using $code AD$$ types in $cref/parallel/ta_in_parallel/$$ execution mode. $head Initialization$$ The following routines must be called at least once before being used in parallel mode: $cref/CheckSimpleVector/CheckSimpleVector/Parallel Mode/$$, $cref/CheckNumericType/CheckNumericType/Parallel Mode/$$, $cref/discrete functions/Discrete/Parallel Mode/$$, $cref/Rosen34/Rosen34/Parallel Mode/$$, $cref/Runge45/Runge45/Parallel Mode/$$. $head Same Thread$$ Some operations must be preformed by the same thread: $cref/ADFun/FunConstruct/Parallel Mode/$$, $cref Independent$$, $cref Dependent$$. $head Parallel Prohibited$$ The following routine cannot be called in parallel mode: $cref/ErrorHandler constructor/ErrorHandler/Constructor/Parallel Mode/$$. $childtable% cppad/core/parallel_ad.hpp% multi_thread/thread_test.cpp %$$ $end cppad-20170000.3/omh/sparse_jac_fun.omh0000644000175200017650000000156313057470463016712 0ustar coincoin-web$Id: sparse_jac_fun.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin sparse_jac_fun.hpp$$ $spell jac ifndef endif $$ $section Source: sparse_jac_fun$$ $mindex source$$ $code # ifndef CPPAD_SPARSE_JAC_FUN_HPP $pre $$ # define CPPAD_SPARSE_JAC_FUN_HPP $srcfile%cppad/speed/sparse_jac_fun.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/license.omh0000644000175200017650000000133013057470467015346 0ustar coincoin-web$Id: license.omh 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin License$$ $spell CppAD $$ $section Your License for the CppAD Software$$ $pre $$ $fixed $verbatim%gpl-3.0.txt%$$ $$ $end cppad-20170000.3/omh/base_require/0002755000175200017650000000000013057470463015666 5ustar coincoin-webcppad-20170000.3/omh/base_require/base_example.omh0000644000175200017650000000155313057470463021022 0ustar coincoin-web// $Id: base_example.omh 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin base_example$$ $section Example AD Base Types That are not AD$$ $contents% example/base_alloc.hpp% example/base_require.cpp% cppad/example/base_adolc.hpp% cppad/core/base_float.hpp% cppad/core/base_double.hpp% cppad/core/base_complex.hpp %$$ $end cppad-20170000.3/omh/base_require/base_identical.omh0000644000175200017650000000735313057470463021327 0ustar coincoin-web// $Id: base_identical.omh 3757 2015-11-30 12:03:07Z bradbell $$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_identical$$ $spell alloc adolc Op const CppAD adolc namespace bool inline $$ $section Base Type Requirements for Identically Equal Comparisons$$ $mindex require$$ $head EqualOpSeq$$ If function $cref EqualOpSeq$$ is used with arguments of type $codei%AD<%Base%>%$$, the type $icode Base$$ must support the syntax $codei% %b% = CppAD::EqualOpSeq(%u%, %v%) %$$ This should return true if and only if $icode u$$ is identically equal to $icode v$$ and it makes no different which one is used. The arguments $icode u$$ and $icode v$$ have prototype $codei% const %Base%& %u% const %Base%& %v% %$$ The return value $icode b$$ has prototype $codei% bool %b% %$$ $subhead The Simple Case$$ If $icode Base$$ is a relatively simple type, the $code EqualOpSeq$$ function can be defined by $codei% namespace CppAD { inline %Base% EqualOpSeq(const %Base%& u, const %Base%& v) { return u == v; } } %$$ For example, see $cref/base_alloc/base_alloc.hpp/EqualOpSeq/$$. $subhead More Complicated Cases$$ The variables $icode u$$ and $icode v$$ are not identically equal in the following case (which CppAD automatically defines $code EqualOpSeq$$ for): The type $icode Base$$ is $codei%AD%$$, $icode x[0] = x[1] = 1.$$, then $cref independent$$ is used to make $icode x$$ the independent variable vector, and then $icode u = x[0]$$, $icode v = x[1]$$, Note that during a future $cref Forward$$ calculation, $icode u$$ and $icode v$$ could correspond to different values. For example, see $cref/adolc EqualOpSeq/base_adolc.hpp/EqualOpSeq/$$. $head Identical$$ $subhead IdenticalPar$$ A $icode Base$$ is a $cref/parameter/glossary/Parameter/$$ when used in an $codei%AD<%Base%>%$$ operation sequence. It is however still possible for a parameter to change its value. For example, the $icode Base$$ value $icode u$$ is not identically a parameter equal in the following case (which CppAD automatically defines $code IdenticalPar$$ for): The type $icode Base$$ is $codei%AD%$$, $icode x[0] = 1.$$, then $cref independent$$ is used to make $icode x$$ the independent variable vector, and then $icode u = x[0]$$, Note that during a future $cref Forward$$ calculation, $icode u$$ could correspond to different values. $subhead Prototypes$$ The argument $icode u$$ has prototype $codei% const %Base% %u% %$$ If it is present, the argument $icode v$$ has prototype $codei% const %Base% %v% %$$ The result $icode b$$ has prototype $codei% bool %b% %$$ $subhead Identical Functions$$ The type $icode Base$$ must support the following functions (in the CppAD namespace): $table $bold Syntax$$ $cnext $bold Result$$ $rnext $icode%b% = IdenticalPar(%u%)%$$ $pre $$ $cnext the $icode Base$$ value will always be the same $rnext $icode%b% = IdenticalZero(%u%)%$$ $pre $$ $cnext $icode u$$ equals zero and $codei%IdenticalPar(%u%)%$$ $rnext $icode%b% = IdenticalOne(%u%)%$$ $pre $$ $cnext $icode u$$ equals one and $codei%IdenticalPar(%u%)%$$ $rnext $icode%b% = IdenticalEqualPar(%u%, %v%)%$$ $pre $$ $cnext $icode u$$ equals $icode v$$, $codei%IdenticalPar(%u%)%$$ and $codei%IdenticalPar(%v%)%$$ $tend $subhead Examples$$ See $cref/base_alloc/base_alloc.hpp/Identical/$$. $end */ cppad-20170000.3/omh/base_require/base_ordered.omh0000644000175200017650000000434713057470463021017 0ustar coincoin-web// $Id: base_ordered.omh 3665 2015-02-26 04:59:01Z bradbell $$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_ordered$$ $spell alloc abs_geq const bool namespace CppAD inline $$ $section Base Type Requirements for Ordered Comparisons$$ $head Purpose$$ The following operations (in the CppAD namespace) are required to use the type $codei%AD<%Base%>%$$: $table $bold Syntax$$ $cnext $bold Result$$ $rnext $icode%b% = GreaterThanZero(%x%)%$$ $pre $$ $cnext $latex x > 0$$ $rnext $icode%b% = GreaterThanOrZero(%x%)%$$ $pre $$ $cnext $latex x \geq 0$$ $rnext $icode%b% = LessThanZero(%x%)%$$ $pre $$ $cnext $latex x < 0$$ $rnext $icode%b% = LessThanOrZero(%x%)%$$ $pre $$ $cnext $latex x \leq 0$$ $rnext $icode%b% = abs_geq(%x%, %y%)%$$ $pre $$ $cnext $latex |x| \geq |y|$$. $tend where the arguments and return value have the prototypes $codei% const %Base%& %x% const %Base%& %y% bool %% %b% %$$ $head Ordered Type$$ If the type $icode Base$$ supports ordered operations, these functions should have their corresponding definitions. For example, $codei% namespace CppAD { inline bool GreaterThanZero(const %Base% &x) { return (x > 0); } } %$$ The other functions would replace $code >$$ by the corresponding operator. For example, see $cref/base_alloc/base_alloc.hpp/Ordered/$$. $head Not Ordered$$ If the type $icode Base$$ does not support ordering, one might (but need not) define $code GreaterThanZero$$ as follows: $codei% namespace CppAD { inline bool GreaterThanZero(const %Base% &x) { // attempt to use GreaterThanZero with a %Base% argument assert(0); return x; } } %$$ The other functions would have the corresponding definition. For example, see $cref/complex Ordered/base_complex.hpp/Ordered/$$. $end */ cppad-20170000.3/omh/base_require/base_member.omh0000644000175200017650000000411413057470463020632 0ustar coincoin-web/* $Id: base_member.omh 3665 2015-02-26 04:59:01Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin base_member$$ $spell bool const op Bool definition alloc $$ $section Required Base Class Member Functions$$ $head Notation$$ $table $bold Symbol$$ $cnext $bold Meaning$$ $rnext $icode Base$$ $cnext The base type corresponding to $codei%AD<%Base%>%$$ $rnext $icode b$$ $cnext An object of type $code bool$$ $rnext $icode d$$ $cnext An object of type $code double$$ $rnext $icode x$$ $cnext An object of type $codei%const %Base%&%$$ $rnext $icode y$$ $cnext An object of type $codei%const %Base%&%$$ $rnext $icode z$$ $cnext An object of type $icode Base$$ $rnext $tend $head Default Constructor$$ $icode%Base z%$$ $head Double Constructor$$ $icode%Base z%(%d%)%$$ $head Copy Constructor$$ $icode%Base z%(%x%)%$$ $head Unary Operators$$ For $code op$$ equal to $code +$$, $code -$$ the following operation must be supported: $codei% %z% = %op% %x%$$ $head Assignment Operators$$ For $icode op$$ equal to $icode =$$, $code +=$$, $code -=$$, $code *=$$, and $code /=$$ the following operation must be supported: $codei% %z% %op% %x%$$ $head Binary Operators$$ For $icode op$$ equal to $code +$$, $code -$$, $code *$$, and $code /$$ the following operation must be supported: $codei% %z% = %x% %op% %y%$$ $head Bool Operators$$ For $icode op$$ equal to $code ==$$, $code !=$$, $code <=$$, the following operation must be supported: $codei% %b% = %x% %op% %y%$$ $head Example$$ See the heading Class Definition in $cref/base_alloc/base_alloc.hpp/Class Definition/$$. $end cppad-20170000.3/omh/mul_level.omh0000644000175200017650000001101213057470463015702 0ustar coincoin-web$Id: mul_level.omh 3735 2015-10-01 13:43:46Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin mul_level$$ $spell Taylor fout const var Cpp Arg $$ $section Using Multiple Levels of AD$$ $head Background$$ If $icode f$$ is an $codei%ADFun<%Base%>%$$ object, the vectors returned by $cref/f.Forward/Forward/$$, and $cref/f.Reverse/Reverse/$$, have values of type $icode Base$$ and not $codei%AD<%Base%>%$$. This reflects the fact that operations used to calculate these function values are not recorded by the tape corresponding to $codei%AD<%Base%>%$$ operations. $head Motivation$$ Suppose that you use derivatives of one or more inner functions as part of the operations needed to compute an outer function. For example, the derivatives returned by $icode%f%.Forward%$$ might be used as part of Taylor's method for solving ordinary differential equations. In addition, we might want to differentiate the solution of a differential equation with respect to parameters in the equation. This can be accomplished in the following way: $list number$$ The function defining the differential equation could be calculated using the class $codei AD< AD >$$. $lnext The operations during the calculation of Taylor's method could be done using the $codei AD$$ class. $lnext Derivatives of the solution of the differential equation could then be calculated using the $code double$$ class. $lend $head Procedure$$ $subhead First Start AD$$ If some of the $cref/parameters/glossary/Parameter/$$ in the $codei AD< AD >$$ recording depend on the $cref/variables/glossary/Variable/$$ in the $codei AD$$ recording, we must first declaring these variables; i.e., $codei% Independent(%a1x%) %$$ where $icode a1x$$ is a $cref SimpleVector$$ with elements of type $codei AD$$. This will start recording a new tape of operations performed using $codei AD$$ class objects. $subhead Start AD< AD > Recording$$ The next step is to declare the independent variables using $codei% Independent(%a2x%) %$$ where $icode a2x$$ is a $cref SimpleVector$$ with elements of type $codei AD< AD >$$. This will start recording a new tape of operations performed using $codei AD< AD >$$ class objects. $subhead Inner Function$$ The next step is to calculation the inner function using $codei AD< AD >$$ class objects. We then stop the recording using $codei% %a1f%.Dependent(%a2x%, %a2y%) %$$ where $icode a2y$$ is a $cref SimpleVector$$ with elements of type $codei AD< AD >$$ and $icode a1f$$ is an $codei%ADFun< AD >%$$ object. $subhead Second Start AD< AD >$$ If none of the $cref/parameters/glossary/Parameter/$$ in the $codei AD< AD >$$ recording depend on the $cref/variables/glossary/Variable/$$ in the $codei AD$$ recording, it is preferred to delay declaring these variables to this point; i.e., $codei% Independent(%a1x%) %$$ where $icode a1x$$ is a $cref SimpleVector$$ with elements of type $codei AD$$. This will start recording a new tape of operations performed using $codei AD$$ class objects. $subhead Outer Function$$ The next step is to calculation the outer function using $codei AD$$ class objects. Note that derivatives of the inner function can be included in the calculation of the outer function using $icode a1f$$. We then stop the recording of $codei AD$$ operations using $codei% %g%.Dependent(%a1x%, %a1y%) %$$ where $icode a1y$$ is a $cref SimpleVector$$ with elements of type $codei AD$$ and $icode g$$ is an $codei%ADFun%$$ object. $subhead Derivatives of Outer Function$$ The AD function object $icode g$$ can then be used to calculate the derivatives of the outer function. $children% example/mul_level.cpp% example/change_param.cpp %$$ $head Example$$ The files $cref mul_level.cpp$$ and $cref change_param.cpp$$ contain an examples and tests of this procedure. They return true if they succeed and false otherwise. The file $cref mul_level_ode.cpp$$ is a more complex example use of multiple tapes. $end cppad-20170000.3/omh/preprocessor.omh0000644000175200017650000000574613057470463016465 0ustar coincoin-web// $Id: preprocessor.omh 3768 2015-12-28 18:58:35Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin preprocessor$$ $spell const nullptr CppADvector Vec $$ $section CppAD API Preprocessor Symbols$$ $mindex CPPAD_ NULL pointer$$ $head Purpose$$ The CppAD include files define preprocessor symbols all of which begin with $code CPPAD_$$. Note that there are some old, deprecated preprocessor symbols that begin with $code CppAD$$. In this section we list all of the CppAD preprocessor symbols that are part of the CppAD Application Interface (API). $head Documented Here$$ $subhead CPPAD_NULL$$ Is a null pointer used by CppAD, instead of just using the value zero which was often done in C++98, which has been replaced by the value $code nullptr$$ in C++11. $subhead CPPAD_PACKAGE_STRING$$ Is a $code const char*$$ representation of this version of CppAD. $subhead CPPAD_USE_CPLUSPLUS_2011$$ This preprocessor symbol has the value has the value $code 1$$ if C++11 features are being used by CppAD. Otherwise it has the value zero. $head Documented Elsewhere$$ $table $cref/CPPAD_BOOL_BINARY/BoolFun/Create Binary/$$ $rnext $cref/CPPAD_BOOL_UNARY/BoolFun/Create Unary/$$ $rnext $cref/CPPAD_DISCRETE_FUNCTION/Discrete/$$ $rnext $cref/CPPAD_MAX_NUM_THREADS/multi_thread/CPPAD_MAX_NUM_THREADS/$$ $rnext $cref/CPPAD_NUMERIC_LIMITS/base_limits/CPPAD_NUMERIC_LIMITS/$$ $rnext $cref/CPPAD_STANDARD_MATH_UNARY/base_std_math/CPPAD_STANDARD_MATH_UNARY/$$ $rnext $cref/CPPAD_TAPE_ADDR_TYPE/cmake/cppad_tape_addr_type/$$ $rnext $cref/CPPAD_TAPE_ID_TYPE/cmake/cppad_tape_id_type/$$ $rnext $cref/CPPAD_TESTVECTOR/testvector/$$ $rnext $cref/CPPAD_TO_STRING/base_to_string/CPPAD_TO_STRING/$$ $tend $head Deprecated$$ $table $cref/CppADCreateDiscrete/Discrete/CppADCreateDiscrete Deprecated 2007-07-28/$$ $rnext $cref/CppADvector/test_vector/Deprecated 2012-07-03/$$ $rnext $cref/CPPAD_TEST_VECTOR/test_vector/$$ $rnext $cref/CPPAD_TRACK_NEW_VEC/TrackNewDel/TrackNewVec/Macro/$$ $rnext $cref/CPPAD_TRACK_DEL_VEC/TrackNewDel/TrackDelVec/Macro/$$ $rnext $cref/CPPAD_TRACK_EXTEND/TrackNewDel/TrackExtend/Macro/$$ $rnext $cref/CPPAD_TRACK_COUNT/TrackNewDel/TrackCount/Macro/$$ $rnext $cref/CPPAD_USER_ATOMIC/old_atomic/$$ $rnext $cref/CppADTrackNewVec/TrackNewDel/TrackNewVec/Previously Deprecated/$$ $rnext $cref/CppADTrackDelVec/TrackNewDel/TrackDelVec/Previously Deprecated/$$ $rnext $cref/CppADTrackExtend/TrackNewDel/TrackExtend/Previously Deprecated/$$ $rnext $cref/CppADTrackCount/TrackNewDel/TrackCount/Previously Deprecated/$$ $tend $end cppad-20170000.3/omh/theory/0002755000175200017650000000000013057470464014533 5ustar coincoin-webcppad-20170000.3/omh/theory/erf_forward.omh0000644000175200017650000000341013057470463017533 0ustar coincoin-web$Id:$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin erf_forward$$ $spell erf Taylor $$ $section Error Function Forward Taylor Polynomial Theory$$ $mindex erf$$ $head Derivatives$$ Given $latex X(t)$$, we define the function $latex \[ Z(t) = \R{erf}[ X(t) ] \]$$ It follows that $latex \[ \begin{array}{rcl} \R{erf}^{(1)} ( u ) & = & ( 2 / \sqrt{\pi} ) \exp \left( - u^2 \right) \\ Z^{(1)} (t) & = & \R{erf}^{(1)} [ X(t) ] X^{(1)} (t) = Y(t) X^{(1)} (t) \end{array} \] $$ where we define the function $latex \[ Y(t) = \frac{2}{ \sqrt{\pi} } \exp \left[ - X(t)^2 \right] \] $$ $head Taylor Coefficients Recursion$$ Suppose that we are given the Taylor coefficients up to order $latex j$$ for the function $latex X(t)$$ and $latex Y(t)$$. We need a formula that computes the coefficient of order $latex j$$ for $latex Z(t)$$. Using the equation above for $latex Z^{(1)} (t)$$, we have $latex \[ \begin{array}{rcl} \sum_{k=1}^j k z^{(k)} t^{k-1} & = & \left[ \sum_{k=0}^j y^{(k)} t^k \right] \left[ \sum_{k=1}^j k x^{(k)} t^{k-1} \right] + o( t^{j-1} ) \end{array} \] $$ Setting the coefficients of $latex t^{j-1}$$ equal, we have $latex \[ \begin{array}{rcl} j z^{(j)} = \sum_{k=1}^j k x^{(k)} y^{(j-k)} \\ z^{(j)} = \frac{1}{j} \sum_{k=1}^j k x^{(k)} y^{(j-k)} \end{array} \] $$ $end cppad-20170000.3/omh/theory/log_forward.omh0000644000175200017650000000406713057470463017551 0ustar coincoin-web$Id: log_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin log_forward$$ $spell Taylor $$ $section Logarithm Function Forward Mode Theory$$ $mindex log1p$$ $head Derivatives$$ If $latex F(x)$$ is $latex \R{log} (x)$$ or $latex \R{log1p} (x)$$ the corresponding derivative satisfies the equation $latex \[ ( \bar{b} + x ) * F^{(1)} (x) - 0 * F (x) = 1 \] $$ where $latex \[ \bar{b} = \left\{ \begin{array}{ll} 0 & \R{if} \; F(x) = \R{log}(x) \\ 1 & \R{if} \; F(x) = \R{log1p}(x) \end{array} \right. \] $$ In the $cref/standard math function differential equation /ForwardTheory /Standard Math Functions /Differential Equation /$$, $latex A(x) = 0$$, $latex B(x) = \bar{b} + x$$, and $latex D(x) = 1$$. We use $latex a$$, $latex b$$, $latex d$$, and $latex z$$ to denote the Taylor coefficients for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, and $latex F [ X(t) ] $$ respectively. $head Taylor Coefficients Recursion$$ For orders $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} z^{(0)} & = & F ( x^{(0)} ) \\ e^{(j)} & = & d^{(j)} + \sum_{k=0}^{j} a^{(j-k)} * z^{(k)} \\ & = & \left\{ \begin{array}{ll} 1 & {\rm if} \; j = 0 \\ 0 & {\rm otherwise} \end{array} \right. \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=1}^{j+1} k x^{(k)} e^{(j+1-k)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \\ & = & \frac{1}{j+1} \frac{1}{ \bar{b} + x^{(0)} } \left( (j+1) x^{(j+1) } - \sum_{k=1}^j k z^{(k)} x^{(j+1-k)} \right) \end{array} \] $$ $end cppad-20170000.3/omh/theory/reverse_theory.omh0000644000175200017650000001235413057470463020307 0ustar coincoin-web$Id: reverse_theory.omh 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin ReverseTheory$$ $spell Taylor Arctangent $$ $section The Theory of Reverse Mode$$ $head Taylor Notation$$ In Taylor notation, each variable corresponds to a function of a single argument which we denote by $icode t$$ (see Section 10.2 of $cref/Evaluating Derivatives/Bib/Evaluating Derivatives/$$). Here and below $latex X(t)$$, $latex Y(t)$$, and $icode Z(t)$$ are scalar valued functions and the corresponding $th p$$ order Taylor coefficients row vectors are $latex x$$, $latex y$$ and $latex z$$; i.e., $latex \[ \begin{array}{lcr} X(t) & = & x^{(0)} + x^{(1)} * t + \cdots + x^{(p)} * t^p + O( t^{p+1} ) \\ Y(t) & = & y^{(0)} + y^{(1)} * t + \cdots + y^{(p)} * t^p + O( t^{p+1} ) \\ Z(t) & = & z^{(0)} + z^{(1)} * t + \cdots + z^{(p)} * t^p + O( t^{p+1} ) \end{array} \] $$ For the purposes of this discussion, we are given the $th p$$ order Taylor coefficient row vectors $latex x$$, $latex y$$, and $latex z$$. In addition, we are given the partial derivatives of a scalar valued function $latex \[ G ( z^{(j)} , \ldots , z^{(0)}, x, y) \] $$ We need to compute the partial derivatives of the scalar valued function $latex \[ H ( z^{(j-1)} , \ldots , z^{(0)}, x, y) = G ( z^{(j)}, z^{(j-1)} , \ldots , z^{(0)}, x , y ) \] $$ where $latex z^{(j)}$$ is expressed as a function of the $th j-1$$ order Taylor coefficient row vector for $latex Z$$ and the vectors $latex x$$, $latex y$$; i.e., $latex z^{(j)}$$ above is a shorthand for $latex \[ z^{(j)} ( z^{(j-1)} , \ldots , z^{(0)}, x, y ) \] $$ If we do not provide a formula for a partial derivative of $latex H$$, then that partial derivative has the same value as for the function $latex G$$. $head Binary Operators$$ $subhead Addition$$ The forward mode formula for $cref/addition/ForwardTheory/Binary Operators/Addition/$$ is $latex \[ z^{(j)} = x^{(j)} + y^{(j)} \] $$ If follows that for $latex k = 0 , \ldots , j$$ and $latex l = 0 , \ldots , j-1$$ $latex \[ \begin{array}{rcl} \D{H}{ x^{(k)} } & = & \D{G}{ x^{(k)} } + \D{G}{ z^{(k)} } \\ \\ \D{H}{ y^{(k)} } & = & \D{G}{ y^{(k)} } + \D{G}{ z^{(k)} } \\ \D{H}{ z^{(l)} } & = & \D{G}{ z^{(l)} } \end{array} \] $$ $subhead Subtraction$$ The forward mode formula for $cref/subtraction/ForwardTheory/Binary Operators/Subtraction/$$ is $latex \[ z^{(j)} = x^{(j)} - y^{(j)} \] $$ If follows that for $latex k = 0 , \ldots , j$$ $latex \[ \begin{array}{rcl} \D{H}{ x^{(k)} } & = & \D{G}{ x^{(k)} } - \D{G}{ z^{(k)} } \\ \\ \D{H}{ y^{(k)} } & = & \D{G}{ y^{(k)} } - \D{G}{ z^{(k)} } \end{array} \] $$ $subhead Multiplication$$ The forward mode formula for $cref/multiplication/ForwardTheory/Binary Operators/Multiplication/$$ is $latex \[ z^{(j)} = \sum_{k=0}^j x^{(j-k)} * y^{(k)} \] $$ If follows that for $latex k = 0 , \ldots , j$$ and $latex l = 0 , \ldots , j-1$$ $latex \[ \begin{array}{rcl} \D{H}{ x^{(j-k)} } & = & \D{G}{ x^{(j-k)} } + \sum_{k=0}^j \D{G}{ z^{(j)} } y^{(k)} \\ \D{H}{ y^{(k)} } & = & \D{G}{ y^{(k)} } + \sum_{k=0}^j \D{G}{ z^{(j)} } x^{(j-k)} \end{array} \] $$ $subhead Division$$ The forward mode formula for $cref/division/ForwardTheory/Binary Operators/Division/$$ is $latex \[ z^{(j)} = \frac{1}{y^{(0)}} \left( x^{(j)} - \sum_{k=1}^j z^{(j-k)} y^{(k)} \right) \] $$ If follows that for $latex k = 1 , \ldots , j$$ $latex \[ \begin{array}{rcl} \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \frac{1}{y^{(0)}} \\ \D{H}{ z^{(j-k)} } & = & \D{G}{ z^{(j-k)} } - \D{G}{ z^{(j)} } \frac{1}{y^{(0)}} y^{(k)} \\ \D{H}{ y^{(k)} } & = & \D{G}{ y^{(k)} } - \D{G}{ z^{(j)} } \frac{1}{y^{(0)}} z^{(j-k)} \\ \D{H}{ y^{(0)} } & = & \D{G}{ y^{(0)} } - \D{G}{ z^{(j)} } \frac{1}{y^{(0)}} \frac{1}{y^{(0)}} \left( x^{(j)} - \sum_{k=1}^j z^{(j-k)} y^{(k)} \right) \\ & = & \D{G}{ y^{(0)} } - \D{G}{ z^{(j)} } \frac{1}{y^{(0)}} z^{(j)} \end{array} \] $$ $head Standard Math Functions$$ The standard math functions have only one argument. Hence we are given the partial derivatives of a scalar valued function $latex \[ G ( z^{(j)} , \ldots , z^{(0)}, x) \] $$ We need to compute the partial derivatives of the scalar valued function $latex \[ H ( z^{(j-1)} , \ldots , z^{(0)}, x) = G ( z^{(j)}, z^{(j-1)} , \ldots , z^{(0)}, x) \] $$ where $latex z^{(j)}$$ is expressed as a function of the $th j-1$$ order Taylor coefficient row vector for $latex Z$$ and the vector $latex x$$; i.e., $latex z^{(j)}$$ above is a shorthand for $latex \[ z^{(j)} ( z^{(j-1)} , \ldots , z^{(0)}, x ) \] $$ $childtable% omh/theory/exp_reverse.omh% omh/theory/log_reverse.omh% omh/theory/sqrt_reverse.omh% omh/theory/sin_cos_reverse.omh% omh/theory/atan_reverse.omh% omh/theory/asin_reverse.omh% omh/theory/acos_reverse.omh% omh/theory/tan_reverse.omh% omh/theory/erf_reverse.omh %$$ $end cppad-20170000.3/omh/theory/tan_forward.omh0000644000175200017650000000446413057470463017553 0ustar coincoin-web$Id: tan_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin tan_forward$$ $spell Taylor $$ $section Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory$$ $mindex tan$$ $head Derivatives$$ $latex \[ \begin{array}{rcl} \tan^{(1)} ( u ) & = & [ \cos (u)^2 + \sin (u)^2 ] / \cos (u)^2 \\ & = & 1 + \tan (u)^2 \\ \tanh^{(1)} ( u ) & = & [ \cosh (u)^2 - \sinh (u)^2 ] / \cosh (u)^2 \\ & = & 1 - \tanh (u)^2 \end{array} \] $$ If $latex F(u)$$ is $latex \tan (u)$$ or $latex \tanh (u)$$ the corresponding derivative is given by $latex \[ F^{(1)} (u) = 1 \pm F(u)^2 \]$$ Given $latex X(t)$$, we define the function $latex Z(t) = F[ X(t) ]$$. It follows that $latex \[ Z^{(1)} (t) = F^{(1)} [ X(t) ] X^{(1)} (t) = [ 1 \pm Y(t) ] X^{(1)} (t) \] $$ where we define the function $latex Y(t) = Z(t)^2$$. $head Taylor Coefficients Recursion$$ Suppose that we are given the Taylor coefficients up to order $latex j$$ for the function $latex X(t)$$ and up to order $latex j-1$$ for the functions $latex Y(t)$$ and $latex Z(t)$$. We need a formula that computes the coefficient of order $latex j$$ for $latex Y(t)$$ and $latex Z(t)$$. Using the equation above for $latex Z^{(1)} (t)$$, we have $latex \[ \begin{array}{rcl} \sum_{k=1}^j k z^{(k)} t^{k-1} & = & \sum_{k=1}^j k x^{(k)} t^{k-1} \pm \left[ \sum_{k=0}^{j-1} y^{(k)} t^k \right] \left[ \sum_{k=1}^j k x^{(k)} t^{k-1} \right] + o( t^{j-1} ) \end{array} \] $$ Setting the coefficients of $latex t^{j-1}$$ equal, we have $latex \[ \begin{array}{rcl} j z^{(j)} = j x^{(j)} \pm \sum_{k=1}^j k x^{(k)} y^{(j-k)} \\ z^{(j)} = x^{(j)} \pm \frac{1}{j} \sum_{k=1}^j k x^{(k)} y^{(j-k)} \end{array} \] $$ Once we have computed $latex z^{(j)}$$, we can compute $latex y^{(j)}$$ as follows: $latex \[ y^{(j)} = \sum_{k=0}^j z^{(k)} z^{(j-k)} \] $$ $end cppad-20170000.3/omh/theory/atan_forward.omh0000644000175200017650000000441013057470464017704 0ustar coincoin-web$Id: atan_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin atan_forward$$ $spell atan atanh Taylor $$ $section Inverse Tangent and Hyperbolic Tangent Forward Mode Theory$$ $mindex atan atanh$$ $head Derivatives$$ $latex \[ \begin{array}{rcl} \R{atan}^{(1)} (x) & = & 1 / ( 1 + x * x ) \\ \R{atanh}^{(1)} (x) & = & 1 / ( 1 - x * x ) \end{array} \] $$ If $latex F(x)$$ is $latex \R{atan} (x)$$ or $latex \R{atanh} (x)$$, the corresponding derivative satisfies the equation $latex \[ (1 \pm x * x ) * F^{(1)} (x) - 0 * F (x) = 1 \] $$ and in the $cref/standard math function differential equation /ForwardTheory /Standard Math Functions /Differential Equation /$$, $latex A(x) = 0$$, $latex B(x) = 1 \pm x * x $$, and $latex D(x) = 1$$. We use $latex a$$, $latex b$$, $latex d$$ and $latex z$$ to denote the Taylor coefficients for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, and $latex F [ X(t) ] $$ respectively. $head Taylor Coefficients Recursion$$ For $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} z^{(0)} & = & F( x^{(0)} ) \\ b^{(j)} & = & \left\{ \begin{array}{ll} 1 \pm x^{(0)} * x^{(0)} & {\rm if} \; j = 0 \\ \pm \sum_{k=0}^j x^{(k)} x^{(j-k)} & {\rm otherwise} \end{array} \right. \\ e^{(j)} & = & d^{(j)} + \sum_{k=0}^{j} a^{(j-k)} * z^{(k)} \\ & = & \left\{ \begin{array}{ll} 1 & {\rm if} \; j = 0 \\ 0 & {\rm otherwise} \end{array} \right. \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=0}^j e^{(k)} (j+1-k) x^{(j+1-k)} - \sum_{k=1}^j b^{(k)} (j+1-k) z^{(j+1-k)} \right) \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( (j+1) x^{(j+1)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \end{array} \] $$ $end cppad-20170000.3/omh/theory/erf_reverse.omh0000644000175200017650000000347113057470464017552 0ustar coincoin-web$Id:$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin erf_reverse$$ $spell erf Taylor $$ $section Error Function Reverse Mode Theory$$ $mindex erf$$ $head Notation$$ We use the reverse theory $cref/standard math function/ReverseTheory/Standard Math Functions/$$ definition for the functions $latex H$$ and $latex G$$. $head Positive Orders Z(t)$$ For order $latex j > 0$$, suppose that $latex H$$ is the same as $latex G$$. $latex \[ z^{(j)} = \frac{1}{j} \sum_{k=1}^j k x^{(k)} y^{(j-k)} \] $$ For $latex k = 1 , \ldots , j$$, the partial of $latex H$$ with respect to $latex x^{(k)}$$ is given by $latex \[ \D{H}{ x^{(k)} } = \D{G}{ x^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(k)} } = \D{G}{ x^{(k)} } + \D{G}{ z^{(j)} } \frac{k}{j} y^{(j-k)} \] $$ For $latex k = 1 , \ldots , j$$ The partial of $latex H$$ with respect to $latex y^{j-k}$$, is given by $latex \[ \D{H}{ y^{(j-k)} } = \D{G}{ y^{(j-k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ y^{(j-k)} } = \D{G}{ y^{(j-k)} } + \D{G}{ z^{(j)} } \frac{k}{j} x^{k} \] $$ $head Order Zero Z(t)$$ The $latex z^{(0)}$$ coefficient is expressed as a function of the Taylor coefficients for $latex X(t)$$ and $latex Y(t)$$ as follows: In this case, $latex \[ \D{H}{ x^{(0)} } = \D{G}{ x^{(0)} } + \D{G}{ z^{(0)} } \D{ z^{(0)} }{ x^{(0)} } = \D{G}{ x^{(0)} } + \D{G}{ z^{(0)} } y^{(0)} \] $$ $end cppad-20170000.3/omh/theory/acos_forward.omh0000644000175200017650000000600413057470464017707 0ustar coincoin-web$Id: acos_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin acos_forward$$ $spell acos acosh Arccosine Taylor $$ $section Inverse Cosine and Hyperbolic Cosine Forward Mode Theory$$ $mindex acos acosh$$ $head Derivatives$$ $latex \[ \begin{array}{rcl} \R{acos}^{(1)} (x) & = & - 1 / \sqrt{ 1 - x * x } \\ \R{acosh}^{(1)} (x) & = & + 1 / \sqrt{ x * x - 1} \end{array} \] $$ If $latex F(x)$$ is $latex \R{acos} (x)$$ or $latex \R{acosh} (x)$$ the corresponding derivative satisfies the equation $latex \[ \sqrt{ \mp ( x * x - 1 ) } * F^{(1)} (x) - 0 * F (u) = \mp 1 \] $$ and in the $cref/standard math function differential equation /ForwardTheory /Standard Math Functions /Differential Equation /$$, $latex A(x) = 0$$, $latex B(x) = \sqrt{ \mp( x * x - 1 ) }$$, and $latex D(x) = \mp 1$$. We use $latex a$$, $latex b$$, $latex d$$ and $latex z$$ to denote the Taylor coefficients for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, and $latex F [ X(t) ] $$ respectively. $head Taylor Coefficients Recursion$$ We define $latex Q(x) = \mp ( x * x - 1 )$$ and let $latex q$$ be the corresponding Taylor coefficients for $latex Q[ X(t) ]$$. It follows that $latex \[ q^{(j)} = \left\{ \begin{array}{ll} \mp ( x^{(0)} * x^{(0)} - 1 ) & {\rm if} \; j = 0 \\ \mp \sum_{k=0}^j x^{(k)} x^{(j-k)} & {\rm otherwise} \end{array} \right. \] $$ It follows that $latex B[ X(t) ] = \sqrt{ Q[ X(t) ] }$$ and from the equations for the $cref/square root/sqrt_forward/$$ that for $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} b^{(0)} & = & \sqrt{ q^{(0)} } \\ b^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \frac{j+1}{2} q^{(j+1) } - \sum_{k=1}^j k b^{(k)} b^{(j+1-k)} \right) \end{array} \] $$ It now follows from the general $xref/ ForwardTheory/ Standard Math Functions/ Taylor Coefficients Recursion Formula/ Taylor coefficients recursion formula/ 1 /$$ that for $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} z^{(0)} & = & F ( x^{(0)} ) \\ e^{(j)} & = & d^{(j)} + \sum_{k=0}^{j} a^{(j-k)} * z^{(k)} \\ & = & \left\{ \begin{array}{ll} \mp 1 & {\rm if} \; j = 0 \\ 0 & {\rm otherwise} \end{array} \right. \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=0}^j e^{(k)} (j+1-k) x^{(j+1-k)} - \sum_{k=1}^j b^{(k)} (j+1-k) z^{(j+1-k)} \right) \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \mp (j+1) x^{(j+1)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \end{array} \] $$ $end cppad-20170000.3/omh/theory/theory.omh0000644000175200017650000000141113057470464016545 0ustar coincoin-web$Id: theory.omh 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin Theory$$ $section The Theory of Derivative Calculations$$ $contents% omh/theory/forward_theory.omh% omh/theory/reverse_theory.omh% omh/theory/reverse_identity.omh%$$ $end cppad-20170000.3/omh/theory/log_reverse.omh0000644000175200017650000000501613057470464017554 0ustar coincoin-web$Id: log_reverse.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin log_reverse$$ $spell Taylor $$ $section Logarithm Function Reverse Mode Theory$$ $mindex log1p$$ We use the reverse theory $cref%standard math function %ReverseTheory %Standard Math Functions %$$ definition for the functions $latex H$$ and $latex G$$. The zero order forward mode formula for the $cref/logarithm/log_forward/$$ is $latex \[ z^{(0)} = F( x^{(0)} ) \] $$ and for $latex j > 0$$, $latex \[ z^{(j)} = \frac{1}{ \bar{b} + x^{(0)} } \frac{1}{j} \left( j x^{(j)} - \sum_{k=1}^{j-1} k z^{(k)} x^{(j-k)} \right) \] $$ where $latex \[ \bar{b} = \left\{ \begin{array}{ll} 0 & \R{if} \; F(x) = \R{log}(x) \\ 1 & \R{if} \; F(x) = \R{log1p}(x) \end{array} \right. \] $$ We note that for $latex j > 0$$ $latex \[ \begin{array}{rcl} \D{ z^{(j)} } { x^{(0)} } & = & - \frac{1}{ \bar{b} + x^{(0)} } \frac{1}{ \bar{b} + x^{(0)} } \frac{1}{j} \left( j x^{(j)} - \sum_{k=1}^{j-1} k z^{(k)} x^{(j-k)} \right) \\ & = & - \frac{z^{(j)}}{ \bar{b} + x^{(0)} } \end{array} \] $$ Removing the zero order partials are given by $latex \[ \begin{array}{rcl} \D{H}{ x^{(0)} } & = & \D{G}{ x^{(0)} } + \D{G}{ z^{(0)} } \D{ z^{(0)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(0)} } + \D{G}{ z^{(0)} } \frac{1}{ \bar{b} + x^{(0)} } \end{array} \] $$ For orders $latex j > 0$$ and for $latex k = 1 , \ldots , j-1$$ $latex \[ \begin{array}{rcl} \D{H}{ x^{(0)} } & = & \D{G}{ x^{(0)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(0)} } - \D{G}{ z^{(j)} } \frac{ z^{(j)} }{ \bar{b} + x^{(0)} } \\ \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(j)} } \\ & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \frac{1}{ \bar{b} + x^{(0)} } \\ \D{H}{ x^{(j-k)} } & = & \D{G}{ x^{(j-k)} } - \D{G}{ z^{(j)} } \frac{1}{ \bar{b} + x^{(0)} } \frac{k}{j} z^{(k)} \\ \D{H}{ z^{(k)} } & = & \D{G}{ z^{(k)} } - \D{G}{ z^{(j)} } \frac{1}{ \bar{b} + x^{(0)} } \frac{k}{j} x^{(j-k)} \end{array} \] $$ $end cppad-20170000.3/omh/theory/tan_reverse.omh0000644000175200017650000000631313057470464017556 0ustar coincoin-web$Id: tan_reverse.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin tan_reverse$$ $spell Taylor $$ $section Tangent and Hyperbolic Tangent Reverse Mode Theory$$ $mindex tan$$ $head Notation$$ We use the reverse theory $cref/standard math function/ReverseTheory/Standard Math Functions/$$ definition for the functions $latex H$$ and $latex G$$. In addition, we use the forward mode notation in $cref tan_forward$$ for $latex X(t)$$, $latex Y(t)$$ and $latex Z(t)$$. $head Eliminating Y(t)$$ For $latex j > 0$$, the forward mode coefficients are given by $latex \[ y^{(j-1)} = \sum_{k=0}^{j-1} z^{(k)} z^{(j-k-1)} \] $$ Fix $latex j > 0$$ and suppose that $latex H$$ is the same as $latex G$$ except that $latex y^{(j-1)}$$ is replaced as a function of the Taylor coefficients for $latex Z(t)$$. To be specific, for $latex k = 0 , \ldots , j-1$$, $latex \[ \begin{array}{rcl} \D{H}{ z^{(k)} } & = & \D{G}{ z^{(k)} } + \D{G}{ y^{(j-1)} } \D{ y^{(j-1)} }{ z^{(k)} } \\ & = & \D{G}{ z^{(k)} } + \D{G}{ y^{(j-1)} } 2 z^{(j-k-1)} \end{array} \] $$ $head Positive Orders Z(t)$$ For order $latex j > 0$$, suppose that $latex H$$ is the same as $latex G$$ except that $latex z^{(j)}$$ is expressed as a function of the coefficients for $latex X(t)$$, and the lower order Taylor coefficients for $latex Y(t)$$, $latex Z(t)$$. $latex \[ z^{(j)} = x^{(j)} \pm \frac{1}{j} \sum_{k=1}^j k x^{(k)} y^{(j-k)} \] $$ For $latex k = 1 , \ldots , j$$, the partial of $latex H$$ with respect to $latex x^{(k)}$$ is given by $latex \[ \begin{array}{rcl} \D{H}{ x^{(k)} } & = & \D{G}{ x^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(k)} } \\ & = & \D{G}{ x^{(k)} } + \D{G}{ z^{(j)} } \left[ \delta ( j - k ) \pm \frac{k}{j} y^{(j-k)} \right] \end{array} \] $$ where $latex \delta ( j - k )$$ is one if $latex j = k$$ and zero otherwise. For $latex k = 1 , \ldots , j$$ The partial of $latex H$$ with respect to $latex y^{j-k}$$, is given by $latex \[ \begin{array}{rcl} \D{H}{ y^{(j-k)} } & = & \D{G}{ y^{(j-k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ y^{(j-k)} } \\ & = & \D{G}{ y^{(j-k)} } \pm \D{G}{ z^{(j)} }\frac{k}{j} x^{k} \end{array} \] $$ $head Order Zero Z(t)$$ The order zero coefficients for the tangent and hyperbolic tangent are $latex \[ \begin{array}{rcl} z^{(0)} & = & \left\{ \begin{array}{c} \tan ( x^{(0)} ) \\ \tanh ( x^{(0)} ) \end{array} \right. \end{array} \] $$ Suppose that $latex H$$ is the same as $latex G$$ except that $latex z^{(0)}$$ is expressed as a function of the Taylor coefficients for $latex X(t)$$. In this case, $latex \[ \begin{array}{rcl} \D{H}{ x^{(0)} } & = & \D{G}{ x^{(0)} } + \D{G}{ z^{(0)} } \D{ z^{(0)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(0)} } + \D{G}{ z^{(0)} } ( 1 \pm y^{(0)} ) \end{array} \] $$ $end cppad-20170000.3/omh/theory/sqrt_forward.omh0000644000175200017650000000367513057470464017766 0ustar coincoin-web$Id: sqrt_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin sqrt_forward$$ $spell sqrt Arctangent Taylor $$ $section Square Root Function Forward Mode Theory$$ $mindex sqrt$$ If $latex F(x) = \sqrt{x} $$ $latex \[ F(x) * F^{(1)} (x) - 0 * F (x) = 1/2 \] $$ and in the $cref/standard math function differential equation /ForwardTheory /Standard Math Functions /Differential Equation /$$, $latex A(x) = 0$$, $latex B(x) = F(x)$$, and $latex D(x) = 1/2$$. We use $latex a$$, $latex b$$, $latex d$$, and $latex z$$ to denote the Taylor coefficients for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, and $latex F [ X(t) ] $$ respectively. It now follows from the general $cref/Taylor coefficients recursion formula /ForwardTheory /Standard Math Functions /Taylor Coefficients Recursion Formula /$$ that for $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} z^{(0)} & = & \sqrt { x^{(0)} } \\ e^{(j)} & = & d^{(j)} + \sum_{k=0}^{j} a^{(j-k)} * z^{(k)} \\ & = & \left\{ \begin{array}{ll} 1/2 & {\rm if} \; j = 0 \\ 0 & {\rm otherwise} \end{array} \right. \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=1}^{j+1} k x^{(k)} e^{(j+1-k)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \\ & = & \frac{1}{j+1} \frac{1}{ z^{(0)} } \left( \frac{j+1}{2} x^{(j+1) } - \sum_{k=1}^j k z^{(k)} z^{(j+1-k)} \right) \end{array} \] $$ $end cppad-20170000.3/omh/theory/asin_forward.omh0000644000175200017650000000572113057470464017721 0ustar coincoin-web$Id: asin_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin asin_forward$$ $spell asinh asin Taylor $$ $section Inverse Sine and Hyperbolic Sine Forward Mode Theory$$ $mindex asin asinh$$ $head Derivatives$$ $latex \[ \begin{array}{rcl} \R{asin}^{(1)} (x) & = & 1 / \sqrt{ 1 - x * x } \\ \R{asinh}^{(1)} (x) & = & 1 / \sqrt{ 1 + x * x } \end{array} \] $$ If $latex F(x)$$ is $latex \R{asin} (x) $$ or $latex \R{asinh} (x)$$ the corresponding derivative satisfies the equation $latex \[ \sqrt{ 1 \mp x * x } * F^{(1)} (x) - 0 * F (u) = 1 \] $$ and in the $cref/standard math function differential equation /ForwardTheory /Standard Math Functions /Differential Equation /$$, $latex A(x) = 0$$, $latex B(x) = \sqrt{1 \mp x * x }$$, and $latex D(x) = 1$$. We use $latex a$$, $latex b$$, $latex d$$ and $latex z$$ to denote the Taylor coefficients for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, and $latex F [ X(t) ] $$ respectively. $head Taylor Coefficients Recursion$$ We define $latex Q(x) = 1 \mp x * x$$ and let $latex q$$ be the corresponding Taylor coefficients for $latex Q[ X(t) ]$$. It follows that $latex \[ q^{(j)} = \left\{ \begin{array}{ll} 1 \mp x^{(0)} * x^{(0)} & {\rm if} \; j = 0 \\ \mp \sum_{k=0}^j x^{(k)} x^{(j-k)} & {\rm otherwise} \end{array} \right. \] $$ It follows that $latex B[ X(t) ] = \sqrt{ Q[ X(t) ] }$$ and from the equations for the $cref/square root/sqrt_forward/$$ that for $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} b^{(0)} & = & \sqrt{ q^{(0)} } \\ b^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \frac{j+1}{2} q^{(j+1) } - \sum_{k=1}^j k b^{(k)} b^{(j+1-k)} \right) \end{array} \] $$ It now follows from the general $xref/ ForwardTheory/ Standard Math Functions/ Taylor Coefficients Recursion Formula/ Taylor coefficients recursion formula/ 1 /$$ that for $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} z^{(0)} & = & F ( x^{(0)} ) \\ e^{(j)} & = & d^{(j)} + \sum_{k=0}^{j} a^{(j-k)} * z^{(k)} \\ & = & \left\{ \begin{array}{ll} 1 & {\rm if} \; j = 0 \\ 0 & {\rm otherwise} \end{array} \right. \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=0}^j e^{(k)} (j+1-k) x^{(j+1-k)} - \sum_{k=1}^j b^{(k)} (j+1-k) z^{(j+1-k)} \right) \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( (j+1) x^{(j+1)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \end{array} \] $$ $end cppad-20170000.3/omh/theory/atan_reverse.omh0000644000175200017650000000664213057470464017724 0ustar coincoin-web$Id: atan_reverse.omh 3682 2015-05-08 21:59:05Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin atan_reverse$$ $spell atan atanh Taylor $$ $section Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory$$ We use the reverse theory $cref%standard math function %ReverseTheory %Standard Math Functions %$$ definition for the functions $latex H$$ and $latex G$$. In addition, we use the forward mode notation in $cref atan_forward$$ for $latex \[ B(t) = 1 \pm X(t) * X(t) \] $$ We use $latex b$$ for the $th p$$ order Taylor coefficient row vectors corresponding to $latex B(t)$$ and replace $latex z^{(j)}$$ by $latex \[ ( z^{(j)} , b^{(j)} ) \] $$ in the definition for $latex G$$ and $latex H$$. The zero order forward mode formulas for the $cref/atan/atan_forward/$$ function are $latex \[ \begin{array}{rcl} z^{(0)} & = & F ( x^{(0)} ) \\ b^{(0)} & = & 1 \pm x^{(0)} x^{(0)} \end{array} \] $$ where $latex F(x) = \R{atan} (x)$$ for $latex +$$ and $latex F(x) = \R{atanh} (x)$$ for $latex -$$. For orders $latex j$$ greater than zero we have $latex \[ \begin{array}{rcl} b^{(j)} & = & \pm \sum_{k=0}^j x^{(k)} x^{(j-k)} \\ z^{(j)} & = & \frac{1}{j} \frac{1}{ b^{(0)} } \left( j x^{(j)} - \sum_{k=1}^{j-1} k z^{(k)} b^{(j-k)} \right) \end{array} \] $$ If $latex j = 0$$, we note that $latex F^{(1)} ( x^{(0)} ) = 1 / b^{(0)}$$ and hence $latex \[ \begin{array}{rcl} \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(0)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \frac{1}{ b^{(0)} } \pm \D{G}{ b^{(j)} } 2 x^{(0)} \end{array} \] $$ If $latex j > 0$$, then for $latex k = 1, \ldots , j-1$$ $latex \[ \begin{array}{rcl} \D{H}{ b^{(0)} } & = & \D{G}{ b^{(0)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ b^{(0)} } \\ & = & \D{G}{ b^{(0)} } - \D{G}{ z^{(j)} } \frac{ z^{(j)} }{ b^{(0)} } \\ \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(j)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ x^{(j)} } \\ & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \frac{1}{ b^{(0)} } \pm \D{G}{ b^{(j)} } 2 x^{(0)} \\ \D{H}{ x^{(0)} } & = & \D{G}{ x^{(0)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(0)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(0)} } \pm \D{G}{ b^{(j)} } 2 x^{(j)} \\ \D{H}{ x^{(k)} } & = & \D{G}{ x^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ x^{(k)} } \\ & = & \D{G}{ x^{(k)} } \pm \D{G}{ b^{(j)} } 2 x^{(j-k)} \\ \D{H}{ z^{(k)} } & = & \D{G}{ z^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ z^{(k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ z^{(k)} } \\ & = & \D{G}{ z^{(k)} } - \D{G}{ z^{(j)} } \frac{k b^{(j-k)} }{ j b^{(0)} } \\ \D{H}{ b^{(j-k)} } & = & \D{G}{ b^{(j-k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ b^{(j-k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ b^{(j-k)} } \\ & = & \D{G}{ b^{(j-k)} } - \D{G}{ z^{(j)} } \frac{k z^{(k)} }{ j b^{(0)} } \end{array} \] $$ $end cppad-20170000.3/omh/theory/exp_forward.omh0000644000175200017650000000377713057470464017574 0ustar coincoin-web$Id: exp_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin exp_forward$$ $spell exp expm1 Taylor $$ $section Exponential Function Forward Mode Theory$$ $mindex exp expm1$$ $head Derivatives$$ If $latex F(x)$$ is $latex \R{exp} (x)$$ or $latex \R{expm1} (x)$$ the corresponding derivative satisfies the equation $latex \[ 1 * F^{(1)} (x) - 1 * F (x) = d^{(0)} = \left\{ \begin{array}{ll} 0 & \R{if} \; F(x) = \R{exp}(x) \\ 1 & \R{if} \; F(x) = \R{expm1}(x) \end{array} \right. \] $$ where the equation above defines $latex d^{(0)}$$. In the $cref/standard math function differential equation /ForwardTheory /Standard Math Functions /Differential Equation /$$, $latex A(x) = 1$$, $latex B(x) = 1$$, and $latex D(x) = d^{(0)}$$. We use $latex a$$, $latex b$$, $latex d$$, and $latex z$$ to denote the Taylor coefficients for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, and $latex F [ X(t) ] $$ respectively. $head Taylor Coefficients Recursion$$ For orders $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} z^{(0)} & = & F ( x^{(0)} ) \\ e^{(0)} & = & d^{(0)} + z^{(0)} \\ e^{(j+1)} & = & d^{(j+1)} + \sum_{k=0}^{j+1} a^{(j+1-k)} * z^{(k)} \\ & = & z^{(j+1)} \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=1}^{j+1} k x^{(k)} e^{(j+1-k)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \\ & = & x^{(j+1)} d^{(0)} + \frac{1}{j+1} \sum_{k=1}^{j+1} k x^{(k)} z^{(j+1-k)} \end{array} \] $$ $end cppad-20170000.3/omh/theory/acos_reverse.omh0000644000175200017650000000773313057470464017730 0ustar coincoin-web$Id: acos_reverse.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin acos_reverse$$ $spell acosh acos Taylor $$ $section Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory$$ $mindex acos acosh$$ We use the reverse theory $cref%standard math function %ReverseTheory %Standard Math Functions %$$ definition for the functions $latex H$$ and $latex G$$. In addition, we use the forward mode notation in $cref acos_forward$$ for $latex \[ \begin{array}{rcl} Q(t) & = & \mp ( X(t) * X(t) - 1 ) \\ B(t) & = & \sqrt{ Q(t) } \end{array} \] $$ We use $latex q$$ and $latex b$$ for the $th p$$ order Taylor coefficient row vectors corresponding to these functions and replace $latex z^{(j)}$$ by $latex \[ ( z^{(j)} , b^{(j)} ) \] $$ in the definition for $latex G$$ and $latex H$$. The zero order forward mode formulas for the $cref/acos/acos_forward/$$ function are $latex \[ \begin{array}{rcl} q^{(0)} & = & \mp ( x^{(0)} x^{(0)} - 1) \\ b^{(0)} & = & \sqrt{ q^{(0)} } \\ z^{(0)} & = & F ( x^{(0)} ) \end{array} \] $$ where $latex F(x) = \R{acos} (x)$$ for $latex -$$ and $latex F(x) = \R{acosh} (x) $$ for $latex +$$. For orders $latex j$$ greater than zero we have $latex \[ \begin{array}{rcl} q^{(j)} & = & \mp \sum_{k=0}^j x^{(k)} x^{(j-k)} \\ b^{(j)} & = & \frac{1}{j} \frac{1}{ b^{(0)} } \left( \frac{j}{2} q^{(j)} - \sum_{k=1}^{j-1} k b^{(k)} b^{(j-k)} \right) \\ z^{(j)} & = & \frac{1}{j} \frac{1}{ b^{(0)} } \left( \mp j x^{(j)} - \sum_{k=1}^{j-1} k z^{(k)} b^{(j-k)} \right) \end{array} \] $$ If $latex j = 0$$, we note that $latex F^{(1)} ( x^{(0)} ) = \mp 1 / b^{(0)}$$ and hence $latex \[ \begin{array}{rcl} \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(0)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ q^{(0)} } \D{ q^{(0)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(j)} } \mp \D{G}{ z^{(j)} } \frac{1}{ b^{(0)} } \mp \D{G}{ b^{(j)} } \frac{ x^{(0)} }{ b^{(0)} } \end{array} \] $$ If $latex j > 0$$, then for $latex k = 1, \ldots , j-1$$ $latex \[ \begin{array}{rcl} \D{H}{ b^{(0)} } & = & \D{G}{ b^{(0)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ b^{(0)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ b^{(0)} } \\ & = & \D{G}{ b^{(0)} } - \D{G}{ z^{(j)} } \frac{ z^{(j)} }{ b^{(0)} } - \D{G}{ b^{(j)} } \frac{ b^{(j)} }{ b^{(0)} } \\ \D{H}{ x^{(0)} } & = & \D{G}{ x^{(0)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ q^{(j)} } \D{ q^{(j)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(0)} } \mp \D{G}{ b^{(j)} } \frac{ x^{(j)} }{ b^{(0)} } \\ \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(j)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ q^{(j)} } \D{ q^{(j)} }{ x^{(j)} } \\ & = & \D{G}{ x^{(j)} } \mp \D{G}{ z^{(j)} } \frac{1}{ b^{(0)} } \mp \D{G}{ b^{(j)} } \frac{ x^{(0)} }{ b^{(0)} } \\ \D{H}{ b^{(j - k)} } & = & \D{G}{ b^{(j - k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ b^{(j - k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ b^{(j - k)} } \\ & = & \D{G}{ b^{(j - k)} } - \D{G}{ z^{(j)} } \frac{k z^{(k)} }{j b^{(0)} } - \D{G}{ b^{(j)} } \frac{ b^{(k)} }{ b^{(0)} } \\ \D{H}{ x^{(k)} } & = & \D{G}{ x^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ q^{(j)} } \D{ q^{(j)} }{ x^{(k)} } \\ & = & \D{G}{ x^{(k)} } \mp \D{G}{ b^{(j)} } \frac{ x^{(j-k)} }{ b^{(0)} } \\ \D{H}{ z^{(k)} } & = & \D{G}{ z^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ z^{(k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ z^{(k)} } \\ & = & \D{G}{ z^{(k)} } - \D{G}{ z^{(j)} } \frac{k b^{(j-k)} }{ j b^{(0)} } \end{array} \] $$ $end cppad-20170000.3/omh/theory/cholesky.omh0000644000175200017650000002241713057470464017065 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin cholesky_theory$$ $spell Taylor Cholesky Sebastian Ph Humboldt Universitat zu $$ $section AD Theory for Cholesky Factorization$$ $head Reference$$ See section 3.6 of Sebastian F. Walter's Ph.D. thesis, $italic Structured Higher-Order Algorithmic Differentiation in the Forward and Reverse Mode with Application in Optimum Experimental Design $$, Humboldt-Universitat zu Berlin, 2011. $head Notation$$ $subhead Cholesky Factor$$ We are given a positive definite symmetric matrix $latex A \in \B{R}^{n \times n}$$ and a Cholesky factorization $latex \[ A = L L^\R{T} \] $$ where $latex L \in \B{R}^{n \times n}$$ is lower triangular. $subhead Taylor Coefficient$$ The matrix $latex A$$ is a function of a scalar argument $latex t$$. For $latex k = 0 , \ldots , K$$, we use $latex A_k$$ for the corresponding Taylor coefficients; i.e., $latex \[ A(t) = o( t^K ) + \sum_{k = 0}^K A_k t^k \] $$ where $latex o( t^K ) / t^K \rightarrow 0 $$ as $latex t \rightarrow 0$$. We use a similar notation for $latex L(t)$$. $subhead Lower Triangular Part$$ For a square matrix $latex C$$, $latex \R{lower} (C)$$ is the lower triangular part of $latex C$$, $latex \R{diag} (C)$$ is the diagonal matrix with the same diagonal as $latex C$$ and $latex \[ \R{low} ( C ) = \R{lower} (C) - \frac{1}{2} \R{diag} (C) \] $$ $head Forward Mode$$ For Taylor coefficient order $latex k = 0 , \ldots , K$$ the coefficients $latex A_k \in \B{R}^{n \times n}$$, and satisfy the equation $latex \[ A_k = \sum_{\ell=0}^k L_\ell L_{k-\ell}^\R{T} \] $$ In the case where $latex k=0$$, the $latex \[ A_0 = L_0 L_0^\R{T} \] $$ The value of $latex L_0$$ can be computed using the Cholesky factorization. In the case where $latex k > 0$$, $latex \[ A_k = L_k L_0^\R{T} + L_0 L_k^\R{T} + B_k \] $$ where $latex \[ B_k = \sum_{\ell=1}^{k-1} L_\ell L_{k-\ell}^\R{T} \] $$ Note that $latex B_k$$ is defined in terms of Taylor coefficients of $latex L(t)$$ that have order less than $latex k$$. We also note that $latex \[ L_0^{-1} ( A_k - B_k ) L_0^\R{-T} = L_0^{-1} L_k + L_k^\R{T} L_0^\R{-T} \] $$ The first matrix on the right hand side is lower triangular, the second is upper triangular, and the diagonals are equal. It follows that $latex \[ L_0^{-1} L_k = \R{low} [ L_0^{-1} ( A_k - B_k ) L_0^\R{-T} ] \] $$ $latex \[ L_k = L_0 \R{low} [ L_0^{-1} ( A_k - B_k ) L_0^\R{-T} ] \] $$ This expresses $latex L_k$$ in term of the Taylor coefficients of $latex A(t)$$ and the lower order coefficients of $latex L(t)$$. $head Lemma 1$$ We use the notation $latex \dot{C}$$ for the derivative of a matrix valued function $latex C(s)$$ with respect to a scalar argument $latex s$$. We use the notation $latex \bar{S}$$ and $latex \bar{L}$$ for the partial derivative of a scalar value function $latex \bar{F}( S, L)$$ with respect to a symmetric matrix $latex S$$ and an lower triangular matrix $latex L$$. Define the scalar valued function $latex \[ \hat{F}( C ) = \bar{F} [ S , \hat{L} (S) ] \] $$ We use $latex \hat{S}$$ for the total derivative of $latex \hat{F}$$ with respect to $latex S$$. Suppose that $latex \hat{L} ( S )$$ is such that $latex \[ \dot{L} = L_0 \R{low} ( L_0^{-1} \dot{S} L_0^\R{-T} ) \] $$ for any $latex S(s)$$. It follows that $latex \[ \hat{S} = \bar{S} + \frac{1}{2} ( M + M^\R{T} ) \] $$ where $latex \[ M = L_0^\R{-T} \R{low}( L_0^\R{T} \bar{L} )^\R{T} L_0^{-1} \] $$ $subhead Proof$$ $latex \[ \partial_s \hat{F} [ S(s) , L(s) ] = \R{tr} ( \bar{S}^\R{T} \dot{S} ) + \R{tr} ( \bar{L}^\R{T} \dot{L} ) \] $$ $latex \[ \R{tr} ( \bar{L}^\R{T} \dot{L} ) = \R{tr} [ \bar{L}^\R{T} L_0 \R{low} ( L_0^{-1} \dot{S} L_0^\R{-T} ) ] \] $$ $latex \[ = \R{tr} [ \R{low} ( L_0^{-1} \dot{S} L_0^\R{-T} )^\R{T} L_0^\R{T} \bar{L} ] \] $$ $latex \[ = \R{tr} [ L_0^{-1} \dot{S} L_0^\R{-T} \R{low}( L_0^\R{T} \bar{L} ) ] \] $$ $latex \[ = \R{tr} [ L_0^\R{-T} \R{low}( L_0^\R{T} \bar{L} ) L_0^{-1} \dot{S} ] \] $$ $latex \[ \partial_s \hat{F} [ S(s) , L(s) ] = \R{tr} ( \bar{S}^\R{T} \dot{S} ) + \R{tr} [ L_0^\R{-T} \R{low}( L_0^\R{T} \bar{L} ) L_0^{-1} \dot{S} ] \] $$ We now consider the $latex (i, j)$$ component function, for a symmetric matrix $latex S(s)$$, defined by $latex \[ S_{k, \ell} (s) = \left\{ \begin{array}{ll} 1 & \R{if} \; k = i \; \R{and} \; \ell = j \\ 1 & \R{if} \; k = j \; \R{and} \; \ell = i \\ 0 & \R{otherwise} \end{array} \right\} \] $$ This shows that the formula in the lemma is correct for $latex \hat{S}_{i,j}$$ and $latex \hat{S}_{j,i}$$. This completes the proof because the component $latex (i, j)$$ was arbitrary. $head Lemma 2$$ We use the same assumptions as in Lemma 1 except that the matrix $latex S$$ is lower triangular (instead of symmetric). It follows that $latex \[ \hat{S} = \bar{S} + \R{lower}(M) \] $$ where $latex \[ M = L_0^\R{-T} \R{low}( L_0^\R{T} \bar{L} )^\R{T} L_0^{-1} \] $$ The proof of this lemma is identical to Lemma 2 except that component function is defined by $latex \[ S_{k, \ell} (s) = \left\{ \begin{array}{ll} 1 & \R{if} \; k = i \; \R{and} \; \ell = j \\ 0 & \R{otherwise} \end{array} \right\} \] $$ $head Reverse Mode$$ $subhead Case k = 0$$ For the case $latex k = 0$$, $latex \[ \dot{A}_0 = \dot{L}_0 L_0^\R{T} + L_0 \dot{L}_0^\R{T} \] $$ $latex \[ L_0^{-1} \dot{A}_0 L_0^\R{-T} = L_0^{-1} \dot{L}_0 + \dot{L}_0^\R{T} L_0^\R{-T} \] $$ $latex \[ \R{low} ( L_0^{-1} \dot{A}_0 L_0^\R{-T} ) = L_0^{-1} \dot{L}_0 \] $$ $latex \[ \dot{L}_0 = L_0 \R{low} ( L_0^{-1} \dot{A}_0 L_0^\R{-T} ) \] $$ It follows from Lemma 1 that $latex \[ \bar{A}_0 \stackrel{+}{=} \frac{1}{2} ( M + M^\R{T} ) \] $$ where $latex \[ M = L_0^\R{-T} \R{low} ( L_0^\R{T} \bar{L}_0 )^\R{T} L_0^{-1} \] $$ and $latex \bar{A}_0$$ is the partial before and after is before and after $latex L_0$$ is removed from the scalar function dependency. $subhead Case k > 0$$ In the case where $latex k > 0$$, $latex \[ A_k = L_k L_0^\R{T} + L_0 L_k^\R{T} + B_k \] $$ where $latex B_k$$ is defined in terms of Taylor coefficients of $latex L(t)$$ that have order less than $latex k$$. It follows that $latex \[ \dot{L}_k L_0^\R{T} + L_0 \dot{L}_k^\R{T} = \dot{A}_k - \dot{B}_k - \dot{L}_0 L_k^\R{T} - L_k \dot{L}_0^\R{T} \] $$ $latex \[ L_0^{-1} \dot{L}_k + \dot{L}_k^\R{T} L_0^\R{-T} = L_0^{-1} ( \dot{A}_k - \dot{B}_k - \dot{L}_0 L_k^\R{T} - L_k \dot{L}_0^\R{T} ) L_0^\R{-T} \] $$ $latex \[ L_0^{-1} \dot{L}_k = \R{low} [ L_0^{-1} ( \dot{A}_k - \dot{B}_k - \dot{L}_0 L_k^\R{T} - L_k \dot{L}_0^\R{T} ) L_0^\R{-T} ] \] $$ $latex \[ \dot{L}_k = L_0 \R{low} [ L_0^{-1} ( \dot{A}_k - \dot{B}_k - \dot{L}_0 L_k^\R{T} - L_k \dot{L}_0^\R{T} ) L_0^\R{-T} ] \] $$ The matrix $latex A_k$$ is symmetric, it follows that $latex \[ \bar{A}_k \stackrel{+}{=} \frac{1}{2} ( M_k + M_k^\R{T} ) \] $$ where $latex \[ M_k = L_0^\R{-T} \R{low} ( L_0^\R{T} \bar{L}_k )^\R{T} L_0^{-1} \] $$ The matrix $latex B_k$$ is also symmetric, hence $latex \[ \bar{B}_k = - \; \frac{1}{2} ( M_k + M_k^\R{T} ) \] $$ We define the symmetric matrix $latex C_k (s)$$ by $latex \[ \dot{C}_k = \dot{L}_0 L_k^\R{T} + L_k \dot{L}_0^\R{T} \] $$ and remove the dependency on $latex C_k$$ with $latex \[ \R{tr}( \bar{C}_k^\R{T} \dot{C}_k ) = \R{tr}( \bar{B}_k^\R{T} \dot{C}_k ) = \R{tr}( \bar{B}_k^\R{T} \dot{L}_0 L_k^\R{T} ) + \R{tr}( \bar{B}_k^\R{T} L_k \dot{L}_0^\R{T} ) \] $$ $latex \[ = \R{tr}( L_k^\R{T} \bar{B}_k^\R{T} \dot{L}_0 ) + \R{tr}( L_k^\R{T} \bar{B}_k \dot{L}_0 ) \] $$ $latex \[ = \R{tr}[ L_k^\R{T} ( \bar{B}_k + \bar{B}_k^\R{T} ) \dot{L}_0 ] \] $$ Thus, removing $latex C_k$$ from the dependency results in the following update to $latex \bar{L}_0$$: $latex \[ \bar{L}_0 \stackrel{+}{=} \R{lower} [ ( \bar{B}_k + \bar{B}_k^\R{T} ) L_k ] \] $$ which is the same as $latex \[ \bar{L}_0 \stackrel{+}{=} 2 \; \R{lower} [ \bar{B}_k L_k ] \] $$ We still need to remove $latex B_k$$ from the dependency. It follows from its definition that $latex \[ \dot{B}_k = \sum_{\ell=1}^{k-1} \dot{L}_\ell L_{k-\ell}^\R{T} + L_\ell \dot{L}_{k-\ell}^\R{T} \]$$ $latex \[ \R{tr}( \bar{B}_k^\R{T} \dot{B}_k ) = \sum_{\ell=1}^{k-1} \R{tr}( \bar{B}_k^\R{T} \dot{L}_\ell L_{k-\ell}^\R{T} ) + \R{tr}( \bar{B}_k^\R{T} L_\ell \dot{L}_{k-\ell}^\R{T} ) \]$$ $latex \[ = \sum_{\ell=1}^{k-1} \R{tr}( L_{k-\ell}^\R{T} \bar{B}_k^\R{T} \dot{L}_\ell ) + \sum_{\ell=1}^{k-1} \R{tr}( L_\ell^\R{T} \bar{B}_k \dot{L}_{k-\ell} ) \]$$ We now use the fact that $latex \bar{B}_k$$ is symmetric to conclude $latex \[ \R{tr}( \bar{B}_k^\R{T} \dot{B}_k ) = 2 \sum_{\ell=1}^{k-1} \R{tr}( L_{k-\ell}^\R{T} \bar{B}_k^\R{T} \dot{L}_\ell ) \] $$ Each of the $latex \dot{L}_\ell$$ matrices is lower triangular. Thus, removing $latex B_k$$ from the dependency results in the following update for $latex \ell = 1 , \ldots , k-1$$: $latex \[ \bar{L}_\ell \stackrel{+}{=} 2 \; \R{lower}( \bar{B}_k L_{k-\ell} ) \] $$ $end cppad-20170000.3/omh/theory/sin_cos_forward.omh0000644000175200017650000000514713057470464020426 0ustar coincoin-web$Id: sin_cos_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin sin_cos_forward$$ $spell sin cos sinh cosh Taylor $$ $section Trigonometric and Hyperbolic Sine and Cosine Forward Theory$$ $mindex sin sinh cos cosh$$ $head Differential Equation$$ The $cref/standard math function differential equation /ForwardTheory /Standard Math Functions /Differential Equation /$$ is $latex \[ B(u) * F^{(1)} (u) - A(u) * F (u) = D(u) \] $$ In this sections we consider forward mode for the following choices: $table $pre $$ $cnext $cnext $latex F(u)$$ $cnext $cnext $latex \sin(u)$$ $cnext $cnext $latex \cos(u)$$ $cnext $cnext $latex \sinh(u)$$ $cnext $cnext $latex \cosh(u)$$ $rnext $cnext $cnext $latex A(u)$$ $cnext $cnext $latex 0$$ $cnext $cnext $latex 0$$ $cnext $cnext $latex 0$$ $cnext $cnext $latex 0$$ $rnext $cnext $cnext $latex B(u)$$ $cnext $cnext $latex 1$$ $cnext $cnext $latex 1$$ $cnext $cnext $latex 1$$ $cnext $cnext $latex 1$$ $rnext $cnext $cnext $latex D(u)$$ $cnext $cnext $latex \cos(u)$$ $cnext $cnext $latex - \sin(u)$$ $cnext $cnext $latex \cosh(u)$$ $cnext $cnext $latex \sinh(u)$$ $tend We use $latex a$$, $latex b$$, $latex d$$ and $latex f$$ for the Taylor coefficients of $latex A [ X (t) ]$$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, and $latex F [ X(t) ] $$ respectively. It now follows from the general $xref/ ForwardTheory/ Standard Math Functions/ Taylor Coefficients Recursion Formula/ Taylor coefficients recursion formula/ 1 /$$ that for $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} f^{(0)} & = & D ( x^{(0)} ) \\ e^{(j)} & = & d^{(j)} + \sum_{k=0}^{j} a^{(j-k)} * f^{(k)} \\ & = & d^{(j)} \\ f^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=1}^{j+1} k x^{(k)} e^{(j+1-k)} - \sum_{k=1}^j k f^{(k)} b^{(j+1-k)} \right) \\ & = & \frac{1}{j+1} \sum_{k=1}^{j+1} k x^{(k)} d^{(j+1-k)} \end{array} \] $$ The formula above generates the order $latex j+1$$ coefficient of $latex F[ X(t) ]$$ from the lower order coefficients for $latex X(t)$$ and $latex D[ X(t) ]$$. $end cppad-20170000.3/omh/theory/reverse_identity.omh0000644000175200017650000001057613057470464020633 0ustar coincoin-web$Id: reverse_identity.omh 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin reverse_identity$$ $spell Taylor Griewank Andreas $$ $section An Important Reverse Mode Identity$$ The theorem and the proof below is a restatement of the results on page 236 of $cref/Evaluating Derivatives/Bib/Evaluating Derivatives/$$. $head Notation$$ Given a function $latex f(u, v)$$ where $latex u \in B^n$$ we use the notation $latex \[ \D{f}{u} (u, v) = \left[ \D{f}{u_1} (u, v) , \cdots , \D{f}{u_n} (u, v) \right] \] $$ $head Reverse Sweep$$ When using $cref/reverse mode/reverse_any/$$ we are given a function $latex F : B^n \rightarrow B^m$$, a matrix of Taylor coefficients $latex x \in B^{n \times p}$$, and a weight vector $latex w \in B^m$$. We define the functions $latex X : B \times B^{n \times p} \rightarrow B^n$$, $latex W : B \times B^{n \times p} \rightarrow B$$, and $latex W_j : B^{n \times p} \rightarrow B$$ by $latex \[ \begin{array}{rcl} X(t , x) & = & x^{(0)} + x^{(1)} t + \cdots + x^{(p-1)} t^{p-1} \\ W(t, x) & = & w_0 F_0 [X(t, x)] + \cdots + w_{m-1} F_{m-1} [X(t, x)] \\ W_j (x) & = & \frac{1}{j!} \Dpow{j}{t} W(0, x) \end{array} \]$$ where $latex x^{(j)}$$ is the $th j$$ column of $latex x \in B^{n \times p}$$. The theorem below implies that $latex \[ \D{ W_j }{ x^{(i)} } (x) = \D{ W_{j-i} }{ x^{(0)} } (x) \] $$ A $cref/general reverse sweep/reverse_any/$$ calculates the values $latex \[ \D{ W_{p-1} }{ x^{(i)} } (x) \hspace{1cm} (i = 0 , \ldots , p-1) \] $$ But the return values for a reverse sweep are specified in terms of the more useful values $latex \[ \D{ W_j }{ x^{(0)} } (x) \hspace{1cm} (j = 0 , \ldots , p-1) \] $$ $head Theorem$$ Suppose that $latex F : B^n \rightarrow B^m$$ is a $latex p$$ times continuously differentiable function. Define the functions $latex Z : B \times B^{n \times p} \rightarrow B^n$$, $latex Y : B \times B^{n \times p }\rightarrow B^m$$, and $latex y^{(j)} : B^{n \times p }\rightarrow B^m$$ by $latex \[ \begin{array}{rcl} Z(t, x) & = & x^{(0)} + x^{(1)} t + \cdots + x^{(p-1)} t^{p-1} \\ Y(t, x) & = & F [ Z(t, x) ] \\ y^{(j)} (x) & = & \frac{1}{j !} \Dpow{j}{t} Y(0, x) \end{array} \] $$ where $latex x^{(j)}$$ denotes the $th j$$ column of $latex x \in B^{n \times p}$$. It follows that for all $latex i, j$$ such that $latex i \leq j < p$$, $latex \[ \begin{array}{rcl} \D{ y^{(j)} }{ x^{(i)} } (x) & = & \D{ y^{(j-i)} }{ x^{(0)} } (x) \end{array} \] $$ $head Proof$$ If follows from the definitions that $latex \[ \begin{array}{rclr} \D{ y^{(j)} }{ x^{(i)} } (x) & = & \frac{1}{j ! } \D{ }{ x^{(i)} } \left[ \Dpow{j}{t} (F \circ Z) (t, x) \right]_{t=0} \\ & = & \frac{1}{j ! } \left[ \Dpow{j}{t} \D{ }{ x^{(i)} } (F \circ Z) (t, x) \right]_{t=0} \\ & = & \frac{1}{j ! } \left\{ \Dpow{j}{t} \left[ t^i ( F^{(1)} \circ Z ) (t, x) \right] \right\}_{t=0} \end{array} \] $$ For $latex k > i$$, the $th k$$ partial of $latex t^i$$ with respect to $latex t$$ is zero. Thus, the partial with respect to $latex t$$ is given by $latex \[ \begin{array}{rcl} \Dpow{j}{t} \left[ t^i ( F^{(1)} \circ Z ) (t, x) \right] & = & \sum_{k=0}^i \left( \begin{array}{c} j \\ k \end{array} \right) \frac{ i ! }{ (i - k) ! } t^{i-k} \; \Dpow{j-k}{t} ( F^{(1)} \circ Z ) (t, x) \\ \left\{ \Dpow{j}{t} \left[ t^i ( F^{(1)} \circ Z ) (t, x) \right] \right\}_{t=0} & = & \left( \begin{array}{c} j \\ i \end{array} \right) i ! \Dpow{j-i}{t} ( F^{(1)} \circ Z ) (t, x) \\ & = & \frac{ j ! }{ (j - i) ! } \Dpow{j-i}{t} ( F^{(1)} \circ Z ) (t, x) \\ \D{ y^{(j)} }{ x^{(i)} } (x) & = & \frac{ 1 }{ (j - i) ! } \Dpow{j-i}{t} ( F^{(1)} \circ Z ) (t, x) \end{array} \] $$ Applying this formula to the case where $latex j$$ is replaced by $latex j - i$$ and $latex i$$ is replaced by zero, we obtain $latex \[ \D{ y^{(j-i)} }{ x^{(0)} } (x) = \frac{ 1 }{ (j - i) ! } \Dpow{j-i}{t} ( F^{(1)} \circ Z ) (t, x) = \D{ y^{(j)} }{ x^{(i)} } (x) \] $$ which completes the proof $end cppad-20170000.3/omh/theory/sqrt_reverse.omh0000644000175200017650000000376713057470464017777 0ustar coincoin-web$Id: sqrt_reverse.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin sqrt_reverse$$ $spell sqrt Taylor $$ $section Square Root Function Reverse Mode Theory$$ $mindex sqrt$$ We use the reverse theory $cref%standard math function %ReverseTheory %Standard Math Functions %$$ definition for the functions $latex H$$ and $latex G$$. The forward mode formulas for the $cref/square root/sqrt_forward/$$ function are $latex \[ z^{(j)} = \sqrt { x^{(0)} } \] $$ for the case $latex j = 0$$, and for $latex j > 0$$, $latex \[ z^{(j)} = \frac{1}{j} \frac{1}{ z^{(0)} } \left( \frac{j}{2} x^{(j) } - \sum_{\ell=1}^{j-1} \ell z^{(\ell)} z^{(j-\ell)} \right) \] $$ If $latex j = 0$$, we have the relation $latex \[ \begin{array}{rcl} \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \frac{1}{2 z^{(0)} } \end{array} \] $$ If $latex j > 0$$, then for $latex k = 1, \ldots , j-1$$ $latex \[ \begin{array}{rcl} \D{H}{ z^{(0)} } & = & \D{G}{ z^{(0)} } + \D{G} { z^{(j)} } \D{ z^{(j)} }{ z^{(0)} } \\ & = & \D{G}{ z^{(0)} } - \D{G}{ z^{(j)} } \frac{ z^{(j)} }{ z^{(0)} } \\ \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(j)} } \\ & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \frac{1}{ 2 z^{(0)} } \\ \D{H}{ z^{(k)} } & = & \D{G}{ z^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ z^{(k)} } \\ & = & \D{G}{ z^{(k)} } - \D{G}{ z^{(j)} } \frac{ z^{(j-k)} }{ z^{(0)} } \end{array} \] $$ $end cppad-20170000.3/omh/theory/asin_reverse.omh0000644000175200017650000000770213057470464017731 0ustar coincoin-web$Id: asin_reverse.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin asin_reverse$$ $spell asinh asin Taylor $$ $section Inverse Sine and Hyperbolic Sine Reverse Mode Theory$$ $mindex asin asinh$$ We use the reverse theory $cref%standard math function %ReverseTheory %Standard Math Functions %$$ definition for the functions $latex H$$ and $latex G$$. In addition, we use the forward mode notation in $cref asin_forward$$ for $latex \[ \begin{array}{rcl} Q(t) & = & 1 \mp X(t) * X(t) \\ B(t) & = & \sqrt{ Q(t) } \end{array} \] $$ We use $latex q$$ and $latex b$$ for the $th p$$ order Taylor coefficient row vectors corresponding to these functions and replace $latex z^{(j)}$$ by $latex \[ ( z^{(j)} , b^{(j)} ) \] $$ in the definition for $latex G$$ and $latex H$$. The zero order forward mode formulas for the $cref/asin/asin_forward/$$ function are $latex \[ \begin{array}{rcl} q^{(0)} & = & 1 \mp x^{(0)} x^{(0)} \\ b^{(0)} & = & \sqrt{ q^{(0)} } \\ z^{(0)} & = & F( x^{(0)} ) \end{array} \] $$ where $latex F(x) = \R{asin} (x)$$ for $latex -$$ and $latex F(x) = \R{asinh} (x) $$ for $latex +$$. For the orders $latex j$$ greater than zero we have $latex \[ \begin{array}{rcl} q^{(j)} & = & \mp \sum_{k=0}^j x^{(k)} x^{(j-k)} \\ b^{(j)} & = & \frac{1}{j} \frac{1}{ b^{(0)} } \left( \frac{j}{2} q^{(j)} - \sum_{k=1}^{j-1} k b^{(k)} b^{(j-k)} \right) \\ z^{(j)} & = & \frac{1}{j} \frac{1}{ b^{(0)} } \left( j x^{(j)} - \sum_{k=1}^{j-1} k z^{(k)} b^{(j-k)} \right) \end{array} \] $$ If $latex j = 0$$, we note that $latex F^{(1)} ( x^{(0)} ) = 1 / b^{(0)}$$ and hence $latex \[ \begin{array}{rcl} \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(0)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ q^{(0)} } \D{ q^{(0)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \frac{1}{ b^{(0)} } \mp \D{G}{ b^{(j)} } \frac{ x^{(0)} }{ b^{(0)} } \end{array} \] $$ If $latex j > 0$$, then for $latex k = 1, \ldots , j-1$$ $latex \[ \begin{array}{rcl} \D{H}{ b^{(0)} } & = & \D{G}{ b^{(0)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ b^{(0)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ b^{(0)} } \\ & = & \D{G}{ b^{(0)} } - \D{G}{ z^{(j)} } \frac{ z^{(j)} }{ b^{(0)} } - \D{G}{ b^{(j)} } \frac{ b^{(j)} }{ b^{(0)} } \\ \D{H}{ x^{(0)} } & = & \D{G}{ x^{(0)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ q^{(j)} } \D{ q^{(j)} }{ x^{(0)} } \\ & = & \D{G}{ x^{(0)} } \mp \D{G}{ b^{(j)} } \frac{ x^{(j)} }{ b^{(0)} } \\ \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(j)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ q^{(j)} } \D{ q^{(j)} }{ x^{(j)} } \\ & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \frac{1}{ b^{(0)} } \mp \D{G}{ b^{(j)} } \frac{ x^{(0)} }{ b^{(0)} } \\ \D{H}{ b^{(j - k)} } & = & \D{G}{ b^{(j - k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ b^{(j - k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ b^{(j - k)} } \\ & = & \D{G}{ b^{(j - k)} } - \D{G}{ z^{(j)} } \frac{k z^{(k)} }{j b^{(0)} } - \D{G}{ b^{(j)} } \frac{ b^{(k)} }{ b^{(0)} } \\ \D{H}{ x^{(k)} } & = & \D{G}{ x^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ q^{(j)} } \D{ q^{(j)} }{ x^{(k)} } \\ & = & \D{G}{ x^{(k)} } \mp \D{G}{ b^{(j)} } \frac{ x^{(j-k)} }{ b^{(0)} } \\ \D{H}{ z^{(k)} } & = & \D{G}{ z^{(k)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ z^{(k)} } + \D{G}{ b^{(j)} } \D{ b^{(j)} }{ z^{(k)} } \\ & = & \D{G}{ z^{(k)} } - \D{G}{ z^{(j)} } \frac{k b^{(j-k)} }{ j b^{(0)} } \end{array} \] $$ $end cppad-20170000.3/omh/theory/exp_reverse.omh0000644000175200017650000000347513057470464017576 0ustar coincoin-web$Id: exp_reverse.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin exp_reverse$$ $spell Taylor exp expm $$ $section Exponential Function Reverse Mode Theory$$ $mindex exp expm1$$ We use the reverse theory $cref%standard math function %ReverseTheory %Standard Math Functions %$$ definition for the functions $latex H$$ and $latex G$$. The zero order forward mode formula for the $cref/exponential/exp_forward/$$ is $latex \[ z^{(0)} = F ( x^{(0)} ) \] $$ and for $latex j > 0$$, $latex \[ z^{(j)} = x^{(j)} d^{(0)} + \frac{1}{j} \sum_{k=1}^{j} k x^{(k)} z^{(j-k)} \] $$ where $latex \[ d^{(0)} = \left\{ \begin{array}{ll} 0 & \R{if} \; F(x) = \R{exp}(x) \\ 1 & \R{if} \; F(x) = \R{expm1}(x) \end{array} \right. \] $$ For order $latex j = 0, 1, \ldots$$ we note that $latex \[ \begin{array}{rcl} \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } \D{ z^{(j)} }{ x^{(j)} } \\ & = & \D{G}{ x^{(j)} } + \D{G}{ z^{(j)} } ( d^{(0)} + z^{(0)} ) \end{array} \] $$ If $latex j > 0$$, then for $latex k = 1 , \ldots , j$$ $latex \[ \begin{array}{rcl} \D{H}{ x^{(k)} } & = & \D{G}{ x^{(k)} } + \D{G}{ z^{(j)} } \frac{1}{j} k z^{(j-k)} \\ \D{H}{ z^{(j-k)} } & = & \D{G}{ z^{(j-k)} } + \D{G}{ z^{(j)} } \frac{1}{j} k x^{(k)} \end{array} \] $$ $end cppad-20170000.3/omh/theory/sin_cos_reverse.omh0000644000175200017650000000520413057470464020427 0ustar coincoin-web$Id: sin_cos_reverse.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin sin_cos_reverse$$ $spell Taylor cos $$ $section Trigonometric and Hyperbolic Sine and Cosine Reverse Theory$$ $mindex sin sinh cos cosh$$ We use the reverse theory $cref%standard math function %ReverseTheory %Standard Math Functions %$$ definition for the functions $latex H$$ and $latex G$$. In addition, we use the following definitions for $latex s$$ and $latex c$$ and the integer $latex \ell$$ $table Coefficients $cnext $cnext $latex s$$ $cnext $cnext $latex c$$ $cnext $cnext $latex \ell$$ $rnext Trigonometric Case $cnext $cnext $latex \sin [ X(t) ]$$ $cnext $cnext $latex \cos [ X(t) ]$$ $cnext $cnext 1 $rnext Hyperbolic Case $cnext $cnext $latex \sinh [ X(t) ]$$ $cnext $cnext $latex \cosh [ X(t) ]$$ $cnext $cnext -1 $tend We use the value $latex \[ z^{(j)} = ( s^{(j)} , c^{(j)} ) \] $$ in the definition for $latex G$$ and $latex H$$. The forward mode formulas for the $cref/sine and cosine/sin_cos_forward/$$ functions are $latex \[ \begin{array}{rcl} s^{(j)} & = & \frac{1 + \ell}{2} \sin ( x^{(0)} ) + \frac{1 - \ell}{2} \sinh ( x^{(0)} ) \\ c^{(j)} & = & \frac{1 + \ell}{2} \cos ( x^{(0)} ) + \frac{1 - \ell}{2} \cosh ( x^{(0)} ) \end{array} \] $$ for the case $latex j = 0$$, and for $latex j > 0$$, $latex \[ \begin{array}{rcl} s^{(j)} & = & \frac{1}{j} \sum_{k=1}^{j} k x^{(k)} c^{(j-k)} \\ c^{(j)} & = & \ell \frac{1}{j} \sum_{k=1}^{j} k x^{(k)} s^{(j-k)} \end{array} \] $$ If $latex j = 0$$, we have the relation $latex \[ \begin{array}{rcl} \D{H}{ x^{(j)} } & = & \D{G}{ x^{(j)} } + \D{G}{ s^{(j)} } c^{(0)} + \ell \D{G}{ c^{(j)} } s^{(0)} \end{array} \] $$ If $latex j > 0$$, then for $latex k = 1, \ldots , j-1$$ $latex \[ \begin{array}{rcl} \D{H}{ x^{(k)} } & = & \D{G}{ x^{(k)} } + \D{G}{ s^{(j)} } \frac{1}{j} k c^{(j-k)} + \ell \D{G}{ c^{(j)} } \frac{1}{j} k s^{(j-k)} \\ \D{H}{ s^{(j-k)} } & = & \D{G}{ s^{(j-k)} } + \ell \D{G}{ c^{(j)} } k x^{(k)} \\ \D{H}{ c^{(j-k)} } & = & \D{G}{ c^{(j-k)} } + \D{G}{ s^{(j)} } k x^{(k)} \end{array} \] $$ $end cppad-20170000.3/omh/theory/forward_theory.omh0000644000175200017650000001301713057470464020276 0ustar coincoin-web$Id: forward_theory.omh 3686 2015-05-11 16:14:25Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin ForwardTheory$$ $spell Taylor $$ $section The Theory of Forward Mode$$ $head Taylor Notation$$ In Taylor notation, each variable corresponds to a function of a single argument which we denote by $icode t$$ (see Section 10.2 of $cref/Evaluating Derivatives/Bib/Evaluating Derivatives/$$). Here and below $latex X(t)$$, $latex Y(t)$$, and $icode Z(t)$$ are scalar valued functions and the corresponding $th p$$ order Taylor coefficients row vectors are $latex x$$, $latex y$$ and $latex z$$; i.e., $latex \[ \begin{array}{lcr} X(t) & = & x^{(0)} + x^{(1)} * t + \cdots + x^{(p)} * t^p + o( t^p ) \\ Y(t) & = & y^{(0)} + y^{(1)} * t + \cdots + y^{(p)} * t^p + o( t^p ) \\ Z(t) & = & z^{(0)} + z^{(1)} * t + \cdots + z^{(p)} * t^p + o( t^p ) \end{array} \] $$ For the purposes of this section, we are given $latex x$$ and $latex y$$ and need to determine $latex z$$. $head Binary Operators$$ $subhead Addition$$ $latex \[ \begin{array}{rcl} Z(t) & = & X(t) + Y(t) \\ \sum_{j=0}^p z^{(j)} * t^j & = & \sum_{j=0}^p x^{(j)} * t^j + \sum_{j=0}^p y^{(j)} * t^j + o( t^p ) \\ z^{(j)} & = & x^{(j)} + y^{(j)} \end{array} \] $$ $subhead Subtraction$$ $latex \[ \begin{array}{rcl} Z(t) & = & X(t) - Y(t) \\ \sum_{j=0}^p z^{(j)} * t^j & = & \sum_{j=0}^p x^{(j)} * t^j - \sum_{j=0}^p y^{(j)} * t^j + o( t^p ) \\ z^{(j)} & = & x^{(j)} - y^{(j)} \end{array} \] $$ $subhead Multiplication$$ $latex \[ \begin{array}{rcl} Z(t) & = & X(t) * Y(t) \\ \sum_{j=0}^p z^{(j)} * t^j & = & \left( \sum_{j=0}^p x^{(j)} * t^j \right) * \left( \sum_{j=0}^p y^{(j)} * t^j \right) + o( t^p ) \\ z^{(j)} & = & \sum_{k=0}^j x^{(j-k)} * y^{(k)} \end{array} \] $$ $subhead Division$$ $latex \[ \begin{array}{rcl} Z(t) & = & X(t) / Y(t) \\ x & = & z * y \\ \sum_{j=0}^p x^{(j)} * t^j & = & \left( \sum_{j=0}^p z^{(j)} * t^j \right) * \left( \sum_{j=0}^p y^{(j)} * t^j \right) + o( t^p ) \\ x^{(j)} & = & \sum_{k=0}^j z^{(j-k)} y^{(k)} \\ z^{(j)} & = & \frac{1}{y^{(0)}} \left( x^{(j)} - \sum_{k=1}^j z^{(j-k)} y^{(k)} \right) \end{array} \] $$ $head Standard Math Functions$$ Suppose that $latex F $$ is a standard math function and $latex \[ Z(t) = F[ X(t) ] \]$$ $subhead Differential Equation$$ All of the standard math functions satisfy a differential equation of the form $latex \[ B(u) * F^{(1)} (u) - A(u) * F (u) = D(u) \] $$ We use $latex a$$, $latex b$$ and $latex d$$ to denote the $th p$$ order Taylor coefficient row vectors for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$ and $latex D [ X (t) ] $$ respectively. We assume that these coefficients are known functions of $latex x$$, the $th p$$ order Taylor coefficients for $latex X(t)$$. $subhead Taylor Coefficients Recursion Formula$$ Our problem here is to express $latex z$$, the $th p$$ order Taylor coefficient row vector for $latex Z(t)$$, in terms of these other known coefficients. It follows from the formulas above that $latex \[ \begin{array}{rcl} Z^{(1)} (t) & = & F^{(1)} [ X(t) ] * X^{(1)} (t) \\ B[ X(t) ] * Z^{(1)} (t) & = & \{ D[ X(t) ] + A[ X(t) ] * Z(t) \} * X^{(1)} (t) \\ B[ X(t) ] * Z^{(1)} (t) & = & E(t) * X^{(1)} (t) \end{array} \] $$ where we define $latex \[ E(t) = D[X(t)] + A[X(t)] * Z(t) \] $$ We can compute the value of $latex z^{(0)}$$ using the formula $latex \[ z^{(0)} = F ( x^{(0)} ) \]$$ Suppose by induction (on $latex j$$) that we are given the Taylor coefficients of $latex E(t)$$ up to order $latex j-1$$; i.e., $latex e^{(k)}$$ for $latex k = 0 , \ldots , j-1$$ and the coefficients $latex z^{(k)}$$ for $latex k = 0 , \ldots , j$$. We can compute $latex e^{(j)}$$ using the formula $latex \[ e^{(j)} = d^{(j)} + \sum_{k=0}^j a^{(j-k)} * z^{(k)} \] $$ We need to complete the induction by finding formulas for $latex z^{(j+1)}$$. It follows for the formula for the $cref/multiplication/ForwardTheory/Binary Operators/Multiplication/$$ operator that $latex \[ \begin{array}{rcl} \left( \sum_{k=0}^j b^{(k)} t^k \right) * \left( \sum_{k=1}^{j+1} k z^{(k)} * t^{k-1} \right) & = & \left( \sum_{k=0}^j e^{(k)} * t^k \right) * \left( \sum_{k=1}^{j+1} k x^{(k)} * t^{k-1} \right) + o( t^p ) \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=0}^j e^{(k)} (j+1-k) x^{(j+1-k)} - \sum_{k=1}^j b^{(k)} (j+1-k) z^{(j+1-k)} \right) \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=1}^{j+1} k x^{(k)} e^{(j+1-k)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \end{array} \] $$ This completes the induction that computes $latex e^{(j)}$$ and $latex z^{(j+1)}$$. $children% omh/theory/exp_forward.omh% omh/theory/log_forward.omh% omh/theory/sqrt_forward.omh% omh/theory/sin_cos_forward.omh% omh/theory/atan_forward.omh% omh/theory/asin_forward.omh% omh/theory/acos_forward.omh% omh/theory/tan_forward.omh% omh/theory/erf_forward.omh %$$ $subhead Cases that Apply Recursion Above$$ $table $rref exp_forward$$ $rref log_forward$$ $rref sqrt_forward$$ $rref sin_cos_forward$$ $rref atan_forward$$ $rref asin_forward$$ $rref acos_forward$$ $tend $subhead Special Cases$$ $table $rref tan_forward$$ $tend $end cppad-20170000.3/omh/det_33_hpp.omh0000644000175200017650000000151213057470464015653 0ustar coincoin-web$Id: det_33_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin det_33.hpp$$ $spell det_33 ifndef endif $$ $section Source: det_33$$ $mindex source$$ $code # ifndef CPPAD_DET_33_HPP $pre $$ # define CPPAD_DET_33_HPP $srcfile%cppad/speed/det_33.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/reverse/0002755000175200017650000000000013057470464014674 5ustar coincoin-webcppad-20170000.3/omh/reverse/reverse.omh0000644000175200017650000000217413057470464017056 0ustar coincoin-web// $Id: reverse.omh 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin Reverse$$ $spell xq $$ $section Reverse Mode$$ $head Multiple Directions$$ Reverse mode after $cref/Forward(q, r, xq)/forward_dir/$$ with number of directions $icode%r% != 1%$$ is not yet supported. There is one exception, $cref reverse_one$$ is allowed because there is only one zero order forward direction. After such an operation, only the zero order forward results are retained (the higher order forward results are lost). $childtable% omh/reverse/reverse_one.omh% omh/reverse/reverse_two.omh% omh/reverse/reverse_any.omh %$$ $end cppad-20170000.3/omh/reverse/reverse_one.omh0000644000175200017650000000561613057470464017723 0ustar coincoin-web// $Id: reverse_one.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin reverse_one$$ $section First Order Reverse Mode$$ $mindex derivative$$ $spell taylor const dw $$ $head Syntax$$ $icode%dw% = %f%.Reverse(1, %w%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The function $latex W : B^n \rightarrow B$$ is defined by $latex \[ W(x) = w_0 * F_0 ( x ) + \cdots + w_{m-1} * F_{m-1} (x) \] $$ The result of this operation is the derivative $latex dw = W^{(1)} (x)$$; i.e., $latex \[ dw = w_0 * F_0^{(1)} ( x ) + \cdots + w_{m-1} * F_{m-1}^{(1)} (x) \] $$ Note that if $latex w$$ is the $th i$$ $cref/elementary vector/glossary/Elementary Vector/$$, $latex dw = F_i^{(1)} (x)$$. $head f$$ The object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ Before this call to $code Reverse$$, the value returned by $codei% %f%.size_order() %$$ must be greater than or equal one (see $cref size_order$$). $head x$$ The vector $icode x$$ in expression for $icode dw$$ above corresponds to the previous call to $cref forward_zero$$ using this ADFun object $icode f$$; i.e., $codei% %f%.Forward(0, %x%) %$$ If there is no previous call with the first argument zero, the value of the $cref/independent/Independent/$$ variables during the recording of the AD sequence of operations is used for $icode x$$. $head w$$ The argument $icode w$$ has prototype $codei% const %Vector% &%w% %$$ (see $cref/Vector/reverse_one/Vector/$$ below) and its size must be equal to $icode m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. $head dw$$ The result $icode dw$$ has prototype $codei% %Vector% %dw% %$$ (see $cref/Vector/reverse_one/Vector/$$ below) and its value is the derivative $latex W^{(1)} (x)$$. The size of $icode dw$$ is equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ $children% example/reverse_one.cpp %$$ The file $cref reverse_one.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end cppad-20170000.3/omh/reverse/reverse_any.omh0000644000175200017650000001411113057470464017717 0ustar coincoin-web// $Id: reverse_any.omh 3799 2016-03-12 12:33:53Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin reverse_any$$ $spell checkpointing typename xk xp dw Ind uj std arg const Taylor $$ $section Any Order Reverse Mode$$ $mindex derivative$$ $head Syntax$$ $icode%dw% = %f%.Reverse(%q%, %w%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. Reverse mode computes the derivative of the $cref Forward$$ mode $cref/Taylor coefficients/glossary/Taylor Coefficient/$$ with respect to the domain variable $latex x$$. To be specific, it computes the derivative $latex W^{(1)} (u)$$ at $latex u = x$$ which is specified by the following notation: $head Notation$$ $subhead u^(k)$$ For $latex k = 0, \ldots , q-1$$, the vector $latex u^{(k)} \in B^n$$ is defined as the value of $icode x_k$$ in the previous calls of the form $codei% %f%.Forward(%k%, %x_k%) %$$ If there is no previous call with $latex k = 0$$, $latex u^{(0)}$$ is the value of the independent variables when the corresponding AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ was recorded. $subhead X(t, u)$$ The function $latex X : B \times B^{n \times q} \rightarrow B^n$$ is defined by $latex \[ X ( t , u ) = u^{(0)} + u^{(1)} * t + \cdots + u^{(q-1)} * t^{q-1} \] $$ Note that for $latex k = 0 , \ldots , q-1$$, $latex u^{(k)}$$ is related to the $th k$$ partial of $latex X(t, u)$$ with respect to $latex t$$ by $latex \[ u^{(k)} = \frac{1}{k !} \Dpow{k}{t} X(0, u) \] $$ $subhead Y(t, u)$$ The function $latex Y : B \times B^{n \times q} \rightarrow B^m$$ is defined by $latex \[ Y(t, u) = F [ X(t,u) ] \]$$ $subhead w^(k)$$ If the argument $icode w$$ has size $icode%m% * %q%$$, for $latex k = 0 , \ldots , q-1$$ and $latex i = 0, \ldots , m-1$$, $latex \[ w_i^{(k)} = w [ i * q + k ] \] $$ If the argument $icode w$$ has size $icode m$$, for $latex k = 0 , \ldots , q-1$$ and $latex i = 0, \ldots , m-1$$, $latex \[ w_i^{(k)} = \left\{ \begin{array}{ll} w [ i ] & {\rm if} \; k = q-1 \\ 0 & {\rm otherwise} \end{array} \right. \] $$ $subhead W(u)$$ The function $latex W : B^{n \times q} \rightarrow B$$ is defined by $latex \[ W(u) = \sum_{k=0}^{q-1} ( w^{(k)} )^\R{T} \frac{1}{k !} \Dpow{k}{t} Y(0, u) \] $$ $head f$$ The object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ Before this call to $code Reverse$$, the value returned by $codei% %f%.size_order() %$$ must be greater than or equal $icode q$$ (see $cref size_order$$). $head q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ and specifies the number of Taylor coefficient orders to be differentiated (for each variable). $head w$$ The argument $icode w$$ has prototype $codei% const %Vector% &%w% %$$ (see $cref/Vector/reverse_any/Vector/$$ below) and its size must be equal to $icode m$$ or $icode%m% * %q%$$, It specifies the weighting vector $icode w$$ in the definition of $cref/W(u)/reverse_any/Notation/W(u)/$$. $head dw$$ The return value $icode dw$$ has prototype $codei% %Vector% %dw% %$$ (see $cref/Vector/reverse_any/Vector/$$ below). It is a vector with size $latex n \times q$$. For $latex j = 0, \ldots, n-1$$ and $latex k = 0 , \ldots , q-1$$ If the argument $icode w$$ has size $icode%m% * %q%$$, $latex \[ dw[ j * q + k ] = W^{(1)} ( x )_{j,k} \] $$ where $latex u = x$$ is value of the Taylor coefficients where the derivative is evaluated. $pre $$ If the argument $icode w$$ has size $icode m$$, $latex \[ dw[ j * q + q - k - 1 ] = W^{(1)} ( x )_{j,k} \] $$ where $latex u = x$$ is value of the Taylor coefficients where the derivative is evaluated. Note the reverse order in which the order indices are stored. This is an unfortunate consequence of keeping $code Reverse$$ backward compatible. $head First Order$$ We consider the case where $icode%q% = 1%$$ and $icode%w%.size() == %m%$$. In this case $latex \[ \begin{array}{rcl} W(u) & = & w_0 Y_0 (0, u) + \cdots + w_m Y_m (0, u) \\ W(u) & = & w_0 F_0 [ X(0, u) ] + \cdots + w_m F_m [ X(0, u) ] \\ W^{(1)} (x) & = & w_0 F_0^{(1)} ( x^{(0)} ) + \cdots + w_m F_m^{(1)} ( x^{(0)} ) \end{array} \] $$ This is the same as the result documented in $cref reverse_one$$. $head Second Order$$ We consider the case where $icode%q% = 2%$$ and $icode%w%.size() == %m%$$. In this case $latex \[ \begin{array}{rcl} W(u) & = & w_0 \partial_t Y_0 (0, u) + \cdots + w_m \partial_t Y_m (0, u) \\ W(u) & = & w_0 \partial_t \{ F_0 [ X(t, u) ] \}_{t = 0} + \cdots + w_m \partial_t \{ F_m [ X(t, u) ] \}_{t = 0} \\ W(u) & = & w_0 F_0^{(1)} ( u^{(0)} ) u^{(1)} + \cdots + w_0 F_m^{(1)} ( u^{(0)} ) u^{(1)} \\ \partial_{u(0)} W(x) & = & w_0 ( x^{(1)} )^\R{T} F_0^{(2)} ( x^{(0)} ) + \cdots + w_m ( x^{(1)} )^\R{T} F_m^{(2)} ( x^{(0)} ) \\ \partial_{u(1)} W(x) & = & w_0 F_0^{(1)} ( x^{(0)} ) + \cdots + w_m F_m^{(1)} ( x^{(0)} ) \end{array} \] $$ where $latex \partial{u(0)} $$ denotes partial with respect to $latex u^{(0)}$$. These are the same as the result documented in $cref reverse_two$$. $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ $children% example/reverse_three.cpp% example/reverse_checkpoint.cpp %$$ $list number$$ The file $cref reverse_three.cpp$$ contains an example and test of using reverse mode to compute third order derivatives. $lnext The file $cref reverse_checkpoint.cpp$$ contains an example and test of the general reverse mode case. $lend $end cppad-20170000.3/omh/reverse/reverse_two.omh0000644000175200017650000001151113057470464017742 0ustar coincoin-web// $Id: reverse_two.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin reverse_two$$ $section Second Order Reverse Mode$$ $mindex derivative$$ $spell taylor const dw $$ $head Syntax$$ $icode%dw% = %f%.Reverse(2, %w%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. Reverse mode computes the derivative of the $cref Forward$$ mode $cref/Taylor coefficients/glossary/Taylor Coefficient/$$ with respect to the domain variable $latex x$$. $head x^(k)$$ For $latex k = 0, 1$$, the vector $latex x^{(k)} \in B^n$$ is defined as the value of $icode x_k$$ in the previous call (counting this call) of the form $codei% %f%.Forward(%k%, %x_k%) %$$ If there is no previous call with $latex k = 0$$, $latex x^{(0)}$$ is the value of the independent variables when the corresponding AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ was recorded. $head W$$ The functions $latex W_0 : B^n \rightarrow B$$ and $latex W_1 : B^n \rightarrow B$$ are defined by $latex \[ \begin{array}{rcl} W_0 ( u ) & = & w_0 * F_0 ( u ) + \cdots + w_{m-1} * F_{m-1} (u) \\ W_1 ( u ) & = & w_0 * F_0^{(1)} ( u ) * x^{(1)} + \cdots + w_{m-1} * F_{m-1}^{(1)} (u) * x^{(1)} \end{array} \] $$ This operation computes the derivatives $latex \[ \begin{array}{rcl} W_0^{(1)} (u) & = & w_0 * F_0^{(1)} ( u ) + \cdots + w_{m-1} * F_{m-1}^{(1)} (u) \\ W_1^{(1)} (u) & = & w_0 * \left( x^{(1)} \right)^\R{T} * F_0^{(2)} ( u ) + \cdots + w_{m-1} * \left( x^{(1)} \right)^\R{T} F_{m-1}^{(2)} (u) \end{array} \] $$ at $latex u = x^{(0)}$$. $head f$$ The object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ Before this call to $code Reverse$$, the value returned by $codei% %f%.size_order() %$$ must be greater than or equal two (see $cref size_order$$). $head w$$ The argument $icode w$$ has prototype $codei% const %Vector% &%w% %$$ (see $cref/Vector/reverse_two/Vector/$$ below) and its size must be equal to $icode m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. $head dw$$ The result $icode dw$$ has prototype $codei% %Vector% %dw% %$$ (see $cref/Vector/reverse_two/Vector/$$ below). It contains both the derivative $latex W^{(1)} (x)$$ and the derivative $latex U^{(1)} (x)$$. The size of $icode dw$$ is equal to $latex n \times 2$$, where $latex n$$ is the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. $subhead First Order Partials$$ For $latex j = 0 , \ldots , n - 1$$, $latex \[ dw [ j * 2 + 0 ] = \D{ W_0 }{ u_j } \left( x^{(0)} \right) = w_0 * \D{ F_0 }{ u_j } \left( x^{(0)} \right) + \cdots + w_{m-1} * \D{ F_{m-1} }{ u_j } \left( x^{(0)} \right) \] $$ This part of $icode dw$$ contains the same values as are returned by $cref reverse_one$$. $subhead Second Order Partials$$ For $latex j = 0 , \ldots , n - 1$$, $latex \[ dw [ j * 2 + 1 ] = \D{ W_1 }{ u_j } \left( x^{(0)} \right) = \sum_{\ell=0}^{n-1} x_\ell^{(1)} \left[ w_0 * \DD{ F_0 }{ u_\ell }{ u_j } \left( x^{(0)} \right) + \cdots + w_{m-1} * \DD{ F_{m-1} }{ u_\ell }{ u_j } \left( x^{(0)} \right) \right] \] $$ $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Hessian Times Direction$$ Suppose that $latex w$$ is the $th i$$ elementary vector. It follows that for $latex j = 0, \ldots, n-1$$ $latex \[ \begin{array}{rcl} dw[ j * 2 + 1 ] & = & w_i \sum_{\ell=0}^{n-1} \DD{F_i}{ u_j }{ u_\ell } \left( x^{(0)} \right) x_\ell^{(1)} \\ & = & \left[ F_i^{(2)} \left( x^{(0)} \right) * x^{(1)} \right]_j \end{array} \] $$ Thus the vector $latex ( dw[1], dw[3], \ldots , dw[ n * q - 1 ] )$$ is equal to the Hessian of $latex F_i (x)$$ times the direction $latex x^{(1)}$$. In the special case where $latex x^{(1)}$$ is the $th l$$ $cref/elementary vector/glossary/Elementary Vector/$$, $latex \[ dw[ j * 2 + 1 ] = \DD{ F_i }{ x_j }{ x_\ell } \left( x^{(0)} \right) \] $$ $head Example$$ $children% example/reverse_two.cpp% example/hes_times_dir.cpp %$$ The files $cref reverse_two.cpp$$ and $cref hes_times_dir.cpp$$ contain a examples and tests of reverse mode calculations. They return true if they succeed and false otherwise. $end cppad-20170000.3/omh/example.omh0000644000175200017650000000300413057470464015354 0ustar coincoin-web$Id: example.omh 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin Example$$ $spell CppAD Cygwin Microsoft chdir nmake mak Workspace dsw exe Example example $$ $section Examples$$ $head Introduction$$ This section organizes the information related to the CppAD examples. Each CppAD operation has its own specific example, for example $cref add.cpp$$ is an example for $cref/addition/ad_binary/$$. Some of the examples are of a more general nature (not connected of a specific feature of CppAD). In addition, there are some utility functions that are used by the examples. $head Running Examples$$ The $cref/installation instructions/Install/$$ show how the examples can be run on your system. $head The CppAD Test Vector Template Class$$ Many of the examples use the $small $cref/CPPAD_TESTVECTOR/testvector/$$ $$ preprocessor symbol to determine which $cref SimpleVector$$ template class is used with the examples. $contents% omh/example_list.omh% cppad/core/testvector.hpp %$$ $end cppad-20170000.3/omh/bib.omh0000644000175200017650000000276113057470464014466 0ustar coincoin-web$Id: bib.omh 3779 2016-01-01 11:26:11Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin Bib$$ $spell ed Bjarne Stroustrup Saul Griewank Andreas Vetterling Flannery Teukolsky Abramowitz Stegun Shampine Rosenbrock $$ $section Bibliography$$ $head Abramowitz and Stegun$$ Handbook of Mathematical Functions, Dover, New York. $head The C++ Programming Language$$ Bjarne Stroustrup, The C++ Programming Language, Special ed., AT&T, 2000 $head Evaluating Derivatives$$ Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Andreas Griewank, SIAM, Philadelphia, 2000 $head Numerical Recipes$$ Numerical Recipes in Fortran: The Art of Scientific Computing, Second Edition, William H. Press, William T. Vetterling, Saul, A. Teukolsky, Brian R. Flannery, Cambridge University Press, 1992 $head Shampine, L.F.$$ Implementation of Rosenbrock Methods, ACM Transactions on Mathematical Software, Vol. 8, No. 2, June 1982. $end cppad-20170000.3/omh/seq_property.omh0000644000175200017650000001430013057470464016456 0ustar coincoin-web$Id: seq_property.omh 3853 2016-12-14 14:40:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin seq_property$$ $spell inuse Addr CppAD sizeof op arg enum Taylor const bool var VecAD $$ $section ADFun Sequence Properties$$ $head Syntax$$ $icode%n% = %f%.Domain() %$$ $icode%m% = %f%.Range() %$$ $icode%p% = %f%.Parameter(%i%) %$$ $icode%s% = %f%.size_var() %$$ $icode%s% = %f%.size_par() %$$ $icode%s% = %f%.size_op() %$$ $icode%s% = %f%.size_op_arg() %$$ $icode%s% = %f%.size_text() %$$ $icode%s% = %f%.size_VecAD() %$$ $icode%s% = %f%.size_op_seq() %$$ $subhead See Also$$ $cref size_order$$, $cref capacity_order$$, $cref number_skip$$. $head Purpose$$ The operations above return properties of the AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ stored in the ADFun object $icode f$$. (If there is no operation sequence stored in $icode f$$, $code size_var$$ returns zero.) $head f$$ The object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ (see $codei%ADFun<%Base%>%$$ $cref/constructor/FunConstruct/$$). $head Domain$$ The result $icode n$$ has prototype $codei% size_t %n% %$$ and is the dimension of the domain space corresponding to $icode f$$. This is equal to the size of the vector $icode x$$ in the call $codei% Independent(%x%) %$$ that starting recording the operation sequence currently stored in $icode f$$ (see $cref FunConstruct$$ and $cref Dependent$$). $head Range$$ The result $icode m$$ has prototype $codei% size_t %m% %$$ and is the dimension of the range space corresponding to $icode f$$. This is equal to the size of the vector $icode y$$ in syntax $codei% ADFun<%Base> %f%(%x%, %y%) %$$ or $codei% %f%.Dependent(%y%) %$$ depending on which stored the operation sequence currently in $icode f$$ (see $cref FunConstruct$$ and $cref Dependent$$). $head Parameter$$ The argument $icode i$$ has prototype $codei% size_t %i% %$$ and $latex 0 \leq i < m$$. The result $icode p$$ has prototype $codei% bool %p% %$$ It is true if the $th i$$ component of range space for $latex F$$ corresponds to a $cref/parameter/glossary/Parameter/$$ in the operation sequence. In this case, the $th i$$ component of $latex F$$ is constant and $latex \[ \D{F_i}{x_j} (x) = 0 \] $$ for $latex j = 0 , \ldots , n-1$$ and all $latex x \in B^n$$. $head size_var$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the number of variables in the operation sequence plus the following: one for a phantom variable with tape address zero, one for each component of the range that is a parameter. The amount of work and memory necessary for computing function values and derivatives using $icode f$$ is roughly proportional to $icode s$$. (The function call $cref/f.size_order()/size_order/$$ returns the number of Taylor coefficient orders, per variable,direction, currently stored in $icode f$$.) $pre $$ If there is no operation sequence stored in $icode f$$, $code size_var$$ returns zero (see $cref/default constructor/FunConstruct/Default Constructor/$$). $head size_par$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the number of parameters in the operation sequence. Parameters differ from variables in that only values (and not derivatives) need to be stored for each parameter. These parameters are considered part of the operation sequence, as opposed to the Taylor coefficients which are considered extra data in the function object $icode f$$. Note that one $icode Base$$ value is required for each parameter. $head size_op$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the number of operations in the operation sequence. Some operators, like comparison operators, do not correspond to a variable. Other operators, like the sine operator, correspond to two variables. Thus, this value will be different from $cref/size_var/seq_property/size_var/$$. Note that one $code enum$$ value is required for each operator. $head size_op_arg$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the total number of operator arguments in the operation sequence. For example, Binary operators (e.g. addition) have two arguments. Note that one integer index is stored in the operation sequence for each argument. Also note that, as of 2013-10-20, there is an extra phantom argument with index 0 that is not used. $head size_text$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the total characters used in the $cref PrintFor$$ commands in this operation sequence. $head size_VecAD$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the number of $cref VecAD$$ vectors, plus the number of elements in the vectors. Only $code VecAD$$ vectors that depend on the independent variables are stored in the operation sequence. $head size_op_seq$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the amount of memory required to store the operation sequence (not counting a small amount of memory required for every operation sequence). For the current version of CppAD, this is given by $codei% %s% = %f%.size_op() * sizeof(CppAD::local::OpCode) + %f%.size_op_arg() * sizeof(%tape_addr_type%) + %f%.size_par() * sizeof(%Base%) + %f%.size_text() * sizeof(char) + %f%.size_VecAD() * sizeof(%tape_addr_type%) %$$ see $cref/tape_addr_type/cmake/cppad_tape_addr_type/$$. Note that this is the minimal amount of memory that can hold the information corresponding to an operation sequence. The actual amount of memory allocated ($cref/inuse/ta_inuse/$$) for the operations sequence may be larger. $head Example$$ $children% example/seq_property.cpp %$$ The file $cref seq_property.cpp$$ contains an example and test of these operations. It returns true if it succeeds and false otherwise. $end cppad-20170000.3/omh/lu_solve_hpp.omh0000644000175200017650000000152313057470464016424 0ustar coincoin-web$Id: lu_solve_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin lu_solve.hpp$$ $spell Lu ifndef endif $$ $section Source: LuSolve$$ $mindex source$$ $code # ifndef CPPAD_LU_SOLVE_HPP $pre $$ # define CPPAD_LU_SOLVE_HPP $srcfile%cppad/utility/lu_solve.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/utility.omh0000644000175200017650000000644213057470464015435 0ustar coincoin-web$Id: utility.omh 3805 2016-03-22 20:01:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin utility$$ $spell CppAD namespace alloc cppad.hpp $$ $section Some General Purpose Utilities$$ These routines can be include individually; for example, $codep # include $$ only includes the definitions necessary for the $code CppAD::vector$$ class. They can also be included as a group, separate from the rest of CppAD, using $codep # include $$ They will also be included, along with the rest of CppAD, using $codep # include $$ $children% cppad/utility/error_handler.hpp% cppad/utility/near_equal.hpp% cppad/utility/speed_test.hpp% cppad/utility/time_test.hpp% omh/numeric_type.omh% cppad/utility/check_numeric_type.hpp% omh/simple_vector.omh% cppad/utility/check_simple_vector.hpp% cppad/utility/nan.hpp% cppad/utility/pow_int.hpp% cppad/utility/poly.hpp% omh/lu_det_and_solve.omh% cppad/utility/romberg_one.hpp% cppad/utility/romberg_mul.hpp% cppad/utility/runge_45.hpp% cppad/utility/rosen_34.hpp% cppad/utility/ode_err_control.hpp% cppad/utility/ode_gear.hpp% cppad/utility/ode_gear_control.hpp% cppad/utility/vector.hpp% omh/thread_alloc.omh% cppad/utility/index_sort.hpp% cppad/utility/to_string.hpp% cppad/utility/set_union.hpp %$$ $head Testing$$ The routines listed below support numerical correctness and speed testing: $table $rref NearEqual$$ $rref time_test$$ $rref speed_test$$ $rref SpeedTest$$ $tend $head C++ Concepts$$ We refer to a the set of classes that satisfy certain conditions as a C++ concept. The following concepts are used by the CppAD Template library: $table $rref NumericType$$ $rref CheckNumericType$$ $rref SimpleVector$$ $rref CheckSimpleVector$$ $tend $head General Numerical Routines$$ The routines listed below are general purpose numerical routines written with the floating point type a C++ template parameter. This enables them to be used with algorithmic differentiation types, as well as for other purposes. $table $rref nan$$ $rref pow_int$$ $rref Poly$$ $rref LuDetAndSolve$$ $rref RombergOne$$ $rref RombergMul$$ $rref Runge45$$ $rref Rosen34$$ $rref OdeErrControl$$ $rref OdeGear$$ $rref OdeGearControl$$ $tend $head Miscellaneous$$ $subhead Error Handler$$ All of the routines in the CppAD namespace use the following general purpose error handler: $table $rref ErrorHandler$$ $tend $subhead Simple Vector Template Class$$ A simple implementation of a template vector class (that is easy to view in a C++ debugger): $table $rref CppAD_vector$$ $tend $subhead Multi-Threading Memory Allocation$$ $table $rref thread_alloc$$ $tend $subhead Sorting Indices$$ $table $rref index_sort$$ $tend $subhead to_string$$ $table $rref to_string$$ $tend $subhead set_union$$ $table $rref set_union$$ $tend $end cppad-20170000.3/omh/sparse_hes_fun.omh0000644000175200017650000000156313057470464016735 0ustar coincoin-web$Id: sparse_hes_fun.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin sparse_hes_fun.hpp$$ $spell hes ifndef endif $$ $section Source: sparse_hes_fun$$ $mindex source$$ $code # ifndef CPPAD_SPARSE_HES_FUN_HPP $pre $$ # define CPPAD_SPARSE_HES_FUN_HPP $srcfile%cppad/speed/sparse_hes_fun.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/wish_list.omh0000644000175200017650000001433613057470464015740 0ustar coincoin-web$Id: wish_list.omh 3856 2016-12-21 05:51:22Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin wish_list$$ $spell op Recomputation optimizer checkpointing grep recomputed iterator std Adolc xml hpp CppAD Atan cppad tapeless Retape $$ $section The CppAD Wish List$$ $comment ----------------------------------------------------------------- $$ $head Optimization$$ $subhead Taping$$ Perhaps some of the optimization done while taping forward mode should be delayed to the $code optimization$$ step. $subhead Special Operators$$ Add special operators that can be implemented more efficiently, e.g., $codei% square(%x%) = %x% * %x% %$$ and have the optimizer recognize when they should be used. (They could also be in the user API, but it would not be expected that the user would use them.) $comment ------------------------------------------------------------------ $$ $head checkpoint$$ $subhead Retape$$ Perhaps there should be a version of the $cref checkpoint$$ class that uses a tapeless AD package to compute the derivative values. This would allow for algorithms where the operations sequence depends on the independent variable values. There is a question as to how sparsity patterns would be determined in this case. Perhaps they would be passed into the constructor. If it was known to be constant, the user could compute the pattern using CppAD. Otherwise, the user could input a conservative estimate of the pattern that would be correct. $subhead Testing$$ There should be some examples and tests for both speed and memory use that demonstrate that checkpointing is useful. $comment -------------------------------------------------------------------$$ $head Sparsity Patterns$$ It may be that each set has a large overhead in a large and very sparse $cref/vector of sets/glossary/Sparsity Pattern/Vector of Sets/$$ representation of a sparsity pattern. The user API for this representation uses $codei% %vector%< std::set > %$$ Perhaps CppAD's API should have a sparse matrix class with the following fields $codei% %vector% %row%; %vector% %col%; %vector%<%Type%> %val%; %$$ where the vectors are arbitrary $cref/simple vectors/SimpleVector/$$. If the $icode val$$ vector has size zero, this would just be a sparsity pattern (and $icode row$$ and $icode col$$ vectors would have the same size). Otherwise, it would be a sparse matrix with elements of type $icode Type$$ and $icode val$$ would have the same size as $icode row$$ and $icode col$$. $head check_finite$$ Sometimes one only gets infinite value during zero order forward and nan when computing corresponding derivatives. Change $cref check_for_nan$$ to $code check_finite$$ (not infinite or nan) so that error detection happens during zero order forward instead of later. $head Compilation Speed$$ Create a library corresponding to $code AD$$ so that one does not need to re-compile all the header files every time. $head Base Requirements$$ Change the $cref/Base requirements/base_require/$$ to use template specialization instead of functions so that there is a default value for each function. The default would result in a $cref/known/cppad_assert/Known/$$ assert when the operation is used and not defined by the base class. An example of this type of template specialization can be found in the implementation of $cref to_string$$. $head Adolc$$ Create a documentation page that shows how to convert Adolc commands to CppAD commands. $head Forward Mode Recomputation$$ If the results of $cref forward_order$$ have already been computed and are still stored in the $cref ADFun$$ object (see $cref size_order$$), then they do not need to be recomputed and the results can just be returned. $head Iterator Interface$$ All of the CppAD simple vector interfaces should also have an iterator version for the following reasons: $list number$$ It would not be necessary to copy information to simple vectors when it was originally stored in a different type of container. $lnext It would not be necessary to reallocate memory for a result that is repeatedly calculated (because an iterator for the result container would be passed in). $lend $head Operation Sequence$$ It is possible to detect if the AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ does not depend on any of the $cref/independent variable/glossary/Tape/Independent Variable/$$ values. This could be returned as an extra $cref seq_property$$. $head Software Guidelines$$ The following is a list of some software guidelines taken from $href%http://www.boost.org/development/requirements.html#Guidelines%boost%$$. These guidelines are not followed by the current CppAD source code, but perhaps they should be: $list number$$ Names (except as noted below) should be all lowercase, with words separated by underscores. For example, acronyms should be treated as ordinary names (xml_parser instead of XML_parser). $lnext Template parameter names should begin with an uppercase letter. $lnext Use spaces rather than tabs. Currently, CppAD uses a tabs stops at column multiples of 5. Five columns were chosen to avoid high levels of indenting and to allow for $codep if( expression ) statement else statement $$ with a tab after the else. Automatic conversion to actual spaces should be easy. $lend $head Tracing$$ Add tracing the operation sequence to the user API and documentation. Tracing the operation sequence is currently done by changing the CppAD source code. Use the command $codep grep '^# *define *CPPAD_.*_TRACE' cppad/local/*.hpp $$ to find all the possible tracing flags. $head atan2$$ The $cref/atan2/Atan2/$$ function could be made faster by adding a special operator for it. $head BenderQuad$$ See the $cref/problem/BenderQuad/Problem/$$ with the current $code BenderQuad$$ specifications. $end cppad-20170000.3/omh/numeric_ad.omh0000644000175200017650000000152213057470464016032 0ustar coincoin-web$Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin numeric_ad$$ $spell CppAD namespace alloc $$ $section Some Numerical AD Utilities$$ The routines listed below are numerical utilities that are designed to work with CppAD in particular. $childtable% cppad/core/bender_quad.hpp% cppad/core/opt_val_hes.hpp% cppad/core/lu_ratio.hpp %$$ $end cppad-20170000.3/omh/lu_det_and_solve.omh0000644000175200017650000000151413057470464017233 0ustar coincoin-web$Id: lu_det_and_solve.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin LuDetAndSolve$$ $section Compute Determinants and Solve Equations by LU Factorization$$ $mindex matrix factor linear$$ $childtable% cppad/utility/lu_solve.hpp% cppad/utility/lu_factor.hpp% cppad/utility/lu_invert.hpp %$$ $end cppad-20170000.3/omh/atomic_base.omh0000644000175200017650000000740413057470464016177 0ustar coincoin-web// $Id: atomic_base.omh 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin atomic_base$$ $spell ctor cppad hpp afun arg vx vy tx ty px py jac hes CppAD checkpointing algo $$ $section User Defined Atomic AD Functions$$ $head Syntax$$ $codei% %atomic_user% %afun%(%ctor_arg_list%) %afun%(%ax%, %ay%) %ok% = %afun%.forward(%p%, %q%, %vx%, %vy%, %tx%, %ty%) %ok% = %afun%.reverse(%q%, %tx%, %ty%, %px%, %py%) %ok% = %afun%.for_sparse_jac(%q%, %r%, %s%) %ok% = %afun%.rev_sparse_jac(%q%, %r%, %s%) %ok% = %afun%.for_sparse_hes(%vx%, %r%, %s%, %h%) %ok% = %afun%.rev_sparse_hes(%vx%, %s%, %t%, %q%, %r%, %u%, %v%) atomic_base<%Base%>::clear()%$$ $head Purpose$$ In some cases, the user knows how to compute derivatives of a function $latex \[ y = f(x) \; {\rm where} \; f : B^n \rightarrow B^m \] $$ more efficiently than by coding it using $codei%AD<%Base%>%$$ $cref/atomic/glossary/Operation/Atomic/$$ operations and letting CppAD do the rest. In this case $codei%atomic_base%<%Base%>%$$ can use the user code for $latex f(x)$$, and its derivatives, as $codei%AD<%Base%>%$$ atomic operations. $head Virtual Functions$$ User defined derivatives are implemented by defining the following virtual functions in the $icode base_atomic$$ class: $cref/forward/atomic_forward/$$, $cref/reverse/atomic_reverse/$$, $cref/for_sparse_jac/atomic_for_sparse_jac/$$, $cref/rev_sparse_jac/atomic_rev_sparse_jac/$$, and $cref/rev_sparse_hes/atomic_rev_sparse_hes/$$. These virtual functions have a default implementation that returns $icode%ok% == false%$$. The $code forward$$ function, for the case $icode%q% == 0%$$, must be implemented. Otherwise, only those functions required by the your calculations need to be implemented. For example, $icode forward$$ for the case $icode%q% == 2%$$ can just return $icode%ok% == false%$$ unless you require forward mode calculation of second derivatives. $childtable% cppad/core/atomic_base.hpp% example/atomic/get_started.cpp% example/atomic/norm_sq.cpp% example/atomic/reciprocal.cpp% example/atomic/set_sparsity.cpp% example/atomic/tangent.cpp% example/atomic/eigen_mat_mul.cpp% example/atomic/eigen_mat_inv.cpp% example/atomic/eigen_cholesky.cpp% example/atomic/mat_mul.cpp %$$ $head Examples$$ $subhead Getting Started$$ The file $cref atomic_get_started.cpp$$ contains an example and test that shows the minimal amount of information required to create a user defined atomic operation. $subhead Scalar Function$$ The file $cref atomic_reciprocal.cpp$$ contains an example and test where the user provides the code for computing derivatives. This example is simple because the domain and range are scalars. $subhead Vector Range$$ The file $cref atomic_tangent.cpp$$ contains another example where the user provides the code for computing derivatives. This example is more complex because the range has two components. $subhead Hessian Sparsity Patterns$$ The file $cref atomic_rev_sparse_hes.cpp$$ contains an minimal example where the user provides the code for computing Hessian sparsity patterns. $head General Case$$ The file $cref atomic_mat_mul.cpp$$ contains a more general example where the user provides the code for computing derivatives. This example is more complex because both the domain and range dimensions are arbitrary. $end cppad-20170000.3/omh/faq.omh0000644000175200017650000001633713057470464014505 0ustar coincoin-web$Id: faq.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin Faq$$ $escape !$$ $spell instantiating cppad@list.coin-or.org faq std whatsnew sqrt cmath Namespace Dvector Gcc CppAD Lu $$ $section Frequently Asked Questions and Answers$$ $mindex FAQ operator reporting ErrorHandler avoid record taping mode CPPAD_TESTVECTOR standard math function storage$$ $head Assignment and Independent$$ Why does the code sequence $codei% Independent(%u%); %v% = %u%[0]; %$$ behave differently from the code sequence $codei% %v% = %u%[0]; Independent(%u%); %$$ Before the call to $cref Independent$$, $icode%u%[0]%$$ is a $cref/parameter/glossary/Parameter/$$ and after the call it is a variable. Thus in the first case, $icode v$$ is a variable and in the second case it is a parameter. $head Bugs$$ What should I do if I suspect that there is a bug in CppAD ? $pre $$ $list number$$ The first step is to search this page for mention of some feature that perhaps you interpreting as a bug (and is not). If this does not solve your problem, continue to the next step. $lnext The second step is to check the $cref whats_new$$ messages from the date of the release that you are using to the current date. If the bug has been mentioned and fixed, then $cref install$$ the current version of CppAD. If this does not solve your problem, continue to the next step. $lnext Create a simple as possible demonstration of the bug; see the file $code bug/template.sh$$ for a template that you can edit for that purpose. The smaller the program, the better the bug report. $lnext Send an e-mail message to the mailing list $href% http://list.coin-or.org/mailman/listinfo/cppad% cppad@list.coin-or.org %$$ with a description of the bug. Attaching your program that demonstrates the bug. $lend $head CompareChange$$ If you attempt to use the $cref CompareChange$$ function when $code NDEBUG$$ is true, you will get an error message stating that $code CompareChange$$ is not a member of the $cref ADFun$$ template class. $head Complex Types$$ Which of the following complex types is better: $codei% AD< std::complex<%Base%> > std::complex< AD<%Base%> > %$$ The $cref/complex abs function/abs/Complex Types/$$ is differentiable with respect to its real and imaginary parts, but it is not complex differentiable. Thus one would prefer to use $codei% std::complex< AD<%Base%> > %$$ On the other hand, the C++ standard only specifies $codei%std::complex<%Type%>%$$ where $icode Type$$ is $code float$$, $code double$$, or $code lone double$$. The effect of instantiating the template complex for any other type is unspecified. $head Exceptions$$ Why, in all the examples, do you pass back a boolean variable instead of throwing an exception ? $pre $$ The examples are also used to test the correctness of CppAD and to check your installation. For these two uses, it is helpful to run all the tests and to know which ones failed. The actual code in CppAD uses the $cref ErrorHandler$$ utility to signal exceptions. Specifications for redefining this action are provided. $head Independent Variables$$ Is it possible to evaluate the same tape recording with different values for the independent variables ? $pre $$ Yes (see $cref forward_zero$$). $head Matrix Inverse$$ Is it possible to differentiate (with respect to the matrix elements) the computation of the inverse of a matrix where the computation of the inverse uses pivoting ? $pre $$ The example routine $cref LuSolve$$ can be used to do this because the inverse is a special case of the solution of linear equations. The examples $cref jac_lu_det.cpp$$ and $cref hes_lu_det.cpp$$ use LuSolve to compute derivatives of the determinant with respect to the components of the matrix. $head Mode: Forward or Reverse$$ When evaluating derivatives, one always has a choice between forward and reverse mode. How does one decide which mode to use ? $pre $$ In general, the best mode depends on the number of domain and range components in the function that your are differentiating. Each call to $cref Forward$$ computes the derivative of all the range directions with respect to one domain direction. Each call to $cref Reverse$$ computes the derivative of one range direction with respect to all the domain directions. The times required for (speed of) calls $code Forward$$ and $code Reverse$$ are about equal. The $cref/Parameter/seq_property/Parameter/$$ function can be used to quickly determine that some range directions have derivative zero. $head Namespace$$ $subhead Test Vector Preprocessor Symbol$$ Why do you use $code CPPAD_TESTVECTOR$$ instead of a namespace for the CppAD $cref testvector$$ class ? $pre $$ The preprocessor symbol $small $cref/CPPAD_TESTVECTOR/testvector/$$ $$ determines which $cref SimpleVector$$ template class is used for extensive testing. The default definition for $code CPPAD_TESTVECTOR$$ is the $cref/CppAD::vector/CppAD_vector/$$ template class, but it can be changed. Note that all the preprocessor symbols that are defined or used by CppAD begin with either $code CPPAD$$ (some old deprecated symbols begin with $code CppAD$$). $subhead Using$$ Why do I have trouble when the following command $codep using namespace CppAD $$ is at the global level (not within a function or some other limited scope). $pre $$ Some versions of $code # include $$ for gcc and Visual C++ define the standard math functions, (for example $codei%double sqrt(double %x%)%$$) at the global level. It is necessary to put your $code using$$ commands within the scope of a function, or some other limited scope, in order to shadow these improper global definitions. $head Speed$$ How do I get the best speed performance out of CppAD ? $subhead NDEBUG$$ You should compile your code with optimization, without debugging, and with the preprocessor symbol $code NDEBUG$$ defined. (The $cref speed_cppad$$ tests do this.) Note that defining $code NDEBUG$$ will turn off all of the error checking and reporting that is done using $cref ErrorHandler$$. $subhead Optimize$$ It is also possible that preforming a tape $cref/optimization/optimize/$$ will improve the speed of evaluation more than the time required for the optimization. $subhead Memory Allocation$$ You may also increase execution speed by calling $code hold_memory$$ with $cref/value/ta_hold_memory/value/$$ equal to true. $head Tape Storage: Disk or Memory$$ Does CppAD store the tape on disk or in memory ? $pre $$ CppAD uses memory to store a different tape for recording operations for each $codei%AD<%Base%>%$$ type that is used. If you have a very large number calculations that are recorded on a tape, the tape will keep growing to hold the necessary information. Eventually, virtual memory may be used to store the tape and the calculations may slow down because of necessary disk access. $end cppad-20170000.3/omh/cos_forward.omh0000644000175200017650000000422613057470464016240 0ustar coincoin-web$Id: cos_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin CosForward$$ $spell cos Taylor $$ $section Cosine Function Forward Taylor Polynomial Theory$$ $mindex cos$$ If $latex F(x) = \cos(x) $$ $latex \[ 1 * F^{(1)} (x) - 0 * F (x) = - \sin(x) \] $$ and in the $xref/ ForwardTheory/ Standard Math Functions/ Differential Equation/ standard math function differential equation/ 1 /$$, $latex A(x) = 0$$, $latex B(x) = 1$$, and $latex D(x) = - \sin(x)$$. We use $latex a$$, $latex b$$, $latex d$$, $latex s$$ and $latex z$$ to denote the Taylor coefficients for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, $latex \sin [ X(t) ]$$, and $latex F [ X(t) ] $$ respectively. It now follows from the general $xref/ ForwardTheory/ Standard Math Functions/ Taylor Coefficients Recursion Formula/ Taylor coefficients recursion formula/ 1 /$$ that for $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} z^{(0)} & = & \cos ( x^{(0)} ) \\ e^{(j)} & = & d^{(j)} + \sum_{k=0}^{j} a^{(j-k)} * z^{(k)} \\ & = & -s^{(j)} \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=1}^{j+1} k x^{(k)} e^{(j+1-k)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \\ & = & - \frac{1}{j+1} \sum_{k=1}^{j+1} k x^{(k)} s^{(j+1-k)} \end{array} \] $$ Using $latex c$$ for the Taylor coefficients of $latex \cos[ X(t) ]$$ the order $latex j+1$$ coefficient can be generated using the lower order coefficients for $latex \sin[ X(t) ]$$ and $latex \cos[ X(t) ]$$ by the following formula: $latex \[ c^{(j+1)} = - \frac{1}{j+1} \sum_{k=1}^{j+1} k x^{(k)} s^{(j+1-k)} \] $$ $end cppad-20170000.3/omh/det_of_minor_hpp.omh0000644000175200017650000000156413057470464017245 0ustar coincoin-web$Id: det_of_minor_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin det_of_minor.hpp$$ $spell det_of_minor ifndef endif $$ $section Source: det_of_minor$$ $mindex source$$ $code # ifndef CPPAD_DET_OF_MINOR_HPP $pre $$ # define CPPAD_DET_OF_MINOR_HPP $srcfile%cppad/speed/det_of_minor.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/det_by_lu_hpp.omh0000644000175200017650000000153713057470464016547 0ustar coincoin-web$Id: det_by_lu_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin det_by_lu.hpp$$ $spell det_by_lu ifndef endif $$ $section Source: det_by_lu$$ $mindex source$$ $code # ifndef CPPAD_DET_BY_LU_HPP $pre $$ # define CPPAD_DET_BY_LU_HPP $srcfile%cppad/speed/det_by_lu.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/sin_forward.omh0000644000175200017650000000421313057470464016241 0ustar coincoin-web$Id: sin_forward.omh 3757 2015-11-30 12:03:07Z bradbell $ // BEGIN SHORT COPYRIGHT /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // END SHORT COPYRIGHT $begin SinForward$$ $spell sin Taylor $$ $section Sine Function Forward Taylor Polynomial Theory$$ $mindex sin$$ If $latex F(x) = \sin(x) $$ $latex \[ 1 * F^{(1)} (x) - 0 * F (x) = \cos(x) \] $$ and in the $xref/ ForwardTheory/ Standard Math Functions/ Differential Equation/ standard math function differential equation/ 1 /$$, $latex A(x) = 0$$, $latex B(x) = 1$$, and $latex D(x) = \cos(x)$$. We use $latex a$$, $latex b$$, $latex d$$, $latex c$$ and $latex z$$ to denote the Taylor coefficients for $latex A [ X (t) ] $$, $latex B [ X (t) ]$$, $latex D [ X (t) ] $$, $latex \cos [ X(t) ]$$, and $latex F [ X(t) ] $$ respectively. It now follows from the general $xref/ ForwardTheory/ Standard Math Functions/ Taylor Coefficients Recursion Formula/ Taylor coefficients recursion formula/ 1 /$$ that for $latex j = 0 , 1, \ldots$$, $latex \[ \begin{array}{rcl} z^{(0)} & = & \sin ( x^{(0)} ) \\ e^{(j)} & = & d^{(j)} + \sum_{k=0}^{j} a^{(j-k)} * z^{(k)} \\ & = & c^{(j)} \\ z^{(j+1)} & = & \frac{1}{j+1} \frac{1}{ b^{(0)} } \left( \sum_{k=1}^{j+1} k x^{(k)} e^{(j+1-k)} - \sum_{k=1}^j k z^{(k)} b^{(j+1-k)} \right) \\ & = & \frac{1}{j+1} \sum_{k=1}^{j+1} k x^{(k)} c^{(j+1-k)} \end{array} \] $$ Using $latex s$$ for the Taylor coefficients of $latex \sin[ X(t) ]$$ the order $latex j+1$$ coefficient can be generated using the lower order coefficients for $latex \sin[ X(t) ]$$ and $latex \cos[ X(t) ]$$ by the following formula: $latex \[ s^{(j+1)} = \frac{1}{j+1} \sum_{k=1}^{j+1} k x^{(k)} c^{(j+1-k)} \] $$ $end cppad-20170000.3/omh/lu_invert_hpp.omh0000644000175200017650000000153113057470464016602 0ustar coincoin-web$Id: lu_invert_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin lu_invert.hpp$$ $spell Lu ifndef endif $$ $section Source: LuInvert$$ $mindex source$$ $code # ifndef CPPAD_LU_INVERT_HPP $pre $$ # define CPPAD_LU_INVERT_HPP $srcfile%cppad/utility/lu_invert.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/speed/0002755000175200017650000000000013057470464014321 5ustar coincoin-webcppad-20170000.3/omh/speed/speed.omh0000644000175200017650000000266113057470464016131 0ustar coincoin-web$Id: speed.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin speed$$ $spell cppad CppAD Cygwin Microsoft chdir Workspace dsw exe sln $$ $section Speed Test an Operator Overloading AD Package$$ $head Purpose$$ CppAD has a set of speed tests that are used to determine if certain changes improve its execution speed. These tests can also be used to compare the AD packages $href% https://projects.coin-or.org/ADOL-C% Adolc %$$, $href% http://www.coin-or.org/CppAD/% CppAD %$$, $href% http://www.fadbad.com/% Fadbad %$$ and $href% http://trilinos.sandia.gov/packages/sacado/% Sacado %$$. The sections below explain how you can run these tests on your computer. $childtable% speed/main.cpp% omh/speed/speed_utility.omh% omh/speed/speed_double.omh% omh/speed/speed_adolc.omh% omh/speed/speed_cppad.omh% omh/speed/speed_fadbad.omh% omh/speed/speed_sacado.omh %$$ $end cppad-20170000.3/omh/speed/speed_fadbad.omh0000644000175200017650000000333413057470464017410 0ustar coincoin-web$Id: speed_fadbad.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin speed_fadbad$$ $spell cmake FadbadDir CppAD Cygwin $$ $section Speed Test Derivatives Using Fadbad$$ $head Purpose$$ CppAD has a set of speed tests that are used to compare Fadbad with other AD packages. This section links to the source code the Fadbad speed tests (any suggestions to make the Fadbad results faster are welcome). $head fadbad_prefix$$ To run these tests, you must include the $cref fadbad_prefix$$ in you $cref/cmake command/cmake/CMake Command/$$. $head Running Tests$$ To build these speed tests, and run their correctness tests, execute the following commands starting in the $cref/build directory/cmake/CMake Command/Build Directory/$$: $codei% cd speed/fadbad make check_speed_fadbad VERBOSE=1 %$$ You can then run the corresponding speed tests with the following command $codei% ./speed_fadbad speed %seed% %$$ where $icode seed$$ is a positive integer. See $cref speed_main$$ for more options. $contents% speed/fadbad/det_minor.cpp% speed/fadbad/det_lu.cpp% speed/fadbad/mat_mul.cpp% speed/fadbad/ode.cpp% speed/fadbad/poly.cpp% speed/fadbad/sparse_hessian.cpp% speed/fadbad/sparse_jacobian.cpp %$$ $end cppad-20170000.3/omh/speed/speed_adolc.omh0000644000175200017650000000335013057470464017267 0ustar coincoin-web$Id: speed_adolc.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin speed_adolc$$ $spell cmake AdolcDir CppAD Cygwin $$ $section Speed Test of Derivatives Using Adolc$$ $head Purpose$$ CppAD has a set of speed tests that are used to compare Adolc with other AD packages. This section links to the source code the Adolc speed tests (any suggestions to make the Adolc results faster are welcome). $head adolc_prefix$$ To run these tests, you must include the $cref adolc_prefix$$ in you $cref/cmake command/cmake/CMake Command/$$. $head Running Tests$$ To build these speed tests, and run their correctness tests, execute the following commands starting in the $cref/build directory/cmake/CMake Command/Build Directory/$$: $codei% cd speed/adolc make check_speed_adolc VERBOSE=1 %$$ You can then run the corresponding speed tests with the following command $codei% ./speed_adolc speed %seed% %$$ where $icode seed$$ is a positive integer. See $cref speed_main$$ for more options. $contents% speed/adolc/det_minor.cpp% speed/adolc/det_lu.cpp% speed/adolc/mat_mul.cpp% speed/adolc/ode.cpp% speed/adolc/poly.cpp% speed/adolc/sparse_hessian.cpp% speed/adolc/sparse_jacobian.cpp% speed/adolc/alloc_mat.cpp %$$ $end cppad-20170000.3/omh/speed/speed_utility.omh0000644000175200017650000000324513057470464017713 0ustar coincoin-web$Id: speed_utility.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin speed_utility$$ $section Speed Testing Utilities$$ $children% cppad/speed/det_by_lu.hpp% cppad/speed/det_of_minor.hpp% cppad/speed/det_by_minor.hpp% cppad/speed/det_33.hpp% cppad/speed/det_grad_33.hpp% cppad/speed/mat_sum_sq.hpp% cppad/speed/ode_evaluate.hpp% cppad/speed/sparse_jac_fun.hpp% cppad/speed/sparse_hes_fun.hpp% cppad/speed/uniform_01.hpp %$$ $head Speed Main Program$$ $table $rref speed_main$$ $tend $head Speed Utility Routines$$ $table $rref det_by_lu$$ $rref det_by_minor$$ $rref det_of_minor$$ $rref det_33$$ $rref det_grad_33$$ $rref mat_sum_sq$$ $rref ode_evaluate$$ $rref sparse_jac_fun$$ $rref sparse_hes_fun$$ $rref uniform_01$$ $tend $head Library Routines$$ $table $rref LuFactor$$ $rref LuInvert$$ $rref LuSolve$$ $rref Poly$$ $tend $head Source Code$$ $table $rref det_by_lu.hpp$$ $rref det_by_minor.hpp$$ $rref det_grad_33.hpp$$ $rref det_of_minor.hpp$$ $rref lu_factor.hpp$$ $rref lu_invert.hpp$$ $rref lu_solve.hpp$$ $rref mat_sum_sq.hpp$$ $rref poly.hpp$$ $rref sparse_jac_fun.hpp$$ $rref sparse_hes_fun.hpp$$ $rref uniform_01.hpp$$ $tend $end cppad-20170000.3/omh/speed/speed_cppad.omh0000644000175200017650000000325513057470464017300 0ustar coincoin-web$Id: speed_cppad.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin speed_cppad$$ $spell cmake cppad CppAD Cygwin Microsoft chdir Workspace dsw exe sln $$ $section Speed Test Derivatives Using CppAD$$ $head Purpose$$ CppAD has a set of speed tests that are used to determine if certain changes improve its execution speed (and to compare CppAD with other AD packages). This section links to the source code the CppAD speed tests (any suggestions to make the CppAD results faster are welcome). $head Running Tests$$ To build these speed tests, and run their correctness tests, execute the following commands starting in the $cref/build directory/cmake/CMake Command/Build Directory/$$: $codei% cd speed/cppad make check_speed_cppad VERBOSE=1 %$$ You can then run the corresponding speed tests with the following command $codei% ./speed_cppad speed %seed% %$$ where $icode seed$$ is a positive integer. See $cref speed_main$$ for more options. $contents% speed/cppad/det_minor.cpp% speed/cppad/det_lu.cpp% speed/cppad/mat_mul.cpp% speed/cppad/ode.cpp% speed/cppad/poly.cpp% speed/cppad/sparse_hessian.cpp% speed/cppad/sparse_jacobian.cpp %$$ $end cppad-20170000.3/omh/speed/speed_double.omh0000644000175200017650000000312413057470464017456 0ustar coincoin-web$Id: speed_double.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin speed_double$$ $spell cmake cppad CppAD Cygwin Microsoft chdir Workspace dsw exe sln $$ $section Speed Test of Functions in Double$$ $head Purpose$$ CppAD has a set of speed tests for just calculating functions (in double precision instead of an AD type). This section links to the source code the function value speed tests. $head Running Tests$$ To build these speed tests, and run their correctness tests, execute the following commands starting in the $cref/build directory/cmake/CMake Command/Build Directory/$$: $codei% cd speed/double make check_speed_double VERBOSE=1 %$$ You can then run the corresponding speed tests with the following command $codei% ./speed_double speed %seed% %$$ where $icode seed$$ is a positive integer. See $cref speed_main$$ for more options. $contents% speed/double/det_minor.cpp% speed/double/det_lu.cpp% speed/double/mat_mul.cpp% speed/double/ode.cpp% speed/double/poly.cpp% speed/double/sparse_hessian.cpp% speed/double/sparse_jacobian.cpp %$$ $end cppad-20170000.3/omh/speed/speed_sacado.omh0000644000175200017650000000333413057470464017441 0ustar coincoin-web$Id: speed_sacado.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin speed_sacado$$ $spell cmake SacadoDir CppAD Cygwin $$ $section Speed Test Derivatives Using Sacado$$ $head Purpose$$ CppAD has a set of speed tests that are used to compare Sacado with other AD packages. This section links to the source code the Sacado speed tests (any suggestions to make the Sacado results faster are welcome). $head sacado_prefix$$ To run these tests, you must include the $cref sacado_prefix$$ in you $cref/cmake command/cmake/CMake Command/$$. $head Running Tests$$ To build these speed tests, and run their correctness tests, execute the following commands starting in the $cref/build directory/cmake/CMake Command/Build Directory/$$: $codei% cd speed/sacado make check_speed_sacado VERBOSE=1 %$$ You can then run the corresponding speed tests with the following command $codei% ./speed_sacado speed %seed% %$$ where $icode seed$$ is a positive integer. See $cref speed_main$$ for more options. $contents% speed/sacado/det_minor.cpp% speed/sacado/det_lu.cpp% speed/sacado/mat_mul.cpp% speed/sacado/ode.cpp% speed/sacado/poly.cpp% speed/sacado/sparse_hessian.cpp% speed/sacado/sparse_jacobian.cpp %$$ $end cppad-20170000.3/omh/mat_sum_sq_hpp.omh0000644000175200017650000000153613057470464016750 0ustar coincoin-web$Id: mat_sum_sq_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin mat_sum_sq.hpp$$ $spell sq ifndef endif $$ $section Source: mat_sum_sq$$ $mindex source$$ $code # ifndef CPPAD_MAT_SUM_SQ_HPP $pre $$ # define CPPAD_MAT_SUM_SQ_HPP $srcfile%cppad/speed/mat_sum_sq.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/thread_alloc.omh0000644000175200017650000000322113057470464016343 0ustar coincoin-web// $Id: thread_alloc.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin thread_alloc$$ $spell openmp cppad/utility/thread_alloc.hpp CppAD $$ $section A Fast Multi-Threading Memory Allocator$$ $mindex allocation$$ $head Syntax$$ $code # include $$ $head Purpose$$ The C++ $code new$$ and $code delete$$ operators are thread safe, but this means that a thread may have to wait for a lock on these operations. Once memory is obtained for a thread, the $code thread_alloc$$ memory allocator keeps that memory $cref/available/ta_available/$$ for the thread so that it can be re-used without waiting for a lock. All the CppAD memory allocations use this utility. The $cref/free_available/ta_free_available/$$ function should be used to return memory to the system (once it is no longer required by a thread). $head Include$$ The routines in sections below are defined by $code cppad/thread_alloc.hpp$$. This file is included by $code cppad/cppad.hpp$$, but it can also be included separately with out the rest of the $code CppAD$$. $childtable% example/thread_alloc.cpp% cppad/utility/thread_alloc.hpp %$$ $end */ cppad-20170000.3/omh/forward/0002755000175200017650000000000013057470464014665 5ustar coincoin-webcppad-20170000.3/omh/forward/compare_change.omh0000644000175200017650000001135213057470464020325 0ustar coincoin-web// $Id: compare_change.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin compare_change$$ $spell op const $$ $section Comparison Changes Between Taping and Zero Order Forward$$ $mindex ADFun compare_change$$ $head Syntax$$ $icode%f%.compare_change_count(%count%) %$$ $icode%number% = %f%.compare_change_number() %$$ $icode%op_index% = %f%.compare_change_op_index() %$$ $bold See Also$$ $cref FunCheck$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$; i.e, given $latex x \in B^n$$, $latex F(x)$$ is defined by $codei% %F%(%x%) = %f%.Forward(0, %x%) %$$ see $cref forward_zero$$. If $latex x$$ is such that all the algorithm $cref/comparison/Compare/$$ operations have the same result as when the algorithm was taped, The function $latex F(x)$$ and the algorithm will have the same values. (This is a sufficient, but not necessary condition). $head f$$ In the $code compare_change_number$$ and $code compare_change_op_index$$ syntax, the object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ In the $code compare_change_count$$ syntax, the object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ $head count$$ The argument $icode count$$ has prototype $icode% size_t %count% %$$ It specifies which comparison change should correspond to the information stored in $icode f$$ during subsequent calls to $cref forward_zero$$; i.e., $codei% %f%.Forward(0, %x%) %$$ For example, if $icode%count% == 1%$$, the operator index corresponding to the first comparison change will be stored. This is the default value used if $icode count$$ is not specified. $subhead Speed$$ The special case where $icode count == 0$$, should be faster because the comparisons are not checked during $codei% %f%.Forward(0, %x%) %$$ $head number$$ The return value $icode number$$ has prototype $codei% size_t %number% %$$ If $icode count$$ is non-zero, $icode number$$ is the number of $codei%AD<%Base%>%$$ $cref/comparison/Compare/$$ operations, corresponding to the previous call to $codei% %f%.Forward(0, %x%) %$$ that have a different result for this value of $icode x$$ than the value used when $icode f$$ was created by taping an algorithm. If $icode count$$ is zero, or if no calls to $icode%f%.Forward(0, %x%)%$$ follow the previous setting of $icode count$$, $icode number$$ is zero. $subhead Discussion$$ If $icode count$$ and $icode number$$ are non-zero, you may want to re-tape the algorithm with the $cref/independent variables/glossary/Tape/Independent Variable/$$ equal to the values in $icode x$$, so the AD operation sequence properly represents the algorithm for this value of independent variables. On the other hand, re-taping the AD operation sequence usually takes significantly more time than evaluation using $cref forward_zero$$. If the functions values have not changed (see $cref FunCheck$$) it may not be worth re-taping a new AD operation sequence. $head op_index$$ The return value $icode op_index$$ has prototype $codei% size_t %op_index% %$$ If $icode count$$ is non-zero, $icode op_index$$ is the operator index corresponding the $icode count$$-th comparison change during the previous call to $codei% %f%.Forward(0, %x%) %$$ If $icode count$$ is greater than the corresponding $icode number$$, there is no such comparison change and $icode op_index$$ will also be zero. If $icode count$$ is zero, if the function $icode f$$ has been $cref/optimized/optimize/$$, or if no calls to $icode%f%.Forward(0, %x%)%$$ follow the previous setting of $icode count$$, $icode op_index$$ is zero. $subhead Purpose$$ The operator index can be used to generate an error during the taping process so that the corresponding algorithm can be inspected. In some cases, it is possible to re-design this part of the algorithm to avoid the particular comparison operation. For example, using an $cref/conditional expression/CondExp/$$ may be appropriate in some cases. See $cref/abort_op_index/Independent/abort_op_index/$$ in the syntax $codei% Independent(%x%, %abort_op_index%) %$$ $children% example/compare_change.cpp %$$ $head Example$$ $cref compare_change.cpp$$ contains an example and test of this operation. It returns true if they succeed and false otherwise. $end cppad-20170000.3/omh/forward/forward_two.omh0000644000175200017650000001050413057470464017725 0ustar coincoin-web// $Id: forward_two.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin forward_two$$ $spell Jacobian Taylor const $$ $section Second Order Forward Mode: Derivative Values$$ $mindex two$$ $head Syntax$$ $icode%y2% = %f%.Forward(1, %x2%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The result of the syntax above is that for $icode%i% = 0 , %...% , %m%-1%$$, $codei% %y2%[%i%]%$$ $latex = F_i^{(1)} (x0) * x2 + \frac{1}{2} x1^T * F_i^{(2)} (x0) * x1$$ $pre $$ where $latex F^{(1)} (x0)$$ is the Jacobian of $latex F$$, and $latex F_i^{(2)} (x0)$$ is the Hessian of th $th i$$ component of $latex F$$, evaluated at $icode x0$$. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$. Before this call to $code Forward$$, the value returned by $codei% %f%.size_order() %$$ must be greater than or equal two. After this call it will be will be three (see $cref size_order$$). $head x0$$ The vector $icode x0$$ in the formula for $icode%y2%[%i%]%$$ corresponds to the previous call to $cref forward_zero$$ using this ADFun object $icode f$$; i.e., $codei% %f%.Forward(0, %x0%) %$$ If there is no previous call with the first argument zero, the value of the $cref/independent/Independent/$$ variables during the recording of the AD sequence of operations is used for $icode x0$$. $head x1$$ The vector $icode x1$$ in the formula for $icode%y2%[%i%]%$$ corresponds to the previous call to $cref forward_one$$ using this ADFun object $icode f$$; i.e., $codei% %f%.Forward(1, %x1%) %$$ $head x2$$ The argument $icode x2$$ has prototype $codei% const %Vector%& %x2% %$$ (see $cref/Vector/forward_two/Vector/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. $head y2$$ The result $icode y2$$ has prototype $codei% %Vector% %y2% %$$ (see $cref/Vector/forward_two/Vector/$$ below) The size of $icode y1$$ is equal to $icode m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. Its value is given element-wise by the formula in the $cref/purpose/forward_two/Purpose/$$ above. $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ The file $cref forward.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $head Special Case$$ This is special case of $cref forward_order$$ where $latex \[ \begin{array}{rcl} Y(t) & = F[ X(t) ] \\ X(t) & = & x^{(0)} t^0 + x^{(1)} * t^1 + \cdots, + x^{(q)} * t^q + o( t^q ) \\ Y(t) & = & y^{(0)} t^0 + y^{(1)} * t^1 + \cdots, + y^{(q)} * t^q + o( t^q ) \end{array} \] $$ and $latex o( t^q ) * t^{-q} \rightarrow 0$$ as $latex t \rightarrow 0$$. For this special case, $latex q = 2$$, $latex x^{(0)}$$ $codei%= %x0%$$, $latex x^{(1)}$$ $codei%= %x1%$$, $latex X(t) = x^{(0)} + x^{(1)} t + x^{(2)} t^2$$, and $latex \[ y^{(0)} + y^{(1)} t + y^{(2)} t^2 = F [ x^{(0)} + x^{(1)} t + x^{(2)} t^2 ] + o(t^2) \] $$ Restricting our attention to the $th i$$ component, and taking the derivative with respect to $latex t$$, we obtain $latex \[ y_i^{(1)} + 2 y_i^{(2)} t = F_i^{(1)} [ x^{(0)} + x^{(1)} t + x^{(2)} t^2 ] [ x^{(1)} + 2 x^{(2)} t ] + o(t) \] $$ Taking a second derivative with respect to $latex t$$, and evaluating at $latex t = 0$$, we obtain $latex \[ 2 y_i^{(2)} = [ x^{(1)} ]^T F_i^{(2)} [ x^{(0)} ] x^{(1)} + F_i^{(1)} [ x^{(0)} ] 2 x^{(2)} \] $$ which agrees with the specification for $icode%y2%[%i%]%$$ in the $cref/purpose/forward_two/Purpose/$$ above. $end cppad-20170000.3/omh/forward/forward_order.omh0000644000175200017650000001465413057470464020241 0ustar coincoin-web// $Id: forward_order.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin forward_order$$ $spell std::cout ostream xk xp yp Ind vp uj Taylor const xq yq $$ $section Multiple Order Forward Mode$$ $mindex any$$ $head Syntax$$ $icode%yq% = %f%.Forward(%q%, %xq% ) %$$ $icode%yq% = %f%.Forward(%q%, %xq%, %s%) %$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. Given a function $latex X : B \rightarrow B^n$$, defined by its $cref/Taylor coefficients/glossary/Taylor Coefficient/$$, forward mode computes the Taylor coefficients for the function $latex \[ Y (t) = F [ X(t) ] \]$$ $subhead Function Values$$ If you are using forward mode to compute values for $latex F(x)$$, $cref forward_zero$$ is simpler to understand than this explanation of the general case. $subhead Derivative Values$$ If you are using forward mode to compute values for $latex F^{(1)} (x) * dx$$, $cref forward_one$$ is simpler to understand than this explanation of the general case. $head Notation$$ $subhead n$$ We use $icode n$$ to denote the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. $subhead m$$ We use $icode m$$ to denote the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. $head f$$ The $cref ADFun$$ object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$. After this call we will have $codei% %f%.size_order() == %q% + 1 %f%.size_direction() == 1 %$$ $head One Order$$ If $icode%xq%.size() == %n%$$, then we are only computing one order. In this case, before this call we must have $codei% %f%.size_order() >= %q% %f%.size_direction() == 1 %$$ $head q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ and specifies the highest order of the Taylor coefficients to be calculated. $head xq$$ The argument $icode xq$$ has prototype $codei% const %Vector%& %xq% %$$ (see $cref/Vector/forward_order/Vector/$$ below). As above, we use $icode n$$ to denote the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. The size of $icode xq$$ must be either $icode n$$ or $icode%n%*(%q%+1)%$$. After this call we will have $codei% %f%.size_order() == %q% + 1 %$$ $subhead One Order$$ If $icode%xq%.size() == %n%$$, the $th q$$ order Taylor coefficient for $latex X(t)$$ is defined by $pre $$ $latex x^{(q)} = $$ $icode xq$$. For $latex k = 0 , \ldots , q-1$$, the Taylor coefficient $latex x^{(k)}$$ is defined by $icode xk$$ in the previous call to $codei% %f%.Forward(%k%, %xk%) %$$ $subhead Multiple Orders$$ If $icode%xq%.size() == %n%*(%q%+1)%$$, For $latex k = 0 , \ldots , q$$, $latex j = 0 , \ldots , n-1$$, the $th j$$ component of the $th k$$ order Taylor coefficient for $latex X(t)$$ is defined by $pre $$ $latex x_j^{(k)} = $$ $icode%%xq%[ (%q%+1) * %j% + %k% ]%$$ $subhead Restrictions$$ Note if $icode f$$ uses $cref old_atomic$$ functions, the size of $icode xq$$ must be $icode n$$. $head s$$ If the argument $icode s$$ is not present, $code std::cout$$ is used in its place. Otherwise, this argument has prototype $codei% std::ostream& %s% %$$ If order zero is begin calculated, $icode s$$ specifies where the output corresponding to $cref PrintFor$$ will be written. If order zero is not being calculated, $icode s$$ is not used $head X(t)$$ The function $latex X : B \rightarrow B^n$$ is defined using the Taylor coefficients $latex x^{(k)} \in B^n$$: $latex \[ X(t) = x^{(0)} * t^0 + x^{(1)} * t^1 + \cdots + x^{(q)} * t^q \] $$ Note that for $latex k = 0 , \ldots , q$$, the $th k$$ derivative of $latex X(t)$$ is related to the Taylor coefficients by the equation $latex \[ x^{(k)} = \frac{1}{k !} X^{(k)} (0) \] $$ $head Y(t)$$ The function $latex Y : B \rightarrow B^m$$ is defined by $latex Y(t) = F[ X(t) ] $$. We use $latex y^{(k)} \in B^m$$ to denote the $th k$$ order Taylor coefficient of $latex Y(t)$$; i.e., $latex \[ Y(t) = y^{(0)} * t^0 + y^{(1)} * t^1 + \cdots + y^{(q)} * t^q + o( t^q ) \] $$ where $latex o( t^q ) * t^{-q} \rightarrow 0$$ as $latex t \rightarrow 0$$. Note that $latex y^{(k)}$$ is related to the $th k$$ derivative of $latex Y(t)$$ by the equation $latex \[ y^{(k)} = \frac{1}{k !} Y^{(k)} (0) \] $$ $head yq$$ The return value $icode yq$$ has prototype $codei% %Vector% %yq% %$$ (see $cref/Vector/forward_order/Vector/$$ below). $subhead One Order$$ If $icode%xq%.size() == %n%$$, the vector $icode yq$$ has size $icode m$$. The $th q$$ order Taylor coefficient for $latex Y(t)$$ is returned as $codei% %yq%$$ $latex = y^{(q)}$$. $subhead Multiple Orders$$ If $icode%xq%.size() == %n%*(%q%+1)%$$, the vector $icode yq$$ has size $icode%m%*(%q%+1)%$$. For $latex k = 0 , \ldots , q$$, for $latex i = 0 , \ldots , m-1$$, the $th i$$ component of the $th k$$ order Taylor coefficient for $latex Y(t)$$ is returned as $codei% %yq%[ (%q%+1) * %i% + %k% ]%$$ $latex = y_i^{(k)}$$ $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Zero Order$$ The case where $latex q = 0$$ and $icode%xq%.size() == %n%$$, corresponds to the zero order $cref/special case/forward_zero/Special Case/$$. $head First Order$$ The case where $latex q = 1$$ and $icode%xq%.size() == %n%$$, corresponds to the first order $cref/special case/forward_one/Special Case/$$. $head Second Order$$ The case where $latex q = 2$$ and $icode%xq%.size() == %n%$$, corresponds to the second order $cref/special case/forward_two/Special Case/$$. $children% example/forward.cpp% example/forward_order.cpp %$$ $head Example$$ The file $cref forward.cpp$$ ( $cref forward_order.cpp$$ ) contains an example and test using one order (multiple orders). They return true if they succeed and false otherwise. $end cppad-20170000.3/omh/forward/forward_dir.omh0000644000175200017650000001362313057470464017677 0ustar coincoin-web// $Id: forward_dir.omh 3823 2016-07-01 12:30:50Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin forward_dir$$ $spell Taylor const dir cpp yq xq xk std::cout ostream $$ $section Multiple Directions Forward Mode$$ $head Syntax$$ $icode%yq% = %f%.Forward(%q%, %r%, %xq%) %$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. Given a function $latex X : B \rightarrow B^n$$, defined by its $cref/Taylor coefficients/glossary/Taylor Coefficient/$$, forward mode computes the Taylor coefficients for the function $latex \[ Y (t) = F [ X(t) ] \]$$ This version of forward mode computes multiple directions as the same time (reducing the number of passes through the tape). This requires more memory, but might be faster in some cases. $head Reverse Mode$$ Reverse mode for multiple directions has not yet been implemented. If you have speed tests that indicate that multiple direction forward mode is faster, and you want to try multiple direction reverse mode, contact the CppAD project manager. $head Notation$$ $subhead n$$ We use $icode n$$ to denote the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. $subhead m$$ We use $icode m$$ to denote the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. $head f$$ The $cref ADFun$$ object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$. After this call we will have $codei% %f%.size_order() == %q% + 1 %f%.size_direction() == %r% %$$ $head q$$ This argument has prototype $codei% size_t %q% %$$ It specifies the order of Taylor Coefficient that we are calculating and must be greater than zero. The zero order coefficients can only have one direction computed and stored in $icode f$$ so use $cref forward_zero$$ to compute the zero order coefficients. $head r$$ This argument has prototype $codei% size_t %r% %$$ It specifies the number of directions that are computed together. If ($icode%r% == 1%$$), you are only using one direction and $cref forward_order$$ is simpler, and should be faster, than this more general case. $head xq$$ The argument $icode xq$$ has prototype $codei% const %Vector%& %xq% %$$ and its size must be $icode%n%*%r%$$ (see $cref/Vector/forward_dir/Vector/$$ below). For $latex \ell = 0 , \ldots , r-1$$, $latex j = 0 , \ldots , n-1$$, the $th j$$ component of the $th q$$ order Taylor coefficient for $latex X_\ell (t)$$ is defined by $pre $$ $latex x_j^{(q),\ell} = $$ $icode%xq%[ %r% * %j% + %ell% ]%$$ $head Zero Order$$ For $latex j = 0 , \ldots , n-1$$, the $th j$$ component of the zero order Taylor coefficient for $latex X_\ell (t)$$ is defined by $pre $$ $latex x_j^{(0)} = $$ $icode%xk%[ %j% ]%$$ where $icode xk$$ corresponds to the previous call $codei% %f%.Forward(%k%, %xk%) %$$ with $icode%k% = 0%$$. $head Non-Zero Lower Orders$$ For $latex \ell = 0 , \ldots , r-1$$, $latex j = 0 , \ldots , n-1$$, $latex k = 1, \ldots , q-1$$, the $th j$$ component of the $th k$$ order Taylor coefficient for $latex X_\ell (t)$$ is defined by $pre $$ $latex x_j^{(k),\ell} = $$ $icode%xk%[ %r% * %j% + %ell% ]%$$ where $icode xk$$ corresponds to the previous call $codei% %f%.Forward(%k%, %r%, %xk%) %$$ Note that $icode r$$ must have the same value in this previous call. $head X(t)$$ For $latex \ell = 0 , \ldots , r-1$$, the function $latex X_\ell : B \rightarrow B^n$$ is defined using the Taylor coefficients $latex x^{(k),\ell} \in B^n$$: $latex \[ X_\ell (t) = x^{(0)} + x^{(1),\ell} * t^1 + \cdots + x^{(q),\ell} t^q \] $$ Note that the $th k$$ derivative of $latex X_\ell (t)$$ is related to its Taylor coefficients by $latex \[ \begin{array}{rcl} x^{(0)} & = & X_\ell (0) \\ x^{(k), \ell} & = & \frac{1}{k !} X_\ell^{(k)} (0) \end{array} \] $$ for $latex k = 1 , \ldots , q$$. $head Y(t)$$ For $latex \ell = 0 , \ldots , r-1$$, the function $latex Y_\ell : B \rightarrow B^m$$ is defined by $latex Y_\ell (t) = F[ X_\ell (t) ] $$. We use $latex y^{(0)}$$ for the zero order coefficient and $latex y^{(k),\ell} \in B^m$$ to denote the hight order coefficients; i.e., $latex \[ Y_\ell (t) = y^{(0)} + y^{(1),\ell} * t^1 + \cdots + y^{(q),\ell} * t^q + o( t^q ) \] $$ where $latex o( t^q ) * t^{-q} \rightarrow 0$$ as $latex t \rightarrow 0$$. Note that the $th k$$ derivative of $latex Y_\ell (t)$$ is related to its Taylor coefficients by $latex \[ \begin{array}{rcl} y^{(0)} & = & Y_\ell (0) \\ y^{(k), \ell} & = & \frac{1}{k !} Y_\ell^{(k)} (0) \end{array} \] $$ for $latex k = 1 , \ldots , q$$. $head yq$$ The argument $icode yq$$ has prototype $codei% %Vector% %yq% %$$ and its size is $icode%m%*%r%$$ (see $cref/Vector/forward_dir/Vector/$$ below). For $latex \ell = 0 , \ldots , r-1$$, $latex i = 0 , \ldots , m-1$$, the $th i$$ component of the $th q$$ order Taylor coefficient for $latex Y_\ell (t)$$ is given by $pre $$ $latex y_i^{(q),\ell} = $$ $icode%yq%[ %r% * %i% + %ell% ]%$$ $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $children% example/forward_dir.cpp %$$ $head Example$$ The file $cref forward_dir.cpp$$ contains an example and test using one order (multiple orders). They return true if they succeed and false otherwise. $end cppad-20170000.3/omh/forward/forward_zero.omh0000644000175200017650000000645113057470464020101 0ustar coincoin-web// $Id: forward_zero.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin forward_zero$$ $spell std::cout ostream const Taylor dy Jacobian $$ $section Zero Order Forward Mode: Function Values$$ $head Syntax$$ $icode%y0% = %f%.Forward(0, %x0%) %$$ $icode%y0% = %f%.Forward(0, %x0%, %s%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The result of the syntax above is $latex \[ y0 = F(x0) \] $$ See the $cref/FunCheck discussion/FunCheck/Discussion/$$ for possible differences between $latex F(x)$$ and the algorithm that defined the operation sequence. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$. After this call to $code Forward$$, the value returned by $codei% %f%.size_order() %$$ will be equal to one (see $cref size_order$$). $head x0$$ The argument $icode x0$$ has prototype $codei% const %Vector%& %x0% %$$ (see $cref/Vector/forward_zero/Vector/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. $head s$$ If the argument $icode s$$ is not present, $code std::cout$$ is used in its place. Otherwise, this argument has prototype $codei% std::ostream& %s% %$$ It specifies where the output corresponding to $cref PrintFor$$, and this zero order forward mode call, will be written. $head y0$$ The result $icode y0$$ has prototype $codei% %Vector% %y0% %$$ (see $cref/Vector/forward_zero/Vector/$$ below) and its value is $latex F(x)$$ at $icode%x% = %x0%$$. The size of $icode y0$$ is equal to $icode m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ The file $cref forward.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $head Special Case$$ This is special case of $cref forward_order$$ where $latex \[ \begin{array}{rcl} Y(t) & = & F[ X(t) ] \\ X(t) & = & x^{(0)} t^0 + x^{(1)} * t^1 + \cdots, + x^{(q)} * t^q + o( t^q ) \\ Y(t) & = & y^{(0)} t^0 + y^{(1)} * t^1 + \cdots, + y^{(q)} * t^q + o( t^q ) \end{array} \] $$ and $latex o( t^q ) * t^{-q} \rightarrow 0$$ as $latex t \rightarrow 0$$. For this special case, $latex q = 0$$, $latex x^{(0)}$$ $codei%= %x0%$$, $latex X(t) = x^{(0)}$$, and $latex \[ y^{(0)} = Y(t) = F[ X(t) ] = F( x^{(0)} ) \] $$ which agrees with the specifications for $icode y0$$ in the $cref/purpose/forward_zero/Purpose/$$ above. $end cppad-20170000.3/omh/forward/forward.omh0000644000175200017650000000164613057470464017043 0ustar coincoin-web// $Id: forward.omh 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin Forward$$ $section Forward Mode$$ $childtable% omh/forward/forward_zero.omh% omh/forward/forward_one.omh% omh/forward/forward_two.omh% omh/forward/forward_order.omh% omh/forward/forward_dir.omh% omh/forward/size_order.omh% omh/forward/compare_change.omh% cppad/core/capacity_order.hpp% cppad/core/num_skip.hpp %$$ $end cppad-20170000.3/omh/forward/forward_one.omh0000644000175200017650000000640513057470464017702 0ustar coincoin-web// $Id: forward_one.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin forward_one$$ $spell Jacobian Taylor const $$ $section First Order Forward Mode: Derivative Values$$ $mindex one$$ $head Syntax$$ $icode%y1% = %f%.Forward(1, %x1%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The result of the syntax above is $latex \[ y1 = F^{(1)} (x0) * x1 \] $$ where $latex F^{(1)} (x0)$$ is the Jacobian of $latex F$$ evaluated at $icode x0$$. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$. Before this call to $code Forward$$, the value returned by $codei% %f%.size_order() %$$ must be greater than or equal one. After this call it will be will be two (see $cref size_order$$). $head x0$$ The vector $icode x0$$ in the formula $latex \[ y1 = F^{(1)} (x0) * x1 \] $$ corresponds to the previous call to $cref forward_zero$$ using this ADFun object $icode f$$; i.e., $codei% %f%.Forward(0, %x0%) %$$ If there is no previous call with the first argument zero, the value of the $cref/independent/Independent/$$ variables during the recording of the AD sequence of operations is used for $icode x0$$. $head x1$$ The argument $icode x1$$ has prototype $codei% const %Vector%& %x1% %$$ (see $cref/Vector/forward_one/Vector/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ The file $cref forward.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $head Special Case$$ This is special case of $cref forward_order$$ where $latex \[ \begin{array}{rcl} Y(t) & = & F[ X(t) ] \\ X(t) & = & x^{(0)} t^0 + x^{(1)} * t^1 + \cdots, + x^{(q)} * t^q + o( t^q ) \\ Y(t) & = & y^{(0)} t^0 + y^{(1)} * t^1 + \cdots, + y^{(q)} * t^q + o( t^q ) \end{array} \] $$ and $latex o( t^q ) * t^{-q} \rightarrow 0$$ as $latex t \rightarrow 0$$. For this special case, $latex q = 1$$, $latex x^{(0)}$$ $codei%= %x0%$$, $latex x^{(1)}$$ $codei%= %x1%$$, $latex X(t) = x^{(0)} + x^{(1)} t$$, and $latex \[ y^{(0)} + y^{(1)} t = F [ x^{(0)} + x^{(1)} t ] + o(t) \] $$ Taking the derivative with respect to $latex t$$, at $latex t = 0$$, we obtain $latex \[ y^{(1)} = F^{(1)} [ x^{(0)} ] x^{(1)} \] $$ which agrees with the specifications for $icode y1$$ in the $cref/purpose/forward_one/Purpose/$$ above. $end cppad-20170000.3/omh/forward/size_order.omh0000644000175200017650000000575513057470464017551 0ustar coincoin-web// $Id: size_order.omh 3779 2016-01-01 11:26:11Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin size_order$$ $spell var Taylor const $$ $section Number Taylor Coefficient Orders Currently Stored$$ $head Syntax$$ $icode%s% = %f%.size_order()%$$ $subhead See Also$$ $cref seq_property$$ $head Purpose$$ Determine the number of Taylor coefficient orders, per variable,direction, currently calculated and stored in the ADFun object $icode f$$. See the discussion under $cref/Constructor/size_order/Constructor/$$, $cref/Forward/size_order/Forward/$$, and $cref/capacity_order/size_order/capacity_order/$$ for a description of when this value can change. $head f$$ The object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ $head s$$ The result $icode s$$ has prototype $codei% size_t %s% %$$ and is the number of Taylor coefficient orders, per variable,direction in the AD operation sequence, currently calculated and stored in the ADFun object $icode f$$. $head Constructor$$ Directly after the $cref FunConstruct$$ syntax $codei% ADFun<%Base%> %f%(%x%, %y%) %$$ the value of $icode s$$ returned by $code size_order$$ is one. This is because there is an implicit call to $code Forward$$ that computes the zero order Taylor coefficients during this constructor. $head Forward$$ After a call to $cref/Forward/forward_order/$$ with the syntax $codei% %f%.Forward(%q%, %x_q%) %$$ the value of $icode s$$ returned by $code size_order$$ would be $latex q + 1$$. The call to $code Forward$$ above uses the lower order Taylor coefficients to compute and store the $th q$$ order Taylor coefficients for all the variables in the operation sequence corresponding to $icode f$$. Thus there are $latex q + 1$$ (order zero through $icode q$$) Taylor coefficients per variable,direction. (You can determine the number of variables in the operation sequence using the $cref/size_var/seq_property/size_var/$$ function.) $head capacity_order$$ If the number of Taylor coefficient orders currently stored in $icode f$$ is less than or equal $icode c$$, a call to $cref capacity_order$$ with the syntax $codei% %f%.capacity_order(%c%) %$$ does not affect the value $icode s$$ returned by $code size_order$$. Otherwise, the value $icode s$$ returned by $code size_order$$ is equal to $icode c$$ (only Taylor coefficients of order zero through $latex c-1$$ have been retained). $head Example$$ The file $cref forward.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end cppad-20170000.3/omh/install/0002755000175200017650000000000013057470464014667 5ustar coincoin-webcppad-20170000.3/omh/install/testvector.omh0000644000175200017650000000400313057470464017571 0ustar coincoin-web// $Id: testvector.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin cppad_testvector$$ $spell CppAD cppad eigen std testvector namespace cmake $$ $section Choosing the CppAD Test Vector Template Class$$ $head Purpose$$ The value $icode cppad_testvector$$ in the $cref/cmake command/cmake/CMake Command/$$ must be one of the following: $code boost$$, $code cppad$$, $code eigen$$, or $code std$$. It specifies which type of vector is corresponds to the template class $cref/CPPAD_TESTVECTOR/testvector/$$ which is used for many of the CppAD examples and tests. $head std$$ If $icode%cppad_testvector%$$ is $icode std$$, the $code std::vector$$ template class is used to define $code CPPAD_TESTVECTOR$$. $head cppad$$ If $icode%cppad_testvector%$$ is $icode cppad$$, the $cref cppad_vector$$ template class is used to define $code CPPAD_TESTVECTOR$$. $head boost$$ If $icode%cppad_testvector%$$ is $icode boost$$, $href% http://www.boost.org/doc/libs/1_52_0/libs/numeric/ublas/doc/vector.htm% boost ublas vector %$$ template class is used to define $code CPPAD_TESTVECTOR$$. In this case, the $href% http://www.cmake.org/cmake/help/cmake2.6docs.html#module:FindBoost% cmake FindBoost %$$ module must be able to automatically figure out where Boost is installed. $head eigen$$ If $icode%cppad_testvector%$$ is $icode eigen$$, one of the eigen template classes is used to define $code CPPAD_TESTVECTOR$$. In this case, $cref eigen_prefix$$ must be specified on the $code cmake$$ command line. $end cppad-20170000.3/omh/install/eigen_prefix.omh0000644000175200017650000000475713057470464020053 0ustar coincoin-web// $Id: eigen_prefix.omh 3810 2016-03-26 14:43:57Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin eigen_prefix$$ $dollar @$$ $spell testvector dir namespace Eigen Cpp includedirs cmake det cppad $$ $section Including the Eigen Examples and Tests$$ $mindex prefix get$$ $head Purpose$$ CppAD can include the following examples and tests that use the linear algebra package $href%http://eigen.tuxfamily.org%Eigen%$$: $comment check list with 'grep eigen omh/example_list.omh'$$ $table $rref eigen_plugin.hpp$$ $rref cppad_eigen.hpp$$ $rref eigen_array.cpp$$ $rref eigen_det.cpp$$ $rref atomic_eigen_mat_mul.hpp$$ $rref atomic_eigen_mat_inv.hpp$$ $tend $head eigen_prefix$$ If Eigen is installed on your system, you can specify a value for its install $icode eigen_prefix$$ on the $cref cmake$$ command line. The value of $icode eigen_prefix$$ must be such that, for one of the directories $icode dir$$ in $cref/cmake_install_includedirs/cmake/cmake_install_includedirs/$$, $codei% %eigen_prefix%/%dir%/Eigen/Core %$$ is a valid way to reference to the include file $code Core$$; $head Examples$$ If you include $icode eigen_prefix$$ on the $cref cmake$$ command line, you will be able to run the Eigen examples list above by executing the following commands starting in the $cref/distribution directory/download/Distribution Directory/$$: $codei% cd build/example make check_example %$$ If you do this, you will see an indication that the examples $code eigen_array$$ and $code eigen_det$$ have passed their correctness check. options to this program. $head Test Vector$$ If you have specified $icode eigen_prefix$$ you can choose $codei% -D cppad_testvector=eigen %$$ on the $cref/cmake command/cmake/CMake Command/$$ line. This we set the CppAD $cref testvector$$ to use Eigen vectors. $children% bin/get_eigen.sh %$$ $head get_eigen$$ If you are using Unix, you can download and install a copy of Eigen using $cref get_eigen.sh$$. The corresponding $icode eigen_prefix$$ would be $code build/prefix$$. $end cppad-20170000.3/omh/install/install.omh0000644000175200017650000000266313057470464017047 0ustar coincoin-web$Id: install.omh 3760 2015-12-01 04:12:28Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin Install$$ $dollar @$$ $spell makefiles nmake cmake tarball CppAD $$ $section CppAD Download, Test, and Install Instructions$$ $head Instructions$$ $subhead Step 1: Download$$ Use the $cref download$$ instructions to obtain a copy or CppAD. $subhead Step 2: Cmake$$ Use the $cref cmake$$ instructions to configure CppAD. $subhead Step 3: Check$$ Use the $cref cmake_check$$ instructions to check the CppAD examples and tests. $subhead Step 4: Installation$$ Use the command $codep make install $$ to install CppAD. If you created $code nmake$$ makefiles, you will have to use $codep nmake install $$ see the $cref/generator/cmake/generator/$$ option for the $code cmake$$ command. $childtable% omh/install/download.omh% omh/install/cmake.omh% omh/install/cmake_check.omh% omh/install/pkgconfig.omh% omh/install/auto_tools.omh %$$ $end cppad-20170000.3/omh/install/download.omh0000644000175200017650000002003413057470464017200 0ustar coincoin-web/* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin download$$ $escape $$ $spell vcdir vcvarsall Microsoft yyyy mkdir cmake nmake Makefiles omhelp svn https org dir exe gpl xzf CppAD cppad gzip yyyymmdd rel lic epl tgz hpp github git git htm $$ $dollar @$$ $section Download The CppAD Source Code$$ $head Purpose$$ CppAD is an include file library and you therefore need the source code to use it. This section discusses how to download the different versions of CppAD. $head Distribution Directory$$ We refer to the CppAD source directory created by the download instruction below as the distribution directory. To be specific, the distribution directory contains the file $code cppad/cppad.hpp$$. $head Compressed Archives$$ These files have been archived using $code tar$$ and compressed using $code gzip$$. We use $icode version$$ to denote the year, month, and day, corresponding to a version of the CppAD API. For example $code 20160101$$ corresponds to January 1, 2016. We use $icode rel$$ to denote the release number. Higher release numbers corresponding to more bug fixes. We use $icode lic$$ to denote the licence corresponding to a compressed archive which can be either $code epl$$ or $code gpl$$ ($code gpl$$ denotes the GNU General Public License and $code epl$$ denotes the Eclipse Public License). The compressed archives names have one of the following formats: $codei% cppad-%version%.%rel%.%lic%.tgz cppad-%version%.%rel%.tgz cppad-%version%.%lic%.tgz %$$ In Unix, you can extract these compressed archives using $code tar$$. For example, $codei% tar -xzf cppad-%version%.%rel%.%lic%.tgz %$$ No matter what the format of the name, the corresponding distribution directory is $codei%cppad-%version%$$. To see that the extraction has been done correctly, check for the following file: $codei% cppad-%version%/cppad/cppad.hpp %$$ $head Current Version$$ $subhead Compressed Archives$$ $table $bold version$$ $pre $$ $cnext $bold license$$ $pre $$ $cnext $bold link$$ $rnext current $cnext EPL $cnext $href% http://www.coin-or.org/download/source/CppAD/cppad-20170000.3.epl.tgz% cppad-20170000.3.epl.tgz%$$ $rnext current $cnext GPL $cnext $href% http://www.coin-or.org/download/source/CppAD/cppad-20170000.3.gpl.tgz% cppad-20170000.3.gpl.tgz%$$ $tend $subhead Subversion$$ The archives above correspond to the current subversion $href%https://projects.coin-or.org/CppAD/browser/trunk%trunk%$$. You can obtain a subversion copy of the current version using the command $codei% svn checkout https://projects.coin-or.org/svn/CppAD/trunk cppad.svn/trunk %$$ This procedure requires that the $href%http://subversion.tigris.org/%subversion%$$ program is installed on your system. $subhead Git$$ The archives above correspond to the current git $href%https://github.com/bradbell/cppad%master%$$. You can a git clone of the current version using the command $codei% git clone https://github.com/coin-or/CppAD.git cppad.git %$$ This procedure requires that the $href|https://en.wikipedia.org/wiki/Git_%28software%29|git|$$ is installed on your system. $head Release Versions$$ $subhead Coin$$ Release versions have the $icode rel$$ field in the compressed archive name. The release version on the $href%http://www.coin-or.org/download/source/CppAD/%Coin download page%$$ have the format $codei% cppad-%version%.%rel%.%lic%.tgz %$$ $subhead github$$ The release versions on the $href%https://github.com/coin-or/CppAD/releases%github download page%$$ have the format $codei% cppad-%version%.%rel%.tgz %$$ $head Monthly Versions$$ Monthly versions of the compressed tar files are available on the $href%http://www.coin-or.org/download/source/CppAD/%Coin download page%$$. These are kept until the end of the current year, when the next release is created. The monthly versions have the form $codei% cppad-%yyyy%0101.%lic%.tgz %$$ where the license code $icode lic$$ is $code gpl$$ or $code epl$$ and $icode yyyy$$ is the current year. $head Daily Versions$$ You can use the git version of the repository to obtain the version corresponding to a specific day as follows: $codei% git clone https://github.com/coin-or/CppAD.git cppad.git cd cppad.git git checkout --quiet %hash_id% %$$ where $icode hash_id$$ is the SHA-1 hash code for the version of the repository for the day of interest. Note that a list of these $icode hash_id$$ values can be found at the CppAD github $href%https://github.com/coin-or/CppAD/commits/master%commits/master%$$. page. $head Windows File Extraction and Testing$$ If you know how to extract the distribution directory from the tar file, just do so. Otherwise, below is one way you can do it. (Note that if $code 7z.exe$$, $code cmake.exe$$, and $code nmake.exe$$ are you your execution path, you will not need to specify their paths below.) $list number$$ Download and install the open source program $href%http://www.7-zip.org%$$. $lnext Download and install the Visual Studio Express; for example $href%http://www.microsoft.com/en-us/download/confirmation.aspx?id=44914 %Visual Studio 2013 %$$ $lnext In a command window, execute the following commands: $codei| set PATH=|path_to_7_zip|;%PATH% set PATH=|path_to_cmake|;%PATH% set VCDIR=|path_to_vcdir|;%PATH% call "%VCDIR%\vcvarsall.bat" x86 |$$ For example, on one machine these paths had the following values: $codei| |path_to_7_zip|=C:\Program Files\7-zip |path_to_cmake|=C:\Program Files (x86)\CMake\bin |path_to_vcdir|=C:\Program Files (x86)\Microsoft Visual Studio 14.0\VC |$$ $lnext Use the following commands to extract the distribution from the compressed archive: $codei% 7z x cppad-%version%.%lic%.tgz 7z x cppad-%version%.%lic%.tar %$$ $lnext To see if this has been done correctly, check for the following file: $codei% cppad-%version%\cppad\cppad.hpp %$$ $lnext The commands below are optional. They run the CppAD tests using the default $cref cmake$$ settings (except for the $cref/generator/cmake/generator/$$ option) $codei% mkdir build cd build cmake -G "NMake Makefiles" .. nmake check %$$ $lend $head Install Instructions$$ The $cref install$$ instructions on this web site correspond to the $cref/current version/download/Current Version/$$ of CppAD. If you are using an old version of CppAD these instructions may work. If you have trouble (or just to be careful), you should follow the instructions in the $code doc$$ subdirectory of the distribution directory. If there is no such documentation, you can build it; see $cref/building documentation /download /No Documentation /Building Documentation /$$. $head No Documentation$$ Some of the download methods do not include documentation. To be specific, the $cref/subversion/download/Current Version/Subversion/$$ method, $cref/git/download/Current Version/Git/$$ method, $cref/daily version/download/Daily Versions/$$ method, and the $cref/github release version/download/Release Versions/github/$$ method. In addition, these methods only provide the $href%http://opensource.org/licenses/EPL-1.0%EPL licensed%$$ version of CppAD. $subhead Building Documentation$$ If you are using one of these download methods, you can build the documentation to get the corresponding install instructions. The documentation for CppAD is built from the source code files using $href%http://www.seanet.com/~bradbell/omhelp/%OMhelp%$$. You will need to install the $code omhelp$$ command so that $codep which omhelp $$ shows it is in your path. Once you have done this, in the distribution directory execute the following command: $codei% bin/run_omhelp.sh htm %$$ You will then be able to follow the install instructions in the $code doc$$ subdirectory of the distribution directory. $end cppad-20170000.3/omh/install/pkgconfig.omh0000644000175200017650000000600113057470464017336 0ustar coincoin-web// $Id: pkgconfig.omh 3760 2015-12-01 04:12:28Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin pkgconfig$$ $spell cmake datadir ipopt CppAD pkg-config Cflags Dir builddir prefixdir cppad pkgconfig uninstalled $$ $section CppAD pkg-config Files$$ $mindex pc$$ $head Purpose$$ The $code pkg-config$$ package helps with the use of installed libraries; see its $href%http://people.freedesktop.org/~dbn/pkg-config-guide.html%guide%$$ for more information. $head Usage$$ The necessary flags for compiling code that includes CppAD can be obtained with the command $codep pkg-config --cflags cppad $$ Note that this command assumes $cref/cppad.pc/pkgconfig/$$ is in the search path $code PKG_CONFIG_PATH$$. If $cref ipopt_prefix$$ is specified, the necessary flags for linking $cref/cppad_ipopt/cppad_ipopt_nlp/$$ can be obtained with the commands $codep pkg-config --libs cppad $$ Note that this command assumes $code ipopt.pc$$ is in the search path $code PKG_CONFIG_PATH$$. $head Defined Fields$$ $table $icode Name$$ $cnext A human-readable name for the CppAD package. $rnext $icode Description$$ $cnext A brief description of the CppAD package. $rnext $icode URL$$ $cnext A URL where people can get more information about the CppAD package. $rnext $icode Version$$ $cnext A string specifically defining the version of the CppAD package. $rnext $icode Cflags$$ $cnext The necessary flags for using any of the CppAD include files. $rnext $icode Libs$$ $cnext If $cref ipopt_prefix$$ is specified, the necessary flags for using the $cref/cppad_ipopt/cppad_ipopt_nlp/$$ library $rnext $icode Requires$$ $cnext If $cref ipopt_prefix$$ is specified, the packages required to use the $cref/cppad_ipopt/cppad_ipopt_nlp/$$ library $tend $head CppAD Configuration Files$$ In the table below, $icode builddir$$ is the build directory; i.e., the directory where the CppAD $cref/cmake command/cmake/CMake Command/$$ is executed. The directory $icode prefix$$ is the value of $cref/cppad_prefix/cmake/cppad_prefix/$$ during configuration. The directory $icode datadir$$ is the value of $cref/cmake_install_datadir/cmake/cmake_install_datadir/$$. The following configuration files contain the information above $table $icode File$$ $cnext $icode Description$$ $rnext $icode%prefix%/%datadir%/pkgconfig/cppad.pc%$$ $cnext for use after $cref/make install/install/Instructions/Step 4: Installation/$$ $rnext $icode%builddir%/pkgconfig/cppad-uninstalled.pc%$$ $cnext for testing before $code make install$$ $tend $end cppad-20170000.3/omh/install/sacado_prefix.omh0000644000175200017650000000413313057470464020202 0ustar coincoin-web// $Id: sacado_prefix.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin sacado_prefix$$ $dollar @$$ $spell dir Sacado includedirs cmake CppAD hpp $$ $section Including the Sacado Speed Tests$$ $mindex prefix get$$ $head Purpose$$ CppAD includes speed comparisons for the AD package $href%http://trilinos.sandia.gov/packages/sacado%Sacado%$$; see $cref speed_sacado$$. $head sacado_prefix$$ If Sacado is installed on your system, you can specify a value for its install $icode sacado_prefix$$ on the $cref cmake$$ command line. The value of $icode sacado_prefix$$ must be such that, for one of the directories $icode dir$$ in $cref/cmake_install_includedirs/cmake/cmake_install_includedirs/$$, $codei% %sacado_prefix%/%dir%/Sacado.hpp %$$ is a valid way to reference to the include file $code Sacado.hpp$$; $head Speed Tests$$ If you include $icode sacado_prefix$$ on the $cref cmake$$ command line, you will be able to run the Sacado speed correctness tests by executing the following commands starting in the $cref/distribution directory/download/Distribution Directory/$$: $codei% cd build/speed/sacado make check_speed_sacado %$$ After executing $code make check_speed_sacado$$, you can run a specific Sacado speed test by executing the command $code ./speed_sacado$$; see $cref speed_main$$ for the meaning of the command line options to this program. $children% bin/get_sacado.sh %$$ $head get_sacado$$ If you are using Unix, you can download and install a copy of Sacado using $cref get_sacado.sh$$. The corresponding $icode sacado_prefix$$ would be $code build/prefix$$. $end cppad-20170000.3/omh/install/auto_tools.omh0000644000175200017650000003714713057470464017576 0ustar coincoin-web$Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin auto_tools$$ $escape $$ $dollar ^$$ $spell ctor testvector Eigen colpack num cxx boostvector inv fopenmp openmp cout Addr sizeof op_arg err_retu const printf avector.h Ipopt Ip gzip Linux fi exp_apx tgz gpl Dev sed cppad gprof config stdvector std ublas hpp adouble badiff usr cygdrive htm xml Dir xvzf gz workspace Makefile exe Cygwin Microsoft dsw CppAD Adolc Fadbad Sacado ls aclocal yum devel $$ $section Auto Tools Unix Test and Installation$$ $mindex speed profile prefix std vector boost eigen sparse internal sets ctor implicit explicit compile flags OpenMP postfix Adolc Fadbad Ipopt Sacado memory usage tape$$ $head Deprecated 2012-12-26$$ These install instructions have been deprecated and no improvements have been added since 2012. For example, this install procedure will not detect any of the $code c++11$$ extensions. You should use the $cref cmake$$ instructions to install CppAD. $head Distribution Directory$$ You must first obtain a copy of the CppAD distribution directory using the $cref download$$ instructions. The install instructions below correspond to the $cref/current version/download/Current Version/$$ which has distribution directory $code cppad-20121230$$. $head Work Directory$$ Create the directory $code cppad-20121230/build$$, which will be referred to as the build directory below. $head Configure$$ Execute the following command in the build directory: $codei% ./configure \ --prefix=%prefix_dir% \ --with-Documentation \ --with-%test%vector \ --with-deprecated \ MAX_NUM_THREADS=%max_num_threads% \ CXX_FLAGS=%cxx_flags% \ OPENMP_FLAGS=%openmp_flags% \ POSTFIX_DIR=%postfix_dir% \ ADOLC_DIR=%adolc_dir% \ BOOST_DIR=%boost_dir% \ EIGEN_DIR=%eigen_dir% \ FADBAD_DIR=%fadbad_dir% \ SADADO_DIR=%sacado_dir% \ IPOPT_DIR=%ipopt_dir% \ TAPE_ADDR_TYPE=%tape_addr_type% \ TAPE_ID_TYPE=%tape_id_type% %$$ where only the $code configure$$ line need appear; i.e., the entries in all of the other lines are optional. The text in italic is replaced values that you choose; see discussion below. $head make$$ CppAD has some object libraries that are used for its correctness tests. (Currently, none of these libraries get installed.) You can build these libraries by executing the command $codei% make %$$ in the build directory. $subhead Examples and Tests$$ Once you have executed the $code make$$ command, you can run the correctness and speed tests. $pre $$ The following command will build all the correctness and speed tests. In addition, it will run all the correctness tests: $codep make test $$ $pre $$ The following links describe how to build and run subsets of these tests: $table $cref/get_started/get_started.cpp/Running/$$ $cnext $title get_started.cpp$$ $rnext $cref/exp_apx_main/exp_apx_main.cpp/Running Tests/$$ $cnext $title exp_apx_main.cpp$$ $rnext $cref/example/example.cpp/Running Tests/$$ $cnext $title example.cpp$$ $rnext $cref/print_for_cout/print_for_cout.cpp/Running/$$ $cnext $title print_for_cout.cpp$$ $rnext $cref/speed_example/speed_example.cpp/Running Tests/$$ $cnext $title speed_example.cpp$$ $rnext $cref/speed_double/speed_double/Running Tests/$$ $cnext $title speed_double$$ $rnext $cref/speed_adolc/speed_adolc/Running Tests/$$ $cnext $title speed_adolc$$ $rnext $cref/speed_cppad/speed_cppad/Running Tests/$$ $cnext $title speed_cppad$$ $rnext $cref/speed_fadbad/speed_fadbad/Running Tests/$$ $cnext $title speed_fadbad$$ $rnext $cref/speed_sacado/speed_sacado/Running Tests/$$ $cnext $title speed_sacado$$ $tend In addition, you can run a large subset of correctness tests (that are not intended to be examples) by executing the following commands starting in the build directory: $codei% cd test_more make test %$$ $head Profiling CppAD$$ The CppAD derivative speed tests mentioned above can be profiled. You can test that the results computed during this profiling are correct by executing the following commands starting in the build directory: $codei% cd speed/profile make test %$$ After executing $code make test$$, you can run a profile speed test by executing the command $code ./profile$$; see $cref speed_main$$ for the meaning of the command line options to this program. $pre $$ After you have run a profiling speed test, you can then obtain the profiling results with $codei% gprof -b profile %$$ If you are using a windows operating system with Cygwin or MinGW, you may have to replace $code profile$$ by $code profile.exe$$ in the $code gprof$$ command above; i.e., $codep gprof -b profile.exe $$ In C++, template parameters and argument types become part of a routines's name. This can make the $code gprof$$ output hard to read (the routine names can be very long). You can remove the template parameters and argument types from the routine names by executing the following command $codep gprof -b profile | sed -f gprof.sed $$ If you are using a windows operating system with Cygwin or MinGW, you would need to use $codep gprof -b profile.exe | sed -f gprof.sed $$ $head prefix_dir$$ The default value for prefix directory is $code ^HOME$$ i.e., by default the CppAD include files will $cref/install/auto_tools/make install/$$ below $code ^HOME$$. If you want to install elsewhere, you will have to use this option. As an example of using the $codei%--prefix=%prefix_dir%$$ option, if you specify $codep ./configure --prefix=/usr/local $$ the CppAD include files will be installed in the directory $codei% /usr/local/include/cppad %$$ If $cref/--with-Documentation/auto_tools/--with-Documentation/$$ is specified, the CppAD documentation files will be installed in the directory $codei% /usr/local/share/doc/cppad-20121230 %$$ $head --with-Documentation$$ If the command line argument $code --with-Documentation$$ is specified, the CppAD documentation HTML and XML files are copied to the directory $codei% %prefix_dir%/share/doc/%postfix_dir%/cppad-20121230 %$$ (see $cref/postfix_dir/auto_tools/postfix_dir/$$). The top of the CppAD HTML documentation tree (with mathematics displayed as LaTex command) will be located at $codei% %prefix_dir%/share/doc/%postfix_dir%/cppad-20121230/cppad.htm %$$ and the top of the XML documentation tree (with mathematics displayed as MathML) will be located at $codei% %prefix_dir%/share/doc/%postfix_dir%/cppad-20121230/cppad.xml %$$ $head --with-testvector$$ The $cref/CPPAD_TESTVECTOR/testvector/$$ template class is used for many of the CppAD examples and tests. The default for this template class is $codei%CppAD::vector<%Scalar%>%$$. If one, and only one, of the following command line arguments is specified: $codep --with-stdvector --with-boostvector --with-eigenvector $$ the corresponding of the following template classes is used $codei% std::vector<%Scalar%> boost::numeric::ublas::vector<%Scalar%> Eigen::matrix<%Scalar%, Eigen::Dynamic, 1> %$$ See also, $cref/boost_dir/auto_tools/boost_dir/$$ and $cref/eigen_dir/auto_tools/eigen_dir/$$. $head --with-deprecated$$ If this configure argument is present, then all the $cref deprecated$$ features are included in the install. Otherwise, they are not included. $head max_num_threads$$ this specifies the value for the default value for the preprocessor symbol $cref/CPPAD_MAX_NUM_THREADS/multi_thread/CPPAD_MAX_NUM_THREADS/$$. It must be greater than or equal to four; i.e., $icode%max_num_threads% >= 4%$$. $head cxx_flags$$ If the command line argument $icode CompilerFlags$$ is present, it specifies compiler flags. For example, $codei% CXX_FLAGS="-Wall -ansi" %$$ would specify that warning flags $code -Wall$$ and $code -ansi$$ should be included in all the C++ compile commands. The error and warning flags chosen must be valid options for the C++ compiler. The default value for $icode CompilerFlags$$ is the empty string. $head openmp_flags$$ If the command line argument $icode OpenmpFlags$$ is present, it specifies the necessary flags so that the compiler will properly interpret OpenMP directives. For example, when using the GNU $code g++$$ compiler, the following setting includes the OpenMP tests: $codei% OPENMP_FLAGS=-fopenmp %$$ If you specify configure command, the CppAD OpenMP correctness and speed tests will be built; see $cref/threading/thread_test.cpp/Running Tests/threading/$$ multi-threading tests. $head postfix_dir$$ By default, the postfix directory is empty; i.e., there is no postfix directory. As an example of using the $codei%POSTFIX_DIR=%postfix_dir%$$ option, if you specify $codep ./configure --prefix=/usr/local POSTFIX_DIR=coin $$ the CppAD include files will be $cref/installed/auto_tools/make install/$$ in the directory $codei% /usr/local/include/coin/cppad %$$ If $cref/--with-Documentation/auto_tools/--with-Documentation/$$ is specified, the CppAD documentation files will be installed in the directory $codei% /usr/local/share/doc/coin/cppad-20121230 %$$ $head adolc_dir$$ If you have $href%https://projects.coin-or.org/ADOL-C%ADOL-C%$$ installed on your system, you can specify a value for $icode adolc_dir$$ in the $cref/configure/auto_tools/Configure/$$ command line. The value of $icode adolc_dir$$ must be such that $codei% %adolc_dir%/include/adolc/adouble.h %$$ is a valid way to reference $code adouble.h$$. In this case, you can run the Adolc speed correctness tests by executing the following commands starting in the build directory: $codei% cd speed/adolc make test %$$ After executing $code make test$$, you can run an Adolc speed tests by executing the command $code ./adolc$$; see $cref speed_main$$ for the meaning of the command line options to this program. Note that these speed tests assume Adolc has been configure with its sparse matrix computations enabled using $codei% --with-colpack=%colpack_dir% %$$ $subhead Linux$$ If you are using Linux, you will have to add $icode%adolc_dir%/lib%$$ to $code LD_LIBRARY_PATH$$. For example, if you use the $code bash$$ shell to run your programs, you could include $codei% LD_LIBRARY_PATH=%adolc_dir%/lib:^{LD_LIBRARY_PATH} export LD_LIBRARY_PATH %$$ in your $code ^HOME/.bash_profile$$ file. $subhead Cygwin$$ If you are using Cygwin, you will have to add to following lines to the file $code .bash_profile$$ in your home directory: $codei% PATH=%adolc_dir%/bin:^{PATH} export PATH %$$ in order for Adolc to run properly. If $icode adolc_dir$$ begins with a disk specification, you must use the Cygwin format for the disk specification. For example, if $code d:/adolc_base$$ is the proper directory, $code /cygdrive/d/adolc_base$$ should be used for $icode adolc_dir$$. $head boost_dir$$ If the command line argument $codei% BOOST_DIR=%boost_dir% %$$ is present, it must be such that files $codei% %boost_dir%/include/boost/numeric/ublas/vector.hpp %boost_dir%/include/boost/thread.hpp %$$ are present. In this case, these files will be used by CppAD. See also, $cref/--with-boostvector/auto_tools/--with-testvector/$$ $head eigen_dir$$ If you have $href%http://eigen.tuxfamily.org%Eigen%$$ installed on your system, you can specify a value for $icode eigen_dir$$. It must be such that $codei% %eigen_dir%/include/Eigen/Core %$$ is a valid include file. In this case CppAD will compile and test the Eigen examples; e.g., $cref eigen_array.cpp$$. See also, $cref/--with-eigenvector/auto_tools/--with-testvector/$$ $head fadbad_dir$$ If you have $href% http://www.fadbad.com/% Fadbad 2.1 %$$ installed on your system, you can specify a value for $icode fadbad_dir$$. It must be such that $codei% %fadbad_dir%/include/FADBAD++/badiff.h %$$ is a valid reference to $code badiff.h$$. In this case, you can run the Fadbad speed correctness tests by executing the following commands starting in the build directory: $codei% cd speed/fadbad make test %$$ After executing $code make test$$, you can run a Fadbad speed tests by executing the command $code ./fadbad$$; see $cref speed_main$$ for the meaning of the command line options to this program. $head ipopt_dir$$ If you have $href% http://www.coin-or.org/projects/Ipopt.xml% Ipopt %$$ installed on your system, you can specify a value for $icode ipopt_dir$$. It must be such that $codei% %ipopt_dir%/include/coin/IpIpoptApplication.hpp %$$ is a valid reference to $code IpIpoptApplication.hpp$$. In this case, the CppAD interface to Ipopt $cref/examples/cppad_ipopt_nlp/Example/$$ can be built and tested by executing the following commands starting in the build directory: $codei% make # cd cppad_ipopt/example make test # cd ../test make test # cd ../speed make test %$$ Once this has been done, you can execute the program $code ./speed$$ in the $code build/cppad_ipopt/speed$$ directory; see $cref ipopt_ode_speed.cpp$$. $head sacado_dir$$ If you have $href% http://trilinos.sandia.gov/packages/sacado/% Sacado %$$ installed on your system, you can specify a value for $icode sacado_dir$$. It must be such that $codei% %sacado_dir%/include/Sacado.hpp %$$ is a valid reference to $code Sacado.hpp$$. In this case, you can run the Sacado speed correctness tests by executing the following commands starting in the build directory: $codei% cd speed/sacado make test %$$ After executing $code make test$$, you can run a Sacado speed tests by executing the command $code ./sacado$$; see $cref speed_main$$ for the meaning of the command line options to this program. $head tape_addr_type$$ If the command line argument $icode tape_addr_type$$ is present, it specifies the type used for address in the AD recordings (tapes). The valid values for this argument are $code unsigned short int$$, $code unsigned int$$, $code size_t$$. The smaller the value of $icode%sizeof(%tape_addr_type%)%$$, the less memory is used. On the other hand, the value $codei% std::numeric_limits<%tape_addr_type%>::max() %$$ must be larger than any of the following: $cref/size_op/seq_property/size_op/$$, $cref/size_op_arg/seq_property/size_op_arg/$$, $cref/size_par/seq_property/size_text/$$, $cref/size_par/seq_property/size_par/$$, $cref/size_par/seq_property/size_VecAD/$$. $head tape_id_type$$ If the command line argument $icode tape_id_type$$ is present, it specifies the type used for identifying tapes. The valid values for this argument are $code unsigned short int$$, $code unsigned int$$, $code size_t$$. The smaller the value of $icode%sizeof(%tape_id_type%)%$$, the less memory is used. On the other hand, the value $codei% std::numeric_limits<%tape_id_type%>::max() %$$ must be larger than the maximum number of tapes per thread times $cref/max_num_threads/auto_tools/max_num_threads/$$. $head make install$$ Once you are satisfied that the tests are giving correct results, you can install CppAD into easy to use directories by executing the command $codep make install $$ This will install CppAD in the location specified by $cref/prefix_dir/auto_tools/prefix_dir/$$. You must have permission to write in the $icode prefix_dir$$ directory to execute this command. You may optionally specify a destination directory for the install; i.e., $codei% make install DESTDIR=%DestinationDirectory% %$$ $end cppad-20170000.3/omh/install/ipopt_prefix.omh0000644000175200017650000000371513057470464020110 0ustar coincoin-web// $Id: ipopt_prefix.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin ipopt_prefix$$ $dollar @$$ $spell IpIpopt dir cppad cmake includedirs hpp $$ $section Including the cppad_ipopt Library and Tests$$ $mindex ipopt cppad prefix get$$ $head Purpose$$ Includes the $cref cppad_ipopt_nlp$$ example and tests as well as installing the $code cppad_ipopt$$ library during the $code make install$$ step. $head ipopt_prefix$$ If you have $href%http://www.coin-or.org/projects/Ipopt.xml%Ipopt%$$ installed on your system, you can specify the value for $icode ipopt_prefix$$ on the $cref cmake$$ command line. The value of $icode ipopt_prefix$$ must be such that, for one of the directories $icode dir$$ in $cref/cmake_install_includedirs/cmake/cmake_install_includedirs/$$, $codei% %ipopt_prefix%/%dir%/coin/IpIpoptApplication.hpp %$$ is a valid way to reference to the include file $code IpIpoptApplication.hpp$$. $head Examples and Tests$$ If you include $icode ipopt_prefix$$ on the $cref cmake$$ command line, you will be able to run the Ipopt examples and tests by executing the following commands starting in the $cref/distribution directory/download/Distribution Directory/$$: $codei% cd cppad_ipopt make check_ipopt %$$ $children% bin/get_ipopt.sh %$$ $head get_ipopt$$ If you are using Unix, you can download and install a copy of Ipopt using $cref get_ipopt.sh$$. The corresponding $icode ipopt_prefix$$ would be $code build/prefix$$. $end cppad-20170000.3/omh/install/colpack_prefix.omh0000644000175200017650000000435513057470464020372 0ustar coincoin-web// $Id: colpack_prefix.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin colpack_prefix$$ $dollar @$$ $spell datadir cppad.hpp namespace std CppAD includedirs colpack cmake dir Jacobians $$ $section Including the ColPack Sparsity Calculations$$ $mindex prefix get$$ $head Purpose$$ If you specify a $icode colpack_prefix$$ on the $cref/cmake command/cmake/CMake Command/$$ line, the CppAD $cref sparse_jacobian$$ calculations use the $href%http://cscapes.cs.purdue.edu/dox/ColPack/html%ColPack%$$ package. $head colpack_prefix$$ If ColPack is installed on your system, you can specify a value for its install $icode colpack_prefix$$ on the $cref cmake$$ command line. The value of $icode colpack_prefix$$ must be such that, for one of the directories $icode dir$$ in $cref/cmake_install_includedirs/cmake/cmake_install_includedirs/$$, $codei% %colpack_prefix%/%dir%/ColPack/ColPackHeaders.h %$$ is a valid way to reference to the include file $code ColPackHeaders.h$$. $head cppad_lib$$ The ColPack header files has a $codei% using namespace std %$$ at the global level. For this reason, CppAD does not include these files. It is therefore necessary to link the object library $code cppad_lib$$ when using ColPack. $children%example/colpack_jac.cpp %example/colpack_hes.cpp %bin/get_colpack.sh %$$ $head Example$$ The file $cref colpack_jac.cpp$$ ($cref colpack_hes.cpp$$) contains an example and test of using ColPack to compute the coloring for sparse Jacobians (Hessians). It returns true, if it succeeds and false otherwise. $head get_colpack$$ If you are using Unix, you can download and install a copy of ColPack using $cref get_colpack.sh$$. The corresponding $icode colpack_prefix$$ would be $code build/prefix$$. $end cppad-20170000.3/omh/install/cmake_check.omh0000644000175200017650000000440213057470464017607 0ustar coincoin-web// $Id: cmake_check.omh 3778 2016-01-01 01:55:33Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin cmake_check$$ $spell nlp cppad makefiles ipopt CppAD cmake nmake $$ $section Checking the CppAD Examples and Tests$$ $head Purpose$$ After you configure your system with the $cref/cmake command/cmake/CMake Command/$$ you can run the CppAD example and tests to make sure that CppAD functions properly on your system. $head Check All$$ In the $code build$$ subdirectory of the $cref/distribution directory/download/Distribution Directory/$$ execute the command $codep make check $$ This will build and run all of the tests that are support by your system and the $cref cmake$$ command options. $subhead Windows$$ If you created $code nmake$$ makefiles, you will have to use $code nmake$$ instead of $code make$$ in the commands above and below; see $cref/windows file extraction and testing /download /Windows File Extraction and Testing /$$. $head Subsets$$ It is possible to build and run the following subsets of the examples and tests: $table Command $cnext Description $rnext $code make check_compare_c$$ $cnext $tref compare_c$$ $rnext $code make check_introduction$$ $cnext the programs in the $cref Introduction$$ $rnext $code make check_example$$ $cnext most of the $cref Example$$ programs $rnext $code make check_print_for$$ $cnext the $cref PrintFor$$ command $rnext $code make check_test_more$$ $cnext correctness tests that are not examples $rnext $code make check_multi_thread$$ $cnext $cref multi_thread$$ tests (run correctness only) $rnext $code make check_speed$$ $cnext single threading $cref speed$$ tests (run correctness only) $rnext $code make check_cppad_ipopt$$ $cnext the $cref cppad_ipopt_nlp$$ speed and correctness tests $rnext $tend $end cppad-20170000.3/omh/install/fadbad_prefix.omh0000644000175200017650000000410013057470464020143 0ustar coincoin-web// $Id: fadbad_prefix.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin fadbad_prefix$$ $dollar @$$ $spell dir CppAD fadbad cmake badiff includedirs $$ $section Including the FADBAD Speed Tests$$ $mindex prefix get$$ $head Purpose$$ CppAD includes speed comparisons for the AD package $href%http://www.fadbad.com%FADBAD%$$; see $cref speed_fadbad$$. $head fadbad_prefix$$ If FADBAD is installed on your system, you can specify a value for its install $icode fadbad_prefix$$ on the $cref cmake$$ command line. The value of $icode fadbad_prefix$$ must be such that, for one of the directories $icode dir$$ in $cref/cmake_install_includedirs/cmake/cmake_install_includedirs/$$, $codei% %fadbad_prefix%/%dir%/FADBAD++/badiff.h %$$ is a valid way to reference to the include file $code badiff.h$$; $head Speed Tests$$ If you include $icode fadbad_prefix$$ on the $cref cmake$$ command line, you will be able to run the FADBAD speed correctness tests by executing the following commands starting in the $cref/distribution directory/download/Distribution Directory/$$: $codei% cd build/speed/fadbad make check_speed_fadbad %$$ After executing $code make check$$, you can run a specific FADBAD speed test by executing the command $code ./speed_fadbad$$; see $cref speed_main$$ for the meaning of the command line options to this program. $children% bin/get_fadbad.sh %$$ $head get_fadbad$$ If you are using Unix, you can download and install a copy of Fadbad using $cref get_fadbad.sh$$. The corresponding $icode fadbad_prefix$$ would be $code build/prefix$$. $end cppad-20170000.3/omh/install/adolc_prefix.omh0000644000175200017650000000751313057470464020037 0ustar coincoin-web// $Id: adolc_prefix.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin adolc_prefix$$ $dollar @$$ $spell dir mul cmake includedirs CppAD adolc adouble colpack cygdrive Cygwin bashrc $$ $section Including the ADOL-C Examples and Tests$$ $mindex adolc prefix get$$ $head Purpose$$ CppAD includes examples and tests that can use the AD package $href%https://projects.coin-or.org/ADOL-C%ADOL-C%$$. The includes speed comparison with other AD packages; see $cref speed_adolc$$. It also includes examples that combine ADOL-C with CppAD; see $table $rref base_adolc.hpp$$ $rref mul_level_adolc.cpp$$ $rref mul_level_adolc_ode.cpp$$ $tend $head adolc_prefix$$ If ADOL-C is installed on your system, you can specify a value for its install $icode adolc_prefix$$ on the $cref cmake$$ command line. The value of $icode adolc_prefix$$ must be such that, for one of the directories $icode dir$$ in $cref/cmake_install_includedirs/cmake/cmake_install_includedirs/$$, $codei% %adolc_prefix%/%dir%/adolc/adouble.h %$$ is a valid way to reference to the include file $code adouble.h$$; Note that CppAD assumes ADOL-C has been configured with its sparse matrix computations enabled; i.e, using $codei% --with-colpack=%adolc_prefix% %$$ In other words ColPack is installed and with the same prefix as ACOL-C; see $cref get_colpack.sh$$. $head Examples$$ If you include $icode adolc_prefix$$ on the $cref cmake$$ command line, you will be able to run the ADOL-C examples listed above by executing the following commands starting in the $cref/distribution directory/download/Distribution Directory/$$: $codei% cd build/example make check_example %$$ If you do this, you will see an indication that the examples $code mul_level_adolc$$ and $code mul_level_adolc_ode$$ have passed their correctness check. $head Speed Tests$$ If you include $icode adolc_prefix$$ on the $cref cmake$$ command line, you will be able to run the ADOL-C speed correctness tests by executing the following commands starting in the $cref/distribution directory/download/Distribution Directory/$$: $codei% cd build/speed/adolc make check_speed_adolc %$$ After executing $code make check_speed_adolc$$, you can run a specific ADOL-C speed tests by executing the command $code ./speed_adolc$$; see $cref speed_main$$ for the meaning of the command line options to this program. $head Unix$$ If you are using Unix, you may have to add $icode adolc_prefix$$ to $code LD_LIBRARY_PATH$$. For example, if you use the $code bash$$ shell to run your programs, you could include $codei% LD_LIBRARY_PATH=%adolc_prefix%/lib:@{LD_LIBRARY_PATH} export LD_LIBRARY_PATH %$$ in your $code @HOME/.bashrc$$ file. $head Cygwin$$ If you are using Cygwin, you may have to add to following lines to the file $code .bashrc$$ in your home directory: $codei% PATH=%adolc_prefix%/bin:@{PATH} export PATH %$$ in order for ADOL-C to run properly. If $icode adolc_prefix$$ begins with a disk specification, you must use the Cygwin format for the disk specification. For example, if $code d:/adolc_base$$ is the proper directory, $code /cygdrive/d/adolc_base$$ should be used for $icode adolc_prefix$$. $children% bin/get_adolc.sh %$$ $head get_adolc$$ If you are using Unix, you can download and install a copy of Adolc using $cref get_adolc.sh$$. The corresponding $icode adolc_prefix$$ would be $code build/prefix$$. $end cppad-20170000.3/omh/install/cmake.omh0000644000175200017650000003057613057470464016465 0ustar coincoin-web$Id: cmake.omh 3857 2016-12-23 13:08:43Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin cmake$$ $escape $$ $spell cstdint uint pkgconfig ctor op arg sizeof testvector std Wshadow namespace adouble colpack dir makefile usr hpp xml ipopt libcppad CppAD txt Microsoft Makefiles cmake Dcmake cppad adolc boost eigen fadbad sacado datadir docdir includedirs libdirs cxx max num postfix id addr grep $$ $section Using CMake to Configure CppAD$$ $mindex makefile install prefix postfix include directories lib datadir documentation package compile flags profile maximum number threads sparsity internal structure vector sets memory usage tape ctor implicit explicit$$ $head The CMake Program$$ The $href%http://www.cmake.org/cmake/help/install.html%cmake%$$ program enables one to create a single set of scripts, called $code CMakeLists.txt$$, that can be used to test and install a program on Unix, Microsoft, or Apple operating systems. For example, one can use it to automatically generate Microsoft project files. $head CMake Command$$ The command below assumes that $code cmake$$ is in your execution path with version greater than or equal 2.8. If not, you can put the path to the version of $code cmake$$ in font the command. Only the $code cmake$$ command and the path to the distribution directory ($code ..$$ at the end of the command below) are required. In other words, the first and last lines below are required and all of the other lines are optional. $subhead Build Directory$$ Create a $code build$$ subdirectory of the $cref/distribution directory/download/Distribution Directory/$$, change into the $code build$$ directory, and execute the following command: $codei% cmake %% \ -D CMAKE_VERBOSE_MAKEFILE=%cmake_verbose_makefile% \ -G %generator% \ \ -D cppad_prefix=%cppad_prefix% \ -D cppad_postfix=%cppad_postfix% \ \ -D cmake_install_includedirs=%cmake_install_includedirs% \ -D cmake_install_libdirs=%cmake_install_libdirs% \ \ -D cmake_install_datadir=%cmake_install_datadir% \ -D cmake_install_docdir=%cmake_install_docdir% \ \ -D adolc_prefix=%adolc_prefix% \ -D colpack_prefix=%colpack_prefix% \ -D eigen_prefix=%eigen_prefix% \ -D fadbad_prefix=%fadbad_prefix% \ -D ipopt_prefix=%ipopt_prefix% \ -D sacado_prefix=%sacado_prefix% \ \ -D cppad_cxx_flags=%cppad_cxx_flags% \ -D cppad_profile_flag=%cppad_profile_flag% \ \ -D cppad_testvector=%cppad_testvector% \ -D cppad_max_num_threads=%cppad_max_num_threads% \ -D cppad_tape_id_type=%cppad_tape_id_type% \ -D cppad_tape_addr_type=%cppad_tape_addr_type% \ -D cppad_deprecated=%cppad_deprecated% \ \ .. %$$ $head make check$$ Important information about the CppAD configuration is output by this command. If you have the $code grep$$ program, and store the output in $code cmake.log$$, you can get a list of all the test options with the command: $codep grep 'make check' cmake.log $$ $head cmake_verbose_makefile$$ This value should be either $code YES$$ or $code NO$$. The default value, when it is not present, is $code NO$$. If it is $code YES$$, then the output of the $code make$$ commands will include all of the files and flags used to run the compiler and linker. This can be useful for seeing how to compile and link your own applications. $head generator$$ The CMake program is capable of generating different kinds of files. Below is a table with a few of the possible files $table $icode generator$$ $cnext Description $rnext $code "Unix Makefiles"$$ $cnext make files for unix operating system $rnext $code "NMake Makefiles"$$ $cnext make files for Visual Studio $tend Other generator choices are available; see the cmake $href%http://www.cmake.org/cmake/help/cmake2.6docs.html#section_Generators% generators%$$ documentation. $head cppad_prefix$$ This is the top level absolute path below which all of the CppAD files are installed by the command $codei% make install %$$ For example, if $icode cppad_prefix$$ is $code /usr$$, $icode cmake_install_includedirs$$ is $code include$$, and $icode cppad_postfix$$ is not specified, the file $code cppad.hpp$$ is installed in the location $codei% /usr/include/cppad/cppad.hpp %$$ The default value for $icode cppad_prefix$$ is $code /usr$$. $head cppad_postfix$$ This is the bottom level relative path below which all of the CppAD files are installed. For example, if $icode cppad_prefix$$ is $code /usr$$, $icode cmake_install_includedirs$$ is $code include$$, and $icode cppad_postfix$$ is $code coin$$, the file $code cppad.hpp$$ is installed in the location $codei% /usr/include/coin/cppad/cppad.hpp %$$ The default value for $icode cppad_postfix$$ is empty; i.e, there is no bottom level relative directory for the installed files. $head cmake_install_includedirs$$ This is one directory, or a list of directories separated by spaces or by semi-colons. This first entry in the list is the middle level relative path below which the CppAD include files are installed. The entire list is used for searching for include files. For example, if $icode cppad_prefix$$ is $code /usr$$, $icode cmake_install_includedirs$$ is $code include$$, and $icode cppad_postfix$$ is not specified, the file $code cppad.hpp$$ is installed in the location $codei% /usr/include/cppad/cppad.hpp %$$ The default value for this directory list is $code include$$. $head cmake_install_libdirs$$ This is one directory, or a list of directories separated by spaces or by semi-colons. This first entry in the list is the middle level relative path below which the CppAD library files are installed. The entire list is used for searching for library files. For example, if $icode cppad_prefix$$ is $code /usr$$, $icode cmake_install_libdirs$$ is $code lib$$, $icode cppad_postfix$$ is not specified, and $icode ipopt_prefix$$ is specified, the file $code libcppad_ipopt.a$$ is installed in the location $codei% /usr/lib/libcppad_ipopt.a %$$ The default value for this directory list is $code lib$$. $head cmake_install_datadir$$ This is the middle level relative path below which the CppAD data files are installed. For example, if $icode cppad_prefix$$ is $code /usr$$, $icode cmake_install_datadir$$ is $code share$$, and $icode cppad_postfix$$ is not specified, the $cref pkgconfig$$ file $code cppad.pc$$ is installed in the location $codei% /usr/share/pkgconfig/cppad.pc %$$ The default value for $icode cmake_install_datadir$$ is $code share$$. $head cmake_install_docdir$$ This is the middle level relative path below which the CppAD documentation files are installed. For example, if $icode cppad_prefix$$ is $code /usr$$, $icode cmake_install_docdir$$ is $code share/doc$$, and $icode cppad_postfix$$ is not specified, the file $code cppad.xml$$ is installed in the location $codei% /usr/share/doc/cppad/cppad.xml %$$ There is no default value for $icode cmake_install_docdir$$. If it is not specified, the documentation files are not installed. $head package_prefix$$ Each of these packages corresponds to optional CppAD examples, that can be compiled and tested if the corresponding prefix is provided: $table $rref adolc_prefix$$ $rref colpack_prefix$$ $rref eigen_prefix$$ $rref fadbad_prefix$$ $rref ipopt_prefix$$ $rref sacado_prefix$$ $tend $head cppad_cxx_flags$$ This specifies the addition compiler flags, besides the debug and release flags, that are used when compiling the CppAD examples and tests. The default value for these flags is the empty string $code ""$$. These flags must be valid for the C++ compiler on your system. For example, if you are using $code g++$$ you could specify $codep -D cppad_cxx_flags="-Wall -ansi -pedantic-errors -std=c++11 -Wshadow" $$ $subhead C++11$$ In order for the compiler to take advantage of features that are new in C++11, the $icode cppad_cxx_flags$$ must enable these features. The compiler may still be used with a flag that disables the new features (unless it is a Microsoft compiler; i.e., $code _MSC_VER$$ is defined). $head cppad_profile_flag$$ This specifies an addition compiler and link flag that is used for $cref/profiling/speed_main/package/profile/$$ the speed tests. A profile version of the speed test is only build when this argument is present. $subhead Eigen and Fadbad$$ The packages $cref/eigen/eigen_prefix/$$ and $cref/fadbad/fadbad_prefix/$$ currently generate a lot of shadowed variable warnings. If the $code -Wshadow$$ flag is present, it is automatically removed when compiling examples and test that use these packages. $head cppad_testvector$$ See $tref cppad_testvector$$. $head cppad_max_num_threads$$ The value $icode cppad_max_num_threads$$ must be greater than or equal to four; i.e., $icode%max_num_threads% >= 4%$$. The current default value for $icode cppad_max_num_threads$$ is 48, but it may change in future versions of CppAD. The value $icode cppad_max_num_threads$$ in turn specifies the default value for the preprocessor symbol $cref/CPPAD_MAX_NUM_THREADS/multi_thread/CPPAD_MAX_NUM_THREADS/$$. $head cppad_tape_id_type$$ The type $icode cppad_tape_id_type$$ is used for identifying different tapes. The valid values for this type are $code unsigned char$$, $code unsigned short int$$, $code unsigned int$$, and $code size_t$$. The smaller the value of $codei%sizeof(%cppad_tape_id_type%)%$$, the less memory is used. On the other hand, the value $codei% std::numeric_limits<%cppad_tape_id_type%>::max() %$$ must be larger than the maximum number of tapes used by one thread times $cref/CPPAD_MAX_NUM_THREADS/multi_thread/CPPAD_MAX_NUM_THREADS/$$. $subhead cstdint$$ If all of the following $code cstdint$$ types are defined, they can also be used as the value of $icode cppad_tape_addr_type$$: $code uint8_t$$, $code uint16_t$$, $code uint32_t$$, $code uint64_t$$. $head cppad_tape_addr_type$$ The type $icode cppad_tape_addr_type$$ is used for address in the AD recordings (tapes). The valid values for this argument are $code unsigned char$$, $code unsigned short int$$, $code unsigned int$$, $code size_t$$. The smaller the value of $codei%sizeof(%cppad_tape_addr_type%)%$$, the less memory is used. On the other hand, the value $codei% std::numeric_limits<%cppad_tape_addr_type%>::max() %$$ must be larger than any of the following: $cref/size_op/seq_property/size_op/$$, $cref/size_op_arg/seq_property/size_op_arg/$$, $cref/size_par/seq_property/size_text/$$, $cref/size_par/seq_property/size_par/$$, $cref/size_par/seq_property/size_VecAD/$$. $subhead cstdint$$ If all of the following $code cstdint$$ types are defined, they can also be used as the value of $icode cppad_tape_addr_type$$: $code uint8_t$$, $code uint16_t$$, $code uint32_t$$, $code uint64_t$$. $head cppad_deprecated$$ The default value for $icode cppad_deprecated$$ is $code NO$$. If it is $code YES$$, then all the CppAD $cref deprecated$$ features are included in the $cref/installation/install/Instructions/Step 4: Installation/$$. Otherwise, some of the deprecated features may be excluded from the installation. (The intention here is to exclude more deprecated features as time marches on.) $children% omh/install/adolc_prefix.omh% omh/install/colpack_prefix.omh% omh/install/eigen_prefix.omh% omh/install/fadbad_prefix.omh% omh/install/ipopt_prefix.omh% omh/install/sacado_prefix.omh% omh/install/testvector.omh %$$ $end cppad-20170000.3/omh/lu_factor_hpp.omh0000644000175200017650000000153113057470464016551 0ustar coincoin-web$Id: lu_factor_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin lu_factor.hpp$$ $spell Lu ifndef endif $$ $section Source: LuFactor$$ $mindex source$$ $code # ifndef CPPAD_LU_FACTOR_HPP $pre $$ # define CPPAD_LU_FACTOR_HPP $srcfile%cppad/utility/lu_factor.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/addon.omh0000644000175200017650000000461613057470464015020 0ustar coincoin-web// $Id$ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin addon$$ $spell Addons addon libdir includedir libcppad adcomp CppAD cppad.hpp ons namespace cg pycppad $$ $section CppAD Addons$$ $head Name$$ Each CppAD addon has a short name which we denote by $icode name$$ below, a longer name $icode longer$$ and a $icode description$$: $table $icode name$$ $pre $$ $cnext $icode longer$$ $pre $$ $cnext $icode description$$ $rnext $href%https://github.com/joaoleal/CppADCodeGen/%cg%$$ $cnext $code CppADCodeGen$$ $cnext C++ Source Code Generation of CppAD Derivative Calculations $rnext $href%http://www.seanet.com/~bradbell/pycppad/pycppad.htm%py%$$ $cnext $code pycppad$$ $cnext A Python Interface to CppAD $rnext $href%https://github.com/kaskr/adcomp%tmb%$$ $cnext $code adcomp$$ $cnext An R Interface to CppAD with Random Effects Modeling Utilities $rnext $href%http://moby.ihme.washington.edu/bradbell/cppad_mixed%mixed%$$ $cnext $code cppad_mixed$$ $cnext A C++ Interface to Random Effects Laplace Approximation $tend $head Include Files$$ If $icode includedir$$ is the directory where the include files are installed, the file $codei% %includedir%/cppad/%name%.hpp %$$ and the directory $codei% %includedir%/cppad/%name% %$$ are reserved for use by the $icode name$$ addon. $head Library Files$$ If $icode libdir$$ is the directory where CppAD library files are installed, files with the name $codei% %libdir%/libcppad_%name%.%ext% %libdir%/libcppad_%name%_%anything%.%ext% %$$ where $icode anything$$ and $icode ext$$ are arbitrary, are reserved for use by the $icode name$$ addon. $head Preprocessor Symbols$$ C++ preprocessor symbols that begin with $codei% CPPAD_%NAME%_ %$$ where $icode NAME$$ is a upper-case version of $icode name$$, are reserved for use by the $icode name$$ addon. $head Namespace$$ The C++ namespace $codei% CppAD::%name% %$$ is reserved for use by the $icode name$$ addon. $end cppad-20170000.3/omh/det_grad_33_hpp.omh0000644000175200017650000000155513057470464016657 0ustar coincoin-web$Id: det_grad_33_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin det_grad_33.hpp$$ $spell det_grad_33 ifndef endif $$ $section Source: det_grad_33$$ $mindex source$$ $code # ifndef CPPAD_DET_GRAD_33_HPP $pre $$ # define CPPAD_DET_GRAD_33_HPP $srcfile%cppad/speed/det_grad_33.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/example_list.omh0000644000175200017650000001557113057470464016423 0ustar coincoin-web$Id: example_list.omh 3855 2016-12-19 00:30:54Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin General$$ $spell Cpp $$ $section General Examples$$ $mindex realistic$$ $head Description$$ Most of the examples in CppAD are part of the documentation for a specific feature; for example, $cref add.cpp$$ is an example using the $cref/addition operator/ad_binary/$$. The examples list in this section are of a more general nature. $childtable% example/ad_fun.cpp% example/ad_in_c.cpp% example/conj_grad.cpp% cppad/example/cppad_eigen.hpp % example/hes_minor_det.cpp% example/hes_lu_det.cpp% example/interface2c.cpp% example/jac_minor_det.cpp% example/jac_lu_det.cpp% omh/mul_level.omh% example/ode_stiff.cpp% example/mul_level_ode.cpp% example/mul_level_adolc_ode.cpp% example/ode_taylor.cpp% example/stack_machine.cpp %$$ $end ----------------------------------------------------------------------------- $begin ExampleUtility$$ $spell CppAD $$ $section Utility Routines used by CppAD Examples$$ $childtable% example/example.cpp% speed/example/example.cpp% example/lu_vec_ad.cpp %$$ $end ----------------------------------------------------------------------------- $begin ListAllExamples$$ $spell CppAD $$ $section List of All the CppAD Examples$$ $comment omit: TestOne.cpp OneCase.cpp lu_vec_ad.cpp $$ $table $rref a11c_bthread.cpp$$ $rref a11c_openmp.cpp$$ $rref a11c_pthread.cpp$$ $rref abort_recording.cpp$$ $rref Abs.cpp$$ $rref acos.cpp$$ $rref acosh.cpp$$ $rref ad_assign.cpp$$ $rref ad_ctor.cpp$$ $rref add.cpp$$ $rref AddEq.cpp$$ $rref ad_fun.cpp$$ $rref ad_in_c.cpp$$ $rref ad_input.cpp$$ $rref ad_output.cpp$$ $rref asin.cpp$$ $rref asinh.cpp$$ $rref atan2.cpp$$ $rref atan.cpp$$ $rref atanh.cpp$$ $rref atomic_eigen_cholesky.cpp$$ $rref atomic_eigen_cholesky.hpp$$ $rref atomic_eigen_mat_inv.cpp$$ $rref atomic_eigen_mat_inv.hpp$$ $rref atomic_eigen_mat_mul.cpp$$ $rref atomic_eigen_mat_mul.hpp$$ $rref checkpoint_extended_ode.cpp$$ $rref atomic_for_sparse_hes.cpp$$ $rref atomic_for_sparse_jac.cpp$$ $rref atomic_forward.cpp$$ $rref atomic_get_started.cpp$$ $rref atomic_mat_mul.cpp$$ $rref atomic_mat_mul.hpp$$ $rref atomic_mul_level.cpp$$ $rref atomic_norm_sq.cpp$$ $rref checkpoint_ode.cpp$$ $rref atomic_reciprocal.cpp$$ $rref atomic_reverse.cpp$$ $rref atomic_rev_sparse_hes.cpp$$ $rref atomic_rev_sparse_jac.cpp$$ $rref atomic_set_sparsity.cpp$$ $rref atomic_tangent.cpp$$ $rref azmul.cpp$$ $rref base_adolc.hpp$$ $rref base_alloc.hpp$$ $rref base_complex.hpp$$ $rref base_require.cpp$$ $rref bender_quad.cpp$$ $rref bool_fun.cpp$$ $rref bool_sparsity.cpp$$ $rref capacity_order.cpp$$ $rref change_param.cpp$$ $rref check_for_nan.cpp$$ $rref check_numeric_type.cpp$$ $rref checkpoint.cpp$$ $rref check_simple_vector.cpp$$ $rref colpack_hes.cpp$$ $rref colpack_jac.cpp$$ $rref compare_change.cpp$$ $rref compare.cpp$$ $rref complex_poly.cpp$$ $rref cond_exp.cpp$$ $rref conj_grad.cpp$$ $rref cos.cpp$$ $rref cosh.cpp$$ $rref cppad_eigen.hpp$$ $rref cppad_vector.cpp$$ $rref dependency.cpp$$ $rref det_by_lu.cpp$$ $rref det_by_minor.cpp$$ $rref det_of_minor.cpp$$ $rref div.cpp$$ $rref div_eq.cpp$$ $rref eigen_array.cpp$$ $rref eigen_det.cpp$$ $rref eigen_plugin.hpp$$ $rref elapsed_seconds.cpp$$ $rref equal_op_seq.cpp$$ $rref erf.cpp$$ $rref error_handler.cpp$$ $rref example.cpp$$ $rref exp.cpp$$ $rref expm1.cpp$$ $rref expm1.cpp$$ $rref for_one.cpp$$ $rref for_sparse_hes.cpp$$ $rref for_sparse_jac.cpp$$ $rref for_two.cpp$$ $rref forward.cpp$$ $rref forward_dir.cpp$$ $rref forward_order.cpp$$ $rref fun_assign.cpp$$ $rref fun_check.cpp$$ $rref get_started.cpp$$ $rref harmonic.cpp$$ $rref harmonic_time.cpp$$ $rref harmonic_work.cpp$$ $rref hes_lagrangian.cpp$$ $rref hes_lu_det.cpp$$ $rref hes_minor_det.cpp$$ $rref hessian.cpp$$ $rref hes_times_dir.cpp$$ $rref independent.cpp$$ $rref index_sort.cpp$$ $rref integer.cpp$$ $rref interface2c.cpp$$ $rref interp_onetape.cpp$$ $rref interp_retape.cpp$$ $rref ipopt_solve_get_started.cpp$$ $rref ipopt_solve_ode_inverse.cpp$$ $rref ipopt_solve_retape.cpp$$ $rref jac_lu_det.cpp$$ $rref jac_minor_det.cpp$$ $rref jacobian.cpp$$ $rref log10.cpp$$ $rref log1p.cpp$$ $rref log.cpp$$ $rref lu_factor.cpp$$ $rref lu_invert.cpp$$ $rref lu_ratio.cpp$$ $rref lu_solve.cpp$$ $rref lu_vec_ad_ok.cpp$$ $rref mat_sum_sq.cpp$$ $rref mul.cpp$$ $rref mul_eq.cpp$$ $rref mul_level_adolc.cpp$$ $rref mul_level_adolc_ode.cpp$$ $rref mul_level.cpp$$ $rref mul_level_ode.cpp$$ $rref multi_newton.cpp$$ $rref multi_newton_time.cpp$$ $rref multi_newton_work.cpp$$ $rref nan.cpp$$ $rref near_equal.cpp$$ $rref near_equal_ext.cpp$$ $rref number_skip.cpp$$ $rref numeric_type.cpp$$ $rref num_limits.cpp$$ $rref ode_err_control.cpp$$ $rref ode_err_maxabs.cpp$$ $rref ode_evaluate.cpp$$ $rref ode_gear_control.cpp$$ $rref ode_gear.cpp$$ $rref ode_stiff.cpp$$ $rref ode_taylor.cpp$$ $rref optimize_compare_op.cpp$$ $rref optimize_conditional_skip.cpp$$ $rref optimize_cumulative_sum.cpp$$ $rref optimize_forward_active.cpp$$ $rref optimize_nest_conditional.cpp$$ $rref optimize_print_for.cpp$$ $rref optimize_reverse_active.cpp$$ $rref opt_val_hes.cpp$$ $rref par_var.cpp$$ $rref poly.cpp$$ $rref pow.cpp$$ $rref pow_int.cpp$$ $rref print_for_cout.cpp$$ $rref print_for_string.cpp$$ $rref reverse_checkpoint.cpp$$ $rref reverse_one.cpp$$ $rref reverse_three.cpp$$ $rref reverse_two.cpp$$ $rref rev_one.cpp$$ $rref rev_sparse_hes.cpp$$ $rref rev_sparse_jac.cpp$$ $rref rev_two.cpp$$ $rref Rombergmul.cpp$$ $rref romberg_one.cpp$$ $rref rosen_34.cpp$$ $rref runge45_1.cpp$$ $rref runge45_2.cpp$$ $rref seq_property.cpp$$ $rref set_union.cpp$$ $rref simple_ad_bthread.cpp$$ $rref simple_ad_openmp.cpp$$ $rref simple_ad_pthread.cpp$$ $rref simple_vector.cpp$$ $rref sin.cpp$$ $rref sinh.cpp$$ $rref sparse_hes_fun.cpp$$ $rref sparse_hessian.cpp$$ $rref sparse_jac_fun.cpp$$ $rref sparse_jacobian.cpp$$ $rref sparse_sub_hes.cpp$$ $rref sparsity_sub.cpp$$ $rref speed_example.cpp$$ $rref speed_program.cpp$$ $rref speed_test.cpp$$ $rref sqrt.cpp$$ $rref stack_machine.cpp$$ $rref sub.cpp$$ $rref sub_eq.cpp$$ $rref sub_sparse_hes.cpp$$ $rref tan.cpp$$ $rref tanh.cpp$$ $rref tape_index.cpp$$ $rref team_bthread.cpp$$ $rref team_example.cpp$$ $rref team_openmp.cpp$$ $rref team_pthread.cpp$$ $rref team_thread.hpp$$ $rref thread_alloc.cpp$$ $rref thread_test.cpp$$ $rref time_test.cpp$$ $rref to_string.cpp$$ $rref unary_minus.cpp$$ $rref unary_plus.cpp$$ $rref value.cpp$$ $rref var2par.cpp$$ $rref vec_ad.cpp$$ $rref vector_bool.cpp$$ $tend $end cppad-20170000.3/omh/uniform_01_hpp.omh0000644000175200017650000000154613057470464016560 0ustar coincoin-web$Id: uniform_01_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin uniform_01.hpp$$ $spell uniform_01 ifndef endif $$ $section Source: uniform_01$$ $mindex source$$ $code # ifndef CPPAD_UNIFORM_01_HPP $pre $$ # define CPPAD_UNIFORM_01_HPP $srcfile%cppad/speed/uniform_01.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/poly_hpp.omh0000644000175200017650000000147413057470464015564 0ustar coincoin-web$Id: poly_hpp.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin poly.hpp$$ $spell Lu ifndef endif $$ $section Source: Poly$$ $mindex source$$ $code # ifndef CPPAD_POLY_HPP $pre $$ # define CPPAD_POLY_HPP $srcfile%cppad/utility/poly.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/ode_evaluate.omh0000644000175200017650000000154213057470464016363 0ustar coincoin-web$Id: ode_evaluate.omh 3788 2016-02-09 15:50:06Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin ode_evaluate.hpp$$ $spell ifndef endif $$ $section Source: ode_evaluate$$ $mindex source$$ $code # ifndef CPPAD_ODE_EVALUATE_HPP $pre $$ # define CPPAD_ODE_EVALUATE_HPP $srcfile%cppad/speed/ode_evaluate.hpp%0%// BEGIN C++%// END C++%$$ # endif $$ $end cppad-20170000.3/omh/omp_alloc_dep.omh0000644000175200017650000000646113057470464016530 0ustar coincoin-web/* $Id: omp_alloc_dep.omh 3740 2015-10-07 03:47:28Z bradbell $ */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin efficient$$ $spell omp_alloc ptr num bool const $$ $section Check If A Memory Allocation is Efficient for Another Use$$ $mindex omp_alloc reuse$$ $head Deprecated 2011-07-29$$ This function has been deprecated because speed tests seem to indicate it is just as fast, or faster, to free and then reallocate the memory. $head Syntax$$ $codei%flag% = omp_alloc::efficient(%v_ptr%, %num_bytes%)%$$ $head Purpose$$ Check if memory that is currently in use is an efficient allocation for a specified number of bytes. $head v_ptr$$ This argument has prototype $codei% const void* %v_ptr% %$$. It must be a pointer to memory that is currently in use; i.e. obtained by a previous call to $cref get_memory$$ and not yet returned. $head num_bytes$$ This argument has prototype $codei% size_t %num_bytes% %$$ It specifies the number of bytes of the memory allocated by $icode v_ptr$$ that we want to use. $head flag$$ The return value has prototype $codei% bool %flag% %$$ It is true, a call to $code get_memory$$ with $cref/min_bytes/get_memory/min_bytes/$$ equal to $icode num_bytes$$ would result in a value for $cref/cap_bytes/get_memory/cap_bytes/$$ that is the same as when $code v_ptr$$ was returned by $code get_memory$$; i.e., $icode v_ptr$$ is an efficient memory block for $icode num_bytes$$ bytes of information. $head Thread$$ Either the $cref/current thread/get_thread_num/$$ must be the same as during the corresponding call to $cref get_memory$$, or the current execution mode must be sequential (not $cref/parallel/in_parallel/$$). $head NDEBUG$$ If $code NDEBUG$$ is defined, $icode v_ptr$$ is not checked (this is faster). Otherwise, a list of in use pointers is searched to make sure that $icode v_ptr$$ is in the list. $end ------------------------------------------------------------------------------- $begin old_max_num_threads$$ $spell inv CppAD num omp_alloc $$ $section Set Maximum Number of Threads for omp_alloc Allocator$$ $mindex max_num_threads parallel OpenMP initialize$$ $head Removed$$ This function has been removed from the CppAD API. Use the function $cref/set_max_num_threads/max_num_threads/$$ in its place. $head Syntax$$ $codei%omp_alloc::max_num_threads(%number%)%$$ $head Purpose$$ By default there is only one thread and all execution is in sequential mode (not $cref/parallel/in_parallel/$$). $head number$$ The argument $icode number$$ has prototype $codei% size_t %number% %$$ It must be greater than zero and specifies the maximum number of OpenMP threads that will be active at one time. $head Restrictions$$ This function must be called before the program enters $cref/parallel/in_parallel/$$ execution mode. $end ------------------------------------------------------------------------------- cppad-20170000.3/omh/subversion.omh0000644000175200017650000000665013057470464016132 0ustar coincoin-web$Id: subversion.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin subversion$$ $spell mkdir omh noframe http www xml htm config yyyymmdd yyyy mm dd omhelp cppad OMhelp CppAD svn https org dir hpp $$ $section Using Subversion To Download Source Code$$ $head File Format$$ The files corresponding to this download procedure are in Unix format; i.e., each line ends with just a line feed. $head Subversion$$ You must have $href%http://subversion.tigris.org/%subversion%$$ installed to use this download procedure. In Unix, you can check if subversion is already installed in your path by entering the command $codep which svn $$ $head OMhelp$$ The documentation for CppAD is built from the source code files using $href%http://www.seanet.com/~bradbell/omhelp/%OMhelp%$$. In Unix, you can check if OMhelp is already installed in your path by entering the command $codep which omhelp $$ $head Current Version$$ The following command will download the current version of the CppAD source code: $codei% svn co https://projects.coin-or.org/svn/CppAD/%dir% %dir% %$$ where $icode dir$$ is replaced by $code trunk$$. To see if this has been done correctly, check for the following file: $codei% %dir%/cppad/cppad.hpp %$$ $head Stable Versions$$ Subversion downloads are available for a set of stable versions (after the specified date, only bug fixes get applied). The following link will list the available $icode dir$$ values corresponding to $href% https://projects.coin-or.org/CppAD/browser/stable% stable versions %$$. The following command will download a stable version of the CppAD source code: $codei% svn co https://projects.coin-or.org/svn/CppAD/stable/%dir% %dir% %$$ To see if this has been done correctly, check for the following file: $codei% %dir%/cppad/cppad.hpp %$$ Note that it will correspond to the most recent release for this stable version. $head Release Versions$$ Subversion downloads are available for a set of release versions (no changes are applied). The following link will list the available $icode dir$$ values corresponding to $href% https://projects.coin-or.org/CppAD/browser/releases% release versions %$$. The following command will download a release version of the CppAD source code: $codei% svn co https://projects.coin-or.org/svn/CppAD/releases/%dir% %dir% %$$ To see if this has been done correctly, check for the following file: $codei% %dir%/cppad/cppad.hpp %$$ $head Build the Documentation$$ Now build the documentation for this version using the commands $codei% cd %dir% ./build.sh configure omhelp %$$ $head Continue with Installation$$ Once the steps above are completed, you can proceed with the install instructions in the documentation you just built. Start by opening the file $codei% %dir%/doc/index.xml %$$ in a web browser and proceeding to the install instructions in that documentation, skipping the Download section and starting with the Configure command. $end cppad-20170000.3/omh/numeric_type.omh0000644000175200017650000000762513057470464016441 0ustar coincoin-web$Id: numeric_type.omh 3757 2015-11-30 12:03:07Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin NumericType$$ $spell const std valarray $$ $section Definition of a Numeric Type$$ $mindex int$$ $head Type Requirements$$ A $icode NumericType$$ is any type that satisfies the requirements below. The following is a list of some numeric types: $code int$$, $code float$$, $code double$$, $code AD$$, $code AD< AD >$$. The routine $cref CheckNumericType$$ can be used to check that a type satisfies these conditions. $head Default Constructor$$ The syntax $codei% %NumericType% %x%; %$$ creates a $icode NumericType$$ object with an unspecified value. $head Constructor From Integer$$ If $icode i$$ is an $code int$$, the syntax $codei% %NumericType% %x%(%i%); %$$ creates a $icode NumericType$$ object with a value equal to $icode i$$ where $icode i$$ can be $code const$$. $head Copy Constructor$$ If $icode x$$ is a $icode NumericType$$ object the syntax $codei% %NumericType% %y%(%x%); %$$ creates a $icode NumericType$$ object $icode y$$ with the same value as $icode x$$ where $icode x$$ can be $code const$$. $head Assignment$$ If $icode x$$ and $icode y$$ are $icode NumericType$$ objects, the syntax $codei% %x% = %y% %$$ sets the value of $icode x$$ equal to the value of $icode y$$ where $icode y$$ can be $code const$$. The expression corresponding to this operation is unspecified; i.e., it could be $code void$$ and hence $codei% %x% = %y% = %z% %$$ may not be legal. $head Operators$$ Suppose $icode x$$, $icode y$$ and $icode z$$ $icode NumericType$$ objects where $icode x$$ and $icode y$$ may be $code const$$. In the result type column, $icode NumericType$$ can be replaced by any type that can be used just like a $icode NumericType$$ object. $table $bold Operation$$ $cnext $bold Description$$ $cnext $bold Result Type$$ $rnext $codei%+%x%$$ $cnext unary plus $cnext $icode NumericType$$ $rnext $codei%-%x%$$ $cnext unary minus $cnext $icode NumericType$$ $rnext $icode%x% + %y%$$ $cnext binary addition $cnext $icode NumericType$$ $rnext $icode%x% - %y%$$ $cnext binary subtraction $cnext $icode NumericType$$ $rnext $icode%x% * %y%$$ $cnext binary multiplication $cnext $icode NumericType$$ $rnext $icode%x% / %y%$$ $cnext binary division $cnext $icode NumericType$$ $rnext $icode%z% += %y%$$ $cnext computed assignment addition $cnext unspecified $rnext $icode%z% -= %y%$$ $cnext computed assignment subtraction $cnext unspecified $rnext $icode%z% *= %y%$$ $cnext computed assignment multiplication $cnext unspecified $rnext $icode%z% /= %y%$$ $cnext computed assignment division $cnext unspecified $tend $head Example$$ $children% example/numeric_type.cpp %$$ The file $cref numeric_type.cpp$$ contains an example and test of using numeric types. It returns true if it succeeds and false otherwise. (It is easy to modify to test additional numeric types.) $head Exercise$$ $list number$$ List three operators that are not supported by every numeric type but that are supported by the numeric types $code int$$, $code float$$, $code double$$. $lnext Which of the following are numeric types: $code std::complex$$, $code std::valarray$$, $code std::vector$$ ? $lend $end cppad-20170000.3/omh/glossary.omh0000644000175200017650000002216313057470464015573 0ustar coincoin-web$Id: glossary.omh 3768 2015-12-28 18:58:35Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin glossary$$ $aindex head subhead$$ $spell std Vec cos bool Op Diff Var Cpp enum Taylor $$ $section Glossary$$ $mindex efficient$$ $head AD Function$$ Given an $cref ADFun$$ object $icode f$$ there is a corresponding AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. This operation sequence defines a function $latex F : B^n \rightarrow B^m $$ where $icode B$$ is the space corresponding to objects of type $icode Base$$, $icode n$$ is the size of the $cref/domain/seq_property/Domain/$$ space, and $icode m$$ is the size of the $cref/range/seq_property/Range/$$ space. We refer to $latex F$$ as the AD function corresponding to the operation sequence stored in the object $icode f$$. (See the $cref/FunCheck discussion/FunCheck/Discussion/$$ for possible differences between $latex F(x)$$ and the algorithm that defined the operation sequence.) $head AD of Base$$ An object is called an AD of $icode Base$$ object its type is either $codei%AD<%Base%>%$$ (see the default and copy $cref/constructors/ad_ctor/$$ or $codei%VecAD<%Base%>::reference%$$ (see $cref VecAD$$) for some $icode Base$$ type. $head AD Type Above Base$$ If $icode Base$$ is a type, an AD type above $icode Base$$ is the following sequence of types: $codei% AD<%Base%> %,% AD< AD<%Base%> > %,% AD< AD< AD<%Base%> > > %,% %...% %$$ $head Base Function$$ A function $latex f : B \rightarrow B$$ is referred to as a $icode Base$$ function, if $icode Base$$ is a C++ type that represent elements of the domain and range space of $icode f$$; i.e. elements of $latex B$$. $head Base Type$$ If $icode x$$ is an $codei%AD<%Base%>%$$ object, $icode Base$$ is referred to as the base type for $icode x$$. $head Elementary Vector$$ The $th j$$ elementary vector $latex e^j \in B^m$$ is defined by $latex \[ e_i^j = \left\{ \begin{array}{ll} 1 & {\rm if} \; i = j \\ 0 & {\rm otherwise} \end{array} \right. \] $$ $head Operation$$ $subhead Atomic$$ An atomic $icode Type$$ operation is an operation that has a $icode Type$$ result and is not made up of other more basic operations. $subhead Sequence$$ A sequence of atomic $icode Type$$ operations is called a $icode Type$$ operation sequence. A sequence of atomic $cref/AD of Base/glossary/AD of Base/$$ operations is referred to as an AD of $icode Base$$ operation sequence. The abbreviated notation AD operation sequence is often used when it is not necessary to specify the base type. $subhead Dependent$$ Suppose that $icode x$$ and $icode y$$ are $icode Type$$ objects and the result of $codei% %x% < %y% %$$ has type $code bool$$ (where $icode Type$$ is not the same as $code bool$$). If one executes the following code $codei% if( %x% < %y% ) %y% = cos(%x%); else %y% = sin(%x%); %$$ the choice above depends on the value of $icode x$$ and $icode y$$ and the two choices result in a different $icode Type$$ operation sequence. In this case, we say that the $icode Type$$ operation sequence depends on $icode x$$ and $icode y$$. $subhead Independent$$ Suppose that $icode i$$ and $icode n$$ are $code size_t$$ objects, and $icode%x%[%i%]%$$, $icode y$$ are $icode Type$$ objects, where $icode Type$$ is different from $code size_t$$. The $icode Type$$ sequence of operations corresponding to $codei% %y% = %Type%(0); for(%i% = 0; %i% < %n%; %i%++) %y% += %x%[%i%]; %$$ does not depend on the value of $icode x$$ or $icode y$$. In this case, we say that the $icode Type$$ operation sequence is independent of $icode y$$ and the elements of $icode x$$. $head Parameter$$ All $icode Base$$ objects are parameters. An $codei%AD<%Base%>%$$ object $icode u$$ is currently a parameter if its value does not depend on the value of an $cref Independent$$ variable vector for an $cref/active tape/glossary/Tape/Active/$$. If $icode u$$ is a parameter, the function $cref/Parameter(u)/ParVar/$$ returns true and $cref/Variable(u)/ParVar/$$ returns false. $head Sparsity Pattern$$ CppAD describes a sparse matrix as a vector of sets with each vector component corresponding to a row and the elements of the set corresponding to the possibly non-zero columns. A vector of $code bool$$ can represent a vector of sets using one bit per element. (Some vectors of $code bool$$ use one byte per element but $cref/vectorBool/CppAD_vector/vectorBool/$$ is an example class that uses one bit per element.) The problem is that this representation uses one bit for both the elements that are there and the ones that are not. $pre $$ A vector of $code std::set$$ does not represent the elements that are not present, but it uses about three $code size_t$$ values for each element that is present. For example, if $code size_t$$ uses 32 bits, a vector of $code std::set$$ uses about 100 bits for each element that is present in the vector of sets. Thus, a vector of $code std::set$$ should be more efficient for very sparse matrix representations. $subhead Vector of Boolean$$ Given a matrix $latex A \in B^{m \times n}$$, a vector of $code bool$$ $latex B$$ of length $latex m \times n$$ is a sparsity pattern for $latex A$$ if for $latex i = 0, \ldots , m-1$$ and $latex j = 0 , \ldots n-1$$, $latex \[ A_{i,j} \neq 0 \; \Rightarrow \; B_{i * n + j} = {\rm true} \] $$ Given two sparsity patterns $latex B$$ and $icode C$$ for a matrix $icode A$$, we say that $icode B$$ is more efficient than $icode C$$ if $icode B$$ has fewer true elements than $icode C$$. For example, if $latex A$$ is the identity matrix, $latex \[ B_{i * n + j} = (i = j) \] $$ defines an efficient sparsity pattern for $latex A$$. $subhead Vector of Sets$$ Given a matrix $latex A \in B^{m \times n}$$, a vector of sets $latex S$$ of length $latex m$$ is a sparsity pattern for $latex A$$ if for $latex i = 0, \ldots , m-1$$ $latex \[ A_{i,j} \neq 0 \; \Rightarrow \; j \in S_i \] $$ Given two sparsity patterns $latex S$$ and $icode T$$ for a matrix $icode A$$, we say that $icode S$$ is more efficient than $icode T$$ if $icode S$$ has fewer elements than $icode T$$. For example, if $latex A$$ is the identity matrix, $latex \[ S_i = \{ i \} \] $$ defines an efficient sparsity pattern for $latex A$$. $head Tape$$ $subhead Active$$ A new tape is created and becomes active after each call of the form (see $cref Independent$$) $codei% Independent(%x%) %$$ All operations that depend on the elements of $icode x$$ are recorded on this active tape. $subhead Inactive$$ The $cref/operation sequence/glossary/Operation/Sequence/$$ stored in a tape must be transferred to a function object using the syntax (see $cref/ADFun f(x, y)/FunConstruct/$$) $codei% ADFun<%Base%> %f%( %x%, %y%) %$$ or using the syntax (see $cref/f.Dependent(x, y)/Dependent/$$) $codei% %f%.Dependent( %x%, %y%) %$$ After such a transfer, the tape becomes inactive. $subhead Independent Variable$$ While the tape is active, we refer to the elements of $icode x$$ as the independent variables for the tape. When the tape becomes inactive, the corresponding objects become $cref/parameters/glossary/Parameter/$$. $subhead Dependent Variables$$ While the tape is active, we use the term dependent variables for the tape for any objects whose value depends on the independent variables for the tape. When the tape becomes inactive, the corresponding objects become $cref/parameters/glossary/Parameter/$$. $head Taylor Coefficient$$ Suppose $latex X : B \rightarrow B^n$$ is a is $latex p$$ times continuously differentiable function in some neighborhood of zero. For $latex k = 0 , \ldots , p$$, we use the column vector $latex x^{(k)} \in B^n$$ for the $th k$$ order Taylor coefficient corresponding to $latex X$$ which is defined by $latex \[ x^{(k)} = \frac{1}{k !} \Dpow{k}{t} X(0) \] $$ It follows that $latex \[ X(t) = x^{(0)} + x^{(1)} t + \cdots + x^{(p)} t^p + R(t) \]$$ where the remainder $latex R(t)$$ divided by $latex t^p$$ converges to zero and $latex t$$ goes to zero. $head Variable$$ An $codei%AD<%Base%>%$$ object $icode u$$ is a variable if its value depends on an independent variable vector for a currently $cref/active tape/glossary/Tape/Active/$$. If $icode u$$ is a variable, $cref/Variable(u)/ParVar/$$ returns true and $cref/Parameter(u)/ParVar/$$ returns false. For example, directly after the code sequence $codei% Independent(%x%); AD %u% = %x%[0]; %$$ the $codei%AD%$$ object $icode u$$ is currently a variable. Directly after the code sequence $codei% Independent(%x%); AD %u% = %x%[0]; %u% = 5; %$$ $icode u$$ is currently a $cref/parameter/glossary/Parameter/$$ (not a variable). $pre $$ Note that we often drop the word currently and just refer to an $codei%AD<%Base%>%$$ object as a variable or parameter. $end cppad-20170000.3/ChangeLog0000644000175200017650000000037111210357004014166 0ustar coincoin-web* 2008-08-26 Brad Bell - A developers ChangeLog can be found in the svn log; e.g., - https://projects.coin-or.org/CppAD/timeline - A user's ChangeLog is located at -- http://www.coin-or.org/CppAD/Doc/whats_new.htm cppad-20170000.3/cppad/0002755000175200017650000000000013057470467013530 5ustar coincoin-webcppad-20170000.3/cppad/CMakeLists.txt0000644000175200017650000002364613057470464016276 0ustar coincoin-web# $Id: CMakeLists.txt 3859 2017-01-01 10:59:24Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # Build the cppad/configure.hpp file. # Inherit environment from ../CMakeLists.txt # ----------------------------------------------------------------------------- MACRO(check_match match_variable match_constant output_variable) STRING(COMPARE EQUAL ${${match_variable}} ${match_constant} match_flag ) IF( match_flag ) SET(${output_variable} 1) ELSE( match_flag ) SET(${output_variable} 0) ENDIF( match_flag ) print_variable(${output_variable}) ENDMACRO(check_match) # ----------------------------------------------------------------------------- # command line arguments # # cppad_testvector command_line_arg(cppad_testvector cppad STRING "Namespace of vector used for testing, one of: boost, cppad, eigen, std" ) # # cppad_max_num_threads command_line_arg(cppad_max_num_threads 48 STRING "maximum number of threads that CppAD can use use" ) # cppad_sparse_list IF( cppad_sparse_list ) MESSAGE(FATAL_ERROR "cppad_sparse_list = ${cppad_sparse_list}" ": this command line argument has been removed" ) ENDIF( cppad_sparse_list ) # # cppad_tape_id_type command_line_arg(cppad_tape_id_type "unsigned int" STRING "type used to identify different tapes, size must be <= sizeof(size_t)" ) # # cppad_tape_addr_type command_line_arg(cppad_tape_addr_type "unsigned int" STRING "type used to identify variables on one tape, size must be <= sizeof(size_t)" ) # # cppad_deprecated command_line_arg(cppad_deprecated NO BOOL "implicit (instead of explicit) conversion from any type to AD" ) # ----------------------------------------------------------------------------- # cppad_deprecated IF( cppad_deprecated ) SET(cppad_deprecated 1) ELSE( cppad_deprecated ) SET(cppad_deprecated 0) ENDIF( cppad_deprecated ) # ----------------------------------------------------------------------------- # cppad_boostvector, cppad_cppadvector, cppad_eigenvector, cppad_stdvector # check_match(cppad_testvector boost cppad_boostvector) check_match(cppad_testvector cppad cppad_cppadvector) check_match(cppad_testvector eigen cppad_eigenvector) check_match(cppad_testvector std cppad_stdvector) IF( NOT cppad_boostvector ) IF( NOT cppad_cppadvector ) IF( NOT cppad_eigenvector ) IF( NOT cppad_stdvector ) MESSAGE(FATAL_ERROR "cppad_testvector not one of following: boost, cppad, eigen, std." ) ENDIF( NOT cppad_stdvector ) ENDIF( NOT cppad_eigenvector ) ENDIF( NOT cppad_cppadvector ) ENDIF( NOT cppad_boostvector ) IF( cppad_boostvector ) # FIND_PACKAGE(Boost) done by ../CMakeLists.txt IF( NOT Boost_FOUND ) MESSAGE(FATAL_ERROR "cppad_testvector == boost but cannot find boost include files" ) ENDIF( NOT Boost_FOUND ) ENDIF( cppad_boostvector ) # IF( cppad_eigenvector ) IF( NOT eigen_prefix ) MESSAGE(FATAL_ERROR "cppad_testvector == eigen but eigen_prefix is not specified" ) ENDIF( NOT eigen_prefix ) ENDIF( cppad_eigenvector ) # ============================================================================= # Begin C++11 features # SET(cppad_cplusplus_201100_ok 1) # ----------------------------------------------------------------------------- # cppad_has_signed_long_long # SET(source " int main(void) { signed long long value = 0; return int(value); }" ) check_source_runs("${source}" cppad_has_signed_long_long ) IF( NOT cppad_has_signed_long_long ) SET(cppad_cplusplus_201100_ok 0) ENDIF( NOT cppad_has_signed_long_long ) # ----------------------------------------------------------------------------- # cppad_has_rvalue # SET(source " int main(void) { int&& value = 1 + 2; if( value != 3 ) return 1; return 0; }" ) check_source_runs("${source}" cppad_has_rvalue) IF( NOT cppad_has_rvalue ) SET(cppad_cplusplus_201100_ok 0) ENDIF( NOT cppad_has_rvalue ) # ----------------------------------------------------------------------------- # cppad_has_nullptr # SET(source " int main(void) { char *c = nullptr; return 0; }" ) check_source_runs("${source}" cppad_has_nullptr) IF( NOT cppad_has_nullptr ) SET(cppad_cplusplus_201100_ok 0) ENDIF( NOT cppad_has_nullptr ) # ----------------------------------------------------------------------------- # cppad_has_cstdint_8_to_64 # SET(source " # include template inline bool is_pod(void) { return false; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } int main(void) { return 0; } " ) check_source_runs("${source}" cppad_has_cstdint_8_to_64) IF( NOT cppad_has_cstdint_8_to_64 ) SET(cppad_cplusplus_201100_ok 0) ENDIF( NOT cppad_has_cstdint_8_to_64 ) # ----------------------------------------------------------------------------- # cppad_compiler_has_erf # cppad_compiler_has_asinh # cppad_compiler_has_acosh # cppad_compiler_has_atanh # cppad_compiler_has_expm1 # SET(source_template " # include int main(void) { std::c11_function(0.0); return 0; } " ) FOREACH(c11_function erf asinh acosh atanh expm1 log1p) STRING(REPLACE "c11_function" ${c11_function} source "${source_template}" ) # really only checking if program compiles check_source_runs("${source}" cppad_compiler_has_${c11_function} ) IF( NOT cppad_compiler_has_${c11_function} ) SET(cppad_cplusplus_201100_ok 0) ENDIF( NOT cppad_compiler_has_${c11_function} ) ENDFOREACH(c11_function) # ----------------------------------------------------------------------------- # cppad_has_steady_clock # SET(source " # include # include # include int main(void) { std::chrono::time_point start, end; start = std::chrono::steady_clock::now(); std::this_thread::sleep_for( std::chrono::milliseconds(1) ); end = std::chrono::steady_clock::now(); std::chrono::duration difference = end - start; double elapsed_seconds = difference.count(); if( elapsed_seconds >= 0.9e-3 ) // 1e-3 = one millisecond return 0; return 1; } " ) check_source_runs("${source}" cppad_has_steady_clock) IF( NOT cppad_has_steady_clock ) SET(cppad_cplusplus_201100_ok 0) ENDIF( NOT cppad_has_steady_clock ) # ============================================================================= # End C++11 features # print_variable(cppad_cplusplus_201100_ok) # ----------------------------------------------------------------------------- # cppad_has_gettimeofday # SET(source " # include int main(void) { struct timeval time; gettimeofday(&time, 0); return 0; }" ) check_source_runs("${source}" cppad_has_gettimeofday) # ----------------------------------------------------------------------------- # cppad_size_t_not_unsigned_int # SET(source " # include template inline bool is_pod(void) { return false; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } int main(void) { return 0; } " ) check_source_runs("${source}" cppad_size_t_not_unsigned_int) # ----------------------------------------------------------------------------- # cppad_tape_addr_type, cppad_tape_id_type # FOREACH(cmake_var cppad_tape_id_type cppad_tape_addr_type ) SET(source " # include int main(void) { bool is_unsigned = ! std::numeric_limits<${${cmake_var}}>::is_signed; return int(! is_unsigned); } " ) check_source_runs("${source}" ${cmake_var}_is_unsigned) IF( ${cmake_var}_is_unsigned STREQUAL 0 ) MESSAGE(STATUS "Warning: using a signed ${cmake_var} is for CppAD developers only !" ) ENDIF( ${cmake_var}_is_unsigned STREQUAL 0 ) ENDFOREACH( cmake_var ) # ----------------------------------------------------------------------------- # check that cppad_max_num_threads is >= 4 # SET(CMAKE_REQUIRED_INCLUDES "") SET(CMAKE_REQUIRED_LIBRARIES "") SET(CMAKE_REQUIRED_FLAGS ) SET(source " int main(void) { const char* number = \"${cppad_max_num_threads}\"; int value = 0; while( *number == ' ' ) number++; while( '0' <= *number && *number <= '9' ) { value = 10 * value + (int)(*number - '0'); number++; } while( *number == ' ' ) number++; if( *number != char(0) ) return 1; if( value < 4 ) return 1; return 0; } " ) # Using CHECK_CXX_SOURCE_RUNS directly (instead of check_source_runs). CHECK_CXX_SOURCE_RUNS("${source}" cppad_max_num_threads_is_integer_ge_4) IF( NOT cppad_max_num_threads_is_integer_ge_4 ) MESSAGE(FATAL_ERROR "cppad_max_num_threads is not an integer greater than or equal 4" ) ENDIF( NOT cppad_max_num_threads_is_integer_ge_4 ) # ----------------------------------------------------------------------------- # cppad_has_mkstemp # SET(source " # include # include int main(void) { char pattern[] = \"/tmp/fileXXXXXX\"; int fd = mkstemp(pattern); return 0; } " ) check_source_runs("${source}" cppad_has_mkstemp ) # ----------------------------------------------------------------------------- # cppad_has_tmpname_s # SET(source " # include int main(void) { char filename[L_tmpnam_s ]; if( tmpnam_s(filename, L_tmpnam_s ) != 0 ) return 1; return 0; } " ) check_source_runs("${source}" cppad_has_tmpnam_s ) # ----------------------------------------------------------------------------- # Copy a file to another location and modify its contents. # configure_file(InputFile OutputFile [COPYONLY] [ESCAPE_QUOTES] [@ONLY]) CONFIGURE_FILE( ${CMAKE_CURRENT_SOURCE_DIR}/configure.hpp.in ${CMAKE_CURRENT_SOURCE_DIR}/configure.hpp ) cppad-20170000.3/cppad/cppad.hpp0000644000175200017650000000521313057470464015324 0ustar coincoin-web// $Id: cppad.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_CPPAD_HPP # define CPPAD_CPPAD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file cppad.hpp \brief includes the entire CppAD package in the necessary order. \namespace CppAD \brief contains all the variables and functions defined by the CppAD package. */ # include // all base type requirements // --------------------------------------------------------------------------- // CppAD general purpose library routines (can be included separately) # include // -------------------------------------------------------------------------- // System routines that can be used by rest of CppAD with out including # include # include # include # include // --------------------------------------------------------------------------- // definitions needed by rest of includes // definitions that come from the installation # include // definitions that are local to the CppAD include files # include // vectors used with CppAD # include // deprecated vectors used with CppAD # include // Declare classes and fucntions that are used before defined # include // --------------------------------------------------------------------------- // declare the AD template class # include // --------------------------------------------------------------------------- # include // AD class methods available to the user // tape that tape for AD acts as a user of Base operations // so user_ad.hpp must come before op.hpp # include // executes taped operations # include // ADFun objects // --------------------------------------------------------------------------- // library routines that require the rest of CppAD # include # include # include // undo definitions in Define.h # include # endif cppad-20170000.3/cppad/deprecated/0002755000175200017650000000000013057470465015626 5ustar coincoin-webcppad-20170000.3/cppad/deprecated/error_handler.hpp0000644000175200017650000000003613057470464021161 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/ErrorHandler.h0000644000175200017650000000003613057470464020362 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/CppAD.h0000644000175200017650000000003613057470464016722 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/runge_45.hpp0000644000175200017650000000003613057470464017763 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/LuSolve.h0000644000175200017650000000003613057470464017364 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/elapsed_seconds.hpp0000644000175200017650000000003613057470464021466 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/Rosen34.h0000644000175200017650000000003613057470464017230 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/time_test.hpp0000644000175200017650000000003613057470464020330 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/speed_test.hpp0000644000175200017650000000003613057470464020472 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/check_numeric_type.hpp0000644000175200017650000000003613057470464022173 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/SpeedTest.h0000644000175200017650000000003613057470464017673 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/track_new_del.hpp0000644000175200017650000000003613057470464021134 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/vector.hpp0000644000175200017650000000003613057470464017635 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/TrackNewDel.h0000644000175200017650000000003613057470464020136 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/OdeGear.h0000644000175200017650000000003613057470464017301 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/CppAD_vector.h0000644000175200017650000000003613057470464020304 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/romberg_mul.hpp0000644000175200017650000000003613057470464020645 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/CheckSimpleVector.h0000644000175200017650000000003613057470464021345 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/RombergMul.h0000644000175200017650000000003613057470464020046 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/near_equal.hpp0000644000175200017650000000003613057470464020447 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/NearEqual.h0000644000175200017650000000003613057470464017650 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/pow_int.hpp0000644000175200017650000000003613057470464020012 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/ode_err_control.hpp0000644000175200017650000000003613057470464021512 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/PowInt.h0000644000175200017650000000003613057470464017213 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/lu_solve.hpp0000644000175200017650000000003613057470464020163 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/Runge45.h0000644000175200017650000000003613057470464017224 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/rosen_34.hpp0000644000175200017650000000003613057470464017767 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/romberg_one.hpp0000644000175200017650000000003613057470464020631 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/RombergOne.h0000644000175200017650000000003613057470464020032 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/CheckNumericType.h0000644000175200017650000000003613057470464021175 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/memory_leak.hpp0000644000175200017650000000003613057470464020637 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/ode_gear.hpp0000644000175200017650000000003613057470465020101 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/ode_gear_control.hpp0000644000175200017650000000003613057470465021641 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/omp_alloc.hpp0000644000175200017650000000003613057470465020301 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/OdeGearControl.h0000644000175200017650000000003613057470465020643 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/lu_invert.hpp0000644000175200017650000000003613057470465020343 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/LuInvert.h0000644000175200017650000000003613057470465017544 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/check_simple_vector.hpp0000644000175200017650000000003613057470465022344 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/nan.hpp0000644000175200017650000000003613057470465017110 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/index_sort.hpp0000644000175200017650000000003613057470465020512 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/lu_factor.hpp0000644000175200017650000000003613057470465020312 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/LuFactor.h0000644000175200017650000000003613057470465017513 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/thread_alloc.hpp0000644000175200017650000000003613057470465020755 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/OdeErrControl.h0000644000175200017650000000003613057470465020515 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/poly.hpp0000644000175200017650000000003613057470465017317 0ustar coincoin-web# include cppad-20170000.3/cppad/deprecated/Poly.h0000644000175200017650000000003613057470465016717 0ustar coincoin-web# include cppad-20170000.3/cppad/speed/0002755000175200017650000000000013057470465014626 5ustar coincoin-webcppad-20170000.3/cppad/speed/det_by_minor.hpp0000644000175200017650000000762713057470465020023 0ustar coincoin-web// $Id: det_by_minor.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_SPEED_DET_BY_MINOR_HPP # define CPPAD_SPEED_DET_BY_MINOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin det_by_minor$$ $spell CppAD cppad typedef const hpp Det namespace $$ $section Determinant Using Expansion by Minors$$ $head Syntax$$ $codei%# include %$$ $codei%det_by_minor<%Scalar%> %det%(%n%) %$$ $icode%d% = %det%(%a%) %$$ $head Inclusion$$ The template class $code det_by_minor$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/det_by_minor.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head Constructor$$ The syntax $codei% det_by_minor<%Scalar%> %det%(%n%) %$$ constructs the object $icode det$$ which can be used for evaluating the determinant of $icode n$$ by $icode n$$ matrices using expansion by minors. $head Scalar$$ The type $icode Scalar$$ must satisfy the same conditions as in the function $cref/det_of_minor/det_of_minor/Scalar/$$. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ $head det$$ The syntax $codei% %d% = %det%(%a%) %$$ returns the determinant of the matrix $icode A$$ using expansion by minors. $subhead a$$ The argument $icode a$$ has prototype $codei% const %Vector% &%a% %$$ It must be a $icode Vector$$ with length $latex n * n$$ and with elements of type $icode Scalar$$. The elements of the $latex n \times n$$ matrix $latex A$$ are defined, for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , n-1$$, by $latex \[ A_{i,j} = a[ i * m + j] \] $$ $subhead d$$ The return value $icode d$$ has prototype $codei% %Scalar% %d% %$$ It is equal to the determinant of $latex A$$. $head Vector$$ If $icode y$$ is a $icode Vector$$ object, it must support the syntax $codei% %y%[%i%] %$$ where $icode i$$ has type $code size_t$$ with value less than $latex n * n$$. This must return a $icode Scalar$$ value corresponding to the $th i$$ element of the vector $icode y$$. This is the only requirement of the type $icode Vector$$. $children% speed/example/det_by_minor.cpp% omh/det_by_minor_hpp.omh %$$ $head Example$$ The file $cref det_by_minor.cpp$$ contains an example and test of $code det_by_minor.hpp$$. It returns true if it succeeds and false otherwise. $head Source Code$$ The file $cref det_by_minor.hpp$$ contains the source for this template function. $end --------------------------------------------------------------------------- */ // BEGIN C++ # include # include // BEGIN CppAD namespace namespace CppAD { template class det_by_minor { private: size_t m_; // made mutable because modified and then restored mutable std::vector r_; mutable std::vector c_; // make mutable because its value does not matter mutable std::vector a_; public: det_by_minor(size_t m) : m_(m) , r_(m + 1) , c_(m + 1), a_(m * m) { size_t i; // values for r and c that correspond to entire matrix for(i = 0; i < m; i++) { r_[i] = i+1; c_[i] = i+1; } r_[m] = 0; c_[m] = 0; } template inline Scalar operator()(const Vector &x) const { size_t i = m_ * m_; while(i--) a_[i] = x[i]; return det_of_minor(a_, m_, m_, r_, c_); } }; } // END CppAD namespace // END C++ # endif cppad-20170000.3/cppad/speed/ode_evaluate.hpp0000644000175200017650000001403113057470465017771 0ustar coincoin-web// $Id: ode_evaluate.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_SPEED_ODE_EVALUATE_HPP # define CPPAD_SPEED_ODE_EVALUATE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ode_evaluate$$ $spell Runge fabs retaped Jacobian const Cpp cppad hpp fp namespace exp $$ $section Evaluate a Function Defined in Terms of an ODE$$ $mindex ode_evaluate$$ $head Syntax$$ $codei%# include %$$ $codei%ode_evaluate(%x%, %p%, %fp%)%$$ $head Purpose$$ This routine evaluates a function $latex f : \B{R}^n \rightarrow \B{R}^n$$ defined by $latex \[ f(x) = y(x, 1) \] $$ where $latex y(x, t)$$ solves the ordinary differential equation $latex \[ \begin{array}{rcl} y(x, 0) & = & x \\ \partial_t y (x, t ) & = & g[ y(x,t) , t ] \end{array} \] $$ where $latex g : \B{R}^n \times \B{R} \rightarrow \B{R}^n$$ is an unspecified function. $head Inclusion$$ The template function $code ode_evaluate$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/ode_evaluate.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head Float$$ $subhead Operation Sequence$$ The type $icode Float$$ must be a $cref NumericType$$. The $icode Float$$ $cref/operation sequence/glossary/Operation/Sequence/$$ for this routine does not depend on the value of the argument $icode x$$, hence it does not need to be retaped for each value of $latex x$$. $subhead fabs$$ If $icode y$$ and $icode z$$ are $icode Float$$ objects, the syntax $codei% %y% = fabs(%z%) %$$ must be supported. Note that it does not matter if the operation sequence for $code fabs$$ depends on $icode z$$ because the corresponding results are not actually used by $code ode_evaluate$$; see $code fabs$$ in $cref/Runge45/Runge45/Scalar/fabs/$$. $head x$$ The argument $icode x$$ has prototype $codei% const CppAD::vector<%Float%>& %x% %$$ It contains he argument value for which the function, or its derivative, is being evaluated. The value $latex n$$ is determined by the size of the vector $icode x$$. $head p$$ The argument $icode p$$ has prototype $codei% size_t %p% %$$ $subhead p == 0$$ In this case a numerical method is used to solve the ode and obtain an accurate approximation for $latex y(x, 1)$$. This numerical method has a fixed that does not depend on $icode x$$. $subhead p = 1$$ In this case an analytic solution for the partial derivative $latex \partial_x y(x, 1)$$ is returned. $head fp$$ The argument $icode fp$$ has prototype $codei% CppAD::vector<%Float%>& %fp% %$$ The input value of the elements of $icode fp$$ does not matter. $subhead Function$$ If $icode p$$ is zero, $icode fp$$ has size equal to $latex n$$ and contains the value of $latex y(x, 1)$$. $subhead Gradient$$ If $icode p$$ is one, $icode fp$$ has size equal to $icode n^2$$ and for $latex i = 0 , \ldots and n-1$$, $latex j = 0 , \ldots , n-1$$ $latex \[ \D{y[i]}{x[j]} (x, 1) = fp [ i \cdot n + j ] \] $$ $children% speed/example/ode_evaluate.cpp% omh/ode_evaluate.omh %$$ $head Example$$ The file $cref ode_evaluate.cpp$$ contains an example and test of $code ode_evaluate.hpp$$. It returns true if it succeeds and false otherwise. $head Source Code$$ The file $cref ode_evaluate.hpp$$ contains the source code for this template function. $end */ // BEGIN C++ # include # include # include namespace CppAD { template class ode_evaluate_fun { public: // Given that y_i (0) = x_i, // the following y_i (t) satisfy the ODE below: // y_0 (t) = x[0] // y_1 (t) = x[1] + x[0] * t // y_2 (t) = x[2] + x[1] * t + x[0] * t^2/2 // y_3 (t) = x[3] + x[2] * t + x[1] * t^2/2 + x[0] * t^3 / 3! // ... void Ode( const Float& t, const CppAD::vector& y, CppAD::vector& f) { size_t n = y.size(); f[0] = 0.; for(size_t k = 1; k < n; k++) f[k] = y[k-1]; } }; // template void ode_evaluate( const CppAD::vector& x , size_t p , CppAD::vector& fp ) { using CppAD::vector; typedef vector VectorFloat; size_t n = x.size(); CPPAD_ASSERT_KNOWN( p == 0 || p == 1, "ode_evaluate: p is not zero or one" ); CPPAD_ASSERT_KNOWN( ((p==0) & (fp.size()==n)) || ((p==1) & (fp.size()==n*n)), "ode_evaluate: the size of fp is not correct" ); if( p == 0 ) { // function that defines the ode ode_evaluate_fun F; // number of Runge45 steps to use size_t M = 10; // initial and final time Float ti = 0.0; Float tf = 1.0; // initial value for y(x, t); i.e. y(x, 0) // (is a reference to x) const VectorFloat& yi = x; // final value for y(x, t); i.e., y(x, 1) // (is a reference to fp) VectorFloat& yf = fp; // Use fourth order Runge-Kutta to solve ODE yf = CppAD::Runge45(F, M, ti, tf, yi); return; } /* Compute derivaitve of y(x, 1) w.r.t x y_0 (x, t) = x[0] y_1 (x, t) = x[1] + x[0] * t y_2 (x, t) = x[2] + x[1] * t + x[0] * t^2/2 y_3 (x, t) = x[3] + x[2] * t + x[1] * t^2/2 + x[0] * t^3 / 3! ... */ size_t i, j, k; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) fp[ i * n + j ] = 0.0; } size_t factorial = 1; for(k = 0; k < n; k++) { if( k > 1 ) factorial *= k; for(i = k; i < n; i++) { // partial w.r.t x[i-k] of x[i-k] * t^k / k! j = i - k; fp[ i * n + j ] += 1.0 / Float(factorial); } } } } // END C++ # endif cppad-20170000.3/cppad/speed/det_grad_33.hpp0000644000175200017650000000665313057470465017425 0ustar coincoin-web// $Id: det_grad_33.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_SPEED_DET_GRAD_33_HPP # define CPPAD_SPEED_DET_GRAD_33_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin det_grad_33$$ $spell cppad CppAD det cppad.hpp namespace const bool $$ $section Check Gradient of Determinant of 3 by 3 matrix$$ $mindex det_grad_33 correct$$ $head Syntax$$ $codei%# include %$$ $icode%ok% = det_grad_33(%x%, %g%)%$$ $head Purpose$$ This routine can be used to check a method for computing the gradient of the determinant of a matrix. $head Inclusion$$ The template function $code det_grad_33$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/det_grad_33.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$. It contains the elements of the matrix $latex X$$ in row major order; i.e., $latex \[ X_{i,j} = x [ i * 3 + j ] \] $$ $head g$$ The argument $icode g$$ has prototype $codei% const %Vector% &%g% %$$. It contains the elements of the gradient of $latex \det ( X )$$ in row major order; i.e., $latex \[ \D{\det (X)}{X(i,j)} = g [ i * 3 + j ] \] $$ $head Vector$$ If $icode y$$ is a $icode Vector$$ object, it must support the syntax $codei% %y%[%i%] %$$ where $icode i$$ has type $code size_t$$ with value less than 9. This must return a $code double$$ value corresponding to the $th i$$ element of the vector $icode y$$. This is the only requirement of the type $icode Vector$$. $head ok$$ The return value $icode ok$$ has prototype $codei% bool %ok% %$$ It is true, if the gradient $icode g$$ passes the test and false otherwise. $children% omh/det_grad_33_hpp.omh %$$ $head Source Code$$ The file $cref det_grad_33.hpp$$ contains the source code for this template function. $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include # include namespace CppAD { template bool det_grad_33(const Vector &x, const Vector &g) { bool ok = true; typedef typename Vector::value_type Float; Float eps = 10. * Float( std::numeric_limits::epsilon() ); // use expansion by minors to compute the derivative by hand double check[9]; check[0] = + ( x[4] * x[8] - x[5] * x[7] ); check[1] = - ( x[3] * x[8] - x[5] * x[6] ); check[2] = + ( x[3] * x[7] - x[4] * x[6] ); // check[3] = - ( x[1] * x[8] - x[2] * x[7] ); check[4] = + ( x[0] * x[8] - x[2] * x[6] ); check[5] = - ( x[0] * x[7] - x[1] * x[6] ); // check[6] = + ( x[1] * x[5] - x[2] * x[4] ); check[7] = - ( x[0] * x[5] - x[2] * x[3] ); check[8] = + ( x[0] * x[4] - x[1] * x[3] ); // for(size_t i = 0; i < 3 * 3; i++) ok &= CppAD::NearEqual(check[i], g[i], eps, eps); return ok; } } // END C++ # endif cppad-20170000.3/cppad/speed/uniform_01.hpp0000644000175200017650000000521113057470465017313 0ustar coincoin-web// $Id: uniform_01.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_SPEED_UNIFORM_01_HPP # define CPPAD_SPEED_UNIFORM_01_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin uniform_01$$ $spell CppAD cppad.hpp namespace $$ $section Simulate a [0,1] Uniform Random Variate$$ $mindex uniform_01$$ $head Syntax$$ $codei%# include %$$ $codei%uniform_01(%seed%) %$$ $codei%uniform_01(%n%, %x%)%$$ $head Purpose$$ This routine is used to create random values for speed testing purposes. $head Inclusion$$ The template function $code uniform_01$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/uniform_01.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head seed$$ The argument $icode seed$$ has prototype $codei% size_t %seed% %$$ It specifies a seed for the uniform random number generator. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ It specifies the number of elements in the random vector $icode x$$. $head x$$ The argument $icode x$$ has prototype $codei% %Vector% &%x% %$$. The input value of the elements of $icode x$$ does not matter. Upon return, the elements of $icode x$$ are set to values randomly sampled over the interval [0,1]. $head Vector$$ If $icode y$$ is a $code double$$ value, the object $icode x$$ must support the syntax $codei% %x%[%i%] = %y% %$$ where $icode i$$ has type $code size_t$$ with value less than or equal $latex n-1$$. This is the only requirement of the type $icode Vector$$. $children% omh/uniform_01_hpp.omh %$$ $head Source Code$$ The file $cref uniform_01.hpp$$ constraints the source code for this template function. $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include namespace CppAD { inline void uniform_01(size_t seed) { std::srand( (unsigned int) seed); } template void uniform_01(size_t n, Vector &x) { static double factor = 1. / double(RAND_MAX); while(n--) x[n] = std::rand() * factor; } } // END C++ # endif cppad-20170000.3/cppad/speed/det_33.hpp0000644000175200017650000000563213057470465016424 0ustar coincoin-web// $Id: det_33.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_SPEED_DET_33_HPP # define CPPAD_SPEED_DET_33_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin det_33$$ $spell cppad CppAD det cppad.hpp namespace const bool $$ $section Check Determinant of 3 by 3 matrix$$ $mindex det_33 correct$$ $head Syntax$$ $codei%# include %$$ $icode%ok% = det_33(%x%, %d%)%$$ $head Purpose$$ This routine can be used to check a method for computing the determinant of a matrix. $head Inclusion$$ The template function $code det_33$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/det_33.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$. It contains the elements of the matrix $latex X$$ in row major order; i.e., $latex \[ X_{i,j} = x [ i * 3 + j ] \] $$ $head d$$ The argument $icode d$$ has prototype $codei% const %Vector% &%d% %$$. It is tested to see if $icode%d%[0]%$$ it is equal to $latex \det ( X )$$. $head Vector$$ If $icode y$$ is a $icode Vector$$ object, it must support the syntax $codei% %y%[%i%] %$$ where $icode i$$ has type $code size_t$$ with value less than 9. This must return a $code double$$ value corresponding to the $th i$$ element of the vector $icode y$$. This is the only requirement of the type $icode Vector$$. (Note that only the first element of the vector $icode d$$ is used.) $head ok$$ The return value $icode ok$$ has prototype $codei% bool %ok% %$$ It is true, if the determinant $icode%d%[0]%$$ passes the test and false otherwise. $children% omh/det_33_hpp.omh %$$ $head Source Code$$ The file $cref det_33.hpp$$ contains the source code for this template function. $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include namespace CppAD { template bool det_33(const Vector &x, const Vector &d) { bool ok = true; // use expansion by minors to compute the determinant by hand double check = 0.; check += x[0] * ( x[4] * x[8] - x[5] * x[7] ); check -= x[1] * ( x[3] * x[8] - x[5] * x[6] ); check += x[2] * ( x[3] * x[7] - x[4] * x[6] ); ok &= CppAD::NearEqual(check, d[0], 1e-10, 1e-10); return ok; } } // END C++ # endif cppad-20170000.3/cppad/speed/sparse_jac_fun.hpp0000644000175200017650000001350213057470465020320 0ustar coincoin-web// $Id: sparse_jac_fun.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_SPEED_SPARSE_JAC_FUN_HPP # define CPPAD_SPEED_SPARSE_JAC_FUN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparse_jac_fun$$ $spell Jacobian jac cppad hpp fp CppAD namespace const bool exp arg $$ $section Evaluate a Function That Has a Sparse Jacobian$$ $mindex sparse_jac_fun$$ $head Syntax$$ $codei%# include %$$ $codei%sparse_jac_fun(%m%, %n%, %x%, %row%, %col%, %p%, %fp%)%$$ $head Purpose$$ This routine evaluates $latex f(x)$$ and $latex f^{(1)} (x)$$ where the Jacobian $latex f^{(1)} (x)$$ is sparse. The function $latex f : \B{R}^n \rightarrow \B{R}^m$$ only depends on the size and contents of the index vectors $icode row$$ and $icode col$$. The non-zero entries in the Jacobian of this function have one of the following forms: $latex \[ \D{ f[row[k]]}{x[col[k]]} \] $$ for some $latex k $$ between zero and $latex K-1$$. All the other terms of the Jacobian are zero. $head Inclusion$$ The template function $code sparse_jac_fun$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/sparse_jac_fun.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head Float$$ The type $icode Float$$ must be a $cref NumericType$$. In addition, if $icode y$$ and $icode z$$ are $icode Float$$ objects, $codei% %y% = exp(%z%) %$$ must set the $icode y$$ equal the exponential of $icode z$$, i.e., the derivative of $icode y$$ with respect to $icode z$$ is equal to $icode y$$. $head FloatVector$$ The type $icode FloatVector$$ is any $cref SimpleVector$$, or it can be a raw pointer, with elements of type $icode Float$$. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ It specifies the dimension for the domain space for $latex f(x)$$. $head m$$ The argument $icode m$$ has prototype $codei% size_t %m% %$$ It specifies the dimension for the range space for $latex f(x)$$. $head x$$ The argument $icode x$$ has prototype $codei% const %FloatVector%& %x% %$$ It contains the argument value for which the function, or its derivative, is being evaluated. We use $latex n$$ to denote the size of the vector $icode x$$. $head row$$ The argument $icode row$$ has prototype $codei% const CppAD::vector& %row% %$$ It specifies indices in the range of $latex f(x)$$ for non-zero components of the Jacobian (see $cref/purpose/sparse_hes_fun/Purpose/$$ above). The value $latex K$$ is defined by $icode%K% = %row%.size()%$$. All the elements of $icode row$$ must be between zero and $icode%m%-1%$$. $head col$$ The argument $icode row$$ has prototype $codei% const CppAD::vector& %col% %$$ and its size must be $latex K$$; i.e., the same as for $icode col$$. It specifies the component of $latex x$$ for the non-zero Jacobian terms. All the elements of $icode col$$ must be between zero and $icode%n%-1%$$. $head p$$ The argument $icode p$$ has prototype $codei% size_t %p% %$$ It is either zero or one and specifies the order of the derivative of $latex f$$ that is being evaluated, i.e., $latex f^{(p)} (x)$$ is evaluated. $head fp$$ The argument $icode fp$$ has prototype $codei% %FloatVector%& %fp% %$$ If $icode%p% = 0%$$, it size is $icode m$$ otherwise its size is $icode K$$. The input value of the elements of $icode fp$$ does not matter. $subhead Function$$ If $icode p$$ is zero, $icode fp$$ has size $latex m$$ and $codei%(%fp%[0]%, ... , %fp%[%m%-1])%$$ is the value of $latex f(x)$$. $subhead Jacobian$$ If $icode p$$ is one, $icode fp$$ has size $icode K$$ and for $latex k = 0 , \ldots , K-1$$, $latex \[ \D{f[ \R{row}[i] ]}{x[ \R{col}[j] ]} = fp [k] \] $$ $children% speed/example/sparse_jac_fun.cpp% omh/sparse_jac_fun.omh %$$ $head Example$$ The file $cref sparse_jac_fun.cpp$$ contains an example and test of $code sparse_jac_fun.hpp$$. It returns true if it succeeds and false otherwise. $head Source Code$$ The file $cref sparse_jac_fun.hpp$$ contains the source code for this template function. $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include # include # include // following needed by gcc under fedora 17 so that exp(double) is defined # include namespace CppAD { template void sparse_jac_fun( size_t m , size_t n , const FloatVector& x , const CppAD::vector& row , const CppAD::vector& col , size_t p , FloatVector& fp ) { // check numeric type specifications CheckNumericType(); // check value of p CPPAD_ASSERT_KNOWN( p == 0 || p == 1, "sparse_jac_fun: p != 0 and p != 1" ); size_t K = row.size(); CPPAD_ASSERT_KNOWN( K >= m, "sparse_jac_fun: row.size() < m" ); size_t i, j, k; if( p == 0 ) for(i = 0; i < m; i++) fp[i] = Float(0); Float t; for(k = 0; k < K; k++) { i = row[k]; j = col[k]; t = exp( x[j] * x[j] / 2.0 ); switch(p) { case 0: fp[i] += t; break; case 1: fp[k] = t * x[j]; break; } } } } // END C++ # endif cppad-20170000.3/cppad/speed/det_of_minor.hpp0000644000175200017650000001634513057470465020012 0ustar coincoin-web// $Id: det_of_minor.hpp 3855 2016-12-19 00:30:54Z bradbell $ # ifndef CPPAD_SPEED_DET_OF_MINOR_HPP # define CPPAD_SPEED_DET_OF_MINOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin det_of_minor$$ $spell CppAD cppad.hpp hpp std Det const namespace $$ $section Determinant of a Minor$$ $mindex det_of_minor matrix$$ $head Syntax$$ $codei%# include %$$ $icode%d% = det_of_minor(%a%, %m%, %n%, %r%, %c%)%$$ $head Inclusion$$ The template function $code det_of_minor$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/det_of_minor.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head Purpose$$ This template function returns the determinant of a minor of the matrix $latex A$$ using expansion by minors. The elements of the $latex n \times n$$ minor $latex M$$ of the matrix $latex A$$ are defined, for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , n-1$$, by $latex \[ M_{i,j} = A_{R(i), C(j)} \]$$ where the functions $latex R(i)$$ is defined by the $cref/argument r/det_of_minor/r/$$ and $latex C(j)$$ is defined by the $cref/argument c/det_of_minor/c/$$. $pre $$ This template function is for example and testing purposes only. Expansion by minors is chosen as an example because it uses a lot of floating point operations yet does not require much source code (on the order of $icode m$$ factorial floating point operations and about 70 lines of source code including comments). This is not an efficient method for computing a determinant; for example, using an LU factorization would be better. $head Determinant of A$$ If the following conditions hold, the minor is the entire matrix $latex A$$ and hence $code det_of_minor$$ will return the determinant of $latex A$$: $list number$$ $latex n = m$$. $lnext for $latex i = 0 , \ldots , m-1$$, $latex r[i] = i+1$$, and $latex r[m] = 0$$. $lnext for $latex j = 0 , \ldots , m-1$$, $latex c[j] = j+1$$, and $latex c[m] = 0$$. $lend $head a$$ The argument $icode a$$ has prototype $codei% const std::vector<%Scalar%>& %a% %$$ and is a vector with size $latex m * m$$ (see description of $cref/Scalar/det_of_minor/Scalar/$$ below). The elements of the $latex m \times m$$ matrix $latex A$$ are defined, for $latex i = 0 , \ldots , m-1$$ and $latex j = 0 , \ldots , m-1$$, by $latex \[ A_{i,j} = a[ i * m + j] \] $$ $head m$$ The argument $icode m$$ has prototype $codei% size_t %m% %$$ and is the number of rows (and columns) in the square matrix $latex A$$. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ and is the number of rows (and columns) in the square minor $latex M$$. $head r$$ The argument $icode r$$ has prototype $codei% std::vector& %r% %$$ and is a vector with $latex m + 1$$ elements. This vector defines the function $latex R(i)$$ which specifies the rows of the minor $latex M$$. To be specific, the function $latex R(i)$$ for $latex i = 0, \ldots , n-1$$ is defined by $latex \[ \begin{array}{rcl} R(0) & = & r[m] \\ R(i+1) & = & r[ R(i) ] \end{array} \] $$ All the elements of $icode r$$ must have value less than or equal $icode m$$. The elements of vector $icode r$$ are modified during the computation, and restored to their original value before the return from $code det_of_minor$$. $head c$$ The argument $icode c$$ has prototype $codei% std::vector& %c% %$$ and is a vector with $latex m + 1$$ elements This vector defines the function $latex C(i)$$ which specifies the rows of the minor $latex M$$. To be specific, the function $latex C(i)$$ for $latex j = 0, \ldots , n-1$$ is defined by $latex \[ \begin{array}{rcl} C(0) & = & c[m] \\ C(j+1) & = & c[ C(j) ] \end{array} \] $$ All the elements of $icode c$$ must have value less than or equal $icode m$$. The elements of vector $icode c$$ are modified during the computation, and restored to their original value before the return from $code det_of_minor$$. $head d$$ The result $icode d$$ has prototype $codei% %Scalar% %d% %$$ and is equal to the determinant of the minor $latex M$$. $head Scalar$$ If $icode x$$ and $icode y$$ are objects of type $icode Scalar$$ and $icode i$$ is an object of type $code int$$, the $icode Scalar$$ must support the following operations: $table $bold Syntax$$ $cnext $bold Description$$ $cnext $bold Result Type$$ $rnext $icode%Scalar% %x%$$ $cnext default constructor for $icode Scalar$$ object. $rnext $icode%x% = %i%$$ $cnext set value of $icode x$$ to current value of $icode i$$ $rnext $icode%x% = %y%$$ $cnext set value of $icode x$$ to current value of $icode y$$ $rnext $icode%x% + %y%$$ $cnext value of $icode x$$ plus $icode y$$ $cnext $icode Scalar$$ $rnext $icode%x% - %y%$$ $cnext value of $icode x$$ minus $icode y$$ $cnext $icode Scalar$$ $rnext $icode%x% * %y%$$ $cnext value of $icode x$$ times value of $icode y$$ $cnext $icode Scalar$$ $tend $children% speed/example/det_of_minor.cpp% omh/det_of_minor_hpp.omh %$$ $head Example$$ The file $cref det_of_minor.cpp$$ contains an example and test of $code det_of_minor.hpp$$. It returns true if it succeeds and false otherwise. $head Source Code$$ The file $cref det_of_minor.hpp$$ contains the source for this template function. $end --------------------------------------------------------------------------- */ // BEGIN C++ namespace CppAD { // BEGIN CppAD namespace template Scalar det_of_minor( const std::vector& a , size_t m , size_t n , std::vector& r , std::vector& c ) { const size_t R0 = r[m]; // R(0) size_t Cj = c[m]; // C(j) (case j = 0) size_t Cj1 = m; // C(j-1) (case j = 0) // check for 1 by 1 case if( n == 1 ) return a[ R0 * m + Cj ]; // initialize determinant of the minor M Scalar detM = Scalar(0); // initialize sign of factor for next sub-minor int s = 1; // remove row with index 0 in M from all the sub-minors of M r[m] = r[R0]; // for each column of M for(size_t j = 0; j < n; j++) { // element with index (0,j) in the minor M Scalar M0j = a[ R0 * m + Cj ]; // remove column with index j in M to form next sub-minor S of M c[Cj1] = c[Cj]; // compute determinant of the current sub-minor S Scalar detS = det_of_minor(a, m, n - 1, r, c); // restore column Cj to represenation of M as a minor of A c[Cj1] = Cj; // include this sub-minor term in the summation if( s > 0 ) detM = detM + M0j * detS; else detM = detM - M0j * detS; // advance to next column of M Cj1 = Cj; Cj = c[Cj]; s = - s; } // restore row zero to the minor representation for M r[m] = R0; // return the determinant of the minor M return detM; } } // END CppAD namespace // END C++ # endif cppad-20170000.3/cppad/speed/sparse_hes_fun.hpp0000644000175200017650000001563113057470465020347 0ustar coincoin-web// $Id: sparse_hes_fun.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_SPEED_SPARSE_HES_FUN_HPP # define CPPAD_SPEED_SPARSE_HES_FUN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparse_hes_fun$$ $spell hes cppad hpp fp CppAD namespace const bool exp arg $$ $section Evaluate a Function That Has a Sparse Hessian$$ $mindex sparse_hes_fun$$ $head Syntax$$ $codei%# include %$$ $codei%sparse_hes_fun(%n%, %x%, %row%, %col%, %p%, %fp%)%$$ $head Purpose$$ This routine evaluates $latex f(x)$$, $latex f^{(1)} (x)$$, or $latex f^{(2)} (x)$$ where the Hessian $latex f^{(2)} (x)$$ is sparse. The function $latex f : \B{R}^n \rightarrow \B{R}$$ only depends on the size and contents of the index vectors $icode row$$ and $icode col$$. The non-zero entries in the Hessian of this function have one of the following forms: $latex \[ \DD{f}{x[row[k]]}{x[row[k]]} \; , \; \DD{f}{x[row[k]]}{x[col[k]]} \; , \; \DD{f}{x[col[k]]}{x[row[k]]} \; , \; \DD{f}{x[col[k]]}{x[col[k]]} \] $$ for some $latex k $$ between zero and $latex K-1 $$. All the other terms of the Hessian are zero. $head Inclusion$$ The template function $code sparse_hes_fun$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/sparse_hes_fun.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head Float$$ The type $icode Float$$ must be a $cref NumericType$$. In addition, if $icode y$$ and $icode z$$ are $icode Float$$ objects, $codei% %y% = exp(%z%) %$$ must set the $icode y$$ equal the exponential of $icode z$$, i.e., the derivative of $icode y$$ with respect to $icode z$$ is equal to $icode y$$. $head FloatVector$$ The type $icode FloatVector$$ is any $cref SimpleVector$$, or it can be a raw pointer, with elements of type $icode Float$$. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ It specifies the dimension for the domain space for $latex f(x)$$. $head x$$ The argument $icode x$$ has prototype $codei% const %FloatVector%& %x% %$$ It contains the argument value for which the function, or its derivative, is being evaluated. We use $latex n$$ to denote the size of the vector $icode x$$. $head row$$ The argument $icode row$$ has prototype $codei% const CppAD::vector& %row% %$$ It specifies one of the first index of $latex x$$ for each non-zero Hessian term (see $cref/purpose/sparse_hes_fun/Purpose/$$ above). All the elements of $icode row$$ must be between zero and $icode%n%-1%$$. The value $latex K$$ is defined by $icode%K% = %row%.size()%$$. $head col$$ The argument $icode col$$ has prototype $codei% const CppAD::vector& %col% %$$ and its size must be $latex K$$; i.e., the same as for $icode col$$. It specifies the second index of $latex x$$ for the non-zero Hessian terms. All the elements of $icode col$$ must be between zero and $icode%n%-1%$$. There are no duplicated entries requested, to be specific, if $icode%k1% != %k2%$$ then $codei% ( %row%[%k1%] , %col%[%k1%] ) != ( %row%[%k2%] , %col%[%k2%] ) %$$ $head p$$ The argument $icode p$$ has prototype $codei% size_t %p% %$$ It is either zero or two and specifies the order of the derivative of $latex f$$ that is being evaluated, i.e., $latex f^{(p)} (x)$$ is evaluated. $head fp$$ The argument $icode fp$$ has prototype $codei% %FloatVector%& %fp% %$$ The input value of the elements of $icode fp$$ does not matter. $subhead Function$$ If $icode p$$ is zero, $icode fp$$ has size one and $icode%fp%[0]%$$ is the value of $latex f(x)$$. $subhead Hessian$$ If $icode p$$ is two, $icode fp$$ has size $icode K$$ and for $latex k = 0 , \ldots , K-1$$, $latex \[ \DD{f}{ x[ \R{row}[k] ] }{ x[ \R{col}[k] ]} = fp [k] \] $$ $children% speed/example/sparse_hes_fun.cpp% omh/sparse_hes_fun.omh %$$ $head Example$$ The file $cref sparse_hes_fun.cpp$$ contains an example and test of $code sparse_hes_fun.hpp$$. It returns true if it succeeds and false otherwise. $head Source Code$$ The file $cref sparse_hes_fun.hpp$$ contains the source code for this template function. $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include # include # include // following needed by gcc under fedora 17 so that exp(double) is defined # include namespace CppAD { template void sparse_hes_fun( size_t n , const FloatVector& x , const CppAD::vector& row , const CppAD::vector& col , size_t p , FloatVector& fp ) { // check numeric type specifications CheckNumericType(); // check value of p CPPAD_ASSERT_KNOWN( p == 0 || p == 2, "sparse_hes_fun: p != 0 and p != 2" ); size_t K = row.size(); size_t i, j, k; if( p == 0 ) fp[0] = Float(0); else { for(k = 0; k < K; k++) fp[k] = Float(0); } // determine which diagonal entries are present in row[k], col[k] CppAD::vector diagonal(n); for(i = 0; i < n; i++) diagonal[i] = K; // no diagonal entry for this row for(k = 0; k < K; k++) { if( row[k] == col[k] ) { CPPAD_ASSERT_UNKNOWN( diagonal[row[k]] == K ); // index of the diagonal entry diagonal[ row[k] ] = k; } } // determine which entries must be multiplied by a factor of two CppAD::vector factor(K); for(k = 0; k < K; k++) { factor[k] = Float(1); for(size_t k1 = 0; k1 < K; k1++) { bool reflected = true; reflected &= k != k1; reflected &= row[k] != col[k]; reflected &= row[k] == col[k1]; reflected &= col[k] == row[k1]; if( reflected ) factor[k] = Float(2); } } Float t; for(k = 0; k < K; k++) { i = row[k]; j = col[k]; t = exp( x[i] * x[j] ); switch(p) { case 0: fp[0] += t; break; case 2: if( i == j ) { // dt_dxi = 2.0 * xi * t fp[k] += ( Float(2) + Float(4) * x[i] * x[i] ) * t; } else { // dt_dxi = xj * t fp[k] += factor[k] * ( Float(1) + x[i] * x[j] ) * t; if( diagonal[i] != K ) { size_t ki = diagonal[i]; fp[ki] += x[j] * x[j] * t; } if( diagonal[j] != K ) { size_t kj = diagonal[j]; fp[kj] += x[i] * x[i] * t; } } break; } } } } // END C++ # endif cppad-20170000.3/cppad/speed/det_by_lu.hpp0000644000175200017650000001070513057470465017306 0ustar coincoin-web// $Id: det_by_lu.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_SPEED_DET_BY_LU_HPP # define CPPAD_SPEED_DET_BY_LU_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin det_by_lu$$ $spell CppAD cppad lu hpp typedef const hpp Det CPPAD_TESTVECTOR namespace $$ $section Determinant Using Expansion by Lu Factorization$$ $mindex det_by_lu factor$$ $head Syntax$$ $codei%# include %$$ $codei%det_by_lu<%Scalar%> %det%(%n%) %$$ $icode%d% = %det%(%a%) %$$ $head Inclusion$$ The template class $code det_by_lu$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/det_by_lu.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head Constructor$$ The syntax $codei% det_by_lu<%Scalar%> %det%(%n%) %$$ constructs the object $icode det$$ which can be used for evaluating the determinant of $icode n$$ by $icode n$$ matrices using LU factorization. $head Scalar$$ The type $icode Scalar$$ can be any $cref NumericType$$ $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ $head det$$ The syntax $codei% %d% = %det%(%a%) %$$ returns the determinant of the matrix $latex A$$ using LU factorization. $subhead a$$ The argument $icode a$$ has prototype $codei% const %Vector% &%a% %$$ It must be a $icode Vector$$ with length $latex n * n$$ and with It must be a $icode Vector$$ with length $latex n * n$$ and with elements of type $icode Scalar$$. The elements of the $latex n \times n$$ matrix $latex A$$ are defined, for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , n-1$$, by $latex \[ A_{i,j} = a[ i * m + j] \] $$ $subhead d$$ The return value $icode d$$ has prototype $codei% %Scalar% %d% %$$ $head Vector$$ If $icode y$$ is a $icode Vector$$ object, it must support the syntax $codei% %y%[%i%] %$$ where $icode i$$ has type $code size_t$$ with value less than $latex n * n$$. This must return a $icode Scalar$$ value corresponding to the $th i$$ element of the vector $icode y$$. This is the only requirement of the type $icode Vector$$. $children% speed/example/det_by_lu.cpp% omh/det_by_lu_hpp.omh %$$ $head Example$$ The file $cref det_by_lu.cpp$$ contains an example and test of $code det_by_lu.hpp$$. It returns true if it succeeds and false otherwise. $head Source Code$$ The file $cref det_by_lu.hpp$$ contains the source for this template function. $end --------------------------------------------------------------------------- */ // BEGIN C++ # include # include // BEGIN CppAD namespace namespace CppAD { // The AD complex case is used by examples by not used by speed tests // Must define a specializatgion of LeqZero,AbsGeq for the ADComplex case typedef std::complex Complex; typedef CppAD::AD ADComplex; CPPAD_BOOL_UNARY(Complex, LeqZero ) CPPAD_BOOL_BINARY(Complex, AbsGeq ) template class det_by_lu { private: const size_t m_; const size_t n_; CPPAD_TESTVECTOR(Scalar) A_; CPPAD_TESTVECTOR(Scalar) B_; CPPAD_TESTVECTOR(Scalar) X_; public: det_by_lu(size_t n) : m_(0), n_(n), A_(n * n) { } template inline Scalar operator()(const Vector &x) { using CppAD::exp; Scalar logdet; Scalar det; int signdet; size_t i; // copy matrix so it is not overwritten for(i = 0; i < n_ * n_; i++) A_[i] = x[i]; // comput log determinant signdet = CppAD::LuSolve( n_, m_, A_, B_, X_, logdet); /* // Do not do this for speed test because it makes floating // point operation sequence very simple. if( signdet == 0 ) det = 0; else det = Scalar( signdet ) * exp( logdet ); */ // convert to determinant det = Scalar( signdet ) * exp( logdet ); # ifdef FADBAD // Fadbad requires tempories to be set to constants for(i = 0; i < n_ * n_; i++) A_[i] = 0; # endif return det; } }; } // END CppAD namespace // END C++ # endif cppad-20170000.3/cppad/speed/mat_sum_sq.hpp0000644000175200017650000000706213057470465017512 0ustar coincoin-web// $Id: mat_sum_sq.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_SPEED_MAT_SUM_SQ_HPP # define CPPAD_SPEED_MAT_SUM_SQ_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin mat_sum_sq$$ $spell sq namespace const CppAD sq cppad.hpp $$ $section Sum Elements of a Matrix Times Itself$$ $mindex mat_sum_sq multiply speed test$$ $head Syntax$$ $codei%# include %$$ $icode%mat_sum_sq(%n%, %x%, %y%, %z%)%$$ $head Purpose$$ This routine is intended for use with the matrix multiply speed tests; to be specific, it computes $latex \[ \begin{array}{rcl} y_{i,j} & = & \sum_{k=0}^{n-1} x_{i,k} x_{k,j} \\ z_0 & = & \sum_{i=0}^{n-1} \sum_{j=0}^{n-1} y_{i,j} \end{array} \] $$ see $cref link_mat_mul$$. $head Inclusion$$ The template function $code mat_sum_sq$$ is defined in the $code CppAD$$ namespace by including the file $code cppad/speed/mat_sum_sq.hpp$$ (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by $cref/cppad.hpp/cppad/$$. $head n$$ This argument has prototype $codei% size_t %n% %$$ It specifies the size of the matrices. $head x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ and $icode%x%.size() == %n% * %n%$$. It contains the elements of $latex x$$ in row major order; i.e., $latex \[ x_{i,j} = x [ i * n + j ] \] $$ $head y$$ The argument $icode y$$ has prototype $codei% %Vector%& %y% %$$ and $icode%y%.size() == %n% * %n%$$. The input value of its elements does not matter. Upon return, $latex \[ \begin{array}{rcl} y_{i,j} & = & \sum_{k=0}^{n-1} x_{i,k} x_{k,j} \\ y[ i * n + j ] & = & y_{i,j} \end{array} \] $$ $head z$$ The argument $icode d$$ has prototype $codei% %Vector%& %z% %$$. The input value of its element does not matter. Upon return $latex \[ \begin{array}{rcl} z_0 & = & \sum_{i=0}^{n-1} \sum_{j=0}^n y_{i,j} \\ z[0] & = & z_0 \end{array} \] $$ $head Vector$$ The type $icode Vector$$ is any $cref SimpleVector$$, or it can be a raw pointer to the vector elements. The element type must support addition, multiplication, and assignment to both its own type and to a double value. $children% speed/example/mat_sum_sq.cpp% omh/mat_sum_sq_hpp.omh %$$ $head Example$$ The file $cref mat_sum_sq.cpp$$ contains an example and test of $code mat_sum_sq.hpp$$. It returns true if it succeeds and false otherwise. $head Source Code$$ The file $cref mat_sum_sq.hpp$$ contains the source for this template function. $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include // namespace CppAD { template void mat_sum_sq(size_t n, Vector& x , Vector& y , Vector& z) { size_t i, j, k; // Very simple computation of y = x * x for speed comparison for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { y[i * n + j] = 0.; for(k = 0; k < n; k++) y[i * n + j] += x[i * n + k] * x[k * n + j]; } } z[0] = 0.; for(i = 0; i < n; i++) { for(j = 0; j < n; j++) z[0] += y[i * n + j]; } return; } } // END C++ # endif cppad-20170000.3/cppad/utility/0002755000175200017650000000000013057470465015231 5ustar coincoin-webcppad-20170000.3/cppad/utility/speed_test.hpp0000644000175200017650000002574113057470465020110 0ustar coincoin-web// $Id: speed_test.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_SPEED_TEST_HPP # define CPPAD_UTILITY_SPEED_TEST_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin speed_test$$ $spell gettimeofday vec cppad.hpp Microsoft namespace std const cout ctime ifdef const endif cpp $$ $section Run One Speed Test and Return Results$$ $mindex speed_test$$ $head Syntax$$ $codei%# include %$$ $icode%rate_vec% = speed_test(%test%, %size_vec%, %time_min%)%$$ $head Purpose$$ The $code speed_test$$ function executes a speed test for various sized problems and reports the rate of execution. $head Motivation$$ It is important to separate small calculation units and test them individually. This way individual changes can be tested in the context of the routine that they are in. On many machines, accurate timing of a very short execution sequences is not possible. In addition, there may be set up and tear down time for a test that we do not really want included in the timing. For this reason $code speed_test$$ automatically determines how many times to repeat the section of the test that we wish to time. $head Include$$ The file $code cppad/speed_test.hpp$$ defines the $code speed_test$$ function. This file is included by $code cppad/cppad.hpp$$ and it can also be included separately with out the rest of the $code CppAD$$ routines. $head Vector$$ We use $icode Vector$$ to denote a $cref/simple vector class/SimpleVector/$$ with elements of type $code size_t$$. $head test$$ The $code speed_test$$ argument $icode test$$ is a function with the syntax $codei% %test%(%size%, %repeat%) %$$ and its return value is $code void$$. $subhead size$$ The $icode test$$ argument $icode size$$ has prototype $codei% size_t %size% %$$ It specifies the size for this test. $subhead repeat$$ The $icode test$$ argument $icode repeat$$ has prototype $codei% size_t %repeat% %$$ It specifies the number of times to repeat the test. $head size_vec$$ The $code speed_test$$ argument $icode size_vec$$ has prototype $codei% const %Vector%& %size_vec% %$$ This vector determines the size for each of the tests problems. $head time_min$$ The argument $icode time_min$$ has prototype $codei% double %time_min% %$$ It specifies the minimum amount of time in seconds that the $icode test$$ routine should take. The $icode repeat$$ argument to $icode test$$ is increased until this amount of execution time is reached. $head rate_vec$$ The return value $icode rate_vec$$ has prototype $codei% %Vector%& %rate_vec% %$$ We use $latex n$$ to denote its size which is the same as the vector $icode size_vec$$. For $latex i = 0 , \ldots , n-1$$, $codei% %rate_vec%[%i%] %$$ is the ratio of $icode repeat$$ divided by time in seconds for the problem with size $icode%size_vec%[%i%]%$$. $head Timing$$ If your system supports the unix $code gettimeofday$$ function, it will be used to measure time. Otherwise, time is measured by the difference in $codep (double) clock() / (double) CLOCKS_PER_SEC $$ in the context of the standard $code $$ definitions. $children% speed/example/speed_test.cpp %$$ $head Example$$ The routine $cref speed_test.cpp$$ is an example and test of $code speed_test$$. $end ----------------------------------------------------------------------- */ # include # include # include # include namespace CppAD { // BEGIN CppAD namespace // implemented as an inline so that can include in multiple link modules // with this same file template inline Vector speed_test( void test(size_t size, size_t repeat), const Vector& size_vec , double time_min ) { // check that size_vec is a simple vector with size_t elements CheckSimpleVector(); size_t n = size_vec.size(); Vector rate_vec(n); size_t i; for(i = 0; i < n; i++) { size_t size = size_vec[i]; size_t repeat = 1; double s0 = elapsed_seconds(); double s1 = elapsed_seconds(); while( s1 - s0 < time_min ) { repeat = 2 * repeat; s0 = elapsed_seconds(); test(size, repeat); s1 = elapsed_seconds(); } rate_vec[i] = (size_t)(.5 + repeat / (s1 - s0)); } return rate_vec; } } // END CppAD namespace /* $begin SpeedTest$$ $spell cppad.hpp Microsoft namespace std const cout ctime ifdef const endif cpp $$ $section Run One Speed Test and Print Results$$ $mindex SpeedTest$$ $head Syntax$$ $codei%# include %$$ $codei%SpeedTest(%Test%, %first%, %inc%, %last%)%$$ $head Purpose$$ The $code SpeedTest$$ function executes a speed test for various sized problems and reports the results on standard output; i.e. $code std::cout$$. The size of each test problem is included in its report (unless $icode first$$ is equal to $icode last$$). $head Motivation$$ It is important to separate small calculation units and test them individually. This way individual changes can be tested in the context of the routine that they are in. On many machines, accurate timing of a very short execution sequences is not possible. In addition, there may be set up time for a test that we do not really want included in the timing. For this reason $code SpeedTest$$ automatically determines how many times to repeat the section of the test that we wish to time. $head Include$$ The file $code speed_test.hpp$$ contains the $code SpeedTest$$ function. This file is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head Test$$ The $code SpeedTest$$ argument $icode Test$$ is a function with the syntax $codei% %name% = %Test%(%size%, %repeat%) %$$ $subhead size$$ The $icode Test$$ argument $icode size$$ has prototype $codei% size_t %size% %$$ It specifies the size for this test. $subhead repeat$$ The $icode Test$$ argument $icode repeat$$ has prototype $codei% size_t %repeat% %$$ It specifies the number of times to repeat the test. $subhead name$$ The $icode Test$$ result $icode name$$ has prototype $codei% std::string %name% %$$ The results for this test are reported on $code std::cout$$ with $icode name$$ as an identifier for the test. It is assumed that, for the duration of this call to $code SpeedTest$$, $icode Test$$ will always return the same value for $icode name$$. If $icode name$$ is the empty string, no test name is reported by $code SpeedTest$$. $head first$$ The $code SpeedTest$$ argument $icode first$$ has prototype $codei% size_t %first% %$$ It specifies the size of the first test problem reported by this call to $code SpeedTest$$. $head last$$ The $code SpeedTest$$ argument $icode last$$ has prototype $codei% size_t %last% %$$ It specifies the size of the last test problem reported by this call to $code SpeedTest$$. $head inc$$ The $code SpeedTest$$ argument $icode inc$$ has prototype $codei% int %inc% %$$ It specifies the increment between problem sizes; i.e., all values of $icode size$$ in calls to $icode Test$$ are given by $codei% %size% = %first% + %j% * %inc% %$$ where $icode j$$ is a positive integer. The increment can be positive or negative but it cannot be zero. The values $icode first$$, $icode last$$ and $icode inc$$ must satisfy the relation $latex \[ inc * ( last - first ) \geq 0 \] $$ $head rate$$ The value displayed in the $code rate$$ column on $code std::cout$$ is defined as the value of $icode repeat$$ divided by the corresponding elapsed execution time in seconds. The elapsed execution time is measured by the difference in $codep (double) clock() / (double) CLOCKS_PER_SEC $$ in the context of the standard $code $$ definitions. $head Errors$$ If one of the restrictions above is violated, the CppAD error handler is used to report the error. You can redefine this action using the instructions in $cref ErrorHandler$$ $head Example$$ $children% speed/example/speed_program.cpp %$$ The program $cref speed_program.cpp$$ is an example usage of $code SpeedTest$$. $end ----------------------------------------------------------------------- */ // BEGIN C++ # include # include # include # include namespace CppAD { // BEGIN CppAD namespace inline void SpeedTestNdigit(size_t value, size_t &ndigit, size_t &pow10) { pow10 = 10; ndigit = 1; while( pow10 <= value ) { pow10 *= 10; ndigit += 1; } } // implemented as an inline so that can include in multiple link modules // with this same file inline void SpeedTest( std::string Test(size_t size, size_t repeat), size_t first, int inc, size_t last ) { using std::cout; using std::endl; size_t size; size_t repeat; size_t rate; size_t digit; size_t ndigit; size_t pow10; size_t maxSize; size_t maxSizeDigit; double s0; double s1; std::string name; CPPAD_ASSERT_KNOWN( inc != 0 && first != 0 && last != 0, "inc, first, or last is zero in call to SpeedTest" ); CPPAD_ASSERT_KNOWN( (inc > 0 && first <= last) || (inc < 0 && first >= last), "SpeedTest: increment is positive and first > last or " "increment is negative and first < last" ); // compute maxSize maxSize = size = first; while( (inc > 0 && size <= last) || (inc < 0 && size >= last) ) { if( size > maxSize ) maxSize = size; // next size if( ((int) size) + inc > 0 ) size += inc; else size = 0; } SpeedTestNdigit(maxSize, maxSizeDigit, pow10); size = first; while( (inc > 0 && size <= last) || (inc < 0 && size >= last) ) { repeat = 1; s0 = elapsed_seconds(); s1 = elapsed_seconds(); while( s1 - s0 < 1. ) { repeat = 2 * repeat; s0 = elapsed_seconds(); name = Test(size, repeat); s1 = elapsed_seconds(); } rate = (size_t)(.5 + repeat / (s1 - s0)); if( size == first && name != "" ) cout << name << endl; if( first != last ) { // convert int(size_t) to avoid warning on _MSC_VER sys std::cout << "size = " << int(size); SpeedTestNdigit(size, ndigit, pow10); while( ndigit < maxSizeDigit ) { cout << " "; ndigit++; } cout << " "; } cout << "rate = "; SpeedTestNdigit(rate, ndigit, pow10); while( ndigit > 0 ) { pow10 /= 10; digit = rate / pow10; // convert int(size_t) to avoid warning on _MSC_VER sys std::cout << int(digit); rate = rate % pow10; ndigit -= 1; if( (ndigit > 0) && (ndigit % 3 == 0) ) cout << ","; } cout << endl; // next size if( ((int) size) + inc > 0 ) size += inc; else size = 0; } return; } } // END CppAD namespace // END C++ # endif cppad-20170000.3/cppad/utility/check_numeric_type.hpp0000644000175200017650000001227413057470465021606 0ustar coincoin-web// $Id: check_numeric_type.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_UTILITY_CHECK_NUMERIC_TYPE_HPP # define CPPAD_UTILITY_CHECK_NUMERIC_TYPE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin CheckNumericType$$ $spell alloc cppad.hpp CppAD $$ $section Check NumericType Class Concept$$ $mindex numeric CheckNumericType$$ $head Syntax$$ $codei%# include %$$ $codei%CheckNumericType<%NumericType%>()%$$ $head Purpose$$ The syntax $codei% CheckNumericType<%NumericType%>() %$$ preforms compile and run time checks that the type specified by $icode NumericType$$ satisfies all the requirements for a $cref NumericType$$ class. If a requirement is not satisfied, a an error message makes it clear what condition is not satisfied. $head Include$$ The file $code cppad/check_numeric_type.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest if the CppAD include files. $head Parallel Mode$$ The routine $cref/thread_alloc::parallel_setup/ta_parallel_setup/$$ must be called before it can be used in $cref/parallel/ta_in_parallel/$$ mode. $head Example$$ $children% example/check_numeric_type.cpp %$$ The file $cref check_numeric_type.cpp$$ contains an example and test of this function. It returns true, if it succeeds an false otherwise. The comments in this example suggest a way to change the example so an error message occurs. $end --------------------------------------------------------------------------- */ # include # include namespace CppAD { # ifdef NDEBUG template void CheckNumericType(void) { } # else template NumericType CheckNumericType(void) { // Section 3.6.2 of ISO/IEC 14882:1998(E) states: "The storage for // objects with static storage duration (3.7.1) shall be zero- // initialized (8.5) before any other initialization takes place." static size_t count[CPPAD_MAX_NUM_THREADS]; size_t thread = thread_alloc::thread_num(); if( count[thread] > 0 ) return NumericType(0); count[thread]++; /* contructors */ NumericType check_NumericType_default_constructor; NumericType check_NumericType_constructor_from_int(1); const NumericType x(1); NumericType check_NumericType_copy_constructor(x); // assignment NumericType check_NumericType_assignment; check_NumericType_assignment = x; /* unary operators */ const NumericType check_NumericType_unary_plus(1); NumericType check_NumericType_unary_plus_result = + check_NumericType_unary_plus; const NumericType check_NumericType_unary_minus(1); NumericType check_NumericType_unary_minus_result = - check_NumericType_unary_minus; /* binary operators */ const NumericType check_NumericType_binary_addition(1); NumericType check_NumericType_binary_addition_result = check_NumericType_binary_addition + x; const NumericType check_NumericType_binary_subtraction(1); NumericType check_NumericType_binary_subtraction_result = check_NumericType_binary_subtraction - x; const NumericType check_NumericType_binary_multiplication(1); NumericType check_NumericType_binary_multiplication_result = check_NumericType_binary_multiplication * x; const NumericType check_NumericType_binary_division(1); NumericType check_NumericType_binary_division_result = check_NumericType_binary_division / x; /* computed assignment operators */ NumericType check_NumericType_computed_assignment_addition(1); check_NumericType_computed_assignment_addition += x; NumericType check_NumericType_computed_assignment_subtraction(1); check_NumericType_computed_assignment_subtraction -= x; NumericType check_NumericType_computed_assignment_multiplication(1); check_NumericType_computed_assignment_multiplication *= x; NumericType check_NumericType_computed_assignment_division(1); check_NumericType_computed_assignment_division /= x; /* use all values so as to avoid warnings */ check_NumericType_default_constructor = x; return + check_NumericType_default_constructor + check_NumericType_constructor_from_int + check_NumericType_copy_constructor + check_NumericType_assignment + check_NumericType_unary_plus_result + check_NumericType_unary_minus_result + check_NumericType_binary_addition_result + check_NumericType_binary_subtraction_result + check_NumericType_binary_multiplication_result + check_NumericType_binary_division_result + check_NumericType_computed_assignment_addition + check_NumericType_computed_assignment_subtraction + check_NumericType_computed_assignment_multiplication + check_NumericType_computed_assignment_division ; } # endif } // end namespace CppAD # endif cppad-20170000.3/cppad/utility/track_new_del.hpp0000644000175200017650000003331413057470465020545 0ustar coincoin-web// $Id: track_new_del.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_TRACK_NEW_DEL_HPP # define CPPAD_UTILITY_TRACK_NEW_DEL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin TrackNewDel$$ $spell cppad.hpp Cpp newptr Vec oldptr newlen ncopy const $$ $section Routines That Track Use of New and Delete$$ $mindex memory NDEBUG CPPAD_TRACK_NEW_VEC CppADTrackNewVec CPPAD_TRACK_DEL_VEC CppADTrackDelVec CPPAD_TRACK_EXTEND CppADTrackExtend CPPAD_TRACK_COUNT thread multi$$ $head Deprecated 2007-07-23$$ All these routines have been deprecated. You should use the $cref thread_alloc$$ memory allocator instead (which works better in both a single thread and properly in multi-threading environment). $head Syntax$$ $codei%# include %$$ $icode%newptr% = TrackNewVec(%file%, %line%, %newlen%, %oldptr%) %$$ $codei%TrackDelVec(%file%, %line%, %oldptr%) %$$ $icode%newptr% = TrackExtend(%file%, %line%, %newlen%, %ncopy%, %oldptr%) %$$ $icode%count% = TrackCount(%file%, %line%)%$$ $head Purpose$$ These routines aid in the use of $code new[]$$ and $code delete[]$$ during the execution of a C++ program. $head Include$$ The file $code cppad/track_new_del.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the CppAD include files. $head file$$ The argument $icode file$$ has prototype $codei% const char *%file% %$$ It should be the source code file name where the call to $code TrackNew$$ is located. The best way to accomplish this is the use the preprocessor symbol $code __FILE__$$ for this argument. $head line$$ The argument $icode line$$ has prototype $codei% int %line% %$$ It should be the source code file line number where the call to $code TrackNew$$ is located. The best way to accomplish this is the use the preprocessor symbol $code __LINE__$$ for this argument. $head oldptr$$ The argument $icode oldptr$$ has prototype $codei% %Type% *%oldptr% %$$ This argument is used to identify the type $icode Type$$. $head newlen$$ The argument $icode newlen$$ has prototype $codei% size_t %newlen% %$$ $head head newptr$$ The return value $icode newptr$$ has prototype $codei% %Type% *%newptr% %$$ It points to the newly allocated vector of objects that were allocated using $codei% new Type[%newlen%] %$$ $head ncopy$$ The argument $icode ncopy$$ has prototype $codei% size_t %ncopy% %$$ This specifies the number of elements that are copied from the old array to the new array. The value of $icode ncopy$$ must be less than or equal $icode newlen$$. $head TrackNewVec$$ If $code NDEBUG$$ is defined, this routine only sets $codei% %newptr% = %Type% new[%newlen%] %$$ The value of $icode oldptr$$ does not matter (except that it is used to identify $icode Type$$). If $code NDEBUG$$ is not defined, $code TrackNewVec$$ also tracks the this memory allocation. In this case, if memory cannot be allocated $cref ErrorHandler$$ is used to generate a message stating that there was not sufficient memory. $subhead Macro$$ The preprocessor macro call $codei% CPPAD_TRACK_NEW_VEC(%newlen%, %oldptr%) %$$ expands to $codei% CppAD::TrackNewVec(__FILE__, __LINE__, %newlen%, %oldptr%) %$$ $subhead Previously Deprecated$$ The preprocessor macro $code CppADTrackNewVec$$ is the same as $code CPPAD_TRACK_NEW_VEC$$ and was previously deprecated. $head TrackDelVec$$ This routine is used to a vector of objects that have been allocated using $code TrackNew$$ or $code TrackExtend$$. If $code NDEBUG$$ is defined, this routine only frees memory with $codei% delete [] %oldptr% %$$ If $code NDEBUG$$ is not defined, $code TrackDelete$$ also checks that $icode oldptr$$ was allocated by $code TrackNew$$ or $code TrackExtend$$ and has not yet been freed. If this is not the case, $cref ErrorHandler$$ is used to generate an error message. $subhead Macro$$ The preprocessor macro call $codei% CPPAD_TRACK_DEL_VEC(%oldptr%) %$$ expands to $codei% CppAD::TrackDelVec(__FILE__, __LINE__, %oldptr%) %$$ $subhead Previously Deprecated$$ The preprocessor macro $code CppADTrackDelVec$$ is the same as $code CPPAD_TRACK_DEL_VEC$$ was previously deprecated. $head TrackExtend$$ This routine is used to allocate a new vector (using $code TrackNewVec$$), copy $icode ncopy$$ elements from the old vector to the new vector. If $icode ncopy$$ is greater than zero, $icode oldptr$$ must have been allocated using $code TrackNewVec$$ or $code TrackExtend$$. In this case, the vector pointed to by $icode oldptr$$ must be have at least $icode ncopy$$ elements and it will be deleted (using $code TrackDelVec$$). Note that the dependence of $code TrackExtend$$ on $code NDEBUG$$ is indirectly through the routines $code TrackNewVec$$ and $code TrackDelVec$$. $subhead Macro$$ The preprocessor macro call $codei% CPPAD_TRACK_EXTEND(%newlen%, %ncopy%, %oldptr%) %$$ expands to $codei% CppAD::TrackExtend(__FILE__, __LINE__, %newlen%, %ncopy%, %oldptr%) %$$ $subhead Previously Deprecated$$ The preprocessor macro $code CppADTrackExtend$$ is the same as $code CPPAD_TRACK_EXTEND$$ and was previously deprecated. $head TrackCount$$ The return value $icode count$$ has prototype $codei% size_t %count% %$$ If $code NDEBUG$$ is defined, $icode count$$ will be zero. Otherwise, it will be the number of vectors that have been allocated (by $code TrackNewVec$$ or $code TrackExtend$$) and not yet freed (by $code TrackDelete$$). $subhead Macro$$ The preprocessor macro call $codei% CPPAD_TRACK_COUNT() %$$ expands to $codei% CppAD::TrackCount(__FILE__, __LINE__) %$$ $subhead Previously Deprecated$$ The preprocessor macro $code CppADTrackCount$$ is the same as $code CPPAD_TRACK_COUNT$$ and was previously deprecated. $head Multi-Threading$$ These routines cannot be used $cref/in_parallel/ta_in_parallel/$$ execution mode. Use the $cref thread_alloc$$ routines instead. $head Example$$ $children% test_more/track_new_del.cpp %$$ The file $cref TrackNewDel.cpp$$ contains an example and test of these functions. It returns true, if it succeeds, and false otherwise. $end ------------------------------------------------------------------------------ */ # include # include # include # include # include # ifndef CPPAD_TRACK_DEBUG # define CPPAD_TRACK_DEBUG 0 # endif // ------------------------------------------------------------------------- # define CPPAD_TRACK_NEW_VEC(newlen, oldptr) \ CppAD::TrackNewVec(__FILE__, __LINE__, newlen, oldptr) # define CPPAD_TRACK_DEL_VEC(oldptr) \ CppAD::TrackDelVec(__FILE__, __LINE__, oldptr) # define CPPAD_TRACK_EXTEND(newlen, ncopy, oldptr) \ CppAD::TrackExtend(__FILE__, __LINE__, newlen, ncopy, oldptr) # define CPPAD_TRACK_COUNT() \ CppAD::TrackCount(__FILE__, __LINE__) // ------------------------------------------------------------------------- # define CppADTrackNewVec CPPAD_TRACK_NEW_VEC # define CppADTrackDelVec CPPAD_TRACK_DEL_VEC # define CppADTrackExtend CPPAD_TRACK_EXTEND # define CppADTrackCount CPPAD_TRACK_COUNT // ------------------------------------------------------------------------- namespace CppAD { // Begin CppAD namespace // TrackElement ------------------------------------------------------------ class TrackElement { public: std::string file; // corresponding file name int line; // corresponding line number void *ptr; // value returned by TrackNew TrackElement *next; // next element in linked list // default contructor (used to initialize root) TrackElement(void) : file(""), line(0), ptr(CPPAD_NULL), next(CPPAD_NULL) { } TrackElement(const char *f, int l, void *p) : file(f), line(l), ptr(p), next(CPPAD_NULL) { CPPAD_ASSERT_UNKNOWN( p != CPPAD_NULL); } // There is only one tracking list and it starts it here static TrackElement *Root(void) { CPPAD_ASSERT_UNKNOWN( ! thread_alloc::in_parallel() ); static TrackElement root; return &root; } // Print one tracking element static void Print(TrackElement* E) { CPPAD_ASSERT_UNKNOWN( ! thread_alloc::in_parallel() ); using std::cout; cout << "E = " << E; cout << ", E->next = " << E->next; cout << ", E->ptr = " << E->ptr; cout << ", E->line = " << E->line; cout << ", E->file = " << E->file; cout << std::endl; } // Print the linked list for a thread static void Print(void) { CPPAD_ASSERT_UNKNOWN( ! thread_alloc::in_parallel() ); using std::cout; using std::endl; TrackElement *E = Root(); // convert int(size_t) to avoid warning on _MSC_VER systems cout << "Begin Track List" << endl; while( E->next != CPPAD_NULL ) { E = E->next; Print(E); } cout << "End Track List:" << endl; cout << endl; } }; // TrackError ---------------------------------------------------------------- inline void TrackError( const char *routine, const char *file, int line, const char *msg ) { CPPAD_ASSERT_UNKNOWN( ! thread_alloc::in_parallel() ); std::ostringstream buf; buf << routine << ": at line " << line << " in file " << file << std::endl << msg; std::string str = buf.str(); size_t n = str.size(); size_t i; char *message = new char[n + 1]; for(i = 0; i < n; i++) message[i] = str[i]; message[n] = '\0'; CPPAD_ASSERT_KNOWN( false , message); } // TrackNewVec --------------------------------------------------------------- # ifdef NDEBUG template inline Type *TrackNewVec( const char *file, int line, size_t len, Type * /* oldptr */ ) { # if CPPAD_TRACK_DEBUG static bool first = true; if( first ) { std::cout << "NDEBUG is defined for TrackNewVec" << std::endl; first = false; } # endif return (new Type[len]); } # else template Type *TrackNewVec( const char *file , int line , size_t len , Type * /* oldptr */ ) { CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "attempt to use TrackNewVec in parallel execution mode." ); // try to allocate the new memrory Type *newptr = CPPAD_NULL; try { newptr = new Type[len]; } catch(...) { TrackError("TrackNewVec", file, line, "Cannot allocate sufficient memory" ); } // create tracking element void *vptr = static_cast(newptr); TrackElement *E = new TrackElement(file, line, vptr); // get the root TrackElement *root = TrackElement::Root(); // put this elemenent at the front of linked list E->next = root->next; root->next = E; # if CPPAD_TRACK_DEBUG std::cout << "TrackNewVec: "; TrackElement::Print(E); # endif return newptr; } # endif // TrackDelVec -------------------------------------------------------------- # ifdef NDEBUG template inline void TrackDelVec(const char *file, int line, Type *oldptr) { # if CPPAD_TRACK_DEBUG static bool first = true; if( first ) { std::cout << "NDEBUG is defined in TrackDelVec" << std::endl; first = false; } # endif delete [] oldptr; } # else template void TrackDelVec( const char *file , int line , Type *oldptr ) { CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "attempt to use TrackDelVec in parallel execution mode." ); TrackElement *P; TrackElement *E; // search list for pointer P = TrackElement::Root(); E = P->next; void *vptr = static_cast(oldptr); while(E != CPPAD_NULL && E->ptr != vptr) { P = E; E = E->next; } // check if pointer was not in list if( E == CPPAD_NULL || E->ptr != vptr ) TrackError( "TrackDelVec", file, line, "Invalid value for the argument oldptr.\n" "Possible linking of debug and NDEBUG compilations of CppAD." ); # if CPPAD_TRACK_DEBUG std::cout << "TrackDelVec: "; TrackElement::Print(E); # endif // remove tracking element from list P->next = E->next; // delete allocated pointer delete [] oldptr; // delete tracking element delete E; return; } # endif // TrackExtend -------------------------------------------------------------- template Type *TrackExtend( const char *file , int line , size_t newlen , size_t ncopy , Type *oldptr ) { CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "attempt to use TrackExtend in parallel execution mode." ); # if CPPAD_TRACK_DEBUG using std::cout; cout << "TrackExtend: file = " << file; cout << ", line = " << line; cout << ", newlen = " << newlen; cout << ", ncopy = " << ncopy; cout << ", oldptr = " << oldptr; cout << std::endl; # endif CPPAD_ASSERT_KNOWN( ncopy <= newlen, "TrackExtend: ncopy is greater than newlen." ); // allocate the new memrory Type *newptr = TrackNewVec(file, line, newlen, oldptr); // copy the data size_t i; for(i = 0; i < ncopy; i++) newptr[i] = oldptr[i]; // delete the old vector if( ncopy > 0 ) TrackDelVec(file, line, oldptr); return newptr; } // TrackCount -------------------------------------------------------------- inline size_t TrackCount(const char *file, int line) { CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "attempt to use TrackCount in parallel execution mode." ); size_t count = 0; TrackElement *E = TrackElement::Root(); while( E->next != CPPAD_NULL ) { ++count; E = E->next; } return count; } // --------------------------------------------------------------------------- } // End CppAD namespace // preprocessor symbols local to this file # undef CPPAD_TRACK_DEBUG # endif cppad-20170000.3/cppad/utility/vector.hpp0000644000175200017650000005762313057470465017257 0ustar coincoin-web// $Id: vector.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_UTILITY_VECTOR_HPP # define CPPAD_UTILITY_VECTOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin CppAD_vector$$ $spell rvalues thread_alloc cppad.hpp Bool resize cout endl std Cpp const vec ostream elem $$ $section The CppAD::vector Template Class$$ $mindex vector CppAD [] push thread_alloc$$ $head Syntax$$ $code%# include $$ $head Description$$ The include file $code cppad/vector.hpp$$ defines the vector template class $code CppAD::vector$$. This is a $cref SimpleVector$$ template class and in addition it has the features listed below: $head Include$$ The file $code cppad/vector.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the CppAD include files. $head capacity$$ If $icode x$$ is a $codei%CppAD::vector<%Scalar%>%$$, and $icode cap$$ is a $code size_t$$ object, $codei% %cap% = %x%.capacity() %$$ set $icode cap$$ to the number of $icode Scalar$$ objects that could fit in the memory currently allocated for $icode x$$. Note that $codei% %x%.size() <= %x%.capacity() %$$ $head Assignment$$ If $icode x$$ and $icode y$$ are $codei%CppAD::vector<%Scalar%>%$$ objects, $codei% %y% = %x% %$$ has all the properties listed for a $cref/simple vector assignment/SimpleVector/Assignment/$$ plus the following: $subhead Check Size$$ The $code CppAD::vector$$ template class will check that the size of $icode x$$ is either zero or the size of $icode y$$ before doing the assignment. If this is not the case, $code CppAD::vector$$ will use $cref ErrorHandler$$ to generate an appropriate error report. Allowing for assignment to a vector with size zero makes the following code work: $codei% CppAD::vector<%Scalar%> %y%; %y% = %x%; %$$ $subhead Return Reference$$ A reference to the vector $icode y$$ is returned. An example use of this reference is in multiple assignments of the form $codei% %z% = %y% = %x% %$$ $subhead Move Semantics$$ If the C++ compiler supports move semantic rvalues using the $code &&$$ syntax, then it will be used during the vector assignment statement. This means that return values and other temporaries are not be copied, but rather pointers are transferred. $head Element Access$$ If $icode x$$ is a $codei%CppAD::vector<%Scalar%>%$$ object and $icode i$$ has type $code size_t$$, $codei% %x%[%i%] %$$ has all the properties listed for a $cref/simple vector element access/SimpleVector/Element Access/$$ plus the following: $pre $$ The object $icode%x%[%i%]%$$ has type $icode Scalar$$ (is not possibly a different type that can be converted to $icode Scalar$$). $pre $$ If $icode i$$ is not less than the size of the $icode x$$, $code CppAD::vector$$ will use $cref ErrorHandler$$ to generate an appropriate error report. $head push_back$$ If $icode x$$ is a $codei%CppAD::vector<%Scalar%>%$$ object with size equal to $icode n$$ and $icode s$$ has type $icode Scalar$$, $codei% %x%.push_back(%s%) %$$ extends the vector $icode x$$ so that its new size is $icode n$$ plus one and $icode%x%[%n%]%$$ is equal to $icode s$$ (equal in the sense of the $icode Scalar$$ assignment operator). $head push_vector$$ If $icode x$$ is a $codei%CppAD::vector<%Scalar%>%$$ object with size equal to $icode n$$ and $icode v$$ is a $cref/simple vector/SimpleVector/$$ with elements of type $icode Scalar$$ and size $icode m$$, $codei% %x%.push_vector(%v%) %$$ extends the vector $icode x$$ so that its new size is $icode%n%+%m%$$ and $icode%x%[%n% + %i%]%$$ is equal to $icode%v%[%i%]%$$ for $icode%i = 1 , ... , m-1%$$ (equal in the sense of the $icode Scalar$$ assignment operator). $head Output$$ If $icode x$$ is a $codei%CppAD::vector<%Scalar%>%$$ object and $icode os$$ is an $code std::ostream$$, and the operation $codei% %os% << %x% %$$ will output the vector $icode x$$ to the standard output stream $icode os$$. The elements of $icode x$$ are enclosed at the beginning by a $code {$$ character, they are separated by $code ,$$ characters, and they are enclosed at the end by $code }$$ character. It is assumed by this operation that if $icode e$$ is an object with type $icode Scalar$$, $codei% %os% << %e% %$$ will output the value $icode e$$ to the standard output stream $icode os$$. $head resize$$ The call $icode%x%.resize(%n%)%$$ set the size of $icode x$$ equal to $icode n$$. If $icode%n% <= %x%.capacity()%$$, no memory is freed or allocated, the capacity of $icode x$$ does not change, and the data in $icode x$$ is preserved. If $icode%n% > %x%.capacity()%$$, new memory is allocated and the data in $icode x$$ is lost (not copied to the new memory location). $head clear$$ All memory allocated for the vector is freed and both its size and capacity are set to zero. This can be useful when using very large vectors and when checking for memory leaks (and there are global vectors) see the $cref/memory/CppAD_vector/Memory and Parallel Mode/$$ discussion. $head data$$ If $icode x$$ is a $codei%CppAD::vector<%Scalar%>%$$ object $codei% %x%.data() %$$ returns a pointer to a $icode Scalar$$ object such that for $codei%0 <= %i% < %x%.size()%$$, $icode%x%[%i%]%$$ and $icode%x%.data()[%i%]%$$ are the same $icode Scalar$$ object. If $icode x$$ is $code const$$, the pointer is $code const$$. If $icode%x%.capacity()%$$ is zero, the value of the pointer is not defined. The pointer may no longer be valid after the following operations on $icode x$$: its destructor, $code clear$$, $code resize$$, $code push_back$$, $code push_vector$$, assignment to another vector when original size of $icode x$$ is zero. $head vectorBool$$ The file $code $$ also defines the class $code CppAD::vectorBool$$. This has the same specifications as $code CppAD::vector$$ with the following exceptions: $subhead Memory$$ The class $code vectorBool$$ conserves on memory (on the other hand, $code CppAD::vector$$ is expected to be faster than $code vectorBool$$). $subhead bit_per_unit$$ The static function call $codei% %s% = vectorBool::bit_per_unit() %$$ returns the $code size_t$$ value $icode s$$ which is equal to the number of boolean values (bits) that are packed into one operational unit. For example, a logical $code or$$ acts on this many boolean values with one operation. $subhead data$$ The $cref/data/CppAD_vector/data/$$ function is not supported by $code vectorBool$$. $subhead Output$$ The $code CppAD::vectorBool$$ output operator prints each boolean value as a $code 0$$ for false, a $code 1$$ for true, and does not print any other output; i.e., the vector is written a long sequence of zeros and ones with no surrounding $code {$$, $code }$$ and with no separating commas or spaces. $subhead Element Type$$ If $icode x$$ has type $code vectorBool$$ and $icode i$$ has type $code size_t$$, the element access value $icode%x%[%i%]%$$ has an unspecified type, referred to here as $icode elementType$$, that supports the following operations: $list number$$ $icode elementType$$ can be converted to $code bool$$; e.g. the following syntax is supported: $codei% static_cast( %x%[%i%] ) %$$ $lnext $icode elementType$$ supports the assignment operator $code =$$ where the right hand side is a $code bool$$ or an $icode elementType$$ object; e.g., if $icode y$$ has type $code bool$$, the following syntax is supported: $codei% %x%[%i%] = %y% %$$ $lnext The result of an assignment to an $icode elementType$$ also has type $icode elementType$$. Thus, if $icode z$$ has type $code bool$$, the following syntax is supported: $codei% %z% = %x%[%i%] = %y% %$$ $lend $head Memory and Parallel Mode$$ These vectors use the multi-threaded fast memory allocator $cref thread_alloc$$: $list number$$ The routine $cref/parallel_setup/ta_parallel_setup/$$ must be called before these vectors can be used $cref/in parallel/ta_in_parallel/$$. $lnext Using these vectors affects the amount of memory $cref/in_use/ta_inuse/$$ and $cref/available/ta_available/$$. $lnext Calling $cref/clear/CppAD_vector/clear/$$, makes the corresponding memory available (though $code thread_alloc$$) to the current thread. $lnext Available memory can then be completely freed using $cref/free_available/ta_free_available/$$. $lend $head Example$$ $children% example/cppad_vector.cpp% example/vector_bool.cpp %$$ The files $cref cppad_vector.cpp$$ and $cref vector_bool.cpp$$ each contain an example and test of this template class. They return true if they succeed and false otherwise. $head Exercise$$ Create and run a program that contains the following code: $codep CppAD::vector x(3); size_t i; for(i = 0; i < 3; i++) x[i] = 4. - i; std::cout << "x = " << x << std::endl; $$ $end $end ------------------------------------------------------------------------ */ # include # include # include # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file vector.hpp File used to define CppAD::vector and CppAD::vectorBool */ // --------------------------------------------------------------------------- /*! The CppAD Simple Vector template class. */ template class vector { private: /// maximum number of Type elements current allocation can hold size_t capacity_; /// number of Type elements currently in this vector size_t length_; /// pointer to the first type elements /// (not defined and should not be used when capacity_ = 0) Type* data_; /// delete data pointer void delete_data(Type* data_ptr) { thread_alloc::delete_array(data_ptr); } public: /// type of the elements in the vector typedef Type value_type; /// default constructor sets capacity_ = length_ = data_ = 0 inline vector(void) : capacity_(0), length_(0), data_(CPPAD_NULL) { } /// sizing constructor inline vector( /// number of elements in this vector size_t n ) : capacity_(0), length_(0), data_(CPPAD_NULL) { resize(n); } /// copy constructor inline vector( /// the *this vector will be a copy of \c x const vector& x ) : capacity_(0), length_(0), data_(CPPAD_NULL) { resize(x.length_); // copy the data for(size_t i = 0; i < length_; i++) data_[i] = x.data_[i]; } /// destructor ~vector(void) { if( capacity_ > 0 ) delete_data(data_); } /// maximum number of elements current allocation can store inline size_t capacity(void) const { return capacity_; } /// number of elements currently in this vector. inline size_t size(void) const { return length_; } /// raw pointer to the data inline Type* data(void) { return data_; } /// const raw pointer to the data inline const Type* data(void) const { return data_; } /// change the number of elements in this vector. inline void resize( /// new number of elements for this vector size_t n ) { length_ = n; // check if we must allocate new memory if( capacity_ < length_ ) { // check if there is old memory to be freed if( capacity_ > 0 ) delete_data(data_); // get new memory and set capacity data_ = thread_alloc::create_array(length_, capacity_); } } /// free memory and set number of elements to zero inline void clear(void) { length_ = 0; // check if there is old memory to be freed if( capacity_ > 0 ) delete_data(data_); capacity_ = 0; } /// vector assignment operator inline vector& operator=( /// right hand size of the assingment operation const vector& x ) { size_t i; // If original lenght is zero, then resize it. // Otherwise a length mismatch is an error. if( length_ == 0 ) resize( x.length_ ); CPPAD_ASSERT_KNOWN( length_ == x.length_ , "vector: size miss match in assignment operation" ); for(i = 0; i < length_; i++) data_[i] = x.data_[i]; return *this; } # if CPPAD_USE_CPLUSPLUS_2011 /// vector assignment operator with move semantics inline vector& operator=( /// right hand size of the assingment operation vector&& x ) { CPPAD_ASSERT_KNOWN( length_ == x.length_ || (length_ == 0), "vector: size miss match in assignment operation" ); if( this != &x ) { clear(); // length_ = x.length_; capacity_ = x.capacity_; data_ = x.data_; // x.length_ = 0; x.capacity_ = 0; x.data_ = CPPAD_NULL; } return *this; } # endif /// non-constant element access; i.e., we can change this element value Type& operator[]( /// element index, must be less than length size_t i ) { CPPAD_ASSERT_KNOWN( i < length_, "vector: index greater than or equal vector size" ); return data_[i]; } /// constant element access; i.e., we cannot change this element value const Type& operator[]( /// element index, must be less than length size_t i ) const { CPPAD_ASSERT_KNOWN( i < length_, "vector: index greater than or equal vector size" ); return data_[i]; } /// add an element to the back of this vector void push_back( /// value of the element const Type& s ) { // case where no allocation is necessary if( length_ + 1 <= capacity_ ) { data_[length_++] = s; return; } CPPAD_ASSERT_UNKNOWN( length_ == capacity_ ); // store old length, capacity and data size_t old_length = length_; size_t old_capacity = capacity_; Type* old_data = data_; // set the new length, capacity and data length_ = 0; capacity_ = 0; resize(old_length + 1); // copy old data values for(size_t i = 0; i < old_length; i++) data_[i] = old_data[i]; // put the new element in the vector CPPAD_ASSERT_UNKNOWN( old_length + 1 <= capacity_ ); data_[old_length] = s; // free old data if( old_capacity > 0 ) delete_data(old_data); CPPAD_ASSERT_UNKNOWN( old_length + 1 == length_ ); CPPAD_ASSERT_UNKNOWN( length_ <= capacity_ ); } /*! add vector to the back of this vector (we could not use push_back because MS V++ 7.1 did not resolve to non-template member function when scalar is used.) */ template void push_vector( /// value of the vector that we are adding const Vector& v ) { CheckSimpleVector(); size_t m = v.size(); // case where no allcoation is necessary if( length_ + m <= capacity_ ) { for(size_t i = 0; i < m; i++) data_[length_++] = v[i]; return; } // store old length, capacity and data size_t old_length = length_; size_t old_capacity = capacity_; Type* old_data = data_; // set new length, capacity and data length_ = 0; capacity_ = 0; resize(old_length + m); // copy old data values for(size_t i = 0; i < old_length; i++) data_[i] = old_data[i]; // put the new elements in the vector CPPAD_ASSERT_UNKNOWN( old_length + m <= capacity_ ); for(size_t i = 0; i < m; i++) data_[old_length + i] = v[i]; // free old data if( old_capacity > 0 ) delete_data(old_data); CPPAD_ASSERT_UNKNOWN( old_length + m == length_ ); CPPAD_ASSERT_UNKNOWN( length_ <= capacity_ ); } }; /// output a vector template inline std::ostream& operator << ( /// stream to write the vector to std::ostream& os , /// vector that is output const CppAD::vector& vec ) { size_t i = 0; size_t n = vec.size(); os << "{ "; while(i < n) { os << vec[i++]; if( i < n ) os << ", "; } os << " }"; return os; } // --------------------------------------------------------------------------- /*! Class that is used to hold a non-constant element of a vector. */ class vectorBoolElement { /// the boolean data is packed with sizeof(UnitType) bits per value typedef size_t UnitType; private: /// pointer to the UnitType value holding this eleemnt UnitType* unit_; /// mask for the bit corresponding to this element /// (all zero except for bit that corresponds to this element) UnitType mask_; public: /// constructor from member values vectorBoolElement( /// unit for this element UnitType* unit , /// mask for this element UnitType mask ) : unit_(unit) , mask_(mask) { } /// constuctor from another element vectorBoolElement( /// other element const vectorBoolElement& e ) : unit_(e.unit_) , mask_(e.mask_) { } /// conversion to a boolean value operator bool() const { return (*unit_ & mask_) != 0; } /// assignment of this element to a bool vectorBoolElement& operator=( /// right hand side for assignment bool bit ) { if(bit) *unit_ |= mask_; else *unit_ &= ~mask_; return *this; } /// assignment of this element to another element vectorBoolElement& operator=(const vectorBoolElement& e) { if( *(e.unit_) & e.mask_ ) *unit_ |= mask_; else *unit_ &= ~mask_; return *this; } }; class vectorBool { /// the boolean data is packed with sizeof(UnitType) bits per value typedef size_t UnitType; private: /// number of bits packed into each UnitType value in data_ static const size_t bit_per_unit_ = std::numeric_limits::digits; /// number of UnitType values in data_ size_t n_unit_; /// number of bits currently stored in this vector size_t length_; /// pointer to where the bits are stored UnitType *data_; /// minimum number of UnitType values that can store length_ bits /// (note that this is really a function of length_) size_t unit_min(void) { if( length_ == 0 ) return 0; return (length_ - 1) / bit_per_unit_ + 1; } public: /// type corresponding to the elements of this vector /// (note that non-const elements actually use vectorBoolElement) typedef bool value_type; // static member function static size_t bit_per_unit(void) { return bit_per_unit_; } /// default constructor (sets all member data to zero) inline vectorBool(void) : n_unit_(0), length_(0), data_(CPPAD_NULL) { } /// sizing constructor inline vectorBool( /// number of bits in this vector size_t n ) : n_unit_(0), length_(n), data_(CPPAD_NULL) { if( length_ > 0 ) { // set n_unit and data size_t min_unit = unit_min(); data_ = thread_alloc::create_array(min_unit, n_unit_); } } /// copy constructor inline vectorBool( /// the *this vector will be a copy of \c v const vectorBool& v ) : n_unit_(0), length_(v.length_), data_(CPPAD_NULL) { if( length_ > 0 ) { // set n_unit and data size_t min_unit = unit_min(); data_ = thread_alloc::create_array(min_unit, n_unit_); // copy values using UnitType assignment operator CPPAD_ASSERT_UNKNOWN( min_unit <= v.n_unit_ ); size_t i; for(i = 0; i < min_unit; i++) data_[i] = v.data_[i]; } } /// destructor ~vectorBool(void) { if( n_unit_ > 0 ) thread_alloc::delete_array(data_); } /// number of elements in this vector inline size_t size(void) const { return length_; } /// maximum number of elements current allocation can store inline size_t capacity(void) const { return n_unit_ * bit_per_unit_; } /// change number of elements in this vector inline void resize( /// new number of elements for this vector size_t n ) { length_ = n; // check if we can use the current memory size_t min_unit = unit_min(); if( n_unit_ >= min_unit ) return; // check if there is old memory to be freed if( n_unit_ > 0 ) thread_alloc::delete_array(data_); // get new memory and set n_unit data_ = thread_alloc::create_array(min_unit, n_unit_); } /// free memory and set number of elements to zero inline void clear(void) { length_ = 0; // check if there is old memory to be freed if( n_unit_ > 0 ) thread_alloc::delete_array(data_); n_unit_ = 0; } /// vector assignment operator inline vectorBool& operator=( /// right hand size of the assingment operation const vectorBool& v ) { size_t i; // If original lenght is zero, then resize it. // Otherwise a length mismatch is an error. if( length_ == 0 ) resize( v.length_ ); CPPAD_ASSERT_KNOWN( length_ == v.length_ , "vectorBool: size miss match in assignment operation" ); size_t min_unit = unit_min(); CPPAD_ASSERT_UNKNOWN( min_unit <= n_unit_ ); CPPAD_ASSERT_UNKNOWN( min_unit <= v.n_unit_ ); for(i = 0; i < min_unit; i++) data_[i] = v.data_[i]; return *this; } # if CPPAD_USE_CPLUSPLUS_2011 /// vector assignment operator with move semantics inline vectorBool& operator=( /// right hand size of the assingment operation vectorBool&& x ) { CPPAD_ASSERT_KNOWN( length_ == x.length_ || (length_ == 0), "vectorBool: size miss match in assignment operation" ); if( this != &x ) { clear(); // length_ = x.length_; n_unit_ = x.n_unit_; data_ = x.data_; // x.length_ = 0; x.n_unit_ = 0; x.data_ = CPPAD_NULL; } return *this; } # endif /// non-constant element access; i.e., we can change this element value vectorBoolElement operator[]( /// element index, must be less than length size_t k ) { size_t i, j; CPPAD_ASSERT_KNOWN( k < length_, "vectorBool: index greater than or equal vector size" ); i = k / bit_per_unit_; j = k - i * bit_per_unit_; return vectorBoolElement(data_ + i , UnitType(1) << j ); } /// constant element access; i.e., we cannot change this element value bool operator[](size_t k) const { size_t i, j; UnitType unit, mask; CPPAD_ASSERT_KNOWN( k < length_, "vectorBool: index greater than or equal vector size" ); i = k / bit_per_unit_; j = k - i * bit_per_unit_; unit = data_[i]; mask = UnitType(1) << j; return (unit & mask) != 0; } /// add an element to the back of this vector void push_back( /// value of the element bool bit ) { CPPAD_ASSERT_UNKNOWN( unit_min() <= n_unit_ ); size_t i, j; UnitType mask; if( length_ + 1 > n_unit_ * bit_per_unit_ ) { CPPAD_ASSERT_UNKNOWN( unit_min() == n_unit_ ); // store old n_unit and data values size_t old_n_unit = n_unit_; UnitType* old_data = data_; // set new n_unit and data values data_ = thread_alloc::create_array(n_unit_+1, n_unit_); // copy old data values for(i = 0; i < old_n_unit; i++) data_[i] = old_data[i]; // free old data if( old_n_unit > 0 ) thread_alloc::delete_array(old_data); } i = length_ / bit_per_unit_; j = length_ - i * bit_per_unit_; mask = UnitType(1) << j; if( bit ) data_[i] |= mask; else data_[i] &= ~mask; length_++; } /// add vector to the back of this vector template void push_vector( /// value of the vector that we are adding const Vector& v ) { CheckSimpleVector(); size_t min_unit = unit_min(); CPPAD_ASSERT_UNKNOWN( length_ <= n_unit_ * bit_per_unit_ ); // some temporaries size_t i, j, k, ell; UnitType mask; bool bit; // store old length size_t old_length = length_; // new length and minium number of units; length_ = length_ + v.size(); min_unit = unit_min(); if( length_ >= n_unit_ * bit_per_unit_ ) { // store old n_unit and data value size_t old_n_unit = n_unit_; UnitType* old_data = data_; // set new n_unit and data values data_ = thread_alloc::create_array(min_unit, n_unit_); // copy old data values for(i = 0; i < old_n_unit; i++) data_[i] = old_data[i]; // free old data if( old_n_unit > 0 ) thread_alloc::delete_array(old_data); } ell = old_length; for(k = 0; k < v.size(); k++) { i = ell / bit_per_unit_; j = ell - i * bit_per_unit_; bit = v[k]; mask = UnitType(1) << j; if( bit ) data_[i] |= mask; else data_[i] &= ~mask; ell++; } CPPAD_ASSERT_UNKNOWN( length_ == ell ); CPPAD_ASSERT_UNKNOWN( length_ <= n_unit_ * bit_per_unit_ ); } }; /// output a vector inline std::ostream& operator << ( /// steam to write the vector to std::ostream& os , /// vector that is output const vectorBool& v ) { size_t i = 0; size_t n = v.size(); while(i < n) os << v[i++]; return os; } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/utility/set_union.hpp0000644000175200017650000000400213057470465017737 0ustar coincoin-web// $Id$ # ifndef CPPAD_UTILITY_SET_UNION_HPP # define CPPAD_UTILITY_SET_UNION_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin set_union$$ $spell set const std $$ $section Union of Standard Sets$$ $head Syntax$$ $icode%result% = set_union(%left%, %right%)%$$ $head Purpose$$ This is a simplified (and restricted) interface to the $code std::union$$ operation. $head Element$$ This is the type of the elements of the sets. $head left$$ This argument has prototype $codei% const std::set<%Element%>& %left% %$$ $head right$$ This argument has prototype $codei% const std::set<%Element%>& %right% %$$ $head result$$ The return value has prototype $codei% std::set<%Element%>& %result% %$$ It contains the union of $icode left$$ and $icode right$$. Note that C++11 detects that the return value is a temporary and uses it for the result instead of making a separate copy. $children% example/set_union.cpp %$$ $head Example$$ The file $cref set_union.cpp$$ contains an example and test of this operation. It returns true if the test passes and false otherwise. $end */ # include # include # include namespace CppAD { template std::set set_union( const std::set& left , const std::set& right ) { std::set result; std::set_union( left.begin() , left.end() , right.begin() , right.end() , std::inserter(result, result.begin()) ); return result; } } # endif cppad-20170000.3/cppad/utility/memory_leak.hpp0000644000175200017650000001517413057470465020254 0ustar coincoin-web// $Id: memory_leak.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_MEMORY_LEAK_HPP # define CPPAD_UTILITY_MEMORY_LEAK_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin memory_leak$$ $spell cppad num alloc hpp bool inuse $$ $section Memory Leak Detection$$ $mindex memory_leak check static$$ $head Deprecated 2012-04-06$$ This routine has been deprecated. You should instead use the routine $cref ta_free_all$$. $head Syntax$$ $codei%# include %$$ $icode%flag% = %memory_leak() %$$ $icode%flag% = %memory_leak(%add_static%)%$$ $head Purpose$$ This routine checks that the are no memory leaks caused by improper use of $cref thread_alloc$$ memory allocator. The deprecated memory allocator $cref TrackNewDel$$ is also checked. Memory errors in the deprecated $cref omp_alloc$$ allocator are reported as being in $code thread_alloc$$. $head thread$$ It is assumed that $cref/in_parallel()/ta_in_parallel/$$ is false and $cref/thread_num/ta_thread_num/$$ is zero when $code memory_leak$$ is called. $head add_static$$ This argument has prototype $codei% size_t %add_static% %$$ and its default value is zero. Static variables hold onto memory forever. If the argument $icode add_static$$ is present (and non-zero), $code memory_leak$$ adds this amount of memory to the $cref/inuse/ta_inuse/$$ sum that corresponds to static variables in the program. A call with $icode add_static$$ should be make after a routine that has static variables which use $cref/get_memory/ta_get_memory/$$ to allocate memory. The value of $icode add_static$$ should be the difference of $codei% thread_alloc::inuse(0) %$$ before and after the call. Since multiple statics may be allocated in different places in the program, it is expected that there will be multiple calls that use this option. $head flag$$ The return value $icode flag$$ has prototype $codei% bool %flag% %$$ If $icode add_static$$ is non-zero, the return value for $code memory_leak$$ is false. Otherwise, the return value for $code memory_leak$$ should be false (indicating that the only allocated memory corresponds to static variables). $head inuse$$ It is assumed that, when $code memory_leak$$ is called, there should not be any memory $cref/inuse/ta_inuse/$$ or $cref omp_inuse$$ for any thread (except for inuse memory corresponding to static variables). If there is, a message is printed and $code memory_leak$$ returns false. $head available$$ It is assumed that, when $code memory_leak$$ is called, there should not be any memory $cref/available/ta_available/$$ or $cref omp_available$$ for any thread; i.e., it all has been returned to the system. If there is memory still available for any thread, $code memory_leak$$ returns false. $head TRACK_COUNT$$ It is assumed that, when $code memory_leak$$ is called, $cref/TrackCount/TrackNewDel/TrackCount/$$ will return a zero value. If it returns a non-zero value, $code memory_leak$$ returns false. $head Error Message$$ If this is the first call to $code memory_leak$$, no message is printed. Otherwise, if it returns true, an error message is printed to standard output describing the memory leak that was detected. $end */ # include # include # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file memory_leak.hpp File that implements a memory check at end of a CppAD program */ /*! Function that checks allocator \c thread_alloc for misuse that results in memory leaks. Deprecated routines in track_new_del.hpp and omp_alloc.hpp are also checked. \param add_static [in] The amount specified by \c add_static is added to the amount of memory that is expected to be used by thread zero for static variables. \return If \c add_static is non-zero, the return value is \c false. Otherwise, if one of the following errors is detected, the return value is \c true: \li Thread zero does not have the expected amount of inuse memory (for static variables). \li A thread, other than thread zero, has any inuse memory. \li Any thread has available memory. \par If an error is detected, diagnostic information is printed to standard output. */ inline bool memory_leak(size_t add_static = 0) { // CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL not necessary given asserts below static size_t thread_zero_static_inuse = 0; using std::cout; using std::endl; using CppAD::thread_alloc; using CppAD::omp_alloc; // -------------------------------------------------------------------- CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel(), "memory_leak: in_parallel() is true." ); CPPAD_ASSERT_KNOWN( thread_alloc::thread_num() == 0, "memory_leak: thread_num() is not zero." ); if( add_static != 0 ) { thread_zero_static_inuse += add_static; return false; } bool leak = false; size_t thread = 0; // check that memory in use for thread zero corresponds to statics size_t num_bytes = thread_alloc::inuse(thread); if( num_bytes != thread_zero_static_inuse ) { leak = true; cout << "thread zero: static inuse = " << thread_zero_static_inuse; cout << "current inuse(thread) = " << num_bytes << endl; } // check that no memory is currently available for this thread num_bytes = thread_alloc::available(thread); if( num_bytes != 0 ) { leak = true; cout << "thread zero: available = "; cout << num_bytes << endl; } for(thread = 1; thread < CPPAD_MAX_NUM_THREADS; thread++) { // check that no memory is currently in use for this thread num_bytes = thread_alloc::inuse(thread); if( num_bytes != 0 ) { leak = true; cout << "thread " << thread << ": inuse(thread) = "; cout << num_bytes << endl; } // check that no memory is currently available for this thread num_bytes = thread_alloc::available(thread); if( num_bytes != 0 ) { leak = true; cout << "thread " << thread << ": available(thread) = "; cout << num_bytes << endl; } } // ---------------------------------------------------------------------- // check track_new_del if( CPPAD_TRACK_COUNT() != 0 ) { leak = true; CppAD::TrackElement::Print(); } return leak; } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/utility/omp_alloc.hpp0000644000175200017650000005045013057470465017711 0ustar coincoin-web// $Id: omp_alloc.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_UTILITY_OMP_ALLOC_HPP # define CPPAD_UTILITY_OMP_ALLOC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # ifdef _OPENMP # include # endif namespace CppAD { // BEGIN_CPPAD_NAMESPACE class omp_alloc{ // ============================================================================ public: /* $begin omp_max_num_threads$$ $spell cppad.hpp inv CppAD num omp_alloc $$ $section Set and Get Maximum Number of Threads for omp_alloc Allocator$$ $head Deprecated 2011-08-31$$ Use the functions $cref/thread_alloc::parallel_setup/ta_parallel_setup/$$ and $cref/thread_alloc:num_threads/ta_num_threads/$$ instead. $head Syntax$$ $codei%# include %$$ $codei%omp_alloc::set_max_num_threads(%number%) %$$ $icode%number% = omp_alloc::get_max_num_threads() %$$ $head Purpose$$ By default there is only one thread and all execution is in sequential mode (not $cref/parallel/omp_in_parallel/$$). $head number$$ The argument and return value $icode number$$ has prototype $codei% size_t %number% %$$ and must be greater than zero. $head set_max_num_threads$$ Informs $cref omp_alloc$$ of the maximum number of OpenMP threads. $head get_max_num_threads$$ Returns the valued used in the previous call to $code set_max_num_threads$$. If there was no such previous call, the value one is returned (and only thread number zero can use $cref omp_alloc$$). $head Restrictions$$ The function $code set_max_num_threads$$ must be called before the program enters $cref/parallel/omp_in_parallel/$$ execution mode. In addition, this function cannot be called while in parallel mode. $end */ /*! Inform omp_alloc of the maximum number of OpenMP threads and enable parallel execution mode by initializing all statics in this file. \param number [in] maximum number of OpenMP threads. */ static void set_max_num_threads(size_t number) { thread_alloc::parallel_setup( number, omp_alloc::in_parallel, omp_alloc::get_thread_num ); thread_alloc::hold_memory(number > 1); } /*! Get the current maximum number of OpenMP threads that omp_alloc can use. \return maximum number of OpenMP threads. */ static size_t get_max_num_threads(void) { return thread_alloc::num_threads(); } /* ----------------------------------------------------------------------- $begin omp_in_parallel$$ $section Is The Current Execution in OpenMP Parallel Mode$$ $mindex in_parallel$$ $spell cppad.hpp omp_alloc bool $$ $head Deprecated 2011-08-31$$ Use the function $cref/thread_alloc::in_parallel/ta_in_parallel/$$ instead. $head Syntax$$ $codei%# include %$$ $icode%flag% = omp_alloc::in_parallel()%$$ $head Purpose$$ Some of the $cref omp_alloc$$ allocation routines have different specifications for parallel (not sequential) execution mode. This routine enables you to determine if the current execution mode is sequential or parallel. $head flag$$ The return value has prototype $codei% bool %flag% %$$ It is true if the current execution is in parallel mode (possibly multi-threaded) and false otherwise (sequential mode). $head Example$$ $cref omp_alloc.cpp$$ $end */ /// Are we in a parallel execution state; i.e., is it possible that /// other threads are currently executing. static bool in_parallel(void) { # ifdef _OPENMP return omp_in_parallel() != 0; # else return false; # endif } /* ----------------------------------------------------------------------- $begin omp_get_thread_num$$ $spell cppad.hpp CppAD num omp_alloc cppad.hpp $$ $section Get the Current OpenMP Thread Number$$ $mindex get_thread_num$$ $head Deprecated 2011-08-31$$ Use the function $cref/thread_alloc::thread_num/ta_thread_num/$$ instead. $head Syntax$$ $codei%# include %$$ $icode%thread% = omp_alloc::get_thread_num()%$$ $head Purpose$$ Some of the $cref omp_alloc$$ allocation routines have a thread number. This routine enables you to determine the current thread. $head thread$$ The return value $icode thread$$ has prototype $codei% size_t %thread% %$$ and is the currently executing thread number. If $code _OPENMP$$ is not defined, $icode thread$$ is zero. $head Example$$ $cref omp_alloc.cpp$$ $end */ /// Get current OpenMP thread number (zero if _OpenMP not defined). static size_t get_thread_num(void) { # ifdef _OPENMP size_t thread = static_cast( omp_get_thread_num() ); return thread; # else return 0; # endif } /* ----------------------------------------------------------------------- $begin omp_get_memory$$ $spell cppad.hpp num ptr omp_alloc $$ $section Get At Least A Specified Amount of Memory$$ $head Deprecated 2011-08-31$$ Use the function $cref/thread_alloc::get_memory/ta_get_memory/$$ instead. $head Syntax$$ $codei%# include %$$ $icode%v_ptr% = omp_alloc::get_memory(%min_bytes%, %cap_bytes%)%$$ $head Purpose$$ Use $cref omp_alloc$$ to obtain a minimum number of bytes of memory (for use by the $cref/current thread/omp_get_thread_num/$$). $head min_bytes$$ This argument has prototype $codei% size_t %min_bytes% %$$ It specifies the minimum number of bytes to allocate. $head cap_bytes$$ This argument has prototype $codei% size_t& %cap_bytes% %$$ It's input value does not matter. Upon return, it is the actual number of bytes (capacity) that have been allocated for use, $codei% %min_bytes% <= %cap_bytes% %$$ $head v_ptr$$ The return value $icode v_ptr$$ has prototype $codei% void* %v_ptr% %$$ It is the location where the $icode cap_bytes$$ of memory that have been allocated for use begins. $head Allocation Speed$$ This allocation should be faster if the following conditions hold: $list number$$ The memory allocated by a previous call to $code get_memory$$ is currently available for use. $lnext The current $icode min_bytes$$ is between the previous $icode min_bytes$$ and previous $icode cap_bytes$$. $lend $head Example$$ $cref omp_alloc.cpp$$ $end */ /*! Use omp_alloc to get a specified amount of memory. If the memory allocated by a previous call to \c get_memory is now avaialable, and \c min_bytes is between its previous value and the previous \c cap_bytes, this memory allocation will have optimal speed. Otherwise, the memory allocation is more complicated and may have to wait for other threads to complete an allocation. \param min_bytes [in] The minimum number of bytes of memory to be obtained for use. \param cap_bytes [out] The actual number of bytes of memory obtained for use. \return pointer to the beginning of the memory allocted for use. */ static void* get_memory(size_t min_bytes, size_t& cap_bytes) { return thread_alloc::get_memory(min_bytes, cap_bytes); } /* ----------------------------------------------------------------------- $begin omp_return_memory$$ $spell cppad.hpp ptr omp_alloc $$ $section Return Memory to omp_alloc$$ $mindex return_memory$$ $head Deprecated 2011-08-31$$ Use the function $cref/thread_alloc::return_memory/ta_return_memory/$$ instead. $head Syntax$$ $codei%# include %$$ $codei%omp_alloc::return_memory(%v_ptr%)%$$ $head Purpose$$ If $cref omp_max_num_threads$$ is one, the memory is returned to the system. Otherwise, the memory is retained by $cref omp_alloc$$ for quick future use by the thread that allocated to memory. $head v_ptr$$ This argument has prototype $codei% void* %v_ptr% %$$. It must be a pointer to memory that is currently in use; i.e. obtained by a previous call to $cref omp_get_memory$$ and not yet returned. $head Thread$$ Either the $cref/current thread/omp_get_thread_num/$$ must be the same as during the corresponding call to $cref omp_get_memory$$, or the current execution mode must be sequential (not $cref/parallel/omp_in_parallel/$$). $head NDEBUG$$ If $code NDEBUG$$ is defined, $icode v_ptr$$ is not checked (this is faster). Otherwise, a list of in use pointers is searched to make sure that $icode v_ptr$$ is in the list. $head Example$$ $cref omp_alloc.cpp$$ $end */ /*! Return memory that was obtained by \c get_memory. If max_num_threads(0) == 1, the memory is returned to the system. Otherwise, it is retained by \c omp_alloc and available for use by \c get_memory for this thread. \param v_ptr [in] Value of the pointer returned by \c get_memory and still in use. After this call, this pointer will available (and not in use). \par We must either be in sequential (not parallel) execution mode, or the current thread must be the same as for the corresponding call to \c get_memory. */ static void return_memory(void* v_ptr) { thread_alloc::return_memory(v_ptr); } /* ----------------------------------------------------------------------- $begin omp_free_available$$ $spell cppad.hpp omp_alloc $$ $section Free Memory Currently Available for Quick Use by a Thread$$ $mindex free_available$$ $head Deprecated 2011-08-31$$ Use the function $cref/thread_alloc::free_available/ta_free_available/$$ instead. $head Syntax$$ $codei%# include %$$ $codei%omp_alloc::free_available(%thread%)%$$ $head Purpose$$ Free memory, currently available for quick use by a specific thread, for general future use. $head thread$$ This argument has prototype $codei% size_t %thread% %$$ Either $cref omp_get_thread_num$$ must be the same as $icode thread$$, or the current execution mode must be sequential (not $cref/parallel/omp_in_parallel/$$). $head Example$$ $cref omp_alloc.cpp$$ $end */ /*! Return all the memory being held as available for a thread to the system. \param thread [in] this thread that will no longer have any available memory after this call. This must either be the thread currently executing, or we must be in sequential (not parallel) execution mode. */ static void free_available(size_t thread) { thread_alloc::free_available(thread); } /* ----------------------------------------------------------------------- $begin omp_inuse$$ $spell cppad.hpp num inuse omp_alloc $$ $section Amount of Memory a Thread is Currently Using$$ $mindex inuse$$ $head Deprecated 2011-08-31$$ $head Syntax$$ $codei%# include %$$ $icode%num_bytes% = omp_alloc::inuse(%thread%)%$$ Use the function $cref/thread_alloc::inuse/ta_inuse/$$ instead. $head Purpose$$ Memory being managed by $cref omp_alloc$$ has two states, currently in use by the specified thread, and quickly available for future use by the specified thread. This function informs the program how much memory is in use. $head thread$$ This argument has prototype $codei% size_t %thread% %$$ Either $cref omp_get_thread_num$$ must be the same as $icode thread$$, or the current execution mode must be sequential (not $cref/parallel/omp_in_parallel/$$). $head num_bytes$$ The return value has prototype $codei% size_t %num_bytes% %$$ It is the number of bytes currently in use by the specified thread. $head Example$$ $cref omp_alloc.cpp$$ $end */ /*! Determine the amount of memory that is currently inuse. \param thread [in] Thread for which we are determining the amount of memory (must be < CPPAD_MAX_NUM_THREADS). Durring parallel execution, this must be the thread that is currently executing. \return The amount of memory in bytes. */ static size_t inuse(size_t thread) { return thread_alloc::inuse(thread); } /* ----------------------------------------------------------------------- $begin omp_available$$ $spell cppad.hpp num omp_alloc $$ $section Amount of Memory Available for Quick Use by a Thread$$ $head Deprecated 2011-08-31$$ Use the function $cref/thread_alloc::available/ta_available/$$ instead. $head Syntax$$ $codei%# include %$$ $icode%num_bytes% = omp_alloc::available(%thread%)%$$ $head Purpose$$ Memory being managed by $cref omp_alloc$$ has two states, currently in use by the specified thread, and quickly available for future use by the specified thread. This function informs the program how much memory is available. $head thread$$ This argument has prototype $codei% size_t %thread% %$$ Either $cref omp_get_thread_num$$ must be the same as $icode thread$$, or the current execution mode must be sequential (not $cref/parallel/omp_in_parallel/$$). $head num_bytes$$ The return value has prototype $codei% size_t %num_bytes% %$$ It is the number of bytes currently available for use by the specified thread. $head Example$$ $cref omp_alloc.cpp$$ $end */ /*! Determine the amount of memory that is currently available for use. \copydetails inuse */ static size_t available(size_t thread) { return thread_alloc::available(thread); } /* ----------------------------------------------------------------------- $begin omp_create_array$$ $spell cppad.hpp omp_alloc sizeof $$ $section Allocate Memory and Create A Raw Array$$ $mindex create_array$$ $head Deprecated 2011-08-31$$ Use the function $cref/thread_alloc::create_array/ta_create_array/$$ instead. $head Syntax$$ $codei%# include %$$ $icode%array% = omp_alloc::create_array<%Type%>(%size_min%, %size_out%)%$$. $head Purpose$$ Create a new raw array using $cref omp_alloc$$ a fast memory allocator that works well in a multi-threading OpenMP environment. $head Type$$ The type of the elements of the array. $head size_min$$ This argument has prototype $codei% size_t %size_min% %$$ This is the minimum number of elements that there can be in the resulting $icode array$$. $head size_out$$ This argument has prototype $codei% size_t& %size_out% %$$ The input value of this argument does not matter. Upon return, it is the actual number of elements in $icode array$$ ($icode% size_min %<=% size_out%$$). $head array$$ The return value $icode array$$ has prototype $codei% %Type%* %array% %$$ It is array with $icode size_out$$ elements. The default constructor for $icode Type$$ is used to initialize the elements of $icode array$$. Note that $cref omp_delete_array$$ should be used to destroy the array when it is no longer needed. $head Delta$$ The amount of memory $cref omp_inuse$$ by the current thread, will increase $icode delta$$ where $codei% sizeof(%Type%) * (%size_out% + 1) > %delta% >= sizeof(%Type%) * %size_out% %$$ The $cref omp_available$$ memory will decrease by $icode delta$$, (and the allocation will be faster) if a previous allocation with $icode size_min$$ between its current value and $icode size_out$$ is available. $head Example$$ $cref omp_alloc.cpp$$ $end */ /*! Use omp_alloc to Create a Raw Array. \tparam Type The type of the elements of the array. \param size_min [in] The minimum number of elements in the array. \param size_out [out] The actual number of elements in the array. \return pointer to the first element of the array. The default constructor is used to initialize all the elements of the array. \par The \c extra_ field, in the \c omp_alloc node before the return value, is set to size_out. */ template static Type* create_array(size_t size_min, size_t& size_out) { return thread_alloc::create_array(size_min, size_out); } /* ----------------------------------------------------------------------- $begin omp_delete_array$$ $spell cppad.hpp omp_alloc sizeof $$ $section Return A Raw Array to The Available Memory for a Thread$$ $mindex delete_array$$ $head Deprecated 2011-08-31$$ Use the function $cref/thread_alloc::delete_array/ta_delete_array/$$ instead. $head Syntax$$ $codei%# include %$$ $codei%omp_alloc::delete_array(%array%)%$$. $head Purpose$$ Returns memory corresponding to a raw array (create by $cref omp_create_array$$) to the $cref omp_available$$ memory pool for the current thread. $head Type$$ The type of the elements of the array. $head array$$ The argument $icode array$$ has prototype $codei% %Type%* %array% %$$ It is a value returned by $cref omp_create_array$$ and not yet deleted. The $icode Type$$ destructor is called for each element in the array. $head Thread$$ The $cref/current thread/omp_get_thread_num/$$ must be the same as when $cref omp_create_array$$ returned the value $icode array$$. There is an exception to this rule: when the current execution mode is sequential (not $cref/parallel/omp_in_parallel/$$) the current thread number does not matter. $head Delta$$ The amount of memory $cref omp_inuse$$ will decrease by $icode delta$$, and the $cref omp_available$$ memory will increase by $icode delta$$, where $cref/delta/omp_create_array/Delta/$$ is the same as for the corresponding call to $code create_array$$. $head Example$$ $cref omp_alloc.cpp$$ $end */ /*! Return Memory Used for a Raw Array to the Available Pool. \tparam Type The type of the elements of the array. \param array [in] A value returned by \c create_array that has not yet been deleted. The \c Type destructor is used to destroy each of the elements of the array. \par Durring parallel execution, the current thread must be the same as during the corresponding call to \c create_array. */ template static void delete_array(Type* array) { thread_alloc::delete_array(array); } }; /* -------------------------------------------------------------------------- $begin omp_efficient$$ $spell cppad.hpp omp_alloc ptr num bool const $$ $section Check If A Memory Allocation is Efficient for Another Use$$ $head Removed$$ This function has been removed because speed tests seem to indicate it is just as fast, or faster, to free and then reallocate the memory. $head Syntax$$ $codei%# include %$$ $icode%flag% = omp_alloc::efficient(%v_ptr%, %num_bytes%)%$$ $head Purpose$$ Check if memory that is currently in use is an efficient allocation for a specified number of bytes. $head v_ptr$$ This argument has prototype $codei% const void* %v_ptr% %$$. It must be a pointer to memory that is currently in use; i.e. obtained by a previous call to $cref omp_get_memory$$ and not yet returned. $head num_bytes$$ This argument has prototype $codei% size_t %num_bytes% %$$ It specifies the number of bytes of the memory allocated by $icode v_ptr$$ that we want to use. $head flag$$ The return value has prototype $codei% bool %flag% %$$ It is true, a call to $code get_memory$$ with $cref/min_bytes/omp_get_memory/min_bytes/$$ equal to $icode num_bytes$$ would result in a value for $cref/cap_bytes/omp_get_memory/cap_bytes/$$ that is the same as when $code v_ptr$$ was returned by $code get_memory$$; i.e., $icode v_ptr$$ is an efficient memory block for $icode num_bytes$$ bytes of information. $head Thread$$ Either the $cref/current thread/omp_get_thread_num/$$ must be the same as during the corresponding call to $cref omp_get_memory$$, or the current execution mode must be sequential (not $cref/parallel/omp_in_parallel/$$). $head NDEBUG$$ If $code NDEBUG$$ is defined, $icode v_ptr$$ is not checked (this is faster). Otherwise, a list of in use pointers is searched to make sure that $icode v_ptr$$ is in the list. $end --------------------------------------------------------------------------- $begin old_max_num_threads$$ $spell cppad.hpp inv CppAD num omp_alloc $$ $section Set Maximum Number of Threads for omp_alloc Allocator$$ $mindex max_num_threads$$ $head Removed$$ This function has been removed from the CppAD API. Use the function $cref/thread_alloc::parallel_setup/ta_parallel_setup/$$ in its place. $head Syntax$$ $codei%# include %$$ $codei%omp_alloc::max_num_threads(%number%)%$$ $head Purpose$$ By default there is only one thread and all execution is in sequential mode (not $cref/parallel/omp_in_parallel/$$). $head number$$ The argument $icode number$$ has prototype $codei% size_t %number% %$$ It must be greater than zero and specifies the maximum number of OpenMP threads that will be active at one time. $head Restrictions$$ This function must be called before the program enters $cref/parallel/omp_in_parallel/$$ execution mode. $end ------------------------------------------------------------------------------- */ } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/utility/ode_gear_control.hpp0000644000175200017650000003326613057470465021257 0ustar coincoin-web// $Id: ode_gear_control.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_UTILITY_ODE_GEAR_CONTROL_HPP # define CPPAD_UTILITY_ODE_GEAR_CONTROL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin OdeGearControl$$ $spell cppad.hpp CppAD xf xi smin smax eabs ef maxabs nstep tf sini erel dep const tb ta exp $$ $section An Error Controller for Gear's Ode Solvers$$ $mindex OdeGearControl Gear differential equation$$ $head Syntax$$ $codei%# include %$$ $icode%xf% = OdeGearControl(%F%, %M%, %ti%, %tf%, %xi%, %smin%, %smax%, %sini%, %eabs%, %erel%, %ef% , %maxabs%, %nstep% )%$$ $head Purpose$$ Let $latex \B{R}$$ denote the real numbers and let $latex f : \B{R} \times \B{R}^n \rightarrow \B{R}^n$$ be a smooth function. We define $latex X : [ti , tf] \rightarrow \B{R}^n$$ by the following initial value problem: $latex \[ \begin{array}{rcl} X(ti) & = & xi \\ X'(t) & = & f[t , X(t)] \end{array} \] $$ The routine $cref OdeGear$$ is a stiff multi-step method that can be used to approximate the solution to this equation. The routine $code OdeGearControl$$ sets up this multi-step method and controls the error during such an approximation. $head Include$$ The file $code cppad/ode_gear_control.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head Notation$$ The template parameter types $cref/Scalar/OdeGearControl/Scalar/$$ and $cref/Vector/OdeGearControl/Vector/$$ are documented below. $head xf$$ The return value $icode xf$$ has the prototype $codei% %Vector% %xf% %$$ and the size of $icode xf$$ is equal to $icode n$$ (see description of $cref/Vector/OdeGear/Vector/$$ below). It is the approximation for $latex X(tf)$$. $head Fun$$ The class $icode Fun$$ and the object $icode F$$ satisfy the prototype $codei% %Fun% &%F% %$$ This must support the following set of calls $codei% %F%.Ode(%t%, %x%, %f%) %F%.Ode_dep(%t%, %x%, %f_x%) %$$ $subhead t$$ The argument $icode t$$ has prototype $codei% const %Scalar% &%t% %$$ (see description of $cref/Scalar/OdeGear/Scalar/$$ below). $subhead x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ and has size $icode N$$ (see description of $cref/Vector/OdeGear/Vector/$$ below). $subhead f$$ The argument $icode f$$ to $icode%F%.Ode%$$ has prototype $codei% %Vector% &%f% %$$ On input and output, $icode f$$ is a vector of size $icode N$$ and the input values of the elements of $icode f$$ do not matter. On output, $icode f$$ is set equal to $latex f(t, x)$$ (see $icode f(t, x)$$ in $cref/Purpose/OdeGear/Purpose/$$). $subhead f_x$$ The argument $icode f_x$$ has prototype $codei% %Vector% &%f_x% %$$ On input and output, $icode f_x$$ is a vector of size $latex N * N$$ and the input values of the elements of $icode f_x$$ do not matter. On output, $latex \[ f\_x [i * n + j] = \partial_{x(j)} f_i ( t , x ) \] $$ $subhead Warning$$ The arguments $icode f$$, and $icode f_x$$ must have a call by reference in their prototypes; i.e., do not forget the $code &$$ in the prototype for $icode f$$ and $icode f_x$$. $head M$$ The argument $icode M$$ has prototype $codei% size_t %M% %$$ It specifies the order of the multi-step method; i.e., the order of the approximating polynomial (after the initialization process). The argument $icode M$$ must greater than or equal one. $head ti$$ The argument $icode ti$$ has prototype $codei% const %Scalar% &%ti% %$$ It specifies the initial time for the integration of the differential equation. $head tf$$ The argument $icode tf$$ has prototype $codei% const %Scalar% &%tf% %$$ It specifies the final time for the integration of the differential equation. $head xi$$ The argument $icode xi$$ has prototype $codei% const %Vector% &%xi% %$$ and size $icode n$$. It specifies value of $latex X(ti)$$. $head smin$$ The argument $icode smin$$ has prototype $codei% const %Scalar% &%smin% %$$ The minimum value of $latex T[M] - T[M-1]$$ in a call to $code OdeGear$$ will be $latex smin$$ except for the last two calls where it may be as small as $latex smin / 2$$. The value of $icode smin$$ must be less than or equal $icode smax$$. $head smax$$ The argument $icode smax$$ has prototype $codei% const %Scalar% &%smax% %$$ It specifies the maximum step size to use during the integration; i.e., the maximum value for $latex T[M] - T[M-1]$$ in a call to $code OdeGear$$. $head sini$$ The argument $icode sini$$ has prototype $codei% %Scalar% &%sini% %$$ The value of $icode sini$$ is the minimum step size to use during initialization of the multi-step method; i.e., for calls to $code OdeGear$$ where $latex m < M$$. The value of $icode sini$$ must be less than or equal $icode smax$$ (and can also be less than $icode smin$$). $head eabs$$ The argument $icode eabs$$ has prototype $codei% const %Vector% &%eabs% %$$ and size $icode n$$. Each of the elements of $icode eabs$$ must be greater than or equal zero. It specifies a bound for the absolute error in the return value $icode xf$$ as an approximation for $latex X(tf)$$. (see the $cref/error criteria discussion/OdeGearControl/Error Criteria Discussion/$$ below). $head erel$$ The argument $icode erel$$ has prototype $codei% const %Scalar% &%erel% %$$ and is greater than or equal zero. It specifies a bound for the relative error in the return value $icode xf$$ as an approximation for $latex X(tf)$$ (see the $cref/error criteria discussion/OdeGearControl/Error Criteria Discussion/$$ below). $head ef$$ The argument value $icode ef$$ has prototype $codei% %Vector% &%ef% %$$ and size $icode n$$. The input value of its elements does not matter. On output, it contains an estimated bound for the absolute error in the approximation $icode xf$$; i.e., $latex \[ ef_i > | X( tf )_i - xf_i | \] $$ $head maxabs$$ The argument $icode maxabs$$ is optional in the call to $code OdeGearControl$$. If it is present, it has the prototype $codei% %Vector% &%maxabs% %$$ and size $icode n$$. The input value of its elements does not matter. On output, it contains an estimate for the maximum absolute value of $latex X(t)$$; i.e., $latex \[ maxabs[i] \approx \max \left\{ | X( t )_i | \; : \; t \in [ti, tf] \right\} \] $$ $head nstep$$ The argument $icode nstep$$ has the prototype $codei% %size_t% &%nstep% %$$ Its input value does not matter and its output value is the number of calls to $cref OdeGear$$ used by $code OdeGearControl$$. $head Error Criteria Discussion$$ The relative error criteria $icode erel$$ and absolute error criteria $icode eabs$$ are enforced during each step of the integration of the ordinary differential equations. In addition, they are inversely scaled by the step size so that the total error bound is less than the sum of the error bounds. To be specific, if $latex \tilde{X} (t)$$ is the approximate solution at time $latex t$$, $icode ta$$ is the initial step time, and $icode tb$$ is the final step time, $latex \[ \left| \tilde{X} (tb)_j - X (tb)_j \right| \leq \frac{tf - ti}{tb - ta} \left[ eabs[j] + erel \; | \tilde{X} (tb)_j | \right] \] $$ If $latex X(tb)_j$$ is near zero for some $latex tb \in [ti , tf]$$, and one uses an absolute error criteria $latex eabs[j]$$ of zero, the error criteria above will force $code OdeGearControl$$ to use step sizes equal to $cref/smin/OdeGearControl/smin/$$ for steps ending near $latex tb$$. In this case, the error relative to $icode maxabs$$ can be judged after $code OdeGearControl$$ returns. If $icode ef$$ is to large relative to $icode maxabs$$, $code OdeGearControl$$ can be called again with a smaller value of $icode smin$$. $head Scalar$$ The type $icode Scalar$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, the following operations must be defined for $icode Scalar$$ objects $icode a$$ and $icode b$$: $table $bold Operation$$ $cnext $bold Description$$ $rnext $icode%a% <= %b%$$ $cnext returns true (false) if $icode a$$ is less than or equal (greater than) $icode b$$. $rnext $icode%a% == %b%$$ $cnext returns true (false) if $icode a$$ is equal to $icode b$$. $rnext $codei%log(%a%)%$$ $cnext returns a $icode Scalar$$ equal to the logarithm of $icode a$$ $rnext $codei%exp(%a%)%$$ $cnext returns a $icode Scalar$$ equal to the exponential of $icode a$$ $tend $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type Scalar/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ $children% example/ode_gear_control.cpp %$$ The file $cref ode_gear_control.cpp$$ contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise. $head Theory$$ Let $latex e(s)$$ be the error as a function of the step size $latex s$$ and suppose that there is a constant $latex K$$ such that $latex e(s) = K s^m$$. Let $latex a$$ be our error bound. Given the value of $latex e(s)$$, a step of size $latex \lambda s$$ would be ok provided that $latex \[ \begin{array}{rcl} a & \geq & e( \lambda s ) (tf - ti) / ( \lambda s ) \\ a & \geq & K \lambda^m s^m (tf - ti) / ( \lambda s ) \\ a & \geq & \lambda^{m-1} s^{m-1} (tf - ti) e(s) / s^m \\ a & \geq & \lambda^{m-1} (tf - ti) e(s) / s \\ \lambda^{m-1} & \leq & \frac{a}{e(s)} \frac{s}{tf - ti} \end{array} \] $$ Thus if the right hand side of the last inequality is greater than or equal to one, the step of size $latex s$$ is ok. $head Source Code$$ The source code for this routine is in the file $code cppad/ode_gear_control.hpp$$. $end -------------------------------------------------------------------------- */ // link exp and log for float and double # include # include namespace CppAD { // Begin CppAD namespace template Vector OdeGearControl( Fun &F , size_t M , const Scalar &ti , const Scalar &tf , const Vector &xi , const Scalar &smin , const Scalar &smax , Scalar &sini , const Vector &eabs , const Scalar &erel , Vector &ef , Vector &maxabs, size_t &nstep ) { // check simple vector class specifications CheckSimpleVector(); // dimension of the state space size_t n = size_t(xi.size()); CPPAD_ASSERT_KNOWN( M >= 1, "Error in OdeGearControl: M is less than one" ); CPPAD_ASSERT_KNOWN( smin <= smax, "Error in OdeGearControl: smin is greater than smax" ); CPPAD_ASSERT_KNOWN( sini <= smax, "Error in OdeGearControl: sini is greater than smax" ); CPPAD_ASSERT_KNOWN( size_t(eabs.size()) == n, "Error in OdeGearControl: size of eabs is not equal to n" ); CPPAD_ASSERT_KNOWN( size_t(maxabs.size()) == n, "Error in OdeGearControl: size of maxabs is not equal to n" ); // some constants const Scalar zero(0); const Scalar one(1); const Scalar one_plus( Scalar(3) / Scalar(2) ); const Scalar two(2); const Scalar ten(10); // temporary indices size_t i, k; // temporary Scalars Scalar step, sprevious, lambda, axi, a, root, r; // vectors of Scalars Vector T (M + 1); Vector X( (M + 1) * n ); Vector e(n); Vector xf(n); // initial integer values size_t m = 1; nstep = 0; // initialize T T[0] = ti; // initialize X, ef, maxabs for(i = 0; i < n; i++) for(i = 0; i < n; i++) { X[i] = xi[i]; ef[i] = zero; X[i] = xi[i]; if( zero <= xi[i] ) maxabs[i] = xi[i]; else maxabs[i] = - xi[i]; } // initial step size step = smin; while( T[m-1] < tf ) { sprevious = step; // check maximum if( smax <= step ) step = smax; // check minimum if( m < M ) { if( step <= sini ) step = sini; } else if( step <= smin ) step = smin; // check if near the end if( tf <= T[m-1] + one_plus * step ) T[m] = tf; else T[m] = T[m-1] + step; // try using this step size nstep++; OdeGear(F, m, n, T, X, e); step = T[m] - T[m-1]; // compute value of lambda for this step lambda = Scalar(10) * sprevious / step; for(i = 0; i < n; i++) { axi = X[m * n + i]; if( axi <= zero ) axi = - axi; a = eabs[i] + erel * axi; if( e[i] > zero ) { if( m == 1 ) root = (a / e[i]) / ten; else { r = ( a / e[i] ) * step / (tf - ti); root = exp( log(r) / Scalar(m-1) ); } if( root <= lambda ) lambda = root; } } bool advance; if( m == M ) advance = one <= lambda || step <= one_plus * smin; else advance = one <= lambda || step <= one_plus * sini; if( advance ) { // accept the results of this time step CPPAD_ASSERT_UNKNOWN( m <= M ); if( m == M ) { // shift for next step for(k = 0; k < m; k++) { T[k] = T[k+1]; for(i = 0; i < n; i++) X[k*n + i] = X[(k+1)*n + i]; } } // update ef and maxabs for(i = 0; i < n; i++) { ef[i] = ef[i] + e[i]; axi = X[m * n + i]; if( axi <= zero ) axi = - axi; if( axi > maxabs[i] ) maxabs[i] = axi; } if( m != M ) m++; // all we need do in this case } // new step suggested by error criteria step = std::min(lambda , ten) * step / two; } for(i = 0; i < n; i++) xf[i] = X[(m-1) * n + i]; return xf; } } // End CppAD namespace # endif cppad-20170000.3/cppad/utility/ode_gear.hpp0000644000175200017650000003063713057470465017516 0ustar coincoin-web// $Id: ode_gear.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_ODE_GEAR_HPP # define CPPAD_UTILITY_ODE_GEAR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin OdeGear$$ $spell cppad.hpp Jan bool const CppAD dep $$ $section An Arbitrary Order Gear Method$$ $mindex OdeGear Ode stiff differential equation$$ $head Syntax$$ $codei%# include %$$ $codei%OdeGear(%F%, %m%, %n%, %T%, %X%, %e%)%$$ $head Purpose$$ This routine applies $cref/Gear's Method/OdeGear/Gear's Method/$$ to solve an explicit set of ordinary differential equations. We are given $latex f : \B{R} \times \B{R}^n \rightarrow \B{R}^n$$ be a smooth function. This routine solves the following initial value problem $latex \[ \begin{array}{rcl} x( t_{m-1} ) & = & x^0 \\ x^\prime (t) & = & f[t , x(t)] \end{array} \] $$ for the value of $latex x( t_m )$$. If your set of ordinary differential equations are not stiff an explicit method may be better (perhaps $cref Runge45$$.) $head Include$$ The file $code cppad/ode_gear.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head Fun$$ The class $icode Fun$$ and the object $icode F$$ satisfy the prototype $codei% %Fun% &%F% %$$ This must support the following set of calls $codei% %F%.Ode(%t%, %x%, %f%) %F%.Ode_dep(%t%, %x%, %f_x%) %$$ $subhead t$$ The argument $icode t$$ has prototype $codei% const %Scalar% &%t% %$$ (see description of $cref/Scalar/OdeGear/Scalar/$$ below). $subhead x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ and has size $icode n$$ (see description of $cref/Vector/OdeGear/Vector/$$ below). $subhead f$$ The argument $icode f$$ to $icode%F%.Ode%$$ has prototype $codei% %Vector% &%f% %$$ On input and output, $icode f$$ is a vector of size $icode n$$ and the input values of the elements of $icode f$$ do not matter. On output, $icode f$$ is set equal to $latex f(t, x)$$ (see $icode f(t, x)$$ in $cref/Purpose/OdeGear/Purpose/$$). $subhead f_x$$ The argument $icode f_x$$ has prototype $codei% %Vector% &%f_x% %$$ On input and output, $icode f_x$$ is a vector of size $latex n * n$$ and the input values of the elements of $icode f_x$$ do not matter. On output, $latex \[ f\_x [i * n + j] = \partial_{x(j)} f_i ( t , x ) \] $$ $subhead Warning$$ The arguments $icode f$$, and $icode f_x$$ must have a call by reference in their prototypes; i.e., do not forget the $code &$$ in the prototype for $icode f$$ and $icode f_x$$. $head m$$ The argument $icode m$$ has prototype $codei% size_t %m% %$$ It specifies the order (highest power of $latex t$$) used to represent the function $latex x(t)$$ in the multi-step method. Upon return from $code OdeGear$$, the $th i$$ component of the polynomial is defined by $latex \[ p_i ( t_j ) = X[ j * n + i ] \] $$ for $latex j = 0 , \ldots , m$$ (where $latex 0 \leq i < n$$). The value of $latex m$$ must be greater than or equal one. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ It specifies the range space dimension of the vector valued function $latex x(t)$$. $head T$$ The argument $icode T$$ has prototype $codei% const %Vector% &%T% %$$ and size greater than or equal to $latex m+1$$. For $latex j = 0 , \ldots m$$, $latex T[j]$$ is the time corresponding to time corresponding to a previous point in the multi-step method. The value $latex T[m]$$ is the time of the next point in the multi-step method. The array $latex T$$ must be monotone increasing; i.e., $latex T[j] < T[j+1]$$. Above and below we often use the shorthand $latex t_j$$ for $latex T[j]$$. $head X$$ The argument $icode X$$ has the prototype $codei% %Vector% &%X% %$$ and size greater than or equal to $latex (m+1) * n$$. On input to $code OdeGear$$, for $latex j = 0 , \ldots , m-1$$, and $latex i = 0 , \ldots , n-1$$ $latex \[ X[ j * n + i ] = x_i ( t_j ) \] $$ Upon return from $code OdeGear$$, for $latex i = 0 , \ldots , n-1$$ $latex \[ X[ m * n + i ] \approx x_i ( t_m ) \] $$ $head e$$ The vector $icode e$$ is an approximate error bound for the result; i.e., $latex \[ e[i] \geq | X[ m * n + i ] - x_i ( t_m ) | \] $$ The order of this approximation is one less than the order of the solution; i.e., $latex \[ e = O ( h^m ) \] $$ where $latex h$$ is the maximum of $latex t_{j+1} - t_j$$. $head Scalar$$ The type $icode Scalar$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, the following operations must be defined for $icode Scalar$$ objects $icode a$$ and $icode b$$: $table $bold Operation$$ $cnext $bold Description$$ $rnext $icode%a% < %b%$$ $cnext less than operator (returns a $code bool$$ object) $tend $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type Scalar/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ $children% example/ode_gear.cpp %$$ The file $cref ode_gear.cpp$$ contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise. $head Source Code$$ The source code for this routine is in the file $code cppad/ode_gear.hpp$$. $head Theory$$ For this discussion we use the shorthand $latex x_j$$ for the value $latex x ( t_j ) \in \B{R}^n$$ which is not to be confused with $latex x_i (t) \in \B{R}$$ in the notation above. The interpolating polynomial $latex p(t)$$ is given by $latex \[ p(t) = \sum_{j=0}^m x_j \frac{ \prod_{i \neq j} ( t - t_i ) }{ \prod_{i \neq j} ( t_j - t_i ) } \] $$ The derivative $latex p^\prime (t)$$ is given by $latex \[ p^\prime (t) = \sum_{j=0}^m x_j \frac{ \sum_{i \neq j} \prod_{k \neq i,j} ( t - t_k ) }{ \prod_{k \neq j} ( t_j - t_k ) } \] $$ Evaluating the derivative at the point $latex t_\ell$$ we have $latex \[ \begin{array}{rcl} p^\prime ( t_\ell ) & = & x_\ell \frac{ \sum_{i \neq \ell} \prod_{k \neq i,\ell} ( t_\ell - t_k ) }{ \prod_{k \neq \ell} ( t_\ell - t_k ) } + \sum_{j \neq \ell} x_j \frac{ \sum_{i \neq j} \prod_{k \neq i,j} ( t_\ell - t_k ) }{ \prod_{k \neq j} ( t_j - t_k ) } \\ & = & x_\ell \sum_{i \neq \ell} \frac{ 1 }{ t_\ell - t_i } + \sum_{j \neq \ell} x_j \frac{ \prod_{k \neq \ell,j} ( t_\ell - t_k ) }{ \prod_{k \neq j} ( t_j - t_k ) } \\ & = & x_\ell \sum_{k \neq \ell} ( t_\ell - t_k )^{-1} + \sum_{j \neq \ell} x_j ( t_j - t_\ell )^{-1} \prod_{k \neq \ell ,j} ( t_\ell - t_k ) / ( t_j - t_k ) \end{array} \] $$ We define the vector $latex \alpha \in \B{R}^{m+1}$$ by $latex \[ \alpha_j = \left\{ \begin{array}{ll} \sum_{k \neq m} ( t_m - t_k )^{-1} & {\rm if} \; j = m \\ ( t_j - t_m )^{-1} \prod_{k \neq m,j} ( t_m - t_k ) / ( t_j - t_k ) & {\rm otherwise} \end{array} \right. \] $$ It follows that $latex \[ p^\prime ( t_m ) = \alpha_0 x_0 + \cdots + \alpha_m x_m \] $$ Gear's method determines $latex x_m$$ by solving the following nonlinear equation $latex \[ f( t_m , x_m ) = \alpha_0 x_0 + \cdots + \alpha_m x_m \] $$ Newton's method for solving this equation determines iterates, which we denote by $latex x_m^k$$, by solving the following affine approximation of the equation above $latex \[ \begin{array}{rcl} f( t_m , x_m^{k-1} ) + \partial_x f( t_m , x_m^{k-1} ) ( x_m^k - x_m^{k-1} ) & = & \alpha_0 x_0^k + \alpha_1 x_1 + \cdots + \alpha_m x_m \\ \left[ \alpha_m I - \partial_x f( t_m , x_m^{k-1} ) \right] x_m & = & \left[ f( t_m , x_m^{k-1} ) - \partial_x f( t_m , x_m^{k-1} ) x_m^{k-1} - \alpha_0 x_0 - \cdots - \alpha_{m-1} x_{m-1} \right] \end{array} \] $$ In order to initialize Newton's method; i.e. choose $latex x_m^0$$ we define the vector $latex \beta \in \B{R}^{m+1}$$ by $latex \[ \beta_j = \left\{ \begin{array}{ll} \sum_{k \neq m-1} ( t_{m-1} - t_k )^{-1} & {\rm if} \; j = m-1 \\ ( t_j - t_{m-1} )^{-1} \prod_{k \neq m-1,j} ( t_{m-1} - t_k ) / ( t_j - t_k ) & {\rm otherwise} \end{array} \right. \] $$ It follows that $latex \[ p^\prime ( t_{m-1} ) = \beta_0 x_0 + \cdots + \beta_m x_m \] $$ We solve the following approximation of the equation above to determine $latex x_m^0$$: $latex \[ f( t_{m-1} , x_{m-1} ) = \beta_0 x_0 + \cdots + \beta_{m-1} x_{m-1} + \beta_m x_m^0 \] $$ $head Gear's Method$$ C. W. Gear, ``Simultaneous Numerical Solution of Differential-Algebraic Equations,'' IEEE Transactions on Circuit Theory, vol. 18, no. 1, pp. 89-95, Jan. 1971. $end -------------------------------------------------------------------------- */ # include # include # include # include # include # include # include namespace CppAD { // BEGIN CppAD namespace template void OdeGear( Fun &F , size_t m , size_t n , const Vector &T , Vector &X , Vector &e ) { // temporary indices size_t i, j, k; typedef typename Vector::value_type Scalar; // check numeric type specifications CheckNumericType(); // check simple vector class specifications CheckSimpleVector(); CPPAD_ASSERT_KNOWN( m >= 1, "OdeGear: m is less than one" ); CPPAD_ASSERT_KNOWN( n > 0, "OdeGear: n is equal to zero" ); CPPAD_ASSERT_KNOWN( size_t(T.size()) >= (m+1), "OdeGear: size of T is not greater than or equal (m+1)" ); CPPAD_ASSERT_KNOWN( size_t(X.size()) >= (m+1) * n, "OdeGear: size of X is not greater than or equal (m+1) * n" ); for(j = 0; j < m; j++) CPPAD_ASSERT_KNOWN( T[j] < T[j+1], "OdeGear: the array T is not monotone increasing" ); // some constants Scalar zero(0); Scalar one(1); // vectors required by method Vector alpha(m + 1); Vector beta(m + 1); Vector f(n); Vector f_x(n * n); Vector x_m0(n); Vector x_m(n); Vector b(n); Vector A(n * n); // compute alpha[m] alpha[m] = zero; for(k = 0; k < m; k++) alpha[m] += one / (T[m] - T[k]); // compute beta[m-1] beta[m-1] = one / (T[m-1] - T[m]); for(k = 0; k < m-1; k++) beta[m-1] += one / (T[m-1] - T[k]); // compute other components of alpha for(j = 0; j < m; j++) { // compute alpha[j] alpha[j] = one / (T[j] - T[m]); for(k = 0; k < m; k++) { if( k != j ) { alpha[j] *= (T[m] - T[k]); alpha[j] /= (T[j] - T[k]); } } } // compute other components of beta for(j = 0; j <= m; j++) { if( j != m-1 ) { // compute beta[j] beta[j] = one / (T[j] - T[m-1]); for(k = 0; k <= m; k++) { if( k != j && k != m-1 ) { beta[j] *= (T[m-1] - T[k]); beta[j] /= (T[j] - T[k]); } } } } // evaluate f(T[m-1], x_{m-1} ) for(i = 0; i < n; i++) x_m[i] = X[(m-1) * n + i]; F.Ode(T[m-1], x_m, f); // solve for x_m^0 for(i = 0; i < n; i++) { x_m[i] = f[i]; for(j = 0; j < m; j++) x_m[i] -= beta[j] * X[j * n + i]; x_m[i] /= beta[m]; } x_m0 = x_m; // evaluate partial w.r.t x of f(T[m], x_m^0) F.Ode_dep(T[m], x_m, f_x); // compute the matrix A = ( alpha[m] * I - f_x ) for(i = 0; i < n; i++) { for(j = 0; j < n; j++) A[i * n + j] = - f_x[i * n + j]; A[i * n + i] += alpha[m]; } // LU factor (and overwrite) the matrix A CppAD::vector ip(n) , jp(n); # ifndef NDEBUG int sign = # endif LuFactor(ip, jp, A); CPPAD_ASSERT_KNOWN( sign != 0, "OdeGear: step size is to large" ); // Iterations of Newton's method for(k = 0; k < 3; k++) { // only evaluate f( T[m] , x_m ) keep f_x during iteration F.Ode(T[m], x_m, f); // b = f + f_x x_m - alpha[0] x_0 - ... - alpha[m-1] x_{m-1} for(i = 0; i < n; i++) { b[i] = f[i]; for(j = 0; j < n; j++) b[i] -= f_x[i * n + j] * x_m[j]; for(j = 0; j < m; j++) b[i] -= alpha[j] * X[ j * n + i ]; } LuInvert(ip, jp, A, b); x_m = b; } // return estimate for x( t[k] ) and the estimated error bound for(i = 0; i < n; i++) { X[m * n + i] = x_m[i]; e[i] = x_m[i] - x_m0[i]; if( e[i] < zero ) e[i] = - e[i]; } } } // End CppAD namespace # endif cppad-20170000.3/cppad/utility/lu_invert.hpp0000644000175200017650000001443513057470465017756 0ustar coincoin-web// $Id: lu_invert.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_LU_INVERT_HPP # define CPPAD_UTILITY_LU_INVERT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin LuInvert$$ $escape #$$ $spell cppad.hpp Lu Cpp jp ip const namespace typename etmp $$ $section Invert an LU Factored Equation$$ $mindex LuInvert linear$$ $pre $$ $head Syntax$$ $codei%# include %$$ $codei%LuInvert(%ip%, %jp%, %LU%, %X%)%$$ $head Description$$ Solves the matrix equation $icode%A% * %X% = %B%$$ using an LU factorization computed by $cref LuFactor$$. $head Include$$ The file $code cppad/lu_invert.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head Matrix Storage$$ All matrices are stored in row major order. To be specific, if $latex Y$$ is a vector that contains a $latex p$$ by $latex q$$ matrix, the size of $latex Y$$ must be equal to $latex p * q $$ and for $latex i = 0 , \ldots , p-1$$, $latex j = 0 , \ldots , q-1$$, $latex \[ Y_{i,j} = Y[ i * q + j ] \] $$ $head ip$$ The argument $icode ip$$ has prototype $codei% const %SizeVector% &%ip% %$$ (see description for $icode SizeVector$$ in $cref/LuFactor/LuFactor/SizeVector/$$ specifications). The size of $icode ip$$ is referred to as $icode n$$ in the specifications below. The elements of $icode ip$$ determine the order of the rows in the permuted matrix. $head jp$$ The argument $icode jp$$ has prototype $codei% const %SizeVector% &%jp% %$$ (see description for $icode SizeVector$$ in $cref/LuFactor/LuFactor/SizeVector/$$ specifications). The size of $icode jp$$ must be equal to $icode n$$. The elements of $icode jp$$ determine the order of the columns in the permuted matrix. $head LU$$ The argument $icode LU$$ has the prototype $codei% const %FloatVector% &%LU% %$$ and the size of $icode LU$$ must equal $latex n * n$$ (see description for $icode FloatVector$$ in $cref/LuFactor/LuFactor/FloatVector/$$ specifications). $subhead L$$ We define the lower triangular matrix $icode L$$ in terms of $icode LU$$. The matrix $icode L$$ is zero above the diagonal and the rest of the elements are defined by $codei% %L%(%i%, %j%) = %LU%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , i$$. $subhead U$$ We define the upper triangular matrix $icode U$$ in terms of $icode LU$$. The matrix $icode U$$ is zero below the diagonal, one on the diagonal, and the rest of the elements are defined by $codei% %U%(%i%, %j%) = %LU%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ for $latex i = 0 , \ldots , n-2$$ and $latex j = i+1 , \ldots , n-1$$. $subhead P$$ We define the permuted matrix $icode P$$ in terms of the matrix $icode L$$ and the matrix $icode U$$ by $icode%P% = %L% * %U%$$. $subhead A$$ The matrix $icode A$$, which defines the linear equations that we are solving, is given by $codei% %P%(%i%, %j%) = %A%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ (Hence $icode LU$$ contains a permuted factorization of the matrix $icode A$$.) $head X$$ The argument $icode X$$ has prototype $codei% %FloatVector% &%X% %$$ (see description for $icode FloatVector$$ in $cref/LuFactor/LuFactor/FloatVector/$$ specifications). The matrix $icode X$$ must have the same number of rows as the matrix $icode A$$. The input value of $icode X$$ is the matrix $icode B$$ and the output value solves the matrix equation $icode%A% * %X% = %B%$$. $children% example/lu_invert.cpp% omh/lu_invert_hpp.omh %$$ $head Example$$ The file $cref lu_solve.hpp$$ is a good example usage of $code LuFactor$$ with $code LuInvert$$. The file $cref lu_invert.cpp$$ contains an example and test of using $code LuInvert$$ by itself. It returns true if it succeeds and false otherwise. $head Source$$ The file $cref lu_invert.hpp$$ contains the current source code that implements these specifications. $end -------------------------------------------------------------------------- */ // BEGIN C++ # include # include # include namespace CppAD { // BEGIN CppAD namespace // LuInvert template void LuInvert( const SizeVector &ip, const SizeVector &jp, const FloatVector &LU, FloatVector &B ) { size_t k; // column index in X size_t p; // index along diagonal in LU size_t i; // row index in LU and X typedef typename FloatVector::value_type Float; // check numeric type specifications CheckNumericType(); // check simple vector class specifications CheckSimpleVector(); CheckSimpleVector(); Float etmp; size_t n = ip.size(); CPPAD_ASSERT_KNOWN( size_t(jp.size()) == n, "Error in LuInvert: jp must have size equal to n * n" ); CPPAD_ASSERT_KNOWN( size_t(LU.size()) == n * n, "Error in LuInvert: Lu must have size equal to n * m" ); size_t m = size_t(B.size()) / n; CPPAD_ASSERT_KNOWN( size_t(B.size()) == n * m, "Error in LuSolve: B must have size equal to a multiple of n" ); // temporary storage for reordered solution FloatVector x(n); // loop over equations for(k = 0; k < m; k++) { // invert the equation c = L * b for(p = 0; p < n; p++) { // solve for c[p] etmp = B[ ip[p] * m + k ] / LU[ ip[p] * n + jp[p] ]; B[ ip[p] * m + k ] = etmp; // subtract off effect on other variables for(i = p+1; i < n; i++) B[ ip[i] * m + k ] -= etmp * LU[ ip[i] * n + jp[p] ]; } // invert the equation x = U * c p = n; while( p > 0 ) { --p; etmp = B[ ip[p] * m + k ]; x[ jp[p] ] = etmp; for(i = 0; i < p; i++ ) B[ ip[i] * m + k ] -= etmp * LU[ ip[i] * n + jp[p] ]; } // copy reordered solution into B for(i = 0; i < n; i++) B[i * m + k] = x[i]; } return; } } // END CppAD namespace // END C++ # endif cppad-20170000.3/cppad/utility/check_simple_vector.hpp0000644000175200017650000001152313057470465021752 0ustar coincoin-web// $Id: check_simple_vector.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_CHECK_SIMPLE_VECTOR_HPP # define CPPAD_UTILITY_CHECK_SIMPLE_VECTOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin CheckSimpleVector$$ $spell alloc const cppad.hpp CppAD $$ $section Check Simple Vector Concept$$ $mindex CheckSimpleVector$$ $head Syntax$$ $codei%# include %$$ $codei%CheckSimpleVector<%Scalar%, %Vector%>()%$$ $pre $$ $codei%CheckSimpleVector<%Scalar%, %Vector%>(%x%, %y%)%$$ $head Purpose$$ Preforms compile and run time checks that the type specified by $icode Vector$$ satisfies all the requirements for a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Scalar$$. If a requirement is not satisfied, a an error message makes it clear what condition is not satisfied. $head x, y$$ If the arguments $icode x$$ and $icode y$$ are present, they have prototype $codei% const %Scalar%& %x% const %Scalar%& %y% %$$ In addition, the check $codei% %x% == %x% %$$ will return the boolean value $code true$$, and $codei% %x% == %y% %$$ will return $code false$$. $head Restrictions$$ If the arguments $icode x$$ and $icode y$$ are not present, the following extra assumption is made by $code CheckSimpleVector$$: If $icode x$$ is a $icode Scalar$$ object $codei% %x% = 0 %y% = 1 %$$ assigns values to the objects $icode x$$ and $icode y$$. In addition, $icode%x% == %x%$$ would return the boolean value $code true$$ and $icode%x% == %y%$$ would return $code false$$. $head Include$$ The file $code cppad/check_simple_vector.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest if the CppAD include files. $head Parallel Mode$$ The routine $cref/thread_alloc::parallel_setup/ta_parallel_setup/$$ must be called before it can be used in $cref/parallel/ta_in_parallel/$$ mode. $head Example$$ $children% example/check_simple_vector.cpp %$$ The file $cref check_simple_vector.cpp$$ contains an example and test of this function where $icode S$$ is the same as $icode T$$. It returns true, if it succeeds an false otherwise. The comments in this example suggest a way to change the example so $icode S$$ is not the same as $icode T$$. $end --------------------------------------------------------------------------- */ # include # include # include # include namespace CppAD { # ifdef NDEBUG template inline void CheckSimpleVector(const Scalar& x, const Scalar& y) { } template inline void CheckSimpleVector(void) { } # else template struct ok_if_S_same_as_T { }; template struct ok_if_S_same_as_T { T value; }; template void CheckSimpleVector(const Scalar& x, const Scalar& y) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL static size_t count; if( count > 0 ) return; count++; // value_type must be type of elements of Vector typedef typename Vector::value_type value_type; // check that elements of Vector have type Scalar struct ok_if_S_same_as_T x_copy; x_copy.value = x; // check default constructor Vector d; // size member function CPPAD_ASSERT_KNOWN( d.size() == 0, "default construtor result does not have size zero" ); // resize to same size as other vectors in test d.resize(1); // check sizing constructor Vector s(1); // check element assignment s[0] = y; CPPAD_ASSERT_KNOWN( s[0] == y, "element assignment failed" ); // check copy constructor s[0] = x_copy.value; const Vector c(s); s[0] = y; CPPAD_ASSERT_KNOWN( c[0] == x, "copy constructor is shallow" ); // vector assignment operator d[0] = x; s = d; s[0] = y; CPPAD_ASSERT_KNOWN( d[0] == x, "assignment operator is shallow" ); // element access, right side const // element assignment, left side not const d[0] = c[0]; CPPAD_ASSERT_KNOWN( d[0] == x, "element assignment from const failed" ); } template void CheckSimpleVector(void) { Scalar x; Scalar y; // use assignment and not constructor x = 0; y = 1; CheckSimpleVector(x, y); } # endif } // end namespace CppAD # endif cppad-20170000.3/cppad/utility/to_string.hpp0000644000175200017650000001115113057470465017747 0ustar coincoin-web// $Id$ # ifndef CPPAD_UTILITY_TO_STRING_HPP # define CPPAD_UTILITY_TO_STRING_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin to_string$$ $spell cppad.hpp long long std const ostringstream $$ $section Convert Certain Types to a String$$ $head Syntax$$ $codei%# include %$$ $icode%s% = to_string(%value%)%$$. $head See Also$$ $cref base_to_string$$, $cref ad_to_string$$ $head Purpose$$ This routine is similar to the C++11 routine $code std::to_string$$ with the following differences: $list number$$ It works with C++98. $lnext It has been extended to the fundamental floating point types. $lnext It has specifications for extending to an arbitrary type; see $cref base_to_string$$. $lnext If $code $$ is included, and it has been extended to a $icode Base$$ type, it automatically extends to the $cref/AD types above Base/glossary/AD Type Above Base/$$. $lend $head value$$ $subhead Integer$$ The argument $icode value$$ can have the following prototype $codei% const %Integer%& %value% %$$ where $icode Integer$$ is any of the fundamental integer types; e.g., $code short int$$ and $code unsigned long$$. Note that if C++11 is supported by this compilation, $code unsigned long long$$ is also a fundamental integer type. $subhead Float$$ The argument $icode value$$ can have the following prototype $codei% const %Float%& %value% %$$ where $icode Float$$ is any of the fundamental floating point types; i.e., $code float$$, $code double$$, and $code long double$$. $head s$$ The return value has prototype $codei% std::string %s% %$$ and contains a representation of the specified $icode value$$. $subhead Integer$$ If $icode value$$ is an $codei Integer$$, the representation is equivalent to $codei%os% << %value%$$ where $icode os$$ is an $code std::ostringstream$$. $subhead Float$$ If $icode value$$ is a $codei Float$$, enough digits are used in the representation so that the result is accurate to withing round off error. $children% example/to_string.cpp %$$ $head Example$$ The file $cref to_string.cpp$$ contains an example and test of this routine. It returns true if it succeeds and false otherwise. $end */ # include # include # include # include # include # define CPPAD_SPECIALIZE_TO_STRING_INTEGER(Type) \ template <> struct to_string_struct\ { std::string operator()(const Type& value) \ { std::stringstream os;\ os << value;\ return os.str();\ }\ }; # define CPPAD_SPECIALIZE_TO_STRING_FLOAT(Float) \ template <> struct to_string_struct\ { std::string operator()(const Float& value) \ { std::stringstream os;\ Float epsilon = std::numeric_limits::epsilon();\ size_t n_digits = 1 - int( std::log10(epsilon) );\ os << std::setprecision(n_digits);\ os << value;\ return os.str();\ }\ }; namespace CppAD { // Default implementation, // each type must define its own specilization. template struct to_string_struct { std::string operator()(const Type& value) { CPPAD_ASSERT_KNOWN( false, "to_string is not implemented for this type" ); // return empty string return std::string(""); } }; // specialization for the fundamental integer types CPPAD_SPECIALIZE_TO_STRING_INTEGER(signed short) CPPAD_SPECIALIZE_TO_STRING_INTEGER(unsigned short) // CPPAD_SPECIALIZE_TO_STRING_INTEGER(signed int) CPPAD_SPECIALIZE_TO_STRING_INTEGER(unsigned int) // CPPAD_SPECIALIZE_TO_STRING_INTEGER(signed long) CPPAD_SPECIALIZE_TO_STRING_INTEGER(unsigned long) // # if CPPAD_USE_CPLUSPLUS_2011 CPPAD_SPECIALIZE_TO_STRING_INTEGER(signed long long) CPPAD_SPECIALIZE_TO_STRING_INTEGER(unsigned long long) # endif // specialization for the fundamental floating point types CPPAD_SPECIALIZE_TO_STRING_FLOAT(float) CPPAD_SPECIALIZE_TO_STRING_FLOAT(double) CPPAD_SPECIALIZE_TO_STRING_FLOAT(long double) // link from function to function object in structure template std::string to_string(const Type& value) { to_string_struct to_str; return to_str(value); } } # undef CPPAD_SPECIALIZE_TO_STRING_FLOAT # undef CPPAD_SPECIALIZE_TO_STRING_INTEGER # endif cppad-20170000.3/cppad/utility/romberg_mul.hpp0000644000175200017650000001717113057470465020261 0ustar coincoin-web// $Id: romberg_mul.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_UTILITY_ROMBERG_MUL_HPP # define CPPAD_UTILITY_ROMBERG_MUL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin RombergMul$$ $spell cppad.hpp bool const Cpp RombergMulMul $$ $section Multi-dimensional Romberg Integration$$ $mindex integrate multi dimensional dimension$$ $head Syntax$$ $codei%# include %$$ $codei%RombergMul<%Fun%, %SizeVector%, %FloatVector%, %m%> %R%$$ $pre $$ $icode%r% = %R%(%F%, %a%, %b%, %n%, %p%, %e%)%$$ $head Description$$ Returns the Romberg integration estimate $latex r$$ for the multi-dimensional integral $latex \[ r = \int_{a[0]}^{b[0]} \cdots \int_{a[m-1]}^{b[m-1]} \; F(x) \; {\bf d} x_0 \cdots {\bf d} x_{m-1} \; + \; \sum_{i=0}^{m-1} O \left[ ( b[i] - a[i] ) / 2^{n[i]-1} \right]^{2(p[i]+1)} \] $$ $head Include$$ The file $code cppad/romberg_mul.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head m$$ The template parameter $icode m$$ must be convertible to a $code size_t$$ object with a value that can be determined at compile time; for example $code 2$$. It determines the dimension of the domain space for the integration. $head r$$ The return value $icode r$$ has prototype $codei% %Float% %r% %$$ It is the estimate computed by $code RombergMul$$ for the integral above (see description of $cref/Float/RombergMul/Float/$$ below). $head F$$ The object $icode F$$ has the prototype $codei% %Fun% &%F% %$$ It must support the operation $codei% %F%(%x%) %$$ The argument $icode x$$ to $icode F$$ has prototype $codei% const %Float% &%x% %$$ The return value of $icode F$$ is a $icode Float$$ object $head a$$ The argument $icode a$$ has prototype $codei% const %FloatVector% &%a% %$$ It specifies the lower limit for the integration (see description of $cref/FloatVector/RombergMul/FloatVector/$$ below). $head b$$ The argument $icode b$$ has prototype $codei% const %FloatVector% &%b% %$$ It specifies the upper limit for the integration. $head n$$ The argument $icode n$$ has prototype $codei% const %SizeVector% &%n% %$$ A total number of $latex 2^{n[i]-1} + 1$$ evaluations of $icode%F%(%x%)%$$ are used to estimate the integral with respect to $latex {\bf d} x_i$$. $head p$$ The argument $icode p$$ has prototype $codei% const %SizeVector% &%p% %$$ For $latex i = 0 , \ldots , m-1$$, $latex n[i]$$ determines the accuracy order in the approximation for the integral that is returned by $code RombergMul$$. The values in $icode p$$ must be less than or equal $icode n$$; i.e., $icode%p%[%i%] <= %n%[%i%]%$$. $head e$$ The argument $icode e$$ has prototype $codei% %Float% &%e% %$$ The input value of $icode e$$ does not matter and its output value is an approximation for the absolute error in the integral estimate. $head Float$$ The type $icode Float$$ is defined as the type of the elements of $cref/FloatVector/RombergMul/FloatVector/$$. The type $icode Float$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, if $icode x$$ and $icode y$$ are $icode Float$$ objects, $codei% %x% < %y% %$$ returns the $code bool$$ value true if $icode x$$ is less than $icode y$$ and false otherwise. $head FloatVector$$ The type $icode FloatVector$$ must be a $cref SimpleVector$$ class. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $children% example/romberg_mul.cpp %$$ $head Example$$ $comment% example/romberg_mul.cpp %$$ The file $cref Rombergmul.cpp$$ contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise. $head Source Code$$ The source code for this routine is in the file $code cppad/romberg_mul.hpp$$. $end */ # include # include # include namespace CppAD { // BEGIN CppAD namespace template class SliceLast { typedef typename FloatVector::value_type Float; private: Fun *F; size_t last; FloatVector x; public: SliceLast( Fun *F_, size_t last_, const FloatVector &x_ ) : F(F_) , last(last_), x(last + 1) { size_t i; for(i = 0; i < last; i++) x[i] = x_[i]; } double operator()(const Float &xlast) { x[last] = xlast; return (*F)(x); } }; template class IntegrateLast { private: Fun *F; const size_t last; const FloatVector a; const FloatVector b; const SizeVector n; const SizeVector p; Float esum; size_t ecount; public: IntegrateLast( Fun *F_ , size_t last_ , const FloatVector &a_ , const FloatVector &b_ , const SizeVector &n_ , const SizeVector &p_ ) : F(F_) , last(last_), a(a_) , b(b_) , n(n_) , p(p_) { } Float operator()(const FloatVector &x) { Float r, e; SliceLast S(F, last, x); r = CppAD::RombergOne( S, a[last], b[last], n[last], p[last], e ); esum = esum + e; ecount++; return r; } void ClearEsum(void) { esum = 0.; } Float GetEsum(void) { return esum; } void ClearEcount(void) { ecount = 0; } size_t GetEcount(void) { return ecount; } }; template class RombergMul { typedef typename FloatVector::value_type Float; public: RombergMul(void) { } Float operator() ( Fun &F , const FloatVector &a , const FloatVector &b , const SizeVector &n , const SizeVector &p , Float &e ) { Float r; typedef IntegrateLast< Fun , SizeVector , FloatVector , Float > IntegrateOne; IntegrateOne Fm1(&F, m-1, a, b, n, p); RombergMul< IntegrateOne, SizeVector , FloatVector , m-1 > RombergMulM1; Fm1.ClearEsum(); Fm1.ClearEcount(); r = RombergMulM1(Fm1, a, b, n, p, e); size_t i, j; Float prod = 1; size_t pow2 = 1; for(i = 0; i < m-1; i++) { prod *= (b[i] - a[i]); for(j = 0; j < (n[i] - 1); j++) pow2 *= 2; } assert( Fm1.GetEcount() == (pow2+1) ); e = e + Fm1.GetEsum() * prod / Fm1.GetEcount(); return r; } }; template class RombergMul { typedef typename FloatVector::value_type Float; public: Float operator() ( Fun &F , const FloatVector &a , const FloatVector &b , const SizeVector &n , const SizeVector &p , Float &e ) { Float r; typedef IntegrateLast< Fun , SizeVector , FloatVector , Float > IntegrateOne; // check simple vector class specifications CheckSimpleVector(); // check numeric type specifications CheckNumericType(); IntegrateOne F0(&F, 0, a, b, n, p); F0.ClearEsum(); F0.ClearEcount(); r = F0(a); assert( F0.GetEcount() == 1 ); e = F0.GetEsum(); return r; } }; } // END CppAD namespace # endif cppad-20170000.3/cppad/utility/near_equal.hpp0000644000175200017650000001355113057470465020061 0ustar coincoin-web// $Id: near_equal.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_NEAR_EQUAL_HPP # define CPPAD_UTILITY_NEAR_EQUAL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin NearEqual$$ $spell cppad.hpp sqrt cout endl Microsoft std Cpp namespace const bool $$ $section Determine if Two Values Are Nearly Equal$$ $mindex NearEqual near absolute difference relative$$ $head Syntax$$ $codei%# include %$$ $icode%b% = NearEqual(%x%, %y%, %r%, %a%)%$$ $head Purpose$$ Returns true, if $icode x$$ and $icode y$$ are nearly equal, and false otherwise. $head x$$ The argument $icode x$$ has one of the following possible prototypes $codei% const %Type% &%x%, const std::complex<%Type%> &%x%, %$$ $head y$$ The argument $icode y$$ has one of the following possible prototypes $codei% const %Type% &%y%, const std::complex<%Type%> &%y%, %$$ $head r$$ The relative error criteria $icode r$$ has prototype $codei% const %Type% &%r% %$$ It must be greater than or equal to zero. The relative error condition is defined as: $latex \[ | x - y | \leq r ( |x| + |y| ) \] $$ $head a$$ The absolute error criteria $icode a$$ has prototype $codei% const %Type% &%a% %$$ It must be greater than or equal to zero. The absolute error condition is defined as: $latex \[ | x - y | \leq a \] $$ $head b$$ The return value $icode b$$ has prototype $codei% bool %b% %$$ If either $icode x$$ or $icode y$$ is infinite or not a number, the return value is false. Otherwise, if either the relative or absolute error condition (defined above) is satisfied, the return value is true. Otherwise, the return value is false. $head Type$$ The type $icode Type$$ must be a $cref NumericType$$. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, the following operations must be defined objects $icode a$$ and $icode b$$ of type $icode Type$$: $table $bold Operation$$ $cnext $bold Description$$ $rnext $icode%a% <= %b%$$ $cnext less that or equal operator (returns a $code bool$$ object) $tend $head Include Files$$ The file $code cppad/near_equal.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head Example$$ $children% example/near_equal.cpp %$$ The file $cref near_equal.cpp$$ contains an example and test of $code NearEqual$$. It return true if it succeeds and false otherwise. $head Exercise$$ Create and run a program that contains the following code: $codep using std::complex; using std::cout; using std::endl; complex one(1., 0), i(0., 1); complex x = one / i; complex y = - i; double r = 1e-12; double a = 0; bool ok = CppAD::NearEqual(x, y, r, a); if( ok ) cout << "Ok" << endl; else cout << "Error" << endl; $$ $end */ # include # include # include # include namespace CppAD { // Begin CppAD namespace // determine if both x and y are finite values template bool near_equal_isfinite(const Type &x , const Type &y) { Type infinity = Type( std::numeric_limits::infinity() ); // handle bug where some compilers return true for nan == nan bool xNan = x != x; bool yNan = y != y; // infinite cases bool xInf = (x == infinity || x == - infinity); bool yInf = (x == infinity || x == - infinity); return ! (xNan | yNan | xInf | yInf); } template bool NearEqual(const Type &x, const Type &y, const Type &r, const Type &a) { CheckNumericType(); Type zero(0); CPPAD_ASSERT_KNOWN( zero <= r, "Error in NearEqual: relative error is less than zero" ); CPPAD_ASSERT_KNOWN( zero <= a, "Error in NearEqual: absolute error is less than zero" ); // check for special cases if( ! CppAD::near_equal_isfinite(x, y) ) return false; Type ax = x; if( ax <= zero ) ax = - ax; Type ay = y; if( ay <= zero ) ay = - ay; Type ad = x - y; if( ad <= zero ) ad = - ad; if( ad <= a ) return true; if( ad <= r * (ax + ay) ) return true; return false; } template bool NearEqual( const std::complex &x , const std::complex &y , const Type &r , const Type & a ) { CheckNumericType(); # ifndef NDEBUG Type zero(0); # endif CPPAD_ASSERT_KNOWN( zero <= r, "Error in NearEqual: relative error is less than zero" ); CPPAD_ASSERT_KNOWN( zero <= a, "Error in NearEqual: absolute error is less than zero" ); // check for special cases if( ! CppAD::near_equal_isfinite(x.real(), x.imag()) ) return false; if( ! CppAD::near_equal_isfinite(y.real(), y.imag()) ) return false; std::complex d = x - y; Type ad = std::abs(d); if( ad <= a ) return true; Type ax = std::abs(x); Type ay = std::abs(y); if( ad <= r * (ax + ay) ) return true; return false; } template bool NearEqual( const std::complex &x , const Type &y , const Type &r , const Type & a ) { return NearEqual(x, std::complex(y, Type(0)), r, a); } template bool NearEqual( const Type &x , const std::complex &y , const Type &r , const Type & a ) { return NearEqual(std::complex(x, Type(0)), y, r, a); } } // END CppAD namespace # endif cppad-20170000.3/cppad/utility/nan.hpp0000644000175200017650000001056013057470465016516 0ustar coincoin-web// $Id: nan.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_NAN_HPP # define CPPAD_UTILITY_NAN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin nan$$ $spell hasnan cppad hpp CppAD isnan bool const $$ $section Obtain Nan or Determine if a Value is Nan$$ $head Syntax$$ $codei%# include %$$ $icode%b% = isnan(%s%) %$$ $icode%b% = hasnan(%v%)%$$ $head Purpose$$ It obtain and check for the value not a number $code nan$$. The IEEE standard specifies that a floating point value $icode a$$ is $code nan$$ if and only if the following returns true $codei% %a% != %a% %$$ $head Include$$ The file $code cppad/nan.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $subhead Macros$$ Some C++ compilers use preprocessor symbols called $code nan$$ and $code isnan$$. These preprocessor symbols will no longer be defined after this file is included. $head isnan$$ This routine determines if a scalar value is $code nan$$. $subhead s$$ The argument $icode s$$ has prototype $codei% const %Scalar% %s% %$$ $subhead b$$ The return value $icode b$$ has prototype $codei% bool %b% %$$ It is true if the value $icode s$$ is $code nan$$. $head hasnan$$ This routine determines if a $cref SimpleVector$$ has an element that is $code nan$$. $subhead v$$ The argument $icode v$$ has prototype $codei% const %Vector% &%v% %$$ (see $cref/Vector/nan/Vector/$$ for the definition of $icode Vector$$). $subhead b$$ The return value $icode b$$ has prototype $codei% bool %b% %$$ It is true if the vector $icode v$$ has a $code nan$$. $head nan(zero)$$ $subhead Deprecated 2015-10-04$$ This routine has been deprecated, use CppAD numeric limits $cref/quiet_NaN/numeric_limits/quiet_NaN/$$ in its place. $subhead Syntax$$ $icode%s% = nan(%z%) %$$ $subhead z$$ The argument $icode z$$ has prototype $codei% const %Scalar% &%z% %$$ and its value is zero (see $cref/Scalar/nan/Scalar/$$ for the definition of $icode Scalar$$). $subhead s$$ The return value $icode s$$ has prototype $codei% %Scalar% %s% %$$ It is the value $code nan$$ for this floating point type. $head Scalar$$ The type $icode Scalar$$ must support the following operations; $table $bold Operation$$ $cnext $bold Description$$ $rnext $icode%a% / %b%$$ $cnext division operator (returns a $icode Scalar$$ object) $rnext $icode%a% == %b%$$ $cnext equality operator (returns a $code bool$$ object) $rnext $icode%a% != %b%$$ $cnext not equality operator (returns a $code bool$$ object) $tend Note that the division operator will be used with $icode a$$ and $icode b$$ equal to zero. For some types (e.g. $code int$$) this may generate an exception. No attempt is made to catch any such exception. $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with elements of type $icode Scalar$$. $children% example/nan.cpp %$$ $head Example$$ The file $cref nan.cpp$$ contains an example and test of this routine. It returns true if it succeeds and false otherwise. $end */ # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include /* # define nan There must be a define for every CppAD undef */ # ifdef nan # undef nan # endif /* # define isnan There must be a define for every CppAD undef */ # ifdef isnan # undef isnan # endif namespace CppAD { // BEGIN CppAD namespace template inline bool isnan(const Scalar &s) { return (s != s); } template bool hasnan(const Vector &v) { bool found_nan; size_t i; i = v.size(); found_nan = false; // on MS Visual Studio 2012, CppAD required in front of isnan ? while(i--) found_nan |= CppAD::isnan(v[i]); return found_nan; } template inline Scalar nan(const Scalar &zero) { return zero / zero; } } // End CppAD namespace # endif cppad-20170000.3/cppad/utility/index_sort.hpp0000644000175200017650000001057713057470465020130 0ustar coincoin-web// $Id: index_sort.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_INDEX_SORT_HPP # define CPPAD_UTILITY_INDEX_SORT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin index_sort$$ $spell cppad.hpp ind const $$ $section Returns Indices that Sort a Vector$$ $mindex index_sort$$ $head Syntax$$ $codei%# include %$$ $codei%index_sort(%keys%, %ind%)%$$ $head keys$$ The argument $icode keys$$ has prototype $codei% const %VectorKey%& %keys% %$$ where $icode VectorKey$$ is a $cref SimpleVector$$ class with elements that support the $code <$$ operation. $head ind$$ The argument $icode ind$$ has prototype $codei% %VectorSize%& %ind% %$$ where $icode VectorSize$$ is a $cref SimpleVector$$ class with elements of type $code size_t$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $subhead Input$$ The size of $icode ind$$ must be the same as the size of $icode keys$$ and the value of its input elements does not matter. $subhead Return$$ Upon return, $icode ind$$ is a permutation of the set of indices that yields increasing order for $icode keys$$. In other words, for all $icode%i% != %j%$$, $codei% %ind%[%i%] != %ind%[%j%] %$$ and for $icode%i% = 0 , %...% , %size%-2%$$, $codei% ( %keys%[ %ind%[%i%+1] ] < %keys%[ %ind%[%i%] ] ) == false %$$ $head Example$$ $children% example/index_sort.cpp %$$ The file $cref index_sort.cpp$$ contains an example and test of this routine. It return true if it succeeds and false otherwise. $end */ # include # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file index_sort.hpp File used to implement the CppAD index sort utility */ /*! Helper class used by index_sort */ template class index_sort_element { private: /// key used to determine position of this element Compare key_; /// index vlaue corresponding to this key size_t index_; public: /// operator requried by std::sort bool operator<(const index_sort_element& other) const { return key_ < other.key_; } /// set the key for this element void set_key(const Compare& value) { key_ = value; } /// set the index for this element void set_index(const size_t& index) { index_ = index; } /// get the key for this element Compare get_key(void) const { return key_; } /// get the index for this element size_t get_index(void) const { return index_; } }; /*! Compute the indices that sort a vector of keys \tparam VectorKey Simple vector type that deterimene the sorting order by \c < operator on its elements. \tparam VectorSize Simple vector type with elements of \c size_t that is used to return index values. \param keys [in] values that determine the sorting order. \param ind [out] must have the same size as \c keys. The input value of its elements does not matter. The output value of its elements satisfy \code ( keys[ ind[i] ] < keys[ ind[i+1] ] ) == false \endcode */ template void index_sort(const VectorKey& keys, VectorSize& ind) { typedef typename VectorKey::value_type Compare; CheckSimpleVector(); typedef index_sort_element element; CPPAD_ASSERT_KNOWN( size_t(keys.size()) == size_t(ind.size()), "index_sort: vector sizes do not match" ); size_t size_work = size_t(keys.size()); size_t size_out; element* work = thread_alloc::create_array(size_work, size_out); // copy initial order into work size_t i; for(i = 0; i < size_work; i++) { work[i].set_key( keys[i] ); work[i].set_index( i ); } // sort the work array std::sort(work, work+size_work); // copy the indices to the output vector for(i = 0; i < size_work; i++) ind[i] = work[i].get_index(); // we are done with this work array thread_alloc::delete_array(work); return; } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/utility/lu_factor.hpp0000644000175200017650000002665513057470465017734 0ustar coincoin-web// $Id: lu_factor.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_LU_FACTOR_HPP # define CPPAD_UTILITY_LU_FACTOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin LuFactor$$ $escape #$$ $spell cppad.hpp Cpp Geq Lu bool const ip jp namespace std typename $$ $section LU Factorization of A Square Matrix$$ $mindex LuFactor linear equation solve$$ $pre $$ $head Syntax$$ $codei%# include %$$ $icode%sign% = LuFactor(%ip%, %jp%, %LU%)%$$ $head Description$$ Computes an LU factorization of the matrix $icode A$$ where $icode A$$ is a square matrix. $head Include$$ The file $code cppad/lu_factor.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head Matrix Storage$$ All matrices are stored in row major order. To be specific, if $latex Y$$ is a vector that contains a $latex p$$ by $latex q$$ matrix, the size of $latex Y$$ must be equal to $latex p * q $$ and for $latex i = 0 , \ldots , p-1$$, $latex j = 0 , \ldots , q-1$$, $latex \[ Y_{i,j} = Y[ i * q + j ] \] $$ $head sign$$ The return value $icode sign$$ has prototype $codei% int %sign% %$$ If $icode A$$ is invertible, $icode sign$$ is plus or minus one and is the sign of the permutation corresponding to the row ordering $icode ip$$ and column ordering $icode jp$$. If $icode A$$ is not invertible, $icode sign$$ is zero. $head ip$$ The argument $icode ip$$ has prototype $codei% %SizeVector% &%ip% %$$ (see description of $cref/SizeVector/LuFactor/SizeVector/$$ below). The size of $icode ip$$ is referred to as $icode n$$ in the specifications below. The input value of the elements of $icode ip$$ does not matter. The output value of the elements of $icode ip$$ determine the order of the rows in the permuted matrix. $head jp$$ The argument $icode jp$$ has prototype $codei% %SizeVector% &%jp% %$$ (see description of $cref/SizeVector/LuFactor/SizeVector/$$ below). The size of $icode jp$$ must be equal to $icode n$$. The input value of the elements of $icode jp$$ does not matter. The output value of the elements of $icode jp$$ determine the order of the columns in the permuted matrix. $head LU$$ The argument $icode LU$$ has the prototype $codei% %FloatVector% &%LU% %$$ and the size of $icode LU$$ must equal $latex n * n$$ (see description of $cref/FloatVector/LuFactor/FloatVector/$$ below). $subhead A$$ We define $icode A$$ as the matrix corresponding to the input value of $icode LU$$. $subhead P$$ We define the permuted matrix $icode P$$ in terms of $icode A$$ by $codei% %P%(%i%, %j%) = %A%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ $subhead L$$ We define the lower triangular matrix $icode L$$ in terms of the output value of $icode LU$$. The matrix $icode L$$ is zero above the diagonal and the rest of the elements are defined by $codei% %L%(%i%, %j%) = %LU%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , i$$. $subhead U$$ We define the upper triangular matrix $icode U$$ in terms of the output value of $icode LU$$. The matrix $icode U$$ is zero below the diagonal, one on the diagonal, and the rest of the elements are defined by $codei% %U%(%i%, %j%) = %LU%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ for $latex i = 0 , \ldots , n-2$$ and $latex j = i+1 , \ldots , n-1$$. $subhead Factor$$ If the return value $icode sign$$ is non-zero, $codei% %L% * %U% = %P% %$$ If the return value of $icode sign$$ is zero, the contents of $icode L$$ and $icode U$$ are not defined. $subhead Determinant$$ If the return value $icode sign$$ is zero, the determinant of $icode A$$ is zero. If $icode sign$$ is non-zero, using the output value of $icode LU$$ the determinant of the matrix $icode A$$ is equal to $codei% %sign% * %LU%[%ip%[0], %jp%[0]] * %...% * %LU%[%ip%[%n%-1], %jp%[%n%-1]] %$$ $head SizeVector$$ The type $icode SizeVector$$ must be a $cref SimpleVector$$ class with $cref/elements of type size_t/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head FloatVector$$ The type $icode FloatVector$$ must be a $cref/simple vector class/SimpleVector/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Float$$ This notation is used to denote the type corresponding to the elements of a $icode FloatVector$$. The type $icode Float$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, the following operations must be defined for any pair of $icode Float$$ objects $icode x$$ and $icode y$$: $table $bold Operation$$ $cnext $bold Description$$ $rnext $codei%log(%x%)%$$ $cnext returns the logarithm of $icode x$$ as a $icode Float$$ object $tend $head AbsGeq$$ Including the file $code lu_factor.hpp$$ defines the template function $codei% template bool AbsGeq<%Float%>(const %Float% &%x%, const %Float% &%y%) %$$ in the $code CppAD$$ namespace. This function returns true if the absolute value of $icode x$$ is greater than or equal the absolute value of $icode y$$. It is used by $code LuFactor$$ to choose the pivot elements. This template function definition uses the operator $code <=$$ to obtain the absolute value for $icode Float$$ objects. If this operator is not defined for your use of $icode Float$$, you will need to specialize this template so that it works for your use of $code LuFactor$$. $pre $$ Complex numbers do not have the operation $code <=$$ defined. The specializations $codei% bool AbsGeq< std::complex > (const std::complex &%x%, const std::complex &%y%) bool AbsGeq< std::complex > (const std::complex &%x%, const std::complex &%y%) %$$ are define by including $code lu_factor.hpp$$ These return true if the sum of the square of the real and imaginary parts of $icode x$$ is greater than or equal the sum of the square of the real and imaginary parts of $icode y$$. $children% example/lu_factor.cpp% omh/lu_factor_hpp.omh %$$ $head Example$$ The file $cref lu_factor.cpp$$ contains an example and test of using $code LuFactor$$ by itself. It returns true if it succeeds and false otherwise. $pre $$ The file $cref lu_solve.hpp$$ provides a useful example usage of $code LuFactor$$ with $code LuInvert$$. $head Source$$ The file $cref lu_factor.hpp$$ contains the current source code that implements these specifications. $end -------------------------------------------------------------------------- */ // BEGIN C++ # include # include # include # include # include namespace CppAD { // BEGIN CppAD namespace // AbsGeq template inline bool AbsGeq(const Float &x, const Float &y) { Float xabs = x; if( xabs <= Float(0) ) xabs = - xabs; Float yabs = y; if( yabs <= Float(0) ) yabs = - yabs; return xabs >= yabs; } inline bool AbsGeq( const std::complex &x, const std::complex &y) { double xsq = x.real() * x.real() + x.imag() * x.imag(); double ysq = y.real() * y.real() + y.imag() * y.imag(); return xsq >= ysq; } inline bool AbsGeq( const std::complex &x, const std::complex &y) { float xsq = x.real() * x.real() + x.imag() * x.imag(); float ysq = y.real() * y.real() + y.imag() * y.imag(); return xsq >= ysq; } // Lines that are different from code in cppad/core/lu_ratio.hpp end with // template // int LuFactor(SizeVector &ip, SizeVector &jp, FloatVector &LU) // { // type of the elements of LU // typedef typename FloatVector::value_type Float; // // check numeric type specifications CheckNumericType(); // check simple vector class specifications CheckSimpleVector(); CheckSimpleVector(); size_t i, j; // some temporary indices const Float zero( 0 ); // the value zero as a Float object size_t imax; // row index of maximum element size_t jmax; // column indx of maximum element Float emax; // maximum absolute value size_t p; // count pivots int sign; // sign of the permutation Float etmp; // temporary element Float pivot; // pivot element // ------------------------------------------------------- size_t n = ip.size(); CPPAD_ASSERT_KNOWN( size_t(jp.size()) == n, "Error in LuFactor: jp must have size equal to n" ); CPPAD_ASSERT_KNOWN( size_t(LU.size()) == n * n, "Error in LuFactor: LU must have size equal to n * m" ); // ------------------------------------------------------- // initialize row and column order in matrix not yet pivoted for(i = 0; i < n; i++) { ip[i] = i; jp[i] = i; } // initialize the sign of the permutation sign = 1; // --------------------------------------------------------- // Reduce the matrix P to L * U using n pivots for(p = 0; p < n; p++) { // determine row and column corresponding to element of // maximum absolute value in remaining part of P imax = jmax = n; emax = zero; for(i = p; i < n; i++) { for(j = p; j < n; j++) { CPPAD_ASSERT_UNKNOWN( (ip[i] < n) & (jp[j] < n) ); etmp = LU[ ip[i] * n + jp[j] ]; // check if maximum absolute value so far if( AbsGeq (etmp, emax) ) { imax = i; jmax = j; emax = etmp; } } } CPPAD_ASSERT_KNOWN( (imax < n) & (jmax < n) , "LuFactor can't determine an element with " "maximum absolute value.\n" "Perhaps original matrix contains not a number or infinity.\n" "Perhaps your specialization of AbsGeq is not correct." ); if( imax != p ) { // switch rows so max absolute element is in row p i = ip[p]; ip[p] = ip[imax]; ip[imax] = i; sign = -sign; } if( jmax != p ) { // switch columns so max absolute element is in column p j = jp[p]; jp[p] = jp[jmax]; jp[jmax] = j; sign = -sign; } // pivot using the max absolute element pivot = LU[ ip[p] * n + jp[p] ]; // check for determinant equal to zero if( pivot == zero ) { // abort the mission return 0; } // Reduce U by the elementary transformations that maps // LU( ip[p], jp[p] ) to one. Only need transform elements // above the diagonal in U and LU( ip[p] , jp[p] ) is // corresponding value below diagonal in L. for(j = p+1; j < n; j++) LU[ ip[p] * n + jp[j] ] /= pivot; // Reduce U by the elementary transformations that maps // LU( ip[i], jp[p] ) to zero. Only need transform elements // above the diagonal in U and LU( ip[i], jp[p] ) is // corresponding value below diagonal in L. for(i = p+1; i < n; i++ ) { etmp = LU[ ip[i] * n + jp[p] ]; for(j = p+1; j < n; j++) { LU[ ip[i] * n + jp[j] ] -= etmp * LU[ ip[p] * n + jp[j] ]; } } } return sign; } } // END CppAD namespace // END C++ # endif cppad-20170000.3/cppad/utility/pow_int.hpp0000644000175200017650000000630013057470465017416 0ustar coincoin-web// $Id: pow_int.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_UTILITY_POW_INT_HPP # define CPPAD_UTILITY_POW_INT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin pow_int$$ $spell cppad.hpp CppAD namespace const $$ $section The Integer Power Function$$ $mindex pow exponent$$ $head Syntax$$ $codei%# include %$$ $icode%z% = pow(%x%, %y%)%$$ $head See Also$$ $cref pow$$ $head Purpose$$ Determines the value of the power function $latex \[ {\rm pow} (x, y) = x^y \] $$ for integer exponents $icode n$$ using multiplication and possibly division to compute the value. The other CppAD $cref pow$$ function may use logarithms and exponentiation to compute derivatives of the same value (which will not work if $icode x$$ is less than or equal zero). $head Include$$ The file $code cppad/pow_int.h$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. Including this file defines this version of the $code pow$$ within the $code CppAD$$ namespace. $head x$$ The argument $icode x$$ has prototype $codei% const %Type%& %x% %$$ $head y$$ The argument $icode y$$ has prototype $codei% const int& %y% %$$ $head z$$ The result $icode z$$ has prototype $codei% %Type% %z% %$$ $head Type$$ The type $icode Type$$ must support the following operations where $icode a$$ and $icode b$$ are $icode Type$$ objects and $icode i$$ is an $code int$$: $table $bold Operation$$ $pre $$ $cnext $bold Description$$ $cnext $bold Result Type$$ $rnext $icode%Type% %a%(%i%)%$$ $cnext construction of a $icode Type$$ object from an $code int$$ $cnext $icode Type$$ $rnext $icode%a% * %b%$$ $cnext binary multiplication of $icode Type$$ objects $cnext $icode Type$$ $rnext $icode%a% / %b%$$ $cnext binary division of $icode Type$$ objects $cnext $icode Type$$ $tend $head Operation Sequence$$ The $icode Type$$ operation sequence used to calculate $icode z$$ is $cref/independent/glossary/Operation/Independent/$$ of $icode x$$. $head Example$$ $children% example/pow_int.cpp %$$ The file $cref pow_int.cpp$$ is an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ namespace CppAD { template inline Type pow (const Type& x, const int& n) { Type p(1); int n2 = n / 2; if( n == 0 ) return p; if( n < 0 ) return p / pow(x, -n); if( n == 1 ) return x; // p = (x^2)^(n/2) p = pow( x * x , n2 ); // n is even case if( n % 2 == 0 ) return p; // n is odd case return p * x; } } # endif cppad-20170000.3/cppad/utility/ode_err_control.hpp0000644000175200017650000003707213057470465021130 0ustar coincoin-web// $Id: ode_err_control.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_ODE_ERR_CONTROL_HPP # define CPPAD_UTILITY_ODE_ERR_CONTROL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin OdeErrControl$$ $spell cppad.hpp nstep maxabs exp scur CppAD xf tf xi smin smax eabs erel ef ta tb xa xb const eb $$ $section An Error Controller for ODE Solvers$$ $mindex OdeErrControl differential equation$$ $head Syntax$$ $codei%# include %$$ $icode%xf% = OdeErrControl(%method%, %ti%, %tf%, %xi%, %smin%, %smax%, %scur%, %eabs%, %erel%, %ef% , %maxabs%, %nstep% )%$$ $head Description$$ Let $latex \B{R}$$ denote the real numbers and let $latex F : \B{R} \times \B{R}^n \rightarrow \B{R}^n$$ be a smooth function. We define $latex X : [ti , tf] \rightarrow \B{R}^n$$ by the following initial value problem: $latex \[ \begin{array}{rcl} X(ti) & = & xi \\ X'(t) & = & F[t , X(t)] \end{array} \] $$ The routine $code OdeErrControl$$ can be used to adjust the step size used an arbitrary integration methods in order to be as fast as possible and still with in a requested error bound. $head Include$$ The file $code cppad/ode_err_control.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head Notation$$ The template parameter types $cref/Scalar/OdeErrControl/Scalar/$$ and $cref/Vector/OdeErrControl/Vector/$$ are documented below. $head xf$$ The return value $icode xf$$ has the prototype $codei% %Vector% %xf% %$$ (see description of $cref/Vector/OdeErrControl/Vector/$$ below). and the size of $icode xf$$ is equal to $icode n$$. If $icode xf$$ contains not a number $cref nan$$, see the discussion of $cref/step/OdeErrControl/Method/Nan/$$. $head Method$$ The class $icode Method$$ and the object $icode method$$ satisfy the following syntax $codei% %Method% &%method% %$$ The object $icode method$$ must support $code step$$ and $code order$$ member functions defined below: $subhead step$$ The syntax $codei% %method%.step(%ta%, %tb%, %xa%, %xb%, %eb%) %$$ executes one step of the integration method. $codei% %ta% %$$ The argument $icode ta$$ has prototype $codei% const %Scalar% &%ta% %$$ It specifies the initial time for this step in the ODE integration. (see description of $cref/Scalar/OdeErrControl/Scalar/$$ below). $codei% %tb% %$$ The argument $icode tb$$ has prototype $codei% const %Scalar% &%tb% %$$ It specifies the final time for this step in the ODE integration. $codei% %xa% %$$ The argument $icode xa$$ has prototype $codei% const %Vector% &%xa% %$$ and size $icode n$$. It specifies the value of $latex X(ta)$$. (see description of $cref/Vector/OdeErrControl/Vector/$$ below). $codei% %xb% %$$ The argument value $icode xb$$ has prototype $codei% %Vector% &%xb% %$$ and size $icode n$$. The input value of its elements does not matter. On output, it contains the approximation for $latex X(tb)$$ that the method obtains. $codei% %eb% %$$ The argument value $icode eb$$ has prototype $codei% %Vector% &%eb% %$$ and size $icode n$$. The input value of its elements does not matter. On output, it contains an estimate for the error in the approximation $icode xb$$. It is assumed (locally) that the error bound in this approximation nearly equal to $latex K (tb - ta)^m$$ where $icode K$$ is a fixed constant and $icode m$$ is the corresponding argument to $code CodeControl$$. $subhead Nan$$ If any element of the vector $icode eb$$ or $icode xb$$ are not a number $code nan$$, the current step is considered to large. If this happens with the current step size equal to $icode smin$$, $code OdeErrControl$$ returns with $icode xf$$ and $icode ef$$ as vectors of $code nan$$. $subhead order$$ If $icode m$$ is $code size_t$$, the object $icode method$$ must also support the following syntax $codei% %m% = %method%.order() %$$ The return value $icode m$$ is the order of the error estimate; i.e., there is a constant K such that if $latex ti \leq ta \leq tb \leq tf$$, $latex \[ | eb(tb) | \leq K | tb - ta |^m \] $$ where $icode ta$$, $icode tb$$, and $icode eb$$ are as in $icode%method%.step(%ta%, %tb%, %xa%, %xb%, %eb%)%$$ $head ti$$ The argument $icode ti$$ has prototype $codei% const %Scalar% &%ti% %$$ It specifies the initial time for the integration of the differential equation. $head tf$$ The argument $icode tf$$ has prototype $codei% const %Scalar% &%tf% %$$ It specifies the final time for the integration of the differential equation. $head xi$$ The argument $icode xi$$ has prototype $codei% const %Vector% &%xi% %$$ and size $icode n$$. It specifies value of $latex X(ti)$$. $head smin$$ The argument $icode smin$$ has prototype $codei% const %Scalar% &%smin% %$$ The step size during a call to $icode method$$ is defined as the corresponding value of $latex tb - ta$$. If $latex tf - ti \leq smin$$, the integration will be done in one step of size $icode tf - ti$$. Otherwise, the minimum value of $icode tb - ta$$ will be $latex smin$$ except for the last two calls to $icode method$$ where it may be as small as $latex smin / 2$$. $head smax$$ The argument $icode smax$$ has prototype $codei% const %Scalar% &%smax% %$$ It specifies the maximum step size to use during the integration; i.e., the maximum value for $latex tb - ta$$ in a call to $icode method$$. The value of $icode smax$$ must be greater than or equal $icode smin$$. $head scur$$ The argument $icode scur$$ has prototype $codei% %Scalar% &%scur% %$$ The value of $icode scur$$ is the suggested next step size, based on error criteria, to try in the next call to $icode method$$. On input it corresponds to the first call to $icode method$$, in this call to $code OdeErrControl$$ (where $latex ta = ti$$). On output it corresponds to the next call to $icode method$$, in a subsequent call to $code OdeErrControl$$ (where $icode ta = tf$$). $head eabs$$ The argument $icode eabs$$ has prototype $codei% const %Vector% &%eabs% %$$ and size $icode n$$. Each of the elements of $icode eabs$$ must be greater than or equal zero. It specifies a bound for the absolute error in the return value $icode xf$$ as an approximation for $latex X(tf)$$. (see the $cref/error criteria discussion/OdeErrControl/Error Criteria Discussion/$$ below). $head erel$$ The argument $icode erel$$ has prototype $codei% const %Scalar% &%erel% %$$ and is greater than or equal zero. It specifies a bound for the relative error in the return value $icode xf$$ as an approximation for $latex X(tf)$$ (see the $cref/error criteria discussion/OdeErrControl/Error Criteria Discussion/$$ below). $head ef$$ The argument value $icode ef$$ has prototype $codei% %Vector% &%ef% %$$ and size $icode n$$. The input value of its elements does not matter. On output, it contains an estimated bound for the absolute error in the approximation $icode xf$$; i.e., $latex \[ ef_i > | X( tf )_i - xf_i | \] $$ If on output $icode ef$$ contains not a number $code nan$$, see the discussion of $cref/step/OdeErrControl/Method/Nan/$$. $head maxabs$$ The argument $icode maxabs$$ is optional in the call to $code OdeErrControl$$. If it is present, it has the prototype $codei% %Vector% &%maxabs% %$$ and size $icode n$$. The input value of its elements does not matter. On output, it contains an estimate for the maximum absolute value of $latex X(t)$$; i.e., $latex \[ maxabs[i] \approx \max \left\{ | X( t )_i | \; : \; t \in [ti, tf] \right\} \] $$ $head nstep$$ The argument $icode nstep$$ is optional in the call to $code OdeErrControl$$. If it is present, it has the prototype $codei% %size_t% &%nstep% %$$ Its input value does not matter and its output value is the number of calls to $icode%method%.step%$$ used by $code OdeErrControl$$. $head Error Criteria Discussion$$ The relative error criteria $icode erel$$ and absolute error criteria $icode eabs$$ are enforced during each step of the integration of the ordinary differential equations. In addition, they are inversely scaled by the step size so that the total error bound is less than the sum of the error bounds. To be specific, if $latex \tilde{X} (t)$$ is the approximate solution at time $latex t$$, $icode ta$$ is the initial step time, and $icode tb$$ is the final step time, $latex \[ \left| \tilde{X} (tb)_j - X (tb)_j \right| \leq \frac{tf - ti}{tb - ta} \left[ eabs[j] + erel \; | \tilde{X} (tb)_j | \right] \] $$ If $latex X(tb)_j$$ is near zero for some $latex tb \in [ti , tf]$$, and one uses an absolute error criteria $latex eabs[j]$$ of zero, the error criteria above will force $code OdeErrControl$$ to use step sizes equal to $cref/smin/OdeErrControl/smin/$$ for steps ending near $latex tb$$. In this case, the error relative to $icode maxabs$$ can be judged after $code OdeErrControl$$ returns. If $icode ef$$ is to large relative to $icode maxabs$$, $code OdeErrControl$$ can be called again with a smaller value of $icode smin$$. $head Scalar$$ The type $icode Scalar$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, the following operations must be defined for $icode Scalar$$ objects $icode a$$ and $icode b$$: $table $bold Operation$$ $cnext $bold Description$$ $rnext $icode%a% <= %b%$$ $cnext returns true (false) if $icode a$$ is less than or equal (greater than) $icode b$$. $rnext $icode%a% == %b%$$ $cnext returns true (false) if $icode a$$ is equal to $icode b$$. $rnext $codei%log(%a%)%$$ $cnext returns a $icode Scalar$$ equal to the logarithm of $icode a$$ $rnext $codei%exp(%a%)%$$ $cnext returns a $icode Scalar$$ equal to the exponential of $icode a$$ $tend $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type Scalar/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ $children% example/ode_err_control.cpp% example/ode_err_maxabs.cpp %$$ The files $cref ode_err_control.cpp$$ and $cref ode_err_maxabs.cpp$$ contain examples and tests of using this routine. They return true if they succeed and false otherwise. $head Theory$$ Let $latex e(s)$$ be the error as a function of the step size $latex s$$ and suppose that there is a constant $latex K$$ such that $latex e(s) = K s^m$$. Let $latex a$$ be our error bound. Given the value of $latex e(s)$$, a step of size $latex \lambda s$$ would be ok provided that $latex \[ \begin{array}{rcl} a & \geq & e( \lambda s ) (tf - ti) / ( \lambda s ) \\ a & \geq & K \lambda^m s^m (tf - ti) / ( \lambda s ) \\ a & \geq & \lambda^{m-1} s^{m-1} (tf - ti) e(s) / s^m \\ a & \geq & \lambda^{m-1} (tf - ti) e(s) / s \\ \lambda^{m-1} & \leq & \frac{a}{e(s)} \frac{s}{tf - ti} \end{array} \] $$ Thus if the right hand side of the last inequality is greater than or equal to one, the step of size $latex s$$ is ok. $head Source Code$$ The source code for this routine is in the file $code cppad/ode_err_control.hpp$$. $end -------------------------------------------------------------------------- */ // link exp and log for float and double # include # include # include # include namespace CppAD { // Begin CppAD namespace template Vector OdeErrControl( Method &method, const Scalar &ti , const Scalar &tf , const Vector &xi , const Scalar &smin , const Scalar &smax , Scalar &scur , const Vector &eabs , const Scalar &erel , Vector &ef , Vector &maxabs, size_t &nstep ) { // check simple vector class specifications CheckSimpleVector(); size_t n = size_t(xi.size()); CPPAD_ASSERT_KNOWN( smin <= smax, "Error in OdeErrControl: smin > smax" ); CPPAD_ASSERT_KNOWN( size_t(eabs.size()) == n, "Error in OdeErrControl: size of eabs is not equal to n" ); CPPAD_ASSERT_KNOWN( size_t(maxabs.size()) == n, "Error in OdeErrControl: size of maxabs is not equal to n" ); size_t m = method.order(); CPPAD_ASSERT_KNOWN( m > 1, "Error in OdeErrControl: m is less than or equal one" ); bool ok; bool minimum_step; size_t i; Vector xa(n), xb(n), eb(n), nan_vec(n); // initialization Scalar zero(0); Scalar one(1); Scalar two(2); Scalar three(3); Scalar m1(m-1); Scalar ta = ti; for(i = 0; i < n; i++) { nan_vec[i] = nan(zero); ef[i] = zero; xa[i] = xi[i]; if( zero <= xi[i] ) maxabs[i] = xi[i]; else maxabs[i] = - xi[i]; } nstep = 0; Scalar tb, step, lambda, axbi, a, r, root; while( ! (ta == tf) ) { // start with value suggested by error criteria step = scur; // check maximum if( smax <= step ) step = smax; // check minimum minimum_step = step <= smin; if( minimum_step ) step = smin; // check if near the end if( tf <= ta + step * three / two ) tb = tf; else tb = ta + step; // try using this step size nstep++; method.step(ta, tb, xa, xb, eb); step = tb - ta; // check if this steps error estimate is ok ok = ! (hasnan(xb) || hasnan(eb)); if( (! ok) && minimum_step ) { ef = nan_vec; return nan_vec; } // compute value of lambda for this step lambda = Scalar(10) * scur / step; for(i = 0; i < n; i++) { if( zero <= xb[i] ) axbi = xb[i]; else axbi = - xb[i]; a = eabs[i] + erel * axbi; if( ! (eb[i] == zero) ) { r = ( a / eb[i] ) * step / (tf - ti); root = exp( log(r) / m1 ); if( root <= lambda ) lambda = root; } } if( ok && ( one <= lambda || step <= smin * three / two) ) { // this step is within error limits or // close to the minimum size ta = tb; for(i = 0; i < n; i++) { xa[i] = xb[i]; ef[i] = ef[i] + eb[i]; if( zero <= xb[i] ) axbi = xb[i]; else axbi = - xb[i]; if( axbi > maxabs[i] ) maxabs[i] = axbi; } } if( ! ok ) { // decrease step an see if method will work this time scur = step / two; } else if( ! (ta == tf) ) { // step suggested by the error criteria is not used // on the last step because it may be very small. scur = lambda * step / two; } } return xa; } template Vector OdeErrControl( Method &method, const Scalar &ti , const Scalar &tf , const Vector &xi , const Scalar &smin , const Scalar &smax , Scalar &scur , const Vector &eabs , const Scalar &erel , Vector &ef ) { Vector maxabs(xi.size()); size_t nstep; return OdeErrControl( method, ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep ); } template Vector OdeErrControl( Method &method, const Scalar &ti , const Scalar &tf , const Vector &xi , const Scalar &smin , const Scalar &smax , Scalar &scur , const Vector &eabs , const Scalar &erel , Vector &ef , Vector &maxabs) { size_t nstep; return OdeErrControl( method, ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep ); } } // End CppAD namespace # endif cppad-20170000.3/cppad/utility/thread_alloc.hpp0000644000175200017650000012456713057470465020400 0ustar coincoin-web// $Id: thread_alloc.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_THREAD_ALLOC_HPP # define CPPAD_UTILITY_THREAD_ALLOC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # ifdef _MSC_VER // Supress warning that Microsoft compiler changed its behavior and is now // doing the correct thing at the statement: // new(array + i) Type(); # pragma warning(disable:4345) # endif # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file thread_alloc.hpp File used to define the CppAD multi-threading allocator class */ /*! \def CPPAD_MAX_NUM_CAPACITY Maximum number of different capacities the allocator will attempt. This must be larger than the log base two of numeric_limit::max(). */ # define CPPAD_MAX_NUM_CAPACITY 100 /*! \def CPPAD_MIN_DOUBLE_CAPACITY Minimum number of double values that will fit in an allocation. */ # define CPPAD_MIN_DOUBLE_CAPACITY 16 /*! \def CPPAD_TRACE_CAPACITY If NDEBUG is not defined, print all calls to \c get_memory and \c return_memory that correspond to this capacity and thread CPPAD_TRACE_THREAD. (Note that if CPPAD_TRACE_CAPACITY is zero, or any other value not in the list of capacities, no tracing will be done.) */ # define CPPAD_TRACE_CAPACITY 0 /*! \def CPPAD_TRACE_THREAD If NDEBUG is not defined, print all calls to \c get_memory and \c return_memory that correspond to this thead and capacity CPPAD_TRACE_CAPACITY. */ # define CPPAD_TRACE_THREAD 0 /* Note that Section 3.6.2 of ISO/IEC 14882:1998(E) states: "The storage for objects with static storage duration (3.7.1) shall be zero-initialized (8.5) before any other initialization takes place." */ /*! Capacity vector for memory allocation block sizes. Only one of these objects should be created and used as a static variable inside of the \c thread_alloc::capacity_info function. */ /*! Allocator class that works well with an multi-threading environment. */ class thread_alloc{ // ============================================================================ private: class capacity_t { public: /// number of capacity values actually used size_t number; /// the different capacity values size_t value[CPPAD_MAX_NUM_CAPACITY]; /// ctor capacity_t(void) { // Cannot figure out how to call thread_alloc::in_parallel here. // CPPAD_ASSERT_UNKNOWN( // ! thread_alloc::in_parallel() , "thread_alloc: " // "parallel mode and parallel_setup not yet called." // ); number = 0; size_t capacity = CPPAD_MIN_DOUBLE_CAPACITY * sizeof(double); while( capacity < std::numeric_limits::max() / 2 ) { CPPAD_ASSERT_UNKNOWN( number < CPPAD_MAX_NUM_CAPACITY ); value[number++] = capacity; // next capactiy is 3/2 times the current one capacity = 3 * ( (capacity + 1) / 2 ); } CPPAD_ASSERT_UNKNOWN( number > 0 ); } }; class block_t { public: /// extra information (currently used by create and delete array) size_t extra_; /// an index that uniquely idenfifies both thread and capacity size_t tc_index_; /// pointer to the next memory allocation with the same tc_index_ void* next_; // ----------------------------------------------------------------- /// make default constructor private. It is only used by constructor /// for `root arrays below. block_t(void) : extra_(0), tc_index_(0), next_(CPPAD_NULL) { } }; // --------------------------------------------------------------------- /// Vector of fixed capacity values for this allocator static const capacity_t* capacity_info(void) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static const capacity_t capacity; return &capacity; } // --------------------------------------------------------------------- /// Structure of information for each thread struct thread_alloc_info { /// count of available bytes for this thread size_t count_inuse_; /// count of inuse bytes for this thread size_t count_available_; /// root of available list for this thread and each capacity block_t root_available_[CPPAD_MAX_NUM_CAPACITY]; /// root of inuse list for this thread and each capacity /// If NDEBUG is true, this memory is not used, but it still /// helps separate this structure from one for the next thread. block_t root_inuse_[CPPAD_MAX_NUM_CAPACITY]; }; // --------------------------------------------------------------------- /*! Set and Get hold available memory flag. \param set [in] if true, the value returned by this return is changed. \param new_value [in] if \a set is true, this is the new value returned by this routine. Otherwise, \c new_value is ignored. \return the current setting for this routine (which is initially false). */ static bool set_get_hold_memory(bool set, bool new_value = false) { static bool value = false; if( set ) value = new_value; return value; } // --------------------------------------------------------------------- /*! Get pointer to the information for this thread. \param thread [in] Is the thread number for this information pointer. \param clear If \a clear is true, then the information pointer for this thread is deleted and the \c CPPAD_NULL pointer is returned. There must be no memory currently in either the inuse or avaialble lists when this routine is called. \return is the current informaiton pointer for this thread. If \a clear is false, and the current pointer is CPPAD_NULL, a new infromation record is allocated and its pointer returned. In this case, if \c info is the retured pointer, info->count_inuse == 0 and info->count_available == 0. In addition, for c = 0 , ... , CPPAD_MAX_NUM_CAPACITY-1 info->root_inuse_[c].next_ == CPPAD_NULL and info->root_available_[c].next_ == CPPAD_NULL. */ static thread_alloc_info* thread_info( size_t thread , bool clear = false ) { static thread_alloc_info* all_info[CPPAD_MAX_NUM_THREADS]; static thread_alloc_info zero_info; CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; CPPAD_ASSERT_UNKNOWN( thread < CPPAD_MAX_NUM_THREADS ); thread_alloc_info* info = all_info[thread]; if( clear ) { if( info != CPPAD_NULL ) { # ifndef NDEBUG CPPAD_ASSERT_UNKNOWN( info->count_inuse_ == 0 && info->count_available_ == 0 ); for(size_t c = 0; c < CPPAD_MAX_NUM_CAPACITY; c++) { CPPAD_ASSERT_UNKNOWN( info->root_inuse_[c].next_ == CPPAD_NULL && info->root_available_[c].next_ == CPPAD_NULL ); } # endif if( thread != 0 ) ::operator delete( reinterpret_cast(info) ); info = CPPAD_NULL; all_info[thread] = info; } } else if( info == CPPAD_NULL ) { if( thread == 0 ) info = &zero_info; else { size_t size = sizeof(thread_alloc_info); void* v_ptr = ::operator new(size); info = reinterpret_cast(v_ptr); } all_info[thread] = info; // initialize the information record for(size_t c = 0; c < CPPAD_MAX_NUM_CAPACITY; c++) { info->root_inuse_[c].next_ = CPPAD_NULL; info->root_available_[c].next_ = CPPAD_NULL; } info->count_inuse_ = 0; info->count_available_ = 0; } return info; } // ----------------------------------------------------------------------- /*! Increase the number of bytes of memory that are currently in use; i.e., that been obtained with \c get_memory and not yet returned. \param inc [in] amount to increase memory in use. \param thread [in] Thread for which we are increasing the number of bytes in use (must be less than \c num_threads). Durring parallel execution, this must be the thread that is currently executing. */ static void inc_inuse(size_t inc, size_t thread) { CPPAD_ASSERT_UNKNOWN( thread < num_threads() ); CPPAD_ASSERT_UNKNOWN( thread == thread_num() || (! in_parallel()) ); thread_alloc_info* info = thread_info(thread); // do the addition size_t result = info->count_inuse_ + inc; CPPAD_ASSERT_UNKNOWN( result >= info->count_inuse_ ); info->count_inuse_ = result; } // ----------------------------------------------------------------------- /*! Increase the number of bytes of memory that are currently avaialble; i.e., have been obtained obtained from the system and are being held future use. \copydetails inc_inuse */ static void inc_available(size_t inc, size_t thread) { CPPAD_ASSERT_UNKNOWN( thread < CPPAD_MAX_NUM_THREADS); CPPAD_ASSERT_UNKNOWN( thread == thread_num() || (! in_parallel()) ); thread_alloc_info* info = thread_info(thread); // do the addition size_t result = info->count_available_ + inc; CPPAD_ASSERT_UNKNOWN( result >= info->count_available_ ); info->count_available_ = result; } // ----------------------------------------------------------------------- /*! Decrease the number of bytes of memory that are currently in use; i.e., that been obtained with \c get_memory and not yet returned. \param dec [in] amount to decrease number of bytes in use. \param thread [in] Thread for which we are decreasing the number of bytes in use (must be less than \c num_threads). Durring parallel execution, this must be the thread that is currently executing. */ static void dec_inuse(size_t dec, size_t thread) { CPPAD_ASSERT_UNKNOWN( thread < num_threads() || (! in_parallel()) ); CPPAD_ASSERT_UNKNOWN( thread == thread_num() || (! in_parallel()) ); thread_alloc_info* info = thread_info(thread); // do the subtraction CPPAD_ASSERT_UNKNOWN( info->count_inuse_ >= dec ); info->count_inuse_ = info->count_inuse_ - dec; } // ----------------------------------------------------------------------- /*! Decrease the number of bytes of memory that are currently avaialble; i.e., have been obtained obtained from the system and are being held future use. \copydetails dec_inuse */ static void dec_available(size_t dec, size_t thread) { CPPAD_ASSERT_UNKNOWN( thread < CPPAD_MAX_NUM_THREADS); CPPAD_ASSERT_UNKNOWN( thread == thread_num() || (! in_parallel()) ); thread_alloc_info* info = thread_info(thread); // do the subtraction CPPAD_ASSERT_UNKNOWN( info->count_available_ >= dec ); info->count_available_ = info->count_available_ - dec; } // ---------------------------------------------------------------------- /*! Set and get the number of threads that are sharing memory. \param number_new If \c number is zero, we are only retreiving the current maximum number of threads. Otherwise, we are setting and retreiving maximum number of threads. \return the number of threads that are sharing memory. If \c number_new is non-zero, the return value is equal to \c number_new. */ static size_t set_get_num_threads(size_t number_new) { static size_t number_user = 1; CPPAD_ASSERT_UNKNOWN( number_new <= CPPAD_MAX_NUM_THREADS ); CPPAD_ASSERT_UNKNOWN( ! in_parallel() || (number_new == 0) ); // case where we are changing the number of threads if( number_new != 0 ) number_user = number_new; return number_user; } /*! Set and call the routine that determine the current thread number. \return returns value for the most recent setting for \a thread_num_new. If \a set is true, or the most recent setting is \c CPPAD_NULL (its initial value), the return value is zero. Otherwise the routine corresponding to the most recent setting is called and its value returned by \c set_get_thread_num. \param thread_num_new [in] If \a set is false, \a thread_num_new it is not used. Otherwise, the current value of \c thread_num_new becomes the most recent setting for thread_num. \param set If \a set is true, then \a thread_num_new is becomes the most recent setting for this \c set_get_thread_num. */ static size_t set_get_thread_num( size_t (*thread_num_new)(void) , bool set = false ) { static size_t (*thread_num_user)(void) = CPPAD_NULL; if( set ) { thread_num_user = thread_num_new; return 0; } if( thread_num_user == CPPAD_NULL ) return 0; size_t thread = thread_num_user(); CPPAD_ASSERT_KNOWN( thread < set_get_num_threads(0) , "parallel_setup: thread_num() >= num_threads" ); return thread; } // ============================================================================ public: /* $begin ta_parallel_setup$$ $spell alloc num bool $$ $section Setup thread_alloc For Use in Multi-Threading Environment$$ $mindex parallel initialize$$ $head Syntax$$ $codei%thread_alloc::parallel_setup(%num_threads%, %in_parallel%, %thread_num%) %$$ $head Purpose$$ By default there is only one thread and all execution is in sequential mode, i.e., multiple threads are not sharing the same memory; i.e. not in parallel mode. $head Speed$$ It should be faster, even when $icode num_thread$$ is equal to one, for $code thread_alloc$$ to hold onto memory. This can be accomplished using the function call $codei% thread_alloc::hold_memory(true) %$$ see $cref/hold_memory/ta_hold_memory/$$. $head num_threads$$ This argument has prototype $codei% size_t %num_threads% %$$ and must be greater than zero. It specifies the number of threads that are sharing memory. The case $icode%num_threads% == 1%$$ is a special case that is used to terminate a multi-threading environment. $head in_parallel$$ This function has prototype $codei% bool %in_parallel%(void) %$$ It must return $code true$$ if there is more than one thread currently executing. Otherwise it can return false. $pre $$ In the special case where $icode%num_threads% == 1%$$, the routine $icode in_parallel$$ is not used. $head thread_num$$ This function has prototype $codei% size_t %thread_num%(void) %$$ It must return a thread number that uniquely identifies the currently executing thread. Furthermore $codei% 0 <= %thread_num%() < %num_threads% %$$. In the special case where $icode%num_threads% == 1%$$, the routine $icode thread_num$$ is not used. $pre $$ Note that this function is called by other routines so, as soon as a new thread is executing, one must be certain that $icode thread_num()$$ will work for that thread. $head Restrictions$$ The function $code parallel_setup$$ must be called before the program enters $cref/parallel/ta_in_parallel/$$ execution mode. In addition, this function cannot be called while in parallel mode. $head Example$$ The files $cref simple_ad_openmp.cpp$$, $cref simple_ad_bthread.cpp$$, and $cref simple_ad_pthread.cpp$$, contain examples and tests that use this function. $end */ /*! Set thread_alloc up for parallel mode usage. \param num_threads [in] Is the number of thread that may be executing at the same time. \param in_parallel [in] Is the routine that determines if we are in parallel mode or not. \param thread_num [in] Is the routine that determines the current thread number (between zero and num_threads minus one). */ static void parallel_setup( size_t num_threads , bool (*in_parallel)(void) , size_t (*thread_num)(void) ) { // Special case where we go back to single thread mode right away // (previous settings may no longer be valid) if( num_threads == 1 ) { bool set = true; set_get_num_threads(num_threads); // emphasize that this routine is outside thread_alloc class CppAD::local::set_get_in_parallel(CPPAD_NULL, set); set_get_thread_num(CPPAD_NULL, set); return; } CPPAD_ASSERT_KNOWN( num_threads <= CPPAD_MAX_NUM_THREADS , "parallel_setup: num_threads is too large" ); CPPAD_ASSERT_KNOWN( num_threads != 0 , "parallel_setup: num_threads == zero" ); CPPAD_ASSERT_KNOWN( in_parallel != CPPAD_NULL , "parallel_setup: num_threads != 1 and in_parallel == CPPAD_NULL" ); CPPAD_ASSERT_KNOWN( thread_num != CPPAD_NULL , "parallel_setup: num_threads != 1 and thread_num == CPPAD_NULL" ); // Make sure that constructors for all static variables in this file // are called in sequential mode. for(size_t thread = 0; thread < num_threads; thread++) thread_info(thread); capacity_info(); size_t cap_bytes; void* v_ptr = get_memory(0, cap_bytes); // free memory allocated by call to get_memory above return_memory(v_ptr); free_available( set_get_thread_num(CPPAD_NULL) ); // delay this so thread_num() call above is in previous mode // (current setings may not yet be valid) if( num_threads > 1 ) { bool set = true; set_get_num_threads(num_threads); // emphasize that this routine is outside thread_alloc class CppAD::local::set_get_in_parallel(in_parallel, set); set_get_thread_num(thread_num, set); } } /* $begin ta_num_threads$$ $spell inv CppAD num alloc $$ $section Get Number of Threads$$ $head Syntax$$ $icode%number% = thread_alloc::num_threads()%$$ $head Purpose$$ Determine the number of threads as set during $cref/parallel_setup/ta_parallel_setup/$$. $head number$$ The return value $icode number$$ has prototype $codei% size_t %number% %$$ and is equal to the value of $cref/num_threads/ta_parallel_setup/num_threads/$$ in the previous call to $icode parallel_setup$$. If there was no such previous call, the value one is returned. $head Example$$ The example and test $cref thread_alloc.cpp$$ uses this routine. $end */ /*! Get the current number of threads that thread_alloc can use. */ static size_t num_threads(void) { return set_get_num_threads(0); } /* ----------------------------------------------------------------------- $begin ta_in_parallel$$ $section Is The Current Execution in Parallel Mode$$ $mindex sequential$$ $spell thread_alloc bool $$ $head Syntax$$ $icode%flag% = thread_alloc::in_parallel()%$$ $head Purpose$$ Some of the $cref thread_alloc$$ allocation routines have different specifications for parallel (not sequential) execution mode. This routine enables you to determine if the current execution mode is sequential or parallel. $head flag$$ The return value has prototype $codei% bool %flag% %$$ It is true if the current execution is in parallel mode (possibly multi-threaded) and false otherwise (sequential mode). $head Example$$ $cref thread_alloc.cpp$$ $end */ /// Are we in a parallel execution state; i.e., is it possible that /// other threads are currently executing. static bool in_parallel(void) { // emphasize that this routine is outside thread_alloc class return CppAD::local::set_get_in_parallel(0); } /* ----------------------------------------------------------------------- $begin ta_thread_num$$ $spell CppAD num thread_alloc cppad.hpp $$ $section Get the Current Thread Number$$ $head Syntax$$ $icode%thread% = thread_alloc::thread_num()%$$ $head Purpose$$ Some of the $cref thread_alloc$$ allocation routines have a thread number. This routine enables you to determine the current thread. $head thread$$ The return value $icode thread$$ has prototype $codei% size_t %thread% %$$ and is the currently executing thread number. $head Example$$ $cref thread_alloc.cpp$$ $end */ /// Get current thread number static size_t thread_num(void) { return set_get_thread_num(CPPAD_NULL); } /* ----------------------------------------------------------------------- $begin ta_get_memory$$ $spell std num ptr thread_alloc $$ $section Get At Least A Specified Amount of Memory$$ $mindex allocate$$ $head Syntax$$ $icode%v_ptr% = thread_alloc::get_memory(%min_bytes%, %cap_bytes%)%$$ $head Purpose$$ Use $cref thread_alloc$$ to obtain a minimum number of bytes of memory (for use by the $cref/current thread/ta_thread_num/$$). $head min_bytes$$ This argument has prototype $codei% size_t %min_bytes% %$$ It specifies the minimum number of bytes to allocate. This value must be less than $codep std::numeric_limits::max() / 2 $$ $head cap_bytes$$ This argument has prototype $codei% size_t& %cap_bytes% %$$ It's input value does not matter. Upon return, it is the actual number of bytes (capacity) that have been allocated for use, $codei% %min_bytes% <= %cap_bytes% %$$ $head v_ptr$$ The return value $icode v_ptr$$ has prototype $codei% void* %v_ptr% %$$ It is the location where the $icode cap_bytes$$ of memory that have been allocated for use begins. $head Allocation Speed$$ This allocation should be faster if the following conditions hold: $list number$$ The memory allocated by a previous call to $code get_memory$$ is currently available for use. $lnext The current $icode min_bytes$$ is between the previous $icode min_bytes$$ and previous $icode cap_bytes$$. $lend $head Alignment$$ We call a memory allocation aligned if the address is a multiple of the number of bytes in a $code size_t$$ value. If the system $code new$$ allocator is aligned, then $icode v_ptr$$ pointer is also aligned. $head Example$$ $cref thread_alloc.cpp$$ $end */ /*! Use thread_alloc to get a specified amount of memory. If the memory allocated by a previous call to \c get_memory is now avaialable, and \c min_bytes is between its previous value and the previous \c cap_bytes, this memory allocation will have optimal speed. Otherwise, the memory allocation is more complicated and may have to wait for other threads to complete an allocation. \param min_bytes [in] The minimum number of bytes of memory to be obtained for use. \param cap_bytes [out] The actual number of bytes of memory obtained for use. \return pointer to the beginning of the memory allocated for use. */ static void* get_memory(size_t min_bytes, size_t& cap_bytes) { // see first_trace below CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; // check that number of requested bytes is not to large CPPAD_ASSERT_KNOWN( min_bytes < std::numeric_limits::max() / 2 , "get_memory(min_bytes, cap_bytes): min_bytes is too large" ); size_t num_cap = capacity_info()->number; using std::cout; using std::endl; // determine the capacity for this request size_t c_index = 0; const size_t* capacity_vec = capacity_info()->value; while( capacity_vec[c_index] < min_bytes ) { ++c_index; CPPAD_ASSERT_UNKNOWN(c_index < num_cap ); } cap_bytes = capacity_vec[c_index]; // determine the thread, capacity, and info for this thread size_t thread = thread_num(); size_t tc_index = thread * num_cap + c_index; thread_alloc_info* info = thread_info(thread); # ifndef NDEBUG // trace allocation static bool first_trace = true; if( cap_bytes == CPPAD_TRACE_CAPACITY && thread == CPPAD_TRACE_THREAD && first_trace ) { cout << endl; cout << "thread_alloc: Trace for Thread = " << thread; cout << " and capacity = " << cap_bytes << endl; if( first_trace ) first_trace = false; } // Root nodes for both lists. Note these are different for different // threads because tc_index is different for different threads. block_t* inuse_root = info->root_inuse_ + c_index; # endif block_t* available_root = info->root_available_ + c_index; // check if we already have a node we can use void* v_node = available_root->next_; block_t* node = reinterpret_cast(v_node); if( node != CPPAD_NULL ) { CPPAD_ASSERT_UNKNOWN( node->tc_index_ == tc_index ); // remove node from available list available_root->next_ = node->next_; // return value for get_memory void* v_ptr = reinterpret_cast(node + 1); # ifndef NDEBUG // add node to inuse list node->next_ = inuse_root->next_; inuse_root->next_ = v_node; // trace allocation if( cap_bytes == CPPAD_TRACE_CAPACITY && thread == CPPAD_TRACE_THREAD ) { cout << "get_memory: v_ptr = " << v_ptr << endl; } # endif // adjust counts inc_inuse(cap_bytes, thread); dec_available(cap_bytes, thread); // return pointer to memory, do not inclue thread_alloc information return v_ptr; } // Create a new node with thread_alloc information at front. // This uses the system allocator, which is thread safe, but slower, // because the thread might wait for a lock on the allocator. v_node = ::operator new(sizeof(block_t) + cap_bytes); node = reinterpret_cast(v_node); node->tc_index_ = tc_index; void* v_ptr = reinterpret_cast(node + 1); # ifndef NDEBUG // add node to inuse list node->next_ = inuse_root->next_; inuse_root->next_ = v_node; // trace allocation if( cap_bytes == CPPAD_TRACE_CAPACITY && thread == CPPAD_TRACE_THREAD ) { cout << "get_memory: v_ptr = " << v_ptr << endl; } # endif // adjust counts inc_inuse(cap_bytes, thread); return v_ptr; } /* ----------------------------------------------------------------------- $begin ta_return_memory$$ $spell num ptr thread_alloc $$ $section Return Memory to thread_alloc$$ $mindex return_memory available$$ $head Syntax$$ $codei%thread_alloc::return_memory(%v_ptr%)%$$ $head Purpose$$ If $cref/hold_memory/ta_hold_memory/$$ is false, the memory is returned to the system. Otherwise, the memory is retained by $cref thread_alloc$$ for quick future use by the thread that allocated to memory. $head v_ptr$$ This argument has prototype $codei% void* %v_ptr% %$$. It must be a pointer to memory that is currently in use; i.e. obtained by a previous call to $cref/get_memory/ta_get_memory/$$ and not yet returned. $head Thread$$ Either the $cref/current thread/ta_thread_num/$$ must be the same as during the corresponding call to $cref/get_memory/ta_get_memory/$$, or the current execution mode must be sequential (not $cref/parallel/ta_in_parallel/$$). $head NDEBUG$$ If $code NDEBUG$$ is defined, $icode v_ptr$$ is not checked (this is faster). Otherwise, a list of in use pointers is searched to make sure that $icode v_ptr$$ is in the list. $head Example$$ $cref thread_alloc.cpp$$ $end */ /*! Return memory that was obtained by \c get_memory. If num_threads() == 1, the memory is returned to the system. Otherwise, it is retained by \c thread_alloc and available for use by \c get_memory for this thread. \param v_ptr [in] Value of the pointer returned by \c get_memory and still in use. After this call, this pointer will available (and not in use). \par We must either be in sequential (not parallel) execution mode, or the current thread must be the same as for the corresponding call to \c get_memory. */ static void return_memory(void* v_ptr) { size_t num_cap = capacity_info()->number; block_t* node = reinterpret_cast(v_ptr) - 1; size_t tc_index = node->tc_index_; size_t thread = tc_index / num_cap; size_t c_index = tc_index % num_cap; size_t capacity = capacity_info()->value[c_index]; CPPAD_ASSERT_UNKNOWN( thread < CPPAD_MAX_NUM_THREADS ); CPPAD_ASSERT_KNOWN( thread == thread_num() || (! in_parallel()), "Attempt to return memory for a different thread " "while in parallel mode" ); thread_alloc_info* info = thread_info(thread); # ifndef NDEBUG // remove node from inuse list void* v_node = reinterpret_cast(node); block_t* inuse_root = info->root_inuse_ + c_index; block_t* previous = inuse_root; while( (previous->next_ != CPPAD_NULL) & (previous->next_ != v_node) ) previous = reinterpret_cast(previous->next_); // check that v_ptr is valid if( previous->next_ != v_node ) { using std::endl; std::ostringstream oss; oss << "return_memory: attempt to return memory not in use"; oss << endl; oss << "v_ptr = " << v_ptr << endl; oss << "thread = " << thread << endl; oss << "capacity = " << capacity << endl; oss << "See CPPAD_TRACE_THREAD & CPPAD_TRACE_CAPACITY in"; oss << endl << "%# include " << endl; // oss.str() returns a string object with a copy of the current // contents in the stream buffer. std::string msg_str = oss.str(); // msg_str.c_str() returns a pointer to the c-string // representation of the string object's value. const char* msg_char_star = msg_str.c_str(); CPPAD_ASSERT_KNOWN(false, msg_char_star ); } // trace option if( capacity==CPPAD_TRACE_CAPACITY && thread==CPPAD_TRACE_THREAD ) { std::cout << "return_memory: v_ptr = " << v_ptr << std::endl; } // remove v_ptr from inuse list previous->next_ = node->next_; # endif // capacity bytes are removed from the inuse pool dec_inuse(capacity, thread); // check for case where we just return the memory to the system if( ! set_get_hold_memory(false) ) { ::operator delete( reinterpret_cast(node) ); return; } // add this node to available list for this thread and capacity block_t* available_root = info->root_available_ + c_index; node->next_ = available_root->next_; available_root->next_ = reinterpret_cast(node); // capacity bytes are added to the available pool inc_available(capacity, thread); } /* ----------------------------------------------------------------------- $begin ta_free_available$$ $spell num thread_alloc $$ $section Free Memory Currently Available for Quick Use by a Thread$$ $mindex free_available$$ $spell inuse $$ $head Syntax$$ $codei%thread_alloc::free_available(%thread%)%$$ $head Purpose$$ Return to the system all the memory that is currently being $cref/held/ta_hold_memory/$$ for quick use by the specified thread. $subhead Extra Memory$$ In the case where $icode%thread% > 0%$$, some extra memory is used to track allocations by the specified thread. If $codei% thread_alloc::inuse(%thread%) == 0 %$$ the extra memory is also returned to the system. $head thread$$ This argument has prototype $codei% size_t %thread% %$$ Either $cref/thread_num/ta_thread_num/$$ must be the same as $icode thread$$, or the current execution mode must be sequential (not $cref/parallel/ta_in_parallel/$$). $head Example$$ $cref thread_alloc.cpp$$ $end */ /*! Return all the memory being held as available for a thread to the system. \param thread [in] this thread that will no longer have any available memory after this call. This must either be the thread currently executing, or we must be in sequential (not parallel) execution mode. */ static void free_available(size_t thread) { CPPAD_ASSERT_KNOWN( thread < CPPAD_MAX_NUM_THREADS, "Attempt to free memory for a thread >= CPPAD_MAX_NUM_THREADS" ); CPPAD_ASSERT_KNOWN( thread == thread_num() || (! in_parallel()), "Attempt to free memory for a different thread " "while in parallel mode" ); size_t num_cap = capacity_info()->number; if( num_cap == 0 ) return; const size_t* capacity_vec = capacity_info()->value; size_t c_index; thread_alloc_info* info = thread_info(thread); for(c_index = 0; c_index < num_cap; c_index++) { size_t capacity = capacity_vec[c_index]; block_t* available_root = info->root_available_ + c_index; void* v_ptr = available_root->next_; while( v_ptr != CPPAD_NULL ) { block_t* node = reinterpret_cast(v_ptr); void* next = node->next_; ::operator delete(v_ptr); v_ptr = next; dec_available(capacity, thread); } available_root->next_ = CPPAD_NULL; } CPPAD_ASSERT_UNKNOWN( available(thread) == 0 ); if( inuse(thread) == 0 ) { // clear the information for this thread thread_info(thread, true); } } /* ----------------------------------------------------------------------- $begin ta_hold_memory$$ $spell alloc num $$ $section Control When Thread Alloc Retains Memory For Future Use$$ $mindex hold$$ $head Syntax$$ $codei%thread_alloc::hold_memory(%value%)%$$ $head Purpose$$ It should be faster, even when $icode num_thread$$ is equal to one, for $code thread_alloc$$ to hold onto memory. Calling $icode hold_memory$$ with $icode value$$ equal to true, instructs $code thread_alloc$$ to hold onto memory, and put it in the $cref/available/ta_available/$$ pool, after each call to $cref/return_memory/ta_return_memory/$$. $head value$$ If $icode value$$ is true, $code thread_alloc$$ with hold onto memory for future quick use. If it is false, future calls to $cref/return_memory/ta_return_memory/$$ will return the corresponding memory to the system. By default (when $code hold_memory$$ has not been called) $code thread_alloc$$ does not hold onto memory. $head free_available$$ Memory that is being held by $code thread_alloc$$ can be returned to the system using $cref/free_available/ta_free_available/$$. $end */ /*! Change the thread_alloc hold memory setting. \param value [in] New value for the thread_alloc hold memory setting. */ static void hold_memory(bool value) { bool set = true; set_get_hold_memory(set, value); } /* ----------------------------------------------------------------------- $begin ta_inuse$$ $spell num inuse thread_alloc $$ $section Amount of Memory a Thread is Currently Using$$ $mindex inuse$$ $head Syntax$$ $icode%num_bytes% = thread_alloc::inuse(%thread%)%$$ $head Purpose$$ Memory being managed by $cref thread_alloc$$ has two states, currently in use by the specified thread, and quickly available for future use by the specified thread. This function informs the program how much memory is in use. $head thread$$ This argument has prototype $codei% size_t %thread% %$$ Either $cref/thread_num/ta_thread_num/$$ must be the same as $icode thread$$, or the current execution mode must be sequential (not $cref/parallel/ta_in_parallel/$$). $head num_bytes$$ The return value has prototype $codei% size_t %num_bytes% %$$ It is the number of bytes currently in use by the specified thread. $head Example$$ $cref thread_alloc.cpp$$ $end */ /*! Determine the amount of memory that is currently inuse. \param thread [in] Thread for which we are determining the amount of memory (must be < CPPAD_MAX_NUM_THREADS). Durring parallel execution, this must be the thread that is currently executing. \return The amount of memory in bytes. */ static size_t inuse(size_t thread) { CPPAD_ASSERT_UNKNOWN( thread < CPPAD_MAX_NUM_THREADS); CPPAD_ASSERT_UNKNOWN( thread == thread_num() || (! in_parallel()) ); thread_alloc_info* info = thread_info(thread); return info->count_inuse_; } /* ----------------------------------------------------------------------- $begin ta_available$$ $spell num thread_alloc $$ $section Amount of Memory Available for Quick Use by a Thread$$ $head Syntax$$ $icode%num_bytes% = thread_alloc::available(%thread%)%$$ $head Purpose$$ Memory being managed by $cref thread_alloc$$ has two states, currently in use by the specified thread, and quickly available for future use by the specified thread. This function informs the program how much memory is available. $head thread$$ This argument has prototype $codei% size_t %thread% %$$ Either $cref/thread_num/ta_thread_num/$$ must be the same as $icode thread$$, or the current execution mode must be sequential (not $cref/parallel/ta_in_parallel/$$). $head num_bytes$$ The return value has prototype $codei% size_t %num_bytes% %$$ It is the number of bytes currently available for use by the specified thread. $head Example$$ $cref thread_alloc.cpp$$ $end */ /*! Determine the amount of memory that is currently available for use. \copydetails inuse */ static size_t available(size_t thread) { CPPAD_ASSERT_UNKNOWN( thread < CPPAD_MAX_NUM_THREADS); CPPAD_ASSERT_UNKNOWN( thread == thread_num() || (! in_parallel()) ); thread_alloc_info* info = thread_info(thread); return info->count_available_; } /* ----------------------------------------------------------------------- $begin ta_create_array$$ $spell inuse thread_alloc sizeof $$ $section Allocate An Array and Call Default Constructor for its Elements$$ $mindex create_array$$ $head Syntax$$ $icode%array% = thread_alloc::create_array<%Type%>(%size_min%, %size_out%)%$$. $head Purpose$$ Create a new raw array using $cref thread_alloc$$ memory allocator (works well in a multi-threading environment) and call default constructor for each element. $head Type$$ The type of the elements of the array. $head size_min$$ This argument has prototype $codei% size_t %size_min% %$$ This is the minimum number of elements that there can be in the resulting $icode array$$. $head size_out$$ This argument has prototype $codei% size_t& %size_out% %$$ The input value of this argument does not matter. Upon return, it is the actual number of elements in $icode array$$ ($icode% size_min %<=% size_out%$$). $head array$$ The return value $icode array$$ has prototype $codei% %Type%* %array% %$$ It is array with $icode size_out$$ elements. The default constructor for $icode Type$$ is used to initialize the elements of $icode array$$. Note that $cref/delete_array/ta_delete_array/$$ should be used to destroy the array when it is no longer needed. $head Delta$$ The amount of memory $cref/inuse/ta_inuse/$$ by the current thread, will increase $icode delta$$ where $codei% sizeof(%Type%) * (%size_out% + 1) > %delta% >= sizeof(%Type%) * %size_out% %$$ The $cref/available/ta_available/$$ memory will decrease by $icode delta$$, (and the allocation will be faster) if a previous allocation with $icode size_min$$ between its current value and $icode size_out$$ is available. $head Alignment$$ We call a memory allocation aligned if the address is a multiple of the number of bytes in a $code size_t$$ value. If the system $code new$$ allocator is aligned, then $icode array$$ pointer is also aligned. $head Example$$ $cref thread_alloc.cpp$$ $end */ /*! Use thread_alloc to allocate an array, then call default construtor for each element. \tparam Type The type of the elements of the array. \param size_min [in] The minimum number of elements in the array. \param size_out [out] The actual number of elements in the array. \return pointer to the first element of the array. The default constructor is used to initialize all the elements of the array. \par The \c extra_ field, in the \c thread_alloc node before the return value, is set to size_out. */ template static Type* create_array(size_t size_min, size_t& size_out) { // minimum number of bytes to allocate size_t min_bytes = size_min * sizeof(Type); // do the allocation size_t num_bytes; void* v_ptr = get_memory(min_bytes, num_bytes); // This is where the array starts Type* array = reinterpret_cast(v_ptr); // number of Type values in the allocation size_out = num_bytes / sizeof(Type); // store this number in the extra field block_t* node = reinterpret_cast(v_ptr) - 1; node->extra_ = size_out; // call default constructor for each element size_t i; for(i = 0; i < size_out; i++) new(array + i) Type(); return array; } /* ----------------------------------------------------------------------- $begin ta_delete_array$$ $spell inuse thread_alloc sizeof deallocate $$ $section Deallocate An Array and Call Destructor for its Elements$$ $mindex delete_array$$ $head Syntax$$ $codei%thread_alloc::delete_array(%array%)%$$. $head Purpose$$ Returns memory corresponding to an array created by (create by $cref/create_array/ta_create_array/$$) to the $cref/available/ta_available/$$ memory pool for the current thread. $head Type$$ The type of the elements of the array. $head array$$ The argument $icode array$$ has prototype $codei% %Type%* %array% %$$ It is a value returned by $cref/create_array/ta_create_array/$$ and not yet deleted. The $icode Type$$ destructor is called for each element in the array. $head Thread$$ The $cref/current thread/ta_thread_num/$$ must be the same as when $cref/create_array/ta_create_array/$$ returned the value $icode array$$. There is an exception to this rule: when the current execution mode is sequential (not $cref/parallel/ta_in_parallel/$$) the current thread number does not matter. $head Delta$$ The amount of memory $cref/inuse/ta_inuse/$$ will decrease by $icode delta$$, and the $cref/available/ta_available/$$ memory will increase by $icode delta$$, where $cref/delta/ta_create_array/Delta/$$ is the same as for the corresponding call to $code create_array$$. $head Example$$ $cref thread_alloc.cpp$$ $end */ /*! Return Memory Used for an Array to the Available Pool (include destructor call for each element). \tparam Type The type of the elements of the array. \param array [in] A value returned by \c create_array that has not yet been deleted. The \c Type destructor is used to destroy each of the elements of the array. \par Durring parallel execution, the current thread must be the same as during the corresponding call to \c create_array. */ template static void delete_array(Type* array) { // determine the number of values in the array block_t* node = reinterpret_cast(array) - 1; size_t size = node->extra_; // call destructor for each element size_t i; for(i = 0; i < size; i++) (array + i)->~Type(); // return the memory to the available pool for this thread thread_alloc::return_memory( reinterpret_cast(array) ); } /* ----------------------------------------------------------------------- $begin ta_free_all$$ $spell alloc bool inuse $$ $section Free All Memory That Was Allocated for Use by thread_alloc$$ $head Syntax$$ $icode%ok% = thread_alloc::free_all()%$$. $head Purpose$$ Returns all memory that was used by $code thread_alloc$$ to the system. $head ok$$ The return value $icode ok$$ has prototype $codei% bool %ok% %$$ Its value will be $code true$$ if all the memory can be freed. This requires that for all $icode thread$$ indices, there is no memory $cref/inuse/ta_inuse/$$; i.e., $codei% 0 == thread_alloc::inuse(%thread%) %$$ Otherwise, the return value will be false. $head Restrictions$$ This function cannot be called while in parallel mode. $head Example$$ $cref thread_alloc.cpp$$ $end */ /*! Return to the system all thread_alloc memory that is not currently inuse. \return If no \c thread_alloc memory is currently inuse, all memory is returned to the system and the return value is true. Otherwise the return value is false. */ static bool free_all(void) { CPPAD_ASSERT_KNOWN( ! in_parallel(), "free_all cannot be used while in parallel execution" ); bool ok = true; size_t thread = CPPAD_MAX_NUM_THREADS; while(thread--) { ok &= inuse(thread) == 0; free_available(thread); } return ok; } }; } // END_CPPAD_NAMESPACE // preprocessor symbols local to this file # undef CPPAD_MAX_NUM_CAPACITY # undef CPPAD_MIN_DOUBLE_CAPACITY # undef CPPAD_TRACE_CAPACITY # undef CPPAD_TRACE_THREAD # endif cppad-20170000.3/cppad/utility/poly.hpp0000644000175200017650000001132713057470465016727 0ustar coincoin-web// $Id: poly.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_UTILITY_POLY_HPP # define CPPAD_UTILITY_POLY_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Poly$$ $spell cppad.hpp CppAD namespace cstddef ifndef endif deg const std da $$ $section Evaluate a Polynomial or its Derivative$$ $mindex Poly template$$ $head Syntax$$ $codei%# include %$$ $icode%p% = Poly(%k%, %a%, %z%)%$$ $head Description$$ Computes the $th k$$ derivative of the polynomial $latex \[ P(z) = a_0 + a_1 z^1 + \cdots + a_d z^d \] $$ If $icode k$$ is equal to zero, the return value is $latex P(z)$$. $head Include$$ The file $code cppad/poly.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. Including this file defines $code Poly$$ within the $code CppAD$$ namespace. $head k$$ The argument $icode k$$ has prototype $codei% size_t %k% %$$ It specifies the order of the derivative to calculate. $head a$$ The argument $icode a$$ has prototype $codei% const %Vector% &%a% %$$ (see $cref/Vector/Poly/Vector/$$ below). It specifies the vector corresponding to the polynomial $latex P(z)$$. $head z$$ The argument $icode z$$ has prototype $codei% const %Type% &%z% %$$ (see $icode Type$$ below). It specifies the point at which to evaluate the polynomial $head p$$ The result $icode p$$ has prototype $codei% %Type% %p% %$$ (see $cref/Type/Poly/Type/$$ below) and it is equal to the $th k$$ derivative of $latex P(z)$$; i.e., $latex \[ p = \frac{k !}{0 !} a_k + \frac{(k+1) !}{1 !} a_{k+1} z^1 + \ldots + \frac{d !}{(d - k) !} a_d z^{d - k} \] $$ If $latex k > d$$, $icode%p% = %Type%(0)%$$. $head Type$$ The type $icode Type$$ is determined by the argument $icode z$$. It is assumed that multiplication and addition of $icode Type$$ objects are commutative. $subhead Operations$$ The following operations must be supported where $icode x$$ and $icode y$$ are objects of type $icode Type$$ and $icode i$$ is an $code int$$: $table $icode%x% = %i%$$ $cnext assignment $rnext $icode%x% = %y%$$ $cnext assignment $rnext $icode%x% *= %y%$$ $cnext multiplication computed assignment $rnext $icode%x% += %y%$$ $cnext addition computed assignment $tend $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Type$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Operation Sequence$$ The $icode Type$$ operation sequence used to calculate $icode p$$ is $cref/independent/glossary/Operation/Independent/$$ of $icode z$$ and the elements of $icode a$$ (it does depend on the size of the vector $icode a$$). $children% example/poly.cpp% omh/poly_hpp.omh %$$ $head Example$$ The file $cref poly.cpp$$ contains an example and test of this routine. It returns true if it succeeds and false otherwise. $head Source$$ The file $cref poly.hpp$$ contains the current source code that implements these specifications. $end ------------------------------------------------------------------------------ */ // BEGIN C++ # include // used to defined size_t # include namespace CppAD { // BEGIN CppAD namespace template Type Poly(size_t k, const Vector &a, const Type &z) { size_t i; size_t d = a.size() - 1; Type tmp; // check Vector is Simple Vector class with Type elements CheckSimpleVector(); // case where derivative order greater than degree of polynomial if( k > d ) { tmp = 0; return tmp; } // case where we are evaluating a derivative if( k > 0 ) { // initialize factor as (k-1) ! size_t factor = 1; for(i = 2; i < k; i++) factor *= i; // set b to coefficient vector corresponding to derivative Vector b(d - k + 1); for(i = k; i <= d; i++) { factor *= i; tmp = factor; b[i - k] = a[i] * tmp; factor /= (i - k + 1); } // value of derivative polynomial return Poly(0, b, z); } // case where we are evaluating the original polynomial Type sum = a[d]; i = d; while(i > 0) { sum *= z; sum += a[--i]; } return sum; } } // END CppAD namespace // END C++ # endif cppad-20170000.3/cppad/utility/error_handler.hpp0000644000175200017650000001430713057470465020573 0ustar coincoin-web// $Id: error_handler.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_ERROR_HANDLER_HPP # define CPPAD_UTILITY_ERROR_HANDLER_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ErrorHandler$$ $spell cppad.hpp CppAD exp bool const $$ $section Replacing the CppAD Error Handler$$ $mindex replace assert exception ErrorHandler$$ $head Syntax$$ $codei%# include %$$ $codei%ErrorHandler %info%(%handler%) %$$ $codei%ErrorHandler::Call(%known%, %line%, %file%, %exp%, %msg%) %$$ $head Constructor$$ When you construct a $code ErrorHandler$$ object, the current CppAD error handler is replaced by $icode handler$$. When the object is destructed, the previous CppAD error handler is restored. $subhead Parallel Mode$$ The $code ErrorHandler$$ constructor and destructor cannot be called in $cref/parallel/ta_in_parallel/$$ execution mode. Furthermore, this rule is not abided by, a raw C++ $code assert$$, instead of one that uses this error handler, will be generated. $head Call$$ When $code ErrorHandler::Call$$ is called, the current CppAD error handler is used to report an error. This starts out as a default error handler and can be replaced using the $code ErrorHandler$$ constructor. $head info$$ The object $icode info$$ is used to store information that is necessary to restore the previous CppAD error handler. This is done when the destructor for $icode info$$ is called. $head handler$$ The argument $icode handler$$ has prototype $codei% void (*%handler%) (bool, int, const char *, const char *, const char *); %$$ When an error is detected, it is called with the syntax $codei% %handler% (%known%, %line%, %file%, %exp%, %msg%) %$$ This routine should not return; i.e., upon detection of the error, the routine calling $icode handler$$ does not know how to proceed. $head known$$ The $icode handler$$ argument $icode known$$ has prototype $codei% bool %known% %$$ If it is true, the error being reported is from a know problem. $head line$$ The $icode handler$$ argument $icode line$$ has prototype $codei% int %line% %$$ It reports the source code line number where the error is detected. $head file$$ The $icode handler$$ argument $icode file$$ has prototype $codei% const char *%file% %$$ and is a $code '\0'$$ terminated character vector. It reports the source code file where the error is detected. $head exp$$ The $icode handler$$ argument $icode exp$$ has prototype $codei% const char *%exp% %$$ and is a $code '\0'$$ terminated character vector. It is a source code boolean expression that should have been true, but is false, and thereby causes this call to $icode handler$$. $head msg$$ The $icode handler$$ argument $icode msg$$ has prototype $codei% const char *%msg% %$$ and is a $code '\0'$$ terminated character vector. It reports the meaning of the error from the C++ programmers point of view. $children% example/error_handler.cpp% cppad/core/cppad_assert.hpp %$$ $head Example$$ The file $cref error_handler.cpp$$ contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise. $end --------------------------------------------------------------------------- */ # include # include # include # include # include namespace CppAD { // BEGIN CppAD namespace class ErrorHandler { template friend void parallel_ad(void); public: typedef void (*Handler) (bool, int, const char *, const char *, const char *); // construct a new handler ErrorHandler(Handler handler) : previous( Current() ) { if( local::set_get_in_parallel(0) ) { bool known = true; int line = __LINE__; const char* file = __FILE__; const char* exp = "! local::set_get_in_parallel(0)"; const char* msg = "Using ErrorHandler constructor in parallel mode."; Call(known, line, file, exp, msg); } Current() = handler; } // destructor for an error handler ~ErrorHandler(void) { if( local::set_get_in_parallel(0) ) { bool known = true; int line = __LINE__; const char* file = __FILE__; const char* exp = "! local::set_get_in_parallel(0)"; const char* msg = "Using ErrorHandler destructor in parallel mode."; Call(known, line, file, exp, msg); } Current() = previous; } // report an error static void Call( bool known, int line , const char *file , const char *exp , const char *msg ) { Handler handler = Current(); handler(known, line, file, exp, msg); } private: const Handler previous; // The default error handler static void Default( bool known, int line , const char *file , const char *exp , const char *msg ) { using std::cerr; using std::endl; cerr << CPPAD_PACKAGE_STRING; if( known ) cerr << " error from a known source:" << endl; else cerr << " error from unknown source" << endl; if( msg[0] != '\0' ) cerr << msg << endl; cerr << "Error detected by false result for" << endl; cerr << " " << exp << endl; cerr << "at line " << line << " in the file " << endl; cerr << " " << file << endl; // terminate program execution assert(false); // termination when NDEBUG is defined std::exit(1); } // current error handler static Handler &Current(void) { static bool first_call = true; static Handler current = Default; if( first_call ) { if( local::set_get_in_parallel(0) ) { bool known = false; int line = __LINE__; const char* file = __FILE__; const char* exp = ""; const char* msg = ""; Call(known, line, file, exp, msg); } first_call = false; } return current; } }; } // END CppAD namespace # endif cppad-20170000.3/cppad/utility/runge_45.hpp0000644000175200017650000002645713057470465017406 0ustar coincoin-web// $Id: runge_45.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_RUNGE_45_HPP # define CPPAD_UTILITY_RUNGE_45_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Runge45$$ $spell std fabs cppad.hpp bool xf templated const Runge-Kutta CppAD xi ti tf Karp $$ $section An Embedded 4th and 5th Order Runge-Kutta ODE Solver$$ $mindex Runge45 Runge Kutta solve differential equation$$ $head Syntax$$ $codei%# include %$$ $icode%xf% = Runge45(%F%, %M%, %ti%, %tf%, %xi%) %$$ $icode%xf% = Runge45(%F%, %M%, %ti%, %tf%, %xi%, %e%) %$$ $head Purpose$$ This is an implementation of the Cash-Karp embedded 4th and 5th order Runge-Kutta ODE solver described in Section 16.2 of $cref/Numerical Recipes/Bib/Numerical Recipes/$$. We use $latex n$$ for the size of the vector $icode xi$$. Let $latex \B{R}$$ denote the real numbers and let $latex F : \B{R} \times \B{R}^n \rightarrow \B{R}^n$$ be a smooth function. The return value $icode xf$$ contains a 5th order approximation for the value $latex X(tf)$$ where $latex X : [ti , tf] \rightarrow \B{R}^n$$ is defined by the following initial value problem: $latex \[ \begin{array}{rcl} X(ti) & = & xi \\ X'(t) & = & F[t , X(t)] \end{array} \] $$ If your set of ordinary differential equations are stiff, an implicit method may be better (perhaps $cref Rosen34$$.) $head Operation Sequence$$ The $cref/operation sequence/glossary/Operation/Sequence/$$ for $icode Runge$$ does not depend on any of its $icode Scalar$$ input values provided that the operation sequence for $codei% %F%.Ode(%t%, %x%, %f%) %$$ does not on any of its $icode Scalar$$ inputs (see below). $head Include$$ The file $code cppad/runge_45.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head xf$$ The return value $icode xf$$ has the prototype $codei% %Vector% %xf% %$$ and the size of $icode xf$$ is equal to $icode n$$ (see description of $cref/Vector/Runge45/Vector/$$ below). $latex \[ X(tf) = xf + O( h^6 ) \] $$ where $latex h = (tf - ti) / M$$ is the step size. If $icode xf$$ contains not a number $cref nan$$, see the discussion for $cref/f/Runge45/Fun/f/$$. $head Fun$$ The class $icode Fun$$ and the object $icode F$$ satisfy the prototype $codei% %Fun% &%F% %$$ The object $icode F$$ (and the class $icode Fun$$) must have a member function named $code Ode$$ that supports the syntax $codei% %F%.Ode(%t%, %x%, %f%) %$$ $subhead t$$ The argument $icode t$$ to $icode%F%.Ode%$$ has prototype $codei% const %Scalar% &%t% %$$ (see description of $cref/Scalar/Runge45/Scalar/$$ below). $subhead x$$ The argument $icode x$$ to $icode%F%.Ode%$$ has prototype $codei% const %Vector% &%x% %$$ and has size $icode n$$ (see description of $cref/Vector/Runge45/Vector/$$ below). $subhead f$$ The argument $icode f$$ to $icode%F%.Ode%$$ has prototype $codei% %Vector% &%f% %$$ On input and output, $icode f$$ is a vector of size $icode n$$ and the input values of the elements of $icode f$$ do not matter. On output, $icode f$$ is set equal to $latex F(t, x)$$ in the differential equation. If any of the elements of $icode f$$ have the value not a number $code nan$$ the routine $code Runge45$$ returns with all the elements of $icode xf$$ and $icode e$$ equal to $code nan$$. $subhead Warning$$ The argument $icode f$$ to $icode%F%.Ode%$$ must have a call by reference in its prototype; i.e., do not forget the $code &$$ in the prototype for $icode f$$. $head M$$ The argument $icode M$$ has prototype $codei% size_t %M% %$$ It specifies the number of steps to use when solving the differential equation. This must be greater than or equal one. The step size is given by $latex h = (tf - ti) / M$$, thus the larger $icode M$$, the more accurate the return value $icode xf$$ is as an approximation for $latex X(tf)$$. $head ti$$ The argument $icode ti$$ has prototype $codei% const %Scalar% &%ti% %$$ (see description of $cref/Scalar/Runge45/Scalar/$$ below). It specifies the initial time for $icode t$$ in the differential equation; i.e., the time corresponding to the value $icode xi$$. $head tf$$ The argument $icode tf$$ has prototype $codei% const %Scalar% &%tf% %$$ It specifies the final time for $icode t$$ in the differential equation; i.e., the time corresponding to the value $icode xf$$. $head xi$$ The argument $icode xi$$ has the prototype $codei% const %Vector% &%xi% %$$ and the size of $icode xi$$ is equal to $icode n$$. It specifies the value of $latex X(ti)$$ $head e$$ The argument $icode e$$ is optional and has the prototype $codei% %Vector% &%e% %$$ If $icode e$$ is present, the size of $icode e$$ must be equal to $icode n$$. The input value of the elements of $icode e$$ does not matter. On output it contains an element by element estimated bound for the absolute value of the error in $icode xf$$ $latex \[ e = O( h^5 ) \] $$ where $latex h = (tf - ti) / M$$ is the step size. If on output, $icode e$$ contains not a number $code nan$$, see the discussion for $cref/f/Runge45/Fun/f/$$. $head Scalar$$ The type $icode Scalar$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. $subhead fabs$$ In addition, the following function must be defined for $icode Scalar$$ objects $icode a$$ and $icode b$$ $codei% %a% = fabs(%b%) %$$ Note that this operation is only used for computing $icode e$$; hence the operation sequence for $icode xf$$ can still be independent of the arguments to $code Runge45$$ even if $codei% fabs(%b%) = std::max(-%b%, %b%) %$$. $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type Scalar/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Parallel Mode$$ For each set of types $cref/Scalar/Runge45/Scalar/$$, $cref/Vector/Runge45/Vector/$$, and $cref/Fun/Runge45/Fun/$$, the first call to $code Runge45$$ must not be $cref/parallel/ta_in_parallel/$$ execution mode. $head Example$$ $children% example/runge45_1.cpp% example/runge45_2.cpp %$$ The file $cref runge45_1.cpp$$ contains a simple example and test of $code Runge45$$. It returns true if it succeeds and false otherwise. $pre $$ The file $cref runge45_2.cpp$$ contains an example using $code Runge45$$ in the context of algorithmic differentiation. It also returns true if it succeeds and false otherwise. $head Source Code$$ The source code for this routine is in the file $code cppad/runge_45.hpp$$. $end -------------------------------------------------------------------------- */ # include # include # include # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { // BEGIN CppAD namespace template Vector Runge45( Fun &F , size_t M , const Scalar &ti , const Scalar &tf , const Vector &xi ) { Vector e( xi.size() ); return Runge45(F, M, ti, tf, xi, e); } template Vector Runge45( Fun &F , size_t M , const Scalar &ti , const Scalar &tf , const Vector &xi , Vector &e ) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; // check numeric type specifications CheckNumericType(); // check simple vector class specifications CheckSimpleVector(); // Cash-Karp parameters for embedded Runge-Kutta method // are static to avoid recalculation on each call and // do not use Vector to avoid possible memory leak static Scalar a[6] = { Scalar(0), Scalar(1) / Scalar(5), Scalar(3) / Scalar(10), Scalar(3) / Scalar(5), Scalar(1), Scalar(7) / Scalar(8) }; static Scalar b[5 * 5] = { Scalar(1) / Scalar(5), Scalar(0), Scalar(0), Scalar(0), Scalar(0), Scalar(3) / Scalar(40), Scalar(9) / Scalar(40), Scalar(0), Scalar(0), Scalar(0), Scalar(3) / Scalar(10), -Scalar(9) / Scalar(10), Scalar(6) / Scalar(5), Scalar(0), Scalar(0), -Scalar(11) / Scalar(54), Scalar(5) / Scalar(2), -Scalar(70) / Scalar(27), Scalar(35) / Scalar(27), Scalar(0), Scalar(1631) / Scalar(55296), Scalar(175) / Scalar(512), Scalar(575) / Scalar(13824), Scalar(44275) / Scalar(110592), Scalar(253) / Scalar(4096) }; static Scalar c4[6] = { Scalar(2825) / Scalar(27648), Scalar(0), Scalar(18575) / Scalar(48384), Scalar(13525) / Scalar(55296), Scalar(277) / Scalar(14336), Scalar(1) / Scalar(4), }; static Scalar c5[6] = { Scalar(37) / Scalar(378), Scalar(0), Scalar(250) / Scalar(621), Scalar(125) / Scalar(594), Scalar(0), Scalar(512) / Scalar(1771) }; CPPAD_ASSERT_KNOWN( M >= 1, "Error in Runge45: the number of steps is less than one" ); CPPAD_ASSERT_KNOWN( e.size() == xi.size(), "Error in Runge45: size of e not equal to size of xi" ); size_t i, j, k, m; // indices size_t n = xi.size(); // number of components in X(t) Scalar ns = Scalar(int(M)); // number of steps as Scalar object Scalar h = (tf - ti) / ns; // step size Scalar zero_or_nan = Scalar(0); // zero (nan if Ode returns has a nan) for(i = 0; i < n; i++) // initialize e = 0 e[i] = zero_or_nan; // vectors used to store values returned by F Vector fh(6 * n), xtmp(n), ftmp(n), x4(n), x5(n), xf(n); xf = xi; // initialize solution for(m = 0; m < M; m++) { // time at beginning of this interval // (convert to int to avoid MS compiler warning) Scalar t = ti * (Scalar(int(M - m)) / ns) + tf * (Scalar(int(m)) / ns); // loop over integration steps x4 = x5 = xf; // start x4 and x5 at same point for each step for(j = 0; j < 6; j++) { // loop over function evaluations for this step xtmp = xf; // location for next function evaluation for(k = 0; k < j; k++) { // loop over previous function evaluations Scalar bjk = b[ (j-1) * 5 + k ]; for(i = 0; i < n; i++) { // loop over elements of x xtmp[i] += bjk * fh[i * 6 + k]; } } // ftmp = F(t + a[j] * h, xtmp) F.Ode(t + a[j] * h, xtmp, ftmp); // if ftmp has a nan, set zero_or_nan to nan for(i = 0; i < n; i++) zero_or_nan *= ftmp[i]; for(i = 0; i < n; i++) { // loop over elements of x Scalar fhi = ftmp[i] * h; fh[i * 6 + j] = fhi; x4[i] += c4[j] * fhi; x5[i] += c5[j] * fhi; x5[i] += zero_or_nan; } } // accumulate error bound for(i = 0; i < n; i++) { // cant use abs because cppad.hpp may not be included Scalar diff = x5[i] - x4[i]; e[i] += fabs(diff); e[i] += zero_or_nan; } // advance xf for this step using x5 xf = x5; } return xf; } } // End CppAD namespace # endif cppad-20170000.3/cppad/utility/lu_solve.hpp0000644000175200017650000002330513057470465017573 0ustar coincoin-web// $Id: lu_solve.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_LU_SOLVE_HPP # define CPPAD_UTILITY_LU_SOLVE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin LuSolve$$ $escape #$$ $spell cppad.hpp det exp Leq typename bool const namespace std Geq Lu CppAD signdet logdet $$ $section Compute Determinant and Solve Linear Equations$$ $mindex LuSolve Lu$$ $pre $$ $head Syntax$$ $codei%# include %$$ $icode%signdet% = LuSolve(%n%, %m%, %A%, %B%, %X%, %logdet%)%$$ $head Description$$ Use an LU factorization of the matrix $icode A$$ to compute its determinant and solve for $icode X$$ in the linear of equation $latex \[ A * X = B \] $$ where $icode A$$ is an $icode n$$ by $icode n$$ matrix, $icode X$$ is an $icode n$$ by $icode m$$ matrix, and $icode B$$ is an $latex n x m$$ matrix. $head Include$$ The file $code cppad/lu_solve.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head Factor and Invert$$ This routine is an easy to user interface to $cref LuFactor$$ and $cref LuInvert$$ for computing determinants and solutions of linear equations. These separate routines should be used if one right hand side $icode B$$ depends on the solution corresponding to another right hand side (with the same value of $icode A$$). In this case only one call to $code LuFactor$$ is required but there will be multiple calls to $code LuInvert$$. $head Matrix Storage$$ All matrices are stored in row major order. To be specific, if $latex Y$$ is a vector that contains a $latex p$$ by $latex q$$ matrix, the size of $latex Y$$ must be equal to $latex p * q $$ and for $latex i = 0 , \ldots , p-1$$, $latex j = 0 , \ldots , q-1$$, $latex \[ Y_{i,j} = Y[ i * q + j ] \] $$ $head signdet$$ The return value $icode signdet$$ is a $code int$$ value that specifies the sign factor for the determinant of $icode A$$. This determinant of $icode A$$ is zero if and only if $icode signdet$$ is zero. $head n$$ The argument $icode n$$ has type $code size_t$$ and specifies the number of rows in the matrices $icode A$$, $icode X$$, and $icode B$$. The number of columns in $icode A$$ is also equal to $icode n$$. $head m$$ The argument $icode m$$ has type $code size_t$$ and specifies the number of columns in the matrices $icode X$$ and $icode B$$. If $icode m$$ is zero, only the determinant of $icode A$$ is computed and the matrices $icode X$$ and $icode B$$ are not used. $head A$$ The argument $icode A$$ has the prototype $codei% const %FloatVector% &%A% %$$ and the size of $icode A$$ must equal $latex n * n$$ (see description of $cref/FloatVector/LuSolve/FloatVector/$$ below). This is the $latex n$$ by $icode n$$ matrix that we are computing the determinant of and that defines the linear equation. $head B$$ The argument $icode B$$ has the prototype $codei% const %FloatVector% &%B% %$$ and the size of $icode B$$ must equal $latex n * m$$ (see description of $cref/FloatVector/LuSolve/FloatVector/$$ below). This is the $latex n$$ by $icode m$$ matrix that defines the right hand side of the linear equations. If $icode m$$ is zero, $icode B$$ is not used. $head X$$ The argument $icode X$$ has the prototype $codei% %FloatVector% &%X% %$$ and the size of $icode X$$ must equal $latex n * m$$ (see description of $cref/FloatVector/LuSolve/FloatVector/$$ below). The input value of $icode X$$ does not matter. On output, the elements of $icode X$$ contain the solution of the equation we wish to solve (unless $icode signdet$$ is equal to zero). If $icode m$$ is zero, $icode X$$ is not used. $head logdet$$ The argument $icode logdet$$ has prototype $codei% %Float% &%logdet% %$$ On input, the value of $icode logdet$$ does not matter. On output, it has been set to the log of the determinant of $icode A$$ (but not quite). To be more specific, the determinant of $icode A$$ is given by the formula $codei% %det% = %signdet% * exp( %logdet% ) %$$ This enables $code LuSolve$$ to use logs of absolute values in the case where $icode Float$$ corresponds to a real number. $head Float$$ The type $icode Float$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, the following operations must be defined for any pair of $icode Float$$ objects $icode x$$ and $icode y$$: $table $bold Operation$$ $cnext $bold Description$$ $rnext $codei%log(%x%)%$$ $cnext returns the logarithm of $icode x$$ as a $icode Float$$ object $tend $head FloatVector$$ The type $icode FloatVector$$ must be a $cref SimpleVector$$ class with $cref/elements of type Float/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head LeqZero$$ Including the file $code lu_solve.hpp$$ defines the template function $codei% template bool LeqZero<%Float%>(const %Float% &%x%) %$$ in the $code CppAD$$ namespace. This function returns true if $icode x$$ is less than or equal to zero and false otherwise. It is used by $code LuSolve$$ to avoid taking the log of zero (or a negative number if $icode Float$$ corresponds to real numbers). This template function definition assumes that the operator $code <=$$ is defined for $icode Float$$ objects. If this operator is not defined for your use of $icode Float$$, you will need to specialize this template so that it works for your use of $code LuSolve$$. $pre $$ Complex numbers do not have the operation or $code <=$$ defined. In addition, in the complex case, one can take the log of a negative number. The specializations $codei% bool LeqZero< std::complex > (const std::complex &%x%) bool LeqZero< std::complex >(const std::complex &%x%) %$$ are defined by including $code lu_solve.hpp$$. These return true if $icode x$$ is zero and false otherwise. $head AbsGeq$$ Including the file $code lu_solve.hpp$$ defines the template function $codei% template bool AbsGeq<%Float%>(const %Float% &%x%, const %Float% &%y%) %$$ If the type $icode Float$$ does not support the $code <=$$ operation and it is not $code std::complex$$ or $code std::complex$$, see the documentation for $code AbsGeq$$ in $cref/LuFactor/LuFactor/AbsGeq/$$. $children% example/lu_solve.cpp% omh/lu_solve_hpp.omh %$$ $head Example$$ The file $cref lu_solve.cpp$$ contains an example and test of using this routine. It returns true if it succeeds and false otherwise. $head Source$$ The file $cref lu_solve.hpp$$ contains the current source code that implements these specifications. $end -------------------------------------------------------------------------- */ // BEGIN C++ # include # include // link exp for float and double cases # include # include # include # include # include # include namespace CppAD { // BEGIN CppAD namespace // LeqZero template inline bool LeqZero(const Float &x) { return x <= Float(0); } inline bool LeqZero( const std::complex &x ) { return x == std::complex(0); } inline bool LeqZero( const std::complex &x ) { return x == std::complex(0); } // LuSolve template int LuSolve( size_t n , size_t m , const FloatVector &A , const FloatVector &B , FloatVector &X , Float &logdet ) { // check numeric type specifications CheckNumericType(); // check simple vector class specifications CheckSimpleVector(); size_t p; // index of pivot element (diagonal of L) int signdet; // sign of the determinant Float pivot; // pivot element // the value zero const Float zero(0); // pivot row and column order in the matrix std::vector ip(n); std::vector jp(n); // ------------------------------------------------------- CPPAD_ASSERT_KNOWN( size_t(A.size()) == n * n, "Error in LuSolve: A must have size equal to n * n" ); CPPAD_ASSERT_KNOWN( size_t(B.size()) == n * m, "Error in LuSolve: B must have size equal to n * m" ); CPPAD_ASSERT_KNOWN( size_t(X.size()) == n * m, "Error in LuSolve: X must have size equal to n * m" ); // ------------------------------------------------------- // copy A so that it does not change FloatVector Lu(A); // copy B so that it does not change X = B; // Lu factor the matrix A signdet = LuFactor(ip, jp, Lu); // compute the log of the determinant logdet = Float(0); for(p = 0; p < n; p++) { // pivot using the max absolute element pivot = Lu[ ip[p] * n + jp[p] ]; // check for determinant equal to zero if( pivot == zero ) { // abort the mission logdet = Float(0); return 0; } // update the determinant if( LeqZero ( pivot ) ) { logdet += log( - pivot ); signdet = - signdet; } else logdet += log( pivot ); } // solve the linear equations LuInvert(ip, jp, Lu, X); // return the sign factor for the determinant return signdet; } } // END CppAD namespace // END C++ # endif cppad-20170000.3/cppad/utility/elapsed_seconds.hpp0000644000175200017650000001164413057470465021101 0ustar coincoin-web// $Id: elapsed_seconds.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_ELAPSED_SECONDS_HPP # define CPPAD_UTILITY_ELAPSED_SECONDS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin elapsed_seconds$$ $spell cppad.hpp Microsoft gettimeofday std chrono $$ $section Returns Elapsed Number of Seconds$$ $mindex elapsed_seconds time$$ $head Syntax$$ $codei%# include %$$ $icode%s% = elapsed_seconds()%$$ $head Purpose$$ This routine is accurate to within .02 seconds (see $cref elapsed_seconds.cpp$$). It does not necessary work for time intervals that are greater than a day. $list number$$ If the C++11 $code std::chrono::steady_clock$$ is available, it will be used for timing. $lnext Otherwise, if running under the Microsoft compiler, $code ::GetSystemTime$$ will be used for timing. $lnext Otherwise, if $code gettimeofday$$ is available, it is used for timing. $lnext Otherwise, $code std::clock()$$ will be used for timing. $lend $head s$$ is a $code double$$ equal to the number of seconds since the first call to $code elapsed_seconds$$. $head Microsoft Systems$$ It you are using $code ::GetSystemTime$$, you will need to link in the external routine called $cref microsoft_timer$$. $children% speed/example/elapsed_seconds.cpp %$$ $head Example$$ The routine $cref elapsed_seconds.cpp$$ is an example and test of this routine. $end ----------------------------------------------------------------------- */ // For some unknown reason under Fedora (which needs to be understood), // if you move this include for cppad_assert.hpp below include for define.hpp, // cd work/speed/example // make test.sh // fails with the error message 'gettimeofday' not defined. # include // define CPPAD_NULL # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include # if CPPAD_USE_CPLUSPLUS_2011 # include # elif _MSC_VER extern double microsoft_timer(void); # elif CPPAD_HAS_GETTIMEOFDAY # include # else # include # endif namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file elapsed_seconds.hpp \brief Function that returns the elapsed seconds from first call. */ /*! Returns the elapsed number since the first call to this function. This routine tries is accurate to within .02 seconds. It does not necessary work for time intervals that are less than a day. \li If running under the Microsoft system, it uses \c ::%GetSystemTime for timing. \li Otherwise, if \c gettimeofday is available, it is used. \li Otherwise, \c std::clock() is used. \return The number of seconds since the first call to \c elapsed_seconds. */ inline double elapsed_seconds(void) // -------------------------------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static bool first_ = true; static std::chrono::time_point start_; if( first_ ) { start_ = std::chrono::steady_clock::now(); first_ = false; return 0.0; } std::chrono::time_point now; now = std::chrono::steady_clock::now(); std::chrono::duration difference = now - start_; return difference.count(); } // -------------------------------------------------------------------------- # elif _MSC_VER { return microsoft_timer(); } // -------------------------------------------------------------------------- # elif CPPAD_HAS_GETTIMEOFDAY { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static bool first_ = true; static struct timeval tv_; struct timeval tv; if( first_ ) { gettimeofday(&tv_, CPPAD_NULL); first_ = false; return 0.; } gettimeofday(&tv, CPPAD_NULL); assert( tv.tv_sec >= tv_.tv_sec ); double sec = double(tv.tv_sec - tv_.tv_sec); double usec = double(tv.tv_usec) - double(tv_.tv_usec); double diff = sec + 1e-6*usec; return diff; } // -------------------------------------------------------------------------- # else // Not CPPAD_USE_CPLUSPLUS_2011 or CPPAD_HAS_GETTIMEOFDAY { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static bool first_ = true; static double tic_; double tic; if( first_ ) { tic_ = double(std::clock()); first_ = false; return 0.; } tic = double( std::clock() ); double diff = (tic - tic_) / double(CLOCKS_PER_SEC); return diff; } # endif // -------------------------------------------------------------------------- } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/utility/rosen_34.hpp0000644000175200017650000003201113057470465017371 0ustar coincoin-web// $Id: rosen_34.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_ROSEN_34_HPP # define CPPAD_UTILITY_ROSEN_34_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Rosen34$$ $spell cppad.hpp bool xf templated const Rosenbrock CppAD xi ti tf Karp Rosen Shampine ind dep $$ $section A 3rd and 4th Order Rosenbrock ODE Solver$$ $mindex Rosen34 solve stiff differential equation$$ $head Syntax$$ $codei%# include %$$ $icode%xf% = Rosen34(%F%, %M%, %ti%, %tf%, %xi%) %$$ $icode%xf% = Rosen34(%F%, %M%, %ti%, %tf%, %xi%, %e%) %$$ $head Description$$ This is an embedded 3rd and 4th order Rosenbrock ODE solver (see Section 16.6 of $cref/Numerical Recipes/Bib/Numerical Recipes/$$ for a description of Rosenbrock ODE solvers). In particular, we use the formulas taken from page 100 of $cref/Shampine, L.F./Bib/Shampine, L.F./$$ (except that the fraction 98/108 has been correction to be 97/108). $pre $$ We use $latex n$$ for the size of the vector $icode xi$$. Let $latex \B{R}$$ denote the real numbers and let $latex F : \B{R} \times \B{R}^n \rightarrow \B{R}^n$$ be a smooth function. The return value $icode xf$$ contains a 5th order approximation for the value $latex X(tf)$$ where $latex X : [ti , tf] \rightarrow \B{R}^n$$ is defined by the following initial value problem: $latex \[ \begin{array}{rcl} X(ti) & = & xi \\ X'(t) & = & F[t , X(t)] \end{array} \] $$ If your set of ordinary differential equations are not stiff an explicit method may be better (perhaps $cref Runge45$$.) $head Include$$ The file $code cppad/rosen_34.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head xf$$ The return value $icode xf$$ has the prototype $codei% %Vector% %xf% %$$ and the size of $icode xf$$ is equal to $icode n$$ (see description of $cref/Vector/Rosen34/Vector/$$ below). $latex \[ X(tf) = xf + O( h^5 ) \] $$ where $latex h = (tf - ti) / M$$ is the step size. If $icode xf$$ contains not a number $cref nan$$, see the discussion of $cref/f/Rosen34/Fun/Nan/$$. $head Fun$$ The class $icode Fun$$ and the object $icode F$$ satisfy the prototype $codei% %Fun% &%F% %$$ This must support the following set of calls $codei% %F%.Ode(%t%, %x%, %f%) %F%.Ode_ind(%t%, %x%, %f_t%) %F%.Ode_dep(%t%, %x%, %f_x%) %$$ $subhead t$$ In all three cases, the argument $icode t$$ has prototype $codei% const %Scalar% &%t% %$$ (see description of $cref/Scalar/Rosen34/Scalar/$$ below). $subhead x$$ In all three cases, the argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ and has size $icode n$$ (see description of $cref/Vector/Rosen34/Vector/$$ below). $subhead f$$ The argument $icode f$$ to $icode%F%.Ode%$$ has prototype $codei% %Vector% &%f% %$$ On input and output, $icode f$$ is a vector of size $icode n$$ and the input values of the elements of $icode f$$ do not matter. On output, $icode f$$ is set equal to $latex F(t, x)$$ (see $icode F(t, x)$$ in $cref/Description/Rosen34/Description/$$). $subhead f_t$$ The argument $icode f_t$$ to $icode%F%.Ode_ind%$$ has prototype $codei% %Vector% &%f_t% %$$ On input and output, $icode f_t$$ is a vector of size $icode n$$ and the input values of the elements of $icode f_t$$ do not matter. On output, the $th i$$ element of $icode f_t$$ is set equal to $latex \partial_t F_i (t, x)$$ (see $icode F(t, x)$$ in $cref/Description/Rosen34/Description/$$). $subhead f_x$$ The argument $icode f_x$$ to $icode%F%.Ode_dep%$$ has prototype $codei% %Vector% &%f_x% %$$ On input and output, $icode f_x$$ is a vector of size $icode%n%*%n%$$ and the input values of the elements of $icode f_x$$ do not matter. On output, the [$icode%i%*%n%+%j%$$] element of $icode f_x$$ is set equal to $latex \partial_{x(j)} F_i (t, x)$$ (see $icode F(t, x)$$ in $cref/Description/Rosen34/Description/$$). $subhead Nan$$ If any of the elements of $icode f$$, $icode f_t$$, or $icode f_x$$ have the value not a number $code nan$$, the routine $code Rosen34$$ returns with all the elements of $icode xf$$ and $icode e$$ equal to $code nan$$. $subhead Warning$$ The arguments $icode f$$, $icode f_t$$, and $icode f_x$$ must have a call by reference in their prototypes; i.e., do not forget the $code &$$ in the prototype for $icode f$$, $icode f_t$$ and $icode f_x$$. $subhead Optimization$$ Every call of the form $codei% %F%.Ode_ind(%t%, %x%, %f_t%) %$$ is directly followed by a call of the form $codei% %F%.Ode_dep(%t%, %x%, %f_x%) %$$ where the arguments $icode t$$ and $icode x$$ have not changed between calls. In many cases it is faster to compute the values of $icode f_t$$ and $icode f_x$$ together and then pass them back one at a time. $head M$$ The argument $icode M$$ has prototype $codei% size_t %M% %$$ It specifies the number of steps to use when solving the differential equation. This must be greater than or equal one. The step size is given by $latex h = (tf - ti) / M$$, thus the larger $icode M$$, the more accurate the return value $icode xf$$ is as an approximation for $latex X(tf)$$. $head ti$$ The argument $icode ti$$ has prototype $codei% const %Scalar% &%ti% %$$ (see description of $cref/Scalar/Rosen34/Scalar/$$ below). It specifies the initial time for $icode t$$ in the differential equation; i.e., the time corresponding to the value $icode xi$$. $head tf$$ The argument $icode tf$$ has prototype $codei% const %Scalar% &%tf% %$$ It specifies the final time for $icode t$$ in the differential equation; i.e., the time corresponding to the value $icode xf$$. $head xi$$ The argument $icode xi$$ has the prototype $codei% const %Vector% &%xi% %$$ and the size of $icode xi$$ is equal to $icode n$$. It specifies the value of $latex X(ti)$$ $head e$$ The argument $icode e$$ is optional and has the prototype $codei% %Vector% &%e% %$$ If $icode e$$ is present, the size of $icode e$$ must be equal to $icode n$$. The input value of the elements of $icode e$$ does not matter. On output it contains an element by element estimated bound for the absolute value of the error in $icode xf$$ $latex \[ e = O( h^4 ) \] $$ where $latex h = (tf - ti) / M$$ is the step size. $head Scalar$$ The type $icode Scalar$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, the following operations must be defined for $icode Scalar$$ objects $icode a$$ and $icode b$$: $table $bold Operation$$ $cnext $bold Description$$ $rnext $icode%a% < %b%$$ $cnext less than operator (returns a $code bool$$ object) $tend $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type Scalar/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Parallel Mode$$ For each set of types $cref/Scalar/Rosen34/Scalar/$$, $cref/Vector/Rosen34/Vector/$$, and $cref/Fun/Rosen34/Fun/$$, the first call to $code Rosen34$$ must not be $cref/parallel/ta_in_parallel/$$ execution mode. $head Example$$ $children% example/rosen_34.cpp %$$ The file $cref rosen_34.cpp$$ contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise. $head Source Code$$ The source code for this routine is in the file $code cppad/rosen_34.hpp$$. $end -------------------------------------------------------------------------- */ # include # include # include # include # include # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { // BEGIN CppAD namespace template Vector Rosen34( Fun &F , size_t M , const Scalar &ti , const Scalar &tf , const Vector &xi ) { Vector e( xi.size() ); return Rosen34(F, M, ti, tf, xi, e); } template Vector Rosen34( Fun &F , size_t M , const Scalar &ti , const Scalar &tf , const Vector &xi , Vector &e ) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; // check numeric type specifications CheckNumericType(); // check simple vector class specifications CheckSimpleVector(); // Parameters for Shampine's Rosenbrock method // are static to avoid recalculation on each call and // do not use Vector to avoid possible memory leak static Scalar a[3] = { Scalar(0), Scalar(1), Scalar(3) / Scalar(5) }; static Scalar b[2 * 2] = { Scalar(1), Scalar(0), Scalar(24) / Scalar(25), Scalar(3) / Scalar(25) }; static Scalar ct[4] = { Scalar(1) / Scalar(2), - Scalar(3) / Scalar(2), Scalar(121) / Scalar(50), Scalar(29) / Scalar(250) }; static Scalar cg[3 * 3] = { - Scalar(4), Scalar(0), Scalar(0), Scalar(186) / Scalar(25), Scalar(6) / Scalar(5), Scalar(0), - Scalar(56) / Scalar(125), - Scalar(27) / Scalar(125), - Scalar(1) / Scalar(5) }; static Scalar d3[3] = { Scalar(97) / Scalar(108), Scalar(11) / Scalar(72), Scalar(25) / Scalar(216) }; static Scalar d4[4] = { Scalar(19) / Scalar(18), Scalar(1) / Scalar(4), Scalar(25) / Scalar(216), Scalar(125) / Scalar(216) }; CPPAD_ASSERT_KNOWN( M >= 1, "Error in Rosen34: the number of steps is less than one" ); CPPAD_ASSERT_KNOWN( e.size() == xi.size(), "Error in Rosen34: size of e not equal to size of xi" ); size_t i, j, k, l, m; // indices size_t n = xi.size(); // number of components in X(t) Scalar ns = Scalar(double(M)); // number of steps as Scalar object Scalar h = (tf - ti) / ns; // step size Scalar zero = Scalar(0); // some constants Scalar one = Scalar(1); Scalar two = Scalar(2); // permutation vectors needed for LU factorization routine CppAD::vector ip(n), jp(n); // vectors used to store values returned by F Vector E(n * n), Eg(n), f_t(n); Vector g(n * 3), x3(n), x4(n), xf(n), ftmp(n), xtmp(n), nan_vec(n); // initialize e = 0, nan_vec = nan for(i = 0; i < n; i++) { e[i] = zero; nan_vec[i] = nan(zero); } xf = xi; // initialize solution for(m = 0; m < M; m++) { // time at beginning of this interval Scalar t = ti * (Scalar(int(M - m)) / ns) + tf * (Scalar(int(m)) / ns); // value of x at beginning of this interval x3 = x4 = xf; // evaluate partial derivatives at beginning of this interval F.Ode_ind(t, xf, f_t); F.Ode_dep(t, xf, E); // E = f_x if( hasnan(f_t) || hasnan(E) ) { e = nan_vec; return nan_vec; } // E = I - f_x * h / 2 for(i = 0; i < n; i++) { for(j = 0; j < n; j++) E[i * n + j] = - E[i * n + j] * h / two; E[i * n + i] += one; } // LU factor the matrix E # ifndef NDEBUG int sign = LuFactor(ip, jp, E); # else LuFactor(ip, jp, E); # endif CPPAD_ASSERT_KNOWN( sign != 0, "Error in Rosen34: I - f_x * h / 2 not invertible" ); // loop over integration steps for(k = 0; k < 3; k++) { // set location for next function evaluation xtmp = xf; for(l = 0; l < k; l++) { // loop over previous function evaluations Scalar bkl = b[(k-1)*2 + l]; for(i = 0; i < n; i++) { // loop over elements of x xtmp[i] += bkl * g[i*3 + l] * h; } } // ftmp = F(t + a[k] * h, xtmp) F.Ode(t + a[k] * h, xtmp, ftmp); if( hasnan(ftmp) ) { e = nan_vec; return nan_vec; } // Form Eg for this integration step for(i = 0; i < n; i++) Eg[i] = ftmp[i] + ct[k] * f_t[i] * h; for(l = 0; l < k; l++) { for(i = 0; i < n; i++) Eg[i] += cg[(k-1)*3 + l] * g[i*3 + l]; } // Solve the equation E * g = Eg LuInvert(ip, jp, E, Eg); // save solution and advance x3, x4 for(i = 0; i < n; i++) { g[i*3 + k] = Eg[i]; x3[i] += h * d3[k] * Eg[i]; x4[i] += h * d4[k] * Eg[i]; } } // Form Eg for last update to x4 only for(i = 0; i < n; i++) Eg[i] = ftmp[i] + ct[3] * f_t[i] * h; for(l = 0; l < 3; l++) { for(i = 0; i < n; i++) Eg[i] += cg[2*3 + l] * g[i*3 + l]; } // Solve the equation E * g = Eg LuInvert(ip, jp, E, Eg); // advance x4 and accumulate error bound for(i = 0; i < n; i++) { x4[i] += h * d4[3] * Eg[i]; // cant use abs because cppad.hpp may not be included Scalar diff = x4[i] - x3[i]; if( diff < zero ) e[i] -= diff; else e[i] += diff; } // advance xf for this step using x4 xf = x4; } return xf; } } // End CppAD namespace # endif cppad-20170000.3/cppad/utility/time_test.hpp0000644000175200017650000001374613057470465017750 0ustar coincoin-web// $Id: time_test.hpp 3855 2016-12-19 00:30:54Z bradbell $ # ifndef CPPAD_UTILITY_TIME_TEST_HPP # define CPPAD_UTILITY_TIME_TEST_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin time_test$$ $spell gettimeofday vec cppad.hpp Microsoft namespace std const cout ctime ifdef const endif cpp $$ $section Determine Amount of Time to Execute a Test$$ $mindex time_test speed$$ $head Syntax$$ $codei%# include %$$ $icode%time% = time_test(%test%, %time_min%) %$$ $icode%time% = time_test(%test%, %time_min%, %test_size%)%$$ $head Purpose$$ The $code time_test$$ function executes a timing test and reports the amount of wall clock time for execution. $head Motivation$$ It is important to separate small calculation units and test them individually. This way individual changes can be tested in the context of the routine that they are in. On many machines, accurate timing of a very short execution sequences is not possible. In addition, there may be set up and tear down time for a test that we do not really want included in the timing. For this reason $code time_test$$ automatically determines how many times to repeat the section of the test that we wish to time. $head Include$$ The file $code cppad/time_test.hpp$$ defines the $code time_test$$ function. This file is included by $code cppad/cppad.hpp$$ and it can also be included separately with out the rest of the $code CppAD$$ routines. $head test$$ The $code time_test$$ argument $icode test$$ is a function, or function object. In the case where $icode test_size$$ is not present, $icode test$$ supports the syntax $codei% %test%(%repeat%) %$$ In the case where $icode test_size$$ is present, $icode test$$ supports the syntax $codei% %test%(%size%, %repeat%) %$$ In either case, the return value for $icode test$$ is $code void$$. $subhead size$$ If the argument $icode size$$ is present, it has prototype $codei% size_t %size% %$$ and is equal to the $icode test_size$$ argument to $code time_test$$. $subhead repeat$$ The $icode test$$ argument $icode repeat$$ has prototype $codei% size_t %repeat% %$$ It will be equal to the $icode size$$ argument to $code time_test$$. $head time_min$$ The argument $icode time_min$$ has prototype $codei% double %time_min% %$$ It specifies the minimum amount of time in seconds that the $icode test$$ routine should take. The $icode repeat$$ argument to $icode test$$ is increased until this amount of execution time (or more) is reached. $head test_size$$ This argument has prototype $codei% size_t %test_size% %$$ It specifies the $icode size$$ argument to $icode test$$. $head time$$ The return value $icode time$$ has prototype $codei% double %time% %$$ and is the number of wall clock seconds that it took to execute $icode test$$ divided by the value used for $icode repeat$$. $head Timing$$ The routine $cref elapsed_seconds$$ will be used to determine the amount of time it took to execute the test. $children% cppad/utility/elapsed_seconds.hpp% speed/example/time_test.cpp %$$ $head Example$$ The routine $cref time_test.cpp$$ is an example and test of $code time_test$$. $end ----------------------------------------------------------------------- */ # include # include # include # include # include # define CPPAD_EXTRA_RUN_BEFORE_TIMING 0 namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file time_test.hpp \brief Function that preforms one timing test (for speed of execution). */ /*! Preform one wall clock execution timing test. \tparam Test Either the type void (*)(size_t) or a function object type that supports the same syntax. \param test The function, or function object, that supports the operation test(repeat) where \c repeat is the number of times to repeat the tests operaiton that is being timed. \param time_min is the minimum amount of time that \c test should take to preform the repetitions of the operation being timed. */ template double time_test(Test test, double time_min ) { # if CPPAD_EXTRA_RUN_BEFORE_TIMING test(1); # endif size_t repeat = 0; double s0 = elapsed_seconds(); double s1 = s0; while( s1 - s0 < time_min ) { repeat = std::max(size_t(1), 2 * repeat); s0 = elapsed_seconds(); test(repeat); s1 = elapsed_seconds(); } double time = (s1 - s0) / double(repeat); return time; } /*! Preform one wall clock execution timing test. \tparam Test Either the type void (*)(size_t, size_t) or a function object type that supports the same syntax. \param test The function, or function object, that supports the operation test(size, repeat) where \c is the size for this test and \c repeat is the number of times to repeat the tests operaiton that is being timed. \param time_min is the minimum amount of time that \c test should take to preform the repetitions of the operation being timed. \param test_size will be used for the value of \c size in the call to \c test. */ template double time_test(Test test, double time_min, size_t test_size) { # if CPPAD_EXTRA_RUN_BEFORE_TIMING test(test_size, 1); # endif size_t repeat = 0; double s0 = elapsed_seconds(); double s1 = s0; while( s1 - s0 < time_min ) { repeat = std::max(size_t(1), 2 * repeat); s0 = elapsed_seconds(); test(test_size, repeat); s1 = elapsed_seconds(); } double time = (s1 - s0) / double(repeat); return time; } } // END_CPPAD_NAMESPACE # undef CPPAD_EXTRA_RUN_BEFORE_TIMING // END PROGRAM # endif cppad-20170000.3/cppad/utility/romberg_one.hpp0000644000175200017650000001226313057470465020242 0ustar coincoin-web// $Id: romberg_one.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_UTILITY_ROMBERG_ONE_HPP # define CPPAD_UTILITY_ROMBERG_ONE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin RombergOne$$ $spell cppad.hpp bool const Cpp RombergOne $$ $section One DimensionalRomberg Integration$$ $mindex integrate Romberg$$ $head Syntax$$ $codei%# include %$$ $icode%r% = RombergOne(%F%, %a%, %b%, %n%, %e%)%$$ $head Description$$ Returns the Romberg integration estimate $latex r$$ for a one dimensional integral $latex \[ r = \int_a^b F(x) {\bf d} x + O \left[ (b - a) / 2^{n-1} \right]^{2(p+1)} \] $$ $head Include$$ The file $code cppad/romberg_one.hpp$$ is included by $code cppad/cppad.hpp$$ but it can also be included separately with out the rest of the $code CppAD$$ routines. $head r$$ The return value $icode r$$ has prototype $codei% %Float% %r% %$$ It is the estimate computed by $code RombergOne$$ for the integral above. $head F$$ The object $icode F$$ can be of any type, but it must support the operation $codei% %F%(%x%) %$$ The argument $icode x$$ to $icode F$$ has prototype $codei% const %Float% &%x% %$$ The return value of $icode F$$ is a $icode Float$$ object (see description of $cref/Float/RombergOne/Float/$$ below). $head a$$ The argument $icode a$$ has prototype $codei% const %Float% &%a% %$$ It specifies the lower limit for the integration. $head b$$ The argument $icode b$$ has prototype $codei% const %Float% &%b% %$$ It specifies the upper limit for the integration. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ A total number of $latex 2^{n-1} + 1$$ evaluations of $icode%F%(%x%)%$$ are used to estimate the integral. $head p$$ The argument $icode p$$ has prototype $codei% size_t %p% %$$ It must be less than or equal $latex n$$ and determines the accuracy order in the approximation for the integral that is returned by $code RombergOne$$. To be specific $latex \[ r = \int_a^b F(x) {\bf d} x + O \left[ (b - a) / 2^{n-1} \right]^{2(p+1)} \] $$ $head e$$ The argument $icode e$$ has prototype $codei% %Float% &%e% %$$ The input value of $icode e$$ does not matter and its output value is an approximation for the error in the integral estimates; i.e., $latex \[ e \approx \left| r - \int_a^b F(x) {\bf d} x \right| \] $$ $head Float$$ The type $icode Float$$ must satisfy the conditions for a $cref NumericType$$ type. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. In addition, if $icode x$$ and $icode y$$ are $icode Float$$ objects, $codei% %x% < %y% %$$ returns the $code bool$$ value true if $icode x$$ is less than $icode y$$ and false otherwise. $children% example/romberg_one.cpp %$$ $head Example$$ $comment% example/romberg_one.cpp %$$ The file $cref romberg_one.cpp$$ contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise. $head Source Code$$ The source code for this routine is in the file $code cppad/romberg_one.hpp$$. $end */ # include # include # include namespace CppAD { // BEGIN CppAD namespace template Float RombergOne( Fun &F , const Float &a , const Float &b , size_t n , size_t p , Float &e ) { size_t ipow2 = 1; size_t k, i; Float pow2, sum, x; Float zero = Float(0); Float two = Float(2); // check specifications for a NumericType CheckNumericType(); CPPAD_ASSERT_KNOWN( n >= 2, "RombergOne: n must be greater than or equal 2" ); CppAD::vector r(n); // set r[i] = trapazoidal rule with 2^i intervals in [a, b] r[0] = ( F(a) + F(b) ) * (b - a) / two; for(i = 1; i < n; i++) { ipow2 *= 2; // there must be a conversion from int to any numeric type pow2 = Float(int(ipow2)); sum = zero; for(k = 1; k < ipow2; k += 2) { // start = a + (b-a)/pow2, increment = 2*(b-a)/pow2 x = ( (pow2 - Float(int(k))) * a + k * b ) / pow2; sum = sum + F(x); } // combine function evaluations in sum with those in T[i-1] r[i] = r[i-1] / two + sum * (b - a) / pow2; } // now compute the higher order estimates size_t ipow4 = 1; // order of accuract for previous estimate Float pow4, pow4minus; for(i = 0; i < p; i++) { // compute estimate accurate to O[ step^(2*(i+1)) ] // put resutls in r[n-1], r[n-2], ... , r[n-i+1] ipow4 *= 4; pow4 = Float(int(ipow4)); pow4minus = Float(ipow4-1); for(k = n-1; k > i; k--) r[k] = ( pow4 * r[k] - r[k-1] ) / pow4minus; } // error estimate for r[n] e = r[n-1] - r[n-2]; if( e < zero ) e = - e; return r[n-1]; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/0002755000175200017650000000000013057470466014457 5ustar coincoin-webcppad-20170000.3/cppad/core/user_ad.hpp0000644000175200017650000000372313057470465016614 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_USER_AD_HPP # define CPPAD_CORE_USER_AD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* --------------------------------------------------------------------------- $begin AD$$ $spell std bool cos Cpp $$ $section AD Objects$$ $mindex require$$ $head Purpose$$ The sections listed below describe the operations that are available to $cref/AD of Base/glossary/AD of Base/$$ objects. These objects are used to $cref/tape/glossary/Tape/$$ an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. This operation sequence can be transferred to an $cref ADFun$$ object where it can be used to evaluate the corresponding function and derivative values. $head Base Type Requirements$$ The $icode Base$$ requirements are provided by the CppAD package for the following base types: $code float$$, $code double$$, $code std::complex$$, $code std::complex$$. Otherwise, see $cref base_require$$. $childtable% cppad/core/ad_ctor.hpp% cppad/core/ad_assign.hpp% cppad/core/convert.hpp% cppad/core/ad_valued.hpp% cppad/core/bool_valued.hpp% cppad/core/vec_ad.hpp% cppad/base_require.hpp %$$ $end --------------------------------------------------------------------------- */ # include # include # include # include # include # include # include # endif cppad-20170000.3/cppad/core/near_equal_ext.hpp0000644000175200017650000001166413057470465020171 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_NEAR_EQUAL_EXT_HPP # define CPPAD_CORE_NEAR_EQUAL_EXT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin NearEqualExt$$ $spell cout endl Microsoft std Cpp namespace const bool $$ $section Compare AD and Base Objects for Nearly Equal$$ $mindex NearEqual with$$ $head Syntax$$ $icode%b% = NearEqual(%x%, %y%, %r%, %a%)%$$ $head Purpose$$ The routine $cref NearEqual$$ determines if two objects of the same type are nearly. This routine is extended to the case where one object can have type $icode Type$$ while the other can have type $codei%AD<%Type%>%$$ or $codei%AD< std::complex<%Type%> >%$$. $head x$$ The arguments $icode x$$ has one of the following possible prototypes: $codei% const %Type% &%x% const AD<%Type%> &%x% const AD< std::complex<%Type%> > &%x% %$$ $head y$$ The arguments $icode y$$ has one of the following possible prototypes: $codei% const %Type% &%y% const AD<%Type%> &%y% const AD< std::complex<%Type%> > &%x% %$$ $head r$$ The relative error criteria $icode r$$ has prototype $codei% const %Type% &%r% %$$ It must be greater than or equal to zero. The relative error condition is defined as: $latex \[ \frac{ | x - y | } { |x| + |y| } \leq r \] $$ $head a$$ The absolute error criteria $icode a$$ has prototype $codei% const %Type% &%a% %$$ It must be greater than or equal to zero. The absolute error condition is defined as: $latex \[ | x - y | \leq a \] $$ $head b$$ The return value $icode b$$ has prototype $codei% bool %b% %$$ If either $icode x$$ or $icode y$$ is infinite or not a number, the return value is false. Otherwise, if either the relative or absolute error condition (defined above) is satisfied, the return value is true. Otherwise, the return value is false. $head Type$$ The type $icode Type$$ must be a $cref NumericType$$. The routine $cref CheckNumericType$$ will generate an error message if this is not the case. If $icode a$$ and $icode b$$ have type $icode Type$$, the following operation must be defined $table $bold Operation$$ $cnext $bold Description$$ $rnext $icode%a% <= %b%$$ $cnext less that or equal operator (returns a $code bool$$ object) $tend $head Operation Sequence$$ The result of this operation is not an $cref/AD of Base/glossary/AD of Base/$$ object. Thus it will not be recorded as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Example$$ $children% example/near_equal_ext.cpp %$$ The file $cref near_equal_ext.cpp$$ contains an example and test of this extension of $cref NearEqual$$. It return true if it succeeds and false otherwise. $end */ // BEGIN CppAD namespace namespace CppAD { // ------------------------------------------------------------------------ // fold into base type and then use template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool NearEqual( const AD &x, const AD &y, const Base &r, const Base &a) { return NearEqual(x.value_, y.value_, r, a); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool NearEqual( const Base &x, const AD &y, const Base &r, const Base &a) { return NearEqual(x, y.value_, r, a); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool NearEqual( const AD &x, const Base &y, const Base &r, const Base &a) { return NearEqual(x.value_, y, r, a); } // fold into AD type and then use cases above template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool NearEqual( const VecAD_reference &x, const VecAD_reference &y, const Base &r, const Base &a) { return NearEqual(x.ADBase(), y.ADBase(), r, a); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool NearEqual(const VecAD_reference &x, const AD &y, const Base &r, const Base &a) { return NearEqual(x.ADBase(), y, r, a); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool NearEqual(const VecAD_reference &x, const Base &y, const Base &r, const Base &a) { return NearEqual(x.ADBase(), y, r, a); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool NearEqual(const AD &x, const VecAD_reference &y, const Base &r, const Base &a) { return NearEqual(x, y.ADBase(), r, a); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool NearEqual(const Base &x, const VecAD_reference &y, const Base &r, const Base &a) { return NearEqual(x, y.ADBase(), r, a); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/num_skip.hpp0000644000175200017650000000711113057470465017012 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_NUM_SKIP_HPP # define CPPAD_CORE_NUM_SKIP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin number_skip$$ $spell optimizer var taylor_ $$ $section Number of Variables that Can be Skipped$$ $mindex number_skip$$ $head Syntax$$ $icode%n% = %f%.number_skip()%$$ $subhead See Also$$ $cref seq_property$$ $head Purpose$$ The $cref/conditional expressions/CondExp/$$ use either the $cref/if_true/CondExp/$$ or $cref/if_false/CondExp/$$. Hence, some terms only need to be evaluated depending on the value of the comparison in the conditional expression. The $cref optimize$$ option is capable of detecting some of these case and determining variables that can be skipped. This routine returns the number such variables. $head n$$ The return value $icode n$$ has type $code size_t$$ is the number of variables that the optimizer has determined can be skipped (given the independent variable values specified by the previous call to $cref/f.Forward/Forward/$$ for order zero). $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ $children% example/number_skip.cpp %$$ $head Example$$ The file $cref number_skip.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ----------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { // This routine is not const because it runs through the operations sequence // 2DO: compute this value during zero order forward operations. template size_t ADFun::number_skip(void) { // must pass through operation sequence to map operations to variables local::OpCode op; size_t i_op; size_t i_var; const addr_t* arg; // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; local::enum_user_state user_state; // number of variables skipped size_t num_var_skip = 0; // start playback user_state = local::start_user; play_.forward_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN(op == local::BeginOp) while(op != local::EndOp) { // next op play_.forward_next(op, arg, i_op, i_var); // if( op == local::UserOp ) { // skip only appears at front or back UserOp of user atomic call bool skip_call = cskip_op_[i_op]; CPPAD_ASSERT_UNKNOWN( user_state == local::start_user ); play_.forward_user( op, user_state, user_old, user_m, user_n, user_i, user_j ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); size_t num_op = user_m + user_n + 1; for(size_t i = 0; i < num_op; i++) { play_.forward_next(op, arg, i_op, i_var); play_.forward_user( op, user_state, user_old, user_m, user_n, user_i, user_j ); if( skip_call ) num_var_skip += NumRes(op); } CPPAD_ASSERT_UNKNOWN( user_state == local::start_user ); } else { if( op == local::CSumOp) play_.forward_csum(op, arg, i_op, i_var); else if (op == local::CSkipOp) play_.forward_cskip(op, arg, i_op, i_var); // if( cskip_op_[i_op] ) num_var_skip += NumRes(op); } } return num_var_skip; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/base_float.hpp0000644000175200017650000001233613057470465017271 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BASE_FLOAT_HPP # define CPPAD_CORE_BASE_FLOAT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include /* $begin base_float.hpp$$ $spell namespaces cppad hpp azmul expm1 atanh acosh asinh erf endif abs_geq acos asin atan cos sqrt tanh std fabs bool Lt Le Eq Ge Gt Rel CppAD CondExpOp namespace inline enum const exp const $$ $section Enable use of AD where Base is float$$ $head CondExpOp$$ The type $code float$$ is a relatively simple type that supports $code <$$, $code <=$$, $code ==$$, $code >=$$, and $code >$$ operators; see $cref/ordered type/base_cond_exp/CondExpTemplate/Ordered Type/$$. Hence its $code CondExpOp$$ function is defined by $srccode%cpp% */ namespace CppAD { inline float CondExpOp( enum CompareOp cop , const float& left , const float& right , const float& exp_if_true , const float& exp_if_false ) { return CondExpTemplate(cop, left, right, exp_if_true, exp_if_false); } } /* %$$ $head CondExpRel$$ The $cref/CPPAD_COND_EXP_REL/base_cond_exp/CondExpRel/$$ macro invocation $srccode%cpp% */ namespace CppAD { CPPAD_COND_EXP_REL(float) } /* %$$ uses $code CondExpOp$$ above to define $codei%CondExp%Rel%$$ for $code float$$ arguments and $icode%Rel%$$ equal to $code Lt$$, $code Le$$, $code Eq$$, $code Ge$$, and $code Gt$$. $head EqualOpSeq$$ The type $code float$$ is simple (in this respect) and so we define $srccode%cpp% */ namespace CppAD { inline bool EqualOpSeq(const float& x, const float& y) { return x == y; } } /* %$$ $head Identical$$ The type $code float$$ is simple (in this respect) and so we define $srccode%cpp% */ namespace CppAD { inline bool IdenticalPar(const float& x) { return true; } inline bool IdenticalZero(const float& x) { return (x == 0.f); } inline bool IdenticalOne(const float& x) { return (x == 1.f); } inline bool IdenticalEqualPar(const float& x, const float& y) { return (x == y); } } /* %$$ $head Integer$$ $srccode%cpp% */ namespace CppAD { inline int Integer(const float& x) { return static_cast(x); } } /* %$$ $head azmul$$ $srccode%cpp% */ namespace CppAD { CPPAD_AZMUL( float ) } /* %$$ $head Ordered$$ The $code float$$ type supports ordered comparisons $srccode%cpp% */ namespace CppAD { inline bool GreaterThanZero(const float& x) { return x > 0.f; } inline bool GreaterThanOrZero(const float& x) { return x >= 0.f; } inline bool LessThanZero(const float& x) { return x < 0.f; } inline bool LessThanOrZero(const float& x) { return x <= 0.f; } inline bool abs_geq(const float& x, const float& y) { return std::fabs(x) >= std::fabs(y); } } /* %$$ $head Unary Standard Math$$ The following macro invocations import the $code float$$ versions of the unary standard math functions into the $code CppAD$$ namespace. Importing avoids ambiguity errors when using both the $code CppAD$$ and $code std$$ namespaces. Note this also defines the $cref/double/base_double.hpp/Unary Standard Math/$$ versions of these functions. $srccode%cpp% */ namespace CppAD { using std::acos; using std::asin; using std::atan; using std::cos; using std::cosh; using std::exp; using std::fabs; using std::log; using std::log10; using std::sin; using std::sinh; using std::sqrt; using std::tan; using std::tanh; # if CPPAD_USE_CPLUSPLUS_2011 using std::erf; using std::asinh; using std::acosh; using std::atanh; using std::expm1; using std::log1p; # endif } /* %$$ The absolute value function is special because its $code std$$ name is $code fabs$$ $srccode%cpp% */ namespace CppAD { inline float abs(const float& x) { return std::fabs(x); } } /* %$$ $head sign$$ The following defines the $code CppAD::sign$$ function that is required to use $code AD$$: $srccode%cpp% */ namespace CppAD { inline float sign(const float& x) { if( x > 0.f ) return 1.f; if( x == 0.f ) return 0.f; return -1.f; } } /* %$$ $head pow$$ The following defines a $code CppAD::pow$$ function that is required to use $code AD$$. As with the unary standard math functions, this has the exact same signature as $code std::pow$$, so use it instead of defining another function. $srccode%cpp% */ namespace CppAD { using std::pow; } /* %$$ $head numeric_limits$$ The following defines the CppAD $cref numeric_limits$$ for the type $code float$$: $srccode%cpp% */ namespace CppAD { CPPAD_NUMERIC_LIMITS(float, float) } /* %$$ $head to_string$$ There is no need to define $code to_string$$ for $code float$$ because it is defined by including $code cppad/utility/to_string.hpp$$; see $cref to_string$$. See $cref/base_complex.hpp/base_complex.hpp/to_string/$$ for an example where it is necessary to define $code to_string$$ for a $icode Base$$ type. $end */ # endif cppad-20170000.3/cppad/core/log1p.hpp0000644000175200017650000000444013057470465016211 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_LOG1P_HPP # define CPPAD_CORE_LOG1P_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin log1p$$ $spell CppAD $$ $section The Logarithm of One Plus Argument: log1p$$ $head Syntax$$ $icode%y% = log1p(%x%)%$$ $head Description$$ Returns the value of the logarithm of one plus argument which is defined by $icode%y% == log(1 + %x%)%$$. $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head CPPAD_USE_CPLUSPLUS_2011$$ $subhead true$$ If this preprocessor symbol is true ($code 1$$), and $icode x$$ is an AD type, this is an $cref/atomic operation/glossary/Operation/Atomic/$$. $subhead false$$ If this preprocessor symbol is false ($code 0$$), CppAD uses the representation $latex \[ \R{log1p} (x) = \log(1 + x) \] $$ to compute this function. $head Example$$ $children% example/log1p.cpp %$$ The file $cref log1p.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ # include # if ! CPPAD_USE_CPLUSPLUS_2011 // BEGIN CppAD namespace namespace CppAD { template Type log1p_template(const Type &x) { return CppAD::log(Type(1) + x); } inline float log1p(const float &x) { return log1p_template(x); } inline double log1p(const double &x) { return log1p_template(x); } template inline AD log1p(const AD &x) { return log1p_template(x); } template inline AD log1p(const VecAD_reference &x) { return log1p_template( x.ADBase() ); } } // END CppAD namespace # endif // CPPAD_USE_CPLUSPLUS_2011 # endif // CPPAD_LOG1P_INCLUDED cppad-20170000.3/cppad/core/parallel_ad.hpp0000644000175200017650000000715313057470465017433 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_PARALLEL_AD_HPP # define CPPAD_CORE_PARALLEL_AD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin parallel_ad$$ $spell CppAD num std $$ $section Enable AD Calculations During Parallel Mode$$ $head Syntax$$ $codei%parallel_ad<%Base%>()%$$ $head Purpose$$ The function $codei%parallel_ad<%Base%>()%$$ must be called before any $codei%AD<%Base>%$$ objects are used in $cref/parallel/ta_in_parallel/$$ mode. In addition, if this routine is called after one is done using parallel mode, it will free extra memory used to keep track of the multiple $codei%AD<%Base%>%$$ tapes required for parallel execution. $head Discussion$$ By default, for each $codei%AD<%Base%>%$$ class there is only one tape that records $cref/AD of Base/glossary/AD of Base/$$ operations. This tape is a global variable and hence it cannot be used by multiple threads at the same time. The $cref/parallel_setup/ta_parallel_setup/$$ function informs CppAD of the maximum number of threads that can be active in parallel mode. This routine does extra setup (and teardown) for the particular $icode Base$$ type. $head CheckSimpleVector$$ This routine has the side effect of calling the routines $codei% CheckSimpleVector< %Type%, CppAD::vector<%Type%> >() %$$ where $icode Type$$ is $icode Base$$ and $codei%AD<%Base%>%$$. $head Example$$ The files $cref team_openmp.cpp$$, $cref team_bthread.cpp$$, and $cref team_pthread.cpp$$, contain examples and tests that implement this function. $head Restriction$$ This routine cannot be called in parallel mode or while there is a tape recording $codei%AD<%Base%>%$$ operations. $end ----------------------------------------------------------------------------- */ # include // BEGIN CppAD namespace namespace CppAD { /*! Enable parallel execution mode with AD by initializing static variables that my be used. */ template void parallel_ad(void) { CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "parallel_ad must be called before entering parallel execution mode." ); CPPAD_ASSERT_KNOWN( AD::tape_ptr() == CPPAD_NULL , "parallel_ad cannot be called while a tape recording is in progress" ); // ensure statics in following functions are initialized elapsed_seconds(); ErrorHandler::Current(); local::NumArg(local::BeginOp); local::NumRes(local::BeginOp); local::one_element_std_set(); local::two_element_std_set(); // the sparse_pack class has member functions with static data local::sparse_pack sp; sp.resize(1, 1); // so can call add_element sp.add_element(0, 0); // has static data sp.clear(0); // has static data sp.is_element(0, 0); // has static data local::sparse_pack::const_iterator itr(sp, 0); // has static data ++itr; // has static data // statics that depend on the value of Base AD::tape_id_handle(0); AD::tape_handle(0); AD::tape_manage(tape_manage_clear); discrete::List(); CheckSimpleVector< Base, CppAD::vector >(); CheckSimpleVector< AD, CppAD::vector< AD > >(); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/rev_two.hpp0000644000175200017650000001403213057470465016652 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_REV_TWO_HPP # define CPPAD_CORE_REV_TWO_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin RevTwo$$ $spell ddw typename Taylor const $$ $section Reverse Mode Second Partial Derivative Driver$$ $mindex order easy$$ $head Syntax$$ $icode%ddw% = %f%.RevTwo(%x%, %i%, %j%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The syntax above sets $latex \[ ddw [ k * p + \ell ] = \DD{ F_{i[ \ell ]} }{ x_{j[ \ell ]} }{ x_k } (x) \] $$ for $latex k = 0 , \ldots , n-1$$ and $latex \ell = 0 , \ldots , p$$, where $latex p$$ is the size of the vectors $icode i$$ and $icode j$$. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/RevTwo Uses Forward/RevTwo/RevTwo Uses Forward/$$ below). $head x$$ The argument $icode x$$ has prototype $codei% const %VectorBase% &%x% %$$ (see $cref/VectorBase/RevTwo/VectorBase/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies that point at which to evaluate the partial derivatives listed above. $head i$$ The argument $icode i$$ has prototype $codei% const %VectorSize_t% &%i% %$$ (see $cref/VectorSize_t/RevTwo/VectorSize_t/$$ below) We use $icode p$$ to denote the size of the vector $icode i$$. All of the indices in $icode i$$ must be less than $icode m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$; i.e., for $latex \ell = 0 , \ldots , p-1$$, $latex i[ \ell ] < m$$. $head j$$ The argument $icode j$$ has prototype $codei% const %VectorSize_t% &%j% %$$ (see $cref/VectorSize_t/RevTwo/VectorSize_t/$$ below) and its size must be equal to $icode p$$, the size of the vector $icode i$$. All of the indices in $icode j$$ must be less than $icode n$$; i.e., for $latex \ell = 0 , \ldots , p-1$$, $latex j[ \ell ] < n$$. $head ddw$$ The result $icode ddw$$ has prototype $codei% %VectorBase% %ddw% %$$ (see $cref/VectorBase/RevTwo/VectorBase/$$ below) and its size is $latex n * p$$. It contains the requested partial derivatives; to be specific, for $latex k = 0 , \ldots , n - 1 $$ and $latex \ell = 0 , \ldots , p - 1$$ $latex \[ ddw [ k * p + \ell ] = \DD{ F_{i[ \ell ]} }{ x_{j[ \ell ]} }{ x_k } (x) \] $$ $head VectorBase$$ The type $icode VectorBase$$ must be a $cref SimpleVector$$ class with $cref/elements of type Base/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head VectorSize_t$$ The type $icode VectorSize_t$$ must be a $cref SimpleVector$$ class with $cref/elements of type size_t/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head RevTwo Uses Forward$$ After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After a call to $code RevTwo$$, the zero order Taylor coefficients correspond to $icode%f%.Forward(0, %x%)%$$ and the other coefficients are unspecified. $head Examples$$ $children% example/rev_two.cpp %$$ The routine $cref/RevTwo/rev_two.cpp/$$ is both an example and test. It returns $code true$$, if it succeeds and $code false$$ otherwise. $end ----------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template template VectorBase ADFun::RevTwo( const VectorBase &x, const VectorSize_t &i, const VectorSize_t &j) { size_t i1; size_t j1; size_t k; size_t l; size_t n = Domain(); size_t m = Range(); size_t p = i.size(); // check VectorBase is Simple Vector class with Base elements CheckSimpleVector(); // check VectorSize_t is Simple Vector class with size_t elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( x.size() == n, "RevTwo: Length of x not equal domain dimension for f." ); CPPAD_ASSERT_KNOWN( i.size() == j.size(), "RevTwo: Lenght of the i and j vectors are not equal." ); // point at which we are evaluating the second partials Forward(0, x); // dimension the return value VectorBase ddw(n * p); // direction vector in argument space VectorBase dx(n); for(j1 = 0; j1 < n; j1++) dx[j1] = Base(0); // direction vector in range space VectorBase w(m); for(i1 = 0; i1 < m; i1++) w[i1] = Base(0); // place to hold the results of a reverse calculation VectorBase r(n * 2); // check the indices in i and j for(l = 0; l < p; l++) { i1 = i[l]; j1 = j[l]; CPPAD_ASSERT_KNOWN( i1 < m, "RevTwo: an eleemnt of i not less than range dimension for f." ); CPPAD_ASSERT_KNOWN( j1 < n, "RevTwo: an element of j not less than domain dimension for f." ); } // loop over all forward directions for(j1 = 0; j1 < n; j1++) { // first order forward mode calculation done bool first_done = false; for(l = 0; l < p; l++) if( j[l] == j1 ) { if( ! first_done ) { first_done = true; // first order forward mode in j1 direction dx[j1] = Base(1); Forward(1, dx); dx[j1] = Base(0); } // execute a reverse in this component direction i1 = i[l]; w[i1] = Base(1); r = Reverse(2, w); w[i1] = Base(0); // place the reverse result in return value for(k = 0; k < n; k++) ddw[k * p + l] = r[k * 2 + 1]; } } return ddw; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/test_vector.hpp0000644000175200017650000001006413057470465017527 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_TEST_VECTOR_HPP # define CPPAD_CORE_TEST_VECTOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin test_vector$$ $spell ifdef undef Microsofts CppADvector hpp std endif ublas Dir valarray stdvector $$ $section Choosing The Vector Testing Template Class$$ $mindex CPPAD_TEST_VECTOR test$$ $head Deprecated 2012-07-03$$ The $code CPPAD_TEST_VECTOR$$ macro has been deprecated, use $cref/CPPAD_TESTVECTOR/testvector/$$ instead. $head Syntax$$ $codei%CPPAD_TEST_VECTOR<%Scalar%> %$$ $head Introduction$$ Many of the CppAD $cref/examples/example/$$ and tests use the $code CPPAD_TEST_VECTOR$$ template class to pass information. The default definition for this template class is $cref/CppAD::vector/CppAD_vector/$$. $head MS Windows$$ The include path for boost is not defined in the Windows project files. If we are using Microsofts compiler, the following code overrides the setting of $code CPPAD_BOOSTVECTOR$$: $srccode%cpp% */ // The next 7 lines are C++ source code. # ifdef _MSC_VER # if CPPAD_BOOSTVECTOR # undef CPPAD_BOOSTVECTOR # define CPPAD_BOOSTVECTOR 0 # undef CPPAD_CPPADVECTOR # define CPPAD_CPPADVECTOR 1 # endif # endif /* %$$ $head CppAD::vector$$ By default $code CPPAD_CPPADVECTOR$$ is true and $code CPPAD_TEST_VECTOR$$ is defined by the following source code $srccode%cpp% */ // The next 3 line are C++ source code. # if CPPAD_CPPADVECTOR # define CPPAD_TEST_VECTOR CppAD::vector # endif /* %$$ If you specify $code --with-eigenvector$$ on the $cref/configure/auto_tools/Configure/$$ command line, $code CPPAD_EIGENVECTOR$$ is true. This vector type cannot be supported by $code CPPAD_TEST_VECTOR$$ (use $cref/CPPAD_TESTVECTOR/testvector/$$ for this support) so $code CppAD::vector$$ is used in this case $srccode%cpp% */ // The next 3 line are C++ source code. # if CPPAD_EIGENVECTOR # define CPPAD_TEST_VECTOR CppAD::vector # endif /* %$$ $head std::vector$$ If you specify $code --with-stdvector$$ on the $cref/configure/auto_tools/Configure/$$ command line during CppAD installation, $code CPPAD_STDVECTOR$$ is true and $code CPPAD_TEST_VECTOR$$ is defined by the following source code $srccode%cpp% */ // The next 4 lines are C++ source code. # if CPPAD_STDVECTOR # include # define CPPAD_TEST_VECTOR std::vector # endif /* %$$ In this case CppAD will use $code std::vector$$ for its examples and tests. Use of $code CppAD::vector$$, $code std::vector$$, and $code std::valarray$$ with CppAD is always tested to some degree. Specifying $code --with-stdvector$$ will increase the amount of $code std::vector$$ testing. $head boost::numeric::ublas::vector$$ If you specify a value for $icode boost_dir$$ on the configure command line during CppAD installation, $code CPPAD_BOOSTVECTOR$$ is true and $code CPPAD_TEST_VECTOR$$ is defined by the following source code $srccode%cpp% */ // The next 4 lines are C++ source code. # if CPPAD_BOOSTVECTOR # include # define CPPAD_TEST_VECTOR boost::numeric::ublas::vector # endif /* %$$ In this case CppAD will use Ublas vectors for its examples and tests. Use of $code CppAD::vector$$, $code std::vector$$, and $code std::valarray$$ with CppAD is always tested to some degree. Specifying $icode boost_dir$$ will increase the amount of Ublas vector testing. $head CppADvector Deprecated 2007-07-28$$ The preprocessor symbol $code CppADvector$$ is defined to have the same value as $code CPPAD_TEST_VECTOR$$ but its use is deprecated: $srccode%cpp% */ # define CppADvector CPPAD_TEST_VECTOR /* %$$ $end ------------------------------------------------------------------------ */ # endif cppad-20170000.3/cppad/core/abs.hpp0000644000175200017650000000554613057470465015744 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ABS_HPP # define CPPAD_CORE_ABS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin abs$$ $spell fabs Vec std faq Taylor Cpp namespace const abs $$ $section AD Absolute Value Functions: abs, fabs$$ $head Syntax$$ $icode%y% = abs(%x%) %$$ $icode%y% = fabs(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ In the case where $icode x$$ is an AD type, this is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Complex Types$$ The functions $code abs$$ and $icode fabs$$ are not defined for the base types $code std::complex$$ or $code std::complex$$ because the complex $code abs$$ function is not complex differentiable (see $cref/complex types faq/Faq/Complex Types/$$). $head Derivative$$ CppAD defines the derivative of the $code abs$$ function is the $cref sign$$ function; i.e., $latex \[ {\rm abs}^{(1)} ( x ) = {\rm sign} (x ) = \left\{ \begin{array}{rl} +1 & {\rm if} \; x > 0 \\ 0 & {\rm if} \; x = 0 \\ -1 & {\rm if} \; x < 0 \end{array} \right. \] $$ The result for $icode%x% == 0%$$ used to be a directional derivative. $head Example$$ $children% example/abs.cpp %$$ The file $cref abs.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD AD::abs_me (void) const { AD result; result.value_ = abs(value_); CPPAD_ASSERT_UNKNOWN( Parameter(result) ); if( Variable(*this) ) { // add this operation to the tape CPPAD_ASSERT_UNKNOWN( local::NumRes(local::AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::AbsOp) == 1 ); local::ADTape *tape = tape_this(); // corresponding operand address tape->Rec_.PutArg(taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::AbsOp); // make result a variable result.tape_id_ = tape->id_; } return result; } template inline AD abs(const AD &x) { return x.abs_me(); } template inline AD abs(const VecAD_reference &x) { return x.ADBase().abs_me(); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/base_complex.hpp0000644000175200017650000003020613057470465017627 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BASE_COMPLEX_HPP # define CPPAD_CORE_BASE_COMPLEX_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include /* $begin base_complex.hpp$$ $spell azmul expm1 atanh acosh asinh endif eps abs_geq Rel Lt Le Eq Ge Gt imag gcc isnan cppad.hpp sqrt exp cos std const CppAD Op inline enum undef acos asin atan erf Cond namespace bool $$ $section Enable use of AD where Base is std::complex$$ $children%example/complex_poly.cpp %$$ $head Example$$ The file $cref complex_poly.cpp$$ contains an example use of $code std::complex$$ type for a CppAD $icode Base$$ type. It returns true if it succeeds and false otherwise. $head Include Order$$ This file is included before $code $$ so it is necessary to define the error handler in addition to including $cref/base_require.hpp/base_require/Include Order/$$ $srccode%cpp% */ # include # include # include # include /* %$$ $head CondExpOp$$ The type $code std::complex$$ does not supports the $code <$$, $code <=$$, $code ==$$, $code >=$$, and $code >$$ operators; see $cref/not ordered/base_cond_exp/CondExpTemplate/Not Ordered/$$. Hence its $code CondExpOp$$ function is defined by $srccode%cpp% */ namespace CppAD { inline std::complex CondExpOp( enum CppAD::CompareOp cop , const std::complex &left , const std::complex &right , const std::complex &trueCase , const std::complex &falseCase ) { CppAD::ErrorHandler::Call( true , __LINE__ , __FILE__ , "std::complex CondExpOp(...)", "Error: cannot use CondExp with a complex type" ); return std::complex(0); } } /* %$$ $head CondExpRel$$ The $cref/CPPAD_COND_EXP_REL/base_cond_exp/CondExpRel/$$ macro invocation $srccode%cpp% */ namespace CppAD { CPPAD_COND_EXP_REL( std::complex ) } /* %$$ used $code CondExpOp$$ above to define $codei%CondExp%Rel%$$ for $code std::complex$$ arguments and $icode%Rel%$$ equal to $code Lt$$, $code Le$$, $code Eq$$, $code Ge$$, and $code Gt$$. $head EqualOpSeq$$ Complex numbers do not carry operation sequence information. Thus they are equal in this sense if and only if there values are equal. $srccode%cpp% */ namespace CppAD { inline bool EqualOpSeq( const std::complex &x , const std::complex &y ) { return x == y; } } /* %$$ $head Identical$$ Complex numbers do not carry operation sequence information. Thus they are all parameters so the identical functions just check values. $srccode%cpp% */ namespace CppAD { inline bool IdenticalPar(const std::complex &x) { return true; } inline bool IdenticalZero(const std::complex &x) { return (x == std::complex(0., 0.) ); } inline bool IdenticalOne(const std::complex &x) { return (x == std::complex(1., 0.) ); } inline bool IdenticalEqualPar( const std::complex &x, const std::complex &y) { return (x == y); } } /* %$$ $head Ordered$$ Complex types do not support comparison operators, $srccode%cpp% */ # undef CPPAD_USER_MACRO # define CPPAD_USER_MACRO(Fun) \ inline bool Fun(const std::complex& x) \ { CppAD::ErrorHandler::Call( \ true , __LINE__ , __FILE__ , \ #Fun"(x)", \ "Error: cannot use " #Fun " with x complex " \ ); \ return false; \ } namespace CppAD { CPPAD_USER_MACRO(LessThanZero) CPPAD_USER_MACRO(LessThanOrZero) CPPAD_USER_MACRO(GreaterThanOrZero) CPPAD_USER_MACRO(GreaterThanZero) inline bool abs_geq( const std::complex& x , const std::complex& y ) { return std::abs(x) >= std::abs(y); } } /* %$$ $head Integer$$ The implementation of this function must agree with the CppAD user specifications for complex arguments to the $cref/Integer/Integer/x/Complex Types/$$ function: $srccode%cpp% */ namespace CppAD { inline int Integer(const std::complex &x) { return static_cast( x.real() ); } } /* %$$ $head azmul$$ $srccode%cpp% */ namespace CppAD { CPPAD_AZMUL( std::complex ) } /* %$$ $head isnan$$ The gcc 4.1.1 complier defines the function $codei% int std::complex::isnan( std::complex %z% ) %$$ (which is not specified in the C++ 1998 standard ISO/IEC 14882). This causes an ambiguity between the function above and the CppAD $cref/isnan/nan/$$ template function. We avoid this ambiguity by defining a non-template version of this function in the CppAD namespace. $srccode%cpp% */ namespace CppAD { inline bool isnan(const std::complex& z) { return (z != z); } } /* %$$ $head Valid Unary Math$$ The following macro invocations define the standard unary math functions that are valid with complex arguments and are required to use $code AD< std::complex >$$. $srccode%cpp% */ namespace CppAD { CPPAD_STANDARD_MATH_UNARY(std::complex, cos) CPPAD_STANDARD_MATH_UNARY(std::complex, cosh) CPPAD_STANDARD_MATH_UNARY(std::complex, exp) CPPAD_STANDARD_MATH_UNARY(std::complex, log) CPPAD_STANDARD_MATH_UNARY(std::complex, sin) CPPAD_STANDARD_MATH_UNARY(std::complex, sinh) CPPAD_STANDARD_MATH_UNARY(std::complex, sqrt) } /* %$$ $head Invalid Unary Math$$ The following macro definition and invocations define the standard unary math functions that are invalid with complex arguments and are required to use $code AD< std::complex >$$. $srccode%cpp% */ # undef CPPAD_USER_MACRO # define CPPAD_USER_MACRO(Fun) \ inline std::complex Fun(const std::complex& x) \ { CppAD::ErrorHandler::Call( \ true , __LINE__ , __FILE__ , \ #Fun"(x)", \ "Error: cannot use " #Fun " with x complex " \ ); \ return std::complex(0); \ } namespace CppAD { CPPAD_USER_MACRO(abs) CPPAD_USER_MACRO(acos) CPPAD_USER_MACRO(asin) CPPAD_USER_MACRO(atan) CPPAD_USER_MACRO(sign) # if CPPAD_USE_CPLUSPLUS_2011 CPPAD_USER_MACRO(erf) CPPAD_USER_MACRO(asinh) CPPAD_USER_MACRO(acosh) CPPAD_USER_MACRO(atanh) CPPAD_USER_MACRO(expm1) CPPAD_USER_MACRO(log1p) # endif } /* %$$ $head pow $$ The following defines a $code CppAD::pow$$ function that is required to use $code AD< std::complex >$$: $srccode%cpp% */ namespace CppAD { inline std::complex pow( const std::complex &x , const std::complex &y ) { return std::pow(x, y); } } /* %$$ $head numeric_limits$$ The following defines the CppAD $cref numeric_limits$$ for the type $code std::complex$$: $srccode%cpp% */ namespace CppAD { CPPAD_NUMERIC_LIMITS(double, std::complex) } /* %$$ $head to_string$$ The following defines the function CppAD $cref to_string$$ for the type $code std::complex$$: $srccode%cpp% */ namespace CppAD { CPPAD_TO_STRING(std::complex) } /* %$$ $end */ # undef CPPAD_USER_MACRO_ONE # define CPPAD_USER_MACRO_ONE(Fun) \ inline bool Fun(const std::complex& x) \ { CppAD::ErrorHandler::Call( \ true , __LINE__ , __FILE__ , \ #Fun"(x)", \ "Error: cannot use " #Fun " with x complex " \ ); \ return false; \ } # undef CPPAD_USER_MACRO_TWO # define CPPAD_USER_MACRO_TWO(Fun) \ inline std::complex Fun(const std::complex& x) \ { CppAD::ErrorHandler::Call( \ true , __LINE__ , __FILE__ , \ #Fun"(x)", \ "Error: cannot use " #Fun " with x complex " \ ); \ return std::complex(0); \ } namespace CppAD { // CondExpOp ------------------------------------------------------ inline std::complex CondExpOp( enum CppAD::CompareOp cop , const std::complex &left , const std::complex &right , const std::complex &trueCase , const std::complex &falseCase ) { CppAD::ErrorHandler::Call( true , __LINE__ , __FILE__ , "std::complex CondExpOp(...)", "Error: cannot use CondExp with a complex type" ); return std::complex(0); } // CondExpRel -------------------------------------------------------- CPPAD_COND_EXP_REL( std::complex ) // EqualOpSeq ----------------------------------------------------- inline bool EqualOpSeq( const std::complex &x , const std::complex &y ) { return x == y; } // Identical ------------------------------------------------------ inline bool IdenticalPar(const std::complex &x) { return true; } inline bool IdenticalZero(const std::complex &x) { return (x == std::complex(0., 0.) ); } inline bool IdenticalOne(const std::complex &x) { return (x == std::complex(1., 0.) ); } inline bool IdenticalEqualPar( const std::complex &x, const std::complex &y) { return (x == y); } // Ordered -------------------------------------------------------- CPPAD_USER_MACRO_ONE(LessThanZero) CPPAD_USER_MACRO_ONE(LessThanOrZero) CPPAD_USER_MACRO_ONE(GreaterThanOrZero) CPPAD_USER_MACRO_ONE(GreaterThanZero) inline bool abs_geq( const std::complex& x , const std::complex& y ) { return std::abs(x) >= std::abs(y); } // Integer ------------------------------------------------------ inline int Integer(const std::complex &x) { return static_cast( x.real() ); } // isnan ------------------------------------------------------------- inline bool isnan(const std::complex& z) { return (z != z); } // Valid standard math functions -------------------------------- CPPAD_STANDARD_MATH_UNARY(std::complex, cos) CPPAD_STANDARD_MATH_UNARY(std::complex, cosh) CPPAD_STANDARD_MATH_UNARY(std::complex, exp) CPPAD_STANDARD_MATH_UNARY(std::complex, log) CPPAD_STANDARD_MATH_UNARY(std::complex, sin) CPPAD_STANDARD_MATH_UNARY(std::complex, sinh) CPPAD_STANDARD_MATH_UNARY(std::complex, sqrt) // Invalid standrd math functions ------------------------------- CPPAD_USER_MACRO_TWO(abs) CPPAD_USER_MACRO_TWO(acos) CPPAD_USER_MACRO_TWO(asin) CPPAD_USER_MACRO_TWO(atan) CPPAD_USER_MACRO_TWO(sign) // The pow function inline std::complex pow( const std::complex &x , const std::complex &y ) { return std::pow(x, y); } // numeric_limits ------------------------------------------------- CPPAD_NUMERIC_LIMITS(float, std::complex) // to_string ------------------------------------------------- CPPAD_TO_STRING(std::complex) } // undefine macros only used by this file # undef CPPAD_USER_MACRO # undef CPPAD_USER_MACRO_ONE # undef CPPAD_USER_MACRO_TWO # endif cppad-20170000.3/cppad/core/erf.hpp0000644000175200017650000000511313057470465015741 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ERF_HPP # define CPPAD_CORE_ERF_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin erf$$ $spell erf const Vec std cmath CppAD Vedder $$ $section The Error Function$$ $head Syntax$$ $icode%y% = erf(%x%)%$$ $head Description$$ Returns the value of the error function which is defined by $latex \[ {\rm erf} (x) = \frac{2}{ \sqrt{\pi} } \int_0^x \exp( - t * t ) \; {\bf d} t \] $$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head CPPAD_USE_CPLUSPLUS_2011$$ $subhead true$$ If this preprocessor symbol is true ($code 1$$), and $icode x$$ is an AD type, this is an $cref/atomic operation/glossary/Operation/Atomic/$$. $subhead false$$ If this preprocessor symbol is false ($code 0$$), CppAD uses a fast approximation (few numerical operations) with relative error bound $latex 4 \times 10^{-4}$$; see Vedder, J.D., $icode Simple approximations for the error function and its inverse$$, American Journal of Physics, v 55, n 8, 1987, p 762-3. $head Example$$ $children% example/erf.cpp %$$ The file $cref erf.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ # include # if ! CPPAD_USE_CPLUSPLUS_2011 // BEGIN CppAD namespace namespace CppAD { template Type erf_template(const Type &x) { using CppAD::exp; const Type a = static_cast(993./880.); const Type b = static_cast(89./880.); return tanh( (a + b * x * x) * x ); } inline float erf(const float &x) { return erf_template(x); } inline double erf(const double &x) { return erf_template(x); } template inline AD erf(const AD &x) { return erf_template(x); } template inline AD erf(const VecAD_reference &x) { return erf_template( x.ADBase() ); } } // END CppAD namespace # endif // CPPAD_USE_CPLUSPLUS_2011 # endif // CPPAD_ERF_INCLUDED cppad-20170000.3/cppad/core/print_for.hpp0000644000175200017650000001376113057470465017177 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_PRINT_FOR_HPP # define CPPAD_CORE_PRINT_FOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin PrintFor$$ $spell pos var VecAD std cout const $$ $section Printing AD Values During Forward Mode$$ $mindex print text output debug$$ $head Syntax$$ $icode%f%.Forward(0, %x%) %$$ $codei%PrintFor(%before%, %var%) %$$ $codei%PrintFor(%pos%, %before%, %var%, %after%) %$$ $head Purpose$$ The $cref/zero order forward/forward_zero/$$ mode command $codei% %f%.Forward(0, %x%) %$$ assigns the $cref/independent variable/glossary/Tape/Independent Variable/$$ vector equal to $icode x$$. It then computes a value for all of the dependent variables in the $cref/operation sequence/glossary/Operation/Sequence/$$ corresponding to $icode f$$. Putting a $code PrintFor$$ in the operation sequence will cause the value of $icode var$$, corresponding to $icode x$$, to be printed during zero order forward operations. $head f.Forward(0, x)$$ The objects $icode f$$, $icode x$$, and the purpose for this operation, are documented in $cref Forward$$. $head pos$$ If present, the argument $icode pos$$ has one of the following prototypes $codei% const AD<%Base%>& %pos% const VecAD<%Base%>::reference& %pos% %$$ In this case the text and $icode var$$ will be printed if and only if $icode pos$$ is not greater than zero and a finite number. $head before$$ The argument $icode before$$ has prototype $codei% const char* %before% %$$ This text is written to $code std::cout$$ before $icode var$$. $head var$$ The argument $icode var$$ has one of the following prototypes $codei% const AD<%Base%>& %var% const VecAD<%Base%>::reference& %var% %$$ The value of $icode var$$, that corresponds to $icode x$$, is written to $code std::cout$$ during the execution of $codei% %f%.Forward(0, %x%) %$$ Note that $icode var$$ may be a $cref/variable/glossary/Variable/$$ or $cref/parameter/glossary/Parameter/$$. (A parameters value does not depend on the value of the independent variable vector $icode x$$.) $head after$$ The argument $icode after$$ has prototype $codei% const char* %after% %$$ This text is written to $code std::cout$$ after $icode var$$. $head Redirecting Output$$ You can redirect this output to any standard output stream; see the $cref/s/forward_order/s/$$ in the forward mode documentation. $head Discussion$$ This is helpful for understanding why tape evaluations have trouble. For example, if one of the operations in $icode f$$ is $codei%log(%var%)%$$ and $icode%var% <= 0%$$, the corresponding result will be $cref nan$$. $head Alternative$$ The $cref ad_output$$ section describes the normal printing of values; i.e., printing when the corresponding code is executed. $head Example$$ $children% print_for/print_for.cpp% example/print_for.cpp %$$ The program $cref print_for_cout.cpp$$ is an example and test that prints to standard output. The output of this program states the conditions for passing and failing the test. The function $cref print_for_string.cpp$$ is an example and test that prints to an standard string stream. This function automatically check for correct output. $end ------------------------------------------------------------------------------ */ # include namespace CppAD { template void PrintFor(const AD& pos, const char *before, const AD& var, const char* after) { CPPAD_ASSERT_NARG_NRES(local::PriOp, 5, 0); // check for case where we are not recording operations local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return; CPPAD_ASSERT_KNOWN( std::strlen(before) <= 1000 , "PrintFor: length of before is greater than 1000 characters" ); CPPAD_ASSERT_KNOWN( std::strlen(after) <= 1000 , "PrintFor: length of after is greater than 1000 characters" ); size_t ind0, ind1, ind2, ind3, ind4; // ind[0] = base 2 representation of the value [Var(pos), Var(var)] ind0 = 0; // ind[1] = address for pos if( Parameter(pos) ) ind1 = tape->Rec_.PutPar(pos.value_); else { ind0 += 1; ind1 = pos.taddr_; } // ind[2] = address of before ind2 = tape->Rec_.PutTxt(before); // ind[3] = address for var if( Parameter(var) ) ind3 = tape->Rec_.PutPar(var.value_); else { ind0 += 2; ind3 = var.taddr_; } // ind[4] = address of after ind4 = tape->Rec_.PutTxt(after); // put the operator in the tape tape->Rec_.PutArg(ind0, ind1, ind2, ind3, ind4); tape->Rec_.PutOp(local::PriOp); } // Fold all other cases into the case above template void PrintFor(const char* before, const AD& var) { PrintFor(AD(0), before, var, "" ); } // template void PrintFor(const char* before, const VecAD_reference& var) { PrintFor(AD(0), before, var.ADBase(), "" ); } // template void PrintFor( const VecAD_reference& pos , const char *before , const VecAD_reference& var , const char *after ) { PrintFor(pos.ADBase(), before, var.ADBase(), after); } // template void PrintFor( const VecAD_reference& pos , const char *before , const AD& var , const char *after ) { PrintFor(pos.ADBase(), before, var, after); } // template void PrintFor( const AD& pos , const char *before , const VecAD_reference& var , const char *after ) { PrintFor(pos, before, var.ADBase(), after); } } # endif cppad-20170000.3/cppad/core/var2par.hpp0000644000175200017650000000365413057470465016552 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_VAR2PAR_HPP # define CPPAD_CORE_VAR2PAR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------ $begin Var2Par$$ $spell var const $$ $section Convert an AD Variable to a Parameter$$ $mindex Var2Par from value_ obtain during taping$$ $head Syntax$$ $icode%y% = Var2Par(%x%)%$$ $head See Also$$ $cref value$$ $head Purpose$$ Returns a $cref/parameter/glossary/Parameter/$$ $icode y$$ with the same value as the $cref/variable/glossary/Variable/$$ $icode x$$. $head x$$ The argument $icode x$$ has prototype $codei% const AD<%Base%> &x %$$ The argument $icode x$$ may be a variable or parameter. $head y$$ The result $icode y$$ has prototype $codei% AD<%Base%> &y %$$ The return value $icode y$$ will be a parameter. $head Example$$ $children% example/var2par.cpp %$$ The file $cref var2par.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------ */ // BEGIN CppAD namespace namespace CppAD { template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION AD Var2Par(const AD &x) { AD y(x.value_); return y; } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION AD Var2Par(const VecAD_reference &x) { AD y(x.ADBase()); y.id_ = 0; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/for_sparse_hes.hpp0000644000175200017650000003660313057470465020177 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_FOR_SPARSE_HES_HPP # define CPPAD_CORE_FOR_SPARSE_HES_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ForSparseHes$$ $spell Andrea Walther std VecAD Jacobian Jac Hessian Hes const Bool Dep proportional var cpp $$ $section Hessian Sparsity Pattern: Forward Mode$$ $head Syntax$$ $icode%h% = %f%.ForSparseHes(%r%, %s%) %$$ $head Purpose$$ We use $latex F : \B{R}^n \rightarrow \B{R}^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. we define $latex \[ \begin{array}{rcl} H(x) & = & \partial_x \left[ \partial_u S \cdot F[ x + R \cdot u ] \right]_{u=0} \\ & = & R^\R{T} \cdot (S \cdot F)^{(2)} ( x ) \cdot R \end{array} \] $$ Where $latex R \in \B{R}^{n \times n}$$ is a diagonal matrix and $latex S \in \B{R}^{1 \times m}$$ is a row vector. Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the diagonal of $latex R$$ and the vector $latex S$$, $code ForSparseHes$$ returns a sparsity pattern for the $latex H(x)$$. $head f$$ The object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ $head x$$ If the operation sequence in $icode f$$ is $cref/independent/glossary/Operation/Independent/$$ of the independent variables in $latex x \in B^n$$, the sparsity pattern is valid for all values of (even if it has $cref CondExp$$ or $cref VecAD$$ operations). $head r$$ The argument $icode r$$ has prototype $codei% const %VectorSet%& %r% %$$ (see $cref/VectorSet/ForSparseHes/VectorSet/$$ below) If it has elements of type $code bool$$, its size is $latex n$$. If it has elements of type $code std::set$$, its size is one and all the elements of $icode%s%[0]%$$ are between zero and $latex n - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the diagonal of $latex R$$. The fewer non-zero elements in this sparsity pattern, the faster the calculation should be and the more sparse $latex H(x)$$ should be. $head s$$ The argument $icode s$$ has prototype $codei% const %VectorSet%& %s% %$$ (see $cref/VectorSet/ForSparseHes/VectorSet/$$ below) If it has elements of type $code bool$$, its size is $latex m$$. If it has elements of type $code std::set$$, its size is one and all the elements of $icode%s%[0]%$$ are between zero and $latex m - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the vector $icode S$$. The fewer non-zero elements in this sparsity pattern, the faster the calculation should be and the more sparse $latex H(x)$$ should be. $head h$$ The result $icode h$$ has prototype $codei% %VectorSet%& %h% %$$ (see $cref/VectorSet/ForSparseHes/VectorSet/$$ below). If $icode h$$ has elements of type $code bool$$, its size is $latex n * n$$. If it has elements of type $code std::set$$, its size is $latex n$$ and all the set elements are between zero and $icode%n%-1%$$ inclusive. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex H(x)$$. $head VectorSet$$ The type $icode VectorSet$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code bool$$ or $code std::set$$; see $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for a discussion of the difference. The type of the elements of $cref/VectorSet/ForSparseHes/VectorSet/$$ must be the same as the type of the elements of $icode r$$. $head Algorithm$$ See Algorithm II in $italic Computing sparse Hessians with automatic differentiation$$ by Andrea Walther. Note that $icode s$$ provides the information so that 'dead ends' are not included in the sparsity pattern. $head Example$$ $children% example/for_sparse_hes.cpp %$$ The file $cref for_sparse_hes.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ----------------------------------------------------------------------------- */ # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file for_sparse_hes.hpp Forward mode Hessian sparsity patterns. */ // =========================================================================== // ForSparseHesCase /*! Private helper function for ForSparseHes(q, s) bool sparsity. All of the description in the public member function ForSparseHes(q, s) applies. \param set_type is a \c bool value. This argument is used to dispatch to the proper source code depending on the vlaue of \c VectorSet::value_type. \param r See \c ForSparseHes(r, s). \param s See \c ForSparseHes(r, s). \param h is the return value for the corresponging call to \c ForSparseJac(q, s). */ template template void ADFun::ForSparseHesCase( bool set_type , const VectorSet& r , const VectorSet& s , VectorSet& h ) { size_t n = Domain(); size_t m = Range(); // // check Vector is Simple VectorSet class with bool elements CheckSimpleVector(); // CPPAD_ASSERT_KNOWN( size_t(r.size()) == n, "ForSparseHes: size of r is not equal to\n" "domain dimension for ADFun object." ); CPPAD_ASSERT_KNOWN( size_t(s.size()) == m, "ForSparseHes: size of s is not equal to\n" "range dimension for ADFun object." ); // // sparsity pattern corresponding to r local::sparse_pack for_jac_sparsity; for_jac_sparsity.resize(num_var_tape_, n + 1); for(size_t i = 0; i < n; i++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] < n + 1 ); // ind_taddr_[i] is operator taddr for i-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp ); // if( r[i] ) for_jac_sparsity.add_element( ind_taddr_[i], ind_taddr_[i] ); } // compute forward Jacobiain sparsity pattern bool dependency = false; local::ForJacSweep( dependency, n, num_var_tape_, &play_, for_jac_sparsity ); // sparsity pattern correspnding to s local::sparse_pack rev_jac_sparsity; rev_jac_sparsity.resize(num_var_tape_, 1); for(size_t i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); if( s[i] ) rev_jac_sparsity.add_element( dep_taddr_[i], 0); } // compute reverse sparsity pattern for dependency analysis // (note that we are only want non-zero derivatives not true dependency) local::RevJacSweep( dependency, n, num_var_tape_, &play_, rev_jac_sparsity ); // vector of sets that will hold the forward Hessain values local::sparse_pack for_hes_sparsity; for_hes_sparsity.resize(n+1, n+1); // // compute the Hessian sparsity patterns local::ForHesSweep( n, num_var_tape_, &play_, for_jac_sparsity, rev_jac_sparsity, for_hes_sparsity ); // initialize return values corresponding to independent variables h.resize(n * n); for(size_t i = 0; i < n; i++) { for(size_t j = 0; j < n; j++) h[ i * n + j ] = false; } // copy to result pattern CPPAD_ASSERT_UNKNOWN( for_hes_sparsity.end() == n+1 ); for(size_t i = 0; i < n; i++) { // ind_taddr_[i] is operator taddr for i-th independent variable CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] == i + 1 ); CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp ); // extract the result from for_hes_sparsity local::sparse_pack::const_iterator itr(for_hes_sparsity, ind_taddr_[i] ); size_t j = *itr; while( j < for_hes_sparsity.end() ) { CPPAD_ASSERT_UNKNOWN( 0 < j ) h[ i * n + (j-1) ] = true; j = *(++itr); } } } /*! Private helper function for ForSparseHes(q, s) set sparsity. All of the description in the public member function ForSparseHes(q, s) applies. \param set_type is a \c std::set value. This argument is used to dispatch to the proper source code depending on the vlaue of \c VectorSet::value_type. \param r See \c ForSparseHes(r, s). \param s See \c ForSparseHes(q, s). \param h is the return value for the corresponging call to \c ForSparseJac(q, s). */ template template void ADFun::ForSparseHesCase( const std::set& set_type , const VectorSet& r , const VectorSet& s , VectorSet& h ) { size_t n = Domain(); # ifndef NDEBUG size_t m = Range(); # endif std::set::const_iterator itr_1; // // check VectorSet is Simple Vector class with sets for elements CheckSimpleVector, VectorSet>( local::one_element_std_set(), local::two_element_std_set() ); CPPAD_ASSERT_KNOWN( r.size() == 1, "ForSparseHes: size of s is not equal to one." ); CPPAD_ASSERT_KNOWN( s.size() == 1, "ForSparseHes: size of s is not equal to one." ); // // sparsity pattern corresponding to r local::sparse_list for_jac_sparsity; for_jac_sparsity.resize(num_var_tape_, n + 1); itr_1 = r[0].begin(); while( itr_1 != r[0].end() ) { size_t i = *itr_1++; CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] < n + 1 ); // ind_taddr_[i] is operator taddr for i-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp ); // for_jac_sparsity.add_element( ind_taddr_[i], ind_taddr_[i] ); } // compute forward Jacobiain sparsity pattern bool dependency = false; local::ForJacSweep( dependency, n, num_var_tape_, &play_, for_jac_sparsity ); // sparsity pattern correspnding to s local::sparse_list rev_jac_sparsity; rev_jac_sparsity.resize(num_var_tape_, 1); itr_1 = s[0].begin(); while( itr_1 != s[0].end() ) { size_t i = *itr_1++; CPPAD_ASSERT_KNOWN( i < m, "ForSparseHes: an element of the set s[0] has value " "greater than or equal m" ); CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); rev_jac_sparsity.add_element( dep_taddr_[i], 0); } // // compute reverse sparsity pattern for dependency analysis // (note that we are only want non-zero derivatives not true dependency) local::RevJacSweep( dependency, n, num_var_tape_, &play_, rev_jac_sparsity ); // // vector of sets that will hold reverse Hessain values local::sparse_list for_hes_sparsity; for_hes_sparsity.resize(n+1, n+1); // // compute the Hessian sparsity patterns local::ForHesSweep( n, num_var_tape_, &play_, for_jac_sparsity, rev_jac_sparsity, for_hes_sparsity ); // return values corresponding to independent variables // j is index corresponding to reverse mode partial h.resize(n); CPPAD_ASSERT_UNKNOWN( for_hes_sparsity.end() == n+1 ); for(size_t i = 0; i < n; i++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] == i + 1 ); CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp ); // extract the result from for_hes_sparsity local::sparse_list::const_iterator itr_2(for_hes_sparsity, ind_taddr_[i] ); size_t j = *itr_2; while( j < for_hes_sparsity.end() ) { CPPAD_ASSERT_UNKNOWN( 0 < j ) h[i].insert(j-1); j = *(++itr_2); } } } // =========================================================================== // ForSparseHes /*! User API for Hessian sparsity patterns using reverse mode. The C++ source code corresponding to this operation is \verbatim h = f.ForSparseHes(q, r) \endverbatim \tparam Base is the base type for this recording. \tparam VectorSet is a simple vector with elements of type \c bool or \c std::set. \param r is a vector with size \c n that specifies the sparsity pattern for the diagonal of the matrix \f$ R \f$, where \c n is the number of independent variables corresponding to the operation sequence stored in \a play. \param s is a vector with size \c m that specifies the sparsity pattern for the vector \f$ S \f$, where \c m is the number of dependent variables corresponding to the operation sequence stored in \a play. \return The return vector is a sparsity pattern for \f$ H(x) \f$ \f[ H(x) = R^T ( S * F)^{(2)} (x) R \f] where \f$ F \f$ is the function corresponding to the operation sequence and \a x is any argument value. */ template template VectorSet ADFun::ForSparseHes( const VectorSet& r, const VectorSet& s ) { VectorSet h; typedef typename VectorSet::value_type Set_type; // Should check to make sure q is same as in previous call to // forward sparse Jacobian. ForSparseHesCase( Set_type() , r , s , h ); return h; } // =========================================================================== // ForSparseHesCheckpoint /*! Hessian sparsity patterns calculation used by checkpoint functions. \tparam Base is the base type for this recording. \param r is a vector with size n that specifies the sparsity pattern for the diagonal of \f$ R \f$, where n is the number of independent variables corresponding to the operation sequence stored in play_. \param s is a vector with size m that specifies the sparsity pattern for the vector \f$ S \f$, where m is the number of dependent variables corresponding to the operation sequence stored in play_. \param h The input size and elements of h do not matter. On output, h is the sparsity pattern for the matrix \f$ H(x) R \f$. \par Assumptions The forward jacobian sparsity pattern must be currently stored in this ADFUN object. */ // The checkpoint class is not yet using forward sparse Hessians. # ifdef CPPAD_NOT_DEFINED template void ADFun::ForSparseHesCheckpoint( vector& r , vector& s , local::sparse_list& h ) { size_t n = Domain(); size_t m = Range(); // checkpoint functions should get this right CPPAD_ASSERT_UNKNOWN( for_jac_sparse_pack_.n_set() == 0 ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse_set_.n_set() == 0 ); CPPAD_ASSERT_UNKNOWN( s.size() == m ); // Array that holds the reverse Jacobiain dependcy flags. // Initialize as true for dependent variables, flase for others. local::pod_vector RevJac; RevJac.extend(num_var_tape_); for(size_t i = 0; i < num_var_tape_; i++) RevJac[i] = false; for(size_t i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ) RevJac[ dep_taddr_[i] ] = s[i]; } // holds forward Hessian sparsity pattern for all variables local::sparse_list for_hes_sparsity; for_hes_sparsity.resize(n+1, n+1); // compute Hessian sparsity pattern for all variables local::ForHesSweep( n, num_var_tape_, &play_, for_jac_sparse_set_, RevJac.data(), for_hes_sparsity ); // dimension the return value if( transpose ) h.resize(n, n); else h.resize(n, n); // j is index corresponding to reverse mode partial for(size_t j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] < num_var_tape_ ); // ind_taddr_[j] is operator taddr for j-th independent variable CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == j + 1 ); CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); // extract the result from for_hes_sparsity CPPAD_ASSERT_UNKNOWN( for_hes_sparsity.end() == q ); local::sparse_list::const_iterator itr(for_hes_sparsity, .j + 1); size_t i = *itr; while( i < q ) { if( transpose ) h.add_element(j, i); else h.add_element(i, j); i = *(++itr); } } } # endif } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/add_eq.hpp0000644000175200017650000000531713057470465016410 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ADD_EQ_HPP # define CPPAD_CORE_ADD_EQ_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD& AD::operator += (const AD &right) { // compute the Base part Base left; left = value_; value_ += right.value_; // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return *this; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_left = tape_id_ == tape_id; bool var_right = right.tape_id_ == tape_id; if( var_left ) { if( var_right ) { // this = variable + variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::AddvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::AddvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(taddr_, right.taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::AddvvOp); // make this a variable CPPAD_ASSERT_UNKNOWN( tape_id_ == tape_id ); } else if( ! IdenticalZero( right.value_ ) ) { // this = variable + parameter // = parameter + variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::AddpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::AddpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(p, taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::AddpvOp); // make this a variable CPPAD_ASSERT_UNKNOWN( tape_id_ == tape_id ); } } else if( var_right ) { if( IdenticalZero(left) ) { // this = 0 + right make_variable(right.tape_id_, right.taddr_); } else { // this = parameter + variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::AddpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::AddpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(left); tape->Rec_.PutArg(p, right.taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::AddpvOp); // make this a variable tape_id_ = tape_id; } } return *this; } CPPAD_FOLD_ASSIGNMENT_OPERATOR(+=) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/opt_val_hes.hpp0000644000175200017650000003341313057470465017474 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_OPT_VAL_HES_HPP # define CPPAD_CORE_OPT_VAL_HES_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin opt_val_hes$$ $spell hes sy Jacobian hes signdet jac Bradley const CppAD $$ $section Jacobian and Hessian of Optimal Values$$ $mindex opt_val_hes$$ $head Syntax$$ $icode%signdet% = opt_val_hes(%x%, %y%, %fun%, %jac%, %hes%)%$$ $head See Also$$ $cref BenderQuad$$ $head Reference$$ Algorithmic differentiation of implicit functions and optimal values, Bradley M. Bell and James V. Burke, Advances in Automatic Differentiation, 2008, Springer. $head Purpose$$ We are given a function $latex S : \B{R}^n \times \B{R}^m \rightarrow \B{R}^\ell$$ and we define $latex F : \B{R}^n \times \B{R}^m \rightarrow \B{R}$$ and $latex V : \B{R}^n \rightarrow \B{R} $$ by $latex \[ \begin{array}{rcl} F(x, y) & = & \sum_{k=0}^{\ell-1} S_k ( x , y) \\ V(x) & = & F [ x , Y(x) ] \\ 0 & = & \partial_y F [x , Y(x) ] \end{array} \] $$ We wish to compute the Jacobian and possibly also the Hessian, of $latex V (x)$$. $head BaseVector$$ The type $icode BaseVector$$ must be a $cref SimpleVector$$ class. We use $icode Base$$ to refer to the type of the elements of $icode BaseVector$$; i.e., $codei% %BaseVector%::value_type %$$ $head x$$ The argument $icode x$$ has prototype $codei% const %BaseVector%& %x% %$$ and its size must be equal to $icode n$$. It specifies the point at which we evaluating the Jacobian $latex V^{(1)} (x)$$ (and possibly the Hessian $latex V^{(2)} (x)$$). $head y$$ The argument $icode y$$ has prototype $codei% const %BaseVector%& %y% %$$ and its size must be equal to $icode m$$. It must be equal to $latex Y(x)$$; i.e., it must solve the implicit equation $latex \[ 0 = \partial_y F ( x , y) \] $$ $head Fun$$ The argument $icode fun$$ is an object of type $icode Fun$$ which must support the member functions listed below. CppAD will may be recording operations of the type $codei%AD<%Base%>%$$ when these member functions are called. These member functions must not stop such a recording; e.g., they must not call $cref/AD::abort_recording/abort_recording/$$. $subhead Fun::ad_vector$$ The type $icode%Fun%::ad_vector%$$ must be a $cref SimpleVector$$ class with elements of type $codei%AD<%Base%>%$$; i.e. $codei% %Fun%::ad_vector::value_type %$$ is equal to $codei%AD<%Base%>%$$. $subhead fun.ell$$ The type $icode Fun$$ must support the syntax $codei% %ell% = %fun%.ell() %$$ where $icode ell$$ has prototype $codei% size_t %ell% %$$ and is the value of $latex \ell$$; i.e., the number of terms in the summation. $pre $$ One can choose $icode ell$$ equal to one, and have $latex S(x,y)$$ the same as $latex F(x, y)$$. Each of the functions $latex S_k (x , y)$$, (in the summation defining $latex F(x, y)$$) is differentiated separately using AD. For very large problems, breaking $latex F(x, y)$$ into the sum of separate simpler functions may reduce the amount of memory necessary for algorithmic differentiation and there by speed up the process. $subhead fun.s$$ The type $icode Fun$$ must support the syntax $codei% %s_k% = %fun%.s(%k%, %x%, %y%) %$$ The $icode%fun%.s%$$ argument $icode k$$ has prototype $codei% size_t %k% %$$ and is between zero and $icode%ell% - 1%$$. The argument $icode x$$ to $icode%fun%.s%$$ has prototype $codei% const %Fun%::ad_vector& %x% %$$ and its size must be equal to $icode n$$. The argument $icode y$$ to $icode%fun%.s%$$ has prototype $codei% const %Fun%::ad_vector& %y% %$$ and its size must be equal to $icode m$$. The $icode%fun%.s%$$ result $icode s_k$$ has prototype $codei% AD<%Base%> %s_k% %$$ and its value must be given by $latex s_k = S_k ( x , y )$$. $subhead fun.sy$$ The type $icode Fun$$ must support the syntax $codei% %sy_k% = %fun%.sy(%k%, %x%, %y%) %$$ The argument $icode k$$ to $icode%fun%.sy%$$ has prototype $codei% size_t %k% %$$ The argument $icode x$$ to $icode%fun%.sy%$$ has prototype $codei% const %Fun%::ad_vector& %x% %$$ and its size must be equal to $icode n$$. The argument $icode y$$ to $icode%fun%.sy%$$ has prototype $codei% const %Fun%::ad_vector& %y% %$$ and its size must be equal to $icode m$$. The $icode%fun%.sy%$$ result $icode sy_k$$ has prototype $codei% %Fun%::ad_vector %sy_k% %$$ its size must be equal to $icode m$$, and its value must be given by $latex sy_k = \partial_y S_k ( x , y )$$. $head jac$$ The argument $icode jac$$ has prototype $codei% %BaseVector%& %jac% %$$ and has size $icode n$$ or zero. The input values of its elements do not matter. If it has size zero, it is not affected. Otherwise, on output it contains the Jacobian of $latex V (x)$$; i.e., for $latex j = 0 , \ldots , n-1$$, $latex \[ jac[ j ] = V^{(1)} (x)_j \] $$ where $icode x$$ is the first argument to $code opt_val_hes$$. $head hes$$ The argument $icode hes$$ has prototype $codei% %BaseVector%& %hes% %$$ and has size $icode%n% * %n%$$ or zero. The input values of its elements do not matter. If it has size zero, it is not affected. Otherwise, on output it contains the Hessian of $latex V (x)$$; i.e., for $latex i = 0 , \ldots , n-1$$, and $latex j = 0 , \ldots , n-1$$, $latex \[ hes[ i * n + j ] = V^{(2)} (x)_{i,j} \] $$ $head signdet$$ If $icode%hes%$$ has size zero, $icode signdet$$ is not defined. Otherwise the return value $icode signdet$$ is the sign of the determinant for $latex \partial_{yy}^2 F(x , y) $$. If it is zero, then the matrix is singular and the Hessian is not computed ($icode hes$$ is not changed). $head Example$$ $children% example/opt_val_hes.cpp %$$ The file $cref opt_val_hes.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ----------------------------------------------------------------------------- */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file opt_val_hes.hpp \brief Computing Jabobians and Hessians of Optimal Values */ /*! Computing Jabobians and Hessians of Optimal Values We are given a function \f$ S : {\rm R}^n \times {\rm R}^m \rightarrow {\rm R}^\ell \f$ and we define \f$ F : {\rm R}^n \times {\rm R}^m \rightarrow {\rm R} \f$ and \f$ V : {\rm R}^n \rightarrow {\rm R} \f$ by \f[ \begin{array}{rcl} F(x, y) & = & \sum_{k=0}^{\ell-1} S_k ( x , y) \\ V(x) & = & F [ x , Y(x) ] \\ 0 & = & \partial_y F [x , Y(x) ] \end{array} \f] We wish to compute the Jacobian and possibly also the Hessian, of \f$ V (x) \f$. \tparam BaseVector The type \c BaseVector must be a SimpleVector class. We use \c Base to refer to the type of the elements of \c BaseVector; i.e., BaseVector::value_type. \param x is a vector with size \c n. It specifies the point at which we evaluating the Jacobian \f$ V^{(1)} (x) \f$ (and possibly the Hessian \f$ V^{(2)} (x) \f$). \param y is a vector with size \c m. It must be equal to \f$ Y(x) \f$; i.e., it must solve the implicit equation \f[ 0 = \partial_y F ( x , y) \f] \param fun The argument \c fun is an object of type \c Fun wich must support the member functions listed below. CppAD will may be recording operations of the type \c AD when these member functions are called. These member functions must not stop such a recording; e.g., they must not call \c AD::abort_recording. \par Fun::ad_vector The type Fun::ad_vector must be a SimpleVector class with elements of type \c AD; i.e. Fun::ad_vector::value_type is equal to \c AD. \par fun.ell the type \c Fun must support the syntax \verbatim ell = fun.ell() \endverbatim where \c ell is a \c size_t value that is set to \f$ \ell \f$; i.e., the number of terms in the summation. \par fun.s The type \c Fun must support the syntax \verbatim s_k = fun.s(k, x, y) \endverbatim The argument \c k has prototype size_t k. The argument \c x has prototype const Fun::ad_vector& x and its size must be equal to \c n. The argument \c y has prototype const Fun::ad_vector& y and its size must be equal to \c m. The return value \c s_k has prototype \c AD s_k and its value must be given by \f$ s_k = S_k ( x , y ) \f$. \par fun.sy The type \c Fun must support the syntax \verbatim sy_k = fun.sy(k, x, y) \endverbatim The argument \c k has prototype size_t k. The argument \c x has prototype const Fun::ad_vector& x and its size must be equal to \c n. The argument \c y has prototype const Fun::ad_vector& y and its size must be equal to \c m. The return value \c sy_k has prototype Fun::ad_vector& sy_k, its size is \c m and its value must be given by \f$ sy_k = \partial_y S_k ( x , y ) \f$. \param jac is a vector with size \c n or zero. The input values of its elements do not matter. If it has size zero, it is not affected. Otherwise, on output it contains the Jacobian of \f$ V (x) \f$; i.e., for \f$ j = 0 , \ldots , n-1 \f$, \f[ jac[ j ] = V^{(1)} (x)_j \f] $$ where \c x is the first argument to \c opt_val_hes. \param hes is a vector with size n * n or zero. The input values of its elements do not matter. If it has size zero, it is not affected. Otherwise, on output it contains the Hessian of \f$ V (x) \f$; i.e., for \f$ i = 0 , \ldots , n-1 \f$, and \f$ j = 0 , \ldots , n-1 \f$, \f[ hes[ i * n + j ] = V^{(2)} (x)_{i,j} \f] \return If hes.size() == 0, the return value is not defined. Otherwise, the return value is the sign of the determinant for \f$ \partial_{yy}^2 F(x , y) \f$$. If it is zero, then the matrix is singular and \c hes is not set to its specified value. */ template int opt_val_hes( const BaseVector& x , const BaseVector& y , Fun fun , BaseVector& jac , BaseVector& hes ) { // determine the base type typedef typename BaseVector::value_type Base; // check that BaseVector is a SimpleVector class with Base elements CheckSimpleVector(); // determine the AD vector type typedef typename Fun::ad_vector ad_vector; // check that ad_vector is a SimpleVector class with AD elements CheckSimpleVector< AD , ad_vector >(); // size of the x and y spaces size_t n = size_t(x.size()); size_t m = size_t(y.size()); // number of terms in the summation size_t ell = fun.ell(); // check size of return values CPPAD_ASSERT_KNOWN( size_t(jac.size()) == n || jac.size() == 0, "opt_val_hes: size of the vector jac is not equal to n or zero" ); CPPAD_ASSERT_KNOWN( size_t(hes.size()) == n * n || hes.size() == 0, "opt_val_hes: size of the vector hes is not equal to n * n or zero" ); // some temporary indices size_t i, j, k; // AD version of S_k(x, y) ad_vector s_k(1); // ADFun version of S_k(x, y) ADFun S_k; // AD version of x ad_vector a_x(n); // AD version of y ad_vector a_y(n); if( jac.size() > 0 ) { // this is the easy part, computing the V^{(1)} (x) which is equal // to \partial_x F (x, y) (see Thoerem 2 of the reference). // copy x and y to AD version for(j = 0; j < n; j++) a_x[j] = x[j]; for(j = 0; j < m; j++) a_y[j] = y[j]; // initialize summation for(j = 0; j < n; j++) jac[j] = Base(0.); // add in \partial_x S_k (x, y) for(k = 0; k < ell; k++) { // start recording Independent(a_x); // record s_k[0] = fun.s(k, a_x, a_y); // stop recording and store in S_k S_k.Dependent(a_x, s_k); // compute partial of S_k with respect to x BaseVector jac_k = S_k.Jacobian(x); // add \partial_x S_k (x, y) to jac for(j = 0; j < n; j++) jac[j] += jac_k[j]; } } // check if we are done if( hes.size() == 0 ) return 0; /* In this case, we need to compute the Hessian. Using Theorem 1 of the reference: Y^{(1)}(x) = - F_yy (x, y)^{-1} F_yx (x, y) Using Theorem 2 of the reference: V^{(2)}(x) = F_xx (x, y) + F_xy (x, y) Y^{(1)}(x) */ // Base and AD version of xy BaseVector xy(n + m); ad_vector a_xy(n + m); for(j = 0; j < n; j++) a_xy[j] = xy[j] = x[j]; for(j = 0; j < m; j++) a_xy[n+j] = xy[n+j] = y[j]; // Initialization summation for Hessian of F size_t nm_sq = (n + m) * (n + m); BaseVector F_hes(nm_sq); for(j = 0; j < nm_sq; j++) F_hes[j] = Base(0.); BaseVector hes_k(nm_sq); // add in Hessian of S_k to hes for(k = 0; k < ell; k++) { // start recording Independent(a_xy); // split out x for(j = 0; j < n; j++) a_x[j] = a_xy[j]; // split out y for(j = 0; j < m; j++) a_y[j] = a_xy[n+j]; // record s_k[0] = fun.s(k, a_x, a_y); // stop recording and store in S_k S_k.Dependent(a_xy, s_k); // when computing the Hessian it pays to optimize the tape S_k.optimize(); // compute Hessian of S_k hes_k = S_k.Hessian(xy, 0); // add \partial_x S_k (x, y) to jac for(j = 0; j < nm_sq; j++) F_hes[j] += hes_k[j]; } // Extract F_yx BaseVector F_yx(m * n); for(i = 0; i < m; i++) { for(j = 0; j < n; j++) F_yx[i * n + j] = F_hes[ (i+n)*(n+m) + j ]; } // Extract F_yy BaseVector F_yy(n * m); for(i = 0; i < m; i++) { for(j = 0; j < m; j++) F_yy[i * m + j] = F_hes[ (i+n)*(n+m) + j + n ]; } // compute - Y^{(1)}(x) = F_yy (x, y)^{-1} F_yx (x, y) BaseVector neg_Y_x(m * n); Base logdet; int signdet = CppAD::LuSolve(m, n, F_yy, F_yx, neg_Y_x, logdet); if( signdet == 0 ) return signdet; // compute hes = F_xx (x, y) + F_xy (x, y) Y^{(1)}(x) for(i = 0; i < n; i++) { for(j = 0; j < n; j++) { hes[i * n + j] = F_hes[ i*(n+m) + j ]; for(k = 0; k < m; k++) hes[i*n+j] -= F_hes[i*(n+m) + k+n] * neg_Y_x[k*n+j]; } } return signdet; } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/base_hash.hpp0000644000175200017650000000460013057470465017102 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BASE_HASH_HPP # define CPPAD_CORE_BASE_HASH_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_hash$$ $spell alloc Cpp adouble valgrind const inline $$ $section Base Type Requirements for Hash Coding Values$$ $head Syntax$$ $icode%code% = hash_code(%x%)%$$ $head Purpose$$ CppAD uses a table of $icode Base$$ type values when recording $codei%AD<%Base%>%$$ operations. A hashing function is used to reduce number of values stored in this table; for example, it is not necessary to store the value 3.0 every time it is used as a $cref/parameter/parvar/$$. $head Default$$ The default hashing function works with the set of bits that correspond to a $icode Base$$ value. In most cases this works well, but in some cases it does not. For example, in the $cref base_adolc.hpp$$ case, an $code adouble$$ value can have fields that are not initialized and $code valgrind$$ reported an error when these are used to form the hash code. $head x$$ This argument has prototype $codei% const %Base%& %x %$$ It is the value we are forming a hash code for. $head code$$ The return value $icode code$$ has prototype $codei% unsigned short %code% %$$ It is the hash code corresponding to $icode x$$. This intention is the commonly used values will have different hash codes. The hash code must satisfy $codei% %code% < CPPAD_HASH_TABLE_SIZE %$$ so that it is a valid index into the hash code table. $head inline$$ If you define this function, it should declare it to be $code inline$$, so that you do not get multiple definitions from different compilation units. $head Example$$ See the $code base_alloc$$ $cref/hash_code/base_alloc.hpp/hash_code/$$ and the $code adouble$$ $cref/hash_code/base_adolc.hpp/hash_code/$$. $end */ /*! \def CPPAD_HASH_TABLE_SIZE the codes retruned by hash_code are between zero and CPPAD_HASH_TABLE_SIZE minus one. */ # define CPPAD_HASH_TABLE_SIZE 10000 # endif cppad-20170000.3/cppad/core/abort_recording.hpp0000644000175200017650000000315313057470465020332 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ABORT_RECORDING_HPP # define CPPAD_CORE_ABORT_RECORDING_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin abort_recording$$ $spell $$ $section Abort Recording of an Operation Sequence$$ $mindex tape$$ $head Syntax$$ $codei%AD<%Base%>::abort_recording()%$$ $head Purpose$$ Sometimes it is necessary to abort the recording of an operation sequence that started with a call of the form $codei% Independent(%x%) %$$ If such a recording is currently in progress, $code abort_recording$$ will stop the recording and delete the corresponding information. Otherwise, $code abort_recording$$ has no effect. $children% example/abort_recording.cpp %$$ $head Example$$ The file $cref abort_recording.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ---------------------------------------------------------------------------- */ namespace CppAD { template void AD::abort_recording(void) { local::ADTape* tape = AD::tape_ptr(); if( tape != CPPAD_NULL ) AD::tape_manage(tape_manage_delete); } } # endif cppad-20170000.3/cppad/core/ad.hpp0000644000175200017650000002162413057470465015556 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AD_HPP # define CPPAD_CORE_AD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // simple AD operations that must be defined for AD as well as base class # include # include // define the template classes that are used by the AD template class # include # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE typedef enum { tape_manage_new, tape_manage_delete, tape_manage_clear } tape_manage_job; template class AD { private : // ----------------------------------------------------------------------- // value_ corresponding to this object Base value_; // Tape identifier corresponding to taddr tape_id_t tape_id_; // taddr_ in tape for this variable addr_t taddr_; // ----------------------------------------------------------------------- // enable use of AD in parallel mode template friend void parallel_ad(void); // template friend functions where template parameter is not bound template friend void Independent(VectorAD &x, size_t abort_op_index); // one argument functions friend bool Parameter (const AD &u); friend bool Parameter (const VecAD &u); friend bool Variable (const AD &u); friend bool Variable (const VecAD &u); friend int Integer (const AD &u); friend AD Var2Par (const AD &u); // power function friend AD pow (const AD &x, const AD &y); // azmul function friend AD azmul (const AD &x, const AD &y); // order determining functions, see ordered.hpp friend bool GreaterThanZero (const AD &x); friend bool GreaterThanOrZero (const AD &x); friend bool LessThanZero (const AD &x); friend bool LessThanOrZero (const AD &x); friend bool abs_geq (const AD& x, const AD& y); // The identical property functions, see identical.hpp friend bool IdenticalPar (const AD &x); friend bool IdenticalZero (const AD &x); friend bool IdenticalOne (const AD &x); friend bool IdenticalEqualPar (const AD &x, const AD &y); // EqualOpSeq function friend bool EqualOpSeq (const AD &u, const AD &v); // NearEqual function friend bool NearEqual ( const AD &x, const AD &y, const Base &r, const Base &a); friend bool NearEqual ( const Base &x, const AD &y, const Base &r, const Base &a); friend bool NearEqual ( const AD &x, const Base &y, const Base &r, const Base &a); // CondExp function friend AD CondExpOp ( enum CompareOp cop , const AD &left , const AD &right , const AD &trueCase , const AD &falseCase ); // classes friend class local::ADTape; friend class ADFun; friend class atomic_base; friend class discrete; friend class VecAD; friend class VecAD_reference; // arithematic binary operators friend AD operator + (const AD &left, const AD &right); friend AD operator - (const AD &left, const AD &right); friend AD operator * (const AD &left, const AD &right); friend AD operator / (const AD &left, const AD &right); // comparison operators friend bool operator < (const AD &left, const AD &right); friend bool operator <= (const AD &left, const AD &right); friend bool operator > (const AD &left, const AD &right); friend bool operator >= (const AD &left, const AD &right); friend bool operator == (const AD &left, const AD &right); friend bool operator != (const AD &left, const AD &right); // input operator friend std::istream& operator >> (std::istream &is, AD &x); // output operations friend std::ostream& operator << (std::ostream &os, const AD &x); friend void PrintFor ( const AD& flag , const char* before , const AD& var , const char* after ); public: // type of value typedef Base value_type; // implicit default constructor inline AD(void); // use default implicit copy constructor and assignment operator // inline AD(const AD &x); // inline AD& operator=(const AD &x); // implicit construction and assingment from base type inline AD(const Base &b); inline AD& operator=(const Base &b); // implicit contructor and assignment from VecAD::reference inline AD(const VecAD_reference &x); inline AD& operator=(const VecAD_reference &x); # if CPPAD_DEPRECATED // implicit construction from some other type (depricated) template inline AD(const T &t); # else // explicit construction from some other type (depricated) template inline explicit AD(const T &t); # endif // assignment from some other type template inline AD& operator=(const T &right); // base type corresponding to an AD object friend Base Value (const AD &x); // computed assignment operators inline AD& operator += (const AD &right); inline AD& operator -= (const AD &right); inline AD& operator *= (const AD &right); inline AD& operator /= (const AD &right); // unary operators inline AD operator +(void) const; inline AD operator -(void) const; // destructor ~AD(void) { } // interface so these functions need not be friends inline AD abs_me(void) const; inline AD acos_me(void) const; inline AD asin_me(void) const; inline AD atan_me(void) const; inline AD cos_me(void) const; inline AD cosh_me(void) const; inline AD exp_me(void) const; inline AD fabs_me(void) const; inline AD log_me(void) const; inline AD sin_me(void) const; inline AD sign_me(void) const; inline AD sinh_me(void) const; inline AD sqrt_me(void) const; inline AD tan_me(void) const; inline AD tanh_me(void) const; # if CPPAD_USE_CPLUSPLUS_2011 inline AD erf_me(void) const; inline AD asinh_me(void) const; inline AD acosh_me(void) const; inline AD atanh_me(void) const; inline AD expm1_me(void) const; inline AD log1p_me(void) const; # endif // ---------------------------------------------------------- // static public member functions // abort current AD recording static void abort_recording(void); // set the maximum number of OpenMP threads (deprecated) static void omp_max_thread(size_t number); // These functions declared public so can be accessed by user through // a macro interface and are not intended for direct use. // The macro interface is documented in bool_fun.hpp. // Developer documentation for these fucntions is in bool_fun.hpp static inline bool UnaryBool( bool FunName(const Base &x), const AD &x ); static inline bool BinaryBool( bool FunName(const Base &x, const Base &y), const AD &x , const AD &y ); private: // // Make this variable a parameter // void make_parameter(void) { CPPAD_ASSERT_UNKNOWN( Variable(*this) ); // currently a var tape_id_ = 0; } // // Make this parameter a new variable // void make_variable(size_t id, size_t taddr) { CPPAD_ASSERT_UNKNOWN( Parameter(*this) ); // currently a par CPPAD_ASSERT_UNKNOWN( taddr > 0 ); // sure valid taddr taddr_ = taddr; tape_id_ = id; } // --------------------------------------------------------------- // tape linking functions // // not static inline local::ADTape* tape_this(void) const; // // static inline static tape_id_t** tape_id_handle(size_t thread); inline static tape_id_t* tape_id_ptr(size_t thread); inline static local::ADTape** tape_handle(size_t thread); static local::ADTape* tape_manage(tape_manage_job job); inline static local::ADTape* tape_ptr(void); inline static local::ADTape* tape_ptr(tape_id_t tape_id); }; // --------------------------------------------------------------------------- } // END_CPPAD_NAMESPACE // tape linking private functions # include // operations that expect the AD template class to be defined # endif cppad-20170000.3/cppad/core/zdouble.hpp0000644000175200017650000003760113057470465016640 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ZDOUBLE_HPP # define CPPAD_CORE_ZDOUBLE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin zdouble$$ $spell zdouble op bool inf CppAD $$ $section zdouble: An AD Base Type With Absolute Zero$$ $head Deprecated 2015-09-26$$ Use the function $cref azmul$$ instead. $head Absolute Zero$$ The $code zdouble$$ class acts like the $code double$$ type with the added property that zero times any value is zero. This includes zero time $cref nan$$ and zero times infinity. In addition, zero divided by any value and any value times zero are also zero. $head Syntax$$ $subhead Constructor and Assignment$$ $codei% zdouble z %$$ $codei% zdouble z(x) %$$ $icode% z1% %op% %x% %$$ where $icode x$$ is a $code double$$ or $code zdouble$$ object and $icode op$$ is $code =$$, $code +=$$, $code -=$$, $code *=$$ or $code /=-$$. $subhead Comparison Operators$$ $icode% b% = %z% %op% %x% %$$ $icode% b% = %x% %op% %z% %$$ where $icode b$$ is a $code bool$$ object, $icode z$$ is a $code zdouble$$ object, $icode x$$ is a $code double$$ or $code zdouble$$ object, and $icode op$$ is $code ==$$, $code !=$$, $code <=$$, $code >=$$, $code <$$ or $code >$$. $subhead Arithmetic Operators$$ $icode% z2% = %z1% %op% %x% %$$ $icode% z2% = %x% %op% %z1% %$$ where $icode z1$$, $icode z2$$ are $code zdouble$$ objects, $icode x$$ is a $code double$$ or $code zdouble$$ object, and $icode op$$ is $code +$$, $code -$$, $code *$$ or $code /$$. $subhead Standard Math$$ $icode% z2% = %fun%(%z1%) %$$ $icode% z3% = pow(%z1%, %z2%) %$$ where $icode z1$$, $icode z2$$, $icode z3$$ are $code zdouble$$ objects and $icode fun$$ is a $cref unary_standard_math$$ function. $subhead Nan$$ There is a specialization of $cref nan$$ so that $icode% z2% = nan(%z1%) %$$ returns 'not a number' when $icode z1$$ has type $code zdouble$$. Note that this template function needs to be specialized because $codei zdouble(0.0) == zdouble(0.0) / zdouble(0.0) $$ $head Motivation$$ $subhead General$$ Often during computing (and more so in parallel computing) alternative values for an expression are computed and one of the alternatives is chosen using some boolean variable. This is often represented by $codei% %result% = %flag% * %value_if_true% + (1 - %flag%) * %value_if_false% %$$ where $icode flag$$ is one for true and zero for false. This representation does not work for $code double$$ when the value being multiplied by zero is $code +inf$$, $code -inf$$, or $code nan$$. $subhead CppAD$$ In CppAD one can use $cref/conditional expressions/CondExp/$$ to achieve the representation $codei% %result% = %flag% * %value_if_true% + (1 - %flag%) * %value_if_false% %$$ This works fine except when there are $cref/multiple levels of AD/mul_level/$$; e.g., when using $codei%AD< AD >%$$. In this case the corresponding AD function objects have type $cref/ADFun< AD >/FunConstruct/$$. When these AD function objects compute derivatives using $cref reverse$$ mode, the conditional expressions are represented use zeros to multiply the expression that is not used. Using $codei%AD< AD >%$$ instead of $code AD< AD >$$ makes this representation work and fixes the problem. $head Base Type Requirements$$ The type $code zdouble$$ satisfies all of the CppAD $cref/base type requirements/base_require/$$. $children% test_more/zdouble.cpp %$$ $head Example$$ The file $cref zdouble.cpp$$ contains an example and test of this class. It returns true if it succeeds and false otherwise. $end */ # include # include /*! \file zdouble.hpp Define a class like double but with an absolute zero. */ /*! \def CPPAD_ZDOUBLE_NORMAL_ASSIGN_OPERATOR(op) Define a computed assignment member operator that functions the same as corresponding double operator. */ # define CPPAD_ZDOUBLE_NORMAL_ASSIGN_OPERATOR(op) \ zdouble& operator op (const zdouble& z) \ { dbl_ op z.dbl_; \ return *this; \ } \ zdouble& operator op (const double& x) \ { dbl_ op x; \ return *this; \ } /*! \def CPPAD_ZDOUBLE_UNARY_OPERATOR(op) Define a unary computed assignment member operator. */ # define CPPAD_ZDOUBLE_UNARY_OPERATOR(op) \ zdouble operator op (void) const \ { return zdouble( op dbl_ ); } /*! # define CPPAD_ZDOUBLE_NORMAL_BINARY_OPERATOR(op) Define a binary arithmetic member operator that functions the same as corresponding double operator. */ # define CPPAD_ZDOUBLE_NORMAL_BINARY_OPERATOR(op) \ zdouble operator op (const zdouble& z) const \ { return zdouble( dbl_ op z.dbl_ ); } \ zdouble operator op (const double& x) const \ { return zdouble( dbl_ op x ); } /*! \def CPPAD_ZDOUBLE_COMPARE_OPERATOR(op) Define a comparison member operator. */ # define CPPAD_ZDOUBLE_COMPARE_OPERATOR(op) \ bool operator op (const zdouble& z) const \ { return dbl_ op z.dbl_; } \ bool operator op (const double& x) const \ { return dbl_ op x; } /*! \def CPPAD_ZDOUBLE_OTHER_BINARY_OPERATOR(op) Define a binary arithmetic operator that is not a member because the double operand is on the left. */ # define CPPAD_ZDOUBLE_OTHER_BINARY_OPERATOR(op) \ inline zdouble operator op(const double& x, const zdouble& z) \ { return zdouble(x) op z; } /*! \def CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR(op, op_switch) Define a comparison operator that is not a member because the double operand is on the left. Convert it to the case where the double operand is on the right by by using op_switch instead of op. */ # define CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR(op, op_switch) \ inline bool operator op(const double& x, const zdouble& z) \ { return z op_switch x; } /*! \def CPPAD_ZDOUBLE_STD_MATH_FRIEND(fun) Declare that a standard math function is a friend. */ # define CPPAD_ZDOUBLE_STD_MATH_FRIEND(fun) \ friend zdouble fun(const zdouble& z); /*! \def CPPAD_ZDOUBLE_STD_MATH(fun) Define a standard math function. */ # define CPPAD_ZDOUBLE_STD_MATH(fun) \ inline zdouble fun(const zdouble& z ) \ { return zdouble( std::fun(z.dbl_) ); } namespace CppAD { // CPPAD_BEGIN_NAMESPACDE /*! Class that is like double, except that it has an absolute zero. */ class zdouble { /*! For zdouble objects z1, z2, and std::ostream os, declare the following friends: \code os << z1 Integer(z1) abs(z1) pow(z1, z2) abs_geq(z1, z2) fun(z1) \endcode where fun is any of the standard math unary functions. */ friend std::ostream& operator << (std::ostream &os, const zdouble& z); friend int Integer(const zdouble& z); friend zdouble abs(const zdouble& x); friend zdouble pow(const zdouble& x, const zdouble& y); friend bool abs_geq(const zdouble& x, const zdouble& y); // CPPAD_ZDOUBLE_STD_MATH_FRIEND(acos) CPPAD_ZDOUBLE_STD_MATH_FRIEND(asin) CPPAD_ZDOUBLE_STD_MATH_FRIEND(atan) CPPAD_ZDOUBLE_STD_MATH_FRIEND(cos) CPPAD_ZDOUBLE_STD_MATH_FRIEND(cosh) CPPAD_ZDOUBLE_STD_MATH_FRIEND(exp) CPPAD_ZDOUBLE_STD_MATH_FRIEND(fabs) CPPAD_ZDOUBLE_STD_MATH_FRIEND(log) CPPAD_ZDOUBLE_STD_MATH_FRIEND(log10) CPPAD_ZDOUBLE_STD_MATH_FRIEND(sin) CPPAD_ZDOUBLE_STD_MATH_FRIEND(sinh) CPPAD_ZDOUBLE_STD_MATH_FRIEND(sqrt) CPPAD_ZDOUBLE_STD_MATH_FRIEND(tan) CPPAD_ZDOUBLE_STD_MATH_FRIEND(tanh) // # if CPPAD_USE_CPLUSPLUS_2011 CPPAD_ZDOUBLE_STD_MATH_FRIEND(erf) CPPAD_ZDOUBLE_STD_MATH_FRIEND(asinh) CPPAD_ZDOUBLE_STD_MATH_FRIEND(acosh) CPPAD_ZDOUBLE_STD_MATH_FRIEND(atanh) CPPAD_ZDOUBLE_STD_MATH_FRIEND(expm1) CPPAD_ZDOUBLE_STD_MATH_FRIEND(log1p) // # endif private: /// The value for this object double dbl_; public: /// Default constructor zdouble(void) : dbl_() { } /// Copy constructor zdouble(const zdouble& z) : dbl_(z.dbl_) { } /// Constructor from double zdouble(const double& dbl) : dbl_(dbl) { } // /// Destructor ~zdouble(void) { } // /// Assignment from zdouble zdouble& operator=(const zdouble& z) { dbl_ = z.dbl_; return *this; } /// Assignment from double zdouble& operator=(const double& dbl) { dbl_ = dbl; return *this; } // /// Normal computed assignment CPPAD_ZDOUBLE_NORMAL_ASSIGN_OPERATOR(+=) /// Normal computed assignment CPPAD_ZDOUBLE_NORMAL_ASSIGN_OPERATOR(-=) /// Normal unary operator CPPAD_ZDOUBLE_UNARY_OPERATOR(+) /// Normal unary operator CPPAD_ZDOUBLE_UNARY_OPERATOR(-) /// Normal compare operator CPPAD_ZDOUBLE_COMPARE_OPERATOR(==) /// Normal compare operator CPPAD_ZDOUBLE_COMPARE_OPERATOR(!=) /// Normal compare operator CPPAD_ZDOUBLE_COMPARE_OPERATOR(<=) /// Normal compare operator CPPAD_ZDOUBLE_COMPARE_OPERATOR(>=) /// Normal compare operator CPPAD_ZDOUBLE_COMPARE_OPERATOR(<) /// Normal compare operator CPPAD_ZDOUBLE_COMPARE_OPERATOR(>) // /// Normal binary arithmetic operator CPPAD_ZDOUBLE_NORMAL_BINARY_OPERATOR(+) /// Normal binary arithmetic operator CPPAD_ZDOUBLE_NORMAL_BINARY_OPERATOR(-) // /// Binary arithmetic * with absolute zero zdouble operator * (const zdouble& z) const { bool zero = (dbl_ == 0.0) || (z.dbl_ == 0.0); return zdouble( zero ? 0.0 : (dbl_ * z.dbl_) ); } /// Binary arithmetic * with absolute zero zdouble operator * (const double& x) const { bool zero = (dbl_ == 0.0) || (x == 0.0); return zdouble( zero ? 0.0 : (dbl_ * x) ); } /// Binary arithmetic / with absolute zero zdouble operator / (const zdouble& z) const { bool zero = (dbl_ == 0.0); return zdouble( zero ? 0.0 : (dbl_ / z.dbl_) ); } /// Binary arithmetic / with absolute zero zdouble operator / (const double& x) const { bool zero = (dbl_ == 0.0); return zdouble( zero ? 0.0 : (dbl_ / x) ); } // /// Compute assignmnet *= with absolute zero zdouble& operator *= (const zdouble& z) { bool zero = (dbl_ == 0.0) || (z.dbl_ == 0.0); zero ? (dbl_ = 0.0) : (dbl_ *= z.dbl_); return *this; } /// Compute assignmnet *= with absolute zero zdouble& operator *= (const double& x) { bool zero = (dbl_ == 0.0) || (x == 0.0); zero ? (dbl_ = 0.0) : (dbl_ *= x); return *this; } // /// Compute assignmnet /= with absolute zero zdouble& operator /= (const zdouble& z) { bool zero = (dbl_ == 0.0); zero ? (dbl_ = 0.0) : (dbl_ /= z.dbl_); return *this; } /// Compute assignmnet /= with absolute zero zdouble& operator /= (const double& x) { bool zero = (dbl_ == 0.0); zero ? (dbl_ = 0.0) : (dbl_ /= x); return *this; } }; // BEGIN nan /// Must specialize CppAD::nan because zdouble 0/0 is not nan. template <> inline zdouble nan(const zdouble& zero) { return zdouble( std::numeric_limits::quiet_NaN() ); } // END nan // /// Normal non-member compare operator CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR(==, ==) /// Normal non-member compare operator CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR(!=, !=) /// Normal non-member compare operator CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR(<=, >=) /// Normal non-member compare operator CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR(>=, <=) /// Normal non-member compare operator CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR(<, >) /// Normal non-member compare operator CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR(>, <) // /// Normal binary arithmetic operator CPPAD_ZDOUBLE_OTHER_BINARY_OPERATOR(+) /// Normal binary arithmetic operator CPPAD_ZDOUBLE_OTHER_BINARY_OPERATOR(-) /// Binary arithmetic operator with absolute zero CPPAD_ZDOUBLE_OTHER_BINARY_OPERATOR(*) /// Binary arithmetic operator with absolute zero CPPAD_ZDOUBLE_OTHER_BINARY_OPERATOR(/) // ------------------------------------------------------------------------- // Base type requirements // ------------------------------------------------------------------------- /// Base type requirement: CondExpOp inline zdouble CondExpOp( enum CompareOp cop , const zdouble& left , const zdouble& right , const zdouble& exp_if_true , const zdouble& exp_if_false ) { return CondExpTemplate(cop, left, right, exp_if_true, exp_if_false); } /// Base type requirement: CondExpRel CPPAD_COND_EXP_REL(zdouble) /// Base type requirement: EqualOpSeq inline bool EqualOpSeq(const zdouble& x, const zdouble& y) { return x == y; } /// Base type requirement: Identical inline bool IdenticalPar(const zdouble& x) { return true; } inline bool IdenticalZero(const zdouble& x) { return (x == 0.0); } inline bool IdenticalOne(const zdouble& x) { return (x == 1.); } inline bool IdenticalEqualPar(const zdouble& x, const zdouble& y) { return (x == y); } /// Base type requirement: output operator inline std::ostream& operator << (std::ostream &os, const zdouble& z) { os << z.dbl_; return os; } /// Base type requirement: Integer inline int Integer(const zdouble& x) { return static_cast(x.dbl_); } /// Base type requirement: azmul inline zdouble azmul(const zdouble& x, const zdouble& y) { return x * y; } /// Base type requirement: Ordered inline bool GreaterThanZero(const zdouble& x) { return x > 0.0; } inline bool GreaterThanOrZero(const zdouble& x) { return x >= 0.0; } inline bool LessThanZero(const zdouble& x) { return x < 0.0; } inline bool LessThanOrZero(const zdouble& x) { return x <= 0.0; } inline bool abs_geq(const zdouble& x, const zdouble& y) { return std::fabs(x.dbl_) >= std::fabs(y.dbl_); } /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(acos) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(asin) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(atan) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(cos) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(cosh) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(exp) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(fabs) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(log) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(log10) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(sin) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(sinh) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(sqrt) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(tan) /// Normal standard math function CPPAD_ZDOUBLE_STD_MATH(tanh) // # if CPPAD_USE_CPLUSPLUS_2011 /// C++2011 standard math function CPPAD_ZDOUBLE_STD_MATH(erf) /// C++2011 standard math function CPPAD_ZDOUBLE_STD_MATH(asinh) /// C++2011 standard math function CPPAD_ZDOUBLE_STD_MATH(acosh) /// C++2011 standard math function CPPAD_ZDOUBLE_STD_MATH(atanh) /// C++2011 standard math function CPPAD_ZDOUBLE_STD_MATH(expm1) /// C++2011 standard math function CPPAD_ZDOUBLE_STD_MATH(log1p) # endif /// Base type requirement: abs inline zdouble abs(const zdouble& x) { return std::fabs(x.dbl_); } /// Base type requirement: sign inline zdouble sign(const zdouble& x) { if( x > 0.0 ) return zdouble(1.); if( x == 0.0 ) return zdouble(0.0); return zdouble(-1.); } /// Base type requirement: pow inline zdouble pow(const zdouble& x, const zdouble& y) { return std::pow(x.dbl_, y.dbl_); } /// Base type requirement: limits template <> class numeric_limits { public: // machine epsilon static zdouble epsilon(void) { return std::numeric_limits::epsilon(); } // minimum positive normalized value static zdouble min(void) { return std::numeric_limits::min(); } // maximum finite value static zdouble max(void) { return std::numeric_limits::max(); } }; } // CPPAD_END_NAMESPACE /// undef all macros defined in this file # undef CPPAD_ZDOUBLE_NORMAL_ASSIGN_OPERATOR # undef CPPAD_ZDOUBLE_UNARY_OPERATOR # undef CPPAD_ZDOUBLE_NORMAL_BINARY_OPERATOR # undef CPPAD_ZDOUBLE_COMPARE_OPERATOR # undef CPPAD_ZDOUBLE_OTHER_BINARY_OPERATOR # undef CPPAD_ZDOUBLE_OTHER_COMPARE_OPERATOR # undef CPPAD_ZDOUBLE_STD_MATH_FRIEND # undef CPPAD_ZDOUBLE_STD_MATH # endif cppad-20170000.3/cppad/core/ad_valued.hpp0000644000175200017650000000257613057470465017123 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AD_VALUED_HPP # define CPPAD_CORE_AD_VALUED_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ADValued$$ $spell $$ $section AD Valued Operations and Functions$$ $comment atomic.omh includes atomic_base.omh which atomic_base.hpp$$ $childtable% cppad/core/arithmetic.hpp% cppad/core/standard_math.hpp% cppad/core/cond_exp.hpp% cppad/core/discrete.hpp% cppad/core/numeric_limits.hpp% omh/atomic.omh %$$ $end */ // include MathOther.h after CondExp.h because some MathOther.h routines use // CondExp.h and CondExp.h is not sufficently declared in Declare.h # include # include # include # include # include # include # include # include # endif cppad-20170000.3/cppad/core/jacobian.hpp0000644000175200017650000001316313057470465016737 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_JACOBIAN_HPP # define CPPAD_CORE_JACOBIAN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Jacobian$$ $spell jac typename Taylor Jacobian DetLu const $$ $section Jacobian: Driver Routine$$ $mindex Jacobian first derivative$$ $head Syntax$$ $icode%jac% = %f%.Jacobian(%x%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The syntax above sets $icode jac$$ to the Jacobian of $icode F$$ evaluated at $icode x$$; i.e., $latex \[ jac = F^{(1)} (x) \] $$ $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/Forward or Reverse/Jacobian/Forward or Reverse/$$ below). $head x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ (see $cref/Vector/Jacobian/Vector/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies that point at which to evaluate the Jacobian. $head jac$$ The result $icode jac$$ has prototype $codei% %Vector% %jac% %$$ (see $cref/Vector/Jacobian/Vector/$$ below) and its size is $latex m * n$$; i.e., the product of the $cref/domain/seq_property/Domain/$$ and $cref/range/seq_property/Range/$$ dimensions for $icode f$$. For $latex i = 0 , \ldots , m - 1 $$ and $latex j = 0 , \ldots , n - 1$$ $latex \[. jac[ i * n + j ] = \D{ F_i }{ x_j } ( x ) \] $$ $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Forward or Reverse$$ This will use order zero Forward mode and either order one Forward or order one Reverse to compute the Jacobian (depending on which it estimates will require less work). After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After a call to $code Jacobian$$, the zero order Taylor coefficients correspond to $icode%f%.Forward(0, %x%)%$$ and the other coefficients are unspecified. $head Example$$ $children% example/jacobian.cpp %$$ The routine $cref/Jacobian/jacobian.cpp/$$ is both an example and test. It returns $code true$$, if it succeeds and $code false$$ otherwise. $end ----------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template void JacobianFor(ADFun &f, const Vector &x, Vector &jac) { size_t i; size_t j; size_t n = f.Domain(); size_t m = f.Range(); // check Vector is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_UNKNOWN( size_t(x.size()) == f.Domain() ); CPPAD_ASSERT_UNKNOWN( size_t(jac.size()) == f.Range() * f.Domain() ); // argument and result for forward mode calculations Vector u(n); Vector v(m); // initialize all the components for(j = 0; j < n; j++) u[j] = Base(0); // loop through the different coordinate directions for(j = 0; j < n; j++) { // set u to the j-th coordinate direction u[j] = Base(1); // compute the partial of f w.r.t. this coordinate direction v = f.Forward(1, u); // reset u to vector of all zeros u[j] = Base(0); // return the result for(i = 0; i < m; i++) jac[ i * n + j ] = v[i]; } } template void JacobianRev(ADFun &f, const Vector &x, Vector &jac) { size_t i; size_t j; size_t n = f.Domain(); size_t m = f.Range(); CPPAD_ASSERT_UNKNOWN( size_t(x.size()) == f.Domain() ); CPPAD_ASSERT_UNKNOWN( size_t(jac.size()) == f.Range() * f.Domain() ); // argument and result for reverse mode calculations Vector u(n); Vector v(m); // initialize all the components for(i = 0; i < m; i++) v[i] = Base(0); // loop through the different coordinate directions for(i = 0; i < m; i++) { if( f.Parameter(i) ) { // return zero for this component of f for(j = 0; j < n; j++) jac[ i * n + j ] = Base(0); } else { // set v to the i-th coordinate direction v[i] = Base(1); // compute the derivative of this component of f u = f.Reverse(1, v); // reset v to vector of all zeros v[i] = Base(0); // return the result for(j = 0; j < n; j++) jac[ i * n + j ] = u[j]; } } } template template Vector ADFun::Jacobian(const Vector &x) { size_t i; size_t n = Domain(); size_t m = Range(); CPPAD_ASSERT_KNOWN( size_t(x.size()) == n, "Jacobian: length of x not equal domain dimension for F" ); // point at which we are evaluating the Jacobian Forward(0, x); // work factor for forward mode size_t workForward = n; // work factor for reverse mode size_t workReverse = 0; for(i = 0; i < m; i++) { if( ! Parameter(i) ) ++workReverse; } // choose the method with the least work Vector jac( n * m ); if( workForward <= workReverse ) JacobianFor(*this, x, jac); else JacobianRev(*this, x, jac); return jac; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/fun_check.hpp0000644000175200017650000001323013057470465017111 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_FUN_CHECK_HPP # define CPPAD_CORE_FUN_CHECK_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin FunCheck$$ $spell exp bool const Taylor $$ $section Check an ADFun Sequence of Operations$$ $head Syntax$$ $icode%ok% = FunCheck(%f%, %g%, %x%, %r%, %a%)%$$ $pre $$ $bold See Also$$ $cref CompareChange$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. We use $latex G : B^n \rightarrow B^m$$ to denote the function corresponding to the C++ function object $icode g$$. This routine check if $latex \[ F(x) = G(x) \]$$ If $latex F(x) \neq G(x)$$, the $cref/operation sequence/glossary/Operation/Sequence/$$ corresponding to $icode f$$ does not represents the algorithm used by $icode g$$ to calculate values for $latex G$$ (see $cref/Discussion/FunCheck/Discussion/$$ below). $head f$$ The $code FunCheck$$ argument $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/Forward/FunCheck/FunCheck Uses Forward/$$ below). $head g$$ The $code FunCheck$$ argument $icode g$$ has prototype $codei% %Fun% &%g% %$$ ($icode Fun$$ is defined the properties of $icode g$$). The C++ function object $icode g$$ supports the syntax $codei% %y% = %g%(%x%) %$$ which computes $latex y = G(x)$$. $subhead x$$ The $icode g$$ argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ (see $cref/Vector/FunCheck/Vector/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. $head y$$ The $icode g$$ result $icode y$$ has prototype $codei% %Vector% %y% %$$ and its value is $latex G(x)$$. The size of $icode y$$ is equal to $icode m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. $head x$$ The $code FunCheck$$ argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. This specifies that point at which to compare the values calculated by $icode f$$ and $icode G$$. $head r$$ The $code FunCheck$$ argument $icode r$$ has prototype $codei% const %Base% &%r% %$$ It specifies the relative error the element by element comparison of the value of $latex F(x)$$ and $latex G(x)$$. $head a$$ The $code FunCheck$$ argument $icode a$$ has prototype $codei% const %Base% &%a% %$$ It specifies the absolute error the element by element comparison of the value of $latex F(x)$$ and $latex G(x)$$. $head ok$$ The $code FunCheck$$ result $icode ok$$ has prototype $codei% bool %ok% %$$ It is true, if for $latex i = 0 , \ldots , m-1$$ either the relative error bound is satisfied $latex \[ | F_i (x) - G_i (x) | \leq r ( | F_i (x) | + | G_i (x) | ) \] $$ or the absolute error bound is satisfied $latex \[ | F_i (x) - G_i (x) | \leq a \] $$ It is false if for some $latex (i, j)$$ neither of these bounds is satisfied. $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head FunCheck Uses Forward$$ After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After $code FunCheck$$, the previous calls to $cref Forward$$ are undefined. $head Discussion$$ Suppose that the algorithm corresponding to $icode g$$ contains $codei% if( %x% >= 0 ) %y% = exp(%x%) else %y% = exp(-%x%) %$$ where $icode x$$ and $icode y$$ are $codei%AD%$$ objects. It follows that the AD of $code double$$ $cref/operation sequence/glossary/Operation/Sequence/$$ depends on the value of $icode x$$. If the sequence of operations stored in $icode f$$ corresponds to $icode g$$ with $latex x \geq 0$$, the function values computed using $icode f$$ when $latex x < 0$$ will not agree with the function values computed by $latex g$$. This is because the operation sequence corresponding to $icode g$$ changed (and hence the object $icode f$$ does not represent the function $latex G$$ for this value of $icode x$$). In this case, you probably want to re-tape the calculations performed by $icode g$$ with the $cref/independent variables/glossary/Tape/Independent Variable/$$ equal to the values in $icode x$$ (so AD operation sequence properly represents the algorithm for this value of independent variables). $head Example$$ $children% example/fun_check.cpp %$$ The file $cref fun_check.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end --------------------------------------------------------------------------- */ namespace CppAD { template bool FunCheck( ADFun &f , Fun &g , const Vector &x , const Base &r , const Base &a ) { bool ok = true; size_t m = f.Range(); Vector yf = f.Forward(0, x); Vector yg = g(x); size_t i; for(i = 0; i < m; i++) ok &= NearEqual(yf[i], yg[i], r, a); return ok; } } # endif cppad-20170000.3/cppad/core/rev_sparse_hes.hpp0000644000175200017650000004174213057470465020205 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_REV_SPARSE_HES_HPP # define CPPAD_CORE_REV_SPARSE_HES_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin RevSparseHes$$ $spell std VecAD Jacobian Jac Hessian Hes const Bool Dep proportional var cpp $$ $section Hessian Sparsity Pattern: Reverse Mode$$ $head Syntax$$ $icode%h% = %f%.RevSparseHes(%q%, %s%) %$$ $icode%h% = %f%.RevSparseHes(%q%, %s%, %transpose%)%$$ $head Purpose$$ We use $latex F : \B{R}^n \rightarrow \B{R}^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. For a fixed matrix $latex R \in \B{R}^{n \times q}$$ and a fixed vector $latex S \in \B{R}^{1 \times m}$$, we define $latex \[ \begin{array}{rcl} H(x) & = & \partial_x \left[ \partial_u S * F[ x + R * u ] \right]_{u=0} \\ & = & R^\R{T} * (S * F)^{(2)} ( x ) \\ H(x)^\R{T} & = & (S * F)^{(2)} ( x ) * R \end{array} \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex R$$ and the vector $latex S$$, $code RevSparseHes$$ returns a sparsity pattern for the $latex H(x)$$. $head f$$ The object $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ $head x$$ If the operation sequence in $icode f$$ is $cref/independent/glossary/Operation/Independent/$$ of the independent variables in $latex x \in B^n$$, the sparsity pattern is valid for all values of (even if it has $cref CondExp$$ or $cref VecAD$$ operations). $head q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of columns in $latex R \in \B{R}^{n \times q}$$ and the number of rows in $latex H(x) \in \B{R}^{q \times n}$$. It must be the same value as in the previous $cref ForSparseJac$$ call $codei% %f%.ForSparseJac(%q%, %r%, %r_transpose%) %$$ Note that if $icode r_transpose$$ is true, $icode r$$ in the call above corresponding to $latex R^\R{T} \in \B{R}^{q \times n}$$ $head transpose$$ The argument $icode transpose$$ has prototype $codei% bool %transpose% %$$ The default value $code false$$ is used when $icode transpose$$ is not present. $head r$$ The matrix $latex R$$ is specified by the previous call $codei% %f%.ForSparseJac(%q%, %r%, %transpose%) %$$ see $cref/r/ForSparseJac/r/$$. The type of the elements of $cref/VectorSet/RevSparseHes/VectorSet/$$ must be the same as the type of the elements of $icode r$$. $head s$$ The argument $icode s$$ has prototype $codei% const %VectorSet%& %s% %$$ (see $cref/VectorSet/RevSparseHes/VectorSet/$$ below) If it has elements of type $code bool$$, its size is $latex m$$. If it has elements of type $code std::set$$, its size is one and all the elements of $icode%s%[0]%$$ are between zero and $latex m - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the vector $icode S$$. $head h$$ The result $icode h$$ has prototype $codei% %VectorSet%& %h% %$$ (see $cref/VectorSet/RevSparseHes/VectorSet/$$ below). $subhead transpose false$$ If $icode h$$ has elements of type $code bool$$, its size is $latex q * n$$. If it has elements of type $code std::set$$, its size is $latex q$$ and all the set elements are between zero and $icode%n%-1%$$ inclusive. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex H(x)$$. $subhead transpose true$$ If $icode h$$ has elements of type $code bool$$, its size is $latex n * q$$. If it has elements of type $code std::set$$, its size is $latex n$$ and all the set elements are between zero and $icode%q%-1%$$ inclusive. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex H(x)^\R{T}$$. $head VectorSet$$ The type $icode VectorSet$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code bool$$ or $code std::set$$; see $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for a discussion of the difference. The type of the elements of $cref/VectorSet/RevSparseHes/VectorSet/$$ must be the same as the type of the elements of $icode r$$. $head Entire Sparsity Pattern$$ Suppose that $latex q = n$$ and $latex R \in \B{R}^{n \times n}$$ is the $latex n \times n$$ identity matrix. Further suppose that the $latex S$$ is the $th k$$ $cref/elementary vector/glossary/Elementary Vector/$$; i.e. $latex \[ S_j = \left\{ \begin{array}{ll} 1 & {\rm if} \; j = k \\ 0 & {\rm otherwise} \end{array} \right. \] $$ In this case, the corresponding value $icode h$$ is a sparsity pattern for the Hessian matrix $latex F_k^{(2)} (x) \in \B{R}^{n \times n}$$. $head Example$$ $children% example/rev_sparse_hes.cpp %example/sparsity_sub.cpp %$$ The file $cref rev_sparse_hes.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. The file $cref/sparsity_sub.cpp/sparsity_sub.cpp/RevSparseHes/$$ contains an example and test of using $code RevSparseHes$$ to compute the sparsity pattern for a subset of the Hessian. $end ----------------------------------------------------------------------------- */ # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file rev_sparse_hes.hpp Reverse mode Hessian sparsity patterns. */ // =========================================================================== // RevSparseHesCase /*! Private helper function for RevSparseHes(q, s) bool sparsity. All of the description in the public member function RevSparseHes(q, s) applies. \param set_type is a \c bool value. This argument is used to dispatch to the proper source code depending on the vlaue of \c VectorSet::value_type. \param transpose See \c RevSparseHes(q, s). \param q See \c RevSparseHes(q, s). \param s See \c RevSparseHes(q, s). \param h is the return value for the corresponging call to \c RevSparseJac(q, s). */ template template void ADFun::RevSparseHesCase( bool set_type , bool transpose , size_t q , const VectorSet& s , VectorSet& h ) { size_t n = Domain(); size_t m = Range(); // h.resize(q * n ); CPPAD_ASSERT_KNOWN( for_jac_sparse_pack_.n_set() > 0, "RevSparseHes: previous stored call to ForSparseJac did not " "use bool for the elements of r." ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse_set_.n_set() == 0 ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse_pack_.n_set() == num_var_tape_ ); // // temporary indices size_t i, j; // check Vector is Simple VectorSet class with bool elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( q == for_jac_sparse_pack_.end(), "RevSparseHes: q is not equal to its value\n" "in the previous call to ForSparseJac with this ADFun object." ); CPPAD_ASSERT_KNOWN( size_t(s.size()) == m, "RevSparseHes: size of s is not equal to\n" "range dimension for ADFun object." ); // Array that will hold reverse Jacobian dependency flag. // Initialize as true for the dependent variables. local::pod_vector RevJac; RevJac.extend(num_var_tape_); for(i = 0; i < num_var_tape_; i++) RevJac[i] = false; for(i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); RevJac[ dep_taddr_[i] ] = s[i]; } // vector of sets that will hold reverse Hessain values local::sparse_pack rev_hes_sparsity; rev_hes_sparsity.resize(num_var_tape_, q); // compute the Hessian sparsity patterns local::RevHesSweep( n, num_var_tape_, &play_, for_jac_sparse_pack_, RevJac.data(), rev_hes_sparsity ); // return values corresponding to independent variables CPPAD_ASSERT_UNKNOWN( size_t(h.size()) == n * q ); for(j = 0; j < n; j++) { for(i = 0; i < q; i++) { if( transpose ) h[ j * q + i ] = false; else h[ i * n + j ] = false; } } // j is index corresponding to reverse mode partial for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] < num_var_tape_ ); // ind_taddr_[j] is operator taddr for j-th independent variable CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == j + 1 ); CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); // extract the result from rev_hes_sparsity CPPAD_ASSERT_UNKNOWN( rev_hes_sparsity.end() == q ); local::sparse_pack::const_iterator itr(rev_hes_sparsity, j + 1); i = *itr; while( i < q ) { if( transpose ) h[ j * q + i ] = true; else h[ i * n + j ] = true; i = *(++itr); } } } /*! Private helper function for RevSparseHes(q, s) set sparsity. All of the description in the public member function RevSparseHes(q, s) applies. \param set_type is a \c std::set value. This argument is used to dispatch to the proper source code depending on the vlaue of \c VectorSet::value_type. \param transpose See \c RevSparseHes(q, s). \param q See \c RevSparseHes(q, s). \param s See \c RevSparseHes(q, s). \param h is the return value for the corresponging call to \c RevSparseJac(q, s). */ template template void ADFun::RevSparseHesCase( const std::set& set_type , bool transpose , size_t q , const VectorSet& s , VectorSet& h ) { size_t n = Domain(); # ifndef NDEBUG size_t m = Range(); # endif // if( transpose ) h.resize(n); else h.resize(q); CPPAD_ASSERT_KNOWN( for_jac_sparse_set_.n_set() > 0, "RevSparseHes: previous stored call to ForSparseJac did not " "use std::set for the elements of r." ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse_pack_.n_set() == 0 ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse_set_.n_set() == num_var_tape_ ); // // temporary indices size_t i, j; std::set::const_iterator itr_1; // check VectorSet is Simple Vector class with sets for elements CheckSimpleVector, VectorSet>( local::one_element_std_set(), local::two_element_std_set() ); CPPAD_ASSERT_KNOWN( q == for_jac_sparse_set_.end(), "RevSparseHes: q is not equal to its value\n" "in the previous call to ForSparseJac with this ADFun object." ); CPPAD_ASSERT_KNOWN( s.size() == 1, "RevSparseHes: size of s is not equal to one." ); // Array that will hold reverse Jacobian dependency flag. // Initialize as true for the dependent variables. local::pod_vector RevJac; RevJac.extend(num_var_tape_); for(i = 0; i < num_var_tape_; i++) RevJac[i] = false; itr_1 = s[0].begin(); while( itr_1 != s[0].end() ) { i = *itr_1++; CPPAD_ASSERT_KNOWN( i < m, "RevSparseHes: an element of the set s[0] has value " "greater than or equal m" ); CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); RevJac[ dep_taddr_[i] ] = true; } // vector of sets that will hold reverse Hessain values local::sparse_list rev_hes_sparsity; rev_hes_sparsity.resize(num_var_tape_, q); // compute the Hessian sparsity patterns local::RevHesSweep( n, num_var_tape_, &play_, for_jac_sparse_set_, RevJac.data(), rev_hes_sparsity ); // return values corresponding to independent variables // j is index corresponding to reverse mode partial CPPAD_ASSERT_UNKNOWN( size_t(h.size()) == q || transpose ); CPPAD_ASSERT_UNKNOWN( size_t(h.size()) == n || ! transpose ); for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] < num_var_tape_ ); CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == j + 1 ); CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); // extract the result from rev_hes_sparsity // and add corresponding elements to result sets in h CPPAD_ASSERT_UNKNOWN( rev_hes_sparsity.end() == q ); local::sparse_list::const_iterator itr_2(rev_hes_sparsity, j+1); i = *itr_2; while( i < q ) { if( transpose ) h[j].insert(i); else h[i].insert(j); i = *(++itr_2); } } } // =========================================================================== // RevSparseHes /*! User API for Hessian sparsity patterns using reverse mode. The C++ source code corresponding to this operation is \verbatim h = f.RevSparseHes(q, r) \endverbatim \tparam Base is the base type for this recording. \tparam VectorSet is a simple vector with elements of type \c bool or \c std::set. \param transpose is true (false) if \c is is equal to \f$ H(x) \f$ (\f$ H(x)^T \f$) where \f[ H(x) = R^T (S * F)^{(2)} (x) \f] where \f$ F \f$ is the function corresponding to the operation sequence and \a x is any argument value. \param q is the value of \a q in the by the previous call of the form \verbatim f.ForSparseJac(q, r, packed) \endverbatim The value \c r in this call is a sparsity pattern for the matrix \f$ R \f$. The type of the element of \c r for the previous call to \c ForSparseJac must be the same as the type of the elements of \c s. \param s is a vector with size \c m that specifies the sparsity pattern for the vector \f$ S \f$, where \c m is the number of dependent variables corresponding to the operation sequence stored in \a play. \return If \c transpose is false (true), the return vector is a sparsity pattern for \f$ H(x) \f$ (\f$ H(x)^T \f$). \f[ H(x) = R^T ( S * F)^{(2)} (x) \f] where \f$ F \f$ is the function corresponding to the operation sequence and \a x is any argument value. */ template template VectorSet ADFun::RevSparseHes( size_t q, const VectorSet& s, bool transpose ) { VectorSet h; typedef typename VectorSet::value_type Set_type; // Should check to make sure q is same as in previous call to // forward sparse Jacobian. RevSparseHesCase( Set_type() , transpose , q , s , h ); return h; } // =========================================================================== // RevSparseHesCheckpoint /*! Hessian sparsity patterns calculation used by checkpoint functions. \tparam Base is the base type for this recording. \param transpose is true (false) h is equal to \f$ H(x) \f$ (\f$ H(x)^T \f$) where \f[ H(x) = R^T (S * F)^{(2)} (x) \f] where \f$ F \f$ is the function corresponding to the operation sequence and \f$ x \f$ is any argument value. \param q is the value of q in the by the previous call of the form \verbatim f.ForSparseJac(q, r) \endverbatim The value r in this call is a sparsity pattern for the matrix \f$ R \f$. \param s is a vector with size m that specifies the sparsity pattern for the vector \f$ S \f$, where m is the number of dependent variables corresponding to the operation sequence stored in play_. \param h The input size and elements of h do not matter. On output, h is the sparsity pattern for the matrix \f$ H(x) \f$ or \f$ H(x)^T \f$ depending on transpose. \par Assumptions The forward jacobian sparsity pattern must be currently stored in this ADFUN object. */ template void ADFun::RevSparseHesCheckpoint( size_t q , vector& s , bool transpose , local::sparse_list& h ) { size_t n = Domain(); size_t m = Range(); // checkpoint functions should get this right CPPAD_ASSERT_UNKNOWN( for_jac_sparse_pack_.n_set() == 0 ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse_set_.n_set() == num_var_tape_ ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse_set_.end() == q ); CPPAD_ASSERT_UNKNOWN( s.size() == m ); // Array that holds the reverse Jacobiain dependcy flags. // Initialize as true for dependent variables, flase for others. local::pod_vector RevJac; RevJac.extend(num_var_tape_); for(size_t i = 0; i < num_var_tape_; i++) RevJac[i] = false; for(size_t i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ) RevJac[ dep_taddr_[i] ] = s[i]; } // holds reverse Hessian sparsity pattern for all variables local::sparse_list rev_hes_sparsity; rev_hes_sparsity.resize(num_var_tape_, q); // compute Hessian sparsity pattern for all variables local::RevHesSweep( n, num_var_tape_, &play_, for_jac_sparse_set_, RevJac.data(), rev_hes_sparsity ); // dimension the return value if( transpose ) h.resize(n, q); else h.resize(q, n); // j is index corresponding to reverse mode partial for(size_t j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] < num_var_tape_ ); // ind_taddr_[j] is operator taddr for j-th independent variable CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == j + 1 ); CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); // extract the result from rev_hes_sparsity CPPAD_ASSERT_UNKNOWN( rev_hes_sparsity.end() == q ); local::sparse_list::const_iterator itr(rev_hes_sparsity, j + 1); size_t i = *itr; while( i < q ) { if( transpose ) h.add_element(j, i); else h.add_element(i, j); i = *(++itr); } } } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/par_var.hpp0000644000175200017650000000576313057470465016632 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_PAR_VAR_HPP # define CPPAD_CORE_PAR_VAR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* --------------------------------------------------------------------------- $begin ParVar$$ $spell VecAD const bool $$ $section Is an AD Object a Parameter or Variable$$ $head Syntax$$ $icode%b% = Parameter(%x%)%$$ $pre $$ $icode%b% = Variable(%x%)%$$ $head Purpose$$ Determine if $icode x$$ is a $cref/parameter/glossary/Parameter/$$ or $cref/variable/glossary/Variable/$$. $head x$$ The argument $icode x$$ has prototype $codei% const AD<%Base%> &%x% const VecAD<%Base%> &%x% %$$ $head b$$ The return value $icode b$$ has prototype $codei% bool %b% %$$ The return value for $code Parameter$$ ($code Variable$$) is true if and only if $icode x$$ is a parameter (variable). Note that a $cref/VecAD/VecAD/$$ object is a variable if any element of the vector depends on the independent variables. $head Operation Sequence$$ The result of this operation is not an $cref/AD of Base/glossary/AD of Base/$$ object. Thus it will not be recorded as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Example$$ $children% example/par_var.cpp %$$ The file $cref par_var.cpp$$ contains an example and test of these functions. It returns true if it succeeds and false otherwise. $end ----------------------------------------------------------------------------- */ namespace CppAD { // Parameter template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool Parameter(const AD &x) { if( x.tape_id_ == 0 ) return true; size_t thread = size_t(x.tape_id_ % CPPAD_MAX_NUM_THREADS); return x.tape_id_ != *AD::tape_id_ptr(thread); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool Parameter(const VecAD &x) { if( x.tape_id_ == 0 ) return true; size_t thread = size_t(x.tape_id_ % CPPAD_MAX_NUM_THREADS); return x.tape_id_ != *AD::tape_id_ptr(thread); } // Variable template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool Variable(const AD &x) { if( x.tape_id_ == 0 ) return false; size_t thread = size_t(x.tape_id_ % CPPAD_MAX_NUM_THREADS); return x.tape_id_ == *AD::tape_id_ptr(thread); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool Variable(const VecAD &x) { if( x.tape_id_ == 0 ) return false; size_t thread = size_t(x.tape_id_ % CPPAD_MAX_NUM_THREADS); return x.tape_id_ == *AD::tape_id_ptr(thread); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/bender_quad.hpp0000644000175200017650000002300713057470465017440 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BENDER_QUAD_HPP # define CPPAD_CORE_BENDER_QUAD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin BenderQuad$$ $spell cppad.hpp BAvector gx gxx CppAD Fy dy Jacobian ADvector const dg ddg $$ $section Computing Jacobian and Hessian of Bender's Reduced Objective$$ $mindex BenderQuad$$ $head Syntax$$ $codei% # include BenderQuad(%x%, %y%, %fun%, %g%, %gx%, %gxx%)%$$ $head See Also$$ $cref opt_val_hes$$ $head Problem$$ The type $cref/ADvector/BenderQuad/ADvector/$$ cannot be determined form the arguments above (currently the type $icode ADvector$$ must be $codei%CPPAD_TESTVECTOR(%Base%)%$$.) This will be corrected in the future by requiring $icode Fun$$ to define $icode%Fun%::vector_type%$$ which will specify the type $icode ADvector$$. $head Purpose$$ We are given the optimization problem $latex \[ \begin{array}{rcl} {\rm minimize} & F(x, y) & {\rm w.r.t.} \; (x, y) \in \B{R}^n \times \B{R}^m \end{array} \] $$ that is convex with respect to $latex y$$. In addition, we are given a set of equations $latex H(x, y)$$ such that $latex \[ H[ x , Y(x) ] = 0 \;\; \Rightarrow \;\; F_y [ x , Y(x) ] = 0 \] $$ (In fact, it is often the case that $latex H(x, y) = F_y (x, y)$$.) Furthermore, it is easy to calculate a Newton step for these equations; i.e., $latex \[ dy = - [ \partial_y H(x, y)]^{-1} H(x, y) \] $$ The purpose of this routine is to compute the value, Jacobian, and Hessian of the reduced objective function $latex \[ G(x) = F[ x , Y(x) ] \] $$ Note that if only the value and Jacobian are needed, they can be computed more quickly using the relations $latex \[ G^{(1)} (x) = \partial_x F [x, Y(x) ] \] $$ $head x$$ The $code BenderQuad$$ argument $icode x$$ has prototype $codei% const %BAvector% &%x% %$$ (see $cref/BAvector/BenderQuad/BAvector/$$ below) and its size must be equal to $icode n$$. It specifies the point at which we evaluating the reduced objective function and its derivatives. $head y$$ The $code BenderQuad$$ argument $icode y$$ has prototype $codei% const %BAvector% &%y% %$$ and its size must be equal to $icode m$$. It must be equal to $latex Y(x)$$; i.e., it must solve the problem in $latex y$$ for this given value of $latex x$$ $latex \[ \begin{array}{rcl} {\rm minimize} & F(x, y) & {\rm w.r.t.} \; y \in \B{R}^m \end{array} \] $$ $head fun$$ The $code BenderQuad$$ object $icode fun$$ must support the member functions listed below. The $codei%AD<%Base%>%$$ arguments will be variables for a tape created by a call to $cref Independent$$ from $code BenderQuad$$ (hence they can not be combined with variables corresponding to a different tape). $subhead fun.f$$ The $code BenderQuad$$ argument $icode fun$$ supports the syntax $codei% %f% = %fun%.f(%x%, %y%) %$$ The $icode%fun%.f%$$ argument $icode x$$ has prototype $codei% const %ADvector% &%x% %$$ (see $cref/ADvector/BenderQuad/ADvector/$$ below) and its size must be equal to $icode n$$. The $icode%fun%.f%$$ argument $icode y$$ has prototype $codei% const %ADvector% &%y% %$$ and its size must be equal to $icode m$$. The $icode%fun%.f%$$ result $icode f$$ has prototype $codei% %ADvector% %f% %$$ and its size must be equal to one. The value of $icode f$$ is $latex \[ f = F(x, y) \] $$. $subhead fun.h$$ The $code BenderQuad$$ argument $icode fun$$ supports the syntax $codei% %h% = %fun%.h(%x%, %y%) %$$ The $icode%fun%.h%$$ argument $icode x$$ has prototype $codei% const %ADvector% &%x% %$$ and its size must be equal to $icode n$$. The $icode%fun%.h%$$ argument $icode y$$ has prototype $codei% const %BAvector% &%y% %$$ and its size must be equal to $icode m$$. The $icode%fun%.h%$$ result $icode h$$ has prototype $codei% %ADvector% %h% %$$ and its size must be equal to $icode m$$. The value of $icode h$$ is $latex \[ h = H(x, y) \] $$. $subhead fun.dy$$ The $code BenderQuad$$ argument $icode fun$$ supports the syntax $codei% %dy% = %fun%.dy(%x%, %y%, %h%) %x% %$$ The $icode%fun%.dy%$$ argument $icode x$$ has prototype $codei% const %BAvector% &%x% %$$ and its size must be equal to $icode n$$. Its value will be exactly equal to the $code BenderQuad$$ argument $icode x$$ and values depending on it can be stored as private objects in $icode f$$ and need not be recalculated. $codei% %y% %$$ The $icode%fun%.dy%$$ argument $icode y$$ has prototype $codei% const %BAvector% &%y% %$$ and its size must be equal to $icode m$$. Its value will be exactly equal to the $code BenderQuad$$ argument $icode y$$ and values depending on it can be stored as private objects in $icode f$$ and need not be recalculated. $codei% %h% %$$ The $icode%fun%.dy%$$ argument $icode h$$ has prototype $codei% const %ADvector% &%h% %$$ and its size must be equal to $icode m$$. $codei% %dy% %$$ The $icode%fun%.dy%$$ result $icode dy$$ has prototype $codei% %ADvector% %dy% %$$ and its size must be equal to $icode m$$. The return value $icode dy$$ is given by $latex \[ dy = - [ \partial_y H (x , y) ]^{-1} h \] $$ Note that if $icode h$$ is equal to $latex H(x, y)$$, $latex dy$$ is the Newton step for finding a zero of $latex H(x, y)$$ with respect to $latex y$$; i.e., $latex y + dy$$ is an approximate solution for the equation $latex H (x, y + dy) = 0$$. $head g$$ The argument $icode g$$ has prototype $codei% %BAvector% &%g% %$$ and has size one. The input value of its element does not matter. On output, it contains the value of $latex G (x)$$; i.e., $latex \[ g[0] = G (x) \] $$ $head gx$$ The argument $icode gx$$ has prototype $codei% %BAvector% &%gx% %$$ and has size $latex n $$. The input values of its elements do not matter. On output, it contains the Jacobian of $latex G (x)$$; i.e., for $latex j = 0 , \ldots , n-1$$, $latex \[ gx[ j ] = G^{(1)} (x)_j \] $$ $head gxx$$ The argument $icode gx$$ has prototype $codei% %BAvector% &%gxx% %$$ and has size $latex n \times n$$. The input values of its elements do not matter. On output, it contains the Hessian of $latex G (x)$$; i.e., for $latex i = 0 , \ldots , n-1$$, and $latex j = 0 , \ldots , n-1$$, $latex \[ gxx[ i * n + j ] = G^{(2)} (x)_{i,j} \] $$ $head BAvector$$ The type $icode BAvector$$ must be a $cref SimpleVector$$ class. We use $icode Base$$ to refer to the type of the elements of $icode BAvector$$; i.e., $codei% %BAvector%::value_type %$$ $head ADvector$$ The type $icode ADvector$$ must be a $cref SimpleVector$$ class with elements of type $codei%AD<%Base%>%$$; i.e., $codei% %ADvector%::value_type %$$ must be the same type as $codei% AD< %BAvector%::value_type > %$$. $head Example$$ $children% example/bender_quad.cpp %$$ The file $cref bender_quad.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ----------------------------------------------------------------------------- */ namespace CppAD { // BEGIN CppAD namespace template void BenderQuad( const BAvector &x , const BAvector &y , Fun fun , BAvector &g , BAvector &gx , BAvector &gxx ) { // determine the base type typedef typename BAvector::value_type Base; // check that BAvector is a SimpleVector class CheckSimpleVector(); // declare the ADvector type typedef CPPAD_TESTVECTOR(AD) ADvector; // size of the x and y spaces size_t n = size_t(x.size()); size_t m = size_t(y.size()); // check the size of gx and gxx CPPAD_ASSERT_KNOWN( g.size() == 1, "BenderQuad: size of the vector g is not equal to 1" ); CPPAD_ASSERT_KNOWN( size_t(gx.size()) == n, "BenderQuad: size of the vector gx is not equal to n" ); CPPAD_ASSERT_KNOWN( size_t(gxx.size()) == n * n, "BenderQuad: size of the vector gxx is not equal to n * n" ); // some temporary indices size_t i, j; // variable versions x ADvector vx(n); for(j = 0; j < n; j++) vx[j] = x[j]; // declare the independent variables Independent(vx); // evaluate h = H(x, y) ADvector h(m); h = fun.h(vx, y); // evaluate dy (x) = Newton step as a function of x through h only ADvector dy(m); dy = fun.dy(x, y, h); // variable version of y ADvector vy(m); for(j = 0; j < m; j++) vy[j] = y[j] + dy[j]; // evaluate G~ (x) = F [ x , y + dy(x) ] ADvector gtilde(1); gtilde = fun.f(vx, vy); // AD function object that corresponds to G~ (x) // We will make heavy use of this tape, so optimize it ADFun Gtilde; Gtilde.Dependent(vx, gtilde); Gtilde.optimize(); // value of G(x) g = Gtilde.Forward(0, x); // initial forward direction vector as zero BAvector dx(n); for(j = 0; j < n; j++) dx[j] = Base(0); // weight, first and second order derivative values BAvector dg(1), w(1), ddw(2 * n); w[0] = 1.; // Jacobian and Hessian of G(x) is equal Jacobian and Hessian of Gtilde for(j = 0; j < n; j++) { // compute partials in x[j] direction dx[j] = Base(1); dg = Gtilde.Forward(1, dx); gx[j] = dg[0]; // restore the dx vector to zero dx[j] = Base(0); // compute second partials w.r.t x[j] and x[l] for l = 1, n ddw = Gtilde.Reverse(2, w); for(i = 0; i < n; i++) gxx[ i * n + j ] = ddw[ i * 2 + 1 ]; } return; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/expm1.hpp0000644000175200017650000000450313057470465016221 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_EXPM1_HPP # define CPPAD_CORE_EXPM1_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin expm1$$ $spell exp expm1 const Vec std cmath CppAD $$ $section The Exponential Function Minus One: expm1$$ $head Syntax$$ $icode%y% = expm1(%x%)%$$ $head Description$$ Returns the value of the exponential function minus one which is defined by $icode%y% == exp(%x%) - 1%$$. $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head CPPAD_USE_CPLUSPLUS_2011$$ $subhead true$$ If this preprocessor symbol is true ($code 1$$), and $icode x$$ is an AD type, this is an $cref/atomic operation/glossary/Operation/Atomic/$$. $subhead false$$ If this preprocessor symbol is false ($code 0$$), CppAD uses the representation $latex \[ \R{expm1} (x) = \exp(x) - 1 \] $$ to compute this function. $head Example$$ $children% example/expm1.cpp %$$ The file $cref expm1.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ # include # if ! CPPAD_USE_CPLUSPLUS_2011 // BEGIN CppAD namespace namespace CppAD { template Type expm1_template(const Type &x) { return CppAD::exp(x) - Type(1); } inline float expm1(const float &x) { return expm1_template(x); } inline double expm1(const double &x) { return expm1_template(x); } template inline AD expm1(const AD &x) { return expm1_template(x); } template inline AD expm1(const VecAD_reference &x) { return expm1_template( x.ADBase() ); } } // END CppAD namespace # endif // CPPAD_USE_CPLUSPLUS_2011 # endif // CPPAD_EXPM1_INCLUDED cppad-20170000.3/cppad/core/reverse.hpp0000644000175200017650000001336113057470465016644 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_REVERSE_HPP # define CPPAD_CORE_REVERSE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file reverse.hpp Compute derivatives using reverse mode. */ /*! Use reverse mode to compute derivative of forward mode Taylor coefficients. The function \f$ X : {\rm R} \times {\rm R}^{n \times q} \rightarrow {\rm R} \f$ is defined by \f[ X(t , u) = \sum_{k=0}^{q-1} u^{(k)} t^k \f] The function \f$ Y : {\rm R} \times {\rm R}^{n \times q} \rightarrow {\rm R} \f$ is defined by \f[ Y(t , u) = F[ X(t, u) ] \f] The function \f$ W : {\rm R}^{n \times q} \rightarrow {\rm R} \f$ is defined by \f[ W(u) = \sum_{k=0}^{q-1} ( w^{(k)} )^{\rm T} \frac{1}{k !} \frac{ \partial^k } { t^k } Y(0, u) \f] \tparam Base base type for the operator; i.e., this operation sequence was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \tparam VectorBase is a Simple Vector class with elements of type \a Base. \param q is the number of the number of Taylor coefficients that are being differentiated (per variable). \param w is the weighting for each of the Taylor coefficients corresponding to dependent variables. If the argument \a w has size m * q , for \f$ k = 0 , \ldots , q-1 \f$ and \f$ i = 0, \ldots , m-1 \f$, \f[ w_i^{(k)} = w [ i * q + k ] \f] If the argument \a w has size \c m , for \f$ k = 0 , \ldots , q-1 \f$ and \f$ i = 0, \ldots , m-1 \f$, \f[ w_i^{(k)} = \left\{ \begin{array}{ll} w [ i ] & {\rm if} \; k = q-1 \\ 0 & {\rm otherwise} \end{array} \right. \f] \return Is a vector \f$ dw \f$ such that for \f$ j = 0 , \ldots , n-1 \f$ and \f$ k = 0 , \ldots , q-1 \f$ \f[ dw[ j * q + k ] = W^{(1)} ( x )_{j,k} \f] where the matrix \f$ x \f$ is the value for \f$ u \f$ that corresponding to the forward mode Taylor coefficients for the independent variables as specified by previous calls to Forward. */ template template VectorBase ADFun::Reverse(size_t q, const VectorBase &w) { // constants const Base zero(0); // temporary indices size_t i, j, k; // number of independent variables size_t n = ind_taddr_.size(); // number of dependent variables size_t m = dep_taddr_.size(); local::pod_vector Partial; Partial.extend(num_var_tape_ * q); // update maximum memory requirement // memoryMax = std::max( memoryMax, // Memory() + num_var_tape_ * q * sizeof(Base) // ); // check VectorBase is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( size_t(w.size()) == m || size_t(w.size()) == (m * q), "Argument w to Reverse does not have length equal to\n" "the dimension of the range for the corresponding ADFun." ); CPPAD_ASSERT_KNOWN( q > 0, "The first argument to Reverse must be greater than zero." ); CPPAD_ASSERT_KNOWN( num_order_taylor_ >= q, "Less that q taylor_ coefficients are currently stored" " in this ADFun object." ); // special case where multiple forward directions have been computed, // but we are only using the one direction zero order results if( (q == 1) & (num_direction_taylor_ > 1) ) { num_order_taylor_ = 1; // number of orders to copy size_t c = cap_order_taylor_; // keep the same capacity setting size_t r = 1; // only keep one direction capacity_order(c, r); } CPPAD_ASSERT_KNOWN( num_direction_taylor_ == 1, "Reverse mode for Forward(q, r, xq) with more than one direction" "\n(r > 1) is not yet supported for q > 1." ); // initialize entire Partial matrix to zero for(i = 0; i < num_var_tape_; i++) for(j = 0; j < q; j++) Partial[i * q + j] = zero; // set the dependent variable direction // (use += because two dependent variables can point to same location) for(i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); if( size_t(w.size()) == m ) Partial[dep_taddr_[i] * q + q - 1] += w[i]; else { for(k = 0; k < q; k++) // ? should use += here, first make test to demonstrate bug Partial[ dep_taddr_[i] * q + k ] = w[i * q + k ]; } } // evaluate the derivatives CPPAD_ASSERT_UNKNOWN( cskip_op_.size() == play_.num_op_rec() ); CPPAD_ASSERT_UNKNOWN( load_op_.size() == play_.num_load_op_rec() ); local::ReverseSweep( q - 1, n, num_var_tape_, &play_, cap_order_taylor_, taylor_.data(), q, Partial.data(), cskip_op_.data(), load_op_ ); // return the derivative values VectorBase value(n * q); for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] < num_var_tape_ ); // independent variable taddr equals its operator taddr CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); // by the Reverse Identity Theorem // partial of y^{(k)} w.r.t. u^{(0)} is equal to // partial of y^{(q-1)} w.r.t. u^{(q - 1 - k)} if( size_t(w.size()) == m ) { for(k = 0; k < q; k++) value[j * q + k ] = Partial[ind_taddr_[j] * q + q - 1 - k]; } else { for(k = 0; k < q; k++) value[j * q + k ] = Partial[ind_taddr_[j] * q + k]; } } CPPAD_ASSERT_KNOWN( ! ( hasnan(value) && check_for_nan_ ) , "dw = f.Reverse(q, w): has a nan,\n" "but none of its Taylor coefficents are nan." ); return value; } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/atanh.hpp0000644000175200017650000000456613057470465016273 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ATANH_HPP # define CPPAD_CORE_ATANH_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin atanh$$ $spell atanh const Vec std cmath CppAD tanh $$ $section The Inverse Hyperbolic Tangent Function: atanh$$ $head Syntax$$ $icode%y% = atanh(%x%)%$$ $head Description$$ The inverse hyperbolic tangent function is defined by $icode%x% == tanh(%y%)%$$. $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head CPPAD_USE_CPLUSPLUS_2011$$ $subhead true$$ If this preprocessor symbol is true ($code 1$$), and $icode x$$ is an AD type, this is an $cref/atomic operation/glossary/Operation/Atomic/$$. $subhead false$$ If this preprocessor symbol is false ($code 0$$), CppAD uses the representation $latex \[ \R{atanh} (x) = \frac{1}{2} \log \left( \frac{1 + x}{1 - x} \right) \] $$ to compute this function. $head Example$$ $children% example/atanh.cpp %$$ The file $cref atanh.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ # include # if ! CPPAD_USE_CPLUSPLUS_2011 // BEGIN CppAD namespace namespace CppAD { template Type atanh_template(const Type &x) { return CppAD::log( (Type(1) + x) / (Type(1) - x) ) / Type(2); } inline float atanh(const float &x) { return atanh_template(x); } inline double atanh(const double &x) { return atanh_template(x); } template inline AD atanh(const AD &x) { return atanh_template(x); } template inline AD atanh(const VecAD_reference &x) { return atanh_template( x.ADBase() ); } } // END CppAD namespace # endif // CPPAD_USE_CPLUSPLUS_2011 # endif // CPPAD_ATANH_INCLUDED cppad-20170000.3/cppad/core/ad_to_string.hpp0000644000175200017650000000347713057470465017654 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AD_TO_STRING_HPP # define CPPAD_CORE_AD_TO_STRING_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ad_to_string$$ $spell const std $$ $section Convert An AD or Base Type to String$$ $head Syntax$$ $icode%s% = to_string(%value%)%$$. $head See Also$$ $cref to_string$$, $cref base_to_string$$ $head value$$ The argument $icode value$$ has prototype $codei% const AD<%Base%>& %value% const %Base%& %value% %$$ where $icode Base$$ is a type that supports the $cref base_to_string$$ type requirement. $head s$$ The return value has prototype $codei% std::string %s% %$$ and contains a representation of the specified $icode value$$. If $icode value$$ is an AD type, the result has the same precision as for the $icode Base$$ type. $head Example$$ The file $cref to_string.cpp$$ includes an example and test of $code to_string$$ with AD types. It returns true if it succeeds and false otherwise. $end */ # include # include namespace CppAD { // Template definition is in cppad/utility/to_string.hpp. // Partial specialzation for AD types template struct to_string_struct< CppAD::AD > { std::string operator()(const CppAD::AD& value) { to_string_struct ts; return ts( Value( Var2Par( value ) ) ); } }; } # endif cppad-20170000.3/cppad/core/value.hpp0000644000175200017650000000423313057470465016303 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_VALUE_HPP # define CPPAD_CORE_VALUE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Value$$ $spell const $$ $section Convert From an AD Type to its Base Type$$ $mindex Value$$ $head Syntax$$ $icode%b% = Value(%x%)%$$ $head See Also$$ $cref var2par$$ $head Purpose$$ Converts from an AD type to the corresponding $cref/base type/glossary/Base Type/$$. $head x$$ The argument $icode x$$ has prototype $codei% const AD<%Base%> &%x% %$$ $head b$$ The return value $icode b$$ has prototype $codei% %Base% %b% %$$ $head Operation Sequence$$ The result of this operation is not an $cref/AD of Base/glossary/AD of Base/$$ object. Thus it will not be recorded as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Restriction$$ If the argument $icode x$$ is a $cref/variable/glossary/Variable/$$ its dependency information would not be included in the $code Value$$ result (see above). For this reason, the argument $icode x$$ must be a $cref/parameter/glossary/Parameter/$$; i.e., it cannot depend on the current $cref/independent variables/glossary/Tape/Independent Variable/$$. $head Example$$ $children% example/value.cpp %$$ The file $cref value.cpp$$ contains an example and test of this operation. $end ------------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION Base Value(const AD &x) { Base result; CPPAD_ASSERT_KNOWN( Parameter(x) , "Value: argument is a variable (not a parameter)" ); result = x.value_; return result; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/hash_code.hpp0000644000175200017650000000305213057470465017102 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_HASH_CODE_HPP # define CPPAD_CORE_HASH_CODE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file core/hash_code.hpp CppAD hashing utility. */ # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! General purpose hash code for an arbitrary value. \tparam Value is the type of the argument being hash coded. It should be a plain old data class; i.e., the values included in the equality operator in the object and not pointed to by the object. \param value the value that we are generating a hash code for. All of the fields in value should have been set before the hash code is computed (otherwise undefined values are used). \return is a hash code that is between zero and CPPAD_HASH_TABLE_SIZE - 1. \par Checked Assertions \li \c std::numeric_limits::max() >= CPPAD_HASH_TABLE_SIZE \li \c sizeof(value) is even \li \c sizeof(unsigned short) == 2 */ template unsigned short hash_code(const Value& value) { return local::local_hash_code(value); } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/sub_eq.hpp0000644000175200017650000000512213057470465016443 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_SUB_EQ_HPP # define CPPAD_CORE_SUB_EQ_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD& AD::operator -= (const AD &right) { // compute the Base part Base left; left = value_; value_ -= right.value_; // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return *this; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_left = tape_id_ == tape_id; bool var_right = right.tape_id_ == tape_id; if( var_left ) { if( var_right ) { // this = variable - variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::SubvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::SubvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(taddr_, right.taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::SubvvOp); // make this a variable CPPAD_ASSERT_UNKNOWN( tape_id_ == tape_id ); } else if( IdenticalZero( right.value_ ) ) { // this = variable - 0 } else { // this = variable - parameter CPPAD_ASSERT_UNKNOWN( local::NumRes(local::SubvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::SubvpOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(taddr_, p); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::SubvpOp); // make this a variable CPPAD_ASSERT_UNKNOWN( tape_id_ == tape_id ); } } else if( var_right ) { // this = parameter - variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::SubpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::SubpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(left); tape->Rec_.PutArg(p, right.taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::SubpvOp); // make this a variable tape_id_ = tape_id; } return *this; } CPPAD_FOLD_ASSIGNMENT_OPERATOR(-=) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/check_for_nan.hpp0000644000175200017650000001242413057470465017747 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_CHECK_FOR_NAN_HPP # define CPPAD_CORE_CHECK_FOR_NAN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin check_for_nan$$ $spell std vec Cpp const bool newline $$ $section Check an ADFun Object For Nan Results$$ $head Syntax$$ $icode%f%.check_for_nan(%b%) %$$ $icode%b% = %f%.check_for_nan() %$$ $codei%get_check_for_nan(%vec%, %file%) %$$ $head Debugging$$ If $code NDEBUG$$ is not defined, and the result of a $cref/forward/forward_order/$$ or $cref/reverse/reverse_any/$$ calculation contains a $cref nan$$, CppAD can halt with an error message. $head f$$ For the syntax where $icode b$$ is an argument, $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ (see $codei%ADFun<%Base%>%$$ $cref/constructor/FunConstruct/$$). For the syntax where $icode b$$ is the result, $icode f$$ has prototype $codei% const ADFun<%Base%> %f% %$$ $head b$$ This argument or result has prototype $codei% bool %b% %$$ Future calls to $icode%f%.Forward%$$ will (will not) check for $code nan$$. depending on if $icode b$$ is true (false). $head Default$$ The value for this setting after construction of $icode f$$) is true. The value of this setting is not affected by calling $cref Dependent$$ for this function object. $head Error Message$$ If this error is detected during zero order forward mode, the values of the independent variables that resulted in the $code nan$$ are written to a temporary binary file. This is so that you can run the original source code with those values to see what is causing the $code nan$$. $subhead vector_size$$ The error message with contain the text $codei%vector_size = %vector_size%$$ followed the newline character $code '\n'$$. The value of $icode vector_size$$ is the number of elements in the independent vector. $subhead file_name$$ The error message with contain the text $codei%file_name = %file_name%$$ followed the newline character $code '\n'$$. The value of $icode file_name$$ is the name of the temporary file that contains the dependent variable values. $subhead index$$ The error message will contain the text $codei%index = %index%$$ followed by the newline character $code '\n'$$. The value of $icode index$$ is the lowest dependent variable index that has the value $code nan$$. $head get_check_for_nan$$ This routine can be used to get the independent variable values that result in a $code nan$$. $subhead vec$$ This argument has prototype $codei% CppAD::vector<%Base%>& %vec% %$$ It size must be equal to the corresponding value of $cref/vector_size/check_for_nan/Error Message/vector_size/$$ in the corresponding error message. The input value of its elements does not matter. Upon return, it will contain the values for the independent variables, in the corresponding call to $cref Independent$$, that resulted in the $code nan$$. (Note that the call to $code Independent$$ uses an vector with elements of type $codei%AD<%Base%>%$$ and $icode vec$$ has elements of type $icode Base$$.) $subhead file$$ This argument has prototype $codei% const std::string& %file% %$$ It must be the value of $cref/file_name/check_for_nan/Error Message/file_name/$$ in the corresponding error message. $head Example$$ $children% example/check_for_nan.cpp %$$ The file $cref check_for_nan.cpp$$ contains an example and test of these operations. It returns true if it succeeds and false otherwise. $end */ # include # include # include # if CPPAD_HAS_MKSTEMP # include # include # else # if CPPAD_HAS_TMPNAM_S # include # else # include # endif # endif namespace CppAD { // BEGIN_CPPAD_NAMESPACE template void put_check_for_nan(const CppAD::vector& vec, std::string& file_name) { size_t char_size = sizeof(Base) * vec.size(); const char* char_ptr = reinterpret_cast( vec.data() ); # if CPPAD_HAS_MKSTEMP char pattern[] = "/tmp/fileXXXXXX"; int fd = mkstemp(pattern); file_name = pattern; write(fd, char_ptr, char_size); close(fd); # else # if CPPAD_HAS_TMPNAM_S std::vector name(L_tmpnam_s); if( tmpnam_s( name.data(), L_tmpnam_s ) != 0 ) { CPPAD_ASSERT_KNOWN( false, "Cannot create a temporary file name" ); } file_name = name.data(); # else file_name = tmpnam( CPPAD_NULL ); # endif std::fstream file_out(file_name.c_str(), std::ios::out|std::ios::binary ); file_out.write(char_ptr, char_size); file_out.close(); # endif return; } template void get_check_for_nan(CppAD::vector& vec, const std::string& file_name) { // size_t n = vec.size(); size_t char_size = sizeof(Base) * n; char* char_ptr = reinterpret_cast( vec.data() ); // std::fstream file_in(file_name.c_str(), std::ios::in|std::ios::binary ); file_in.read(char_ptr, char_size); // return; } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/for_two.hpp0000644000175200017650000001447513057470465016657 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_FOR_TWO_HPP # define CPPAD_CORE_FOR_TWO_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ForTwo$$ $spell ddy typename Taylor const $$ $section Forward Mode Second Partial Derivative Driver$$ $mindex order easy$$ $head Syntax$$ $icode%ddy% = %f%.ForTwo(%x%, %j%, %k%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The syntax above sets $latex \[ ddy [ i * p + \ell ] = \DD{ F_i }{ x_{j[ \ell ]} }{ x_{k[ \ell ]} } (x) \] $$ for $latex i = 0 , \ldots , m-1$$ and $latex \ell = 0 , \ldots , p$$, where $latex p$$ is the size of the vectors $icode j$$ and $icode k$$. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/ForTwo Uses Forward/ForTwo/ForTwo Uses Forward/$$ below). $head x$$ The argument $icode x$$ has prototype $codei% const %VectorBase% &%x% %$$ (see $cref/VectorBase/ForTwo/VectorBase/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies that point at which to evaluate the partial derivatives listed above. $head j$$ The argument $icode j$$ has prototype $codei% const %VectorSize_t% &%j% %$$ (see $cref/VectorSize_t/ForTwo/VectorSize_t/$$ below) We use $icode p$$ to denote the size of the vector $icode j$$. All of the indices in $icode j$$ must be less than $icode n$$; i.e., for $latex \ell = 0 , \ldots , p-1$$, $latex j[ \ell ] < n$$. $head k$$ The argument $icode k$$ has prototype $codei% const %VectorSize_t% &%k% %$$ (see $cref/VectorSize_t/ForTwo/VectorSize_t/$$ below) and its size must be equal to $icode p$$, the size of the vector $icode j$$. All of the indices in $icode k$$ must be less than $icode n$$; i.e., for $latex \ell = 0 , \ldots , p-1$$, $latex k[ \ell ] < n$$. $head ddy$$ The result $icode ddy$$ has prototype $codei% %VectorBase% %ddy% %$$ (see $cref/VectorBase/ForTwo/VectorBase/$$ below) and its size is $latex m * p$$. It contains the requested partial derivatives; to be specific, for $latex i = 0 , \ldots , m - 1 $$ and $latex \ell = 0 , \ldots , p - 1$$ $latex \[ ddy [ i * p + \ell ] = \DD{ F_i }{ x_{j[ \ell ]} }{ x_{k[ \ell ]} } (x) \] $$ $head VectorBase$$ The type $icode VectorBase$$ must be a $cref SimpleVector$$ class with $cref/elements of type Base/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head VectorSize_t$$ The type $icode VectorSize_t$$ must be a $cref SimpleVector$$ class with $cref/elements of type size_t/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head ForTwo Uses Forward$$ After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After a call to $code ForTwo$$, the zero order Taylor coefficients correspond to $icode%f%.Forward(0, %x%)%$$ and the other coefficients are unspecified. $head Examples$$ $children% example/for_two.cpp %$$ The routine $cref/ForTwo/for_two.cpp/$$ is both an example and test. It returns $code true$$, if it succeeds and $code false$$ otherwise. $end ----------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template template VectorBase ADFun::ForTwo( const VectorBase &x, const VectorSize_t &j, const VectorSize_t &k) { size_t i; size_t j1; size_t k1; size_t l; size_t n = Domain(); size_t m = Range(); size_t p = j.size(); // check VectorBase is Simple Vector class with Base type elements CheckSimpleVector(); // check VectorSize_t is Simple Vector class with size_t elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( x.size() == n, "ForTwo: Length of x not equal domain dimension for f." ); CPPAD_ASSERT_KNOWN( j.size() == k.size(), "ForTwo: Lenght of the j and k vectors are not equal." ); // point at which we are evaluating the second partials Forward(0, x); // dimension the return value VectorBase ddy(m * p); // allocate memory to hold all possible diagonal Taylor coefficients // (for large sparse cases, this is not efficient) VectorBase D(m * n); // boolean flag for which diagonal coefficients are computed CppAD::vector c(n); for(j1 = 0; j1 < n; j1++) c[j1] = false; // direction vector in argument space VectorBase dx(n); for(j1 = 0; j1 < n; j1++) dx[j1] = Base(0); // result vector in range space VectorBase dy(m); // compute the diagonal coefficients that are needed for(l = 0; l < p; l++) { j1 = j[l]; k1 = k[l]; CPPAD_ASSERT_KNOWN( j1 < n, "ForTwo: an element of j not less than domain dimension for f." ); CPPAD_ASSERT_KNOWN( k1 < n, "ForTwo: an element of k not less than domain dimension for f." ); size_t count = 2; while(count) { count--; if( ! c[j1] ) { // diagonal term in j1 direction c[j1] = true; dx[j1] = Base(1); Forward(1, dx); dx[j1] = Base(0); dy = Forward(2, dx); for(i = 0; i < m; i++) D[i * n + j1 ] = dy[i]; } j1 = k1; } } // compute all the requested cross partials for(l = 0; l < p; l++) { j1 = j[l]; k1 = k[l]; if( j1 == k1 ) { for(i = 0; i < m; i++) ddy[i * p + l] = Base(2) * D[i * n + j1]; } else { // cross term in j1 and k1 directions dx[j1] = Base(1); dx[k1] = Base(1); Forward(1, dx); dx[j1] = Base(0); dx[k1] = Base(0); dy = Forward(2, dx); // place result in return value for(i = 0; i < m; i++) ddy[i * p + l] = dy[i] - D[i*n+j1] - D[i*n+k1]; } } return ddy; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/convert.hpp0000644000175200017650000000226713057470465016654 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_CONVERT_HPP # define CPPAD_CORE_CONVERT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Convert$$ $spell $$ $section Conversion and I/O of AD Objects$$ $mindex convert from$$ $children% cppad/core/value.hpp% cppad/core/integer.hpp% cppad/core/ad_to_string.hpp% cppad/core/ad_io.hpp% cppad/core/print_for.hpp% cppad/core/var2par.hpp %$$ $table $rref Value$$ $rref Integer$$ $rref ad_output$$ $rref PrintFor$$ $rref Var2Par$$ $tend $end */ # include # include # include # include # include # include # endif cppad-20170000.3/cppad/core/div.hpp0000644000175200017650000000575213057470465015760 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_DIV_HPP # define CPPAD_CORE_DIV_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD operator / (const AD &left , const AD &right) { // compute the Base part AD result; result.value_ = left.value_ / right.value_; CPPAD_ASSERT_UNKNOWN( Parameter(result) ); // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return result; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_left = left.tape_id_ == tape_id; bool var_right = right.tape_id_ == tape_id; if( var_left ) { if( var_right ) { // result = variable / variable CPPAD_ASSERT_KNOWN( left.tape_id_ == right.tape_id_, "Dividing AD objects that are" " variables on different tapes." ); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::DivvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::DivvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(left.taddr_, right.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::DivvvOp); // make result a variable result.tape_id_ = tape_id; } else if( IdenticalOne(right.value_) ) { // result = variable / 1 result.make_variable(left.tape_id_, left.taddr_); } else { // result = variable / parameter CPPAD_ASSERT_UNKNOWN( local::NumRes(local::DivvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::DivvpOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(left.taddr_, p); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::DivvpOp); // make result a variable result.tape_id_ = tape_id; } } else if( var_right ) { if( IdenticalZero(left.value_) ) { // result = 0 / variable } else { // result = parameter / variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::DivpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::DivpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(left.value_); tape->Rec_.PutArg(p, right.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::DivpvOp); // make result a variable result.tape_id_ = tape_id; } } return result; } // convert other cases into the case above CPPAD_FOLD_AD_VALUED_BINARY_OPERATOR(/) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/mul_eq.hpp0000644000175200017650000000561513057470465016456 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_MUL_EQ_HPP # define CPPAD_CORE_MUL_EQ_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD& AD::operator *= (const AD &right) { // compute the Base part Base left; left = value_; value_ *= right.value_; // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return *this; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_left = tape_id_ == tape_id; bool var_right = right.tape_id_ == tape_id; if( var_left ) { if( var_right ) { // this = variable * variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::MulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::MulvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(taddr_, right.taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::MulvvOp); // make this a variable CPPAD_ASSERT_UNKNOWN( tape_id_ == tape_id ); } else if( IdenticalOne( right.value_ ) ) { // this = variable * 1 } else if( IdenticalZero( right.value_ ) ) { // this = variable * 0 make_parameter(); } else { // this = variable * parameter // = parameter * variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::MulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::MulpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(p, taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::MulpvOp); // make this a variable CPPAD_ASSERT_UNKNOWN( tape_id_ == tape_id ); } } else if( var_right ) { if( IdenticalZero(left) ) { // this = 0 * right } else if( IdenticalOne(left) ) { // this = 1 * right make_variable(right.tape_id_, right.taddr_); } else { // this = parameter * variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::MulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::MulpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(left); tape->Rec_.PutArg(p, right.taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::MulpvOp); // make this a variable tape_id_ = tape_id; } } return *this; } CPPAD_FOLD_ASSIGNMENT_OPERATOR(*=) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/numeric_limits.hpp0000644000175200017650000001240213057470465020207 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_NUMERIC_LIMITS_HPP # define CPPAD_CORE_NUMERIC_LIMITS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------ $begin numeric_limits$$ $spell std eps CppAD namespace const $$ $section Numeric Limits For an AD and Base Types$$ $head Syntax$$ $icode%eps% = numeric_limits<%Float%>::epsilon() %$$ $icode%min% = numeric_limits<%Float%>::min() %$$ $icode%max% = numeric_limits<%Float%>::max() %$$ $icode%nan% = numeric_limits<%Float%>::quiet_NaN() %$$ $head CppAD::numeric_limits$$ These functions and have the prototype $codei% static %Float% CppAD::numeric_limits<%Float%>::%fun%(%void%) %$$ where $icode fun$$ is $code epsilon$$, $code min$$, $code max$$, and $code quiet_NaN$$. $head std::numeric_limits$$ CppAD does not use a specialization of $code std::numeric_limits$$ because this would be to restrictive. The C++ standard specifies that Non-fundamental standard types, such as $cref/std::complex/base_complex.hpp/$$ shall not have specializations of $code std::numeric_limits$$; see Section 18.2 of ISO/IEC 14882:1998(E). In addition, since C++11, a only literal types can have a specialization of $code std::numeric_limits$$. $head Float$$ These functions are defined for all $codei%AD<%Base%>%$$, and for all corresponding $icode Base$$ types; see $icode Base$$ type $cref base_limits$$. $head epsilon$$ The result $icode eps$$ is equal to machine epsilon and has prototype $codei% %Float% %eps% %$$ The file $cref num_limits.cpp$$ tests the value $icode eps$$ by checking that the following are true $codei% 1 != 1 + %eps% 1 == 1 + %eps% / 2 %$$ where all the values, and calculations, are done with the precision corresponding to $icode Float$$. $head min$$ The result $icode min$$ is equal to the minimum positive normalized value and has prototype $codei% %Float% %min% %$$ The file $cref num_limits.cpp$$ tests the value $icode min$$ by checking that the following are true $codei% abs( ((%min% / 100) * 100) / %min% - 1 ) > 3 * %eps% abs( ((%min% * 100) / 100) / %min% - 1 ) < 3 * %eps% %$$ where all the values, and calculations, are done with the precision corresponding to $icode Float$$. $head max$$ The result $icode max$$ is equal to the maximum finite value and has prototype $codei% %Float% %max% %$$ The file $cref num_limits.cpp$$ tests the value $icode max$$ by checking that the following are true $codei% abs( ((%max% * 100) / 100) / %max% - 1 ) > 3 * %eps% abs( ((%max% / 100) * 100) / %max% - 1 ) < 3 * %eps% %$$ where all the values, and calculations, are done with the precision corresponding to $icode Float$$. $head quiet_NaN$$ The result $icode nan$$ is not a number and has prototype $codei% %Float% %nan% %$$ The file $cref num_limits.cpp$$ tests the value $icode nan$$ by checking that the following is true $codei% %nan% != %nan% %$$ $head Example$$ $children% example/num_limits.cpp %$$ The file $cref num_limits.cpp$$ contains an example and test of these functions. $end ------------------------------------------------------------------------------ */ # include # include # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file numeric_limits.hpp File that defines CppAD numeric_limits for AD types */ /// Default value for all undefined numeric_limits types template class numeric_limits { public: /// machine epsilon static Float epsilon(void) { CPPAD_ASSERT_KNOWN( false, "numeric_limits::epsilon() is not specialized for this Float" ); return Float(0); } /// minimum positive normalized value static Float min(void) { CPPAD_ASSERT_KNOWN( false, "numeric_limits::min() is not specialized for this Float" ); return Float(0); } /// maximum finite value static Float max(void) { CPPAD_ASSERT_KNOWN( false, "numeric_limits::max() is not specialized for this Float" ); return Float(0); } /// not a number static Float quiet_NaN(void) { CPPAD_ASSERT_KNOWN( false, "numeric_limits::quiet_NaN() is not specialized for this Float" ); return Float(0); } }; /// Partial specialization that defines limits for for all AD types template class numeric_limits< AD > { public: /// machine epsilon static AD epsilon(void) { return AD( numeric_limits::epsilon() ); } /// minimum positive normalized value static AD min(void) { return AD( numeric_limits::min() ); } /// maximum finite value static AD max(void) { return AD( numeric_limits::max() ); } /// note a number static AD quiet_NaN(void) { return AD( numeric_limits::quiet_NaN() ); } }; } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/ordered.hpp0000644000175200017650000000545413057470465016621 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ORDERED_HPP # define CPPAD_CORE_ORDERED_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file ordered.hpp Check and AD values ordering properties relative to zero. */ // GreaterThanZero ============================================================ /*! Check if an AD is greater than zero. \param x value we are checking. \return returns true iff the \c x is greater than zero. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool GreaterThanZero(const AD &x) { return GreaterThanZero(x.value_); } // GreaterThanOrZero ========================================================= /*! Check if an AD is greater than or equal zero. \param x value we are checking. \return returns true iff the \c x is greater than or equal zero. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool GreaterThanOrZero(const AD &x) { return GreaterThanOrZero(x.value_); } // LessThanZero ============================================================ /*! Check if an AD is less than zero. \param x value we are checking. \return returns true iff the \c x is less than zero. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool LessThanZero(const AD &x) { return LessThanZero(x.value_); } // LessThanOrZero ========================================================= /*! Check if an AD is less than or equal zero. \param x value we are checking. \return returns true iff the \c x is less than or equal zero. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool LessThanOrZero(const AD &x) { return LessThanOrZero(x.value_); } // abs_geq ========================================================= /*! Check if absolute value of one AD is greater or equal another. \param x value we are checking if it is greater than or equal other. \param y value we are checking if it is less than other. \return returns true iff the absolute value of \c x is greater than or equal absolute value of \c y. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool abs_geq(const AD& x, const AD& y) { return abs_geq(x.value_, y.value_); } // ============================================================================ } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/for_one.hpp0000644000175200017650000000776413057470465016632 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_FOR_ONE_HPP # define CPPAD_CORE_FOR_ONE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ForOne$$ $spell dy typename Taylor const $$ $section First Order Partial Derivative: Driver Routine$$ $mindex easy$$ $head Syntax$$ $icode%dy% = %f%.ForOne(%x%, %j%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The syntax above sets $icode dy$$ to the partial of $latex F$$ with respect to $latex x_j$$; i.e., $latex \[ dy = \D{F}{ x_j } (x) = \left[ \D{ F_0 }{ x_j } (x) , \cdots , \D{ F_{m-1} }{ x_j } (x) \right] \] $$ $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/ForOne Uses Forward/ForOne/ForOne Uses Forward/$$ below). $head x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ (see $cref/Vector/ForOne/Vector/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies that point at which to evaluate the partial derivative. $head j$$ The argument $icode j$$ has prototype $codei% size_t %j% %$$ an is less than $icode n$$, $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies the component of $icode F$$ for which we are computing the partial derivative. $head dy$$ The result $icode dy$$ has prototype $codei% %Vector% %dy% %$$ (see $cref/Vector/ForOne/Vector/$$ below) and its size is $latex m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. The value of $icode dy$$ is the partial of $latex F$$ with respect to $latex x_j$$ evaluated at $icode x$$; i.e., for $latex i = 0 , \ldots , m - 1$$ $latex \[. dy[i] = \D{ F_i }{ x_j } ( x ) \] $$ $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head ForOne Uses Forward$$ After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After a call to $code ForOne$$, the zero order Taylor coefficients correspond to $icode%f%.Forward(0,%x%)%$$ and the other coefficients are unspecified. $head Example$$ $children% example/for_one.cpp %$$ The routine $cref/ForOne/for_one.cpp/$$ is both an example and test. It returns $code true$$, if it succeeds and $code false$$ otherwise. $end ----------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template template Vector ADFun::ForOne(const Vector &x, size_t j) { size_t j1; size_t n = Domain(); size_t m = Range(); // check Vector is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( x.size() == n, "ForOne: Length of x not equal domain dimension for f" ); CPPAD_ASSERT_KNOWN( j < n, "ForOne: the index j is not less than domain dimension for f" ); // point at which we are evaluating the second partials Forward(0, x); // direction in which are are taking the derivative Vector dx(n); for(j1 = 0; j1 < n; j1++) dx[j1] = Base(0); dx[j] = Base(1); // dimension the return value Vector dy(m); // compute the return value dy = Forward(1, dx); return dy; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/add.hpp0000644000175200017650000000571613057470465015726 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ADD_HPP # define CPPAD_CORE_ADD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD operator + (const AD &left , const AD &right) { // compute the Base part of this AD object AD result; result.value_ = left.value_ + right.value_; CPPAD_ASSERT_UNKNOWN( Parameter(result) ); // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return result; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_left = left.tape_id_ == tape_id; bool var_right = right.tape_id_ == tape_id; if( var_left ) { if( var_right ) { // result = variable + variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::AddvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::AddvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(left.taddr_, right.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::AddvvOp); // make result a variable result.tape_id_ = tape_id; } else if( IdenticalZero(right.value_) ) { // result = variable + 0 result.make_variable(left.tape_id_, left.taddr_); } else { // result = variable + parameter // = parameter + variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::AddpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::AddpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(p, left.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::AddpvOp); // make result a variable result.tape_id_ = tape_id; } } else if( var_right ) { if( IdenticalZero(left.value_) ) { // result = 0 + variable result.make_variable(right.tape_id_, right.taddr_); } else { // result = parameter + variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::AddpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::AddpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(left.value_); tape->Rec_.PutArg(p, right.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::AddpvOp); // make result a variable result.tape_id_ = tape_id; } } return result; } // convert other cases into the case above CPPAD_FOLD_AD_VALUED_BINARY_OPERATOR(+) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/base_limits.hpp0000644000175200017650000000405713057470465017466 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BASE_LIMITS_HPP # define CPPAD_CORE_BASE_LIMITS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_limits$$ $spell std namespace CppAD $$ $section Base Type Requirements for Numeric Limits$$ $head CppAD::numeric_limits$$ A specialization for $cref/CppAD::numeric_limits/numeric_limits/$$ must be defined in order to use the type $codei%AD<%Base%>%$$. CppAD does not use a specialization of $codei%std::numeric_limits<%Base%>%$$. Since C++11, using a specialization of $codei%std::numeric_limits<%Base%>%$$ would require that $icode Base$$ be a literal type. $head CPPAD_NUMERIC_LIMITS$$ In most cases, this macro can be used to define the specialization where the numeric limits for the type $icode Base$$ are the same as the standard numeric limits for the type $icode Other$$. For most $icode Base$$ types, there is a choice of $icode Other$$, for which the following preprocessor macro invocation suffices: $codei% namespace CppAD { CPPAD_NUMERIC_LIMITS(%Other%, %Base%) } %$$ where the macro is defined by $srccode%cpp% */ # define CPPAD_NUMERIC_LIMITS(Other, Base) \ template <> class numeric_limits\ {\ public:\ static Base min(void) \ { return static_cast( std::numeric_limits::min() ); }\ static Base max(void) \ { return static_cast( std::numeric_limits::max() ); }\ static Base epsilon(void) \ { return static_cast( std::numeric_limits::epsilon() ); }\ static Base quiet_NaN(void) \ { return static_cast( std::numeric_limits::quiet_NaN() ); }\ }; /* %$$ $end */ # endif cppad-20170000.3/cppad/core/fun_construct.hpp0000644000175200017650000003275113057470465020071 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_FUN_CONSTRUCT_HPP # define CPPAD_CORE_FUN_CONSTRUCT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin FunConstruct$$ $spell alloc num Jac bool taylor var ADvector const Jacobian $$ $spell $$ $section Construct an ADFun Object and Stop Recording$$ $mindex tape$$ $head Syntax$$ $codei%ADFun<%Base%> %f%, %g% %$$ $codei%ADFun<%Base%> %f%(%x%, %y%) %$$ $icode%g% = %f% %$$ $head Purpose$$ The $codei%AD<%Base%>%$$ object $icode f$$ can store an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. It can then be used to calculate derivatives of the corresponding $cref/AD function/glossary/AD Function/$$ $latex \[ F : B^n \rightarrow B^m \] $$ where $latex B$$ is the space corresponding to objects of type $icode Base$$. $head x$$ If the argument $icode x$$ is present, it has prototype $codei% const %VectorAD% &%x% %$$ It must be the vector argument in the previous call to $cref Independent$$. Neither its size, or any of its values, are allowed to change between calling $codei% Independent(%x%) %$$ and $codei% ADFun<%Base%> %f%(%x%, %y%) %$$ $head y$$ If the argument $icode y$$ is present, it has prototype $codei% const %VectorAD% &%y% %$$ The sequence of operations that map $icode x$$ to $icode y$$ are stored in the ADFun object $icode f$$. $head VectorAD$$ The type $icode VectorAD$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $codei%AD<%Base%>%$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Default Constructor$$ The default constructor $codei% ADFun<%Base%> %f% %$$ creates an $codei%AD<%Base%>%$$ object with no corresponding operation sequence; i.e., $codei% %f%.size_var() %$$ returns the value zero (see $cref/size_var/seq_property/size_var/$$). $head Sequence Constructor$$ The sequence constructor $codei% ADFun<%Base%> %f%(%x%, %y%) %$$ creates the $codei%AD<%Base%>%$$ object $icode f$$, stops the recording of AD of $icode Base$$ operations corresponding to the call $codei% Independent(%x%) %$$ and stores the corresponding operation sequence in the object $icode f$$. It then stores the zero order Taylor coefficients (corresponding to the value of $icode x$$) in $icode f$$. This is equivalent to the following steps using the default constructor: $list number$$ Create $icode f$$ with the default constructor $codei% ADFun<%Base%> %f%; %$$ $lnext Stop the tape and storing the operation sequence using $codei% %f%.Dependent(%x%, %y%); %$$ (see $cref Dependent$$). $lnext Calculate the zero order Taylor coefficients for all the variables in the operation sequence using $codei% %f%.Forward(%p%, %x_p%) %$$ with $icode p$$ equal to zero and the elements of $icode x_p$$ equal to the corresponding elements of $icode x$$ (see $cref Forward$$). $lend $head Copy Constructor$$ It is an error to attempt to use the $codei%ADFun<%Base%>%$$ copy constructor; i.e., the following syntax is not allowed: $codei% ADFun<%Base%> %g%(%f%) %$$ where $icode f$$ is an $codei%ADFun<%Base%>%$$ object. Use its $cref/default constructor/FunConstruct/Default Constructor/$$ instead and its assignment operator. $head Assignment Operator$$ The $codei%ADFun<%Base%>%$$ assignment operation $codei% %g% = %f% %$$ makes a copy of the operation sequence currently stored in $icode f$$ in the object $icode g$$. The object $icode f$$ is not affected by this operation and can be $code const$$. All of information (state) stored in $icode f$$ is copied to $icode g$$ and any information originally in $icode g$$ is lost. $subhead Taylor Coefficients$$ The Taylor coefficient information currently stored in $icode f$$ (computed by $cref/f.Forward/Forward/$$) is copied to $icode g$$. Hence, directly after this operation $codei% %g%.size_order() == %f%.size_order() %$$ $subhead Sparsity Patterns$$ The forward Jacobian sparsity pattern currently stored in $icode f$$ (computed by $cref/f.ForSparseJac/ForSparseJac/$$) is copied to $icode g$$. Hence, directly after this operation $codei% %g%.size_forward_bool() == %f%.size_forward_bool() %g%.size_forward_set() == %f%.size_forward_set() %$$ $head Parallel Mode$$ The call to $code Independent$$, and the corresponding call to $codei% ADFun<%Base%> %f%( %x%, %y%) %$$ or $codei% %f%.Dependent( %x%, %y%) %$$ or $cref abort_recording$$, must be preformed by the same thread; i.e., $cref/thread_alloc::thread_num/ta_thread_num/$$ must be the same. $head Example$$ $subhead Sequence Constructor$$ The file $cref independent.cpp$$ contains an example and test of the sequence constructor. It returns true if it succeeds and false otherwise. $subhead Default Constructor$$ The files $cref fun_check.cpp$$ and $cref hes_lagrangian.cpp$$ contain an examples and tests using the default constructor. They return true if they succeed and false otherwise. $children% example/fun_assign.cpp %$$ $subhead Assignment Operator$$ The file $cref fun_assign.cpp$$ contains an example and test of the $codei%ADFun<%Base%>%$$ assignment operator. It returns true if it succeeds and false otherwise. $end ---------------------------------------------------------------------------- */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file fun_construct.hpp ADFun function constructors and assignment operator. */ /*! ADFun default constructor The C++ syntax for this operation is \verbatim ADFun f \endverbatim An empty ADFun object is created. The Dependent member function, or the ADFun assingment operator, can then be used to put an operation sequence in this ADFun object. \tparam Base is the base for the recording that can be stored in this ADFun object; i.e., operation sequences that were recorded using the type \c AD. */ template ADFun::ADFun(void) : has_been_optimized_(false), check_for_nan_(true) , compare_change_count_(1), compare_change_number_(0), compare_change_op_index_(0), num_var_tape_(0) { } /*! ADFun assignment operator The C++ syntax for this operation is \verbatim g = f \endverbatim where \c g and \c f are ADFun ADFun objects. A copy of the the operation sequence currently stored in \c f is placed in this ADFun object (called \c g above). Any information currently stored in this ADFun object is lost. \tparam Base is the base for the recording that can be stored in this ADFun object; i.e., operation sequences that were recorded using the type \c AD. \param f ADFun object containing the operation sequence to be copied. */ template void ADFun::operator=(const ADFun& f) { size_t m = f.Range(); size_t n = f.Domain(); size_t i; // go through member variables in ad_fun.hpp order // // size_t objects has_been_optimized_ = f.has_been_optimized_; check_for_nan_ = f.check_for_nan_; compare_change_count_ = f.compare_change_count_; compare_change_number_ = f.compare_change_number_; compare_change_op_index_ = f.compare_change_op_index_; num_order_taylor_ = f.num_order_taylor_; cap_order_taylor_ = f.cap_order_taylor_; num_direction_taylor_ = f.num_direction_taylor_; num_var_tape_ = f.num_var_tape_; // // CppAD::vector objects ind_taddr_.resize(n); ind_taddr_ = f.ind_taddr_; dep_taddr_.resize(m); dep_taddr_ = f.dep_taddr_; dep_parameter_.resize(m); dep_parameter_ = f.dep_parameter_; // // pod_vector objects taylor_ = f.taylor_; cskip_op_ = f.cskip_op_; load_op_ = f.load_op_; // // player play_ = f.play_; // // sparse_pack for_jac_sparse_pack_.resize(0, 0); size_t n_set = f.for_jac_sparse_pack_.n_set(); size_t end = f.for_jac_sparse_pack_.end(); if( n_set > 0 ) { CPPAD_ASSERT_UNKNOWN( n_set == num_var_tape_ ); CPPAD_ASSERT_UNKNOWN( f.for_jac_sparse_set_.n_set() == 0 ); for_jac_sparse_pack_.resize(n_set, end); for(i = 0; i < num_var_tape_ ; i++) { for_jac_sparse_pack_.assignment( i , i , f.for_jac_sparse_pack_ ); } } // // sparse_set for_jac_sparse_set_.resize(0, 0); n_set = f.for_jac_sparse_set_.n_set(); end = f.for_jac_sparse_set_.end(); if( n_set > 0 ) { CPPAD_ASSERT_UNKNOWN( n_set == num_var_tape_ ); CPPAD_ASSERT_UNKNOWN( f.for_jac_sparse_pack_.n_set() == 0 ); for_jac_sparse_set_.resize(n_set, end); for(i = 0; i < num_var_tape_; i++) { for_jac_sparse_set_.assignment( i , i , f.for_jac_sparse_set_ ); } } } /*! ADFun constructor from an operation sequence. The C++ syntax for this operation is \verbatim ADFun f(x, y) \endverbatim The operation sequence that started with the previous call \c Independent(x), and that ends with this operation, is stored in this \c ADFun object \c f. \tparam Base is the base for the recording that will be stored in the object \c f; i.e., the operations were recorded using the type \c AD. \tparam VectorAD is a simple vector class with elements of typea \c AD. \param x is the independent variable vector for this ADFun object. The domain dimension of this object will be the size of \a x. \param y is the dependent variable vector for this ADFun object. The range dimension of this object will be the size of \a y. \par Taylor Coefficients A zero order forward mode sweep is done, and if NDEBUG is not defined the resulting values for the depenedent variables are checked against the values in \a y. Thus, the zero order Taylor coefficients corresponding to the value of the \a x vector are stored in this ADFun object. */ template template ADFun::ADFun(const VectorAD &x, const VectorAD &y) { CPPAD_ASSERT_KNOWN( x.size() > 0, "ADFun: independent variable vector has size zero." ); CPPAD_ASSERT_KNOWN( Variable(x[0]), "ADFun: independent variable vector has been changed." ); local::ADTape* tape = AD::tape_ptr(x[0].tape_id_); CPPAD_ASSERT_KNOWN( tape->size_independent_ == size_t ( x.size() ), "ADFun: independent variable vector has been changed." ); size_t j, n = x.size(); # ifndef NDEBUG size_t i, m = y.size(); for(j = 0; j < n; j++) { CPPAD_ASSERT_KNOWN( size_t(x[j].taddr_) == (j+1), "ADFun: independent variable vector has been changed." ); CPPAD_ASSERT_KNOWN( x[j].tape_id_ == x[0].tape_id_, "ADFun: independent variable vector has been changed." ); } for(i = 0; i < m; i++) { CPPAD_ASSERT_KNOWN( CppAD::Parameter( y[i] ) | (y[i].tape_id_ == x[0].tape_id_) , "ADFun: dependent vector contains variables for" "\na different tape than the independent variables." ); } # endif // stop the tape and store the operation sequence Dependent(tape, y); // ad_fun.hpp member values not set by dependent check_for_nan_ = true; // allocate memory for one zero order taylor_ coefficient CPPAD_ASSERT_UNKNOWN( num_order_taylor_ == 0 ); CPPAD_ASSERT_UNKNOWN( num_direction_taylor_ == 0 ); size_t c = 1; size_t r = 1; capacity_order(c, r); CPPAD_ASSERT_UNKNOWN( cap_order_taylor_ == c ); CPPAD_ASSERT_UNKNOWN( num_direction_taylor_ == r ); // set zero order coefficients corresponding to indpendent variables CPPAD_ASSERT_UNKNOWN( n == ind_taddr_.size() ); for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == (j+1) ); CPPAD_ASSERT_UNKNOWN( size_t(x[j].taddr_) == (j+1) ); taylor_[ ind_taddr_[j] ] = x[j].value_; } // use independent variable values to fill in values for others CPPAD_ASSERT_UNKNOWN( cskip_op_.size() == play_.num_op_rec() ); CPPAD_ASSERT_UNKNOWN( load_op_.size() == play_.num_load_op_rec() ); local::forward0sweep(std::cout, false, n, num_var_tape_, &play_, cap_order_taylor_, taylor_.data(), cskip_op_.data(), load_op_, compare_change_count_, compare_change_number_, compare_change_op_index_ ); CPPAD_ASSERT_UNKNOWN( compare_change_count_ == 1 ); CPPAD_ASSERT_UNKNOWN( compare_change_number_ == 0 ); CPPAD_ASSERT_UNKNOWN( compare_change_op_index_ == 0 ); // now set the number of orders stored num_order_taylor_ = 1; # ifndef NDEBUG // on MS Visual Studio 2012, CppAD required in front of isnan ? for(i = 0; i < m; i++) if( taylor_[dep_taddr_[i]] != y[i].value_ || CppAD::isnan( y[i].value_ ) ) { using std::endl; std::ostringstream buf; buf << "A dependent variable value is not equal to " << "its tape evaluation value," << endl << "perhaps it is nan." << endl << "Dependent variable value = " << y[i].value_ << endl << "Tape evaluation value = " << taylor_[dep_taddr_[i]] << endl << "Difference = " << y[i].value_ - taylor_[dep_taddr_[i]] << endl ; // buf.str() returns a string object with a copy of the current // contents in the stream buffer. std::string msg_str = buf.str(); // msg_str.c_str() returns a pointer to the c-string // representation of the string object's value. const char* msg_char_star = msg_str.c_str(); CPPAD_ASSERT_KNOWN( 0, msg_char_star ); } # endif } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/cond_exp.hpp0000644000175200017650000002225213057470465016767 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_COND_EXP_HPP # define CPPAD_CORE_COND_EXP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin CondExp$$ $spell Atan2 CondExp Taylor std Cpp namespace inline const abs Rel bool Lt Le Eq Ge Gt $$ $section AD Conditional Expressions$$ $mindex assign$$ $head Syntax$$ $icode%result% = CondExp%Rel%(%left%, %right%, %if_true%, %if_false%)%$$ $head Purpose$$ Record, as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$, the conditional result $codei% if( %left% %Cop% %right% ) %result% = %if_true% else %result% = %if_false% %$$ The relational $icode Rel$$ and comparison operator $icode Cop$$ above have the following correspondence: $codei% %Rel% Lt Le Eq Ge Gt %Cop% < <= == >= > %$$ If $icode f$$ is the $cref ADFun$$ object corresponding to the AD operation sequence, the assignment choice for $icode result$$ in an AD conditional expression is made each time $cref/f.Forward/Forward/$$ is used to evaluate the zero order Taylor coefficients with new values for the $cref/independent variables/glossary/Tape/Independent Variable/$$. This is in contrast to the $cref/AD comparison operators/Compare/$$ which are boolean valued and not included in the AD operation sequence. $head Rel$$ In the syntax above, the relation $icode Rel$$ represents one of the following two characters: $code Lt$$, $code Le$$, $code Eq$$, $code Ge$$, $code Gt$$. As in the table above, $icode Rel$$ determines which comparison operator $icode Cop$$ is used when comparing $icode left$$ and $icode right$$. $head Type$$ These functions are defined in the CppAD namespace for arguments of $icode Type$$ is $code float$$ , $code double$$, or any type of the form $codei%AD<%Base%>%$$. (Note that all four arguments must have the same type.) $head left$$ The argument $icode left$$ has prototype $codei% const %Type%& %left% %$$ It specifies the value for the left side of the comparison operator. $head right$$ The argument $icode right$$ has prototype $codei% const %Type%& %right% %$$ It specifies the value for the right side of the comparison operator. $head if_true$$ The argument $icode if_true$$ has prototype $codei% const %Type%& %if_true% %$$ It specifies the return value if the result of the comparison is true. $head if_false$$ The argument $icode if_false$$ has prototype $codei% const %Type%& %if_false% %$$ It specifies the return value if the result of the comparison is false. $head result$$ The $icode result$$ has prototype $codei% %Type%& %if_false% %$$ $head Optimize$$ The $cref optimize$$ method will optimize conditional expressions in the following way: During $cref/zero order forward mode/forward_zero/$$, once the value of the $icode left$$ and $icode right$$ have been determined, it is known if the true or false case is required. From this point on, values corresponding to the case that is not required are not computed. This optimization is done for the rest of zero order forward mode as well as forward and reverse derivatives calculations. $head Deprecate 2005-08-07$$ Previous versions of CppAD used $codei% CondExp(%flag%, %if_true%, %if_false%) %$$ for the same meaning as $codei% CondExpGt(%flag%, %Type%(0), %if_true%, %if_false%) %$$ Use of $code CondExp$$ is deprecated, but continues to be supported. $head Operation Sequence$$ This is an AD of $icode Base$$ $cref/atomic operation/glossary/Operation/Atomic/$$ and hence is part of the current AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Example$$ $head Test$$ $children% example/cond_exp.cpp %$$ The file $cref cond_exp.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $head Atan2$$ The following implementation of the AD $cref atan2$$ function is a more complex example of using conditional expressions: $code $srcfile%cppad/core/atan2.hpp%0%BEGIN CondExp%// END CondExp%$$ $$ $end ------------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION AD CondExpOp( enum CompareOp cop , const AD &left , const AD &right , const AD &if_true , const AD &if_false ) { AD returnValue; CPPAD_ASSERT_UNKNOWN( Parameter(returnValue) ); // check first case where do not need to tape if( IdenticalPar(left) & IdenticalPar(right) ) { switch( cop ) { case CompareLt: if( left.value_ < right.value_ ) returnValue = if_true; else returnValue = if_false; break; case CompareLe: if( left.value_ <= right.value_ ) returnValue = if_true; else returnValue = if_false; break; case CompareEq: if( left.value_ == right.value_ ) returnValue = if_true; else returnValue = if_false; break; case CompareGe: if( left.value_ >= right.value_ ) returnValue = if_true; else returnValue = if_false; break; case CompareGt: if( left.value_ > right.value_ ) returnValue = if_true; else returnValue = if_false; break; default: CPPAD_ASSERT_UNKNOWN(0); returnValue = if_true; } return returnValue; } // must use CondExp incase Base is an AD type and recording returnValue.value_ = CondExpOp(cop, left.value_, right.value_, if_true.value_, if_false.value_); local::ADTape *tape = CPPAD_NULL; if( Variable(left) ) tape = left.tape_this(); if( Variable(right) ) tape = right.tape_this(); if( Variable(if_true) ) tape = if_true.tape_this(); if( Variable(if_false) ) tape = if_false.tape_this(); // add this operation to the tape if( tape != CPPAD_NULL ) tape->RecordCondExp(cop, returnValue, left, right, if_true, if_false); return returnValue; } // --- RecordCondExp(cop, returnValue, left, right, if_true, if_false) ----- /// All these operations are done in \c Rec_, so we should move this /// routine to recorder. template void local::ADTape::RecordCondExp( enum CompareOp cop , AD &returnValue , const AD &left , const AD &right , const AD &if_true , const AD &if_false ) { size_t ind0, ind1, ind2, ind3, ind4, ind5; size_t returnValue_taddr; // taddr_ of this variable CPPAD_ASSERT_UNKNOWN( NumRes(CExpOp) == 1 ); returnValue_taddr = Rec_.PutOp(CExpOp); // ind[0] = cop ind0 = addr_t( cop ); // ind[1] = base 2 represenation of the value // [Var(left), Var(right), Var(if_true), Var(if_false)] ind1 = 0; // Make sure returnValue is in the list of variables and set its taddr if( Parameter(returnValue) ) returnValue.make_variable(id_, returnValue_taddr ); else returnValue.taddr_ = returnValue_taddr; // ind[2] = left address if( Parameter(left) ) ind2 = Rec_.PutPar(left.value_); else { ind1 += 1; ind2 = left.taddr_; } // ind[3] = right address if( Parameter(right) ) ind3 = Rec_.PutPar(right.value_); else { ind1 += 2; ind3 = right.taddr_; } // ind[4] = if_true address if( Parameter(if_true) ) ind4 = Rec_.PutPar(if_true.value_); else { ind1 += 4; ind4 = if_true.taddr_; } // ind[5] = if_false address if( Parameter(if_false) ) ind5 = Rec_.PutPar(if_false.value_); else { ind1 += 8; ind5 = if_false.taddr_; } CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); CPPAD_ASSERT_UNKNOWN( ind1 > 0 ); Rec_.PutArg(ind0, ind1, ind2, ind3, ind4, ind5); // check that returnValue is a dependent variable CPPAD_ASSERT_UNKNOWN( Variable(returnValue) ); } // ------------ CondExpOp(left, right, if_true, if_false) ---------------- # define CPPAD_COND_EXP(Name) \ template \ CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION \ AD CondExp##Name( \ const AD &left , \ const AD &right , \ const AD &if_true , \ const AD &if_false ) \ { \ return CondExpOp(Compare##Name, \ left, right, if_true, if_false); \ } // AD CPPAD_COND_EXP(Lt) CPPAD_COND_EXP(Le) CPPAD_COND_EXP(Eq) CPPAD_COND_EXP(Ge) CPPAD_COND_EXP(Gt) template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION AD CondExp( const AD &flag , const AD &if_true , const AD &if_false ) { return CondExpOp(CompareGt, flag, AD(0), if_true, if_false); } # undef CPPAD_COND_EXP } // END CppAD namespace # endif cppad-20170000.3/cppad/core/unary_plus.hpp0000644000175200017650000000376013057470465017374 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_UNARY_PLUS_HPP # define CPPAD_CORE_UNARY_PLUS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin UnaryPlus$$ $spell Vec const inline $$ $section AD Unary Plus Operator$$ $mindex +$$ $head Syntax$$ $icode%y% = + %x%$$ $head Purpose$$ Performs the unary plus operation (the result $icode y$$ is equal to the operand $icode x$$). $head x$$ The operand $icode x$$ has one of the following prototypes $codei% const AD<%Base%> &%x% const VecAD<%Base%>::reference &%x% %$$ $head y$$ The result $icode y$$ has type $codei% AD<%Base%> %y% %$$ It is equal to the operand $icode x$$. $head Operation Sequence$$ This is an AD of $icode Base$$ $cref/atomic operation/glossary/Operation/Atomic/$$ and hence is part of the current AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Derivative$$ If $latex f$$ is a $cref/Base function/glossary/Base Function/$$, $latex \[ \D{[ + f(x) ]}{x} = \D{f(x)}{x} \] $$ $head Example$$ $children% example/unary_plus.cpp %$$ The file $cref unary_plus.cpp$$ contains an example and test of this operation. $end ------------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template inline AD AD::operator + (void) const { AD result(*this); return result; } template inline AD operator + (const VecAD_reference &right) { return right.ADBase(); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/asinh.hpp0000644000175200017650000000453313057470465016274 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ASINH_HPP # define CPPAD_CORE_ASINH_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin asinh$$ $spell asinh const Vec std cmath CppAD $$ $section The Inverse Hyperbolic Sine Function: asinh$$ $head Syntax$$ $icode%y% = asinh(%x%)%$$ $head Description$$ The inverse hyperbolic sine function is defined by $icode%x% == sinh(%y%)%$$. $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head CPPAD_USE_CPLUSPLUS_2011$$ $subhead true$$ If this preprocessor symbol is true ($code 1$$), and $icode x$$ is an AD type, this is an $cref/atomic operation/glossary/Operation/Atomic/$$. $subhead false$$ If this preprocessor symbol is false ($code 0$$), CppAD uses the representation $latex \[ \R{asinh} (x) = \log \left( x + \sqrt{ 1 + x^2 } \right) \] $$ to compute this function. $head Example$$ $children% example/asinh.cpp %$$ The file $cref asinh.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ # include # if ! CPPAD_USE_CPLUSPLUS_2011 // BEGIN CppAD namespace namespace CppAD { template Type asinh_template(const Type &x) { return CppAD::log( x + CppAD::sqrt( Type(1) + x * x ) ); } inline float asinh(const float &x) { return asinh_template(x); } inline double asinh(const double &x) { return asinh_template(x); } template inline AD asinh(const AD &x) { return asinh_template(x); } template inline AD asinh(const VecAD_reference &x) { return asinh_template( x.ADBase() ); } } // END CppAD namespace # endif // CPPAD_USE_CPLUSPLUS_2011 # endif // CPPAD_ASINH_INCLUDED cppad-20170000.3/cppad/core/forward.hpp0000644000175200017650000003014213057470465016631 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_FORWARD_HPP # define CPPAD_CORE_FORWARD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // documened after Forward but included here so easy to see # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file forward.hpp User interface to forward mode computations. */ /*! Multiple orders, one direction, forward mode Taylor coefficieints. \tparam Base The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD. \tparam VectorBase is a Simple Vector class with eleements of type Base. \param q is the hightest order for this forward mode computation; i.e., after this calculation there will be q+1 Taylor coefficients per variable. \param xq contains Taylor coefficients for the independent variables. The size of xq must either be n or (q+1)*n, We define p = q + 1 - xq.size()/n. For j = 0 , ... , n-1, k = p, ... , q, are xq[ (q+1-p)*j + k - p ] is the k-th order coefficient for the j-th independent variable. \param s Is the stream where output corresponding to PriOp operations will written. \return contains Taylor coefficients for the dependent variables. The size of the return value y is m*(q+1-p). For i = 0, ... , m-1, k = p, ..., q, y[(q+1-p)*i + (k-p)] is the k-th order coefficient for the i-th dependent variable. \par taylor_ The Taylor coefficients up to order p-1 are inputs and the coefficents from order p through q are outputs. Let N = num_var_tape_, and C = cap_order_taylor_. Note that for i = 1 , ..., N-1, k = 0 , ..., q, taylor_[ C*i + k ] is the k-th order cofficent, for the i-th varaible on the tape. (The first independent variable has index one on the tape and there is no variable with index zero.) */ template template VectorBase ADFun::Forward( size_t q , const VectorBase& xq , std::ostream& s ) { // temporary indices size_t i, j, k; // number of independent variables size_t n = ind_taddr_.size(); // number of dependent variables size_t m = dep_taddr_.size(); // check Vector is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( size_t(xq.size()) == n || size_t(xq.size()) == n*(q+1), "Forward(q, xq): xq.size() is not equal n or n*(q+1)" ); // lowest order we are computing size_t p = q + 1 - size_t(xq.size()) / n; CPPAD_ASSERT_UNKNOWN( p == 0 || p == q ); CPPAD_ASSERT_KNOWN( q <= num_order_taylor_ || p == 0, "Forward(q, xq): Number of Taylor coefficient orders stored in this" " ADFun\nis less than q and xq.size() != n*(q+1)." ); CPPAD_ASSERT_KNOWN( p <= 1 || num_direction_taylor_ == 1, "Forward(q, xq): computing order q >= 2" " and number of directions is not one." "\nMust use Forward(q, r, xq) for this case" ); // does taylor_ need more orders or fewer directions if( (cap_order_taylor_ <= q) | (num_direction_taylor_ != 1) ) { if( p == 0 ) { // no need to copy old values during capacity_order num_order_taylor_ = 0; } else num_order_taylor_ = q; size_t c = std::max(q + 1, cap_order_taylor_); size_t r = 1; capacity_order(c, r); } CPPAD_ASSERT_UNKNOWN( cap_order_taylor_ > q ); CPPAD_ASSERT_UNKNOWN( num_direction_taylor_ == 1 ); // short hand notation for order capacity size_t C = cap_order_taylor_; // set Taylor coefficients for independent variables for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] < num_var_tape_ ); // ind_taddr_[j] is operator taddr for j-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); if( p == q ) taylor_[ C * ind_taddr_[j] + q] = xq[j]; else { for(k = 0; k <= q; k++) taylor_[ C * ind_taddr_[j] + k] = xq[ (q+1)*j + k]; } } // evaluate the derivatives CPPAD_ASSERT_UNKNOWN( cskip_op_.size() == play_.num_op_rec() ); CPPAD_ASSERT_UNKNOWN( load_op_.size() == play_.num_load_op_rec() ); if( q == 0 ) { local::forward0sweep(s, true, n, num_var_tape_, &play_, C, taylor_.data(), cskip_op_.data(), load_op_, compare_change_count_, compare_change_number_, compare_change_op_index_ ); } else { local::forward1sweep(s, true, p, q, n, num_var_tape_, &play_, C, taylor_.data(), cskip_op_.data(), load_op_, compare_change_count_, compare_change_number_, compare_change_op_index_ ); } // return Taylor coefficients for dependent variables VectorBase yq; if( p == q ) { yq.resize(m); for(i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); yq[i] = taylor_[ C * dep_taddr_[i] + q]; } } else { yq.resize(m * (q+1) ); for(i = 0; i < m; i++) { for(k = 0; k <= q; k++) yq[ (q+1) * i + k] = taylor_[ C * dep_taddr_[i] + k ]; } } # ifndef NDEBUG if( check_for_nan_ ) { bool ok = true; size_t index = m; if( p == 0 ) { for(i = 0; i < m; i++) { // Visual Studio 2012, CppAD required in front of isnan ? if( CppAD::isnan( yq[ (q+1) * i + 0 ] ) ) { ok = false; if( index == m ) index = i; } } } if( ! ok ) { CPPAD_ASSERT_UNKNOWN( index < m ); // CppAD::vector x0(n); for(j = 0; j < n; j++) x0[j] = taylor_[ C * ind_taddr_[j] + 0 ]; std::string file_name; put_check_for_nan(x0, file_name); std::stringstream ss; ss << "yq = f.Forward(q, xq): a zero order Taylor coefficient is nan.\n" "Corresponding independent variables vector was written " "to binary a file.\n" "vector_size = " << n << "\n" << "file_name = " << file_name << "\n" << "index = " << index << "\n"; // ss.str() returns a string object with a copy of the current // contents in the stream buffer. std::string msg_str = ss.str(); // msg_str.c_str() returns a pointer to the c-string // representation of the string object's value. const char* msg_char_star = msg_str.c_str(); ErrorHandler::Call( true, __LINE__, __FILE__, "if( CppAD::isnan( yq[ (q+1) * index + 0 ] )", msg_char_star ); } CPPAD_ASSERT_KNOWN(ok, "with the value nan." ); if( 0 < q ) { for(i = 0; i < m; i++) { for(k = p; k <= q; k++) { // Studio 2012, CppAD required in front of isnan ? ok &= ! CppAD::isnan( yq[ (q+1-p)*i + k-p ] ); } } } CPPAD_ASSERT_KNOWN(ok, "yq = f.Forward(q, xq): has a non-zero order Taylor coefficient\n" "with the value nan (but zero order coefficients are not nan)." ); } # endif // now we have q + 1 taylor_ coefficient orders per variable num_order_taylor_ = q + 1; return yq; } /*! One order, multiple directions, forward mode Taylor coefficieints. \tparam Base The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD. \tparam VectorBase is a Simple Vector class with eleements of type Base. \param q is the order for this forward mode computation, q > 0. There must be at least q Taylor coefficients per variable before this call. After this call there will be q+1 Taylor coefficients per variable. \param r is the number of directions for this calculation. If q != 1, \c r must be the same as in the previous call to Forward where \c q was equal to one. \param xq contains Taylor coefficients for the independent variables. The size of xq must either be r*n, For j = 0 , ... , n-1, ell = 0, ... , r-1, xq[ ( r*j + ell ] is the q-th order coefficient for the j-th independent variable and the ell-th direction. \return contains Taylor coefficients for the dependent variables. The size of the return value \c y is r*m. For i = 0, ... , m-1, ell = 0, ... , r-1, y[ r*i + ell ] is the q-th order coefficient for the i-th dependent variable and the ell-th direction. \par taylor_ The Taylor coefficients up to order q-1 are inputs and the coefficents of order \c q are outputs. Let N = num_var_tape_, and C = cap_order_taylor_. Note that for i = 1 , ..., N-1, taylor_[ (C-1)*r*i + i + 0 ] is the zero order cofficent, for the i-th varaible, and all directions. For i = 1 , ..., N-1, k = 1 , ..., q, ell = 0 , ..., r-1, taylor_[ (C-1)*r*i + i + (k-1)*r + ell + 1 ] is the k-th order cofficent, for the i-th varaible, and ell-th direction. (The first independent variable has index one on the tape and there is no variable with index zero.) */ template template VectorBase ADFun::Forward( size_t q , size_t r , const VectorBase& xq ) { // temporary indices size_t i, j, ell; // number of independent variables size_t n = ind_taddr_.size(); // number of dependent variables size_t m = dep_taddr_.size(); // check Vector is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( q > 0, "Forward(q, r, xq): q == 0" ); CPPAD_ASSERT_KNOWN( size_t(xq.size()) == r * n, "Forward(q, r, xq): xq.size() is not equal r * n" ); CPPAD_ASSERT_KNOWN( q <= num_order_taylor_ , "Forward(q, r, xq): Number of Taylor coefficient orders stored in" " this ADFun is less than q" ); CPPAD_ASSERT_KNOWN( q == 1 || num_direction_taylor_ == r , "Forward(q, r, xq): q > 1 and number of Taylor directions r" " is not same as previous Forward(1, r, xq)" ); // does taylor_ need more orders or new number of directions if( cap_order_taylor_ <= q || num_direction_taylor_ != r ) { if( num_direction_taylor_ != r ) num_order_taylor_ = 1; size_t c = std::max(q + 1, cap_order_taylor_); capacity_order(c, r); } CPPAD_ASSERT_UNKNOWN( cap_order_taylor_ > q ); CPPAD_ASSERT_UNKNOWN( num_direction_taylor_ == r ) // short hand notation for order capacity size_t c = cap_order_taylor_; // set Taylor coefficients for independent variables for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] < num_var_tape_ ); // ind_taddr_[j] is operator taddr for j-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); for(ell = 0; ell < r; ell++) { size_t index = ((c-1)*r + 1)*ind_taddr_[j] + (q-1)*r + ell + 1; taylor_[ index ] = xq[ r * j + ell ]; } } // evaluate the derivatives CPPAD_ASSERT_UNKNOWN( cskip_op_.size() == play_.num_op_rec() ); CPPAD_ASSERT_UNKNOWN( load_op_.size() == play_.num_load_op_rec() ); local::forward2sweep( q, r, n, num_var_tape_, &play_, c, taylor_.data(), cskip_op_.data(), load_op_ ); // return Taylor coefficients for dependent variables VectorBase yq; yq.resize(r * m); for(i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); for(ell = 0; ell < r; ell++) { size_t index = ((c-1)*r + 1)*dep_taddr_[i] + (q-1)*r + ell + 1; yq[ r * i + ell ] = taylor_[ index ]; } } # ifndef NDEBUG if( check_for_nan_ ) { bool ok = true; for(i = 0; i < m; i++) { for(ell = 0; ell < r; ell++) { // Studio 2012, CppAD required in front of isnan ? ok &= ! CppAD::isnan( yq[ r * i + ell ] ); } } CPPAD_ASSERT_KNOWN(ok, "yq = f.Forward(q, r, xq): has a non-zero order Taylor coefficient\n" "with the value nan (but zero order coefficients are not nan)." ); } # endif // now we have q + 1 taylor_ coefficient orders per variable num_order_taylor_ = q + 1; return yq; } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/tape_link.hpp0000644000175200017650000002365113057470465017142 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_TAPE_LINK_HPP # define CPPAD_CORE_TAPE_LINK_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file tape_link.hpp Routines that Link AD and local::ADTape Objects. The routines that connect the AD class to the corresponding tapes (one for each thread). */ /*! Handle to the tape identifier for this AD class and the specific thread. \tparam Base is the base type for this AD class. \param thread is the thread number. The following condition must hold \code (! thread_alloc::in_parallel()) || thread == thread_alloc::thread_num() \endcode \return is a handle to the tape identifier for this thread and AD class. */ template inline tape_id_t** AD::tape_id_handle(size_t thread) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static tape_id_t* tape_id_table[CPPAD_MAX_NUM_THREADS]; CPPAD_ASSERT_UNKNOWN( (! thread_alloc::in_parallel()) || thread == thread_alloc::thread_num() ); return tape_id_table + thread; } /*! Pointer to the tape identifier for this AD class and the specific thread. \tparam Base is the base type for this AD class. \param thread is the thread number; i.e., \code thread == thread_alloc::thread_num() \endcode If this condition is not satisfied, and \c NDEBUG is not defined, a CPPAD_ASSERT_UNKNOWN is generated. \return is a pointer to the tape identifier for this thread and AD class. \par Restrictions This routine should only be called if there was a tape created for the specified thread (it may no longer be recording). */ template inline tape_id_t* AD::tape_id_ptr(size_t thread) { CPPAD_ASSERT_UNKNOWN( *tape_id_handle(thread) != CPPAD_NULL ) return *tape_id_handle(thread); } /*! Handle for the tape for this AD class and the specific thread. \tparam Base is the base type for this AD class. \param thread is the thread number; i.e., \code thread == thread_alloc::thread_num() \endcode If this condition is not satisfied, and \c NDEBUG is not defined, a CPPAD_ASSERT_UNKNOWN is generated. \return is a handle for the AD class and the specified thread. */ template inline local::ADTape** AD::tape_handle(size_t thread) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static local::ADTape* tape_table[CPPAD_MAX_NUM_THREADS]; CPPAD_ASSERT_UNKNOWN( thread == thread_alloc::thread_num() ); return tape_table + thread; } /*! Pointer for the tape for this AD class and the current thread. \code thread == thread_alloc::thread_num() \endcode \tparam Base is the base type corresponding to AD operations. \return is a pointer to the tape that is currently recording AD operations for the current thread. If this value is \c CPPAD_NULL, there is no tape currently recording AD operations for this thread. */ template inline local::ADTape* AD::tape_ptr(void) { size_t thread = thread_alloc::thread_num(); return *tape_handle(thread); } /*! Pointer for the tape for this AD class and the specified tape identifier. \tparam Base is the base type corresponding to AD operations. \param tape_id is the identifier for the tape that is currently recording AD operations for the current thread. It must hold that the current thread is \code thread = size_t( tape_id % CPPAD_MAX_NUM_THREADS ) \endcode and that there is a tape recording AD operations for this thread. If this is not the currently executing thread, a variable from a different thread is being recorded on the tape for this thread which is a user error. \return is a pointer to the tape that is currently recording AD operations for the current thread (and it is not \c CPPAD_NULL). \par Restrictions This routine should only be called if there is a tape recording operaitons for the specified thread. */ template inline local::ADTape* AD::tape_ptr(tape_id_t tape_id) { size_t thread = size_t( tape_id % CPPAD_MAX_NUM_THREADS ); CPPAD_ASSERT_KNOWN( thread == thread_alloc::thread_num(), "Attempt to use an AD variable with two different threads." ); CPPAD_ASSERT_UNKNOWN( tape_id == *tape_id_ptr(thread) ); CPPAD_ASSERT_UNKNOWN( *tape_handle(thread) != CPPAD_NULL ); return *tape_handle(thread); } /*! Create and delete tapes that record AD operations for current thread. \par thread the current thread is given by \code thread = thread_alloc::thread_num() \endcode \tparam Base is the base type corresponding to AD operations. \param job This argument determines if we are creating a new tape, or deleting an old one. - \c tape_manage_new : Creates and a new tape. It is assumed that there is no tape recording AD operations for this thread when \c tape_manage is called. It the input value of *tape_id_handle(thread) is \c CPPAD_NULL, it will be changed to a non-zero pointer and the corresponding value of *tape_id_ptr(thread) will be set to thread + CPPAD_MAX_NUM_THREADS. - \c tape_manage_delete : It is assumed that there is a tape recording AD operations for this thread when \c tape_manage is called. The value of *tape_id_ptr(thread) will be advanced by \c CPPAD_MAX_NUM_THREADS. \return - job == tape_manage_new: a pointer to the new tape is returned. - job == tape_manage_delete: the value \c CPPAD_NULL is returned. */ template local::ADTape* AD::tape_manage(tape_manage_job job) { // this routine has static variables so first call cannot be in parallel CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL // The tape for the master thread static local::ADTape tape_zero; // Pointer to the tape for each thread static local::ADTape* tape_table[CPPAD_MAX_NUM_THREADS]; // The id current being used for each of the tapes static tape_id_t tape_id_save[CPPAD_MAX_NUM_THREADS]; // Thread corresponding to this call size_t thread = thread_alloc::thread_num(); // tape_manage_clear if( job == tape_manage_clear ) { // This operation cannot be done in parallel CPPAD_ASSERT_UNKNOWN(thread == 0 && (! thread_alloc::in_parallel())); for(thread = 0; thread < CPPAD_MAX_NUM_THREADS; thread++) { // if this thread has a tape if( tape_table[thread] != CPPAD_NULL ) { // id corresponding to this thread tape_id_save[thread] = tape_table[thread]->id_; *tape_id_handle(thread) = &tape_id_save[thread]; // delete all but the master thread if( thread != 0 ) delete( tape_table[thread] ); // set the tape pointer to null tape_table[thread] = CPPAD_NULL; } } return CPPAD_NULL; } // id and tape fpor this thread tape_id_t** tape_id = tape_id_handle(thread); local::ADTape** tape = tape_handle(thread); // check if there is no tape currently attached to this thread if( tape_table[thread] == CPPAD_NULL ) { // allocate separate memroy to avoid false sharing if( thread == 0 ) { // mastert tape is a static in this routine tape_table[thread] = &tape_zero; } else { // other tapes are allocated tape_table[thread] = new local::ADTape(); } // current id and pointer to this tape tape_table[thread]->id_ = tape_id_save[thread]; *tape_id = &tape_table[thread]->id_; // if id is zero, initialize it so that // thread == tape id % CPPAD_MAX_NUM_THREADS if( **tape_id == 0 ) **tape_id = thread + CPPAD_MAX_NUM_THREADS; } // make sure tape_id_handle(thread) is pointing to the proper place CPPAD_ASSERT_UNKNOWN( *tape_id == &tape_table[thread]->id_ ); // make sure tape_id value is valid for this thread CPPAD_ASSERT_UNKNOWN( size_t( **tape_id % CPPAD_MAX_NUM_THREADS ) == thread ); switch(job) { case tape_manage_new: // tape for this thread must be null at the start CPPAD_ASSERT_UNKNOWN( *tape == CPPAD_NULL ); *tape = tape_table[thread]; break; case tape_manage_delete: CPPAD_ASSERT_UNKNOWN( *tape == tape_table[thread] ); CPPAD_ASSERT_KNOWN( std::numeric_limits::max() - CPPAD_MAX_NUM_THREADS > **tape_id, "To many different tapes given the type used for " "CPPAD_TAPE_ID_TYPE" ); // advance tape identfier so all AD variables become parameters **tape_id += CPPAD_MAX_NUM_THREADS; // free memory corresponding to recording in the old tape tape_table[thread]->Rec_.free(); // inform rest of CppAD that no tape recording for this thread *tape = CPPAD_NULL; break; case tape_manage_clear: CPPAD_ASSERT_UNKNOWN(false); } return *tape; } /*! Get a pointer to tape that records AD operations for the current thread. \tparam Base is the base type corresponding to AD operations. \par thread The current thread must be given by \code thread = this->tape_id_ % CPPAD_MAX_NUM_THREADS \endcode \return is a pointer to the tape that is currently recording AD operations for the current thread. This value must not be \c CPPAD_NULL; i.e., there must be a tape currently recording AD operations for this thread. */ template inline local::ADTape *AD::tape_this(void) const { size_t thread = size_t( tape_id_ % CPPAD_MAX_NUM_THREADS ); CPPAD_ASSERT_UNKNOWN( tape_id_ == *tape_id_ptr(thread) ); CPPAD_ASSERT_UNKNOWN( *tape_handle(thread) != CPPAD_NULL ); return *tape_handle(thread); } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/dependent.hpp0000644000175200017650000002204013057470465017131 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_DEPENDENT_HPP # define CPPAD_CORE_DEPENDENT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Dependent$$ $spell alloc num taylor_ ADvector const $$ $spell $$ $section Stop Recording and Store Operation Sequence$$ $mindex ADFun tape Dependent$$ $head Syntax$$ $icode%f%.Dependent(%x%, %y%)%$$ $head Purpose$$ Stop recording and the AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ that started with the call $codei% Independent(%x%) %$$ and store the operation sequence in $icode f$$. The operation sequence defines an $cref/AD function/glossary/AD Function/$$ $latex \[ F : B^n \rightarrow B^m \] $$ where $latex B$$ is the space corresponding to objects of type $icode Base$$. The value $latex n$$ is the dimension of the $cref/domain/seq_property/Domain/$$ space for the operation sequence. The value $latex m$$ is the dimension of the $cref/range/seq_property/Range/$$ space for the operation sequence (which is determined by the size of $icode y$$). $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ The AD of $icode Base$$ operation sequence is stored in $icode f$$; i.e., it becomes the operation sequence corresponding to $icode f$$. If a previous operation sequence was stored in $icode f$$, it is deleted. $head x$$ The argument $icode x$$ must be the vector argument in a previous call to $cref Independent$$. Neither its size, or any of its values, are allowed to change between calling $codei% Independent(%x%) %$$ and $codei% %f%.Dependent(%x%, %y%) %$$. $head y$$ The vector $icode y$$ has prototype $codei% const %ADvector% &%y% %$$ (see $cref/ADvector/FunConstruct/$$ below). The length of $icode y$$ must be greater than zero and is the dimension of the range space for $icode f$$. $head ADvector$$ The type $icode ADvector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $codei%AD<%Base%>%$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Taping$$ The tape, that was created when $codei%Independent(%x%)%$$ was called, will stop recording. The AD operation sequence will be transferred from the tape to the object $icode f$$ and the tape will then be deleted. $head Forward$$ No $cref Forward$$ calculation is preformed during this operation. Thus, directly after this operation, $codei% %f%.size_order() %$$ is zero (see $cref size_order$$). $head Parallel Mode$$ The call to $code Independent$$, and the corresponding call to $codei% ADFun<%Base%> %f%( %x%, %y%) %$$ or $codei% %f%.Dependent( %x%, %y%) %$$ or $cref abort_recording$$, must be preformed by the same thread; i.e., $cref/thread_alloc::thread_num/ta_thread_num/$$ must be the same. $head Example$$ The file $cref fun_check.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ---------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { /*! \file dependent.hpp Different versions of Dependent function. */ /*! Determine the \c tape corresponding to this exeuction thread and then use Dependent(tape, y) to store this tapes recording in a function. \param y [in] The dependent variable vector for the corresponding function. */ template template void ADFun::Dependent(const ADvector &y) { local::ADTape* tape = AD::tape_ptr(); CPPAD_ASSERT_KNOWN( tape != CPPAD_NULL, "Can't store current operation sequence in this ADFun object" "\nbecause there is no active tape (for this thread)." ); // code above just determines the tape and checks for errors Dependent(tape, y); } /*! Determine the \c tape corresponding to this exeuction thread and then use Dependent(tape, y) to store this tapes recording in a function. \param x [in] The independent variable vector for this tape. This informaiton is also stored in the tape so a check is done to make sure it is correct (if NDEBUG is not defined). \param y [in] The dependent variable vector for the corresponding function. */ template template void ADFun::Dependent(const ADvector &x, const ADvector &y) { CPPAD_ASSERT_KNOWN( x.size() > 0, "Dependent: independent variable vector has size zero." ); CPPAD_ASSERT_KNOWN( Variable(x[0]), "Dependent: independent variable vector has been changed." ); local::ADTape *tape = AD::tape_ptr(x[0].tape_id_); CPPAD_ASSERT_KNOWN( tape->size_independent_ == size_t( x.size() ), "Dependent: independent variable vector has been changed." ); # ifndef NDEBUG size_t i, j; for(j = 0; j < size_t(x.size()); j++) { CPPAD_ASSERT_KNOWN( size_t(x[j].taddr_) == (j+1), "ADFun: independent variable vector has been changed." ); CPPAD_ASSERT_KNOWN( x[j].tape_id_ == x[0].tape_id_, "ADFun: independent variable vector has been changed." ); } for(i = 0; i < size_t(y.size()); i++) { CPPAD_ASSERT_KNOWN( CppAD::Parameter( y[i] ) | (y[i].tape_id_ == x[0].tape_id_) , "ADFun: dependent vector contains a variable for" "\na different tape (thread) than the independent variables." ); } # endif // code above just determines the tape and checks for errors Dependent(tape, y); } /*! Replace the floationg point operations sequence for this function object. \param tape is a tape that contains the new floating point operation sequence for this function. After this operation, all memory allocated for this tape is deleted. \param y The dependent variable vector for the function being stored in this object. \par All of the private member data in ad_fun.hpp is set to correspond to the new tape except for check_for_nan_. */ template template void ADFun::Dependent(local::ADTape *tape, const ADvector &y) { size_t m = y.size(); size_t n = tape->size_independent_; size_t i, j; size_t y_taddr; // check ADvector is Simple Vector class with AD elements CheckSimpleVector< AD, ADvector>(); CPPAD_ASSERT_KNOWN( y.size() > 0, "ADFun operation sequence dependent variable size is zero size" ); // --------------------------------------------------------------------- // Begin setting ad_fun.hpp private member data // --------------------------------------------------------------------- // dep_parameter_, dep_taddr_ CPPAD_ASSERT_UNKNOWN( local::NumRes(local::ParOp) == 1 ); dep_parameter_.resize(m); dep_taddr_.resize(m); for(i = 0; i < m; i++) { dep_parameter_[i] = CppAD::Parameter(y[i]); if( dep_parameter_[i] ) { // make a tape copy of dependent variables that are parameters, y_taddr = tape->RecordParOp( y[i].value_ ); } else y_taddr = y[i].taddr_; CPPAD_ASSERT_UNKNOWN( y_taddr > 0 ); dep_taddr_[i] = y_taddr; } // put an EndOp at the end of the tape tape->Rec_.PutOp(local::EndOp); // some size_t values in ad_fun.hpp has_been_optimized_ = false; compare_change_count_ = 1; compare_change_number_ = 0; compare_change_op_index_ = 0; num_order_taylor_ = 0; num_direction_taylor_ = 0; cap_order_taylor_ = 0; // num_var_tape_ // Now that all the variables are in the tape, we can set this value. num_var_tape_ = tape->Rec_.num_var_rec(); // taylor_ taylor_.erase(); // cskip_op_ cskip_op_.erase(); cskip_op_.extend( tape->Rec_.num_op_rec() ); // load_op_ load_op_.erase(); load_op_.extend( tape->Rec_.num_load_op_rec() ); // play_ // Now that each dependent variable has a place in the tape, // and there is a EndOp at the end of the tape, we can transfer the // recording to the player and and erase the tape. play_.get(tape->Rec_); // ind_taddr_ // Note that play_ has been set, we can use it to check operators ind_taddr_.resize(n); CPPAD_ASSERT_UNKNOWN( n < num_var_tape_); for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( play_.GetOp(j+1) == local::InvOp ); ind_taddr_[j] = j+1; } // for_jac_sparse_pack_, for_jac_sparse_set_ for_jac_sparse_pack_.resize(0, 0); for_jac_sparse_set_.resize(0,0); // --------------------------------------------------------------------- // End set ad_fun.hpp private member data // --------------------------------------------------------------------- // now we can delete the tape AD::tape_manage(tape_manage_delete); // total number of varables in this recording CPPAD_ASSERT_UNKNOWN( num_var_tape_ == play_.num_var_rec() ); // used to determine if there is an operation sequence in *this CPPAD_ASSERT_UNKNOWN( num_var_tape_ > 0 ); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/div_eq.hpp0000644000175200017650000000524213057470465016437 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_DIV_EQ_HPP # define CPPAD_CORE_DIV_EQ_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD& AD::operator /= (const AD &right) { // compute the Base part Base left; left = value_; value_ /= right.value_; // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return *this; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_left = tape_id_ == tape_id; bool var_right = right.tape_id_ == tape_id; if( var_left ) { if( var_right ) { // this = variable / variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::DivvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::DivvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(taddr_, right.taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::DivvvOp); // make this a variable CPPAD_ASSERT_UNKNOWN( tape_id_ == tape_id ); } else if( IdenticalOne( right.value_ ) ) { // this = variable * 1 } else { // this = variable / parameter CPPAD_ASSERT_UNKNOWN( local::NumRes(local::DivvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::DivvpOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(taddr_, p); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::DivvpOp); // make this a variable CPPAD_ASSERT_UNKNOWN( tape_id_ == tape_id ); } } else if( var_right ) { if( IdenticalZero(left) ) { // this = 0 / variable } else { // this = parameter / variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::DivpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::DivpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(left); tape->Rec_.PutArg(p, right.taddr_); // put operator in the tape taddr_ = tape->Rec_.PutOp(local::DivpvOp); // make this a variable tape_id_ = tape_id; } } return *this; } CPPAD_FOLD_ASSIGNMENT_OPERATOR(/=) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/epsilon.hpp0000644000175200017650000000273313057470465016643 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_EPSILON_HPP # define CPPAD_CORE_EPSILON_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------ $begin epsilon$$ $spell std eps CppAD namespace const $$ $section Machine Epsilon For AD Types$$ $head Deprecated 2012-06-17$$ This routine has been deprecated. You should use the $cref numeric_limits$$ $code epsilon$$ instead. $head Syntax$$ $icode%eps% = epsilon<%Float%>()%$$ $head Purpose$$ Obtain the value of machine epsilon corresponding to the type $icode%Float%$$. $head Float$$ this type can either be $codei%AD<%Base%>%$$, or it can be $icode Base$$ for any $codei%AD<%Base%>%$$ type. $head eps$$ The result $icode eps$$ has prototype $codei% %Float% eps %$$ $end ------------------------------------------------------------------------------ */ namespace CppAD { template inline Type epsilon(void) { return Type ( numeric_limits::epsilon() ); } } # endif cppad-20170000.3/cppad/core/equal_op_seq.hpp0000644000175200017650000000564613057470465017655 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_EQUAL_OP_SEQ_HPP # define CPPAD_CORE_EQUAL_OP_SEQ_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------ $begin EqualOpSeq$$ $spell Op const bool $$ $section Check if Two Value are Identically Equal$$ $mindex EqualOpSeq operation sequence$$ $head Syntax$$ $icode%b% = EqualOpSeq(%x%, %y%)%$$ $head Purpose$$ Determine if two $icode x$$ and $icode y$$ are identically equal; i.e., not only is $icode%x% == %y%$$ true, but if they are $cref/variables/glossary/Variable/$$, they correspond have the same $cref/operation sequence/glossary/Operation/Sequence/$$. $head Motivation$$ Sometimes it is useful to cache information and only recalculate when a function's arguments change. In the case of AD variables, it may be important not only when the argument values are equal, but when they are related to the $cref/independent variables/glossary/Tape/Independent Variable/$$ by the same operation sequence. After the assignment $codei% %y% = %x% %$$ these two AD objects would not only have equal values, but would also correspond to the same operation sequence. $head x$$ The argument $icode x$$ has prototype $codei% const AD<%Base%> &%x% %$$ $head y$$ The argument $icode y$$ has prototype $codei% const AD<%Base%> &%y% %$$ $head b$$ The result $icode b$$ has prototype $codei% bool %b% %$$ The result is true if and only if one of the following cases holds: $list number$$ Both $icode x$$ and $icode y$$ are variables and correspond to the same operation sequence. $lnext Both $icode x$$ and $icode y$$ are parameters, $icode Base$$ is an AD type, and $codei%EqualOpSeq( Value(%x%) , Value(%y%) )%$$ is true. $lnext Both $icode x$$ and $icode y$$ are parameters, $icode Base$$ is not an AD type, and $icode%x% == %y%%$$ is true. $lend $head Example$$ $children% example/equal_op_seq.cpp %$$ The file $cref equal_op_seq.cpp$$ contains an example and test of $code EqualOpSeq$$. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------ */ namespace CppAD { template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool EqualOpSeq(const AD &x, const AD &y) { if( Parameter(x) ) { if( Parameter(y) ) return EqualOpSeq(x.value_, y.value_); else return false; } else if( Parameter(y) ) return false; return (x.taddr_ == y.taddr_); } } # endif cppad-20170000.3/cppad/core/drivers.hpp0000644000175200017650000000237113057470465016646 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_DRIVERS_HPP # define CPPAD_CORE_DRIVERS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Drivers$$ $spell $$ $section First and Second Derivatives: Easy Drivers$$ $mindex forward reverse$$ $childtable% cppad/core/jacobian.hpp% cppad/core/for_one.hpp% cppad/core/rev_one.hpp% cppad/core/hessian.hpp% cppad/core/for_two.hpp% cppad/core/rev_two.hpp% cppad/core/sparse_jacobian.hpp% cppad/core/sparse_hessian.hpp %$$ $end */ # include # include # include # include # include # include # include # include # endif cppad-20170000.3/cppad/core/vec_ad.hpp0000644000175200017650000004761513057470465016423 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_VEC_AD_HPP # define CPPAD_CORE_VEC_AD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin VecAD$$ $spell cppad.hpp CondExpGt grep Ld vp Lu wc op Ldp Ldv Taylor VecAD const Cpp $$ $section AD Vectors that Record Index Operations$$ $mindex VecAD tape reference VecAD$$ $head Syntax$$ $codei%VecAD<%Base%> %v%(%n%)%$$ $pre $$ $icode%v%.size()%$$ $pre $$ $icode%b% = %v%[%i%]%$$ $pre $$ $icode%r% = %v%[%x%]%$$ $head Purpose$$ If either $icode v$$ or $icode x$$ is a $cref/variable/glossary/Variable/$$, the indexing operation $codei% %r% = %v%[%x%] %$$ is recorded in the corresponding AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ and transferred to the corresponding $cref ADFun$$ object $icode f$$. Such an index can change each time zero order $cref/f.Forward/Forward/$$ is used; i.e., $icode f$$ is evaluated with new value for the $cref/independent variables/glossary/Tape/Independent Variable/$$. Note that the value of $icode y$$ depends on the value of $icode x$$ in a discrete fashion and CppAD computes its partial derivative with respect to $icode x$$ as zero. $head Alternatives$$ If only the values in the vector, and not the indices, depend on the independent variables, the class $icode%Vector%< AD<%Base%> >%$$ is much more efficient for storing AD values where $icode Vector$$ is any $cref SimpleVector$$ template class, If only the indices, and not the values in the vector, depend on the independent variables, The $cref Discrete$$ functions are a much more efficient way to represent these vectors. $head VecAD::reference$$ The result $icode r$$ has type $codei% VecAD<%Base%>::reference %$$ which is very much like the $codei%AD<%Base%>%$$ type with some notable exceptions: $subhead Exceptions$$ $list number$$ The object $icode r$$ cannot be used with the $cref Value$$ function to compute the corresponding $icode Base$$ value. If $icode v$$ and $icode i$$ are not $cref/variables/glossary/Variable/$$ $codei% %b% = v[%i%] %$$ can be used to compute the corresponding $icode Base$$ value. $lnext The object $icode r$$ cannot be used with the $cref/computed assignments operators/Arithmetic/$$ $code +=$$, $code -=$$, $code *=$$, or $code /=$$. For example, the following syntax is not valid: $codei% %v%[%x%] += %z%; %$$ no matter what the types of $icode z$$. $lnext Assignment to $icode r$$ returns a $code void$$. For example, the following syntax is not valid: $codei% %z% = %v%[%x%] = %u%; %$$ no matter what the types of $icode z$$, and $icode u$$. $lnext The $cref CondExp$$ functions do not accept $codei%VecAD<%Base%>::reference%$$ arguments. For example, the following syntax is not valid: $codei% CondExpGt(%v%[%x%], %z%, %u%, %v%) %$$ no matter what the types of $icode z$$, $icode u$$, and $icode v$$. $lnext The $cref/Parameter and Variable/ParVar/$$ functions cannot be used with $codei%VecAD<%Base%>::reference%$$ arguments like $icode r$$, use the entire $codei%VecAD<%Base%>%$$ vector instead; i.e. $icode v$$. $lnext The vectors passed to $cref Independent$$ must have elements of type $codei%AD<%Base%>%$$; i.e., $cref VecAD$$ vectors cannot be passed to $code Independent$$. $lnext If one uses this type in a AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$, $cref/sparsity pattern/glossary/Sparsity Pattern/$$ calculations ($cref Sparse$$) are less efficient because the dependence of different elements of the vector cannot be separated. $lend $head Constructor$$ $subhead v$$ The syntax $codei% VecAD<%Base%> %v%(%n%) %$$ creates an $code VecAD$$ object $icode v$$ with $icode n$$ elements. The initial value of the elements of $icode v$$ is unspecified. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ $head size$$ The syntax $codei% %v%.size() %$$ returns the number of elements in the vector $icode v$$; i.e., the value of $icode n$$ when it was constructed. $head size_t Indexing$$ We refer to the syntax $codei% %b% = %v%[%i%] %$$ as $code size_t$$ indexing of a $code VecAD$$ object. This indexing is only valid if the vector $icode v$$ is a $cref/parameter/ParVar/$$; i.e., it does not depend on the independent variables. $subhead i$$ The operand $icode i$$ has prototype $codei% size_t %i% %$$ It must be greater than or equal zero and less than $icode n$$; i.e., less than the number of elements in $icode v$$. $subhead b$$ The result $icode b$$ has prototype $codei% %Base% %b% %$$ and is a reference to the $th i$$ element in the vector $icode v$$. It can be used to change the element value; for example, $codei% %v%[%i%] = %c% %$$ is valid where $icode c$$ is a $icode Base$$ object. The reference $icode b$$ is no longer valid once the destructor for $icode v$$ is called; for example, when $icode v$$ falls out of scope. $head AD Indexing$$ We refer to the syntax $codei% %r% = %v%[%x%] %$$ as AD indexing of a $code VecAD$$ object. $subhead x$$ The argument $icode x$$ has prototype $codei% const AD<%Base%> &%x% %$$ The value of $icode x$$ must be greater than or equal zero and less than $icode n$$; i.e., less than the number of elements in $icode v$$. $subhead r$$ The result $icode r$$ has prototype $codei% VecAD<%Base%>::reference %r% %$$ The object $icode r$$ has an AD type and its operations are recorded as part of the same AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ as for $codei%AD<%Base%>%$$ objects. It acts as a reference to the element with index $latex {\rm floor} (x)$$ in the vector $icode v$$ ($latex {\rm floor} (x)$$ is the greatest integer less than or equal $icode x$$). Because it is a reference, it can be used to change the element value; for example, $codei% %v%[%x%] = %z% %$$ is valid where $icode z$$ is an $codei%VecAD<%Base%>::reference%$$ object. As a reference, $icode r$$ is no longer valid once the destructor for $icode v$$ is called; for example, when $icode v$$ falls out of scope. $head Example$$ $children% example/vec_ad.cpp %$$ The file $cref vec_ad.cpp$$ contains an example and test using $code VecAD$$ vectors. It returns true if it succeeds and false otherwise. $head Speed and Memory$$ The $cref VecAD$$ vector type is inefficient because every time an element of a vector is accessed, a new CppAD $cref/variable/glossary/Variable/$$ is created on the tape using either the $code Ldp$$ or $code Ldv$$ operation (unless all of the elements of the vector are $cref/parameters/glossary/Parameter/$$). The effect of this can be seen by executing the following steps: $list number$$ In the file $code cppad/local/forward1sweep.h$$, change the definition of $code CPPAD_FORWARD1SWEEP_TRACE$$ to $codep # define CPPAD_FORWARD1SWEEP_TRACE 1 $$ $lnext In the $code Example$$ directory, execute the command $codep ./test_one.sh lu_vec_ad_ok.cpp lu_vec_ad.cpp -DNDEBUG > lu_vec_ad_ok.log $$ This will write a trace of all the forward tape operations, for the test case $cref lu_vec_ad_ok.cpp$$, to the file $code lu_vec_ad_ok.log$$. $lnext In the $code Example$$ directory execute the commands $codep grep "op=" lu_vec_ad_ok.log | wc -l grep "op=Ld[vp]" lu_vec_ad_ok.log | wc -l grep "op=St[vp][vp]" lu_vec_ad_ok.log | wc -l $$ The first command counts the number of operators in the tracing, the second counts the number of VecAD load operations, and the third counts the number of VecAD store operations. (For CppAD version 05-11-20 these counts were 956, 348, and 118 respectively.) $lend $end ------------------------------------------------------------------------ */ # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file vec_ad.hpp Defines the VecAD class. */ /*! \def CPPAD_VEC_AD_COMPUTED_ASSIGNMENT(op, name) Prints an error message if the correspinding computed assignment is used. THis macro is used to print an error message if any of the computed assignments are used with the VecAD_reference class. The argument \c op is one of the following: += , -= , *= , /=. The argument \c name, is a string literal with the name of the computed assignment \c op. */ # define CPPAD_VEC_AD_COMPUTED_ASSIGNMENT(op, name) \ VecAD_reference& operator op (const VecAD_reference &right) \ { CPPAD_ASSERT_KNOWN( \ false, \ "Cannot use a ADVec element on left side of" name \ ); \ return *this; \ } \ VecAD_reference& operator op (const AD &right) \ { CPPAD_ASSERT_KNOWN( \ false, \ "Cannot use a ADVec element on left side of" name \ ); \ return *this; \ } \ VecAD_reference& operator op (const Base &right) \ { CPPAD_ASSERT_KNOWN( \ false, \ "Cannot use a ADVec element on left side of" name \ ); \ return *this; \ } /*! Class used to hold a reference to an element of a VecAD object. \tparam Base Elements of this class act like an AD (in a restricted sense), in addition they track (on the tape) the index they correspond to. */ template class VecAD_reference { friend bool Parameter (const VecAD &vec); friend bool Variable (const VecAD &vec); friend class VecAD; friend class local::ADTape; private: /// pointer to vecad vector that this is a element of VecAD *vec_; /// index in vecad vector that this element corresponds to AD ind_; // index for this element public: /*! consructor \param vec value of vec_ \param ind value of ind_ */ VecAD_reference(VecAD *vec, const AD& ind) : vec_( vec ) , ind_(ind) { } // assignment operators inline void operator = (const VecAD_reference &right); void operator = (const AD &right); void operator = (const Base &right); void operator = (int right); // computed assignments CPPAD_VEC_AD_COMPUTED_ASSIGNMENT( += , " += " ) CPPAD_VEC_AD_COMPUTED_ASSIGNMENT( -= , " -= " ) CPPAD_VEC_AD_COMPUTED_ASSIGNMENT( *= , " *= " ) CPPAD_VEC_AD_COMPUTED_ASSIGNMENT( /= , " /= " ) /// Conversion from VecAD_reference to AD. /// puts the correspond vecad load instruction in the tape. AD ADBase(void) const { AD result; size_t i = static_cast( Integer(ind_) ); CPPAD_ASSERT_UNKNOWN( i < vec_->length_ ); // AD value corresponding to this element result.value_ = vec_->data_[i]; // this address will be recorded in tape and must be // zero for parameters CPPAD_ASSERT_UNKNOWN( Parameter(result) ); result.taddr_ = 0; // index corresponding to this element if( Variable(*vec_) ) { local::ADTape* tape = AD::tape_ptr(vec_->tape_id_); CPPAD_ASSERT_UNKNOWN( tape != CPPAD_NULL ); CPPAD_ASSERT_UNKNOWN( vec_->offset_ > 0 ); size_t load_op_index = tape->Rec_.num_load_op_rec(); if( IdenticalPar(ind_) ) { CPPAD_ASSERT_UNKNOWN( local::NumRes(local::LdpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::LdpOp) == 3 ); // put operand addresses in tape tape->Rec_.PutArg( vec_->offset_, i, load_op_index ); // put operator in the tape, ind_ is a parameter result.taddr_ = tape->Rec_.PutLoadOp(local::LdpOp); // change result to variable for this load result.tape_id_ = tape->id_; } else { CPPAD_ASSERT_UNKNOWN( local::NumRes(local::LdvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::LdvOp) == 3 ); addr_t ind_taddr; if( Parameter(ind_) ) { // kludge that should not be needed // if ind_ instead of i is used for index // in the tape ind_taddr = tape->RecordParOp( ind_.value_ ); } else ind_taddr = ind_.taddr_; CPPAD_ASSERT_UNKNOWN( ind_taddr > 0 ); // put operand addresses in tape // (value of third arugment does not matter) tape->Rec_.PutArg( vec_->offset_, ind_taddr, load_op_index ); // put operator in the tape, ind_ is a variable result.taddr_ = tape->Rec_.PutLoadOp(local::LdvOp); // change result to variable for this load result.tape_id_ = tape->id_; } } return result; } }; /*! Vector of AD objects that tracks indexing operations on the tape. */ template class VecAD { friend bool Parameter (const VecAD &vec); friend bool Variable (const VecAD &vec); friend class local::ADTape; friend class VecAD_reference; friend std::ostream& operator << (std::ostream &os, const VecAD &vec_); private: /// size of this VecAD vector const size_t length_; /// elements of this vector local::pod_vector data_; /// offset in cummulate vector corresponding to this object size_t offset_; /// tape id corresponding to the offset tape_id_t tape_id_; public: /// declare the user's view of this type here typedef VecAD_reference reference; /// default constructor /// initialize tape_id_ same as for default constructor; see default.hpp VecAD(void) : length_(0) , offset_(0) , tape_id_(0) { CPPAD_ASSERT_UNKNOWN( Parameter(*this) ); } /// sizing constructor /// initialize tape_id_ same as for parameters; see ad_copy.hpp VecAD(size_t n) : length_(n) , offset_(0) , tape_id_(0) { if( length_ > 0 ) { size_t i; Base zero(0); data_.extend(length_); // Initialize data to zero so all have same value. // This uses less memory and avoids a valgrind error // during TapeRec::PutPar for(i = 0; i < length_; i++) data_[i] = zero; } CPPAD_ASSERT_UNKNOWN( Parameter(*this) ); } /// destructor ~VecAD(void) { } /// number of elements in the vector size_t size(void) { return length_; } /// element access (not taped) /// /// \param i /// element index Base &operator[](size_t i) { CPPAD_ASSERT_KNOWN( Parameter(*this), "VecAD: cannot use size_t indexing because this" " VecAD vector is a variable." ); CPPAD_ASSERT_KNOWN( i < length_, "VecAD: element index is >= vector length" ); return data_[i]; } /*! delayed taped elemement access \param x element index \par This operation may convert this vector from a parameter to a variable */ VecAD_reference operator[](const AD &x) { CPPAD_ASSERT_KNOWN( 0 <= Integer(x), "VecAD: element index is less than zero" ); CPPAD_ASSERT_KNOWN( static_cast( Integer(x) ) < length_, "VecAD: element index is >= vector length" ); // if no need to track indexing operation, return now if( Parameter(*this) & Parameter(x) ) return VecAD_reference(this, x); CPPAD_ASSERT_KNOWN( Parameter(*this) | Parameter(x) | (tape_id_ == x.tape_id_), "VecAD: vector and index are variables for" " different tapes." ); if( Parameter(*this) ) { // must place a copy of vector in tape offset_ = AD::tape_ptr(x.tape_id_)->AddVec(length_, data_); // Advance pointer by one so starts at first component of this // vector; i.e., skip lenght at begining (so is always > 0) offset_++; // tape id corresponding to this offest tape_id_ = x.tape_id_; } return VecAD_reference(this, x); } }; /*! Taped setting of element to a value. \param y value that element is set to. */ template void VecAD_reference::operator=(const AD &y) { if( Parameter(y) ) { // fold into the Base type assignment *this = y.value_; return; } CPPAD_ASSERT_UNKNOWN( y.taddr_ > 0 ); CPPAD_ASSERT_KNOWN( Parameter(*vec_) | (vec_->tape_id_ == y.tape_id_), "VecAD assignment: vector and new element value are variables" "\nfor different tapes." ); local::ADTape* tape = AD::tape_ptr(y.tape_id_); CPPAD_ASSERT_UNKNOWN( tape != CPPAD_NULL ); if( Parameter(*vec_) ) { // must place a copy of vector in tape vec_->offset_ = tape->AddVec(vec_->length_, vec_->data_); // advance offset to be start of vector plus one (vec_->offset_)++; // tape id corresponding to this offest vec_->tape_id_ = y.tape_id_; } CPPAD_ASSERT_UNKNOWN( Variable(*vec_) ); // index in vector for this element size_t i = static_cast( Integer(ind_) ); CPPAD_ASSERT_UNKNOWN( i < vec_->length_ ); // assign value for this element (as an AD object) vec_->data_[i] = y.value_; // record the setting of this array element CPPAD_ASSERT_UNKNOWN( vec_->offset_ > 0 ); if( Parameter(ind_) ) { CPPAD_ASSERT_UNKNOWN( local::NumArg(local::StpvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::StpvOp) == 0 ); // put operand addresses in tape tape->Rec_.PutArg(vec_->offset_, i, y.taddr_); // put operator in the tape, ind_ is parameter, y is variable tape->Rec_.PutOp(local::StpvOp); } else { CPPAD_ASSERT_UNKNOWN( local::NumArg(local::StvvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::StvvOp) == 0 ); CPPAD_ASSERT_UNKNOWN( ind_.taddr_ > 0 ); // put operand addresses in tape tape->Rec_.PutArg(vec_->offset_, ind_.taddr_, y.taddr_); // put operator in the tape, ind_ is variable, y is variable tape->Rec_.PutOp(local::StvvOp); } } /*! Taped setting of element to a value. \param y value that element is set to. */ template void VecAD_reference::operator=(const Base &y) { size_t i = static_cast( Integer(ind_) ); CPPAD_ASSERT_UNKNOWN( i < vec_->length_ ); // assign value for this element vec_->data_[i] = y; // check if this ADVec object is a parameter if( Parameter(*vec_) ) return; local::ADTape* tape = AD::tape_ptr(vec_->tape_id_); CPPAD_ASSERT_UNKNOWN( tape != CPPAD_NULL ); // put value of the parameter y in the tape addr_t p = tape->Rec_.PutPar(y); // record the setting of this array element CPPAD_ASSERT_UNKNOWN( vec_->offset_ > 0 ); if( Parameter(ind_) ) { CPPAD_ASSERT_UNKNOWN( local::NumArg(local::StppOp) == 3 ); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::StppOp) == 0 ); // put operand addresses in tape tape->Rec_.PutArg(vec_->offset_, i, p); // put operator in the tape, ind_ is parameter, y is parameter tape->Rec_.PutOp(local::StppOp); } else { CPPAD_ASSERT_UNKNOWN( local::NumArg(local::StvpOp) == 3 ); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::StvpOp) == 0 ); CPPAD_ASSERT_UNKNOWN( ind_.taddr_ > 0 ); // put operand addresses in tape tape->Rec_.PutArg(vec_->offset_, ind_.taddr_, p); // put operator in the tape, ind_ is variable, y is parameter tape->Rec_.PutOp(local::StvpOp); } } /*! Taped setting of element to a value. \param y value that element is set to. \par this case gets folded into case where value is AD. */ template inline void VecAD_reference::operator= (const VecAD_reference &y) { *this = y.ADBase(); } /*! Taped setting of element to a value. \param y value that element is set to. \par this case gets folded into case where value is Base. */ template inline void VecAD_reference::operator=(int y) { *this = Base(y); } } // END_CPPAD_NAMESPACE // preprocessor symbols that are local to this file # undef CPPAD_VEC_AD_COMPUTED_ASSIGNMENT # endif cppad-20170000.3/cppad/core/sparse_jacobian.hpp0000644000175200017650000007615613057470465020327 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_SPARSE_JACOBIAN_HPP # define CPPAD_CORE_SPARSE_JACOBIAN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // maximum number of sparse directions to compute at the same time // # define CPPAD_SPARSE_JACOBIAN_MAX_MULTIPLE_DIRECTION 1 # define CPPAD_SPARSE_JACOBIAN_MAX_MULTIPLE_DIRECTION 64 /* $begin sparse_jacobian$$ $spell cppad colpack cmake recomputed valarray std CppAD Bool jac Jacobian Jacobians const Taylor $$ $section Sparse Jacobian: Easy Driver$$ $mindex SparseJacobian$$ $head Syntax$$ $icode%jac% = %f%.SparseJacobian(%x%) %jac% = %f%.SparseJacobian(%x%, %p%) %n_sweep% = %f%.SparseJacobianForward(%x%, %p%, %row%, %col%, %jac%, %work%) %n_sweep% = %f%.SparseJacobianReverse(%x%, %p%, %row%, %col%, %jac%, %work%) %$$ $head Purpose$$ We use $latex n$$ for the $cref/domain/seq_property/Domain/$$ size, and $latex m$$ for the $cref/range/seq_property/Range/$$ size of $icode f$$. We use $latex F : \B{R}^n \rightarrow \B{R}^m$$ do denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The syntax above sets $icode jac$$ to the Jacobian $latex \[ jac = F^{(1)} (x) \] $$ This routine takes advantage of the sparsity of the Jacobian in order to reduce the amount of computation necessary. If $icode row$$ and $icode col$$ are present, it also takes advantage of the reduced set of elements of the Jacobian that need to be computed. One can use speed tests (e.g. $cref speed_test$$) to verify that results are computed faster than when using the routine $cref Jacobian$$. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/Uses Forward/sparse_jacobian/Uses Forward/$$ below). $head x$$ The argument $icode x$$ has prototype $codei% const %VectorBase%& %x% %$$ (see $cref/VectorBase/sparse_jacobian/VectorBase/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies that point at which to evaluate the Jacobian. $head p$$ The argument $icode p$$ is optional and has prototype $codei% const %VectorSet%& %p% %$$ (see $cref/VectorSet/sparse_jacobian/VectorSet/$$ below). If it has elements of type $code bool$$, its size is $latex m * n$$. If it has elements of type $code std::set$$, its size is $latex m$$ and all its set elements are between zero and $latex n - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the Jacobian $latex F^{(1)} (x)$$. $pre $$ If this sparsity pattern does not change between calls to $codei SparseJacobian$$, it should be faster to calculate $icode p$$ once (using $cref ForSparseJac$$ or $cref RevSparseJac$$) and then pass $icode p$$ to $codei SparseJacobian$$. Furthermore, if you specify $icode work$$ in the calling sequence, it is not necessary to keep the sparsity pattern; see the heading $cref/p/sparse_jacobian/work/p/$$ under the $icode work$$ description. $pre $$ In addition, if you specify $icode p$$, CppAD will use the same type of sparsity representation (vectors of $code bool$$ or vectors of $code std::set$$) for its internal calculations. Otherwise, the representation for the internal calculations is unspecified. $head row, col$$ The arguments $icode row$$ and $icode col$$ are optional and have prototype $codei% const %VectorSize%& %row% const %VectorSize%& %col% %$$ (see $cref/VectorSize/sparse_jacobian/VectorSize/$$ below). They specify which rows and columns of $latex F^{(1)} (x)$$ are computes and in what order. Not all the non-zero entries in $latex F^{(1)} (x)$$ need be computed, but all the entries specified by $icode row$$ and $icode col$$ must be possibly non-zero in the sparsity pattern. We use $latex K$$ to denote the value $icode%jac%.size()%$$ which must also equal the size of $icode row$$ and $icode col$$. Furthermore, for $latex k = 0 , \ldots , K-1$$, it must hold that $latex row[k] < m$$ and $latex col[k] < n$$. $head jac$$ The result $icode jac$$ has prototype $codei% %VectorBase%& %jac% %$$ In the case where the arguments $icode row$$ and $icode col$$ are not present, the size of $icode jac$$ is $latex m * n$$ and for $latex i = 0 , \ldots , m-1$$, $latex j = 0 , \ldots , n-1$$, $latex \[ jac [ i * n + j ] = \D{ F_i }{ x_j } (x) \] $$ $pre $$ In the case where the arguments $icode row$$ and $icode col$$ are present, we use $latex K$$ to denote the size of $icode jac$$. The input value of its elements does not matter. Upon return, for $latex k = 0 , \ldots , K - 1$$, $latex \[ jac [ k ] = \D{ F_i }{ x_j } (x) \; , \; \; {\rm where} \; i = row[k] \; {\rm and } \; j = col[k] \] $$ $head work$$ If this argument is present, it has prototype $codei% sparse_jacobian_work& %work% %$$ This object can only be used with the routines $code SparseJacobianForward$$ and $code SparseJacobianReverse$$. During its the first use, information is stored in $icode work$$. This is used to reduce the work done by future calls to the same mode (forward or reverse), the same $icode f$$, $icode p$$, $icode row$$, and $icode col$$. If a future call is for a different mode, or any of these values have changed, you must first call $icode%work%.clear()%$$ to inform CppAD that this information needs to be recomputed. $subhead color_method$$ The coloring algorithm determines which columns (forward mode) or rows (reverse mode) can be computed during the same sweep. This field has prototype $codep% std::string %work%.color_method %$$ and its default value (after a constructor or $code clear()$$) is $code "cppad"$$. If $cref colpack_prefix$$ is specified on the $cref/cmake command/cmake/CMake Command/$$ line, you can set this method to $code "colpack"$$. This value only matters on the first call to $code sparse_jacobian$$ that follows the $icode work$$ constructor or a call to $icode%work%.clear()%$$. $subhead p$$ If $icode work$$ is present, and it is not the first call after its construction or a clear, the sparsity pattern $icode p$$ is not used. This enables one to free the sparsity pattern and still compute corresponding sparse Jacobians. $head n_sweep$$ The return value $icode n_sweep$$ has prototype $codei% size_t %n_sweep% %$$ If $code SparseJacobianForward$$ ($code SparseJacobianReverse$$) is used, $icode n_sweep$$ is the number of first order forward (reverse) sweeps used to compute the requested Jacobian values. (This is also the number of colors determined by the coloring method mentioned above). This is proportional to the total work that $code SparseJacobian$$ does, not counting the zero order forward sweep, or the work to combine multiple columns (rows) into a single sweep. $head VectorBase$$ The type $icode VectorBase$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head VectorSet$$ The type $icode VectorSet$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code bool$$ or $code std::set$$; see $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for a discussion of the difference. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $subhead Restrictions$$ If $icode VectorSet$$ has elements of $code std::set$$, then $icode%p%[%i%]%$$ must return a reference (not a copy) to the corresponding set. According to section 26.3.2.3 of the 1998 C++ standard, $code std::valarray< std::set >$$ does not satisfy this condition. $head VectorSize$$ The type $icode VectorSize$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code size_t$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Uses Forward$$ After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After a call to any of the sparse Jacobian routines, the zero order Taylor coefficients correspond to $icode%f%.Forward(0, %x%)%$$ and the other coefficients are unspecified. After $code SparseJacobian$$, the previous calls to $cref Forward$$ are undefined. $head Example$$ $children% example/sparse_jacobian.cpp %$$ The routine $cref sparse_jacobian.cpp$$ is examples and tests of $code sparse_jacobian$$. It return $code true$$, if it succeeds and $code false$$ otherwise. $end ============================================================================== */ # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file sparse_jacobian.hpp Sparse Jacobian driver routine and helper functions. */ // =========================================================================== /*! class used by SparseJacobian to hold information so it does not need to be recomputed. */ class sparse_jacobian_work { public: /// Coloring method: "cppad", or "colpack" /// (this field is set by user) std::string color_method; /// indices that sort the user row and col arrays by color CppAD::vector order; /// results of the coloring algorithm CppAD::vector color; /// constructor sparse_jacobian_work(void) : color_method("cppad") { } /// reset coloring method to its default and /// inform CppAD that color and order need to be recomputed void clear(void) { color_method = "cppad"; order.clear(); color.clear(); } }; // =========================================================================== /*! Private helper function forward mode cases \tparam Base is the base type for the recording that is stored in this ADFun object. \tparam VectorBase is a simple vector class with elements of type \a Base. \tparam VectorSet is either sparse_pack or sparse_list. \tparam VectorSize is a simple vector class with elements of type \c size_t. \param x [in] is a vector specifing the point at which to compute the Jacobian. \param p_transpose [in] If work.color.size() != 0, then \c p_transpose is not used. Otherwise, it is a sparsity pattern for the transpose of the Jacobian of this ADFun object. Note that we do not change the values in \c p_transpose, but is not \c const because we use its iterator facility. \param row [in] is the vector of row indices for the returned Jacobian values. \param col [in] is the vector of columns indices for the returned Jacobian values. It must have the same size as \c row. \param jac [out] is the vector of Jacobian values. We use \c K to denote the size of \c jac. The return value jac[k] is the partial of the row[k] range component of the function with respect the the col[k] domain component of its argument. \param work work.color_method is an input. The rest of this structure contains information that is computed by \c SparseJacobainFor. If the sparsity pattern, \c row vector, or \c col vectors are not the same between calls to \c SparseJacobianFor, \c work.clear() must be called to reinitialize \c work. \return Is the number of first order forward sweeps used to compute the requested Jacobian values. The total work, not counting the zero order forward sweep, or the time to combine computations, is proportional to this return value. */ template template size_t ADFun::SparseJacobianFor( const VectorBase& x , VectorSet& p_transpose , const VectorSize& row , const VectorSize& col , VectorBase& jac , sparse_jacobian_work& work ) { size_t j, k, ell; CppAD::vector& order(work.order); CppAD::vector& color(work.color); size_t m = Range(); size_t n = Domain(); // some values const Base zero(0); const Base one(1); // check VectorBase is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_UNKNOWN( size_t(x.size()) == n ); CPPAD_ASSERT_UNKNOWN( color.size() == 0 || color.size() == n ); // number of components of Jacobian that are required size_t K = size_t(jac.size()); CPPAD_ASSERT_UNKNOWN( size_t( row.size() ) == K ); CPPAD_ASSERT_UNKNOWN( size_t( col.size() ) == K ); // Point at which we are evaluating the Jacobian Forward(0, x); // check for case where nothing (except Forward above) to do if( K == 0 ) return 0; if( color.size() == 0 ) { CPPAD_ASSERT_UNKNOWN( p_transpose.n_set() == n ); CPPAD_ASSERT_UNKNOWN( p_transpose.end() == m ); // execute coloring algorithm color.resize(n); if( work.color_method == "cppad" ) local::color_general_cppad(p_transpose, col, row, color); else if( work.color_method == "colpack" ) { # if CPPAD_HAS_COLPACK local::color_general_colpack(p_transpose, col, row, color); # else CPPAD_ASSERT_KNOWN( false, "SparseJacobianForward: work.color_method = colpack " "and colpack_prefix missing from cmake command line." ); # endif } else CPPAD_ASSERT_KNOWN( false, "SparseJacobianForward: work.color_method is not valid." ); // put sorting indices in color order VectorSize key(K); order.resize(K); for(k = 0; k < K; k++) key[k] = color[ col[k] ]; index_sort(key, order); } size_t n_color = 1; for(j = 0; j < n; j++) if( color[j] < n ) n_color = std::max(n_color, color[j] + 1); // initialize the return value for(k = 0; k < K; k++) jac[k] = zero; # if CPPAD_SPARSE_JACOBIAN_MAX_MULTIPLE_DIRECTION == 1 // direction vector and return values for calls to forward VectorBase dx(n), dy(m); // loop over colors k = 0; for(ell = 0; ell < n_color; ell++) { CPPAD_ASSERT_UNKNOWN( color[ col[ order[k] ] ] == ell ); // combine all columns with this color for(j = 0; j < n; j++) { dx[j] = zero; if( color[j] == ell ) dx[j] = one; } // call forward mode for all these columns at once dy = Forward(1, dx); // set the corresponding components of the result while( k < K && color[ col[order[k]] ] == ell ) { jac[ order[k] ] = dy[row[order[k]]]; k++; } } # else // abbreviation for this value size_t max_r = CPPAD_SPARSE_JACOBIAN_MAX_MULTIPLE_DIRECTION; CPPAD_ASSERT_UNKNOWN( max_r > 1 ); // count the number of colors done so far size_t count_color = 0; // count the sparse matrix entries done so far k = 0; while( count_color < n_color ) { // number of colors we will do this time size_t r = std::min(max_r , n_color - count_color); VectorBase dx(n * r), dy(m * r); // loop over colors we will do this tme for(ell = 0; ell < r; ell++) { // combine all columns with this color for(j = 0; j < n; j++) { dx[j * r + ell] = zero; if( color[j] == ell + count_color ) dx[j * r + ell] = one; } } size_t q = 1; dy = Forward(q, r, dx); // store results for(ell = 0; ell < r; ell++) { // set the components of the result for this color while( k < K && color[ col[order[k]] ] == ell + count_color ) { jac[ order[k] ] = dy[ row[order[k]] * r + ell ]; k++; } } count_color += r; } # endif return n_color; } /*! Private helper function for reverse mode cases. \tparam Base is the base type for the recording that is stored in this ADFun object. \tparam VectorBase is a simple vector class with elements of type \a Base. \tparam VectorSet is either sparse_pack or sparse_list. \tparam VectorSize is a simple vector class with elements of type \c size_t. \param x [in] is a vector specifing the point at which to compute the Jacobian. \param p [in] If work.color.size() != 0, then \c p is not used. Otherwise, it is a sparsity pattern for the Jacobian of this ADFun object. Note that we do not change the values in \c p, but is not \c const because we use its iterator facility. \param row [in] is the vector of row indices for the returned Jacobian values. \param col [in] is the vector of columns indices for the returned Jacobian values. It must have the same size as \c row. \param jac [out] is the vector of Jacobian values. It must have the same size as \c row. The return value jac[k] is the partial of the row[k] range component of the function with respect the the col[k] domain component of its argument. \param work work.color_method is an input. The rest of This structure contains information that is computed by \c SparseJacobainRev. If the sparsity pattern, \c row vector, or \c col vectors are not the same between calls to \c SparseJacobianRev, \c work.clear() must be called to reinitialize \c work. \return Is the number of first order reverse sweeps used to compute the reverse Jacobian values. The total work, not counting the zero order forward sweep, or the time to combine computations, is proportional to this return value. */ template template size_t ADFun::SparseJacobianRev( const VectorBase& x , VectorSet& p , const VectorSize& row , const VectorSize& col , VectorBase& jac , sparse_jacobian_work& work ) { size_t i, k, ell; CppAD::vector& order(work.order); CppAD::vector& color(work.color); size_t m = Range(); size_t n = Domain(); // some values const Base zero(0); const Base one(1); // check VectorBase is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_UNKNOWN( size_t(x.size()) == n ); CPPAD_ASSERT_UNKNOWN (color.size() == m || color.size() == 0 ); // number of components of Jacobian that are required size_t K = size_t(jac.size()); CPPAD_ASSERT_UNKNOWN( size_t( size_t( row.size() ) ) == K ); CPPAD_ASSERT_UNKNOWN( size_t( size_t( col.size() ) ) == K ); // Point at which we are evaluating the Jacobian Forward(0, x); // check for case where nothing (except Forward above) to do if( K == 0 ) return 0; if( color.size() == 0 ) { CPPAD_ASSERT_UNKNOWN( p.n_set() == m ); CPPAD_ASSERT_UNKNOWN( p.end() == n ); // execute the coloring algorithm color.resize(m); if( work.color_method == "cppad" ) local::color_general_cppad(p, row, col, color); else if( work.color_method == "colpack" ) { # if CPPAD_HAS_COLPACK local::color_general_colpack(p, row, col, color); # else CPPAD_ASSERT_KNOWN( false, "SparseJacobianReverse: work.color_method = colpack " "and colpack_prefix missing from cmake command line." ); # endif } else CPPAD_ASSERT_KNOWN( false, "SparseJacobianReverse: work.color_method is not valid." ); // put sorting indices in color order VectorSize key(K); order.resize(K); for(k = 0; k < K; k++) key[k] = color[ row[k] ]; index_sort(key, order); } size_t n_color = 1; for(i = 0; i < m; i++) if( color[i] < m ) n_color = std::max(n_color, color[i] + 1); // weighting vector for calls to reverse VectorBase w(m); // location for return values from Reverse VectorBase dw(n); // initialize the return value for(k = 0; k < K; k++) jac[k] = zero; // loop over colors k = 0; for(ell = 0; ell < n_color; ell++) { CPPAD_ASSERT_UNKNOWN( color[ row[ order[k] ] ] == ell ); // combine all the rows with this color for(i = 0; i < m; i++) { w[i] = zero; if( color[i] == ell ) w[i] = one; } // call reverse mode for all these rows at once dw = Reverse(1, w); // set the corresponding components of the result while( k < K && color[ row[order[k]] ] == ell ) { jac[ order[k] ] = dw[col[order[k]]]; k++; } } return n_color; } // ========================================================================== // Public Member functions // ========================================================================== /*! Compute user specified subset of a sparse Jacobian using forward mode. The C++ source code corresponding to this operation is \verbatim SparceJacobianForward(x, p, row, col, jac, work) \endverbatim \tparam Base is the base type for the recording that is stored in this ADFun object. \tparam VectorBase is a simple vector class with elements of type \a Base. \tparam VectorSet is a simple vector class with elements of type \c bool or \c std::set. \tparam VectorSize is a simple vector class with elements of type \c size_t. \param x [in] is a vector specifing the point at which to compute the Jacobian. \param p [in] is the sparsity pattern for the Jacobian that we are calculating. \param row [in] is the vector of row indices for the returned Jacobian values. \param col [in] is the vector of columns indices for the returned Jacobian values. It must have the same size as \c row. \param jac [out] is the vector of Jacobian values. It must have the same size as \c row. The return value jac[k] is the partial of the row[k] range component of the function with respect the the col[k] domain component of its argument. \param work [in,out] this structure contains information that depends on the function object, sparsity pattern, \c row vector, and \c col vector. If they are not the same between calls to \c SparseJacobianForward, \c work.clear() must be called to reinitialize them. \return Is the number of first order forward sweeps used to compute the requested Jacobian values. The total work, not counting the zero order forward sweep, or the time to combine computations, is proportional to this return value. */ template template size_t ADFun::SparseJacobianForward( const VectorBase& x , const VectorSet& p , const VectorSize& row , const VectorSize& col , VectorBase& jac , sparse_jacobian_work& work ) { size_t n = Domain(); size_t m = Range(); size_t K = jac.size(); # ifndef NDEBUG size_t k; CPPAD_ASSERT_KNOWN( size_t(x.size()) == n , "SparseJacobianForward: size of x not equal domain dimension for f." ); CPPAD_ASSERT_KNOWN( size_t(row.size()) == K && size_t(col.size()) == K , "SparseJacobianForward: either r or c does not have " "the same size as jac." ); CPPAD_ASSERT_KNOWN( work.color.size() == 0 || work.color.size() == n, "SparseJacobianForward: invalid value in work." ); for(k = 0; k < K; k++) { CPPAD_ASSERT_KNOWN( row[k] < m, "SparseJacobianForward: invalid value in r." ); CPPAD_ASSERT_KNOWN( col[k] < n, "SparseJacobianForward: invalid value in c." ); } if( work.color.size() != 0 ) for(size_t j = 0; j < n; j++) CPPAD_ASSERT_KNOWN( work.color[j] <= n, "SparseJacobianForward: invalid value in work." ); # endif // check for case where there is nothing to compute size_t n_sweep = 0; if( K == 0 ) return n_sweep; typedef typename VectorSet::value_type Set_type; typedef typename local::internal_sparsity::pattern_type Pattern_type; Pattern_type s_transpose; if( work.color.size() == 0 ) { bool transpose = true; const char* error_msg = "SparseJacobianForward: transposed sparsity" " pattern does not have proper row or column dimension"; sparsity_user2internal(s_transpose, p, n, m, transpose, error_msg); } n_sweep = SparseJacobianFor(x, s_transpose, row, col, jac, work); return n_sweep; } /*! Compute user specified subset of a sparse Jacobian using forward mode. The C++ source code corresponding to this operation is \verbatim SparceJacobianReverse(x, p, row, col, jac, work) \endverbatim \tparam Base is the base type for the recording that is stored in this ADFun object. \tparam VectorBase is a simple vector class with elements of type \a Base. \tparam VectorSet is a simple vector class with elements of type \c bool or \c std::set. \tparam VectorSize is a simple vector class with elements of type \c size_t. \param x [in] is a vector specifing the point at which to compute the Jacobian. \param p [in] is the sparsity pattern for the Jacobian that we are calculating. \param row [in] is the vector of row indices for the returned Jacobian values. \param col [in] is the vector of columns indices for the returned Jacobian values. It must have the same size as \c row. \param jac [out] is the vector of Jacobian values. It must have the same size as \c row. The return value jac[k] is the partial of the row[k] range component of the function with respect the the col[k] domain component of its argument. \param work [in,out] this structure contains information that depends on the function object, sparsity pattern, \c row vector, and \c col vector. If they are not the same between calls to \c SparseJacobianReverse, \c work.clear() must be called to reinitialize them. \return Is the number of first order reverse sweeps used to compute the reverse Jacobian values. The total work, not counting the zero order forward sweep, or the time to combine computations, is proportional to this return value. */ template template size_t ADFun::SparseJacobianReverse( const VectorBase& x , const VectorSet& p , const VectorSize& row , const VectorSize& col , VectorBase& jac , sparse_jacobian_work& work ) { size_t m = Range(); size_t n = Domain(); size_t K = jac.size(); # ifndef NDEBUG size_t k; CPPAD_ASSERT_KNOWN( size_t(x.size()) == n , "SparseJacobianReverse: size of x not equal domain dimension for f." ); CPPAD_ASSERT_KNOWN( size_t(row.size()) == K && size_t(col.size()) == K , "SparseJacobianReverse: either r or c does not have " "the same size as jac." ); CPPAD_ASSERT_KNOWN( work.color.size() == 0 || work.color.size() == m, "SparseJacobianReverse: invalid value in work." ); for(k = 0; k < K; k++) { CPPAD_ASSERT_KNOWN( row[k] < m, "SparseJacobianReverse: invalid value in r." ); CPPAD_ASSERT_KNOWN( col[k] < n, "SparseJacobianReverse: invalid value in c." ); } if( work.color.size() != 0 ) for(size_t i = 0; i < m; i++) CPPAD_ASSERT_KNOWN( work.color[i] <= m, "SparseJacobianReverse: invalid value in work." ); # endif // check for case where there is nothing to compute size_t n_sweep = 0; if( K == 0 ) return n_sweep; typedef typename VectorSet::value_type Set_type; typedef typename local::internal_sparsity::pattern_type Pattern_type; Pattern_type s; if( work.color.size() == 0 ) { bool transpose = false; const char* error_msg = "SparseJacobianReverse: sparsity" " pattern does not have proper row or column dimension"; sparsity_user2internal(s, p, m, n, transpose, error_msg); } n_sweep = SparseJacobianRev(x, s, row, col, jac, work); return n_sweep; } /*! Compute a sparse Jacobian. The C++ source code corresponding to this operation is \verbatim jac = SparseJacobian(x, p) \endverbatim \tparam Base is the base type for the recording that is stored in this ADFun object. \tparam VectorBase is a simple vector class with elements of type \a Base. \tparam VectorSet is a simple vector class with elements of type \c bool or \c std::set. \param x [in] is a vector specifing the point at which to compute the Jacobian. \param p [in] is the sparsity pattern for the Jacobian that we are calculating. \return Will be a vector if size \c m * n containing the Jacobian at the specified point (in row major order). */ template template VectorBase ADFun::SparseJacobian( const VectorBase& x, const VectorSet& p ) { size_t i, j, k; size_t m = Range(); size_t n = Domain(); VectorBase jac(m * n); CPPAD_ASSERT_KNOWN( size_t(x.size()) == n, "SparseJacobian: size of x not equal domain size for f." ); CheckSimpleVector(); typedef typename VectorSet::value_type Set_type; typedef typename local::internal_sparsity::pattern_type Pattern_type; // initialize the return value as zero Base zero(0); for(i = 0; i < m; i++) for(j = 0; j < n; j++) jac[i * n + j] = zero; sparse_jacobian_work work; CppAD::vector row; CppAD::vector col; if( n <= m ) { // need an internal copy of sparsity pattern Pattern_type s_transpose; bool transpose = true; const char* error_msg = "SparseJacobian: transposed sparsity" " pattern does not have proper row or column dimension"; sparsity_user2internal(s_transpose, p, n, m, transpose, error_msg); k = 0; for(j = 0; j < n; j++) { typename Pattern_type::const_iterator itr(s_transpose, j); i = *itr; while( i != s_transpose.end() ) { row.push_back(i); col.push_back(j); k++; i = *(++itr); } } size_t K = k; VectorBase J(K); // now we have folded this into the following case SparseJacobianFor(x, s_transpose, row, col, J, work); // now set the non-zero return values for(k = 0; k < K; k++) jac[ row[k] * n + col[k] ] = J[k]; } else { // need an internal copy of sparsity pattern Pattern_type s; bool transpose = false; const char* error_msg = "SparseJacobian: sparsity" " pattern does not have proper row or column dimension"; sparsity_user2internal(s, p, m, n, transpose, error_msg); k = 0; for(i = 0; i < m; i++) { typename Pattern_type::const_iterator itr(s, i); j = *itr; while( j != s.end() ) { row.push_back(i); col.push_back(j); k++; j = *(++itr); } } size_t K = k; VectorBase J(K); // now we have folded this into the following case SparseJacobianRev(x, s, row, col, J, work); // now set the non-zero return values for(k = 0; k < K; k++) jac[ row[k] * n + col[k] ] = J[k]; } return jac; } /*! Compute a sparse Jacobian. The C++ source code corresponding to this operation is \verbatim jac = SparseJacobian(x) \endverbatim \tparam Base is the base type for the recording that is stored in this ADFun object. \tparam VectorBase is a simple vector class with elements of the \a Base. \param x [in] is a vector specifing the point at which to compute the Jacobian. \return Will be a vector of size \c m * n containing the Jacobian at the specified point (in row major order). */ template template VectorBase ADFun::SparseJacobian( const VectorBase& x ) { typedef CppAD::vectorBool VectorBool; size_t m = Range(); size_t n = Domain(); // sparsity pattern for Jacobian VectorBool p(m * n); if( n <= m ) { size_t j, k; // use forward mode VectorBool r(n * n); for(j = 0; j < n; j++) { for(k = 0; k < n; k++) r[j * n + k] = false; r[j * n + j] = true; } p = ForSparseJac(n, r); } else { size_t i, k; // use reverse mode VectorBool s(m * m); for(i = 0; i < m; i++) { for(k = 0; k < m; k++) s[i * m + k] = false; s[i * m + i] = true; } p = RevSparseJac(m, s); } return SparseJacobian(x, p); } } // END_CPPAD_NAMESPACE # undef CPPAD_SPARSE_JACOBIAN_MAX_MULTIPLE_DIRECTION # endif cppad-20170000.3/cppad/core/compare.hpp0000644000175200017650000002520113057470465016613 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_COMPARE_HPP # define CPPAD_CORE_COMPARE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin Compare$$ $spell cos Op bool const $$ $section AD Binary Comparison Operators$$ $mindex compare < <= > >= == !=$$ $head Syntax$$ $icode%b% = %x% %Op% %y%$$ $head Purpose$$ Compares two operands where one of the operands is an $codei%AD<%Base%>%$$ object. The comparison has the same interpretation as for the $icode Base$$ type. $head Op$$ The operator $icode Op$$ is one of the following: $table $bold Op$$ $pre $$ $cnext $bold Meaning$$ $rnext $code <$$ $cnext is $icode x$$ less than $icode y$$ $rnext $code <=$$ $cnext is $icode x$$ less than or equal $icode y$$ $rnext $code >$$ $cnext is $icode x$$ greater than $icode y$$ $rnext $code >=$$ $cnext is $icode x$$ greater than or equal $icode y$$ $rnext $code ==$$ $cnext is $icode x$$ equal to $icode y$$ $rnext $code !=$$ $cnext is $icode x$$ not equal to $icode y$$ $tend $head x$$ The operand $icode x$$ has prototype $codei% const %Type% &%x% %$$ where $icode Type$$ is $codei%AD<%Base%>%$$, $icode Base$$, or $code int$$. $head y$$ The operand $icode y$$ has prototype $codei% const %Type% &%y% %$$ where $icode Type$$ is $codei%AD<%Base%>%$$, $icode Base$$, or $code int$$. $head b$$ The result $icode b$$ has type $codei% bool %b% %$$ $head Operation Sequence$$ The result of this operation is a $code bool$$ value (not an $cref/AD of Base/glossary/AD of Base/$$ object). Thus it will not be recorded as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $pre $$ For example, suppose $icode x$$ and $icode y$$ are $codei%AD<%Base%>%$$ objects, the tape corresponding to $codei%AD<%Base%>%$$ is recording, $icode b$$ is true, and the subsequent code is $codei% if( %b% ) %y% = cos(%x%); else %y% = sin(%x%); %$$ only the assignment $icode%y% = cos(%x%)%$$ is recorded on the tape (if $icode x$$ is a $cref/parameter/glossary/Parameter/$$, nothing is recorded). The $cref CompareChange$$ function can yield some information about changes in comparison operation results. You can use $cref CondExp$$ to obtain comparison operations that depends on the $cref/independent variable/glossary/Tape/Independent Variable/$$ values with out re-taping the AD sequence of operations. $head Assumptions$$ If one of the $icode Op$$ operators listed above is used with an $codei%AD<%Base%>%$$ object, it is assumed that the same operator is supported by the base type $icode Base$$. $head Example$$ $children% example/compare.cpp %$$ The file $cref compare.cpp$$ contains an example and test of these operations. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { // -------------------------------- < -------------------------- template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool operator < (const AD &left , const AD &right) { bool result = (left.value_ < right.value_); bool var_left = Variable(left); bool var_right = Variable(right); local::ADTape *tape = CPPAD_NULL; if( var_left ) { tape = left.tape_this(); if( var_right ) { if( result ) { tape->Rec_.PutOp(local::LtvvOp); tape->Rec_.PutArg(left.taddr_, right.taddr_); } else { tape->Rec_.PutOp(local::LevvOp); tape->Rec_.PutArg(right.taddr_, left.taddr_); } } else { addr_t arg1 = tape->Rec_.PutPar(right.value_); if( result ) { tape->Rec_.PutOp(local::LtvpOp); tape->Rec_.PutArg(left.taddr_, arg1); } else { tape->Rec_.PutOp(local::LepvOp); tape->Rec_.PutArg(arg1, left.taddr_); } } } else if ( var_right ) { tape = right.tape_this(); addr_t arg0 = tape->Rec_.PutPar(left.value_); if( result ) { tape->Rec_.PutOp(local::LtpvOp); tape->Rec_.PutArg(arg0, right.taddr_); } else { tape->Rec_.PutOp(local::LevpOp); tape->Rec_.PutArg(right.taddr_, arg0); } } return result; } // convert other cases into the case above CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR(<) // -------------------------------- <= ------------------------- template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool operator <= (const AD &left , const AD &right) { bool result = (left.value_ <= right.value_); bool var_left = Variable(left); bool var_right = Variable(right); local::ADTape *tape = CPPAD_NULL; if( var_left ) { tape = left.tape_this(); if( var_right ) { if( result ) { tape->Rec_.PutOp(local::LevvOp); tape->Rec_.PutArg(left.taddr_, right.taddr_); } else { tape->Rec_.PutOp(local::LtvvOp); tape->Rec_.PutArg(right.taddr_, left.taddr_); } } else { addr_t arg1 = tape->Rec_.PutPar(right.value_); if( result ) { tape->Rec_.PutOp(local::LevpOp); tape->Rec_.PutArg(left.taddr_, arg1); } else { tape->Rec_.PutOp(local::LtpvOp); tape->Rec_.PutArg(arg1, left.taddr_); } } } else if ( var_right ) { tape = right.tape_this(); addr_t arg0 = tape->Rec_.PutPar(left.value_); if( result ) { tape->Rec_.PutOp(local::LepvOp); tape->Rec_.PutArg(arg0, right.taddr_); } else { tape->Rec_.PutOp(local::LtvpOp); tape->Rec_.PutArg(right.taddr_, arg0); } } return result; } // convert other cases into the case above CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR(<=) // -------------------------------- > -------------------------- template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool operator > (const AD &left , const AD &right) { bool result = (left.value_ > right.value_); bool var_left = Variable(left); bool var_right = Variable(right); local::ADTape *tape = CPPAD_NULL; if( var_left ) { tape = left.tape_this(); if( var_right ) { if( result ) { tape->Rec_.PutOp(local::LtvvOp); tape->Rec_.PutArg(right.taddr_, left.taddr_); } else { tape->Rec_.PutOp(local::LevvOp); tape->Rec_.PutArg(left.taddr_, right.taddr_); } } else { addr_t arg1 = tape->Rec_.PutPar(right.value_); if( result ) { tape->Rec_.PutOp(local::LtpvOp); tape->Rec_.PutArg(arg1, left.taddr_); } else { tape->Rec_.PutOp(local::LevpOp); tape->Rec_.PutArg(left.taddr_, arg1); } } } else if ( var_right ) { tape = right.tape_this(); addr_t arg0 = tape->Rec_.PutPar(left.value_); if( result ) { tape->Rec_.PutOp(local::LtvpOp); tape->Rec_.PutArg(right.taddr_, arg0); } else { tape->Rec_.PutOp(local::LepvOp); tape->Rec_.PutArg(arg0, right.taddr_); } } return result; } // convert other cases into the case above CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR(>) // -------------------------------- >= ------------------------- template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool operator >= (const AD &left , const AD &right) { bool result = (left.value_ >= right.value_); bool var_left = Variable(left); bool var_right = Variable(right); local::ADTape *tape = CPPAD_NULL; if( var_left ) { tape = left.tape_this(); if( var_right ) { if( result ) { tape->Rec_.PutOp(local::LevvOp); tape->Rec_.PutArg(right.taddr_, left.taddr_); } else { tape->Rec_.PutOp(local::LtvvOp); tape->Rec_.PutArg(left.taddr_, right.taddr_); } } else { addr_t arg1 = tape->Rec_.PutPar(right.value_); if( result ) { tape->Rec_.PutOp(local::LepvOp); tape->Rec_.PutArg(arg1, left.taddr_); } else { tape->Rec_.PutOp(local::LtvpOp); tape->Rec_.PutArg(left.taddr_, arg1); } } } else if ( var_right ) { tape = right.tape_this(); addr_t arg0 = tape->Rec_.PutPar(left.value_); if( result ) { tape->Rec_.PutOp(local::LevpOp); tape->Rec_.PutArg(right.taddr_, arg0); } else { tape->Rec_.PutOp(local::LtpvOp); tape->Rec_.PutArg(arg0, right.taddr_); } } return result; } // convert other cases into the case above CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR(>=) // -------------------------------- == ------------------------- template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool operator == (const AD &left , const AD &right) { bool result = (left.value_ == right.value_); bool var_left = Variable(left); bool var_right = Variable(right); local::ADTape *tape = CPPAD_NULL; if( var_left ) { tape = left.tape_this(); if( var_right ) { tape->Rec_.PutArg(left.taddr_, right.taddr_); if( result ) tape->Rec_.PutOp(local::EqvvOp); else tape->Rec_.PutOp(local::NevvOp); } else { addr_t arg1 = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(arg1, left.taddr_); if( result ) tape->Rec_.PutOp(local::EqpvOp); else tape->Rec_.PutOp(local::NepvOp); } } else if ( var_right ) { tape = right.tape_this(); addr_t arg0 = tape->Rec_.PutPar(left.value_); tape->Rec_.PutArg(arg0, right.taddr_); if( result ) tape->Rec_.PutOp(local::EqpvOp); else tape->Rec_.PutOp(local::NepvOp); } return result; } // convert other cases into the case above CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR(==) // -------------------------------- != ------------------------- template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool operator != (const AD &left , const AD &right) { bool result = (left.value_ != right.value_); bool var_left = Variable(left); bool var_right = Variable(right); local::ADTape *tape = CPPAD_NULL; if( var_left ) { tape = left.tape_this(); if( var_right ) { tape->Rec_.PutArg(left.taddr_, right.taddr_); if( result ) tape->Rec_.PutOp(local::NevvOp); else tape->Rec_.PutOp(local::EqvvOp); } else { addr_t arg1 = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(arg1, left.taddr_); if( result ) tape->Rec_.PutOp(local::NepvOp); else tape->Rec_.PutOp(local::EqpvOp); } } else if ( var_right ) { tape = right.tape_this(); addr_t arg0 = tape->Rec_.PutPar(left.value_); tape->Rec_.PutArg(arg0, right.taddr_); if( result ) tape->Rec_.PutOp(local::NepvOp); else tape->Rec_.PutOp(local::EqpvOp); } return result; } // convert other cases into the case above CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR(!=) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/checkpoint.hpp0000644000175200017650000010120213057470465017310 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_CHECKPOINT_HPP # define CPPAD_CORE_CHECKPOINT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file checkpoint.hpp defining checkpoint functions. */ /* $begin checkpoint$$ $spell sv var cppad.hpp CppAD checkpoint checkpointing algo atom_fun const enum bool recomputed $$ $section Checkpointing Functions$$ $head Syntax$$ $codei%checkpoint<%Base%> %atom_fun%( %name%, %algo%, %ax%, %ay%, %sparsity%, %optimize% ) %sv% = %atom_fun%.size_var() %atom_fun%.option(%option_value%) %algo%(%ax%, %ay%) %atom_fun%(%ax%, %ay%) checkpoint<%Base%>::clear()%$$ $head See Also$$ $cref reverse_checkpoint.cpp$$ $head Purpose$$ $subhead Reduce Memory$$ You can reduce the size of the tape and memory required for AD by checkpointing functions of the form $latex y = f(x)$$ where $latex f : B^n \rightarrow B^m$$. $subhead Faster Recording$$ It may also reduce the time to make a recording the same function for different values of the independent variable. Note that the operation sequence for a recording that uses $latex f(x)$$ may depend on its independent variables. $subhead Repeating Forward$$ Normally, CppAD store $cref forward$$ mode results until they freed using $cref capacity_order$$ or the corresponding $cref ADFun$$ object is deleted. This is not true for checkpoint functions because a checkpoint function may be used repeatedly with different arguments in the same tape. Thus, forward mode results are recomputed each time a checkpoint function is used during a forward or reverse mode sweep. $subhead Restriction$$ The $cref/operation sequence/glossary/Operation/Sequence/$$ representing $latex f(x)$$ cannot depend on the value of $latex x$$. The approach in the $cref reverse_checkpoint.cpp$$ example case be applied when the operation sequence depends on $latex x$$. $subhead Multiple Level AD$$ If $icode Base$$ is an AD type, it is possible to record $icode Base$$ operations. Note that $icode atom_fun$$ will treat $icode algo$$ as an atomic operation while recording $codei%AD%<%Base%>%$$ operations, but not while recording $icode Base$$ operations. See the $cref atomic_mul_level.cpp$$ example. $head Method$$ The $code checkpoint$$ class is derived from $code atomic_base$$ and makes this easy. It implements all the $code atomic_base$$ $cref/virtual functions/atomic_base/Virtual Functions/$$ and hence its source code $code cppad/core/checkpoint.hpp$$ provides an example implementation of $cref atomic_base$$. The difference is that $code checkpoint.hpp$$ uses AD instead of user provided derivatives. $head constructor$$ The syntax for the checkpoint constructor is $codei% checkpoint<%Base%> %atom_fun%(%name%, %algo%, %ax%, %ay%) %$$ $list number$$ This constructor cannot be called in $cref/parallel/ta_in_parallel/$$ mode. $lnext You cannot currently be recording $codei%AD<%Base%>%$$ operations when the constructor is called. $lnext This object $icode atom_fun$$ must not be destructed for as long as any $codei%ADFun<%Base%>%$$ object uses its atomic operation. $lnext This class is implemented as a derived class of $cref/atomic_base/atomic_ctor/atomic_base/$$ and hence some of its error message will refer to $code atomic_base$$. $lend $head Base$$ The type $icode Base$$ specifies the base type for AD operations. $head ADVector$$ The type $icode ADVector$$ must be a $cref/simple vector class/SimpleVector/$$ with elements of type $codei%AD<%Base%>%$$. $head name$$ This $icode checkpoint$$ constructor argument has prototype $codei% const char* %name% %$$ It is the name used for error reporting. The suggested value for $icode name$$ is $icode atom_fun$$; i.e., the same name as used for the object being constructed. $head ax$$ This argument has prototype $codei% const %ADVector%& %ax% %$$ and size must be equal to $icode n$$. It specifies vector $latex x \in B^n$$ at which an $codei%AD<%Base%>%$$ version of $latex y = f(x)$$ is to be evaluated. $head ay$$ This argument has prototype $codei% %ADVector%& %ay% %$$ Its input size must be equal to $icode m$$ and does not change. The input values of its elements do not matter. Upon return, it is an $codei%AD<%Base%>%$$ version of $latex y = f(x)$$. $head sparsity$$ This argument has prototype $codei% atomic_base<%Base%>::option_enum %sparsity% %$$ It specifies $cref/sparsity/atomic_ctor/atomic_base/sparsity/$$ in the $code atomic_base$$ constructor and must be either $codei%atomic_base<%Base%>::pack_sparsity_enum%$$, $codei%atomic_base<%Base%>::bool_sparsity_enum%$$, or $codei%atomic_base<%Base%>::set_sparsity_enum%$$. This argument is optional and its default value is unspecified. $head optimize$$ This argument has prototype $codei% bool %optimize% %$$ It specifies if the recording corresponding to the atomic function should be $cref/optimized/optimize/$$. One expects to use a checkpoint function many times, so it should be worth the time to optimize its operation sequence. For debugging purposes, it may be useful to use the original operation sequence (before optimization) because it corresponds more closely to $icode algo$$. This argument is optional and its default value is true. $head size_var$$ This $code size_var$$ member function return value has prototype $codei% size_t %sv% %$$ It is the $cref/size_var/seq_property/size_var/$$ for the $codei%ADFun<%Base%>%$$ object is used to store the operation sequence corresponding to $icode algo$$. $head option$$ The $code option$$ syntax can be used to set the type of sparsity pattern used by $icode atom_fun$$. This is an $codei%atomic_base<%Base%>%$$ function and its documentation can be found at $cref atomic_option$$. $head algo$$ The type of $icode algo$$ is arbitrary, except for the fact that the syntax $codei% %algo%(%ax%, %ay%) %$$ must evaluate the function $latex y = f(x)$$ using $codei%AD<%Base%>%$$ operations. In addition, we assume that the $cref/operation sequence/glossary/Operation/Sequence/$$ does not depend on the value of $icode ax$$. $head atom_fun$$ Given $icode ax$$ it computes the corresponding value of $icode ay$$ using the operation sequence corresponding to $icode algo$$. If $codei%AD<%Base%>%$$ operations are being recorded, it enters the computation as single operation in the recording see $cref/start recording/Independent/Start Recording/$$. (Currently each use of $icode atom_fun$$ actually corresponds to $icode%m%+%n%+2%$$ operations and creates $icode m$$ new variables, but this is not part of the CppAD specifications and my change.) $head clear$$ The $code atomic_base$$ class holds onto static work space in order to increase speed by avoiding system memory allocation calls. This call makes to work space $cref/available/ta_available/$$ to for other uses by the same thread. This should be called when you are done using the user atomic functions for a specific value of $icode Base$$. $subhead Restriction$$ The $code clear$$ routine cannot be called while in $cref/parallel/ta_in_parallel/$$ execution mode. $children%example/atomic/checkpoint.cpp %example/atomic/mul_level.cpp %example/atomic/ode.cpp %example/atomic/extended_ode.cpp %$$ $head Example$$ The file $cref checkpoint.cpp$$ contains an example and test of these operations. It returns true if it succeeds and false if it fails. $end */ template class checkpoint : public atomic_base { // --------------------------------------------------------------------------- private: /// same as option_enum in base class typedef typename atomic_base::option_enum option_enum; // /// AD function corresponding to this checkpoint object ADFun f_; // /// sparsity for entire Jacobian f(x)^{(1)} does not change so can cache it local::sparse_list jac_sparse_set_; vectorBool jac_sparse_bool_; // /// sparsity for sum_i f_i(x)^{(2)} does not change so can cache it local::sparse_list hes_sparse_set_; vectorBool hes_sparse_bool_; // ------------------------------------------------------------------------ option_enum sparsity(void) { return static_cast< atomic_base* >(this)->sparsity(); } // ------------------------------------------------------------------------ /// set jac_sparse_set_ void set_jac_sparse_set(void) { CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.n_set() == 0 ); bool transpose = false; bool dependency = true; size_t n = f_.Domain(); size_t m = f_.Range(); // Use the choice for forward / reverse that results in smaller // size for the sparsity pattern of all variables in the tape. if( n <= m ) { local::sparse_list identity; identity.resize(n, n); for(size_t j = 0; j < n; j++) identity.add_element(j, j); f_.ForSparseJacCheckpoint( n, identity, transpose, dependency, jac_sparse_set_ ); f_.size_forward_set(0); } else { local::sparse_list identity; identity.resize(m, m); for(size_t i = 0; i < m; i++) identity.add_element(i, i); f_.RevSparseJacCheckpoint( m, identity, transpose, dependency, jac_sparse_set_ ); } CPPAD_ASSERT_UNKNOWN( f_.size_forward_set() == 0 ); CPPAD_ASSERT_UNKNOWN( f_.size_forward_bool() == 0 ); } /// set jac_sparse_bool_ void set_jac_sparse_bool(void) { CPPAD_ASSERT_UNKNOWN( jac_sparse_bool_.size() == 0 ); bool transpose = false; bool dependency = true; size_t n = f_.Domain(); size_t m = f_.Range(); // Use the choice for forward / reverse that results in smaller // size for the sparsity pattern of all variables in the tape. if( n <= m ) { vectorBool identity(n * n); for(size_t j = 0; j < n; j++) { for(size_t i = 0; i < n; i++) identity[ i * n + j ] = (i == j); } jac_sparse_bool_ = f_.ForSparseJac( n, identity, transpose, dependency ); f_.size_forward_bool(0); } else { vectorBool identity(m * m); for(size_t j = 0; j < m; j++) { for(size_t i = 0; i < m; i++) identity[ i * m + j ] = (i == j); } jac_sparse_bool_ = f_.RevSparseJac( m, identity, transpose, dependency ); } CPPAD_ASSERT_UNKNOWN( f_.size_forward_bool() == 0 ); CPPAD_ASSERT_UNKNOWN( f_.size_forward_set() == 0 ); } // ------------------------------------------------------------------------ /// set hes_sparse_set_ void set_hes_sparse_set(void) { CPPAD_ASSERT_UNKNOWN( hes_sparse_set_.n_set() == 0 ); size_t n = f_.Domain(); size_t m = f_.Range(); // // set version of sparsity for vector of all ones vector all_one(m); for(size_t i = 0; i < m; i++) all_one[i] = true; // set version of sparsity for n by n idendity matrix local::sparse_list identity; identity.resize(n, n); for(size_t j = 0; j < n; j++) identity.add_element(j, j); // compute sparsity pattern for H(x) = sum_i f_i(x)^{(2)} bool transpose = false; bool dependency = false; f_.ForSparseJacCheckpoint( n, identity, transpose, dependency, jac_sparse_set_ ); f_.RevSparseHesCheckpoint( n, all_one, transpose, hes_sparse_set_ ); CPPAD_ASSERT_UNKNOWN( hes_sparse_set_.n_set() == n ); CPPAD_ASSERT_UNKNOWN( hes_sparse_set_.end() == n ); // // drop the forward sparsity results from f_ f_.size_forward_set(0); } /// set hes_sparse_bool_ void set_hes_sparse_bool(void) { CPPAD_ASSERT_UNKNOWN( hes_sparse_bool_.size() == 0 ); size_t n = f_.Domain(); size_t m = f_.Range(); // // set version of sparsity for vector of all ones vectorBool all_one(m); for(size_t i = 0; i < m; i++) all_one[i] = true; // set version of sparsity for n by n idendity matrix vectorBool identity(n * n); for(size_t j = 0; j < n; j++) { for(size_t i = 0; i < n; i++) identity[ i * n + j ] = (i == j); } // compute sparsity pattern for H(x) = sum_i f_i(x)^{(2)} bool transpose = false; bool dependency = false; f_.ForSparseJac(n, identity, transpose, dependency); hes_sparse_bool_ = f_.RevSparseHes(n, all_one, transpose); CPPAD_ASSERT_UNKNOWN( hes_sparse_bool_.size() == n * n ); // // drop the forward sparsity results from f_ f_.size_forward_bool(0); CPPAD_ASSERT_UNKNOWN( f_.size_forward_bool() == 0 ); CPPAD_ASSERT_UNKNOWN( f_.size_forward_set() == 0 ); } // ------------------------------------------------------------------------ /*! Link from user_atomic to forward sparse Jacobian pack and bool \copydetails atomic_base::for_sparse_jac */ template bool for_sparse_jac( size_t q , const sparsity_type& r , sparsity_type& s , const vector& x ) { // during user sparsity calculations size_t m = f_.Range(); size_t n = f_.Domain(); if( jac_sparse_bool_.size() == 0 ) set_jac_sparse_bool(); if( jac_sparse_set_.n_set() != 0 ) jac_sparse_set_.resize(0, 0); CPPAD_ASSERT_UNKNOWN( jac_sparse_bool_.size() == m * n ); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.n_set() == 0 ); CPPAD_ASSERT_UNKNOWN( r.size() == n * q ); CPPAD_ASSERT_UNKNOWN( s.size() == m * q ); // bool ok = true; for(size_t i = 0; i < m; i++) { for(size_t k = 0; k < q; k++) s[i * q + k] = false; } // sparsity for s = jac_sparse_bool_ * r for(size_t i = 0; i < m; i++) { for(size_t k = 0; k < q; k++) { // initialize sparsity for S(i,k) bool s_ik = false; // S(i,k) = sum_j J(i,j) * R(j,k) for(size_t j = 0; j < n; j++) { bool J_ij = jac_sparse_bool_[ i * n + j]; bool R_jk = r[j * q + k ]; s_ik |= ( J_ij & R_jk ); } s[i * q + k] = s_ik; } } return ok; } // ------------------------------------------------------------------------ /*! Link from user_atomic to reverse sparse Jacobian pack and bool \copydetails atomic_base::rev_sparse_jac */ template bool rev_sparse_jac( size_t q , const sparsity_type& rt , sparsity_type& st , const vector& x ) { // during user sparsity calculations size_t m = f_.Range(); size_t n = f_.Domain(); if( jac_sparse_bool_.size() == 0 ) set_jac_sparse_bool(); if( jac_sparse_set_.n_set() != 0 ) jac_sparse_set_.resize(0, 0); CPPAD_ASSERT_UNKNOWN( jac_sparse_bool_.size() == m * n ); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.n_set() == 0 ); CPPAD_ASSERT_UNKNOWN( rt.size() == m * q ); CPPAD_ASSERT_UNKNOWN( st.size() == n * q ); bool ok = true; // // S = R * J where J is jacobian for(size_t i = 0; i < q; i++) { for(size_t j = 0; j < n; j++) { // initialize sparsity for S(i,j) bool s_ij = false; // S(i,j) = sum_k R(i,k) * J(k,j) for(size_t k = 0; k < m; k++) { // sparsity for R(i, k) bool R_ik = rt[ k * q + i ]; bool J_kj = jac_sparse_bool_[ k * n + j ]; s_ij |= (R_ik & J_kj); } // set sparsity for S^T st[ j * q + i ] = s_ij; } } return ok; } /*! Link from user_atomic to reverse sparse Hessian bools \copydetails atomic_base::rev_sparse_hes */ template bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const sparsity_type& r , const sparsity_type& u , sparsity_type& v , const vector& x ) { size_t n = f_.Domain(); # ifndef NDEBUG size_t m = f_.Range(); # endif CPPAD_ASSERT_UNKNOWN( vx.size() == n ); CPPAD_ASSERT_UNKNOWN( s.size() == m ); CPPAD_ASSERT_UNKNOWN( t.size() == n ); CPPAD_ASSERT_UNKNOWN( r.size() == n * q ); CPPAD_ASSERT_UNKNOWN( u.size() == m * q ); CPPAD_ASSERT_UNKNOWN( v.size() == n * q ); // bool ok = true; // make sure hes_sparse_bool_ has been set if( hes_sparse_bool_.size() == 0 ) set_hes_sparse_bool(); if( hes_sparse_set_.n_set() != 0 ) hes_sparse_set_.resize(0, 0); CPPAD_ASSERT_UNKNOWN( hes_sparse_bool_.size() == n * n ); CPPAD_ASSERT_UNKNOWN( hes_sparse_set_.n_set() == 0 ); // compute sparsity pattern for T(x) = S(x) * f'(x) t = f_.RevSparseJac(1, s); # ifndef NDEBUG for(size_t j = 0; j < n; j++) CPPAD_ASSERT_UNKNOWN( vx[j] || ! t[j] ) # endif // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // compute sparsity pattern for A(x) = f'(x)^T * U(x) bool transpose = true; sparsity_type a(n * q); a = f_.RevSparseJac(q, u, transpose); // Need sparsity pattern for H(x) = (S(x) * f(x))''(x) * R, // but use less efficient sparsity for f(x)''(x) * R so that // hes_sparse_set_ can be used every time this is needed. for(size_t i = 0; i < n; i++) { for(size_t k = 0; k < q; k++) { // initialize sparsity pattern for H(i,k) bool h_ik = false; // H(i,k) = sum_j f''(i,j) * R(j,k) for(size_t j = 0; j < n; j++) { bool f_ij = hes_sparse_bool_[i * n + j]; bool r_jk = r[j * q + k]; h_ik |= ( f_ij & r_jk ); } // sparsity for H(i,k) v[i * q + k] = h_ik; } } // compute sparsity pattern for V(x) = A(x) + H(x) for(size_t i = 0; i < n; i++) { for(size_t k = 0; k < q; k++) // v[ i * q + k ] |= a[ i * q + k]; v[ i * q + k ] = bool(v[ i * q + k]) | bool(a[ i * q + k]); } return ok; } public: // ------------------------------------------------------------------------ /*! Constructor of a checkpoint object \param name [in] is the user's name for the AD version of this atomic operation. \param algo [in/out] user routine that compute AD function values (not const because state may change during evaluation). \param ax [in] argument value where algo operation sequence is taped. \param ay [out] function value at specified argument value. \param sparsity [in] what type of sparsity patterns are computed by this function, pack_sparsity_enum bool_sparsity_enum, or set_sparsity_enum. The default value is unspecified. \param optimize [in] l should the operation sequence corresponding to the algo be optimized. The default value is true, but it is sometimes useful to use false for debugging purposes. */ template checkpoint( const char* name , Algo& algo , const ADVector& ax , ADVector& ay , option_enum sparsity = atomic_base::pack_sparsity_enum , bool optimize = true ) : atomic_base(name, sparsity) { CheckSimpleVector< CppAD::AD , ADVector>(); // make a copy of ax because Independent modifies AD information ADVector x_tmp(ax); // delcare x_tmp as the independent variables Independent(x_tmp); // record mapping from x_tmp to ay algo(x_tmp, ay); // create function f_ : x -> y f_.Dependent(ay); if( optimize ) { // suppress checking for nan in f_ results // (see optimize documentation for atomic functions) f_.check_for_nan(false); // // now optimize f_.optimize(); } // now disable checking of comparison operations // 2DO: add a debugging mode that checks for changes and aborts f_.compare_change_count(0); } // ------------------------------------------------------------------------ /*! Implement the user call to atom_fun.size_var(). */ size_t size_var(void) { return f_.size_var(); } // ------------------------------------------------------------------------ /*! Implement the user call to atom_fun(ax, ay). \tparam ADVector A simple vector class with elements of type AD. \param id optional parameter which must be zero if present. \param ax is the argument vector for this call, ax.size() determines the number of arguments. \param ay is the result vector for this call, ay.size() determines the number of results. */ template void operator()(const ADVector& ax, ADVector& ay, size_t id = 0) { CPPAD_ASSERT_KNOWN( id == 0, "checkpoint: id is non-zero in atom_fun(ax, ay, id)" ); this->atomic_base::operator()(ax, ay, id); } // ------------------------------------------------------------------------ /*! Link from user_atomic to forward mode \copydetails atomic_base::forward */ virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { size_t n = f_.Domain(); size_t m = f_.Range(); // CPPAD_ASSERT_UNKNOWN( f_.size_var() > 0 ); CPPAD_ASSERT_UNKNOWN( tx.size() % (q+1) == 0 ); CPPAD_ASSERT_UNKNOWN( ty.size() % (q+1) == 0 ); CPPAD_ASSERT_UNKNOWN( n == tx.size() / (q+1) ); CPPAD_ASSERT_UNKNOWN( m == ty.size() / (q+1) ); bool ok = true; // if( vx.size() == 0 ) { // during user forward mode if( jac_sparse_set_.n_set() != 0 ) jac_sparse_set_.resize(0,0); if( jac_sparse_bool_.size() != 0 ) jac_sparse_bool_.clear(); // if( hes_sparse_set_.n_set() != 0 ) hes_sparse_set_.resize(0,0); if( hes_sparse_bool_.size() != 0 ) hes_sparse_bool_.clear(); } if( vx.size() > 0 ) { // need Jacobian sparsity pattern to determine variable relation // during user recording using checkpoint functions if( sparsity() == atomic_base::set_sparsity_enum ) { if( jac_sparse_set_.n_set() == 0 ) set_jac_sparse_set(); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.n_set() == m ); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.end() == n ); // for(size_t i = 0; i < m; i++) { vy[i] = false; local::sparse_list::const_iterator set_itr(jac_sparse_set_, i); size_t j = *set_itr; while(j < n ) { // y[i] depends on the value of x[j] // cast avoid Microsoft warning (should not be needed) vy[i] |= static_cast( vx[j] ); j = *(++set_itr); } } } else { if( jac_sparse_set_.n_set() != 0 ) jac_sparse_set_.resize(0, 0); if( jac_sparse_bool_.size() == 0 ) set_jac_sparse_bool(); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.n_set() == 0 ); CPPAD_ASSERT_UNKNOWN( jac_sparse_bool_.size() == m * n ); // for(size_t i = 0; i < m; i++) { vy[i] = false; for(size_t j = 0; j < n; j++) { if( jac_sparse_bool_[ i * n + j ] ) { // y[i] depends on the value of x[j] // cast avoid Microsoft warning vy[i] |= static_cast( vx[j] ); } } } } } // compute forward results for orders zero through q ty = f_.Forward(q, tx); // no longer need the Taylor coefficients in f_ // (have to reconstruct them every time) // Hold onto sparsity pattern because it is always good. size_t c = 0; size_t r = 0; f_.capacity_order(c, r); return ok; } // ------------------------------------------------------------------------ /*! Link from user_atomic to reverse mode \copydetails atomic_base::reverse */ virtual bool reverse( size_t q , const vector& tx , const vector& ty , vector& px , const vector& py ) { # ifndef NDEBUG size_t n = f_.Domain(); size_t m = f_.Range(); # endif CPPAD_ASSERT_UNKNOWN( n == tx.size() / (q+1) ); CPPAD_ASSERT_UNKNOWN( m == ty.size() / (q+1) ); CPPAD_ASSERT_UNKNOWN( f_.size_var() > 0 ); CPPAD_ASSERT_UNKNOWN( tx.size() % (q+1) == 0 ); CPPAD_ASSERT_UNKNOWN( ty.size() % (q+1) == 0 ); bool ok = true; // put proper forward mode coefficients in f_ # ifdef NDEBUG // compute forward results for orders zero through q f_.Forward(q, tx); # else CPPAD_ASSERT_UNKNOWN( px.size() == n * (q+1) ); CPPAD_ASSERT_UNKNOWN( py.size() == m * (q+1) ); size_t i, j, k; // // compute forward results for orders zero through q vector check_ty = f_.Forward(q, tx); for(i = 0; i < m; i++) { for(k = 0; k <= q; k++) { j = i * (q+1) + k; CPPAD_ASSERT_UNKNOWN( check_ty[j] == ty[j] ); } } # endif // now can run reverse mode px = f_.Reverse(q+1, py); // no longer need the Taylor coefficients in f_ // (have to reconstruct them every time) size_t c = 0; size_t r = 0; f_.capacity_order(c, r); return ok; } // ------------------------------------------------------------------------ /*! Link from user_atomic to forward sparse Jacobian pack \copydetails atomic_base::for_sparse_jac */ virtual bool for_sparse_jac( size_t q , const vectorBool& r , vectorBool& s , const vector& x ) { return for_sparse_jac< vectorBool >(q, r, s, x); } /*! Link from user_atomic to forward sparse Jacobian bool \copydetails atomic_base::for_sparse_jac */ virtual bool for_sparse_jac( size_t q , const vector& r , vector& s , const vector& x ) { return for_sparse_jac< vector >(q, r, s, x); } /*! Link from user_atomic to forward sparse Jacobian sets \copydetails atomic_base::for_sparse_jac */ virtual bool for_sparse_jac( size_t q , const vector< std::set >& r , vector< std::set >& s , const vector& x ) { // during user sparsity calculations size_t m = f_.Range(); size_t n = f_.Domain(); if( jac_sparse_bool_.size() != 0 ) jac_sparse_bool_.clear(); if( jac_sparse_set_.n_set() == 0 ) set_jac_sparse_set(); CPPAD_ASSERT_UNKNOWN( jac_sparse_bool_.size() == 0 ); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.n_set() == m ); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.end() == n ); CPPAD_ASSERT_UNKNOWN( r.size() == n ); CPPAD_ASSERT_UNKNOWN( s.size() == m ); bool ok = true; for(size_t i = 0; i < m; i++) s[i].clear(); // sparsity for s = jac_sparse_set_ * r for(size_t i = 0; i < m; i++) { // compute row i of the return pattern local::sparse_list::const_iterator set_itr(jac_sparse_set_, i); size_t j = *set_itr; while(j < n ) { std::set::const_iterator itr_j; const std::set& r_j( r[j] ); for(itr_j = r_j.begin(); itr_j != r_j.end(); itr_j++) { size_t k = *itr_j; CPPAD_ASSERT_UNKNOWN( k < q ); s[i].insert(k); } j = *(++set_itr); } } return ok; } // ------------------------------------------------------------------------ /*! Link from user_atomic to reverse sparse Jacobian pack \copydetails atomic_base::rev_sparse_jac */ virtual bool rev_sparse_jac( size_t q , const vectorBool& rt , vectorBool& st , const vector& x ) { return rev_sparse_jac< vectorBool >(q, rt, st, x); } /*! Link from user_atomic to reverse sparse Jacobian bool \copydetails atomic_base::rev_sparse_jac */ virtual bool rev_sparse_jac( size_t q , const vector& rt , vector& st , const vector& x ) { return rev_sparse_jac< vector >(q, rt, st, x); } /*! Link from user_atomic to reverse Jacobian sets \copydetails atomic_base::rev_sparse_jac */ virtual bool rev_sparse_jac( size_t q , const vector< std::set >& rt , vector< std::set >& st , const vector& x ) { // during user sparsity calculations size_t m = f_.Range(); size_t n = f_.Domain(); if( jac_sparse_bool_.size() != 0 ) jac_sparse_bool_.clear(); if( jac_sparse_set_.n_set() == 0 ) set_jac_sparse_set(); CPPAD_ASSERT_UNKNOWN( jac_sparse_bool_.size() == 0 ); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.n_set() == m ); CPPAD_ASSERT_UNKNOWN( jac_sparse_set_.end() == n ); CPPAD_ASSERT_UNKNOWN( rt.size() == m ); CPPAD_ASSERT_UNKNOWN( st.size() == n ); // bool ok = true; // for(size_t j = 0; j < n; j++) st[j].clear(); // // sparsity for s = r * jac_sparse_set_ // s^T = jac_sparse_set_^T * r^T for(size_t i = 0; i < m; i++) { // i is the row index in r^T std::set::const_iterator itr_i; const std::set& r_i( rt[i] ); for(itr_i = r_i.begin(); itr_i != r_i.end(); itr_i++) { // k is the column index in r^T size_t k = *itr_i; CPPAD_ASSERT_UNKNOWN( k < q ); // // i is column index in jac_sparse_set^T local::sparse_list::const_iterator set_itr(jac_sparse_set_, i); size_t j = *set_itr; while( j < n ) { // j is row index in jac_sparse_set^T st[j].insert(k); j = *(++set_itr); } } } return ok; } // ------------------------------------------------------------------------ /*! Link from user_atomic to reverse sparse Hessian pack \copydetails atomic_base::rev_sparse_hes */ virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vectorBool& r , const vectorBool& u , vectorBool& v , const vector& x ) { return rev_sparse_hes< vectorBool >(vx, s, t, q, r, u, v, x); } /*! Link from user_atomic to reverse sparse Hessian bool \copydetails atomic_base::rev_sparse_hes */ virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vector& r , const vector& u , vector& v , const vector& x ) { return rev_sparse_hes< vector >(vx, s, t, q, r, u, v, x); } /*! Link from user_atomic to reverse sparse Hessian sets \copydetails atomic_base::rev_sparse_hes */ virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vector< std::set >& r , const vector< std::set >& u , vector< std::set >& v , const vector& x ) { size_t n = f_.Domain(); # ifndef NDEBUG size_t m = f_.Range(); # endif CPPAD_ASSERT_UNKNOWN( vx.size() == n ); CPPAD_ASSERT_UNKNOWN( s.size() == m ); CPPAD_ASSERT_UNKNOWN( t.size() == n ); CPPAD_ASSERT_UNKNOWN( r.size() == n ); CPPAD_ASSERT_UNKNOWN( u.size() == m ); CPPAD_ASSERT_UNKNOWN( v.size() == n ); // bool ok = true; // make sure hes_sparse_set_ has been set if( hes_sparse_bool_.size() != 0 ) hes_sparse_bool_.clear(); if( hes_sparse_set_.n_set() == 0 ) set_hes_sparse_set(); CPPAD_ASSERT_UNKNOWN( hes_sparse_bool_.size() == 0 ); CPPAD_ASSERT_UNKNOWN( hes_sparse_set_.n_set() == n ); CPPAD_ASSERT_UNKNOWN( hes_sparse_set_.end() == n ); // compute sparsity pattern for T(x) = S(x) * f'(x) t = f_.RevSparseJac(1, s); # ifndef NDEBUG for(size_t j = 0; j < n; j++) CPPAD_ASSERT_UNKNOWN( vx[j] || ! t[j] ) # endif // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // compute sparsity pattern for A(x) = f'(x)^T * U(x) // 2DO: change a to use INTERNAL_SPARSE_SET bool transpose = true; vector< std::set > a(n); a = f_.RevSparseJac(q, u, transpose); // Need sparsity pattern for H(x) = (S(x) * f(x))''(x) * R, // but use less efficient sparsity for f(x)''(x) * R so that // hes_sparse_set_ can be used every time this is needed. for(size_t i = 0; i < n; i++) { v[i].clear(); local::sparse_list::const_iterator set_itr(hes_sparse_set_, i); size_t j = *set_itr; while( j < n ) { std::set::const_iterator itr_j; const std::set& r_j( r[j] ); for(itr_j = r_j.begin(); itr_j != r_j.end(); itr_j++) { size_t k = *itr_j; v[i].insert(k); } j = *(++set_itr); } } // compute sparsity pattern for V(x) = A(x) + H(x) std::set::const_iterator itr; for(size_t i = 0; i < n; i++) { for(itr = a[i].begin(); itr != a[i].end(); itr++) { size_t j = *itr; CPPAD_ASSERT_UNKNOWN( j < q ); v[i].insert(j); } } return ok; } }; } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/azmul.hpp0000644000175200017650000001323513057470465016321 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AZMUL_HPP # define CPPAD_CORE_AZMUL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin azmul$$ $spell azmul const namespace Vec $$ $section Absolute Zero Multiplication$$ $head Syntax$$ $icode%z% = azmul(%x%, %y%)%$$ $head Purpose$$ Evaluates multiplication with an absolute zero for any of the possible types listed below. The result is given by $latex \[ z = \left\{ \begin{array}{ll} 0 & {\rm if} \; x = 0 \\ x \cdot y & {\rm otherwise} \end{array} \right. \] $$ Note if $icode x$$ is zero and $icode y$$ is infinity, ieee multiplication would result in not a number whereas $icode z$$ would be zero. $head Base$$ If $icode Base$$ satisfies the $cref/base type requirements/base_require/$$ and arguments $icode x$$, $icode y$$ have prototypes $codei% const %Base%& %x% const %Base%& %y% %$$ then the result $icode z$$ has prototype $codei% %Base% %z% %$$ $head AD$$ If the arguments $icode x$$, $icode y$$ have prototype $codei% const AD<%Base%>& %x% const AD<%Base%>& %y% %$$ then the result $icode z$$ has prototype $codei% AD<%Base%> %z% %$$ $head VecAD$$ If the arguments $icode x$$, $icode y$$ have prototype $codei% const VecAD<%Base%>::reference& %x% const VecAD<%Base%>::reference& %y% %$$ then the result $icode z$$ has prototype $codei% AD<%Base%> %z% %$$ $head Example$$ $children% example/azmul.cpp %$$ The file $cref azmul.cpp$$ is an examples and tests of this function. It returns true if it succeeds and false otherwise. $end */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE // ========================================================================== // case where x and y are AD ------------------------------------------- template AD azmul(const AD& x, const AD& y) { // compute the Base part AD result; result.value_ = azmul(x.value_, y.value_); // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return result; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_x = x.tape_id_ == tape_id; bool var_y = y.tape_id_ == tape_id; if( var_x ) { if( var_y ) { // result = azmul(variable, variable) CPPAD_ASSERT_UNKNOWN( local::NumRes(local::ZmulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::ZmulvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(x.taddr_, y.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::ZmulvvOp); // make result a variable result.tape_id_ = tape_id; } else if( IdenticalZero( y.value_ ) ) { // result = variable * 0 } else if( IdenticalOne( y.value_ ) ) { // result = variable * 1 result.make_variable(x.tape_id_, x.taddr_); } else { // result = zmul(variable, parameter) CPPAD_ASSERT_UNKNOWN( local::NumRes(local::ZmulvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::ZmulvpOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(y.value_); tape->Rec_.PutArg(x.taddr_, p); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::ZmulvpOp); // make result a variable result.tape_id_ = tape_id; } } else if( var_y ) { if( IdenticalZero(x.value_) ) { // result = 0 * variable } else if( IdenticalOne( x.value_ ) ) { // result = 1 * variable result.make_variable(y.tape_id_, y.taddr_); } else { // result = zmul(parameter, variable) CPPAD_ASSERT_UNKNOWN( local::NumRes(local::ZmulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::ZmulpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(x.value_); tape->Rec_.PutArg(p, y.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::ZmulpvOp); // make result a variable result.tape_id_ = tape_id; } } return result; } // ========================================================================= // Fold operations into case above // ------------------------------------------------------------------------- // Operations with VecAD_reference and AD only template AD azmul(const AD& x, const VecAD_reference& y) { return azmul(x, y.ADBase()); } template AD azmul(const VecAD_reference& x, const VecAD_reference& y) { return azmul(x.ADBase(), y.ADBase()); } template AD azmul(const VecAD_reference& x, const AD& y) { return azmul(x.ADBase(), y); } // ------------------------------------------------------------------------- // Operations with Base template AD azmul(const Base& x, const AD& y) { return azmul(AD(x), y); } template AD azmul(const Base& x, const VecAD_reference& y) { return azmul(AD(x), y.ADBase()); } template AD azmul(const AD& x, const Base& y) { return azmul(x, AD(y)); } template AD azmul(const VecAD_reference& x, const Base& y) { return azmul(x.ADBase(), AD(y)); } // ========================================================================== } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/ad_assign.hpp0000644000175200017650000000612113057470465017115 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AD_ASSIGN_HPP # define CPPAD_CORE_AD_ASSIGN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------ $begin ad_assign$$ $spell Vec const $$ $section AD Assignment Operator$$ $mindex assign Base VecAD$$ $head Syntax$$ $icode%y% = %x%$$ $head Purpose$$ Assigns the value in $icode x$$ to the object $icode y$$. In either case, $head x$$ The argument $icode x$$ has prototype $codei% const %Type% &%x% %$$ where $icode Type$$ is $codei%VecAD<%Base%>::reference%$$, $codei%AD<%Base%>%$$, $icode Base$$, or any type that has an implicit constructor of the form $icode%Base%(%x%)%$$. $head y$$ The target $icode y$$ has prototype $codei% AD<%Base%> %y% %$$ $head Example$$ $children% example/ad_assign.cpp %$$ The file $cref ad_assign.cpp$$ contain examples and tests of these operations. It test returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------ */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file ad_assign.hpp AD constructors and and copy operations. */ /*! \page AD_default_assign Use default assignment operator because they may be optimized better than the code below: \code template inline AD& AD::operator=(const AD &right) { value_ = right.value_; tape_id_ = right.tape_id_; taddr_ = right.taddr_; return *this; } \endcode */ /*! Assignment to Base type value. \tparam Base Base type for this AD object. \param b is the Base type value being assignment to this AD object. The tape identifier will be an invalid tape identifier, so this object is initially a parameter. */ template inline AD& AD::operator=(const Base &b) { value_ = b; tape_id_ = 0; // check that this is a parameter CPPAD_ASSERT_UNKNOWN( Parameter(*this) ); return *this; } /*! Assignment to an ADVec element drops the vector information. \tparam Base Base type for this AD object. */ template inline AD& AD::operator=(const VecAD_reference &x) { return *this = x.ADBase(); } /*! Assignment from any other type, converts to Base type, and then uses assignment from Base type. \tparam Base Base type for this AD object. \tparam T is the the type that is being assigned to AD. There must be an assignment for Base from Type. \param t is the object that is being assigned to an AD object. */ template template inline AD& AD::operator=(const T &t) { return *this = Base(t); } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/arithmetic.hpp0000644000175200017650000000225113057470465017316 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ARITHMETIC_HPP # define CPPAD_CORE_ARITHMETIC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin Arithmetic$$ $spell Op const $$ $section AD Arithmetic Operators and Computed Assignments$$ $childtable% cppad/core/unary_plus.hpp% cppad/core/unary_minus.hpp% cppad/core/ad_binary.hpp% cppad/core/compute_assign.hpp %$$ $end ------------------------------------------------------------------------------- */ # include # include # include # include # endif cppad-20170000.3/cppad/core/hessian.hpp0000644000175200017650000001210713057470465016620 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_HESSIAN_HPP # define CPPAD_CORE_HESSIAN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Hessian$$ $spell hes typename Taylor HesLuDet const $$ $section Hessian: Easy Driver$$ $mindex second derivative$$ $head Syntax$$ $icode%hes% = %f%.Hessian(%x%, %w%) %$$ $icode%hes% = %f%.Hessian(%x%, %l%) %$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The syntax above sets $icode hes$$ to the Hessian The syntax above sets $icode h$$ to the Hessian $latex \[ hes = \dpow{2}{x} \sum_{i=1}^m w_i F_i (x) \] $$ The routine $cref sparse_hessian$$ may be faster in the case where the Hessian is sparse. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/Hessian Uses Forward/Hessian/Hessian Uses Forward/$$ below). $head x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ (see $cref/Vector/Hessian/Vector/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies that point at which to evaluate the Hessian. $head l$$ If the argument $icode l$$ is present, it has prototype $codei% size_t %l% %$$ and is less than $icode m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. It specifies the component of $icode F$$ for which we are evaluating the Hessian. To be specific, in the case where the argument $icode l$$ is present, $latex \[ w_i = \left\{ \begin{array}{ll} 1 & i = l \\ 0 & {\rm otherwise} \end{array} \right. \] $$ $head w$$ If the argument $icode w$$ is present, it has prototype $codei% const %Vector% &%w% %$$ and size $latex m$$. It specifies the value of $latex w_i$$ in the expression for $icode h$$. $head hes$$ The result $icode hes$$ has prototype $codei% %Vector% %hes% %$$ (see $cref/Vector/Hessian/Vector/$$ below) and its size is $latex n * n$$. For $latex j = 0 , \ldots , n - 1 $$ and $latex \ell = 0 , \ldots , n - 1$$ $latex \[ hes [ j * n + \ell ] = \DD{ w^{\rm T} F }{ x_j }{ x_\ell } ( x ) \] $$ $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Hessian Uses Forward$$ After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After a call to $code Hessian$$, the zero order Taylor coefficients correspond to $icode%f%.Forward(0, %x%)%$$ and the other coefficients are unspecified. $head Example$$ $children% example/hessian.cpp% example/hes_lagrangian.cpp %$$ The routines $cref hessian.cpp$$ and $cref hes_lagrangian.cpp$$ are examples and tests of $code Hessian$$. They return $code true$$, if they succeed and $code false$$ otherwise. $end ----------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template template Vector ADFun::Hessian(const Vector &x, size_t l) { size_t i, m = Range(); CPPAD_ASSERT_KNOWN( l < m, "Hessian: index i is not less than range dimension for f" ); Vector w(m); for(i = 0; i < m; i++) w[i] = Base(0); w[l] = Base(1); return Hessian(x, w); } template template Vector ADFun::Hessian(const Vector &x, const Vector &w) { size_t j; size_t k; size_t n = Domain(); // check Vector is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( size_t(x.size()) == n, "Hessian: length of x not equal domain dimension for f" ); CPPAD_ASSERT_KNOWN( size_t(w.size()) == Range(), "Hessian: length of w not equal range dimension for f" ); // point at which we are evaluating the Hessian Forward(0, x); // define the return value Vector hes(n * n); // direction vector for calls to forward Vector u(n); for(j = 0; j < n; j++) u[j] = Base(0); // location for return values from Reverse Vector ddw(n * 2); // loop over forward directions for(j = 0; j < n; j++) { // evaluate partials of entire function w.r.t. j-th coordinate u[j] = Base(1); Forward(1, u); u[j] = Base(0); // evaluate derivative of partial corresponding to F_i ddw = Reverse(2, w); // return desired components for(k = 0; k < n; k++) hes[k * n + j] = ddw[k * 2 + 1]; } return hes; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/define.hpp0000644000175200017650000004230013057470465016416 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_DEFINE_HPP # define CPPAD_CORE_DEFINE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file define.hpp Define processor symbols and macros that are used by CppAD. */ // ---------------------------------------------------------------------------- /*! \def CPPAD_OP_CODE_TYPE Is the type used to store enum OpCode values. If not the same as OpCode, then sizeof(CPPAD_OP_CODE_TYPE) <= sizeof( enum OpCode ) to conserve memory. This type must support \c std::numeric_limits, the \c <= operator, and conversion to \c size_t. Make sure that the type chosen returns true for is_pod in pod_vector.hpp. */ # define CPPAD_OP_CODE_TYPE unsigned char // ---------------------------------------------------------------------------- /*! \def CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION A version of the inline command that works with MC compiler. Microsoft Visual C++ version 9.0 generates a warning if a template function is declared as a friend (this was not a problem for version 7.0). The warning identifier is \verbatim warning C4396 \endverbatim and it contains the text \verbatim the inline specifier cannot be used when a friend declaration refers to a specialization of a function template \endverbatim This happens even if the function is not a specialization. This macro is defined as empty for Microsoft compilers. */ # ifdef _MSC_VER # define CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION # else # define CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION inline # endif // ---------------------------------------------------------------------------- /*! \def CPPAD_LIB_EXPORT Special macro for exporting windows DLL symbols; see https://cmake.org/Wiki/BuildingWinDLL */ # ifdef _MSC_VER # ifdef cppad_lib_EXPORTS # define CPPAD_LIB_EXPORT __declspec(dllexport) # else # define CPPAD_LIB_EXPORT __declspec(dllimport) # endif // cppad_lib_EXPORTS # else // _MSC_VER # define CPPAD_LIB_EXPORT # endif // ============================================================================ /*! \def CPPAD_FOLD_ASSIGNMENT_OPERATOR(Op) Declares automatic coercion for certain AD assignment operations. This macro assumes that the operator \verbatim left Op right \endverbatim is defined for the case where left and right have type AD. It uses this case to define the cases where left has type AD and right has type VecAD_reference, Base, or double. The argument right is const and call by reference. This macro converts the operands to AD and then uses the definition of the same operation for that case. */ # define CPPAD_FOLD_ASSIGNMENT_OPERATOR(Op) \ /* ----------------------------------------------------------------*/ \ template \ inline AD& operator Op \ (AD &left, double right) \ { return left Op AD(right); } \ \ template \ inline AD& operator Op \ (AD &left, const Base &right) \ { return left Op AD(right); } \ \ inline AD& operator Op \ (AD &left, const double &right) \ { return left Op AD(right); } \ \ template \ inline AD& operator Op \ (AD &left, const VecAD_reference &right) \ { return left Op right.ADBase(); } // ===================================================================== /*! \def CPPAD_FOLD_AD_VALUED_BINARY_OPERATOR(Op) Declares automatic coercion for certain binary operations with AD result. This macro assumes that the operator \verbatim left Op right \endverbatim is defined for the case where left and right and the result of the operation all have type AD. It uses this case to define the cases either left or right has type VecAD_reference or AD and the type of the other operand is one of the following: VecAD_reference, AD, Base, double. All of the arguments are const and call by reference. This macro converts the operands to AD and then uses the definition of the same operation for that case. */ # define CPPAD_FOLD_AD_VALUED_BINARY_OPERATOR(Op) \ /* ----------------------------------------------------------------*/ \ /* Operations with VecAD_reference and AD only*/ \ \ template \ inline AD operator Op \ (const AD &left, const VecAD_reference &right) \ { return left Op right.ADBase(); } \ \ template \ inline AD operator Op \ (const VecAD_reference &left, const VecAD_reference &right)\ { return left.ADBase() Op right.ADBase(); } \ \ template \ inline AD operator Op \ (const VecAD_reference &left, const AD &right) \ { return left.ADBase() Op right; } \ /* ----------------------------------------------------------------*/ \ /* Operations Base */ \ \ template \ inline AD operator Op \ (const Base &left, const AD &right) \ { return AD(left) Op right; } \ \ template \ inline AD operator Op \ (const Base &left, const VecAD_reference &right) \ { return AD(left) Op right.ADBase(); } \ \ template \ inline AD operator Op \ (const AD &left, const Base &right) \ { return left Op AD(right); } \ \ template \ inline AD operator Op \ (const VecAD_reference &left, const Base &right) \ { return left.ADBase() Op AD(right); } \ \ /* ----------------------------------------------------------------*/ \ /* Operations double */ \ \ template \ inline AD operator Op \ (const double &left, const AD &right) \ { return AD(left) Op right; } \ \ template \ inline AD operator Op \ (const double &left, const VecAD_reference &right) \ { return AD(left) Op right.ADBase(); } \ \ template \ inline AD operator Op \ (const AD &left, const double &right) \ { return left Op AD(right); } \ \ template \ inline AD operator Op \ (const VecAD_reference &left, const double &right) \ { return left.ADBase() Op AD(right); } \ /* ----------------------------------------------------------------*/ \ /* Special case to avoid ambuigity when Base is double */ \ \ inline AD operator Op \ (const double &left, const AD &right) \ { return AD(left) Op right; } \ \ inline AD operator Op \ (const double &left, const VecAD_reference &right) \ { return AD(left) Op right.ADBase(); } \ \ inline AD operator Op \ (const AD &left, const double &right) \ { return left Op AD(right); } \ \ inline AD operator Op \ (const VecAD_reference &left, const double &right) \ { return left.ADBase() Op AD(right); } // ======================================================================= /*! \def CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR(Op) Declares automatic coercion for certain binary operations with bool result. This macro assumes that the operator \verbatim left Op right \endverbatim is defined for the case where left and right have type AD and the result has type bool. It uses this case to define the cases either left or right has type VecAD_reference or AD and the type of the other operand is one of the following: VecAD_reference, AD, Base, double. All of the arguments are const and call by reference. This macro converts the operands to AD and then uses the definition of the same operation for that case. */ # define CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR(Op) \ /* ----------------------------------------------------------------*/ \ /* Operations with VecAD_reference and AD only*/ \ \ template \ inline bool operator Op \ (const AD &left, const VecAD_reference &right) \ { return left Op right.ADBase(); } \ \ template \ inline bool operator Op \ (const VecAD_reference &left, const VecAD_reference &right)\ { return left.ADBase() Op right.ADBase(); } \ \ template \ inline bool operator Op \ (const VecAD_reference &left, const AD &right) \ { return left.ADBase() Op right; } \ /* ----------------------------------------------------------------*/ \ /* Operations Base */ \ \ template \ inline bool operator Op \ (const Base &left, const AD &right) \ { return AD(left) Op right; } \ \ template \ inline bool operator Op \ (const Base &left, const VecAD_reference &right) \ { return AD(left) Op right.ADBase(); } \ \ template \ inline bool operator Op \ (const AD &left, const Base &right) \ { return left Op AD(right); } \ \ template \ inline bool operator Op \ (const VecAD_reference &left, const Base &right) \ { return left.ADBase() Op AD(right); } \ \ /* ----------------------------------------------------------------*/ \ /* Operations double */ \ \ template \ inline bool operator Op \ (const double &left, const AD &right) \ { return AD(left) Op right; } \ \ template \ inline bool operator Op \ (const double &left, const VecAD_reference &right) \ { return AD(left) Op right.ADBase(); } \ \ template \ inline bool operator Op \ (const AD &left, const double &right) \ { return left Op AD(right); } \ \ template \ inline bool operator Op \ (const VecAD_reference &left, const double &right) \ { return left.ADBase() Op AD(right); } \ /* ----------------------------------------------------------------*/ \ /* Special case to avoid ambuigity when Base is double */ \ \ inline bool operator Op \ (const double &left, const AD &right) \ { return AD(left) Op right; } \ \ inline bool operator Op \ (const double &left, const VecAD_reference &right) \ { return AD(left) Op right.ADBase(); } \ \ inline bool operator Op \ (const AD &left, const double &right) \ { return left Op AD(right); } \ \ inline bool operator Op \ (const VecAD_reference &left, const double &right) \ { return left.ADBase() Op AD(right); } # endif cppad-20170000.3/cppad/core/base_std_math.hpp0000644000175200017650000001211113057470466017757 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BASE_STD_MATH_HPP # define CPPAD_CORE_BASE_STD_MATH_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_std_math$$ $spell expm1 atanh acosh asinh inline fabs isnan alloc std acos asin atan cos exp sqrt const CppAD namespace erf $$ $section Base Type Requirements for Standard Math Functions$$ $head Purpose$$ These definitions are required for the user's code to use the type $codei%AD<%Base%>%$$: $head Unary Standard Math$$ The type $icode Base$$ must support the following functions unary standard math functions (in the CppAD namespace): $table $bold Syntax$$ $cnext $bold Result$$ $rnext $icode%y% = abs(%x%)%$$ $cnext absolute value $rnext $icode%y% = acos(%x%)%$$ $cnext inverse cosine $rnext $icode%y% = asin(%x%)%$$ $cnext inverse sine $rnext $icode%y% = atan(%x%)%$$ $cnext inverse tangent $rnext $icode%y% = cos(%x%)%$$ $cnext cosine $rnext $icode%y% = cosh(%x%)%$$ $cnext hyperbolic cosine $rnext $icode%y% = exp(%x%)%$$ $cnext exponential $rnext $icode%y% = fabs(%x%)%$$ $cnext absolute value $rnext $icode%y% = log(%x%)%$$ $cnext natural logarithm $rnext $icode%y% = sin(%x%)%$$ $cnext sine $rnext $icode%y% = sinh(%x%)%$$ $cnext hyperbolic sine $rnext $icode%y% = sqrt(%x%)%$$ $cnext square root $rnext $icode%y% = tan(%x%)%$$ $cnext tangent $tend where the arguments and return value have the prototypes $codei% const %Base%& %x% %Base% %y% %$$ For example, $cref/base_alloc/base_alloc.hpp/Unary Standard Math/$$, $head CPPAD_STANDARD_MATH_UNARY$$ The macro invocation, within the CppAD namespace, $codei% CPPAD_STANDARD_MATH_UNARY(%Base%, %Fun%) %$$ defines the syntax $codei% %y% = CppAD::%Fun%(%x%) %$$ This macro uses the functions $codei%std::%Fun%$$ which must be defined and have the same prototype as $codei%CppAD::%Fun%$$. For example, $cref/float/base_float.hpp/Unary Standard Math/$$. $head erf, asinh, acosh, atanh, expm1, log1p$$ If this preprocessor symbol $code CPPAD_USE_CPLUSPLUS_2011$$ is true ($code 1$$), when compiling for c++11, the type $code double$$ is supported for the functions listed below. In this case, the type $icode Base$$ must also support these functions: $table $bold Syntax$$ $cnext $bold Result$$ $rnext $icode%y% = erf(%x%)%$$ $cnext error function $rnext $icode%y% = asinh(%x%)%$$ $cnext inverse hyperbolic sin $rnext $icode%y% = acosh(%x%)%$$ $cnext inverse hyperbolic cosine $rnext $icode%y% = atanh(%x%)%$$ $cnext inverse hyperbolic tangent $rnext $icode%y% = expm1(%x%)%$$ $cnext exponential of x minus one $rnext $icode%y% = log1p(%x%)%$$ $cnext logarithm of one plus x $tend where the arguments and return value have the prototypes $codei% const %Base%& %x% %Base% %y% %$$ $head sign$$ The type $icode Base$$ must support the syntax $codei% %y% = CppAD::sign(%x%) %$$ which computes $latex \[ y = \left\{ \begin{array}{ll} +1 & {\rm if} \; x > 0 \\ 0 & {\rm if} \; x = 0 \\ -1 & {\rm if} \; x < 0 \end{array} \right. \] $$ where $icode x$$ and $icode y$$ have the same prototype as above. For example, see $cref/base_alloc/base_alloc.hpp/sign/$$. Note that, if ordered comparisons are not defined for the type $icode Base$$, the $code code sign$$ function should generate an assert if it is used; see $cref/complex invalid unary math/base_complex.hpp/Invalid Unary Math/$$. $head pow$$ The type $icode Base$$ must support the syntax $codei% %z% = CppAD::pow(%x%, %y%) %$$ which computes $latex z = x^y$$. The arguments $icode x$$ and $icode y$$ have prototypes $codei% const %Base%& %x% const %Base%& %y% %$$ and the return value $icode z$$ has prototype $codei% %Base% %z% %$$ For example, see $cref/base_alloc/base_alloc.hpp/pow/$$. $head isnan$$ If $icode Base$$ defines the $code isnan$$ function, you may also have to provide a definition in the CppAD namespace (to avoid a function ambiguity). For example, see $cref/base_complex/base_complex.hpp/isnan/$$. $end ------------------------------------------------------------------------------- */ # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file base_std_math.hpp Defintions that aid meeting Base type requirements for standard math functions. */ /*! \def CPPAD_STANDARD_MATH_UNARY(Type, Fun) This macro defines the function \verbatim y = CppAD:Fun(x) \endverbatim where the argument \c x and return value \c y have type \c Type using the corresponding function std::Fun. */ # define CPPAD_STANDARD_MATH_UNARY(Type, Fun) \ inline Type Fun(const Type& x) \ { return std::Fun(x); } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/acosh.hpp0000644000175200017650000000453613057470466016273 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ACOSH_HPP # define CPPAD_CORE_ACOSH_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin acosh$$ $spell acosh const Vec std cmath CppAD $$ $section The Inverse Hyperbolic Cosine Function: acosh$$ $head Syntax$$ $icode%y% = acosh(%x%)%$$ $head Description$$ The inverse hyperbolic cosine function is defined by $icode%x% == cosh(%y%)%$$. $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head CPPAD_USE_CPLUSPLUS_2011$$ $subhead true$$ If this preprocessor symbol is true ($code 1$$), and $icode x$$ is an AD type, this is an $cref/atomic operation/glossary/Operation/Atomic/$$. $subhead false$$ If this preprocessor symbol is false ($code 0$$), CppAD uses the representation $latex \[ \R{acosh} (x) = \log \left( x + \sqrt{ x^2 - 1 } \right) \] $$ to compute this function. $head Example$$ $children% example/acosh.cpp %$$ The file $cref acosh.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ # include # if ! CPPAD_USE_CPLUSPLUS_2011 // BEGIN CppAD namespace namespace CppAD { template Type acosh_template(const Type &x) { return CppAD::log( x + CppAD::sqrt( x * x - Type(1) ) ); } inline float acosh(const float &x) { return acosh_template(x); } inline double acosh(const double &x) { return acosh_template(x); } template inline AD acosh(const AD &x) { return acosh_template(x); } template inline AD acosh(const VecAD_reference &x) { return acosh_template( x.ADBase() ); } } // END CppAD namespace # endif // CPPAD_USE_CPLUSPLUS_2011 # endif // CPPAD_ACOSH_INCLUDED cppad-20170000.3/cppad/core/independent.hpp0000644000175200017650000001157613057470466017475 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_INDEPENDENT_HPP # define CPPAD_CORE_INDEPENDENT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* --------------------------------------------------------------------------- $begin Independent$$ $spell op alloc num Cpp bool const var typename $$ $section Declare Independent Variables and Start Recording$$ $head Syntax$$ $codei%Independent(%x%) %$$ $codei%Independent(%x%, %abort_op_index%) %$$ $head Purpose$$ Start recording $cref/AD of Base/glossary/AD of Base/$$ operations with $icode x$$ as the independent variable vector. Once the $cref/operation sequence/glossary/Operation/Sequence/$$ is completed, it must be transferred to a function object; see below. $head Start Recording$$ An operation sequence recording is started by the commands $codei% Independent(%x%) Independent(%x%, %abort_op_index%) %$$ $head Stop Recording$$ The recording is stopped, and the operation sequence is transferred to the AD function object $icode f$$, using either the $cref/function constructor/FunConstruct/$$ $codei% ADFun<%Base%> %f%(%x%, %y%) %$$ or the $cref/dependent variable specifier/Dependent/$$ $codei% %f%.Dependent(%x%, %y%) %$$ The only other way to stop a recording is using $cref abort_recording$$. Between when the recording is started and when it stopped, we refer to the elements of $icode x$$, and the values that depend on the elements of $icode x$$, as $codei%AD<%Base%>%$$ variables. $head x$$ The vector $icode x$$ has prototype $codei% %VectorAD% &%x% %$$ (see $icode VectorAD$$ below). The size of the vector $icode x$$, must be greater than zero, and is the number of independent variables for this AD operation sequence. $head abort_op_index$$ It specifies the operator index at which the execution is be aborted by calling the CppAD $cref/error handler/ErrorHandler/$$. When this error handler leads to an assert, the user can inspect the call stack to see the source code corresponding to this operator index; see $cref/purpose/compare_change/op_index/Purpose/$$. No abort will occur if $icode abort_op_index$$ is zero, of if $cref/NDEBUG/Faq/Speed/NDEBUG/$$ is defined. $head VectorAD$$ The type $icode VectorAD$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $codei%AD<%Base%>%$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Parallel Mode$$ Each thread can have one, and only one, active recording. A call to $code Independent$$ starts the recording for the current thread. The recording must be stopped by a corresponding call to $codei% ADFun<%Base%> %f%( %x%, %y%) %$$ or $codei% %f%.Dependent( %x%, %y%) %$$ or $cref abort_recording$$ preformed by the same thread; i.e., $cref/thread_alloc::thread_num/ta_thread_num/$$ must be the same. $head Example$$ $children% example/independent.cpp %$$ The file $cref independent.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ----------------------------------------------------------------------------- */ # include /*! \file core/independent.hpp Declare the independent variables */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! Declaration of independent variables. \tparam VectorAD This is simple vector type with elements of type AD. \param x Vector of the independent variablerd. \param abort_op_index operator index at which execution will be aborted (during the recording of operations). The value zero corresponds to not aborting (will not match). */ template inline void Independent(VectorAD &x, size_t abort_op_index) { typedef typename VectorAD::value_type ADBase; typedef typename ADBase::value_type Base; CPPAD_ASSERT_KNOWN( ADBase::tape_ptr() == CPPAD_NULL, "Independent: cannot create a new tape because\n" "a previous tape is still active (for this thread).\n" "AD::abort_recording() would abort this previous recording." ); local::ADTape* tape = ADBase::tape_manage(tape_manage_new); tape->Independent(x, abort_op_index); } /*! Declaration of independent variables without abort option. \tparam VectorAD This is simple vector type with elements of type AD. \param x Vector of the independent variablerd. */ template inline void Independent(VectorAD &x) { size_t abort_op_index = 0; Independent(x, abort_op_index); } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/sparse.hpp0000644000175200017650000000205413057470466016464 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_SPARSE_HPP # define CPPAD_CORE_SPARSE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Sparse$$ $spell $$ $section Calculating Sparsity Patterns$$ $childtable% cppad/core/for_sparse_jac.hpp% cppad/core/rev_sparse_jac.hpp% example/dependency.cpp% cppad/core/rev_sparse_hes.hpp% cppad/core/for_sparse_hes.hpp% example/bool_sparsity.cpp %$$ $end */ # include # include # include # include # endif cppad-20170000.3/cppad/core/optimize.hpp0000644000175200017650000002277413057470466017042 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_OPTIMIZE_HPP # define CPPAD_CORE_OPTIMIZE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin optimize$$ $spell enum jac bool Taylor CppAD cppad std const onetape op $$ $section Optimize an ADFun Object Tape$$ $mindex sequence operations speed memory NDEBUG$$ $head Syntax$$ $icode%f%.optimize() %$$ $icode%f%.optimize(%options%) %$$ $head Purpose$$ The operation sequence corresponding to an $cref ADFun$$ object can be very large and involve many operations; see the size functions in $cref seq_property$$. The $icode%f%.optimize%$$ procedure reduces the number of operations, and thereby the time and the memory, required to compute function and derivative values. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ $head options$$ This argument has prototype $codei% const std::string& %options% %$$ The default for $icode options$$ is the empty string. If it is present, it must consist of one or more of the options below separated by a single space character. $subhead no_conditional_skip$$ The $code optimize$$ function can create conditional skip operators to improve the speed of conditional expressions; see $cref/optimize/CondExp/Optimize/$$. If the sub-string $code no_conditional_skip$$ appears in $icode options$$, conditional skip operations are not be generated. This may make the optimize routine use significantly less memory and take less time to optimize $icode f$$. If conditional skip operations are generated, it may save a significant amount of time when using $icode f$$ for $cref forward$$ or $cref reverse$$ mode calculations; see $cref number_skip$$. $subhead no_compare_op$$ If the sub-string $code no_compare_op$$ appears in $icode options$$, comparison operators will be removed from the optimized function. These operators are necessary for the $cref compare_change$$ functions to be meaningful. On the other hand, they are not necessary, and take extra time, when the compare_change functions are not used. $subhead no_print_for_op$$ If the sub-string $code no_compare_op$$ appears in $icode options$$, $cref PrintFor$$ operations will be removed form the optimized function. These operators are useful for reporting problems evaluating derivatives at independent variable values different from those used to record a function. $head Examples$$ $children% example/optimize/forward_active.cpp %example/optimize/reverse_active.cpp %example/optimize/compare_op.cpp %example/optimize/print_for.cpp %example/optimize/conditional_skip.cpp %example/optimize/nest_conditional.cpp %example/optimize/cumulative_sum.cpp %$$ $table $cref/forward_active.cpp/optimize_forward_active.cpp/$$ $cnext $title optimize_forward_active.cpp$$ $rnext $cref/reverse_active.cpp/optimize_reverse_active.cpp/$$ $cnext $title optimize_reverse_active.cpp$$ $rnext $cref/compare_op.cpp/optimize_compare_op.cpp/$$ $cnext $title optimize_compare_op.cpp$$ $rnext $cref/print_for_op.cpp/optimize_print_for.cpp/$$ $cnext $title optimize_print_for.cpp$$ $rnext $cref/conditional_skip.cpp/optimize_conditional_skip.cpp/$$ $cnext $title optimize_conditional_skip.cpp$$ $rnext $cref/nest_conditional.cpp/optimize_nest_conditional.cpp/$$ $cnext $title optimize_nest_conditional.cpp$$ $rnext $cref/cumulative_sum.cpp/optimize_cumulative_sum.cpp/$$ $cnext $title optimize_cumulative_sum.cpp$$ $tend $head Efficiency$$ If a $cref/zero order forward/forward_zero/$$ calculation is done during the construction of $icode f$$, it will require more memory and time than required after the optimization procedure. In addition, it will need to be redone. For this reason, it is more efficient to use $codei% ADFun<%Base%> %f%; %f%.Dependent(%x%, %y%); %f%.optimize(); %$$ instead of $codei% ADFun<%Base%> %f%(%x%, %y%) %f%.optimize(); %$$ See the discussion about $cref/sequence constructors/FunConstruct/Sequence Constructor/$$. $head Speed Testing$$ You can run the CppAD $cref/speed/speed_main/$$ tests and see the corresponding changes in number of variables and execution time. Note that there is an interaction between using $cref/optimize/speed_main/Global Options/optimize/$$ and $cref/onetape/speed_main/Global Options/onetape/$$. If $icode onetape$$ is true and $icode optimize$$ is true, the optimized tape will be reused many times. If $icode onetape$$ is false and $icode optimize$$ is true, the tape will be re-optimized for each test. $head Atomic Functions$$ There are some subtitle issue with optimized $cref atomic$$ functions $latex v = g(u)$$: $subhead rev_sparse_jac$$ The $cref atomic_rev_sparse_jac$$ function is be used to determine which components of $icode u$$ affect the dependent variables of $icode f$$. For each atomic operation, the current $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ setting is used to determine if $code pack_sparsity_enum$$, $code bool_sparsity_enum$$, or $code set_sparsity_enum$$ is used to determine dependency relations between argument and result variables. $subhead nan$$ If $icode%u%[%i%]%$$ does not affect the value of the dependent variables for $icode f$$, the value of $icode%u%[%i%]%$$ is set to $cref nan$$. $head Checking Optimization$$ If $cref/NDEBUG/Faq/Speed/NDEBUG/$$ is not defined, and $cref/f.size_order()/size_order/$$ is greater than zero, a $cref forward_zero$$ calculation is done using the optimized version of $icode f$$ and the results are checked to see that they are the same as before. If they are not the same, the $cref ErrorHandler$$ is called with a known error message related to $icode%f%.optimize()%$$. $end ----------------------------------------------------------------------------- */ # include /*! \file optimize.hpp Optimize a player object operation sequence */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! Optimize a player object operation sequence The operation sequence for this object is replaced by one with fewer operations but the same funcition and derivative values. \tparam Base base type for the operator; i.e., this operation was recorded using AD and computations by this routine are done using type \a Base. \param options \li If the sub-string "no_conditional_skip" appears, conditional skip operations will not be generated. This may make the optimize routine use significantly less memory and take significantly less time. \li If the sub-string "no_compare_op" appears, then comparison operators will be removed from the optimized tape. These operators are necessary for the compare_change function to be be meaningful in the resulting recording. On the other hand, they are not necessary and take extra time when compare_change is not used. */ template void ADFun::optimize(const std::string& options) { // place to store the optimized version of the recording local::recorder rec; // number of independent variables size_t n = ind_taddr_.size(); # ifndef NDEBUG size_t i, j, m = dep_taddr_.size(); CppAD::vector x(n), y(m), check(m); Base max_taylor(0); bool check_zero_order = num_order_taylor_ > 0; if( check_zero_order ) { // zero order coefficients for independent vars for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( play_.GetOp(j+1) == local::InvOp ); CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == j+1 ); x[j] = taylor_[ ind_taddr_[j] * cap_order_taylor_ + 0]; } // zero order coefficients for dependent vars for(i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); y[i] = taylor_[ dep_taddr_[i] * cap_order_taylor_ + 0]; } // maximum zero order coefficient not counting BeginOp at beginning // (which is correpsonds to uninitialized memory). for(i = 1; i < num_var_tape_; i++) { if( abs_geq(taylor_[i*cap_order_taylor_+0] , max_taylor) ) max_taylor = taylor_[i*cap_order_taylor_+0]; } } # endif // create the optimized recording local::optimize::optimize_run(options, n, dep_taddr_, &play_, &rec); // number of variables in the recording num_var_tape_ = rec.num_var_rec(); // now replace the recording play_.get(rec); // set flag so this function knows it has been optimized has_been_optimized_ = true; // free memory allocated for sparse Jacobian calculation // (the results are no longer valid) for_jac_sparse_pack_.resize(0, 0); for_jac_sparse_set_.resize(0,0); // free old Taylor coefficient memory taylor_.free(); num_order_taylor_ = 0; cap_order_taylor_ = 0; // resize and initilaize conditional skip vector // (must use player size because it now has the recoreder information) cskip_op_.erase(); cskip_op_.extend( play_.num_op_rec() ); # ifndef NDEBUG if( check_zero_order ) { // zero order forward calculation using new operation sequence check = Forward(0, x); // check results Base eps = 10. * CppAD::numeric_limits::epsilon(); for(i = 0; i < m; i++) CPPAD_ASSERT_KNOWN( abs_geq( eps * max_taylor , check[i] - y[i] ) , "Error during check of f.optimize()." ); // Erase memory that this calculation was done so NDEBUG gives // same final state for this object (from users perspective) num_order_taylor_ = 0; } # endif } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/sign.hpp0000644000175200017650000000504413057470466016131 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_SIGN_HPP # define CPPAD_CORE_SIGN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sign$$ $spell CppAD Dirac $$ $section The Sign: sign$$ $head Syntax$$ $icode%y% = sign(%x%)%$$ $head Description$$ Evaluates the $code sign$$ function which is defined by $latex \[ {\rm sign} (x) = \left\{ \begin{array}{rl} +1 & {\rm if} \; x > 0 \\ 0 & {\rm if} \; x = 0 \\ -1 & {\rm if} \; x < 0 \end{array} \right. \] $$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ CppAD computes the derivative of the $code sign$$ function as zero for all argument values $icode x$$. The correct mathematical derivative is different and is given by $latex \[ {\rm sign}^{(1)} (x) = 2 \delta (x) \] $$ where $latex \delta (x)$$ is the Dirac Delta function. $head Example$$ $children% example/sign.cpp %$$ The file $cref sign.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD AD::sign_me (void) const { AD result; result.value_ = sign(value_); CPPAD_ASSERT_UNKNOWN( Parameter(result) ); if( Variable(*this) ) { // add this operation to the tape CPPAD_ASSERT_UNKNOWN( local::NumRes(local::SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::SignOp) == 1 ); local::ADTape *tape = tape_this(); // corresponding operand address tape->Rec_.PutArg(taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::SignOp); // make result a variable result.tape_id_ = tape->id_; } return result; } template inline AD sign(const AD &x) { return x.sign_me(); } template inline AD sign(const VecAD_reference &x) { return x.ADBase().sign_me(); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/testvector.hpp0000644000175200017650000000620413057470466017372 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_TESTVECTOR_HPP # define CPPAD_CORE_TESTVECTOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin testvector$$ $spell CppAD cmake testvector cppad Eigen ifdef hpp std endif ublas $$ $section Using The CppAD Test Vector Template Class$$ $mindex CPPAD_TESTVECTOR$$ $head Syntax$$ $codei%CPPAD_TESTVECTOR(%Scalar%) %$$ $head Introduction$$ Many of the CppAD $cref/examples/example/$$ and tests use the $code CPPAD_TESTVECTOR$$ template class to pass information to CppAD. This is not a true template class because it's syntax uses $codei%(%Scalar%)%$$ instead of $codei%<%Scalar%>%$$. This enables us to use $codei% Eigen::Matrix<%Scalar%, Eigen::Dynamic, 1> %$$ as one of the possible cases for this 'template class'. $head CppAD::vector$$ If in the $cref/cmake command/cmake/CMake Command/$$ you specify $cref cppad_testvector$$ to be $code cppad$$, $code CPPAD_CPPADVECTOR$$ will be true. In this case, $code CPPAD_TESTVECTOR$$ is defined by the following source code: $srccode%cpp% */ # if CPPAD_CPPADVECTOR # define CPPAD_TESTVECTOR(Scalar) CppAD::vector< Scalar > # endif /* %$$ In this case CppAD will use its own vector for many of its examples and tests. $head std::vector$$ If in the cmake command you specify $icode cppad_testvector$$ to be $code std$$, $code CPPAD_STDVECTOR$$ will be true. In this case, $code CPPAD_TESTVECTOR$$ is defined by the following source code: $srccode%cpp% */ # if CPPAD_STDVECTOR # include # define CPPAD_TESTVECTOR(Scalar) std::vector< Scalar > # endif /* %$$ In this case CppAD will use standard vector for many of its examples and tests. $head boost::numeric::ublas::vector$$ If in the cmake command you specify $icode cppad_testvector$$ to be $code boost$$, $code CPPAD_BOOSTVECTOR$$ will be true. In this case, $code CPPAD_TESTVECTOR$$ is defined by the following source code: $srccode%cpp% */ # if CPPAD_BOOSTVECTOR # include # define CPPAD_TESTVECTOR(Scalar) boost::numeric::ublas::vector< Scalar > # endif /* %$$ In this case CppAD will use this boost vector for many of its examples and tests. $head Eigen Vectors$$ If in the cmake command you specify $icode cppad_testvector$$ to be $code eigen$$, $code CPPAD_EIGENVECTOR$$ will be true. In this case, $code CPPAD_TESTVECTOR$$ is defined by the following source code: $srccode%cpp% */ # if CPPAD_EIGENVECTOR # include # define CPPAD_TESTVECTOR(Scalar) Eigen::Matrix< Scalar , Eigen::Dynamic, 1> # endif /* %$$ In this case CppAD will use the Eigen vector for many of its examples and tests. $end ------------------------------------------------------------------------ */ # endif cppad-20170000.3/cppad/core/discrete.hpp0000644000175200017650000001773113057470466017001 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_DISCRETE_HPP # define CPPAD_CORE_DISCRETE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin Discrete$$ $spell retaping namespace std Eq Cpp const inline Geq $$ $section Discrete AD Functions$$ $mindex CPPAD_DISCRETE_FUNCTION$$ $head Syntax$$ $codei%CPPAD_DISCRETE_FUNCTION(%Base%, %name%) %$$ $icode%y% = %name%(%x%) %$$ $icode%ay% = %name%(%ax%) %$$ $head Purpose$$ Record the evaluation of a discrete function as part of an $codei%AD<%Base%>%$$ $cref/operation sequence/glossary/Operation/Sequence/$$. The value of a discrete function can depend on the $cref/independent variables/glossary/Tape/Independent Variable/$$, but its derivative is identically zero. For example, suppose that the integer part of a $cref/variable/glossary/Variable/$$ $icode x$$ is the index into an array of values. $head Base$$ This is the $cref/base type/base_require/$$ corresponding to the operations sequence; i.e., use of the $icode name$$ with arguments of type $codei%AD<%Base%>%$$ can be recorded in an operation sequence. $head name$$ This is the name of the function (as it is used in the source code). The user must provide a version of $icode name$$ where the argument has type $icode Base$$. CppAD uses this to create a version of $icode name$$ where the argument has type $codei%AD<%Base%>%$$. $head x$$ The argument $icode x$$ has prototype $codei% const %Base%& %x% %$$ It is the value at which the user provided version of $icode name$$ is to be evaluated. $head y$$ The result $icode y$$ has prototype $codei% %Base% %y% %$$ It is the return value for the user provided version of $icode name$$. $head ax$$ The argument $icode ax$$ has prototype $codei% const AD<%Base%>& %ax% %$$ It is the value at which the CppAD provided version of $icode name$$ is to be evaluated. $head ay$$ The result $icode ay$$ has prototype $codei% AD<%Base%> %ay% %$$ It is the return value for the CppAD provided version of $icode name$$. $head Create AD Version$$ The preprocessor macro invocation $codei% CPPAD_DISCRETE_FUNCTION(%Base%, %name%) %$$ defines the $codei%AD<%Base%>%$$ version of $icode name$$. This can be with in a namespace (not the $code CppAD$$ namespace) but must be outside of any routine. $head Operation Sequence$$ This is an AD of $icode Base$$ $cref/atomic operation/glossary/Operation/Atomic/$$ and hence is part of the current AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Derivatives$$ During a zero order $cref Forward$$ operation, an $cref ADFun$$ object will compute the value of $icode name$$ using the user provided $icode Base$$ version of this routine. All the derivatives of $icode name$$ will be evaluated as zero. $head Parallel Mode$$ The first call to $codei% %ay% = %name%(%ax%) %$$ must not be in $cref/parallel/ta_in_parallel/$$ execution mode. $head Example$$ $children% example/tape_index.cpp% example/interp_onetape.cpp% example/interp_retape.cpp %$$ The file $cref tape_index.cpp$$ contains an example and test that uses a discrete function to vary an array index during $cref Forward$$ mode calculations. The file $cref interp_onetape.cpp$$ contains an example and test that uses discrete functions to avoid retaping a calculation that requires interpolation. (The file $cref interp_retape.cpp$$ shows how interpolation can be done with retaping.) $head CppADCreateDiscrete Deprecated 2007-07-28$$ The preprocessor symbol $code CppADCreateDiscrete$$ is defined to be the same as $code CPPAD_DISCRETE_FUNCTION$$ but its use is deprecated. $end ------------------------------------------------------------------------------ */ # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file discrete.hpp user define discrete functions */ /*! \def CPPAD_DISCRETE_FUNCTION(Base, name) Defines the function name(ax, ay) where \c ax and \c ay are vectors with AD elements. \par Base is the base type for the discrete function. \par name is the name of the user defined function that corresponding to this operation. */ # define CPPAD_DISCRETE_FUNCTION(Base, name) \ inline CppAD::AD name (const CppAD::AD& ax) \ { \ static CppAD::discrete fun(#name, name); \ \ return fun.ad(ax); \ } # define CppADCreateDiscrete CPPAD_DISCRETE_FUNCTION /* Class that acutally implemnets the ay = name(ax) call. A new discrete function is generated for ech time the user invokes the CPPAD_DISCRETE_FUNCTION macro; see static object in that macro. */ template class discrete { /// parallel_ad needs to call List to initialize static template friend void parallel_ad(void); /// type for the user routine that computes function values typedef Base (*F) (const Base& x); private: /// name of this user defined function const std::string name_; /// user's implementation of the function for Base operations const F f_; /// index of this objec in the vector of all objects for this class const size_t index_; /*! List of all objects in this class. If we use CppAD::vector for this vector, it will appear that there is a memory leak because this list is not distroyed before thread_alloc::free_available(thread) is called by the testing routines. */ static std::vector& List(void) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static std::vector list; return list; } public: /*! Constructor called for each invocation of CPPAD_DISCRETE_FUNCTION. Put this object in the list of all objects for this class and set the constant private data name_, f_, and index_. \param Name is the user's name for this discrete function. \param f user routine that implements this function for \c Base class. \par This constructor can ont be used in parallel mode because it changes the static object \c List. */ discrete(const char* Name, F f) : name_(Name) , f_(f) , index_( List().size() ) { CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "discrete: First call the function *Name is in parallel mode." ); List().push_back(this); } /*! Implement the user call to ay = name(ax). \param ax is the argument for this call. \return the return value is called \c ay above. */ AD ad(const AD &ax) const { AD ay; ay.value_ = f_(ax.value_); if( Variable(ax) ) { local::ADTape *tape = ax.tape_this(); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::DisOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::DisOp) == 2 ); // put operand addresses in the tape tape->Rec_.PutArg(index_, ax.taddr_); // put operator in the tape ay.taddr_ = tape->Rec_.PutOp(local::DisOp); // make result a variable ay.tape_id_ = tape->id_; CPPAD_ASSERT_UNKNOWN( Variable(ay) ); } return ay; } /// Name corresponding to a discrete object static const char* name(size_t index) { return List()[index]->name_.c_str(); } /*! Link from forward mode sweep to users routine \param index index for this function in the list of all discrete object \param x argument value at which to evaluate this function */ static Base eval(size_t index, const Base& x) { CPPAD_ASSERT_UNKNOWN(index < List().size() ); return List()[index]->f_(x); } }; } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/bool_fun.hpp0000644000175200017650000001435113057470466016775 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BOOL_FUN_HPP # define CPPAD_CORE_BOOL_FUN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin BoolFun$$ $spell namespace bool CppAD const $$ $section AD Boolean Functions$$ $mindex bool CPPAD_BOOL_UNARY CPPAD_BOOL_BINARY$$ $head Syntax$$ $codei%CPPAD_BOOL_UNARY(%Base%, %unary_name%) %$$ $icode%b% = %unary_name%(%u%) %$$ $icode%b% = %unary_name%(%x%) %$$ $codei%CPPAD_BOOL_BINARY(%Base%, %binary_name%) %$$ $icode%b% = %binary_name%(%u%, %v%) %$$ $icode%b% = %binary_name%(%x%, %y%)%$$ $head Purpose$$ Create a $code bool$$ valued function that has $codei%AD<%Base%>%$$ arguments. $head unary_name$$ This is the name of the $code bool$$ valued function with one argument (as it is used in the source code). The user must provide a version of $icode unary_name$$ where the argument has type $icode Base$$. CppAD uses this to create a version of $icode unary_name$$ where the argument has type $codei%AD<%Base%>%$$. $head u$$ The argument $icode u$$ has prototype $codei% const %Base% &%u% %$$ It is the value at which the user provided version of $icode unary_name$$ is to be evaluated. It is also used for the first argument to the user provided version of $icode binary_name$$. $head x$$ The argument $icode x$$ has prototype $codei% const AD<%Base%> &%x% %$$ It is the value at which the CppAD provided version of $icode unary_name$$ is to be evaluated. It is also used for the first argument to the CppAD provided version of $icode binary_name$$. $head b$$ The result $icode b$$ has prototype $codei% bool %b% %$$ $head Create Unary$$ The preprocessor macro invocation $codei% CPPAD_BOOL_UNARY(%Base%, %unary_name%) %$$ defines the version of $icode unary_name$$ with a $codei%AD<%Base%>%$$ argument. This can with in a namespace (not the $code CppAD$$ namespace) but must be outside of any routine. $head binary_name$$ This is the name of the $code bool$$ valued function with two arguments (as it is used in the source code). The user must provide a version of $icode binary_name$$ where the arguments have type $icode Base$$. CppAD uses this to create a version of $icode binary_name$$ where the arguments have type $codei%AD<%Base%>%$$. $head v$$ The argument $icode v$$ has prototype $codei% const %Base% &%v% %$$ It is the second argument to the user provided version of $icode binary_name$$. $head y$$ The argument $icode x$$ has prototype $codei% const AD<%Base%> &%y% %$$ It is the second argument to the CppAD provided version of $icode binary_name$$. $head Create Binary$$ The preprocessor macro invocation $codei% CPPAD_BOOL_BINARY(%Base%, %binary_name%) %$$ defines the version of $icode binary_name$$ with $codei%AD<%Base%>%$$ arguments. This can with in a namespace (not the $code CppAD$$ namespace) but must be outside of any routine. $head Operation Sequence$$ The result of this operation is not an $cref/AD of Base/glossary/AD of Base/$$ object. Thus it will not be recorded as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Example$$ $children% example/bool_fun.cpp %$$ The file $cref bool_fun.cpp$$ contains an example and test of these operations. It returns true if it succeeds and false otherwise. $head Deprecated 2007-07-31$$ The preprocessor symbols $code CppADCreateUnaryBool$$ and $code CppADCreateBinaryBool$$ are defined to be the same as $code CPPAD_BOOL_UNARY$$ and $code CPPAD_BOOL_BINARY$$ respectively (but their use is deprecated). $end */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file bool_fun.hpp Routines and macros that implement functions from AD to bool. */ /*! Macro that defines a unary function bool F(AD x) using bool F(Base x). \param Base base for the AD type of arguments to this unary bool valued function. \param unary_name name of this unary function; i.e., \c F. */ # define CPPAD_BOOL_UNARY(Base, unary_name) \ inline bool unary_name (const CppAD::AD &x) \ { \ return CppAD::AD::UnaryBool(unary_name, x); \ } /*! Deprecated name for CPPAD_BOOL_UNARY */ # define CppADCreateUnaryBool CPPAD_BOOL_UNARY /*! Link a function name, and AD value pair to function call with base argument and bool retrun value. \param FunName is the name of the function that we are linking. \param x is the argument where we are evaluating the function. */ template inline bool AD::UnaryBool( bool FunName(const Base &x), const AD &x ) { return FunName(x.value_); } /*! Macro that defines a binary function bool F(AD x, AD y) using bool F(Base x, Base y). \param Base base for the AD type of arguments to this binary bool valued function. \param binary_name name of this binary function; i.e., \c F. */ # define CPPAD_BOOL_BINARY(Base, binary_name) \ inline bool binary_name ( \ const CppAD::AD &x, const CppAD::AD &y) \ { \ return CppAD::AD::BinaryBool(binary_name, x, y); \ } /*! Deprecated name for CPPAD_BOOL_BINARY */ # define CppADCreateBinaryBool CPPAD_BOOL_BINARY /*! Link a function name, and two AD values to function call with base arguments and bool retrun value. \param FunName is the name of the function that we are linking. \param x is the first argument where we are evaluating the function at. \param y is the second argument where we are evaluating the function at. */ template inline bool AD::BinaryBool( bool FunName(const Base &x, const Base &y), const AD &x, const AD &y ) { return FunName(x.value_, y.value_); } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/base_double.hpp0000644000175200017650000001237113057470466017436 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BASE_DOUBLE_HPP # define CPPAD_CORE_BASE_DOUBLE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include /* $begin base_double.hpp$$ $spell namespaces cppad hpp azmul expm1 atanh acosh asinh erf endif abs_geq acos asin atan cos sqrt tanh std fabs bool Lt Le Eq Ge Gt Rel CppAD CondExpOp namespace inline enum const exp const $$ $section Enable use of AD where Base is double$$ $head CondExpOp$$ The type $code double$$ is a relatively simple type that supports $code <$$, $code <=$$, $code ==$$, $code >=$$, and $code >$$ operators; see $cref/ordered type/base_cond_exp/CondExpTemplate/Ordered Type/$$. Hence its $code CondExpOp$$ function is defined by $srccode%cpp% */ namespace CppAD { inline double CondExpOp( enum CompareOp cop , const double& left , const double& right , const double& exp_if_true , const double& exp_if_false ) { return CondExpTemplate(cop, left, right, exp_if_true, exp_if_false); } } /* %$$ $head CondExpRel$$ The $cref/CPPAD_COND_EXP_REL/base_cond_exp/CondExpRel/$$ macro invocation $srccode%cpp% */ namespace CppAD { CPPAD_COND_EXP_REL(double) } /* %$$ uses $code CondExpOp$$ above to define $codei%CondExp%Rel%$$ for $code double$$ arguments and $icode%Rel%$$ equal to $code Lt$$, $code Le$$, $code Eq$$, $code Ge$$, and $code Gt$$. $head EqualOpSeq$$ The type $code double$$ is simple (in this respect) and so we define $srccode%cpp% */ namespace CppAD { inline bool EqualOpSeq(const double& x, const double& y) { return x == y; } } /* %$$ $head Identical$$ The type $code double$$ is simple (in this respect) and so we define $srccode%cpp% */ namespace CppAD { inline bool IdenticalPar(const double& x) { return true; } inline bool IdenticalZero(const double& x) { return (x == 0.); } inline bool IdenticalOne(const double& x) { return (x == 1.); } inline bool IdenticalEqualPar(const double& x, const double& y) { return (x == y); } } /* %$$ $head Integer$$ $srccode%cpp% */ namespace CppAD { inline int Integer(const double& x) { return static_cast(x); } } /* %$$ $head azmul$$ $srccode%cpp% */ namespace CppAD { CPPAD_AZMUL( double ) } /* %$$ $head Ordered$$ The $code double$$ type supports ordered comparisons $srccode%cpp% */ namespace CppAD { inline bool GreaterThanZero(const double& x) { return x > 0.; } inline bool GreaterThanOrZero(const double& x) { return x >= 0.; } inline bool LessThanZero(const double& x) { return x < 0.; } inline bool LessThanOrZero(const double& x) { return x <= 0.; } inline bool abs_geq(const double& x, const double& y) { return std::fabs(x) >= std::fabs(y); } } /* %$$ $head Unary Standard Math$$ The following macro invocations import the $code double$$ versions of the unary standard math functions into the $code CppAD$$ namespace. Importing avoids ambiguity errors when using both the $code CppAD$$ and $code std$$ namespaces. Note this also defines the $cref/float/base_float.hpp/Unary Standard Math/$$ versions of these functions. $srccode%cpp% */ namespace CppAD { using std::acos; using std::asin; using std::atan; using std::cos; using std::cosh; using std::exp; using std::fabs; using std::log; using std::log10; using std::sin; using std::sinh; using std::sqrt; using std::tan; using std::tanh; # if CPPAD_USE_CPLUSPLUS_2011 using std::erf; using std::asinh; using std::acosh; using std::atanh; using std::expm1; using std::log1p; # endif } /* %$$ The absolute value function is special because its $code std$$ name is $code fabs$$ $srccode%cpp% */ namespace CppAD { inline double abs(const double& x) { return std::fabs(x); } } /* %$$ $head sign$$ The following defines the $code CppAD::sign$$ function that is required to use $code AD$$: $srccode%cpp% */ namespace CppAD { inline double sign(const double& x) { if( x > 0. ) return 1.; if( x == 0. ) return 0.; return -1.; } } /* %$$ $head pow$$ The following defines a $code CppAD::pow$$ function that is required to use $code AD$$. As with the unary standard math functions, this has the exact same signature as $code std::pow$$, so use it instead of defining another function. $srccode%cpp% */ namespace CppAD { using std::pow; } /* %$$ $head numeric_limits$$ The following defines the CppAD $cref numeric_limits$$ for the type $code double$$: $srccode%cpp% */ namespace CppAD { CPPAD_NUMERIC_LIMITS(double, double) } /* %$$ $head to_string$$ There is no need to define $code to_string$$ for $code double$$ because it is defined by including $code cppad/utility/to_string.hpp$$; see $cref to_string$$. See $cref/base_complex.hpp/base_complex.hpp/to_string/$$ for an example where it is necessary to define $code to_string$$ for a $icode Base$$ type. $end */ # endif cppad-20170000.3/cppad/core/atan2.hpp0000644000175200017650000000650513057470466016201 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ATAN2_HPP # define CPPAD_CORE_ATAN2_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin atan2$$ $spell Vec CppAD namespace std atan const $$ $section AD Two Argument Inverse Tangent Function$$ $mindex tan atan2$$ $head Syntax$$ $icode%theta% = atan2(%y%, %x%)%$$ $head Purpose$$ Determines an angle $latex \theta \in [ - \pi , + \pi ]$$ such that $latex \[ \begin{array}{rcl} \sin ( \theta ) & = & y / \sqrt{ x^2 + y^2 } \\ \cos ( \theta ) & = & x / \sqrt{ x^2 + y^2 } \end{array} \] $$ $head y$$ The argument $icode y$$ has one of the following prototypes $codei% const AD<%Base%> &%y% const VecAD<%Base%>::reference &%y% %$$ $head x$$ The argument $icode x$$ has one of the following prototypes $codei% const AD<%Base%> &%x% const VecAD<%Base%>::reference &%x% %$$ $head theta$$ The result $icode theta$$ has prototype $codei% AD<%Base%> %theta% %$$ $head Operation Sequence$$ The AD of $icode Base$$ operation sequence used to calculate $icode theta$$ is $cref/independent/glossary/Operation/Independent/$$ of $icode x$$ and $icode y$$. $head Example$$ $children% example/atan2.cpp %$$ The file $cref atan2.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ namespace CppAD { // BEGIN CppAD namespace inline float atan2(float x, float y) { return std::atan2(x, y); } inline double atan2(double x, double y) { return std::atan2(x, y); } // The code below is used as an example by the CondExp documentation. // BEGIN CondExp template AD atan2 (const AD &y, const AD &x) { AD alpha; AD beta; AD theta; AD zero(0.); AD pi2(2. * atan(1.)); AD pi(2. * pi2); AD ax = abs(x); AD ay = abs(y); // if( ax > ay ) // theta = atan(ay / ax); // else theta = pi2 - atan(ax / ay); alpha = atan(ay / ax); beta = pi2 - atan(ax / ay); theta = CondExpGt(ax, ay, alpha, beta); // use of CondExp // if( x <= 0 ) // theta = pi - theta; theta = CondExpLe(x, zero, pi - theta, theta); // use of CondExp // if( y <= 0 ) // theta = - theta; theta = CondExpLe(y, zero, -theta, theta); // use of CondExp return theta; } // END CondExp template inline AD atan2 (const VecAD_reference &y, const AD &x) { return atan2( y.ADBase() , x ); } template inline AD atan2 (const AD &y, const VecAD_reference &x) { return atan2( y , x.ADBase() ); } template inline AD atan2 (const VecAD_reference &y, const VecAD_reference &x) { return atan2( y.ADBase() , x.ADBase() ); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/atomic_base.hpp0000644000175200017650000014406113057470466017442 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_ATOMIC_BASE_HPP # define CPPAD_CORE_ATOMIC_BASE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file atomic_base.hpp Base class for atomic user operations. */ template class atomic_base { // =================================================================== public: enum option_enum { pack_sparsity_enum , bool_sparsity_enum , set_sparsity_enum }; private: // ------------------------------------------------------ // constants // /// index of this object in class_object const size_t index_; // ----------------------------------------------------- // variables // /// sparsity pattern this object is currently using /// (set by constructor and option member functions) option_enum sparsity_; /// temporary work space used afun, declared here to avoid memory /// allocation/deallocation for each call to afun vector afun_vx_[CPPAD_MAX_NUM_THREADS]; vector afun_vy_[CPPAD_MAX_NUM_THREADS]; vector afun_tx_[CPPAD_MAX_NUM_THREADS]; vector afun_ty_[CPPAD_MAX_NUM_THREADS]; // ----------------------------------------------------- // static member functions // /// List of all the object in this class static std::vector& class_object(void) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static std::vector list_; return list_; } /// List of names for each object in this class static std::vector& class_name(void) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static std::vector list_; return list_; } // ===================================================================== public: // ----------------------------------------------------- // member functions not in user API // /// current sparsity setting option_enum sparsity(void) const { return sparsity_; } /// Name corresponding to a base_atomic object const std::string& afun_name(void) const { return class_name()[index_]; } /* $begin atomic_ctor$$ $spell enum sq std afun arg CppAD bool ctor const mat_mul_xam.cpp hpp $$ $section Atomic Function Constructor$$ $head Syntax$$ $icode%atomic_user afun%(%ctor_arg_list%) %$$ $codei%atomic_base<%Base%>(%name%, %sparsity%) %$$ $head atomic_user$$ $subhead ctor_arg_list$$ Is a list of arguments for the $icode atomic_user$$ constructor. $subhead afun$$ The object $icode afun$$ must stay in scope for as long as the corresponding atomic function is used. This includes use by any $cref/ADFun/ADFun/$$ that has this $icode atomic_user$$ operation in its $cref/operation sequence/glossary/Operation/Sequence/$$. $subhead Implementation$$ The user defined $icode atomic_user$$ class is a publicly derived class of $codei%atomic_base<%Base%>%$$. It should be declared as follows: $codei% class %atomic_user% : public CppAD::atomic_base<%Base%> { public: %atomic_user%(%ctor_arg_list%) : atomic_base<%Base%>(%name%, %sparsity%) %...% }; %$$ where $icode ...$$ denotes the rest of the implementation of the derived class. This includes completing the constructor and all the virtual functions that have their $code atomic_base$$ implementations replaced by $icode atomic_user$$ implementations. $head atomic_base$$ $subhead Restrictions$$ The $code atomic_base$$ constructor cannot be called in $cref/parallel/ta_in_parallel/$$ mode. $subhead Base$$ The template parameter determines the $icode Base$$ type for this $codei%AD<%Base%>%$$ atomic operation. $subhead name$$ This $code atomic_base$$ constructor argument has the following prototype $codei% const std::string& %name% %$$ It is the name for this atomic function and is used for error reporting. The suggested value for $icode name$$ is $icode afun$$ or $icode atomic_user$$, i.e., the name of the corresponding atomic object or class. $subhead sparsity$$ This $code atomic_base$$ constructor argument has prototype $codei% atomic_base<%Base%>::option_enum %sparsity% %$$ The current $icode sparsity$$ for an $code atomic_base$$ object determines which type of sparsity patterns it uses and its value is one of the following: $table $icode sparsity$$ $cnext sparsity patterns $rnext $codei%atomic_base<%Base%>::pack_sparsity_enum%$$ $pre $$ $cnext $cref/vectorBool/CppAD_vector/vectorBool/$$ $rnext $codei%atomic_base<%Base%>::bool_sparsity_enum%$$ $pre $$ $cnext $cref/vector/CppAD_vector/$$$code $$ $rnext $codei%atomic_base<%Base%>::set_sparsity_enum%$$ $pre $$ $cnext $cref/vector/CppAD_vector/$$$code >$$ $tend There is a default value for $icode sparsity$$ if it is not included in the constructor (which may be either the bool or set option). $head Example$$ $subhead Define Constructor$$ The following is an example of a user atomic function constructor definitions: $cref%get_started.cpp%atomic_get_started.cpp%Constructor%$$. $subhead Use Constructor$$ The following is an example using a user atomic function constructor: $cref%get_started.cpp%atomic_get_started.cpp%Use Atomic Function%Constructor%$$. $end */ /*! Base class for atomic_user functions. \tparam Base This class is used for defining an AD atomic operation y = f(x). */ /// make sure user does not invoke the default constructor atomic_base(void) { CPPAD_ASSERT_KNOWN(false, "Attempt to use the atomic_base default constructor" ); } /*! Constructor \param name name used for error reporting \param sparsity [in] what type of sparsity patterns are computed by this function, bool_sparsity_enum or set_sparsity_enum. Default value is bool sparsity patterns. */ atomic_base( const std::string& name, option_enum sparsity = bool_sparsity_enum ) : index_( class_object().size() ) , sparsity_( sparsity ) { CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "atomic_base: constructor cannot be called in parallel mode." ); class_object().push_back(this); class_name().push_back(name); CPPAD_ASSERT_UNKNOWN( class_object().size() == class_name().size() ); } /// destructor informs CppAD that this atomic function with this index /// has dropped out of scope by setting its pointer to null virtual ~atomic_base(void) { CPPAD_ASSERT_UNKNOWN( class_object().size() > index_ ); // change object pointer to null, but leave name for error reporting class_object()[index_] = CPPAD_NULL; } /// atomic_base function object corresponding to a certain index static atomic_base* class_object(size_t index) { CPPAD_ASSERT_UNKNOWN( class_object().size() > index ); return class_object()[index]; } /// atomic_base function name corresponding to a certain index static const std::string& class_name(size_t index) { CPPAD_ASSERT_UNKNOWN( class_name().size() > index ); return class_name()[index]; } /* $begin atomic_option$$ $spell sq enum afun bool CppAD std typedef $$ $section Set Atomic Function Options$$ $head Syntax$$ $icode%afun%.option(%option_value%)%$$ These settings do not apply to individual $icode afun$$ calls, but rather all subsequent uses of the corresponding atomic operation in an $cref ADFun$$ object. $head atomic_sparsity$$ Note that, if you use $cref optimize$$, these sparsity patterns are used to determine the $cref/dependency/dependency.cpp/$$ relationship between argument and result variables. $subhead pack_sparsity_enum$$ If $icode option_value$$ is $codei%atomic_base<%Base%>::pack_sparsity_enum%$$, then the type used by $icode afun$$ for $cref/sparsity patterns/glossary/Sparsity Pattern/$$, (after the option is set) will be $codei% typedef CppAD::vectorBool %atomic_sparsity% %$$ If $icode r$$ is a sparsity pattern for a matrix $latex R \in B^{p \times q}$$: $icode%r%.size() == %p% * %q%$$. $subhead bool_sparsity_enum$$ If $icode option_value$$ is $codei%atomic_base<%Base%>::bool_sparsity_enum%$$, then the type used by $icode afun$$ for $cref/sparsity patterns/glossary/Sparsity Pattern/$$, (after the option is set) will be $codei% typedef CppAD::vector %atomic_sparsity% %$$ If $icode r$$ is a sparsity pattern for a matrix $latex R \in B^{p \times q}$$: $icode%r%.size() == %p% * %q%$$. $subhead set_sparsity_enum$$ If $icode option_value$$ is $icode%atomic_base<%Base%>::set_sparsity_enum%$$, then the type used by $icode afun$$ for $cref/sparsity patterns/glossary/Sparsity Pattern/$$, (after the option is set) will be $codei% typedef CppAD::vector< std::set > %atomic_sparsity% %$$ If $icode r$$ is a sparsity pattern for a matrix $latex R \in B^{p \times q}$$: $icode%r%.size() == %p%$$, and for $latex i = 0 , \ldots , p-1$$, the elements of $icode%r%[%i%]%$$ are between zero and $latex q-1$$ inclusive. $end */ void option(enum option_enum option_value) { switch( option_value ) { case pack_sparsity_enum: case bool_sparsity_enum: case set_sparsity_enum: sparsity_ = option_value; break; default: CPPAD_ASSERT_KNOWN( false, "atoic_base::option: option_value is not valid" ); } return; } /* ----------------------------------------------------------------------------- $begin atomic_afun$$ $spell sq mul afun const CppAD mat_mul.cpp $$ $section Using AD Version of Atomic Function$$ $head Syntax$$ $icode%afun%(%ax%, %ay%)%$$ $head Purpose$$ Given $icode ax$$, this call computes the corresponding value of $icode ay$$. If $codei%AD<%Base%>%$$ operations are being recorded, it enters the computation as an atomic operation in the recording; see $cref/start recording/Independent/Start Recording/$$. $head ADVector$$ The type $icode ADVector$$ must be a $cref/simple vector class/SimpleVector/$$ with elements of type $codei%AD<%Base%>%$$; see $cref/Base/atomic_ctor/atomic_base/Base/$$. $head afun$$ is a $cref/atomic_user/atomic_ctor/atomic_user/$$ object and this $icode afun$$ function call is implemented by the $cref/atomic_base/atomic_ctor/atomic_base/$$ class. $head ax$$ This argument has prototype $codei% const %ADVector%& %ax% %$$ and size must be equal to $icode n$$. It specifies vector $latex x \in B^n$$ at which an $codei%AD<%Base%>%$$ version of $latex y = f(x)$$ is to be evaluated; see $cref/Base/atomic_ctor/atomic_base/Base/$$. $head ay$$ This argument has prototype $codei% %ADVector%& %ay% %$$ and size must be equal to $icode m$$. The input values of its elements are not specified (must not matter). Upon return, it is an $codei%AD<%Base%>%$$ version of $latex y = f(x)$$. $head Examples$$ The following files contain example uses of the AD version of atomic functions during recording: $cref%get_started.cpp%atomic_get_started.cpp%Use Atomic Function%Recording%$$, $cref%norm_sq.cpp%atomic_norm_sq.cpp%Use Atomic Function%Recording%$$, $cref%reciprocal.cpp%atomic_reciprocal.cpp%Use Atomic Function%Recording%$$, $cref%tangent.cpp%atomic_tangent.cpp%Use Atomic Function%Recording%$$, $cref%mat_mul.cpp%atomic_mat_mul.cpp%Use Atomic Function%Recording%$$. $end ----------------------------------------------------------------------------- */ /*! Implement the user call to afun(ax, ay) and old_atomic call to afun(ax, ay, id). \tparam ADVector A simple vector class with elements of type AD. \param id optional extra information vector that is just passed through by CppAD, and used by old_atomic derived class (not other derived classes). This is an extra parameter to the virtual callbacks for old_atomic; see the set_old member function. \param ax is the argument vector for this call, ax.size() determines the number of arguments. \param ay is the result vector for this call, ay.size() determines the number of results. */ template void operator()( const ADVector& ax , ADVector& ay , size_t id = 0 ) { size_t i, j; size_t n = ax.size(); size_t m = ay.size(); # ifndef NDEBUG bool ok; std::string msg = "atomic_base: " + afun_name() + ".eval: "; if( (n == 0) | (m == 0) ) { msg += "ax.size() or ay.size() is zero"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif size_t thread = thread_alloc::thread_num(); vector & tx = afun_tx_[thread]; vector & ty = afun_ty_[thread]; vector & vx = afun_vx_[thread]; vector & vy = afun_vy_[thread]; // if( vx.size() != n ) { vx.resize(n); tx.resize(n); } if( vy.size() != m ) { vy.resize(m); ty.resize(m); } // // Determine tape corresponding to variables in ax tape_id_t tape_id = 0; local::ADTape* tape = CPPAD_NULL; for(j = 0; j < n; j++) { tx[j] = ax[j].value_; vx[j] = Variable( ax[j] ); if( vx[j] ) { if( tape_id == 0 ) { tape = ax[j].tape_this(); tape_id = ax[j].tape_id_; CPPAD_ASSERT_UNKNOWN( tape != CPPAD_NULL ); } # ifndef NDEBUG if( tape_id != ax[j].tape_id_ ) { msg += afun_name() + ": ax contains variables from different threads."; CPPAD_ASSERT_KNOWN(false, msg.c_str()); } # endif } } // Use zero order forward mode to compute values size_t p = 0, q = 0; set_old(id); # ifdef NDEBUG forward(p, q, vx, vy, tx, ty); # else ok = forward(p, q, vx, vy, tx, ty); if( ! ok ) { msg += afun_name() + ": ok is false for " "zero order forward mode calculation."; CPPAD_ASSERT_KNOWN(false, msg.c_str()); } # endif bool record_operation = false; for(i = 0; i < m; i++) { // pass back values ay[i].value_ = ty[i]; // initialize entire vector parameters (not in tape) ay[i].tape_id_ = 0; ay[i].taddr_ = 0; // we need to record this operation if // any of the eleemnts of ay are variables, record_operation |= vy[i]; } # ifndef NDEBUG if( record_operation & (tape == CPPAD_NULL) ) { msg += "all elements of vx are false but vy contains a true element"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif // if tape is not null, ay is on the tape if( record_operation ) { // Operator that marks beginning of this atomic operation CPPAD_ASSERT_UNKNOWN( local::NumRes(local::UserOp) == 0 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::UserOp) == 4 ); tape->Rec_.PutArg(index_, id, n, m); tape->Rec_.PutOp(local::UserOp); // Now put n operators, one for each element of argument vector CPPAD_ASSERT_UNKNOWN( local::NumRes(local::UsravOp) == 0 ); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::UsrapOp) == 0 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::UsravOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::UsrapOp) == 1 ); for(j = 0; j < n; j++) { if( vx[j] ) { // information for an argument that is a variable tape->Rec_.PutArg(ax[j].taddr_); tape->Rec_.PutOp(local::UsravOp); } else { // information for an argument that is parameter addr_t par = tape->Rec_.PutPar(ax[j].value_); tape->Rec_.PutArg(par); tape->Rec_.PutOp(local::UsrapOp); } } // Now put m operators, one for each element of result vector CPPAD_ASSERT_UNKNOWN( local::NumArg(local::UsrrpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::UsrrpOp) == 0 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::UsrrvOp) == 0 ); CPPAD_ASSERT_UNKNOWN( local::NumRes(local::UsrrvOp) == 1 ); for(i = 0; i < m; i++) { if( vy[i] ) { ay[i].taddr_ = tape->Rec_.PutOp(local::UsrrvOp); ay[i].tape_id_ = tape_id; } else { addr_t par = tape->Rec_.PutPar(ay[i].value_); tape->Rec_.PutArg(par); tape->Rec_.PutOp(local::UsrrpOp); } } // Put a duplicate UserOp at end of UserOp sequence tape->Rec_.PutArg(index_, id, n, m); tape->Rec_.PutOp(local::UserOp); } return; } /* ----------------------------------------------------------------------------- $begin atomic_forward$$ $spell sq mul.hpp hes afun vx vy ty Taylor const CppAD bool $$ $section Atomic Forward Mode$$ $mindex callback virtual$$ $head Syntax$$ $icode%ok% = %afun%.forward(%p%, %q%, %vx%, %vy%, %tx%, %ty%)%$$ $head Purpose$$ This virtual function is used by $cref atomic_afun$$ to evaluate function values. It is also used buy $cref/forward/Forward/$$ to compute function vales and derivatives. $head Implementation$$ This virtual function must be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. It can just return $icode%ok% == false%$$ (and not compute anything) for values of $icode%q% > 0%$$ that are greater than those used by your $cref/forward/Forward/$$ mode calculations. $head p$$ The argument $icode p$$ has prototype $codei% size_t %p% %$$ It specifies the lowest order Taylor coefficient that we are evaluating. During calls to $cref atomic_afun$$, $icode%p% == 0%$$. $head q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the highest order Taylor coefficient that we are evaluating. During calls to $cref atomic_afun$$, $icode%q% == 0%$$. $head vx$$ The $code forward$$ argument $icode vx$$ has prototype $codei% const CppAD::vector& %vx% %$$ The case $icode%vx%.size() > 0%$$ only occurs while evaluating a call to $cref atomic_afun$$. In this case, $icode%p% == %q% == 0%$$, $icode%vx%.size() == %n%$$, and for $latex j = 0 , \ldots , n-1$$, $icode%vx%[%j%]%$$ is true if and only if $icode%ax%[%j%]%$$ is a $cref/variable/glossary/Variable/$$ in the corresponding call to $codei% %afun%(%ax%, %ay%) %$$ If $icode%vx%.size() == 0%$$, then $icode%vy%.size() == 0%$$ and neither of these vectors should be used. $head vy$$ The $code forward$$ argument $icode vy$$ has prototype $codei% CppAD::vector& %vy% %$$ If $icode%vy%.size() == 0%$$, it should not be used. Otherwise, $icode%q% == 0%$$ and $icode%vy%.size() == %m%$$. The input values of the elements of $icode vy$$ are not specified (must not matter). Upon return, for $latex j = 0 , \ldots , m-1$$, $icode%vy%[%i%]%$$ is true if and only if $icode%ay%[%i%]%$$ is a variable (CppAD uses $icode vy$$ to reduce the necessary computations). $head tx$$ The argument $icode tx$$ has prototype $codei% const CppAD::vector<%Base%>& %tx% %$$ and $icode%tx%.size() == (%q%+1)*%n%$$. For $latex j = 0 , \ldots , n-1$$ and $latex k = 0 , \ldots , q$$, we use the Taylor coefficient notation $latex \[ \begin{array}{rcl} x_j^k & = & tx [ j * ( q + 1 ) + k ] \\ X_j (t) & = & x_j^0 + x_j^1 t^1 + \cdots + x_j^q t^q \end{array} \] $$ Note that superscripts represent an index for $latex x_j^k$$ and an exponent for $latex t^k$$. Also note that the Taylor coefficients for $latex X(t)$$ correspond to the derivatives of $latex X(t)$$ at $latex t = 0$$ in the following way: $latex \[ x_j^k = \frac{1}{ k ! } X_j^{(k)} (0) \] $$ $head ty$$ The argument $icode ty$$ has prototype $codei% CppAD::vector<%Base%>& %ty% %$$ and $icode%tx%.size() == (%q%+1)*%m%$$. Upon return, For $latex i = 0 , \ldots , m-1$$ and $latex k = 0 , \ldots , q$$, $latex \[ \begin{array}{rcl} Y_i (t) & = & f_i [ X(t) ] \\ Y_i (t) & = & y_i^0 + y_i^1 t^1 + \cdots + y_i^q t^q + o ( t^q ) \\ ty [ i * ( q + 1 ) + k ] & = & y_i^k \end{array} \] $$ where $latex o( t^q ) / t^q \rightarrow 0$$ as $latex t \rightarrow 0$$. Note that superscripts represent an index for $latex y_j^k$$ and an exponent for $latex t^k$$. Also note that the Taylor coefficients for $latex Y(t)$$ correspond to the derivatives of $latex Y(t)$$ at $latex t = 0$$ in the following way: $latex \[ y_j^k = \frac{1}{ k ! } Y_j^{(k)} (0) \] $$ If $latex p > 0$$, for $latex i = 0 , \ldots , m-1$$ and $latex k = 0 , \ldots , p-1$$, the input of $icode ty$$ satisfies $latex \[ ty [ i * ( q + 1 ) + k ] = y_i^k \]$$ and hence the corresponding elements need not be recalculated. $head ok$$ If the required results are calculated, $icode ok$$ should be true. Otherwise, it should be false. $head Discussion$$ For example, suppose that $icode%q% == 2%$$, and you know how to compute the function $latex f(x)$$, its first derivative $latex f^{(1)} (x)$$, and it component wise Hessian $latex f_i^{(2)} (x)$$. Then you can compute $icode ty$$ using the following formulas: $latex \[ \begin{array}{rcl} y_i^0 & = & Y(0) = f_i ( x^0 ) \\ y_i^1 & = & Y^{(1)} ( 0 ) = f_i^{(1)} ( x^0 ) X^{(1)} ( 0 ) = f_i^{(1)} ( x^0 ) x^1 \\ y_i^2 & = & \frac{1}{2 !} Y^{(2)} (0) \\ & = & \frac{1}{2} X^{(1)} (0)^\R{T} f_i^{(2)} ( x^0 ) X^{(1)} ( 0 ) + \frac{1}{2} f_i^{(1)} ( x^0 ) X^{(2)} ( 0 ) \\ & = & \frac{1}{2} (x^1)^\R{T} f_i^{(2)} ( x^0 ) x^1 + f_i^{(1)} ( x^0 ) x^2 \end{array} \] $$ For $latex i = 0 , \ldots , m-1$$, and $latex k = 0 , 1 , 2$$, $latex \[ ty [ i * (q + 1) + k ] = y_i^k \] $$ $children% example/atomic/forward.cpp %$$ $head Examples$$ The file $cref atomic_forward.cpp$$ contains an example and test that uses this routine. It returns true if the test passes and false if it fails. $end ----------------------------------------------------------------------------- */ /*! Link from atomic_base to forward mode \param p [in] lowerest order for this forward mode calculation. \param q [in] highest order for this forward mode calculation. \param vx [in] if size not zero, which components of \c x are variables \param vy [out] if size not zero, which components of \c y are variables \param tx [in] Taylor coefficients corresponding to \c x for this calculation. \param ty [out] Taylor coefficient corresponding to \c y for this calculation See the forward mode in user's documentation for base_atomic */ virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { return false; } /* ----------------------------------------------------------------------------- $begin atomic_reverse$$ $spell sq mul.hpp afun ty px py Taylor const CppAD $$ $section Atomic Reverse Mode$$ $spell bool $$ $head Syntax$$ $icode%ok% = %afun%.reverse(%q%, %tx%, %ty%, %px%, %py%)%$$ $head Purpose$$ This function is used by $cref/reverse/Reverse/$$ to compute derivatives. $head Implementation$$ If you are using $cref/reverse/Reverse/$$ mode, this virtual function must be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. It can just return $icode%ok% == false%$$ (and not compute anything) for values of $icode q$$ that are greater than those used by your $cref/reverse/Reverse/$$ mode calculations. $head q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the highest order Taylor coefficient that computing the derivative of. $head tx$$ The argument $icode tx$$ has prototype $codei% const CppAD::vector<%Base%>& %tx% %$$ and $icode%tx%.size() == (%q%+1)*%n%$$. For $latex j = 0 , \ldots , n-1$$ and $latex k = 0 , \ldots , q$$, we use the Taylor coefficient notation $latex \[ \begin{array}{rcl} x_j^k & = & tx [ j * ( q + 1 ) + k ] \\ X_j (t) & = & x_j^0 + x_j^1 t^1 + \cdots + x_j^q t^q \end{array} \] $$ Note that superscripts represent an index for $latex x_j^k$$ and an exponent for $latex t^k$$. Also note that the Taylor coefficients for $latex X(t)$$ correspond to the derivatives of $latex X(t)$$ at $latex t = 0$$ in the following way: $latex \[ x_j^k = \frac{1}{ k ! } X_j^{(k)} (0) \] $$ $head ty$$ The argument $icode ty$$ has prototype $codei% const CppAD::vector<%Base%>& %ty% %$$ and $icode%tx%.size() == (%q%+1)*%m%$$. For $latex i = 0 , \ldots , m-1$$ and $latex k = 0 , \ldots , q$$, we use the Taylor coefficient notation $latex \[ \begin{array}{rcl} Y_i (t) & = & f_i [ X(t) ] \\ Y_i (t) & = & y_i^0 + y_i^1 t^1 + \cdots + y_i^q t^q + o ( t^q ) \\ y_i^k & = & ty [ i * ( q + 1 ) + k ] \end{array} \] $$ where $latex o( t^q ) / t^q \rightarrow 0$$ as $latex t \rightarrow 0$$. Note that superscripts represent an index for $latex y_j^k$$ and an exponent for $latex t^k$$. Also note that the Taylor coefficients for $latex Y(t)$$ correspond to the derivatives of $latex Y(t)$$ at $latex t = 0$$ in the following way: $latex \[ y_j^k = \frac{1}{ k ! } Y_j^{(k)} (0) \] $$ $head F$$ We use the notation $latex \{ x_j^k \} \in B^{n \times (q+1)}$$ for $latex \[ \{ x_j^k \W{:} j = 0 , \ldots , n-1, k = 0 , \ldots , q \} \]$$ We use the notation $latex \{ y_i^k \} \in B^{m \times (q+1)}$$ for $latex \[ \{ y_i^k \W{:} i = 0 , \ldots , m-1, k = 0 , \ldots , q \} \]$$ We define the function $latex F : B^{n \times (q+1)} \rightarrow B^{m \times (q+1)}$$ by $latex \[ y_i^k = F_i^k [ \{ x_j^k \} ] \] $$ Note that $latex \[ F_i^0 ( \{ x_j^k \} ) = f_i ( X(0) ) = f_i ( x^0 ) \] $$ We also note that $latex F_i^\ell ( \{ x_j^k \} )$$ is a function of $latex x^0 , \ldots , x^\ell$$ and is determined by the derivatives of $latex f_i (x)$$ up to order $latex \ell$$. $head G, H$$ We use $latex G : B^{m \times (q+1)} \rightarrow B$$ to denote an arbitrary scalar valued function of $latex \{ y_i^k \}$$. We use $latex H : B^{n \times (q+1)} \rightarrow B$$ defined by $latex \[ H ( \{ x_j^k \} ) = G[ F( \{ x_j^k \} ) ] \] $$ $head py$$ The argument $icode py$$ has prototype $codei% const CppAD::vector<%Base%>& %py% %$$ and $icode%py%.size() == m * (%q%+1)%$$. For $latex i = 0 , \ldots , m-1$$, $latex k = 0 , \ldots , q$$, $latex \[ py[ i * (q + 1 ) + k ] = \partial G / \partial y_i^k \] $$ $subhead px$$ The $icode px$$ has prototype $codei% CppAD::vector<%Base%>& %px% %$$ and $icode%px%.size() == n * (%q%+1)%$$. The input values of the elements of $icode px$$ are not specified (must not matter). Upon return, for $latex j = 0 , \ldots , n-1$$ and $latex \ell = 0 , \ldots , q$$, $latex \[ \begin{array}{rcl} px [ j * (q + 1) + \ell ] & = & \partial H / \partial x_j^\ell \\ & = & ( \partial G / \partial \{ y_i^k \} ) \cdot ( \partial \{ y_i^k \} / \partial x_j^\ell ) \\ & = & \sum_{k=0}^q \sum_{i=0}^{m-1} ( \partial G / \partial y_i^k ) ( \partial y_i^k / \partial x_j^\ell ) \\ & = & \sum_{k=\ell}^q \sum_{i=0}^{m-1} py[ i * (q + 1 ) + k ] ( \partial F_i^k / \partial x_j^\ell ) \end{array} \] $$ Note that we have used the fact that for $latex k < \ell$$, $latex \partial F_i^k / \partial x_j^\ell = 0$$. $head ok$$ The return value $icode ok$$ has prototype $codei% bool %ok% %$$ If it is $code true$$, the corresponding evaluation succeeded, otherwise it failed. $children% example/atomic/reverse.cpp %$$ $head Examples$$ The file $cref atomic_forward.cpp$$ contains an example and test that uses this routine. It returns true if the test passes and false if it fails. $end ----------------------------------------------------------------------------- */ /*! Link from reverse mode sweep to users routine. \param q [in] highest order for this reverse mode calculation. \param tx [in] Taylor coefficients corresponding to \c x for this calculation. \param ty [in] Taylor coefficient corresponding to \c y for this calculation \param px [out] Partials w.r.t. the \c x Taylor coefficients. \param py [in] Partials w.r.t. the \c y Taylor coefficients. See atomic_reverse mode use documentation */ virtual bool reverse( size_t q , const vector& tx , const vector& ty , vector& px , const vector& py ) { return false; } /* -------------------------------------- --------------------------------------- $begin atomic_for_sparse_jac$$ $spell sq mul.hpp afun Jacobian jac const CppAD std bool std $$ $section Atomic Forward Jacobian Sparsity Patterns$$ $head Syntax$$ $icode%ok% = %afun%.for_sparse_jac(%q%, %r%, %s%, %x%) %$$ $head Deprecated 2016-06-27$$ $icode%ok% = %afun%.for_sparse_jac(%q%, %r%, %s%) %$$ $head Purpose$$ This function is used by $cref ForSparseJac$$ to compute Jacobian sparsity patterns. For a fixed matrix $latex R \in B^{n \times q}$$, the Jacobian of $latex f( x + R * u)$$ with respect to $latex u \in B^q$$ is $latex \[ S(x) = f^{(1)} (x) * R \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex R$$, $code for_sparse_jac$$ computes a sparsity pattern for $latex S(x)$$. $head Implementation$$ If you are using $cref ForSparseJac$$, $cref ForSparseHes$$, or $cref RevSparseHes$$, one of the versions of this virtual function must be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. $subhead q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of columns in $latex R \in B^{n \times q}$$ and the Jacobian $latex S(x) \in B^{m \times q}$$. $subhead r$$ This argument has prototype $codei% const %atomic_sparsity%& %r% %$$ and is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for $latex R \in B^{n \times q}$$. $subhead s$$ This argument has prototype $codei% %atomic_sparsity%& %s% %$$ The input values of its elements are not specified (must not matter). Upon return, $icode s$$ is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for $latex S(x) \in B^{m \times q}$$. $subhead x$$ $index deprecated$$ The argument has prototype $codei% const CppAD::vector<%Base%>& %x% %$$ and size is equal to the $icode n$$. This is the $cref Value$$ value corresponding to the parameters in the vector $cref/ax/atomic_afun/ax/$$ (when the atomic function was called). To be specific, if $codei% if( Parameter(%ax%[%i%]) == true ) %x%[%i%] = Value( %ax%[%i%] ); else %x%[%i%] = CppAD::numeric_limits<%Base%>::quiet_NaN(); %$$ The version of this function with out the $icode x$$ argument is deprecated; i.e., you should include the argument even if you do not use it. $head ok$$ The return value $icode ok$$ has prototype $codei% bool %ok% %$$ If it is $code true$$, the corresponding evaluation succeeded, otherwise it failed. $children% example/atomic/for_sparse_jac.cpp %$$ $head Examples$$ The file $cref atomic_for_sparse_jac.cpp$$ contains an example and test that uses this routine. It returns true if the test passes and false if it fails. $end ----------------------------------------------------------------------------- */ /*! Link from forward Jacobian sparsity sweep to atomic_base \param q is the column dimension for the Jacobian sparsity partterns. \param r is the Jacobian sparsity pattern for the argument vector x \param s is the Jacobian sparsity pattern for the result vector y \param x is the integer value for x arguments that are parameters. */ virtual bool for_sparse_jac( size_t q , const vector< std::set >& r , vector< std::set >& s , const vector& x ) { return false; } virtual bool for_sparse_jac( size_t q , const vector& r , vector& s , const vector& x ) { return false; } virtual bool for_sparse_jac( size_t q , const vectorBool& r , vectorBool& s , const vector& x ) { return false; } // deprecated versions virtual bool for_sparse_jac( size_t q , const vector< std::set >& r , vector< std::set >& s ) { return false; } virtual bool for_sparse_jac( size_t q , const vector& r , vector& s ) { return false; } virtual bool for_sparse_jac( size_t q , const vectorBool& r , vectorBool& s ) { return false; } /* -------------------------------------- --------------------------------------- $begin atomic_rev_sparse_jac$$ $spell sq mul.hpp rt afun Jacobian jac CppAD std bool const hes $$ $section Atomic Reverse Jacobian Sparsity Patterns$$ $head Syntax$$ $icode%ok% = %afun%.rev_sparse_jac(%q%, %rt%, %st%, %x%) %$$ $head Deprecated 2016-06-27$$ $icode%ok% = %afun%.rev_sparse_jac(%q%, %rt%, %st%) %$$ $head Purpose$$ This function is used by $cref RevSparseJac$$ to compute Jacobian sparsity patterns. If you are using $cref RevSparseJac$$, one of the versions of this virtual function must be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. $pre $$ For a fixed matrix $latex R \in B^{q \times m}$$, the Jacobian of $latex R * f( x )$$ with respect to $latex x \in B^n$$ is $latex \[ S(x) = R * f^{(1)} (x) \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex R$$, $code rev_sparse_jac$$ computes a sparsity pattern for $latex S(x)$$. $head Implementation$$ If you are using $cref RevSparseJac$$ or $cref ForSparseHes$$, this virtual function must be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. $subhead q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of rows in $latex R \in B^{q \times m}$$ and the Jacobian $latex S(x) \in B^{q \times n}$$. $subhead rt$$ This argument has prototype $codei% const %atomic_sparsity%& %rt% %$$ and is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for $latex R^\R{T} \in B^{m \times q}$$. $subhead st$$ This argument has prototype $codei% %atomic_sparsity%& %st% %$$ The input value of its elements are not specified (must not matter). Upon return, $icode s$$ is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for $latex S(x)^\R{T} \in B^{n \times q}$$. $subhead x$$ $index deprecated$$ The argument has prototype $codei% const CppAD::vector<%Base%>& %x% %$$ and size is equal to the $icode n$$. This is the $cref Value$$ corresponding to the parameters in the vector $cref/ax/atomic_afun/ax/$$ (when the atomic function was called). To be specific, if $codei% if( Parameter(%ax%[%i%]) == true ) %x%[%i%] = Value( %ax%[%i%] ); else %x%[%i%] = CppAD::numeric_limits<%Base%>::quiet_NaN(); %$$ The version of this function with out the $icode x$$ argument is deprecated; i.e., you should include the argument even if you do not use it. $head ok$$ The return value $icode ok$$ has prototype $codei% bool %ok% %$$ If it is $code true$$, the corresponding evaluation succeeded, otherwise it failed. $children% example/atomic/rev_sparse_jac.cpp %$$ $head Examples$$ The file $cref atomic_rev_sparse_jac.cpp$$ contains an example and test that uses this routine. It returns true if the test passes and false if it fails. $end ----------------------------------------------------------------------------- */ /*! Link from reverse Jacobian sparsity sweep to atomic_base \param q [in] is the row dimension for the Jacobian sparsity partterns \param rt [out] is the tansposed Jacobian sparsity pattern w.r.t to range variables y \param st [in] is the tansposed Jacobian sparsity pattern for the argument variables x \param x is the integer value for x arguments that are parameters. */ virtual bool rev_sparse_jac( size_t q , const vector< std::set >& rt , vector< std::set >& st , const vector& x ) { return false; } virtual bool rev_sparse_jac( size_t q , const vector& rt , vector& st , const vector& x ) { return false; } virtual bool rev_sparse_jac( size_t q , const vectorBool& rt , vectorBool& st , const vector& x ) { return false; } // deprecated versions virtual bool rev_sparse_jac( size_t q , const vector< std::set >& rt , vector< std::set >& st ) { return false; } virtual bool rev_sparse_jac( size_t q , const vector& rt , vector& st ) { return false; } virtual bool rev_sparse_jac( size_t q , const vectorBool& rt , vectorBool& st ) { return false; } /* -------------------------------------- --------------------------------------- $begin atomic_for_sparse_hes$$ $spell sq mul.hpp vx afun Jacobian jac CppAD std bool hes const $$ $section Atomic Forward Hessian Sparsity Patterns$$ $head Syntax$$ $icode%ok% = %afun%.for_sparse_hes(%vx%, %r%, %s%, %h%, %x%)%$$ $head Deprecated 2016-06-27$$ $icode%ok% = %afun%.for_sparse_hes(%vx%, %r%, %s%, %h%)%$$ $head Purpose$$ This function is used by $cref ForSparseHes$$ to compute Hessian sparsity patterns. If you are using $cref ForSparseHes$$, one of the versions of this virtual function must be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. $pre $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for a diagonal matrix $latex R \in B^{n \times n}$$, and a row vector $latex S \in B^{1 \times m}$$, this routine computes the sparsity pattern for $latex \[ H(x) = R^\R{T} \cdot (S \cdot f)^{(2)}( x ) \cdot R \] $$ $head Implementation$$ If you are using and $cref ForSparseHes$$, this virtual function must be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. $subhead vx$$ The argument $icode vx$$ has prototype $codei% const CppAD:vector& %vx% %$$ $icode%vx%.size() == %n%$$, and for $latex j = 0 , \ldots , n-1$$, $icode%vx%[%j%]%$$ is true if and only if $icode%ax%[%j%]%$$ is a $cref/variable/glossary/Variable/$$ in the corresponding call to $codei% %afun%(%ax%, %ay%) %$$ $subhead r$$ This argument has prototype $codei% const CppAD:vector& %r% %$$ and is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for the diagonal of $latex R \in B^{n \times n}$$. $subhead s$$ The argument $icode s$$ has prototype $codei% const CppAD:vector& %s% %$$ and its size is $icode m$$. It is a sparsity pattern for $latex S \in B^{1 \times m}$$. $subhead h$$ This argument has prototype $codei% %atomic_sparsity%& %h% %$$ The input value of its elements are not specified (must not matter). Upon return, $icode h$$ is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for $latex H(x) \in B^{n \times n}$$ which is defined above. $subhead x$$ $index deprecated$$ The argument has prototype $codei% const CppAD::vector<%Base%>& %x% %$$ and size is equal to the $icode n$$. This is the $cref Value$$ value corresponding to the parameters in the vector $cref/ax/atomic_afun/ax/$$ (when the atomic function was called). To be specific, if $codei% if( Parameter(%ax%[%i%]) == true ) %x%[%i%] = Value( %ax%[%i%] ); else %x%[%i%] = CppAD::numeric_limits<%Base%>::quiet_NaN(); %$$ The version of this function with out the $icode x$$ argument is deprecated; i.e., you should include the argument even if you do not use it. $children% example/atomic/for_sparse_hes.cpp %$$ $head Examples$$ The file $cref atomic_for_sparse_hes.cpp$$ contains an example and test that uses this routine. It returns true if the test passes and false if it fails. $end ----------------------------------------------------------------------------- */ /*! Link from forward Hessian sparsity sweep to base_atomic \param vx [in] which componens of x are variables. \param r [in] is the forward Jacobian sparsity pattern w.r.t the argument vector x. \param s [in] is the reverse Jacobian sparsity pattern w.r.t the result vector y. \param h [out] is the Hessian sparsity pattern w.r.t the argument vector x. \param x is the integer value of the x arguments that are parameters. */ virtual bool for_sparse_hes( const vector& vx , const vector& r , const vector& s , vector< std::set >& h , const vector& x ) { return false; } virtual bool for_sparse_hes( const vector& vx , const vector& r , const vector& s , vector& h , const vector& x ) { return false; } virtual bool for_sparse_hes( const vector& vx , const vector& r , const vector& s , vectorBool& h , const vector& x ) // deprecated { return false; } virtual bool for_sparse_hes( const vector& vx , const vector& r , const vector& s , vector< std::set >& h ) { return false; } // deprecated versions virtual bool for_sparse_hes( const vector& vx , const vector& r , const vector& s , vector& h ) { return false; } virtual bool for_sparse_hes( const vector& vx , const vector& r , const vector& s , vectorBool& h ) { return false; } /* -------------------------------------- --------------------------------------- $begin atomic_rev_sparse_hes$$ $spell sq mul.hpp vx afun Jacobian jac CppAD std bool hes const $$ $section Atomic Reverse Hessian Sparsity Patterns$$ $head Syntax$$ $icode%ok% = %afun%.rev_sparse_hes(%vx%, %s%, %t%, %q%, %r%, %u%, %v%, %x%)%$$ $head Deprecated 2016-06-27$$ $icode%ok% = %afun%.rev_sparse_hes(%vx%, %s%, %t%, %q%, %r%, %u%, %v%)%$$ $head Purpose$$ This function is used by $cref RevSparseHes$$ to compute Hessian sparsity patterns. If you are using $cref RevSparseHes$$ to compute one of the versions of this virtual function muse be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. $pre $$ There is an unspecified scalar valued function $latex g : B^m \rightarrow B$$. Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex R \in B^{n \times q}$$, and information about the function $latex z = g(y)$$, this routine computes the sparsity pattern for $latex \[ V(x) = (g \circ f)^{(2)}( x ) R \] $$ $head Implementation$$ If you are using and $cref RevSparseHes$$, this virtual function must be defined by the $cref/atomic_user/atomic_ctor/atomic_user/$$ class. $subhead vx$$ The argument $icode vx$$ has prototype $codei% const CppAD:vector& %vx% %$$ $icode%vx%.size() == %n%$$, and for $latex j = 0 , \ldots , n-1$$, $icode%vx%[%j%]%$$ is true if and only if $icode%ax%[%j%]%$$ is a $cref/variable/glossary/Variable/$$ in the corresponding call to $codei% %afun%(%ax%, %ay%) %$$ $subhead s$$ The argument $icode s$$ has prototype $codei% const CppAD:vector& %s% %$$ and its size is $icode m$$. It is a sparsity pattern for $latex S(x) = g^{(1)} [ f(x) ] \in B^{1 \times m}$$. $subhead t$$ This argument has prototype $codei% CppAD:vector& %t% %$$ and its size is $icode m$$. The input values of its elements are not specified (must not matter). Upon return, $icode t$$ is a sparsity pattern for $latex T(x) \in B^{1 \times n}$$ where $latex \[ T(x) = (g \circ f)^{(1)} (x) = S(x) * f^{(1)} (x) \]$$ $subhead q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of columns in $latex R \in B^{n \times q}$$, $latex U(x) \in B^{m \times q}$$, and $latex V(x) \in B^{n \times q}$$. $subhead r$$ This argument has prototype $codei% const %atomic_sparsity%& %r% %$$ and is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for $latex R \in B^{n \times q}$$. $head u$$ This argument has prototype $codei% const %atomic_sparsity%& %u% %$$ and is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for $latex U(x) \in B^{m \times q}$$ which is defined by $latex \[ \begin{array}{rcl} U(x) & = & \{ \partial_u \{ \partial_y g[ y + f^{(1)} (x) R u ] \}_{y=f(x)} \}_{u=0} \\ & = & \partial_u \{ g^{(1)} [ f(x) + f^{(1)} (x) R u ] \}_{u=0} \\ & = & g^{(2)} [ f(x) ] f^{(1)} (x) R \end{array} \] $$ $subhead v$$ This argument has prototype $codei% %atomic_sparsity%& %v% %$$ The input value of its elements are not specified (must not matter). Upon return, $icode v$$ is a $cref/atomic_sparsity/atomic_option/atomic_sparsity/$$ pattern for $latex V(x) \in B^{n \times q}$$ which is defined by $latex \[ \begin{array}{rcl} V(x) & = & \partial_u [ \partial_x (g \circ f) ( x + R u ) ]_{u=0} \\ & = & \partial_u [ (g \circ f)^{(1)}( x + R u ) ]_{u=0} \\ & = & (g \circ f)^{(2)}( x ) R \\ & = & f^{(1)} (x)^\R{T} g^{(2)} [ f(x) ] f^{(1)} (x) R + \sum_{i=1}^m g_i^{(1)} [ f(x) ] \; f_i^{(2)} (x) R \\ & = & f^{(1)} (x)^\R{T} U(x) + \sum_{i=1}^m S_i (x) \; f_i^{(2)} (x) R \end{array} \] $$ $subhead x$$ $index deprecated$$ The argument has prototype $codei% const CppAD::vector<%Base%>& %x% %$$ and size is equal to the $icode n$$. This is the $cref Value$$ value corresponding to the parameters in the vector $cref/ax/atomic_afun/ax/$$ (when the atomic function was called). To be specific, if $codei% if( Parameter(%ax%[%i%]) == true ) %x%[%i%] = Value( %ax%[%i%] ); else %x%[%i%] = CppAD::numeric_limits<%Base%>::quiet_NaN(); %$$ The version of this function with out the $icode x$$ argument is deprecated; i.e., you should include the argument even if you do not use it. $children% example/atomic/rev_sparse_hes.cpp %$$ $head Examples$$ The file $cref atomic_rev_sparse_hes.cpp$$ contains an example and test that uses this routine. It returns true if the test passes and false if it fails. $end ----------------------------------------------------------------------------- */ /*! Link from reverse Hessian sparsity sweep to base_atomic \param vx [in] which componens of x are variables. \param s [in] is the reverse Jacobian sparsity pattern w.r.t the result vector y. \param t [out] is the reverse Jacobian sparsity pattern w.r.t the argument vector x. \param q [in] is the column dimension for the sparsity partterns. \param r [in] is the forward Jacobian sparsity pattern w.r.t the argument vector x \param u [in] is the Hessian sparsity pattern w.r.t the result vector y. \param v [out] is the Hessian sparsity pattern w.r.t the argument vector x. \param x [in] is the integer value of the x arguments that are parameters. */ virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vector< std::set >& r , const vector< std::set >& u , vector< std::set >& v , const vector& x ) { return false; } virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vector& r , const vector& u , vector& v , const vector& x ) { return false; } virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vectorBool& r , const vectorBool& u , vectorBool& v , const vector& x ) { return false; } // deprecated virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vector< std::set >& r , const vector< std::set >& u , vector< std::set >& v ) { return false; } virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vector& r , const vector& u , vector& v ) { return false; } virtual bool rev_sparse_hes( const vector& vx , const vector& s , vector& t , size_t q , const vectorBool& r , const vectorBool& u , vectorBool& v ) { return false; } /* ------------------------------------------------------------------------------ $begin atomic_base_clear$$ $spell sq alloc $$ $section Free Static Variables$$ $mindex clear$$ $head Syntax$$ $codei%atomic_base<%Base%>::clear()%$$ $head Purpose$$ Each $code atomic_base$$ objects holds onto work space in order to avoid repeated memory allocation calls and thereby increase speed (until it is deleted). If an the $code atomic_base$$ object is global or static because, the it does not get deleted. This is a problem when using $code thread_alloc$$ $cref/free_all/ta_free_all/$$ to check that all allocated memory has been freed. Calling this $code clear$$ function will free all the memory currently being held onto by the $codei%atomic_base<%Base%>%$$ class. $head Future Use$$ If there is future use of an $code atomic_base$$ object, after a call to $code clear$$, the work space will be reallocated and held onto. $head Restriction$$ This routine cannot be called while in $cref/parallel/ta_in_parallel/$$ execution mode. $end ------------------------------------------------------------------------------ */ /*! Free all thread_alloc static memory held by atomic_base (avoids reallocations). (This does not include class_object() which is an std::vector.) */ /// Free vector memory used by this class (work space) static void clear(void) { CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "cannot use atomic_base clear during parallel execution" ); size_t i = class_object().size(); while(i--) { size_t thread = CPPAD_MAX_NUM_THREADS; while(thread--) { atomic_base* op = class_object()[i]; if( op != CPPAD_NULL ) { op->afun_vx_[thread].clear(); op->afun_vy_[thread].clear(); op->afun_tx_[thread].clear(); op->afun_ty_[thread].clear(); } } } return; } // ------------------------------------------------------------------------- /*! Set value of id (used by deprecated old_atomic class) This function is called just before calling any of the virtual function and has the corresponding id of the corresponding virtual call. */ virtual void set_old(size_t id) { } // --------------------------------------------------------------------------- }; } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/sparse_hessian.hpp0000644000175200017650000005735613057470466020215 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_SPARSE_HESSIAN_HPP # define CPPAD_CORE_SPARSE_HESSIAN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin sparse_hessian$$ $spell jacobian recomputed CppAD valarray std Bool hes const Taylor cppad cmake colpack $$ $section Sparse Hessian: Easy Driver$$ $mindex SparseHessian$$ $head Syntax$$ $icode%hes% = %f%.SparseHessian(%x%, %w%) %hes% = %f%.SparseHessian(%x%, %w%, %p%) %n_sweep% = %f%.SparseHessian(%x%, %w%, %p%, %row%, %col%, %hes%, %work%) %$$ $head Purpose$$ We use $latex n$$ for the $cref/domain/seq_property/Domain/$$ size, and $latex m$$ for the $cref/range/seq_property/Range/$$ size of $icode f$$. We use $latex F : \B{R}^n \rightarrow \B{R}^m$$ do denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The syntax above sets $icode hes$$ to the Hessian $latex \[ H(x) = \dpow{2}{x} \sum_{i=1}^m w_i F_i (x) \] $$ This routine takes advantage of the sparsity of the Hessian in order to reduce the amount of computation necessary. If $icode row$$ and $icode col$$ are present, it also takes advantage of the reduced set of elements of the Hessian that need to be computed. One can use speed tests (e.g. $cref speed_test$$) to verify that results are computed faster than when using the routine $cref Hessian$$. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/Uses Forward/sparse_hessian/Uses Forward/$$ below). $head x$$ The argument $icode x$$ has prototype $codei% const %VectorBase%& %x% %$$ (see $cref/VectorBase/sparse_hessian/VectorBase/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies that point at which to evaluate the Hessian. $head w$$ The argument $icode w$$ has prototype $codei% const %VectorBase%& %w% %$$ and size $latex m$$. It specifies the value of $latex w_i$$ in the expression for $icode hes$$. The more components of $latex w$$ that are identically zero, the more sparse the resulting Hessian may be (and hence the more efficient the calculation of $icode hes$$ may be). $head p$$ The argument $icode p$$ is optional and has prototype $codei% const %VectorSet%& %p% %$$ (see $cref/VectorSet/sparse_hessian/VectorSet/$$ below) If it has elements of type $code bool$$, its size is $latex n * n$$. If it has elements of type $code std::set$$, its size is $latex n$$ and all its set elements are between zero and $latex n - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the Hessian $latex H(x)$$. $subhead Purpose$$ If this sparsity pattern does not change between calls to $codei SparseHessian$$, it should be faster to calculate $icode p$$ once and pass this argument to $codei SparseHessian$$. If you specify $icode p$$, CppAD will use the same type of sparsity representation (vectors of $code bool$$ or vectors of $code std::set$$) for its internal calculations. Otherwise, the representation for the internal calculations is unspecified. $subhead work$$ If you specify $icode work$$ in the calling sequence, it is not necessary to keep the sparsity pattern; see the heading $cref/p/sparse_hessian/work/p/$$ under the $icode work$$ description. $subhead Column Subset$$ If the arguments $icode row$$ and $icode col$$ are present, and $cref/color_method/sparse_hessian/work/color_method/$$ is $code cppad.general$$ or $code cppad.symmetric$$, it is not necessary to compute the entire sparsity pattern. Only the following subset of column values will matter: $codei% { %col%[%k%] : %k% = 0 , %...% , %K%-1 } %$$. $head row, col$$ The arguments $icode row$$ and $icode col$$ are optional and have prototype $codei% const %VectorSize%& %row% const %VectorSize%& %col% %$$ (see $cref/VectorSize/sparse_hessian/VectorSize/$$ below). They specify which rows and columns of $latex H (x)$$ are returned and in what order. We use $latex K$$ to denote the value $icode%hes%.size()%$$ which must also equal the size of $icode row$$ and $icode col$$. Furthermore, for $latex k = 0 , \ldots , K-1$$, it must hold that $latex row[k] < n$$ and $latex col[k] < n$$. In addition, all of the $latex (row[k], col[k])$$ pairs must correspond to a true value in the sparsity pattern $icode p$$. $head hes$$ The result $icode hes$$ has prototype $codei% %VectorBase% %hes% %$$ In the case where $icode row$$ and $icode col$$ are not present, the size of $icode hes$$ is $latex n * n$$ and its size is $latex n * n$$. In this case, for $latex i = 0 , \ldots , n - 1 $$ and $latex ell = 0 , \ldots , n - 1$$ $latex \[ hes [ j * n + \ell ] = \DD{ w^{\rm T} F }{ x_j }{ x_\ell } ( x ) \] $$ $pre $$ In the case where the arguments $icode row$$ and $icode col$$ are present, we use $latex K$$ to denote the size of $icode hes$$. The input value of its elements does not matter. Upon return, for $latex k = 0 , \ldots , K - 1$$, $latex \[ hes [ k ] = \DD{ w^{\rm T} F }{ x_j }{ x_\ell } (x) \; , \; \; {\rm where} \; j = row[k] \; {\rm and } \; \ell = col[k] \] $$ $head work$$ If this argument is present, it has prototype $codei% sparse_hessian_work& %work% %$$ This object can only be used with the routines $code SparseHessian$$. During its the first use, information is stored in $icode work$$. This is used to reduce the work done by future calls to $code SparseHessian$$ with the same $icode f$$, $icode p$$, $icode row$$, and $icode col$$. If a future call is made where any of these values have changed, you must first call $icode%work%.clear()%$$ to inform CppAD that this information needs to be recomputed. $subhead color_method$$ The coloring algorithm determines which rows and columns can be computed during the same sweep. This field has prototype $codei% std::string %work%.color_method %$$ This value only matters on the first call to $code sparse_hessian$$ that follows the $icode work$$ constructor or a call to $icode%work%.clear()%$$. $codei% "cppad.symmetric" %$$ This is the default coloring method (after a constructor or $code clear()$$). It takes advantage of the fact that the Hessian matrix is symmetric to find a coloring that requires fewer $cref/sweeps/sparse_hessian/n_sweep/$$. $codei% "cppad.general" %$$ This is the same as the $code "cppad"$$ method for the $cref/sparse_jacobian/sparse_jacobian/work/color_method/$$ calculation. $codei% "colpack.star" %$$ This method requires that $cref colpack_prefix$$ was specified on the $cref/cmake command/cmake/CMake Command/$$ line. It also takes advantage of the fact that the Hessian matrix is symmetric. $subhead p$$ If $icode work$$ is present, and it is not the first call after its construction or a clear, the sparsity pattern $icode p$$ is not used. This enables one to free the sparsity pattern and still compute corresponding sparse Hessians. $head n_sweep$$ The return value $icode n_sweep$$ has prototype $codei% size_t %n_sweep% %$$ It is the number of first order forward sweeps used to compute the requested Hessian values. Each first forward sweep is followed by a second order reverse sweep so it is also the number of reverse sweeps. This is proportional to the total work that $code SparseHessian$$ does, not counting the zero order forward sweep, or the work to combine multiple columns into a single forward-reverse sweep pair. $head VectorBase$$ The type $icode VectorBase$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head VectorSet$$ The type $icode VectorSet$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code bool$$ or $code std::set$$; see $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for a discussion of the difference. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $subhead Restrictions$$ If $icode VectorSet$$ has elements of $code std::set$$, then $icode%p%[%i%]%$$ must return a reference (not a copy) to the corresponding set. According to section 26.3.2.3 of the 1998 C++ standard, $code std::valarray< std::set >$$ does not satisfy this condition. $head VectorSize$$ The type $icode VectorSize$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code size_t$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Uses Forward$$ After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After a call to any of the sparse Hessian routines, the zero order Taylor coefficients correspond to $icode%f%.Forward(0, %x%)%$$ and the other coefficients are unspecified. $children% example/sparse_hessian.cpp% example/sub_sparse_hes.cpp% example/sparse_sub_hes.cpp %$$ $head Example$$ The routine $cref sparse_hessian.cpp$$ is examples and tests of $code sparse_hessian$$. It return $code true$$, if it succeeds and $code false$$ otherwise. $head Subset Hessian$$ The routines $cref sub_sparse_hes.cpp$$ and $cref sparse_sub_hes.cpp$$ are examples and tests that compute a sparse Hessian for a subset of the variables. They return $code true$$, if they succeed and $code false$$ otherwise. $end ----------------------------------------------------------------------------- */ # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file sparse_hessian.hpp Sparse Hessian driver routine and helper functions. */ // =========================================================================== /*! class used by SparseHessian to hold information so it does not need to be recomputed. */ class sparse_hessian_work { public: /// Coloring method: "cppad", or "colpack" /// (this field is set by user) std::string color_method; /// row and column indicies for return values /// (some may be reflected by star coloring algorithm) CppAD::vector row; CppAD::vector col; /// indices that sort the user row and col arrays by color CppAD::vector order; /// results of the coloring algorithm CppAD::vector color; /// constructor sparse_hessian_work(void) : color_method("cppad.symmetric") { } /// inform CppAD that this information needs to be recomputed void clear(void) { color_method = "cppad.symmetric"; row.clear(); col.clear(); order.clear(); color.clear(); } }; // =========================================================================== /*! Private helper function that does computation for all Sparse Hessian cases. \tparam Base is the base type for the recording that is stored in this ADFun. \tparam VectorSize is sparse_pack or sparse_list. \param x [in] is a vector specifing the point at which to compute the Hessian. \param w [in] is the weighting vector that defines a scalar valued function by a weighted sum of the components of the vector valued function $latex F(x)$$. \param sparsity [in] is the sparsity pattern for the Hessian that we are calculating. \param user_row [in] is the vector of row indices for the returned Hessian values. \param user_col [in] is the vector of columns indices for the returned Hessian values. It must have the same size as user_row. \param hes [out] is the vector of Hessian values. It must have the same size as user_row. The return value hes[k] is the second partial of \f$ w^{\rm T} F(x)\f$ with respect to the row[k] and col[k] component of \f$ x\f$. \param work This structure contains information that is computed by \c SparseHessianCompute. If the sparsity pattern, \c row vector, or \c col vectors are not the same between calls to \c SparseHessianCompute, \c work.clear() must be called to reinitialize \c work. \return Is the number of first order forward sweeps used to compute the requested Hessian values. (This is also equal to the number of second order reverse sweeps.) The total work, not counting the zero order forward sweep, or the time to combine computations, is proportional to this return value. */ template template size_t ADFun::SparseHessianCompute( const VectorBase& x , const VectorBase& w , VectorSet& sparsity , const VectorSize& user_row , const VectorSize& user_col , VectorBase& hes , sparse_hessian_work& work ) { using CppAD::vectorBool; size_t i, k, ell; CppAD::vector& row(work.row); CppAD::vector& col(work.col); CppAD::vector& color(work.color); CppAD::vector& order(work.order); size_t n = Domain(); // some values const Base zero(0); const Base one(1); // check VectorBase is Simple Vector class with Base type elements CheckSimpleVector(); // number of components of Hessian that are required size_t K = hes.size(); CPPAD_ASSERT_UNKNOWN( size_t( user_row.size() ) == K ); CPPAD_ASSERT_UNKNOWN( size_t( user_col.size() ) == K ); CPPAD_ASSERT_UNKNOWN( size_t(x.size()) == n ); CPPAD_ASSERT_UNKNOWN( color.size() == 0 || color.size() == n ); CPPAD_ASSERT_UNKNOWN( row.size() == 0 || row.size() == K ); CPPAD_ASSERT_UNKNOWN( col.size() == 0 || col.size() == K ); // Point at which we are evaluating the Hessian Forward(0, x); // check for case where nothing (except Forward above) to do if( K == 0 ) return 0; // Rows of the Hessian (i below) correspond to the forward mode index // and columns (j below) correspond to the reverse mode index. if( color.size() == 0 ) { CPPAD_ASSERT_UNKNOWN( sparsity.n_set() == n ); CPPAD_ASSERT_UNKNOWN( sparsity.end() == n ); // copy user rwo and col to work space row.resize(K); col.resize(K); for(k = 0; k < K; k++) { row[k] = user_row[k]; col[k] = user_col[k]; } // execute coloring algorithm color.resize(n); if( work.color_method == "cppad.general" ) local::color_general_cppad(sparsity, row, col, color); else if( work.color_method == "cppad.symmetric" ) local::color_symmetric_cppad(sparsity, row, col, color); else if( work.color_method == "colpack.star" ) { # if CPPAD_HAS_COLPACK local::color_symmetric_colpack(sparsity, row, col, color); # else CPPAD_ASSERT_KNOWN( false, "SparseHessian: work.color_method = colpack.star" "and colpack_prefix missing from cmake command line." ); # endif } else { CPPAD_ASSERT_KNOWN( false, "SparseHessian: work.color_method is not valid." ); } // put sorting indices in color order VectorSize key(K); order.resize(K); for(k = 0; k < K; k++) key[k] = color[ row[k] ]; index_sort(key, order); } size_t n_color = 1; for(ell = 0; ell < n; ell++) if( color[ell] < n ) n_color = std::max(n_color, color[ell] + 1); // direction vector for calls to forward (rows of the Hessian) VectorBase u(n); // location for return values from reverse (columns of the Hessian) VectorBase ddw(2 * n); // initialize the return value for(k = 0; k < K; k++) hes[k] = zero; // loop over colors k = 0; for(ell = 0; ell < n_color; ell++) { CPPAD_ASSERT_UNKNOWN( color[ row[ order[k] ] ] == ell ); // combine all rows with this color for(i = 0; i < n; i++) { u[i] = zero; if( color[i] == ell ) u[i] = one; } // call forward mode for all these rows at once Forward(1, u); // evaluate derivative of w^T * F'(x) * u ddw = Reverse(2, w); // set the corresponding components of the result while( k < K && color[ row[ order[k] ] ] == ell ) { hes[ order[k] ] = ddw[ col[ order[k] ] * 2 + 1 ]; k++; } } return n_color; } // =========================================================================== // Public Member Functions // =========================================================================== /*! Compute user specified subset of a sparse Hessian. The C++ source code corresponding to this operation is \verbatim SparceHessian(x, w, p, row, col, hes, work) \endverbatim \tparam Base is the base type for the recording that is stored in this ADFun. \tparam VectorSize is a simple vector class with elements of type \c size_t. \param x [in] is a vector specifing the point at which to compute the Hessian. \param w [in] is the weighting vector that defines a scalar valued function by a weighted sum of the components of the vector valued function $latex F(x)$$. \param p [in] is the sparsity pattern for the Hessian that we are calculating. \param row [in] is the vector of row indices for the returned Hessian values. \param col [in] is the vector of columns indices for the returned Hessian values. It must have the same size are r. \param hes [out] is the vector of Hessian values. It must have the same size are r. The return value hes[k] is the second partial of \f$ w^{\rm T} F(x)\f$ with respect to the row[k] and col[k] component of \f$ x\f$. \param work This structure contains information that is computed by \c SparseHessianCompute. If the sparsity pattern, \c row vector, or \c col vectors are not the same between calls to \c SparseHessian, \c work.clear() must be called to reinitialize \c work. \return Is the number of first order forward sweeps used to compute the requested Hessian values. (This is also equal to the number of second order reverse sweeps.) The total work, not counting the zero order forward sweep, or the time to combine computations, is proportional to this return value. */ template template size_t ADFun::SparseHessian( const VectorBase& x , const VectorBase& w , const VectorSet& p , const VectorSize& row , const VectorSize& col , VectorBase& hes , sparse_hessian_work& work ) { size_t n = Domain(); size_t K = hes.size(); # ifndef NDEBUG size_t k; CPPAD_ASSERT_KNOWN( size_t(x.size()) == n , "SparseHessian: size of x not equal domain dimension for f." ); CPPAD_ASSERT_KNOWN( size_t(row.size()) == K && size_t(col.size()) == K , "SparseHessian: either r or c does not have the same size as ehs." ); CPPAD_ASSERT_KNOWN( work.color.size() == 0 || work.color.size() == n, "SparseHessian: invalid value in work." ); for(k = 0; k < K; k++) { CPPAD_ASSERT_KNOWN( row[k] < n, "SparseHessian: invalid value in r." ); CPPAD_ASSERT_KNOWN( col[k] < n, "SparseHessian: invalid value in c." ); } if( work.color.size() != 0 ) for(size_t j = 0; j < n; j++) CPPAD_ASSERT_KNOWN( work.color[j] <= n, "SparseHessian: invalid value in work." ); # endif // check for case where there is nothing to compute size_t n_sweep = 0; if( K == 0 ) return n_sweep; typedef typename VectorSet::value_type Set_type; typedef typename local::internal_sparsity::pattern_type Pattern_type; Pattern_type s; if( work.color.size() == 0 ) { bool transpose = false; const char* error_msg = "SparseHessian: sparsity pattern" " does not have proper row or column dimension"; sparsity_user2internal(s, p, n, n, transpose, error_msg); } n_sweep = SparseHessianCompute(x, w, s, row, col, hes, work); return n_sweep; } /*! Compute a sparse Hessian. The C++ source code coresponding to this operation is \verbatim hes = SparseHessian(x, w, p) \endverbatim \tparam Base is the base type for the recording that is stored in this ADFun. \param x [in] is a vector specifing the point at which to compute the Hessian. \param w [in] The Hessian is computed for a weighted sum of the components of the function corresponding to this ADFun object. The argument \a w specifies the weights for each component. It must have size equal to the range dimension for this ADFun object. \param p [in] is a sparsity pattern for the Hessian. \return Will be a vector of size \c n * n containing the Hessian of at the point specified by \a x (where \c n is the domain dimension for this ADFun object). */ template template VectorBase ADFun::SparseHessian( const VectorBase& x, const VectorBase& w, const VectorSet& p ) { size_t i, j, k; size_t n = Domain(); VectorBase hes(n * n); CPPAD_ASSERT_KNOWN( size_t(x.size()) == n, "SparseHessian: size of x not equal domain size for f." ); typedef typename VectorSet::value_type Set_type; typedef typename local::internal_sparsity::pattern_type Pattern_type; // initialize the return value as zero Base zero(0); for(i = 0; i < n; i++) for(j = 0; j < n; j++) hes[i * n + j] = zero; // arguments to SparseHessianCompute Pattern_type s; CppAD::vector row; CppAD::vector col; sparse_hessian_work work; bool transpose = false; const char* error_msg = "SparseHessian: sparsity pattern" " does not have proper row or column dimension"; sparsity_user2internal(s, p, n, n, transpose, error_msg); k = 0; for(i = 0; i < n; i++) { typename Pattern_type::const_iterator itr(s, i); j = *itr; while( j != s.end() ) { row.push_back(i); col.push_back(j); k++; j = *(++itr); } } size_t K = k; VectorBase H(K); // now we have folded this into the following case SparseHessianCompute(x, w, s, row, col, H, work); // now set the non-zero return values for(k = 0; k < K; k++) hes[ row[k] * n + col[k] ] = H[k]; return hes; } /*! Compute a sparse Hessian The C++ source code coresponding to this operation is \verbatim hes = SparseHessian(x, w) \endverbatim \tparam Base is the base type for the recording that is stored in this ADFun object. The argument \a w specifies the weights for each component. It must have size equal to the range dimension for this ADFun object. \return Will be a vector of size \c n * n containing the Hessian of at the point specified by \a x (where \c n is the domain dimension for this ADFun object). */ template template VectorBase ADFun::SparseHessian(const VectorBase &x, const VectorBase &w) { size_t i, j, k; typedef CppAD::vectorBool VectorBool; size_t m = Range(); size_t n = Domain(); // determine the sparsity pattern p for Hessian of w^T F VectorBool r(n * n); for(j = 0; j < n; j++) { for(k = 0; k < n; k++) r[j * n + k] = false; r[j * n + j] = true; } ForSparseJac(n, r); // VectorBool s(m); for(i = 0; i < m; i++) s[i] = w[i] != 0; VectorBool p = RevSparseHes(n, s); // compute sparse Hessian return SparseHessian(x, w, p); } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/standard_math.hpp0000644000175200017650000000671613057470466020011 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_STANDARD_MATH_HPP # define CPPAD_CORE_STANDARD_MATH_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin unary_standard_math$$ $spell const VecAD fabs $$ $section The Unary Standard Math Functions$$ $head Syntax$$ $icode%y% = %fun%(%x%)%$$ $head Purpose$$ Evaluates the standard math function $icode fun$$. $head Possible Types$$ $subhead Base$$ If $icode Base$$ satisfies the $cref/base type requirements/base_require/$$ and argument $icode x$$ has prototype $codei% const %Base%& %x% %$$ then the result $icode y$$ has prototype $codei% %Base% %y% %$$ $subhead AD$$ If the argument $icode x$$ has prototype $codei% const AD<%Base%>& %x% %$$ then the result $icode y$$ has prototype $codei% AD<%Base%> %y% %$$ $subhead VecAD$$ If the argument $icode x$$ has prototype $codei% const VecAD<%Base%>::reference& %x% %$$ then the result $icode y$$ has prototype $codei% AD<%Base%> %y% %$$ $children%cppad/core/std_math_98.hpp %cppad/core/abs.hpp %cppad/core/acosh.hpp %cppad/core/asinh.hpp %cppad/core/atanh.hpp %cppad/core/erf.hpp %cppad/core/expm1.hpp %cppad/core/log1p.hpp %cppad/core/sign.hpp %$$ $head fun$$ The possible values for $icode fun$$ are $table $icode fun$$ $pre $$ $cnext Description $rnext $cref abs$$ $cnext $title abs$$ $rnext $cref acos$$ $cnext $title acos$$ $rnext $cref acosh$$ $cnext $title acosh$$ $rnext $cref asin$$ $cnext $title asin$$ $rnext $cref asinh$$ $cnext $title asinh$$ $rnext $cref atan$$ $cnext $title atan$$ $rnext $cref atanh$$ $cnext $title atanh$$ $rnext $cref cos$$ $cnext $title cos$$ $rnext $cref cosh$$ $cnext $title cosh$$ $rnext $cref erf$$ $cnext $title erf$$ $rnext $cref exp$$ $cnext $title exp$$ $rnext $cref expm1$$ $cnext $title expm1$$ $rnext $cref/fabs/abs/$$ $cnext $title abs$$ $rnext $cref log10$$ $cnext $title log10$$ $rnext $cref log1p$$ $cnext $title log1p$$ $rnext $cref log$$ $cnext $title log$$ $rnext $cref sign$$ $cnext $title sign$$ $rnext $cref sin$$ $cnext $title sin$$ $rnext $cref sinh$$ $cnext $title sinh$$ $rnext $cref sqrt$$ $cnext $title sqrt$$ $rnext $cref tan$$ $cnext $title tan$$ $rnext $cref tanh$$ $cnext $title tanh$$ $tend $end */ # include # include # include # include # include # include # include # include # include /* $begin binary_math$$ $section The Binary Math Functions$$ $childtable%cppad/core/atan2.hpp %cppad/core/pow.hpp %cppad/core/azmul.hpp %$$ $end */ # include # include # endif cppad-20170000.3/cppad/core/unary_minus.hpp0000644000175200017650000000441513057470466017543 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_UNARY_MINUS_HPP # define CPPAD_CORE_UNARY_MINUS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin UnaryMinus$$ $spell Vec const inline $$ $section AD Unary Minus Operator$$ $mindex -$$ $head Syntax$$ $icode%y% = - %x%$$ $head Purpose$$ Computes the negative of $icode x$$. $head Base$$ The operation in the syntax above must be supported for the case where the operand is a $code const$$ $icode Base$$ object. $head x$$ The operand $icode x$$ has one of the following prototypes $codei% const AD<%Base%> &%x% const VecAD<%Base%>::reference &%x% %$$ $head y$$ The result $icode y$$ has type $codei% AD<%Base%> %y% %$$ It is equal to the negative of the operand $icode x$$. $head Operation Sequence$$ This is an AD of $icode Base$$ $cref/atomic operation/glossary/Operation/Atomic/$$ and hence is part of the current AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Derivative$$ If $latex f$$ is a $cref/Base function/glossary/Base Function/$$, $latex \[ \D{[ - f(x) ]}{x} = - \D{f(x)}{x} \] $$ $head Example$$ $children% example/unary_minus.cpp %$$ The file $cref unary_minus.cpp$$ contains an example and test of this operation. $end ------------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { // Broken g++ compiler inhibits declaring unary minus a member or friend template inline AD AD::operator - (void) const { // should make a more efficient version by adding unary minus to // Operator.h (some day) AD result(0); result -= *this; return result; } template inline AD operator - (const VecAD_reference &right) { return - right.ADBase(); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/ad_ctor.hpp0000644000175200017650000000722713057470466016611 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AD_CTOR_HPP # define CPPAD_CORE_AD_CTOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------ $begin ad_ctor$$ $spell cppad ctor initializes Vec const $$ $section AD Constructors $$ $mindex convert Base VecAD$$ $head Syntax$$ $codei%AD<%Base%> %y%() %$$ $codei%AD<%Base%> %y%(%x%) %$$ $head Purpose$$ creates a new $codei%AD<%Base%>%$$ object $icode y$$ and initializes its value as equal to $icode x$$. $head x$$ $subhead implicit$$ There is an implicit constructor where $icode x$$ has one of the following prototypes: $codei% const %Base%& %x% const VecAD<%Base%>& %x% %$$ $subhead explicit$$ There is an explicit constructor where $icode x$$ has prototype $codei% const %Type%& %x% %$$ for any type that has an explicit constructor of the form $icode%Base%(%x%)%$$. $subhead Deprecated 2013-12-31$$ If you set $cref/cppad_deprecated/cmake/cppad_deprecated/$$ to be $code YES$$ during the install procedure, you will get an implicit constructor with prototype $codei% const %Type%& %x% %$$ for any type that has an explicit constructor of the form $icode%Base%(%x%)%$$. $head y$$ The target $icode y$$ has prototype $codei% AD<%Base%> %y% %$$ $head Example$$ $children% example/ad_ctor.cpp %$$ The files $cref ad_ctor.cpp$$ contain examples and tests of these operations. It test returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------ */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file ad_ctor.hpp AD constructors and and copy operations. */ /*! \page AD_default_ctor Use default copy constructor because they may be optimized better than the code below: \code template inline AD::AD(const AD &x) { value_ = x.value_; tape_id_ = x.tape_id_; taddr_ = x.taddr_; return; } \endcode */ /*! Default Constructor. \tparam Base Base type for this AD object. */ template inline AD::AD(void) : value_() , tape_id_(0) , taddr_(0) { } /*! Constructor from Base type. \tparam Base Base type for this AD object. \param b is the Base type value corresponding to this AD object. The tape identifier will be an invalid tape identifier, so this object is initially a parameter. */ template inline AD::AD(const Base &b) : value_(b) , tape_id_(0) , taddr_(0) { // check that this is a parameter CPPAD_ASSERT_UNKNOWN( Parameter(*this) ); } /*! Constructor from an ADVec element drops the vector information. \tparam Base Base type for this AD object. */ template inline AD::AD(const VecAD_reference &x) { *this = x.ADBase(); } /*! Constructor from any other type, converts to Base type, and uses constructor from Base type. \tparam Base Base type for this AD object. \tparam T is the the type that is being converted to AD. There must be a constructor for Base from Type. \param t is the object that is being converted from T to AD. */ template template inline AD::AD(const T &t) : value_(Base(t)) , tape_id_(0) , taddr_(0) { } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/ad_io.hpp0000644000175200017650000001252013057470466016241 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AD_IO_HPP # define CPPAD_CORE_AD_IO_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ad_input$$ $spell VecAD std istream const $$ $section AD Output Stream Operator$$ $mindex >> input write$$ $head Syntax$$ $icode%is% >> %x%$$ $head Purpose$$ Sets $icode x$$ to a $cref/parameter/glossary/Parameter/$$ with value $icode b$$ corresponding to $codei% %is% >> %b% %$$ where $icode b$$ is a $icode Base$$ object. It is assumed that this $icode Base$$ input operation returns a reference to $icode is$$. $head is$$ The operand $icode is$$ has prototype $codei% std::istream& %is% %$$ $head x$$ The operand $icode x$$ has one of the following prototypes $codei% AD<%Base%>& %x% %$$ $head Result$$ The result of this operation can be used as a reference to $icode is$$. For example, if the operand $icode y$$ has prototype $codei% AD<%Base%> %y% %$$ then the syntax $codei% %is% >> %x% >> %y% %$$ will first read the $icode Base$$ value of $icode x$$ from $icode is$$, and then read the $icode Base$$ value to $icode y$$. $head Operation Sequence$$ The result of this operation is not an $cref/AD of Base/glossary/AD of Base/$$ object. Thus it will not be recorded as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Example$$ $children% example/ad_input.cpp %$$ The file $cref ad_input.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------ $begin ad_output$$ $spell VecAD std ostream const $$ $section AD Output Stream Operator$$ $mindex <<$$ $head Syntax$$ $icode%os% << %x%$$ $head Purpose$$ Writes the $icode Base$$ value, corresponding to $icode x$$, to the output stream $icode os$$. $head Assumption$$ If $icode b$$ is a $icode Base$$ object, $codei% %os% << %b% %$$ returns a reference to $icode os$$. $head os$$ The operand $icode os$$ has prototype $codei% std::ostream& %os% %$$ $head x$$ The operand $icode x$$ has one of the following prototypes $codei% const AD<%Base%>& %x% const VecAD<%Base%>::reference& %x% %$$ $head Result$$ The result of this operation can be used as a reference to $icode os$$. For example, if the operand $icode y$$ has prototype $codei% AD<%Base%> %y% %$$ then the syntax $codei% %os% << %x% << %y% %$$ will output the value corresponding to $icode x$$ followed by the value corresponding to $icode y$$. $head Operation Sequence$$ The result of this operation is not an $cref/AD of Base/glossary/AD of Base/$$ object. Thus it will not be recorded as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Example$$ $children% example/ad_output.cpp %$$ The file $cref ad_output.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------ */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file ad_io.hpp AD input and ouput stream operators. */ // --------------------------------------------------------------------------- /*! Read an AD object from an input stream. \tparam Base Base type for the AD object. \param is [in,out] Is the input stream from which that value is read. \param x [out] is the object that is being set to a value. Upone return, x.value_ is read from the input stream and x.tape_is_ is zero; i.e., x is a parameter. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION std::istream& operator >> (std::istream& is, AD& x) { // like assignment to a base type value x.tape_id_ = 0; CPPAD_ASSERT_UNKNOWN( Parameter(x) ); return (is >> x.value_); } // --------------------------------------------------------------------------- /*! Write an AD object to an output stream. \tparam Base Base type for the AD object. \param os [in,out] Is the output stream to which that value is written. \param x is the object that is being written to the output stream. This is equivalent to writing x.value_ to the output stream. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION std::ostream& operator << (std::ostream &os, const AD &x) { return (os << x.value_); } // --------------------------------------------------------------------------- /*! Write a VecAD_reference object to an output stream. \tparam Base Base type for the VecAD_reference object. \param os [in,out] Is the output stream to which that value is written. \param x is the element of the VecAD object that is being written to the output stream. This is equivalent to writing the corresponing Base value to the stream. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION std::ostream& operator << (std::ostream &os, const VecAD_reference &x) { return (os << x.ADBase()); } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/lu_ratio.hpp0000644000175200017650000002457213057470466017016 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_LU_RATIO_HPP # define CPPAD_CORE_LU_RATIO_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin LuRatio$$ $spell cppad.hpp xk Cpp Lu bool const ip jp std ADvector $$ $section LU Factorization of A Square Matrix and Stability Calculation$$ $mindex LuRatio linear equation solve$$ $head Syntax$$ $code# include $$ $pre $$ $icode%sign% = LuRatio(%ip%, %jp%, %LU%, %ratio%)%$$ $head Description$$ Computes an LU factorization of the matrix $icode A$$ where $icode A$$ is a square matrix. A measure of the numerical stability called $icode ratio$$ is calculated. This ratio is useful when the results of $code LuRatio$$ are used as part of an $cref ADFun$$ object. $head Include$$ This routine is designed to be used with AD objects and requires the $code cppad/cppad.hpp$$ file to be included. $head Matrix Storage$$ All matrices are stored in row major order. To be specific, if $latex Y$$ is a vector that contains a $latex p$$ by $latex q$$ matrix, the size of $latex Y$$ must be equal to $latex p * q $$ and for $latex i = 0 , \ldots , p-1$$, $latex j = 0 , \ldots , q-1$$, $latex \[ Y_{i,j} = Y[ i * q + j ] \] $$ $head sign$$ The return value $icode sign$$ has prototype $codei% int %sign% %$$ If $icode A$$ is invertible, $icode sign$$ is plus or minus one and is the sign of the permutation corresponding to the row ordering $icode ip$$ and column ordering $icode jp$$. If $icode A$$ is not invertible, $icode sign$$ is zero. $head ip$$ The argument $icode ip$$ has prototype $codei% %SizeVector% &%ip% %$$ (see description of $cref/SizeVector/LuFactor/SizeVector/$$ below). The size of $icode ip$$ is referred to as $icode n$$ in the specifications below. The input value of the elements of $icode ip$$ does not matter. The output value of the elements of $icode ip$$ determine the order of the rows in the permuted matrix. $head jp$$ The argument $icode jp$$ has prototype $codei% %SizeVector% &%jp% %$$ (see description of $cref/SizeVector/LuFactor/SizeVector/$$ below). The size of $icode jp$$ must be equal to $icode n$$. The input value of the elements of $icode jp$$ does not matter. The output value of the elements of $icode jp$$ determine the order of the columns in the permuted matrix. $head LU$$ The argument $icode LU$$ has the prototype $codei% %ADvector% &%LU% %$$ and the size of $icode LU$$ must equal $latex n * n$$ (see description of $cref/ADvector/LuRatio/ADvector/$$ below). $subhead A$$ We define $icode A$$ as the matrix corresponding to the input value of $icode LU$$. $subhead P$$ We define the permuted matrix $icode P$$ in terms of $icode A$$ by $codei% %P%(%i%, %j%) = %A%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ $subhead L$$ We define the lower triangular matrix $icode L$$ in terms of the output value of $icode LU$$. The matrix $icode L$$ is zero above the diagonal and the rest of the elements are defined by $codei% %L%(%i%, %j%) = %LU%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , i$$. $subhead U$$ We define the upper triangular matrix $icode U$$ in terms of the output value of $icode LU$$. The matrix $icode U$$ is zero below the diagonal, one on the diagonal, and the rest of the elements are defined by $codei% %U%(%i%, %j%) = %LU%[ %ip%[%i%] * %n% + %jp%[%j%] ] %$$ for $latex i = 0 , \ldots , n-2$$ and $latex j = i+1 , \ldots , n-1$$. $subhead Factor$$ If the return value $icode sign$$ is non-zero, $codei% %L% * %U% = %P% %$$ If the return value of $icode sign$$ is zero, the contents of $icode L$$ and $icode U$$ are not defined. $subhead Determinant$$ If the return value $icode sign$$ is zero, the determinant of $icode A$$ is zero. If $icode sign$$ is non-zero, using the output value of $icode LU$$ the determinant of the matrix $icode A$$ is equal to $codei% %sign% * %LU%[%ip%[0], %jp%[0]] * %...% * %LU%[%ip%[%n%-1], %jp%[%n%-1]] %$$ $head ratio$$ The argument $icode ratio$$ has prototype $codei% AD<%Base%> &%ratio% %$$ On input, the value of $icode ratio$$ does not matter. On output it is a measure of how good the choice of pivots is. For $latex p = 0 , \ldots , n-1$$, the $th p$$ pivot element is the element of maximum absolute value of a $latex (n-p) \times (n-p)$$ sub-matrix. The ratio of each element of sub-matrix divided by the pivot element is computed. The return value of $icode ratio$$ is the maximum absolute value of such ratios over with respect to all elements and all the pivots. $subhead Purpose$$ Suppose that the execution of a call to $code LuRatio$$ is recorded in the $codei%ADFun<%Base%>%$$ object $icode F$$. Then a call to $cref Forward$$ of the form $codei% %F%.Forward(%k%, %xk%) %$$ with $icode k$$ equal to zero will revaluate this Lu factorization with the same pivots and a new value for $icode A$$. In this case, the resulting $icode ratio$$ may not be one. If $icode ratio$$ is too large (the meaning of too large is up to you), the current pivots do not yield a stable LU factorization of $icode A$$. A better choice for the pivots (for this value of $icode A$$) will be made if you recreate the $code ADFun$$ object starting with the $cref Independent$$ variable values that correspond to the vector $icode xk$$. $head SizeVector$$ The type $icode SizeVector$$ must be a $cref SimpleVector$$ class with $cref/elements of type size_t/SimpleVector/Elements of Specified Type/$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head ADvector$$ The type $icode ADvector$$ must be a $cref/simple vector class/SimpleVector/$$ with elements of type $codei%AD<%Base%>%$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head Example$$ $children% example/lu_ratio.cpp %$$ The file $cref lu_ratio.cpp$$ contains an example and test of using $code LuRatio$$. It returns true if it succeeds and false otherwise. $end -------------------------------------------------------------------------- */ namespace CppAD { // BEGIN CppAD namespace // Lines different from the code in cppad/lu_factor.hpp end with // template // int LuRatio(SizeVector &ip, SizeVector &jp, ADvector &LU, AD &ratio) // { typedef ADvector FloatVector; // typedef AD Float; // // check numeric type specifications CheckNumericType(); // check simple vector class specifications CheckSimpleVector(); CheckSimpleVector(); size_t i, j; // some temporary indices const Float zero( 0 ); // the value zero as a Float object size_t imax; // row index of maximum element size_t jmax; // column indx of maximum element Float emax; // maximum absolute value size_t p; // count pivots int sign; // sign of the permutation Float etmp; // temporary element Float pivot; // pivot element // ------------------------------------------------------- size_t n = size_t(ip.size()); CPPAD_ASSERT_KNOWN( size_t(jp.size()) == n, "Error in LuFactor: jp must have size equal to n" ); CPPAD_ASSERT_KNOWN( size_t(LU.size()) == n * n, "Error in LuFactor: LU must have size equal to n * m" ); // ------------------------------------------------------- // initialize row and column order in matrix not yet pivoted for(i = 0; i < n; i++) { ip[i] = i; jp[i] = i; } // initialize the sign of the permutation sign = 1; // initialize the ratio // ratio = Float(1); // // --------------------------------------------------------- // Reduce the matrix P to L * U using n pivots for(p = 0; p < n; p++) { // determine row and column corresponding to element of // maximum absolute value in remaining part of P imax = jmax = n; emax = zero; for(i = p; i < n; i++) { for(j = p; j < n; j++) { CPPAD_ASSERT_UNKNOWN( (ip[i] < n) & (jp[j] < n) ); etmp = LU[ ip[i] * n + jp[j] ]; // check if maximum absolute value so far if( AbsGeq (etmp, emax) ) { imax = i; jmax = j; emax = etmp; } } } for(i = p; i < n; i++) // { for(j = p; j < n; j++) // { etmp = abs(LU[ ip[i] * n + jp[j] ] / emax); // ratio = // CondExpGt(etmp, ratio, etmp, ratio); // } // } // CPPAD_ASSERT_KNOWN( (imax < n) & (jmax < n) , "AbsGeq must return true when second argument is zero" ); if( imax != p ) { // switch rows so max absolute element is in row p i = ip[p]; ip[p] = ip[imax]; ip[imax] = i; sign = -sign; } if( jmax != p ) { // switch columns so max absolute element is in column p j = jp[p]; jp[p] = jp[jmax]; jp[jmax] = j; sign = -sign; } // pivot using the max absolute element pivot = LU[ ip[p] * n + jp[p] ]; // check for determinant equal to zero if( pivot == zero ) { // abort the mission return 0; } // Reduce U by the elementary transformations that maps // LU( ip[p], jp[p] ) to one. Only need transform elements // above the diagonal in U and LU( ip[p] , jp[p] ) is // corresponding value below diagonal in L. for(j = p+1; j < n; j++) LU[ ip[p] * n + jp[j] ] /= pivot; // Reduce U by the elementary transformations that maps // LU( ip[i], jp[p] ) to zero. Only need transform elements // above the diagonal in U and LU( ip[i], jp[p] ) is // corresponding value below diagonal in L. for(i = p+1; i < n; i++ ) { etmp = LU[ ip[i] * n + jp[p] ]; for(j = p+1; j < n; j++) { LU[ ip[i] * n + jp[j] ] -= etmp * LU[ ip[p] * n + jp[j] ]; } } } return sign; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/compute_assign.hpp0000644000175200017650000000661113057470466020212 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_COMPUTE_ASSIGN_HPP # define CPPAD_CORE_COMPUTE_ASSIGN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin compute_assign$$ $spell Op VecAD const $$ $section AD Computed Assignment Operators$$ $mindex + add plus - subtract minus * multiply times / divide multiple$$ $head Syntax$$ $icode%x% %Op% %y%$$ $head Purpose$$ Performs computed assignment operations where either $icode x$$ has type $codei%AD<%Base%>%$$. $head Op$$ The operator $icode Op$$ is one of the following $table $bold Op$$ $cnext $bold Meaning$$ $rnext $code +=$$ $cnext $icode x$$ is assigned $icode x$$ plus $icode y$$ $rnext $code -=$$ $cnext $icode x$$ is assigned $icode x$$ minus $icode y$$ $rnext $code *=$$ $cnext $icode x$$ is assigned $icode x$$ times $icode y$$ $rnext $code /=$$ $cnext $icode x$$ is assigned $icode x$$ divided by $icode y$$ $tend $head Base$$ The type $icode Base$$ is determined by the operand $icode x$$. $head x$$ The operand $icode x$$ has the following prototype $codei% AD<%Base%> &%x% %$$ $head y$$ The operand $icode y$$ has the following prototype $codei% const %Type% &%y% %$$ where $icode Type$$ is $codei%VecAD<%Base%>::reference%$$, $codei%AD<%Base%>%$$, $icode Base$$, or $code double$$. $head Result$$ The result of this assignment can be used as a reference to $icode x$$. For example, if $icode z$$ has the following type $codei% AD<%Base%> %z% %$$ then the syntax $codei% %z% = %x% += %y% %$$ will compute $icode x$$ plus $icode y$$ and then assign this value to both $icode x$$ and $icode z$$. $head Operation Sequence$$ This is an $cref/atomic/glossary/Operation/Atomic/$$ $cref/AD of Base/glossary/AD of Base/$$ operation and hence it is part of the current AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $children% example/add_eq.cpp% example/sub_eq.cpp% example/mul_eq.cpp% example/div_eq.cpp %$$ $head Example$$ The following files contain examples and tests of these functions. Each test returns true if it succeeds and false otherwise. $table $rref AddEq.cpp$$ $rref sub_eq.cpp$$ $rref mul_eq.cpp$$ $rref div_eq.cpp$$ $tend $head Derivative$$ If $latex f$$ and $latex g$$ are $cref/Base functions/glossary/Base Function/$$ $subhead Addition$$ $latex \[ \D{[ f(x) + g(x) ]}{x} = \D{f(x)}{x} + \D{g(x)}{x} \] $$ $subhead Subtraction$$ $latex \[ \D{[ f(x) - g(x) ]}{x} = \D{f(x)}{x} - \D{g(x)}{x} \] $$ $subhead Multiplication$$ $latex \[ \D{[ f(x) * g(x) ]}{x} = g(x) * \D{f(x)}{x} + f(x) * \D{g(x)}{x} \] $$ $subhead Division$$ $latex \[ \D{[ f(x) / g(x) ]}{x} = [1/g(x)] * \D{f(x)}{x} - [f(x)/g(x)^2] * \D{g(x)}{x} \] $$ $end ----------------------------------------------------------------------------- */ # include # include # include # include # endif cppad-20170000.3/cppad/core/capacity_order.hpp0000644000175200017650000001636613057470466020172 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_CAPACITY_ORDER_HPP # define CPPAD_CORE_CAPACITY_ORDER_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin capacity_order$$ $spell var taylor_ xq yq $$ $section Controlling Taylor Coefficients Memory Allocation$$ $mindex Forward capacity_order control$$ $head Syntax$$ $icode%f%.capacity_order(%c%)%$$ $subhead See Also$$ $cref seq_property$$ $head Purpose$$ The Taylor coefficients calculated by $cref Forward$$ mode calculations are retained in an $cref ADFun$$ object for subsequent use during $cref Reverse$$ mode and higher order Forward mode calculations. For example, a call to $cref/Forward/forward_order/$$ with the syntax $codei% %yq% = %f%.Forward(%q%, %xq%) %$$ where $icode%q% > 0%$$ and $code%xq%.size() == %f%.Domain()%$$, uses the lower order Taylor coefficients and computes the $th q$$ order Taylor coefficients for all the variables in the operation sequence corresponding to $icode f$$. The $code capacity_order$$ operation allows you to control that amount of memory that is retained by an AD function object (to hold $code Forward$$ results for subsequent calculations). $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ $head c$$ The argument $icode c$$ has prototype $codei% size_t %c% %$$ It specifies the number of Taylor coefficient orders that are allocated in the AD operation sequence corresponding to $icode f$$. $subhead Pre-Allocating Memory$$ If you plan to make calls to $code Forward$$ with the maximum value of $icode q$$ equal to $icode Q$$, it should be faster to pre-allocate memory for these calls using $codei% %f%.capacity_order(%c%) %$$ with $icode c$$ equal to $latex Q + 1$$. If you do no do this, $code Forward$$ will automatically allocate memory and will copy the results to a larger buffer, when necessary. $pre $$ Note that each call to $cref Dependent$$ frees the old memory connected to the function object and sets the corresponding taylor capacity to zero. $subhead Freeing Memory$$ If you no longer need the Taylor coefficients of order $icode q$$ and higher (that are stored in $icode f$$), you can reduce the memory allocated to $icode f$$ using $codei% %f%.capacity_order(%c%) %$$ with $icode c$$ equal to $icode q$$. Note that, if $cref ta_hold_memory$$ is true, this memory is not actually returned to the system, but rather held for future use by the same thread. $head Original State$$ If $icode f$$ is $cref/constructed/FunConstruct/$$ with the syntax $codei% ADFun<%Base%> %f%(%x%, %y%) %$$, there is an implicit call to $cref forward_zero$$ with $icode xq$$ equal to the value of the $cref/independent variables/glossary/Tape/Independent Variable/$$ when the AD operation sequence was recorded. This corresponds to $icode%c% == 1%$$. $children% example/capacity_order.cpp %$$ $head Example$$ The file $cref capacity_order.cpp$$ contains an example and test of these operations. It returns true if it succeeds and false otherwise. $end ----------------------------------------------------------------------------- */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file capacity_order.hpp Control of number of orders allocated. \} */ /*! Control of number of orders and directions allocated. \tparam Base The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD. \param c is the number of orders to allocate memory for. If c == 0 then \c r must also be zero. In this case num_order_taylor_, cap_order_taylor_, and num_direction_taylor_ are all set to zero. In addition, taylor_.free() is called. \param r is the number of directions to allocate memory for. If c == 1 then \c r must also be one. In all cases, it must hold that r == num_direction_taylor_ || num_order_taylor <= 1 Upon return, num_direction_taylor_ is equal to r. \par num_order_taylor_ The output value of num_order_taylor_ is the mininumum of its input value and c. This minimum is the number of orders that are copied to the new taylor coefficient buffer. \par num_direction_taylor_ The output value of num_direction_taylor_ is equal to \c r. */ template void ADFun::capacity_order(size_t c, size_t r) { // temporary indices size_t i, k, ell; if( (c == cap_order_taylor_) & (r == num_direction_taylor_) ) return; if( c == 0 ) { CPPAD_ASSERT_UNKNOWN( r == 0 ); taylor_.free(); num_order_taylor_ = 0; cap_order_taylor_ = 0; num_direction_taylor_ = r; return; } CPPAD_ASSERT_UNKNOWN(r==num_direction_taylor_ || num_order_taylor_<=1); // Allocate new taylor with requested number of orders and directions size_t new_len = ( (c-1)*r + 1 ) * num_var_tape_; local::pod_vector new_taylor; new_taylor.extend(new_len); // number of orders to copy size_t p = std::min(num_order_taylor_, c); if( p > 0 ) { // old order capacity size_t C = cap_order_taylor_; // old number of directions size_t R = num_direction_taylor_; // copy the old data into the new matrix CPPAD_ASSERT_UNKNOWN( p == 1 || r == R ); for(i = 0; i < num_var_tape_; i++) { // copy zero order size_t old_index = ((C-1) * R + 1) * i + 0; size_t new_index = ((c-1) * r + 1) * i + 0; new_taylor[ new_index ] = taylor_[ old_index ]; // copy higher orders for(k = 1; k < p; k++) { for(ell = 0; ell < R; ell++) { old_index = ((C-1) * R + 1) * i + (k-1) * R + ell + 1; new_index = ((c-1) * r + 1) * i + (k-1) * r + ell + 1; new_taylor[ new_index ] = taylor_[ old_index ]; } } } } // replace taylor_ by new_taylor taylor_.swap(new_taylor); cap_order_taylor_ = c; num_order_taylor_ = p; num_direction_taylor_ = r; // note that the destructor for new_taylor will free the old taylor memory return; } /*! User API control of number of orders allocated. \tparam Base The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD. \param c is the number of orders to allocate memory for. If c == 0, num_order_taylor_, cap_order_taylor_, and num_direction_taylor_ are all set to zero. In addition, taylor_.free() is called. \par num_order_taylor_ The output value of num_order_taylor_ is the mininumum of its input value and c. This minimum is the number of orders that are copied to the new taylor coefficient buffer. \par num_direction_taylor_ If \c is zero (one), \c num_direction_taylor_ is set to zero (one). Otherwise, if \c num_direction_taylor_ is zero, it is set to one. Othwerwise, \c num_direction_taylor_ is not modified. */ template void ADFun::capacity_order(size_t c) { size_t r; if( (c == 0) | (c == 1) ) { r = c; capacity_order(c, r); return; } r = num_direction_taylor_; if( r == 0 ) r = 1; capacity_order(c, r); return; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/ad_binary.hpp0000644000175200017650000000655313057470466017127 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AD_BINARY_HPP # define CPPAD_CORE_AD_BINARY_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin ad_binary$$ $spell Op VecAD const $$ $section AD Binary Arithmetic Operators$$ $mindex + add plus - subtract minus * multiply times / divide$$ $head Syntax$$ $icode%z% = %x% %Op% %y%$$ $head Purpose$$ Performs arithmetic operations where either $icode x$$ or $icode y$$ has type $codei%AD<%Base%>%$$ or $cref%VecAD::reference%VecAD%VecAD::reference%$$. $head Op$$ The operator $icode Op$$ is one of the following $table $bold Op$$ $cnext $bold Meaning$$ $rnext $code +$$ $cnext $icode z$$ is $icode x$$ plus $icode y$$ $rnext $code -$$ $cnext $icode z$$ is $icode x$$ minus $icode y$$ $rnext $code *$$ $cnext $icode z$$ is $icode x$$ times $icode y$$ $rnext $code /$$ $cnext $icode z$$ is $icode x$$ divided by $icode y$$ $tend $head Base$$ The type $icode Base$$ is determined by the operand that has type $codei%AD<%Base%>%$$ or $codei%VecAD<%Base%>::reference%$$. $head x$$ The operand $icode x$$ has the following prototype $codei% const %Type% &%x% %$$ where $icode Type$$ is $codei%VecAD<%Base%>::reference%$$, $codei%AD<%Base%>%$$, $icode Base$$, or $code double$$. $head y$$ The operand $icode y$$ has the following prototype $codei% const %Type% &%y% %$$ where $icode Type$$ is $codei%VecAD<%Base%>::reference%$$, $codei%AD<%Base%>%$$, $icode Base$$, or $code double$$. $head z$$ The result $icode z$$ has the following prototype $codei% %Type% %z% %$$ where $icode Type$$ is $codei%AD<%Base%>%$$. $head Operation Sequence$$ This is an $cref/atomic/glossary/Operation/Atomic/$$ $cref/AD of Base/glossary/AD of Base/$$ operation and hence it is part of the current AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $children% example/add.cpp% example/sub.cpp% example/mul.cpp% example/div.cpp %$$ $head Example$$ The following files contain examples and tests of these functions. Each test returns true if it succeeds and false otherwise. $table $rref add.cpp$$ $rref sub.cpp$$ $rref mul.cpp$$ $rref div.cpp$$ $tend $head Derivative$$ If $latex f$$ and $latex g$$ are $cref/Base functions/glossary/Base Function/$$ $subhead Addition$$ $latex \[ \D{[ f(x) + g(x) ]}{x} = \D{f(x)}{x} + \D{g(x)}{x} \] $$ $subhead Subtraction$$ $latex \[ \D{[ f(x) - g(x) ]}{x} = \D{f(x)}{x} - \D{g(x)}{x} \] $$ $subhead Multiplication$$ $latex \[ \D{[ f(x) * g(x) ]}{x} = g(x) * \D{f(x)}{x} + f(x) * \D{g(x)}{x} \] $$ $subhead Division$$ $latex \[ \D{[ f(x) / g(x) ]}{x} = [1/g(x)] * \D{f(x)}{x} - [f(x)/g(x)^2] * \D{g(x)}{x} \] $$ $end ----------------------------------------------------------------------------- */ # include # include # include # include # endif cppad-20170000.3/cppad/core/sub.hpp0000644000175200017650000000540613057470466015764 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_SUB_HPP # define CPPAD_CORE_SUB_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD operator - (const AD &left , const AD &right) { // compute the Base part AD result; result.value_ = left.value_ - right.value_; CPPAD_ASSERT_UNKNOWN( Parameter(result) ); // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return result; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_left = left.tape_id_ == tape_id; bool var_right = right.tape_id_ == tape_id; if( var_left ) { if( var_right ) { // result = variable - variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::SubvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::SubvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(left.taddr_, right.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::SubvvOp); // make result a variable result.tape_id_ = tape_id; } else if( IdenticalZero(right.value_) ) { // result = variable - 0 result.make_variable(left.tape_id_, left.taddr_); } else { // result = variable - parameter CPPAD_ASSERT_UNKNOWN( local::NumRes(local::SubvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::SubvpOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(left.taddr_, p); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::SubvpOp); // make result a variable result.tape_id_ = tape_id; } } else if( var_right ) { // result = parameter - variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::SubpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::SubpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(left.value_); tape->Rec_.PutArg(p, right.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::SubpvOp); // make result a variable result.tape_id_ = tape_id; } return result; } // convert other cases into the case above CPPAD_FOLD_AD_VALUED_BINARY_OPERATOR(-) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/ad_fun.hpp0000644000175200017650000004754713057470466016443 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_AD_FUN_HPP # define CPPAD_CORE_AD_FUN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ADFun$$ $spell xk Ind bool taylor_ sizeof const std ind_taddr_ dep_taddr_ $$ $spell $$ $section ADFun Objects$$ $head Purpose$$ An AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$ is stored in an $code ADFun$$ object by its $cref FunConstruct$$. The $code ADFun$$ object can then be used to calculate function values, derivative values, and other values related to the corresponding function. $childtable% cppad/core/independent.hpp% cppad/core/fun_construct.hpp% cppad/core/dependent.hpp% cppad/core/abort_recording.hpp% omh/seq_property.omh% cppad/core/fun_eval.hpp% cppad/core/drivers.hpp% cppad/core/fun_check.hpp% cppad/core/optimize.hpp% cppad/core/check_for_nan.hpp %$$ $end */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file ad_fun.hpp File used to define the ADFun class. */ /*! Class used to hold function objects \tparam Base A function object has a recording of AD operations. It does it calculations using \c Base operations. */ template class ADFun { // ------------------------------------------------------------ // Private member variables private: /// Has this ADFun object been optmized bool has_been_optimized_; /// Check for nan's and report message to user (default value is true). bool check_for_nan_; /// If zero, ignoring comparison operators. Otherwise is the /// compare change count at which to store the operator index. size_t compare_change_count_; /// If compare_change_count_ is zero, compare_change_number_ is also zero. /// Otherwise, it is set to the number of comparison operations that had a /// different result during the subsequent zero order forward. size_t compare_change_number_; /// If compare_change_count is zero, compare_change_op_index_ is also /// zero. Otherwise it is the operator index for the comparison operator //// that corresponded to the number changing from count-1 to count. size_t compare_change_op_index_; /// number of orders stored in taylor_ size_t num_order_taylor_; /// maximum number of orders that will fit in taylor_ size_t cap_order_taylor_; /// number of directions stored in taylor_ size_t num_direction_taylor_; /// number of variables in the recording (play_) size_t num_var_tape_; /// tape address for the independent variables CppAD::vector ind_taddr_; /// tape address and parameter flag for the dependent variables CppAD::vector dep_taddr_; /// which dependent variables are actually parameters CppAD::vector dep_parameter_; /// results of the forward mode calculations local::pod_vector taylor_; /// which operations can be conditionally skipped /// Set during forward pass of order zero local::pod_vector cskip_op_; /// Variable on the tape corresponding to each vecad load operation /// (if zero, the operation corresponds to a parameter). local::pod_vector load_op_; /// the operation sequence corresponding to this object local::player play_; /// Packed results of the forward mode Jacobian sparsity calculations. /// for_jac_sparse_pack_.n_set() != 0 implies other sparsity results /// are empty local::sparse_pack for_jac_sparse_pack_; /// Set results of the forward mode Jacobian sparsity calculations /// for_jac_sparse_set_.n_set() != 0 implies for_sparse_pack_ is empty. local::sparse_list for_jac_sparse_set_; // ------------------------------------------------------------ // Private member functions /// change the operation sequence corresponding to this object template void Dependent(local::ADTape *tape, const ADvector &y); // ------------------------------------------------------------ // vector of bool version of ForSparseJac // (see doxygen in for_sparse_jac.hpp) template void ForSparseJacCase( bool set_type , bool transpose , bool dependency, size_t q , const VectorSet& r , VectorSet& s ); // vector of std::set version of ForSparseJac // (see doxygen in for_sparse_jac.hpp) template void ForSparseJacCase( const std::set& set_type , bool transpose , bool dependency, size_t q , const VectorSet& r , VectorSet& s ); // ------------------------------------------------------------ // vector of bool version of RevSparseJac // (see doxygen in rev_sparse_jac.hpp) template void RevSparseJacCase( bool set_type , bool transpose , bool dependency, size_t p , const VectorSet& s , VectorSet& r ); // vector of std::set version of RevSparseJac // (see doxygen in rev_sparse_jac.hpp) template void RevSparseJacCase( const std::set& set_type , bool transpose , bool dependency, size_t p , const VectorSet& s , VectorSet& r ); // ------------------------------------------------------------ // vector of bool version of ForSparseHes // (see doxygen in rev_sparse_hes.hpp) template void ForSparseHesCase( bool set_type , const VectorSet& r , const VectorSet& s , VectorSet& h ); // vector of std::set version of ForSparseHes // (see doxygen in rev_sparse_hes.hpp) template void ForSparseHesCase( const std::set& set_type , const VectorSet& r , const VectorSet& s , VectorSet& h ); // ------------------------------------------------------------ // vector of bool version of RevSparseHes // (see doxygen in rev_sparse_hes.hpp) template void RevSparseHesCase( bool set_type , bool transpose , size_t q , const VectorSet& s , VectorSet& h ); // vector of std::set version of RevSparseHes // (see doxygen in rev_sparse_hes.hpp) template void RevSparseHesCase( const std::set& set_type , bool transpose , size_t q , const VectorSet& s , VectorSet& h ); // ------------------------------------------------------------ // Forward mode version of SparseJacobian // (see doxygen in sparse_jacobian.hpp) template size_t SparseJacobianFor( const VectorBase& x , VectorSet& p_transpose , const VectorSize& row , const VectorSize& col , VectorBase& jac , sparse_jacobian_work& work ); // Reverse mode version of SparseJacobian // (see doxygen in sparse_jacobian.hpp) template size_t SparseJacobianRev( const VectorBase& x , VectorSet& p , const VectorSize& row , const VectorSize& col , VectorBase& jac , sparse_jacobian_work& work ); // ------------------------------------------------------------ // combined sparse_list and sparse_pack version of // SparseHessian (see doxygen in sparse_hessian.hpp) template size_t SparseHessianCompute( const VectorBase& x , const VectorBase& w , VectorSet& sparsity , const VectorSize& row , const VectorSize& col , VectorBase& hes , sparse_hessian_work& work ); // ------------------------------------------------------------ public: /// copy constructor ADFun(const ADFun& g) : num_var_tape_(0) { CppAD::ErrorHandler::Call( true, __LINE__, __FILE__, "ADFun(const ADFun& g)", "Attempting to use the ADFun copy constructor.\n" "Perhaps you are passing an ADFun object " "by value instead of by reference." ); } /// default constructor ADFun(void); // assignment operator // (see doxygen in fun_construct.hpp) void operator=(const ADFun& f); /// sequence constructor template ADFun(const ADvector &x, const ADvector &y); /// destructor ~ADFun(void) { } /// set value of check_for_nan_ void check_for_nan(bool value) { check_for_nan_ = value; } bool check_for_nan(void) const { return check_for_nan_; } /// assign a new operation sequence template void Dependent(const ADvector &x, const ADvector &y); /// forward mode user API, one order multiple directions. template VectorBase Forward(size_t q, size_t r, const VectorBase& x); /// forward mode user API, multiple directions one order. template VectorBase Forward(size_t q, const VectorBase& x, std::ostream& s = std::cout ); /// reverse mode sweep template VectorBase Reverse(size_t p, const VectorBase &v); // forward mode Jacobian sparsity // (see doxygen documentation in for_sparse_jac.hpp) template VectorSet ForSparseJac( size_t q, const VectorSet &r, bool transpose = false, bool dependency = false ); // reverse mode Jacobian sparsity // (see doxygen documentation in rev_sparse_jac.hpp) template VectorSet RevSparseJac( size_t q, const VectorSet &s, bool transpose = false, bool dependency = false ); // forward mode Hessian sparsity // (see doxygen documentation in rev_sparse_hes.hpp) template VectorSet ForSparseHes( const VectorSet &r, const VectorSet &s ); // internal set sparsity version of ForSparseHes // (used by checkpoint functions only) void ForSparseHesCheckpoint( vector& r , vector& s , local::sparse_list& h ); // reverse mode Hessian sparsity // (see doxygen documentation in rev_sparse_hes.hpp) template VectorSet RevSparseHes( size_t q, const VectorSet &s, bool transpose = false ); // internal set sparsity version of RevSparseHes // (used by checkpoint functions only) void RevSparseHesCheckpoint( size_t q , vector& s , bool transpose , local::sparse_list& h ); // internal set sparsity version of RevSparseJac // (used by checkpoint functions only) void RevSparseJacCheckpoint( size_t q , const local::sparse_list& r , bool transpose , bool dependency , local::sparse_list& s ); // internal set sparsity version of RevSparseJac // (used by checkpoint functions only) void ForSparseJacCheckpoint( size_t q , const local::sparse_list& r , bool transpose , bool dependency , local::sparse_list& s ); /// amount of memory used for Jacobain sparsity pattern size_t size_forward_bool(void) const { return for_jac_sparse_pack_.memory(); } /// free memory used for Jacobain sparsity pattern void size_forward_bool(size_t zero) { CPPAD_ASSERT_KNOWN( zero == 0, "size_forward_bool: argument not equal to zero" ); for_jac_sparse_pack_.resize(0, 0); } /// total number of elements used for Jacobian sparsity pattern size_t size_forward_set(void) const { return for_jac_sparse_set_.number_elements(); } /// free memory used for Jacobain sparsity pattern void size_forward_set(size_t zero) { CPPAD_ASSERT_KNOWN( zero == 0, "size_forward_bool: argument not equal to zero" ); for_jac_sparse_set_.resize(0, 0); } /// number of operators in the operation sequence size_t size_op(void) const { return play_.num_op_rec(); } /// number of operator arguments in the operation sequence size_t size_op_arg(void) const { return play_.num_op_arg_rec(); } /// amount of memory required for the operation sequence size_t size_op_seq(void) const { return play_.Memory(); } /// number of parameters in the operation sequence size_t size_par(void) const { return play_.num_par_rec(); } /// number taylor coefficient orders calculated size_t size_order(void) const { return num_order_taylor_; } /// number taylor coefficient directions calculated size_t size_direction(void) const { return num_direction_taylor_; } /// number of characters in the operation sequence size_t size_text(void) const { return play_.num_text_rec(); } /// number of variables in opertion sequence size_t size_var(void) const { return num_var_tape_; } /// number of VecAD indices in the operation sequence size_t size_VecAD(void) const { return play_.num_vec_ind_rec(); } /// set number of orders currently allocated (user API) void capacity_order(size_t c); /// set number of orders and directions currently allocated void capacity_order(size_t c, size_t r); /// number of variables in conditional expressions that can be skipped size_t number_skip(void); /// number of independent variables size_t Domain(void) const { return ind_taddr_.size(); } /// number of dependent variables size_t Range(void) const { return dep_taddr_.size(); } /// is variable a parameter bool Parameter(size_t i) { CPPAD_ASSERT_KNOWN( i < dep_taddr_.size(), "Argument to Parameter is >= dimension of range space" ); return dep_parameter_[i]; } /// Deprecated: number of comparison operations that changed /// for the previous zero order forward (than when function was recorded) size_t CompareChange(void) const { return compare_change_number_; } /// count as which to store operator index void compare_change_count(size_t count) { compare_change_count_ = count; compare_change_number_ = 0; compare_change_op_index_ = 0; } /// number of comparison operations that changed size_t compare_change_number(void) const { return compare_change_number_; } /// operator index for the count-th comparison change size_t compare_change_op_index(void) const { if( has_been_optimized_ ) return 0; return compare_change_op_index_; } /// calculate entire Jacobian template VectorBase Jacobian(const VectorBase &x); /// calculate Hessian for one component of f template VectorBase Hessian(const VectorBase &x, const VectorBase &w); template VectorBase Hessian(const VectorBase &x, size_t i); /// forward mode calculation of partial w.r.t one domain component template VectorBase ForOne( const VectorBase &x , size_t j ); /// reverse mode calculation of derivative of one range component template VectorBase RevOne( const VectorBase &x , size_t i ); /// forward mode calculation of a subset of second order partials template VectorBase ForTwo( const VectorBase &x , const VectorSize_t &J , const VectorSize_t &K ); /// reverse mode calculation of a subset of second order partials template VectorBase RevTwo( const VectorBase &x , const VectorSize_t &I , const VectorSize_t &J ); /// calculate sparse Jacobians template VectorBase SparseJacobian( const VectorBase &x ); template VectorBase SparseJacobian( const VectorBase &x , const VectorSet &p ); template size_t SparseJacobianForward( const VectorBase& x , const VectorSet& p , const VectorSize& r , const VectorSize& c , VectorBase& jac , sparse_jacobian_work& work ); template size_t SparseJacobianReverse( const VectorBase& x , const VectorSet& p , const VectorSize& r , const VectorSize& c , VectorBase& jac , sparse_jacobian_work& work ); /// calculate sparse Hessians template VectorBase SparseHessian( const VectorBase& x , const VectorBase& w ); template VectorBase SparseHessian( const VectorBase& x , const VectorBase& w , const VectorBool& p ); template size_t SparseHessian( const VectorBase& x , const VectorBase& w , const VectorSet& p , const VectorSize& r , const VectorSize& c , VectorBase& hes , sparse_hessian_work& work ); // Optimize the tape // (see doxygen documentation in optimize.hpp) void optimize( const std::string& options = "" ); // ------------------- Deprecated ----------------------------- /// deprecated: assign a new operation sequence template void Dependent(const ADvector &y); /// Deprecated: number of variables in opertion sequence size_t Size(void) const { return num_var_tape_; } /// Deprecated: # taylor_ coefficients currently stored /// (per variable,direction) size_t Order(void) const { return num_order_taylor_ - 1; } /// Deprecated: amount of memory for this object /// Note that an approximation is used for the std::set memory size_t Memory(void) const { size_t pervar = cap_order_taylor_ * sizeof(Base) + for_jac_sparse_pack_.memory() + 3 * sizeof(size_t) * for_jac_sparse_set_.number_elements(); size_t total = num_var_tape_ * pervar + play_.Memory(); return total; } /// Deprecated: # taylor_ coefficient orderss stored /// (per variable,direction) size_t taylor_size(void) const { return num_order_taylor_; } /// Deprecated: Does this AD operation sequence use /// VecAD::reference operands bool use_VecAD(void) const { return play_.num_vec_ind_rec() > 0; } /// Deprecated: # taylor_ coefficient orders calculated /// (per variable,direction) size_t size_taylor(void) const { return num_order_taylor_; } /// Deprecated: set number of orders currently allocated /// (per variable,direction) void capacity_taylor(size_t per_var); }; // --------------------------------------------------------------------------- } // END_CPPAD_NAMESPACE // non-user interfaces # include # include # include # include # include # include # include # include // user interfaces # include # include # include # include # include # include # include # include # include # include # endif cppad-20170000.3/cppad/core/identical.hpp0000644000175200017650000000627513057470466017134 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_IDENTICAL_HPP # define CPPAD_CORE_IDENTICAL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file identical.hpp Check if certain properties is true for any possible AD tape play back. */ // --------------------------------------------------------------------------- /*! Determine if an AD object is a parameter, and could never have a different value during any tape playback. An AD object \c x is identically a parameter if and only if all of the objects in the following chain are parameters: \code x , x.value , x.value.value , ... \endcode In such a case, the value of the object will always be the same no matter what the independent variable values are at any level. \param x values that we are checking for identically a pamameter. \return returns true iff \c x is identically a parameter. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool IdenticalPar(const AD &x) { return Parameter(x) && IdenticalPar(x.value_); } // Zero ============================================================== /*! Determine if an AD is equal to zero, and must be equal zero during any tape playback. \param x object that we are checking. \return returns true if and only if \c x is equals zero and is identically a parameter \ref IdenticalPar. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool IdenticalZero(const AD &x) { return Parameter(x) && IdenticalZero(x.value_); } // One ============================================================== /*! Determine if an AD is equal to one, and must be equal one during any tape playback. \param x object that we are checking. \return returns true if and only if \c x is equals one and is identically a parameter \ref IdenticalPar. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool IdenticalOne(const AD &x) { return Parameter(x) && IdenticalOne(x.value_); } // Equal =================================================================== /*! Determine if two AD objects are equal, and must be equal during any tape playback. \param x first of two objects we are checking for equal. \param y second of two objects we are checking for equal. \return returns true if and only if the arguments are equal and both identically parameters \ref IdenticalPar. */ template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION bool IdenticalEqualPar (const AD &x, const AD &y) { bool parameter; parameter = ( Parameter(x) & Parameter(y) ); return parameter && IdenticalEqualPar(x.value_, y.value_); } // ========================================================================== } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/integer.hpp0000644000175200017650000000533613057470466016632 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_INTEGER_HPP # define CPPAD_CORE_INTEGER_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------ $begin Integer$$ $spell std VecAD CppAD namespace const bool $$ $section Convert From AD to Integer$$ $head Syntax$$ $icode%i% = Integer(%x%)%$$ $head Purpose$$ Converts from an AD type to the corresponding integer value. $head i$$ The result $icode i$$ has prototype $codei% int %i% %$$ $head x$$ $subhead Real Types$$ If the argument $icode x$$ has either of the following prototypes: $codei% const float %% &%x% const double %% &%x% %$$ the fractional part is dropped to form the integer value. For example, if $icode x$$ is 1.5, $icode i$$ is 1. In general, if $latex x \geq 0$$, $icode i$$ is the greatest integer less than or equal $icode x$$. If $latex x \leq 0$$, $icode i$$ is the smallest integer greater than or equal $icode x$$. $subhead Complex Types$$ If the argument $icode x$$ has either of the following prototypes: $codei% const std::complex %% &%x% const std::complex %% &%x% %$$ The result $icode i$$ is given by $codei% %i% = Integer(%x%.real()) %$$ $subhead AD Types$$ If the argument $icode x$$ has either of the following prototypes: $codei% const AD<%Base%> &%x% const VecAD<%Base%>::reference &%x% %$$ $icode Base$$ must support the $code Integer$$ function and the conversion has the same meaning as for $icode Base$$. $head Operation Sequence$$ The result of this operation is not an $cref/AD of Base/glossary/AD of Base/$$ object. Thus it will not be recorded as part of an AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Example$$ $children% example/integer.cpp %$$ The file $cref integer.cpp$$ contains an example and test of this operation. $end ------------------------------------------------------------------------------ */ namespace CppAD { template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION int Integer(const AD &x) { return Integer(x.value_); } template CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION int Integer(const VecAD_reference &x) { return Integer( x.ADBase() ); } } # endif cppad-20170000.3/cppad/core/mul.hpp0000644000175200017650000000605013057470466015764 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_MUL_HPP # define CPPAD_CORE_MUL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template AD operator * (const AD &left , const AD &right) { // compute the Base part AD result; result.value_ = left.value_ * right.value_; CPPAD_ASSERT_UNKNOWN( Parameter(result) ); // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return result; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_left = left.tape_id_ == tape_id; bool var_right = right.tape_id_ == tape_id; if( var_left ) { if( var_right ) { // result = variable * variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::MulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::MulvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(left.taddr_, right.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::MulvvOp); // make result a variable result.tape_id_ = tape_id; } else if( IdenticalZero(right.value_) ) { // result = variable * 0 } else if( IdenticalOne(right.value_) ) { // result = variable * 1 result.make_variable(left.tape_id_, left.taddr_); } else { // result = variable * parameter CPPAD_ASSERT_UNKNOWN( local::NumRes(local::MulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::MulpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(right.value_); tape->Rec_.PutArg(p, left.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::MulpvOp); // make result a variable result.tape_id_ = tape_id; } } else if( var_right ) { if( IdenticalZero(left.value_) ) { // result = 0 * variable } else if( IdenticalOne(left.value_) ) { // result = 1 * variable result.make_variable(right.tape_id_, right.taddr_); } else { // result = parameter * variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::MulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::MulpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(left.value_); tape->Rec_.PutArg(p, right.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::MulpvOp); // make result a variable result.tape_id_ = tape_id; } } return result; } // convert other cases into the case above CPPAD_FOLD_AD_VALUED_BINARY_OPERATOR(*) } // END CppAD namespace # endif cppad-20170000.3/cppad/core/rev_one.hpp0000644000175200017650000000771313057470466016633 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_REV_ONE_HPP # define CPPAD_CORE_REV_ONE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin RevOne$$ $spell dw Taylor const $$ $section First Order Derivative: Driver Routine$$ $mindex derivative easy$$ $head Syntax$$ $icode%dw% = %f%.RevOne(%x%, %i%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. The syntax above sets $icode dw$$ to the derivative of $latex F_i$$ with respect to $latex x$$; i.e., $latex \[ dw = F_i^{(1)} (x) = \left[ \D{ F_i }{ x_0 } (x) , \cdots , \D{ F_i }{ x_{n-1} } (x) \right] \] $$ $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$ (see $cref/RevOne Uses Forward/RevOne/RevOne Uses Forward/$$ below). $head x$$ The argument $icode x$$ has prototype $codei% const %Vector% &%x% %$$ (see $cref/Vector/RevOne/Vector/$$ below) and its size must be equal to $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. It specifies that point at which to evaluate the derivative. $head i$$ The index $icode i$$ has prototype $codei% size_t %i% %$$ and is less than $latex m$$, the dimension of the $cref/range/seq_property/Range/$$ space for $icode f$$. It specifies the component of $latex F$$ that we are computing the derivative of. $head dw$$ The result $icode dw$$ has prototype $codei% %Vector% %dw% %$$ (see $cref/Vector/RevOne/Vector/$$ below) and its size is $icode n$$, the dimension of the $cref/domain/seq_property/Domain/$$ space for $icode f$$. The value of $icode dw$$ is the derivative of $latex F_i$$ evaluated at $icode x$$; i.e., for $latex j = 0 , \ldots , n - 1 $$ $latex \[. dw[ j ] = \D{ F_i }{ x_j } ( x ) \] $$ $head Vector$$ The type $icode Vector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $icode Base$$. The routine $cref CheckSimpleVector$$ will generate an error message if this is not the case. $head RevOne Uses Forward$$ After each call to $cref Forward$$, the object $icode f$$ contains the corresponding $cref/Taylor coefficients/glossary/Taylor Coefficient/$$. After a call to $code RevOne$$, the zero order Taylor coefficients correspond to $icode%f%.Forward(0, %x%)%$$ and the other coefficients are unspecified. $head Example$$ $children% example/rev_one.cpp %$$ The routine $cref/RevOne/rev_one.cpp/$$ is both an example and test. It returns $code true$$, if it succeeds and $code false$$ otherwise. $end ----------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template template Vector ADFun::RevOne(const Vector &x, size_t i) { size_t i1; size_t n = Domain(); size_t m = Range(); // check Vector is Simple Vector class with Base type elements CheckSimpleVector(); CPPAD_ASSERT_KNOWN( x.size() == n, "RevOne: Length of x not equal domain dimension for f" ); CPPAD_ASSERT_KNOWN( i < m, "RevOne: the index i is not less than range dimension for f" ); // point at which we are evaluating the derivative Forward(0, x); // component which are are taking the derivative of Vector w(m); for(i1 = 0; i1 < m; i1++) w[i1] = 0.; w[i] = Base(1); // dimension the return value Vector dw(n); // compute the return value dw = Reverse(1, w); return dw; } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/fun_eval.hpp0000644000175200017650000000164713057470466016775 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_FUN_EVAL_HPP # define CPPAD_CORE_FUN_EVAL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin FunEval$$ $spell $$ $section Evaluate ADFun Functions, Derivatives, and Sparsity Patterns$$ $childtable% omh/forward/forward.omh% omh/reverse/reverse.omh% cppad/core/sparse.hpp %$$ $end */ # include # include # include # endif cppad-20170000.3/cppad/core/undef.hpp0000644000175200017650000000762713057470466016303 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_UNDEF_HPP # define CPPAD_CORE_UNDEF_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ---------------------------------------------------------------------------- Preprecessor definitions that presist after cppad/cppad.hpp is included: # undef CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL used by CPPAD_USER_ATOMIC # undef CPPAD_ASSERT_KNOWN used by cppad_ipopt # undef CPPAD_ASSERT_UNKNOWN used by cppad_ipopt # undef CPPAD_HASH_TABLE_SIZE used by test_more/optimize.cpp # undef EIGEN_MATRIXBASE_PLUGIN example use of Eigen with CppAD # undef CPPAD_HAS_COLPACK used by speed/cppad/sparse_*.cpp # undef CPPAD_BOOL_BINARY in user api # undef CPPAD_BOOL_UNARY in user api # undef CPPAD_DISCRETE_FUNCTION in user api # undef CPPAD_EIGENVECTOR in user api # undef CPPAD_MAX_NUM_THREADS in user api # undef CPPAD_NUMERIC_LIMITS in user api # undef CPPAD_NULL in user api # undef CPPAD_PACKAGE_STRING in user api # undef CPPAD_STANDARD_MATH_UNARY in user api # undef CPPAD_TAPE_ADDR_TYPE in user api # undef CPPAD_TAPE_ID_TYPE in user api # undef CPPAD_TESTVECTOR in user api # undef CPPAD_TO_STRING in user api # undef CPPAD_USE_CPLUSPLUS_2011 in user api # undef CPPAD_TRACK_COUNT in deprecated api # undef CPPAD_TRACK_DEL_VEC in deprecated api # undef CPPAD_TRACK_EXTEND in deprecated api # undef CPPAD_TRACK_NEW_VEC in deprecated api # undef CPPAD_USER_ATOMIC in deprecated api # undef CPPAD_TEST_VECTOR deprecated verssion of CPPAD_TESTVECTOR # undef CppADCreateBinaryBool deprecated version of CPPAD_BOOL_BINARY # undef CppADCreateDiscrete deprecated version of CPPAD_DISCRETE_FUNCTION # undef CppADCreateUnaryBool deprecated version of CPPAD_BOOL_UNARY # undef CppADTrackCount deprecated version of CPPAD_TRACK_COUNT # undef CppADTrackDelVec deprecated version of CPPAD_TRACK_DEL_VEC # undef CppADTrackExtend deprecated version of CPPAD_TRACK_EXTEND # undef CppADTrackNewVec deprecated version of CPPAD_TRACK_NEW_VEC # undef CppADvector deprecated version of CPPAD_TEST_VECTOR // for conditional testing when implicit conversion is not present # undef CPPAD_DEPRECATED ----------------------------------------------------------------------------- */ // Preprecessor definitions that do not presist # undef CPPAD_ASSERT_NARG_NRES # undef CPPAD_ASSERT_ARG_BEFORE_RESULT # undef CPPAD_AZMUL # undef CPPAD_BOOSTVECTOR # undef CPPAD_COND_EXP # undef CPPAD_COND_EXP_BASE_REL # undef CPPAD_COND_EXP_REL # undef CPPAD_CPPADVECTOR # undef CPPAD_FOLD_AD_VALUED_BINARY_OPERATOR # undef CPPAD_FOLD_ASSIGNMENT_OPERATOR # undef CPPAD_FOLD_BOOL_VALUED_BINARY_OPERATOR # undef CPPAD_FOR_JAC_SWEEP_TRACE # undef CPPAD_HAS_GETTIMEOFDAY # undef CPPAD_HAS_MKSTEMP # undef CPPAD_HAS_TMPNAM_S # undef CPPAD_INLINE_FRIEND_TEMPLATE_FUNCTION # undef CPPAD_LIB_EXPORT # undef CPPAD_MAX_NUM_CAPACITY # undef CPPAD_MIN_DOUBLE_CAPACITY # undef CPPAD_OP_CODE_TYPE # undef CPPAD_REVERSE_SWEEP_TRACE # undef CPPAD_REV_HES_SWEEP_TRACE # undef CPPAD_REV_JAC_SWEEP_TRACE # undef CPPAD_SIZE_T_NOT_UNSIGNED_INT # undef CPPAD_STANDARD_MATH_UNARY_AD # undef CPPAD_STDVECTOR # undef CPPAD_TRACE_CAPACITY # undef CPPAD_TRACE_THREAD # undef CPPAD_TRACK_DEBUG # undef CPPAD_USER_MACRO # undef CPPAD_USER_MACRO_ONE # undef CPPAD_USER_MACRO_TWO # undef CPPAD_VEC_AD_COMPUTED_ASSIGNMENT # endif cppad-20170000.3/cppad/core/base_to_string.hpp0000644000175200017650000000367013057470466020176 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BASE_TO_STRING_HPP # define CPPAD_CORE_BASE_TO_STRING_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_to_string$$ $spell std namespace CppAD struct const stringstream setprecision str $$ $section Extending to_string To Another Floating Point Type$$ $head Base Requirement$$ If the function $cref to_string$$ is used by an $cref/AD type above Base/glossary/AD Type Above Base/$$, A specialization for the template structure $code CppAD::to_string_struct$$ must be defined. $head CPPAD_TO_STRING$$ For most $icode Base$$ types, the following can be used to define the specialization: $codei% namespace CppAD { CPPAD_TO_STRING(%Base%) } %$$ Note that the $code CPPAD_TO_STRING$$ macro assumes that the $cref base_limits$$ and $cref base_std_math$$ have already been defined for this type. This macro is defined as follows: $srccode%cpp% */ # define CPPAD_TO_STRING(Base) \ template <> struct to_string_struct\ { std::string operator()(const Base& value) \ { std::stringstream os;\ Base epsilon = CppAD::numeric_limits::epsilon();\ Base log10 = CppAD::log( epsilon ) / CppAD::log(Base(10.));\ size_t n_digits = 1 - Integer( log10 );\ os << std::setprecision(n_digits);\ os << value;\ return os.str();\ }\ }; /* %$$ $end ------------------------------------------------------------------------------ */ // make sure to_string has been included # include # endif cppad-20170000.3/cppad/core/pow.hpp0000644000175200017650000001632513057470466016002 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_POW_HPP # define CPPAD_CORE_POW_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin pow$$ $spell Vec std namespace CppAD const $$ $section The AD Power Function$$ $mindex pow exponent$$ $head Syntax$$ $icode%z% = pow(%x%, %y%)%$$ $head See Also$$ $cref pow_int$$ $head Purpose$$ Determines the value of the power function which is defined by $latex \[ {\rm pow} (x, y) = x^y \] $$ This version of the $code pow$$ function may use logarithms and exponentiation to compute derivatives. This will not work if $icode x$$ is less than or equal zero. If the value of $icode y$$ is an integer, the $cref pow_int$$ function is used to compute this value using only multiplication (and division if $icode y$$ is negative). (This will work even if $icode x$$ is less than or equal zero.) $head x$$ The argument $icode x$$ has one of the following prototypes $codei% const %Base%& %x% const AD<%Base%>& %x% const VecAD<%Base%>::reference& %x% %$$ $head y$$ The argument $icode y$$ has one of the following prototypes $codei% const %Base%& %y% const AD<%Base%>& %y% const VecAD<%Base%>::reference& %y% %$$ $head z$$ If both $icode x$$ and $icode y$$ are $icode Base$$ objects, the result $icode z$$ is also a $icode Base$$ object. Otherwise, it has prototype $codei% AD<%Base%> %z% %$$ $head Operation Sequence$$ This is an AD of $icode Base$$ $cref/atomic operation/glossary/Operation/Atomic/$$ and hence is part of the current AD of $icode Base$$ $cref/operation sequence/glossary/Operation/Sequence/$$. $head Example$$ $children% example/pow.cpp %$$ The file $cref pow.cpp$$ is an examples and tests of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { // case where x and y are AD ----------------------------------------- template AD pow(const AD& x, const AD& y) { // compute the Base part AD result; result.value_ = pow(x.value_, y.value_); CPPAD_ASSERT_UNKNOWN( Parameter(result) ); // check if there is a recording in progress local::ADTape* tape = AD::tape_ptr(); if( tape == CPPAD_NULL ) return result; tape_id_t tape_id = tape->id_; // tape_id cannot match the default value for tape_id_; i.e., 0 CPPAD_ASSERT_UNKNOWN( tape_id > 0 ); bool var_x = x.tape_id_ == tape_id; bool var_y = y.tape_id_ == tape_id; if( var_x ) { if( var_y ) { // result = variable^variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::PowvvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::PowvvOp) == 2 ); // put operand addresses in tape tape->Rec_.PutArg(x.taddr_, y.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::PowvvOp); // make result a variable result.tape_id_ = tape_id; } else if( IdenticalZero( y.value_ ) ) { // result = variable^0 } else { // result = variable^parameter CPPAD_ASSERT_UNKNOWN( local::NumRes(local::PowvpOp) == 3 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::PowvpOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(y.value_); tape->Rec_.PutArg(x.taddr_, p); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::PowvpOp); // make result a variable result.tape_id_ = tape_id; } } else if( var_y ) { if( IdenticalZero(x.value_) ) { // result = 0^variable } else { // result = parameter^variable CPPAD_ASSERT_UNKNOWN( local::NumRes(local::PowpvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( local::NumArg(local::PowpvOp) == 2 ); // put operand addresses in tape addr_t p = tape->Rec_.PutPar(x.value_); tape->Rec_.PutArg(p, y.taddr_); // put operator in the tape result.taddr_ = tape->Rec_.PutOp(local::PowpvOp); // make result a variable result.tape_id_ = tape_id; } } return result; } // ========================================================================= // Fold operations in same way as CPPAD_FOLD_AD_VALUED_BINARY_OPERATOR(Op) // ------------------------------------------------------------------------- // Operations with VecAD_reference and AD only template AD pow(const AD& x, const VecAD_reference& y) { return pow(x, y.ADBase()); } template AD pow(const VecAD_reference& x, const VecAD_reference& y) { return pow(x.ADBase(), y.ADBase()); } template AD pow(const VecAD_reference& x, const AD& y) { return pow(x.ADBase(), y); } // ------------------------------------------------------------------------- // Operations with Base template AD pow(const Base& x, const AD& y) { return pow(AD(x), y); } template AD pow(const Base& x, const VecAD_reference& y) { return pow(AD(x), y.ADBase()); } template AD pow(const AD& x, const Base& y) { return pow(x, AD(y)); } template AD pow(const VecAD_reference& x, const Base& y) { return pow(x.ADBase(), AD(y)); } // ------------------------------------------------------------------------- // Operations with double template AD pow(const double& x, const AD& y) { return pow(AD(x), y); } template AD pow(const double& x, const VecAD_reference& y) { return pow(AD(x), y.ADBase()); } template AD pow(const AD& x, const double& y) { return pow(x, AD(y)); } template AD pow(const VecAD_reference& x, const double& y) { return pow(x.ADBase(), AD(y)); } // ------------------------------------------------------------------------- // Special case to avoid ambuigity when Base is double inline AD pow(const double& x, const AD& y) { return pow(AD(x), y); } inline AD pow(const double& x, const VecAD_reference& y) { return pow(AD(x), y.ADBase()); } inline AD pow(const AD& x, const double& y) { return pow(x, AD(y)); } inline AD pow(const VecAD_reference& x, const double& y) { return pow(x.ADBase(), AD(y)); } // ========================================================================= // Fold operations for the cases where x is an int, // but let cppad/pow_int.hpp handle the cases where y is an int. // ------------------------------------------------------------------------- template AD pow (const int& x, const VecAD_reference& y) { return pow(AD(x), y.ADBase()); } template AD pow (const int& x, const AD& y) { return pow(AD(x), y); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/cppad_assert.hpp0000644000175200017650000001456713057470466017653 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_CPPAD_ASSERT_HPP # define CPPAD_CORE_CPPAD_ASSERT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file cppad_assert.hpp Define the CppAD error checking macros (all of which begin with CPPAD_ASSERT_) */ /* ------------------------------------------------------------------------------- $begin cppad_assert$$ $spell CppAD exp const bool $$ $section CppAD Assertions During Execution$$ $mindex assert macro CPPAD_ASSERT_KNOWN CPPAD_ASSERT_UNKNOWN$$ $head Syntax$$ $codei%CPPAD_ASSERT_KNOWN(%exp%, %msg%) %$$ $codei%CPPAD_ASSERT_UNKNOWN(%exp%)%$$ $head Purpose$$ These CppAD macros are used to detect and report errors. They are documented here because they correspond to the C++ source code that the error is reported at. $head NDEBUG$$ If the preprocessor symbol $cref/NDEBUG/Faq/Speed/NDEBUG/$$ is defined, these macros do nothing; i.e., they are optimized out. $head Restriction$$ The CppAD user should not uses these macros. You can however write your own macros that do not begin with $code CPPAD$$ and that call the $cref/CppAD error handler/ErrorHandler/$$. $head Known$$ The $code CPPAD_ASSERT_KNOWN$$ macro is used to check for an error with a known cause. For example, many CppAD routines uses these macros to make sure their arguments conform to their specifications. $head Unknown$$ The $code CPPAD_ASSERT_UNKNOWN$$ macro is used to check that the CppAD internal data structures conform as expected. If this is not the case, CppAD does not know why the error has occurred; for example, the user may have written past the end of an allocated array. $head Exp$$ The argument $icode exp$$ is a C++ source code expression that results in a $code bool$$ value that should be true. If it is false, an error has occurred. This expression may be execute any number of times (including zero times) so it must have not side effects. $head Msg$$ The argument $icode msg$$ has prototype $codei% const char *%msg% %$$ and contains a $code '\0'$$ terminated character string. This string is a description of the error corresponding to $icode exp$$ being false. $head Error Handler$$ These macros use the $cref/CppAD error handler/ErrorHandler/$$ to report errors. This error handler can be replaced by the user. $end ------------------------------------------------------------------------------ */ # include # include # include /*! \def CPPAD_ASSERT_KNOWN(exp, msg) Check that \a exp is true, if not print \a msg and terminate execution. The C++ expression \a exp is expected to be true. If it is false, the CppAD use has made an error that is described by \a msg. If the preprocessor symbol \a NDEBUG is not defined, and \a exp is false, this macro will report the source code line number at which this expected result occurred. In addition, it will print the specified error message \a msg. */ # ifdef NDEBUG # define CPPAD_ASSERT_KNOWN(exp, msg) // do nothing # else # define CPPAD_ASSERT_KNOWN(exp, msg) \ { if( ! ( exp ) ) \ CppAD::ErrorHandler::Call( \ true , \ __LINE__ , \ __FILE__ , \ #exp , \ msg ); \ } # endif /*! \def CPPAD_ASSERT_UNKNOWN(exp) Check that \a exp is true, if not terminate execution. The C++ expression \a exp is expected to be true. If it is false, CppAD has detected an error but does not know the cause of the error. If the preprocessor symbol \a NDEBUG is not defined, and \a exp is false, this macro will report the source code line number at which this expected result occurred. */ # ifdef NDEBUG # define CPPAD_ASSERT_UNKNOWN(exp) // do nothing # else # define CPPAD_ASSERT_UNKNOWN(exp) \ { if( ! ( exp ) ) \ CppAD::ErrorHandler::Call( \ false , \ __LINE__ , \ __FILE__ , \ #exp , \ "" ); \ } # endif /*! \def CPPAD_ASSERT_NARG_NRES(op, n_arg, n_res) Check that operator \a op has the specified number of of arguments and results. If \a NDEBUG is not defined and either the number of arguments or the number of results are not as expected, execution is terminated and the source code line number is reported. */ # define CPPAD_ASSERT_NARG_NRES(op, n_arg, n_res) \ CPPAD_ASSERT_UNKNOWN( NumArg(op) == n_arg ) \ CPPAD_ASSERT_UNKNOWN( NumRes(op) == n_res ) /*! \def CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL Check that the first call to a routine is not during parallel execution mode. If \c NDEBUG is defined, this macro has no effect (not even the definition of (\c assert_first_call). Otherwise, the variable \code static bool assert_first_call \endcode is defined and if the first call is executed in parallel mode, execution is terminated and the source code line number is reported. */ # ifdef NDEBUG # define CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # else # define CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL \ static bool assert_first_call = true; \ if( assert_first_call ) \ { CPPAD_ASSERT_KNOWN( \ ! (CppAD::thread_alloc::in_parallel() ), \ "In parallel mode and parallel_setup has not been called." \ ); \ assert_first_call = false; \ } # endif /*! \def CPPAD_ASSERT_ARG_BEFORE_RESULT Check that operator arguments come before result. If \c NDEBUG is defined, this macro has no effect, otherwise it calls the function assert_arg_before_result. */ # ifdef NDEBUG # define CPPAD_ASSERT_ARG_BEFORE_RESULT(op, arg, result) # else # define CPPAD_ASSERT_ARG_BEFORE_RESULT(op, arg, result) \ assert_arg_before_result(op, arg, result) # endif # endif cppad-20170000.3/cppad/core/old_atomic.hpp0000644000175200017650000010174413057470466017307 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_OLD_ATOMIC_HPP # define CPPAD_CORE_OLD_ATOMIC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin old_atomic$$ $spell hes std Jacobian jac Tvector afun vx vy bool namespace CppAD const Taylor tx ty px py $$ $section User Defined Atomic AD Functions$$ $mindex operation old_atomic$$ $head Deprecated 2013-05-27$$ Using $code CPPAD_USER_ATOMIC$$ has been deprecated. Use $cref atomic_base$$ instead. $head Syntax Function$$ $codei%CPPAD_USER_ATOMIC(%afun%, %Tvector%, %Base%, %forward%, %reverse%, %for_jac_sparse%, %rev_jac_sparse%, %rev_hes_sparse% ) %$$ $subhead Use Function$$ $icode%afun%(%id%, %ax%, %ay%) %$$ $subhead Callback Routines$$ $icode%ok% = %forward%(%id%, %k%, %n%, %m%, %vx%, %vy%, %tx%, %ty%) %$$ $icode%ok% = %reverse%(%id%, %k%, %n%, %m%, %tx%, %ty%, %px%, %py%) %$$ $icode%ok% = %for_jac_sparse%(%id%, %n%, %m%, %q%, %r%, %s%) %$$ $icode%ok% = %rev_jac_sparse%(%id%, %n%, %m%, %q%, %r%, %s%) %$$ $icode%ok% = %rev_hes_sparse%(%id%, %n%, %m%, %q%, %r%, %s%, %t%, %u%, %v%) %$$ $subhead Free Static Memory$$ $codei%user_atomic<%Base%>::clear()%$$ $head Purpose$$ In some cases, the user knows how to compute the derivative of a function $latex \[ y = f(x) \; {\rm where} \; f : B^n \rightarrow B^m \] $$ more efficiently than by coding it using $codei%AD<%Base%>%$$ $cref/atomic/glossary/Operation/Atomic/$$ operations and letting CppAD do the rest. In this case, $code CPPAD_USER_ATOMIC$$ can be used add the user code for $latex f(x)$$, and its derivatives, to the set of $codei%AD<%Base%>%$$ atomic operations. $pre $$ Another possible purpose is to reduce the size of the tape; see $cref/use AD/old_atomic/Example/Use AD/$$ $head Partial Implementation$$ The routines $cref/forward/old_atomic/forward/$$, $cref/reverse/old_atomic/reverse/$$, $cref/for_jac_sparse/old_atomic/for_jac_sparse/$$, $cref/rev_jac_sparse/old_atomic/rev_jac_sparse/$$, and $cref/rev_hes_sparse/old_atomic/rev_hes_sparse/$$, must be defined by the user. The $icode forward$$ the routine, for the case $icode%k% = 0%$$, must be implemented. Functions with the correct prototype, that just return $code false$$, can be used for the other cases (unless they are required by your calculations). For example, you need not implement $icode forward$$ for the case $icode%k% == 2%$$ until you require forward mode calculation of second derivatives. $head CPPAD_USER_ATOMIC$$ The macro $codei% CPPAD_USER_ATOMIC(%afun%, %Tvector%, %Base%, %forward%, %reverse%, %for_jac_sparse%, %rev_jac_sparse%, %rev_hes_sparse% ) %$$ defines the $codei%AD<%Base%>%$$ routine $icode afun$$. This macro can be placed within a namespace (not the $code CppAD$$ namespace) but must be outside of any routine. $subhead Tvector$$ The macro argument $icode Tvector$$ must be a $cref/simple vector template class/SimpleVector/$$. It determines the type of vectors used as arguments to the routine $icode afun$$. $subhead Base$$ The macro argument $icode Base$$ specifies the $cref/base type/base_require/$$ corresponding to $codei%AD<%Base>%$$ operation sequences. Calling the routine $icode afun$$ will add the operator defined by this macro to an $codei%AD<%Base>%$$ operation sequence. $head ok$$ For all routines documented below, the return value $icode ok$$ has prototype $codei% bool %ok% %$$ If it is $code true$$, the corresponding evaluation succeeded, otherwise it failed. $head id$$ For all routines documented below, the argument $icode id$$ has prototype $codei% size_t %id% %$$ Its value in all other calls is the same as in the corresponding call to $icode afun$$. It can be used to store and retrieve extra information about a specific call to $icode afun$$. $head k$$ For all routines documented below, the argument $icode k$$ has prototype $codei% size_t %k% %$$ The value $icode%k%$$ is the order of the Taylor coefficient that we are evaluating ($cref/forward/old_atomic/forward/$$) or taking the derivative of ($cref/reverse/old_atomic/reverse/$$). $head n$$ For all routines documented below, the argument $icode n$$ has prototype $codei% size_t %n% %$$ It is the size of the vector $icode ax$$ in the corresponding call to $icode%afun%(%id%, %ax%, %ay%)%$$; i.e., the dimension of the domain space for $latex y = f(x)$$. $head m$$ For all routines documented below, the argument $icode m$$ has prototype $codei% size_t %m% %$$ It is the size of the vector $icode ay$$ in the corresponding call to $icode%afun%(%id%, %ax%, %ay%)%$$; i.e., the dimension of the range space for $latex y = f(x)$$. $head tx$$ For all routines documented below, the argument $icode tx$$ has prototype $codei% const CppAD::vector<%Base%>& %tx% %$$ and $icode%tx%.size() >= (%k% + 1) * %n%$$. For $latex j = 0 , \ldots , n-1$$ and $latex \ell = 0 , \ldots , k$$, we use the Taylor coefficient notation $latex \[ \begin{array}{rcl} x_j^\ell & = & tx [ j * ( k + 1 ) + \ell ] \\ X_j (t) & = & x_j^0 + x_j^1 t^1 + \cdots + x_j^k t^k \end{array} \] $$ If $icode%tx%.size() > (%k% + 1) * %n%$$, the other components of $icode tx$$ are not specified and should not be used. Note that superscripts represent an index for $latex x_j^\ell$$ and an exponent for $latex t^\ell$$. Also note that the Taylor coefficients for $latex X(t)$$ correspond to the derivatives of $latex X(t)$$ at $latex t = 0$$ in the following way: $latex \[ x_j^\ell = \frac{1}{ \ell ! } X_j^{(\ell)} (0) \] $$ $head ty$$ In calls to $cref/forward/old_atomic/forward/$$, the argument $icode ty$$ has prototype $codei% CppAD::vector<%Base%>& %ty% %$$ while in calls to $cref/reverse/old_atomic/reverse/$$ it has prototype $codei% const CppAD::vector<%Base%>& %ty% %$$ For all calls, $icode%tx%.size() >= (%k% + 1) * %m%$$. For $latex i = 0 , \ldots , m-1$$ and $latex \ell = 0 , \ldots , k$$, we use the Taylor coefficient notation $latex \[ \begin{array}{rcl} y_i^\ell & = & ty [ i * ( k + 1 ) + \ell ] \\ Y_i (t) & = & y_i^0 + y_i^1 t^1 + \cdots + y_i^k t^k + o ( t^k ) \end{array} \] $$ where $latex o( t^k ) / t^k \rightarrow 0$$ as $latex t \rightarrow 0$$. If $icode%ty%.size() > (%k% + 1) * %m%$$, the other components of $icode ty$$ are not specified and should not be used. Note that superscripts represent an index for $latex y_j^\ell$$ and an exponent for $latex t^\ell$$. Also note that the Taylor coefficients for $latex Y(t)$$ correspond to the derivatives of $latex Y(t)$$ at $latex t = 0$$ in the following way: $latex \[ y_j^\ell = \frac{1}{ \ell ! } Y_j^{(\ell)} (0) \] $$ $subhead forward$$ In the case of $icode forward$$, for $latex i = 0 , \ldots , m-1$$, $latex ty[ i *( k + 1) + k ]$$ is an output and all the other components of $icode ty$$ are inputs. $subhead reverse$$ In the case of $icode reverse$$, all the components of $icode ty$$ are inputs. $head afun$$ The macro argument $icode afun$$, is the name of the AD function corresponding to this atomic operation (as it is used in the source code). CppAD uses the other functions, where the arguments are vectors with elements of type $icode Base$$, to implement the function $codei% %afun%(%id%, %ax%, %ay%) %$$ where the argument are vectors with elements of type $codei%AD<%Base%>%$$. $subhead ax$$ The $icode afun$$ argument $icode ax$$ has prototype $codei% const %Tvector%< AD<%Base%> >& %ax% %$$ It is the argument vector $latex x \in B^n$$ at which the $codei%AD<%Base%>%$$ version of $latex y = f(x)$$ is to be evaluated. The dimension of the domain space for $latex y = f (x)$$ is specified by $cref/n/old_atomic/n/$$ $codei%= %ax%.size()%$$, which must be greater than zero. $subhead ay$$ The $icode afun$$ result $icode ay$$ has prototype $codei% %Tvector%< AD<%Base%> >& %ay% %$$ The input values of its elements are not specified (must not matter). Upon return, it is the $codei%AD<%Base%>%$$ version of the result vector $latex y = f(x)$$. The dimension of the range space for $latex y = f (x)$$ is specified by $cref/m/old_atomic/m/$$ $codei%= %ay%.size()%$$, which must be greater than zero. $subhead Parallel Mode$$ The first call to $codei% %afun%(%id%, %ax%, %ay%) %$$ must not be in $cref/parallel/ta_in_parallel/$$ mode. In addition, the $cref/old_atomic clear/old_atomic/clear/$$ routine cannot be called while in parallel mode. $head forward$$ The macro argument $icode forward$$ is a user defined function $codei% %ok% = %forward%(%id%, %k%, %n%, %m%, %vx%, %vy%, %tx%, %ty%) %$$ that computes results during a $cref/forward/Forward/$$ mode sweep. For this call, we are given the Taylor coefficients in $icode tx$$ form order zero through $icode k$$, and the Taylor coefficients in $icode ty$$ with order less than $icode k$$. The $icode forward$$ routine computes the $icode k$$ order Taylor coefficients for $latex y$$ using the definition $latex Y(t) = f[ X(t) ]$$. For example, for $latex i = 0 , \ldots , m-1$$, $latex \[ \begin{array}{rcl} y_i^0 & = & Y(0) = f_i ( x^0 ) \\ y_i^1 & = & Y^{(1)} ( 0 ) = f_i^{(1)} ( x^0 ) X^{(1)} ( 0 ) = f_i^{(1)} ( x^0 ) x^1 \\ y_i^2 & = & \frac{1}{2 !} Y^{(2)} (0) \\ & = & \frac{1}{2} X^{(1)} (0)^\R{T} f_i^{(2)} ( x^0 ) X^{(1)} ( 0 ) + \frac{1}{2} f_i^{(1)} ( x^0 ) X^{(2)} ( 0 ) \\ & = & \frac{1}{2} (x^1)^\R{T} f_i^{(2)} ( x^0 ) x^1 + f_i^{(1)} ( x^0 ) x^2 \end{array} \] $$ Then, for $latex i = 0 , \ldots , m-1$$, it sets $latex \[ ty [ i * (k + 1) + k ] = y_i^k \] $$ The other components of $icode ty$$ must be left unchanged. $subhead Usage$$ This routine is used, with $icode%vx%.size() > 0%$$ and $icode%k% == 0%$$, by calls to $icode afun$$. It is used, with $icode%vx%.size() = 0%$$ and $icode k$$ equal to the order of the derivative begin computed, by calls to $cref/forward/forward_order/$$. $subhead vx$$ The $icode forward$$ argument $icode vx$$ has prototype $codei% const CppAD::vector& %vx% %$$ The case $icode%vx%.size() > 0%$$ occurs once for each call to $icode afun$$, during the call, and before any of the other callbacks corresponding to that call. Hence such a call can be used to cache information attached to the corresponding $icode id$$ (such as the elements of $icode vx$$). If $icode%vx%.size() > 0%$$ then $icode%k% == 0%$$, $icode%vx%.size() >= %n%$$, and for $latex j = 0 , \ldots , n-1$$, $icode%vx%[%j%]%$$ is true if and only if $icode%ax%[%j%]%$$ is a $cref/variable/glossary/Variable/$$. $pre $$ If $icode%vx%.size() == 0%$$, then $icode%vy%.size() == 0%$$ and neither of these vectors should be used. $subhead vy$$ The $icode forward$$ argument $icode vy$$ has prototype $codei% CppAD::vector& %vy% %$$ If $icode%vy%.size() == 0%$$, it should not be used. Otherwise, $icode%k% == 0%$$ and $icode%vy%.size() >= %m%$$. The input values of the elements of $icode vy$$ are not specified (must not matter). Upon return, for $latex j = 0 , \ldots , m-1$$, $icode%vy%[%i%]%$$ is true if and only if $icode%ay%[%j%]%$$ is a variable. (CppAD uses $icode vy$$ to reduce the necessary computations.) $head reverse$$ The macro argument $icode reverse$$ is a user defined function $codei% %ok% = %reverse%(%id%, %k%, %n%, %m%, %tx%, %ty%, %px%, %py%) %$$ that computes results during a $cref/reverse/Reverse/$$ mode sweep. The input value of the vectors $icode tx$$ and $icode ty$$ contain Taylor coefficient, up to order $icode k$$, for $latex X(t)$$ and $latex Y(t)$$ respectively. We use the $latex \{ x_j^\ell \}$$ and $latex \{ y_i^\ell \}$$ to denote these Taylor coefficients where the implicit range indices are $latex i = 0 , \ldots , m-1$$, $latex j = 0 , \ldots , n-1$$, $latex \ell = 0 , \ldots , k$$. Using the calculations done by $cref/forward/old_atomic/forward/$$, the Taylor coefficients $latex \{ y_i^\ell \}$$ are a function of the Taylor coefficients for $latex \{ x_j^\ell \}$$; i.e., given $latex y = f(x)$$ we define the function $latex F : B^{n \times (k+1)} \rightarrow B^{m \times (k+1)}$$ by $latex \[ y_i^\ell = F_i^\ell ( \{ x_j^\ell \} ) \] $$ We use $latex G : B^{m \times (k+1)} \rightarrow B$$ to denote an arbitrary scalar valued function of the Taylor coefficients for $latex Y(t)$$ and write $latex z = G( \{ y_i^\ell \} )$$. The $code reverse$$ routine is given the derivative of $latex z$$ with respect to $latex \{ y_i^\ell \}$$ and computes its derivative with respect to $latex \{ x_j^\ell \}$$. $subhead Usage$$ This routine is used, with $icode%k% + 1%$$ equal to the order of the derivative being calculated, by calls to $cref/reverse/reverse_any/$$. $subhead py$$ The $icode reverse$$ argument $icode py$$ has prototype $codei% const CppAD::vector<%Base%>& %py% %$$ and $icode%py%.size() >= (%k% + 1) * %m%$$. For $latex i = 0 , \ldots , m-1$$ and $latex \ell = 0 , \ldots , k$$, $latex \[ py[ i * (k + 1 ) + \ell ] = \partial G / \partial y_i^\ell \] $$ If $icode%py%.size() > (%k% + 1) * %m%$$, the other components of $icode py$$ are not specified and should not be used. $subhead px$$ We define the function $latex \[ H ( \{ x_j^\ell \} ) = G[ F( \{ x_j^\ell \} ) ] \] $$ The $icode reverse$$ argument $icode px$$ has prototype $codei% CppAD::vector<%Base%>& %px% %$$ and $icode%px%.size() >= (%k% + 1) * %n%$$. The input values of the elements of $icode px$$ are not specified (must not matter). Upon return, for $latex j = 0 , \ldots , n-1$$ and $latex p = 0 , \ldots , k$$, $latex \[ \begin{array}{rcl} px [ j * (k + 1) + p ] & = & \partial H / \partial x_j^p \\ & = & ( \partial G / \partial \{ y_i^\ell \} ) ( \partial \{ y_i^\ell \} / \partial x_j^p ) \\ & = & \sum_{i=0}^{m-1} \sum_{\ell=0}^k ( \partial G / \partial y_i^\ell ) ( \partial y_i^\ell / \partial x_j^p ) \\ & = & \sum_{i=0}^{m-1} \sum_{\ell=p}^k py[ i * (k + 1 ) + \ell ] ( \partial F_i^\ell / \partial x_j^p ) \end{array} \] $$ Note that we have used the fact that for $latex \ell < p$$, $latex \partial F_i^\ell / \partial x_j^p = 0$$. If $icode%px%.size() > (%k% + 1) * %n%$$, the other components of $icode px$$ are not specified and should not be used. $head for_jac_sparse$$ The macro argument $icode for_jac_sparse$$ is a user defined function $codei% %ok% = %for_jac_sparse%(%id%, %n%, %m%, %q%, %r%, %s%) %$$ that is used to compute results during a forward Jacobian sparsity sweep. For a fixed $latex n \times q$$ matrix $latex R$$, the Jacobian of $latex f( x + R * u)$$ with respect to $latex u \in B^q$$ is $latex \[ S(x) = f^{(1)} (x) * R \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex R$$, $icode for_jac_sparse$$ computes a sparsity pattern for $latex S(x)$$. $subhead Usage$$ This routine is used by calls to $cref ForSparseJac$$. $subhead q$$ The $icode for_jac_sparse$$ argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of columns in $latex R \in B^{n \times q}$$ and the Jacobian $latex S(x) \in B^{m \times q}$$. $subhead r$$ The $icode for_jac_sparse$$ argument $icode r$$ has prototype $codei% const CppAD::vector< std::set >& %r% %$$ and $icode%r%.size() >= %n%$$. For $latex j = 0 , \ldots , n-1$$, all the elements of $icode%r%[%j%]%$$ are between zero and $icode%q%-1%$$ inclusive. This specifies a sparsity pattern for the matrix $latex R$$. $subhead s$$ The $icode for_jac_sparse$$ return value $icode s$$ has prototype $codei% CppAD::vector< std::set >& %s% %$$ and $icode%s%.size() >= %m%%$$. The input values of its sets are not specified (must not matter). Upon return for $latex i = 0 , \ldots , m-1$$, all the elements of $icode%s%[%i%]%$$ are between zero and $icode%q%-1%$$ inclusive. This represents a sparsity pattern for the matrix $latex S(x)$$. $head rev_jac_sparse$$ The macro argument $icode rev_jac_sparse$$ is a user defined function $codei% %ok% = %rev_jac_sparse%(%id%, %n%, %m%, %q%, %r%, %s%) %$$ that is used to compute results during a reverse Jacobian sparsity sweep. For a fixed $latex q \times m$$ matrix $latex S$$, the Jacobian of $latex S * f( x )$$ with respect to $latex x \in B^n$$ is $latex \[ R(x) = S * f^{(1)} (x) \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex S$$, $icode rev_jac_sparse$$ computes a sparsity pattern for $latex R(x)$$. $subhead Usage$$ This routine is used by calls to $cref RevSparseJac$$ and to $cref optimize$$. $subhead q$$ The $icode rev_jac_sparse$$ argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of rows in $latex S \in B^{q \times m}$$ and the Jacobian $latex R(x) \in B^{q \times n}$$. $subhead s$$ The $icode rev_jac_sparse$$ argument $icode s$$ has prototype $codei% const CppAD::vector< std::set >& %s% %$$ and $icode%s%.size() >= %m%$$. For $latex i = 0 , \ldots , m-1$$, all the elements of $icode%s%[%i%]%$$ are between zero and $icode%q%-1%$$ inclusive. This specifies a sparsity pattern for the matrix $latex S^\R{T}$$. $subhead r$$ The $icode rev_jac_sparse$$ return value $icode r$$ has prototype $codei% CppAD::vector< std::set >& %r% %$$ and $icode%r%.size() >= %n%$$. The input values of its sets are not specified (must not matter). Upon return for $latex j = 0 , \ldots , n-1$$, all the elements of $icode%r%[%j%]%$$ are between zero and $icode%q%-1%$$ inclusive. This represents a sparsity pattern for the matrix $latex R(x)^\R{T}$$. $head rev_hes_sparse$$ The macro argument $icode rev_hes_sparse$$ is a user defined function $codei% %ok% = %rev_hes_sparse%(%id%, %n%, %m%, %q%, %r%, %s%, %t%, %u%, %v%) %$$ There is an unspecified scalar valued function $latex g : B^m \rightarrow B$$. Given a sparsity pattern for $latex R$$ and information about the function $latex z = g(y)$$, this routine computes the sparsity pattern for $latex \[ V(x) = (g \circ f)^{(2)}( x ) R \] $$ $subhead Usage$$ This routine is used by calls to $cref RevSparseHes$$. $subhead q$$ The $icode rev_hes_sparse$$ argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of columns in the sparsity patterns. $subhead r$$ The $icode rev_hes_sparse$$ argument $icode r$$ has prototype $codei% const CppAD::vector< std::set >& %r% %$$ and $icode%r%.size() >= %n%$$. For $latex j = 0 , \ldots , n-1$$, all the elements of $icode%r%[%j%]%$$ are between zero and $icode%q%-1%$$ inclusive. This specifies a sparsity pattern for the matrix $latex R \in B^{n \times q}$$. $subhead s$$ The $icode rev_hes_sparse$$ argument $icode s$$ has prototype $codei% const CppAD::vector& %s% %$$ and $icode%s%.size() >= %m%$$. This specifies a sparsity pattern for the matrix $latex S(x) = g^{(1)} (y) \in B^{1 \times m}$$. $subhead t$$ The $icode rev_hes_sparse$$ argument $icode t$$ has prototype $codei% CppAD::vector& %t% %$$ and $icode%t%.size() >= %n%$$. The input values of its elements are not specified (must not matter). Upon return it represents a sparsity pattern for the matrix $latex T(x) \in B^{1 \times n}$$ defined by $latex \[ T(x) = (g \circ f)^{(1)} (x) = S(x) * f^{(1)} (x) \] $$ $subhead u$$ The $icode rev_hes_sparse$$ argument $icode u$$ has prototype $codei% const CppAD::vector< std::set >& %u% %$$ and $icode%u%.size() >= %m%$$. For $latex i = 0 , \ldots , m-1$$, all the elements of $icode%u%[%i%]%$$ are between zero and $icode%q%-1%$$ inclusive. This specifies a sparsity pattern for the matrix $latex U(x) \in B^{m \times q}$$ defined by $latex \[ \begin{array}{rcl} U(x) & = & \partial_u \{ \partial_y g[ y + f^{(1)} (x) R u ] \}_{u=0} \\ & = & \partial_u \{ g^{(1)} [ y + f^{(1)} (x) R u ] \}_{u=0} \\ & = & g^{(2)} (y) f^{(1)} (x) R \end{array} \] $$ $subhead v$$ The $icode rev_hes_sparse$$ argument $icode v$$ has prototype $codei% CppAD::vector< std::set >& %v% %$$ and $icode%v%.size() >= %n%$$. The input values of its elements are not specified (must not matter). Upon return, for $latex j = 0, \ldots , n-1$$, all the elements of $icode%v%[%j%]%$$ are between zero and $icode%q%-1%$$ inclusive. This represents a sparsity pattern for the matrix $latex V(x) \in B^{n \times q}$$ defined by $latex \[ \begin{array}{rcl} V(x) & = & \partial_u [ \partial_x (g \circ f) ( x + R u ) ]_{u=0} \\ & = & \partial_u [ (g \circ f)^{(1)}( x + R u ) ]_{u=0} \\ & = & (g \circ f)^{(2)}( x ) R \\ & = & f^{(1)} (x)^\R{T} g^{(2)} ( y ) f^{(1)} (x) R + \sum_{i=1}^m [ g^{(1)} (y) ]_i \; f_i^{(2)} (x) R \\ & = & f^{(1)} (x)^\R{T} U(x) + \sum_{i=1}^m S(x)_i \; f_i^{(2)} (x) R \end{array} \] $$ $head clear$$ User atomic functions hold onto static work space in order to increase speed by avoiding system memory allocation calls. The function call $codei% user_atomic<%Base%>::clear() %$$ makes to work space $cref/available/ta_available/$$ to for other uses by the same thread. This should be called when you are done using the user atomic functions for a specific value of $icode Base$$. $subhead Restriction$$ The user atomic $code clear$$ routine cannot be called while in $cref/parallel/ta_in_parallel/$$ execution mode. $children% test_more/old_reciprocal.cpp% test_more/old_usead_1.cpp% test_more/old_usead_2.cpp% test_more/old_tan.cpp% test_more/old_mat_mul.cpp %$$ $head Example$$ $subhead Simple$$ The file $cref old_reciprocal.cpp$$ contains the simplest example and test of a user atomic operation. $subhead Use AD$$ The examples $cref old_usead_1.cpp$$ and $cref old_usead_2.cpp$$ use AD to compute the derivatives inside a user defined atomic function. This may have the advantage of reducing the size of the tape, because a repeated section of code would only be taped once. $subhead Tangent Function$$ The file $cref old_tan.cpp$$ contains an example and test implementation of the tangent function as a user atomic operation. $subhead Matrix Multiplication$$ The file $cref old_mat_mul.cpp$$ contains an example and test implementation of matrix multiplication a a user atomic operation. $end ------------------------------------------------------------------------------ */ # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file old_atomic.hpp user defined atomic operations. */ /*! \def CPPAD_USER_ATOMIC(afun, Tvector, forward, reverse, for_jac_sparse, rev_jac_sparse, rev_hes_sparse ) Defines the function afun(id, ax, ay) where \c id is \c ax and \c ay are vectors with AD elements. \par Tvector the Simple Vector template class for this function. \par Base the base type for the atomic operation. \par afun name of the CppAD defined function that corresponding to this operation. Note that \c afun, preceeded by a pound sign, is a version of \c afun with quotes arround it. \par forward name of the user defined function that computes corresponding results during forward mode. \par reverse name of the user defined function that computes corresponding results during reverse mode. \par for_jac_sparse name of the user defined routine that computes corresponding results during forward mode jacobian sparsity sweeps. \par rev_jac_sparse name of the user defined routine that computes corresponding results during reverse mode jacobian sparsity sweeps. \par rev_hes_sparse name of the user defined routine that computes corresponding results during reverse mode Hessian sparsity sweeps. \par memory allocation Note that old_atomic is used as a static object, so its objects do note get deallocated until the program terminates. */ # define CPPAD_USER_ATOMIC( \ afun , \ Tvector , \ Base , \ forward , \ reverse , \ for_jac_sparse , \ rev_jac_sparse , \ rev_hes_sparse \ ) \ inline void afun ( \ size_t id , \ const Tvector< CppAD::AD >& ax , \ Tvector< CppAD::AD >& ay \ ) \ { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; \ static CppAD::old_atomic fun( \ #afun , \ forward , \ reverse , \ for_jac_sparse , \ rev_jac_sparse , \ rev_hes_sparse \ ); \ fun(id, ax, ay); \ } /// link so that user_atomic::clear() still works template class user_atomic : public atomic_base { }; /*! Class that actually implements the afun(id, ax, ay) calls. A new old_atomic object is generated each time the user invokes the CPPAD_USER_ATOMIC macro; see static object in that macro. */ template class old_atomic : public atomic_base { public: /// disable old_atomic::clear(void) static void clear(void) { CPPAD_ASSERT_KNOWN( false, "Depreacted API uses user_atomic::clear()" ); } /// type for user routine that computes forward mode results typedef bool (*F) ( size_t id , size_t k , size_t n , size_t m , const vector& vx , vector& vy , const vector& tx , vector& ty ); /// type for user routine that computes reverse mode results typedef bool (*R) ( size_t id , size_t k , size_t n , size_t m , const vector& tx , const vector& ty , vector& px , const vector& py ); /// type for user routine that computes forward mode Jacobian sparsity typedef bool (*FJS) ( size_t id , size_t n , size_t m , size_t q , const vector< std::set >& r , vector< std::set >& s ); /// type for user routine that computes reverse mode Jacobian sparsity typedef bool (*RJS) ( size_t id , size_t n , size_t m , size_t q , vector< std::set >& r , const vector< std::set >& s ); /// type for user routine that computes reverse mode Hessian sparsity typedef bool (*RHS) ( size_t id , size_t n , size_t m , size_t q , const vector< std::set >& r , const vector& s , vector& t , const vector< std::set >& u , vector< std::set >& v ); private: /// id value corresponding to next virtual callback size_t id_; /// user's implementation of forward mode const F f_; /// user's implementation of reverse mode const R r_; /// user's implementation of forward jacobian sparsity calculations const FJS fjs_; /// user's implementation of reverse jacobian sparsity calculations const RJS rjs_; /// user's implementation of reverse Hessian sparsity calculations const RHS rhs_; public: /*! Constructor called for each invocation of CPPAD_USER_ATOMIC. Put this object in the list of all objects for this class and set the constant private data f_, r_, fjs_, rjs_, rhs_. \param afun is the user's name for the AD version of this atomic operation. \param f user routine that does forward mode calculations for this operation. \param r user routine that does reverse mode calculations for this operation. \param fjs user routine that does forward Jacobian sparsity calculations. \param rjs user routine that does reverse Jacobian sparsity calculations. \param rhs user routine that does reverse Hessian sparsity calculations. \par This constructor can not be used in parallel mode because atomic_base has this restriction. */ old_atomic(const char* afun, F f, R r, FJS fjs, RJS rjs, RHS rhs) : atomic_base(afun) // name = afun , f_(f) , r_(r) , fjs_(fjs) , rjs_(rjs) , rhs_(rhs) { this->option( atomic_base::set_sparsity_enum ); } /*! Implement the user call to afun(id, ax, ay). \tparam ADVector A simple vector class with elements of type AD. \param id extra information vector that is just passed through by CppAD, and possibly used by user's routines. \param ax is the argument vector for this call, ax.size() determines the number of arguments. \param ay is the result vector for this call, ay.size() determines the number of results. */ template void operator()(size_t id, const ADVector& ax, ADVector& ay) { // call atomic_base function object this->atomic_base::operator()(ax, ay, id); return; } /*! Store id for next virtual function callback \param id id value corresponding to next virtual callback */ virtual void set_old(size_t id) { id_ = id; } /*! Link from old_atomic to forward mode \copydetails atomic_base::forward */ virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { CPPAD_ASSERT_UNKNOWN( tx.size() % (q+1) == 0 ); CPPAD_ASSERT_UNKNOWN( ty.size() % (q+1) == 0 ); size_t n = tx.size() / (q+1); size_t m = ty.size() / (q+1); size_t i, j, k, ell; vector x(n * (q+1)); vector y(m * (q+1)); vector empty; // old_atomic interface can only handel one order at a time // so must just throuh hoops to get multiple orders at one time. bool ok = true; for(k = p; k <= q; k++) { for(j = 0; j < n; j++) for(ell = 0; ell <= k; ell++) x[ j * (k+1) + ell ] = tx[ j * (q+1) + ell ]; for(i = 0; i < m; i++) for(ell = 0; ell < k; ell++) y[ i * (k+1) + ell ] = ty[ i * (q+1) + ell ]; if( k == 0 ) ok &= f_(id_, k, n, m, vx, vy, x, y); else ok &= f_(id_, k, n, m, empty, empty, x, y); for(i = 0; i < m; i++) ty[ i * (q+1) + k ] = y[ i * (k+1) + k]; } return ok; } /*! Link from old_atomic to reverse mode \copydetails atomic_base::reverse */ virtual bool reverse( size_t q , const vector& tx , const vector& ty , vector& px , const vector& py ) { CPPAD_ASSERT_UNKNOWN( tx.size() % (q+1) == 0 ); CPPAD_ASSERT_UNKNOWN( ty.size() % (q+1) == 0 ); size_t n = tx.size() / (q+1); size_t m = ty.size() / (q+1); bool ok = r_(id_, q, n, m, tx, ty, px, py); return ok; } /*! Link from forward Jacobian sparsity sweep to old_atomic \copydetails atomic_base::for_sparse_jac */ virtual bool for_sparse_jac( size_t q , const vector< std::set >& r , vector< std::set >& s , const vector& x ) { size_t n = r.size(); size_t m = s.size(); bool ok = fjs_(id_, n, m, q, r, s); return ok; } /*! Link from reverse Jacobian sparsity sweep to old_atomic. \copydetails atomic_base::rev_sparse_jac */ virtual bool rev_sparse_jac( size_t q , const vector< std::set >& rt , vector< std::set >& st , const vector& x ) { size_t n = st.size(); size_t m = rt.size(); bool ok = rjs_(id_, n, m, q, st, rt); return ok; } /*! Link from reverse Hessian sparsity sweep to old_atomic \copydetails atomic_base::rev_sparse_hes */ virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t q , const vector< std::set >& r , const vector< std::set >& u , vector< std::set >& v , const vector& x ) { size_t m = u.size(); size_t n = v.size(); CPPAD_ASSERT_UNKNOWN( r.size() == n ); CPPAD_ASSERT_UNKNOWN( s.size() == m ); CPPAD_ASSERT_UNKNOWN( t.size() == n ); // // old interface used id instead of vx bool ok = rhs_(id_, n, m, q, r, s, t, u, v); return ok; } }; } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/for_sparse_jac.hpp0000644000175200017650000005045413057470466020156 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_FOR_SPARSE_JAC_HPP # define CPPAD_CORE_FOR_SPARSE_JAC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ForSparseJac$$ $spell std var Jacobian Jac const Bool proportional VecAD CondExpRel optimizer cpp $$ $section Jacobian Sparsity Pattern: Forward Mode$$ $head Syntax$$ $icode%s% = %f%.ForSparseJac(%q%, %r%) %$$ $icode%s% = %f%.ForSparseJac(%q%, %r%, %transpose%, %dependency%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. For a fixed $latex n \times q$$ matrix $latex R$$, the Jacobian of $latex F[ x + R * u ]$$ with respect to $latex u$$ at $latex u = 0$$ is $latex \[ S(x) = F^{(1)} ( x ) * R \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex R$$, $code ForSparseJac$$ returns a sparsity pattern for the $latex S(x)$$. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ Note that the $cref ADFun$$ object $icode f$$ is not $code const$$. After a call to $code ForSparseJac$$, the sparsity pattern for each of the variables in the operation sequence is held in $icode f$$ (for possible later use by $cref RevSparseHes$$). These sparsity patterns are stored with elements of type $code bool$$ or elements of type $code std::set$$ (see $cref/VectorSet/ForSparseJac/VectorSet/$$ below). $subhead size_forward_bool$$ After $code ForSparseJac$$, if $icode k$$ is a $code size_t$$ object, $codei% %k% = %f%.size_forward_bool() %$$ sets $icode k$$ to the amount of memory (in unsigned character units) used to store the sparsity pattern with elements of type $code bool$$ in the function object $icode f$$. If the sparsity patterns for the previous $code ForSparseJac$$ used elements of type $code bool$$, the return value for $code size_forward_bool$$ will be non-zero. Otherwise, its return value will be zero. This sparsity pattern is stored for use by $cref RevSparseHes$$ and when it is not longer needed, it can be deleted (and the corresponding memory freed) using $codei% %f%.size_forward_bool(0) %$$ After this call, $icode%f%.size_forward_bool()%$$ will return zero. $subhead size_forward_set$$ After $code ForSparseJac$$, if $icode k$$ is a $code size_t$$ object, $codei% %k% = %f%.size_forward_set() %$$ sets $icode s$$ to the total number of elements in all the sets corresponding to the sparsity pattern stored in the function object $icode f$$. If the sparsity patterns for this operation use elements of type $code bool$$, the return value for $code size_forward_set$$ will be zero. Otherwise, its return value will be non-zero (unless the entire sparsity pattern is false). This sparsity pattern is stored for use by $cref RevSparseHes$$ and when it is not longer needed, it can be deleted (and the corresponding memory freed) using $codei% %f%.size_forward_set(0) %$$ After this call, $icode%f%.size_forward_set()%$$ will return zero. $head x$$ If the operation sequence in $icode f$$ is $cref/independent/glossary/Operation/Independent/$$ of the independent variables in $latex x \in B^n$$, the sparsity pattern is valid for all values of (even if it has $cref CondExp$$ or $cref VecAD$$ operations). $head q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of columns in $latex R \in B^{n \times q}$$ and the Jacobian $latex S(x) \in B^{m \times q}$$. $head transpose$$ The argument $icode transpose$$ has prototype $codei% bool %transpose% %$$ The default value $code false$$ is used when $icode transpose$$ is not present. $head dependency$$ The argument $icode dependency$$ has prototype $codei% bool %dependency% %$$ If $icode dependency$$ is true, the $cref/dependency pattern/dependency.cpp/Dependency Pattern/$$ (instead of sparsity pattern) is computed. $head r$$ The argument $icode r$$ has prototype $codei% const %VectorSet%& %r% %$$ see $cref/VectorSet/ForSparseJac/VectorSet/$$ below. $subhead transpose false$$ If $icode r$$ has elements of type $code bool$$, its size is $latex n * q$$. If it has elements of type $code std::set$$, its size is $latex n$$ and all the set elements must be between zero and $icode%q%-1%$$ inclusive. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex R \in B^{n \times q}$$. $subhead transpose true$$ If $icode r$$ has elements of type $code bool$$, its size is $latex q * n$$. If it has elements of type $code std::set$$, its size is $latex q$$ and all the set elements must be between zero and $icode%n%-1%$$ inclusive. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex R^\R{T} \in B^{q \times n}$$. $head s$$ The return value $icode s$$ has prototype $codei% %VectorSet% %s% %$$ see $cref/VectorSet/ForSparseJac/VectorSet/$$ below. $subhead transpose false$$ If $icode s$$ has elements of type $code bool$$, its size is $latex m * q$$. If it has elements of type $code std::set$$, its size is $latex m$$ and all its set elements are between zero and $icode%q%-1%$$ inclusive. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex S(x) \in B^{m \times q}$$. $subhead transpose true$$ If $icode s$$ has elements of type $code bool$$, its size is $latex q * m$$. If it has elements of type $code std::set$$, its size is $latex q$$ and all its set elements are between zero and $icode%m%-1%$$ inclusive. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex S(x)^\R{T} \in B^{q \times m}$$. $head VectorSet$$ The type $icode VectorSet$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code bool$$ or $code std::set$$; see $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for a discussion of the difference. $head Entire Sparsity Pattern$$ Suppose that $latex q = n$$ and $latex R$$ is the $latex n \times n$$ identity matrix. In this case, the corresponding value for $icode s$$ is a sparsity pattern for the Jacobian $latex S(x) = F^{(1)} ( x )$$. $head Example$$ $children% example/for_sparse_jac.cpp %$$ The file $cref for_sparse_jac.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. The file $cref/sparsity_sub.cpp/sparsity_sub.cpp/ForSparseJac/$$ contains an example and test of using $code ForSparseJac$$ to compute the sparsity pattern for a subset of the Jacobian. $end ----------------------------------------------------------------------------- */ # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file for_sparse_jac.hpp Forward mode Jacobian sparsity patterns. */ // --------------------------------------------------------------------------- /*! Private helper function for ForSparseJac(q, r) boolean sparsity patterns. All of the description in the public member function ForSparseJac(q, r) applies. \param set_type is a \c bool value. This argument is used to dispatch to the proper source code depending on the value of \c VectorSet::value_type. \param transpose See \c ForSparseJac(q, r, transpose, dependency). \param dependency See \c ForSparseJac(q, r, transpose, dependency). \param q See \c ForSparseJac(q, r, transpose, dependency). \param r See \c ForSparseJac(q, r, transpose, dependency). \param s is the return value for the corresponding call to \c ForSparseJac(q, r). */ template template void ADFun::ForSparseJacCase( bool set_type , bool transpose , bool dependency , size_t q , const VectorSet& r , VectorSet& s ) { size_t m = Range(); size_t n = Domain(); // check VectorSet is Simple Vector class with bool elements CheckSimpleVector(); // dimension size of result vector s.resize( m * q ); // temporary indices size_t i, j; // CPPAD_ASSERT_KNOWN( q > 0, "ForSparseJac: q is not greater than zero" ); CPPAD_ASSERT_KNOWN( size_t(r.size()) == n * q, "ForSparseJac: size of r is not equal to\n" "q times domain dimension for ADFun object." ); // // allocate memory for the requested sparsity calculation result for_jac_sparse_pack_.resize(num_var_tape_, q); // set values corresponding to independent variables for(i = 0; i < n; i++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] < num_var_tape_ ); // ind_taddr_[i] is operator taddr for i-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp ); // set bits that are true if( transpose ) { for(j = 0; j < q; j++) if( r[ j * n + i ] ) for_jac_sparse_pack_.add_element( ind_taddr_[i], j); } else { for(j = 0; j < q; j++) if( r[ i * q + j ] ) for_jac_sparse_pack_.add_element( ind_taddr_[i], j); } } // evaluate the sparsity patterns local::ForJacSweep( dependency, n, num_var_tape_, &play_, for_jac_sparse_pack_ ); // return values corresponding to dependent variables CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == m * q ); for(i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); // extract the result from for_jac_sparse_pack_ if( transpose ) { for(j = 0; j < q; j++) s[ j * m + i ] = false; } else { for(j = 0; j < q; j++) s[ i * q + j ] = false; } CPPAD_ASSERT_UNKNOWN( for_jac_sparse_pack_.end() == q ); local::sparse_pack::const_iterator itr(for_jac_sparse_pack_, dep_taddr_[i] ); j = *itr; while( j < q ) { if( transpose ) s[j * m + i] = true; else s[i * q + j] = true; j = *(++itr); } } } // --------------------------------------------------------------------------- /*! Private helper function for \c ForSparseJac(q, r) set sparsity. All of the description in the public member function \c ForSparseJac(q, r) applies. \param set_type is a \c std::set object. This argument is used to dispatch to the proper source code depending on the value of \c VectorSet::value_type. \param transpose See \c ForSparseJac(q, r, transpose, dependency). \param dependency See \c ForSparseJac(q, r, transpose, dependency). \param q See \c ForSparseJac(q, r, transpose, dependency). \param r See \c ForSparseJac(q, r, transpose, dependency). \param s is the return value for the corresponding call to \c ForSparseJac(q, r). */ template template void ADFun::ForSparseJacCase( const std::set& set_type , bool transpose , bool dependency , size_t q , const VectorSet& r , VectorSet& s ) { size_t m = Range(); size_t n = Domain(); // check VectorSet is Simple Vector class with sets for elements CheckSimpleVector, VectorSet>( local::one_element_std_set(), local::two_element_std_set() ); // dimension size of result vector if( transpose ) s.resize(q); else s.resize( m ); // temporary indices size_t i, j; std::set::const_iterator itr_1; // CPPAD_ASSERT_KNOWN( q > 0, "ForSparseJac: q is not greater than zero" ); CPPAD_ASSERT_KNOWN( size_t(r.size()) == n || transpose, "ForSparseJac: size of r is not equal to n and transpose is false." ); CPPAD_ASSERT_KNOWN( size_t(r.size()) == q || ! transpose, "ForSparseJac: size of r is not equal to q and transpose is true." ); // // allocate memory for the requested sparsity calculation for_jac_sparse_set_.resize(num_var_tape_, q); // set values corresponding to independent variables if( transpose ) { for(i = 0; i < q; i++) { // add the elements that are present itr_1 = r[i].begin(); while( itr_1 != r[i].end() ) { j = *itr_1++; CPPAD_ASSERT_KNOWN( j < n, "ForSparseJac: transpose is true and element of the set\n" "r[j] has value greater than or equal n." ); CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] < num_var_tape_ ); // operator for j-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); for_jac_sparse_set_.add_element( ind_taddr_[j], i); } } } else { for(i = 0; i < n; i++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[i] < num_var_tape_ ); // ind_taddr_[i] is operator taddr for i-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[i] ) == local::InvOp ); // add the elements that are present itr_1 = r[i].begin(); while( itr_1 != r[i].end() ) { j = *itr_1++; CPPAD_ASSERT_KNOWN( j < q, "ForSparseJac: an element of the set r[i] " "has value greater than or equal q." ); for_jac_sparse_set_.add_element( ind_taddr_[i], j); } } } // evaluate the sparsity patterns local::ForJacSweep( dependency, n, num_var_tape_, &play_, for_jac_sparse_set_ ); // return values corresponding to dependent variables CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == m || transpose ); CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == q || ! transpose ); for(i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); // extract results from for_jac_sparse_set_ // and add corresponding elements to sets in s CPPAD_ASSERT_UNKNOWN( for_jac_sparse_set_.end() == q ); local::sparse_list::const_iterator itr_2(for_jac_sparse_set_, dep_taddr_[i] ); j = *itr_2; while( j < q ) { if( transpose ) s[j].insert(i); else s[i].insert(j); j = *(++itr_2); } } } // --------------------------------------------------------------------------- /*! User API for Jacobian sparsity patterns using forward mode. The C++ source code corresponding to this operation is \verbatim s = f.ForSparseJac(q, r, transpose, dependency) \endverbatim \tparam Base is the base type for this recording. \tparam VectorSet is a simple vector with elements of type \c bool or \c std::set. \param q is the number of columns in the matrix \f$ R \f$. \param r is a sparsity pattern for the matrix \f$ R \f$. \param transpose are sparsity patterns for \f$ R \f$ and \f$ S(x) \f$ transposed. \param dependency Are the derivatives with respect to left and right of the expression below considered to be non-zero: \code CondExpRel(left, right, if_true, if_false) \endcode This is used by the optimizer to obtain the correct dependency relations. \return The value of \c transpose is false (true), the return value is a sparsity pattern for \f$ S(x) \f$ (\f$ S(x)^T \f$) where \f[ S(x) = F^{(1)} (x) * R \f] where \f$ F \f$ is the function corresponding to the operation sequence and \a x is any argument value. If \c VectorSet::value_type is \c bool, the return value has size \f$ m * q \f$ (\f$ q * m \f$). where \c m is the number of dependent variables corresponding to the operation sequence stored in \c f. If \c VectorSet::value_type is \c std::set, the return value has size \f$ m \f$ ( \f$ q \f$ ) and with all its elements between zero and \f$ q - 1 \f$ ( \f$ m - 1 \f$). \par Side Effects If \c VectorSet::value_type is \c bool, the forward sparsity pattern for all of the variables on the tape is stored in \c for_jac_sparse_pack__. In this case \verbatim for_jac_sparse_pack_.n_set() == num_var_tape_ for_jac_sparse_pack_.end() == q for_jac_sparse_set_.n_set() == 0 for_jac_sparse_set_.end() == 0 \endverbatim \n \n If \c VectorSet::value_type is \c std::set, the forward sparsity pattern for all of the variables on the tape is stored in \c for_jac_sparse_set__. In this case \verbatim for_jac_sparse_set_.n_set() == num_var_tape_ for_jac_sparse_set_.end() == q for_jac_sparse_pack_.n_set() == 0 for_jac_sparse_pack_.end() == 0 \endverbatim */ template template VectorSet ADFun::ForSparseJac( size_t q , const VectorSet& r , bool transpose , bool dependency ) { VectorSet s; typedef typename VectorSet::value_type Set_type; // free all memory currently in sparsity patterns for_jac_sparse_pack_.resize(0, 0); for_jac_sparse_set_.resize(0, 0); ForSparseJacCase( Set_type() , transpose , dependency , q , r , s ); return s; } // =========================================================================== // ForSparseJacCheckpoint /*! Forward mode Jacobian sparsity calculation used by checkpoint functions. \tparam Base is the base type for this recording. \param transpose is true (false) s is equal to \f$ S(x) \f$ (\f$ S(x)^T \f$) where \f[ S(x) = F^{(1)} (x) * R \f] where \f$ F \f$ is the function corresponding to the operation sequence and \f$ x \f$ is any argument value. \param q is the number of columns in the matrix \f$ R \f$. \param r is a sparsity pattern for the matrix \f$ R \f$. \param transpose are the sparsity patterns for \f$ R \f$ and \f$ S(x) \f$ transposed. \param dependency Are the derivatives with respect to left and right of the expression below considered to be non-zero: \code CondExpRel(left, right, if_true, if_false) \endcode This is used by the optimizer to obtain the correct dependency relations. \param s The input size and elements of s do not matter. On output, s is the sparsity pattern for the matrix \f$ S(x) \f$ or \f$ S(x)^T \f$ depending on transpose. \par Side Effects If \c VectorSet::value_type is \c bool, the forward sparsity pattern for all of the variables on the tape is stored in \c for_jac_sparse_pack__. In this case \verbatim for_jac_sparse_pack_.n_set() == num_var_tape_ for_jac_sparse_pack_.end() == q for_jac_sparse_set_.n_set() == 0 for_jac_sparse_set_.end() == 0 \endverbatim \n \n If \c VectorSet::value_type is \c std::set, the forward sparsity pattern for all of the variables on the tape is stored in \c for_jac_sparse_set__. In this case \verbatim for_jac_sparse_set_.n_set() == num_var_tape_ for_jac_sparse_set_.end() == q for_jac_sparse_pack_.n_set() == 0 for_jac_sparse_pack_.end() == 0 \endverbatim */ template void ADFun::ForSparseJacCheckpoint( size_t q , const local::sparse_list& r , bool transpose , bool dependency , local::sparse_list& s ) { size_t n = Domain(); size_t m = Range(); # ifndef NDEBUG if( transpose ) { CPPAD_ASSERT_UNKNOWN( r.n_set() == q ); CPPAD_ASSERT_UNKNOWN( r.end() == n ); } else { CPPAD_ASSERT_UNKNOWN( r.n_set() == n ); CPPAD_ASSERT_UNKNOWN( r.end() == q ); } for(size_t j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == (j+1) ); CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); } # endif // free all memory currently in sparsity patterns for_jac_sparse_pack_.resize(0, 0); for_jac_sparse_set_.resize(0, 0); // allocate new sparsity pattern for_jac_sparse_set_.resize(num_var_tape_, q); // set sparsity pattern for dependent variables if( transpose ) { for(size_t i = 0; i < q; i++) { local::sparse_list::const_iterator itr(r, i); size_t j = *itr; while( j < n ) { for_jac_sparse_set_.add_element( ind_taddr_[j], i ); j = *(++itr); } } } else { for(size_t j = 0; j < n; j++) { local::sparse_list::const_iterator itr(r, j); size_t i = *itr; while( i < q ) { for_jac_sparse_set_.add_element( ind_taddr_[j], i ); i = *(++itr); } } } // evaluate the sparsity pattern for all variables local::ForJacSweep( dependency, n, num_var_tape_, &play_, for_jac_sparse_set_ ); // dimension the return value if( transpose ) s.resize(q, m); else s.resize(m, q); // return values corresponding to dependent variables for(size_t i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); // extract the result from for_jac_sparse_set_ CPPAD_ASSERT_UNKNOWN( for_jac_sparse_set_.end() == q ); local::sparse_list::const_iterator itr(for_jac_sparse_set_, dep_taddr_[i] ); size_t j = *itr; while( j < q ) { if( transpose ) s.add_element(j, i); else s.add_element(i, j); j = *(++itr); } } } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/std_math_98.hpp0000644000175200017650000003412113057470466017312 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_STD_MATH_98_HPP # define CPPAD_CORE_STD_MATH_98_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* ------------------------------------------------------------------------------- $begin acos$$ $spell acos $$ $section Inverse Sine Function: acos$$ $head Syntax$$ $icode%y% = acos(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{acos}^{(1)} (x) & = & - (1 - x * x)^{-1/2} \end{array} \] $$ $head Example$$ $children% example/acos.cpp %$$ The file $cref acos.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin asin$$ $spell asin $$ $section Inverse Sine Function: asin$$ $head Syntax$$ $icode%y% = asin(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{asin}^{(1)} (x) & = & (1 - x * x)^{-1/2} \end{array} \] $$ $head Example$$ $children% example/asin.cpp %$$ The file $cref asin.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin atan$$ $spell atan $$ $section Inverse Tangent Function: atan$$ $head Syntax$$ $icode%y% = atan(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{atan}^{(1)} (x) & = & \frac{1}{1 + x^2} \end{array} \] $$ $head Example$$ $children% example/atan.cpp %$$ The file $cref atan.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin cos$$ $spell cos $$ $section The Cosine Function: cos$$ $head Syntax$$ $icode%y% = cos(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{cos}^{(1)} (x) & = & - \sin(x) \end{array} \] $$ $head Example$$ $children% example/cos.cpp %$$ The file $cref cos.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin cosh$$ $spell cosh $$ $section The Hyperbolic Cosine Function: cosh$$ $head Syntax$$ $icode%y% = cosh(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{cosh}^{(1)} (x) & = & \sinh(x) \end{array} \] $$ $head Example$$ $children% example/cosh.cpp %$$ The file $cref cosh.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin exp$$ $spell exp $$ $section The Exponential Function: exp$$ $head Syntax$$ $icode%y% = exp(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{exp}^{(1)} (x) & = & \exp(x) \end{array} \] $$ $head Example$$ $children% example/exp.cpp %$$ The file $cref exp.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin log$$ $spell $$ $section The Exponential Function: log$$ $head Syntax$$ $icode%y% = log(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{log}^{(1)} (x) & = & \frac{1}{x} \end{array} \] $$ $head Example$$ $children% example/log.cpp %$$ The file $cref log.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin log10$$ $spell CppAD $$ $section The Base 10 Logarithm Function: log10$$ $head Syntax$$ $icode%y% = log10(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Method$$ CppAD uses the representation $latex \[ \begin{array}{lcr} {\rm log10} (x) & = & \log(x) / \log(10) \end{array} \] $$ $head Example$$ $children% example/log10.cpp %$$ The file $cref log10.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin sin$$ $spell sin $$ $section The Sine Function: sin$$ $head Syntax$$ $icode%y% = sin(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{sin}^{(1)} (x) & = & \cos(x) \end{array} \] $$ $head Example$$ $children% example/sin.cpp %$$ The file $cref sin.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin sinh$$ $spell sinh $$ $section The Hyperbolic Sine Function: sinh$$ $head Syntax$$ $icode%y% = sinh(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{sinh}^{(1)} (x) & = & \cosh(x) \end{array} \] $$ $head Example$$ $children% example/sinh.cpp %$$ The file $cref sinh.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin sqrt$$ $spell sqrt $$ $section The Square Root Function: sqrt$$ $head Syntax$$ $icode%y% = sqrt(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{sqrt}^{(1)} (x) & = & \frac{1}{2 \R{sqrt} (x) } \end{array} \] $$ $head Example$$ $children% example/sqrt.cpp %$$ The file $cref sqrt.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin tan$$ $spell tan $$ $section The Tangent Function: tan$$ $head Syntax$$ $icode%y% = tan(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{tan}^{(1)} (x) & = & 1 + \tan (x)^2 \end{array} \] $$ $head Example$$ $children% example/tan.cpp %$$ The file $cref tan.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- $begin tanh$$ $spell tanh $$ $section The Hyperbolic Tangent Function: tanh$$ $head Syntax$$ $icode%y% = tanh(%x%)%$$ $head x, y$$ See the $cref/possible types/unary_standard_math/Possible Types/$$ for a unary standard math function. $head Atomic$$ This is an $cref/atomic operation/glossary/Operation/Atomic/$$. $head Derivative$$ $latex \[ \begin{array}{lcr} \R{tanh}^{(1)} (x) & = & 1 - \tanh (x)^2 \end{array} \] $$ $head Example$$ $children% example/tanh.cpp %$$ The file $cref tanh.cpp$$ contains an example and test of this function. It returns true if it succeeds and false otherwise. $end ------------------------------------------------------------------------------- */ /*! \file std_math_98.hpp Define AD standard math functions (using their Base versions) */ /*! \def CPPAD_STANDARD_MATH_UNARY_AD(Name, Op) Defines function Name with argument type AD and tape operation Op The macro defines the function x.Name() where x has type AD. It then uses this funciton to define Name(x) where x has type AD or VecAD_reference. If x is a variable, the tape unary operator Op is used to record the operation and the result is identified as correspoding to this operation; i.e., Name(x).taddr_ idendifies the operation and Name(x).tape_id_ identifies the tape. This macro is used to define AD versions of acos, asin, atan, cos, cosh, exp, fabs, log, sin, sinh, sqrt, tan, tanh. */ # define CPPAD_STANDARD_MATH_UNARY_AD(Name, Op) \ template \ inline AD Name(const AD &x) \ { return x.Name##_me(); } \ template \ inline AD AD::Name##_me (void) const \ { \ AD result; \ result.value_ = CppAD::Name(value_); \ CPPAD_ASSERT_UNKNOWN( Parameter(result) ); \ \ if( Variable(*this) ) \ { CPPAD_ASSERT_UNKNOWN( NumArg(Op) == 1 ); \ local::ADTape *tape = tape_this(); \ tape->Rec_.PutArg(taddr_); \ result.taddr_ = tape->Rec_.PutOp(Op); \ result.tape_id_ = tape->id_; \ } \ return result; \ } \ template \ inline AD Name(const VecAD_reference &x) \ { return x.ADBase().Name##_me(); } // BEGIN CppAD namespace namespace CppAD { CPPAD_STANDARD_MATH_UNARY_AD(acos, local::AcosOp) CPPAD_STANDARD_MATH_UNARY_AD(asin, local::AsinOp) CPPAD_STANDARD_MATH_UNARY_AD(atan, local::AtanOp) CPPAD_STANDARD_MATH_UNARY_AD(cos, local::CosOp) CPPAD_STANDARD_MATH_UNARY_AD(cosh, local::CoshOp) CPPAD_STANDARD_MATH_UNARY_AD(exp, local::ExpOp) CPPAD_STANDARD_MATH_UNARY_AD(fabs, local::AbsOp) CPPAD_STANDARD_MATH_UNARY_AD(log, local::LogOp) CPPAD_STANDARD_MATH_UNARY_AD(sin, local::SinOp) CPPAD_STANDARD_MATH_UNARY_AD(sinh, local::SinhOp) CPPAD_STANDARD_MATH_UNARY_AD(sqrt, local::SqrtOp) CPPAD_STANDARD_MATH_UNARY_AD(tan, local::TanOp) CPPAD_STANDARD_MATH_UNARY_AD(tanh, local::TanhOp) # if CPPAD_USE_CPLUSPLUS_2011 CPPAD_STANDARD_MATH_UNARY_AD(asinh, local::AsinhOp) CPPAD_STANDARD_MATH_UNARY_AD(acosh, local::AcoshOp) CPPAD_STANDARD_MATH_UNARY_AD(atanh, local::AtanhOp) CPPAD_STANDARD_MATH_UNARY_AD(expm1, local::Expm1Op) CPPAD_STANDARD_MATH_UNARY_AD(log1p, local::Log1pOp) # endif # if CPPAD_USE_CPLUSPLUS_2011 // Error function is a special case template inline AD erf(const AD &x) { return x.erf_me(); } template inline AD AD::erf_me (void) const { AD result; result.value_ = CppAD::erf(value_); CPPAD_ASSERT_UNKNOWN( Parameter(result) ); if( Variable(*this) ) { CPPAD_ASSERT_UNKNOWN( local::NumArg(local::ErfOp) == 3 ); local::ADTape *tape = tape_this(); // arg[0] = argument to erf function tape->Rec_.PutArg(taddr_); // arg[1] = zero addr_t p = tape->Rec_.PutPar( Base(0) ); tape->Rec_.PutArg(p); // arg[2] = 2 / sqrt(pi) p = tape->Rec_.PutPar(Base( 1.0 / std::sqrt( std::atan(1.0) ) )); tape->Rec_.PutArg(p); // result.taddr_ = tape->Rec_.PutOp(local::ErfOp); result.tape_id_ = tape->id_; } return result; } template inline AD erf(const VecAD_reference &x) { return x.ADBase().erf_me(); } # endif /*! Compute the log of base 10 of x where has type AD \tparam Base is the base type (different from base for log) for this AD type, see base_require. \param x is the argument for the log10 function. \result if the result is y, then \f$ x = 10^y \f$. */ template inline AD log10(const AD &x) { return CppAD::log(x) / CppAD::log( Base(10) ); } template inline AD log10(const VecAD_reference &x) { return CppAD::log(x.ADBase()) / CppAD::log( Base(10) ); } } # undef CPPAD_STANDARD_MATH_UNARY_AD # endif cppad-20170000.3/cppad/core/rev_sparse_jac.hpp0000644000175200017650000004034013057470466020155 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_REV_SPARSE_JAC_HPP # define CPPAD_CORE_REV_SPARSE_JAC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin RevSparseJac$$ $spell optimizer nz CondExpRel std VecAD var Jacobian Jac const Bool Dep proportional $$ $section Jacobian Sparsity Pattern: Reverse Mode$$ $mindex RevSparseJac sparse$$ $head Syntax$$ $icode%s% = %f%.RevSparseJac(%q%, %r%) %$$ $icode%s% = %f%.RevSparseJac(%q%, %r%, %transpose%, %dependency%)%$$ $head Purpose$$ We use $latex F : B^n \rightarrow B^m$$ to denote the $cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$. For a fixed matrix $latex R \in B^{q \times m}$$, the Jacobian of $latex R * F( x )$$ with respect to $latex x$$ is $latex \[ S(x) = R * F^{(1)} ( x ) \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex R$$, $code RevSparseJac$$ returns a sparsity pattern for the $latex S(x)$$. $head f$$ The object $icode f$$ has prototype $codei% ADFun<%Base%> %f% %$$ $head x$$ If the operation sequence in $icode f$$ is $cref/independent/glossary/Operation/Independent/$$ of the independent variables in $latex x \in B^n$$, the sparsity pattern is valid for all values of (even if it has $cref CondExp$$ or $cref VecAD$$ operations). $head q$$ The argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of rows in $latex R \in B^{q \times m}$$ and the Jacobian $latex S(x) \in B^{q \times n}$$. $head transpose$$ The argument $icode transpose$$ has prototype $codei% bool %transpose% %$$ The default value $code false$$ is used when $icode transpose$$ is not present. $head dependency$$ The argument $icode dependency$$ has prototype $codei% bool %dependency% %$$ If $icode dependency$$ is true, the $cref/dependency pattern/dependency.cpp/Dependency Pattern/$$ (instead of sparsity pattern) is computed. $head r$$ The argument $icode s$$ has prototype $codei% const %VectorSet%& %r% %$$ see $cref/VectorSet/RevSparseJac/VectorSet/$$ below. $subhead transpose false$$ If $icode r$$ has elements of type $code bool$$, its size is $latex q * m$$. If it has elements of type $code std::set$$, its size is $icode q$$ and all its set elements are between zero and $latex m - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex R \in B^{q \times m}$$. $subhead transpose true$$ If $icode r$$ has elements of type $code bool$$, its size is $latex m * q$$. If it has elements of type $code std::set$$, its size is $icode m$$ and all its set elements are between zero and $latex q - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex R^\R{T} \in B^{m \times q}$$. $head s$$ The return value $icode s$$ has prototype $codei% %VectorSet% %s% %$$ see $cref/VectorSet/RevSparseJac/VectorSet/$$ below. $subhead transpose false$$ If it has elements of type $code bool$$, its size is $latex q * n$$. If it has elements of type $code std::set$$, its size is $icode q$$ and all its set elements are between zero and $latex n - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex S(x) \in {q \times n}$$. $subhead transpose true$$ If it has elements of type $code bool$$, its size is $latex n * q$$. If it has elements of type $code std::set$$, its size is $icode n$$ and all its set elements are between zero and $latex q - 1$$. It specifies a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for the matrix $latex S(x)^\R{T} \in {n \times q}$$. $head VectorSet$$ The type $icode VectorSet$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code bool$$ or $code std::set$$; see $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for a discussion of the difference. $head Entire Sparsity Pattern$$ Suppose that $latex q = m$$ and $latex R$$ is the $latex m \times m$$ identity matrix. In this case, the corresponding value for $icode s$$ is a sparsity pattern for the Jacobian $latex S(x) = F^{(1)} ( x )$$. $head Example$$ $children% example/rev_sparse_jac.cpp %$$ The file $cref rev_sparse_jac.cpp$$ contains an example and test of this operation. It returns true if it succeeds and false otherwise. $end ----------------------------------------------------------------------------- */ # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file rev_sparse_jac.hpp Reverse mode Jacobian sparsity patterns. */ // ========================================================================= // RevSparseJacCase /*! Private helper function for RevSparseJac(q, r, transpose) boolean sparsity. All of the description in the public member function \c RevSparseJac(q, r, transpose) apply. \param set_type is a \c bool value. This argument is used to dispatch to the proper source code depending on the value of \c VectorSet::value_type. \param transpose See \c RevSparseJac(q, r, transpose, dependency) \param dependency See \c RevSparseJac(q, r, transpose, dependency) \param q See \c RevSparseJac(q, r, transpose, dependency) \param r See \c RevSparseJac(q, r, transpose, dependency) \param s is the return value for the corresponding call to RevSparseJac(q, r, transpose). */ template template void ADFun::RevSparseJacCase( bool set_type , bool transpose , bool dependency , size_t q , const VectorSet& r , VectorSet& s ) { size_t n = Domain(); size_t m = Range(); // dimension of the result vector s.resize( q * n ); // temporary indices size_t i, j; // check VectorSet is Simple Vector class with bool elements CheckSimpleVector(); // CPPAD_ASSERT_KNOWN( q > 0, "RevSparseJac: q is not greater than zero" ); CPPAD_ASSERT_KNOWN( size_t(r.size()) == q * m, "RevSparseJac: size of r is not equal to\n" "q times range dimension for ADFun object." ); // // vector of sets that will hold the results local::sparse_pack var_sparsity; var_sparsity.resize(num_var_tape_, q); // The sparsity pattern corresponding to the dependent variables for(i = 0; i < m; i++) { CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); if( transpose ) { for(j = 0; j < q; j++) if( r[ i * q + j ] ) var_sparsity.add_element( dep_taddr_[i], j ); } else { for(j = 0; j < q; j++) if( r[ j * m + i ] ) var_sparsity.add_element( dep_taddr_[i], j ); } } // evaluate the sparsity patterns local::RevJacSweep( dependency, n, num_var_tape_, &play_, var_sparsity ); // return values corresponding to dependent variables CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == q * n ); for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == (j+1) ); // ind_taddr_[j] is operator taddr for j-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); // extract the result from var_sparsity if( transpose ) { for(i = 0; i < q; i++) s[ j * q + i ] = false; } else { for(i = 0; i < q; i++) s[ i * n + j ] = false; } CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == q ); local::sparse_pack::const_iterator itr(var_sparsity, j+1); i = *itr; while( i < q ) { if( transpose ) s[ j * q + i ] = true; else s[ i * n + j ] = true; i = *(++itr); } } } /*! Private helper function for RevSparseJac(q, r, transpose) set sparsity All of the description in the public member function \c RevSparseJac(q, r, transpose) apply. \param set_type is a \c std::set object. This argument is used to dispatch to the proper source code depending on the value of \c VectorSet::value_type. \param transpose See \c RevSparseJac(q, r, transpose, dependency) \param dependency See \c RevSparseJac(q, r, transpose, dependency) \param q See \c RevSparseJac(q, r, transpose, dependency) \param r See \c RevSparseJac(q, r, transpose, dependency) \param s is the return value for the corresponding call to RevSparseJac(q, r, transpose) */ template template void ADFun::RevSparseJacCase( const std::set& set_type , bool transpose , bool dependency , size_t q , const VectorSet& r , VectorSet& s ) { // dimension of the result vector if( transpose ) s.resize( Domain() ); else s.resize( q ); // temporary indices size_t i, j; std::set::const_iterator itr_1; // check VectorSet is Simple Vector class with sets for elements CheckSimpleVector, VectorSet>( local::one_element_std_set(), local::two_element_std_set() ); // domain dimensions for F size_t n = ind_taddr_.size(); size_t m = dep_taddr_.size(); CPPAD_ASSERT_KNOWN( q > 0, "RevSparseJac: q is not greater than zero" ); CPPAD_ASSERT_KNOWN( size_t(r.size()) == q || transpose, "RevSparseJac: size of r is not equal to q and transpose is false." ); CPPAD_ASSERT_KNOWN( size_t(r.size()) == m || ! transpose, "RevSparseJac: size of r is not equal to m and transpose is true." ); // vector of lists that will hold the results local::sparse_list var_sparsity; var_sparsity.resize(num_var_tape_, q); // The sparsity pattern corresponding to the dependent variables if( transpose ) { for(i = 0; i < m; i++) { itr_1 = r[i].begin(); while(itr_1 != r[i].end()) { j = *itr_1++; CPPAD_ASSERT_KNOWN( j < q, "RevSparseJac: transpose is true and element of the set\n" "r[i] has value greater than or equal q." ); CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); var_sparsity.add_element( dep_taddr_[i], j ); } } } else { for(i = 0; i < q; i++) { itr_1 = r[i].begin(); while(itr_1 != r[i].end()) { j = *itr_1++; CPPAD_ASSERT_KNOWN( j < m, "RevSparseJac: transpose is false and element of the set\n" "r[i] has value greater than or equal range dimension." ); CPPAD_ASSERT_UNKNOWN( dep_taddr_[j] < num_var_tape_ ); var_sparsity.add_element( dep_taddr_[j], i ); } } } // evaluate the sparsity patterns local::RevJacSweep( dependency, n, num_var_tape_, &play_, var_sparsity ); // return values corresponding to dependent variables CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == q || transpose ); CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == n || ! transpose ); for(j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == (j+1) ); // ind_taddr_[j] is operator taddr for j-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == q ); local::sparse_list::const_iterator itr_2(var_sparsity, j+1); i = *itr_2; while( i < q ) { if( transpose ) s[j].insert(i); else s[i].insert(j); i = *(++itr_2); } } } // ========================================================================= // RevSparseJac /*! User API for Jacobian sparsity patterns using reverse mode. The C++ source code corresponding to this operation is \verbatim s = f.RevSparseJac(q, r, transpose, dependency) \endverbatim \tparam Base is the base type for this recording. \tparam VectorSet is a simple vector with elements of type \c bool. or \c std::set. \param q is the number of rows in the matrix \f$ R \f$. \param r is a sparsity pattern for the matrix \f$ R \f$. \param transpose are the sparsity patterns for \f$ R \f$ and \f$ S(x) \f$ transposed. \param dependency Are the derivatives with respect to left and right of the expression below considered to be non-zero: \code CondExpRel(left, right, if_true, if_false) \endcode This is used by the optimizer to obtain the correct dependency relations. \return If \c transpose is false (true), the return value is a sparsity pattern for \f$ S(x) \f$ (\f$ S(x)^T \f$) where \f[ S(x) = R * F^{(1)} (x) \f] and \f$ F \f$ is the function corresponding to the operation sequence and \a x is any argument value. If \c VectorSet::value_type is \c bool, the return value has size \f$ q * n \f$ ( \f$ n * q \f$). If \c VectorSet::value_type is \c std::set, the return value has size \f$ q \f$ ( \f$ n \f$) and with all its elements between zero and \f$ n - 1 \f$ (\f$ q - 1 \f$). */ template template VectorSet ADFun::RevSparseJac( size_t q , const VectorSet& r , bool transpose , bool dependency ) { VectorSet s; typedef typename VectorSet::value_type Set_type; RevSparseJacCase( Set_type() , transpose , dependency , q , r , s ); return s; } // =========================================================================== // RevSparseJacCheckpoint /*! Reverse mode Jacobian sparsity calculation used by checkpoint functions. \tparam Base is the base type for this recording. \param transpose is true (false) s is equal to \f$ S(x) \f$ (\f$ S(x)^T \f$) where \f[ S(x) = R * F^{(1)} (x) \f] where \f$ F \f$ is the function corresponding to the operation sequence and \f$ x \f$ is any argument value. \param q is the number of rows in the matrix \f$ R \f$. \param r is a sparsity pattern for the matrix \f$ R \f$. \param transpose are the sparsity patterns for \f$ R \f$ and \f$ S(x) \f$ transposed. \param dependency Are the derivatives with respect to left and right of the expression below considered to be non-zero: \code CondExpRel(left, right, if_true, if_false) \endcode This is used by the optimizer to obtain the correct dependency relations. \param s The input size and elements of s do not matter. On output, s is the sparsity pattern for the matrix \f$ S(x) \f$ or \f$ S(x)^T \f$ depending on transpose. */ template void ADFun::RevSparseJacCheckpoint( size_t q , const local::sparse_list& r , bool transpose , bool dependency , local::sparse_list& s ) { size_t n = Domain(); size_t m = Range(); # ifndef NDEBUG if( transpose ) { CPPAD_ASSERT_UNKNOWN( r.n_set() == m ); CPPAD_ASSERT_UNKNOWN( r.end() == q ); } else { CPPAD_ASSERT_UNKNOWN( r.n_set() == q ); CPPAD_ASSERT_UNKNOWN( r.end() == m ); } for(size_t i = 0; i < m; i++) CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ ); # endif // holds reverse Jacobian sparsity pattern for all variables local::sparse_list var_sparsity; var_sparsity.resize(num_var_tape_, q); // set sparsity pattern for dependent variables if( transpose ) { for(size_t i = 0; i < m; i++) { local::sparse_list::const_iterator itr(r, i); size_t j = *itr; while( j < q ) { var_sparsity.add_element( dep_taddr_[i], j ); j = *(++itr); } } } else { for(size_t j = 0; j < q; j++) { local::sparse_list::const_iterator itr(r, j); size_t i = *itr; while( i < m ) { var_sparsity.add_element( dep_taddr_[i], j ); i = *(++itr); } } } // evaluate the sparsity pattern for all variables local::RevJacSweep( dependency, n, num_var_tape_, &play_, var_sparsity ); // dimension the return value if( transpose ) s.resize(n, m); else s.resize(m, n); // return values corresponding to independent variables for(size_t j = 0; j < n; j++) { CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == (j+1) ); // ind_taddr_[j] is operator taddr for j-th independent variable CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp ); // extract the result from var_sparsity CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == q ); local::sparse_list::const_iterator itr(var_sparsity, j+1); size_t i = *itr; while( i < q ) { if( transpose ) s.add_element(j, i); else s.add_element(i, j); i = *(++itr); } } } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/omp_max_thread.hpp0000644000175200017650000000512213057470466020155 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_OMP_MAX_THREAD_HPP # define CPPAD_CORE_OMP_MAX_THREAD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin omp_max_thread$$ $spell alloc num omp OpenMp CppAD $$ $section OpenMP Parallel Setup$$ $mindex omp_max_thread$$ $head Deprecated 2011-06-23$$ Use $cref/thread_alloc::parallel_setup/ta_parallel_setup/$$ to set the number of threads. $head Syntax$$ $codei%AD<%Base%>::omp_max_thread(%number%) %$$ $head Purpose$$ By default, for each $codei%AD<%Base%>%$$ class there is only one tape that records $cref/AD of Base/glossary/AD of Base/$$ operations. This tape is a global variable and hence it cannot be used by multiple OpenMP threads at the same time. The $code omp_max_thread$$ function is used to set the maximum number of OpenMP threads that can be active. In this case, there is a different tape corresponding to each $codei%AD<%Base%>%$$ class and thread pair. $head number$$ The argument $icode number$$ has prototype $codei% size_t %number% %$$ It must be greater than zero and specifies the maximum number of OpenMp threads that will be active at one time. $head Independent$$ Each call to $cref/Independent(x)/Independent/$$ creates a new $cref/active/glossary/Tape/Active/$$ tape. All of the operations with the corresponding variables must be preformed by the same OpenMP thread. This includes the corresponding call to $cref/f.Dependent(x,y)/Dependent/$$ or the $cref/ADFun f(x, y)/FunConstruct/Sequence Constructor/$$ during which the tape stops recording and the variables become parameters. $head Restriction$$ No tapes can be $cref/active/glossary/Tape/Active/$$ when this function is called. $end ----------------------------------------------------------------------------- */ // BEGIN CppAD namespace namespace CppAD { template void AD::omp_max_thread(size_t number) { # ifdef _OPENMP thread_alloc::parallel_setup( number, omp_alloc::in_parallel, omp_alloc::get_thread_num ); # else CPPAD_ASSERT_KNOWN( number == 1, "omp_max_thread: number > 1 and _OPENMP is not defined" ); # endif parallel_ad(); } } // END CppAD namespace # endif cppad-20170000.3/cppad/core/base_cond_exp.hpp0000644000175200017650000001624213057470466017764 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BASE_COND_EXP_HPP # define CPPAD_CORE_BASE_COND_EXP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_cond_exp$$ $spell alloc Rel hpp enum namespace Op Lt Le Eq Ge Gt Ne cond exp const adolc CppAD inline $$ $section Base Type Requirements for Conditional Expressions$$ $mindex CondExp require CPPAD_COND_EXP_REL$$ $head Purpose$$ These definitions are required by the user's code to support the $codei%AD<%Base%>%$$ type for $cref CondExp$$ operations: $head CompareOp$$ The following $code enum$$ type is used in the specifications below: $codep namespace CppAD { // The conditional expression operator enum type enum CompareOp { CompareLt, // less than CompareLe, // less than or equal CompareEq, // equal CompareGe, // greater than or equal CompareGt, // greater than CompareNe // not equal }; } $$ $head CondExpTemplate$$ The type $icode Base$$ must support the syntax $codei% %result% = CppAD::CondExpOp( %cop%, %left%, %right%, %exp_if_true%, %exp_if_false% ) %$$ which computes implements the corresponding $cref CondExp$$ function when the result has prototype $codei% %Base% %result% %$$ The argument $icode cop$$ has prototype $codei% enum CppAD::CompareOp %cop% %$$ The other arguments have the prototype $codei% const %Base%& %left% const %Base%& %right% const %Base%& %exp_if_true% const %Base%& %exp_if_false% %$$ $subhead Ordered Type$$ If $icode Base$$ is a relatively simple type that supports $code <$$, $code <=$$, $code ==$$, $code >=$$, and $code >$$ operators its $code CondExpOp$$ function can be defined by $codei% namespace CppAD { inline %Base% CondExpOp( enum CppAD::CompareOp cop , const %Base% &left , const %Base% &right , const %Base% &exp_if_true , const %Base% &exp_if_false ) { return CondExpTemplate( cop, left, right, trueCase, falseCase); } } %$$ For example, see $cref/double CondExpOp/base_alloc.hpp/CondExpOp/$$. For an example of and implementation of $code CondExpOp$$ with a more involved $icode Base$$ type see $cref/adolc CondExpOp/base_adolc.hpp/CondExpOp/$$. $subhead Not Ordered$$ If the type $icode Base$$ does not support ordering, the $code CondExpOp$$ function does not make sense. In this case one might (but need not) define $code CondExpOp$$ as follows: $codei% namespace CppAD { inline %Base% CondExpOp( enum CompareOp cop , const %Base% &left , const %Base% &right , const %Base% &exp_if_true , const %Base% &exp_if_false ) { // attempt to use CondExp with a %Base% argument assert(0); return %Base%(0); } } %$$ For example, see $cref/complex CondExpOp/base_complex.hpp/CondExpOp/$$. $head CondExpRel$$ The macro invocation $codei% CPPAD_COND_EXP_REL(%Base%) %$$ uses $code CondExpOp$$ above to define the following functions $codei% CondExpLt(%left%, %right%, %exp_if_true%, %exp_if_false%) CondExpLe(%left%, %right%, %exp_if_true%, %exp_if_false%) CondExpEq(%left%, %right%, %exp_if_true%, %exp_if_false%) CondExpGe(%left%, %right%, %exp_if_true%, %exp_if_false%) CondExpGt(%left%, %right%, %exp_if_true%, %exp_if_false%) %$$ where the arguments have type $icode Base$$. This should be done inside of the CppAD namespace. For example, see $cref/base_alloc/base_alloc.hpp/CondExpRel/$$. $end */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file base_cond_exp.hpp CondExp operations that aid in meeting Base type requirements. */ /*! \def CPPAD_COND_EXP_BASE_REL(Type, Rel, Op) This macro defines the operation \verbatim CondExpRel(left, right, exp_if_true, exp_if_false) \endverbatim The argument \c Type is the \c Base type for this base require operation. The argument \c Rel is one of \c Lt, \c Le, \c Eq, \c Ge, \c Gt. The argument \c Op is the corresponding \c CompareOp value. */ # define CPPAD_COND_EXP_BASE_REL(Type, Rel, Op) \ inline Type CondExp##Rel( \ const Type& left , \ const Type& right , \ const Type& exp_if_true , \ const Type& exp_if_false ) \ { return CondExpOp(Op, left, right, exp_if_true, exp_if_false); \ } /*! \def CPPAD_COND_EXP_REL(Type) The macro defines the operations \verbatim CondExpLt(left, right, exp_if_true, exp_if_false) CondExpLe(left, right, exp_if_true, exp_if_false) CondExpEq(left, right, exp_if_true, exp_if_false) CondExpGe(left, right, exp_if_true, exp_if_false) CondExpGt(left, right, exp_if_true, exp_if_false) \endverbatim The argument \c Type is the \c Base type for this base require operation. */ # define CPPAD_COND_EXP_REL(Type) \ CPPAD_COND_EXP_BASE_REL(Type, Lt, CompareLt) \ CPPAD_COND_EXP_BASE_REL(Type, Le, CompareLe) \ CPPAD_COND_EXP_BASE_REL(Type, Eq, CompareEq) \ CPPAD_COND_EXP_BASE_REL(Type, Ge, CompareGe) \ CPPAD_COND_EXP_BASE_REL(Type, Gt, CompareGt) /*! Template function to implement Conditional Expressions for simple types that have comparision operators. \tparam CompareType is the type of the left and right operands to the comparision operator. \tparam ResultType is the type of the result, which is the same as \c CompareType except during forward and reverse mode sparese calculations. \param cop specifices which comparision to use; i.e., $code <$$, $code <=$$, $code ==$$, $code >=$$, $code >$$, or $code !=$$. \param left is the left operand to the comparision operator. \param right is the right operand to the comparision operator. \param exp_if_true is the return value is the comparision results in true. \param exp_if_false is the return value is the comparision results in false. \return see \c exp_if_true and \c exp_if_false above. */ template ResultType CondExpTemplate( enum CompareOp cop , const CompareType& left , const CompareType& right , const ResultType& exp_if_true , const ResultType& exp_if_false ) { ResultType returnValue; switch( cop ) { case CompareLt: if( left < right ) returnValue = exp_if_true; else returnValue = exp_if_false; break; case CompareLe: if( left <= right ) returnValue = exp_if_true; else returnValue = exp_if_false; break; case CompareEq: if( left == right ) returnValue = exp_if_true; else returnValue = exp_if_false; break; case CompareGe: if( left >= right ) returnValue = exp_if_true; else returnValue = exp_if_false; break; case CompareGt: if( left > right ) returnValue = exp_if_true; else returnValue = exp_if_false; break; default: CPPAD_ASSERT_UNKNOWN(0); returnValue = exp_if_true; } return returnValue; } } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/core/bool_valued.hpp0000644000175200017650000000224513057470466017464 0ustar coincoin-web// $Id$ # ifndef CPPAD_CORE_BOOL_VALUED_HPP # define CPPAD_CORE_BOOL_VALUED_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin BoolValued$$ $spell Bool $$ $section Bool Valued Operations and Functions with AD Arguments$$ $children% cppad/core/compare.hpp% cppad/core/near_equal_ext.hpp% cppad/core/bool_fun.hpp% cppad/core/par_var.hpp% cppad/core/equal_op_seq.hpp %$$ $table $rref Compare$$ $rref NearEqualExt$$ $rref BoolFun$$ $rref ParVar$$ $rref EqualOpSeq$$ $tend $end */ # include # include # include # include # include # endif cppad-20170000.3/cppad/utility.hpp0000644000175200017650000000334713057470466015750 0ustar coincoin-web// $Id$ # ifndef CPPAD_UTILITY_HPP # define CPPAD_UTILITY_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # endif cppad-20170000.3/cppad/local/0002755000175200017650000000000013057470467014622 5ustar coincoin-webcppad-20170000.3/cppad/local/sparse_pack.hpp0000644000175200017650000003442513057470466017633 0ustar coincoin-web// $Id: sparse_pack.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_SPARSE_PACK_HPP # define CPPAD_LOCAL_SPARSE_PACK_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sparse_pack.hpp Vector of sets of positive integers stored as a packed array of bools. */ // ========================================================================== /*! Vector of sets of postivie integers, each set stored as a packed boolean array. */ class sparse_pack_const_iterator; class sparse_pack { friend class sparse_pack_const_iterator; private: /// Type used to pack elements (should be the same as corresponding /// typedef in multiple_n_bit() in test_more/sparse_hacobian.cpp) typedef size_t Pack; /// Number of bits per Pack value static const size_t n_bit_ = std::numeric_limits::digits; /// Number of sets that we are representing /// (set by constructor and resize). size_t n_set_; /// Possible elements in each set are 0, 1, ..., end_ - 1 /// (set by constructor and resize). size_t end_; /// Number of \c Pack values necessary to represent \c end_ bits. /// (set by constructor and resize). size_t n_pack_; /// Data for all the sets. pod_vector data_; public: /// declare a const iterator typedef sparse_pack_const_iterator const_iterator; // ----------------------------------------------------------------- /*! Default constructor (no sets) */ sparse_pack(void) : n_set_(0) , end_(0) , n_pack_(0) { } // ----------------------------------------------------------------- /*! Make use of copy constructor an error \param v vector that we are attempting to make a copy of. */ sparse_pack(const sparse_pack& v) { // Error: // Probably a sparse_pack argument has been passed by value CPPAD_ASSERT_UNKNOWN(0); } // ----------------------------------------------------------------- /*! Destructor */ ~sparse_pack(void) { } // ----------------------------------------------------------------- /*! Change number of sets, set end, and initialize all sets as empty If \c n_set_in is zero, any memory currently allocated for this object is freed. Otherwise, new memory may be allocated for the sets (if needed). \param n_set_in is the number of sets in this vector of sets. \param end_in is the maximum element plus one. The minimum element is 0 and end must be greater than zero (unless n_set is also zero). */ void resize(size_t n_set_in, size_t end_in) { CPPAD_ASSERT_UNKNOWN( n_set_in == 0 || 0 < end_in ); n_set_ = n_set_in; end_ = end_in; if( n_set_ == 0 ) { data_.free(); return; } // now start a new vector with empty sets Pack zero(0); data_.erase(); n_pack_ = ( 1 + (end_ - 1) / n_bit_ ); size_t i = n_set_ * n_pack_; if( i > 0 ) { data_.extend(i); while(i--) data_[i] = zero; } } // ----------------------------------------------------------------- /*! Add one element to a set. \param index is the index for this set in the vector of sets. \param element is the element we are adding to the set. \par Checked Assertions \li index < n_set_ \li element < end_ */ void add_element(size_t index, size_t element) { static Pack one(1); CPPAD_ASSERT_UNKNOWN( index < n_set_ ); CPPAD_ASSERT_UNKNOWN( element < end_ ); size_t j = element / n_bit_; size_t k = element - j * n_bit_; Pack mask = one << k; data_[ index * n_pack_ + j] |= mask; } // ----------------------------------------------------------------- /*! Is an element of a set. \param index is the index for this set in the vector of sets. \param element is the element we are checking to see if it is in the set. \par Checked Assertions \li index < n_set_ \li element < end_ */ bool is_element(size_t index, size_t element) const { static Pack one(1); static Pack zero(0); CPPAD_ASSERT_UNKNOWN( index < n_set_ ); CPPAD_ASSERT_UNKNOWN( element < end_ ); size_t j = element / n_bit_; size_t k = element - j * n_bit_; Pack mask = one << k; return (data_[ index * n_pack_ + j] & mask) != zero; } // ----------------------------------------------------------------- /*! Assign the empty set to one of the sets. \param target is the index of the set we are setting to the empty set. \par Checked Assertions \li target < n_set_ */ void clear(size_t target) { // value with all its bits set to false static Pack zero(0); CPPAD_ASSERT_UNKNOWN( target < n_set_ ); size_t t = target * n_pack_; size_t j = n_pack_; while(j--) data_[t++] = zero; } // ----------------------------------------------------------------- /*! Assign one set equal to another set. \param this_target is the index (in this \c sparse_pack object) of the set being assinged. \param other_value is the index (in the other \c sparse_pack object) of the that we are using as the value to assign to the target set. \param other is the other \c sparse_pack object (which may be the same as this \c sparse_pack object). \par Checked Assertions \li this_target < n_set_ \li other_value < other.n_set_ \li n_pack_ == other.n_pack_ */ void assignment( size_t this_target , size_t other_value , const sparse_pack& other ) { CPPAD_ASSERT_UNKNOWN( this_target < n_set_ ); CPPAD_ASSERT_UNKNOWN( other_value < other.n_set_ ); CPPAD_ASSERT_UNKNOWN( n_pack_ == other.n_pack_ ); size_t t = this_target * n_pack_; size_t v = other_value * n_pack_; size_t j = n_pack_; while(j--) data_[t++] = other.data_[v++]; } // ----------------------------------------------------------------- /*! Assing a set equal to the union of two other sets. \param this_target is the index (in this \c sparse_pack object) of the set being assinged. \param this_left is the index (in this \c sparse_pack object) of the left operand for the union operation. It is OK for \a this_target and \a this_left to be the same value. \param other_right is the index (in the other \c sparse_pack object) of the right operand for the union operation. It is OK for \a this_target and \a other_right to be the same value. \param other is the other \c sparse_pack object (which may be the same as this \c sparse_pack object). \par Checked Assertions \li this_target < n_set_ \li this_left < n_set_ \li other_right < other.n_set_ \li n_pack_ == other.n_pack_ */ void binary_union( size_t this_target , size_t this_left , size_t other_right , const sparse_pack& other ) { CPPAD_ASSERT_UNKNOWN( this_target < n_set_ ); CPPAD_ASSERT_UNKNOWN( this_left < n_set_ ); CPPAD_ASSERT_UNKNOWN( other_right < other.n_set_ ); CPPAD_ASSERT_UNKNOWN( n_pack_ == other.n_pack_ ); size_t t = this_target * n_pack_; size_t l = this_left * n_pack_; size_t r = other_right * n_pack_; size_t j = n_pack_; while(j--) data_[t++] = ( data_[l++] | other.data_[r++] ); } // ----------------------------------------------------------------- /*! Assing a set equal to the intersection of two other sets. \par Warning This operation is not implemented for sparse_list and hence cannot be used for the sparsity calculations. \param this_target is the index (in this \c sparse_pack object) of the set being assinged. \param this_left is the index (in this \c sparse_pack object) of the left operand for the intersection operation. It is OK for \a this_target and \a this_left to be the same value. \param other_right is the index (in the other \c sparse_pack object) of the right operand for the intersection operation. It is OK for \a this_target and \a other_right to be the same value. \param other is the other \c sparse_pack object (which may be the same as this \c sparse_pack object). \par Checked Assertions \li this_target < n_set_ \li this_left < n_set_ \li other_right < other.n_set_ \li n_pack_ == other.n_pack_ */ void binary_intersection( size_t this_target , size_t this_left , size_t other_right , const sparse_pack& other ) { CPPAD_ASSERT_UNKNOWN( this_target < n_set_ ); CPPAD_ASSERT_UNKNOWN( this_left < n_set_ ); CPPAD_ASSERT_UNKNOWN( other_right < other.n_set_ ); CPPAD_ASSERT_UNKNOWN( n_pack_ == other.n_pack_ ); size_t t = this_target * n_pack_; size_t l = this_left * n_pack_; size_t r = other_right * n_pack_; size_t j = n_pack_; while(j--) data_[t++] = ( data_[l++] & other.data_[r++] ); } // ----------------------------------------------------------------- /*! Amount of memory used by this vector of sets \return The amount of memory in units of type unsigned char memory. */ size_t memory(void) const { return n_set_ * n_pack_ * sizeof(Pack); } // ----------------------------------------------------------------- /*! Fetch n_set for vector of sets object. \return Number of from sets for this vector of sets object */ size_t n_set(void) const { return n_set_; } // ----------------------------------------------------------------- /*! Fetch end for this vector of sets object. \return is the maximum element value plus one (the minimum element value is 0). */ size_t end(void) const { return end_; } }; // ========================================================================== /*! cons_iterator for one set of positive integers in a sparse_pack object. */ class sparse_pack_const_iterator { private: /// Type used to pack elements in sparse_pack typedef sparse_pack::Pack Pack; /// data for the entire vector of sets const pod_vector& data_; /// Number of bits per Pack value const size_t n_bit_; /// Number of Pack values necessary to represent end_ bits. const size_t n_pack_; /// Possible elements in each set are 0, 1, ..., end_ - 1; const size_t end_; /// index of this set in the vector of sets; const size_t index_; /// value of the next element in this set /// (use end_ for no such element exists; i.e., past end of the set). size_t next_element_; public: /// construct a const_iterator for a set in a sparse_pack object sparse_pack_const_iterator (const sparse_pack& pack, size_t index) : data_ ( pack.data_ ) , n_bit_ ( pack.n_bit_ ) , n_pack_ ( pack.n_pack_ ) , end_ ( pack.end_ ) , index_ ( index ) { static Pack one(1); CPPAD_ASSERT_UNKNOWN( index < pack.n_set_ ); // next_element_ = 0; if( next_element_ < end_ ) { Pack check = data_[ index_ * n_pack_ + 0 ]; if( check & one ) return; } // element with index zero is not in this set of integers, // advance to first element or end ++(*this); } /// advance to next element in this set sparse_pack_const_iterator& operator++(void) { static Pack one(1); CPPAD_ASSERT_UNKNOWN( next_element_ <= end_ ); if( next_element_ == end_ ) return *this; // ++next_element_; if( next_element_ == end_ ) return *this; // // initialize packed data index size_t j = next_element_ / n_bit_; // initialize bit index size_t k = next_element_ - j * n_bit_; // initialize mask size_t mask = one << k; // start search at this packed value Pack check = data_[ index_ * n_pack_ + j ]; // while( true ) { // check if this element is in the set if( check & mask ) return *this; // increment next element before checking this one next_element_++; if( next_element_ == end_ ) return *this; // shift mask to left one bit so corresponds to next_element_ // (use mask <<= 1. not one << k, so compiler knows value) k++; mask <<= 1; CPPAD_ASSERT_UNKNOWN( k <= n_bit_ ); // check if we must go to next packed data index if( k == n_bit_ ) { // get next packed value k = 0; mask = one; j++; CPPAD_ASSERT_UNKNOWN( j < n_pack_ ); check = data_[ index_ * n_pack_ + j ]; } } // should never get here CPPAD_ASSERT_UNKNOWN(false); return *this; } /// obtain value of this element of the set of positive integers /// (end_ for no such element) size_t operator*(void) const { return next_element_; } }; // ========================================================================== /*! Copy a user vector of sets sparsity pattern to an internal sparse_pack object. \tparam VectorSet is a simple vector with elements of type std::set. \param internal The input value of sparisty does not matter. Upon return it contains the same sparsity pattern as \c user (or the transposed sparsity pattern). \param user sparsity pattern that we are placing internal. \param n_set number of sets (rows) in the internal sparsity pattern. \param end end of set value (number of columns) in the interanl sparsity pattern. \param transpose if true, the user sparsity patter is the transposed. \param error_msg is the error message to display if some values in the user sparstiy pattern are not valid. */ template void sparsity_user2internal( sparse_pack& internal , const VectorSet& user , size_t n_set , size_t end , bool transpose , const char* error_msg ) { CPPAD_ASSERT_KNOWN(size_t( user.size() ) == n_set * end, error_msg ); // size of internal sparsity pattern internal.resize(n_set, end); if( transpose ) { // transposed pattern case for(size_t j = 0; j < end; j++) { for(size_t i = 0; i < n_set; i++) { if( user[ j * n_set + i ] ) internal.add_element(i, j); } } return; } else { for(size_t i = 0; i < n_set; i++) { for(size_t j = 0; j < end; j++) { if( user[ i * end + j ] ) internal.add_element(i, j); } } } return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/tanh_op.hpp0000644000175200017650000001345613057470466016771 0ustar coincoin-web// $Id: tanh_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_TANH_OP_HPP # define CPPAD_LOCAL_TANH_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file tanh_op.hpp Forward and reverse mode calculations for z = tanh(x). */ /*! Compute forward mode Taylor coefficient for result of op = TanOp. The C++ source code corresponding to this operation is \verbatim z = tanh(x) \endverbatim The auxillary result is \verbatim y = tanh(x)^2 \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_tanh_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* y = z - cap_order; size_t k; if( p == 0 ) { z[0] = tanh( x[0] ); y[0] = z[0] * z[0]; p++; } for(size_t j = p; j <= q; j++) { Base base_j = static_cast(j); z[j] = x[j]; for(k = 1; k <= j; k++) z[j] -= Base(k) * x[k] * y[j-k] / base_j; y[j] = z[0] * z[j]; for(k = 1; k <= j; k++) y[j] += z[k] * z[j-k]; } } /*! Multiple directions forward mode Taylor coefficient for op = TanOp. The C++ source code corresponding to this operation is \verbatim z = tanh(x) \endverbatim The auxillary result is \verbatim y = tanh(x)^2 \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_tanh_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; Base* y = z - num_taylor_per_var; size_t k; size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = Base(q) * ( x[m+ell] - x[m+ell] * y[0] ); for(k = 1; k < q; k++) z[m+ell] -= Base(k) * x[(k-1)*r+1+ell] * y[(q-k-1)*r+1+ell]; z[m+ell] /= Base(q); // y[m+ell] = Base(2) * z[m+ell] * z[0]; for(k = 1; k < q; k++) y[m+ell] += z[(k-1)*r+1+ell] * z[(q-k-1)*r+1+ell]; } } /*! Compute zero order forward mode Taylor coefficient for result of op = TanOp. The C++ source code corresponding to this operation is \verbatim z = tanh(x) \endverbatim The auxillary result is \verbatim y = cos(x) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_tanh_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; // called z in documentation Base* y = z - cap_order; // called y in documentation z[0] = tanh( x[0] ); y[0] = z[0] * z[0]; } /*! Compute reverse mode partial derivatives for result of op = TanOp. The C++ source code corresponding to this operation is \verbatim z = tanh(x) \endverbatim The auxillary result is \verbatim y = cos(x) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_tanh_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* z = taylor + i_z * cap_order; // called z in doc Base* pz = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* y = z - cap_order; // called y in documentation Base* py = pz - nc_partial; size_t j = d; size_t k; Base base_two(2); while(j) { px[j] += pz[j]; pz[j] /= Base(j); for(k = 1; k <= j; k++) { px[k] -= azmul(pz[j], y[j-k]) * Base(k); py[j-k] -= azmul(pz[j], x[k]) * Base(k); } for(k = 0; k < j; k++) pz[k] += azmul(py[j-1], z[j-k-1]) * base_two; --j; } px[0] += azmul(pz[0], Base(1) - y[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/mul_op.hpp0000644000175200017650000002257413057470466016635 0ustar coincoin-web// $Id: mul_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_MUL_OP_HPP # define CPPAD_LOCAL_MUL_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file mul_op.hpp Forward and reverse mode calculations for z = x * y. */ // --------------------------- Mulvv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = MulvvOp. The C++ source code corresponding to this operation is \verbatim z = x * y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op */ template inline void forward_mulvv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; size_t k; for(size_t d = p; d <= q; d++) { z[d] = Base(0); for(k = 0; k <= d; k++) z[d] += x[d-k] * y[k]; } } /*! Multiple directions forward mode Taylor coefficients for op = MulvvOp. The C++ source code corresponding to this operation is \verbatim z = x * y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_dir */ template inline void forward_mulvv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var; Base* y = taylor + arg[1] * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; size_t k, ell, m; for(ell = 0; ell < r; ell++) { m = (q-1)*r + ell + 1; z[m] = x[0] * y[m] + x[m] * y[0]; for(k = 1; k < q; k++) z[m] += x[(q-k-1)*r + ell + 1] * y[(k-1)*r + ell + 1]; } } /*! Compute zero order forward mode Taylor coefficients for result of op = MulvvOp. The C++ source code corresponding to this operation is \verbatim z = x * y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_0 */ template inline void forward_mulvv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x[0] * y[0]; } /*! Compute reverse mode partial derivatives for result of op = MulvvOp. The C++ source code corresponding to this operation is \verbatim z = x * y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails reverse_binary_op */ template inline void reverse_mulvv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Arguments const Base* x = taylor + arg[0] * cap_order; const Base* y = taylor + arg[1] * cap_order; // Partial derivatives corresponding to arguments and result Base* px = partial + arg[0] * nc_partial; Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t j = d + 1; size_t k; while(j) { --j; for(k = 0; k <= j; k++) { px[j-k] += azmul(pz[j], y[k]); py[k] += azmul(pz[j], x[j-k]); } } } // --------------------------- Mulpv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = MulpvOp. The C++ source code corresponding to this operation is \verbatim z = x * y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op */ template inline void forward_mulpv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; // Paraemter value Base x = parameter[ arg[0] ]; for(size_t d = p; d <= q; d++) z[d] = x * y[d]; } /*! Multiple directions forward mode Taylor coefficients for op = MulpvOp. The C++ source code corresponding to this operation is \verbatim z = x * y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_dir */ template inline void forward_mulpv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; size_t m = (q-1) * r + 1; Base* y = taylor + arg[1] * num_taylor_per_var + m; Base* z = taylor + i_z * num_taylor_per_var + m; // Paraemter value Base x = parameter[ arg[0] ]; for(size_t ell = 0; ell < r; ell++) z[ell] = x * y[ell]; } /*! Compute zero order forward mode Taylor coefficient for result of op = MulpvOp. The C++ source code corresponding to this operation is \verbatim z = x * y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_0 */ template inline void forward_mulpv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 ); // Paraemter value Base x = parameter[ arg[0] ]; // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x * y[0]; } /*! Compute reverse mode partial derivative for result of op = MulpvOp. The C++ source code corresponding to this operation is \verbatim z = x * y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails reverse_binary_op */ template inline void reverse_mulpv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Arguments Base x = parameter[ arg[0] ]; // Partial derivatives corresponding to arguments and result Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t j = d + 1; while(j) { --j; py[j] += azmul(pz[j], x); } } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/sparse_list.hpp0000644000175200017650000006533613057470466017675 0ustar coincoin-web# ifndef CPPAD_LOCAL_SPARSE_LIST_HPP # define CPPAD_LOCAL_SPARSE_LIST_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sparse_list.hpp Vector of sets of positive integers stored as singly linked lists in with the element values strictly increasing. */ // ========================================================================= /*! Vector of sets of positive integers, each set stored as a singly linked list. */ class sparse_list_const_iterator; class sparse_list { friend class sparse_list_const_iterator; public: /// declare a const iterator typedef sparse_list_const_iterator const_iterator; /// type used for each entry in a singly linked list. struct pair_size_t { /// For the first entry in each list, this is the reference count. /// For the other entries in the list this is an element of the set. size_t value; /// This is the index in data_ of the next entry in the list. /// If there are no more entries in the list, this value is zero. /// (The first entry in data_ is not used.) size_t next; }; private: // ----------------------------------------------------------------- /// Possible elements in each set are 0, 1, ..., end_ - 1; size_t end_; /// number of elements in data_ that have been allocated /// and are no longer being used. size_t data_not_used_; /*! The number of elements in this vector is the number of sets, which is also the number of singly linked lists. \li If the i-th set has no elements, start_[i] is zero. \li If the i-th set is non-empty, start_[i] is the index in data_ for the first entry in the i-th singly linked list for this set. In this case and data_[ start_[i] ].value is the reference count for this list and data_[ start_[i] ].next is not zero because there is at least one entry in this list. */ pod_vector start_; /// The data for all the singly linked lists. pod_vector data_; // ----------------------------------------------------------------- /*! Private member functiont that counts references to sets. \param index is the index of the set that we are counting the references to. \return if the set is empty, the return value is empty. Otherwise it is the number of sets that share the same linked list */ size_t reference_count(size_t index) const { size_t ret = start_[index]; if( ret != 0 ) { CPPAD_ASSERT_UNKNOWN( data_[ret].value != 0 ); CPPAD_ASSERT_UNKNOWN( data_[ret].next != 0 ); ret = data_[ret].value; } return ret; } // ----------------------------------------------------------------- /*! Private member function that counts number of elements in a set. \param index is the index in start_ of the set we are counting the elements of. */ size_t number_elements(size_t index) const { CPPAD_ASSERT_UNKNOWN(index < start_.size() ); size_t count = 0; size_t start = start_[index]; // check if the set is empty if( start == 0 ) return count; CPPAD_ASSERT_UNKNOWN( reference_count(index) > 0 ); // advance to the first element in the set size_t next = data_[start].next; while( next != 0 ) { CPPAD_ASSERT_UNKNOWN( data_[next].value < end_ ); count++; next = data_[next].next; } CPPAD_ASSERT_UNKNOWN( count > 0 ); return count; } // ----------------------------------------------------------------- /*! Member function that checks the number of data elements not used (effectively const, but modifies and restores values) */ void check_data_not_used(void) { // number of sets size_t n_set = start_.size(); // // save the reference counters pod_vector ref_count; ref_count.extend(n_set); for(size_t i = 0; i < n_set; i++) ref_count[i] = reference_count(i); // count the number of entries in the singly linked lists size_t number_list_entries = 0; for(size_t i = 0; i < start_.size(); i++) { size_t start = start_[i]; if( start != 0 ) { CPPAD_ASSERT_UNKNOWN( data_[start].value > 0 ); // decrement the reference counter data_[start].value--; // copy the list when we hit zero if( data_[start].value == 0 ) { // This should be the last reference to this linked list. // Restore reference count data_[start].value = ref_count[i]; // count number of entries in this list // (is one more than number in set) number_list_entries += number_elements(i) + 1; } } } CPPAD_ASSERT_UNKNOWN( number_list_entries + data_not_used_ == data_.size() ); return; } // ----------------------------------------------------------------- /*! Check if one of two sets is a subset of the other set \param one_this is the index in this sparse_list object of the first set. \param two_other is the index in other sparse_list object of the second set. \param other is the other sparse_list object (which may be the same as this sparse_list object). \return If zero, niether set is a subset of the other. If one, then set one is a subset of set two. If two, then set two is a subset of set one. If the two sets are equal, the value two is returned; i.e., the set in the other object is identified as a subset of the set in this object. */ size_t is_subset( size_t one_this , size_t two_other , const sparse_list& other ) const { CPPAD_ASSERT_UNKNOWN( one_this < start_.size() ); CPPAD_ASSERT_UNKNOWN( two_other < other.start_.size() ); CPPAD_ASSERT_UNKNOWN( end_ == other.end_ ); // // start size_t start_one = start_[one_this]; size_t start_two = other.start_[two_other]; if( start_two == 0 ) return 2; if( start_one == 0 ) return 1; // // next size_t next_one = data_[start_one].next; size_t next_two = other.data_[start_two].next; // // value size_t value_one = data_[next_one].value; size_t value_two = other.data_[next_two].value; // bool one_subset = true; bool two_subset = true; size_t value_union = std::min(value_one, value_two); while( (one_subset | two_subset) & (value_union < end_) ) { if( value_one > value_union ) two_subset = false; else { next_one = data_[next_one].next; if( next_one == 0 ) value_one = end_; else value_one = data_[next_one].value; } if( value_two > value_union ) one_subset = false; else { next_two = other.data_[next_two].next; if( next_two == 0 ) value_two = end_; else value_two = other.data_[next_two].value; } value_union = std::min(value_one, value_two); } if( two_subset ) return 2; if( one_subset ) return 1; return 0; } // ----------------------------------------------------------------- /*! Private member functions that does garbage collection. This routine should be called when the number entries in data_ that are not being used is greater that data_.size() / 2. Note that the size of data_ should equal the number of entries in the singly linked lists plust the number of entries in data_ that are not being used. (Note that data_[0] never gets used.) */ void collect_garbage(void) { CPPAD_ASSERT_UNKNOWN( data_not_used_ > data_.size() / 2 ); # ifndef NDEBUG check_data_not_used(); # endif // // number of sets including empty ones size_t n_set = start_.size(); // // copy the sets to a temporary data vector pod_vector data_tmp; data_tmp.extend(1); // data_tmp[0] will not be used // pod_vector start_tmp; start_tmp.extend(n_set); for(size_t i = 0; i < n_set; i++) { size_t start = start_[i]; if( start == 0 ) start_tmp[i] = 0; else { // check if this linked list has already been copied if( data_[start].next == 0 ) { // starting address in data_tmp has been stored here start_tmp[i] = data_[start].value; } else { size_t count = data_[start].value; size_t next = data_[start].next; // size_t tmp_start = data_tmp.extend(2); size_t next_tmp = tmp_start + 1; start_tmp[i] = tmp_start; data_tmp[tmp_start].value = count; data_tmp[tmp_start].next = next_tmp; // CPPAD_ASSERT_UNKNOWN( next != 0 ); while( next != 0 ) { CPPAD_ASSERT_UNKNOWN( data_[next].value < end_ ); data_tmp[next_tmp].value = data_[next].value; // next = data_[next].next; if( next == 0 ) data_tmp[next_tmp].next = 0; else { // data_tmp[next_tmp].next = data_tmp.extend(1); // does not seem to work ? size_t tmp = data_tmp.extend(1); data_tmp[next_tmp].next = tmp; next_tmp = tmp; } } // store the starting address here data_[start].value = tmp_start; // flag that indicates this link list already copied data_[start].next = 0; } } } // swap the tmp and old data vectors start_.swap(start_tmp); data_.swap(data_tmp); // all of the elements, except the first, are used data_not_used_ = 1; } // ----------------------------------------------------------------- /*! Make a separate copy of the shared list \param index is the index, in the vector of sets, for this list. */ void separate_copy(size_t index) { size_t ref_count = reference_count(index); if( ref_count <= 1 ) return; // size_t start = start_[index]; size_t next = data_[start].next; size_t value = data_[next].value; // size_t copy_cur = data_.extend(2); size_t copy_next = copy_cur + 1; start_[index] = copy_cur; data_[copy_cur].value = 1; data_[copy_cur].next = copy_next; copy_cur = copy_next; // CPPAD_ASSERT_UNKNOWN( value < end_ ); while( value < end_ ) { data_[copy_cur].value = value; // next = data_[next].next; if( next == 0 ) { value = end_; data_[copy_cur].next = 0; } else { value = data_[next].value; data_[copy_cur].next = data_.extend(1); } } CPPAD_ASSERT_UNKNOWN( next == 0 ); // // decrement reference count CPPAD_ASSERT_UNKNOWN( data_[start].value == ref_count ); data_[start].value--; // } // ----------------------------------------------------------------- /*! Using copy constructor is a programing (not user) error \param v vector of sets that we are attempting to make a copy of. */ sparse_list(const sparse_list& v) { // Error: Probably a sparse_list argument has been passed by value CPPAD_ASSERT_UNKNOWN(false); } public: // ----------------------------------------------------------------- /*! Default constructor (no sets) */ sparse_list(void) : end_(0) , data_not_used_(0) { } // ----------------------------------------------------------------- /// Destructor ~sparse_list(void) { } // ----------------------------------------------------------------- /*! Start a new vector of sets. \param n_set_in is the number of sets in this vector of sets. \li If n_set_in is zero, any memory currently allocated for this object is freed. Otherwise, new memory may be allocated for the sets (if needed). \li If n_set_in is non-zero, a vector of n_set_in is created and all the sets are initilaized as empty. \param end_in is the maximum element plus one (the minimum element is 0). */ void resize(size_t n_set_in, size_t end_in) { if( n_set_in == 0 ) { // restore object to start after constructor // (no memory allocated for this object) data_.free(); start_.free(); data_not_used_ = 0; end_ = 0; // return; } end_ = end_in; // start_.erase(); start_.extend(n_set_in); for(size_t i = 0; i < n_set_in; i++) start_[i] = 0; // data_.erase(); data_.extend(1); // first element is not used data_not_used_ = 1; } // ----------------------------------------------------------------- /*! check an element is in a set. \param index is the index for this set in the vector of sets. \param element is the element we are checking to see if it is in the set. */ bool is_element(size_t index, size_t element) const { CPPAD_ASSERT_UNKNOWN( index < start_.size() ); CPPAD_ASSERT_UNKNOWN( element < end_ ); // size_t start = start_[index]; if( start == 0 ) return false; // CPPAD_ASSERT_UNKNOWN( data_[start].value > 0 ); CPPAD_ASSERT_UNKNOWN( data_[start].next > 0 ); // size_t next = data_[start].next; size_t value = data_[next].value; while( value < element ) { next = data_[next].next; if( next == 0 ) value = end_; else value = data_[next].value; } return element == value; } // ----------------------------------------------------------------- /*! Add one element to a set. \param index is the index for this set in the vector of sets. \param element is the element we are adding to the set. */ void add_element(size_t index, size_t element) { CPPAD_ASSERT_UNKNOWN( index < start_.size() ); CPPAD_ASSERT_UNKNOWN( element < end_ ); // check if element is already in the set if( is_element(index, element) ) return; // check for case where starting set is empty size_t start = start_[index]; if( start == 0 ) { start = data_.extend(2); start_[index] = start; size_t next = start + 1; data_[start].value = 1; // reference count data_[start].next = next; data_[next].value = element; data_[next].next = 0; return; } // make sure that we have a separate copy of this set separate_copy(index); // CPPAD_ASSERT_UNKNOWN( reference_count(index) == 1 ); size_t previous = start_[index]; size_t next = data_[previous].next; size_t value = data_[next].value; CPPAD_ASSERT_UNKNOWN( value < end_ ); while( value < element ) { previous = next; next = data_[next].next; if( next == 0 ) value = end_; else value = data_[next].value; } CPPAD_ASSERT_UNKNOWN( element < value ) // size_t insert = data_.extend(1); data_[insert].next = next; data_[previous].next = insert; data_[insert].value = element; // } // ----------------------------------------------------------------- /*! Assign the empty set to one of the sets. \param target is the index of the set we are setting to the empty set. \par data_not_used_ increments this value by number of data_ elements that are lost (unlinked) by this operation. */ void clear(size_t target) { CPPAD_ASSERT_UNKNOWN( target < start_.size() ); // number of references to this set size_t ref_count = reference_count(target); // case by reference count if( ref_count > 1 ) { // just remove this reference size_t start = start_[target]; start_[target] = 0; CPPAD_ASSERT_UNKNOWN( data_[start].value == ref_count ); data_[start].value--; } else if( ref_count == 1 ) { // number of data_ elements that will be lost by this operation size_t number_delete = number_elements(target) + 1; // delete the elements from the set start_[target] = 0; // adjust data_not_used_ data_not_used_ += number_delete; if( data_not_used_ > data_.size() / 2 ) collect_garbage(); } // } // ----------------------------------------------------------------- /*! Assign one set equal to another set. \param this_target is the index in this sparse_list object of the set being assinged. \param other_source is the index in the other \c sparse_list object of the set that we are using as the value to assign to the target set. \param other is the other sparse_list object (which may be the same as this sparse_list object). This must have the same value for end_. \par data_not_used_ increments this value by number of elements lost. */ void assignment( size_t this_target , size_t other_source , const sparse_list& other ) { CPPAD_ASSERT_UNKNOWN( this_target < start_.size() ); CPPAD_ASSERT_UNKNOWN( other_source < other.start_.size() ); CPPAD_ASSERT_UNKNOWN( end_ == other.end_ ); // check if we are assigning a set to itself if( (this == &other) & (this_target == other_source) ) return; // number of list elements that will be deleted by this operation size_t number_delete = 0; size_t ref_count = reference_count(this_target); size_t start = start_[this_target]; if( ref_count == 1 ) number_delete = number_elements(this_target) + 1; else if (ref_count > 1 ) { // decrement reference counter CPPAD_ASSERT_UNKNOWN( data_[start].value > 1 ) data_[start].value--; } // If this and other are the same, use another reference to same list size_t other_start = other.start_[other_source]; if( this == &other ) { start_[this_target] = other_start; if( other_start != 0 ) { data_[other_start].value++; // increment reference count CPPAD_ASSERT_UNKNOWN( data_[other_start].value > 1 ); } } else if( other_start == 0 ) { // the target list is empty start_[this_target] = 0; } else { // make a copy of the other list in this sparse_list size_t this_start = data_.extend(2); size_t this_next = this_start + 1; start_[this_target] = this_start; data_[this_start].value = 1; // reference count data_[this_start].next = this_next; // size_t next = other.data_[other_start].next; CPPAD_ASSERT_UNKNOWN( next != 0 ); while( next != 0 ) { data_[this_next].value = other.data_[next].value; next = other.data_[next].next; if( next == 0 ) data_[this_next].next = 0; else { size_t tmp = data_.extend(1); data_[this_next].next = tmp; this_next = tmp; } } } // adjust data_not_used_ data_not_used_ += number_delete; // check if time for garbage collection if( data_not_used_ > data_.size() / 2 ) collect_garbage(); // } // ----------------------------------------------------------------- /*! Assign a set equal to the union of two other sets. \param this_target is the index in this sparse_list object of the set being assinged. \param this_left is the index in this sparse_list object of the left operand for the union operation. It is OK for this_target and this_left to be the same value. \param other_right is the index in the other sparse_list object of the right operand for the union operation. It is OK for this_target and other_right to be the same value. \param other is the other sparse_list object (which may be the same as this sparse_list object). */ void binary_union( size_t this_target , size_t this_left , size_t other_right , const sparse_list& other ) { CPPAD_ASSERT_UNKNOWN( this_target < start_.size() ); CPPAD_ASSERT_UNKNOWN( this_left < start_.size() ); CPPAD_ASSERT_UNKNOWN( other_right < other.start_.size() ); CPPAD_ASSERT_UNKNOWN( end_ == other.end_ ); // check if one of the two operands is a subset of the the other size_t subset = is_subset(this_left, other_right, other); // case where right is a subset of left or right and left are equal if( subset == 2 ) { assignment(this_target, this_left, *this); return; } // case where the left is a subset of right and they are not equal if( subset == 1 ) { assignment(this_target, other_right, other); return; } // if niether case holds, then both left and right are non-empty CPPAD_ASSERT_UNKNOWN( reference_count(this_left) > 0 ); CPPAD_ASSERT_UNKNOWN( other.reference_count(other_right) > 0 ); // must get all the start indices before modify start_this // (incase start_this is the same as start_left or start_right) size_t start_target = start_[this_target]; size_t start_left = start_[this_left]; size_t start_right = other.start_[other_right]; // number of list elements that will be deleted by this operation size_t number_delete = 0; size_t ref_count = reference_count(this_target); if( ref_count == 1 ) number_delete = number_elements(this_target) + 1; else if (ref_count > 1 ) { // decrement reference counter CPPAD_ASSERT_UNKNOWN( data_[start_target].value > 1 ) data_[start_target].value--; } // start the new list size_t start = data_.extend(1); size_t next = start; start_[this_target] = start; data_[start].value = 1; // reference count // next for left and right lists size_t next_left = data_[start_left].next; size_t next_right = other.data_[start_right].next; // value for left and right sets size_t value_left = data_[next_left].value; size_t value_right = other.data_[next_right].value; CPPAD_ASSERT_UNKNOWN( value_left < end_ && value_right < end_ ); while( (value_left < end_) | (value_right < end_) ) { if( value_left == value_right ) { // advance right so left and right are no longer equal next_right = other.data_[next_right].next; if( next_right == 0 ) value_right = end_; else value_right = other.data_[next_right].value; } if( value_left < value_right ) { size_t tmp = data_.extend(1); data_[next].next = tmp; next = tmp; data_[next].value = value_left; // advance left to its next element next_left = data_[next_left].next; if( next_left == 0 ) value_left = end_; else value_left = data_[next_left].value; } else { CPPAD_ASSERT_UNKNOWN( value_right < value_left ) size_t tmp = data_.extend(1); data_[next].next = tmp; next = tmp; data_[next].value = value_right; // advance right to its next element next_right = other.data_[next_right].next; if( next_right == 0 ) value_right = end_; else value_right = other.data_[next_right].value; } } data_[next].next = 0; // adjust data_not_used_ data_not_used_ += number_delete; if( data_not_used_ > data_.size() / 2 ) collect_garbage(); // } // ----------------------------------------------------------------- /*! Fetch n_set for vector of sets object. \return Number of from sets for this vector of sets object */ size_t n_set(void) const { return start_.size(); } // ----------------------------------------------------------------- /*! Fetch end for this vector of sets object. \return is the maximum element value plus one (the minimum element value is 0). */ size_t end(void) const { return end_; } // ----------------------------------------------------------------- /*! Sum over all sets of the number of elements /return The the total number of elements */ size_t number_elements(void) const { size_t i, count; count = 0; for(i = 0; i < start_.size(); i++) count += number_elements(i); return count; } }; // ========================================================================= /*! cons_iterator for one set of positive integers in a sparse_list object. */ class sparse_list_const_iterator { private: /// type used by sparse_list to represent one element of the list typedef sparse_list::pair_size_t pair_size_t; /// data for the entire vector of sets const pod_vector& data_; /// Possible elements in a list are 0, 1, ..., end_ - 1; const size_t end_; /// next element in the singly linked list /// (next_pair_.value == end_ for past end of list) pair_size_t next_pair_; public: /// construct a const_iterator for a list in a sparse_list object sparse_list_const_iterator (const sparse_list& list, size_t index) : data_( list.data_ ) , end_ ( list.end_ ) { CPPAD_ASSERT_UNKNOWN( index < list.start_.size() ); size_t start = list.start_[index]; if( start == 0 ) { next_pair_.next = 0; next_pair_.value = end_; } else { // value for this entry is reference count for list CPPAD_ASSERT_UNKNOWN( data_[start].value > 0 ); // index where list truely starts size_t next = data_[start].next; CPPAD_ASSERT_UNKNOWN( next != 0 ); // true first entry in the list next_pair_ = data_[next]; CPPAD_ASSERT_UNKNOWN( next_pair_.value < end_ ); } } /// advance to next element in this list sparse_list_const_iterator& operator++(void) { if( next_pair_.next == 0 ) next_pair_.value = end_; else { next_pair_ = data_[next_pair_.next]; CPPAD_ASSERT_UNKNOWN( next_pair_.value < end_ ); } return *this; } /// obtain value of this element of the set of positive integers /// (end_ for no such element) size_t operator*(void) { return next_pair_.value; } }; // ========================================================================= // Tell pod_vector class that each pair_size_t is plain old data and hence // the corresponding constructor need not be called. template <> inline bool is_pod(void) { return true; } /*! Copy a user vector of sets sparsity pattern to an internal sparse_list object. \tparam VectorSet is a simple vector with elements of type std::set. \param internal The input value of sparisty does not matter. Upon return it contains the same sparsity pattern as \c user (or the transposed sparsity pattern). \param user sparsity pattern that we are placing internal. \param n_set number of sets (rows) in the internal sparsity pattern. \param end end of set value (number of columns) in the interanl sparsity pattern. \param transpose if true, the user sparsity patter is the transposed. \param error_msg is the error message to display if some values in the user sparstiy pattern are not valid. */ template void sparsity_user2internal( sparse_list& internal , const VectorSet& user , size_t n_set , size_t end , bool transpose , const char* error_msg ) { # ifndef NDEBUG if( transpose ) CPPAD_ASSERT_KNOWN( size_t(end) == user.size(), error_msg); if( ! transpose ) CPPAD_ASSERT_KNOWN( size_t(n_set) == user.size(), error_msg); # endif // iterator for user set std::set::const_iterator itr; // size of internal sparsity pattern internal.resize(n_set, end); if( transpose ) { // transposed pattern case for(size_t j = 0; j < end; j++) { itr = user[j].begin(); while(itr != user[j].end()) { size_t i = *itr++; CPPAD_ASSERT_KNOWN(i < n_set, error_msg); internal.add_element(i, j); } } } else { for(size_t i = 0; i < n_set; i++) { itr = user[i].begin(); while(itr != user[i].end()) { size_t j = *itr++; CPPAD_ASSERT_KNOWN( j < end, error_msg); internal.add_element(i, j); } } } return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/user_state.hpp0000644000175200017650000000201013057470466017477 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_USER_STATE_HPP # define CPPAD_LOCAL_USER_STATE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE enum enum_user_state { /// next UserOp marks beginning of a user atomic call start_user, /// next UsrapOp (UsravOp) is a parameter (variable) argument arg_user, /// next UsrrpOp (UsrrvOp) is a parameter (variable) result ret_user, /// next UserOp marks end of a user atomic call end_user }; } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/forward1sweep.hpp0000644000175200017650000006546313057470466020137 0ustar coincoin-web// $Id: forward1sweep.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_FORWARD1SWEEP_HPP # define CPPAD_LOCAL_FORWARD1SWEEP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file forward1sweep.hpp Compute one Taylor coefficient for each order requested. */ /* \def CPPAD_ATOMIC_CALL This avoids warnings when NDEBUG is defined and user_ok is not used. If NDEBUG is defined, this resolves to \code user_atom->forward \endcode otherwise, it respolves to \code user_ok = user_atom->forward \endcode This macro is undefined at the end of this file to facillitate its use with a different definition in other files. */ # ifdef NDEBUG # define CPPAD_ATOMIC_CALL user_atom->forward # else # define CPPAD_ATOMIC_CALL user_ok = user_atom->forward # endif /*! \def CPPAD_FORWARD1SWEEP_TRACE This value is either zero or one. Zero is the normal operational value. If it is one, a trace of every forward1sweep computation is printed. */ # define CPPAD_FORWARD1SWEEP_TRACE 0 /*! Compute arbitrary order forward mode Taylor coefficients. \tparam Base The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD. \param s_out Is the stream where output corresponding to PriOp operations will be written. \param print If print is false, suppress the output that is otherwise generated by the c PriOp instructions. \param n is the number of independent variables on the tape. \param numvar is the total number of variables on the tape. This is also equal to the number of rows in the matrix taylor; i.e., play->num_var_rec(). \param play The information stored in play is a recording of the operations corresponding to the function \f[ F : {\bf R}^n \rightarrow {\bf R}^m \f] where \f$ n \f$ is the number of independent variables and \f$ m \f$ is the number of dependent variables. \n \n The object play is effectly constant. The exception to this is that while palying back the tape the object play holds information about the current location with in the tape and this changes during palyback. \param J Is the number of columns in the coefficient matrix taylor. This must be greater than or equal one. \param cskip_op Is a vector with size play->num_op_rec(). \n \n p = 0 \n In this case, the input value of the elements does not matter. Upon return, if cskip_op[i] is true, the operator with index i does not affect any of the dependent variable (given the value of the independent variables). \n \n p > 0 \n In this case cskip_op is not modified and has the same meaning as its return value above. \param var_by_load_op is a vector with size play->num_load_op_rec(). \n \n p == 0 \n In this case, The input value of the elements does not matter. Upon return, it is the variable index corresponding the result for each load operator. In the case where the index is zero, the load operator results in a parameter (not a variable). Note that the is no variable with index zero on the tape. \n \n p > 0 \n In this case var_by_load_op is not modified and has the meaning as its return value above. \param p is the lowest order of the Taylor coefficients that are computed during this call. \param q is the highest order of the Taylor coefficients that are computed during this call. \param taylor \n \b Input: For i = 1 , ... , numvar-1, k = 0 , ... , p-1, taylor[ J*i + k] is the k-th order Taylor coefficient corresponding to the i-th variable. \n \n \b Input: For i = 1 , ... , n, k = p , ... , q, taylor[ J*j + k] is the k-th order Taylor coefficient corresponding to the i-th variable (these are the independent varaibles). \n \n \b Output: For i = n+1 , ... , numvar-1, and k = 0 , ... , p-1, taylor[ J*i + k] is the k-th order Taylor coefficient corresponding to the i-th variable. \param compare_change_count Is the count value for changing number and op_index during zero order foward mode. \param compare_change_number If p is non-zero, this value is not changed, otherwise: If compare_change_count is zero, this value is set to zero, otherwise: this value is set to the number of comparision operations that have a different result from when the information in play was recorded. \param compare_change_op_index if p is non-zero, this value is not changed, otherwise: If compare_change_count is zero, this value is set to zero. Otherwise it is the operator index (see forward_next) for the count-th comparision operation that has a different result from when the information in play was recorded. */ template void forward1sweep( std::ostream& s_out, const bool print, const size_t p, const size_t q, const size_t n, const size_t numvar, local::player* play, const size_t J, Base* taylor, bool* cskip_op, pod_vector& var_by_load_op, size_t compare_change_count, size_t& compare_change_number, size_t& compare_change_op_index ) { // number of directions const size_t r = 1; CPPAD_ASSERT_UNKNOWN( p <= q ); CPPAD_ASSERT_UNKNOWN( J >= q + 1 ); CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar ); /* */ // op code for current instruction OpCode op; // index for current instruction size_t i_op; // next variables size_t i_var; // operation argument indices const addr_t* arg = CPPAD_NULL; // initialize the comparision operator counter if( p == 0 ) { compare_change_number = 0; compare_change_op_index = 0; } // If this includes a zero calculation, initialize this information pod_vector isvar_by_ind; pod_vector index_by_ind; if( p == 0 ) { size_t i; // this includes order zero calculation, initialize vector indices size_t num = play->num_vec_ind_rec(); if( num > 0 ) { isvar_by_ind.extend(num); index_by_ind.extend(num); for(i = 0; i < num; i++) { index_by_ind[i] = play->GetVecInd(i); isvar_by_ind[i] = false; } } // includes zero order, so initialize conditional skip flags num = play->num_op_rec(); for(i = 0; i < num; i++) cskip_op[i] = false; } // work space used by UserOp. vector user_vx; // empty vecotor vector user_vy; // empty vecotor vector user_tx; // argument vector Taylor coefficients vector user_ty; // result vector Taylor coefficients // atomic_base* user_atom = CPPAD_NULL; // user's atomic op calculator # ifndef NDEBUG bool user_ok = false; // atomic op return value # endif // // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state = start_user; // proper initialization // length of the parameter vector (used by CppAD assert macros) const size_t num_par = play->num_par_rec(); // pointer to the beginning of the parameter vector const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // length of the text vector (used by CppAD assert macros) const size_t num_text = play->num_text_rec(); // pointer to the beginning of the text vector const char* text = CPPAD_NULL; if( num_text > 0 ) text = play->GetTxt(0); /* */ // temporary indices size_t i, k; // number of orders for this user calculation // (not needed for order zero) const size_t user_q1 = q+1; // variable indices for results vector // (done differently for order zero). vector user_iy; // skip the BeginOp at the beginning of the recording play->forward_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == BeginOp ); // # if CPPAD_FORWARD1SWEEP_TRACE bool user_trace = false; std::cout << std::endl; # endif // bool flag; // a temporary flag to use in switch cases bool more_operators = true; while(more_operators) { // this op play->forward_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( (i_op > n) | (op == InvOp) ); CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) ); CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() ); CPPAD_ASSERT_ARG_BEFORE_RESULT(op, arg, i_var); // check if we are skipping this operation while( cskip_op[i_op] ) { switch(op) { case CSumOp: // CSumOp has a variable number of arguments play->forward_csum(op, arg, i_op, i_var); break; case CSkipOp: // CSkip has a variable number of arguments play->forward_cskip(op, arg, i_op, i_var); break; case UserOp: { // skip all operations in this user atomic call CPPAD_ASSERT_UNKNOWN( user_state == start_user ); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); size_t n_skip = user_m + user_n + 1; for(i = 0; i < n_skip; i++) { play->forward_next(op, arg, i_op, i_var); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); } CPPAD_ASSERT_UNKNOWN( user_state == start_user ); } break; default: break; } play->forward_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() ); } // action depends on the operator switch( op ) { case AbsOp: forward_abs_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case AddvvOp: forward_addvv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case AddpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_addpv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case AcosOp: // sqrt(1 - x * x), acos(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_acos_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AcoshOp: // sqrt(x * x - 1), acosh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_acosh_op(p, q, i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case AsinOp: // sqrt(1 - x * x), asin(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_asin_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AsinhOp: // sqrt(1 + x * x), asinh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_asinh_op(p, q, i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case AtanOp: // 1 + x * x, atan(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_atan_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AtanhOp: // 1 - x * x, atanh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_atanh_op(p, q, i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case CExpOp: forward_cond_op( p, q, i_var, arg, num_par, parameter, J, taylor ); break; // --------------------------------------------------- case CosOp: // sin(x), cos(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_cos_op(p, q, i_var, arg[0], J, taylor); break; // --------------------------------------------------- case CoshOp: // sinh(x), cosh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_cosh_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case CSkipOp: // CSkipOp has a variable number of arguments and // forward_next thinks it has no arguments. // we must inform forward_next of this special case. if( p == 0 ) { forward_cskip_op_0( i_var, arg, num_par, parameter, J, taylor, cskip_op ); } play->forward_cskip(op, arg, i_op, i_var); break; // ------------------------------------------------- case CSumOp: // CSumOp has a variable number of arguments and // forward_next thinks it has no arguments. // we must inform forward_next of this special case. forward_csum_op( p, q, i_var, arg, num_par, parameter, J, taylor ); play->forward_csum(op, arg, i_op, i_var); break; // ------------------------------------------------- case DisOp: forward_dis_op(p, q, r, i_var, arg, J, taylor); break; // ------------------------------------------------- case DivvvOp: forward_divvv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case DivpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_divpv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case DivvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_divvp_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case EndOp: CPPAD_ASSERT_NARG_NRES(op, 0, 0); more_operators = false; break; // ------------------------------------------------- case EqpvOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_eqpv_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; // ------------------------------------------------- case EqvvOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_eqvv_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case ErfOp: CPPAD_ASSERT_UNKNOWN( CPPAD_USE_CPLUSPLUS_2011 ); forward_erf_op(p, q, i_var, arg, parameter, J, taylor); break; # endif // ------------------------------------------------- case ExpOp: forward_exp_op(p, q, i_var, arg[0], J, taylor); break; // --------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Expm1Op: forward_expm1_op(p, q, i_var, arg[0], J, taylor); break; # endif // --------------------------------------------------- case InvOp: CPPAD_ASSERT_NARG_NRES(op, 0, 1); break; // ------------------------------------------------- case LdpOp: if( p == 0 ) { forward_load_p_op_0( play, i_var, arg, parameter, J, taylor, isvar_by_ind.data(), index_by_ind.data(), var_by_load_op.data() ); if( p < q ) forward_load_op( play, op, p+1, q, r, J, i_var, arg, var_by_load_op.data(), taylor ); } else forward_load_op( play, op, p, q, r, J, i_var, arg, var_by_load_op.data(), taylor ); break; // ------------------------------------------------- case LdvOp: if( p == 0 ) { forward_load_v_op_0( play, i_var, arg, parameter, J, taylor, isvar_by_ind.data(), index_by_ind.data(), var_by_load_op.data() ); if( p < q ) forward_load_op( play, op, p+1, q, r, J, i_var, arg, var_by_load_op.data(), taylor ); } else forward_load_op( play, op, p, q, r, J, i_var, arg, var_by_load_op.data(), taylor ); break; // ------------------------------------------------- case LepvOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_lepv_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; case LevpOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_levp_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; // ------------------------------------------------- case LevvOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_levv_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; // ------------------------------------------------- case LogOp: forward_log_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Log1pOp: forward_log1p_op(p, q, i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case LtpvOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_ltpv_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; case LtvpOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_ltvp_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; // ------------------------------------------------- case LtvvOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_ltvv_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; // ------------------------------------------------- case MulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_mulpv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case MulvvOp: forward_mulvv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case NepvOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_nepv_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; // ------------------------------------------------- case NevvOp: if( ( p == 0 ) & ( compare_change_count > 0 ) ) { forward_nevv_op_0( compare_change_number, arg, parameter, J, taylor ); if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } break; // ------------------------------------------------- case ParOp: i = p; if( i == 0 ) { forward_par_op_0( i_var, arg, num_par, parameter, J, taylor ); i++; } while(i <= q) { taylor[ i_var * J + i] = Base(0); i++; } break; // ------------------------------------------------- case PowvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_powvp_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PowpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_powpv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PowvvOp: forward_powvv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PriOp: if( (p == 0) & print ) forward_pri_0(s_out, arg, num_text, text, num_par, parameter, J, taylor ); break; // ------------------------------------------------- case SignOp: // sign(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sign_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SinOp: // cos(x), sin(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sin_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SinhOp: // cosh(x), sinh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sinh_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SqrtOp: forward_sqrt_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case StppOp: if( p == 0 ) { forward_store_pp_op_0( i_var, arg, num_par, J, taylor, isvar_by_ind.data(), index_by_ind.data() ); } break; // ------------------------------------------------- case StpvOp: if( p == 0 ) { forward_store_pv_op_0( i_var, arg, num_par, J, taylor, isvar_by_ind.data(), index_by_ind.data() ); } break; // ------------------------------------------------- case StvpOp: if( p == 0 ) { forward_store_vp_op_0( i_var, arg, num_par, J, taylor, isvar_by_ind.data(), index_by_ind.data() ); } break; // ------------------------------------------------- case StvvOp: if( p == 0 ) { forward_store_vv_op_0( i_var, arg, num_par, J, taylor, isvar_by_ind.data(), index_by_ind.data() ); } break; // ------------------------------------------------- case SubvvOp: forward_subvv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case SubpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_subpv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case SubvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_subvp_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case TanOp: // tan(x)^2, tan(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_tan_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case TanhOp: // tanh(x)^2, tanh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_tanh_op(p, q, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case UserOp: // start or end an atomic operation sequence flag = user_state == start_user; user_atom = play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( flag ) { user_tx.resize(user_n * user_q1); user_ty.resize(user_m * user_q1); user_iy.resize(user_m); } else { // call users function for this operation user_atom->set_old(user_old); CPPAD_ATOMIC_CALL( p, q, user_vx, user_vy, user_tx, user_ty ); # ifndef NDEBUG if( ! user_ok ) { std::string msg = user_atom->afun_name() + ": atomic_base.forward: returned false"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif for(i = 0; i < user_m; i++) if( user_iy[i] > 0 ) for(k = p; k <= q; k++) taylor[ user_iy[i] * J + k ] = user_ty[ i * user_q1 + k ]; # if CPPAD_FORWARD1SWEEP_TRACE user_trace = true; # endif } break; case UsrapOp: // parameter argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); user_tx[user_j * user_q1 + 0] = parameter[ arg[0]]; for(k = 1; k < user_q1; k++) user_tx[user_j * user_q1 + k] = Base(0); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsravOp: // variable argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var ); for(k = 0; k < user_q1; k++) user_tx[user_j * user_q1 + k] = taylor[ arg[0] * J + k]; play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrpOp: // parameter result in an atomic operation sequence user_iy[user_i] = 0; user_ty[user_i * user_q1 + 0] = parameter[ arg[0]]; for(k = 1; k < p; k++) user_ty[user_i * user_q1 + k] = Base(0); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrvOp: // variable result in an atomic operation sequence user_iy[user_i] = i_var; for(k = 0; k < p; k++) user_ty[user_i * user_q1 + k] = taylor[ i_var * J + k]; play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; // ------------------------------------------------- case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_zmulpv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_zmulvp_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case ZmulvvOp: forward_zmulvv_op(p, q, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- default: CPPAD_ASSERT_UNKNOWN(0); } # if CPPAD_FORWARD1SWEEP_TRACE if( user_trace ) { user_trace = false; CPPAD_ASSERT_UNKNOWN( op == UserOp ); CPPAD_ASSERT_UNKNOWN( NumArg(UsrrvOp) == 0 ); for(i = 0; i < user_m; i++) if( user_iy[i] > 0 ) { size_t i_tmp = (i_op + i) - user_m; printOp( std::cout, play, i_tmp, user_iy[i], UsrrvOp, CPPAD_NULL ); Base* Z_tmp = taylor + user_iy[i] * J; printOpResult( std::cout, q + 1, Z_tmp, 0, (Base *) CPPAD_NULL ); std::cout << std::endl; } } Base* Z_tmp = taylor + J * i_var; const addr_t* arg_tmp = arg; if( op == CSumOp ) arg_tmp = arg - arg[-1] - 4; if( op == CSkipOp ) arg_tmp = arg - arg[-1] - 7; if( op != UsrrvOp ) { printOp( std::cout, play, i_op, i_var, op, arg_tmp ); if( NumRes(op) > 0 ) printOpResult( std::cout, q + 1, Z_tmp, 0, (Base *) CPPAD_NULL ); std::cout << std::endl; } } std::cout << std::endl; # else } # endif CPPAD_ASSERT_UNKNOWN( user_state == start_user ); CPPAD_ASSERT_UNKNOWN( i_var + 1 == play->num_var_rec() ); if( (p == 0) & (compare_change_count == 0) ) compare_change_number = 0; return; } // preprocessor symbols that are local to this file # undef CPPAD_FORWARD1SWEEP_TRACE # undef CPPAD_ATOMIC_CALL } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/atanh_op.hpp0000644000175200017650000001401513057470466017122 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_ATANH_OP_HPP # define CPPAD_LOCAL_ATANH_OP_HPP # if CPPAD_USE_CPLUSPLUS_2011 /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file atanh_op.hpp Forward and reverse mode calculations for z = atanh(x). */ /*! Forward mode Taylor coefficient for result of op = AtanhOp. The C++ source code corresponding to this operation is \verbatim z = atanh(x) \endverbatim The auxillary result is \verbatim y = 1 - x * x \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_atanh_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AtanhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AtanhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation size_t k; if( p == 0 ) { z[0] = atanh( x[0] ); b[0] = Base(1) - x[0] * x[0]; p++; } for(size_t j = p; j <= q; j++) { b[j] = - Base(2) * x[0] * x[j]; z[j] = Base(0); for(k = 1; k < j; k++) { b[j] -= x[k] * x[j-k]; z[j] -= Base(k) * z[k] * b[j-k]; } z[j] /= Base(j); z[j] += x[j]; z[j] /= b[0]; } } /*! Multiple direction Taylor coefficient for op = AtanhOp. The C++ source code corresponding to this operation is \verbatim z = atanh(x) \endverbatim The auxillary result is \verbatim y = 1 - x * x \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_atanh_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AtanhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AtanhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; Base* b = z - num_taylor_per_var; // called y in documentation size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { b[m+ell] = - Base(2) * x[m+ell] * x[0]; z[m+ell] = Base(q) * x[m+ell]; for(size_t k = 1; k < q; k++) { b[m+ell] -= x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell]; z[m+ell] -= Base(k) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; } z[m+ell] /= ( Base(q) * b[0] ); } } /*! Zero order forward mode Taylor coefficient for result of op = AtanhOp. The C++ source code corresponding to this operation is \verbatim z = atanh(x) \endverbatim The auxillary result is \verbatim y = 1 - x * x \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_atanh_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AtanhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AtanhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation z[0] = atanh( x[0] ); b[0] = Base(1) - x[0] * x[0]; } /*! Reverse mode partial derivatives for result of op = AtanhOp. The C++ source code corresponding to this operation is \verbatim z = atanh(x) \endverbatim The auxillary result is \verbatim y = 1 - x * x \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_atanh_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AtanhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AtanhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* b = z - cap_order; // called y in documentation Base* pb = pz - nc_partial; Base inv_b0 = Base(1) / b[0]; // number of indices to access size_t j = d; size_t k; while(j) { // scale partials w.r.t z[j] and b[j] pz[j] = azmul(pz[j], inv_b0); pb[j] *= Base(2); pb[0] -= azmul(pz[j], z[j]); px[j] += pz[j] - azmul(pb[j], x[0]); px[0] -= azmul(pb[j], x[j]); // more scaling of partials w.r.t z[j] pz[j] /= Base(j); for(k = 1; k < j; k++) { pb[j-k] -= Base(k) * azmul(pz[j], z[k]); pz[k] -= Base(k) * azmul(pz[j], b[j-k]); px[k] -= azmul(pb[j], x[j-k]); } --j; } px[0] += azmul(pz[0], inv_b0) - Base(2) * azmul(pb[0], x[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif # endif cppad-20170000.3/cppad/local/player.hpp0000644000175200017650000010132113057470466016622 0ustar coincoin-web// $Id: player.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_PLAYER_HPP # define CPPAD_LOCAL_PLAYER_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file player.hpp File used to define the player class. */ /*! Class used to store and play back an operation sequence recording. \tparam Base These were AD< Base > operations when recorded. Operations during playback are done using the type Base . */ template class player { private: // ---------------------------------------------------------------------- // Variables that define the recording // ---------------------------------------------------------------------- /// Number of variables in the recording. size_t num_var_rec_; /// number of vecad load opeations in the reconding size_t num_load_op_rec_; /// Number of VecAD vectors in the recording size_t num_vecad_vec_rec_; /// The operators in the recording. pod_vector op_rec_; /// The VecAD indices in the recording. pod_vector vecad_ind_rec_; /// The operation argument indices in the recording pod_vector op_arg_rec_; /// The parameters in the recording. /// Note that Base may not be plain old data, so use false in consructor. pod_vector par_rec_; /// Character strings ('\\0' terminated) in the recording. pod_vector text_rec_; // ---------------------------------------------------------------------- // Variables used for iterating thorough operators in the recording // ---------------------------------------------------------------------- /// Current operator OpCode op_; /// Index in recording corresponding to current operator size_t op_index_; /// Current offset of the argument indices in op_arg_rec_ const addr_t* op_arg_; /// Index for primary (last) variable corresponding to current operator size_t var_index_; /// index for the current user atomic function size_t user_index_; # ifndef NDEBUG /// Flag indicating that a special function must be called before next bool special_before_next_; # endif public: // ================================================================= /// constructor player(void) : num_var_rec_(0) , num_load_op_rec_(0) , op_rec_( std::numeric_limits::max() ) , vecad_ind_rec_( std::numeric_limits::max() ) , op_arg_rec_( std::numeric_limits::max() ) , par_rec_( std::numeric_limits::max() ) , text_rec_( std::numeric_limits::max() ) { } // ================================================================= /// destructor ~player(void) { } // =============================================================== /*! Moving an operation sequence from a recorder to this player \param rec the object that was used to record the operation sequence. After this operation, the state of the recording is no longer defined. For example, the pod_vector member variables in this have been swapped with rec . */ void get(recorder& rec) { size_t i; // just set size_t values num_var_rec_ = rec.num_var_rec_; num_load_op_rec_ = rec.num_load_op_rec_; // op_rec_ op_rec_.swap(rec.op_rec_); // vec_ind_rec_ vecad_ind_rec_.swap(rec.vecad_ind_rec_); // op_arg_rec_ op_arg_rec_.swap(rec.op_arg_rec_); // par_rec_ par_rec_.swap(rec.par_rec_); // text_rec_ text_rec_.swap(rec.text_rec_); // set the number of VecAD vectors num_vecad_vec_rec_ = 0; for(i = 0; i < vecad_ind_rec_.size(); i += vecad_ind_rec_[i] + 1) num_vecad_vec_rec_++; // vecad_ind_rec_ contains size of each VecAD followed by // the parameter indices used to iniialize it. CPPAD_ASSERT_UNKNOWN( i == vecad_ind_rec_.size() ); } // =============================================================== /*! Copying an operation sequence from another player to this one \param play the object that contains the operatoion sequence to copy. */ void operator=(const player& play) { num_var_rec_ = play.num_var_rec_; num_load_op_rec_ = play.num_load_op_rec_; op_rec_ = play.op_rec_; num_vecad_vec_rec_ = play.num_vecad_vec_rec_; vecad_ind_rec_ = play.vecad_ind_rec_; op_arg_rec_ = play.op_arg_rec_; par_rec_ = play.par_rec_; text_rec_ = play.text_rec_; } // =============================================================== /// Erase the recording stored in the player void Erase(void) { num_var_rec_ = 0; num_load_op_rec_ = 0; num_vecad_vec_rec_ = 0; op_rec_.erase(); vecad_ind_rec_.erase(); op_arg_rec_.erase(); par_rec_.erase(); text_rec_.erase(); } // ================================================================ // const functions that retrieve infromation from this player // ================================================================ /*! \brief fetch an operator from the recording. \return the i-th operator in the recording. \param i the index of the operator in recording */ OpCode GetOp (size_t i) const { return OpCode(op_rec_[i]); } /*! \brief Fetch a VecAD index from the recording. \return the i-th VecAD index in the recording. \param i the index of the VecAD index in recording */ size_t GetVecInd (size_t i) const { return vecad_ind_rec_[i]; } /*! \brief Fetch a parameter from the recording. \return the i-th parameter in the recording. \param i the index of the parameter in recording */ Base GetPar(size_t i) const { return par_rec_[i]; } /*! \brief Fetch entire parameter vector from the recording. \return the entire parameter vector. */ const Base* GetPar(void) const { return par_rec_.data(); } /*! \brief Fetch a '\\0' terminated string from the recording. \return the beginning of the string. \param i the index where the string begins. */ const char *GetTxt(size_t i) const { CPPAD_ASSERT_UNKNOWN(i < text_rec_.size() ); return text_rec_.data() + i; } /// Fetch number of variables in the recording. size_t num_var_rec(void) const { return num_var_rec_; } /// Fetch number of vecad load operations size_t num_load_op_rec(void) const { return num_load_op_rec_; } /// Fetch number of operators in the recording. size_t num_op_rec(void) const { return op_rec_.size(); } /// Fetch number of VecAD indices in the recording. size_t num_vec_ind_rec(void) const { return vecad_ind_rec_.size(); } /// Fetch number of VecAD vectors in the recording size_t num_vecad_vec_rec(void) const { return num_vecad_vec_rec_; } /// Fetch number of argument indices in the recording. size_t num_op_arg_rec(void) const { return op_arg_rec_.size(); } /// Fetch number of parameters in the recording. size_t num_par_rec(void) const { return par_rec_.size(); } /// Fetch number of characters (representing strings) in the recording. size_t num_text_rec(void) const { return text_rec_.size(); } /// Fetch a rough measure of amount of memory used to store recording /// (just lengths, not capacities). size_t Memory(void) const { return op_rec_.size() * sizeof(OpCode) + op_arg_rec_.size() * sizeof(addr_t) + par_rec_.size() * sizeof(Base) + text_rec_.size() * sizeof(char) + vecad_ind_rec_.size() * sizeof(addr_t) ; } // ===================================================================== // Forward iteration over operations in this player // ===================================================================== /*! Start a play back of the recording during a forward sweep. Use repeated calls to forward_next to play back one operator at a time. \param op [out] The input value of op does not matter. Its output value is the first operator in the recording; i.e., BeginOp. \param op_arg [out] The input value of op_arg does not matter. Its output value is the beginning of the vector of argument indices for the first operation; i.e., 0 \param op_index [out] The input value of op_index does not matter. Its output value is the index of the next first operator in the recording; i.e., 0. \param var_index [out] The input value of var_index does not matter. Its output value is the index of the primary (last) result corresponding to the the first operator (which must be a BeginOp); i.e., 0. */ void forward_start( OpCode& op , const addr_t*& op_arg , size_t& op_index , size_t& var_index ) { op = op_ = OpCode( op_rec_[0] ); op_arg = op_arg_ = op_arg_rec_.data(); op_index = op_index_ = 0; var_index = var_index_ = 0; # ifndef NDEBUG special_before_next_ = false; CPPAD_ASSERT_UNKNOWN( op_ == BeginOp ); CPPAD_ASSERT_NARG_NRES(op_, 1, 1); # endif return; } /*! Fetch the next operator during a forward sweep. Use forward_start to initialize forward play back to the first operator; i.e., the BeginOp at the beginning of the recording. We use the notation forward_routine to denote the set forward_start, forward_next, forward_csum, forward_cskip, forward_user. \param op [in,out] The input value of op must be its output value from the previous call to a forward_routine. Its output value is the next operator in the recording. For speed, forward_next does not check for the special cases where op == CSumOp (op == CSkipOp). In this case some of the return values from forward_next must be corrected by a call to forward_csum (forward_cskip). In addition, for speed, extra information that is only used by the UserOp, UsrapOp, UsravOp, UsrrpOp, UsrrvOp operations is not returned for all operations. If this information is needed, then forward_user should be called after each call to forward_next. \param op_arg [in,out] The input value of op_arg must be its output value form the previous call to a forward routine. Its output value is the beginning of the vector of argument indices for this operation. \param op_index [in,out] The input value of op_index must be its output value form the previous call to a forward routine. Its output value is the index of this operator in the recording. Thus the ouput value following the previous call to forward_start is one. In addition, the output value increases by one with each call to forward_next. \param var_index [in,out] The input value of var_index must be its output value form the previous call to a forward routine. Its output value is the index of the primary (last) result corresponding to the operator op. */ void forward_next( OpCode& op , const addr_t*& op_arg , size_t& op_index , size_t& var_index ) { CPPAD_ASSERT_UNKNOWN( ! special_before_next_ ); CPPAD_ASSERT_UNKNOWN( op_ == op ); CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_index == op_index_ ); CPPAD_ASSERT_UNKNOWN( var_index == var_index_ ); // index for the next operator op_index = ++op_index_; // first argument for next operator op_arg = op_arg_ += NumArg(op_); // next operator op = op_ = OpCode( op_rec_[ op_index_ ] ); // index for last result for next operator var_index = var_index_ += NumRes(op); # ifndef NDEBUG special_before_next_ = (op == CSumOp) | (op == CSkipOp); // CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_arg_ + NumArg(op) <= op_arg_rec_.data() + op_arg_rec_.size() ); CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ ); # endif } /*! Correct forward_next return values when op == CSumOp. \param op [in] The input value of op must be the return value from the previous call to forward_next and must be CSumOp. It is not modified. \param op_arg [in,out] The input value of op_arg must be the return value from the previous call to forward_next. Its output value is the beginning of the vector of argument indices for the next operation. \param op_index [in] The input value of op_index must be the return value from the previous call to forward_next. Its is not modified. \param var_index [in] The input value of var_index must be the return value from the previous call to forward_next. It is not modified. */ void forward_csum( const OpCode& op , const addr_t*& op_arg , const size_t& op_index , const size_t& var_index ) { CPPAD_ASSERT_UNKNOWN( op_ == op ); CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_index == op_index_ ); CPPAD_ASSERT_UNKNOWN( var_index == var_index_ ); CPPAD_ASSERT_UNKNOWN( op == CSumOp ); CPPAD_ASSERT_UNKNOWN( NumArg(CSumOp) == 0 ); CPPAD_ASSERT_UNKNOWN( op_arg[0] + op_arg[1] == op_arg[ 3 + op_arg[0] + op_arg[1] ] ); /* The only thing that really needs fixing is op_arg_. Actual number of arugments for this operator is op_arg[0] + op_arg[1] + 4. We must change op_arg_ so that when you add NumArg(CSumOp) you get first argument for next operator in sequence. */ op_arg = op_arg_ += op_arg[0] + op_arg[1] + 4; # ifndef NDEBUG CPPAD_ASSERT_UNKNOWN( special_before_next_ ); special_before_next_ = false; // CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_arg_ + NumArg(op) <= op_arg_rec_.data() + op_arg_rec_.size() ); CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ ); # endif } /*! Correct forward_next return values when op == CSkipOp. \param op [in] The input value of op must be the return value from the previous call to forward_next and must be CSkipOp. It is not modified. \param op_arg [in,out] The input value of op_arg must be the return value from the previous call to forward_next. Its output value is the beginning of the vector of argument indices for the next operation. \param op_index [in] The input value of op_index must be the return value from the previous call to forward_next. Its is not modified. \param var_index [in] The input value of var_index must be the return value from the previous call to forward_next. It is not modified. */ void forward_cskip( const OpCode& op , const addr_t*& op_arg , const size_t& op_index , const size_t& var_index ) { CPPAD_ASSERT_UNKNOWN( op_ == op ); CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_index == op_index_ ); CPPAD_ASSERT_UNKNOWN( var_index == var_index_ ); CPPAD_ASSERT_UNKNOWN( op == CSkipOp ); CPPAD_ASSERT_UNKNOWN( NumArg(CSkipOp) == 0 ); CPPAD_ASSERT_UNKNOWN( op_arg[4] + op_arg[5] == op_arg[ 6 + op_arg[4] + op_arg[5] ] ); /* The only thing that really needs fixing is op_arg_. Actual number of arugments for this operator is 7 + op_arg[4] + op_arg[5] We must change op_arg_ so that when you add NumArg(CSkipOp) you get first argument for next operator in sequence. */ op_arg = op_arg_ += 7 + op_arg[4] + op_arg[5]; # ifndef NDEBUG CPPAD_ASSERT_UNKNOWN( special_before_next_ ); special_before_next_ = false; // CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_arg_ + NumArg(op) <= op_arg_rec_.data() + op_arg_rec_.size() ); CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ ); # endif } /*! Extra information when forward_next returns one of the following op values: UserOp, UsrapOp, UsravOp, UsrrpOp, UsrrvOp. \param op [in] The value of op must be the return value from the previous call to forward_next and one of those listed above. \param user_state [in,out] This should be initialized to start_user before each call to forward_start and not otherwise changed by the calling program. Upon return it is the state of the user atomic call as follows: \li start_user next user operator will be UserOp at beginning of a call \li arg_user next operator will be UsrapOp or UsravOp. \li ret_user next operator will be UsrrpOp or UsrrvOp. \li end_user next operator will be UserOp at end of a call \param user_old [in,out] This should not be changed by the calling program. Upon return it is the extra information used by the old_atomic interface. \param user_m [in,out] This should not be changed by the calling program. Upon return it is the number of results for this user atomic function. \param user_n [in,out] This should not be changed by the calling program. Upon return it is the number of arguments to this user atomic function. \param user_i [in,out] This should not be changed by the calling program. Upon return it is the index for the next result for this user atomic function; i.e., the next UsrrpOp or UsrrvOp. If there are no more results, the return value is user_m. \param user_j [in,out] This should not be changed by the calling program. Upon return it is the index for the next argument for this user atomic function; i.e., the next UsrapOp or UsravOp. If there are no more arguments, the return value is user_n. \return the return value is a pointer to the atomic_base object for the correspnding function. If the corresponding user function has been deleted, an CPPAD_ASSERT_KNOWN is generated and a null pointer is returned. \par Initialization The initial value of user_old, user_m, user_n, user_i, user_j do not matter. They may be initialized to avoid compiler warnings. */ atomic_base* forward_user( const OpCode& op , enum_user_state& user_state , size_t& user_old , size_t& user_m , size_t& user_n , size_t& user_i , size_t& user_j ) { atomic_base* user_atom; switch(op) { case UserOp: CPPAD_ASSERT_NARG_NRES(op, 4, 0); if( user_state == start_user ) { // forward_user arguments determined by values in UserOp user_index_ = op_arg_[0]; user_old = op_arg_[1]; user_n = op_arg_[2]; user_m = op_arg_[3]; CPPAD_ASSERT_UNKNOWN( user_n > 0 ); // other forward_user arguments user_j = 0; user_i = 0; user_state = arg_user; # ifndef NDEBUG user_atom = atomic_base::class_object(user_index_); if( user_atom == CPPAD_NULL ) { // user_atom is null so cannot use user_atom->afun_name() std::string msg = atomic_base::class_name(user_index_) + ": atomic_base function has been deleted"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif } else { // copy of UsrOp at end of this atomic sequence CPPAD_ASSERT_UNKNOWN( user_state == end_user ); CPPAD_ASSERT_UNKNOWN( user_index_ == size_t(op_arg_[0]) ); CPPAD_ASSERT_UNKNOWN( user_old == size_t(op_arg_[1]) ); CPPAD_ASSERT_UNKNOWN( user_n == size_t(op_arg_[2]) ); CPPAD_ASSERT_UNKNOWN( user_m == size_t(op_arg_[3]) ); CPPAD_ASSERT_UNKNOWN( user_j == user_n ); CPPAD_ASSERT_UNKNOWN( user_i == user_m ); user_state = start_user; } break; case UsrapOp: case UsravOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 ); CPPAD_ASSERT_UNKNOWN( user_state == arg_user ); CPPAD_ASSERT_UNKNOWN( user_i == 0 ); CPPAD_ASSERT_UNKNOWN( user_j < user_n ); ++user_j; if( user_j == user_n ) user_state = ret_user; break; case UsrrpOp: case UsrrvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 || op == UsrrvOp ); CPPAD_ASSERT_UNKNOWN( NumArg(op) == 0 || op == UsrrpOp ); CPPAD_ASSERT_UNKNOWN( user_state == ret_user ); CPPAD_ASSERT_UNKNOWN( user_i < user_m ); CPPAD_ASSERT_UNKNOWN( user_j == user_n ); ++user_i; if( user_i == user_m ) user_state = end_user; break; default: CPPAD_ASSERT_UNKNOWN(false); } // the atomic_base object corresponding to this user function user_atom = atomic_base::class_object(user_index_); CPPAD_ASSERT_UNKNOWN( user_atom != CPPAD_NULL ); return user_atom; } // ===================================================================== // Reverse iteration over operations in this player // ===================================================================== /*! Start a play back of the recording during a reverse sweep. Use repeated calls to reverse_next to play back one operator at a time. \param op [out] The input value of op does not matter. Its output value is the last operator in the recording; i.e., EndOp. \param op_arg [out] The input value of op_arg does not matter. Its output value is the beginning of the vector of argument indices for the last operation; (there are no arguments for the last operation so op_arg is invalid). \param op_index [out[ The input value of op_index does not matter. Its output value is the index of the last operator in the recording. \param var_index [out] The input value of var_index does not matter. Its output value is the index of the primary (last) result corresponding to the the last operator (which must be a EndOp). (there are no results for the last operation so var_index is invalid). */ void reverse_start( OpCode& op , const addr_t*& op_arg , size_t& op_index , size_t& var_index ) { op_arg = op_arg_ = op_arg_rec_.data() + op_arg_rec_.size(); op_index = op_index_ = op_rec_.size() - 1; var_index = var_index_ = num_var_rec_ - 1; op = op_ = OpCode( op_rec_[ op_index_ ] ); # ifndef NDEBUG special_before_next_ = false; CPPAD_ASSERT_UNKNOWN( op_ == EndOp ); CPPAD_ASSERT_NARG_NRES(op, 0, 0); # endif return; } /*! Fetch the next operator during a reverse sweep. Use reverse_start to initialize reverse play back to the last operator; i.e., the EndOp at the end of the recording. We use the notation reverse_routine to denote the set reverse_start, reverse_next, reverse_csum, reverse_cskip, reverse_user. \param op [in,out] The input value of op must be its output value from the previous call to a reverse_routine. Its output value is the next operator in the recording (in reverse order). For speed, reverse_next does not check for the special cases where op == CSumOp (op == CSkipOp). In this case some of the return values from reverse_next must be corrected by a call to reverse_csum (reverse_cskip). In addition, for speed, extra information that is only used by the UserOp, UsrapOp, UsravOp, UsrrpOp, UsrrvOp operations is not returned for all operations. If this information is needed, then reverse_user should be called after each call to reverse_next. \param op_arg [in,out] The input value of op_arg must be its output value from the previous call to a reverse_routine. Its output value is the beginning of the vector of argument indices for this operation. \param op_index [in,out] The input value of op_index must be its output value from the previous call to a reverse_routine. Its output value is the index of this operator in the recording. Thus the output value following the previous call to reverse_start is equal to the number of operators in the recording minus one. In addition, the output value decreases by one with each call to reverse_next. The last operator, BeginOp, sets op_index equal to 0. \param var_index [in,out] The input value of var_index must be its output value from the previous call to a reverse_routine. Its output value is the index of the primary (last) result corresponding to the operator op. The last operator sets var_index equal to 0 (corresponding to BeginOp at beginning of operation sequence). */ void reverse_next( OpCode& op , const addr_t*& op_arg , size_t& op_index , size_t& var_index ) { CPPAD_ASSERT_UNKNOWN( ! special_before_next_ ); CPPAD_ASSERT_UNKNOWN( op_ == op ); CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_index == op_index_ ); CPPAD_ASSERT_UNKNOWN( var_index == var_index_ ); // index of the last result for the next operator CPPAD_ASSERT_UNKNOWN( var_index_ >= NumRes(op_) ); var_index = var_index_ -= NumRes(op_); // next operator CPPAD_ASSERT_UNKNOWN( op_index_ > 0 ); op_index = --op_index_; // index op = op_ = OpCode( op_rec_[ op_index_ ] ); // value // first argument for next operator op_arg = op_arg_ -= NumArg(op); # ifndef NDEBUG special_before_next_ = (op == CSumOp) | (op == CSkipOp); // CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_arg_ + NumArg(op) <= op_arg_rec_.data() + op_arg_rec_.size() ); # endif } /*! Correct reverse_next return values when op == CSumOp. \param op [in] The input value of op must be the return value from the previous call to reverse_next and must be CSumOp. It is not modified. \param op_arg [in,out] The input value of op_arg must be the return value from the previous call to reverse_next. Its output value is the beginning of the vector of argument indices for this operation. \param op_index [in] The input value of op_index must be the return value from the previous call to reverse_next. It is not modified. \param var_index [in] The input value of var_index must be the return value from the previous call to reverse_next. It is not modified. */ void reverse_csum( const OpCode& op , const addr_t*& op_arg , const size_t& op_index , const size_t& var_index ) { CPPAD_ASSERT_UNKNOWN( op_ == op ); CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_index == op_index_ ); CPPAD_ASSERT_UNKNOWN( var_index == var_index_ ); CPPAD_ASSERT_UNKNOWN( op == CSumOp ); CPPAD_ASSERT_UNKNOWN( NumArg(CSumOp) == 0 ); /* The variables that need fixing are op_arg_ and op_arg. Currently, op_arg points to the last argument for the previous operator. */ // last argument for this csum operation --op_arg; // first argument for this csum operation op_arg = op_arg_ -= (op_arg[0] + 4); // now op_arg points to the first argument for this csum operator CPPAD_ASSERT_UNKNOWN( op_arg[0] + op_arg[1] == op_arg[ 3 + op_arg[0] + op_arg[1] ] ); # ifndef NDEBUG CPPAD_ASSERT_UNKNOWN( special_before_next_ ); special_before_next_ = false; // CPPAD_ASSERT_UNKNOWN( op_index_ < op_rec_.size() ); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ ); CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ ); # endif } /*! Correct reverse_next return values when op == CSkipOp. \param op [int] The input value of op must be the return value from the previous call to reverse_next and must be CSkipOp. It is not modified. \param op_arg [in,out] The input value of op_arg must be the return value from the previous call to reverse_next. Its output value is the beginning of the vector of argument indices for this operation. \param op_index [in] The input value of op_index must be the return value from the previous call to reverse_next. It is not modified. \param var_index [in] The input value of var_index must be the return value from the previous call to reverse_next. It is not modified. */ void reverse_cskip( const OpCode& op , const addr_t*& op_arg , const size_t& op_index , const size_t& var_index ) { CPPAD_ASSERT_UNKNOWN( op_ == op ); CPPAD_ASSERT_UNKNOWN( op_arg == op_arg_ ); CPPAD_ASSERT_UNKNOWN( op_index == op_index_ ); CPPAD_ASSERT_UNKNOWN( var_index == var_index_ ); CPPAD_ASSERT_UNKNOWN( op == CSkipOp ); CPPAD_ASSERT_UNKNOWN( NumArg(CSkipOp) == 0 ); /* The variables that need fixing are op_arg_ and op_arg. Currently, op_arg points to the last arugment for the previous operator. */ // last argument for this cskip operation --op_arg; // first argument for this cskip operation op_arg = op_arg_ -= (op_arg[0] + 7); CPPAD_ASSERT_UNKNOWN( op_arg[4] + op_arg[5] == op_arg[ 6 + op_arg[4] + op_arg[5] ] ); # ifndef NDEBUG CPPAD_ASSERT_UNKNOWN( special_before_next_ ); special_before_next_ = false; // CPPAD_ASSERT_UNKNOWN( op_index_ < op_rec_.size() ); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.data() <= op_arg_ ); CPPAD_ASSERT_UNKNOWN( var_index_ < num_var_rec_ ); # endif } /*! Extra information when reverse_next returns one of the following op values: UserOp, UsrapOp, UsravOp, UsrrpOp, UsrrvOp. \param op [in] The value of op must be the return value from the previous call to reverse_next and one of those listed above. \param user_state [in,out] This should be initialized to end_user before each call to reverse_start and not otherwise changed by the calling program. Upon return it is the state of the user atomic call as follows: \li end_user next user operator will be UserOp at end of a call \li ret_user next operator will be UsrrpOp or UsrrvOp. \li arg_user next operator will be UsrapOp or UsravOp. \li start_user next operator will be UserOp at beginning of a call \param user_old [in,out] This should not be changed by the calling program. Upon return it is the extra information used by the old_atomic interface. \param user_m [in,out] This should not be changed by the calling program. Upon return it is the number of results for this user atomic function. \param user_n [in,out] This should not be changed by the calling program. Upon return it is the number of arguments to this user atomic function. \param user_i [in,out] This should not be changed by the calling program. Upon return it is the index for this result for this user atomic function; i.e., this UsrrpOp or UsrrvOp. If the input value of user_state is end_user, the return value is user_m. \param user_j [in,out] This should not be changed by the calling program. Upon return it is the index for this argument for this user atomic function; i.e., this UsrapOp or UsravOp. If the input value of user_state is end_user, the return value is user_n. \return the return value is a pointer to the atomic_base object for the correspnding function. If the corresponding user function has been deleted, an CPPAD_ASSERT_KNOWN is generated and a null pointer is returned. \par Initialization The initial value of user_old, user_m, user_n, user_i, user_j do not matter. They may be initialized to avoid compiler warnings. */ atomic_base* reverse_user( const OpCode& op , enum_user_state& user_state , size_t& user_old , size_t& user_m , size_t& user_n , size_t& user_i , size_t& user_j ) { atomic_base* user_atom; switch(op) { case UserOp: CPPAD_ASSERT_NARG_NRES(op, 4, 0); if( user_state == end_user ) { // reverse_user arguments determined by values in UserOp user_index_ = op_arg_[0]; user_old = op_arg_[1]; user_n = op_arg_[2]; user_m = op_arg_[3]; CPPAD_ASSERT_UNKNOWN( user_n > 0 ); // other reverse_user arguments user_j = user_n; user_i = user_m; user_state = ret_user; // the atomic_base object corresponding to this user function # ifndef NDEBUG user_atom = atomic_base::class_object(user_index_); if( user_atom == CPPAD_NULL ) { // user_atom is null so cannot use user_atom->afun_name() std::string msg = atomic_base::class_name(user_index_) + ": atomic_base function has been deleted"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif } else { // copy of UsrOp at end of this atomic sequence CPPAD_ASSERT_UNKNOWN( user_state == start_user ); CPPAD_ASSERT_UNKNOWN( user_index_ == size_t(op_arg_[0]) ); CPPAD_ASSERT_UNKNOWN( user_old == size_t(op_arg_[1]) ); CPPAD_ASSERT_UNKNOWN( user_n == size_t(op_arg_[2]) ); CPPAD_ASSERT_UNKNOWN( user_m == size_t(op_arg_[3]) ); CPPAD_ASSERT_UNKNOWN( user_j == 0 ); CPPAD_ASSERT_UNKNOWN( user_i == 0 ); user_state = end_user; } break; case UsrapOp: case UsravOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 ); CPPAD_ASSERT_UNKNOWN( user_state == arg_user ); CPPAD_ASSERT_UNKNOWN( user_i == 0 ); CPPAD_ASSERT_UNKNOWN( user_j <= user_n ); CPPAD_ASSERT_UNKNOWN( 0 < user_j ); --user_j; if( user_j == 0 ) user_state = start_user; break; case UsrrpOp: case UsrrvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 || op == UsrrvOp ); CPPAD_ASSERT_UNKNOWN( NumArg(op) == 0 || op == UsrrpOp ); CPPAD_ASSERT_UNKNOWN( user_state == ret_user ); CPPAD_ASSERT_UNKNOWN( user_i <= user_m ); CPPAD_ASSERT_UNKNOWN( user_j == user_n ); CPPAD_ASSERT_UNKNOWN( 0 < user_i ); --user_i; if( user_i == 0 ) user_state = arg_user; break; default: CPPAD_ASSERT_UNKNOWN(false); } // the atomic_base object corresponding to this user function user_atom = atomic_base::class_object(user_index_); CPPAD_ASSERT_UNKNOWN( user_atom != CPPAD_NULL ); return user_atom; } }; } } // END_CPPAD_lOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/store_op.hpp0000644000175200017650000003432413057470466017170 0ustar coincoin-web// $Id: store_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_STORE_OP_HPP # define CPPAD_LOCAL_STORE_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file store_op.hpp Changing the current value of a VecAD element. */ /* ============================================================================== The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: ============================================================================== */ /*! Shared documentation for zero order forward implementation of op = StppOp, StpvOp, StvpOp, or StvvOp (not called). The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: \tparam Base base type for the operator; i.e., this operation was recorded using AD and computations by this routine are done using type Base. \param i_z is the index corresponding to the previous variable on the tape (only used for error checking). \param arg \n arg[0] \n is the offset of this VecAD vector relative to the beginning of the isvar_by_ind and index_by_ind arrays. \n \n arg[1] \n If this is a StppOp or StpvOp operation (if x is a parameter), i_vec is defined by \verbatim i_vec = arg[1] \endverbatim If this is a StvpOp or StvvOp operation (if x is a variable), i_vec is defined by \verbatim i_vec = floor( taylor[ arg[1] * cap_order + 0 ] ) \endverbatim where floor(c) is the greatest integer less that or equal c. \n \n arg[2] \n index corresponding to the third operand for this operator; i.e. the index corresponding to y. \param num_par is the total number of parameters on the tape (only used for error checking). \param cap_order number of columns in the matrix containing the Taylor coefficients. \param taylor In StvpOp and StvvOp cases, is used to compute the index in the definition of i_vec above. \param isvar_by_ind If y is a varable (StpvOp and StvvOp cases), isvar_by_ind[ arg[0] + i_vec ] is set to true. Otherwise y is a paraemter (StppOp and StvpOp cases) and isvar_by_ind[ arg[0] + i_vec ] is set to false. \param index_by_ind index_by_ind[ arg[0] - 1 ] is the number of elements in the user vector containing this element. The value index_by_ind[ arg[0] + i_vec] is set equal to arg[2]. \par Check User Errors \li Check that the index is with in range; i.e. i_vec < index_by_ind[ arg[0] - 1 ] Note that, if x is a parameter, the corresponding vector index and it does not change. In this case, the error above should be detected during tape recording. \par Checked Assertions \li NumArg(op) == 3 \li NumRes(op) == 0 \li 0 < arg[0] \li if y is a parameter, arg[2] < num_par */ template inline void forward_store_op_0( size_t i_z , const addr_t* arg , size_t num_par , size_t cap_order , Base* taylor , bool* isvar_by_ind , size_t* index_by_ind ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Shared documnetation for sparsity operations corresponding to op = StpvOp or StvvOp (not called). \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param op is the code corresponding to this operator; i.e., StpvOp, StvpOp, or StvvOp. \param arg \n \a arg[0] is the offset corresponding to this VecAD vector in the combined array. \n \n \a arg[2] \n The set with index \a arg[2] in \a var_sparsity is the sparsity pattern corresponding to y. (Note that \a arg[2] > 0 because y is a variable.) \param num_combined is the total number of elements in the VecAD address array. \param combined \a combined [ arg[0] - 1 ] is the index of the set in \a vecad_sparsity corresponding to the sparsity pattern for the vector v. We use the notation i_v below which is defined by \verbatim i_v = combined[ \a arg[0] - 1 ] \endverbatim \param var_sparsity The set with index \a arg[2] in \a var_sparsity is the sparsity pattern for y. This is an input for forward mode operations. For reverse mode operations: The sparsity pattern for v is added to the spartisy pattern for y. \param vecad_sparsity The set with index \a i_v in \a vecad_sparsity is the sparsity pattern for v. This is an input for reverse mode operations. For forward mode operations, the sparsity pattern for y is added to the sparsity pattern for the vector v. \par Checked Assertions \li NumArg(op) == 3 \li NumRes(op) == 0 \li 0 < \a arg[0] \li \a arg[0] < \a num_combined \li \a arg[2] < \a var_sparsity.n_set() \li i_v < \a vecad_sparsity.n_set() */ template inline void sparse_store_op( OpCode op , const addr_t* arg , size_t num_combined , const size_t* combined , Vector_set& var_sparsity , Vector_set& vecad_sparsity ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Zero order forward mode implementation of op = StppOp. \copydetails forward_store_op_0 */ template inline void forward_store_pp_op_0( size_t i_z , const addr_t* arg , size_t num_par , size_t cap_order , Base* taylor , bool* isvar_by_ind , size_t* index_by_ind ) { size_t i_vec = arg[1]; // Because the index is a parameter, this indexing error should be // caught and reported to the user when the tape is recording. CPPAD_ASSERT_UNKNOWN( i_vec < index_by_ind[ arg[0] - 1 ] ); CPPAD_ASSERT_UNKNOWN( NumArg(StppOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(StppOp) == 0 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); isvar_by_ind[ arg[0] + i_vec ] = false; index_by_ind[ arg[0] + i_vec ] = arg[2]; } /*! Zero order forward mode implementation of op = StpvOp. \copydetails forward_store_op_0 */ template inline void forward_store_pv_op_0( size_t i_z , const addr_t* arg , size_t num_par , size_t cap_order , Base* taylor , bool* isvar_by_ind , size_t* index_by_ind ) { size_t i_vec = arg[1]; // Because the index is a parameter, this indexing error should be // caught and reported to the user when the tape is recording. CPPAD_ASSERT_UNKNOWN( i_vec < index_by_ind[ arg[0] - 1 ] ); CPPAD_ASSERT_UNKNOWN( NumArg(StpvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(StpvOp) == 0 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); isvar_by_ind[ arg[0] + i_vec ] = true; index_by_ind[ arg[0] + i_vec ] = arg[2]; } /*! Zero order forward mode implementation of op = StvpOp. \copydetails forward_store_op_0 */ template inline void forward_store_vp_op_0( size_t i_z , const addr_t* arg , size_t num_par , size_t cap_order , Base* taylor , bool* isvar_by_ind , size_t* index_by_ind ) { size_t i_vec = Integer( taylor[ arg[1] * cap_order + 0 ] ); CPPAD_ASSERT_KNOWN( i_vec < index_by_ind[ arg[0] - 1 ] , "VecAD: index during zero order forward sweep is out of range" ); CPPAD_ASSERT_UNKNOWN( NumArg(StvpOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(StvpOp) == 0 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); isvar_by_ind[ arg[0] + i_vec ] = false; index_by_ind[ arg[0] + i_vec ] = arg[2]; } /*! Zero order forward mode implementation of op = StvvOp. \copydetails forward_store_op_0 */ template inline void forward_store_vv_op_0( size_t i_z , const addr_t* arg , size_t num_par , size_t cap_order , Base* taylor , bool* isvar_by_ind , size_t* index_by_ind ) { size_t i_vec = Integer( taylor[ arg[1] * cap_order + 0 ] ); CPPAD_ASSERT_KNOWN( i_vec < index_by_ind[ arg[0] - 1 ] , "VecAD: index during zero order forward sweep is out of range" ); CPPAD_ASSERT_UNKNOWN( NumArg(StvpOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(StvpOp) == 0 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); isvar_by_ind[ arg[0] + i_vec ] = true; index_by_ind[ arg[0] + i_vec ] = arg[2]; } /*! Forward mode sparsity operations for StpvOp and StvvOp The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: \param dependency is this a dependency (or sparsity) calculation. \copydetails sparse_store_op */ template inline void forward_sparse_store_op( bool dependency , OpCode op , const addr_t* arg , size_t num_combined , const size_t* combined , Vector_set& var_sparsity , Vector_set& vecad_sparsity ) { CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_combined ); size_t i_v = combined[ arg[0] - 1 ]; CPPAD_ASSERT_UNKNOWN( i_v < vecad_sparsity.n_set() ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < var_sparsity.n_set() ); if( dependency & ( (op == StvvOp) | (op == StvpOp) ) ) vecad_sparsity.binary_union(i_v, i_v, arg[1], var_sparsity); if( (op == StpvOp) | (op == StvvOp ) ) vecad_sparsity.binary_union(i_v, i_v, arg[2], var_sparsity); return; } /*! Reverse mode sparsity operations for StpvOp, StvpOp, and StvvOp The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: This routine is given the sparsity patterns for G(v[x], y , w , u ... ) and it uses them to compute the sparsity patterns for \verbatim H(y , w , u , ... ) = G[ v[x], y , w , u , ... ] \endverbatim \param dependency is this a dependency (or sparsity) calculation. \copydetails sparse_store_op */ template inline void reverse_sparse_jacobian_store_op( bool dependency , OpCode op , const addr_t* arg , size_t num_combined , const size_t* combined , Vector_set& var_sparsity , Vector_set& vecad_sparsity ) { CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_combined ); size_t i_v = combined[ arg[0] - 1 ]; CPPAD_ASSERT_UNKNOWN( i_v < vecad_sparsity.n_set() ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < var_sparsity.n_set() ); if( dependency & ( (op == StvpOp) | (op == StvvOp) ) ) var_sparsity.binary_union(arg[1], arg[1], i_v, vecad_sparsity); if( (op == StpvOp) | (op == StvvOp) ) var_sparsity.binary_union(arg[2], arg[2], i_v, vecad_sparsity); return; } /*! Reverse mode sparsity operations for StpvOp and StvvOp The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: This routine is given the sparsity patterns for G(v[x], y , w , u ... ) and it uses them to compute the sparsity patterns for \verbatim H(y , w , u , ... ) = G[ v[x], y , w , u , ... ] \endverbatim \copydetails sparse_store_op \param var_jacobian \a var_jacobian[ \a arg[2] ] is false (true) if the Jacobian of G with respect to y is always zero (may be non-zero). \param vecad_jacobian \a vecad_jacobian[i_v] is false (true) if the Jacobian with respect to x is always zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. */ template inline void reverse_sparse_hessian_store_op( OpCode op , const addr_t* arg , size_t num_combined , const size_t* combined , Vector_set& var_sparsity , Vector_set& vecad_sparsity , bool* var_jacobian , bool* vecad_jacobian ) { CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_combined ); size_t i_v = combined[ arg[0] - 1 ]; CPPAD_ASSERT_UNKNOWN( i_v < vecad_sparsity.n_set() ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < var_sparsity.n_set() ); var_sparsity.binary_union(arg[2], arg[2], i_v, vecad_sparsity); var_jacobian[ arg[2] ] |= vecad_jacobian[i_v]; return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/independent.hpp0000644000175200017650000000453313057470466017632 0ustar coincoin-web// $Id: independent.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_INDEPENDENT_HPP # define CPPAD_LOCAL_INDEPENDENT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /* \file local/independent.hpp Implement the declaration of the independent variables */ /*! Implementation of the declaration of independent variables (in local namespace). \tparam VectorAD This is simple vector type with elements of type AD. \param x Vector of the independent variablerd. \param abort_op_index operator index at which execution will be aborted (during the recording of operations). The value zero corresponds to not aborting (will not match). */ template template void ADTape::Independent(VectorAD &x, size_t abort_op_index) { // check VectorAD is Simple Vector class with AD elements CheckSimpleVector< AD, VectorAD>(); // dimension of the domain space size_t n = x.size(); CPPAD_ASSERT_KNOWN( n > 0, "Indepdendent: the argument vector x has zero size" ); CPPAD_ASSERT_UNKNOWN( Rec_.num_var_rec() == 0 ); // set the abort index before doing anything else Rec_.set_abort_op_index(abort_op_index); // mark the beginning of the tape and skip the first variable index // (zero) because parameters use taddr zero CPPAD_ASSERT_NARG_NRES(BeginOp, 1, 1); Rec_.PutOp(BeginOp); Rec_.PutArg(0); // place each of the independent variables in the tape CPPAD_ASSERT_NARG_NRES(InvOp, 0, 1); size_t j; for(j = 0; j < n; j++) { // tape address for this independent variable x[j].taddr_ = Rec_.PutOp(InvOp); x[j].tape_id_ = id_; CPPAD_ASSERT_UNKNOWN( size_t(x[j].taddr_) == j+1 ); CPPAD_ASSERT_UNKNOWN( Variable(x[j] ) ); } // done specifying all of the independent variables size_independent_ = n; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/cosh_op.hpp0000644000175200017650000001451013057470466016763 0ustar coincoin-web// $Id: cosh_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_COSH_OP_HPP # define CPPAD_LOCAL_COSH_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file cosh_op.hpp Forward and reverse mode calculations for z = cosh(x). */ /*! Compute forward mode Taylor coefficient for result of op = CoshOp. The C++ source code corresponding to this operation is \verbatim z = cosh(x) \endverbatim The auxillary result is \verbatim y = sinh(x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_cosh_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(CoshOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(CoshOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* c = taylor + i_z * cap_order; Base* s = c - cap_order; // rest of this routine is identical for the following cases: // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op. // (except that there is a sign difference for hyperbolic case). size_t k; if( p == 0 ) { s[0] = sinh( x[0] ); c[0] = cosh( x[0] ); p++; } for(size_t j = p; j <= q; j++) { s[j] = Base(0); c[j] = Base(0); for(k = 1; k <= j; k++) { s[j] += Base(k) * x[k] * c[j-k]; c[j] += Base(k) * x[k] * s[j-k]; } s[j] /= Base(j); c[j] /= Base(j); } } /*! Compute forward mode Taylor coefficient for result of op = CoshOp. The C++ source code corresponding to this operation is \verbatim z = cosh(x) \endverbatim The auxillary result is \verbatim y = sinh(x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_cosh_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(CoshOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(CoshOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* s = taylor + i_z * num_taylor_per_var; Base* c = s - num_taylor_per_var; // rest of this routine is identical for the following cases: // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op // (except that there is a sign difference for the hyperbolic case). size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { s[m+ell] = Base(q) * x[m + ell] * c[0]; c[m+ell] = Base(q) * x[m + ell] * s[0]; for(size_t k = 1; k < q; k++) { s[m+ell] += Base(k) * x[(k-1)*r+1+ell] * c[(q-k-1)*r+1+ell]; c[m+ell] += Base(k) * x[(k-1)*r+1+ell] * s[(q-k-1)*r+1+ell]; } s[m+ell] /= Base(q); c[m+ell] /= Base(q); } } /*! Compute zero order forward mode Taylor coefficient for result of op = CoshOp. The C++ source code corresponding to this operation is \verbatim z = cosh(x) \endverbatim The auxillary result is \verbatim y = sinh(x) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_cosh_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(CoshOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(CoshOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* c = taylor + i_z * cap_order; // called z in documentation Base* s = c - cap_order; // called y in documentation c[0] = cosh( x[0] ); s[0] = sinh( x[0] ); } /*! Compute reverse mode partial derivatives for result of op = CoshOp. The C++ source code corresponding to this operation is \verbatim z = cosh(x) \endverbatim The auxillary result is \verbatim y = sinh(x) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_cosh_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(CoshOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(CoshOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* c = taylor + i_z * cap_order; // called z in doc Base* pc = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* s = c - cap_order; // called y in documentation Base* ps = pc - nc_partial; // rest of this routine is identical for the following cases: // reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op. size_t j = d; size_t k; while(j) { ps[j] /= Base(j); pc[j] /= Base(j); for(k = 1; k <= j; k++) { px[k] += Base(k) * azmul(ps[j], c[j-k]); px[k] += Base(k) * azmul(pc[j], s[j-k]); ps[j-k] += Base(k) * azmul(pc[j], x[k]); pc[j-k] += Base(k) * azmul(ps[j], x[k]); } --j; } px[0] += azmul(ps[0], c[0]); px[0] += azmul(pc[0], s[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/acosh_op.hpp0000644000175200017650000001533113057470466017126 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_ACOSH_OP_HPP # define CPPAD_LOCAL_ACOSH_OP_HPP # if CPPAD_USE_CPLUSPLUS_2011 /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file acosh_op.hpp Forward and reverse mode calculations for z = acosh(x). */ /*! Compute forward mode Taylor coefficient for result of op = AcoshOp. The C++ source code corresponding to this operation is \verbatim z = acosh(x) \endverbatim The auxillary result is \verbatim y = sqrt(x * x - 1) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_acosh_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcoshOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcoshOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation size_t k; Base uj; if( p == 0 ) { z[0] = acosh( x[0] ); uj = x[0] * x[0] - Base(1); b[0] = sqrt( uj ); p++; } for(size_t j = p; j <= q; j++) { uj = Base(0); for(k = 0; k <= j; k++) uj += x[k] * x[j-k]; b[j] = Base(0); z[j] = Base(0); for(k = 1; k < j; k++) { b[j] -= Base(k) * b[k] * b[j-k]; z[j] -= Base(k) * z[k] * b[j-k]; } b[j] /= Base(j); z[j] /= Base(j); // b[j] += uj / Base(2); z[j] += x[j]; // b[j] /= b[0]; z[j] /= b[0]; } } /*! Multiple directions forward mode Taylor coefficient for op = AcoshOp. The C++ source code corresponding to this operation is \verbatim z = acosh(x) \endverbatim The auxillary result is \verbatim y = sqrt(x * x - 1) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_acosh_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcoshOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcoshOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; Base* b = z - num_taylor_per_var; // called y in documentation size_t k, ell; size_t m = (q-1) * r + 1; for(ell = 0; ell < r; ell ++) { Base uq = 2.0 * x[m + ell] * x[0]; for(k = 1; k < q; k++) uq += x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell]; b[m+ell] = Base(0); z[m+ell] = Base(0); for(k = 1; k < q; k++) { b[m+ell] += Base(k) * b[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; z[m+ell] += Base(k) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; } b[m+ell] = ( uq / Base(2) - b[m+ell] / Base(q) ) / b[0]; z[m+ell] = ( x[m+ell] - z[m+ell] / Base(q) ) / b[0]; } } /*! Compute zero order forward mode Taylor coefficient for result of op = AcoshOp. The C++ source code corresponding to this operation is \verbatim z = acosh(x) \endverbatim The auxillary result is \verbatim y = sqrt( x * x - 1 ) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_acosh_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcoshOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcoshOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation z[0] = acosh( x[0] ); b[0] = sqrt( x[0] * x[0] - Base(1) ); } /*! Compute reverse mode partial derivatives for result of op = AcoshOp. The C++ source code corresponding to this operation is \verbatim z = acosh(x) \endverbatim The auxillary result is \verbatim y = sqrt( x * x - 1 ) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_acosh_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcoshOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcoshOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* b = z - cap_order; // called y in documentation Base* pb = pz - nc_partial; Base inv_b0 = Base(1) / b[0]; // number of indices to access size_t j = d; size_t k; while(j) { // scale partials w.r.t b[j] by 1 / b[0] pb[j] = azmul(pb[j], inv_b0); // scale partials w.r.t z[j] by 1 / b[0] pz[j] = azmul(pz[j], inv_b0); // update partials w.r.t b^0 pb[0] -= azmul(pz[j], z[j]) + azmul(pb[j], b[j]); // update partial w.r.t. x^0 px[0] += azmul(pb[j], x[j]); // update partial w.r.t. x^j px[j] += pz[j] + azmul(pb[j], x[0]); // further scale partial w.r.t. z[j] by 1 / j pz[j] /= Base(j); for(k = 1; k < j; k++) { // update partials w.r.t b^(j-k) pb[j-k] -= Base(k) * azmul(pz[j], z[k]) + azmul(pb[j], b[k]); // update partials w.r.t. x^k px[k] += azmul(pb[j], x[j-k]); // update partials w.r.t. z^k pz[k] -= Base(k) * azmul(pz[j], b[j-k]); } --j; } // j == 0 case px[0] += azmul(pz[0] + azmul(pb[0], x[0]), inv_b0); } } } // END_CPPAD_LOCAL_NAMESPACE # endif # endif cppad-20170000.3/cppad/local/abs_op.hpp0000644000175200017650000001015213057470466016572 0ustar coincoin-web// $Id: abs_op.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_ABS_OP_HPP # define CPPAD_LOCAL_ABS_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file abs_op.hpp Forward and reverse mode calculations for z = abs(x). */ /*! Compute forward mode Taylor coefficient for result of op = AbsOp. The C++ source code corresponding to this operation is \verbatim z = abs(x) \endverbatim \copydetails forward_unary1_op */ template inline void forward_abs_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; for(size_t j = p; j <= q; j++) z[j] = sign(x[0]) * x[j]; } /*! Multiple directions forward mode Taylor coefficient for op = AbsOp. The C++ source code corresponding to this operation is \verbatim z = abs(x) \endverbatim \copydetails forward_unary1_op_dir */ template inline void forward_abs_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) z[m + ell] = sign(x[0]) * x[m + ell]; } /*! Compute zero order forward mode Taylor coefficient for result of op = AbsOp. The C++ source code corresponding to this operation is \verbatim z = abs(x) \endverbatim \copydetails forward_unary1_op_0 */ template inline void forward_abs_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base x0 = *(taylor + i_x * cap_order); Base* z = taylor + i_z * cap_order; z[0] = abs(x0); } /*! Compute reverse mode partial derivatives for result of op = AbsOp. The C++ source code corresponding to this operation is \verbatim z = abs(x) \endverbatim \copydetails reverse_unary1_op */ template inline void reverse_abs_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { size_t j; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AbsOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to result Base* pz = partial + i_z * nc_partial; // do not need azmul because sign is either +1, -1, or zero for(j = 0; j <= d; j++) px[j] += sign(x[0]) * pz[j]; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/comp_op.hpp0000644000175200017650000001775713057470466017005 0ustar coincoin-web// $Id: comp_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_COMP_OP_HPP # define CPPAD_LOCAL_COMP_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file comp_op.hpp Zero order forward mode check how many comparisons changed. */ // -------------------------------- <= ----------------------------------- /*! Zero order forward mode comparison check that left <= right \param count It the condition is not true, ths counter is incremented by one. \param arg parameter[ arg[0] ] is the left operand and taylor[ arg[1] * cap_order + 0 ] is the zero order Taylor coefficient for the right operand. \param parameter vector of parameter values. \param cap_order number of Taylor coefficients allocated for each variable \param taylor vector of taylor coefficients. */ template inline void forward_lepv_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LepvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(LepvOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base x = parameter[ arg[0] ]; Base* y = taylor + arg[1] * cap_order; count += GreaterThanZero(x - y[0]); } /*! Zero order forward mode comparison check that left <= right \param count It the condition is not true, ths counter is incremented by one. \param arg taylor[ arg[0] * cap_order + 0 ] is the zero order Taylor coefficient for the left operand and parameter[ arg[1] ] is the right operand \param parameter vector of parameter values. \param cap_order number of Taylor coefficients allocated for each variable \param taylor vector of taylor coefficients. */ template inline void forward_levp_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LevpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(LevpOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base y = parameter[ arg[1] ]; count += GreaterThanZero(x[0] - y); } /*! Zero order forward mode comparison check that left <= right \param count It the condition is not true, ths counter is incremented by one. \param arg taylor[ arg[0] * cap_order + 0 ] is the zero order Taylor coefficient for the left operand and taylor[ arg[1] * cap_order + 0 ] is the zero order Taylor coefficient for the right operand. \param parameter vector of parameter values. \param cap_order number of Taylor coefficients allocated for each variable \param taylor vector of taylor coefficients. */ template inline void forward_levv_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LevvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(LevvOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; count += GreaterThanZero(x[0] - y[0]); } // ------------------------------- < ------------------------------------- /*! Zero order forward mode comparison check that left < right \copydetails forward_lepv_op_0 */ template inline void forward_ltpv_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LtpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(LtpvOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base x = parameter[ arg[0] ]; Base* y = taylor + arg[1] * cap_order; count += GreaterThanOrZero(x - y[0]); } /*! Zero order forward mode comparison check that left < right \copydetails forward_levp_op_0 */ template inline void forward_ltvp_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LtvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(LtvpOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base y = parameter[ arg[1] ]; count += GreaterThanOrZero(x[0] - y); } /*! Zero order forward mode comparison check that left < right \copydetails forward_levv_op_0 */ template inline void forward_ltvv_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LtvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(LtvvOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; count += GreaterThanOrZero(x[0] - y[0]); } // ------------------------------ == ------------------------------------- /*! Zero order forward mode comparison check that left == right \copydetails forward_lepv_op_0 */ template inline void forward_eqpv_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(EqpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(EqpvOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base x = parameter[ arg[0] ]; Base* y = taylor + arg[1] * cap_order; count += (x != y[0]); } /*! Zero order forward mode comparison check that left == right \copydetails forward_levv_op_0 */ template inline void forward_eqvv_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(EqvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(EqvvOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; count += (x[0] != y[0]); } // -------------------------------- != ----------------------------------- /*! Zero order forward mode comparison check that left != right \copydetails forward_lepv_op_0 */ template inline void forward_nepv_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(NepvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(NepvOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base x = parameter[ arg[0] ]; Base* y = taylor + arg[1] * cap_order; count += (x == y[0]); } /*! Zero order forward mode comparison check that left != right \copydetails forward_levv_op_0 */ template inline void forward_nevv_op_0( size_t& count , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(NevvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(NevvOp) == 0 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; count += (x[0] == y[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/prototype_op.hpp0000644000175200017650000012405713057470466020104 0ustar coincoin-web// $Id: prototype_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_PROTOTYPE_OP_HPP # define CPPAD_LOCAL_PROTOTYPE_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file prototype_op.hpp Documentation for generic cases (these generic cases are never used). */ // ==================== Unary operators with one result ==================== /*! Prototype for forward mode unary operator with one result (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param p lowest order of the Taylor coefficient that we are computing. \param q highest order of the Taylor coefficient that we are computing. \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param i_x variable index corresponding to the argument for this operator; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: taylor [ i_x * cap_order + k ], for k = 0 , ... , q, is the k-th order Taylor coefficient corresponding to x. \n \b Input: taylor [ i_z * cap_order + k ], for k = 0 , ... , p-1, is the k-th order Taylor coefficient corresponding to z. \n \b Output: taylor [ i_z * cap_order + k ], for k = p , ... , q, is the k-th order Taylor coefficient corresponding to z. \par Checked Assertions \li NumArg(op) == 1 \li NumRes(op) == 1 \li q < cap_order \li p <= q */ template inline void forward_unary1_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for multiple direction forward mode unary operator with one result (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param q order of the Taylor coefficients that we are computing. \param r number of directions for Taylor coefficients that we are computing. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. \param i_x variable index corresponding to the argument for this operator; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the \c taylor array. \par tpv We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable \param taylor \b Input: If x is a variable, taylor [ arg[0] * tpv + 0 ], is the zero order Taylor coefficient for all directions and taylor [ arg[0] * tpv + (k-1)*r + ell + 1 ], for k = 1 , ... , q, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to x and the ell-th direction. \n \b Input: taylor [ i_z * tpv + 0 ], is the zero order Taylor coefficient for all directions and taylor [ i_z * tpv + (k-1)*r + ell + 1 ], for k = 1 , ... , q-1, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to z and the ell-th direction. \n \b Output: taylor [ i_z * tpv + (q-1)*r + ell + 1], ell = 0, ..., r-1, is the q-th order Taylor coefficient corresponding to z and the ell-th direction. \par Checked Assertions \li NumArg(op) == 1 \li NumRes(op) == 2 \li i_x < i_z \li 0 < q \li q < cap_order */ template inline void forward_unary1_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for zero order forward mode unary operator with one result (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param i_x variable index corresponding to the argument for this operator; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: \a taylor [ \a i_x * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to x. \n \b Output: \a taylor [ \a i_z * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to z. \par Checked Assertions \li NumArg(op) == 1 \li NumRes(op) == 1 \li \a i_x < \a i_z \li \a 0 < \a cap_order */ template inline void forward_unary1_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for reverse mode unary operator with one result (not used). This routine is given the partial derivatives of a function G(z , x , w, u ... ) and it uses them to compute the partial derivatives of \verbatim H( x , w , u , ... ) = G[ z(x) , x , w , u , ... ] \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param d highest order Taylor coefficient that we are computing the partial derivatives with respect to. \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor to z. \param i_x variable index corresponding to the argument for this operation; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \a taylor [ \a i_x * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to x. \n \a taylor [ \a i_z * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to z. \param nc_partial number of colums in the matrix containing all the partial derivatives. \param partial \b Input: \a partial [ \a i_x * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Input: \a partial [ \a i_z * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , x , w , u , ... ) with respect to the k-th order Taylor coefficient for z. \n \b Output: \a partial [ \a i_x * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of H( x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Output: \a partial [ \a i_z * \a nc_partial + k ] for k = 0 , ... , \a d may be used as work space; i.e., may change in an unspecified manner. \par Checked Assumptions \li NumArg(op) == 1 \li NumRes(op) == 1 \li \a i_x < \a i_z \li \a d < \a cap_order \li \a d < \a nc_partial */ template inline void reverse_unary1_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } // ==================== Unary operators with two results ==================== /*! Prototype for forward mode unary operator with two results (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param p lowest order of the Taylor coefficients that we are computing. \param q highest order of the Taylor coefficients that we are computing. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. The auxillary result is called y has index \a i_z - 1. \param i_x variable index corresponding to the argument for this operator; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: taylor [ i_x * cap_order + k ] for k = 0 , ... , q, is the k-th order Taylor coefficient corresponding to x. \n \b Input: taylor [ i_z * cap_order + k ] for k = 0 , ... , p - 1, is the k-th order Taylor coefficient corresponding to z. \n \b Input: taylor [ ( i_z - 1) * cap_order + k ] for k = 0 , ... , p-1, is the k-th order Taylor coefficient corresponding to the auxillary result y. \n \b Output: taylor [ i_z * cap_order + k ], for k = p , ... , q, is the k-th order Taylor coefficient corresponding to z. \n \b Output: taylor [ ( i_z - 1 ) * cap_order + k ], for k = p , ... , q, is the k-th order Taylor coefficient corresponding to the autillary result y. \par Checked Assertions \li NumArg(op) == 1 \li NumRes(op) == 2 \li i_x + 1 < i_z \li q < cap_order \li p <= q */ template inline void forward_unary2_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for multiple direction forward mode unary operator with two results (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param q order of the Taylor coefficients that we are computing. \param r number of directions for Taylor coefficients that we are computing. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. The auxillary result is called y has index \a i_z - 1. \param i_x variable index corresponding to the argument for this operator; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the \c taylor array. \par tpv We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable \param taylor \b Input: taylor [ i_x * tpv + 0 ] is the zero order Taylor coefficient for all directions and taylor [ i_x * tpv + (k-1)*r + ell + 1 for k = 1 , ... , q, ell = 0 , ..., r-1, is the k-th order Taylor coefficient corresponding to x and the ell-th direction. \n \b Input: taylor [ i_z * tpv + 0 ], is the zero order Taylor coefficient for all directions and taylor [ i_z * tpv + (k-1)*r + ell + 1 ], for k = 1 , ... , q-1, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to z and the ell-th direction. \n \b Input: taylor [ (i_z-1) * tpv + 0 ], is the zero order Taylor coefficient for all directions and taylor [ (i_z-1) * tpv + (k-1)*r + ell + 1 ], for k = 1 , ... , q-1, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to the auxillary result y and the ell-th direction. \n \b Output: taylor [ i_z * tpv + (q-1)*r + ell + 1], ell = 0, ..., r-1, is the q-th order Taylor coefficient corresponding to z and the ell-th direction. \par Checked Assertions \li NumArg(op) == 1 \li NumRes(op) == 2 \li i_x + 1 < i_z \li 0 < q \li q < cap_order */ template inline void forward_unary2_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for zero order forward mode unary operator with two results (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. The auxillary result is called y and has index \a i_z - 1. \param i_x variable index corresponding to the argument for this operator; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: \a taylor [ \a i_x * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to x. \n \b Output: \a taylor [ \a i_z * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to z. \n \b Output: \a taylor [ ( \a i_z - 1 ) * \a cap_order + j ] is the j-th order Taylor coefficient corresponding to the autillary result y. \par Checked Assertions \li NumArg(op) == 1 \li NumRes(op) == 2 \li \a i_x + 1 < \a i_z \li \a j < \a cap_order */ template inline void forward_unary2_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for reverse mode unary operator with two results (not used). This routine is given the partial derivatives of a function G( z , y , x , w , ... ) and it uses them to compute the partial derivatives of \verbatim H( x , w , u , ... ) = G[ z(x) , y(x), x , w , u , ... ] \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param d highest order Taylor coefficient that we are computing the partial derivatives with respect to. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor to z. The auxillary result is called y and has index \a i_z - 1. \param i_x variable index corresponding to the argument for this operation; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \a taylor [ \a i_x * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to x. \n \a taylor [ \a i_z * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to z. \n \a taylor [ ( \a i_z - 1) * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to the auxillary variable y. \param nc_partial number of colums in the matrix containing all the partial derivatives. \param partial \b Input: \a partial [ \a i_x * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Input: \a partial [ \a i_z * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for z. \n \b Input: \a partial [ ( \a i_z - 1) * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , x , w , u , ... ) with respect to the k-th order Taylor coefficient for the auxillary variable y. \n \b Output: \a partial [ \a i_x * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of H( x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Output: \a partial [ \a ( i_z - j ) * \a nc_partial + k ] for j = 0 , 1 , and for k = 0 , ... , \a d may be used as work space; i.e., may change in an unspecified manner. \par Checked Assumptions \li NumArg(op) == 1 \li NumRes(op) == 2 \li \a i_x + 1 < \a i_z \li \a d < \a cap_order \li \a d < \a nc_partial */ template inline void reverse_unary2_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } // =================== Binary operators with one result ==================== /*! Prototype forward mode x op y (not used) \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param p lowest order of the Taylor coefficient that we are computing. \param q highest order of the Taylor coefficient that we are computing. \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param arg \a arg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x. \n \a arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y. \param parameter If x is a parameter, \a parameter [ \a arg[0] ] is the value corresponding to x. \n If y is a parameter, \a parameter [ \a arg[1] ] is the value corresponding to y. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: If x is a variable, taylor [ arg[0] * cap_order + k ], for k = 0 , ... , q, is the k-th order Taylor coefficient corresponding to x. \n \b Input: If y is a variable, taylor [ arg[1] * cap_order + k ], for k = 0 , ... , q, is the k-th order Taylor coefficient corresponding to y. \n \b Input: taylor [ i_z * cap_order + k ], for k = 0 , ... , p-1, is the k-th order Taylor coefficient corresponding to z. \n \b Output: taylor [ i_z * cap_order + k ], for k = p, ... , q, is the k-th order Taylor coefficient corresponding to z. \par Checked Assertions \li NumArg(op) == 2 \li NumRes(op) == 1 \li q < cap_order \li p <= q */ template inline void forward_binary_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype multiple direction forward mode x op y (not used) \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param q is the order of the Taylor coefficients that we are computing. \param r number of directions for Taylor coefficients that we are computing \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param arg \a arg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x. \n \a arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y. \param parameter If x is a parameter, \a parameter [ \a arg[0] ] is the value corresponding to x. \n If y is a parameter, \a parameter [ \a arg[1] ] is the value corresponding to y. \param cap_order maximum number of orders that will fit in the \c taylor array. \par tpv We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable \param taylor \b Input: If x is a variable, taylor [ arg[0] * tpv + 0 ], is the zero order Taylor coefficient for all directions and taylor [ arg[0] * tpv + (k-1)*r + ell + 1 ], for k = 1 , ... , q, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to x and the ell-th direction. \n \b Input: If y is a variable, taylor [ arg[1] * tpv + 0 ], is the zero order Taylor coefficient for all directions and taylor [ arg[1] * tpv + (k-1)*r + ell + 1 ], for k = 1 , ... , q, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to y and the ell-th direction. \n \b Input: taylor [ i_z * tpv + 0 ], is the zero order Taylor coefficient for all directions and taylor [ i_z * tpv + (k-1)*r + ell + 1 ], for k = 1 , ... , q-1, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to z and the ell-th direction. \n \b Output: taylor [ i_z * tpv + (q-1)*r + ell + 1], ell = 0, ..., r-1, is the q-th order Taylor coefficient corresponding to z and the ell-th direction. \par Checked Assertions \li NumArg(op) == 2 \li NumRes(op) == 1 \li 0 < q < cap_order */ template inline void forward_binary_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype zero order forward mode x op y (not used) \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param arg \a arg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x. \n \a arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y. \param parameter If x is a parameter, \a parameter [ \a arg[0] ] is the value corresponding to x. \n If y is a parameter, \a parameter [ \a arg[1] ] is the value corresponding to y. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: If x is a variable, \a taylor [ \a arg[0] * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to x. \n \b Input: If y is a variable, \a taylor [ \a arg[1] * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to y. \n \b Output: \a taylor [ \a i_z * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to z. \par Checked Assertions \li NumArg(op) == 2 \li NumRes(op) == 1 */ template inline void forward_binary_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for reverse mode binary operator x op y (not used). This routine is given the partial derivatives of a function G( z , y , x , w , ... ) and it uses them to compute the partial derivatives of \verbatim H( y , x , w , u , ... ) = G[ z(x , y) , y , x , w , u , ... ] \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param d highest order Taylor coefficient that we are computing the partial derivatives with respect to. \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param arg \a arg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x. \n \a arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y. \param parameter If x is a parameter, \a parameter [ \a arg[0] ] is the value corresponding to x. \n If y is a parameter, \a parameter [ \a arg[1] ] is the value corresponding to y. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \a taylor [ \a i_z * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to z. \n If x is a variable, \a taylor [ \a arg[0] * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to x. \n If y is a variable, \a taylor [ \a arg[1] * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to y. \param nc_partial number of colums in the matrix containing all the partial derivatives. \param partial \b Input: \a partial [ \a i_z * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for z. \n \b Input: If x is a variable, \a partial [ \a arg[0] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Input: If y is a variable, \a partial [ \a arg[1] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , x , w , u , ... ) with respect to the k-th order Taylor coefficient for the auxillary variable y. \n \b Output: If x is a variable, \a partial [ \a arg[0] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of H( y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Output: If y is a variable, \a partial [ \a arg[1] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of H( y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for y. \n \b Output: \a partial [ \a i_z * \a nc_partial + k ] for k = 0 , ... , \a d may be used as work space; i.e., may change in an unspecified manner. \par Checked Assumptions \li NumArg(op) == 2 \li NumRes(op) == 1 \li \a If x is a variable, arg[0] < \a i_z \li \a If y is a variable, arg[1] < \a i_z \li \a d < \a cap_order \li \a d < \a nc_partial */ template inline void reverse_binary_op( size_t d , size_t i_z , addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } // ======================= Pow Function =================================== /*! Prototype for forward mode z = pow(x, y) (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param p lowest order of the Taylor coefficient that we are computing. \param q highest order of the Taylor coefficient that we are computing. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. Note that there are three results for this operation, below they are referred to as z_0, z_1, z_2 and correspond to \verbatim z_0 = log(x) z_1 = z0 * y z_2 = exp(z1) \endverbatim It follows that the final result is equal to z; i.e., z = z_2 = pow(x, y). \param arg \a arg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x. \n \a arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y. \param parameter If x is a parameter, \a parameter [ \a arg[0] ] is the value corresponding to x. \n If y is a parameter, \a parameter [ \a arg[1] ] is the value corresponding to y. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: If x is a variable, taylor [ arg[0] * cap_order + k ] for k = 0 , ... , q, is the k-th order Taylor coefficient corresponding to x. \n \b Input: If y is a variable, taylor [ arg[1] * cap_order + k ] for k = 0 , ... , q is the k-th order Taylor coefficient corresponding to y. \n \b Input: taylor [ (i_z-2+j) * cap_order + k ], for j = 0, 1, 2 , for k = 0 , ... , p-1, is the k-th order Taylor coefficient corresponding to z_j. \n \b Output: taylor [ (i_z-2+j) * cap_order + k ], is the k-th order Taylor coefficient corresponding to z_j. \par Checked Assertions \li NumArg(op) == 2 \li NumRes(op) == 3 \li If x is a variable, arg[0] < i_z - 2 \li If y is a variable, arg[1] < i_z - 2 \li q < cap_order \li p <= q */ template inline void forward_pow_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for multiple direction forward mode z = pow(x, y) (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param q order of the Taylor coefficient that we are computing. \param r is the number of Taylor coefficient directions that we are computing \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. Note that there are three results for this operation, below they are referred to as z_0, z_1, z_2 and correspond to \verbatim z_0 = log(x) z_1 = z0 * y z_2 = exp(z1) \endverbatim It follows that the final result is equal to z; i.e., z = z_2 = pow(x, y). \param arg \a arg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x. \n \a arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y. \param parameter If x is a parameter, \a parameter [ \a arg[0] ] is the value corresponding to x. \n If y is a parameter, \a parameter [ \a arg[1] ] is the value corresponding to y. \param cap_order maximum number of orders that will fit in the \c taylor array. \par tpv We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable \param taylor \b Input: If x is a variable, taylor [ arg[0] * tpv + 0 ] is the zero order coefficient corresponding to x and taylor [ arg[0] * tpv + (k-1)*r+1+ell ] for k = 1 , ... , q, ell = 0 , ... , r-1, is the k-th order Taylor coefficient corresponding to x for the ell-th direction. \n \n \b Input: If y is a variable, taylor [ arg[1] * tpv + 0 ] is the zero order coefficient corresponding to y and taylor [ arg[1] * tpv + (k-1)*r+1+ell ] for k = 1 , ... , q, ell = 0 , ... , r-1, is the k-th order Taylor coefficient corresponding to y for the ell-th direction. \n \n \b Input: taylor [ (i_z-2+j) * tpv + 0 ], is the zero order coefficient corresponding to z_j and taylor [ (i_z-2+j) * tpv + (k-1)*r+1+ell ], for j = 0, 1, 2 , k = 0 , ... , q-1, ell = 0, ... , r-1, is the k-th order Taylor coefficient corresponding to z_j for the ell-th direction. \n \n \b Output: taylor [ (i_z-2+j) * tpv + (q-1)*r+1+ell ], for j = 0, 1, 2 , ell = 0, ... , r-1, is the q-th order Taylor coefficient corresponding to z_j for the ell-th direction. \par Checked Assertions \li NumArg(op) == 2 \li NumRes(op) == 3 \li If x is a variable, arg[0] < i_z - 2 \li If y is a variable, arg[1] < i_z - 2 \li 0 < q \li q < cap_order */ template inline void forward_pow_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for zero order forward mode z = pow(x, y) (not used). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. Note that there are three results for this operation, below they are referred to as z_0, z_1, z_2 and correspond to \verbatim z_0 = log(x) z_1 = z0 * y z_2 = exp(z1) \endverbatim It follows that the final result is equal to z; i.e., z = z_2 = pow(x, y). \param arg \a arg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x. \n \a arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y. \param parameter If x is a parameter, \a parameter [ \a arg[0] ] is the value corresponding to x. \n If y is a parameter, \a parameter [ \a arg[1] ] is the value corresponding to y. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: If x is a variable, \a taylor [ \a arg[0] * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to x. \n \b Input: If y is a variable, \a taylor [ \a arg[1] * \a cap_order + 0 ] is the k-th order Taylor coefficient corresponding to y. \n \b Output: \a taylor [ \a (i_z - 2 + j) * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to z_j. \par Checked Assertions \li NumArg(op) == 2 \li NumRes(op) == 3 \li If x is a variable, \a arg[0] < \a i_z - 2 \li If y is a variable, \a arg[1] < \a i_z - 2 */ template inline void forward_pow_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for reverse mode z = pow(x, y) (not used). This routine is given the partial derivatives of a function G( z , y , x , w , ... ) and it uses them to compute the partial derivatives of \verbatim H( y , x , w , u , ... ) = G[ pow(x , y) , y , x , w , u , ... ] \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param d highest order Taylor coefficient that we are computing the partial derivatives with respect to. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. Note that there are three results for this operation, below they are referred to as z_0, z_1, z_2 and correspond to \verbatim z_0 = log(x) z_1 = z0 * y z_2 = exp(z1) \endverbatim It follows that the final result is equal to z; i.e., z = z_2 = pow(x, y). \param arg \a arg[0] index corresponding to the left operand for this operator; i.e. the index corresponding to x. \n \a arg[1] index corresponding to the right operand for this operator; i.e. the index corresponding to y. \param parameter If x is a parameter, \a parameter [ \a arg[0] ] is the value corresponding to x. \n If y is a parameter, \a parameter [ \a arg[1] ] is the value corresponding to y. \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \a taylor [ \a (i_z - 2 + j) * \a cap_order + k ] for j = 0, 1, 2 and k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to z_j. \n If x is a variable, \a taylor [ \a arg[0] * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to x. \n If y is a variable, \a taylor [ \a arg[1] * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to y. \param nc_partial number of colums in the matrix containing all the partial derivatives. \param partial \b Input: \a partial [ \a (i_z - 2 + j) * \a nc_partial + k ] for j = 0, 1, 2, and k = 0 , ... , \a d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for z_j. \n \b Input: If x is a variable, \a partial [ \a arg[0] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Input: If y is a variable, \a partial [ \a arg[1] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G( z , x , w , u , ... ) with respect to the k-th order Taylor coefficient for the auxillary variable y. \n \b Output: If x is a variable, \a partial [ \a arg[0] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of H( y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Output: If y is a variable, \a partial [ \a arg[1] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of H( y , x , w , u , ... ) with respect to the k-th order Taylor coefficient for y. \n \b Output: \a partial [ \a ( i_z - j ) * \a nc_partial + k ] for j = 0 , 1 , 2 and for k = 0 , ... , \a d may be used as work space; i.e., may change in an unspecified manner. \par Checked Assumptions \li NumArg(op) == 2 \li NumRes(op) == 3 \li \a If x is a variable, arg[0] < \a i_z - 2 \li \a If y is a variable, arg[1] < \a i_z - 2 \li \a d < \a cap_order \li \a d < \a nc_partial */ template inline void reverse_pow_op( size_t d , size_t i_z , addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } // ==================== Sparsity Calculations ============================== /*! Prototype for reverse mode Hessian sparsity unary operators. This routine is given the forward mode Jacobian sparsity patterns for x. It is also given the reverse mode dependence of G on z. In addition, it is given the revese mode Hessian sparsity for the quanity of interest G(z , y , ... ) and it uses them to compute the sparsity patterns for \verbatim H( x , w , u , ... ) = G[ z(x) , x , w , u , ... ] \endverbatim \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e. the row index in sparsity corresponding to z. \param i_x variable index corresponding to the argument for this operator; i.e. the row index in sparsity corresponding to x. \param rev_jacobian \a rev_jacobian[i_z] is all false (true) if the Jacobian of G with respect to z must be zero (may be non-zero). \n \n \a rev_jacobian[i_x] is all false (true) if the Jacobian with respect to x must be zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. \param for_jac_sparsity The set with index \a i_x in for_jac_sparsity is the forward mode Jacobian sparsity pattern for the variable x. \param rev_hes_sparsity The set with index \a i_z in in \a rev_hes_sparsity is the Hessian sparsity pattern for the fucntion G where one of the partials derivative is with respect to z. \n \n The set with index \a i_x in \a rev_hes_sparsity is the Hessian sparsity pattern where one of the partials derivative is with respect to x. On input, it corresponds to the function G, and on output it corresponds to the function H. \par Checked Assertions: \li \a i_x < \a i_z */ template inline void reverse_sparse_hessian_unary_op( size_t i_z , size_t i_x , bool* rev_jacobian , Vector_set& for_jac_sparsity , Vector_set& rev_hes_sparsity ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Prototype for reverse mode Hessian sparsity binary operators. This routine is given the sparsity patterns the Hessian of a function G(z, y, x, ... ) and it uses them to compute the sparsity patterns for the Hessian of \verbatim H( y, x, w , u , ... ) = G[ z(x,y) , y , x , w , u , ... ] \endverbatim \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e. the row index in sparsity corresponding to z. \param arg \a arg[0] variable index corresponding to the left operand for this operator; i.e. the set with index \a arg[0] in \a var_sparsity is the spasity pattern correspoding to x. \n \n arg[1] variable index corresponding to the right operand for this operator; i.e. the row index in sparsity patterns corresponding to y. \param jac_reverse \a jac_reverse[i_z] is false (true) if the Jacobian of G with respect to z is always zero (may be non-zero). \n \n \a jac_reverse[ \a arg[0] ] is false (true) if the Jacobian with respect to x is always zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. \n \n \a jac_reverse[ \a arg[1] ] is false (true) if the Jacobian with respect to y is always zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. \param for_jac_sparsity The set with index \a arg[0] in \a for_jac_sparsity for the is the forward Jacobian sparsity pattern for x. \n \n The set with index \a arg[1] in \a for_jac_sparsity is the forward sparsity pattern for y. \param rev_hes_sparsity The set wiht index \a i_x in \a rev_hes_sparsity is the Hessian sparsity pattern for the function G where one of the partial derivatives is with respect to z. \n \n The set with index \a arg[0] in \a rev_hes_sparsity is the Hessian sparsity pattern where one of the partial derivatives is with respect to x. On input, it corresponds to the function G, and on output it correspondst to H. \n \n The set with index \a arg[1] in \a rev_hes_sparsity is the Hessian sparsity pattern where one of the partial derivatives is with respect to y. On input, it corresponds to the function G, and on output it correspondst to H. \par Checked Assertions: \li \a arg[0] < \a i_z \li \a arg[1] < \a i_z */ template inline void reverse_sparse_hessian_binary_op( size_t i_z , const addr_t* arg , bool* jac_reverse , Vector_set& for_jac_sparsity , Vector_set& rev_hes_sparsity ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/rev_hes_sweep.hpp0000644000175200017650000006424313057470466020177 0ustar coincoin-web// $Id: rev_hes_sweep.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_REV_HES_SWEEP_HPP # define CPPAD_LOCAL_REV_HES_SWEEP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file rev_hes_sweep.hpp Compute Reverse mode Hessian sparsity patterns. */ /*! \def CPPAD_REV_HES_SWEEP_TRACE This value is either zero or one. Zero is the normal operational value. If it is one, a trace of every rev_hes_sweep computation is printed. */ # define CPPAD_REV_HES_SWEEP_TRACE 0 /*! Given the forward Jacobian sparsity pattern for all the variables, and the reverse Jacobian sparsity pattern for the dependent variables, RevHesSweep computes the Hessian sparsity pattern for all the independent variables. \tparam Base base type for the operator; i.e., this operation sequence was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param n is the number of independent variables on the tape. \param numvar is the total number of variables on the tape; i.e., \a play->num_var_rec(). This is also the number of rows in the entire sparsity pattern \a rev_hes_sparse. \param play The information stored in \a play is a recording of the operations corresponding to a function \f[ F : {\bf R}^n \rightarrow {\bf R}^m \f] where \f$ n \f$ is the number of independent variables and \f$ m \f$ is the number of dependent variables. The object \a play is effectly constant. It is not declared const because while playing back the tape the object \a play holds information about the current location with in the tape and this changes during playback. \param for_jac_sparse For i = 0 , ... , \a numvar - 1, (for all the variables on the tape), the forward Jacobian sparsity pattern for the variable with index i corresponds to the set with index i in \a for_jac_sparse. \param RevJac \b Input: For i = 0, ... , \a numvar - 1 the if the variable with index i on the tape is an dependent variable and included in the Hessian, \a RevJac[ i ] is equal to true, otherwise it is equal to false. \n \n \b Output: The values in \a RevJac upon return are not specified; i.e., it is used for temporary work space. \param rev_hes_sparse The reverse Hessian sparsity pattern for the variable with index i corresponds to the set with index i in \a rev_hes_sparse. \n \n \b Input: For i = 0 , ... , \a numvar - 1 the reverse Hessian sparsity pattern for the variable with index i is empty. \n \n \b Output: For j = 1 , ... , \a n, the reverse Hessian sparsity pattern for the independent dependent variable with index (j-1) is given by the set with index j in \a rev_hes_sparse. The values in the rest of \a rev_hes_sparse are not specified; i.e., they are used for temporary work space. */ template void RevHesSweep( size_t n, size_t numvar, local::player* play, const Vector_set& for_jac_sparse, bool* RevJac, Vector_set& rev_hes_sparse ) { OpCode op; size_t i_op; size_t i_var; const addr_t* arg = CPPAD_NULL; // length of the parameter vector (used by CppAD assert macros) const size_t num_par = play->num_par_rec(); size_t i, j, k; // check numvar argument CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse.n_set() == numvar ); CPPAD_ASSERT_UNKNOWN( rev_hes_sparse.n_set() == numvar ); CPPAD_ASSERT_UNKNOWN( numvar > 0 ); // upper limit exclusive for set elements size_t limit = rev_hes_sparse.end(); CPPAD_ASSERT_UNKNOWN( for_jac_sparse.end() == limit ); // check number of sets match CPPAD_ASSERT_UNKNOWN( for_jac_sparse.n_set() == rev_hes_sparse.n_set() ); // vecad_sparsity contains a sparsity pattern for each VecAD object. // vecad_ind maps a VecAD index (beginning of the VecAD object) // to the index for the corresponding set in vecad_sparsity. size_t num_vecad_ind = play->num_vec_ind_rec(); size_t num_vecad_vec = play->num_vecad_vec_rec(); Vector_set vecad_sparse; vecad_sparse.resize(num_vecad_vec, limit); pod_vector vecad_ind; pod_vector vecad_jac; if( num_vecad_vec > 0 ) { size_t length; vecad_ind.extend(num_vecad_ind); vecad_jac.extend(num_vecad_vec); j = 0; for(i = 0; i < num_vecad_vec; i++) { // length of this VecAD length = play->GetVecInd(j); // set vecad_ind to proper index for this VecAD vecad_ind[j] = i; // make all other values for this vector invalid for(k = 1; k <= length; k++) vecad_ind[j+k] = num_vecad_vec; // start of next VecAD j += length + 1; // initialize this vector's reverse jacobian value vecad_jac[i] = false; } CPPAD_ASSERT_UNKNOWN( j == play->num_vec_ind_rec() ); } // work space used by UserOp. vector user_x; // parameters in x as integers; vector user_ix; // variable indices for argument vector x // typedef std::set size_set; size_set::iterator set_itr; // iterator for a standard set size_set::iterator set_end; // end of iterator sequence vector< size_set > set_r; // forward Jacobian sparsity for x vector< size_set > set_u; // reverse Hessian sparsity for y vector< size_set > set_v; // reverse Hessian sparsity for x // vector bool_r; // bool forward Jacobian sparsity for x vector bool_u; // bool reverse Hessian sparsity for y vector bool_v; // bool reverse Hessian sparsity for x // vectorBool pack_r; // pack forward Jacobian sparsity for x vectorBool pack_u; // pack reverse Hessian sparsity for y vectorBool pack_v; // pack reverse Hessian sparsity for x // vector user_vx; // which components of x are variables vector user_s; // reverse Jacobian sparsity for y vector user_t; // reverse Jacobian sparsity for x const size_t user_q = limit; // maximum element plus one // atomic_base* user_atom = CPPAD_NULL; // user's atomic op calculator bool user_pack = false; // sparsity pattern type is pack bool user_bool = false; // sparsity pattern type is bool bool user_set = false; // sparsity pattern type is set bool user_ok = false; // atomic op return value // // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state = end_user; // proper initialization // // pointer to the beginning of the parameter vector // (used by atomic functions const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // // Initialize play->reverse_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == EndOp ); # if CPPAD_REV_HES_SWEEP_TRACE std::cout << std::endl; CppAD::vectorBool zf_value(limit); CppAD::vectorBool zh_value(limit); # endif bool more_operators = true; while(more_operators) { bool flag; // temporary for use in switch cases // // next op play->reverse_next(op, arg, i_op, i_var); # ifndef NDEBUG if( i_op <= n ) { CPPAD_ASSERT_UNKNOWN((op == InvOp) | (op == BeginOp)); } else CPPAD_ASSERT_UNKNOWN((op != InvOp) & (op != BeginOp)); # endif // rest of information depends on the case switch( op ) { case AbsOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1) reverse_sparse_hessian_linear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case AddvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_addsub_op( i_var, arg, RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case AddpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_linear_unary_op( i_var, arg[1], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case AcosOp: // sqrt(1 - x * x), acos(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AcoshOp: // sqrt(x * x - 1), acosh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; # endif // ------------------------------------------------- case AsinOp: // sqrt(1 - x * x), asin(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AsinhOp: // sqrt(1 + x * x), asinh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; # endif // ------------------------------------------------- case AtanOp: // 1 + x * x, atan(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AtanhOp: // 1 - x * x, atanh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; # endif // ------------------------------------------------- case BeginOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1) more_operators = false; break; // ------------------------------------------------- case CSkipOp: // CSkipOp has a variable number of arguments and // reverse_next thinks it one has one argument. // We must inform reverse_next of this special case. play->reverse_cskip(op, arg, i_op, i_var); break; // ------------------------------------------------- case CSumOp: // CSumOp has a variable number of arguments and // reverse_next thinks it one has one argument. // We must inform reverse_next of this special case. play->reverse_csum(op, arg, i_op, i_var); reverse_sparse_hessian_csum_op( i_var, arg, RevJac, rev_hes_sparse ); break; // ------------------------------------------------- case CExpOp: reverse_sparse_hessian_cond_op( i_var, arg, num_par, RevJac, rev_hes_sparse ); break; // --------------------------------------------------- case CosOp: // sin(x), cos(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // --------------------------------------------------- case CoshOp: // sinh(x), cosh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case DisOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) // derivativve is identically zero break; // ------------------------------------------------- case DivvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_div_op( i_var, arg, RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case DivpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[1], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case DivvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_linear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case ErfOp: // arg[1] is always the parameter 0 // arg[2] is always the parameter 2 / sqrt(pi) CPPAD_ASSERT_NARG_NRES(op, 3, 5); reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case ExpOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Expm1Op: CPPAD_ASSERT_NARG_NRES(op, 1, 1) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; # endif // ------------------------------------------------- case InvOp: CPPAD_ASSERT_NARG_NRES(op, 0, 1) // Z is already defined break; // ------------------------------------------------- case LdpOp: reverse_sparse_hessian_load_op( op, i_var, arg, num_vecad_ind, vecad_ind.data(), rev_hes_sparse, vecad_sparse, RevJac, vecad_jac.data() ); break; // ------------------------------------------------- case LdvOp: reverse_sparse_hessian_load_op( op, i_var, arg, num_vecad_ind, vecad_ind.data(), rev_hes_sparse, vecad_sparse, RevJac, vecad_jac.data() ); break; // ------------------------------------------------- case EqpvOp: case EqvvOp: case LtpvOp: case LtvpOp: case LtvvOp: case LepvOp: case LevpOp: case LevvOp: case NepvOp: case NevvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 0); break; // ------------------------------------------------- case LogOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Log1pOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; # endif // ------------------------------------------------- case MulpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_linear_unary_op( i_var, arg[1], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case MulvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_mul_op( i_var, arg, RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case ParOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1) break; // ------------------------------------------------- case PowpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[1], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case PowvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case PowvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3) reverse_sparse_hessian_pow_op( i_var, arg, RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case PriOp: CPPAD_ASSERT_NARG_NRES(op, 5, 0); break; // ------------------------------------------------- case SignOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); // Derivative is identiaclly zero break; // ------------------------------------------------- case SinOp: // cos(x), sin(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case SinhOp: // cosh(x), sinh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case SqrtOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case StppOp: // sparsity cannot propagate through a parameter CPPAD_ASSERT_NARG_NRES(op, 3, 0) break; // ------------------------------------------------- case StpvOp: reverse_sparse_hessian_store_op( op, arg, num_vecad_ind, vecad_ind.data(), rev_hes_sparse, vecad_sparse, RevJac, vecad_jac.data() ); break; // ------------------------------------------------- case StvpOp: // sparsity cannot propagate through a parameter CPPAD_ASSERT_NARG_NRES(op, 3, 0) break; // ------------------------------------------------- case StvvOp: reverse_sparse_hessian_store_op( op, arg, num_vecad_ind, vecad_ind.data(), rev_hes_sparse, vecad_sparse, RevJac, vecad_jac.data() ); break; // ------------------------------------------------- case SubvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_addsub_op( i_var, arg, RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case SubpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_linear_unary_op( i_var, arg[1], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case SubvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_linear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case TanOp: // tan(x)^2, tan(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case TanhOp: // tanh(x)^2, tanh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2) reverse_sparse_hessian_nonlinear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case UserOp: // start or end an atomic operation sequence flag = user_state == end_user; user_atom = play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( flag ) { user_pack = user_atom->sparsity() == atomic_base::pack_sparsity_enum; user_bool = user_atom->sparsity() == atomic_base::bool_sparsity_enum; user_set = user_atom->sparsity() == atomic_base::set_sparsity_enum; CPPAD_ASSERT_UNKNOWN( user_pack || user_bool || user_set ); user_x.resize(user_n); user_ix.resize(user_n); user_vx.resize(user_n); user_s.resize(user_m); user_t.resize(user_n); // simpler to initialize all sparsity patterns as empty for(i = 0; i < user_m; i++) user_s[i] = false; for(i = 0; i < user_n; i++) user_t[i] = false; if( user_pack ) { pack_r.resize(user_n * user_q); pack_u.resize(user_m * user_q); pack_v.resize(user_n * user_q); // simpler to initialize all patterns as empty for(i = 0; i < user_m; i++) { for(j = 0; j < user_q; j++) pack_u[ i * user_q + j] = false; } for(i = 0; i < user_n; i++) { for(j = 0; j < user_q; j++) { pack_r[ i * user_q + j] = false; pack_v[ i * user_q + j] = false; } } } if( user_bool ) { bool_r.resize(user_n * user_q); bool_u.resize(user_m * user_q); bool_v.resize(user_n * user_q); // simpler to initialize all patterns as empty for(i = 0; i < user_m; i++) { for(j = 0; j < user_q; j++) bool_u[ i * user_q + j] = false; } for(i = 0; i < user_n; i++) { for(j = 0; j < user_q; j++) { bool_r[ i * user_q + j] = false; bool_v[ i * user_q + j] = false; } } } if( user_set ) { set_r.resize(user_n); set_u.resize(user_m); set_v.resize(user_n); for(i = 0; i < user_m; i++) set_u[i].clear(); for(i = 0; i < user_n; i++) { set_r[i].clear(); set_v[i].clear(); } } } else { // call users function for this operation user_atom->set_old(user_old); if( user_pack ) { user_ok = user_atom->rev_sparse_hes(user_vx, user_s, user_t, user_q, pack_r, pack_u, pack_v, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_hes( user_vx, user_s, user_t, user_q, pack_r, pack_u, pack_v ); } if( user_bool ) { user_ok = user_atom->rev_sparse_hes(user_vx, user_s, user_t, user_q, bool_r, bool_u, bool_v, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_hes( user_vx, user_s, user_t, user_q, bool_r, bool_u, bool_v ); } if( user_set ) { user_ok = user_atom->rev_sparse_hes(user_vx, user_s, user_t, user_q, set_r, set_u, set_v, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_hes( user_vx, user_s, user_t, user_q, set_r, set_u, set_v ); } if( ! user_ok ) { std::string msg = user_atom->afun_name() + ": atomic_base.rev_sparse_hes: returned false\n"; if( user_pack ) msg += "sparsity = pack_sparsity_enum"; if( user_bool ) msg += "sparsity = bool_sparsity_enum"; if( user_set ) msg += "sparsity = set_sparsity_enum"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } for(i = 0; i < user_n; i++) if( user_ix[i] > 0 ) { size_t i_x = user_ix[i]; if( user_t[i] ) RevJac[i_x] = true; if( user_pack ) { for(j = 0; j < user_q; j++) if( pack_v[ i * user_q + j ] ) rev_hes_sparse.add_element(i_x, j); } if( user_bool ) { for(j = 0; j < user_q; j++) if( bool_v[ i * user_q + j ] ) rev_hes_sparse.add_element(i_x, j); } if( user_set ) { set_itr = set_v[i].begin(); set_end = set_v[i].end(); while( set_itr != set_end ) rev_hes_sparse.add_element(i_x, *set_itr++); } } } break; case UsrapOp: // parameter argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); user_ix[user_j] = 0; user_vx[user_j] = false; // // parameters as integers user_x[user_j] = parameter[arg[0]]; // break; case UsravOp: // variable argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); user_ix[user_j] = arg[0]; user_vx[user_j] = true; // // variable as integers user_x[user_j] = CppAD::numeric_limits::quiet_NaN(); // { typename Vector_set::const_iterator itr(for_jac_sparse, arg[0]); i = *itr; while( i < user_q ) { if( user_pack ) pack_r[ user_j * user_q + i ] = true; if( user_bool ) bool_r[ user_j * user_q + i ] = true; if( user_set ) set_r[user_j].insert(i); i = *(++itr); } } break; case UsrrpOp: // parameter result in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrvOp: // variable result in an atomic operation sequence play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( RevJac[i_var] ) { user_s[user_i] = true; } { typename Vector_set::const_iterator itr(rev_hes_sparse, i_var); j = *itr; while( j < user_q ) { if( user_pack ) pack_u[user_i * user_q + j] = true; if( user_bool ) bool_u[user_i * user_q + j] = true; if( user_set ) set_u[user_i].insert(j); j = *(++itr); } } break; // ------------------------------------------------- case ZmulpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_linear_unary_op( i_var, arg[1], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case ZmulvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_linear_unary_op( i_var, arg[0], RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- case ZmulvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) reverse_sparse_hessian_mul_op( i_var, arg, RevJac, for_jac_sparse, rev_hes_sparse ); break; // ------------------------------------------------- default: CPPAD_ASSERT_UNKNOWN(0); } # if CPPAD_REV_HES_SWEEP_TRACE for(j = 0; j < limit; j++) { zf_value[j] = false; zh_value[j] = false; } typename Vector_set::const_iterator itr_jac(for_jac_sparse, i_var); j = *itr_jac; while( j < limit ) { zf_value[j] = true; j = *(++itr_jac); } typename Vector_set::const_iterator itr_hes(rev_hes_sparse, i_var); j = *itr_hes; while( j < limit ) { zh_value[j] = true; j = *(++itr_hes); } printOp( std::cout, play, i_op, i_var, op, arg ); // should also print RevJac[i_var], but printOpResult does not // yet allow for this if( NumRes(op) > 0 && op != BeginOp ) printOpResult( std::cout, 1, &zf_value, 1, &zh_value ); std::cout << std::endl; } std::cout << std::endl; # else } # endif // values corresponding to BeginOp CPPAD_ASSERT_UNKNOWN( i_op == 0 ); CPPAD_ASSERT_UNKNOWN( i_var == 0 ); return; } } } // END_CPPAD_LOCAL_NAMESPACE // preprocessor symbols that are local to this file # undef CPPAD_REV_HES_SWEEP_TRACE # endif cppad-20170000.3/cppad/local/pow_op.hpp0000644000175200017650000004036313057470466016641 0ustar coincoin-web// $Id: pow_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_POW_OP_HPP # define CPPAD_LOCAL_POW_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file pow_op.hpp Forward and reverse mode calculations for z = pow(x, y). */ // --------------------------- Powvv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = PowvvOp. In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_pow_op */ template inline void forward_powvv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // 2 = NumRes(PowvvOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // z_0 = log(x) forward_log_op(p, q, i_z, arg[0], cap_order, taylor); // z_1 = z_0 * y addr_t adr[2]; adr[0] = i_z; adr[1] = arg[1]; forward_mulvv_op(p, q, i_z+1, adr, parameter, cap_order, taylor); // z_2 = exp(z_1) // final result for zero order case is exactly the same as for Base if( p == 0 ) { // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z_2 = taylor + (i_z+2) * cap_order; z_2[0] = pow(x[0], y[0]); p++; } if( p <= q ) forward_exp_op(p, q, i_z+2, i_z+1, cap_order, taylor); } /*! Multiple directions forward mode Taylor coefficients for op = PowvvOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_pow_op_dir */ template inline void forward_powvv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // 2 = NumRes(PowvvOp) - 1 // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // z_0 = log(x) forward_log_op_dir(q, r, i_z, arg[0], cap_order, taylor); // z_1 = y * z_0 addr_t adr[2]; adr[0] = i_z; adr[1] = arg[1]; forward_mulvv_op_dir(q, r, i_z+1, adr, parameter, cap_order, taylor); // z_2 = exp(z_1) forward_exp_op_dir(q, r, i_z+2, i_z+1, cap_order, taylor); } /*! Compute zero order forward mode Taylor coefficients for result of op = PowvvOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_pow_op_0 */ template inline void forward_powvv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // NumRes(PowvvOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z_0 = taylor + i_z * cap_order; Base* z_1 = z_0 + cap_order; Base* z_2 = z_1 + cap_order; z_0[0] = log( x[0] ); z_1[0] = z_0[0] * y[0]; z_2[0] = pow(x[0], y[0]); } /*! Compute reverse mode partial derivatives for result of op = PowvvOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails reverse_pow_op */ template inline void reverse_powvv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // convert from final result to first result i_z -= 2; // NumRes(PowvvOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // z_2 = exp(z_1) reverse_exp_op( d, i_z+2, i_z+1, cap_order, taylor, nc_partial, partial ); // z_1 = z_0 * y addr_t adr[2]; adr[0] = i_z; adr[1] = arg[1]; reverse_mulvv_op( d, i_z+1, adr, parameter, cap_order, taylor, nc_partial, partial ); // z_0 = log(x) reverse_log_op( d, i_z, arg[0], cap_order, taylor, nc_partial, partial ); } // --------------------------- Powpv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = PowpvOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_pow_op */ template inline void forward_powpv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // 2 = NumRes(PowpvOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowpvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* z_0 = taylor + i_z * cap_order; // z_0 = log(x) Base x = parameter[ arg[0] ]; size_t d; for(d = p; d <= q; d++) { if( d == 0 ) z_0[d] = log(x); else z_0[d] = Base(0); } // z_1 = z_0 * y addr_t adr[2]; // offset of z_i in taylor (as if it were a parameter); i.e., log(x) adr[0] = i_z * cap_order; // offset of y in taylor (as a variable) adr[1] = arg[1]; // Trick: use taylor both for the parameter vector and variable values forward_mulpv_op(p, q, i_z+1, adr, taylor, cap_order, taylor); // z_2 = exp(z_1) // zero order case exactly same as Base type operation if( p == 0 ) { Base* y = taylor + arg[1] * cap_order; Base* z_2 = taylor + (i_z+2) * cap_order; z_2[0] = pow(x, y[0]); p++; } if( p <= q ) forward_exp_op(p, q, i_z+2, i_z+1, cap_order, taylor); } /*! Multiple directions forward mode Taylor coefficients for op = PowpvOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_pow_op_dir */ template inline void forward_powpv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // 2 = NumRes(PowpvOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowpvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* z_0 = taylor + i_z * num_taylor_per_var; // z_0 = log(x) size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) z_0[m+ell] = Base(0); // z_1 = z_0 * y addr_t adr[2]; // offset of z_0 in taylor (as if it were a parameter); i.e., log(x) adr[0] = i_z * num_taylor_per_var; // ofset of y in taylor (as a variable) adr[1] = arg[1]; // Trick: use taylor both for the parameter vector and variable values forward_mulpv_op_dir(q, r, i_z+1, adr, taylor, cap_order, taylor); // z_2 = exp(z_1) forward_exp_op_dir(q, r, i_z+2, i_z+1, cap_order, taylor); } /*! Compute zero order forward mode Taylor coefficient for result of op = PowpvOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_pow_op_0 */ template inline void forward_powpv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // NumRes(PowpvOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowpvOp) == 3 ); // Paraemter value Base x = parameter[ arg[0] ]; // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z_0 = taylor + i_z * cap_order; Base* z_1 = z_0 + cap_order; Base* z_2 = z_1 + cap_order; // z_0 = log(x) z_0[0] = log(x); // z_1 = z_0 * y z_1[0] = z_0[0] * y[0]; // z_2 = exp(z_1) // zero order case exactly same as Base type operation z_2[0] = pow(x, y[0]); } /*! Compute reverse mode partial derivative for result of op = PowpvOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails reverse_pow_op */ template inline void reverse_powpv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // convert from final result to first result i_z -= 2; // NumRes(PowpvOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // z_2 = exp(z_1) reverse_exp_op( d, i_z+2, i_z+1, cap_order, taylor, nc_partial, partial ); // z_1 = z_0 * y addr_t adr[2]; adr[0] = i_z * cap_order; // offset of z_0[0] in taylor adr[1] = arg[1]; // index of y in taylor and partial // use taylor both for parameter and variable values reverse_mulpv_op( d, i_z+1, adr, taylor, cap_order, taylor, nc_partial, partial ); // z_0 = log(x) // x is a parameter } // --------------------------- Powvp ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = PowvpOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_pow_op */ template inline void forward_powvp_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // 2 = NumRes(PowvpOp) - 1 // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvpOp) == 3 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // z_0 = log(x) forward_log_op(p, q, i_z, arg[0], cap_order, taylor); // z_1 = y * z_0 addr_t adr[2]; adr[0] = arg[1]; adr[1] = i_z; forward_mulpv_op(p, q, i_z+1, adr, parameter, cap_order, taylor); // z_2 = exp(z_1) // zero order case exactly same as Base type operation if( p == 0 ) { Base* z_2 = taylor + (i_z+2) * cap_order; Base* x = taylor + arg[0] * cap_order; Base y = parameter[ arg[1] ]; z_2[0] = pow(x[0], y); p++; } if( p <= q ) forward_exp_op(p, q, i_z+2, i_z+1, cap_order, taylor); } /*! Multiple directions forward mode Taylor coefficients for op = PowvpOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_pow_op_dir */ template inline void forward_powvp_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // 2 = NumRes(PowvpOp) - 1 // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvpOp) == 3 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // z_0 = log(x) forward_log_op_dir(q, r, i_z, arg[0], cap_order, taylor); // z_1 = y * z_0 addr_t adr[2]; adr[0] = arg[1]; adr[1] = i_z; forward_mulpv_op_dir(q, r, i_z+1, adr, parameter, cap_order, taylor); // z_2 = exp(z_1) forward_exp_op_dir(q, r, i_z+2, i_z+1, cap_order, taylor); } /*! Compute zero order forward mode Taylor coefficients for result of op = PowvpOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_pow_op_0 */ template inline void forward_powvp_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // convert from final result to first result i_z -= 2; // NumRes(PowvpOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvpOp) == 3 ); // Paraemter value Base y = parameter[ arg[1] ]; // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* z_0 = taylor + i_z * cap_order; Base* z_1 = z_0 + cap_order; Base* z_2 = z_1 + cap_order; // z_0 = log(x) z_0[0] = log(x[0]); // z_1 = z_0 * y z_1[0] = z_0[0] * y; // z_2 = exp(z_1) // zero order case exactly same as Base type operation z_2[0] = pow(x[0], y); } /*! Compute reverse mode partial derivative for result of op = PowvpOp. The C++ source code corresponding to this operation is \verbatim z = pow(x, y) \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails reverse_pow_op */ template inline void reverse_powvp_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // convert from final result to first result i_z -= 2; // NumRes(PowvpOp) - 1; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(PowvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(PowvpOp) == 3 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // z_2 = exp(z_1) reverse_exp_op( d, i_z+2, i_z+1, cap_order, taylor, nc_partial, partial ); // z_1 = y * z_0 addr_t adr[2]; adr[0] = arg[1]; adr[1] = i_z; reverse_mulpv_op( d, i_z+1, adr, parameter, cap_order, taylor, nc_partial, partial ); // z_0 = log(x) reverse_log_op( d, i_z, arg[0], cap_order, taylor, nc_partial, partial ); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/sign_op.hpp0000644000175200017650000000743513057470466016777 0ustar coincoin-web// $Id: sign_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_SIGN_OP_HPP # define CPPAD_LOCAL_SIGN_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sign_op.hpp Forward and reverse mode calculations for z = sign(x). */ /*! Compute forward mode Taylor coefficient for result of op = SignOp. The C++ source code corresponding to this operation is \verbatim z = sign(x) \endverbatim \copydetails forward_unary1_op */ template inline void forward_sign_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; if( p == 0 ) { z[0] = sign(x[0]); p++; } for(size_t j = p; j <= q; j++) z[j] = Base(0.); } /*! Multiple direction forward mode Taylor coefficient for op = SignOp. The C++ source code corresponding to this operation is \verbatim z = sign(x) \endverbatim \copydetails forward_unary1_op_dir */ template inline void forward_sign_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; size_t m = (q - 1) * r + 1; Base* z = taylor + i_z * num_taylor_per_var; for(size_t ell = 0; ell < r; ell++) z[m+ell] = Base(0.); } /*! Compute zero order forward mode Taylor coefficient for result of op = SignOp. The C++ source code corresponding to this operation is \verbatim z = sign(x) \endverbatim \copydetails forward_unary1_op_0 */ template inline void forward_sign_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base x0 = *(taylor + i_x * cap_order); Base* z = taylor + i_z * cap_order; z[0] = sign(x0); } /*! Compute reverse mode partial derivatives for result of op = SignOp. The C++ source code corresponding to this operation is \verbatim z = sign(x) \endverbatim \copydetails reverse_unary1_op */ template inline void reverse_sign_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SignOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // nothing to do because partials of sign are zero return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/csum_op.hpp0000644000175200017650000004252313057470466017003 0ustar coincoin-web// $Id: csum_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_CSUM_OP_HPP # define CPPAD_LOCAL_CSUM_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file csum_op.hpp Forward, reverse and sparsity calculations for cummulative summation. */ /*! Compute forward mode Taylor coefficients for result of op = CsumOp. This operation is \verbatim z = s + x(1) + ... + x(m) - y(1) - ... - y(n). \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param p lowest order of the Taylor coefficient that we are computing. \param q highest order of the Taylor coefficient that we are computing. \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param arg \a arg[0] is the number of addition variables in this cummulative summation; i.e., m. \n \a arg[1] is the number of subtraction variables in this cummulative summation; i.e., \c m. \n parameter[ arg[2] ] is the parameter value \c s in this cummunative summation. \n arg[2+i] for i = 1 , ... , m is the variable index of x(i). \n arg[2+arg[0]+i] for i = 1 , ... , n is the variable index of y(i). \param num_par is the number of parameters in \a parameter. \param parameter is the parameter vector for this operation sequence. \param cap_order number of colums in the matrix containing all the Taylor coefficients. \param taylor \b Input: taylor [ arg[2+i] * cap_order + k ] for i = 1 , ... , m and k = 0 , ... , q is the k-th order Taylor coefficient corresponding to x(i) \n \b Input: taylor [ arg[2+m+i] * cap_order + k ] for i = 1 , ... , n and k = 0 , ... , q is the k-th order Taylor coefficient corresponding to y(i) \n \b Input: taylor [ i_z * cap_order + k ] for k = 0 , ... , p, is the k-th order Taylor coefficient corresponding to z. \n \b Output: taylor [ i_z * cap_order + k ] for k = p , ... , q, is the \a k-th order Taylor coefficient corresponding to z. */ template inline void forward_csum_op( size_t p , size_t q , size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order , Base* taylor ) { Base zero(0); size_t i, j, k; // check assumptions CPPAD_ASSERT_UNKNOWN( NumRes(CSumOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); CPPAD_ASSERT_UNKNOWN( arg[0] + arg[1] == arg[ arg[0] + arg[1] + 3 ] ); // Taylor coefficients corresponding to result Base* z = taylor + i_z * cap_order; for(k = p; k <= q; k++) z[k] = zero; if( p == 0 ) z[p] = parameter[ arg[2] ]; Base* x; i = arg[0]; j = 2; while(i--) { CPPAD_ASSERT_UNKNOWN( size_t(arg[j+1]) < i_z ); x = taylor + arg[++j] * cap_order; for(k = p; k <= q; k++) z[k] += x[k]; } i = arg[1]; while(i--) { CPPAD_ASSERT_UNKNOWN( size_t(arg[j+1]) < i_z ); x = taylor + arg[++j] * cap_order; for(k = p; k <= q; k++) z[k] -= x[k]; } } /*! Multiple direction forward mode Taylor coefficients for op = CsumOp. This operation is \verbatim z = s + x(1) + ... + x(m) - y(1) - ... - y(n). \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD and computations by this routine are done using type \a Base. \param q order ot the Taylor coefficients that we are computing. \param r number of directions for Taylor coefficients that we are computing. \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param arg \a arg[0] is the number of addition variables in this cummulative summation; i.e., m. \n \a arg[1] is the number of subtraction variables in this cummulative summation; i.e., \c m. \n parameter[ arg[2] ] is the parameter value \c s in this cummunative summation. \n arg[2+i] for i = 1 , ... , m is the variable index of x(i). \n arg[2+arg[0]+i] for i = 1 , ... , n is the variable index of y(i). \param num_par is the number of parameters in \a parameter. \param parameter is the parameter vector for this operation sequence. \param cap_order number of colums in the matrix containing all the Taylor coefficients. \param taylor \b Input: taylor [ arg[2+i]*((cap_order-1)*r + 1) + 0 ] for i = 1 , ... , m is the 0-th order Taylor coefficient corresponding to x(i) and taylor [ arg[2+i]*((cap_order-1)*r + 1) + (q-1)*r + ell + 1 ] for i = 1 , ... , m, ell = 0 , ... , r-1 is the q-th order Taylor coefficient corresponding to x(i) and direction ell. \n \b Input: taylor [ arg[2+m+i]*((cap_order-1)*r + 1) + 0 ] for i = 1 , ... , n is the 0-th order Taylor coefficient corresponding to y(i) and taylor [ arg[2+m+i]*((cap_order-1)*r + 1) + (q-1)*r + ell + 1 ] for i = 1 , ... , n, ell = 0 , ... , r-1 is the q-th order Taylor coefficient corresponding to y(i) and direction ell. \n \b Output: taylor [ i_z*((cap_order-1)*r+1) + (q-1)*r + ell + 1 ] is the \a q-th order Taylor coefficient corresponding to z for direction ell = 0 , ... , r-1. */ template inline void forward_csum_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order , Base* taylor ) { Base zero(0); size_t i, j, ell; // check assumptions CPPAD_ASSERT_UNKNOWN( NumRes(CSumOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); CPPAD_ASSERT_UNKNOWN( arg[0] + arg[1] == arg[ arg[0] + arg[1] + 3 ] ); // Taylor coefficients corresponding to result size_t num_taylor_per_var = (cap_order-1) * r + 1; size_t m = (q-1)*r + 1; Base* z = taylor + i_z * num_taylor_per_var + m; for(ell = 0; ell < r; ell++) z[ell] = zero; Base* x; i = arg[0]; j = 2; while(i--) { CPPAD_ASSERT_UNKNOWN( size_t(arg[j+1]) < i_z ); x = taylor + arg[++j] * num_taylor_per_var + m; for(ell = 0; ell < r; ell++) z[ell] += x[ell]; } i = arg[1]; while(i--) { CPPAD_ASSERT_UNKNOWN( size_t(arg[j+1]) < i_z ); x = taylor + arg[++j] * num_taylor_per_var + m; for(ell = 0; ell < r; ell++) z[ell] -= x[ell]; } } /*! Compute reverse mode Taylor coefficients for result of op = CsumOp. This operation is \verbatim z = q + x(1) + ... + x(m) - y(1) - ... - y(n). H(y, x, w, ...) = G[ z(x, y), y, x, w, ... ] \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param d order the highest order Taylor coefficient that we are computing the partial derivatives with respect to. \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param arg \a arg[0] is the number of addition variables in this cummulative summation; i.e., m. \n \a arg[1] is the number of subtraction variables in this cummulative summation; i.e., \c m. \n parameter[ arg[2] ] is the parameter value \c q in this cummunative summation. \n arg[2+i] for i = 1 , ... , m is the value x(i). \n arg[2+arg[0]+i] for i = 1 , ... , n is the value y(i). \param nc_partial number of colums in the matrix containing all the partial derivatives. \param partial \b Input: partial [ arg[2+i] * nc_partial + k ] for i = 1 , ... , m and k = 0 , ... , d is the partial derivative of G(z, y, x, w, ...) with respect to the k-th order Taylor coefficient corresponding to x(i) \n \b Input: partial [ arg[2+m+i] * nc_partial + k ] for i = 1 , ... , n and k = 0 , ... , d is the partial derivative of G(z, y, x, w, ...) with respect to the k-th order Taylor coefficient corresponding to y(i) \n \b Input: partial [ i_z * nc_partial + k ] for i = 1 , ... , n and k = 0 , ... , d is the partial derivative of G(z, y, x, w, ...) with respect to the k-th order Taylor coefficient corresponding to \c z. \n \b Output: partial [ arg[2+i] * nc_partial + k ] for i = 1 , ... , m and k = 0 , ... , d is the partial derivative of H(y, x, w, ...) with respect to the k-th order Taylor coefficient corresponding to x(i) \n \b Output: partial [ arg[2+m+i] * nc_partial + k ] for i = 1 , ... , n and k = 0 , ... , d is the partial derivative of H(y, x, w, ...) with respect to the k-th order Taylor coefficient corresponding to y(i) */ template inline void reverse_csum_op( size_t d , size_t i_z , const addr_t* arg , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumRes(CSumOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partial derivative corresponding to result Base* pz = partial + i_z * nc_partial; Base* px; size_t i, j, k; size_t d1 = d + 1; i = arg[0]; j = 2; while(i--) { CPPAD_ASSERT_UNKNOWN( size_t(arg[j+1]) < i_z ); px = partial + arg[++j] * nc_partial; k = d1; while(k--) px[k] += pz[k]; } i = arg[1]; while(i--) { CPPAD_ASSERT_UNKNOWN( size_t(arg[j+1]) < i_z ); px = partial + arg[++j] * nc_partial; k = d1; while(k--) px[k] -= pz[k]; } } /*! Forward mode Jacobian sparsity pattern for CSumOp operator. This operation is \verbatim z = q + x(1) + ... + x(m) - y(1) - ... - y(n). \endverbatim \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e. the index in \a sparsity corresponding to z. \param arg \a arg[0] is the number of addition variables in this cummulative summation; i.e., m + n. \n \a arg[1] is the number of subtraction variables in this cummulative summation; i.e., \c m. \n parameter[ arg[2] ] is the parameter value \c q in this cummunative summation. \n arg[2+i] for i = 1 , ... , m is the value x(i). \n arg[2+arg[1]+i] for i = 1 , ... , n is the value y(i). \param sparsity \b Input: For i = 1 , ... , m, the set with index \a arg[2+i] in \a sparsity is the sparsity bit pattern for x(i). This identifies which of the independent variables the variable x(i) depends on. \n \b Input: For i = 1 , ... , n, the set with index \a arg[2+arg[0]+i] in \a sparsity is the sparsity bit pattern for x(i). This identifies which of the independent variables the variable y(i) depends on. \n \b Output: The set with index \a i_z in \a sparsity is the sparsity bit pattern for z. This identifies which of the independent variables the variable z depends on. */ template inline void forward_sparse_jacobian_csum_op( size_t i_z , const addr_t* arg , Vector_set& sparsity ) { sparsity.clear(i_z); size_t i, j; i = arg[0] + arg[1]; j = 2; while(i--) { CPPAD_ASSERT_UNKNOWN( size_t(arg[j+1]) < i_z ); sparsity.binary_union( i_z , // index in sparsity for result i_z , // index in sparsity for left operand arg[++j] , // index for right operand sparsity // sparsity vector for right operand ); } } /*! Reverse mode Jacobian sparsity pattern for CSumOp operator. This operation is \verbatim z = q + x(1) + ... + x(m) - y(1) - ... - y(n). H(y, x, w, ...) = G[ z(x, y), y, x, w, ... ] \endverbatim \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e. the index in \a sparsity corresponding to z. \param arg \a arg[0] is the number of addition variables in this cummulative summation; i.e., m + n. \n \a arg[1] is the number of subtraction variables in this cummulative summation; i.e., \c m. \n parameter[ arg[2] ] is the parameter value \c q in this cummunative summation. \n arg[2+i] for i = 1 , ... , m is the value x(i). \n arg[2+arg[1]+i] for i = 1 , ... , n is the value y(i). \param sparsity For i = 1 , ... , m, the set with index \a arg[2+i] in \a sparsity is the sparsity bit pattern for x(i). This identifies which of the dependent variables depend on x(i). On input, the sparsity patter corresponds to \c G, and on ouput it corresponds to \c H. \n For i = 1 , ... , m, the set with index \a arg[2+arg[0]+i] in \a sparsity is the sparsity bit pattern for y(i). This identifies which of the dependent variables depend on y(i). On input, the sparsity patter corresponds to \c G, and on ouput it corresponds to \c H. \n \b Input: The set with index \a i_z in \a sparsity is the sparsity bit pattern for z. On input it corresponds to \c G and on output it is undefined. */ template inline void reverse_sparse_jacobian_csum_op( size_t i_z , const addr_t* arg , Vector_set& sparsity ) { size_t i, j; i = arg[0] + arg[1]; j = 2; while(i--) { ++j; CPPAD_ASSERT_UNKNOWN( size_t(arg[j]) < i_z ); sparsity.binary_union( arg[j] , // index in sparsity for result arg[j] , // index in sparsity for left operand i_z , // index for right operand sparsity // sparsity vector for right operand ); } } /*! Reverse mode Hessian sparsity pattern for CSumOp operator. This operation is \verbatim z = q + x(1) + ... + x(m) - y(1) - ... - y(n). H(y, x, w, ...) = G[ z(x, y), y, x, w, ... ] \endverbatim \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e. the index in \a sparsity corresponding to z. \param arg \a arg[0] is the number of addition variables in this cummulative summation; i.e., m + n. \n \a arg[1] is the number of subtraction variables in this cummulative summation; i.e., \c m. \n parameter[ arg[2] ] is the parameter value \c q in this cummunative summation. \n arg[2+i] for i = 1 , ... , m is the value x(i). \n arg[2+arg[0]+i] for i = 1 , ... , n is the value y(i). \param rev_jacobian rev_jacobian[i_z] is all false (true) if the Jabobian of G with respect to z must be zero (may be non-zero). \n \n For i = 1 , ... , m rev_jacobian[ arg[2+i] ] is all false (true) if the Jacobian with respect to x(i) is zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. \n \n For i = 1 , ... , n rev_jacobian[ arg[2+arg[0]+i] ] is all false (true) if the Jacobian with respect to y(i) is zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. \param rev_hes_sparsity The set with index \a i_z in in \a rev_hes_sparsity is the Hessian sparsity pattern for the fucntion G where one of the partials derivative is with respect to z. \n \n For i = 1 , ... , m The set with index arg[2+i] in \a rev_hes_sparsity is the Hessian sparsity pattern where one of the partials derivative is with respect to x(i). On input, it corresponds to the function G, and on output it corresponds to the function H. \n \n For i = 1 , ... , n The set with index arg[2+arg[0]+i] in \a rev_hes_sparsity is the Hessian sparsity pattern where one of the partials derivative is with respect to y(i). On input, it corresponds to the function G, and on output it corresponds to the function H. */ template inline void reverse_sparse_hessian_csum_op( size_t i_z , const addr_t* arg , bool* rev_jacobian , Vector_set& rev_hes_sparsity ) { size_t i, j; i = arg[0] + arg[1]; j = 2; while(i--) { ++j; CPPAD_ASSERT_UNKNOWN( size_t(arg[j]) < i_z ); rev_hes_sparsity.binary_union( arg[j] , // index in sparsity for result arg[j] , // index in sparsity for left operand i_z , // index for right operand rev_hes_sparsity // sparsity vector for right operand ); rev_jacobian[arg[j]] |= rev_jacobian[i_z]; } } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/declare_ad.hpp0000644000175200017650000001411413057470466017374 0ustar coincoin-web// $Id: declare_ad.hpp 3846 2016-11-19 11:35:04Z bradbell $ # ifndef CPPAD_LOCAL_DECLARE_AD_HPP # define CPPAD_LOCAL_DECLARE_AD_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # if CPPAD_USE_CPLUSPLUS_2011 # include # endif /*! \file declare_ad.hpp CppAD forward declarations; i.e., before definition */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE template class ADTape; template class player; template class recorder; } } // END_CPPAD_LOCAL_NAMESPACE namespace CppAD { // The conditional expression operator enum type enum CompareOp { CompareLt, // less than CompareLe, // less than or equal CompareEq, // equal CompareGe, // greater than or equal CompareGt, // greater than CompareNe // not equal }; // simple typedefs typedef CPPAD_TAPE_ADDR_TYPE addr_t; typedef CPPAD_TAPE_ID_TYPE tape_id_t; // classes class sparse_jacobian_work; class sparse_hessian_work; template class AD; template class ADFun; template class atomic_base; template class discrete; template class VecAD; template class VecAD_reference; // functions with one VecAD argument template bool Parameter (const VecAD &u); template bool Variable (const VecAD &u); // functions with one AD argument template int Integer (const AD &u); template bool Parameter (const AD &u); template bool Variable (const AD &u); template bool IdenticalZero (const AD &u); template bool IdenticalOne (const AD &u); template bool IdenticalPar (const AD &u); template bool LessThanZero (const AD &u); template bool LessThanOrZero (const AD &u); template bool GreaterThanZero (const AD &u); template bool GreaterThanOrZero (const AD &u); template AD Var2Par (const AD &u); template AD abs (const AD &u); template AD acos (const AD &u); template AD asin (const AD &u); template AD atan (const AD &u); template AD cos (const AD &u); template AD cosh (const AD &u); template AD exp (const AD &u); template AD log (const AD &u); template AD log10 (const AD &u); template AD sin (const AD &u); template AD sinh (const AD &u); template AD sqrt (const AD &u); template AD tan (const AD &u); // arithematic operators template AD operator + ( const AD &left, const AD &right); template AD operator - ( const AD &left, const AD &right); template AD operator * ( const AD &left, const AD &right); template AD operator / ( const AD &left, const AD &right); // comparison operators template bool operator < ( const AD &left, const AD &right); template bool operator <= ( const AD &left, const AD &right); template bool operator > ( const AD &left, const AD &right); template bool operator >= ( const AD &left, const AD &right); template bool operator == ( const AD &left, const AD &right); template bool operator != ( const AD &left, const AD &right); // pow template AD pow ( const AD &x, const AD &y); // azmul template AD azmul ( const AD &x, const AD &y); // NearEqual template bool NearEqual( const AD &x, const AD &y, const Base &r, const Base &a); template bool NearEqual( const Base &x, const AD &y, const Base &r, const Base &a); template bool NearEqual( const AD &x, const Base &y, const Base &r, const Base &a); // CondExpOp template AD CondExpOp ( enum CompareOp cop , const AD &left , const AD &right , const AD &trueCase , const AD &falseCase ); // IdenticalEqualPar template bool IdenticalEqualPar (const AD &u, const AD &v); // EqualOpSeq template bool EqualOpSeq (const AD &u, const AD &v); // PrintFor template void PrintFor( const AD& flag , const char* before , const AD& var , const char* after ); // Value template Base Value(const AD &x); // Pow function template AD pow (const AD &x, const AD &y); // input operator template std::istream& operator >> (std::istream &is, AD &x); // output operator template std::ostream& operator << (std::ostream &os, const AD &x); template std::ostream& operator << (std::ostream &os, const VecAD_reference &e); template std::ostream& operator << (std::ostream &os, const VecAD &vec); } # endif cppad-20170000.3/cppad/local/rev_jac_sweep.hpp0000644000175200017650000005500113057470466020145 0ustar coincoin-web// $Id: rev_jac_sweep.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_REV_JAC_SWEEP_HPP # define CPPAD_LOCAL_REV_JAC_SWEEP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file rev_jac_sweep.hpp Compute Reverse mode Jacobian sparsity patterns. */ /*! \def CPPAD_REV_JAC_SWEEP_TRACE This value is either zero or one. Zero is the normal operational value. If it is one, a trace of every rev_jac_sweep computation is printed. */ # define CPPAD_REV_JAC_SWEEP_TRACE 0 /*! Given the sparsity pattern for the dependent variables, RevJacSweep computes the sparsity pattern for all the independent variables. \tparam Base base type for the operator; i.e., this operation sequence was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param dependency Are the derivatives with respect to left and right of the expression below considered to be non-zero: \code CondExpRel(left, right, if_true, if_false) \endcode This is used by the optimizer to obtain the correct dependency relations. \param n is the number of independent variables on the tape. \param numvar is the total number of variables on the tape; i.e., \a play->num_var_rec(). This is also the number of rows in the entire sparsity pattern \a RevJac. \param play The information stored in \a play is a recording of the operations corresponding to a function \f[ F : {\bf R}^n \rightarrow {\bf R}^m \f] where \f$ n \f$ is the number of independent variables and \f$ m \f$ is the number of dependent variables. The object \a play is effectly constant. It is not declared const because while playing back the tape the object \a play holds information about the current location with in the tape and this changes during playback. \param var_sparsity For i = 0 , ... , \a numvar - 1, (all the variables on the tape) the forward Jacobian sparsity pattern for variable i corresponds to the set with index i in \a var_sparsity. \b \b \b Input: For i = 0 , ... , \a numvar - 1, the forward Jacobian sparsity pattern for variable i is an input if i corresponds to a dependent variable. Otherwise the sparsity patten is empty. \n \n \b Output: For j = 1 , ... , \a n, the sparsity pattern for the dependent variable with index (j-1) is given by the set with index index j in \a var_sparsity. */ template void RevJacSweep( bool dependency, size_t n, size_t numvar, local::player* play, Vector_set& var_sparsity ) { OpCode op; size_t i_op; size_t i_var; const addr_t* arg = CPPAD_NULL; size_t i, j, k; // length of the parameter vector (used by CppAD assert macros) const size_t num_par = play->num_par_rec(); // check numvar argument CPPAD_ASSERT_UNKNOWN( numvar > 0 ); CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar ); CPPAD_ASSERT_UNKNOWN( var_sparsity.n_set() == numvar ); // upper limit (exclusive) for elements in the set size_t limit = var_sparsity.end(); // vecad_sparsity contains a sparsity pattern for each VecAD object. // vecad_ind maps a VecAD index (beginning of the VecAD object) // to the index of the corresponding set in vecad_sparsity. size_t num_vecad_ind = play->num_vec_ind_rec(); size_t num_vecad_vec = play->num_vecad_vec_rec(); Vector_set vecad_sparsity; vecad_sparsity.resize(num_vecad_vec, limit); pod_vector vecad_ind; if( num_vecad_vec > 0 ) { size_t length; vecad_ind.extend(num_vecad_ind); j = 0; for(i = 0; i < num_vecad_vec; i++) { // length of this VecAD length = play->GetVecInd(j); // set to proper index for this VecAD vecad_ind[j] = i; for(k = 1; k <= length; k++) vecad_ind[j+k] = num_vecad_vec; // invalid index // start of next VecAD j += length + 1; } CPPAD_ASSERT_UNKNOWN( j == play->num_vec_ind_rec() ); } // work space used by UserOp. // vector user_x; // parameters in x as integers vector user_ix; // variable indices for argument vector // typedef std::set size_set; size_set::iterator set_itr; // iterator for a standard set size_set::iterator set_end; // end of iterator sequence vector< size_set > set_r; // set sparsity pattern for the argument x vector< size_set > set_s; // set sparisty pattern for the result y // vector bool_r; // bool sparsity pattern for the argument x vector bool_s; // bool sparisty pattern for the result y // vectorBool pack_r; // pack sparsity pattern for the argument x vectorBool pack_s; // pack sparisty pattern for the result y // const size_t user_q = limit; // maximum element plus one atomic_base* user_atom = CPPAD_NULL; // user's atomic op calculator bool user_pack = false; // sparsity pattern type is pack bool user_bool = false; // sparsity pattern type is bool bool user_set = false; // sparsity pattern type is set bool user_ok = false; // atomic op return value // // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state = end_user; // proper initialization // // pointer to the beginning of the parameter vector // (used by atomic functions const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // // Initialize play->reverse_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == EndOp ); # if CPPAD_REV_JAC_SWEEP_TRACE std::cout << std::endl; CppAD::vectorBool z_value(limit); # endif bool more_operators = true; while(more_operators) { bool flag; // temporary for use in switch cases // // next op play->reverse_next(op, arg, i_op, i_var); # ifndef NDEBUG if( i_op <= n ) { CPPAD_ASSERT_UNKNOWN((op == InvOp) | (op == BeginOp)); } else CPPAD_ASSERT_UNKNOWN((op != InvOp) & (op != BeginOp)); # endif // rest of information depends on the case switch( op ) { case AbsOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case AddvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case AddpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case AcosOp: // sqrt(1 - x * x), acos(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AcoshOp: // sqrt(x * x - 1), acosh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case AsinOp: // sqrt(1 - x * x), asin(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AsinhOp: // sqrt(1 + x * x), asinh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case AtanOp: // 1 + x * x, atan(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AtanhOp: // 1 - x * x, atanh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case BeginOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); more_operators = false; break; // ------------------------------------------------- case CSkipOp: // CSkipOp has a variable number of arguments and // reverse_next thinks it one has one argument. // We must inform reverse_next of this special case. play->reverse_cskip(op, arg, i_op, i_var); break; // ------------------------------------------------- case CSumOp: // CSumOp has a variable number of arguments and // reverse_next thinks it one has one argument. // We must inform reverse_next of this special case. play->reverse_csum(op, arg, i_op, i_var); reverse_sparse_jacobian_csum_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case CExpOp: reverse_sparse_jacobian_cond_op( dependency, i_var, arg, num_par, var_sparsity ); break; // --------------------------------------------------- case CosOp: // sin(x), cos(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // --------------------------------------------------- case CoshOp: // sinh(x), cosh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case DisOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); // derivative is identically zero but dependency is not if( dependency ) reverse_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case DivvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case DivpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case DivvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case ErfOp: // arg[1] is always the parameter 0 // arg[0] is always the parameter 2 / sqrt(pi) CPPAD_ASSERT_NARG_NRES(op, 3, 5); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case ExpOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Expm1Op: CPPAD_ASSERT_NARG_NRES(op, 1, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case InvOp: CPPAD_ASSERT_NARG_NRES(op, 0, 1); break; // ------------------------------------------------- case LdpOp: reverse_sparse_jacobian_load_op( dependency, op, i_var, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case LdvOp: reverse_sparse_jacobian_load_op( dependency, op, i_var, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case EqpvOp: case EqvvOp: case LtpvOp: case LtvpOp: case LtvvOp: case LepvOp: case LevpOp: case LevvOp: case NepvOp: case NevvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 0); break; // ------------------------------------------------- case LogOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Log1pOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case MulpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case MulvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case ParOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); break; // ------------------------------------------------- case PowvpOp: reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case PowpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3); reverse_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case PowvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3); reverse_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case PriOp: CPPAD_ASSERT_NARG_NRES(op, 5, 0); break; // ------------------------------------------------- case SignOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); // derivative is identically zero but dependency is not if( dependency ) reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case SinOp: // cos(x), sin(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case SinhOp: // cosh(x), sinh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case SqrtOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case StppOp: // does not affect sparsity or dependency when both are parameters CPPAD_ASSERT_NARG_NRES(op, 3, 0); break; // ------------------------------------------------- case StpvOp: reverse_sparse_jacobian_store_op( dependency, op, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case StvpOp: CPPAD_ASSERT_NARG_NRES(op, 3, 0); // storing a parameter only affects dependency reverse_sparse_jacobian_store_op( dependency, op, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case StvvOp: reverse_sparse_jacobian_store_op( dependency, op, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case SubvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case SubpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case SubvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case TanOp: // tan(x)^2, tan(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case TanhOp: // tanh(x)^2, tanh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case UserOp: // start or end atomic operation sequence flag = user_state == end_user; user_atom = play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( flag ) { user_x.resize( user_n ); user_ix.resize( user_n ); // user_pack = user_atom->sparsity() == atomic_base::pack_sparsity_enum; user_bool = user_atom->sparsity() == atomic_base::bool_sparsity_enum; user_set = user_atom->sparsity() == atomic_base::set_sparsity_enum; CPPAD_ASSERT_UNKNOWN( user_pack || user_bool || user_set ); if( user_pack ) { pack_r.resize( user_m * user_q ); pack_s.resize( user_n * user_q ); for(i = 0; i < user_m; i++) for(j = 0; j < user_q; j++) pack_r[ i * user_q + j] = false; } if( user_bool ) { bool_r.resize( user_m * user_q ); bool_s.resize( user_n * user_q ); for(i = 0; i < user_m; i++) for(j = 0; j < user_q; j++) bool_r[ i * user_q + j] = false; } if( user_set ) { set_r.resize(user_m); set_s.resize(user_n); for(i = 0; i < user_m; i++) set_r[i].clear(); } } else { // call users function for this operation user_atom->set_old(user_old); if( user_pack ) { user_ok = user_atom->rev_sparse_jac( user_q, pack_r, pack_s, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_jac( user_q, pack_r, pack_s ); } if( user_bool ) { user_ok = user_atom->rev_sparse_jac( user_q, bool_r, bool_s, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_jac( user_q, bool_r, bool_s ); } if( user_set ) { user_ok = user_atom->rev_sparse_jac( user_q, set_r, set_s, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_jac( user_q, set_r, set_s ); } if( ! user_ok ) { std::string msg = user_atom->afun_name() + ": atomic_base.rev_sparse_jac: returned false\n"; if( user_pack ) msg += "sparsity = pack_sparsity_enum"; if( user_bool ) msg += "sparsity = bool_sparsity_enum"; if( user_set ) msg += "sparsity = set_sparsity_enum"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } // // 2DO: It might be faster if we add set union to var_sparsity // where one of the sets is not in var_sparsity. for(j = 0; j < user_n; j++) if( user_ix[j] > 0 ) { if( user_pack ) { for(k = 0; k < user_q; k++) if( pack_s[ j * user_q + k ] ) var_sparsity.add_element(user_ix[j], k); } if( user_bool ) { for(k = 0; k < user_q; k++) if( bool_s[ j * user_q + k ] ) var_sparsity.add_element(user_ix[j], k); } if( user_set ) { set_itr = set_s[j].begin(); set_end = set_s[j].end(); while( set_itr != set_end ) var_sparsity.add_element(user_ix[j], *set_itr++); } } } break; case UsrapOp: // parameter argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); user_ix[user_j] = 0; // // parameters as integers user_x[user_j] = parameter[arg[0]]; // break; case UsravOp: // variable argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); user_ix[user_j] = arg[0]; // // variable as integers user_x[user_j] = CppAD::numeric_limits::quiet_NaN(); break; case UsrrpOp: // parameter result in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrvOp: // variable result in an atomic operation sequence play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); { typename Vector_set::const_iterator itr(var_sparsity, i_var); i = *itr; while( i < user_q ) { if( user_pack ) pack_r[ user_i * user_q + i ] = true; if( user_bool ) bool_r[ user_i * user_q + i ] = true; if( user_set ) set_r[user_i].insert(i); i = *(++itr); } } if( user_i == 0 ) user_state = arg_user; break; // ------------------------------------------------- case ZmulpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case ZmulvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case ZmulvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); reverse_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- default: CPPAD_ASSERT_UNKNOWN(0); } # if CPPAD_REV_JAC_SWEEP_TRACE for(j = 0; j < limit; j++) z_value[j] = false; typename Vector_set::const_iterator itr(var_sparsity, i_var); j = *itr; while( j < limit ) { z_value[j] = true; j = *(++itr); } printOp( std::cout, play, i_op, i_var, op, arg ); if( NumRes(op) > 0 && op != BeginOp ) printOpResult( std::cout, 0, (CppAD::vectorBool *) CPPAD_NULL, 1, &z_value ); std::cout << std::endl; } std::cout << std::endl; # else } # endif // values corresponding to BeginOp CPPAD_ASSERT_UNKNOWN( i_op == 0 ); CPPAD_ASSERT_UNKNOWN( i_var == 0 ); return; } } } // END_CPPAD_LOCAL_NAMESPACE // preprocessor symbols that are local to this file # undef CPPAD_REV_JAC_SWEEP_TRACE # undef CPPAD_ATOMIC_CALL # endif cppad-20170000.3/cppad/local/std_set.hpp0000644000175200017650000000274013057470466017000 0ustar coincoin-web// $Id: std_set.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_STD_SET_HPP # define CPPAD_LOCAL_STD_SET_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file std_set.hpp Two constant standard sets (currently used for concept checking). */ /*! A standard set with one element. */ template const std::set& one_element_std_set(void) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static std::set one; if( one.empty() ) one.insert(1); return one; } /*! A standard set with a two elements. */ template const std::set& two_element_std_set(void) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; static std::set two; if( two.empty() ) { two.insert(1); two.insert(2); } return two; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/hash_code.hpp0000644000175200017650000001530313057470466017247 0ustar coincoin-web// $Id: hash_code.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_HASH_CODE_HPP # define CPPAD_LOCAL_HASH_CODE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include /*! \file local/hash_code.hpp CppAD hashing utility. */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! General purpose hash code for an arbitrary value. \tparam Value is the type of the argument being hash coded. It should be a plain old data class; i.e., the values included in the equality operator in the object and not pointed to by the object. \param value the value that we are generating a hash code for. All of the fields in value should have been set before the hash code is computed (otherwise undefined values are used). \return is a hash code that is between zero and CPPAD_HASH_TABLE_SIZE - 1. \par Checked Assertions \li \c std::numeric_limits::max() >= CPPAD_HASH_TABLE_SIZE \li \c sizeof(value) is even \li \c sizeof(unsigned short) == 2 */ template unsigned short local_hash_code(const Value& value) { CPPAD_ASSERT_UNKNOWN( std::numeric_limits::max() >= CPPAD_HASH_TABLE_SIZE ); CPPAD_ASSERT_UNKNOWN( sizeof(unsigned short) == 2 ); CPPAD_ASSERT_UNKNOWN( sizeof(value) % 2 == 0 ); # const unsigned short* v = reinterpret_cast(& value); # size_t i = sizeof(value) / 2 - 1; # unsigned short code = v[i]; # while(i--) code += v[i]; return code % CPPAD_HASH_TABLE_SIZE; } /*! Specialized hash code for a CppAD operator and its arguments. \param op is the operator that we are computing a hash code for. If it is not one of the following operartors, the operator is not hash coded and zero is returned: \li unary operators: AbsOp, AcosOp, AcoshOp, AsinOp, AsinhOp, AtanOp, AtanhOp, CosOp, CoshOp ExpOp, Expm1Op, LogOp, Log1pOp, SinOp, SinhOp, SqrtOp, TanOp, TanhOp \li binary operators where first argument is a parameter: AddpvOp, DivpvOp, MulpvOp, PowpvOp, SubpvOp, ZmulpvOp \li binary operators where second argument is a parameter: DivvpOp, PowvpOp, SubvpOp, Zmulvp \li binary operators where first is an index and second is a variable: DisOp \li binary operators where both arguments are variables: AddvvOp, DivvvOp, MulvvOp, PowvvOp, SubvvOp, ZmulvvOp \param arg is a vector of length \c NumArg(op) or 2 (which ever is smaller), containing the corresponding argument indices for this operator. \param npar is the number of parameters corresponding to this operation sequence. \param par is a vector of length \a npar containing the parameters for this operation sequence; i.e., given a parameter index of \c i, the corresponding parameter value is \a par[i]. \return is a hash code that is between zero and CPPAD_HASH_TABLE_SIZE - 1. \par Checked Assertions \c op must be one of the operators specified above. In addition, \li \c std::numeric_limits::max() >= CPPAD_HASH_TABLE_SIZE \li \c sizeof(size_t) is even \li \c sizeof(Base) is even \li \c sizeof(unsigned short) == 2 \li \c size_t(op) < size_t(NumberOp) <= CPPAD_HASH_TABLE_SIZE \li if the j-th argument for this operation is a parameter, arg[j] < npar. */ template unsigned short local_hash_code( OpCode op , const addr_t* arg , size_t npar , const Base* par ) { CPPAD_ASSERT_UNKNOWN( std::numeric_limits::max() >= CPPAD_HASH_TABLE_SIZE ); CPPAD_ASSERT_UNKNOWN( size_t (op) < size_t(NumberOp) ); CPPAD_ASSERT_UNKNOWN( sizeof(unsigned short) == 2 ); CPPAD_ASSERT_UNKNOWN( sizeof(addr_t) % 2 == 0 ); CPPAD_ASSERT_UNKNOWN( sizeof(Base) % 2 == 0 ); unsigned short op_fac = static_cast ( CPPAD_HASH_TABLE_SIZE / static_cast(NumberOp) ); CPPAD_ASSERT_UNKNOWN( op_fac > 0 ); // number of shorts per addr_t value size_t short_addr_t = sizeof(addr_t) / 2; // number of shorts per Base value size_t short_base = sizeof(Base) / 2; // initialize with value that separates operators as much as possible unsigned short code = static_cast( static_cast(op) * op_fac ); // now code in the operands size_t i; const unsigned short* v; // first argument switch(op) { // Binary operators where first arugment is a parameter. // Code parameters by value instead of // by index for two reasons. One, it gives better separation. // Two, different indices can be same parameter value. case AddpvOp: case DivpvOp: case MulpvOp: case PowpvOp: case SubpvOp: case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 2 ); v = reinterpret_cast(par + arg[0]); i = short_base; while(i--) code += v[i]; v = reinterpret_cast(arg + 1); i = short_addr_t; while(i--) code += v[i]; break; // Binary operator where first argument is an index and // second is a variable (same as both variables). case DisOp: // Binary operators where both arguments are variables case AddvvOp: case DivvvOp: case MulvvOp: case PowvvOp: case SubvvOp: case ZmulvvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 2 ); v = reinterpret_cast(arg + 0); i = 2 * short_addr_t; while(i--) code += v[i]; break; // Binary operators where second arugment is a parameter. case DivvpOp: case PowvpOp: case SubvpOp: case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 2 ); v = reinterpret_cast(arg + 0); i = short_addr_t; while(i--) code += v[i]; v = reinterpret_cast(par + arg[1]); i = short_base; while(i--) code += v[i]; break; // Unary operators case AbsOp: case AcosOp: case AcoshOp: case AsinOp: case AsinhOp: case AtanOp: case AtanhOp: case CosOp: case CoshOp: case ErfOp: case ExpOp: case Expm1Op: case LogOp: case Log1pOp: case SignOp: case SinOp: case SinhOp: case SqrtOp: case TanOp: case TanhOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 || op == ErfOp ); v = reinterpret_cast(arg + 0); i = short_addr_t; while(i--) code += v[i]; break; // should have been one of he cases above default: CPPAD_ASSERT_UNKNOWN(false); } return code % CPPAD_HASH_TABLE_SIZE; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/sparse_unary_op.hpp0000644000175200017650000001525613057470466020552 0ustar coincoin-web// $Id: sparse_unary_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_SPARSE_UNARY_OP_HPP # define CPPAD_LOCAL_SPARSE_UNARY_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sparse_unary_op.hpp Forward and reverse mode sparsity patterns for unary operators. */ /*! Forward mode Jacobian sparsity pattern for all unary operators. The C++ source code corresponding to a unary operation has the form \verbatim z = fun(x) \endverbatim where fun is a C++ unary function, or it has the form \verbatim z = x op q \endverbatim where op is a C++ binary unary operator and q is a parameter. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e., z. \param i_x variable index corresponding to the argument for this operator; i.e., x. \param sparsity \b Input: The set with index \a arg[0] in \a sparsity is the sparsity bit pattern for x. This identifies which of the independent variables the variable x depends on. \n \n \b Output: The set with index \a i_z in \a sparsity is the sparsity bit pattern for z. This identifies which of the independent variables the variable z depends on. \n \par Checked Assertions: \li \a i_x < \a i_z */ template inline void forward_sparse_jacobian_unary_op( size_t i_z , size_t i_x , Vector_set& sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( i_x < i_z ); sparsity.assignment(i_z, i_x, sparsity); } /*! Reverse mode Jacobian sparsity pattern for all unary operators. The C++ source code corresponding to a unary operation has the form \verbatim z = fun(x) \endverbatim where fun is a C++ unary function, or it has the form \verbatim z = x op q \endverbatim where op is a C++ bianry operator and q is a parameter. This routine is given the sparsity patterns for a function G(z, y, ... ) and it uses them to compute the sparsity patterns for \verbatim H( x , w , u , ... ) = G[ z(x) , x , w , u , ... ] \endverbatim \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e. the row index in sparsity corresponding to z. \param i_x variable index corresponding to the argument for this operator; i.e. the row index in sparsity corresponding to x. \param sparsity \b Input: The set with index \a i_z in \a sparsity is the sparsity bit pattern for G with respect to the variable z. \n \b Input: The set with index \a i_x in \a sparsity is the sparsity bit pattern for G with respect to the variable x. \n \b Output: The set with index \a i_x in \a sparsity is the sparsity bit pattern for H with respect to the variable x. \par Checked Assertions: \li \a i_x < \a i_z */ template inline void reverse_sparse_jacobian_unary_op( size_t i_z , size_t i_x , Vector_set& sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( i_x < i_z ); sparsity.binary_union(i_x, i_x, i_z, sparsity); return; } // --------------------------------------------------------------------------- /*! Reverse mode Hessian sparsity pattern for linear unary operators. The C++ source code corresponding to this operation is \verbatim z = fun(x) \endverbatim where fun is a linear functions; e.g. abs, or \verbatim z = x op q \endverbatim where op is a C++ binary operator and q is a parameter. \copydetails reverse_sparse_hessian_unary_op */ template inline void reverse_sparse_hessian_linear_unary_op( size_t i_z , size_t i_x , bool* rev_jacobian , const Vector_set& for_jac_sparsity , Vector_set& rev_hes_sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( i_x < i_z ); rev_hes_sparsity.binary_union(i_x, i_x, i_z, rev_hes_sparsity); rev_jacobian[i_x] |= rev_jacobian[i_z]; return; } /*! Reverse mode Hessian sparsity pattern for non-linear unary operators. The C++ source code corresponding to this operation is \verbatim z = fun(x) \endverbatim where fun is a non-linear functions; e.g. sin. or \verbatim z = q / x \endverbatim where q is a parameter. \copydetails reverse_sparse_hessian_unary_op */ template inline void reverse_sparse_hessian_nonlinear_unary_op( size_t i_z , size_t i_x , bool* rev_jacobian , const Vector_set& for_jac_sparsity , Vector_set& rev_hes_sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( i_x < i_z ); rev_hes_sparsity.binary_union(i_x, i_x, i_z, rev_hes_sparsity); if( rev_jacobian[i_z] ) rev_hes_sparsity.binary_union(i_x, i_x, i_x, for_jac_sparsity); rev_jacobian[i_x] |= rev_jacobian[i_z]; return; } // --------------------------------------------------------------------------- /*! Forward mode Hessian sparsity pattern for non-linear unary operators. The C++ source code corresponding to this operation is \verbatim w(x) = fun( v(x) ) \endverbatim where fun is a non-linear function. \param i_v is the index of the argument variable v \param for_jac_sparsity for_jac_sparsity(i_v) constains the Jacobian sparsity for v(x). \param for_hes_sparsity On input, for_hes_sparsity includes the Hessian sparsity for v(x); i.e., the sparsity can be a super set. Upon return it includes the Hessian sparsity for w(x) */ template inline void forward_sparse_hessian_nonlinear_unary_op( size_t i_v , const Vector_set& for_jac_sparsity , Vector_set& for_hes_sparsity ) { // set of independent variables that v depends on typename Vector_set::const_iterator itr(for_jac_sparsity, i_v); // next independent variables that v depends on size_t i_x = *itr; // loop over dependent variables with non-zero partial while( i_x < for_jac_sparsity.end() ) { // N(i_x) = N(i_x) union L(i_v) for_hes_sparsity.binary_union(i_x, i_x, i_v, for_jac_sparsity); i_x = *(++itr); } return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/erf_op.hpp0000644000175200017650000003645713057470466016621 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_ERF_OP_HPP # define CPPAD_LOCAL_ERF_OP_HPP # if CPPAD_USE_CPLUSPLUS_2011 /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file erf_op.hpp Forward and reverse mode calculations for z = erf(x). */ /*! Forward mode Taylor coefficient for result of op = ErfOp. The C++ source code corresponding to this operation is \verbatim z = erf(x) \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param p lowest order of the Taylor coefficients that we are computing. \param q highest order of the Taylor coefficients that we are computing. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. The auxillary results are called y_j have index \a i_z - j. \param arg arg[0]: is the variable index corresponding to x. \n arg[1]: is the parameter index corresponding to the value zero. \n \arg[2]: is the parameter index correspodning to the value 2 / sqrt(pi). \param parameter parameter[ arg[1] ] is the value zero, and parameter[ arg[2] ] is the value 2 / sqrt(pi). \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: taylor [ arg[0] * cap_order + k ] for k = 0 , ... , q, is the k-th order Taylor coefficient corresponding to x. \n \b Input: taylor [ i_z * cap_order + k ] for k = 0 , ... , p - 1, is the k-th order Taylor coefficient corresponding to z. \n \b Input: taylor [ ( i_z - j) * cap_order + k ] for k = 0 , ... , p-1, and j = 0 , ... , 4, is the k-th order Taylor coefficient corresponding to the j-th result for z. \n \b Output: taylor [ (i_z-j) * cap_order + k ], for k = p , ... , q, and j = 0 , ... , 4, is the k-th order Taylor coefficient corresponding to the j-th result for z. \par Checked Assertions \li NumArg(op) == 3 \li NumRes(op) == 5 \li q < cap_order \li p <= q */ template inline void forward_erf_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ErfOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(ErfOp) == 5 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // array used to pass parameter values for sub-operations addr_t addr[2]; // convert from final result to first result i_z -= 4; // 4 = NumRes(ErfOp) - 1; // z_0 = x * x addr[0] = arg[0]; // x addr[1] = arg[0]; // x forward_mulvv_op(p, q, i_z+0, addr, parameter, cap_order, taylor); // z_1 = - x * x addr[0] = arg[1]; // zero addr[1] = i_z; // z_0 forward_subpv_op(p, q, i_z+1, addr, parameter, cap_order, taylor); // z_2 = exp( - x * x ) forward_exp_op(p, q, i_z+2, i_z+1, cap_order, taylor); // z_3 = (2 / sqrt(pi)) * exp( - x * x ) addr[0] = arg[2]; // 2 / sqrt(pi) addr[1] = i_z + 2; // z_2 forward_mulpv_op(p, q, i_z+3, addr, parameter, cap_order, taylor); // pointers to taylor coefficients for x , z_3, and z_4 Base* x = taylor + arg[0] * cap_order; Base* z_3 = taylor + (i_z+3) * cap_order; Base* z_4 = taylor + (i_z+4) * cap_order; // calculte z_4 coefficients if( p == 0 ) { // z4 (t) = erf[x(t)] z_4[0] = erf(x[0]); p++; } for(size_t j = p; j <= q; j++) { // z_4' (t) = erf'[x(t)] * x'(t) = z3(t) * x'(t) // z_4[1] + 2 * z_4[2] * t + ... = // (z_3[0] + z_3[1] * t + ...) * (x[1] + 2 * x[2] * t + ...) Base base_j = static_cast(j); z_4[j] = static_cast(0); for(size_t k = 1; k <= j; k++) z_4[j] += (Base(k) / base_j) * x[k] * z_3[j-k]; } } /*! Zero order Forward mode Taylor coefficient for result of op = ErfOp. The C++ source code corresponding to this operation is \verbatim z = erf(x) \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. The auxillary results are called y_j have index \a i_z - j. \param arg arg[0]: is the variable index corresponding to x. \n arg[1]: is the parameter index corresponding to the value zero. \n \arg[2]: is the parameter index correspodning to the value 2 / sqrt(pi). \param parameter parameter[ arg[1] ] is the value zero, and parameter[ arg[2] ] is the value 2 / sqrt(pi). \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: taylor [ arg[0] * cap_order + 0 ] is the zero order Taylor coefficient corresponding to x. \n \b Input: taylor [ i_z * cap_order + 0 ] is the zero order Taylor coefficient corresponding to z. \n \b Output: taylor [ (i_z-j) * cap_order + 0 ], for j = 0 , ... , 4, is the zero order Taylor coefficient for j-th result corresponding to z. \par Checked Assertions \li NumArg(op) == 3 \li NumRes(op) == 5 \li q < cap_order \li p <= q */ template inline void forward_erf_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ErfOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(ErfOp) == 5 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // array used to pass parameter values for sub-operations addr_t addr[2]; // convert from final result to first result i_z -= 4; // 4 = NumRes(ErfOp) - 1; // z_0 = x * x addr[0] = arg[0]; // x addr[1] = arg[0]; // x forward_mulvv_op_0(i_z+0, addr, parameter, cap_order, taylor); // z_1 = - x * x addr[0] = arg[1]; // zero addr[1] = i_z; // z_0 forward_subpv_op_0(i_z+1, addr, parameter, cap_order, taylor); // z_2 = exp( - x * x ) forward_exp_op_0(i_z+2, i_z+1, cap_order, taylor); // z_3 = (2 / sqrt(pi)) * exp( - x * x ) addr[0] = arg[2]; // 2 / sqrt(pi) addr[1] = i_z + 2; // z_2 forward_mulpv_op_0(i_z+3, addr, parameter, cap_order, taylor); // zero order Taylor coefficient for z_4 Base* x = taylor + arg[0] * cap_order; Base* z_4 = taylor + (i_z + 4) * cap_order; z_4[0] = erf(x[0]); } /*! Forward mode Taylor coefficient for result of op = ErfOp. The C++ source code corresponding to this operation is \verbatim z = erf(x) \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param q order of the Taylor coefficients that we are computing. \param r number of directions for the Taylor coefficients that we afre computing. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. The auxillary results have index i_z - j for j = 0 , ... , 4 (and include z). \param arg arg[0]: is the variable index corresponding to x. \n arg[1]: is the parameter index corresponding to the value zero. \n \arg[2]: is the parameter index correspodning to the value 2 / sqrt(pi). \param parameter parameter[ arg[1] ] is the value zero, and parameter[ arg[2] ] is the value 2 / sqrt(pi). \param cap_order maximum number of orders that will fit in the \c taylor array. \par tpv We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable \param taylor \b Input: If x is a variable, taylor [ arg[0] * tpv + 0 ], is the zero order Taylor coefficient for all directions and taylor [ arg[0] * tpv + (k-1)*r + ell + 1 ], for k = 1 , ... , q, ell = 0, ..., r-1, is the k-th order Taylor coefficient corresponding to x and the ell-th direction. \n \b Input: taylor [ (i_z - j) * tpv + 0 ] is the zero order Taylor coefficient for all directions and the j-th result for z. for k = 1 , ... , q-1, ell = 0, ... , r-1, taylor[ (i_z - j) * tpv + (k-1)*r + ell + 1] is the Taylor coefficient for the k-th order, ell-th direction, and j-th auzillary result. \n \b Output: taylor [ (i_z-j) * tpv + (q-1)*r + ell + 1 ], for ell = 0 , ... , r-1, is the Taylor coefficient for the q-th order, ell-th direction, and j-th auzillary result. \par Checked Assertions \li NumArg(op) == 3 \li NumRes(op) == 5 \li 0 < q < cap_order */ template inline void forward_erf_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ErfOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(ErfOp) == 5 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( 0 < q ); // array used to pass parameter values for sub-operations addr_t addr[2]; // convert from final result to first result i_z -= 4; // 4 = NumRes(ErfOp) - 1; // z_0 = x * x addr[0] = arg[0]; // x addr[1] = arg[0]; // x forward_mulvv_op_dir(q, r, i_z+0, addr, parameter, cap_order, taylor); // z_1 = - x * x addr[0] = arg[1]; // zero addr[1] = i_z; // z_0 forward_subpv_op_dir(q, r, i_z+1, addr, parameter, cap_order, taylor); // z_2 = exp( - x * x ) forward_exp_op_dir(q, r, i_z+2, i_z+1, cap_order, taylor); // z_3 = (2 / sqrt(pi)) * exp( - x * x ) addr[0] = arg[2]; // 2 / sqrt(pi) addr[1] = i_z + 2; // z_2 forward_mulpv_op_dir(q, r, i_z+3, addr, parameter, cap_order, taylor); // pointers to taylor coefficients for x , z_3, and z_4 size_t num_taylor_per_var = (cap_order - 1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var; Base* z_3 = taylor + (i_z+3) * num_taylor_per_var; Base* z_4 = taylor + (i_z+4) * num_taylor_per_var; // z_4' (t) = erf'[x(t)] * x'(t) = z3(t) * x'(t) // z_4[1] + 2 * z_4[2] * t + ... = // (z_3[0] + z_3[1] * t + ...) * (x[1] + 2 * x[2] * t + ...) Base base_q = static_cast(q); for(size_t ell = 0; ell < r; ell++) { // index in z_4 and x for q-th order term size_t m = (q-1)*r + ell + 1; // initialize q-th order term summation z_4[m] = z_3[0] * x[m]; for(size_t k = 1; k < q; k++) { size_t x_index = (k-1)*r + ell + 1; size_t z3_index = (q-k-1)*r + ell + 1; z_4[m] += (Base(k) / base_q) * x[x_index] * z_3[z3_index]; } } } /*! Compute reverse mode partial derivatives for result of op = ErfOp. The C++ source code corresponding to this operation is \verbatim z = erf(x) \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param d highest order Taylor of the Taylor coefficients that we are computing the partial derivatives with respect to. \param i_z variable index corresponding to the last (primary) result for this operation; i.e. the row index in \a taylor corresponding to z. The auxillary results are called y_j have index \a i_z - j. \param arg arg[0]: is the variable index corresponding to x. \n arg[1]: is the parameter index corresponding to the value zero. \n \arg[2]: is the parameter index correspodning to the value 2 / sqrt(pi). \param parameter parameter[ arg[1] ] is the value zero, and parameter[ arg[2] ] is the value 2 / sqrt(pi). \param cap_order maximum number of orders that will fit in the \c taylor array. \param taylor \b Input: taylor [ arg[0] * cap_order + k ] for k = 0 , ... , d, is the k-th order Taylor coefficient corresponding to x. \n taylor [ (i_z - j) * cap_order + k ] for k = 0 , ... , d, and for j = 0 , ... , 4, is the k-th order Taylor coefficient corresponding to the j-th result for this operation. \param nc_partial number of columns in the matrix containing all the partial derivatives \param partial \b Input: partial [ arg[0] * nc_partial + k ] for k = 0 , ... , d, is the partial derivative of G( z , x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Input: partial [ (i_z - j) * nc_partial + k ] for k = 0 , ... , d, and for j = 0 , ... , 4, is the partial derivative of G( z , x , w , u , ... ) with respect to the k-th order Taylor coefficient for the j-th result of this operation. \n \b Output: partial [ arg[0] * nc_partial + k ] for k = 0 , ... , d, is the partial derivative of H( x , w , u , ... ) with respect to the k-th order Taylor coefficient for x. \n \b Output: partial [ (i_z-j) * nc_partial + k ] for k = 0 , ... , d, and for j = 0 , ... , 4, may be used as work space; i.e., may change in an unspecified manner. \par Checked Assertions \li NumArg(op) == 3 \li NumRes(op) == 5 \li q < cap_order \li p <= q */ template inline void reverse_erf_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ErfOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(ErfOp) == 5 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); // array used to pass parameter values for sub-operations addr_t addr[2]; // If pz is zero, make sure this operation has no effect // (zero times infinity or nan would be non-zero). Base* pz = partial + i_z * nc_partial; bool skip(true); for(size_t i_d = 0; i_d <= d; i_d++) skip &= IdenticalZero(pz[i_d]); if( skip ) return; // convert from final result to first result i_z -= 4; // 4 = NumRes(ErfOp) - 1; // Taylor coefficients and partials corresponding to x const Base* x = taylor + arg[0] * cap_order; Base* px = partial + arg[0] * nc_partial; // Taylor coefficients and partials corresponding to z_3 const Base* z_3 = taylor + (i_z+3) * cap_order; Base* pz_3 = partial + (i_z+3) * nc_partial; // Taylor coefficients and partials corresponding to z_4 Base* pz_4 = partial + (i_z+4) * nc_partial; // Reverse z_4 size_t j = d; while(j) { pz_4[j] /= Base(j); for(size_t k = 1; k <= j; k++) { px[k] += azmul(pz_4[j], z_3[j-k]) * Base(k); pz_3[j-k] += azmul(pz_4[j], x[k]) * Base(k); } j--; } px[0] += azmul(pz_4[0], z_3[0]); // z_3 = (2 / sqrt(pi)) * exp( - x * x ) addr[0] = arg[2]; // 2 / sqrt(pi) addr[1] = i_z + 2; // z_2 reverse_mulpv_op( d, i_z+3, addr, parameter, cap_order, taylor, nc_partial, partial ); // z_2 = exp( - x * x ) reverse_exp_op( d, i_z+2, i_z+1, cap_order, taylor, nc_partial, partial ); // z_1 = - x * x addr[0] = arg[1]; // zero addr[1] = i_z; // z_0 reverse_subpv_op( d, i_z+1, addr, parameter, cap_order, taylor, nc_partial, partial ); // z_0 = x * x addr[0] = arg[0]; // x addr[1] = arg[0]; // x reverse_mulvv_op( d, i_z+0, addr, parameter, cap_order, taylor, nc_partial, partial ); } } } // END_CPPAD_LOCAL_NAMESPACE # endif // CPPAD_USE_CPLUSPLUS_2011 # endif // CPPAD_ERF_OP_INCLUDED cppad-20170000.3/cppad/local/reverse_sweep.hpp0000644000175200017650000005322313057470466020213 0ustar coincoin-web// $Id: reverse_sweep.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_REVERSE_SWEEP_HPP # define CPPAD_LOCAL_REVERSE_SWEEP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file reverse_sweep.hpp Compute derivatives of arbitrary order Taylor coefficients. */ /* \def CPPAD_ATOMIC_CALL This avoids warnings when NDEBUG is defined and user_ok is not used. If \c NDEBUG is defined, this resolves to \code user_atom->reverse \endcode otherwise, it respolves to \code user_ok = user_atom->reverse \endcode This maco is undefined at the end of this file to facillitate is use with a different definition in other files. */ # ifdef NDEBUG # define CPPAD_ATOMIC_CALL user_atom->reverse # else # define CPPAD_ATOMIC_CALL user_ok = user_atom->reverse # endif /*! \def CPPAD_REVERSE_SWEEP_TRACE This value is either zero or one. Zero is the normal operational value. If it is one, a trace of every reverse_sweep computation is printed. */ # define CPPAD_REVERSE_SWEEP_TRACE 0 /*! Compute derivative of arbitrary order forward mode Taylor coefficients. \tparam Base base type for the operator; i.e., this operation sequence was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param d is the highest order Taylor coefficients that we are computing the derivative of. \param n is the number of independent variables on the tape. \param numvar is the total number of variables on the tape. This is also equal to the number of rows in the matrix \a Taylor; i.e., play->num_var_rec(). \param play The information stored in \a play is a recording of the operations corresponding to the function \f[ F : {\bf R}^n \rightarrow {\bf R}^m \f] where \f$ n \f$ is the number of independent variables and \f$ m \f$ is the number of dependent variables. We define \f$ u^{(k)} \f$ as the value of x_k in the previous call of the form f.Forward(k, x_k) We define \f$ X : {\bf R}^{n \times d} \rightarrow {\bf R}^n \f$ by \f[ X(t, u) = u^{(0)} + u^{(1)} t + \cdots + u^{(d)} t^d \f] We define \f$ Y : {\bf R}^{n \times d} \rightarrow {\bf R}^m \f$ by \f[ Y(t, u) = F[ X(t, u) ] \f] We define the function \f$ W : {\bf R}^{n \times d} \rightarrow {\bf R} \f$ by \f[ W(u) = \sum_{k=0}^{d} ( w^{(k)} )^{\rm T} \frac{1}{k !} \frac{\partial^k}{\partial t^k} Y(0, u) \f] (The matrix \f$ w \in {\bf R}^m \f$, is defined below under the heading Partial.) Note that the scale factor 1 / k converts the k-th partial derivative to the k-th order Taylor coefficient. This routine computes the derivative of \f$ W(u) \f$ with respect to all the Taylor coefficients \f$ u^{(k)} \f$ for \f$ k = 0 , ... , d \f$. \n \n The object \a play is effectly constant. There is an exception to this, while palying back the tape the object \a play holds information about the current location with in the tape and this changes during palyback. \param J Is the number of columns in the coefficient matrix \a Taylor. This must be greater than or equal \a d + 1. \param Taylor For i = 1 , ... , \a numvar, and for k = 0 , ... , \a d, \a Taylor [ i * J + k ] is the k-th order Taylor coefficient corresponding to variable with index i on the tape. The value \f$ u \in {\bf R}^{n \times d} \f$, at which the derivative is computed, is defined by \f$ u_j^{(k)} \f$ = \a Taylor [ j * J + k ] for j = 1 , ... , \a n, and for k = 0 , ... , \a d. \param K Is the number of columns in the partial derivative matrix \a Partial. It must be greater than or equal \a d + 1. \param Partial \b Input: The last \f$ m \f$ rows of \a Partial are inputs. The matrix \f$ w \f$, used to define \f$ W(u) \f$, is specified by these rows. For i = 0 , ... , m - 1, for k = 0 , ... , d, Partial [ (numvar - m + i ) * K + k ] = w[i,k]. \n \n \b Temporary: For i = n+1 , ... , \a numvar - 1 and for k = 0 , ... , d, the value of \a Partial [ i * K + k ] is used for temporary work space and its output value is not defined. \n \n \b Output: For j = 1 , ... , n and for k = 0 , ... , d, \a Partial [ j * K + k ] is the partial derivative of \f$ W( u ) \f$ with respect to \f$ u_j^{(k)} \f$. \param cskip_op Is a vector with size play->num_op_rec(). If cskip_op[i] is true, the operator index i in the recording does not affect any of the dependent variable (given the value of the independent variables). Note that all the operators in an atomic function call are skipped as a block, so only the last UserOp fore each call needs to have cskip_op[i] true. \param var_by_load_op is a vector with size play->num_load_op_rec(). Is the variable index corresponding to each load instruction. In the case where the index is zero, the instruction corresponds to a parameter (not variable). \par Assumptions The first operator on the tape is a BeginOp, and the next \a n operators are InvOp operations for the corresponding independent variables. */ template void ReverseSweep( size_t d, size_t n, size_t numvar, local::player* play, size_t J, const Base* Taylor, size_t K, Base* Partial, bool* cskip_op, const pod_vector& var_by_load_op ) { OpCode op; size_t i_op; size_t i_var; const addr_t* arg = CPPAD_NULL; // check numvar argument CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar ); CPPAD_ASSERT_UNKNOWN( numvar > 0 ); // length of the parameter vector (used by CppAD assert macros) const size_t num_par = play->num_par_rec(); // pointer to the beginning of the parameter vector const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // work space used by UserOp. const size_t user_k = d; // highest order we are differentiating const size_t user_k1 = d+1; // number of orders for this calculation vector user_ix; // variable indices for argument vector vector user_tx; // argument vector Taylor coefficients vector user_ty; // result vector Taylor coefficients vector user_px; // partials w.r.t argument vector vector user_py; // partials w.r.t. result vector // atomic_base* user_atom = CPPAD_NULL; // user's atomic op calculator # ifndef NDEBUG bool user_ok = false; // atomic op return value # endif // // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state = end_user; // proper initialization // temporary indices size_t j, ell; // Initialize play->reverse_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == EndOp ); # if CPPAD_REVERSE_SWEEP_TRACE std::cout << std::endl; # endif bool more_operators = true; while(more_operators) { bool flag; // temporary for use in switch cases // // next op play->reverse_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN((i_op > n) | (op == InvOp) | (op == BeginOp)); CPPAD_ASSERT_UNKNOWN((i_op <= n) | (op != InvOp) | (op != BeginOp)); CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() ); // check if we are skipping this operation while( cskip_op[i_op] ) { switch(op) { case CSumOp: // CSumOp has a variable number of arguments play->reverse_csum(op, arg, i_op, i_var); break; case CSkipOp: // CSkip has a variable number of arguments play->reverse_cskip(op, arg, i_op, i_var); break; case UserOp: { // skip all operations in this user atomic call CPPAD_ASSERT_UNKNOWN( user_state == end_user ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); size_t n_skip = user_m + user_n + 1; for(size_t i = 0; i < n_skip; i++) { play->reverse_next(op, arg, i_op, i_var); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); } CPPAD_ASSERT_UNKNOWN( user_state == end_user ); } break; default: break; } play->reverse_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() ); } // rest of informaiton depends on the case # if CPPAD_REVERSE_SWEEP_TRACE if( op == CSumOp ) { // CSumOp has a variable number of arguments play->reverse_csum(op, arg, i_op, i_var); } if( op == CSkipOp ) { // CSkip has a variable number of arguments play->reverse_cskip(op, arg, i_op, i_var); } size_t i_tmp = i_var; const Base* Z_tmp = Taylor + i_var * J; const Base* pZ_tmp = Partial + i_var * K; printOp( std::cout, play, i_op, i_tmp, op, arg ); if( NumRes(op) > 0 && op != BeginOp ) printOpResult( std::cout, d + 1, Z_tmp, d + 1, pZ_tmp ); std::cout << std::endl; # endif switch( op ) { case AbsOp: reverse_abs_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- case AcosOp: // sqrt(1 - x * x), acos(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_acos_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AcoshOp: // sqrt(x * x - 1), acosh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_acosh_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; # endif // -------------------------------------------------- case AddvvOp: reverse_addvv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case AddpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); reverse_addpv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case AsinOp: // sqrt(1 - x * x), asin(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_asin_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AsinhOp: // sqrt(1 + x * x), asinh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_asinh_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; # endif // -------------------------------------------------- case AtanOp: // 1 + x * x, atan(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_atan_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AtanhOp: // 1 - x * x, atanh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_atanh_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; # endif // ------------------------------------------------- case BeginOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); more_operators = false; break; // -------------------------------------------------- case CSkipOp: // CSkipOp has a variable number of arguments and // forward_next thinks it one has one argument. // we must inform reverse_next of this special case. # if ! CPPAD_REVERSE_SWEEP_TRACE play->reverse_cskip(op, arg, i_op, i_var); # endif break; // ------------------------------------------------- case CSumOp: // CSumOp has a variable number of arguments and // reverse_next thinks it one has one argument. // We must inform reverse_next of this special case. # if ! CPPAD_REVERSE_SWEEP_TRACE play->reverse_csum(op, arg, i_op, i_var); # endif reverse_csum_op( d, i_var, arg, K, Partial ); // end of a cummulative summation break; // ------------------------------------------------- case CExpOp: reverse_cond_op( d, i_var, arg, num_par, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case CosOp: CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_cos_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- case CoshOp: CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_cosh_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- case DisOp: // Derivative of discrete operation is zero so no // contribution passes through this operation. break; // -------------------------------------------------- case DivvvOp: reverse_divvv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case DivpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); reverse_divpv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case DivvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); reverse_divvp_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case ErfOp: reverse_erf_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; # endif // -------------------------------------------------- case ExpOp: reverse_exp_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Expm1Op: reverse_expm1_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; # endif // -------------------------------------------------- case InvOp: break; // -------------------------------------------------- case LdpOp: reverse_load_op( op, d, i_var, arg, J, Taylor, K, Partial, var_by_load_op.data() ); break; // ------------------------------------------------- case LdvOp: reverse_load_op( op, d, i_var, arg, J, Taylor, K, Partial, var_by_load_op.data() ); break; // -------------------------------------------------- case EqpvOp: case EqvvOp: case LtpvOp: case LtvpOp: case LtvvOp: case LepvOp: case LevpOp: case LevvOp: case NepvOp: case NevvOp: break; // ------------------------------------------------- case LogOp: reverse_log_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Log1pOp: reverse_log1p_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; # endif // -------------------------------------------------- case MulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); reverse_mulpv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case MulvvOp: reverse_mulvv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case ParOp: break; // -------------------------------------------------- case PowvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); reverse_powvp_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // ------------------------------------------------- case PowpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); reverse_powpv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // ------------------------------------------------- case PowvvOp: reverse_powvv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case PriOp: // no result so nothing to do break; // -------------------------------------------------- case SignOp: CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_sign_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // ------------------------------------------------- case SinOp: CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_sin_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // ------------------------------------------------- case SinhOp: CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_sinh_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- case SqrtOp: reverse_sqrt_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- case StppOp: break; // -------------------------------------------------- case StpvOp: break; // ------------------------------------------------- case StvpOp: break; // ------------------------------------------------- case StvvOp: break; // -------------------------------------------------- case SubvvOp: reverse_subvv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case SubpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); reverse_subpv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case SubvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); reverse_subvp_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // ------------------------------------------------- case TanOp: CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_tan_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // ------------------------------------------------- case TanhOp: CPPAD_ASSERT_UNKNOWN( i_var < numvar ); reverse_tanh_op( d, i_var, arg[0], J, Taylor, K, Partial ); break; // -------------------------------------------------- case UserOp: // start or end an atomic operation sequence flag = user_state == end_user; user_atom = play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( flag ) { user_ix.resize(user_n); if(user_tx.size() != user_n * user_k1) { user_tx.resize(user_n * user_k1); user_px.resize(user_n * user_k1); } if(user_ty.size() != user_m * user_k1) { user_ty.resize(user_m * user_k1); user_py.resize(user_m * user_k1); } } else { // call users function for this operation user_atom->set_old(user_old); CPPAD_ATOMIC_CALL( user_k, user_tx, user_ty, user_px, user_py ); # ifndef NDEBUG if( ! user_ok ) { std::string msg = user_atom->afun_name() + ": atomic_base.reverse: returned false"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif for(j = 0; j < user_n; j++) if( user_ix[j] > 0 ) { for(ell = 0; ell < user_k1; ell++) Partial[user_ix[j] * K + ell] += user_px[j * user_k1 + ell]; } } break; case UsrapOp: // parameter argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); user_ix[user_j] = 0; user_tx[user_j * user_k1 + 0] = parameter[ arg[0]]; for(ell = 1; ell < user_k1; ell++) user_tx[user_j * user_k1 + ell] = Base(0.); break; case UsravOp: // variable argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); user_ix[user_j] = arg[0]; for(ell = 0; ell < user_k1; ell++) user_tx[user_j*user_k1 + ell] = Taylor[ arg[0] * J + ell]; break; case UsrrpOp: // parameter result in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); for(ell = 0; ell < user_k1; ell++) { user_py[user_i * user_k1 + ell] = Base(0.); user_ty[user_i * user_k1 + ell] = Base(0.); } user_ty[user_i * user_k1 + 0] = parameter[ arg[0] ]; break; case UsrrvOp: // variable result in an atomic operation sequence play->reverse_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); for(ell = 0; ell < user_k1; ell++) { user_py[user_i * user_k1 + ell] = Partial[i_var * K + ell]; user_ty[user_i * user_k1 + ell] = Taylor[i_var * J + ell]; } break; // ------------------------------------------------------------ case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); reverse_zmulpv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); reverse_zmulvp_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- case ZmulvvOp: reverse_zmulvv_op( d, i_var, arg, parameter, J, Taylor, K, Partial ); break; // -------------------------------------------------- default: CPPAD_ASSERT_UNKNOWN(false); } } # if CPPAD_REVERSE_SWEEP_TRACE std::cout << std::endl; # endif // values corresponding to BeginOp CPPAD_ASSERT_UNKNOWN( i_op == 0 ); CPPAD_ASSERT_UNKNOWN( i_var == 0 ); } } } // END_CPPAD_LOCAL_NAMESPACE // preprocessor symbols that are local to this file # undef CPPAD_REVERSE_SWEEP_TRACE # undef CPPAD_ATOMIC_CALL # endif cppad-20170000.3/cppad/local/parameter_op.hpp0000644000175200017650000000505213057470466020010 0ustar coincoin-web// $Id: parameter_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_PARAMETER_OP_HPP # define CPPAD_LOCAL_PARAMETER_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file parameter_op.hpp Zero order forward mode for ParOp */ /*! Compute zero order forward mode Taylor coefficient for result of op = ParOp. The C++ source code corresponding to this operation is one of the following \verbatim ADFun f(x, y) f.Dependent(x, y) \endverbatim where some of the components of the vector y are parameters. \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to the component of y that is a parameter. \param arg \a arg[0] \n index corresponding to the parameter value for this operator. \param num_par is the number of parameters in \a parameter. \param parameter \b Input: \a parameter[ \a arg[0] ] is the value of a component of y that is a parameter. \param cap_order number of colums in the matrix containing all the Taylor coefficients. \param taylor \b Output: \a taylor [ \a i_z * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to z. \par Checked Assertions where op is the unary operator with one result: \li NumArg(op) == 1 \li NumRes(op) == 1 \li \a size_t(arg[0]) < num_par \li \a 0 < \a cap_order */ template inline void forward_par_op_0( size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ParOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(ParOp) == 1 ); CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); Base* z = taylor + i_z * cap_order; z[0] = parameter[ arg[0] ]; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/acos_op.hpp0000644000175200017650000001531513057470466016760 0ustar coincoin-web// $Id: acos_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_ACOS_OP_HPP # define CPPAD_LOCAL_ACOS_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file acos_op.hpp Forward and reverse mode calculations for z = acos(x). */ /*! Compute forward mode Taylor coefficient for result of op = AcosOp. The C++ source code corresponding to this operation is \verbatim z = acos(x) \endverbatim The auxillary result is \verbatim y = sqrt(1 - x * x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_acos_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation size_t k; Base uj; if( p == 0 ) { z[0] = acos( x[0] ); uj = Base(1) - x[0] * x[0]; b[0] = sqrt( uj ); p++; } for(size_t j = p; j <= q; j++) { uj = Base(0); for(k = 0; k <= j; k++) uj -= x[k] * x[j-k]; b[j] = Base(0); z[j] = Base(0); for(k = 1; k < j; k++) { b[j] -= Base(k) * b[k] * b[j-k]; z[j] -= Base(k) * z[k] * b[j-k]; } b[j] /= Base(j); z[j] /= Base(j); // b[j] += uj / Base(2); z[j] -= x[j]; // b[j] /= b[0]; z[j] /= b[0]; } } /*! Multiple directions forward mode Taylor coefficient for op = AcosOp. The C++ source code corresponding to this operation is \verbatim z = acos(x) \endverbatim The auxillary result is \verbatim y = sqrt(1 - x * x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_acos_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; Base* b = z - num_taylor_per_var; // called y in documentation size_t k, ell; size_t m = (q-1) * r + 1; for(ell = 0; ell < r; ell ++) { Base uq = - 2.0 * x[m + ell] * x[0]; for(k = 1; k < q; k++) uq -= x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell]; b[m+ell] = Base(0); z[m+ell] = Base(0); for(k = 1; k < q; k++) { b[m+ell] += Base(k) * b[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; z[m+ell] += Base(k) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; } b[m+ell] = ( uq / Base(2) - b[m+ell] / Base(q) ) / b[0]; z[m+ell] = -( x[m+ell] + z[m+ell] / Base(q) ) / b[0]; } } /*! Compute zero order forward mode Taylor coefficient for result of op = AcosOp. The C++ source code corresponding to this operation is \verbatim z = acos(x) \endverbatim The auxillary result is \verbatim y = sqrt( 1 - x * x ) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_acos_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation z[0] = acos( x[0] ); b[0] = sqrt( Base(1) - x[0] * x[0] ); } /*! Compute reverse mode partial derivatives for result of op = AcosOp. The C++ source code corresponding to this operation is \verbatim z = acos(x) \endverbatim The auxillary result is \verbatim y = sqrt( 1 - x * x ) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_acos_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* b = z - cap_order; // called y in documentation Base* pb = pz - nc_partial; Base inv_b0 = Base(1) / b[0]; // number of indices to access size_t j = d; size_t k; while(j) { // scale partials w.r.t b[j] by 1 / b[0] pb[j] = azmul(pb[j], inv_b0); // scale partials w.r.t z[j] by 1 / b[0] pz[j] = azmul(pz[j], inv_b0); // update partials w.r.t b^0 pb[0] -= azmul(pz[j], z[j]) + azmul(pb[j], b[j]); // update partial w.r.t. x^0 px[0] -= azmul(pb[j], x[j]); // update partial w.r.t. x^j px[j] -= pz[j] + azmul(pb[j], x[0]); // further scale partial w.r.t. z[j] by 1 / j pz[j] /= Base(j); for(k = 1; k < j; k++) { // update partials w.r.t b^(j-k) pb[j-k] -= Base(k) * azmul(pz[j], z[k]) + azmul(pb[j], b[k]); // update partials w.r.t. x^k px[k] -= azmul(pb[j], x[j-k]); // update partials w.r.t. z^k pz[k] -= Base(k) * azmul(pz[j], b[j-k]); } --j; } // j == 0 case px[0] -= azmul( pz[0] + azmul(pb[0], x[0]), inv_b0); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/cppad_colpack.hpp0000644000175200017650000000676413057470466020130 0ustar coincoin-web// $Id: cppad_colpack.hpp 3845 2016-11-19 01:50:47Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # ifndef CPPAD_LOCAL_CPPAD_COLPACK_HPP # define CPPAD_LOCAL_CPPAD_COLPACK_HPP # if CPPAD_HAS_COLPACK namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file cppad_colpack.hpp External interface to Colpack routines used by cppad. */ // --------------------------------------------------------------------------- /*! Link from CppAD to ColPack used for general sparse matrices. This CppAD library routine is necessary because ColPack/ColPackHeaders.h has a using namespace std at the global level. \param m [in] is the number of rows in the sparse matrix \param n [in] is the nubmer of columns in the sparse matrix. \param adolc_pattern [in] This vector has size \c m, adolc_pattern[i][0] is the number of non-zeros in row \c i. For j = 1 , ... , adolc_sparsity[i], adolc_pattern[i][j] is the column index (base zero) for the non-zeros in row \c i. \param color [out] is a vector with size \c m. The input value of its elements does not matter. Upon return, it is a coloring for the rows of the sparse matrix. \n \n If for some \c i, color[i] == m, then adolc_pattern[i][0] == 0. Otherwise, color[i] < m. \n \n Suppose two differen rows, i != r have the same color. It follows that for all column indices \c j; it is not the case that both (i, j) and (r, j) appear in the sparsity pattern. \n \n This routine tries to minimize, with respect to the choice of colors, the number of colors. */ extern void cppad_colpack_general( CppAD::vector& color , size_t m , size_t n , const CppAD::vector& adolc_pattern ); /*! Link from CppAD to ColPack used for symmetric sparse matrices (not yet used or tested). This CppAD library routine is necessary because ColPack/ColPackHeaders.h has a using namespace std at the global level. \param n [in] is the nubmer of rows and columns in the symmetric sparse matrix. \param adolc_pattern [in] This vector has size \c n, adolc_pattern[i][0] is the number of non-zeros in row \c i. For j = 1 , ... , adolc_sparsity[i], adolc_pattern[i][j] is the column index (base zero) for the non-zeros in row \c i. \param color [out] The input value of its elements does not matter. Upon return, it is a coloring for the rows of the sparse matrix. The properties of this coloring have not yet been determined; see Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation (pdf/ad/gebemedhin14.pdf) */ extern void cppad_colpack_symmetric( CppAD::vector& color , size_t n , const CppAD::vector& adolc_pattern ); } } // END_CPPAD_LOCAL_NAMESPACE # endif # endif cppad-20170000.3/cppad/local/zmul_op.hpp0000644000175200017650000003310413057470466017016 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_ZMUL_OP_HPP # define CPPAD_LOCAL_ZMUL_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file mul_op.hpp Forward and reverse mode calculations for z = azmul(x, y). */ // --------------------------- Zmulvv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = ZmulvvOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op */ template inline void forward_zmulvv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; size_t k; for(size_t d = p; d <= q; d++) { z[d] = Base(0); for(k = 0; k <= d; k++) z[d] += azmul(x[d-k], y[k]); } } /*! Multiple directions forward mode Taylor coefficients for op = ZmulvvOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_dir */ template inline void forward_zmulvv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var; Base* y = taylor + arg[1] * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; size_t k, ell, m; for(ell = 0; ell < r; ell++) { m = (q-1)*r + ell + 1; z[m] = azmul(x[0], y[m]) + azmul(x[m], y[0]); for(k = 1; k < q; k++) z[m] += azmul(x[(q-k-1)*r + ell + 1], y[(k-1)*r + ell + 1]); } } /*! Compute zero order forward mode Taylor coefficients for result of op = ZmulvvOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_0 */ template inline void forward_zmulvv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulvvOp) == 1 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = azmul(x[0], y[0]); } /*! Compute reverse mode partial derivatives for result of op = ZmulvvOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails reverse_binary_op */ template inline void reverse_zmulvv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Arguments const Base* x = taylor + arg[0] * cap_order; const Base* y = taylor + arg[1] * cap_order; // Partial derivatives corresponding to arguments and result Base* px = partial + arg[0] * nc_partial; Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t j = d + 1; size_t k; while(j) { --j; for(k = 0; k <= j; k++) { px[j-k] += azmul(pz[j], y[k]); py[k] += azmul(pz[j], x[j-k]); } } } // --------------------------- Zmulpv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = ZmulpvOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op */ template inline void forward_zmulpv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; // Paraemter value Base x = parameter[ arg[0] ]; for(size_t d = p; d <= q; d++) z[d] = azmul(x, y[d]); } /*! Multiple directions forward mode Taylor coefficients for op = ZmulpvOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_dir */ template inline void forward_zmulpv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; size_t m = (q-1) * r + 1; Base* y = taylor + arg[1] * num_taylor_per_var + m; Base* z = taylor + i_z * num_taylor_per_var + m; // Paraemter value Base x = parameter[ arg[0] ]; for(size_t ell = 0; ell < r; ell++) z[ell] = azmul(x, y[ell]); } /*! Compute zero order forward mode Taylor coefficient for result of op = ZmulpvOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_0 */ template inline void forward_zmulpv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulpvOp) == 1 ); // Paraemter value Base x = parameter[ arg[0] ]; // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = azmul(x, y[0]); } /*! Compute reverse mode partial derivative for result of op = ZmulpvOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails reverse_binary_op */ template inline void reverse_zmulpv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Arguments Base x = parameter[ arg[0] ]; // Partial derivatives corresponding to arguments and result Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t j = d + 1; while(j) { --j; py[j] += azmul(pz[j], x); } } // --------------------------- Zmulvp ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = ZmulvpOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op */ template inline void forward_zmulvp_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* z = taylor + i_z * cap_order; // Paraemter value Base y = parameter[ arg[1] ]; for(size_t d = p; d <= q; d++) z[d] = azmul(x[d], y); } /*! Multiple directions forward mode Taylor coefficients for op = ZmulvpOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_dir */ template inline void forward_zmulvp_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; size_t m = (q-1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var + m; Base* z = taylor + i_z * num_taylor_per_var + m; // Paraemter value Base y = parameter[ arg[1] ]; for(size_t ell = 0; ell < r; ell++) z[ell] = azmul(x[ell], y); } /*! Compute zero order forward mode Taylor coefficient for result of op = ZmulvpOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_0 */ template inline void forward_zmulvp_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulvpOp) == 1 ); // Paraemter value Base y = parameter[ arg[1] ]; // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = azmul(x[0], y); } /*! Compute reverse mode partial derivative for result of op = ZmulvpOp. The C++ source code corresponding to this operation is \verbatim z = azmul(x, y) \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails reverse_binary_op */ template inline void reverse_zmulvp_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ZmulvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(ZmulvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Arguments Base y = parameter[ arg[1] ]; // Partial derivatives corresponding to arguments and result Base* px = partial + arg[0] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t j = d + 1; while(j) { --j; px[j] += azmul(pz[j], y); } } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/expm1_op.hpp0000644000175200017650000001154713057470466017070 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_EXPM1_OP_HPP # define CPPAD_LOCAL_EXPM1_OP_HPP # if CPPAD_USE_CPLUSPLUS_2011 /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file expm1_op.hpp Forward and reverse mode calculations for z = expm1(x). */ /*! Forward mode Taylor coefficient for result of op = Expm1Op. The C++ source code corresponding to this operation is \verbatim z = expm1(x) \endverbatim \copydetails forward_unary1_op */ template inline void forward_expm1_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; size_t k; if( p == 0 ) { z[0] = expm1( x[0] ); p++; } for(size_t j = p; j <= q; j++) { z[j] = x[1] * z[j-1]; for(k = 2; k <= j; k++) z[j] += Base(k) * x[k] * z[j-k]; z[j] /= Base(j); z[j] += x[j]; } } /*! Multiple direction forward mode Taylor coefficient for op = Expm1Op. The C++ source code corresponding to this operation is \verbatim z = expm1(x) \endverbatim \copydetails forward_unary1_op_dir */ template inline void forward_expm1_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( 0 < q ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; size_t m = (q-1)*r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = Base(q) * x[m+ell] * z[0]; for(size_t k = 1; k < q; k++) z[m+ell] += Base(k) * x[(k-1)*r+ell+1] * z[(q-k-1)*r+ell+1]; z[m+ell] /= Base(q); z[m+ell] += x[m+ell]; } } /*! Zero order forward mode Taylor coefficient for result of op = Expm1Op. The C++ source code corresponding to this operation is \verbatim z = expm1(x) \endverbatim \copydetails forward_unary1_op_0 */ template inline void forward_expm1_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; z[0] = expm1( x[0] ); } /*! Reverse mode partial derivatives for result of op = Expm1Op. The C++ source code corresponding to this operation is \verbatim z = expm1(x) \endverbatim \copydetails reverse_unary1_op */ template inline void reverse_expm1_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; // If pz is zero, make sure this operation has no effect // (zero times infinity or nan would be non-zero). bool skip(true); for(size_t i_d = 0; i_d <= d; i_d++) skip &= IdenticalZero(pz[i_d]); if( skip ) return; // loop through orders in reverse size_t j, k; j = d; while(j) { px[j] += pz[j]; // scale partial w.r.t z[j] pz[j] /= Base(j); for(k = 1; k <= j; k++) { px[k] += Base(k) * azmul(pz[j], z[j-k]); pz[j-k] += Base(k) * azmul(pz[j], x[k]); } --j; } px[0] += pz[0] + azmul(pz[0], z[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif # endif cppad-20170000.3/cppad/local/forward2sweep.hpp0000644000175200017650000005361213057470466020131 0ustar coincoin-web// $Id: forward2sweep.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_FORWARD2SWEEP_HPP # define CPPAD_LOCAL_FORWARD2SWEEP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file forward2sweep.hpp Compute one Taylor coefficient for each direction requested. */ /* \def CPPAD_ATOMIC_CALL This avoids warnings when NDEBUG is defined and user_ok is not used. If NDEBUG is defined, this resolves to \code user_atom->forward \endcode otherwise, it respolves to \code user_ok = user_atom->forward \endcode This macro is undefined at the end of this file to facillitate its use with a different definition in other files. */ # ifdef NDEBUG # define CPPAD_ATOMIC_CALL user_atom->forward # else # define CPPAD_ATOMIC_CALL user_ok = user_atom->forward # endif /*! \def CPPAD_FORWARD2SWEEP_TRACE This value is either zero or one. Zero is the normal operational value. If it is one, a trace of every forward2sweep computation is printed. */ # define CPPAD_FORWARD2SWEEP_TRACE 0 /*! Compute multiple directions forward mode Taylor coefficients. \tparam Base The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD. \param q is the order of the Taylor coefficients that are computed during this call; q > 0. \param r is the number of Taylor coefficients that are computed during this call. \param n is the number of independent variables on the tape. \param numvar is the total number of variables on the tape. This is also equal to the number of rows in the matrix taylor; i.e., play->num_var_rec(). \param play The information stored in play is a recording of the operations corresponding to the function \f[ F : {\bf R}^n \rightarrow {\bf R}^m \f] where \f$ n \f$ is the number of independent variables and \f$ m \f$ is the number of dependent variables. \n \n The object play is effectly constant. The exception to this is that while palying back the tape the object play holds information about the current location with in the tape and this changes during palyback. \param J Is the number of columns in the coefficient matrix taylor. This must be greater than or equal one. \param taylor \n \b Input: For i = 1 , ... , numvar-1, taylor[ (J-1)*r*i + i + 0 ] is the zero order Taylor coefficient corresponding to the i-th variable and all directions. For i = 1 , ... , numvar-1, For k = 1 , ... , q-1, ell = 0 , ... , r-1, taylor[ (J-1)*r*i + i + (k-1)*r + ell + 1 ] is the k-th order Taylor coefficient corresponding to the i-th variabel and ell-th direction. \n \n \b Input: For i = 1 , ... , n, ell = 0 , ... , r-1, taylor[ (J-1)*r*i + i + (q-1)*r + ell + 1 ] is the q-th order Taylor coefficient corresponding to the i-th variable and ell-th direction (these are the independent varaibles). \n \n \b Output: For i = n+1 , ... , numvar-1, ell = 0 , ... , r-1, taylor[ (J-1)*r*i + i + (q-1)*r + ell + 1 ] is the q-th order Taylor coefficient corresponding to the i-th variable and ell-th direction. \param cskip_op Is a vector with size play->num_op_rec(). If cskip_op[i] is true, the operator with index i does not affect any of the dependent variable (given the value of the independent variables). \param var_by_load_op is a vector with size play->num_load_op_rec(). It is the variable index corresponding to each the load instruction. In the case where the index is zero, the instruction corresponds to a parameter (not variable). */ template void forward2sweep( const size_t q, const size_t r, const size_t n, const size_t numvar, local::player* play, const size_t J, Base* taylor, const bool* cskip_op, const pod_vector& var_by_load_op ) { CPPAD_ASSERT_UNKNOWN( q > 0 ); CPPAD_ASSERT_UNKNOWN( J >= q + 1 ); CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar ); // used to avoid compiler errors until all operators are implemented size_t p = q; // op code for current instruction OpCode op; // index for current instruction size_t i_op; // next variables size_t i_var; // operation argument indices const addr_t* arg = CPPAD_NULL; // work space used by UserOp. vector user_vx; // empty vecotor vector user_vy; // empty vecotor vector user_tx_one; // argument vector Taylor coefficients vector user_tx_all; vector user_ty_one; // result vector Taylor coefficients vector user_ty_all; // // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state = start_user; // proper initialization // atomic_base* user_atom = CPPAD_NULL; // user's atomic op calculator # ifndef NDEBUG bool user_ok = false; // atomic op return value # endif // length of the parameter vector (used by CppAD assert macros) const size_t num_par = play->num_par_rec(); // pointer to the beginning of the parameter vector const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // temporary indices size_t i, j, k, ell; // number of orders for this user calculation // (not needed for order zero) const size_t user_q1 = q+1; // variable indices for results vector // (done differently for order zero). vector user_iy; // skip the BeginOp at the beginning of the recording play->forward_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == BeginOp ); # if CPPAD_FORWARD2SWEEP_TRACE bool user_trace = false; std::cout << std::endl; CppAD::vector Z_vec(q+1); # endif bool flag; // a temporary flag to use in switch cases bool more_operators = true; while(more_operators) { // this op play->forward_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( (i_op > n) | (op == InvOp) ); CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) ); CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() ); CPPAD_ASSERT_ARG_BEFORE_RESULT(op, arg, i_var); // check if we are skipping this operation while( cskip_op[i_op] ) { switch(op) { case CSumOp: // CSumOp has a variable number of arguments play->forward_csum(op, arg, i_op, i_var); break; case CSkipOp: // CSkip has a variable number of arguments play->forward_cskip(op, arg, i_op, i_var); break; case UserOp: { // skip all operations in this user atomic call CPPAD_ASSERT_UNKNOWN( user_state == start_user ); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); size_t n_skip = user_m + user_n + 1; for(i = 0; i < n_skip; i++) { play->forward_next(op, arg, i_op, i_var); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); } CPPAD_ASSERT_UNKNOWN( user_state == start_user ); } break; default: break; } play->forward_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() ); } // action depends on the operator switch( op ) { case AbsOp: forward_abs_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case AddvvOp: forward_addvv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case AddpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_addpv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case AcosOp: // sqrt(1 - x * x), acos(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_acos_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AcoshOp: // sqrt(x * x - 1), acosh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_acosh_op_dir(q, r, i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case AsinOp: // sqrt(1 - x * x), asin(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_asin_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AsinhOp: // sqrt(1 + x * x), asinh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_asinh_op_dir(q, r, i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case AtanOp: // 1 + x * x, atan(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_atan_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AtanhOp: // 1 - x * x, atanh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_atanh_op_dir(q, r, i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case CExpOp: forward_cond_op_dir( q, r, i_var, arg, num_par, parameter, J, taylor ); break; // --------------------------------------------------- case CosOp: // sin(x), cos(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_cos_op_dir(q, r, i_var, arg[0], J, taylor); break; // --------------------------------------------------- case CoshOp: // sinh(x), cosh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_cosh_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case CSkipOp: // CSkipOp has a variable number of arguments and // forward_next thinks it has no arguments. // we must inform forward_next of this special case. play->forward_cskip(op, arg, i_op, i_var); break; // ------------------------------------------------- case CSumOp: // CSumOp has a variable number of arguments and // forward_next thinks it has no arguments. // we must inform forward_next of this special case. forward_csum_op_dir( q, r, i_var, arg, num_par, parameter, J, taylor ); play->forward_csum(op, arg, i_op, i_var); break; // ------------------------------------------------- case DisOp: forward_dis_op(p, q, r, i_var, arg, J, taylor); break; // ------------------------------------------------- case DivvvOp: forward_divvv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case DivpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_divpv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case DivvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_divvp_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case EndOp: // needed for sparse_jacobian test CPPAD_ASSERT_NARG_NRES(op, 0, 0); more_operators = false; break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case ErfOp: forward_erf_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- # endif case ExpOp: forward_exp_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Expm1Op: forward_expm1_op_dir(q, r, i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case InvOp: CPPAD_ASSERT_NARG_NRES(op, 0, 1); break; // ------------------------------------------------- case LdpOp: case LdvOp: forward_load_op( play, op, p, q, r, J, i_var, arg, var_by_load_op.data(), taylor ); break; // --------------------------------------------------- case EqpvOp: case EqvvOp: case LtpvOp: case LtvpOp: case LtvvOp: case LepvOp: case LevpOp: case LevvOp: case NepvOp: case NevvOp: CPPAD_ASSERT_UNKNOWN(q > 0 ); break; // ------------------------------------------------- case LogOp: forward_log_op_dir(q, r, i_var, arg[0], J, taylor); break; // --------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Log1pOp: forward_log1p_op_dir(q, r, i_var, arg[0], J, taylor); break; # endif // --------------------------------------------------- case MulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_mulpv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case MulvvOp: forward_mulvv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case ParOp: k = i_var*(J-1)*r + i_var + (q-1)*r + 1; for(ell = 0; ell < r; ell++) taylor[k + ell] = Base(0); break; // ------------------------------------------------- case PowpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_powpv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PowvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_powvp_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PowvvOp: forward_powvv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PriOp: CPPAD_ASSERT_UNKNOWN(q > 0); break; // ------------------------------------------------- case SignOp: // sign(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sign_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SinOp: // cos(x), sin(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sin_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SinhOp: // cosh(x), sinh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sinh_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SqrtOp: forward_sqrt_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case StppOp: case StpvOp: case StvpOp: case StvvOp: CPPAD_ASSERT_UNKNOWN(q > 0 ); break; // ------------------------------------------------- case SubvvOp: forward_subvv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case SubpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_subpv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case SubvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_subvp_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case TanOp: // tan(x)^2, tan(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_tan_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case TanhOp: // tanh(x)^2, tanh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_tanh_op_dir(q, r, i_var, arg[0], J, taylor); break; // ------------------------------------------------- case UserOp: // start or end an atomic operation sequence flag = user_state == start_user; user_atom = play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( flag ) { user_tx_one.resize(user_n * user_q1); user_tx_all.resize(user_n * (q * r + 1)); // user_ty_one.resize(user_m * user_q1); user_ty_all.resize(user_m * (q * r + 1)); // user_iy.resize(user_m); } else { // call users function for this operation user_atom->set_old(user_old); for(ell = 0; ell < r; ell++) { // set user_tx for(j = 0; j < user_n; j++) { size_t j_all = j * (q * r + 1); size_t j_one = j * user_q1; user_tx_one[j_one+0] = user_tx_all[j_all+0]; for(k = 1; k < user_q1; k++) { size_t k_all = j_all + (k-1)*r+1+ell; size_t k_one = j_one + k; user_tx_one[k_one] = user_tx_all[k_all]; } } // set user_ty for(i = 0; i < user_m; i++) { size_t i_all = i * (q * r + 1); size_t i_one = i * user_q1; user_ty_one[i_one+0] = user_ty_all[i_all+0]; for(k = 1; k < q; k++) { size_t k_all = i_all + (k-1)*r+1+ell; size_t k_one = i_one + k; user_ty_one[k_one] = user_ty_all[k_all]; } } CPPAD_ATOMIC_CALL( q, q, user_vx, user_vy, user_tx_one, user_ty_one ); # ifndef NDEBUG if( ! user_ok ) { std::string msg = user_atom->afun_name() + ": atomic_base.forward: returned false"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif for(i = 0; i < user_m; i++) { if( user_iy[i] > 0 ) { size_t i_taylor = user_iy[i]*((J-1)*r+1); size_t q_taylor = i_taylor + (q-1)*r+1+ell; size_t q_one = i * user_q1 + q; taylor[q_taylor] = user_ty_one[q_one]; } } } # if CPPAD_FORWARD2SWEEP_TRACE user_trace = true; # endif } break; case UsrapOp: // parameter argument in an atomic operation sequence user_tx_all[user_j*(q*r+1) + 0] = parameter[ arg[0]]; for(ell = 0; ell < r; ell++) for(k = 1; k < user_q1; k++) user_tx_all[user_j*(q*r+1) + (k-1)*r+1+ell] = Base(0); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsravOp: // variable argument in an atomic operation sequence user_tx_all[user_j*(q*r+1)+0] = taylor[arg[0]*((J-1)*r+1)+0]; for(ell = 0; ell < r; ell++) { for(k = 1; k < user_q1; k++) { user_tx_all[user_j*(q*r+1) + (k-1)*r+1+ell] = taylor[arg[0]*((J-1)*r+1) + (k-1)*r+1+ell]; } } play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrpOp: // parameter result in an atomic operation sequence user_iy[user_i] = 0; user_ty_all[user_i*(q*r+1) + 0] = parameter[ arg[0]]; for(ell = 0; ell < r; ell++) for(k = 1; k < user_q1; k++) user_ty_all[user_i*(q*r+1) + (k-1)*r+1+ell] = Base(0); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrvOp: // variable result in an atomic operation sequence user_iy[user_i] = i_var; user_ty_all[user_i*(q*r+1)+0] = taylor[i_var*((J-1)*r+1)+0]; for(ell = 0; ell < r; ell++) { for(k = 1; k < user_q1; k++) { user_ty_all[user_i*(q*r+1) + (k-1)*r+1+ell] = taylor[i_var*((J-1)*r+1) + (k-1)*r+1+ell]; } } play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; // ------------------------------------------------- case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_zmulpv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_zmulvp_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case ZmulvvOp: forward_zmulvv_op_dir(q, r, i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- default: CPPAD_ASSERT_UNKNOWN(0); } # if CPPAD_FORWARD2SWEEP_TRACE if( user_trace ) { user_trace = false; CPPAD_ASSERT_UNKNOWN( op == UserOp ); CPPAD_ASSERT_UNKNOWN( NumArg(UsrrvOp) == 0 ); for(i = 0; i < user_m; i++) if( user_iy[i] > 0 ) { size_t i_tmp = (i_op + i) - user_m; printOp( std::cout, play, i_tmp, user_iy[i], UsrrvOp, CPPAD_NULL ); Base* Z_tmp = taylor + user_iy[i]*((J-1) * r + 1); { Z_vec[0] = Z_tmp[0]; for(ell = 0; ell < r; ell++) { std::cout << std::endl << " "; for(size_t p_tmp = 1; p_tmp <= q; p_tmp++) Z_vec[p_tmp] = Z_tmp[(p_tmp-1)*r+ell+1]; printOpResult( std::cout, q + 1, Z_vec.data(), 0, (Base *) CPPAD_NULL ); } } std::cout << std::endl; } } const addr_t* arg_tmp = arg; if( op == CSumOp ) arg_tmp = arg - arg[-1] - 4; if( op == CSkipOp ) arg_tmp = arg - arg[-1] - 7; if( op != UsrrvOp ) { printOp( std::cout, play, i_op, i_var, op, arg_tmp ); Base* Z_tmp = CPPAD_NULL; if( op == UsravOp ) Z_tmp = taylor + arg[0]*((J-1) * r + 1); else if( NumRes(op) > 0 ) Z_tmp = taylor + i_var*((J-1)*r + 1); if( Z_tmp != CPPAD_NULL ) { Z_vec[0] = Z_tmp[0]; for(ell = 0; ell < r; ell++) { std::cout << std::endl << " "; for(size_t p_tmp = 1; p_tmp <= q; p_tmp++) Z_vec[p_tmp] = Z_tmp[ (p_tmp-1)*r + ell + 1]; printOpResult( std::cout, q + 1, Z_vec.data(), 0, (Base *) CPPAD_NULL ); } } std::cout << std::endl; } } std::cout << std::endl; # else } # endif CPPAD_ASSERT_UNKNOWN( user_state == start_user ); CPPAD_ASSERT_UNKNOWN( i_var + 1 == play->num_var_rec() ); return; } // preprocessor symbols that are local to this file # undef CPPAD_FORWARD2SWEEP_TRACE # undef CPPAD_ATOMIC_CALL } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/ad_tape.hpp0000644000175200017650000001524313057470466016732 0ustar coincoin-web# ifndef CPPAD_LOCAL_AD_TAPE_HPP # define CPPAD_LOCAL_AD_TAPE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL__NAMESPACE /*! Class used to hold tape that records AD operations. \tparam Base An AD object is used to recording AD operations. */ template class ADTape { // Friends ============================================================= // classes ------------------------------------------------------------- friend class AD; friend class ADFun; friend class atomic_base; friend class discrete; friend class VecAD; friend class VecAD_reference; // functions ----------------------------------------------------------- // PrintFor friend void CppAD::PrintFor ( const AD& flag , const char* before , const AD& var , const char* after ); // CondExpOp friend AD CppAD::CondExpOp ( enum CompareOp cop , const AD &left , const AD &right , const AD &trueCase , const AD &falseCase ); // pow friend AD CppAD::pow (const AD &x, const AD &y); // azmul friend AD CppAD::azmul (const AD &x, const AD &y); // Parameter friend bool CppAD::Parameter (const AD &u); // Variable friend bool CppAD::Variable (const AD &u); // operators ----------------------------------------------------------- // arithematic binary operators friend AD CppAD::operator + (const AD &left, const AD &right); friend AD CppAD::operator - (const AD &left, const AD &right); friend AD CppAD::operator * (const AD &left, const AD &right); friend AD CppAD::operator / (const AD &left, const AD &right); // comparison operators friend bool CppAD::operator < (const AD &left, const AD &right); friend bool CppAD::operator <= (const AD &left, const AD &right); friend bool CppAD::operator > (const AD &left, const AD &right); friend bool CppAD::operator >= (const AD &left, const AD &right); friend bool CppAD::operator == (const AD &left, const AD &right); friend bool CppAD::operator != (const AD &left, const AD &right); // ====================================================================== // -------------------------------------------------------------------------- private: // ---------------------------------------------------------------------- // private data /*! Unique identifier for this tape. It is always greater than CPPAD_MAX_NUM_THREADS, and different for every tape (even ones that have been deleted). In addition, id_ % CPPAD_MAX_NUM_THREADS is the thread number for this tape. Set by Independent and effectively const */ tape_id_t id_; /// Number of independent variables in this tapes reconding. /// Set by Independent and effectively const size_t size_independent_; /// This is where the information is recorded. local::recorder Rec_; // ---------------------------------------------------------------------- // private functions // // add a parameter to the tape size_t RecordParOp(const Base &x); // see CondExp.h void RecordCondExp( enum CompareOp cop , AD &returnValue , const AD &left , const AD &right , const AD &trueCase , const AD &falseCase ); // place a VecAD object in the tape size_t AddVec( size_t length, const pod_vector& data ); public: // default constructor and destructor // public function only used by CppAD::Independent template void Independent(VectorADBase &u); template void Independent(VectorADBase &u, size_t abort_op_index); }; // --------------------------------------------------------------------------- // Private functions // /*! Place a parameter in the tape. On rare occations it is necessary to place a parameter in the tape; e.g., when it is one of the dependent variabes. \param z value of the parameter that we are placing in the tape. \return variable index (for this recording) correpsonding to the parameter. \par 2DO All these operates are preformed in \c Rec_, so we should move this routine from ADTape to recorder. */ template size_t ADTape::RecordParOp(const Base &z) { size_t z_taddr; size_t ind; CPPAD_ASSERT_UNKNOWN( NumRes(ParOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumArg(ParOp) == 1 ); z_taddr = Rec_.PutOp(ParOp); ind = Rec_.PutPar(z); Rec_.PutArg(ind); return z_taddr; } /*! Put initialization for a VecAD object in the tape. This routine should be called once for each VecAD object when just before it changes from a parameter to a variable. \param length size of the VecAD object. \param data initial values for the VecAD object (values before it becomes a variable). \return index of the start of this vector in the list of vector indices. The value for this vector index is the length of the vector. There are \c length indices following for this vector. The values for these vector indices are the corresponding parameter indices in the tape for the initial value of the corresponding vec_ad element. \par 2DO All these operates are preformed in \c Rec_, so we should move this routine from ADTape to recorder. */ template size_t ADTape::AddVec(size_t length, const pod_vector& data) { CPPAD_ASSERT_UNKNOWN( length > 0 ); size_t i; size_t value_index; // store the length in VecInd size_t start = Rec_.PutVecInd(length); // store indices of the values in VecInd for(i = 0; i < length; i++) { value_index = Rec_.PutPar( data[i] ); Rec_.PutVecInd( value_index ); } // return the taddr of the length (where the vector starts) return start; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/recorder.hpp0000644000175200017650000004142413057470466017142 0ustar coincoin-web// $Id: recorder.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_RECORDER_HPP # define CPPAD_LOCAL_RECORDER_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file recorder.hpp File used to define the recorder class. */ /*! Class used to store an operation sequence while it is being recorded (the operation sequence is copied to the player class for playback). \tparam Base This is an AD< \a Base > operation sequence recording; i.e., it records operations of type AD< \a Base >. */ template class recorder { friend class player; private: /// operator index at which to abort recording with an error /// (do not abort when zero) size_t abort_op_index_; /// offset for this thread in the static hash table const size_t thread_offset_; /// Number of variables in the recording. size_t num_var_rec_; /// Number vecad load operations (LdpOp or LdvOp) currently in recording. size_t num_load_op_rec_; /// The operators in the recording. pod_vector op_rec_; /// The VecAD indices in the recording. pod_vector vecad_ind_rec_; /// The argument indices in the recording pod_vector op_arg_rec_; /// The parameters in the recording. /// Note that Base may not be plain old data, so use false in consructor. pod_vector par_rec_; /// Character strings ('\\0' terminated) in the recording. pod_vector text_rec_; // ---------------------- Public Functions ----------------------------------- public: /// Default constructor recorder(void) : thread_offset_( thread_alloc::thread_num() * CPPAD_HASH_TABLE_SIZE ) , num_var_rec_(0) , num_load_op_rec_(0) , op_rec_( std::numeric_limits::max() ) , vecad_ind_rec_( std::numeric_limits::max() ) , op_arg_rec_( std::numeric_limits::max() ) , par_rec_( std::numeric_limits::max() ) , text_rec_( std::numeric_limits::max() ) { abort_op_index_ = 0; } /// Set the abort index void set_abort_op_index(size_t abort_op_index) { abort_op_index_ = abort_op_index; } /// Get the abort index size_t get_abort_op_index(void) { return abort_op_index_; } /// Destructor ~recorder(void) { } /*! Frees all information in recording. Frees the operation sequence store in this recording (the operation sequence is empty after this operation). The buffers used to store the current recording are returned to the system (so as to conserve on memory). */ void free(void) { num_var_rec_ = 0; num_load_op_rec_ = 0; op_rec_.free(); vecad_ind_rec_.free(); op_arg_rec_.free(); par_rec_.free(); text_rec_.free(); } /// Put next operator in the operation sequence. inline size_t PutOp(OpCode op); /// Put a vecad load operator in the operation sequence (special case) inline size_t PutLoadOp(OpCode op); /// Add a value to the end of the current vector of VecAD indices. inline size_t PutVecInd(size_t vec_ind); /// Find or add a parameter to the current vector of parameters. inline size_t PutPar(const Base &par); /// Put one operation argument index in the recording inline void PutArg(addr_t arg0); /// Put two operation argument index in the recording inline void PutArg(addr_t arg0, addr_t arg1); /// Put three operation argument index in the recording inline void PutArg(addr_t arg0, addr_t arg1, addr_t arg2); /// Put four operation argument index in the recording inline void PutArg(addr_t arg0, addr_t arg1, addr_t arg2, addr_t arg3); /// Put five operation argument index in the recording inline void PutArg(addr_t arg0, addr_t arg1, addr_t arg2, addr_t arg3, addr_t arg4); /// Put six operation argument index in the recording inline void PutArg(addr_t arg0, addr_t arg1, addr_t arg2, addr_t arg3, addr_t arg4, addr_t arg5); // Reserve space for a specified number of arguments inline size_t ReserveArg(size_t n_arg); // Replace an argument value void ReplaceArg(size_t i_arg, size_t value); /// Put a character string in the text for this recording. inline size_t PutTxt(const char *text); /// Number of variables currently stored in the recording. size_t num_var_rec(void) const { return num_var_rec_; } /// Number of LdpOp and LdvOp operations currently in the recording. size_t num_load_op_rec(void) const { return num_load_op_rec_; } /// Number of operators currently stored in the recording. size_t num_op_rec(void) const { return op_rec_.size(); } /// Approximate amount of memory used by the recording size_t Memory(void) const { return op_rec_.capacity() * sizeof(CPPAD_OP_CODE_TYPE) + vecad_ind_rec_.capacity() * sizeof(size_t) + op_arg_rec_.capacity() * sizeof(addr_t) + par_rec_.capacity() * sizeof(Base) + text_rec_.capacity() * sizeof(char); } }; /*! Put next operator in the operation sequence. This sets the op code for the next operation in this recording. This call must be followed by putting the corresponding \verbatim NumArg(op) \endverbatim argument indices in the recording. \param op Is the op code corresponding to the the operation that is being recorded (which must not be LdpOp or LdvOp). \return The return value is the index of the primary (last) variable corresponding to the result of this operation. The number of variables corresponding to the operation is given by \verbatim NumRes(op) \endverbatim With each call to PutOp or PutLoadOp, the return index increases by the number of variables corresponding to the call. This index starts at zero after the default constructor and after each call to Erase. */ template inline size_t recorder::PutOp(OpCode op) { size_t i = op_rec_.extend(1); CPPAD_ASSERT_KNOWN( (abort_op_index_ == 0) || (abort_op_index_ != i), "Operator index equals abort_op_index in Independent" ); op_rec_[i] = static_cast(op); CPPAD_ASSERT_UNKNOWN( op_rec_.size() == i + 1 ); CPPAD_ASSERT_UNKNOWN( (op != LdpOp) & (op != LdvOp) ); // first operator should be a BeginOp and NumRes( BeginOp ) > 0 num_var_rec_ += NumRes(op); CPPAD_ASSERT_UNKNOWN( num_var_rec_ > 0 ); return num_var_rec_ - 1; } /*! Put next LdpOp or LdvOp operator in operation sequence (special cases). This sets the op code for the next operation in this recording. This call must be followed by putting the corresponding \verbatim NumArg(op) \endverbatim argument indices in the recording. \param op Is the op code corresponding to the the operation that is being recorded (which must be LdpOp or LdvOp). \return The return value is the index of the primary (last) variable corresponding to the result of this operation. The number of variables corresponding to the operation is given by \verbatim NumRes(op) \endverbatim which must be one for this operation. With each call to PutLoadOp or PutOp, the return index increases by the number of variables corresponding to this call to the call. This index starts at zero after the default constructor and after each call to Erase. \par num_load_op_rec() The return value for num_load_op_rec() increases by one after each call to this function (and starts at zero after the default constructor or Erase). */ template inline size_t recorder::PutLoadOp(OpCode op) { size_t i = op_rec_.extend(1); CPPAD_ASSERT_KNOWN( (abort_op_index_ == 0) || (abort_op_index_ != i), "This is the abort operator index specified by " "Independent(x, abort_op_index)." ); op_rec_[i] = static_cast(op); CPPAD_ASSERT_UNKNOWN( op_rec_.size() == i + 1 ); CPPAD_ASSERT_UNKNOWN( (op == LdpOp) | (op == LdvOp) ); // first operator should be a BeginOp and NumRes( BeginOp ) > 0 num_var_rec_ += NumRes(op); CPPAD_ASSERT_UNKNOWN( num_var_rec_ > 0 ); // count this vecad load operation num_load_op_rec_++; return num_var_rec_ - 1; } /*! Add a value to the end of the current vector of VecAD indices. For each VecAD vector, this routine is used to store the length of the vector followed by the parameter index corresponding to each value in the vector. This value for the elements of the VecAD vector corresponds to the beginning of the operation sequence. \param vec_ind is the index to be palced at the end of the vector of VecAD indices. \return is the index in the vector of VecAD indices corresponding to this value. This index starts at zero after the recorder default constructor and after each call to Erase. It increments by one for each call to PutVecInd.. */ template inline size_t recorder::PutVecInd(size_t vec_ind) { size_t i = vecad_ind_rec_.extend(1); vecad_ind_rec_[i] = vec_ind; CPPAD_ASSERT_UNKNOWN( vecad_ind_rec_.size() == i + 1 ); return i; } /*! Find or add a parameter to the current vector of parameters. \param par is the parameter to be found or placed in the vector of parameters. \return is the index in the parameter vector corresponding to this parameter value. This value is not necessarily placed at the end of the vector (because values that are identically equal may be reused). */ template size_t recorder::PutPar(const Base &par) { static size_t hash_table[CPPAD_HASH_TABLE_SIZE * CPPAD_MAX_NUM_THREADS]; size_t i; size_t code; CPPAD_ASSERT_UNKNOWN( thread_offset_ / CPPAD_HASH_TABLE_SIZE == thread_alloc::thread_num() ); // get hash code for this value code = static_cast( hash_code(par) ); CPPAD_ASSERT_UNKNOWN( code < CPPAD_HASH_TABLE_SIZE ); // If we have a match, return the parameter index i = hash_table[code + thread_offset_]; if( i < par_rec_.size() && IdenticalEqualPar(par_rec_[i], par) ) return i; // place a new value in the table i = par_rec_.extend(1); par_rec_[i] = par; CPPAD_ASSERT_UNKNOWN( par_rec_.size() == i + 1 ); // make the hash code point to this new value hash_table[code + thread_offset_] = i; // return the parameter index return i; } // -------------------------- PutArg -------------------------------------- /*! Prototype for putting operation argument indices in the recording. The following syntax \verbatim rec.PutArg(arg0) rec.PutArg(arg0, arg1) . . . rec.PutArg(arg0, arg1, ..., arg5) \endverbatim places the values passed to PutArg at the current end of the operation argument indices for the recording. \a arg0 comes before \a arg1, etc. The proper number of operation argument indices corresponding to the operation code op is given by \verbatim NumArg(op) \endverbatim The number of the operation argument indices starts at zero after the default constructor and each call to Erase. It increases by the number of indices placed by each call to PutArg. */ inline void prototype_put_arg(void) { // This routine should not be called CPPAD_ASSERT_UNKNOWN(false); } /*! Put one operation argument index in the recording \param arg0 The operation argument index \copydetails prototype_put_arg */ template inline void recorder::PutArg(addr_t arg0) { size_t i = op_arg_rec_.extend(1); op_arg_rec_[i] = static_cast( arg0 ); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.size() == i + 1 ); } /*! Put two operation argument index in the recording \param arg0 First operation argument index. \param arg1 Second operation argument index. \copydetails prototype_put_arg */ template inline void recorder::PutArg(addr_t arg0, addr_t arg1) { size_t i = op_arg_rec_.extend(2); op_arg_rec_[i++] = static_cast( arg0 ); op_arg_rec_[i] = static_cast( arg1 ); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.size() == i + 1 ); } /*! Put three operation argument index in the recording \param arg0 First operation argument index. \param arg1 Second operation argument index. \param arg2 Third operation argument index. \copydetails prototype_put_arg */ template inline void recorder::PutArg(addr_t arg0, addr_t arg1, addr_t arg2) { size_t i = op_arg_rec_.extend(3); op_arg_rec_[i++] = static_cast( arg0 ); op_arg_rec_[i++] = static_cast( arg1 ); op_arg_rec_[i] = static_cast( arg2 ); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.size() == i + 1 ); } /*! Put four operation argument index in the recording \param arg0 First operation argument index. \param arg1 Second operation argument index. \param arg2 Third operation argument index. \param arg3 Fourth operation argument index. \copydetails prototype_put_arg */ template inline void recorder::PutArg(addr_t arg0, addr_t arg1, addr_t arg2, addr_t arg3) { size_t i = op_arg_rec_.extend(4); op_arg_rec_[i++] = static_cast( arg0 ); op_arg_rec_[i++] = static_cast( arg1 ); op_arg_rec_[i++] = static_cast( arg2 ); op_arg_rec_[i] = static_cast( arg3 ); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.size() == i + 1 ); } /*! Put five operation argument index in the recording \param arg0 First operation argument index. \param arg1 Second operation argument index. \param arg2 Third operation argument index. \param arg3 Fourth operation argument index. \param arg4 Fifth operation argument index. \copydetails prototype_put_arg */ template inline void recorder::PutArg(addr_t arg0, addr_t arg1, addr_t arg2, addr_t arg3, addr_t arg4) { size_t i = op_arg_rec_.extend(5); op_arg_rec_[i++] = static_cast( arg0 ); op_arg_rec_[i++] = static_cast( arg1 ); op_arg_rec_[i++] = static_cast( arg2 ); op_arg_rec_[i++] = static_cast( arg3 ); op_arg_rec_[i] = static_cast( arg4 ); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.size() == i + 1 ); } /*! Put six operation argument index in the recording \param arg0 First operation argument index. \param arg1 Second operation argument index. \param arg2 Third operation argument index. \param arg3 Fourth operation argument index. \param arg4 Fifth operation argument index. \param arg5 Sixth operation argument index. \copydetails prototype_put_arg */ template inline void recorder::PutArg(addr_t arg0, addr_t arg1, addr_t arg2, addr_t arg3, addr_t arg4, addr_t arg5) { size_t i = op_arg_rec_.extend(6); op_arg_rec_[i++] = static_cast( arg0 ); op_arg_rec_[i++] = static_cast( arg1 ); op_arg_rec_[i++] = static_cast( arg2 ); op_arg_rec_[i++] = static_cast( arg3 ); op_arg_rec_[i++] = static_cast( arg4 ); op_arg_rec_[i] = static_cast( arg5 ); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.size() == i + 1 ); } // -------------------------------------------------------------------------- /*! Reserve space for arguments, but delay placing values there. \param n_arg number of arguements to reserve space for \return is the index in the argument vector corresponding to the first of the arguments being reserved. */ template inline size_t recorder::ReserveArg(size_t n_arg) { size_t i = op_arg_rec_.extend(n_arg); CPPAD_ASSERT_UNKNOWN( op_arg_rec_.size() == i + n_arg ); return i; } /*! \brief Replace an argument value in the recording (intended to fill in reserved values). \param i_arg is the index, in argument vector, for the value that is replaced. \param value is the new value for the argument with the specified index. */ template inline void recorder::ReplaceArg(size_t i_arg, size_t value) { op_arg_rec_[i_arg] = static_cast( value ); } // -------------------------------------------------------------------------- /*! Put a character string in the text for this recording. \param text is a '\\0' terminated character string that is to be put in the vector of characters corresponding to this recording. The terminator '\\0' will be included. \return is the offset with in the text vector for this recording at which the character string starts. */ template inline size_t recorder::PutTxt(const char *text) { // determine length of the text including terminating '\0' size_t n = 0; while( text[n] != '\0' ) n++; CPPAD_ASSERT_UNKNOWN( n <= 1000 ); n++; CPPAD_ASSERT_UNKNOWN( text[n-1] == '\0' ); // copy text including terminating '\0' size_t i = text_rec_.extend(n); size_t j; for(j = 0; j < n; j++) text_rec_[i + j] = text[j]; CPPAD_ASSERT_UNKNOWN( text_rec_.size() == i + n ); return i; } // ------------------------------------------------------------------------- } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/for_jac_sweep.hpp0000644000175200017650000005613113057470466020144 0ustar coincoin-web// $Id: for_jac_sweep.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_FOR_JAC_SWEEP_HPP # define CPPAD_LOCAL_FOR_JAC_SWEEP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file for_jac_sweep.hpp Compute Forward mode Jacobian sparsity patterns. */ /*! \def CPPAD_FOR_JAC_SWEEP_TRACE This value is either zero or one. Zero is the normal operational value. If it is one, a trace of every for_jac_sweep computation is printed. */ # define CPPAD_FOR_JAC_SWEEP_TRACE 0 /*! Given the sparsity pattern for the independent variables, ForJacSweep computes the sparsity pattern for all the other variables. \tparam Base base type for the operator; i.e., this operation sequence was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param dependency Are the derivatives with respect to left and right of the expression below considered to be non-zero: \code CondExpRel(left, right, if_true, if_false) \endcode This is used by the optimizer to obtain the correct dependency relations. \param n is the number of independent variables on the tape. \param numvar is the total number of variables on the tape; i.e., \a play->num_var_rec(). \param play The information stored in \a play is a recording of the operations corresponding to a function \f[ F : {\bf R}^n \rightarrow {\bf R}^m \f] where \f$ n \f$ is the number of independent variables and \f$ m \f$ is the number of dependent variables. The object \a play is effectly constant. It is not declared const because while playing back the tape the object \a play holds information about the current location with in the tape and this changes during playback. \param var_sparsity \b Input: For j = 1 , ... , \a n, the sparsity pattern for the independent variable with index (j-1) corresponds to the set with index j in \a var_sparsity. \n \n \b Output: For i = \a n + 1 , ... , \a numvar - 1, the sparsity pattern for the variable with index i on the tape corresponds to the set with index i in \a var_sparsity. \par Checked Assertions: \li numvar == var_sparsity.n_set() \li numvar == play->num_var_rec() */ template void ForJacSweep( bool dependency , size_t n , size_t numvar , local::player* play , Vector_set& var_sparsity ) { OpCode op; size_t i_op; size_t i_var; const addr_t* arg = CPPAD_NULL; size_t i, j, k; // check numvar argument CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar ); CPPAD_ASSERT_UNKNOWN( var_sparsity.n_set() == numvar ); // length of the parameter vector (used by CppAD assert macros) const size_t num_par = play->num_par_rec(); // cum_sparsity accumulates sparsity pattern a cummulative sum size_t limit = var_sparsity.end(); // vecad_sparsity contains a sparsity pattern from each VecAD object // to all the other variables. // vecad_ind maps a VecAD index (the beginning of the // VecAD object) to its from index in vecad_sparsity size_t num_vecad_ind = play->num_vec_ind_rec(); size_t num_vecad_vec = play->num_vecad_vec_rec(); Vector_set vecad_sparsity; vecad_sparsity.resize(num_vecad_vec, limit); pod_vector vecad_ind; if( num_vecad_vec > 0 ) { size_t length; vecad_ind.extend(num_vecad_ind); j = 0; for(i = 0; i < num_vecad_vec; i++) { // length of this VecAD length = play->GetVecInd(j); // set to proper index for this VecAD vecad_ind[j] = i; for(k = 1; k <= length; k++) vecad_ind[j+k] = num_vecad_vec; // invalid index // start of next VecAD j += length + 1; } CPPAD_ASSERT_UNKNOWN( j == play->num_vec_ind_rec() ); } // -------------------------------------------------------------- // work space used by UserOp. // vector user_x; // parameters in x as integers // typedef std::set size_set; size_set::iterator set_itr; // iterator for a standard set size_set::iterator set_end; // end of iterator sequence vector< size_set > set_r; // set sparsity pattern for the argument x vector< size_set > set_s; // set sparisty pattern for the result y // vector bool_r; // bool sparsity pattern for the argument x vector bool_s; // bool sparisty pattern for the result y // vectorBool pack_r; // pack sparsity pattern for the argument x vectorBool pack_s; // pack sparisty pattern for the result y // const size_t user_q = limit; // maximum element plus one // // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state = start_user; // proper initialization // atomic_base* user_atom = CPPAD_NULL; // user's atomic op calculator bool user_pack = false; // sparsity pattern type is pack bool user_bool = false; // sparsity pattern type is bool bool user_set = false; // sparsity pattern type is set bool user_ok = false; // atomic op return value // // pointer to the beginning of the parameter vector // (used by user atomic functions) const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // -------------------------------------------------------------- # if CPPAD_FOR_JAC_SWEEP_TRACE std::cout << std::endl; CppAD::vectorBool z_value(limit); # endif // skip the BeginOp at the beginning of the recording play->forward_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == BeginOp ); bool more_operators = true; while(more_operators) { bool flag; // temporary for use in switch cases. // this op play->forward_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( (i_op > n) | (op == InvOp) ); CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) ); CPPAD_ASSERT_ARG_BEFORE_RESULT(op, arg, i_var); // rest of information depends on the case switch( op ) { case AbsOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case AddvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case AddpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case AcosOp: // sqrt(1 - x * x), acos(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AcoshOp: // sqrt(x * x - 1), acosh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case AsinOp: // sqrt(1 - x * x), asin(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AsinhOp: // sqrt(1 + x * x), asinh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case AtanOp: // 1 + x * x, atan(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AtanhOp: // 1 - x * x, atanh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case CSkipOp: // CSipOp has a variable number of arguments and // forward_next thinks it has no arguments. // we must inform forward_next of this special case. play->forward_cskip(op, arg, i_op, i_var); break; // ------------------------------------------------- case CSumOp: // CSumOp has a variable number of arguments and // forward_next thinks it has no arguments. // we must inform forward_next of this special case. forward_sparse_jacobian_csum_op( i_var, arg, var_sparsity ); play->forward_csum(op, arg, i_op, i_var); break; // ------------------------------------------------- case CExpOp: forward_sparse_jacobian_cond_op( dependency, i_var, arg, num_par, var_sparsity ); break; // -------------------------------------------------- case CosOp: // sin(x), cos(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // --------------------------------------------------- case CoshOp: // sinh(x), cosh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case DisOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); // derivative is identically zero but dependency is not if( dependency ) forward_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); else var_sparsity.clear(i_var); break; // ------------------------------------------------- case DivvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case DivpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case DivvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case EndOp: CPPAD_ASSERT_NARG_NRES(op, 0, 0); more_operators = false; break; // ------------------------------------------------- case ErfOp: // arg[1] is always the parameter 0 // arg[0] is always the parameter 2 / sqrt(pi) CPPAD_ASSERT_NARG_NRES(op, 3, 5); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case ExpOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Expm1Op: CPPAD_ASSERT_NARG_NRES(op, 1, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case InvOp: CPPAD_ASSERT_NARG_NRES(op, 0, 1); // sparsity pattern is already defined break; // ------------------------------------------------- case LdpOp: forward_sparse_load_op( dependency, op, i_var, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case LdvOp: forward_sparse_load_op( dependency, op, i_var, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case EqpvOp: case EqvvOp: case LtpvOp: case LtvpOp: case LtvvOp: case LepvOp: case LevpOp: case LevvOp: case NepvOp: case NevvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 0); break; // ------------------------------------------------- case LogOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Log1pOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; # endif // ------------------------------------------------- case MulpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case MulvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case ParOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); var_sparsity.clear(i_var); break; // ------------------------------------------------- case PowvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case PowpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3); forward_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case PowvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3); forward_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case PriOp: CPPAD_ASSERT_NARG_NRES(op, 5, 0); break; // ------------------------------------------------- case SignOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); // derivative is identically zero but dependency is not if( dependency ) forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); else var_sparsity.clear(i_var); break; // ------------------------------------------------- case SinOp: // cos(x), sin(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case SinhOp: // cosh(x), sinh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case SqrtOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case StppOp: CPPAD_ASSERT_NARG_NRES(op, 3, 0); // if both arguments are parameters does not affect sparsity // or dependency break; // ------------------------------------------------- case StpvOp: forward_sparse_store_op( dependency, op, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case StvpOp: CPPAD_ASSERT_NARG_NRES(op, 3, 0); forward_sparse_store_op( dependency, op, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case StvvOp: forward_sparse_store_op( dependency, op, arg, num_vecad_ind, vecad_ind.data(), var_sparsity, vecad_sparsity ); break; // ------------------------------------------------- case SubvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- case SubpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case SubvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case TanOp: // tan(x)^2, tan(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case TanhOp: // tanh(x)^2, tanh(x) CPPAD_ASSERT_NARG_NRES(op, 1, 2); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case UserOp: // start or end an atomic operation sequence flag = user_state == start_user; user_atom = play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( flag ) { user_x.resize( user_n ); // user_pack = user_atom->sparsity() == atomic_base::pack_sparsity_enum; user_bool = user_atom->sparsity() == atomic_base::bool_sparsity_enum; user_set = user_atom->sparsity() == atomic_base::set_sparsity_enum; CPPAD_ASSERT_UNKNOWN( user_pack || user_bool || user_set ); if( user_pack ) { pack_r.resize( user_n * user_q ); pack_s.resize( user_m * user_q ); for(i = 0; i < user_n; i++) for(j = 0; j < user_q; j++) pack_r[ i * user_q + j] = false; } if( user_bool ) { bool_r.resize( user_n * user_q ); bool_s.resize( user_m * user_q ); for(i = 0; i < user_n; i++) for(j = 0; j < user_q; j++) bool_r[ i * user_q + j] = false; } if( user_set) { set_r.resize(user_n); set_s.resize(user_m); for(i = 0; i < user_n; i++) set_r[i].clear(); } } else { # ifndef NDEBUG if( ! user_ok ) { std::string msg = user_atom->afun_name() + ": atomic_base.for_sparse_jac: returned false\n"; if( user_pack ) msg += "sparsity = pack_sparsity_enum"; if( user_bool ) msg += "sparsity = bool_sparsity_enum"; if( user_set ) msg += "sparsity = set_sparsity_enum"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif } break; case UsrapOp: // parameter argument in an atomic operation sequence user_x[user_j] = parameter[arg[0]]; // // set row user_j to empty sparsity pattern play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( user_j == user_n ) { // call users function for this operation user_atom->set_old(user_old); if( user_pack ) { user_ok = user_atom->for_sparse_jac( user_q, pack_r, pack_s, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_jac( user_q, pack_r, pack_s ); } if( user_bool ) { user_ok = user_atom->for_sparse_jac( user_q, bool_r, bool_s, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_jac( user_q, bool_r, bool_s ); } if( user_set ) { user_ok = user_atom->for_sparse_jac( user_q, set_r, set_s, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_jac( user_q, set_r, set_s ); } } break; case UsravOp: // variable argument in an atomic operation sequence // variable as integers user_x[user_j] = CppAD::numeric_limits::quiet_NaN(); // set row user_j to sparsity pattern for variable arg[0] { typename Vector_set::const_iterator itr(var_sparsity, arg[0]); i = *itr; while( i < user_q ) { if( user_pack ) pack_r[user_j * user_q + i] = true; if( user_bool ) bool_r[user_j * user_q + i] = true; if( user_set ) set_r[user_j].insert(i); i = *(++itr); } } play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( user_j == user_n ) { // call users function for this operation user_atom->set_old(user_old); if( user_pack ) { user_ok = user_atom->for_sparse_jac( user_q, pack_r, pack_s, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_jac( user_q, pack_r, pack_s ); } if( user_bool ) { user_ok = user_atom->for_sparse_jac( user_q, bool_r, bool_s, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_jac( user_q, bool_r, bool_s ); } if( user_set ) { user_ok = user_atom->for_sparse_jac( user_q, set_r, set_s, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_jac( user_q, set_r, set_s ); } } break; case UsrrpOp: // parameter result in an atomic operation sequence play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrvOp: // variable result in an atomic operation sequence // It might be faster if we add set union to var_sparsity // where one of the sets is not in var_sparsity if( user_pack ) { for(j = 0; j < user_q; j++) if( pack_s[ user_i * user_q + j ] ) var_sparsity.add_element(i_var, j); } if( user_bool ) { for(j = 0; j < user_q; j++) if( bool_s[ user_i * user_q + j ] ) var_sparsity.add_element(i_var, j); } if( user_set ) { set_itr = set_s[user_i].begin(); set_end = set_s[user_i].end(); while( set_itr != set_end ) var_sparsity.add_element(i_var, *set_itr++); } play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; // ------------------------------------------------- case ZmulpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_unary_op( i_var, arg[1], var_sparsity ); break; // ------------------------------------------------- case ZmulvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_unary_op( i_var, arg[0], var_sparsity ); break; // ------------------------------------------------- case ZmulvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1); forward_sparse_jacobian_binary_op( i_var, arg, var_sparsity ); break; // ------------------------------------------------- default: CPPAD_ASSERT_UNKNOWN(0); } # if CPPAD_FOR_JAC_SWEEP_TRACE const addr_t* arg_tmp = arg; if( op == CSumOp ) arg_tmp = arg - arg[-1] - 4; if( op == CSkipOp ) arg_tmp = arg - arg[-1] - 7; // // value for this variable for(j = 0; j < limit; j++) z_value[j] = false; typename Vector_set::const_iterator itr(var_sparsity, i_var); j = *itr; while( j < limit ) { z_value[j] = true; j = *(++itr); } printOp( std::cout, play, i_op, i_var, op, arg_tmp ); if( NumRes(op) > 0 ) printOpResult( std::cout, 1, &z_value, 0, (CppAD::vectorBool *) CPPAD_NULL ); std::cout << std::endl; } std::cout << std::endl; # else } # endif CPPAD_ASSERT_UNKNOWN( i_var + 1 == play->num_var_rec() ); return; } } } // END_CPPAD_LOCAL_NAMESPACE // preprocessor symbols that are local to this file # undef CPPAD_FOR_JAC_SWEEP_TRACE # endif cppad-20170000.3/cppad/local/color_symmetric.hpp0000644000175200017650000002316313057470466020547 0ustar coincoin-web// $Id: color_symmetric.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_COLOR_SYMMETRIC_HPP # define CPPAD_LOCAL_COLOR_SYMMETRIC_HPP # include # include /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file color_symmetric.hpp Coloring algorithm for a symmetric sparse matrix. */ // -------------------------------------------------------------------------- /*! CppAD algorithm for determining which rows of a symmetric sparse matrix can be computed together. \tparam VectorSize is a simple vector class with elements of type size_t. \tparam VectorSet is an unspecified type with the exception that it must support the operations under pattern and the following operations where p is a VectorSet object: \n VectorSet p Constructs a new vector of sets object. \n p.resize(ns, ne) resizes \c p to ns sets with elements between zero and \c ne. All of the sets are initially empty. \n p.add_element(s, e) add element \c e to set with index \c s. \param pattern [in] Is a representation of the sparsity pattern for the matrix. \n m = pattern.n_set() \n sets m to the number of rows (and columns) in the sparse matrix. All of the row indices are less than this value. \n n = pattern.end() \n sets n to the number of columns in the sparse matrix (which must be equal to the number of rows). All of the column indices are less than this value. \n VectorSet::const_iterator itr(pattern, i) constructs an iterator that starts iterating over columns in the i-th row of the sparsity pattern. \n j = *itr Sets j to the next possibly non-zero column. \n ++itr Advances to the next possibly non-zero column. \n \param row [in/out] is a vector specifying which row indices to compute. \param col [in/out] is a vector, with the same size as row, that specifies which column indices to compute. \n \n Input: For each valid index \c k, the index pair (row[k], col[k]) must be present in the sparsity pattern. It may be that some entries in the sparsity pattern do not need to be computed; i.e, do not appear in the set of (row[k], col[k]) entries. \n \n Output: On output, some of row and column indices may have been swapped \code std::swap( row[k], col[k] ) \endcode So the the the color for row[k] can be used to compute entry (row[k], col[k]). \param color [out] is a vector with size m. The input value of its elements does not matter. Upon return, it is a coloring for the rows of the sparse matrix. Note that if color[i] == m, then ther is no index k for which row[k] == i (for the return value of row). \n \n Fix any (i, j) in the sparsity pattern. Suppose that there is a row index i1 with i1 != i, color[i1] == color[i] and (i1, j) is in the sparsity pattern. If follows that for all j1 with j1 != j and color[j1] == color[j], (j1, i ) is not in the sparsity pattern. \n \n This routine tries to minimize, with respect to the choice of colors, the maximum, with respect to k, of color[ row[k] ]. */ template void color_symmetric_cppad( const VectorSet& pattern , CppAD::vector& row , CppAD::vector& col , CppAD::vector& color ) { size_t o1, o2, i1, i2, j1, j2, k1, c1, c2; size_t K = row.size(); size_t m = pattern.n_set(); CPPAD_ASSERT_UNKNOWN( m == pattern.end() ); CPPAD_ASSERT_UNKNOWN( color.size() == m ); CPPAD_ASSERT_UNKNOWN( col.size() == K ); // row, column pairs that appear in ( row[k], col[k] ) CppAD::vector< std::set > pair_needed(m); std::set::iterator itr1, itr2; for(k1 = 0; k1 < K; k1++) { CPPAD_ASSERT_UNKNOWN( pattern.is_element(row[k1], col[k1]) ); pair_needed[ row[k1] ].insert( col[k1] ); pair_needed[ col[k1] ].insert( row[k1] ); } // order the rows decending by number of pairs needed CppAD::vector key(m), order2row(m); for(i1 = 0; i1 < m; i1++) { CPPAD_ASSERT_UNKNOWN( pair_needed[i1].size() <= m ); key[i1] = m - pair_needed[i1].size(); } CppAD::index_sort(key, order2row); // mapping from order index to row index CppAD::vector row2order(m); for(o1 = 0; o1 < m; o1++) row2order[ order2row[o1] ] = o1; // initial coloring color.resize(m); c1 = 0; for(o1 = 0; o1 < m; o1++) { i1 = order2row[o1]; if( pair_needed[i1].empty() ) color[i1] = m; else color[i1] = c1++; } // which colors are forbidden for this row CppAD::vector forbidden(m); // must start with row zero so that we remove results computed for it for(o1 = 0; o1 < m; o1++) // for each row that appears (in order) if( color[ order2row[o1] ] < m ) { i1 = order2row[o1]; c1 = color[i1]; // initial all colors as ok for this row // (value of forbidden for c > c1 does not matter) for(c2 = 0; c2 <= c1; c2++) forbidden[c2] = false; // ----------------------------------------------------- // Forbid grouping with rows that would destroy results that are // needed for this row. itr1 = pair_needed[i1].begin(); while( itr1 != pair_needed[i1].end() ) { // entry (i1, j1) is needed for this row j1 = *itr1; // Forbid rows i2 != i1 that have non-zero sparsity at (i2, j1). // Note that this is the same as non-zero sparsity at (j1, i2) typename VectorSet::const_iterator pattern_itr(pattern, j1); i2 = *pattern_itr; while( i2 != pattern.end() ) { c2 = color[i2]; if( c2 < c1 ) forbidden[c2] = true; i2 = *(++pattern_itr); } itr1++; } // ----------------------------------------------------- // Forbid grouping with rows that this row would destroy results for for(o2 = 0; o2 < o1; o2++) { i2 = order2row[o2]; c2 = color[i2]; itr2 = pair_needed[i2].begin(); while( itr2 != pair_needed[i2].end() ) { j2 = *itr2; // row i2 needs pair (i2, j2). // Forbid grouping with i1 if (i1, j2) has non-zero sparsity if( pattern.is_element(i1, j2) ) forbidden[c2] = true; itr2++; } } // pick the color with smallest index c2 = 0; while( forbidden[c2] ) { c2++; CPPAD_ASSERT_UNKNOWN( c2 <= c1 ); } color[i1] = c2; // no longer need results that are computed by this row itr1 = pair_needed[i1].begin(); while( itr1 != pair_needed[i1].end() ) { j1 = *itr1; if( row2order[j1] > o1 ) { itr2 = pair_needed[j1].find(i1); if( itr2 != pair_needed[j1].end() ) { pair_needed[j1].erase(itr2); if( pair_needed[j1].empty() ) color[j1] = m; } } itr1++; } } // determine which sparsity entries need to be reflected for(k1 = 0; k1 < row.size(); k1++) { i1 = row[k1]; j1 = col[k1]; itr1 = pair_needed[i1].find(j1); if( itr1 == pair_needed[i1].end() ) { row[k1] = j1; col[k1] = i1; # ifndef NDEBUG itr1 = pair_needed[j1].find(i1); CPPAD_ASSERT_UNKNOWN( itr1 != pair_needed[j1].end() ); # endif } } return; } // -------------------------------------------------------------------------- /*! Colpack algorithm for determining which rows of a symmetric sparse matrix can be computed together. \copydetails color_symmetric_cppad */ template void color_symmetric_colpack( const VectorSet& pattern , CppAD::vector& row , CppAD::vector& col , CppAD::vector& color ) { # if ! CPPAD_HAS_COLPACK CPPAD_ASSERT_UNKNOWN(false); return; # else size_t i, j, k; size_t m = pattern.n_set(); CPPAD_ASSERT_UNKNOWN( m == pattern.end() ); CPPAD_ASSERT_UNKNOWN( row.size() == col.size() ); // Determine number of non-zero entries in each row CppAD::vector n_nonzero(m); size_t n_nonzero_total = 0; for(i = 0; i < m; i++) { n_nonzero[i] = 0; typename VectorSet::const_iterator pattern_itr(pattern, i); j = *pattern_itr; while( j != pattern.end() ) { n_nonzero[i]++; j = *(++pattern_itr); } n_nonzero_total += n_nonzero[i]; } // Allocate memory and fill in Adolc sparsity pattern CppAD::vector adolc_pattern(m); CppAD::vector adolc_memory(m + n_nonzero_total); size_t i_memory = 0; for(i = 0; i < m; i++) { adolc_pattern[i] = adolc_memory.data() + i_memory; adolc_pattern[i][0] = n_nonzero[i]; typename VectorSet::const_iterator pattern_itr(pattern, i); j = *pattern_itr; k = 1; while(j != pattern.end() ) { adolc_pattern[i][k++] = j; j = *(++pattern_itr); } CPPAD_ASSERT_UNKNOWN( k == 1 + n_nonzero[i] ); i_memory += k; } CPPAD_ASSERT_UNKNOWN( i_memory == m + n_nonzero_total ); // Must use an external routine for this part of the calculation because // ColPack/ColPackHeaders.h has as 'using namespace std' at global level. cppad_colpack_symmetric(color, m, adolc_pattern); // determine which sparsity entries need to be reflected size_t i1, i2, j1, j2, k1, k2; for(k1 = 0; k1 < row.size(); k1++) { i1 = row[k1]; j1 = col[k1]; bool reflect = false; for(i2 = 0; i2 < m; i2++) if( (i1 != i2) & (color[i1]==color[i2]) ) { for(k2 = 1; k2 <= adolc_pattern[i2][0]; k2++) { j2 = adolc_pattern[i2][k2]; reflect |= (j1 == j2); } } if( reflect ) { row[k1] = j1; col[k1] = i1; } } return; # endif // CPPAD_HAS_COLPACK } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/color_general.hpp0000644000175200017650000002122113057470466020141 0ustar coincoin-web// $Id: color_general.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_COLOR_GENERAL_HPP # define CPPAD_LOCAL_COLOR_GENERAL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file color_general.hpp Coloring algorithm for a general sparse matrix. */ // -------------------------------------------------------------------------- /*! Determine which rows of a general sparse matrix can be computed together; i.e., do not have non-zero entries with the same column index. \tparam VectorSize is a simple vector class with elements of type size_t. \tparam VectorSet is an unspecified type with the exception that it must support the operations under pattern and the following operations where p is a VectorSet object: \n VectorSet p Constructs a new vector of sets object. \n p.resize(ns, ne) resizes \c p to \c ns sets with elements between zero \c ne. All of the \c ns sets are initially empty. \n p.add_element(s, e) add element \c e to set with index \c s. \param pattern [in] Is a representation of the sparsity pattern for the matrix. \n m = pattern.n_set() \n sets \c m to the number of rows in the sparse matrix. All of the row indices are less than this value. \n n = pattern.end() \n sets \c n to the number of columns in the sparse matrix. All of the column indices are less than this value. \n VectorSet::const_iterator itr(pattern, i) constructs an iterator that starts iterating over columns in the i-th row of the sparsity pattern. \n j = *itr Sets j to the next possibly non-zero column. \n ++itr Advances to the next possibly non-zero column. \param row [in] is a vector specifying which row indices to compute. \param col [in] is a vector, with the same size as row, that specifies which column indices to compute. For each valid index k, the index pair (row[k], col[k]) must be present in the sparsity pattern. It may be that some entries in the sparsity pattern do not need to be computed; i.e, do not appear in the set of (row[k], col[k]) entries. \param color [out] is a vector with size m. The input value of its elements does not matter. Upon return, it is a coloring for the rows of the sparse matrix. \n \n If for some i, color[i] == m, then the i-th row does not appear in the vector row. Otherwise, color[i] < m. \n \n Suppose two differen rows, i != r have the same color and column index j is such that both of the pairs (i, j) and (r, j) appear in the sparsity pattern. It follows that neither of these pairs appear in the set of (row[k], col[k]) entries. \n \n This routine tries to minimize, with respect to the choice of colors, the maximum, with respct to k, of color[ row[k] ] (not counting the indices k for which row[k] == m). */ template void color_general_cppad( const VectorSet& pattern , const VectorSize& row , const VectorSize& col , CppAD::vector& color ) { size_t i, j, k, ell, r; size_t K = row.size(); size_t m = pattern.n_set(); size_t n = pattern.end(); CPPAD_ASSERT_UNKNOWN( size_t( col.size() ) == K ); CPPAD_ASSERT_UNKNOWN( size_t( color.size() ) == m ); // We define the set of rows, columns, and pairs that appear // by the set ( row[k], col[k] ) for k = 0, ... , K-1. // initialize rows that appear CppAD::vector row_appear(m); for(i = 0; i < m; i++) row_appear[i] = false; // rows and columns that appear VectorSet c2r_appear, r2c_appear; c2r_appear.resize(n, m); r2c_appear.resize(m, n); for(k = 0; k < K; k++) { CPPAD_ASSERT_UNKNOWN( pattern.is_element(row[k], col[k]) ); row_appear[ row[k] ] = true; c2r_appear.add_element(col[k], row[k]); r2c_appear.add_element(row[k], col[k]); } // for each column, which rows are non-zero and do not appear VectorSet not_appear; not_appear.resize(n, m); for(i = 0; i < m; i++) { typename VectorSet::const_iterator pattern_itr(pattern, i); j = *pattern_itr; while( j != pattern.end() ) { if( ! c2r_appear.is_element(j , i) ) not_appear.add_element(j, i); j = *(++pattern_itr); } } // initial coloring color.resize(m); ell = 0; for(i = 0; i < m; i++) { if( row_appear[i] ) color[i] = ell++; else color[i] = m; } /* See GreedyPartialD2Coloring Algorithm Section 3.6.2 of Graph Coloring in Optimization Revisited by Assefaw Gebremedhin, Fredrik Maane, Alex Pothen The algorithm above was modified (by Brad Bell) to take advantage of the fact that only the entries (subset of the sparsity pattern) specified by row and col need to be computed. */ CppAD::vector forbidden(m); for(i = 1; i < m; i++) // for each row that appears if( color[i] < m ) { // initial all colors as ok for this row // (value of forbidden for ell > initial color[i] does not matter) for(ell = 0; ell <= color[i]; ell++) forbidden[ell] = false; // ----------------------------------------------------- // Forbid colors for which this row would destroy results: // // for each column that is non-zero for this row typename VectorSet::const_iterator pattern_itr(pattern, i); j = *pattern_itr; while( j != pattern.end() ) { // for each row that appears with this column typename VectorSet::const_iterator c2r_itr(c2r_appear, j); r = *c2r_itr; while( r != c2r_appear.end() ) { // if this is not the same row, forbid its color if( (r < i) & (color[r] < m) ) forbidden[ color[r] ] = true; r = *(++c2r_itr); } j = *(++pattern_itr); } // ----------------------------------------------------- // Forbid colors that destroy results needed for this row. // // for each column that appears with this row typename VectorSet::const_iterator r2c_itr(r2c_appear, i); j = *r2c_itr; while( j != r2c_appear.end() ) { // For each row that is non-zero for this column // (the appear rows have already been checked above). typename VectorSet::const_iterator not_itr(not_appear, j); r = *not_itr; while( r != not_appear.end() ) { // if this is not the same row, forbid its color if( (r < i) & (color[r] < m) ) forbidden[ color[r] ] = true; r = *(++not_itr); } j = *(++r2c_itr); } // pick the color with smallest index ell = 0; while( forbidden[ell] ) { ell++; CPPAD_ASSERT_UNKNOWN( ell <= color[i] ); } color[i] = ell; } return; } # if CPPAD_HAS_COLPACK /*! Colpack version of determining which rows of a sparse matrix can be computed together. \copydetails color_general */ template void color_general_colpack( const VectorSet& pattern , const VectorSize& row , const VectorSize& col , CppAD::vector& color ) { size_t i, j, k; size_t m = pattern.n_set(); size_t n = pattern.end(); // Determine number of non-zero entries in each row CppAD::vector n_nonzero(m); size_t n_nonzero_total = 0; for(i = 0; i < m; i++) { n_nonzero[i] = 0; typename VectorSet::const_iterator pattern_itr(pattern, i); j = *pattern_itr; while( j != pattern.end() ) { n_nonzero[i]++; j = *(++pattern_itr); } n_nonzero_total += n_nonzero[i]; } // Allocate memory and fill in Adolc sparsity pattern CppAD::vector adolc_pattern(m); CppAD::vector adolc_memory(m + n_nonzero_total); size_t i_memory = 0; for(i = 0; i < m; i++) { adolc_pattern[i] = adolc_memory.data() + i_memory; adolc_pattern[i][0] = n_nonzero[i]; typename VectorSet::const_iterator pattern_itr(pattern, i); j = *pattern_itr; k = 1; while(j != pattern.end() ) { adolc_pattern[i][k++] = j; j = *(++pattern_itr); } CPPAD_ASSERT_UNKNOWN( k == 1 + n_nonzero[i] ); i_memory += k; } CPPAD_ASSERT_UNKNOWN( i_memory == m + n_nonzero_total ); // Must use an external routine for this part of the calculation because // ColPack/ColPackHeaders.h has as 'using namespace std' at global level. cppad_colpack_general(color, m, n, adolc_pattern); return; } # endif // CPPAD_HAS_COLPACK } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/load_op.hpp0000644000175200017650000004650013057470466016752 0ustar coincoin-web// $Id: load_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_LOAD_OP_HPP # define CPPAD_LOCAL_LOAD_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file load_op.hpp Setting a variable so that it corresponds to current value of a VecAD element. */ /* ============================================================================== The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: ============================================================================== */ /*! Shared documentation for zero order forward mode implementation of op = LdpOp or LdvOp (not called). The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: \tparam Base base type for the operator; i.e., this operation was recorded using AD and computations by this routine are done using type Base. \param play is the tape that this operation appears in. This is for error detection and not used when NDEBUG is defined. \param i_z is the AD variable index corresponding to the variable z. \param arg \n arg[0] is the offset of this VecAD vector relative to the beginning of the isvar_by_ind and index_by_ind arrays. \n \n arg[1] \n If this is the LdpOp operation (if x is a parameter), i_vec is defined by \verbatim i_vec = arg[1] \endverbatim If this is the LdvOp operation (if x is a variable), i_vec is defined by \verbatim i_vec = floor( taylor[ arg[1] * cap_order + 0 ] ) \endverbatim where floor(c) is the greatest integer less that or equal c. \n \n arg[2] Is the index of this vecad load instruction in the var_by_load_op array. \param parameter If v[x] is a parameter, parameter[ i_v_x ] is its value. This vector has size play->num_par_rec(). \param cap_order number of columns in the matrix containing the Taylor coefficients. \param taylor \n Input \n In LdvOp case, taylor[ arg[1] * cap_order + 0 ] is used to compute the index in the definition of i_vec above. If v[x] is a variable, taylor[ i_v_x * cap_order + 0 ] is the zero order Taylor coefficient for v[x]. \n \n Output \n taylor[ i_z * cap_order + 0 ] is set to the zero order Taylor coefficient for the variable z. \param isvar_by_ind If isvar_by_ind[ arg[0] + i_vec ] is true, v[x] is a variable. Otherwise it is a parameter. This vector has size play->num_vec_ind_rec(). \param index_by_ind index_by_ind[ arg[0] - 1 ] is the number of elements in the user vector containing this element. index_by_ind[ arg[0] + i_vec ] is the variable or parameter index for this element, This array has size play->num_vec_ind_rec(). \param var_by_load_op is a vector with size play->num_load_op_rec(). The input value of its elements does not matter. Upon return, it contains the variable index corresponding to each load instruction. In the case where the index is zero, the instruction corresponds to a parameter (not variable). This array has size play->num_load_op_rec(). \par Check User Errors \li In the LdvOp case check that the index is with in range; i.e. i_vec < index_by_ind[ arg[0] - 1 ]. Note that, if x is a parameter, the corresponding vector index and it does not change. In this case, the error above should be detected during tape recording. */ template inline void forward_load_op_0( local::player* play , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor , bool* isvar_by_ind , size_t* index_by_ind , addr_t* var_by_load_op ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Shared documentation for sparsity operations corresponding to op = LdpOp or LdvOp (not called). The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param op is the code corresponding to this operator; i.e., LdpOp or LdvOp. \param i_z is the AD variable index corresponding to the variable z; i.e., the set with index \a i_z in \a var_sparsity is the sparsity pattern correpsonding to z. \param arg \n \a arg[0] is the offset corresponding to this VecAD vector in the VecAD combined array. \param num_combined is the total number of elements in the VecAD combinded array. \param combined is the VecAD combined array. \n \n \a combined[ \a arg[0] - 1 ] is the index of the set corresponding to the vector v in \a vecad_sparsity. We use the notation i_v for this value; i.e., \verbatim i_v = combined[ \a arg[0] - 1 ] \endverbatim \param var_sparsity The set with index \a i_z in \a var_sparsity is the sparsity pattern for z. This is an output for forward mode operations, and an input for reverse mode operations. \param vecad_sparsity The set with index \a i_v is the sparsity pattern for the vector v. This is an input for forward mode operations. For reverse mode operations, the sparsity pattern for z is added to the sparsity pattern for v. \par Checked Assertions \li NumArg(op) == 3 \li NumRes(op) == 1 \li 0 < \a arg[0] \li \a arg[0] < \a num_combined \li i_v < \a vecad_sparsity.n_set() */ template inline void sparse_load_op( OpCode op , size_t i_z , const addr_t* arg , size_t num_combined , const size_t* combined , Vector_set& var_sparsity , Vector_set& vecad_sparsity ) { // This routine is only for documentaiton, it should not be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Zero order forward mode implementation of op = LdpOp. \copydetails forward_load_op_0 */ template inline void forward_load_p_op_0( local::player* play , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor , bool* isvar_by_ind , size_t* index_by_ind , addr_t* var_by_load_op ) { CPPAD_ASSERT_UNKNOWN( NumArg(LdpOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(LdpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < play->num_load_op_rec() ); // Because the index is a parameter, this indexing error should have been // caught and reported to the user when the tape is recording. size_t i_vec = arg[1]; CPPAD_ASSERT_UNKNOWN( i_vec < index_by_ind[ arg[0] - 1 ] ); CPPAD_ASSERT_UNKNOWN( arg[0] + i_vec < play->num_vec_ind_rec() ); size_t i_v_x = index_by_ind[ arg[0] + i_vec ]; Base* z = taylor + i_z * cap_order; if( isvar_by_ind[ arg[0] + i_vec ] ) { CPPAD_ASSERT_UNKNOWN( i_v_x < i_z ); var_by_load_op[ arg[2] ] = i_v_x; Base* v_x = taylor + i_v_x * cap_order; z[0] = v_x[0]; } else { CPPAD_ASSERT_UNKNOWN( i_v_x < play->num_par_rec() ); var_by_load_op[ arg[2] ] = 0; Base v_x = parameter[i_v_x]; z[0] = v_x; } } /*! Zero order forward mode implementation of op = LdvOp. \copydetails forward_load_op_0 */ template inline void forward_load_v_op_0( local::player* play , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor , bool* isvar_by_ind , size_t* index_by_ind , addr_t* var_by_load_op ) { CPPAD_ASSERT_UNKNOWN( NumArg(LdvOp) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(LdvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < play->num_load_op_rec() ); size_t i_vec = Integer( taylor[ arg[1] * cap_order + 0 ] ); CPPAD_ASSERT_KNOWN( i_vec < index_by_ind[ arg[0] - 1 ] , "VecAD: index during zero order forward sweep is out of range" ); CPPAD_ASSERT_UNKNOWN( arg[0] + i_vec < play->num_vec_ind_rec() ); size_t i_v_x = index_by_ind[ arg[0] + i_vec ]; Base* z = taylor + i_z * cap_order; if( isvar_by_ind[ arg[0] + i_vec ] ) { CPPAD_ASSERT_UNKNOWN( i_v_x < i_z ); var_by_load_op[ arg[2] ] = i_v_x; Base* v_x = taylor + i_v_x * cap_order; z[0] = v_x[0]; } else { CPPAD_ASSERT_UNKNOWN( i_v_x < play->num_par_rec() ); var_by_load_op[ arg[2] ] = 0; Base v_x = parameter[i_v_x]; z[0] = v_x; } } /*! Forward mode, except for zero order, for op = LdpOp or op = LdvOp The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: \tparam Base base type for the operator; i.e., this operation was recorded using AD and computations by this routine are done using type Base. \param play is the tape that this operation appears in. This is for error detection and not used when NDEBUG is defined. \param op is the code corresponding to this operator; i.e., LdpOp or LdvOp (only used for error checking). \param p is the lowest order of the Taylor coefficient that we are computing. \param q is the highest order of the Taylor coefficient that we are computing. \param r is the number of directions for the Taylor coefficients that we are computing. \param cap_order number of columns in the matrix containing the Taylor coefficients. \par tpv We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable \param i_z is the AD variable index corresponding to the variable z. \param arg arg[2] Is the index of this vecad load instruction in the var_by_load_op array. \param var_by_load_op is a vector with size play->num_load_op_rec(). It contains the variable index corresponding to each load instruction. In the case where the index is zero, the instruction corresponds to a parameter (not variable). \par i_var We use the notation \verbatim i_var = size_t( var_by_load_op[ arg[2] ] ) \endverbatim \param taylor \n Input \n If i_var > 0, v[x] is a variable and for k = 1 , ... , q taylor[ i_var * tpv + (k-1)*r+1+ell ] is the k-th order coefficient for v[x] in the ell-th direction, \n \n Output \n for k = p , ... , q, taylor[ i_z * tpv + (k-1)*r+1+ell ] is set to the k-order Taylor coefficient for z in the ell-th direction. */ template inline void forward_load_op( const local::player* play , OpCode op , size_t p , size_t q , size_t r , size_t cap_order , size_t i_z , const addr_t* arg , const addr_t* var_by_load_op , Base* taylor ) { CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( 0 < r); CPPAD_ASSERT_UNKNOWN( 0 < p); CPPAD_ASSERT_UNKNOWN( p <= q ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < play->num_load_op_rec() ); size_t i_var = size_t( var_by_load_op[ arg[2] ] ); CPPAD_ASSERT_UNKNOWN( i_var < i_z ); size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* z = taylor + i_z * num_taylor_per_var; if( i_var > 0 ) { Base* v_x = taylor + i_var * num_taylor_per_var; for(size_t ell = 0; ell < r; ell++) { for(size_t k = p; k <= q; k++) { size_t m = (k-1) * r + 1 + ell; z[m] = v_x[m]; } } } else { for(size_t ell = 0; ell < r; ell++) { for(size_t k = p; k <= q; k++) { size_t m = (k-1) * r + 1 + ell; z[m] = Base(0); } } } } /*! Reverse mode for op = LdpOp or LdvOp. The C++ source code corresponding to this operation is \verbatim v[x] = y \endverbatim where v is a VecAD vector, x is an AD object, and y is AD or Base objects. We define the index corresponding to v[x] by \verbatim i_v_x = index_by_ind[ arg[0] + i_vec ] \endverbatim where i_vec is defined under the heading arg[1] below: This routine is given the partial derivatives of a function G(z , y[x] , w , u ... ) and it uses them to compute the partial derivatives of \verbatim H( y[x] , w , u , ... ) = G[ z( y[x] ) , y[x] , w , u , ... ] \endverbatim \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param op is the code corresponding to this operator; i.e., LdpOp or LdvOp (only used for error checking). \param d highest order the Taylor coefficient that we are computing the partial derivative with respect to. \param i_z is the AD variable index corresponding to the variable z. \param arg \a arg[2] Is the index of this vecad load instruction in the var_by_load_op array. \param cap_order number of columns in the matrix containing the Taylor coefficients (not used). \param taylor matrix of Taylor coefficients (not used). \param nc_partial number of colums in the matrix containing all the partial derivatives (not used if \a arg[2] is zero). \param partial If \a arg[2] is zero, y[x] is a parameter and no values need to be modified; i.e., \a partial is not used. Otherwise, y[x] is a variable and: \n \n \a partial [ \a i_z * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative of G with respect to the k-th order Taylor coefficient for z. \n \n If \a arg[2] is not zero, \a partial [ \a arg[2] * \a nc_partial + k ] for k = 0 , ... , \a d is the partial derivative with respect to the k-th order Taylor coefficient for x. On input, it corresponds to the function G, and on output it corresponds to the the function H. \param var_by_load_op is a vector with size play->num_load_op_rec(). It contains the variable index corresponding to each load instruction. In the case where the index is zero, the instruction corresponds to a parameter (not variable). \par Checked Assertions \li NumArg(op) == 3 \li NumRes(op) == 1 \li d < cap_order \li size_t(arg[2]) < i_z */ template inline void reverse_load_op( OpCode op , size_t d , size_t i_z , const addr_t* arg , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial , const addr_t* var_by_load_op ) { size_t i_load = size_t( var_by_load_op[ arg[2] ] ); CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( i_load < i_z ); if( i_load > 0 ) { Base* pz = partial + i_z * nc_partial; Base* py_x = partial + i_load * nc_partial; size_t j = d + 1; while(j--) py_x[j] += pz[j]; } } /*! Forward mode sparsity operations for LdpOp and LdvOp \param dependency is this a dependency (or sparsity) calculation. \copydetails sparse_load_op */ template inline void forward_sparse_load_op( bool dependency , OpCode op , size_t i_z , const addr_t* arg , size_t num_combined , const size_t* combined , Vector_set& var_sparsity , Vector_set& vecad_sparsity ) { CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_combined ); size_t i_v = combined[ arg[0] - 1 ]; CPPAD_ASSERT_UNKNOWN( i_v < vecad_sparsity.n_set() ); var_sparsity.assignment(i_z, i_v, vecad_sparsity); if( dependency & (op == LdvOp) ) var_sparsity.binary_union(i_z, i_z, arg[1], var_sparsity); return; } /*! Reverse mode Jacobian sparsity operations for LdpOp and LdvOp \param dependency is this a dependency (or sparsity) calculation. \copydetails sparse_load_op */ template inline void reverse_sparse_jacobian_load_op( bool dependency , OpCode op , size_t i_z , const addr_t* arg , size_t num_combined , const size_t* combined , Vector_set& var_sparsity , Vector_set& vecad_sparsity ) { CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_combined ); size_t i_v = combined[ arg[0] - 1 ]; CPPAD_ASSERT_UNKNOWN( i_v < vecad_sparsity.n_set() ); vecad_sparsity.binary_union(i_v, i_v, i_z, var_sparsity); if( dependency & (op == LdvOp) ) var_sparsity.binary_union(arg[1], arg[1], i_z, var_sparsity); return; } /*! Reverse mode Hessian sparsity operations for LdpOp and LdvOp \copydetails sparse_load_op \param var_jacobian \a var_jacobian[i_z] is false (true) if the Jacobian of G with respect to z is always zero (many be non-zero). \param vecad_jacobian \a vecad_jacobian[i_v] is false (true) if the Jacobian with respect to x is always zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. */ template inline void reverse_sparse_hessian_load_op( OpCode op , size_t i_z , const addr_t* arg , size_t num_combined , const size_t* combined , Vector_set& var_sparsity , Vector_set& vecad_sparsity , bool* var_jacobian , bool* vecad_jacobian ) { CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); CPPAD_ASSERT_UNKNOWN( NumRes(op) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_combined ); size_t i_v = combined[ arg[0] - 1 ]; CPPAD_ASSERT_UNKNOWN( i_v < vecad_sparsity.n_set() ); vecad_sparsity.binary_union(i_v, i_v, i_z, var_sparsity); vecad_jacobian[i_v] |= var_jacobian[i_z]; return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/cos_op.hpp0000644000175200017650000001445713057470466016625 0ustar coincoin-web// $Id: cos_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_COS_OP_HPP # define CPPAD_LOCAL_COS_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file cos_op.hpp Forward and reverse mode calculations for z = cos(x). */ /*! Compute forward mode Taylor coefficient for result of op = CosOp. The C++ source code corresponding to this operation is \verbatim z = cos(x) \endverbatim The auxillary result is \verbatim y = sin(x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_cos_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* c = taylor + i_z * cap_order; Base* s = c - cap_order; // rest of this routine is identical for the following cases: // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op. // (except that there is a sign difference for the hyperbolic case). size_t k; if( p == 0 ) { s[0] = sin( x[0] ); c[0] = cos( x[0] ); p++; } for(size_t j = p; j <= q; j++) { s[j] = Base(0); c[j] = Base(0); for(k = 1; k <= j; k++) { s[j] += Base(k) * x[k] * c[j-k]; c[j] -= Base(k) * x[k] * s[j-k]; } s[j] /= Base(j); c[j] /= Base(j); } } /*! Compute forward mode Taylor coefficient for result of op = CosOp. The C++ source code corresponding to this operation is \verbatim z = cos(x) \endverbatim The auxillary result is \verbatim y = sin(x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_cos_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* c = taylor + i_z * num_taylor_per_var; Base* s = c - num_taylor_per_var; // rest of this routine is identical for the following cases: // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op // (except that there is a sign difference for the hyperbolic case). size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { s[m+ell] = Base(q) * x[m + ell] * c[0]; c[m+ell] = - Base(q) * x[m + ell] * s[0]; for(size_t k = 1; k < q; k++) { s[m+ell] += Base(k) * x[(k-1)*r+1+ell] * c[(q-k-1)*r+1+ell]; c[m+ell] -= Base(k) * x[(k-1)*r+1+ell] * s[(q-k-1)*r+1+ell]; } s[m+ell] /= Base(q); c[m+ell] /= Base(q); } } /*! Compute zero order forward mode Taylor coefficient for result of op = CosOp. The C++ source code corresponding to this operation is \verbatim z = cos(x) \endverbatim The auxillary result is \verbatim y = sin(x) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_cos_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* c = taylor + i_z * cap_order; // called z in documentation Base* s = c - cap_order; // called y in documentation c[0] = cos( x[0] ); s[0] = sin( x[0] ); } /*! Compute reverse mode partial derivatives for result of op = CosOp. The C++ source code corresponding to this operation is \verbatim z = cos(x) \endverbatim The auxillary result is \verbatim y = sin(x) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_cos_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* c = taylor + i_z * cap_order; // called z in doc Base* pc = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* s = c - cap_order; // called y in documentation Base* ps = pc - nc_partial; // rest of this routine is identical for the following cases: // reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op. size_t j = d; size_t k; while(j) { ps[j] /= Base(j); pc[j] /= Base(j); for(k = 1; k <= j; k++) { px[k] += Base(k) * azmul(ps[j], c[j-k]); px[k] -= Base(k) * azmul(pc[j], s[j-k]); ps[j-k] -= Base(k) * azmul(pc[j], x[k]); pc[j-k] += Base(k) * azmul(ps[j], x[k]); } --j; } px[0] += azmul(ps[0], c[0]); px[0] -= azmul(pc[0], s[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/add_op.hpp0000644000175200017650000002172513057470466016565 0ustar coincoin-web// $Id: add_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_ADD_OP_HPP # define CPPAD_LOCAL_ADD_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file add_op.hpp Forward and reverse mode calculations for z = x + y. */ // --------------------------- Addvv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = AddvvOp. The C++ source code corresponding to this operation is \verbatim z = x + y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op */ template inline void forward_addvv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AddvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(AddvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; for(size_t j = p; j <= q; j++) z[j] = x[j] + y[j]; } /*! Multiple directions forward mode Taylor coefficients for op = AddvvOp. The C++ source code corresponding to this operation is \verbatim z = x + y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_dir */ template inline void forward_addvv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AddvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(AddvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( 0 < q ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var; Base* y = taylor + arg[1] * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; size_t m = (q-1)*r + 1 ; for(size_t ell = 0; ell < r; ell++) z[m+ell] = x[m+ell] + y[m+ell]; } /*! Compute zero order forward mode Taylor coefficients for result of op = AddvvOp. The C++ source code corresponding to this operation is \verbatim z = x + y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_0 */ template inline void forward_addvv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AddvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(AddvvOp) == 1 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x[0] + y[0]; } /*! Compute reverse mode partial derivatives for result of op = AddvvOp. The C++ source code corresponding to this operation is \verbatim z = x + y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails reverse_binary_op */ template inline void reverse_addvv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AddvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(AddvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Partial derivatives corresponding to arguments and result Base* px = partial + arg[0] * nc_partial; Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t i = d + 1; while(i) { --i; px[i] += pz[i]; py[i] += pz[i]; } } // --------------------------- Addpv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = AddpvOp. The C++ source code corresponding to this operation is \verbatim z = x + y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op */ template inline void forward_addpv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AddpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(AddpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; if( p == 0 ) { // Paraemter value Base x = parameter[ arg[0] ]; z[0] = x + y[0]; p++; } for(size_t j = p; j <= q; j++) z[j] = y[j]; } /*! Multiple directions forward mode Taylor coefficients for op = AddpvOp. The C++ source code corresponding to this operation is \verbatim z = x + y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_dir */ template inline void forward_addpv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AddpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(AddpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; size_t m = (q-1) * r + 1; Base* y = taylor + arg[1] * num_taylor_per_var + m; Base* z = taylor + i_z * num_taylor_per_var + m; for(size_t ell = 0; ell < r; ell++) z[ell] = y[ell]; } /*! Compute zero order forward mode Taylor coefficient for result of op = AddpvOp. The C++ source code corresponding to this operation is \verbatim z = x + y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_0 */ template inline void forward_addpv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AddpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(AddpvOp) == 1 ); // Paraemter value Base x = parameter[ arg[0] ]; // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x + y[0]; } /*! Compute reverse mode partial derivative for result of op = AddpvOp. The C++ source code corresponding to this operation is \verbatim z = x + y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails reverse_binary_op */ template inline void reverse_addpv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AddvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(AddvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Partial derivatives corresponding to arguments and result Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t i = d + 1; while(i) { --i; py[i] += pz[i]; } } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/asin_op.hpp0000644000175200017650000001531213057470466016762 0ustar coincoin-web// $Id: asin_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_ASIN_OP_HPP # define CPPAD_LOCAL_ASIN_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file asin_op.hpp Forward and reverse mode calculations for z = asin(x). */ /*! Compute forward mode Taylor coefficient for result of op = AsinOp. The C++ source code corresponding to this operation is \verbatim z = asin(x) \endverbatim The auxillary result is \verbatim y = sqrt(1 - x * x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_asin_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AsinOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AsinOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation size_t k; Base uj; if( p == 0 ) { z[0] = asin( x[0] ); uj = Base(1) - x[0] * x[0]; b[0] = sqrt( uj ); p++; } for(size_t j = p; j <= q; j++) { uj = Base(0); for(k = 0; k <= j; k++) uj -= x[k] * x[j-k]; b[j] = Base(0); z[j] = Base(0); for(k = 1; k < j; k++) { b[j] -= Base(k) * b[k] * b[j-k]; z[j] -= Base(k) * z[k] * b[j-k]; } b[j] /= Base(j); z[j] /= Base(j); // b[j] += uj / Base(2); z[j] += x[j]; // b[j] /= b[0]; z[j] /= b[0]; } } /*! Multiple directions forward mode Taylor coefficient for op = AsinOp. The C++ source code corresponding to this operation is \verbatim z = asin(x) \endverbatim The auxillary result is \verbatim y = sqrt(1 - x * x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_asin_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; Base* b = z - num_taylor_per_var; // called y in documentation size_t k, ell; size_t m = (q-1) * r + 1; for(ell = 0; ell < r; ell ++) { Base uq = - 2.0 * x[m + ell] * x[0]; for(k = 1; k < q; k++) uq -= x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell]; b[m+ell] = Base(0); z[m+ell] = Base(0); for(k = 1; k < q; k++) { b[m+ell] += Base(k) * b[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; z[m+ell] += Base(k) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; } b[m+ell] = ( uq / Base(2) - b[m+ell] / Base(q) ) / b[0]; z[m+ell] = ( x[m+ell] - z[m+ell] / Base(q) ) / b[0]; } } /*! Compute zero order forward mode Taylor coefficient for result of op = AsinOp. The C++ source code corresponding to this operation is \verbatim z = asin(x) \endverbatim The auxillary result is \verbatim y = sqrt( 1 - x * x ) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_asin_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AsinOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AsinOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation z[0] = asin( x[0] ); b[0] = sqrt( Base(1) - x[0] * x[0] ); } /*! Compute reverse mode partial derivatives for result of op = AsinOp. The C++ source code corresponding to this operation is \verbatim z = asin(x) \endverbatim The auxillary result is \verbatim y = sqrt( 1 - x * x ) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_asin_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AsinOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AsinOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* b = z - cap_order; // called y in documentation Base* pb = pz - nc_partial; Base inv_b0 = Base(1) / b[0]; // number of indices to access size_t j = d; size_t k; while(j) { // scale partials w.r.t b[j] by 1 / b[0] pb[j] = azmul(pb[j], inv_b0); // scale partials w.r.t z[j] by 1 / b[0] pz[j] = azmul(pz[j], inv_b0); // update partials w.r.t b^0 pb[0] -= azmul(pz[j], z[j]) + azmul(pb[j], b[j]); // update partial w.r.t. x^0 px[0] -= azmul(pb[j], x[j]); // update partial w.r.t. x^j px[j] += pz[j] - azmul(pb[j], x[0]); // further scale partial w.r.t. z[j] by 1 / j pz[j] /= Base(j); for(k = 1; k < j; k++) { // update partials w.r.t b^(j-k) pb[j-k] -= Base(k) * azmul(pz[j], z[k]) + azmul(pb[j], b[k]); // update partials w.r.t. x^k px[k] -= azmul(pb[j], x[j-k]); // update partials w.r.t. z^k pz[k] -= Base(k) * azmul(pz[j], b[j-k]); } --j; } // j == 0 case px[0] += azmul(pz[0] - azmul(pb[0], x[0]), inv_b0); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/for_hes_sweep.hpp0000644000175200017650000004233013057470466020162 0ustar coincoin-web# ifndef CPPAD_LOCAL_FOR_HES_SWEEP_HPP # define CPPAD_LOCAL_FOR_HES_SWEEP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file for_hes_sweep.hpp Compute Forward mode Hessian sparsity patterns. */ /*! \def CPPAD_FOR_HES_SWEEP_TRACE This value is either zero or one. Zero is the normal operational value. If it is one, a trace of every rev_hes_sweep computation is printed. */ # define CPPAD_FOR_HES_SWEEP_TRACE 0 /*! Given the forward Jacobian sparsity pattern for all the variables, and the reverse Jacobian sparsity pattern for the dependent variables, ForHesSweep computes the Hessian sparsity pattern for all the independent variables. \tparam Base base type for the operator; i.e., this operation sequence was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param n is the number of independent variables on the tape. \param numvar is the total number of variables on the tape; i.e., \a play->num_var_rec(). This is also the number of rows in the entire sparsity pattern \a for_hes_sparse. \param play The information stored in \a play is a recording of the operations corresponding to a function \f[ F : {\bf R}^n \rightarrow {\bf R}^m \f] where \f$ n \f$ is the number of independent variables and \f$ m \f$ is the number of dependent variables. The object \a play is effectly constant. It is not declared const because while playing back the tape the object \a play holds information about the current location with in the tape and this changes during playback. \param for_jac_sparse For i = 0 , ... , \a numvar - 1, (for all the variables on the tape), the forward Jacobian sparsity pattern for the variable with index i corresponds to the set with index i in \a for_jac_sparse. \param rev_jac_sparse \b Input: For i = 0, ... , \a numvar - 1 the if the function we are computing the Hessian for has a non-zero derivative w.r.t. variable with index i, the set with index i has element zero. Otherwise it has no elements. \param for_hes_sparse The forward Hessian sparsity pattern for the variable with index i corresponds to the set with index i in \a for_hes_sparse. The number of rows in this sparsity patter is n+1 and the row with index zero is not used. \n \n \b Input: For i = 1 , ... , \a n the forward Hessian sparsity pattern for the variable with index i is empty. \n \n \b Output: For j = 1 , ... , \a n, the forward Hessian sparsity pattern for the independent dependent variable with index (j-1) is given by the set with index j in \a for_hes_sparse. */ template void ForHesSweep( size_t n, size_t numvar, local::player* play, const Vector_set& for_jac_sparse, const Vector_set& rev_jac_sparse, Vector_set& for_hes_sparse ) { OpCode op; size_t i_op; size_t i_var; const addr_t* arg = CPPAD_NULL; // length of the parameter vector (used by CppAD assert macros) const size_t num_par = play->num_par_rec(); size_t i, j, k; // check numvar argument size_t limit = n+1; CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar ); CPPAD_ASSERT_UNKNOWN( for_jac_sparse.n_set() == numvar ); CPPAD_ASSERT_UNKNOWN( for_hes_sparse.n_set() == limit ); CPPAD_ASSERT_UNKNOWN( numvar > 0 ); // upper limit exclusive for set elements CPPAD_ASSERT_UNKNOWN( for_jac_sparse.end() == limit ); CPPAD_ASSERT_UNKNOWN( for_hes_sparse.end() == limit ); // vecad_sparsity contains a sparsity pattern for each VecAD object. // vecad_ind maps a VecAD index (beginning of the VecAD object) // to the index for the corresponding set in vecad_sparsity. size_t num_vecad_ind = play->num_vec_ind_rec(); size_t num_vecad_vec = play->num_vecad_vec_rec(); Vector_set vecad_sparse; vecad_sparse.resize(num_vecad_vec, limit); pod_vector vecad_ind; pod_vector vecad_jac; if( num_vecad_vec > 0 ) { size_t length; vecad_ind.extend(num_vecad_ind); vecad_jac.extend(num_vecad_vec); j = 0; for(i = 0; i < num_vecad_vec; i++) { // length of this VecAD length = play->GetVecInd(j); // set vecad_ind to proper index for this VecAD vecad_ind[j] = i; // make all other values for this vector invalid for(k = 1; k <= length; k++) vecad_ind[j+k] = num_vecad_vec; // start of next VecAD j += length + 1; // initialize this vector's reverse jacobian value vecad_jac[i] = false; } CPPAD_ASSERT_UNKNOWN( j == play->num_vec_ind_rec() ); } // work space used by UserOp. vector user_ix; // variable indices for argument vector x vector user_x; // parameters in x as integers // // typedef std::set size_set; vector< size_set > set_h; // forward Hessian sparsity vector bool_h; // forward Hessian sparsity vectorBool pack_h; // forward Hessian sparstiy // vector user_vx; // which components of x are variables vector user_r; // forward Jacobian sparsity for x vector user_s; // reverse Jacobian sparsity for y // // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state = start_user; // proper initialization // atomic_base* user_atom = CPPAD_NULL; // user's atomic op calculator bool user_pack = false; // sparsity pattern type is pack bool user_bool = false; // sparsity pattern type is bool bool user_set = false; // sparsity pattern type is set bool user_ok = false; // atomic op return value // // pointer to the beginning of the parameter vector // (used by user atomic functions) const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // Initialize play->forward_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == BeginOp ); bool more_operators = true; # if CPPAD_FOR_HES_SWEEP_TRACE std::cout << std::endl; CppAD::vectorBool zf_value(limit); CppAD::vectorBool zh_value(limit * limit); # endif bool flag; // temporary for use in switch cases below while(more_operators) { // next op play->forward_next(op, arg, i_op, i_var); # ifndef NDEBUG if( i_op <= n ) { CPPAD_ASSERT_UNKNOWN((op == InvOp) | (op == BeginOp)); } else CPPAD_ASSERT_UNKNOWN((op != InvOp) & (op != BeginOp)); # endif // does the Hessian in question have a non-zero derivative // with respect to this variable bool include = rev_jac_sparse.is_element(i_var, 0); // // operators to include even if derivative is zero include |= op == EndOp; include |= op == CSkipOp; include |= op == CSumOp; include |= op == UserOp; include |= op == UsrapOp; include |= op == UsravOp; include |= op == UsrrpOp; include |= op == UsrrvOp; // if( include ) switch( op ) { // operators that should not occurr // case BeginOp // ------------------------------------------------- // operators that do not affect hessian case AbsOp: case AddvvOp: case AddpvOp: case CExpOp: case DisOp: case DivvpOp: case InvOp: case LdpOp: case LdvOp: case MulpvOp: case ParOp: case PriOp: case SignOp: case StppOp: case StpvOp: case StvpOp: case StvvOp: case SubvvOp: case SubpvOp: case SubvpOp: case ZmulpvOp: case ZmulvpOp: break; // ------------------------------------------------- // nonlinear unary operators case AcosOp: case AsinOp: case AtanOp: case CosOp: case CoshOp: case ExpOp: case LogOp: case SinOp: case SinhOp: case SqrtOp: case TanOp: case TanhOp: # if CPPAD_USE_CPLUSPLUS_2011 case AcoshOp: case AsinhOp: case AtanhOp: case Expm1Op: case Log1pOp: # endif CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 ) forward_sparse_hessian_nonlinear_unary_op( arg[0], for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- case CSkipOp: // CSkipOp has a variable number of arguments and // reverse_next thinks it one has one argument. // We must inform reverse_next of this special case. play->forward_cskip(op, arg, i_op, i_var); break; // ------------------------------------------------- case CSumOp: // CSumOp has a variable number of arguments and // reverse_next thinks it one has one argument. // We must inform reverse_next of this special case. play->forward_csum(op, arg, i_op, i_var); break; // ------------------------------------------------- case DivvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) forward_sparse_hessian_div_op( arg, for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- case DivpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) forward_sparse_hessian_nonlinear_unary_op( arg[1], for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- case EndOp: CPPAD_ASSERT_NARG_NRES(op, 0, 0); more_operators = false; break; // ------------------------------------------------- case ErfOp: // arg[1] is always the parameter 0 // arg[2] is always the parameter 2 / sqrt(pi) CPPAD_ASSERT_NARG_NRES(op, 3, 5); forward_sparse_hessian_nonlinear_unary_op( arg[0], for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- // ------------------------------------------------- // logical comparision operators case EqpvOp: case EqvvOp: case LtpvOp: case LtvpOp: case LtvvOp: case LepvOp: case LevpOp: case LevvOp: case NepvOp: case NevvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 0); break; // ------------------------------------------------- case MulvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) forward_sparse_hessian_mul_op( arg, for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- case PowpvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3) forward_sparse_hessian_nonlinear_unary_op( arg[1], for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- case PowvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3) forward_sparse_hessian_nonlinear_unary_op( arg[0], for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- case PowvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 3) forward_sparse_hessian_pow_op( arg, for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- case UserOp: // start or end an atomic operation sequence flag = user_state == start_user; user_atom = play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( flag ) { user_x.resize( user_n ); // user_pack = user_atom->sparsity() == atomic_base::pack_sparsity_enum; user_bool = user_atom->sparsity() == atomic_base::bool_sparsity_enum; user_set = user_atom->sparsity() == atomic_base::set_sparsity_enum; CPPAD_ASSERT_UNKNOWN( user_pack || user_bool || user_set ); user_ix.resize(user_n); user_vx.resize(user_n); user_r.resize(user_n); user_s.resize(user_m); // simpler to initialize sparsity patterns as empty for(i = 0; i < user_m; i++) user_s[i] = false; for(i = 0; i < user_n; i++) user_r[i] = false; if( user_pack ) { pack_h.resize(user_n * user_n); for(i = 0; i < user_n; i++) { for(j = 0; j < user_n; j++) pack_h[ i * user_n + j] = false; } } if( user_bool ) { bool_h.resize(user_n * user_n); for(i = 0; i < user_n; i++) { for(j = 0; j < user_n; j++) bool_h[ i * user_n + j] = false; } } if( user_set ) { set_h.resize(user_n); for(i = 0; i < user_n; i++) set_h[i].clear(); } } else { // call users function for this operation user_atom->set_old(user_old); if( user_pack ) { user_ok = user_atom->for_sparse_hes( user_vx, user_r, user_s, pack_h, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_hes( user_vx, user_r, user_s, pack_h ); } if( user_bool ) { user_ok = user_atom->for_sparse_hes( user_vx, user_r, user_s, bool_h, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_hes( user_vx, user_r, user_s, bool_h ); } if( user_set ) { user_ok = user_atom->for_sparse_hes( user_vx, user_r, user_s, set_h, user_x ); if( ! user_ok ) user_ok = user_atom->for_sparse_hes( user_vx, user_r, user_s, set_h ); } if( ! user_ok ) { std::string msg = user_atom->afun_name() + ": atomic_base.for_sparse_hes: returned false\n"; if( user_pack ) msg += "sparsity = pack_sparsity_enum"; if( user_bool ) msg += "sparsity = bool_sparsity_enum"; if( user_set ) msg += "sparsity = set_sparsity_enum"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } for(i = 0; i < user_n; i++) for(j = 0; j < user_n; j++) { if( user_ix[i] > 0 && user_ix[j] > 0 ) { flag = false; if( user_pack ) flag = pack_h[i * user_n + j]; if( user_bool ) flag = bool_h[i * user_n + j]; if( user_set ) flag = set_h[i].find(j) != set_h[i].end(); if( flag ) { size_t i_x = user_ix[i]; size_t j_x = user_ix[j]; { typename Vector_set::const_iterator itr_i(for_jac_sparse, i_x); size_t ix = *itr_i; while( ix < for_jac_sparse.end() ) { for_hes_sparse.binary_union( ix, ix, j_x, for_jac_sparse ); ix = *(++itr_i); } typename Vector_set::const_iterator itr_j(for_jac_sparse, j_x); size_t jx = *itr_j; while( jx < for_jac_sparse.end() ) { for_hes_sparse.binary_union( jx, jx, i_x, for_jac_sparse ); jx = *(++itr_j); } } } } } } break; case UsrapOp: // parameter argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); user_ix[user_j] = 0; user_vx[user_j] = false; // // parameters as integers user_x[user_j] = parameter[arg[0]]; // play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsravOp: // variable argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); user_ix[user_j] = arg[0]; user_vx[user_j] = true; // variables as integers user_x[user_j] = CppAD::numeric_limits::quiet_NaN(); // { typename Vector_set::const_iterator itr_1(for_jac_sparse, arg[0]); i = *itr_1; if( i < for_jac_sparse.end() ) user_r[user_j] = true; } play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrpOp: // parameter result in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrvOp: // variable result in an atomic operation sequence if( rev_jac_sparse.is_element(i_var, 0) ) user_s[user_i] = true; play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; // ------------------------------------------------- case ZmulvvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 1) forward_sparse_hessian_mul_op( arg, for_jac_sparse, for_hes_sparse ); break; // ------------------------------------------------- default: CPPAD_ASSERT_UNKNOWN(0); } # if CPPAD_FOR_HES_SWEEP_TRACE if( include ) { for(i = 0; i < limit; i++) { zf_value[i] = false; for(j = 0; j < limit; j++) zh_value[i * limit + j] = false; } typename Vector_set::const_iterator itr_2(for_jac_sparse, i_var); j = *itr_2; while( j < limit ) { zf_value[j] = true; j = *(++itr_2); } for(i = 0; i < limit; i++) { typename Vector_set::const_iterator itr_3(for_hes_sparse, i); j = *itr_3; while( j < limit ) { zh_value[i * limit + j] = true; j = *(++itr_3); } } printOp( std::cout, play, i_op, i_var, op, arg ); // should also print RevJac[i_var], but printOpResult does not // yet allow for this if( NumRes(op) > 0 && op != BeginOp ) printOpResult( std::cout, 1, &zf_value, 1, &zh_value ); std::cout << std::endl; } } std::cout << std::endl; # else } # endif // value corresponding to EndOp CPPAD_ASSERT_UNKNOWN( i_var + 1 == play->num_var_rec() ); return; } } } // END_CPPAD_LOCAL_NAMESPACE // preprocessor symbols that are local to this file # undef CPPAD_FOR_HES_SWEEP_TRACE # endif cppad-20170000.3/cppad/local/print_op.hpp0000644000175200017650000000737313057470466017174 0ustar coincoin-web// $Id: print_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_PRINT_OP_HPP # define CPPAD_LOCAL_PRINT_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! Print operation for parameters; i.e., op = PriOp. The C++ source code corresponding to this operation is \verbatim f.Forward(0, x) PrintFor(before, var) PrintFor(pos, before, var, after) \endverbatim The PrintFor call puts the print operation on the tape and the print occurs during the zero order forward mode computation. \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param s_out the results are printed on this output stream. \param arg \a arg[0] & 1 \n If this is zero, \a pos is a parameter. Otherwise it is a variable. \n \a arg[0] & 2 \n If this is zero, \a var is a parameter. Otherwise it is a variable. \n \n \a arg[1] \n If \a pos is a parameter, parameter[arg[1]] is its value. Othwise taylor[ arg[1] * cap_order + 0 ] is the zero order Taylor coefficient for \a pos. \n \n \a arg[2] \n index of the text to be printed before \a var if \a pos is not a positive value. \n \n \a arg[3] \n If \a var is a parameter, parameter[arg[3]] is its value. Othwise taylor[ arg[3] * cap_order + 0 ] is the zero order Taylor coefficient for \a var. \n \n \a arg[4] \n index of the text to be printed after \a var if \a pos is not a positive value. \param num_text is the total number of text characters on the tape (only used for error checking). \param text \b Input: text[arg[1]] is the first character of the text that will be printed. All the characters from there to (but not including) the first '\\0' are printed. \param num_par is the total number of values in the \a parameter vector \param parameter Contains the value of parameters. \param cap_order number of colums in the matrix containing all the Taylor coefficients. \param taylor Contains the value of variables. \par Checked Assertions: \li NumArg(PriOp) == 5 \li NumRes(PriOp) == 0 \li text != CPPAD_NULL \li arg[1] < num_text \li if \a pos is a parameter, arg[1] < num_par \li if \a var is a parameter, arg[3] < num_par */ template inline void forward_pri_0( std::ostream& s_out , const addr_t* arg , size_t num_text , const char* text , size_t num_par , const Base* parameter , size_t cap_order , const Base* taylor ) { Base pos, var; const char* before; const char* after; CPPAD_ASSERT_NARG_NRES(PriOp, 5, 0); // pos if( arg[0] & 1 ) { pos = taylor[ arg[1] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); pos = parameter[ arg[1] ]; } // before CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_text ); before = text + arg[2]; // var if( arg[0] & 2 ) { var = taylor[ arg[3] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[3]) < num_par ); var = parameter[ arg[3] ]; } // after CPPAD_ASSERT_UNKNOWN( size_t(arg[4]) < num_text ); after = text + arg[4]; if( ! GreaterThanZero( pos ) ) s_out << before << var << after; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/set_get_in_parallel.hpp0000644000175200017650000000424213057470466021326 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_SET_GET_IN_PARALLEL_HPP # define CPPAD_LOCAL_SET_GET_IN_PARALLEL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file set_get_in_parallel.hpp File used to set and get user in_parallel routine. */ /*! Set and call the routine that determine if we are in parallel execution mode. \return value retuned by most recent setting for in_parallel_new. If set is true, or the most recent setting is CPPAD_NULL (its initial value), the return value is false. Otherwise the function corresponding to the most recent setting is called and its value returned by set_get_in_parallel. \param in_parallel_new [in] If set is false, in_parallel_new it is not used. Otherwise, the current value of in_parallel_new becomes the most recent setting for in_parallel_user. \param set If set is true, then parallel_new is becomes the most recent setting for this set_get_in_parallel. In this case, it is assumed that we are currently in sequential execution mode. */ static bool set_get_in_parallel( bool (*in_parallel_new)(void) , bool set = false ) { static bool (*in_parallel_user)(void) = CPPAD_NULL; if( set ) { in_parallel_user = in_parallel_new; // Doing a raw assert in this case because set_get_in_parallel is used // by ErrorHandler and hence cannot use ErrorHandler. // CPPAD_ASSERT_UNKNOWN( in_parallel_user() == false ) assert(in_parallel_user == CPPAD_NULL || in_parallel_user() == false); return false; } // if( in_parallel_user == CPPAD_NULL ) return false; // return in_parallel_user(); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/sinh_op.hpp0000644000175200017650000001451013057470466016770 0ustar coincoin-web// $Id: sinh_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_SINH_OP_HPP # define CPPAD_LOCAL_SINH_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sinh_op.hpp Forward and reverse mode calculations for z = sinh(x). */ /*! Compute forward mode Taylor coefficient for result of op = SinhOp. The C++ source code corresponding to this operation is \verbatim z = sinh(x) \endverbatim The auxillary result is \verbatim y = cosh(x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_sinh_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SinhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SinhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* s = taylor + i_z * cap_order; Base* c = s - cap_order; // rest of this routine is identical for the following cases: // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op // (except that there is a sign difference for hyperbolic case). size_t k; if( p == 0 ) { s[0] = sinh( x[0] ); c[0] = cosh( x[0] ); p++; } for(size_t j = p; j <= q; j++) { s[j] = Base(0); c[j] = Base(0); for(k = 1; k <= j; k++) { s[j] += Base(k) * x[k] * c[j-k]; c[j] += Base(k) * x[k] * s[j-k]; } s[j] /= Base(j); c[j] /= Base(j); } } /*! Compute forward mode Taylor coefficient for result of op = SinhOp. The C++ source code corresponding to this operation is \verbatim z = sinh(x) \endverbatim The auxillary result is \verbatim y = cosh(x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_sinh_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SinhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SinhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* s = taylor + i_z * num_taylor_per_var; Base* c = s - num_taylor_per_var; // rest of this routine is identical for the following cases: // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op // (except that there is a sign difference for the hyperbolic case). size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { s[m+ell] = Base(q) * x[m + ell] * c[0]; c[m+ell] = Base(q) * x[m + ell] * s[0]; for(size_t k = 1; k < q; k++) { s[m+ell] += Base(k) * x[(k-1)*r+1+ell] * c[(q-k-1)*r+1+ell]; c[m+ell] += Base(k) * x[(k-1)*r+1+ell] * s[(q-k-1)*r+1+ell]; } s[m+ell] /= Base(q); c[m+ell] /= Base(q); } } /*! Compute zero order forward mode Taylor coefficient for result of op = SinhOp. The C++ source code corresponding to this operation is \verbatim z = sinh(x) \endverbatim The auxillary result is \verbatim y = cosh(x) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_sinh_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SinhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SinhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* s = taylor + i_z * cap_order; // called z in documentation Base* c = s - cap_order; // called y in documentation s[0] = sinh( x[0] ); c[0] = cosh( x[0] ); } /*! Compute reverse mode partial derivatives for result of op = SinhOp. The C++ source code corresponding to this operation is \verbatim z = sinh(x) \endverbatim The auxillary result is \verbatim y = cosh(x) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_sinh_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SinhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SinhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* s = taylor + i_z * cap_order; // called z in doc Base* ps = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* c = s - cap_order; // called y in documentation Base* pc = ps - nc_partial; // rest of this routine is identical for the following cases: // reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op. size_t j = d; size_t k; while(j) { ps[j] /= Base(j); pc[j] /= Base(j); for(k = 1; k <= j; k++) { px[k] += Base(k) * azmul(ps[j], c[j-k]); px[k] += Base(k) * azmul(pc[j], s[j-k]); ps[j-k] += Base(k) * azmul(pc[j], x[k]); pc[j-k] += Base(k) * azmul(ps[j], x[k]); } --j; } px[0] += azmul(ps[0], c[0]); px[0] += azmul(pc[0], s[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/sparse_binary_op.hpp0000644000175200017650000003454113057470466020676 0ustar coincoin-web// $Id: sparse_binary_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_SPARSE_BINARY_OP_HPP # define CPPAD_LOCAL_SPARSE_BINARY_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sparse_binary_op.hpp Forward and reverse mode sparsity patterns for binary operators. */ /*! Forward mode Jacobian sparsity pattern for all binary operators. The C++ source code corresponding to a binary operation has the form \verbatim z = fun(x, y) \endverbatim where fun is a C++ binary function and both x and y are variables, or it has the form \verbatim z = x op y \endverbatim where op is a C++ binary unary operator and both x and y are variables. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e., z. \param arg \a arg[0] variable index corresponding to the left operand for this operator; i.e., x. \n \n arg[1] variable index corresponding to the right operand for this operator; i.e., y. \param sparsity \b Input: The set with index \a arg[0] in \a sparsity is the sparsity bit pattern for x. This identifies which of the independent variables the variable x depends on. \n \n \b Input: The set with index \a arg[1] in \a sparsity is the sparsity bit pattern for y. This identifies which of the independent variables the variable y depends on. \n \n \b Output: The set with index \a i_z in \a sparsity is the sparsity bit pattern for z. This identifies which of the independent variables the variable z depends on. \par Checked Assertions: \li \a arg[0] < \a i_z \li \a arg[1] < \a i_z */ template inline void forward_sparse_jacobian_binary_op( size_t i_z , const addr_t* arg , Vector_set& sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < i_z ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < i_z ); sparsity.binary_union(i_z, arg[0], arg[1], sparsity); return; } /*! Reverse mode Jacobian sparsity pattern for all binary operators. The C++ source code corresponding to a unary operation has the form \verbatim z = fun(x, y) \endverbatim where fun is a C++ unary function and x and y are variables, or it has the form \verbatim z = x op y \endverbatim where op is a C++ bianry operator and x and y are variables. This routine is given the sparsity patterns for a function G(z, y, x, ... ) and it uses them to compute the sparsity patterns for \verbatim H( y, x, w , u , ... ) = G[ z(x,y) , y , x , w , u , ... ] \endverbatim \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z variable index corresponding to the result for this operation; i.e., z. \param arg \a arg[0] variable index corresponding to the left operand for this operator; i.e., x. \n \n arg[1] variable index corresponding to the right operand for this operator; i.e., y. \param sparsity The set with index \a i_z in \a sparsity is the sparsity pattern for z corresponding ot the function G. \n \n The set with index \a arg[0] in \a sparsity is the sparsity pattern for x. On input, it corresponds to the function G, and on output it corresponds to H. \n \n The set with index \a arg[1] in \a sparsity is the sparsity pattern for y. On input, it corresponds to the function G, and on output it corresponds to H. \n \n \par Checked Assertions: \li \a arg[0] < \a i_z \li \a arg[1] < \a i_z */ template inline void reverse_sparse_jacobian_binary_op( size_t i_z , const addr_t* arg , Vector_set& sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < i_z ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < i_z ); sparsity.binary_union(arg[0], arg[0], i_z, sparsity); sparsity.binary_union(arg[1], arg[1], i_z, sparsity); return; } // --------------------------------------------------------------------------- /*! Reverse mode Hessian sparsity pattern for add and subtract operators. The C++ source code corresponding to a unary operation has the form \verbatim z = x op y \endverbatim where op is + or - and x, y are variables. \copydetails reverse_sparse_hessian_binary_op */ template inline void reverse_sparse_hessian_addsub_op( size_t i_z , const addr_t* arg , bool* jac_reverse , const Vector_set& for_jac_sparsity , Vector_set& rev_hes_sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < i_z ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < i_z ); rev_hes_sparsity.binary_union(arg[0], arg[0], i_z, rev_hes_sparsity); rev_hes_sparsity.binary_union(arg[1], arg[1], i_z, rev_hes_sparsity); jac_reverse[arg[0]] |= jac_reverse[i_z]; jac_reverse[arg[1]] |= jac_reverse[i_z]; return; } /*! Reverse mode Hessian sparsity pattern for multiplication operator. The C++ source code corresponding to a unary operation has the form \verbatim z = x * y \endverbatim where x and y are variables. \copydetails reverse_sparse_hessian_binary_op */ template inline void reverse_sparse_hessian_mul_op( size_t i_z , const addr_t* arg , bool* jac_reverse , const Vector_set& for_jac_sparsity , Vector_set& rev_hes_sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < i_z ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < i_z ); rev_hes_sparsity.binary_union(arg[0], arg[0], i_z, rev_hes_sparsity); rev_hes_sparsity.binary_union(arg[1], arg[1], i_z, rev_hes_sparsity); if( jac_reverse[i_z] ) { rev_hes_sparsity.binary_union( arg[0], arg[0], arg[1], for_jac_sparsity); rev_hes_sparsity.binary_union( arg[1], arg[1], arg[0], for_jac_sparsity); } jac_reverse[arg[0]] |= jac_reverse[i_z]; jac_reverse[arg[1]] |= jac_reverse[i_z]; return; } /*! Reverse mode Hessian sparsity pattern for division operator. The C++ source code corresponding to a unary operation has the form \verbatim z = x / y \endverbatim where x and y are variables. \copydetails reverse_sparse_hessian_binary_op */ template inline void reverse_sparse_hessian_div_op( size_t i_z , const addr_t* arg , bool* jac_reverse , const Vector_set& for_jac_sparsity , Vector_set& rev_hes_sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < i_z ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < i_z ); rev_hes_sparsity.binary_union(arg[0], arg[0], i_z, rev_hes_sparsity); rev_hes_sparsity.binary_union(arg[1], arg[1], i_z, rev_hes_sparsity); if( jac_reverse[i_z] ) { rev_hes_sparsity.binary_union( arg[0], arg[0], arg[1], for_jac_sparsity); rev_hes_sparsity.binary_union( arg[1], arg[1], arg[0], for_jac_sparsity); rev_hes_sparsity.binary_union( arg[1], arg[1], arg[1], for_jac_sparsity); } jac_reverse[arg[0]] |= jac_reverse[i_z]; jac_reverse[arg[1]] |= jac_reverse[i_z]; return; } /*! Reverse mode Hessian sparsity pattern for power function. The C++ source code corresponding to a unary operation has the form \verbatim z = pow(x, y) \endverbatim where x and y are variables. \copydetails reverse_sparse_hessian_binary_op */ template inline void reverse_sparse_hessian_pow_op( size_t i_z , const addr_t* arg , bool* jac_reverse , const Vector_set& for_jac_sparsity , Vector_set& rev_hes_sparsity ) { // check assumptions CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < i_z ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < i_z ); rev_hes_sparsity.binary_union(arg[0], arg[0], i_z, rev_hes_sparsity); rev_hes_sparsity.binary_union(arg[1], arg[1], i_z, rev_hes_sparsity); if( jac_reverse[i_z] ) { rev_hes_sparsity.binary_union( arg[0], arg[0], arg[0], for_jac_sparsity); rev_hes_sparsity.binary_union( arg[0], arg[0], arg[1], for_jac_sparsity); rev_hes_sparsity.binary_union( arg[1], arg[1], arg[0], for_jac_sparsity); rev_hes_sparsity.binary_union( arg[1], arg[1], arg[1], for_jac_sparsity); } // I cannot think of a case where this is necessary, but it including // it makes it like the other cases. jac_reverse[arg[0]] |= jac_reverse[i_z]; jac_reverse[arg[1]] |= jac_reverse[i_z]; return; } // --------------------------------------------------------------------------- /*! Forward mode Hessian sparsity pattern for multiplication operator. The C++ source code corresponding to this operation is \verbatim w(x) = v0(x) * v1(x) \endverbatim \param arg is the index of the argument vector for the multiplication operation; i.e., arg[0], arg[1] are the left and right operands. \param for_jac_sparsity for_jac_sparsity(arg[0]) constains the Jacobian sparsity for v0(x), for_jac_sparsity(arg[1]) constains the Jacobian sparsity for v1(x). \param for_hes_sparsity On input, for_hes_sparsity includes the Hessian sparsity for v0(x) and v1(x); i.e., the sparsity can be a super set. Upon return it includes the Hessian sparsity for w(x) */ template inline void forward_sparse_hessian_mul_op( const addr_t* arg , const Vector_set& for_jac_sparsity , Vector_set& for_hes_sparsity ) { // -------------------------------------------------- // set of independent variables that v0 depends on typename Vector_set::const_iterator itr_0(for_jac_sparsity, arg[0]); // loop over dependent variables with non-zero partial size_t i_x = *itr_0; while( i_x < for_jac_sparsity.end() ) { // N(i_x) = N(i_x) union L(v1) for_hes_sparsity.binary_union(i_x, i_x, arg[1], for_jac_sparsity); i_x = *(++itr_0); } // -------------------------------------------------- // set of independent variables that v1 depends on typename Vector_set::const_iterator itr_1(for_jac_sparsity, arg[1]); // loop over dependent variables with non-zero partial i_x = *itr_1; while( i_x < for_jac_sparsity.end() ) { // N(i_x) = N(i_x) union L(v0) for_hes_sparsity.binary_union(i_x, i_x, arg[0], for_jac_sparsity); i_x = *(++itr_1); } return; } /*! Forward mode Hessian sparsity pattern for division operator. The C++ source code corresponding to this operation is \verbatim w(x) = v0(x) / v1(x) \endverbatim \param arg is the index of the argument vector for the division operation; i.e., arg[0], arg[1] are the left and right operands. \param for_jac_sparsity for_jac_sparsity(arg[0]) constains the Jacobian sparsity for v0(x), for_jac_sparsity(arg[1]) constains the Jacobian sparsity for v1(x). \param for_hes_sparsity On input, for_hes_sparsity includes the Hessian sparsity for v0(x) and v1(x); i.e., the sparsity can be a super set. Upon return it includes the Hessian sparsity for w(x) */ template inline void forward_sparse_hessian_div_op( const addr_t* arg , const Vector_set& for_jac_sparsity , Vector_set& for_hes_sparsity ) { // -------------------------------------------------- // set of independent variables that v0 depends on typename Vector_set::const_iterator itr_0(for_jac_sparsity, arg[0]); // loop over dependent variables with non-zero partial size_t i_x = *itr_0; while( i_x < for_jac_sparsity.end() ) { // N(i_x) = N(i_x) union L(v1) for_hes_sparsity.binary_union(i_x, i_x, arg[1], for_jac_sparsity); i_x = *(++itr_0); } // -------------------------------------------------- // set of independent variables that v1 depends on typename Vector_set::const_iterator itr_1(for_jac_sparsity, arg[1]); // loop over dependent variables with non-zero partial i_x = *itr_1; while( i_x < for_jac_sparsity.end() ) { // N(i_x) = N(i_x) union L(v0) for_hes_sparsity.binary_union(i_x, i_x, arg[0], for_jac_sparsity); // N(i_x) = N(i_x) union L(v1) for_hes_sparsity.binary_union(i_x, i_x, arg[1], for_jac_sparsity); i_x = *(++itr_1); } return; } /*! Forward mode Hessian sparsity pattern for power operator. The C++ source code corresponding to this operation is \verbatim w(x) = pow( v0(x) , v1(x) ) \endverbatim \param arg is the index of the argument vector for the power operation; i.e., arg[0], arg[1] are the left and right operands. \param for_jac_sparsity for_jac_sparsity(arg[0]) constains the Jacobian sparsity for v0(x), for_jac_sparsity(arg[1]) constains the Jacobian sparsity for v1(x). \param for_hes_sparsity On input, for_hes_sparsity includes the Hessian sparsity for v0(x) and v1(x); i.e., the sparsity can be a super set. Upon return it includes the Hessian sparsity for w(x) */ template inline void forward_sparse_hessian_pow_op( const addr_t* arg , const Vector_set& for_jac_sparsity , Vector_set& for_hes_sparsity ) { // -------------------------------------------------- // set of independent variables that v0 depends on typename Vector_set::const_iterator itr_0(for_jac_sparsity, arg[0]); // loop over dependent variables with non-zero partial size_t i_x = *itr_0; while( i_x < for_jac_sparsity.end() ) { // N(i_x) = N(i_x) union L(v0) for_hes_sparsity.binary_union(i_x, i_x, arg[0], for_jac_sparsity); // N(i_x) = N(i_x) union L(v1) for_hes_sparsity.binary_union(i_x, i_x, arg[1], for_jac_sparsity); i_x = *(++itr_0); } // -------------------------------------------------- // set of independent variables that v1 depends on typename Vector_set::const_iterator itr_1(for_jac_sparsity, arg[1]); // loop over dependent variables with non-zero partial i_x = *itr_1; while( i_x < for_jac_sparsity.end() ) { // N(i_x) = N(i_x) union L(v0) for_hes_sparsity.binary_union(i_x, i_x, arg[0], for_jac_sparsity); // N(i_x) = N(i_x) union L(v1) for_hes_sparsity.binary_union(i_x, i_x, arg[1], for_jac_sparsity); i_x = *(++itr_1); } return; } // --------------------------------------------------------------------------- } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/discrete_op.hpp0000644000175200017650000000672213057470466017637 0ustar coincoin-web// $Id: discrete_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_DISCRETE_OP_HPP # define CPPAD_LOCAL_DISCRETE_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file discrete_op.hpp Forward mode for z = f(x) where f is piecewise constant. */ /*! forward mode Taylor coefficient for result of op = DisOp. The C++ source code corresponding to this operation is \verbatim z = f(x) \endverbatim where f is a piecewise constant function (and it's derivative is always calculated as zero). \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base . \param p is the lowest order Taylor coefficient that will be calculated. \param q is the highest order Taylor coefficient that will be calculated. \param r is the number of directions, for each order, that will be calculated (except for order zero wich only has one direction). \param i_z variable index corresponding to the result for this operation; i.e. the row index in \a taylor corresponding to z. \param arg \a arg[0] \n is the index, in the order of the discrete functions defined by the user, for this discrete function. \n \n \a arg[1] variable index corresponding to the argument for this operator; i.e. the row index in \a taylor corresponding to x. \param cap_order maximum number of orders that will fit in the taylor array. \par tpv We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable \param taylor \b Input: taylor [ arg[1] * tpv + 0 ] is the zero order Taylor coefficient corresponding to x. \n \b Output: if p == 0 taylor [ i_z * tpv + 0 ] is the zero order Taylor coefficient corresponding to z. For k = max(p, 1), ... , q, taylor [ i_z * tpv + (k-1)*r + 1 + ell ] is the k-th order Taylor coefficient corresponding to z (which is zero). \par Checked Assertions where op is the unary operator with one result: \li NumArg(op) == 2 \li NumRes(op) == 1 \li q < cap_order \li 0 < r */ template inline void forward_dis_op( size_t p , size_t q , size_t r , size_t i_z , const addr_t* arg , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DisOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DisOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( 0 < r ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + arg[1] * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; if( p == 0 ) { z[0] = discrete::eval(arg[0], x[0]); p++; } for(size_t ell = 0; ell < r; ell++) for(size_t k = p; k <= q; k++) z[ (k-1) * r + 1 + ell ] = Base(0); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/asinh_op.hpp0000644000175200017650000001532513057470466017136 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_ASINH_OP_HPP # define CPPAD_LOCAL_ASINH_OP_HPP # if CPPAD_USE_CPLUSPLUS_2011 /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file asinh_op.hpp Forward and reverse mode calculations for z = asinh(x). */ /*! Compute forward mode Taylor coefficient for result of op = AsinhOp. The C++ source code corresponding to this operation is \verbatim z = asinh(x) \endverbatim The auxillary result is \verbatim y = sqrt(1 + x * x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_asinh_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AsinhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AsinhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation size_t k; Base uj; if( p == 0 ) { z[0] = asinh( x[0] ); uj = Base(1) + x[0] * x[0]; b[0] = sqrt( uj ); p++; } for(size_t j = p; j <= q; j++) { uj = Base(0); for(k = 0; k <= j; k++) uj += x[k] * x[j-k]; b[j] = Base(0); z[j] = Base(0); for(k = 1; k < j; k++) { b[j] -= Base(k) * b[k] * b[j-k]; z[j] -= Base(k) * z[k] * b[j-k]; } b[j] /= Base(j); z[j] /= Base(j); // b[j] += uj / Base(2); z[j] += x[j]; // b[j] /= b[0]; z[j] /= b[0]; } } /*! Multiple directions forward mode Taylor coefficient for op = AsinhOp. The C++ source code corresponding to this operation is \verbatim z = asinh(x) \endverbatim The auxillary result is \verbatim y = sqrt(1 + x * x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_asinh_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; Base* b = z - num_taylor_per_var; // called y in documentation size_t k, ell; size_t m = (q-1) * r + 1; for(ell = 0; ell < r; ell ++) { Base uq = 2.0 * x[m + ell] * x[0]; for(k = 1; k < q; k++) uq += x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell]; b[m+ell] = Base(0); z[m+ell] = Base(0); for(k = 1; k < q; k++) { b[m+ell] += Base(k) * b[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; z[m+ell] += Base(k) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; } b[m+ell] = ( uq / Base(2) - b[m+ell] / Base(q) ) / b[0]; z[m+ell] = ( x[m+ell] - z[m+ell] / Base(q) ) / b[0]; } } /*! Compute zero order forward mode Taylor coefficient for result of op = AsinhOp. The C++ source code corresponding to this operation is \verbatim z = asinh(x) \endverbatim The auxillary result is \verbatim y = sqrt( 1 + x * x ) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_asinh_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AsinhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AsinhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation z[0] = asinh( x[0] ); b[0] = sqrt( Base(1) + x[0] * x[0] ); } /*! Compute reverse mode partial derivatives for result of op = AsinhOp. The C++ source code corresponding to this operation is \verbatim z = asinh(x) \endverbatim The auxillary result is \verbatim y = sqrt( 1 + x * x ) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_asinh_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AsinhOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AsinhOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* b = z - cap_order; // called y in documentation Base* pb = pz - nc_partial; Base inv_b0 = Base(1) / b[0]; // number of indices to access size_t j = d; size_t k; while(j) { // scale partials w.r.t b[j] by 1 / b[0] pb[j] = azmul(pb[j], inv_b0); // scale partials w.r.t z[j] by 1 / b[0] pz[j] = azmul(pz[j], inv_b0); // update partials w.r.t b^0 pb[0] -= azmul(pz[j], z[j]) + azmul(pb[j], b[j]); // update partial w.r.t. x^0 px[0] += azmul(pb[j], x[j]); // update partial w.r.t. x^j px[j] += pz[j] + azmul(pb[j], x[0]); // further scale partial w.r.t. z[j] by 1 / j pz[j] /= Base(j); for(k = 1; k < j; k++) { // update partials w.r.t b^(j-k) pb[j-k] -= Base(k) * azmul(pz[j], z[k]) + azmul(pb[j], b[k]); // update partials w.r.t. x^k px[k] += azmul(pb[j], x[j-k]); // update partials w.r.t. z^k pz[k] -= Base(k) * azmul(pz[j], b[j-k]); } --j; } // j == 0 case px[0] += azmul(pz[0] + azmul(pb[0], x[0]), inv_b0); } } } // END_CPPAD_LOCAL_NAMESPACE # endif # endif cppad-20170000.3/cppad/local/pod_vector.hpp0000644000175200017650000002317213057470466017501 0ustar coincoin-web// $Id: pod_vector.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_POD_VECTOR_HPP # define CPPAD_LOCAL_POD_VECTOR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # if CPPAD_CSTDINT_HAS_8_TO_64 # include # endif # include # include # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file pod_vector.hpp File used to define pod_vector class */ /* A list of which Types pod_vector consideres to be plain old data */ /// default value is false template inline bool is_pod(void) { return false; } /// system pod types so far: template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } # if CPPAD_CSTDINT_HAS_8_TO_64 template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } // template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } # else // CPPAD_CSTDINT_HAS_8_TO_64 template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } // template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } template <> inline bool is_pod(void) { return true; } # if CPPAD_SIZE_T_NOT_UNSIGNED_INT template <> inline bool is_pod(void) { return true; } # endif # endif // CPPAD_CSTDINT_HAS_8_TO_64 /// CppAD pod types so far: template <> inline bool is_pod(void) { return true; } // --------------------------------------------------------------------------- /*! A vector class with Type element that does not use element constructors or destructors when Type is Plain Old Data (pod). */ template class pod_vector { private: /// maximum number of elements that should ever be in this vector size_t max_length_; /// number of elements currently in this vector size_t length_; /// maximum number of Type elements current allocation can hold size_t capacity_; /// pointer to the first type elements /// (not defined and should not be used when capacity_ = 0) Type *data_; /// do not use the copy constructor explicit pod_vector(const pod_vector& ) { CPPAD_ASSERT_UNKNOWN(false); } public: /// Constructors set capacity, length, and data to zero. /// /// \param max_length /// value for maximum number of elements in this vector. inline pod_vector( size_t max_length = std::numeric_limits::max() ) : max_length_(max_length), length_(0), capacity_(0), data_(CPPAD_NULL) { } // ---------------------------------------------------------------------- /// Destructor: returns allocated memory to \c thread_alloc; /// see \c extend. If this is not plain old data, /// the destructor for each element is called. ~pod_vector(void) { if( capacity_ > 0 ) { void* v_ptr = reinterpret_cast( data_ ); if( ! is_pod() ) { // call destructor for each element size_t i; for(i = 0; i < capacity_; i++) (data_ + i)->~Type(); } thread_alloc::return_memory(v_ptr); } } // ---------------------------------------------------------------------- /// current number of elements in this vector. inline size_t size(void) const { return length_; } /// current capacity (amount of allocated storage) for this vector. inline size_t capacity(void) const { return capacity_; } /// current data pointer, no longer valid after any of the following: /// extend, erase, operator=, and ~pod_vector. /// Take extreem care when using this function. inline Type* data(void) { return data_; } /// const version of \c data pointer inline const Type* data(void) const { return data_; } // ---------------------------------------------------------------------- /*! Increase the number of elements the end of this vector. \param n is the number of elements to add to end of this vector. \return is the number of elements in the vector before \c extend was extended. - If \c Type is plain old data, new elements are not initialized; i.e., their constructor is not called. Otherwise, the constructor is called for each new element. - This is the only routine that allocates memory for \c pod_vector. and it uses thread_alloc for this allocation, hence this determines which thread corresponds to this vector (when in parallel mode). - If the resulting length of the vector would be more than \c max_length_, and \c NDEBUG is not defined, a CPPAD_ASSERT is generated. */ inline size_t extend(size_t n) { size_t old_length = length_; length_ += n; CPPAD_ASSERT_KNOWN( length_ <= max_length_ , "pod_vector.hpp: attempt to create to large a vector.\n" "If Type is CPPAD_TYPE_ADDR_TYPE, tape is too long for Type." ); // check if we can use current memory if( capacity_ >= length_ ) return old_length; // save more old information size_t old_capacity = capacity_; Type* old_data = data_; // get new memory and set capacity size_t length_bytes = length_ * sizeof(Type); size_t capacity_bytes; void* v_ptr = thread_alloc::get_memory(length_bytes, capacity_bytes); capacity_ = capacity_bytes / sizeof(Type); data_ = reinterpret_cast(v_ptr); CPPAD_ASSERT_UNKNOWN( length_ <= capacity_ ); size_t i; if( ! is_pod() ) { // call constructor for each new element for(i = 0; i < capacity_; i++) new(data_ + i) Type(); } // copy old data to new data for(i = 0; i < old_length; i++) data_[i] = old_data[i]; // return old memory to available pool if( old_capacity > 0 ) { v_ptr = reinterpret_cast( old_data ); if( ! is_pod() ) { for(i = 0; i < old_capacity; i++) (old_data + i)->~Type(); } thread_alloc::return_memory(v_ptr); } // return value for extend(n) is the old length return old_length; } // ---------------------------------------------------------------------- /// non-constant element access; i.e., we can change this element value Type& operator[]( /// element index, must be less than length size_t i ) { CPPAD_ASSERT_UNKNOWN( i < length_ ); return data_[i]; } // ---------------------------------------------------------------------- /// constant element access; i.e., we cannot change this element value const Type& operator[]( /// element index, must be less than length size_t i ) const { CPPAD_ASSERT_UNKNOWN( i < length_ ); return data_[i]; } // ---------------------------------------------------------------------- /*! Remove all the elements from this vector but leave the capacity and data pointer as is. */ void erase(void) { length_ = 0; return; } // ---------------------------------------------------------------------- /*! Remove all the elements from this vector and delete its memory. */ void free(void) { if( capacity_ > 0 ) { void* v_ptr = reinterpret_cast( data_ ); if( ! is_pod() ) { // call destructor for each element size_t i; for(i = 0; i < capacity_; i++) (data_ + i)->~Type(); } thread_alloc::return_memory(v_ptr); } data_ = CPPAD_NULL; capacity_ = 0; length_ = 0; } /// vector assignment operator /// If the resulting length of the vector would be more than /// \c max_length_, and \c NDEBUG is not defined, /// a CPPAD_ASSERT is generated. void operator=( /// right hand size of the assingment operation const pod_vector& x ) { size_t i; if( x.length_ <= capacity_ ) { // use existing allocation for this vector length_ = x.length_; CPPAD_ASSERT_KNOWN( length_ <= max_length_ , "pod_vector.hpp: attempt to create to large a vector.\n" "If Type is CPPAD_TYPE_ADDR_TYPE, tape long for Type." ); } else { // free old memory and get new memory of sufficient length if( capacity_ > 0 ) { void* v_ptr = reinterpret_cast( data_ ); if( ! is_pod() ) { // call destructor for each element for(i = 0; i < capacity_; i++) (data_ + i)->~Type(); } thread_alloc::return_memory(v_ptr); } length_ = capacity_ = 0; extend( x.length_ ); } CPPAD_ASSERT_UNKNOWN( length_ == x.length_ ); for(i = 0; i < length_; i++) { data_[i] = x.data_[i]; } } /*! Swap all properties of this vector with another. \param other is the other vector that we are swapping this vector with. */ void swap(pod_vector& other) { std::swap(capacity_, other.capacity_); std::swap(length_, other.length_); std::swap(data_, other.data_); } }; } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/cskip_op.hpp0000644000175200017650000001242013057470466017136 0ustar coincoin-web// $Id: cskip_op.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_CSKIP_OP_HPP # define CPPAD_LOCAL_CSKIP_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file cskip_op.hpp Zero order forward mode set which operations to skip. */ /*! Zero order forward mode execution of op = CSkipOp. \par Parameters and Variables The terms parameter and variable depend on if we are referring to its AD or Base value. We use Base parameter and Base variable to refer to the correspond Base value. We use AD parameter and AD variable to refer to the correspond AD value. \tparam Base base type for the operator; i.e., this operation was recorded using AD and computations by this routine are done using type Base. \param i_z variable index corresponding to the result of the previous operation. This is used for error checking. To be specific, the left and right operands for the CExpOp operation must have indexes less than or equal this value. \param arg [in] \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, left is an AD parameter. Otherwise it is an AD variable. \n \n \a arg[1] & 2 \n If this is zero, right is an AD parameter. Otherwise it is an AD variable. \n \a arg[2] is the index corresponding to left in comparision. \n \a arg[3] is the index corresponding to right in comparision. \n \a arg[4] is the number of operations to skip if the comparision result is true. \n \a arg[5] is the number of operations to skip if the comparision result is false. \n arg[5+i] for i = 1 , ... , arg[4] are the operations to skip if the comparision result is true and both left and right are identically Base parameters. \n arg[5+arg[4]+i] for i = 1 , ... , arg[5] are the operations to skip if the comparision result is false and both left and right are identically Base parameters. \param num_par [in] is the total number of values in the vector parameter. \param parameter [in] If left is an AD parameter, parameter [ arg[2] ] is its value. If right is an AD parameter, parameter [ arg[3] ] is its value. \param cap_order [in] number of columns in the matrix containing the Taylor coefficients. \param taylor [in] If left is an AD variable, taylor [ arg[2] * cap_order + 0 ] is the zeroth order Taylor coefficient corresponding to left. If right is an AD variable, taylor [ arg[3] * cap_order + 0 ] is the zeroth order Taylor coefficient corresponding to right. \param cskip_op [in,out] is vector specifying which operations are at this point are know to be unecessary and can be skipped. This is both an input and an output. */ template inline void forward_cskip_op_0( size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order , Base* taylor , bool* cskip_op ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < size_t(CompareNe) ); CPPAD_ASSERT_UNKNOWN( arg[1] != 0 ); Base left, right; if( arg[1] & 1 ) { // If variable arg[2] <= i_z, it has already been computed, // but it will be skipped for higher orders. left = taylor[ arg[2] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); left = parameter[ arg[2] ]; } if( arg[1] & 2 ) { // If variable arg[3] <= i_z, it has already been computed, // but it will be skipped for higher orders. right = taylor[ arg[3] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[3]) < num_par ); right = parameter[ arg[3] ]; } bool ok_to_skip = IdenticalPar(left) & IdenticalPar(right); if( ! ok_to_skip ) return; // initialize to avoid compiler warning bool true_case = false; Base diff = left - right; switch( CompareOp( arg[0] ) ) { case CompareLt: true_case = LessThanZero(diff); break; case CompareLe: true_case = LessThanOrZero(diff); break; case CompareEq: true_case = IdenticalZero(diff); break; case CompareGe: true_case = GreaterThanOrZero(diff); break; case CompareGt: true_case = GreaterThanZero(diff); break; case CompareNe: true_case = ! IdenticalZero(diff); break; default: CPPAD_ASSERT_UNKNOWN(false); } if( true_case ) { for(size_t i = 0; i < size_t(arg[4]); i++) cskip_op[ arg[6+i] ] = true; } else { for(size_t i = 0; i < size_t(arg[5]); i++) cskip_op[ arg[6+arg[4]+i] ] = true; } return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/op_code.hpp0000644000175200017650000006514113057470466016747 0ustar coincoin-web// $Id: op_code.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_OP_CODE_HPP # define CPPAD_LOCAL_OP_CODE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file op_code.hpp Defines the OpCode enum type and functions related to it. */ /*! Type used to distinguish different AD< \a Base > atomic operations. Each of the operators ends with the characters Op. Ignoring the Op at the end, the operators appear in alphabetical order. Binary operation where both operands have type AD< \a Base > use the following convention for thier endings: \verbatim Ending Left-Operand Right-Operand pvOp parameter variable vpOp variable parameter vvOp variable variable \endverbatim For example, AddpvOp represents the addition operator where the left operand is a parameter and the right operand is a variable. */ // alphabetical order is checked by bin/check_op_code.sh enum OpCode { AbsOp, // abs(variable) AcosOp, // acos(variable) AcoshOp, // acosh(variable) AddpvOp, // parameter + variable AddvvOp, // variable + variable AsinOp, // asin(variable) AsinhOp, // asinh(variable) AtanOp, // atan(variable) AtanhOp, // atanh(variable) BeginOp, // used to mark the beginning of the tape CExpOp, // CondExpRel(left, right, trueCase, falseCase) // arg[0] = the Rel operator: Lt, Le, Eq, Ge, Gt, or Ne // arg[1] & 1 = is left a variable // arg[1] & 2 = is right a variable // arg[1] & 4 = is trueCase a variable // arg[1] & 8 = is falseCase a variable // arg[2] = index correspoding to left // arg[3] = index correspoding to right // arg[4] = index correspoding to trueCase // arg[5] = index correspoding to falseCase CosOp, // cos(variable) CoshOp, // cosh(variable) CSkipOp, // Conditional skip // arg[0] = the Rel operator: Lt, Le, Eq, Ge, Gt, or Ne // arg[1] & 1 = is left a variable // arg[1] & 2 = is right a variable // arg[2] = index correspoding to left // arg[3] = index correspoding to right // arg[4] = number of operations to skip if CExpOp comparision is true // arg[5] = number of operations to skip if CExpOp comparision is false // arg[6] -> arg[5+arg[4]] = skip operations if true // arg[6+arg[4]] -> arg[5+arg[4]+arg[5]] = skip operations if false // arg[6+arg[4]+arg[5]] = arg[4] + arg[5] CSumOp, // Cummulative summation // arg[0] = number of addition variables in summation // arg[1] = number of subtraction variables in summation // arg[2] = index of parameter that initializes summation // arg[3] -> arg[2+arg[0]] = index for positive variables // arg[3+arg[0]] -> arg[2+arg[0]+arg[1]] = index for minus variables // arg[3+arg[0]+arg[1]] = arg[0] + arg[1] DisOp, // discrete::eval(index, variable) DivpvOp, // parameter / variable DivvpOp, // variable / parameter DivvvOp, // variable / variable EndOp, // used to mark the end of the tape EqpvOp, // parameter == variable EqvvOp, // variable == variable ErfOp, // erf(variable) ExpOp, // exp(variable) Expm1Op, // expm1(variable) InvOp, // independent variable LdpOp, // z[parameter] LdvOp, // z[variable] LepvOp, // parameter <= variable LevpOp, // variable <= parameter LevvOp, // variable <= variable LogOp, // log(variable) Log1pOp, // log1p(variable) LtpvOp, // parameter < variable LtvpOp, // variable < parameter LtvvOp, // variable < variable MulpvOp, // parameter * variable MulvvOp, // variable * variable NepvOp, // parameter != variable NevvOp, // variable != variable ParOp, // parameter PowpvOp, // pow(parameter, variable) PowvpOp, // pow(variable, parameter) PowvvOp, // pow(variable, variable) PriOp, // PrintFor(text, parameter or variable, parameter or variable) SignOp, // sign(variable) SinOp, // sin(variable) SinhOp, // sinh(variable) SqrtOp, // sqrt(variable) StppOp, // z[parameter] = parameter StpvOp, // z[parameter] = variable StvpOp, // z[variable] = parameter StvvOp, // z[variable] = variable SubpvOp, // parameter - variable SubvpOp, // variable - parameter SubvvOp, // variable - variable TanOp, // tan(variable) TanhOp, // tan(variable) // user atomic operation codes UserOp, // start of a user atomic operaiton // arg[0] = index of the operation if atomic_base class // arg[1] = extra information passed trough by deprecated old atomic class // arg[2] = number of arguments to this atomic function // arg[3] = number of results for this atomic function UsrapOp, // this user atomic argument is a parameter UsravOp, // this user atomic argument is a variable UsrrpOp, // this user atomic result is a parameter UsrrvOp, // this user atomic result is a variable ZmulpvOp, // azmul(parameter, variable) ZmulvpOp, // azmul(variabe, parameter) ZmulvvOp, // azmul(variable, variable) NumberOp // number of operator codes (not an operator) }; // Note that bin/check_op_code.sh assumes the pattern '^\tNumberOp$' occurs // at the end of this list and only at the end of this list. /*! Number of arguments for a specified operator. \return Number of arguments corresponding to the specified operator. \param op Operator for which we are fetching the number of arugments. \par NumArgTable this table specifes the number of arguments stored for each occurance of the operator that is the i-th value in the OpCode enum type. For example, for the first three OpCode enum values we have \verbatim OpCode j NumArgTable[j] Meaning AbsOp 0 1 index of variable we are taking absolute value of AcosOp 1 1 index of variable we are taking acos of AcoshOp 2 1 index of variable we are taking acosh of \endverbatim Note that the meaning of the arguments depends on the operator. */ inline size_t NumArg( OpCode op) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; // agreement with OpCode is checked by bin/check_op_code.sh static const size_t NumArgTable[] = { 1, // AbsOp 1, // AcosOp 1, // AcoshOp 2, // AddpvOp 2, // AddvvOp 1, // AsinOp 1, // AsinhOp 1, // AtanOp 1, // AtanhOp 1, // BeginOp offset first real argument to have index 1 6, // CExpOp 1, // CosOp 1, // CoshOp 0, // CSkipOp (actually has a variable number of arguments, not zero) 0, // CSumOp (actually has a variable number of arguments, not zero) 2, // DisOp 2, // DivpvOp 2, // DivvpOp 2, // DivvvOp 0, // EndOp 2, // EqpvOp 2, // EqvvOp 3, // ErfOp 1, // ExpOp 1, // Expm1Op 0, // InvOp 3, // LdpOp 3, // LdvOp 2, // LepvOp 2, // LevpOp 2, // LevvOp 1, // LogOp 1, // Log1pOp 2, // LtpvOp 2, // LtvpOp 2, // LtvvOp 2, // MulpvOp 2, // MulvvOp 2, // NepvOp 2, // NevvOp 1, // ParOp 2, // PowpvOp 2, // PowvpOp 2, // PowvvOp 5, // PriOp 1, // SignOp 1, // SinOp 1, // SinhOp 1, // SqrtOp 3, // StppOp 3, // StpvOp 3, // StvpOp 3, // StvvOp 2, // SubpvOp 2, // SubvpOp 2, // SubvvOp 1, // TanOp 1, // TanhOp 4, // UserOp 1, // UsrapOp 1, // UsravOp 1, // UsrrpOp 0, // UsrrvOp 2, // ZmulpvOp 2, // ZmulvpOp 2, // ZmulvvOp 0 // NumberOp not used }; # ifndef NDEBUG // only do these checks once to save time static bool first = true; if( first ) { CPPAD_ASSERT_UNKNOWN( size_t(NumberOp) + 1 == sizeof(NumArgTable) / sizeof(NumArgTable[0]) ); CPPAD_ASSERT_UNKNOWN( size_t(NumberOp) <= std::numeric_limits::max() ); first = false; } // do this check every time CPPAD_ASSERT_UNKNOWN( size_t(op) < size_t(NumberOp) ); # endif return NumArgTable[op]; } /*! Number of variables resulting from the specified operation. \param op Operator for which we are fecching the number of results. \par NumResTable table specifes the number of varibles that result for each occurance of the operator that is the i-th value in the OpCode enum type. For example, for the first three OpCode enum values we have \verbatim OpCode j NumResTable[j] Meaning AbsOp 0 1 variable that is the result of the absolute value AcosOp 1 2 acos(x) and sqrt(1-x*x) are required for this op AcoshOp 2 2 acosh(x) and sqrt(x*x-1) are required for this op \endverbatim */ inline size_t NumRes(OpCode op) { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; // agreement with OpCode is checked by bin/check_op_code.sh static const size_t NumResTable[] = { 1, // AbsOp 2, // AcosOp 2, // AcoshOp 1, // AddpvOp 1, // AddvvOp 2, // AsinOp 2, // AsinhOp 2, // AtanOp 2, // AtanhOp 1, // BeginOp offsets first variable to have index one (not zero) 1, // CExpOp 2, // CosOp 2, // CoshOp 0, // CSkipOp 1, // CSumOp 1, // DisOp 1, // DivpvOp 1, // DivvpOp 1, // DivvvOp 0, // EndOp 0, // EqpvOp 0, // EqvvOp 5, // ErfOp 1, // ExpOp 1, // Expm1Op 1, // InvOp 1, // LdpOp 1, // LdvOp 0, // LepvOp 0, // LevpOp 0, // LevvOp 1, // LogOp 1, // Log1pOp 0, // LtpvOp 0, // LtvpOp 0, // LtvvOp 1, // MulpvOp 1, // MulvvOp 0, // NepvOp 0, // NevvOp 1, // ParOp 3, // PowpvOp 3, // PowvpOp 3, // PowvvOp 0, // PriOp 1, // SignOp 2, // SinOp 2, // SinhOp 1, // SqrtOp 0, // StppOp 0, // StpvOp 0, // StvpOp 0, // StvvOp 1, // SubpvOp 1, // SubvpOp 1, // SubvvOp 2, // TanOp 2, // TanhOp 0, // UserOp 0, // UsrapOp 0, // UsravOp 0, // UsrrpOp 1, // UsrrvOp 1, // ZmulpvOp 1, // ZmulvpOp 1, // ZmulvvOp 0 // NumberOp not used and avoids g++ 4.3.2 warn when pycppad builds }; // check ensuring conversion to size_t is as expected CPPAD_ASSERT_UNKNOWN( size_t(NumberOp) + 1 == sizeof(NumResTable) / sizeof(NumResTable[0]) ); // this test ensures that all indices are within the table CPPAD_ASSERT_UNKNOWN( size_t(op) < size_t(NumberOp) ); return NumResTable[op]; } /*! Fetch the name for a specified operation. \return name of the specified operation. \param op Operator for which we are fetching the name */ inline const char* OpName(OpCode op) { // agreement with OpCode is checked by bin/check_op_code.sh static const char *OpNameTable[] = { "Abs" , "Acos" , "Acosh" , "Addpv" , "Addvv" , "Asin" , "Asinh" , "Atan" , "Atanh" , "Begin" , "CExp" , "Cos" , "Cosh" , "CSkip" , "CSum" , "Dis" , "Divpv" , "Divvp" , "Divvv" , "End" , "Eqpv" , "Eqvv" , "Erf" , "Exp" , "Expm1" , "Inv" , "Ldp" , "Ldv" , "Lepv" , "Levp" , "Levv" , "Log" , "Log1p" , "Ltpv" , "Ltvp" , "Ltvv" , "Mulpv" , "Mulvv" , "Nepv" , "Nevv" , "Par" , "Powpv" , "Powvp" , "Powvv" , "Pri" , "Sign" , "Sin" , "Sinh" , "Sqrt" , "Stpp" , "Stpv" , "Stvp" , "Stvv" , "Subpv" , "Subvp" , "Subvv" , "Tan" , "Tanh" , "User" , "Usrap" , "Usrav" , "Usrrp" , "Usrrv" , "Zmulpv", "Zmulvp", "Zmulvv", "Number" // not used }; // check ensuring conversion to size_t is as expected CPPAD_ASSERT_UNKNOWN( size_t(NumberOp) + 1 == sizeof(OpNameTable)/sizeof(OpNameTable[0]) ); // this test ensures that all indices are within the table CPPAD_ASSERT_UNKNOWN( size_t(op) < size_t(NumberOp) ); return OpNameTable[op]; } /*! Prints a single field corresponding to an operator. A specified leader is printed in front of the value and then the value is left justified in the following width character. \tparam Type is the type of the value we are printing. \param os is the stream that we are printing to. \param leader are characters printed before the value. \param value is the value being printed. \param width is the number of character to print the value in. If the value does not fit in the width, the value is replace by width '*' characters. */ template void printOpField( std::ostream &os , const char * leader , const Type &value , size_t width ) { std::ostringstream buffer; std::string str; // first print the leader os << leader; // print the value into an internal buffer buffer << std::setw(width) << value; str = buffer.str(); // length of the string size_t len = str.size(); if( len > width ) { size_t i; for(i = 0; i < width-1; i++) os << str[i]; os << "*"; return; } // count number of spaces at begining size_t nspace = 0; while(str[nspace] == ' ' && nspace < len) nspace++; // left justify the string size_t i = nspace; while( i < len ) os << str[i++]; i = width - len + nspace; while(i--) os << " "; } /*! Prints a single operator and its operands \tparam Base Is the base type for these AD< \a Base > operations. \param os is the output stream that the information is printed on. \param play Is the entire recording for the tape that this operator is in. \param i_op is the index for the operator corresponding to this operation. \param i_var is the index for the variable corresponding to the result of this operation (if NumRes(op) > 0). \param op The operator code (OpCode) for this operation. \param ind is the vector of argument indices for this operation (must have NumArg(op) elements). */ template void printOp( std::ostream& os , const local::player* play , size_t i_op , size_t i_var , OpCode op , const addr_t* ind ) { size_t i; CPPAD_ASSERT_KNOWN( ! thread_alloc::in_parallel() , "cannot print trace of AD operations in parallel mode" ); static const char *CompareOpName[] = { "Lt", "Le", "Eq", "Ge", "Gt", "Ne" }; // print operator printOpField(os, "o=", i_op, 5); if( NumRes(op) > 0 && op != BeginOp ) printOpField(os, "v=", i_var, 5); else printOpField(os, "v=", "", 5); if( op == CExpOp || op == CSkipOp ) { printOpField(os, "", OpName(op), 5); printOpField(os, "", CompareOpName[ ind[0] ], 3); } else printOpField(os, "", OpName(op), 8); // print other fields size_t ncol = 5; switch( op ) { case CSkipOp: /* ind[0] = the Rel operator: Lt, Le, Eq, Ge, Gt, or Ne ind[1] & 1 = is left a variable ind[1] & 2 = is right a variable ind[2] = index correspoding to left ind[3] = index correspoding to right ind[4] = number of operations to skip if CExpOp comparision is true ind[5] = number of operations to skip if CExpOp comparision is false ind[6] -> ind[5+ind[4]] = skip operations if true ind[6+ind[4]] -> ind[5+ind[4]+ind[5]] = skip operations if false ind[6+ind[4]+ind[5]] = ind[4] + ind[5] */ CPPAD_ASSERT_UNKNOWN( ind[6+ind[4]+ind[5]] == ind[4]+ind[5] ); CPPAD_ASSERT_UNKNOWN(ind[1] != 0); if( ind[1] & 1 ) printOpField(os, " vl=", ind[2], ncol); else printOpField(os, " pl=", play->GetPar(ind[2]), ncol); if( ind[1] & 2 ) printOpField(os, " vr=", ind[3], ncol); else printOpField(os, " pr=", play->GetPar(ind[3]), ncol); if( size_t(ind[4]) < 3 ) { for(i = 0; i < size_t(ind[4]); i++) printOpField(os, " ot=", ind[6+i], ncol); } else { printOpField(os, "\n\tot=", ind[6+0], ncol); for(i = 1; i < size_t(ind[4]); i++) printOpField(os, " ot=", ind[6+i], ncol); } if( size_t(ind[5]) < 3 ) { for(i = 0; i < size_t(ind[5]); i++) printOpField(os, " of=", ind[6+ind[4]+i], ncol); } else { printOpField(os, "\n\tof=", ind[6+ind[4]+0], ncol); { for(i = 1; i < size_t(ind[5]); i++) printOpField(os, " of=", ind[6+ind[4]+i], ncol); } } break; case CSumOp: /* ind[0] = number of addition variables in summation ind[1] = number of subtraction variables in summation ind[2] = index of parameter that initializes summation ind[3], ... , ind[2+ind[0]] = index for positive variables ind[3+ind[0]], ..., ind[2+ind[0]+ind[1]] = negative variables ind[3+ind[0]+ind[1]] == ind[0] + ind[1] */ CPPAD_ASSERT_UNKNOWN( ind[3+ind[0]+ind[1]] == ind[0]+ind[1] ); printOpField(os, " pr=", play->GetPar(ind[2]), ncol); for(i = 0; i < size_t(ind[0]); i++) printOpField(os, " +v=", ind[3+i], ncol); for(i = 0; i < size_t(ind[1]); i++) printOpField(os, " -v=", ind[3+ind[0]+i], ncol); break; case LdpOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); printOpField(os, "off=", ind[0], ncol); printOpField(os, "idx=", ind[1], ncol); break; case LdvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); printOpField(os, "off=", ind[0], ncol); printOpField(os, " v=", ind[1], ncol); break; case StppOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); printOpField(os, "off=", ind[0], ncol); printOpField(os, "idx=", ind[1], ncol); printOpField(os, " pr=", play->GetPar(ind[2]), ncol); break; case StpvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); printOpField(os, "off=", ind[0], ncol); printOpField(os, "idx=", ind[1], ncol); printOpField(os, " vr=", ind[2], ncol); break; case StvpOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); printOpField(os, "off=", ind[0], ncol); printOpField(os, " vl=", ind[1], ncol); printOpField(os, " pr=", play->GetPar(ind[2]), ncol); break; case StvvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); printOpField(os, "off=", ind[0], ncol); printOpField(os, " vl=", ind[1], ncol); printOpField(os, " vr=", ind[2], ncol); break; case AddvvOp: case DivvvOp: case EqvvOp: case LevvOp: case LtvvOp: case NevvOp: case MulvvOp: case PowvvOp: case SubvvOp: case ZmulvvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 2 ); printOpField(os, " vl=", ind[0], ncol); printOpField(os, " vr=", ind[1], ncol); break; case AddpvOp: case EqpvOp: case DivpvOp: case LepvOp: case LtpvOp: case NepvOp: case SubpvOp: case MulpvOp: case PowpvOp: case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 2 ); printOpField(os, " pl=", play->GetPar(ind[0]), ncol); printOpField(os, " vr=", ind[1], ncol); break; case DivvpOp: case LevpOp: case LtvpOp: case PowvpOp: case SubvpOp: case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 2 ); printOpField(os, " vl=", ind[0], ncol); printOpField(os, " pr=", play->GetPar(ind[1]), ncol); break; case AbsOp: case AcosOp: case AcoshOp: case AsinOp: case AsinhOp: case AtanOp: case AtanhOp: case CosOp: case CoshOp: case ExpOp: case Expm1Op: case LogOp: case Log1pOp: case SignOp: case SinOp: case SinhOp: case SqrtOp: case UsravOp: case TanOp: case TanhOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 ); printOpField(os, " v=", ind[0], ncol); break; case ErfOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 3 ); // ind[1] points to the parameter 0 // ind[2] points to the parameter 2 / sqrt(pi) printOpField(os, " v=", ind[0], ncol); break; case ParOp: case UsrapOp: case UsrrpOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 ); printOpField(os, " p=", play->GetPar(ind[0]), ncol); break; case UserOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 4 ); { std::string name = atomic_base::class_name(ind[0]); printOpField(os, " f=", name.c_str(), ncol); printOpField(os, " i=", ind[1], ncol); printOpField(os, " n=", ind[2], ncol); printOpField(os, " m=", ind[3], ncol); } break; case PriOp: CPPAD_ASSERT_NARG_NRES(op, 5, 0); if( ind[0] & 1 ) printOpField(os, " v=", ind[1], ncol); else printOpField(os, " p=", play->GetPar(ind[1]), ncol); os << "before=\"" << play->GetTxt(ind[2]) << "\""; if( ind[0] & 2 ) printOpField(os, " v=", ind[3], ncol); else printOpField(os, " p=", play->GetPar(ind[3]), ncol); os << "after=\"" << play->GetTxt(ind[4]) << "\""; break; case BeginOp: // argument not used (created by independent) CPPAD_ASSERT_UNKNOWN( NumArg(op) == 1 ); break; case EndOp: case InvOp: case UsrrvOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 0 ); break; case DisOp: CPPAD_ASSERT_UNKNOWN( NumArg(op) == 2 ); { const char* name = discrete::name(ind[0]); printOpField(os, " f=", name, ncol); printOpField(os, " x=", ind[1], ncol); } break; case CExpOp: CPPAD_ASSERT_UNKNOWN(ind[1] != 0); CPPAD_ASSERT_UNKNOWN( NumArg(op) == 6 ); if( ind[1] & 1 ) printOpField(os, " vl=", ind[2], ncol); else printOpField(os, " pl=", play->GetPar(ind[2]), ncol); if( ind[1] & 2 ) printOpField(os, " vr=", ind[3], ncol); else printOpField(os, " pr=", play->GetPar(ind[3]), ncol); if( ind[1] & 4 ) printOpField(os, " vt=", ind[4], ncol); else printOpField(os, " pt=", play->GetPar(ind[4]), ncol); if( ind[1] & 8 ) printOpField(os, " vf=", ind[5], ncol); else printOpField(os, " pf=", play->GetPar(ind[5]), ncol); break; default: CPPAD_ASSERT_UNKNOWN(0); } } /*! Prints the result values correspnding to an operator. \tparam Base Is the base type for these AD< \a Base > operations. \tparam Value Determines the type of the values that we are printing. \param os is the output stream that the information is printed on. \param nfz is the number of forward sweep calculated values of type Value that correspond to this operation (ignored if NumRes(op) == 0). \param fz points to the first forward calculated value that correspond to this operation (ignored if NumRes(op) == 0). \param nrz is the number of reverse sweep calculated values of type Value that correspond to this operation (ignored if NumRes(op) == 0). \param rz points to the first reverse calculated value that correspond to this operation (ignored if NumRes(op) == 0). */ template void printOpResult( std::ostream &os , size_t nfz , const Value *fz , size_t nrz , const Value *rz ) { size_t k; for(k = 0; k < nfz; k++) os << "| fz[" << k << "]=" << fz[k]; for(k = 0; k < nrz; k++) os << "| rz[" << k << "]=" << rz[k]; } /*! If NDEBUG is not defined, assert that arguments come before result. \param op Operator for which we are checking order. All the operators are checked except for those of the form UserOp or Usr..Op. \param result is the variable index for the result. \param arg is a vector of lenght NumArg(op) pointing to the arguments for this operation. */ inline void assert_arg_before_result( OpCode op, const addr_t* arg, size_t result ) { switch( op ) { // These cases are not included below case UserOp: case UsrapOp: case UsravOp: case UsrrpOp: case UsrrvOp: break; // ------------------------------------------------------------------ // 0 arguments case CSkipOp: case CSumOp: case EndOp: case InvOp: break; // ------------------------------------------------------------------ // 1 argument, but is not used case BeginOp: break; // 1 argument , 1 result case AbsOp: case ExpOp: case Expm1Op: case LogOp: case Log1pOp: case ParOp: case SignOp: case SqrtOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < result ); break; // 1 argument, 2 results case AcosOp: case AcoshOp: case AsinOp: case AsinhOp: case AtanOp: case AtanhOp: case CosOp: case CoshOp: case SinOp: case SinhOp: case TanOp: case TanhOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) + 1 < result ); break; // 1 argument, 5 results case ErfOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) + 4 < result ); break; // ------------------------------------------------------------------ // 2 arguments, no results case LepvOp: case LtpvOp: case EqpvOp: case NepvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) <= result ); break; // case LevpOp: case LtvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= result ); break; // case LevvOp: case LtvvOp: case EqvvOp: case NevvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= result ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) <= result ); break; // 2 arguments (both variables), 1 results case AddvvOp: case DivvvOp: case MulvvOp: case SubvvOp: case ZmulvvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < result ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < result ); break; // 2 arguments (first variables), 1 results case DivvpOp: case SubvpOp: case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < result ); break; // 2 arguments (second variables), 1 results case AddpvOp: case DisOp: case DivpvOp: case MulpvOp: case SubpvOp: case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < result ); break; // 2 arguments (both variables), 3 results case PowvvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) + 2 < result ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) + 2 < result ); break; // 2 arguments (first variable), 3 results case PowvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) + 2 < result ); break; // 2 arguments (second variable), 3 results case PowpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) + 2 < result ); break; // ------------------------------------------------------------------ // 3 arguments, none variables case LdpOp: case StppOp: break; // 3 arguments, second variable, 1 result case LdvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < result ); break; // 3 arguments, third variable, no result case StpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) <= result ); break; // 3 arguments, second variable, no result case StvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) <= result ); break; // 3 arguments, second and third variable, no result case StvvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) <= result ); CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) <= result ); break; // ------------------------------------------------------------------ // 5 arguments, no result case PriOp: if( arg[0] & 1 ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) <= result ); } if( arg[0] & 2 ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[3]) <= result ); } break; // ------------------------------------------------------------------ // 6 arguments, 1 result case CExpOp: if( arg[1] & 1 ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < result ); } if( arg[1] & 2 ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[3]) < result ); } if( arg[1] & 4 ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[4]) < result ); } if( arg[1] & 8 ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[5]) < result ); } break; // ------------------------------------------------------------------ default: CPPAD_ASSERT_UNKNOWN(false); break; } return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/0002755000175200017650000000000013057470466016461 5ustar coincoin-webcppad-20170000.3/cppad/local/optimize/csum_variable.hpp0000644000175200017650000000267313057470466022014 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_CSUM_VARIABLE_HPP # define CPPAD_LOCAL_OPTIMIZE_CSUM_VARIABLE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include // defines addr_t /*! \file csum_variable.hpp Information about one old variable that is part of a new CSumOp operation. */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Information about one old variable that is part of a new CSumOp operation. */ struct struct_csum_variable { /// Pointer to first argument (child) for this old operator. /// Set by the reverse sweep at beginning of optimization. const addr_t* arg; /// Was this old variable added to the summation /// (if not it was subtracted) bool add; /// Operator for which this old variable is the result, NumRes(op) > 0. OpCode op; }; } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/hash_code.hpp0000644000175200017650000000304113057470466021103 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_HASH_CODE_HPP # define CPPAD_LOCAL_OPTIMIZE_HASH_CODE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file local/optimize/hash_code.hpp CppAD hashing utility. */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Specialized hash code for a CppAD operator and its arguments (used during optimization). \param op is the operator that we are computing a hash code for. \param num_arg number of elements of arg to include in the hash code (num_arg <= 2). \param arg is a vector of length num_arg containing the corresponding argument indices for this operator. \return is a hash code that is between zero and CPPAD_HASH_TABLE_SIZE - 1. */ inline size_t optimize_hash_code( OpCode op , size_t num_arg , const addr_t* arg ) { // CPPAD_ASSERT_UNKNOWN(num_arg <= 2 ); size_t sum = size_t(arg[0]) + size_t(op); if( 1 < num_arg ) sum += size_t(arg[1]); // return sum % CPPAD_HASH_TABLE_SIZE; } } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/csum_stacks.hpp0000644000175200017650000000247613057470466021520 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_CSUM_STACKS_HPP # define CPPAD_LOCAL_OPTIMIZE_CSUM_STACKS_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include /*! \file csum_stacks.hpp Information about one cumulative summation operation. */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Information about one cumulative summation operation. */ struct struct_csum_stacks { /// old operator indices for this cummulative summation std::stack op_stack; /// old variable indices to be added std::stack add_stack; /// old variavle indices to be subtracted std::stack sub_stack; }; } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/record_pv.hpp0000644000175200017650000000652013057470466021156 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_RECORD_PV_HPP # define CPPAD_LOCAL_OPTIMIZE_RECORD_PV_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file record_pv.hpp Record an operation of the form (parameter op variable). */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Record an operation of the form (parameter op variable). \param var2op mapping from old variable index to old operator index. \param op_info mapping from old index to operator index to operator information \param old2new mapping from old operator index to information about the new recording. \param current is the index in the old operation sequence for the variable corresponding to the result for the current operator. We use the notation i_op = var2op[current]. It follows that NumRes( op_info[i_op].op ) > 0. If 0 < j_op < i_op, either op_info[j_op].csum_connected, op_info[j_op].usage = 0, or old2new[j_op].new_var != 0. \param npar is the number of parameters corresponding to the old operation sequence. \param par is a vector of length npar containing the parameters the old operation sequence; i.e., given a parameter index i < npar, the corresponding parameter value is par[i]. \param rec is the object that will record the new operations. \return is the operator and variable indices in the new operation sequence. \param op is the operator that we are recording which must be one of the following: AddpvOp, DivpvOp, MulpvOp, PowpvOp, SubpvOp, ZmulpvOp. \param arg is the vector of arguments for this operator. */ template struct_size_pair record_pv( const vector& var2op , const vector& op_info , const CppAD::vector& old2new , size_t current , size_t npar , const Base* par , recorder* rec , OpCode op , const addr_t* arg ) { # ifndef NDEBUG switch(op) { case AddpvOp: case DivpvOp: case MulpvOp: case PowpvOp: case SubpvOp: case ZmulpvOp: break; default: CPPAD_ASSERT_UNKNOWN(false); } # endif CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < npar ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < current ); addr_t new_arg[2]; new_arg[0] = rec->PutPar( par[arg[0]] ); new_arg[1] = old2new[ var2op[arg[1]] ].new_var; rec->PutArg( new_arg[0], new_arg[1] ); struct_size_pair ret; ret.i_op = rec->num_op_rec(); ret.i_var = rec->PutOp(op); CPPAD_ASSERT_UNKNOWN( 0 < new_arg[1] && size_t(new_arg[1]) < ret.i_var ); return ret; } } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/record_vp.hpp0000644000175200017650000000643713057470466021165 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_RECORD_VP_HPP # define CPPAD_LOCAL_OPTIMIZE_RECORD_VP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file record_vp.hpp Record an operation of the form (variable op parameter). */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Record an operation of the form (variable op parameter). \param var2op mapping from old variable index to old operator index. \param op_info mapping from old index to operator index to operator information \param old2new mapping from old operator index to information about the new recording. \param current is the index in the old operation sequence for the variable corresponding to the result for the current operator. We use the notation i_op = var2op[current]. It follows that NumRes( op_info[i_op].op ) > 0. If 0 < j_op < i_op, either op_info[j_op].csum_connected, op_info[j_op].usage = 0, or old2new[j_op].new_var != 0. \param npar is the number of parameters corresponding to the old operation sequence. \param par is a vector of length npar containing the parameters the old operation sequence; i.e., given a parameter index i < npar, the corresponding parameter value is par[i]. \param rec is the object that will record the new operations. \return is the operator and variable indices in the new operation sequence. \param op is the operator that we are recording which must be one of the following: DivvpOp, PowvpOp, SubvpOp, ZmulvpOp. \param arg is the vector of arguments for this operator. */ template struct_size_pair record_vp( const vector& var2op , const vector& op_info , const CppAD::vector& old2new , size_t current , size_t npar , const Base* par , recorder* rec , OpCode op , const addr_t* arg ) { # ifndef NDEBUG switch(op) { case DivvpOp: case PowvpOp: case SubvpOp: case ZmulvpOp: break; default: CPPAD_ASSERT_UNKNOWN(false); } # endif CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < current ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < npar ); addr_t new_arg[2]; new_arg[0] = old2new[ var2op[arg[0]] ].new_var; new_arg[1] = rec->PutPar( par[arg[1]] ); rec->PutArg( new_arg[0], new_arg[1] ); struct_size_pair ret; ret.i_op = rec->num_op_rec(); ret.i_var = rec->PutOp(op); CPPAD_ASSERT_UNKNOWN( 0 < new_arg[0] && size_t(new_arg[0]) < ret.i_var ); return ret; } } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/optimize_run.hpp0000644000175200017650000006362113057470466021724 0ustar coincoin-web # ifndef CPPAD_LOCAL_OPTIMIZE_OPTIMIZE_RUN_HPP # define CPPAD_LOCAL_OPTIMIZE_OPTIMIZE_RUN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # include # include # include # include # include # include # include # include # include # include # include /*! \file optimize_run.hpp Convert a player object to an optimized recorder object */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Convert a player object to an optimized recorder object \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param options \li If the sub-string "no_conditional_skip" appears, conditional skip operations will not be generated. This may make the optimize routine use significantly less memory and take significantly less time. \li If the sub-string "no_compare_op" appears, then comparison operators will be removed from the optimized tape. These operators are necessary for the compare_change function to be be meaningful in the resulting recording. On the other hand, they are not necessary and take extra time when compare_change is not used. \li If the sub-string "no_print_for" appears, then print forward (PriOp) operators will be removed from the optimized tape. These operators are useful for reporting problems evaluating derivatives at independent variable values different from those used to record a function. \param n is the number of independent variables on the tape. \param dep_taddr On input this vector contains the indices for each of the dependent variable values in the operation sequence corresponding to \a play. Upon return it contains the indices for the same variables but in the operation sequence corresponding to \a rec. \param play This is the operation sequence that we are optimizing. It is essentially const, except for play back state which changes while it plays back the operation seqeunce. \param rec The input contents of this recording does not matter. Upon return, it contains an optimized verison of the operation sequence corresponding to \a play. */ template void optimize_run( const std::string& options , size_t n , CppAD::vector& dep_taddr , player* play , recorder* rec ) { bool conditional_skip = true; bool compare_op = true; bool print_for_op = true; size_t index = 0; while( index < options.size() ) { while( index < options.size() && options[index] == ' ' ) ++index; std::string option; while( index < options.size() && options[index] != ' ' ) option += options[index++]; if( option != "" ) { if( option == "no_conditional_skip" ) conditional_skip = false; else if( option == "no_compare_op" ) compare_op = false; else if( option == "no_print_for_op" ) print_for_op = false; else { option += " is not a valid optimize option"; CPPAD_ASSERT_KNOWN( false , option.c_str() ); } } } // number of operators in the player const size_t num_op = play->num_op_rec(); CPPAD_ASSERT_UNKNOWN( num_op < size_t( std::numeric_limits::max() ) ); // number of variables in the player const size_t num_var = play->num_var_rec(); // number of VecAD indices size_t num_vecad_ind = play->num_vec_ind_rec(); // number of VecAD vectors size_t num_vecad_vec = play->num_vecad_vec_rec(); // operator information vector var2op; vector cexp_info; vector vecad_used; vector op_info; get_op_info( conditional_skip, compare_op, print_for_op, play, dep_taddr, var2op, cexp_info, vecad_used, op_info ); // nan with type Base Base base_nan = Base( std::numeric_limits::quiet_NaN() ); // ------------------------------------------------------------- // information for current operator size_t i_op; // index OpCode op; // operator const addr_t* arg; // arguments size_t i_var; // variable index of primary (last) result enum_user_state user_state; // ------------------------------------------------------------- // conditional expression information // // Size of the conditional expression information structure. // This is equal to the number of conditional expressions when // conditional_skip is true, otherwise it is zero. size_t num_cexp = cexp_info.size(); CPPAD_ASSERT_UNKNOWN( conditional_skip || num_cexp == 0 ); // // sort the conditional expression information by max_left_right // this is the conditional skip order vector cskip_order(num_cexp); if( num_cexp > 0 ) { CppAD::vector keys(num_cexp); for(size_t i = 0; i < num_cexp; i++) keys[i] = cexp_info[i].max_left_right; CppAD::index_sort(keys, cskip_order); } // initial index in conditional skip order size_t cskip_order_next = 0; // // initialize index in conditional expression order size_t cexp_next = 0; // mapping from conditional expression index to conditional skip // information on new tape vector cskip_new(num_cexp); // // flag used to indicate that there is no conditional skip // for this conditional expression for(size_t i = 0; i < num_cexp; i++) cskip_new[i].i_arg = 0; // ------------------------------------------------------------- // Erase all information in the old recording rec->free(); // initialize mapping from old VecAD index to new VecAD index CppAD::vector new_vecad_ind(num_vecad_ind); for(size_t i = 0; i < num_vecad_ind; i++) new_vecad_ind[i] = num_vecad_ind; // invalid index { size_t j = 0; // index into the old set of indices for(size_t i = 0; i < num_vecad_vec; i++) { // length of this VecAD size_t length = play->GetVecInd(j); if( vecad_used[i] ) { // Put this VecAD vector in new recording CPPAD_ASSERT_UNKNOWN(length < num_vecad_ind); new_vecad_ind[j] = rec->PutVecInd(length); for(size_t k = 1; k <= length; k++) new_vecad_ind[j+k] = rec->PutVecInd( rec->PutPar( play->GetPar( play->GetVecInd(j+k) ) ) ); } // start of next VecAD j += length + 1; } CPPAD_ASSERT_UNKNOWN( j == num_vecad_ind ); } // // Mapping from old operator index to new operator information // (zero is invalid except for old2new[0].new_op and old2new[0].i_var) vector old2new(num_op); for(size_t i = 0; i < num_op; i++) { old2new[i].new_op = 0; old2new[i].new_var = 0; } // temporary buffer for new argument values addr_t new_arg[6]; // temporary work space used by record_csum // (decalared here to avoid realloaction of memory) struct_csum_stacks csum_work; // tempory used to hold a size_pair struct_size_pair size_pair; user_state = start_user; for(i_op = 0; i_op < num_op; ++i_op) { addr_t mask; // temporary used in some switch cases // // this operator information op = op_info[i_op].op; arg = op_info[i_op].arg; i_var = op_info[i_op].i_var; // // determine if we should insert a conditional skip here bool skip = conditional_skip; skip &= cskip_order_next < num_cexp; skip &= op != BeginOp; skip &= op != InvOp; skip &= user_state == start_user; if( skip ) { size_t j = cskip_order[cskip_order_next]; if( NumRes(op) > 0 ) skip &= cexp_info[j].max_left_right < i_var; else skip &= cexp_info[j].max_left_right <= i_var; } if( skip ) { size_t j = cskip_order[cskip_order_next]; cskip_order_next++; struct_cexp_info info = cexp_info[j]; size_t n_true = info.skip_op_true.size(); size_t n_false = info.skip_op_false.size(); skip &= n_true > 0 || n_false > 0; if( skip ) { CPPAD_ASSERT_UNKNOWN( NumRes(CSkipOp) == 0 ); size_t n_arg = 7 + n_true + n_false; // reserve space for the arguments to this operator but // delay setting them until we have all the new addresses cskip_new[j].i_arg = rec->ReserveArg(n_arg); // i_arg == 0 is used to check if conditional expression // has been skipped. CPPAD_ASSERT_UNKNOWN( cskip_new[j].i_arg > 0 ); // There is no corresponding old operator in this case rec->PutOp(CSkipOp); } } if( op == UserOp ) { if( user_state == start_user ) user_state = end_user; else { CPPAD_ASSERT_UNKNOWN( user_state == end_user ); user_state = start_user; } } size_t previous; // if( op_info[i_op].usage != yes_usage ) { if( op == CExpOp ) ++cexp_next; } else switch( op ) { case BeginOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); // Put BeginOp at beginning of recording old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutOp(BeginOp); rec->PutArg(arg[0]); break; // -------------------------------------------------------------- // Unary operator where operand is arg[0] case AbsOp: case AcosOp: case AcoshOp: case AsinOp: case AsinhOp: case AtanOp: case AtanhOp: case CosOp: case CoshOp: case ErfOp: case ExpOp: case Expm1Op: case LogOp: case Log1pOp: case SignOp: case SinOp: case SinhOp: case SqrtOp: case TanOp: case TanhOp: previous = op_info[i_op].previous; if( previous > 0 ) { size_t j_op = previous; old2new[i_op].new_var = old2new[j_op].new_var; } else { // new_arg[0] = old2new[ var2op[arg[0]] ].new_var; rec->PutArg( new_arg[0] ); // old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutOp(op); CPPAD_ASSERT_UNKNOWN( new_arg[0] < old2new[var2op[i_var]].new_var ); if( op == ErfOp ) { // Error function is a special case // second argument is always the parameter 0 // third argument is always the parameter 2 / sqrt(pi) CPPAD_ASSERT_UNKNOWN( NumArg(ErfOp) == 3 ); rec->PutArg( rec->PutPar( Base(0) ) ); rec->PutArg( rec->PutPar( Base( 1.0 / std::sqrt( std::atan(1.0) ) ) ) ); } } break; // --------------------------------------------------- // Binary operators where // left is a variable and right is a parameter case SubvpOp: // check if this is the top of a csum connection if( op_info[i_op].usage == csum_usage ) break; if( op_info[ var2op[arg[0]] ].usage == csum_usage ) { // convert to a sequence of summation operators size_pair = record_csum( var2op , op_info , old2new , i_var , play->num_par_rec() , play->GetPar() , rec , csum_work ); old2new[i_op].new_op = size_pair.i_op; old2new[i_op].new_var = size_pair.i_var; // abort rest of this case break; } case DivvpOp: case PowvpOp: case ZmulvpOp: previous = op_info[i_op].previous; if( previous > 0 ) { size_t j_op = previous; old2new[i_op].new_var = old2new[j_op].new_var; } else { // size_pair = record_vp( var2op , op_info , old2new , i_var , play->num_par_rec() , play->GetPar() , rec , op , arg ); old2new[i_op].new_op = size_pair.i_op; old2new[i_op].new_var = size_pair.i_var; } break; // --------------------------------------------------- // Binary operators where // left is an index and right is a variable case DisOp: previous = op_info[i_op].previous; if( previous > 0 ) { size_t j_op = previous; old2new[i_op].new_var = old2new[j_op].new_var; } else { // new_arg[0] = arg[0]; new_arg[1] = old2new[ var2op[arg[1]] ].new_var; rec->PutArg( new_arg[0], new_arg[1] ); // old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutOp(op); CPPAD_ASSERT_UNKNOWN( new_arg[1] < old2new[var2op[i_var]].new_var ); } break; // --------------------------------------------------- // Binary operators where // left is a parameter and right is a variable case SubpvOp: case AddpvOp: // check if this is the top of a csum connection if( op_info[i_op].usage == csum_usage ) break; if( op_info[ var2op[arg[1]] ].usage == csum_usage ) { // convert to a sequence of summation operators size_pair = record_csum( var2op , op_info , old2new , i_var , play->num_par_rec() , play->GetPar() , rec , csum_work ); old2new[i_op].new_op = size_pair.i_op; old2new[i_op].new_var = size_pair.i_var; // abort rest of this case break; } case DivpvOp: case MulpvOp: case PowpvOp: case ZmulpvOp: previous = op_info[i_op].previous; if( previous > 0 ) { size_t j_op = previous; old2new[i_op].new_var = old2new[j_op].new_var; } else { // size_pair = record_pv( var2op , op_info , old2new , i_var , play->num_par_rec() , play->GetPar() , rec , op , arg ); old2new[i_op].new_op = size_pair.i_op; old2new[i_op].new_var = size_pair.i_var; } break; // --------------------------------------------------- // Binary operator where both operands are variables case AddvvOp: case SubvvOp: // check if this is the top of a csum connection if( op_info[i_op].usage == csum_usage ) break; if( op_info[ var2op[arg[0]] ].usage == csum_usage || op_info[ var2op[arg[1]] ].usage == csum_usage ) { // convert to a sequence of summation operators size_pair = record_csum( var2op , op_info , old2new , i_var , play->num_par_rec() , play->GetPar() , rec , csum_work ); old2new[i_op].new_op = size_pair.i_op; old2new[i_op].new_var = size_pair.i_var; // abort rest of this case break; } case DivvvOp: case MulvvOp: case PowvvOp: case ZmulvvOp: previous = op_info[i_op].previous; if( previous > 0 ) { size_t j_op = previous; old2new[i_op].new_var = old2new[j_op].new_var; } else { // size_pair = record_vv( var2op , op_info , old2new , i_var , play->num_par_rec() , play->GetPar() , rec , op , arg ); old2new[i_op].new_op = size_pair.i_op; old2new[i_op].new_var = size_pair.i_var; } break; // --------------------------------------------------- // Conditional expression operators case CExpOp: CPPAD_ASSERT_NARG_NRES(op, 6, 1); new_arg[0] = arg[0]; new_arg[1] = arg[1]; mask = 1; for(size_t i = 2; i < 6; i++) { if( arg[1] & mask ) { new_arg[i] = old2new[ var2op[arg[i]] ].new_var; CPPAD_ASSERT_UNKNOWN( size_t(new_arg[i]) < num_var ); } else new_arg[i] = rec->PutPar( play->GetPar( arg[i] ) ); mask = mask << 1; } rec->PutArg( new_arg[0] , new_arg[1] , new_arg[2] , new_arg[3] , new_arg[4] , new_arg[5] ); old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutOp(op); // // The new addresses for left and right are used during // fill in the arguments for the CSkip operations. This does not // affect max_left_right which is used during this sweep. if( conditional_skip ) { CPPAD_ASSERT_UNKNOWN( cexp_next < num_cexp ); CPPAD_ASSERT_UNKNOWN( cexp_info[cexp_next].i_op == i_op ); cskip_new[ cexp_next ].left = new_arg[2]; cskip_new[ cexp_next ].right = new_arg[3]; ++cexp_next; } break; // --------------------------------------------------- // Operations with no arguments and no results case EndOp: CPPAD_ASSERT_NARG_NRES(op, 0, 0); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(op); break; // --------------------------------------------------- // Operations with two arguments and no results case LepvOp: case LtpvOp: case EqpvOp: case NepvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 0); new_arg[0] = rec->PutPar( play->GetPar(arg[0]) ); new_arg[1] = old2new[ var2op[arg[1]] ].new_var; rec->PutArg(new_arg[0], new_arg[1]); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(op); break; // case LevpOp: case LtvpOp: CPPAD_ASSERT_NARG_NRES(op, 2, 0); new_arg[0] = old2new[ var2op[arg[0]] ].new_var; new_arg[1] = rec->PutPar( play->GetPar(arg[1]) ); rec->PutArg(new_arg[0], new_arg[1]); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(op); break; // case LevvOp: case LtvvOp: case EqvvOp: case NevvOp: CPPAD_ASSERT_NARG_NRES(op, 2, 0); new_arg[0] = old2new[ var2op[arg[0]] ].new_var; new_arg[1] = old2new[ var2op[arg[1]] ].new_var; rec->PutArg(new_arg[0], new_arg[1]); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(op); break; // --------------------------------------------------- // Operations with no arguments and one result case InvOp: CPPAD_ASSERT_NARG_NRES(op, 0, 1); old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutOp(op); break; // --------------------------------------------------- // Operations with one argument that is a parameter case ParOp: CPPAD_ASSERT_NARG_NRES(op, 1, 1); new_arg[0] = rec->PutPar( play->GetPar(arg[0] ) ); rec->PutArg( new_arg[0] ); // old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutOp(op); break; // --------------------------------------------------- // print forward operator case PriOp: CPPAD_ASSERT_NARG_NRES(op, 5, 0); // arg[0] new_arg[0] = arg[0]; // // arg[1] if( arg[0] & 1 ) { new_arg[1] = old2new[ var2op[arg[1]] ].new_var; CPPAD_ASSERT_UNKNOWN( size_t(new_arg[1]) < num_var ); } else { new_arg[1] = rec->PutPar( play->GetPar( arg[1] ) ); } // // arg[3] if( arg[0] & 2 ) { new_arg[3] = old2new[ var2op[arg[3]] ].new_var; CPPAD_ASSERT_UNKNOWN( size_t(new_arg[3]) < num_var ); } else { new_arg[3] = rec->PutPar( play->GetPar( arg[3] ) ); } new_arg[2] = rec->PutTxt( play->GetTxt(arg[2]) ); new_arg[4] = rec->PutTxt( play->GetTxt(arg[4]) ); // rec->PutArg( new_arg[0] , new_arg[1] , new_arg[2] , new_arg[3] , new_arg[4] ); // new operator old2new[i_op].new_op = rec->num_op_rec(); // no new variable rec->PutOp(op); break; // --------------------------------------------------- // VecAD operators // Load using a parameter index case LdpOp: CPPAD_ASSERT_NARG_NRES(op, 3, 1); new_arg[0] = new_vecad_ind[ arg[0] ]; new_arg[1] = arg[1]; new_arg[2] = rec->num_load_op_rec(); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[0]) < num_vecad_ind ); rec->PutArg( new_arg[0], new_arg[1], new_arg[2] ); old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutLoadOp(op); break; // Load using a variable index case LdvOp: CPPAD_ASSERT_NARG_NRES(op, 3, 1); new_arg[0] = new_vecad_ind[ arg[0] ]; new_arg[1] = old2new[ var2op[arg[1]] ].new_var; new_arg[2] = rec->num_load_op_rec(); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[0]) < num_vecad_ind ); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[1]) < num_var ); rec->PutArg( new_arg[0], new_arg[1], new_arg[2] ); old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutLoadOp(op); break; // Store a parameter using a parameter index case StppOp: CPPAD_ASSERT_NARG_NRES(op, 3, 0); new_arg[0] = new_vecad_ind[ arg[0] ]; new_arg[1] = rec->PutPar( play->GetPar(arg[1]) ); new_arg[2] = rec->PutPar( play->GetPar(arg[2]) ); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[0]) < num_vecad_ind ); rec->PutArg( new_arg[0], new_arg[1], new_arg[2] ); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(op); break; // Store a parameter using a variable index case StvpOp: CPPAD_ASSERT_NARG_NRES(op, 3, 0); new_arg[0] = new_vecad_ind[ arg[0] ]; new_arg[1] = old2new[ var2op[arg[1]] ].new_var; new_arg[2] = rec->PutPar( play->GetPar(arg[2]) ); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[0]) < num_vecad_ind ); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[1]) < num_var ); rec->PutArg( new_arg[0], new_arg[1], new_arg[2] ); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(op); break; // Store a variable using a parameter index case StpvOp: CPPAD_ASSERT_NARG_NRES(op, 3, 0); new_arg[0] = new_vecad_ind[ arg[0] ]; new_arg[1] = rec->PutPar( play->GetPar(arg[1]) ); new_arg[2] = old2new[ var2op[arg[2]] ].new_var; CPPAD_ASSERT_UNKNOWN( size_t(new_arg[0]) < num_vecad_ind ); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[1]) < num_var ); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[2]) < num_var ); rec->PutArg( new_arg[0], new_arg[1], new_arg[2] ); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(op); break; // Store a variable using a variable index case StvvOp: CPPAD_ASSERT_NARG_NRES(op, 3, 0); new_arg[0] = new_vecad_ind[ arg[0] ]; new_arg[1] = old2new[ var2op[arg[1]] ].new_var; new_arg[2] = old2new[ var2op[arg[2]] ].new_var; CPPAD_ASSERT_UNKNOWN( size_t(new_arg[0]) < num_vecad_ind ); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[1]) < num_var ); CPPAD_ASSERT_UNKNOWN( size_t(new_arg[2]) < num_var ); rec->PutArg( new_arg[0], new_arg[1], new_arg[2] ); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(op); break; // ----------------------------------------------------------- // user atomic function call operators case UserOp: CPPAD_ASSERT_NARG_NRES(op, 4, 0); // user_old, user_n, user_m rec->PutArg(arg[0], arg[1], arg[2], arg[3]); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(UserOp); break; case UsrapOp: CPPAD_ASSERT_NARG_NRES(op, 1, 0); new_arg[0] = rec->PutPar( play->GetPar(arg[0]) ); rec->PutArg(new_arg[0]); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(UsrapOp); break; case UsravOp: CPPAD_ASSERT_NARG_NRES(op, 1, 0); new_arg[0] = old2new[ var2op[arg[0]] ].new_var; if( size_t(new_arg[0]) < num_var ) { rec->PutArg(new_arg[0]); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(UsravOp); } else { // This argument does not affect the result and // has been optimized out so use nan in its place. new_arg[0] = rec->PutPar( base_nan ); rec->PutArg(new_arg[0]); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(UsrapOp); } break; case UsrrpOp: CPPAD_ASSERT_NARG_NRES(op, 1, 0); new_arg[0] = rec->PutPar( play->GetPar(arg[0]) ); rec->PutArg(new_arg[0]); old2new[i_op].new_op = rec->num_op_rec(); rec->PutOp(UsrrpOp); break; case UsrrvOp: CPPAD_ASSERT_NARG_NRES(op, 0, 1); old2new[i_op].new_op = rec->num_op_rec(); old2new[i_op].new_var = rec->PutOp(UsrrvOp); break; // --------------------------------------------------- // all cases should be handled above default: CPPAD_ASSERT_UNKNOWN(false); } } // modify the dependent variable vector to new indices for(size_t i = 0; i < dep_taddr.size(); i++ ) { dep_taddr[i] = old2new[ var2op[dep_taddr[i]] ].new_var; CPPAD_ASSERT_UNKNOWN( size_t(dep_taddr[i]) < num_var ); } # ifndef NDEBUG for(i_op = 0; i_op < num_op; i_op++) if( NumRes( op_info[i_op].op ) > 0 ) CPPAD_ASSERT_UNKNOWN( size_t(old2new[i_op].new_op) < rec->num_op_rec() ); # endif // make sure that all the conditional expressions have been // checked to see if they are still present CPPAD_ASSERT_UNKNOWN( cskip_order_next == num_cexp ); // fill in the arguments for the CSkip operations for(size_t i = 0; i < num_cexp; i++) { // if cskip_new[i].i_arg == 0, this conditional expression was skipped if( cskip_new[i].i_arg > 0 ) { struct_cexp_info info = cexp_info[i]; size_t n_true = info.skip_op_true.size(); size_t n_false = info.skip_op_false.size(); size_t i_arg = cskip_new[i].i_arg; size_t left = cskip_new[i].left; size_t right = cskip_new[i].right; rec->ReplaceArg(i_arg++, info.cop ); rec->ReplaceArg(i_arg++, info.flag ); rec->ReplaceArg(i_arg++, left ); rec->ReplaceArg(i_arg++, right ); rec->ReplaceArg(i_arg++, n_true ); rec->ReplaceArg(i_arg++, n_false ); for(size_t j = 0; j < info.skip_op_true.size(); j++) { i_op = cexp_info[i].skip_op_true[j]; // op_info[i_op].usage == yes_usage CPPAD_ASSERT_UNKNOWN( old2new[i_op].new_op != 0 ); rec->ReplaceArg(i_arg++, old2new[i_op].new_op ); } for(size_t j = 0; j < info.skip_op_false.size(); j++) { i_op = cexp_info[i].skip_op_false[j]; // op_info[i_op].usage == yes_usage CPPAD_ASSERT_UNKNOWN( old2new[i_op].new_op != 0 ); rec->ReplaceArg(i_arg++, old2new[i_op].new_op ); } rec->ReplaceArg(i_arg++, n_true + n_false); # ifndef NDEBUG size_t n_arg = 7 + n_true + n_false; CPPAD_ASSERT_UNKNOWN( cskip_new[i].i_arg + n_arg == i_arg ); # endif } } } } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/usage.hpp0000644000175200017650000000223313057470466020274 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_USAGE_HPP # define CPPAD_LOCAL_OPTIMIZE_USAGE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { enum enum_usage { /// This operator is not used. no_usage, /// This operator is used one or more times. yes_usage, /*! This operator is only used once, it is a summation operator, and its parrent is a summation operator. Furthermore, its result is not a dependent variable. Hence case it can be removed as part of a cumulative summation starting at its parent or above. */ csum_usage }; } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/record_csum.hpp0000644000175200017650000002032613057470466021500 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_RECORD_CSUM_HPP # define CPPAD_LOCAL_OPTIMIZE_RECORD_CSUM_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file record_csum.hpp Recording a cummulative cummulative summation. */ # include // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Recording a cummulative cummulative summation. \param var2op mapping from old variable index to old operator index. \param op_info mapping from old index to operator index to operator information \param old2new mapping from old operator index to information about the new recording. \param current is the index in the old operation sequence for the variable corresponding to the result for the current operator. We use the notation i_op = var2op[current]. It follows that NumRes( op_info[i_op].op ) > 0. If 0 < j_op < i_op, either op_info[j_op].usage == csum_usage, op_info[j_op].usage = no_usage, or old2new[j_op].new_var != 0. \param npar is the number of parameters corresponding to the old operation sequence. \param par is a vector of length npar containing the parameters the old operation sequence; i.e., given a parameter index i < npar, the corresponding parameter value is par[i]. \param rec is the object that will record the new operations. \return is the operator and variable indices in the new operation sequence. \param work Is temporary work space. On input and output, work.op_stack, work.add_stack, and work.sub_stack, are all empty. These stacks are passed in so that they are created once and then be reused with calls to record_csum. \par Assumptions op_info[i_o].op must be one of AddpvOp, AddvvOp, SubpvOp, SubvpOp, SubvvOp. op_info[i_op].usage != no_usage and ! op_info[i_op].usage == csum_usage. Furthermore op_info[j_op].usage == csum_usage is true from some j_op that corresponds to a variable that is an argument to op_info[i_op]. */ template struct_size_pair record_csum( const vector& var2op , const vector& op_info , const CppAD::vector& old2new , size_t current , size_t npar , const Base* par , recorder* rec , // local information passed so stacks need not be allocated for every call struct_csum_stacks& work ) { // check assumption about work space CPPAD_ASSERT_UNKNOWN( work.op_stack.empty() ); CPPAD_ASSERT_UNKNOWN( work.add_stack.empty() ); CPPAD_ASSERT_UNKNOWN( work.sub_stack.empty() ); // size_t i_op = var2op[current]; CPPAD_ASSERT_UNKNOWN( ! ( op_info[i_op].usage == csum_usage ) ); // size_t i; OpCode op; const addr_t* arg; bool add; struct struct_csum_variable var; // // information corresponding to the root node in the cummulative summation var.op = op_info[i_op].op; // this operator var.arg = op_info[i_op].arg; // arguments for this operator var.add = true; // was parrent operator positive or negative // // initialize stack as containing this one operator work.op_stack.push( var ); // // initialize sum of parameter values as zero Base sum_par(0); // # ifndef NDEBUG bool ok = false; struct_op_info info = op_info[i_op]; if( var.op == SubvpOp ) ok = op_info[ var2op[info.arg[0]] ].usage == csum_usage; if( var.op == AddpvOp || var.op == SubpvOp ) ok = op_info[ var2op[info.arg[1]] ].usage == csum_usage; if( var.op == AddvvOp || var.op == SubvvOp ) { ok = op_info[ var2op[info.arg[0]] ].usage == csum_usage; ok |= op_info[ var2op[info.arg[1]] ].usage == csum_usage; } CPPAD_ASSERT_UNKNOWN( ok ); # endif // // while there are operators left on the stack while( ! work.op_stack.empty() ) { // get this summation operator var = work.op_stack.top(); work.op_stack.pop(); op = var.op; arg = var.arg; add = var.add; // // process first argument to this operator switch(op) { // cases where first argument is a parameter case AddpvOp: case SubpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < npar ); // first argument has same sign as parent node if( add ) sum_par += par[arg[0]]; else sum_par -= par[arg[0]]; break; // cases where first argument is a variable case AddvvOp: case SubvpOp: case SubvvOp: // // check if the first argument has csum usage if( op_info[var2op[arg[0]]].usage == csum_usage ) { CPPAD_ASSERT_UNKNOWN( size_t( old2new[ var2op[arg[0]] ].new_var) == 0 ); // push the operator corresponding to the first argument var.op = op_info[ var2op[arg[0]] ].op; var.arg = op_info[ var2op[arg[0]] ].arg; // first argument has same sign as parent node var.add = add; work.op_stack.push( var ); } else { // there are no nodes below this one CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < current ); if( add ) work.add_stack.push(arg[0]); else work.sub_stack.push(arg[0]); } break; default: CPPAD_ASSERT_UNKNOWN(false); } // process second argument to this operator switch(op) { // cases where second argument is a parameter case SubvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < npar ); // second argument has opposite sign of parent node if( add ) sum_par -= par[arg[1]]; else sum_par += par[arg[1]]; break; // cases where second argument is a variable and has opposite sign case SubvvOp: case SubpvOp: add = ! add; // cases where second argument is a variable and has same sign case AddvvOp: case AddpvOp: // check if the second argument has csum usage if( op_info[var2op[arg[1]]].usage == csum_usage ) { CPPAD_ASSERT_UNKNOWN( size_t( old2new[ var2op[arg[1]] ].new_var) == 0 ); // push the operator corresoponding to the second arugment var.op = op_info[ var2op[arg[1]] ].op; var.arg = op_info[ var2op[arg[1]] ].arg; var.add = add; work.op_stack.push( var ); } else { // there are no nodes below this one CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < current ); if( add ) work.add_stack.push(arg[1]); else work.sub_stack.push(arg[1]); } break; default: CPPAD_ASSERT_UNKNOWN(false); } } // number of variables to add in this cummulative sum operator size_t n_add = work.add_stack.size(); // number of variables to subtract in this cummulative sum operator size_t n_sub = work.sub_stack.size(); // rec->PutArg(n_add); // arg[0] rec->PutArg(n_sub); // arg[1] size_t new_arg = rec->PutPar(sum_par); rec->PutArg(new_arg); // arg[2] // addition arguments for(i = 0; i < n_add; i++) { CPPAD_ASSERT_UNKNOWN( ! work.add_stack.empty() ); size_t old_arg = work.add_stack.top(); new_arg = old2new[ var2op[old_arg] ].new_var; CPPAD_ASSERT_UNKNOWN( 0 < new_arg && new_arg < current ); rec->PutArg(new_arg); // arg[3+i] work.add_stack.pop(); } // subtraction arguments for(i = 0; i < n_sub; i++) { CPPAD_ASSERT_UNKNOWN( ! work.sub_stack.empty() ); size_t old_arg = work.sub_stack.top(); new_arg = old2new[ var2op[old_arg] ].new_var; CPPAD_ASSERT_UNKNOWN( 0 < new_arg && new_arg < current ); rec->PutArg(new_arg); // arg[3 + arg[0] + i] work.sub_stack.pop(); } // number of additions plus number of subtractions rec->PutArg(n_add + n_sub); // arg[3 + arg[0] + arg[1]] // // return value struct_size_pair ret; ret.i_op = rec->num_op_rec(); ret.i_var = rec->PutOp(CSumOp); // return ret; } } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/size_pair.hpp0000644000175200017650000000210013057470466021146 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_SIZE_PAIR_HPP # define CPPAD_LOCAL_OPTIMIZE_SIZE_PAIR_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file size_pair.hpp Information for one variable and one operation sequence. */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! \file size_pair.hpp Information for one variable in one operation sequence. */ struct struct_size_pair { size_t i_op; /// operator index for this variable size_t i_var; /// variable index for this variable }; } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/get_op_info.hpp0000644000175200017650000007724013057470466021472 0ustar coincoin-web# ifndef CPPAD_LOCAL_OPTIMIZE_GET_OP_INFO_HPP # define CPPAD_LOCAL_OPTIMIZE_GET_OP_INFO_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file op_info.hpp Create operator information tables */ # include # include # include # include // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /// Is this an addition or subtraction operator inline bool add_or_subtract(OpCode op) { bool result; switch(op) { case AddpvOp: case AddvvOp: case SubpvOp: case SubvpOp: case SubvvOp: result = true; break; default: result = false; break; } return result; } /*! Increarse argument usage and propagate cexp_set from parent to argument. \param sum_parent is parent an addition or subtraction operator (passed for speed so do not need to call add_or_subtract for parent). \param i_parent is the operator index for the parent operator. \param i_arg is the operator index for the argument to the parent operator. \param op_info structure that holds the information for each of the operators. The output value of op_info[i_arg].usage is increased; to be specific, If sum_parent is true and the input value of op_info[i_arg].usage is no_usage, its output value is csum_usage. Otherwise, the output value of op_info[i_arg].usage is yes_usage. \param cexp_set This is a vector of sets with one set for each operator. We denote the i-th set by set[i]. \li In the special case where cexp_set.n_set() is zero, cexp_set is not changed. \li If cexp_set.n_set() != 0 and op_info[i_arg].usage == no_usage, the input value of set[i_arg] must be empty. In this case the output value if set[i_arg] is equal to set[i_parent] (which may also be empty). \li If cexp_set.n_set() != 0 and op_info[i_arg].usage != no_usage, the output value of set[i_arg] is the intersection of its input value and set[i_parent]. */ inline void usage_cexp_parent2arg( bool sum_parent , size_t i_parent , size_t i_arg , vector& op_info , sparse_pack& cexp_set ) { // cexp_set if( cexp_set.n_set() > 0 ) { if( op_info[i_arg].usage == no_usage ) { // set[i_arg] = set[i_parent] cexp_set.assignment(i_arg, i_parent, cexp_set); } else { // set[i_arg] = set[i_arg] intersect set[i_parent] cexp_set.binary_intersection(i_arg, i_arg, i_parent, cexp_set); } } // usage bool csum = sum_parent && op_info[i_arg].usage == no_usage; if( csum ) csum = add_or_subtract( op_info[i_arg].op ); if( csum ) op_info[i_arg].usage = csum_usage; else op_info[i_arg].usage = yes_usage; // return; } /*! Get variable to operator map and operator basic operator information \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param conditional_skip If conditional_skip this is true, the conditional expression information cexp_info will be calculated. This may be time intensive and may not have much benefit in the optimized recording. \param compare_op if this is true, arguments are considered used if they appear in compare operators. This is a side effect because compare operators have boolean results (and the result is not in the tape; i.e. NumRes(op) is zero for these operators. (This is an example of a side effect.) \param print_for_op if this is true, arguments are considered used if they appear in print forward operators; i.e., PriOp. This is also a side effect; i.e. NumRes(PriOp) is zero. \param play This is the operation sequence. It is essentially const, except for play back state which changes while it plays back the operation seqeunce. \param dep_taddr is a vector of variable indices for the dependent variables. \param var2op The input size of this vector must be zero. Upone return it has size equal to the number of variables in the operation sequence; i.e., num_var = play->nun_var_rec(). It maps each variable index to the operator that created the variable. This is only true for the primary variables. If the index i_var corresponds to an auxillary variable, var2op[i_var] is equalt to num_op (which is not a valid operator index). \param cexp_info The input size of this vector must be zero. If conditional_skip is false, cexp_info is not changed. Otherwise, upon return cexp_info has size equal to the number of conditional expressions in the operation sequence; i.e., the number of CExpOp operators. The value cexp_info[j] is the information corresponding to the j-th conditional expression in the operation sequence. This vector is in the same order as the operation sequence; i.e. if j1 > j2, cexp_info[j1].i_op > cexp_info[j2].i_op. \param vecad_used The input size of this vector must be zero. Upon retun it has size equal to the number of VecAD vectors in the operations sequences; i.e., play->num_vecad_vec_rec(). The VecAD vectors are indexed in the order that thier indices apprear in the one large play->GetVecInd that holds all the VecAD vectors. \param op_info The input size of this vector must be zero. Upon return it has size equal to the number of operators in the operation sequence; i.e., num_op = play->nun_var_rec(). The value op_info[i] have been set to the values corresponding to the i-th operator in the operation sequence. */ template void get_op_info( bool conditional_skip , bool compare_op , bool print_for_op , player* play , const vector& dep_taddr , vector& var2op , vector& cexp_info , vector& vecad_used , vector& op_info ) { CPPAD_ASSERT_UNKNOWN( var2op.size() == 0 ); CPPAD_ASSERT_UNKNOWN( cexp_info.size() == 0 ); CPPAD_ASSERT_UNKNOWN( vecad_used.size() == 0 ); CPPAD_ASSERT_UNKNOWN( op_info.size() == 0 ); // number of operators in the tape const size_t num_op = play->num_op_rec(); op_info.resize( num_op ); // // number of variables in the tape const size_t num_var = play->num_var_rec(); var2op.resize( num_var ); // // initialize mapping from variable index to operator index for(size_t i = 0; i < num_var; i++) var2op[i] = num_op; // invalid (used for auxillary variables) // // information set by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state; // // information set by forward_next OpCode op; // operator const addr_t* arg; // arguments size_t i_op; // operator index size_t i_var; // variable index of first result // // ---------------------------------------------------------------------- // Forward pass to compute op, arg, i_var for each operator and var2op // ---------------------------------------------------------------------- play->forward_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == BeginOp ); CPPAD_ASSERT_UNKNOWN( NumRes(BeginOp) == 1 ); CPPAD_ASSERT_UNKNOWN( i_op == 0 ); CPPAD_ASSERT_UNKNOWN( i_var == 0 ); op_info[i_op].op = op; op_info[i_op].arg = arg; op_info[i_op].i_var = i_var; // // This variaible index, 0, is automatically created, but it should // not used because variable index 0 represents a paraemeter during // the recording process. So we set var2op[i_var] = num_op; // size_t num_cexp_op = 0; user_state = start_user; while(op != EndOp) { // next operator play->forward_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( size_t( std::numeric_limits::max() ) > i_var ); // // information for this operator op_info[i_op].op = op; op_info[i_op].arg = arg; op_info[i_op].i_var = i_var; // // mapping from variable index to operator index if( NumRes(op) > 0 ) var2op[i_var] = i_op; // switch( op ) { case CSumOp: // must correct arg before next operator play->forward_csum(op, arg, i_op, i_var); break; case CSkipOp: // must correct arg before next operator play->forward_csum(op, arg, i_op, i_var); break; case UserOp: case UsrapOp: case UsravOp: case UsrrpOp: case UsrrvOp: play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case CExpOp: // Set the operator index for this conditional expression and // count the number of conditional expressions. ++num_cexp_op; break; default: break; } } // vector that maps conditional expression index to operator index vector cexp2op( num_cexp_op ); // ---------------------------------------------------------------------- // Reverse pass to compute usage and cexp_set for each operator // ---------------------------------------------------------------------- // work space used by user defined atomic functions typedef std::set size_set; vector user_x; // parameters in x as integers vector user_ix; // variables indices for argument vector vector user_r_set; // set sparsity pattern for result vector user_s_set; // set sparisty pattern for argument vector user_r_bool; // bool sparsity pattern for result vector user_s_bool; // bool sparisty pattern for argument vectorBool user_r_pack; // pack sparsity pattern for result vectorBool user_s_pack; // pack sparisty pattern for argument // atomic_base* user_atom = CPPAD_NULL; // current user atomic function bool user_pack = false; // sparsity pattern type is pack bool user_bool = false; // sparsity pattern type is bool bool user_set = false; // sparsity pattern type is set // ----------------------------------------------------------------------- // vecad information size_t num_vecad = play->num_vecad_vec_rec(); size_t num_vecad_ind = play->num_vec_ind_rec(); // vecad_used.resize(num_vecad); for(size_t i = 0; i < num_vecad; i++) vecad_used[i] = false; // vector arg2vecad(num_vecad_ind); for(size_t i = 0; i < num_vecad_ind; i++) arg2vecad[i] = num_vecad; // invalid value size_t arg_0 = 1; // value of arg[0] for theh first vecad for(size_t i = 0; i < num_vecad; i++) { // mapping from arg[0] value to index for this vecad object. arg2vecad[arg_0] = i; // // length of this vecad object size_t length = play->GetVecInd(arg_0 - 1); // // set to proper index in GetVecInd for next VecAD arg[0] value arg_0 += length + 1; } CPPAD_ASSERT_UNKNOWN( arg_0 == num_vecad_ind + 1 ); // ----------------------------------------------------------------------- // parameter information (used by atomic function calls) size_t num_par = play->num_par_rec(); const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // ----------------------------------------------------------------------- // Set of conditional expressions comparisons that usage of each /// operator depends on. The operator can be skipped if any of the // comparisons results in the set holds. A set for operator i_op is // not defined and left empty when op_info[i_op].usage = no_usage. /// It is also left empty for the result of any VecAD operations. sparse_pack cexp_set; // // number of sets size_t num_set = 0; if( conditional_skip && num_cexp_op > 0) num_set = num_op; // // conditional expression index = element / 2 // conditional expression compare = bool ( element % 2) size_t end_set = 2 * num_cexp_op; // cexp_set.resize(num_set, end_set); // ----------------------------------------------------------------------- // // initialize operator usage for(size_t i = 0; i < num_op; i++) op_info[i].usage = no_usage; for(size_t i = 0; i < dep_taddr.size(); i++) { i_op = var2op[ dep_taddr[i] ]; op_info[i_op].usage = yes_usage; // dependent variables } // // Initialize reverse pass size_t last_user_i_op = 0; size_t cexp_index = num_cexp_op; user_state = end_user; i_op = num_op; while(i_op != 0 ) { --i_op; // // this operator information op = op_info[i_op].op; arg = op_info[i_op].arg; i_var = op_info[i_op].i_var; // // Is the result of this operation used. // (This only makes sense when NumRes(op) > 0.) enum_usage use_result = op_info[i_op].usage; // bool sum_op = false; switch( op ) { // ============================================================= // normal operators // ============================================================= // Only one variable with index arg[0] case SubvpOp: sum_op = true; // case AbsOp: case AcosOp: case AcoshOp: case AsinOp: case AsinhOp: case AtanOp: case AtanhOp: case CosOp: case CoshOp: case DivvpOp: case ErfOp: case ExpOp: case Expm1Op: case LogOp: case Log1pOp: case PowvpOp: case SignOp: case SinOp: case SinhOp: case SqrtOp: case TanOp: case TanhOp: case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) > 0 ); if( use_result != no_usage ) { size_t j_op = var2op[ arg[0] ]; usage_cexp_parent2arg(sum_op, i_op, j_op, op_info, cexp_set); } break; // -------------------------------------------- // Only one variable with index arg[1] case AddpvOp: case SubpvOp: sum_op = true; // case DisOp: case DivpvOp: case MulpvOp: case PowpvOp: case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) > 0 ); if( use_result != no_usage ) { size_t j_op = var2op[ arg[1] ]; usage_cexp_parent2arg(sum_op, i_op, j_op, op_info, cexp_set); } break; // -------------------------------------------- // arg[0] and arg[1] are the only variables case AddvvOp: case SubvvOp: sum_op = true; // case DivvvOp: case MulvvOp: case PowvvOp: case ZmulvvOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) > 0 ); if( use_result != no_usage ) { for(size_t i = 0; i < 2; i++) { size_t j_op = var2op[ arg[i] ]; usage_cexp_parent2arg( sum_op, i_op, j_op, op_info, cexp_set ); } } break; // -------------------------------------------- // Conditional expression operators // arg[2], arg[3], arg[4], arg[5] are parameters or variables case CExpOp: --cexp_index; cexp2op[ cexp_index ] = i_op; CPPAD_ASSERT_UNKNOWN( NumRes(op) > 0 ); if( use_result != no_usage ) { CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); addr_t mask[] = {1, 2, 4, 8}; for(size_t i = 0; i < 4; i++) { if( arg[1] & mask[i] ) { size_t j_op = var2op[ arg[2 + i] ]; usage_cexp_parent2arg( sum_op, i_op, j_op, op_info, cexp_set ); } } // here is where we add elements to cexp_set if( conditional_skip ) { bool same_variable = bool(arg[1] & 4) && bool(arg[1] & 8); same_variable &= arg[4] == arg[5]; if( ( arg[1] & 4 ) && (! same_variable) ) { // arg[4] is a variable size_t j_op = var2op[ arg[4] ]; CPPAD_ASSERT_UNKNOWN(op_info[j_op].usage != no_usage); // j_op corresponds to the value used when the // comparison result is true. It can be skipped when // the comparison is false (0). size_t element = 2 * cexp_index + 0; cexp_set.add_element(j_op, element); } if( ( arg[1] & 8 ) && (! same_variable) ) { // arg[5] is a variable size_t j_op = var2op[ arg[5] ]; CPPAD_ASSERT_UNKNOWN(op_info[j_op].usage != no_usage); // j_op corresponds to the value used when the // comparison result is false. It can be skipped when // the comparison is true (1). size_t element = 2 * cexp_index + 1; cexp_set.add_element(j_op, element); } } } break; // -------------------------------------------- // Operations that are never used // (new CSkip options are generated if conditional_skip is true) case CSkipOp: case ParOp: break; // Operators that are always used case InvOp: case BeginOp: case EndOp: op_info[i_op].usage = yes_usage; break; // ----------------------------------------------- // The print forward operator case PriOp: CPPAD_ASSERT_NARG_NRES(op, 5, 0); if( print_for_op ) { op_info[i_op].usage = yes_usage; if( arg[0] & 1 ) { // arg[1] is a variable size_t j_op = var2op[ arg[1] ]; usage_cexp_parent2arg( sum_op, i_op, j_op, op_info, cexp_set ); } if( arg[0] & 2 ) { // arg[3] is a variable size_t j_op = var2op[ arg[3] ]; usage_cexp_parent2arg( sum_op, i_op, j_op, op_info, cexp_set ); } } break; // ----------------------------------------------------- // ============================================================= // Comparison operators // ============================================================= // Compare operators where arg[1] is only variable case LepvOp: case LtpvOp: case EqpvOp: case NepvOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); if( compare_op ) { op_info[i_op].usage = yes_usage; // size_t j_op = var2op[ arg[1] ]; usage_cexp_parent2arg(sum_op, i_op, j_op, op_info, cexp_set); } break; // ---------------------------------------------- // Compare operators where arg[0] is only variable case LevpOp: case LtvpOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); if( compare_op ) { op_info[i_op].usage = yes_usage; // size_t j_op = var2op[ arg[0] ]; usage_cexp_parent2arg(sum_op, i_op, j_op, op_info, cexp_set); } break; // ---------------------------------------------- // Compare operators where arg[0] and arg[1] are variables case LevvOp: case LtvvOp: case EqvvOp: case NevvOp: if( compare_op ) CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); if( compare_op ) { op_info[i_op].usage = yes_usage; // for(size_t i = 0; i < 2; i++) { size_t j_op = var2op[ arg[i] ]; usage_cexp_parent2arg( sum_op, i_op, j_op, op_info, cexp_set ); } } break; // ---------------------------------------------- // ============================================================= // VecAD operators // ============================================================= // load operator using a parameter index case LdpOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) > 0 ); if( use_result != no_usage ) { size_t i_vec = arg2vecad[ arg[0] ]; vecad_used[i_vec] = true; } break; // -------------------------------------------- // load operator using a variable index case LdvOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) > 0 ); if( use_result != no_usage ) { size_t i_vec = arg2vecad[ arg[0] ]; vecad_used[i_vec] = true; // size_t j_op = var2op[ arg[1] ]; op_info[j_op].usage = yes_usage; } break; // -------------------------------------------- // Store a variable using a parameter index case StpvOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); if( vecad_used[ arg2vecad[ arg[0] ] ] ) { op_info[i_op].usage = yes_usage; // size_t j_op = var2op[ arg[2] ]; op_info[j_op].usage = yes_usage; } break; // -------------------------------------------- // Store a variable using a variable index case StvvOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) == 0 ); if( vecad_used[ arg2vecad[ arg[0] ] ] ) { op_info[i_op].usage = yes_usage; // size_t j_op = var2op[ arg[1] ]; op_info[j_op].usage = yes_usage; size_t k_op = var2op[ arg[2] ]; op_info[k_op].usage = yes_usage; } break; // ----------------------------------------------------- // ============================================================= // cumuilative summation operator // ============================================================ case CSumOp: CPPAD_ASSERT_UNKNOWN( NumRes(op) == 1 ); { size_t num_add = size_t( arg[0] ); size_t num_sub = size_t( arg[1] ); for(size_t i = 0; i < num_add + num_sub; i++) { size_t j_op = var2op[ arg[3 + i] ]; usage_cexp_parent2arg( sum_op, i_op, j_op, op_info, cexp_set ); } } // ============================================================= // user defined atomic operators // ============================================================ case UserOp: // start or end atomic operation sequence if( user_state == end_user ) { // revese_user using op_info instead of play size_t user_index = arg[0]; user_old = arg[1]; user_n = arg[2]; user_m = arg[3]; user_j = user_n; user_i = user_m; user_state = ret_user; user_atom = atomic_base::class_object(user_index); // ------------------------------------------------------- last_user_i_op = i_op; CPPAD_ASSERT_UNKNOWN( i_op > user_n + user_m + 1 ); CPPAD_ASSERT_UNKNOWN(op_info[last_user_i_op].usage==no_usage); # ifndef NDEBUG if( cexp_set.n_set() > 0 ) { sparse_pack_const_iterator itr(cexp_set, last_user_i_op); CPPAD_ASSERT_UNKNOWN( *itr == cexp_set.end() ); } # endif // user_x.resize( user_n ); user_ix.resize( user_n ); // user_pack = user_atom->sparsity() == atomic_base::pack_sparsity_enum; user_bool = user_atom->sparsity() == atomic_base::bool_sparsity_enum; user_set = user_atom->sparsity() == atomic_base::set_sparsity_enum; CPPAD_ASSERT_UNKNOWN( user_pack || user_bool || user_set ); // // Note that q is one for this call the sparsity calculation if( user_pack ) { user_r_pack.resize( user_m ); user_s_pack.resize( user_n ); for(size_t i = 0; i < user_m; i++) user_r_pack[ i ] = false; } if( user_bool ) { user_r_bool.resize( user_m ); user_s_bool.resize( user_n ); for(size_t i = 0; i < user_m; i++) user_r_bool[ i ] = false; } if( user_set ) { user_s_set.resize(user_n); user_r_set.resize(user_m); for(size_t i = 0; i < user_m; i++) user_r_set[i].clear(); } } else { // reverse_user using op_info instead of play CPPAD_ASSERT_UNKNOWN( user_state == start_user ); CPPAD_ASSERT_UNKNOWN( user_n == size_t(arg[2]) ); CPPAD_ASSERT_UNKNOWN( user_m == size_t(arg[3]) ); CPPAD_ASSERT_UNKNOWN( user_j == 0 ); CPPAD_ASSERT_UNKNOWN( user_i == 0 ); user_state = end_user; // ------------------------------------------------------- CPPAD_ASSERT_UNKNOWN( i_op + user_n + user_m + 1 == last_user_i_op ); // call users function for this operation user_atom->set_old(user_old); bool user_ok = false; size_t user_q = 1; // as if sum of dependent variables if( user_pack ) { user_ok = user_atom->rev_sparse_jac( user_q, user_r_pack, user_s_pack, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_jac( user_q, user_r_pack, user_s_pack ); } if( user_bool ) { user_ok = user_atom->rev_sparse_jac( user_q, user_r_bool, user_s_bool, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_jac( user_q, user_r_bool, user_s_bool ); } if( user_set ) { user_ok = user_atom->rev_sparse_jac( user_q, user_r_set, user_s_set, user_x ); if( ! user_ok ) user_ok = user_atom->rev_sparse_jac( user_q, user_r_set, user_s_set ); } if( ! user_ok ) { std::string s = "Optimizing an ADFun object" " that contains the atomic function\n\t"; s += user_atom->afun_name(); s += "\nCurrent atomic_sparsity is set to "; // if( user_set ) s += "set_sparsity_enum.\n"; if( user_bool ) s += "bool_sparsity_enum.\n"; if( user_pack ) s += "pack_sparsity_enum.\n"; // s += "This version of rev_sparse_jac returned false"; CPPAD_ASSERT_KNOWN(false, s.c_str() ); } if( op_info[last_user_i_op].usage != no_usage ) for(size_t j = 0; j < user_n; j++) if( user_ix[j] > 0 ) { // This user argument is a variable bool use_arg_j = false; if( user_set ) { if( ! user_s_set[j].empty() ) use_arg_j = true; } if( user_bool ) { if( user_s_bool[j] ) use_arg_j = true; } if( user_pack ) { if( user_s_pack[j] ) use_arg_j = true; } if( use_arg_j ) { size_t j_op = var2op[ user_ix[j] ]; usage_cexp_parent2arg( sum_op, last_user_i_op, j_op, op_info, cexp_set ); } } // copy set infomation from last to first if( cexp_set.n_set() > 0 ) cexp_set.assignment(i_op, last_user_i_op, cexp_set); // copy user information from last to all the user operators // for this call for(size_t j = 0; j < user_n + user_m + 1; ++j) op_info[i_op + j].usage = op_info[last_user_i_op].usage; } break; // ------------------------------------------------------- case UsrapOp: // parameter argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); // // reverse_user using op_info instead of play CPPAD_ASSERT_NARG_NRES(op, 1, 0); CPPAD_ASSERT_UNKNOWN( 0 < user_j && user_j < user_n ); --user_j; if( user_j == 0 ) user_state = start_user; // ------------------------------------------------------------- user_ix[user_j] = 0; // // parameter arguments user_x[user_j] = parameter[arg[0]]; // break; case UsravOp: // variable argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( arg[0] <= op_info[i_op].i_var ); CPPAD_ASSERT_UNKNOWN( 0 < arg[0] ); // // reverse_user using op_info instead of play CPPAD_ASSERT_NARG_NRES(op, 1, 0); CPPAD_ASSERT_UNKNOWN( 0 < user_j && user_j <= user_n ); --user_j; if( user_j == 0 ) user_state = start_user; // ------------------------------------------------------------- user_ix[user_j] = arg[0]; // // variable arguments as parameters user_x[user_j] = CppAD::numeric_limits::quiet_NaN(); // break; case UsrrvOp: // variable result in an atomic operation sequence // // reverse_user using op_info instead of play CPPAD_ASSERT_NARG_NRES(op, 0, 1); CPPAD_ASSERT_UNKNOWN( 0 < user_i && user_i <= user_m ); --user_i; if( user_i == 0 ) user_state = arg_user; // ------------------------------------------------------------- if( use_result ) { if( user_set ) user_r_set[user_i].insert(0); if( user_bool ) user_r_bool[user_i] = true; if( user_pack ) user_r_pack[user_i] = true; // usage_cexp_parent2arg( sum_op, i_op, last_user_i_op, op_info, cexp_set ); } break; // -------------------------------------------------------- case UsrrpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); // // reverse_user using op_info instead of play CPPAD_ASSERT_NARG_NRES(op, 0, 1); CPPAD_ASSERT_UNKNOWN( 0 < user_i && user_i < user_m ); --user_i; if( user_i == 0 ) user_state = arg_user; break; // ============================================================ // all cases should be handled above default: CPPAD_ASSERT_UNKNOWN(0); } } // ---------------------------------------------------------------------- // compute previous in op_info // ---------------------------------------------------------------------- sparse_list hash_table_op; hash_table_op.resize(CPPAD_HASH_TABLE_SIZE, num_op); // user_state = start_user; for(i_op = 0; i_op < num_op; ++i_op) { op_info[i_op].previous = 0; if( op_info[i_op].usage == yes_usage ) switch( op_info[i_op].op ) { case NumberOp: CPPAD_ASSERT_UNKNOWN(false); break; case BeginOp: case CExpOp: case CSkipOp: case CSumOp: case EndOp: case InvOp: case LdpOp: case LdvOp: case ParOp: case PriOp: case StppOp: case StpvOp: case StvpOp: case StvvOp: case UserOp: case UsrapOp: case UsravOp: case UsrrpOp: case UsrrvOp: // these operators never match pevious operators break; case AbsOp: case AcosOp: case AcoshOp: case AddpvOp: case AddvvOp: case AsinOp: case AsinhOp: case AtanOp: case AtanhOp: case CosOp: case CoshOp: case DisOp: case DivpvOp: case DivvpOp: case DivvvOp: case EqpvOp: case EqvvOp: case ErfOp: case ExpOp: case Expm1Op: case LepvOp: case LevpOp: case LevvOp: case LogOp: case Log1pOp: case LtpvOp: case LtvpOp: case LtvvOp: case MulpvOp: case MulvvOp: case NepvOp: case NevvOp: case PowpvOp: case PowvpOp: case PowvvOp: case SignOp: case SinOp: case SinhOp: case SqrtOp: case SubpvOp: case SubvpOp: case SubvvOp: case TanOp: case TanhOp: case ZmulpvOp: case ZmulvpOp: case ZmulvvOp: // check for a previous match match_op( var2op, op_info, i_op, hash_table_op ); if( op_info[i_op].previous != 0 ) { // like a unary operator that assigns i_op equal to previous. size_t previous = op_info[i_op].previous; bool sum_op = false; CPPAD_ASSERT_UNKNOWN( previous < i_op ); usage_cexp_parent2arg( sum_op, i_op, previous, op_info, cexp_set ); } break; } } // ---------------------------------------------------------------------- // compute cexp_info // ---------------------------------------------------------------------- if( cexp_set.n_set() == 0 ) return; // // initialize information for each conditional expression cexp_info.resize(num_cexp_op); for(size_t i = 0; i < num_cexp_op; i++) { CPPAD_ASSERT_UNKNOWN( op_info[i].previous == 0 || op_info[i].usage == yes_usage ); i_op = cexp2op[i]; arg = op_info[i_op].arg; CPPAD_ASSERT_UNKNOWN( op_info[i_op].op == CExpOp ); // struct_cexp_info info; info.i_op = i_op; info.cop = CompareOp( arg[0] ); info.flag = arg[1]; info.left = arg[2]; info.right = arg[3]; // // max_left_right size_t index = 0; if( arg[1] & 1 ) index = std::max(index, info.left); if( arg[1] & 2 ) index = std::max(index, info.right); CPPAD_ASSERT_UNKNOWN( index > 0 ); info.max_left_right = index; // cexp_info[i] = info; }; // Determine which operators can be conditionally skipped i_op = 0; while(i_op < num_op) { size_t j_op = i_op; bool keep = op_info[i_op].usage != no_usage; keep &= op_info[i_op].usage != csum_usage; keep &= op_info[i_op].previous == 0; if( keep ) { sparse_pack_const_iterator itr(cexp_set, i_op); if( *itr != cexp_set.end() ) { if( op_info[i_op].op == UserOp ) { // i_op is the first operations in this user atomic call. // Find the last operation in this call. ++j_op; while( op_info[j_op].op != UserOp ) { switch( op_info[j_op].op ) { case UsrapOp: case UsravOp: case UsrrpOp: case UsrrvOp: break; default: CPPAD_ASSERT_UNKNOWN(false); } ++j_op; } } } while( *itr != cexp_set.end() ) { size_t element = *itr; size_t index = element / 2; bool compare = bool( element % 2 ); if( compare == false ) { cexp_info[index].skip_op_false.push_back(i_op); if( j_op != i_op ) cexp_info[index].skip_op_false.push_back(j_op); } else { cexp_info[index].skip_op_true.push_back(i_op); if( j_op != i_op ) cexp_info[index].skip_op_true.push_back(j_op); } ++itr; } } CPPAD_ASSERT_UNKNOWN( i_op <= j_op ); i_op += (1 + j_op) - i_op; } return; } } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/op_info.hpp0000644000175200017650000000300113057470466020613 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_OP_INFO_HPP # define CPPAD_LOCAL_OPTIMIZE_OP_INFO_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /// information for one operator struct struct_op_info { /// arguments const addr_t* arg; /// Primary (not auxillary) variable index for this operator. If the // operator has not results, this is num_var (an invalid variable index). addr_t i_var; /*! previous operator that can be used in place of this operator. \li If previous == 0, no such operator was found. \li If previous != 0, op_info[pevious].previous == 0 and op_info[previous].usage == yes_usage. */ addr_t previous; /// op code OpCode op; /// How is this operator used to compute the dependent variables. /// If usage = csum_usage or usage = no_usage, previous = 0. enum_usage usage; }; } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/record_vv.hpp0000644000175200017650000000663713057470466021175 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_RECORD_VV_HPP # define CPPAD_LOCAL_OPTIMIZE_RECORD_VV_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file record_vv.hpp Record an operation of the form (variable op variable). */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Record an operation of the form (variable op variable). \param var2op mapping from old variable index to old operator index. \param op_info mapping from old index to operator index to operator information \param old2new mapping from old operator index to information about the new recording. \param current is the index in the old operation sequence for the variable corresponding to the result for the current operator. We use the notation i_op = var2op[current]. It follows that NumRes( op_info[i_op].op ) > 0. If 0 < j_op < i_op, either op_info[j_op].csum_connected, op_info[j_op].usage = 0, or old2new[j_op].new_var != 0. \param npar is the number of parameters corresponding to the old operation sequence. \param par is a vector of length npar containing the parameters the old operation sequence; i.e., given a parameter index i < npar, the corresponding parameter value is par[i]. \param rec is the object that will record the new operations. \return is the operator and variable indices in the new operation sequence. \param op is the operator that we are recording which must be one of the following: AddvvOp, DivvvOp, MulvvOp, PowvvOp, SubvvOp, ZmulvvOp. \param arg is the vector of arguments for this operator. */ template struct_size_pair record_vv( const vector& var2op , const vector& op_info , const CppAD::vector& old2new , size_t current , size_t npar , const Base* par , recorder* rec , OpCode op , const addr_t* arg ) { # ifndef NDEBUG switch(op) { case AddvvOp: case DivvvOp: case MulvvOp: case PowvvOp: case SubvvOp: case ZmulvvOp: break; default: CPPAD_ASSERT_UNKNOWN(false); } # endif CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < current ); CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < current ); addr_t new_arg[2]; new_arg[0] = old2new[ var2op[arg[0]] ].new_var; new_arg[1] = old2new[ var2op[arg[1]] ].new_var; rec->PutArg( new_arg[0], new_arg[1] ); struct_size_pair ret; ret.i_op = rec->num_op_rec(); ret.i_var = rec->PutOp(op); CPPAD_ASSERT_UNKNOWN( 0 < new_arg[0] && size_t(new_arg[0]) < ret.i_var ); CPPAD_ASSERT_UNKNOWN( 0 < new_arg[1] && size_t(new_arg[1]) < ret.i_var ); return ret; } } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/cexp_info.hpp0000644000175200017650000000472713057470466021154 0ustar coincoin-web# ifndef CPPAD_LOCAL_OPTIMIZE_CEXP_INFO_HPP # define CPPAD_LOCAL_OPTIMIZE_CEXP_INFO_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include // defines CompareOp # include /*! \file cexp_info.hpp Information about one conditional expression. */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Information about one conditional expression. */ struct struct_cexp_info { /// The operator index for this conditional expression operation size_t i_op; /// (flag & 1) is true if and only if left is a variable /// (flag & 2) is true if and only if right is a variable size_t flag; /// variable or parameter index for left comparison operand size_t left; /// variable or parameter index for right comparison operand size_t right; /// maximum variable index between left and right (ignoring parameters). size_t max_left_right; /// set of operator that are not used when comparison result is true /// Note that UsrapOp, UsravOp, UsrrpOp, and UsrrvOp, are not in this /// vector and should be skipped when the corresponding UserOp are skipped. CppAD::vector skip_op_true; /// set of variables that are not used when comparison result is false /// Note that UsrapOp, UsravOp, UsrrpOp, and UsrrvOp, are not in this /// vector and should be skipped when the corresponding UserOp are skipped. CppAD::vector skip_op_false; /// comparision operator for this conditional expression CompareOp cop; }; // Information about the conditional skip in the new operation sequence struct struct_cskip_new { /// new variable or parameter index for left comparison operand size_t left; /// new variable or parameter index for right comparison operand size_t right; /// maximum variable index between left and right (ignoring parameters). size_t max_left_right; /// index where this conditional skips arguments start size_t i_arg; }; } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/match_op.hpp0000644000175200017650000001643313057470466020771 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_MATCH_OP_HPP # define CPPAD_LOCAL_OPTIMIZE_MATCH_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include /*! \file match_op.hpp Check if current operator matches a previous operator. */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Search for a previous operator that matches the current one. If an argument for the current operator is a variable, and the argument has previous match, the previous match for the argument is used when checking for a match for the current operator. \param var2op mapping from variable index to operator index. \param op_info Mapping from operator index to operator information. The input value of op_info[current].previous is assumed to be zero. If a match if found, the output value of op_info[current].previous is set to the matching operator index, otherwise it is left as is. Note that op_info[current].previous < current. \param current is the index of the current operator which must be an unary or binary operator. Note that NumArg(ErfOp) == 3 but it is effectivey a unary operator and is allowed otherwise NumArg( op_info[current].op) < 3. It is assumed that hash_table_op is initialized as a vector of emtpy sets. After this initialization, the value of current inceases with each call to match_op. \li This must be a unary or binary operator; hence, NumArg( op_info[current].op ) is one or two. There is one exception, NumRes( ErfOp ) == 3, but arg[0] is the only true arguments (the others are always the same). \li This must not be a VecAD load or store operation; i.e., LtpvOp, LtvpOp, LtvvOp, StppOp, StpvOp, StvpOp, StvvOp. It also must not be an independent variable operator InvOp. \param hash_table_op is a vector of sets, hash_table_op.n_set() == CPPAD_HASH_TABLE_SIZE and hash_table_op.end() == op_info.size(). If i_op is an element of set[j], then the operation op_info[i_op] has hash code j, and op_info[i_op] does not match any other element of set[j]. An entry will be added each time match_op is called and a match for the current operator is not found. */ inline void match_op( const vector& var2op , vector& op_info , size_t current , sparse_list& hash_table_op ) { size_t num_op = op_info.size(); // CPPAD_ASSERT_UNKNOWN( op_info[current].previous == 0 ); CPPAD_ASSERT_UNKNOWN( hash_table_op.n_set() == CPPAD_HASH_TABLE_SIZE ); CPPAD_ASSERT_UNKNOWN( hash_table_op.end() == num_op ); CPPAD_ASSERT_UNKNOWN( current < num_op ); // // current operator OpCode op = op_info[current].op; const addr_t* arg = op_info[current].arg; // // which arguments are variable size_t num_arg = NumArg(op); // bool variable[2]; variable[0] = false; variable[1] = false; switch(op) { // case ErfOp: num_arg = 1; // other arugments are always the same // case AbsOp: case AcosOp: case AcoshOp: case AsinOp: case AsinhOp: case AtanOp: case AtanhOp: case CosOp: case CoshOp: case ExpOp: case Expm1Op: case LogOp: case Log1pOp: case SignOp: case SinOp: case SinhOp: case SqrtOp: case TanOp: case TanhOp: CPPAD_ASSERT_UNKNOWN( num_arg == 1 ); variable[0] = true; break; case AddpvOp: case DisOp: case DivpvOp: case EqpvOp: case LepvOp: case LtpvOp: case MulpvOp: case NepvOp: case PowpvOp: case SubpvOp: case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( num_arg == 2 ); variable[1] = true; break; case DivvpOp: case LevpOp: case LtvpOp: case PowvpOp: case SubvpOp: case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( num_arg == 2 ); variable[0] = true; break; case AddvvOp: case DivvvOp: case EqvvOp: case LevvOp: case LtvvOp: case MulvvOp: case NevvOp: case PowvvOp: case SubvvOp: case ZmulvvOp: CPPAD_ASSERT_UNKNOWN( num_arg == 2 ); variable[0] = true; variable[1] = true; break; default: CPPAD_ASSERT_UNKNOWN(false); } // // If i-th argument to current operator has a previous operator, // this is the i-th argument for previous operator. // Otherwise, it is the i-th argument for the current operator // (if a previous variable exists) addr_t arg_match[2]; for(size_t j = 0; j < num_arg; ++j) { arg_match[j] = arg[j]; if( variable[j] ) { size_t previous = op_info[ var2op[arg[j]] ].previous; if( previous != 0 ) { CPPAD_ASSERT_UNKNOWN( op_info[previous].previous == 0 ); // arg_match[j] = op_info[previous].i_var; } } } unsigned short code = optimize_hash_code(op, num_arg, arg_match); // // iterator for the set with this hash code sparse_list_const_iterator itr(hash_table_op, code); // // check for a match size_t count = 0; while( *itr != num_op ) { ++count; // // candidate previous for current operator size_t candidate = *itr; CPPAD_ASSERT_UNKNOWN( candidate < current ); CPPAD_ASSERT_UNKNOWN( op_info[candidate].previous == 0 ); // // check for a match bool match = op == op_info[candidate].op; if( match ) { for(size_t j = 0; j < num_arg; j++) { if( variable[j] ) { size_t previous = op_info[ var2op[op_info[candidate].arg[j]] ].previous; if( previous != 0 ) { CPPAD_ASSERT_UNKNOWN(op_info[previous].previous == 0); // match &= arg_match[j] == addr_t( op_info[previous].i_var ); } else match &= arg_match[j] == op_info[candidate].arg[j]; } } } if( match ) { op_info[current].previous = candidate; return; } ++itr; } // special case where operator is commutative if( (op == AddvvOp) | (op == MulvvOp ) ) { CPPAD_ASSERT_UNKNOWN( NumArg(op) == 2 ); std::swap( arg_match[0], arg_match[1] ); // code = optimize_hash_code(op, num_arg, arg_match); sparse_list_const_iterator itr_swap(hash_table_op, code); while( *itr_swap != num_op ) { size_t candidate = *itr_swap; CPPAD_ASSERT_UNKNOWN( candidate < current ); CPPAD_ASSERT_UNKNOWN( op_info[candidate].previous == 0 ); // bool match = op == op_info[candidate].op; if( match ) { for(size_t j = 0; j < num_arg; j++) { CPPAD_ASSERT_UNKNOWN( variable[j] ) size_t previous = op_info[ var2op[op_info[candidate].arg[j]] ].previous; if( previous != 0 ) { CPPAD_ASSERT_UNKNOWN(op_info[previous].previous == 0); // match &= arg_match[j] == addr_t( op_info[previous].i_var ); } else match &= arg_match[j] == op_info[candidate].arg[j]; } } if( match ) { op_info[current].previous = candidate; return; } ++itr_swap; } } CPPAD_ASSERT_UNKNOWN( count < 11 ); if( count == 10 ) { // restart the list hash_table_op.clear(code); } // no match was found, add this operator the the set for this hash code hash_table_op.add_element(code, current); } } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/optimize/old2new.hpp0000644000175200017650000000214713057470466020546 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_OPTIMIZE_OLD2NEW_HPP # define CPPAD_LOCAL_OPTIMIZE_OLD2NEW_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*! \file old2new.hpp Information that maps old an old operator to a new opeator and new variable. */ // BEGIN_CPPAD_LOCAL_OPTIMIZE_NAMESPACE namespace CppAD { namespace local { namespace optimize { /*! Information that maps old an old operator to a new opeator and new variable. */ struct struct_old2new { /// New operator index for this old operator. addr_t new_op; /// New varaible index for this old operator. addr_t new_var; }; } } } // END_CPPAD_LOCAL_OPTIMIZE_NAMESPACE # endif cppad-20170000.3/cppad/local/op.hpp0000644000175200017650000000413613057470466015752 0ustar coincoin-web// $Id: op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_OP_HPP # define CPPAD_LOCAL_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // used by the sparse operators # include // operations # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # include # endif cppad-20170000.3/cppad/local/log_op.hpp0000644000175200017650000001143213057470466016610 0ustar coincoin-web// $Id: log_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_LOG_OP_HPP # define CPPAD_LOCAL_LOG_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file log_op.hpp Forward and reverse mode calculations for z = log(x). */ /*! Compute forward mode Taylor coefficient for result of op = LogOp. The C++ source code corresponding to this operation is \verbatim z = log(x) \endverbatim \copydetails forward_unary1_op */ template inline void forward_log_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { size_t k; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LogOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(LogOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; if( p == 0 ) { z[0] = log( x[0] ); p++; if( q == 0 ) return; } if ( p == 1 ) { z[1] = x[1] / x[0]; p++; } for(size_t j = p; j <= q; j++) { z[j] = -z[1] * x[j-1]; for(k = 2; k < j; k++) z[j] -= Base(k) * z[k] * x[j-k]; z[j] /= Base(j); z[j] += x[j]; z[j] /= x[0]; } } /*! Muiltiple directions Taylor coefficient for op = LogOp. The C++ source code corresponding to this operation is \verbatim z = log(x) \endverbatim \copydetails forward_unary1_op_dir */ template inline void forward_log_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LogOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(LogOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = Base(q) * x[m+ell]; for(size_t k = 1; k < q; k++) z[m+ell] -= Base(k) * z[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell]; z[m+ell] /= (Base(q) * x[0]); } } /*! Compute zero order forward mode Taylor coefficient for result of op = LogOp. The C++ source code corresponding to this operation is \verbatim z = log(x) \endverbatim \copydetails forward_unary1_op_0 */ template inline void forward_log_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LogOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(LogOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; z[0] = log( x[0] ); } /*! Compute reverse mode partial derivatives for result of op = LogOp. The C++ source code corresponding to this operation is \verbatim z = log(x) \endverbatim \copydetails reverse_unary1_op */ template inline void reverse_log_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { size_t j, k; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(LogOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(LogOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; Base inv_x0 = Base(1) / x[0]; j = d; while(j) { // scale partial w.r.t z[j] pz[j] = azmul(pz[j] , inv_x0); px[0] -= azmul(pz[j], z[j]); px[j] += pz[j]; // further scale partial w.r.t. z[j] pz[j] /= Base(j); for(k = 1; k < j; k++) { pz[k] -= Base(k) * azmul(pz[j], x[j-k]); px[j-k] -= Base(k) * azmul(pz[j], z[k]); } --j; } px[0] += azmul(pz[0], inv_x0); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/atan_op.hpp0000644000175200017650000001377213057470466016763 0ustar coincoin-web// $Id: atan_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_ATAN_OP_HPP # define CPPAD_LOCAL_ATAN_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file atan_op.hpp Forward and reverse mode calculations for z = atan(x). */ /*! Forward mode Taylor coefficient for result of op = AtanOp. The C++ source code corresponding to this operation is \verbatim z = atan(x) \endverbatim The auxillary result is \verbatim y = 1 + x * x \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_atan_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AtanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation size_t k; if( p == 0 ) { z[0] = atan( x[0] ); b[0] = Base(1) + x[0] * x[0]; p++; } for(size_t j = p; j <= q; j++) { b[j] = Base(2) * x[0] * x[j]; z[j] = Base(0); for(k = 1; k < j; k++) { b[j] += x[k] * x[j-k]; z[j] -= Base(k) * z[k] * b[j-k]; } z[j] /= Base(j); z[j] += x[j]; z[j] /= b[0]; } } /*! Multiple direction Taylor coefficient for op = AtanOp. The C++ source code corresponding to this operation is \verbatim z = atan(x) \endverbatim The auxillary result is \verbatim y = 1 + x * x \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_atan_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AtanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; Base* b = z - num_taylor_per_var; // called y in documentation size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { b[m+ell] = Base(2) * x[m+ell] * x[0]; z[m+ell] = Base(q) * x[m+ell]; for(size_t k = 1; k < q; k++) { b[m+ell] += x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell]; z[m+ell] -= Base(k) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell]; } z[m+ell] /= ( Base(q) * b[0] ); } } /*! Zero order forward mode Taylor coefficient for result of op = AtanOp. The C++ source code corresponding to this operation is \verbatim z = atan(x) \endverbatim The auxillary result is \verbatim y = 1 + x * x \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_atan_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AtanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* b = z - cap_order; // called y in documentation z[0] = atan( x[0] ); b[0] = Base(1) + x[0] * x[0]; } /*! Reverse mode partial derivatives for result of op = AtanOp. The C++ source code corresponding to this operation is \verbatim z = atan(x) \endverbatim The auxillary result is \verbatim y = 1 + x * x \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_atan_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(AtanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* b = z - cap_order; // called y in documentation Base* pb = pz - nc_partial; Base inv_b0 = Base(1) / b[0]; // number of indices to access size_t j = d; size_t k; while(j) { // scale partials w.r.t z[j] and b[j] pz[j] = azmul(pz[j], inv_b0); pb[j] *= Base(2); pb[0] -= azmul(pz[j], z[j]); px[j] += pz[j] + azmul(pb[j], x[0]); px[0] += azmul(pb[j], x[j]); // more scaling of partials w.r.t z[j] pz[j] /= Base(j); for(k = 1; k < j; k++) { pb[j-k] -= Base(k) * azmul(pz[j], z[k]); pz[k] -= Base(k) * azmul(pz[j], b[j-k]); px[k] += azmul(pb[j], x[j-k]); } --j; } px[0] += azmul(pz[0], inv_b0) + Base(2) * azmul(pb[0], x[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/sqrt_op.hpp0000644000175200017650000001125513057470466017023 0ustar coincoin-web// $Id: sqrt_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_SQRT_OP_HPP # define CPPAD_LOCAL_SQRT_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sqrt_op.hpp Forward and reverse mode calculations for z = sqrt(x). */ /*! Compute forward mode Taylor coefficient for result of op = SqrtOp. The C++ source code corresponding to this operation is \verbatim z = sqrt(x) \endverbatim \copydetails forward_unary1_op */ template inline void forward_sqrt_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SqrtOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SqrtOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; size_t k; if( p == 0 ) { z[0] = sqrt( x[0] ); p++; } for(size_t j = p; j <= q; j++) { z[j] = Base(0); for(k = 1; k < j; k++) z[j] -= Base(k) * z[k] * z[j-k]; z[j] /= Base(j); z[j] += x[j] / Base(2); z[j] /= z[0]; } } /*! Multiple direction forward mode Taylor coefficient for op = SqrtOp. The C++ source code corresponding to this operation is \verbatim z = sqrt(x) \endverbatim \copydetails forward_unary1_op_dir */ template inline void forward_sqrt_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SqrtOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SqrtOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* z = taylor + i_z * num_taylor_per_var; Base* x = taylor + i_x * num_taylor_per_var; size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = Base(0); for(size_t k = 1; k < q; k++) z[m+ell] -= Base(k) * z[(k-1)*r+1+ell] * z[(q-k-1)*r+1+ell]; z[m+ell] /= Base(q); z[m+ell] += x[m+ell] / Base(2); z[m+ell] /= z[0]; } } /*! Compute zero order forward mode Taylor coefficient for result of op = SqrtOp. The C++ source code corresponding to this operation is \verbatim z = sqrt(x) \endverbatim \copydetails forward_unary1_op_0 */ template inline void forward_sqrt_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SqrtOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SqrtOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; z[0] = sqrt( x[0] ); } /*! Compute reverse mode partial derivatives for result of op = SqrtOp. The C++ source code corresponding to this operation is \verbatim z = sqrt(x) \endverbatim \copydetails reverse_unary1_op */ template inline void reverse_sqrt_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SqrtOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SqrtOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; Base inv_z0 = Base(1) / z[0]; // number of indices to access size_t j = d; size_t k; while(j) { // scale partial w.r.t. z[j] pz[j] = azmul(pz[j], inv_z0); pz[0] -= azmul(pz[j], z[j]); px[j] += pz[j] / Base(2); for(k = 1; k < j; k++) pz[k] -= azmul(pz[j], z[j-k]); --j; } px[0] += azmul(pz[0], inv_z0) / Base(2); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/sub_op.hpp0000644000175200017650000003175613057470467016634 0ustar coincoin-web// $Id: sub_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_SUB_OP_HPP # define CPPAD_LOCAL_SUB_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sub_op.hpp Forward and reverse mode calculations for z = x - y. */ // --------------------------- Subvv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = SubvvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op */ template inline void forward_subvv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; for(size_t d = p; d <= q; d++) z[d] = x[d] - y[d]; } /*! Multiple directions forward mode Taylor coefficients for op = SubvvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_dir */ template inline void forward_subvv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; size_t m = (q-1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var + m; Base* y = taylor + arg[1] * num_taylor_per_var + m; Base* z = taylor + i_z * num_taylor_per_var + m; for(size_t ell = 0; ell < r; ell++) z[ell] = x[ell] - y[ell]; } /*! Compute zero order forward mode Taylor coefficients for result of op = SubvvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_0 */ template inline void forward_subvv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvvOp) == 1 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x[0] - y[0]; } /*! Compute reverse mode partial derivatives for result of op = SubvvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails reverse_binary_op */ template inline void reverse_subvv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Partial derivatives corresponding to arguments and result Base* px = partial + arg[0] * nc_partial; Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t i = d + 1; while(i) { --i; px[i] += pz[i]; py[i] -= pz[i]; } } // --------------------------- Subpv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = SubpvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op */ template inline void forward_subpv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; // Paraemter value Base x = parameter[ arg[0] ]; if( p == 0 ) { z[0] = x - y[0]; p++; } for(size_t d = p; d <= q; d++) z[d] = - y[d]; } /*! Multiple directions forward mode Taylor coefficients for op = SubpvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_dir */ template inline void forward_subpv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; size_t m = (q-1) * r + 1; Base* y = taylor + arg[1] * num_taylor_per_var + m; Base* z = taylor + i_z * num_taylor_per_var + m; // Paraemter value for(size_t ell = 0; ell < r; ell++) z[ell] = - y[ell]; } /*! Compute zero order forward mode Taylor coefficient for result of op = SubpvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_0 */ template inline void forward_subpv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubpvOp) == 1 ); // Paraemter value Base x = parameter[ arg[0] ]; // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x - y[0]; } /*! Compute reverse mode partial derivative for result of op = SubpvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails reverse_binary_op */ template inline void reverse_subpv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Partial derivatives corresponding to arguments and result Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t i = d + 1; while(i) { --i; py[i] -= pz[i]; } } // --------------------------- Subvp ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = SubvvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_binary_op */ template inline void forward_subvp_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* z = taylor + i_z * cap_order; // Parameter value Base y = parameter[ arg[1] ]; if( p == 0 ) { z[0] = x[0] - y; p++; } for(size_t d = p; d <= q; d++) z[d] = x[d]; } /*! Multiple directions forward mode Taylor coefficients for op = SubvvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_binary_op_dir */ template inline void forward_subvp_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; // Parameter value size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) z[m+ell] = x[m+ell]; } /*! Compute zero order forward mode Taylor coefficients for result of op = SubvvOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_binary_op_0 */ template inline void forward_subvp_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvpOp) == 1 ); // Parameter value Base y = parameter[ arg[1] ]; // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x[0] - y; } /*! Compute reverse mode partial derivative for result of op = SubvpOp. The C++ source code corresponding to this operation is \verbatim z = x - y \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails reverse_binary_op */ template inline void reverse_subvp_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SubvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(SubvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Partial derivatives corresponding to arguments and result Base* px = partial + arg[0] * nc_partial; Base* pz = partial + i_z * nc_partial; // number of indices to access size_t i = d + 1; while(i) { --i; px[i] += pz[i]; } } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/sin_op.hpp0000644000175200017650000001446113057470467016626 0ustar coincoin-web// $Id: sin_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_SIN_OP_HPP # define CPPAD_LOCAL_SIN_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sin_op.hpp Forward and reverse mode calculations for z = sin(x). */ /*! Compute forward mode Taylor coefficient for result of op = SinOp. The C++ source code corresponding to this operation is \verbatim z = sin(x) \endverbatim The auxillary result is \verbatim y = cos(x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_sin_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* s = taylor + i_z * cap_order; Base* c = s - cap_order; // rest of this routine is identical for the following cases: // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op. // (except that there is a sign difference for the hyperbolic case). size_t k; if( p == 0 ) { s[0] = sin( x[0] ); c[0] = cos( x[0] ); p++; } for(size_t j = p; j <= q; j++) { s[j] = Base(0); c[j] = Base(0); for(k = 1; k <= j; k++) { s[j] += Base(k) * x[k] * c[j-k]; c[j] -= Base(k) * x[k] * s[j-k]; } s[j] /= Base(j); c[j] /= Base(j); } } /*! Compute forward mode Taylor coefficient for result of op = SinOp. The C++ source code corresponding to this operation is \verbatim z = sin(x) \endverbatim The auxillary result is \verbatim y = cos(x) \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_sin_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* s = taylor + i_z * num_taylor_per_var; Base* c = s - num_taylor_per_var; // rest of this routine is identical for the following cases: // forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op // (except that there is a sign difference for the hyperbolic case). size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { s[m+ell] = Base(q) * x[m + ell] * c[0]; c[m+ell] = - Base(q) * x[m + ell] * s[0]; for(size_t k = 1; k < q; k++) { s[m+ell] += Base(k) * x[(k-1)*r+1+ell] * c[(q-k-1)*r+1+ell]; c[m+ell] -= Base(k) * x[(k-1)*r+1+ell] * s[(q-k-1)*r+1+ell]; } s[m+ell] /= Base(q); c[m+ell] /= Base(q); } } /*! Compute zero order forward mode Taylor coefficient for result of op = SinOp. The C++ source code corresponding to this operation is \verbatim z = sin(x) \endverbatim The auxillary result is \verbatim y = cos(x) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_sin_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* s = taylor + i_z * cap_order; // called z in documentation Base* c = s - cap_order; // called y in documentation s[0] = sin( x[0] ); c[0] = cos( x[0] ); } /*! Compute reverse mode partial derivatives for result of op = SinOp. The C++ source code corresponding to this operation is \verbatim z = sin(x) \endverbatim The auxillary result is \verbatim y = cos(x) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_sin_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* s = taylor + i_z * cap_order; // called z in doc Base* ps = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* c = s - cap_order; // called y in documentation Base* pc = ps - nc_partial; // rest of this routine is identical for the following cases: // reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op. size_t j = d; size_t k; while(j) { ps[j] /= Base(j); pc[j] /= Base(j); for(k = 1; k <= j; k++) { px[k] += Base(k) * azmul(ps[j], c[j-k]); px[k] -= Base(k) * azmul(pc[j], s[j-k]); ps[j-k] -= Base(k) * azmul(pc[j], x[k]); pc[j-k] += Base(k) * azmul(ps[j], x[k]); } --j; } px[0] += azmul(ps[0], c[0]); px[0] -= azmul(pc[0], s[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/forward0sweep.hpp0000644000175200017650000006132213057470467020125 0ustar coincoin-web// $Id: forward0sweep.hpp 3853 2016-12-14 14:40:11Z bradbell $ # ifndef CPPAD_LOCAL_FORWARD0SWEEP_HPP # define CPPAD_LOCAL_FORWARD0SWEEP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file forward0sweep.hpp Compute zero order forward mode Taylor coefficients. */ /* \def CPPAD_ATOMIC_CALL This avoids warnings when NDEBUG is defined and user_ok is not used. If NDEBUG is defined, this resolves to \code user_atom->forward \endcode otherwise, it respolves to \code user_ok = user_atom->forward \endcode This maco is undefined at the end of this file to facillitate is use with a different definition in other files. */ # ifdef NDEBUG # define CPPAD_ATOMIC_CALL user_atom->forward # else # define CPPAD_ATOMIC_CALL user_ok = user_atom->forward # endif /*! \def CPPAD_FORWARD0SWEEP_TRACE This value is either zero or one. Zero is the normal operational value. If it is one, a trace of every forward0sweep computation is printed. (Note that forward0sweep is not used if CPPAD_USE_FORWARD0SWEEP is zero). */ # define CPPAD_FORWARD0SWEEP_TRACE 0 /*! Compute zero order forward mode Taylor coefficients. \tparam Base The type used during the forward mode computations; i.e., the corresponding recording of operations used the type AD. \param s_out Is the stream where output corresponding to PriOp operations will be written. \param print If print is false, suppress the output that is otherwise generated by the c PriOp instructions. \param n is the number of independent variables on the tape. \param numvar is the total number of variables on the tape. This is also equal to the number of rows in the matrix taylor; i.e., play->num_var_rec(). \param play The information stored in play is a recording of the operations corresponding to the function \f[ F : {\bf R}^n \rightarrow {\bf R}^m \f] where \f$ n \f$ is the number of independent variables and \f$ m \f$ is the number of dependent variables. \n \n The object play is effectly constant. The exception to this is that while palying back the tape the object play holds information about the current location with in the tape and this changes during palyback. \param J Is the number of columns in the coefficient matrix taylor. This must be greater than or equal one. \param taylor \n \b Input: For i = 1 , ... , n, taylor [i * J + 0] variable with index j on the tape (these are the independent variables). \n \n \b Output: For i = n + 1, ... , numvar - 1, taylor [i * J + 0] is the zero order Taylor coefficient for the variable with index i on the tape. \param cskip_op Is a vector with size play->num_op_rec(). The input value of the elements does not matter. Upon return, if cskip_op[i] is true, the operator index i does not affect any of the dependent variable (given the value of the independent variables). \param var_by_load_op Is a vector with size play->num_load_op_rec(). The input value of the elements does not matter. Upon return, it is the variable index corresponding the result for each load operator. In the case where the index is zero, the load operator results in a parameter (not a variable). Note that the is no variable with index zero on the tape. \param compare_change_count Is the count value for changing number and op_index during zero order foward mode. \param compare_change_number If compare_change_count is zero, this value is set to zero. Otherwise, the return value is the number of comparision operations that have a different result from when the information in play was recorded. \param compare_change_op_index If compare_change_count is zero, this value is set to zero. Otherwise it is the operator index (see forward_next) for the count-th comparision operation that has a different result from when the information in play was recorded. */ template void forward0sweep( std::ostream& s_out, bool print, size_t n, size_t numvar, local::player* play, size_t J, Base* taylor, bool* cskip_op, pod_vector& var_by_load_op, size_t compare_change_count, size_t& compare_change_number, size_t& compare_change_op_index ) { CPPAD_ASSERT_UNKNOWN( J >= 1 ); CPPAD_ASSERT_UNKNOWN( play->num_var_rec() == numvar ); // use p, q, r so other forward sweeps can use code defined here size_t p = 0; size_t q = 0; size_t r = 1; /* */ // op code for current instruction OpCode op; // index for current instruction size_t i_op; // next variables size_t i_var; // operation argument indices const addr_t* arg = CPPAD_NULL; // initialize the comparision operator counter if( p == 0 ) { compare_change_number = 0; compare_change_op_index = 0; } // If this includes a zero calculation, initialize this information pod_vector isvar_by_ind; pod_vector index_by_ind; if( p == 0 ) { size_t i; // this includes order zero calculation, initialize vector indices size_t num = play->num_vec_ind_rec(); if( num > 0 ) { isvar_by_ind.extend(num); index_by_ind.extend(num); for(i = 0; i < num; i++) { index_by_ind[i] = play->GetVecInd(i); isvar_by_ind[i] = false; } } // includes zero order, so initialize conditional skip flags num = play->num_op_rec(); for(i = 0; i < num; i++) cskip_op[i] = false; } // work space used by UserOp. vector user_vx; // empty vecotor vector user_vy; // empty vecotor vector user_tx; // argument vector Taylor coefficients vector user_ty; // result vector Taylor coefficients // atomic_base* user_atom = CPPAD_NULL; // user's atomic op calculator # ifndef NDEBUG bool user_ok = false; // atomic op return value # endif // // information defined by forward_user size_t user_old=0, user_m=0, user_n=0, user_i=0, user_j=0; enum_user_state user_state = start_user; // proper initialization // length of the parameter vector (used by CppAD assert macros) const size_t num_par = play->num_par_rec(); // pointer to the beginning of the parameter vector const Base* parameter = CPPAD_NULL; if( num_par > 0 ) parameter = play->GetPar(); // length of the text vector (used by CppAD assert macros) const size_t num_text = play->num_text_rec(); // pointer to the beginning of the text vector const char* text = CPPAD_NULL; if( num_text > 0 ) text = play->GetTxt(0); /* */ # if CPPAD_FORWARD0SWEEP_TRACE // flag as to when to trace user function values bool user_trace = false; // variable indices for results vector // (done differently for order zero). vector user_iy; # endif // skip the BeginOp at the beginning of the recording play->forward_start(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( op == BeginOp ); # if CPPAD_FORWARD0SWEEP_TRACE std::cout << std::endl; # endif bool flag; // a temporary flag to use in switch cases bool more_operators = true; while(more_operators) { // this op play->forward_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( (i_op > n) | (op == InvOp) ); CPPAD_ASSERT_UNKNOWN( (i_op <= n) | (op != InvOp) ); CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() ); CPPAD_ASSERT_ARG_BEFORE_RESULT(op, arg, i_var); // check if we are skipping this operation while( cskip_op[i_op] ) { switch(op) { case CSumOp: // CSumOp has a variable number of arguments play->forward_csum(op, arg, i_op, i_var); break; case CSkipOp: // CSkip has a variable number of arguments play->forward_cskip(op, arg, i_op, i_var); break; case UserOp: { // skip all operations in this user atomic call CPPAD_ASSERT_UNKNOWN( user_state == start_user ); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); size_t n_skip = user_m + user_n + 1; for(size_t i = 0; i < n_skip; i++) { play->forward_next(op, arg, i_op, i_var); play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); } CPPAD_ASSERT_UNKNOWN( user_state == start_user ); } break; default: break; } play->forward_next(op, arg, i_op, i_var); CPPAD_ASSERT_UNKNOWN( i_op < play->num_op_rec() ); } // action to take depends on the case switch( op ) { case AbsOp: forward_abs_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- case AddvvOp: forward_addvv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case AddpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_addpv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case AcosOp: // sqrt(1 - x * x), acos(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_acos_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AcoshOp: // sqrt(x * x - 1), acosh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_acosh_op_0(i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case AsinOp: // sqrt(1 - x * x), asin(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_asin_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AsinhOp: // sqrt(1 + x * x), asinh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_asinh_op_0(i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case AtanOp: // 1 + x * x, atan(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_atan_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case AtanhOp: // 1 - x * x, atanh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_atanh_op_0(i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case CExpOp: // Use the general case with d == 0 // (could create an optimzied verison for this case) forward_cond_op_0( i_var, arg, num_par, parameter, J, taylor ); break; // --------------------------------------------------- case CosOp: // sin(x), cos(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_cos_op_0(i_var, arg[0], J, taylor); break; // --------------------------------------------------- case CoshOp: // sinh(x), cosh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_cosh_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- case CSkipOp: // CSkipOp has a variable number of arguments and // forward_next thinks it has no arguments. // we must inform forward_next of this special case. forward_cskip_op_0( i_var, arg, num_par, parameter, J, taylor, cskip_op ); play->forward_cskip(op, arg, i_op, i_var); break; // ------------------------------------------------- case CSumOp: // CSumOp has a variable number of arguments and // forward_next thinks it has no arguments. // we must inform forward_next of this special case. forward_csum_op( 0, 0, i_var, arg, num_par, parameter, J, taylor ); play->forward_csum(op, arg, i_op, i_var); break; // ------------------------------------------------- case DisOp: forward_dis_op(p, q, r, i_var, arg, J, taylor); break; // ------------------------------------------------- case DivvvOp: forward_divvv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case DivpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_divpv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case DivvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_divvp_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case EndOp: CPPAD_ASSERT_NARG_NRES(op, 0, 0); more_operators = false; break; // ------------------------------------------------- case EqpvOp: if( compare_change_count ) { forward_eqpv_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case EqvvOp: if( compare_change_count ) { forward_eqvv_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case ErfOp: forward_erf_op_0(i_var, arg, parameter, J, taylor); break; # endif // ------------------------------------------------- case ExpOp: forward_exp_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Expm1Op: forward_expm1_op_0(i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case InvOp: CPPAD_ASSERT_NARG_NRES(op, 0, 1); break; // --------------------------------------------------- case LdpOp: forward_load_p_op_0( play, i_var, arg, parameter, J, taylor, isvar_by_ind.data(), index_by_ind.data(), var_by_load_op.data() ); break; // ------------------------------------------------- case LdvOp: forward_load_v_op_0( play, i_var, arg, parameter, J, taylor, isvar_by_ind.data(), index_by_ind.data(), var_by_load_op.data() ); break; // ------------------------------------------------- case LepvOp: if( compare_change_count ) { forward_lepv_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case LevpOp: if( compare_change_count ) { forward_levp_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case LevvOp: if( compare_change_count ) { forward_levv_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case LogOp: forward_log_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- # if CPPAD_USE_CPLUSPLUS_2011 case Log1pOp: forward_log1p_op_0(i_var, arg[0], J, taylor); break; # endif // ------------------------------------------------- case LtpvOp: if( compare_change_count ) { forward_ltpv_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case LtvpOp: if( compare_change_count ) { forward_ltvp_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case LtvvOp: if( compare_change_count ) { forward_ltvv_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case MulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_mulpv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case MulvvOp: forward_mulvv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case NepvOp: if( compare_change_count ) { forward_nepv_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case NevvOp: if( compare_change_count ) { forward_nevv_op_0( compare_change_number, arg, parameter, J, taylor ); { if( compare_change_count == compare_change_number ) compare_change_op_index = i_op; } } break; // ------------------------------------------------- case ParOp: forward_par_op_0( i_var, arg, num_par, parameter, J, taylor ); break; // ------------------------------------------------- case PowvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_powvp_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PowpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_powpv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PowvvOp: forward_powvv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case PriOp: if( print ) forward_pri_0(s_out, arg, num_text, text, num_par, parameter, J, taylor ); break; // ------------------------------------------------- case SignOp: // cos(x), sin(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sign_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SinOp: // cos(x), sin(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sin_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SinhOp: // cosh(x), sinh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_sinh_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- case SqrtOp: forward_sqrt_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- case StppOp: forward_store_pp_op_0( i_var, arg, num_par, J, taylor, isvar_by_ind.data(), index_by_ind.data() ); break; // ------------------------------------------------- case StpvOp: forward_store_pv_op_0( i_var, arg, num_par, J, taylor, isvar_by_ind.data(), index_by_ind.data() ); break; // ------------------------------------------------- case StvpOp: forward_store_vp_op_0( i_var, arg, num_par, J, taylor, isvar_by_ind.data(), index_by_ind.data() ); break; // ------------------------------------------------- case StvvOp: forward_store_vv_op_0( i_var, arg, num_par, J, taylor, isvar_by_ind.data(), index_by_ind.data() ); break; // ------------------------------------------------- case SubvvOp: forward_subvv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case SubpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_subpv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case SubvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_subvp_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case TanOp: // tan(x)^2, tan(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_tan_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- case TanhOp: // tanh(x)^2, tanh(x) CPPAD_ASSERT_UNKNOWN( i_var < numvar ); forward_tanh_op_0(i_var, arg[0], J, taylor); break; // ------------------------------------------------- case UserOp: // start or end an atomic operation sequence flag = user_state == start_user; user_atom = play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( flag ) { user_tx.resize(user_n); user_ty.resize(user_m); # if CPPAD_FORWARD0SWEEP_TRACE user_iy.resize(user_m); # endif } else { # ifndef NDEBUG if( ! user_ok ) { std::string msg = user_atom->afun_name() + ": atomic_base.forward: returned false"; CPPAD_ASSERT_KNOWN(false, msg.c_str() ); } # endif # if CPPAD_FORWARD0SWEEP_TRACE user_trace = true; # endif } break; case UsrapOp: // parameter argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t( arg[0] ) < num_par ); user_tx[user_j] = parameter[ arg[0] ]; play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( user_j == user_n ) { // call users function for this operation user_atom->set_old(user_old); CPPAD_ATOMIC_CALL(p, q, user_vx, user_vy, user_tx, user_ty ); } break; case UsravOp: // variable argument in an atomic operation sequence CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) <= i_var ); user_tx[user_j] = taylor[ arg[0] * J + 0 ]; play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); if( user_j == user_n ) { // call users function for this operation user_atom->set_old(user_old); CPPAD_ATOMIC_CALL(p, q, user_vx, user_vy, user_tx, user_ty ); } break; case UsrrpOp: // parameter result in an atomic operation sequence # if CPPAD_FORWARD0SWEEP_TRACE user_iy[user_i] = 0; # endif play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; case UsrrvOp: // variable result in an atomic operation sequence # if CPPAD_FORWARD0SWEEP_TRACE user_iy[user_i] = i_var; # endif taylor[ i_var * J + 0 ] = user_ty[user_i]; play->forward_user(op, user_state, user_old, user_m, user_n, user_i, user_j ); break; // ------------------------------------------------- case ZmulpvOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < num_par ); forward_zmulpv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case ZmulvpOp: CPPAD_ASSERT_UNKNOWN( size_t(arg[1]) < num_par ); forward_zmulvp_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- case ZmulvvOp: forward_zmulvv_op_0(i_var, arg, parameter, J, taylor); break; // ------------------------------------------------- default: CPPAD_ASSERT_UNKNOWN(false); } # if CPPAD_FORWARD0SWEEP_TRACE size_t d = 0; if( user_trace ) { user_trace = false; CPPAD_ASSERT_UNKNOWN( op == UserOp ); CPPAD_ASSERT_UNKNOWN( NumArg(UsrrvOp) == 0 ); for(size_t i = 0; i < user_m; i++) if( user_iy[i] > 0 ) { size_t i_tmp = (i_op + i) - user_m; printOp( std::cout, play, i_tmp, user_iy[i], UsrrvOp, CPPAD_NULL ); Base* Z_tmp = taylor + user_iy[i] * J; printOpResult( std::cout, d + 1, Z_tmp, 0, (Base *) CPPAD_NULL ); std::cout << std::endl; } } Base* Z_tmp = taylor + i_var * J; const addr_t* arg_tmp = arg; if( op == CSumOp ) arg_tmp = arg - arg[-1] - 4; if( op == CSkipOp ) arg_tmp = arg - arg[-1] - 7; if( op != UsrrvOp ) { printOp( std::cout, play, i_op, i_var, op, arg_tmp ); if( NumRes(op) > 0 ) printOpResult( std::cout, d + 1, Z_tmp, 0, (Base *) CPPAD_NULL ); std::cout << std::endl; } } std::cout << std::endl; # else } # endif CPPAD_ASSERT_UNKNOWN( user_state == start_user ); CPPAD_ASSERT_UNKNOWN( i_var + 1 == play->num_var_rec() ); return; } } } // END_CPPAD_LOCAL_NAMESPACE // preprocessor symbols that are local to this file # undef CPPAD_FORWARD0SWEEP_TRACE # undef CPPAD_ATOMIC_CALL # endif cppad-20170000.3/cppad/local/sparse_pattern.hpp0000644000175200017650000000331513057470467020365 0ustar coincoin-web// $Id: sparse_pattern.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_SPARSE_PATTERN_HPP # define CPPAD_LOCAL_SPARSE_PATTERN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ // necessary definitions # include # include # include namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file sparse_pattern.hpp Determine internal spasity pattern from correpsonding element type. */ /*! Template structure used obtain the internal sparsity pattern type form the corresponding element type. The general form is not valid, must use a specialization. \tparam Element_type type of an element in the sparsity structrue. \par internal_sparsity::pattern_type is the type of the corresponding internal sparsity pattern. */ template struct internal_sparsity; /*! Specilization for \c bool elements. */ template <> struct internal_sparsity { typedef sparse_pack pattern_type; }; /*! Specilization for std::set elements. */ template <> struct internal_sparsity< std::set > { typedef sparse_list pattern_type; }; } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/exp_op.hpp0000644000175200017650000001137213057470467016627 0ustar coincoin-web// $Id: exp_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_EXP_OP_HPP # define CPPAD_LOCAL_EXP_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file exp_op.hpp Forward and reverse mode calculations for z = exp(x). */ /*! Forward mode Taylor coefficient for result of op = ExpOp. The C++ source code corresponding to this operation is \verbatim z = exp(x) \endverbatim \copydetails forward_unary1_op */ template inline void forward_exp_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(ExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; size_t k; if( p == 0 ) { z[0] = exp( x[0] ); p++; } for(size_t j = p; j <= q; j++) { z[j] = x[1] * z[j-1]; for(k = 2; k <= j; k++) z[j] += Base(k) * x[k] * z[j-k]; z[j] /= Base(j); } } /*! Multiple direction forward mode Taylor coefficient for op = ExpOp. The C++ source code corresponding to this operation is \verbatim z = exp(x) \endverbatim \copydetails forward_unary1_op_dir */ template inline void forward_exp_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(ExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( 0 < q ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; size_t m = (q-1)*r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = Base(q) * x[m+ell] * z[0]; for(size_t k = 1; k < q; k++) z[m+ell] += Base(k) * x[(k-1)*r+ell+1] * z[(q-k-1)*r+ell+1]; z[m+ell] /= Base(q); } } /*! Zero order forward mode Taylor coefficient for result of op = ExpOp. The C++ source code corresponding to this operation is \verbatim z = exp(x) \endverbatim \copydetails forward_unary1_op_0 */ template inline void forward_exp_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(ExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; z[0] = exp( x[0] ); } /*! Reverse mode partial derivatives for result of op = ExpOp. The C++ source code corresponding to this operation is \verbatim z = exp(x) \endverbatim \copydetails reverse_unary1_op */ template inline void reverse_exp_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(ExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(ExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; // If pz is zero, make sure this operation has no effect // (zero times infinity or nan would be non-zero). bool skip(true); for(size_t i_d = 0; i_d <= d; i_d++) skip &= IdenticalZero(pz[i_d]); if( skip ) return; // loop through orders in reverse size_t j, k; j = d; while(j) { // scale partial w.r.t z[j] pz[j] /= Base(j); for(k = 1; k <= j; k++) { px[k] += Base(k) * azmul(pz[j], z[j-k]); pz[j-k] += Base(k) * azmul(pz[j], x[k]); } --j; } px[0] += azmul(pz[0], z[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/div_op.hpp0000644000175200017650000003557213057470467016625 0ustar coincoin-web// $Id: div_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_DIV_OP_HPP # define CPPAD_LOCAL_DIV_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file div_op.hpp Forward and reverse mode calculations for z = x / y. */ // --------------------------- Divvv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = DivvvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op */ template inline void forward_divvv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; // Using CondExp, it can make sense to divide by zero, // so do not make it an error. size_t k; for(size_t d = p; d <= q; d++) { z[d] = x[d]; for(k = 1; k <= d; k++) z[d] -= z[d-k] * y[k]; z[d] /= y[0]; } } /*! Multiple directions forward mode Taylor coefficients for op = DivvvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_dir */ template inline void forward_divvv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var; Base* y = taylor + arg[1] * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; // Using CondExp, it can make sense to divide by zero, // so do not make it an error. size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = x[m+ell] - z[0] * y[m+ell]; for(size_t k = 1; k < q; k++) z[m+ell] -= z[(q-k-1)*r+1+ell] * y[(k-1)*r+1+ell]; z[m+ell] /= y[0]; } } /*! Compute zero order forward mode Taylor coefficients for result of op = DivvvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails forward_binary_op_0 */ template inline void forward_divvv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 1 ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x[0] / y[0]; } /*! Compute reverse mode partial derivatives for result of op = DivvvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where both x and y are variables and the argument \a parameter is not used. \copydetails reverse_binary_op */ template inline void reverse_divvv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Arguments const Base* y = taylor + arg[1] * cap_order; const Base* z = taylor + i_z * cap_order; // Partial derivatives corresponding to arguments and result Base* px = partial + arg[0] * nc_partial; Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // Using CondExp, it can make sense to divide by zero // so do not make it an error. Base inv_y0 = Base(1) / y[0]; size_t k; // number of indices to access size_t j = d + 1; while(j) { --j; // scale partial w.r.t. z[j] pz[j] = azmul(pz[j], inv_y0); px[j] += pz[j]; for(k = 1; k <= j; k++) { pz[j-k] -= azmul(pz[j], y[k] ); py[k] -= azmul(pz[j], z[j-k]); } py[0] -= azmul(pz[j], z[j]); } } // --------------------------- Divpv ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = DivpvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op */ template inline void forward_divpv_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; // Paraemter value Base x = parameter[ arg[0] ]; // Using CondExp, it can make sense to divide by zero, // so do not make it an error. size_t k; if( p == 0 ) { z[0] = x / y[0]; p++; } for(size_t d = p; d <= q; d++) { z[d] = Base(0); for(k = 1; k <= d; k++) z[d] -= z[d-k] * y[k]; z[d] /= y[0]; } } /*! Multiple directions forward mode Taylor coefficients for op = DivpvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_dir */ template inline void forward_divpv_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivpvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* y = taylor + arg[1] * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; // Using CondExp, it can make sense to divide by zero, // so do not make it an error. size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = - z[0] * y[m+ell]; for(size_t k = 1; k < q; k++) z[m+ell] -= z[(q-k-1)*r+1+ell] * y[(k-1)*r+1+ell]; z[m+ell] /= y[0]; } } /*! Compute zero order forward mode Taylor coefficient for result of op = DivpvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails forward_binary_op_0 */ template inline void forward_divpv_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivpvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivpvOp) == 1 ); // Paraemter value Base x = parameter[ arg[0] ]; // Taylor coefficients corresponding to arguments and result Base* y = taylor + arg[1] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x / y[0]; } /*! Compute reverse mode partial derivative for result of op = DivpvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where x is a parameter and y is a variable. \copydetails reverse_binary_op */ template inline void reverse_divpv_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvvOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvvOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Arguments const Base* y = taylor + arg[1] * cap_order; const Base* z = taylor + i_z * cap_order; // Partial derivatives corresponding to arguments and result Base* py = partial + arg[1] * nc_partial; Base* pz = partial + i_z * nc_partial; // Using CondExp, it can make sense to divide by zero so do not // make it an error. Base inv_y0 = Base(1) / y[0]; size_t k; // number of indices to access size_t j = d + 1; while(j) { --j; // scale partial w.r.t z[j] pz[j] = azmul(pz[j], inv_y0); for(k = 1; k <= j; k++) { pz[j-k] -= azmul(pz[j], y[k] ); py[k] -= azmul(pz[j], z[j-k] ); } py[0] -= azmul(pz[j], z[j]); } } // --------------------------- Divvp ----------------------------------------- /*! Compute forward mode Taylor coefficients for result of op = DivvvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_binary_op */ template inline void forward_divvp_op( size_t p , size_t q , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* z = taylor + i_z * cap_order; // Parameter value Base y = parameter[ arg[1] ]; // Using CondExp and multiple levels of AD, it can make sense // to divide by zero so do not make it an error. for(size_t d = p; d <= q; d++) z[d] = x[d] / y; } /*! Multiple direction forward mode Taylor coefficients for op = DivvvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_binary_op_dir */ template inline void forward_divvp_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( 0 < q ); // Taylor coefficients corresponding to arguments and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + arg[0] * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; // Parameter value Base y = parameter[ arg[1] ]; // Using CondExp and multiple levels of AD, it can make sense // to divide by zero so do not make it an error. size_t m = (q-1)*r + 1; for(size_t ell = 0; ell < r; ell++) z[m + ell] = x[m + ell] / y; } /*! Compute zero order forward mode Taylor coefficients for result of op = DivvvOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails forward_binary_op_0 */ template inline void forward_divvp_op_0( size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvpOp) == 1 ); // Parameter value Base y = parameter[ arg[1] ]; // Taylor coefficients corresponding to arguments and result Base* x = taylor + arg[0] * cap_order; Base* z = taylor + i_z * cap_order; z[0] = x[0] / y; } /*! Compute reverse mode partial derivative for result of op = DivvpOp. The C++ source code corresponding to this operation is \verbatim z = x / y \endverbatim In the documentation below, this operations is for the case where x is a variable and y is a parameter. \copydetails reverse_binary_op */ template inline void reverse_divvp_op( size_t d , size_t i_z , const addr_t* arg , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(DivvpOp) == 2 ); CPPAD_ASSERT_UNKNOWN( NumRes(DivvpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Argument values Base y = parameter[ arg[1] ]; // Partial derivatives corresponding to arguments and result Base* px = partial + arg[0] * nc_partial; Base* pz = partial + i_z * nc_partial; // Using CondExp, it can make sense to divide by zero // so do not make it an error. Base inv_y = Base(1) / y; // number of indices to access size_t j = d + 1; while(j) { --j; px[j] += azmul(pz[j], inv_y); } } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/tan_op.hpp0000644000175200017650000001343613057470467016620 0ustar coincoin-web// $Id: tan_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_TAN_OP_HPP # define CPPAD_LOCAL_TAN_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file tan_op.hpp Forward and reverse mode calculations for z = tan(x). */ /*! Compute forward mode Taylor coefficient for result of op = TanOp. The C++ source code corresponding to this operation is \verbatim z = tan(x) \endverbatim The auxillary result is \verbatim y = tan(x)^2 \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op */ template inline void forward_tan_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; Base* y = z - cap_order; size_t k; if( p == 0 ) { z[0] = tan( x[0] ); y[0] = z[0] * z[0]; p++; } for(size_t j = p; j <= q; j++) { Base base_j = static_cast(j); z[j] = x[j]; for(k = 1; k <= j; k++) z[j] += Base(k) * x[k] * y[j-k] / base_j; y[j] = z[0] * z[j]; for(k = 1; k <= j; k++) y[j] += z[k] * z[j-k]; } } /*! Multiple directions forward mode Taylor coefficient for op = TanOp. The C++ source code corresponding to this operation is \verbatim z = tan(x) \endverbatim The auxillary result is \verbatim y = tan(x)^2 \endverbatim The value of y, and its derivatives, are computed along with the value and derivatives of z. \copydetails forward_unary2_op_dir */ template inline void forward_tan_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; Base* y = z - num_taylor_per_var; size_t k; size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = Base(q) * ( x[m+ell] + x[m+ell] * y[0]); for(k = 1; k < q; k++) z[m+ell] += Base(k) * x[(k-1)*r+1+ell] * y[(q-k-1)*r+1+ell]; z[m+ell] /= Base(q); // y[m+ell] = Base(2) * z[m+ell] * z[0]; for(k = 1; k < q; k++) y[m+ell] += z[(k-1)*r+1+ell] * z[(q-k-1)*r+1+ell]; } } /*! Compute zero order forward mode Taylor coefficient for result of op = TanOp. The C++ source code corresponding to this operation is \verbatim z = tan(x) \endverbatim The auxillary result is \verbatim y = cos(x) \endverbatim The value of y is computed along with the value of z. \copydetails forward_unary2_op_0 */ template inline void forward_tan_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; // called z in documentation Base* y = z - cap_order; // called y in documentation z[0] = tan( x[0] ); y[0] = z[0] * z[0]; } /*! Compute reverse mode partial derivatives for result of op = TanOp. The C++ source code corresponding to this operation is \verbatim z = tan(x) \endverbatim The auxillary result is \verbatim y = cos(x) \endverbatim The value of y is computed along with the value of z. \copydetails reverse_unary2_op */ template inline void reverse_tan_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 2 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to first result const Base* z = taylor + i_z * cap_order; // called z in doc Base* pz = partial + i_z * nc_partial; // Taylor coefficients and partials corresponding to auxillary result const Base* y = z - cap_order; // called y in documentation Base* py = pz - nc_partial; size_t j = d; size_t k; Base base_two(2); while(j) { px[j] += pz[j]; pz[j] /= Base(j); for(k = 1; k <= j; k++) { px[k] += azmul(pz[j], y[j-k]) * Base(k); py[j-k] += azmul(pz[j], x[k]) * Base(k); } for(k = 0; k < j; k++) pz[k] += azmul(py[j-1], z[j-k-1]) * base_two; --j; } px[0] += azmul(pz[0], Base(1) + y[0]); } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/local/log1p_op.hpp0000644000175200017650000001157013057470467017055 0ustar coincoin-web// $Id$ # ifndef CPPAD_LOCAL_LOG1P_OP_HPP # define CPPAD_LOCAL_LOG1P_OP_HPP # if CPPAD_USE_CPLUSPLUS_2011 /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file log1p_op.hpp Forward and reverse mode calculations for z = log1p(x). */ /*! Compute forward mode Taylor coefficient for result of op = Log1pOp. The C++ source code corresponding to this operation is \verbatim z = log1p(x) \endverbatim \copydetails forward_unary1_op */ template inline void forward_log1p_op( size_t p , size_t q , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { size_t k; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(Log1pOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(Log1pOp) == 1 ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); CPPAD_ASSERT_UNKNOWN( p <= q ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; if( p == 0 ) { z[0] = log1p( x[0] ); p++; if( q == 0 ) return; } if ( p == 1 ) { z[1] = x[1] / (Base(1) + x[0]); p++; } for(size_t j = p; j <= q; j++) { z[j] = -z[1] * x[j-1]; for(k = 2; k < j; k++) z[j] -= Base(k) * z[k] * x[j-k]; z[j] /= Base(j); z[j] += x[j]; z[j] /= (Base(1) + x[0]); } } /*! Muiltiple directions Taylor coefficient for op = Log1pOp. The C++ source code corresponding to this operation is \verbatim z = log1p(x) \endverbatim \copydetails forward_unary1_op_dir */ template inline void forward_log1p_op_dir( size_t q , size_t r , size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(Log1pOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(Log1pOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); // Taylor coefficients corresponding to argument and result size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* x = taylor + i_x * num_taylor_per_var; Base* z = taylor + i_z * num_taylor_per_var; size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { z[m+ell] = Base(q) * x[m+ell]; for(size_t k = 1; k < q; k++) z[m+ell] -= Base(k) * z[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell]; z[m+ell] /= (Base(q) + Base(q) * x[0]); } } /*! Compute zero order forward mode Taylor coefficient for result of op = Log1pOp. The C++ source code corresponding to this operation is \verbatim z = log1p(x) \endverbatim \copydetails forward_unary1_op_0 */ template inline void forward_log1p_op_0( size_t i_z , size_t i_x , size_t cap_order , Base* taylor ) { // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(Log1pOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(Log1pOp) == 1 ); CPPAD_ASSERT_UNKNOWN( 0 < cap_order ); // Taylor coefficients corresponding to argument and result Base* x = taylor + i_x * cap_order; Base* z = taylor + i_z * cap_order; z[0] = log1p( x[0] ); } /*! Compute reverse mode partial derivatives for result of op = Log1pOp. The C++ source code corresponding to this operation is \verbatim z = log1p(x) \endverbatim \copydetails reverse_unary1_op */ template inline void reverse_log1p_op( size_t d , size_t i_z , size_t i_x , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { size_t j, k; // check assumptions CPPAD_ASSERT_UNKNOWN( NumArg(Log1pOp) == 1 ); CPPAD_ASSERT_UNKNOWN( NumRes(Log1pOp) == 1 ); CPPAD_ASSERT_UNKNOWN( d < cap_order ); CPPAD_ASSERT_UNKNOWN( d < nc_partial ); // Taylor coefficients and partials corresponding to argument const Base* x = taylor + i_x * cap_order; Base* px = partial + i_x * nc_partial; // Taylor coefficients and partials corresponding to result const Base* z = taylor + i_z * cap_order; Base* pz = partial + i_z * nc_partial; Base inv_1px0 = Base(1) / (Base(1) + x[0]); j = d; while(j) { // scale partial w.r.t z[j] pz[j] = azmul(pz[j] , inv_1px0); px[0] -= azmul(pz[j], z[j]); px[j] += pz[j]; // further scale partial w.r.t. z[j] pz[j] /= Base(j); for(k = 1; k < j; k++) { pz[k] -= Base(k) * azmul(pz[j], x[j-k]); px[j-k] -= Base(k) * azmul(pz[j], z[k]); } --j; } px[0] += azmul(pz[0], inv_1px0); } } } // END_CPPAD_LOCAL_NAMESPACE # endif # endif cppad-20170000.3/cppad/local/cond_op.hpp0000644000175200017650000007612613057470467016766 0ustar coincoin-web// $Id: cond_op.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_LOCAL_COND_OP_HPP # define CPPAD_LOCAL_COND_OP_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE /*! \file cond_op.hpp Forward, reverse, and sparse operations for conditional expressions. */ /*! Shared documentation for conditional expressions (not called). The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \param parameter For j = 0, 1, 2, 3, if y_j is a parameter, \a parameter [ arg[2 + j] ] is its value. \param cap_order number of columns in the matrix containing the Taylor coefficients. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. */ template inline void conditional_exp_op( size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order ) { // This routine is only for documentation, it should never be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Shared documentation for conditional expression sparse operations (not called). The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. */ template inline void sparse_conditional_exp_op( size_t i_z , const addr_t* arg , size_t num_par ) { // This routine is only for documentation, it should never be used CPPAD_ASSERT_UNKNOWN( false ); } /*! Compute forward mode Taylor coefficients for op = CExpOp. The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \param parameter For j = 0, 1, 2, 3, if y_j is a parameter, \a parameter [ arg[2 + j] ] is its value. \param cap_order number of columns in the matrix containing the Taylor coefficients. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. \param p is the lowest order of the Taylor coefficient of z that we are computing. \param q is the highest order of the Taylor coefficient of z that we are computing. \param taylor \b Input: For j = 0, 1, 2, 3 and k = 0 , ... , q, if y_j is a variable then taylor [ arg[2+j] * cap_order + k ] is the k-th order Taylor coefficient corresponding to y_j. \n \b Input: taylor [ i_z * cap_order + k ] for k = 0 , ... , p-1, is the k-th order Taylor coefficient corresponding to z. \n \b Output: taylor [ i_z * cap_order + k ] for k = p , ... , q, is the k-th order Taylor coefficient corresponding to z. */ template inline void forward_cond_op( size_t p , size_t q , size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order , Base* taylor ) { Base y_0, y_1, y_2, y_3; Base zero(0); Base* z = taylor + i_z * cap_order; CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < static_cast (CompareNe) ); CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); CPPAD_ASSERT_UNKNOWN( NumRes(CExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( arg[1] != 0 ); if( arg[1] & 1 ) { y_0 = taylor[ arg[2] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); y_0 = parameter[ arg[2] ]; } if( arg[1] & 2 ) { y_1 = taylor[ arg[3] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[3]) < num_par ); y_1 = parameter[ arg[3] ]; } if( p == 0 ) { if( arg[1] & 4 ) { y_2 = taylor[ arg[4] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[4]) < num_par ); y_2 = parameter[ arg[4] ]; } if( arg[1] & 8 ) { y_3 = taylor[ arg[5] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[5]) < num_par ); y_3 = parameter[ arg[5] ]; } z[0] = CondExpOp( CompareOp( arg[0] ), y_0, y_1, y_2, y_3 ); p++; } for(size_t d = p; d <= q; d++) { if( arg[1] & 4 ) { y_2 = taylor[ arg[4] * cap_order + d]; } else y_2 = zero; if( arg[1] & 8 ) { y_3 = taylor[ arg[5] * cap_order + d]; } else y_3 = zero; z[d] = CondExpOp( CompareOp( arg[0] ), y_0, y_1, y_2, y_3 ); } return; } /*! Multiple directions forward mode Taylor coefficients for op = CExpOp. The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \param parameter For j = 0, 1, 2, 3, if y_j is a parameter, \a parameter [ arg[2 + j] ] is its value. \param cap_order number of columns in the matrix containing the Taylor coefficients. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. \param q is order of the Taylor coefficient of z that we are computing. \param r is the number of Taylor coefficient directions that we are computing. \par tpv We use the notation tpv = (cap_order-1) * r + 1 which is the number of Taylor coefficients per variable \param taylor \b Input: For j = 0, 1, 2, 3, k = 1, ..., q, if y_j is a variable then taylor [ arg[2+j] * tpv + 0 ] is the zero order Taylor coefficient corresponding to y_j and taylor [ arg[2+j] * tpv + (k-1)*r+1+ell is its k-th order Taylor coefficient in the ell-th direction. \n \b Input: For j = 0, 1, 2, 3, k = 1, ..., q-1, taylor [ i_z * tpv + 0 ] is the zero order Taylor coefficient corresponding to z and taylor [ i_z * tpv + (k-1)*r+1+ell is its k-th order Taylor coefficient in the ell-th direction. \n \b Output: taylor [ i_z * tpv + (q-1)*r+1+ell ] is the q-th order Taylor coefficient corresponding to z in the ell-th direction. */ template inline void forward_cond_op_dir( size_t q , size_t r , size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order , Base* taylor ) { Base y_0, y_1, y_2, y_3; Base zero(0); size_t num_taylor_per_var = (cap_order-1) * r + 1; Base* z = taylor + i_z * num_taylor_per_var; CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < static_cast (CompareNe) ); CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); CPPAD_ASSERT_UNKNOWN( NumRes(CExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( arg[1] != 0 ); CPPAD_ASSERT_UNKNOWN( 0 < q ); CPPAD_ASSERT_UNKNOWN( q < cap_order ); if( arg[1] & 1 ) { y_0 = taylor[ arg[2] * num_taylor_per_var + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); y_0 = parameter[ arg[2] ]; } if( arg[1] & 2 ) { y_1 = taylor[ arg[3] * num_taylor_per_var + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[3]) < num_par ); y_1 = parameter[ arg[3] ]; } size_t m = (q-1) * r + 1; for(size_t ell = 0; ell < r; ell++) { if( arg[1] & 4 ) { y_2 = taylor[ arg[4] * num_taylor_per_var + m + ell]; } else y_2 = zero; if( arg[1] & 8 ) { y_3 = taylor[ arg[5] * num_taylor_per_var + m + ell]; } else y_3 = zero; z[m+ell] = CondExpOp( CompareOp( arg[0] ), y_0, y_1, y_2, y_3 ); } return; } /*! Compute zero order forward mode Taylor coefficients for op = CExpOp. The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \param parameter For j = 0, 1, 2, 3, if y_j is a parameter, \a parameter [ arg[2 + j] ] is its value. \param cap_order number of columns in the matrix containing the Taylor coefficients. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. \param taylor \b Input: For j = 0, 1, 2, 3, if y_j is a variable then \a taylor [ \a arg[2+j] * cap_order + 0 ] is the zero order Taylor coefficient corresponding to y_j. \n \b Output: \a taylor [ \a i_z * \a cap_order + 0 ] is the zero order Taylor coefficient corresponding to z. */ template inline void forward_cond_op_0( size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order , Base* taylor ) { Base y_0, y_1, y_2, y_3; Base* z; CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < static_cast (CompareNe) ); CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); CPPAD_ASSERT_UNKNOWN( NumRes(CExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( arg[1] != 0 ); if( arg[1] & 1 ) { y_0 = taylor[ arg[2] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); y_0 = parameter[ arg[2] ]; } if( arg[1] & 2 ) { y_1 = taylor[ arg[3] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[3]) < num_par ); y_1 = parameter[ arg[3] ]; } if( arg[1] & 4 ) { y_2 = taylor[ arg[4] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[4]) < num_par ); y_2 = parameter[ arg[4] ]; } if( arg[1] & 8 ) { y_3 = taylor[ arg[5] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[5]) < num_par ); y_3 = parameter[ arg[5] ]; } z = taylor + i_z * cap_order; z[0] = CondExpOp( CompareOp( arg[0] ), y_0, y_1, y_2, y_3 ); return; } /*! Compute reverse mode Taylor coefficients for op = CExpOp. This routine is given the partial derivatives of a function G( z , y , x , w , ... ) and it uses them to compute the partial derivatives of \verbatim H( y , x , w , u , ... ) = G[ z(y) , y , x , w , u , ... ] \endverbatim where y above represents y_0, y_1, y_2, y_3. The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Base base type for the operator; i.e., this operation was recorded using AD< \a Base > and computations by this routine are done using type \a Base. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \param parameter For j = 0, 1, 2, 3, if y_j is a parameter, \a parameter [ arg[2 + j] ] is its value. \param cap_order number of columns in the matrix containing the Taylor coefficients. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. \param d is the order of the Taylor coefficient of z that we are computing. \param taylor \b Input: For j = 0, 1, 2, 3 and k = 0 , ... , \a d, if y_j is a variable then \a taylor [ \a arg[2+j] * cap_order + k ] is the k-th order Taylor coefficient corresponding to y_j. \n \a taylor [ \a i_z * \a cap_order + k ] for k = 0 , ... , \a d is the k-th order Taylor coefficient corresponding to z. \param nc_partial number of columns in the matrix containing the Taylor coefficients. \param partial \b Input: For j = 0, 1, 2, 3 and k = 0 , ... , \a d, if y_j is a variable then \a partial [ \a arg[2+j] * nc_partial + k ] is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient corresponding to y_j. \n \b Input: \a partial [ \a i_z * \a cap_order + k ] for k = 0 , ... , \a d is the partial derivative of G( z , y , x , w , u , ... ) with respect to the k-th order Taylor coefficient corresponding to z. \n \b Output: For j = 0, 1, 2, 3 and k = 0 , ... , \a d, if y_j is a variable then \a partial [ \a arg[2+j] * nc_partial + k ] is the partial derivative of H( y , x , w , u , ... ) with respect to the k-th order Taylor coefficient corresponding to y_j. */ template inline void reverse_cond_op( size_t d , size_t i_z , const addr_t* arg , size_t num_par , const Base* parameter , size_t cap_order , const Base* taylor , size_t nc_partial , Base* partial ) { Base y_0, y_1; Base zero(0); Base* pz; Base* py_2; Base* py_3; CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < static_cast (CompareNe) ); CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); CPPAD_ASSERT_UNKNOWN( NumRes(CExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( arg[1] != 0 ); pz = partial + i_z * nc_partial + 0; if( arg[1] & 1 ) { y_0 = taylor[ arg[2] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[2]) < num_par ); y_0 = parameter[ arg[2] ]; } if( arg[1] & 2 ) { y_1 = taylor[ arg[3] * cap_order + 0 ]; } else { CPPAD_ASSERT_UNKNOWN( size_t(arg[3]) < num_par ); y_1 = parameter[ arg[3] ]; } if( arg[1] & 4 ) { py_2 = partial + arg[4] * nc_partial; size_t j = d + 1; while(j--) { py_2[j] += CondExpOp( CompareOp( arg[0] ), y_0, y_1, pz[j], zero ); } } if( arg[1] & 8 ) { py_3 = partial + arg[5] * nc_partial; size_t j = d + 1; while(j--) { py_3[j] += CondExpOp( CompareOp( arg[0] ), y_0, y_1, zero, pz[j] ); } } return; } /*! Compute forward Jacobian sparsity patterns for op = CExpOp. The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. \param dependency Are the derivatives with respect to left and right of the expression below considered to be non-zero: \code CondExpRel(left, right, if_true, if_false) \endcode This is used by the optimizer to obtain the correct dependency relations. \param sparsity \b Input: if y_2 is a variable, the set with index t is the sparsity pattern corresponding to y_2. This identifies which of the independent variables the variable y_2 depends on. \n \b Input: if y_3 is a variable, the set with index t is the sparsity pattern corresponding to y_3. This identifies which of the independent variables the variable y_3 depends on. \n \b Output: The set with index T is the sparsity pattern corresponding to z. This identifies which of the independent variables the variable z depends on. */ template inline void forward_sparse_jacobian_cond_op( bool dependency , size_t i_z , const addr_t* arg , size_t num_par , Vector_set& sparsity ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < static_cast (CompareNe) ); CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); CPPAD_ASSERT_UNKNOWN( NumRes(CExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( arg[1] != 0 ); # ifndef NDEBUG size_t k = 1; for( size_t j = 0; j < 4; j++) { if( ! ( arg[1] & k ) ) CPPAD_ASSERT_UNKNOWN( size_t(arg[2+j]) < num_par ); k *= 2; } # endif sparsity.clear(i_z); if( dependency ) { if( arg[1] & 1 ) sparsity.binary_union(i_z, i_z, arg[2], sparsity); if( arg[1] & 2 ) sparsity.binary_union(i_z, i_z, arg[3], sparsity); } if( arg[1] & 4 ) sparsity.binary_union(i_z, i_z, arg[4], sparsity); if( arg[1] & 8 ) sparsity.binary_union(i_z, i_z, arg[5], sparsity); return; } /*! Compute reverse Jacobian sparsity patterns for op = CExpOp. This routine is given the sparsity patterns for a function G(z, y, x, ... ) and it uses them to compute the sparsity patterns for \verbatim H( y, x, w , u , ... ) = G[ z(x,y) , y , x , w , u , ... ] \endverbatim where y represents the combination of y_0, y_1, y_2, and y_3. The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. \param dependency Are the derivatives with respect to left and right of the expression below considered to be non-zero: \code CondExpRel(left, right, if_true, if_false) \endcode This is used by the optimizer to obtain the correct dependency relations. \param sparsity if y_2 is a variable, the set with index t is the sparsity pattern corresponding to y_2. This identifies which of the dependent variables depend on the variable y_2. On input, this pattern corresponds to the function G. On ouput, it corresponds to the function H. \n \n if y_3 is a variable, the set with index t is the sparsity pattern corresponding to y_3. This identifies which of the dependent variables depeond on the variable y_3. On input, this pattern corresponds to the function G. On ouput, it corresponds to the function H. \n \b Output: The set with index T is the sparsity pattern corresponding to z. This identifies which of the dependent variables depend on the variable z. On input and output, this pattern corresponds to the function G. */ template inline void reverse_sparse_jacobian_cond_op( bool dependency , size_t i_z , const addr_t* arg , size_t num_par , Vector_set& sparsity ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < static_cast (CompareNe) ); CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); CPPAD_ASSERT_UNKNOWN( NumRes(CExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( arg[1] != 0 ); # ifndef NDEBUG size_t k = 1; for( size_t j = 0; j < 4; j++) { if( ! ( arg[1] & k ) ) CPPAD_ASSERT_UNKNOWN( size_t(arg[2+j]) < num_par ); k *= 2; } # endif if( dependency ) { if( arg[1] & 1 ) sparsity.binary_union(arg[2], arg[2], i_z, sparsity); if( arg[1] & 2 ) sparsity.binary_union(arg[3], arg[3], i_z, sparsity); } // -------------------------------------------------------------------- if( arg[1] & 4 ) sparsity.binary_union(arg[4], arg[4], i_z, sparsity); if( arg[1] & 8 ) sparsity.binary_union(arg[5], arg[5], i_z, sparsity); return; } /*! Compute reverse Hessian sparsity patterns for op = CExpOp. This routine is given the sparsity patterns for a function G(z, y, x, ... ) and it uses them to compute the sparsity patterns for \verbatim H( y, x, w , u , ... ) = G[ z(x,y) , y , x , w , u , ... ] \endverbatim where y represents the combination of y_0, y_1, y_2, and y_3. The C++ source code coresponding to this operation is \verbatim z = CondExpRel(y_0, y_1, y_2, y_3) \endverbatim where Rel is one of the following: Lt, Le, Eq, Ge, Gt. \tparam Vector_set is the type used for vectors of sets. It can be either sparse_pack or sparse_list. \param i_z is the AD variable index corresponding to the variable z. \param arg \n \a arg[0] is static cast to size_t from the enum type \verbatim enum CompareOp { CompareLt, CompareLe, CompareEq, CompareGe, CompareGt, CompareNe } \endverbatim for this operation. Note that arg[0] cannot be equal to CompareNe. \n \n \a arg[1] & 1 \n If this is zero, y_0 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 2 \n If this is zero, y_1 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 4 \n If this is zero, y_2 is a parameter. Otherwise it is a variable. \n \n \a arg[1] & 8 \n If this is zero, y_3 is a parameter. Otherwise it is a variable. \n \n \a arg[2 + j ] for j = 0, 1, 2, 3 \n is the index corresponding to y_j. \param num_par is the total number of values in the vector \a parameter. \par Checked Assertions \li NumArg(CExpOp) == 6 \li NumRes(CExpOp) == 1 \li arg[0] < static_cast ( CompareNe ) \li arg[1] != 0; i.e., not all of y_0, y_1, y_2, y_3 are parameters. \li For j = 0, 1, 2, 3 if y_j is a parameter, arg[2+j] < num_par. \param jac_reverse \a jac_reverse[i_z] is false (true) if the Jacobian of G with respect to z is always zero (may be non-zero). \n \n \a jac_reverse[ arg[4] ] If y_2 is a variable, \a jac_reverse[ arg[4] ] is false (true) if the Jacobian with respect to y_2 is always zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. \n \n \a jac_reverse[ arg[5] ] If y_3 is a variable, \a jac_reverse[ arg[5] ] is false (true) if the Jacobian with respect to y_3 is always zero (may be non-zero). On input, it corresponds to the function G, and on output it corresponds to the function H. \param hes_sparsity The set with index \a i_z in \a hes_sparsity is the Hessian sparsity pattern for the function G where one of the partials is with respect to z. \n \n If y_2 is a variable, the set with index \a arg[4] in \a hes_sparsity is the Hessian sparsity pattern where one of the partials is with respect to y_2. On input, this pattern corresponds to the function G. On output, this pattern corresponds to the function H. \n \n If y_3 is a variable, the set with index \a arg[5] in \a hes_sparsity is the Hessian sparsity pattern where one of the partials is with respect to y_3. On input, this pattern corresponds to the function G. On output, this pattern corresponds to the function H. */ template inline void reverse_sparse_hessian_cond_op( size_t i_z , const addr_t* arg , size_t num_par , bool* jac_reverse , Vector_set& hes_sparsity ) { CPPAD_ASSERT_UNKNOWN( size_t(arg[0]) < static_cast (CompareNe) ); CPPAD_ASSERT_UNKNOWN( NumArg(CExpOp) == 6 ); CPPAD_ASSERT_UNKNOWN( NumRes(CExpOp) == 1 ); CPPAD_ASSERT_UNKNOWN( arg[1] != 0 ); # ifndef NDEBUG size_t k = 1; for( size_t j = 0; j < 4; j++) { if( ! ( arg[1] & k ) ) CPPAD_ASSERT_UNKNOWN( size_t(arg[2+j]) < num_par ); k *= 2; } # endif if( arg[1] & 4 ) { hes_sparsity.binary_union(arg[4], arg[4], i_z, hes_sparsity); jac_reverse[ arg[4] ] |= jac_reverse[i_z]; } if( arg[1] & 8 ) { hes_sparsity.binary_union(arg[5], arg[5], i_z, hes_sparsity); jac_reverse[ arg[5] ] |= jac_reverse[i_z]; } return; } } } // END_CPPAD_LOCAL_NAMESPACE # endif cppad-20170000.3/cppad/example/0002755000175200017650000000000013057470467015163 5ustar coincoin-webcppad-20170000.3/cppad/example/eigen_mat_inv.hpp0000644000175200017650000003012513057470467020477 0ustar coincoin-web// $Id$ # ifndef CPPAD_EXAMPLE_EIGEN_MAT_INV_HPP # define CPPAD_EXAMPLE_EIGEN_MAT_INV_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_eigen_mat_inv.hpp$$ $spell Eigen Taylor $$ $section Atomic Eigen Matrix Inversion Class$$ $head Purpose$$ Construct an atomic operation that computes the matrix inverse $latex R = A^{-1}$$ for any positive integer $latex p$$ and invertible matrix $latex A \in \B{R}^{p \times p}$$. $head Matrix Dimensions$$ This example puts the matrix dimension $latex p$$ in the atomic function arguments, instead of the $cref/constructor/atomic_ctor/$$, so it can be different for different calls to the atomic function. $head Theory$$ $subhead Forward$$ The zero order forward mode Taylor coefficient is give by $latex \[ R_0 = A_0^{-1} \]$$ For $latex k = 1 , \ldots$$, the $th k$$ order Taylor coefficient of $latex A R$$ is given by $latex \[ 0 = \sum_{\ell=0}^k A_\ell R_{k-\ell} \] $$ Solving for $latex R_k$$ in terms of the coefficients for $latex A$$ and the lower order coefficients for $latex R$$ we have $latex \[ R_k = - R_0 \left( \sum_{\ell=1}^k A_\ell R_{k-\ell} \right) \] $$ Furthermore, once we have $latex R_k$$ we can compute the sum using $latex \[ A_0 R_k = - \left( \sum_{\ell=1}^k A_\ell R_{k-\ell} \right) \] $$ $subhead Product of Three Matrices$$ Suppose $latex \bar{E}$$ is the derivative of the scalar value function $latex s(E)$$ with respect to $latex E$$; i.e., $latex \[ \bar{E}_{i,j} = \frac{ \partial s } { \partial E_{i,j} } \] $$ Also suppose that $latex t$$ is a scalar valued argument and $latex \[ E(t) = B(t) C(t) D(t) \] $$ It follows that $latex \[ E'(t) = B'(t) C(t) D(t) + B(t) C'(t) D(t) + B(t) C(t) D'(t) \] $$ $latex \[ (s \circ E)'(t) = \R{tr} [ \bar{E}^\R{T} E'(t) ] \] $$ $latex \[ = \R{tr} [ \bar{E}^\R{T} B'(t) C(t) D(t) ] + \R{tr} [ \bar{E}^\R{T} B(t) C'(t) D(t) ] + \R{tr} [ \bar{E}^\R{T} B(t) C(t) D'(t) ] \] $$ $latex \[ = \R{tr} [ B(t) D(t) \bar{E}^\R{T} B'(t) ] + \R{tr} [ D(t) \bar{E}^\R{T} B(t) C'(t) ] + \R{tr} [ \bar{E}^\R{T} B(t) C(t) D'(t) ] \] $$ $latex \[ \bar{B} = \bar{E} (C D)^\R{T} \W{,} \bar{C} = B^\R{T} \bar{E} D^\R{T} \W{,} \bar{D} = (B C)^\R{T} \bar{E} \] $$ $subhead Reverse$$ For $latex k > 0$$, reverse mode eliminates $latex R_k$$ and expresses the function values $latex s$$ in terms of the coefficients of $latex A$$ and the lower order coefficients of $latex R$$. The effect on $latex \bar{R}_0$$ (of eliminating $latex R_k$$) is $latex \[ \bar{R}_0 = \bar{R}_0 - \bar{R}_k \left( \sum_{\ell=1}^k A_\ell R_{k-\ell} \right)^\R{T} = \bar{R}_0 + \bar{R}_k ( A_0 R_k )^\R{T} \] $$ For $latex \ell = 1 , \ldots , k$$, the effect on $latex \bar{R}_{k-\ell}$$ and $latex A_\ell$$ (of eliminating $latex R_k$$) is $latex \[ \bar{A}_\ell = \bar{A}_\ell - R_0^\R{T} \bar{R}_k R_{k-\ell}^\R{T} \] $$ $latex \[ \bar{R}_{k-\ell} = \bar{R}_{k-\ell} - ( R_0 A_\ell )^\R{T} \bar{R}_k \] $$ We note that $latex \[ R_0 '(t) A_0 (t) + R_0 (t) A_0 '(t) = 0 \] $$ $latex \[ R_0 '(t) = - R_0 (t) A_0 '(t) R_0 (t) \] $$ The reverse mode formula that eliminates $latex R_0$$ is $latex \[ \bar{A}_0 = \bar{A}_0 - R_0^\R{T} \bar{R}_0 R_0^\R{T} \]$$ $nospell $head Start Class Definition$$ $srccode%cpp% */ # include # include # include /* %$$ $head Public$$ $subhead Types$$ $srccode%cpp% */ namespace { // BEGIN_EMPTY_NAMESPACE template class atomic_eigen_mat_inv : public CppAD::atomic_base { public: // ----------------------------------------------------------- // type of elements during calculation of derivatives typedef Base scalar; // type of elements during taping typedef CppAD::AD ad_scalar; // type of matrix during calculation of derivatives typedef Eigen::Matrix< scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> matrix; // type of matrix during taping typedef Eigen::Matrix< ad_scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > ad_matrix; /* %$$ $subhead Constructor$$ $srccode%cpp% */ // constructor atomic_eigen_mat_inv(void) : CppAD::atomic_base( "atom_eigen_mat_inv" , CppAD::atomic_base::set_sparsity_enum ) { } /* %$$ $subhead op$$ $srccode%cpp% */ // use atomic operation to invert an AD matrix ad_matrix op(const ad_matrix& arg) { size_t nr = size_t( arg.rows() ); size_t ny = nr * nr; size_t nx = 1 + ny; assert( nr == size_t( arg.cols() ) ); // ------------------------------------------------------------------- // packed version of arg CPPAD_TESTVECTOR(ad_scalar) packed_arg(nx); packed_arg[0] = ad_scalar( nr ); for(size_t i = 0; i < ny; i++) packed_arg[1 + i] = arg.data()[i]; // ------------------------------------------------------------------- // packed version of result = arg^{-1}. // This is an atomic_base function call that CppAD uses to // store the atomic operation on the tape. CPPAD_TESTVECTOR(ad_scalar) packed_result(ny); (*this)(packed_arg, packed_result); // ------------------------------------------------------------------- // unpack result matrix ad_matrix result(nr, nr); for(size_t i = 0; i < ny; i++) result.data()[i] = packed_result[i]; return result; } /* %$$ $head Private$$ $subhead Variables$$ $srccode%cpp% */ private: // ------------------------------------------------------------- // one forward mode vector of matrices for argument and result CppAD::vector f_arg_, f_result_; // one reverse mode vector of matrices for argument and result CppAD::vector r_arg_, r_result_; // ------------------------------------------------------------- /* %$$ $subhead forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( // lowest order Taylor coefficient we are evaluating size_t p , // highest order Taylor coefficient we are evaluating size_t q , // which components of x are variables const CppAD::vector& vx , // which components of y are variables CppAD::vector& vy , // tx [ j * (q+1) + k ] is x_j^k const CppAD::vector& tx , // ty [ i * (q+1) + k ] is y_i^k CppAD::vector& ty ) { size_t n_order = q + 1; size_t nr = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) ); size_t ny = nr * nr; size_t nx = 1 + ny; assert( vx.size() == 0 || nx == vx.size() ); assert( vx.size() == 0 || ny == vy.size() ); assert( nx * n_order == tx.size() ); assert( ny * n_order == ty.size() ); // // ------------------------------------------------------------------- // make sure f_arg_ and f_result_ are large enough assert( f_arg_.size() == f_result_.size() ); if( f_arg_.size() < n_order ) { f_arg_.resize(n_order); f_result_.resize(n_order); // for(size_t k = 0; k < n_order; k++) { f_arg_[k].resize(nr, nr); f_result_[k].resize(nr, nr); } } // ------------------------------------------------------------------- // unpack tx into f_arg_ for(size_t k = 0; k < n_order; k++) { // unpack arg values for this order for(size_t i = 0; i < ny; i++) f_arg_[k].data()[i] = tx[ (1 + i) * n_order + k ]; } // ------------------------------------------------------------------- // result for each order // (we could avoid recalculting f_result_[k] for k=0,...,p-1) // f_result_[0] = f_arg_[0].inverse(); for(size_t k = 1; k < n_order; k++) { // initialize sum matrix f_sum = matrix::Zero(nr, nr); // compute sum for(size_t ell = 1; ell <= k; ell++) f_sum -= f_arg_[ell] * f_result_[k-ell]; // result_[k] = arg_[0]^{-1} * sum_ f_result_[k] = f_result_[0] * f_sum; } // ------------------------------------------------------------------- // pack result_ into ty for(size_t k = 0; k < n_order; k++) { for(size_t i = 0; i < ny; i++) ty[ i * n_order + k ] = f_result_[k].data()[i]; } // ------------------------------------------------------------------- // check if we are computing vy if( vx.size() == 0 ) return true; // ------------------------------------------------------------------ // This is a very dumb algorithm that over estimates which // elements of the inverse are variables (which is not efficient). bool var = false; for(size_t i = 0; i < ny; i++) var |= vx[1 + i]; for(size_t i = 0; i < ny; i++) vy[i] = var; return true; } /* %$$ $subhead reverse$$ $srccode%cpp% */ // reverse mode routine called by CppAD virtual bool reverse( // highest order Taylor coefficient that we are computing derivative of size_t q , // forward mode Taylor coefficients for x variables const CppAD::vector& tx , // forward mode Taylor coefficients for y variables const CppAD::vector& ty , // upon return, derivative of G[ F[ {x_j^k} ] ] w.r.t {x_j^k} CppAD::vector& px , // derivative of G[ {y_i^k} ] w.r.t. {y_i^k} const CppAD::vector& py ) { size_t n_order = q + 1; size_t nr = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) ); size_t ny = nr * nr; size_t nx = 1 + ny; // assert( nx * n_order == tx.size() ); assert( ny * n_order == ty.size() ); assert( px.size() == tx.size() ); assert( py.size() == ty.size() ); // ------------------------------------------------------------------- // make sure f_arg_ is large enough assert( f_arg_.size() == f_result_.size() ); // must have previous run forward with order >= n_order assert( f_arg_.size() >= n_order ); // ------------------------------------------------------------------- // make sure r_arg_, r_result_ are large enough assert( r_arg_.size() == r_result_.size() ); if( r_arg_.size() < n_order ) { r_arg_.resize(n_order); r_result_.resize(n_order); // for(size_t k = 0; k < n_order; k++) { r_arg_[k].resize(nr, nr); r_result_[k].resize(nr, nr); } } // ------------------------------------------------------------------- // unpack tx into f_arg_ for(size_t k = 0; k < n_order; k++) { // unpack arg values for this order for(size_t i = 0; i < ny; i++) f_arg_[k].data()[i] = tx[ (1 + i) * n_order + k ]; } // ------------------------------------------------------------------- // unpack py into r_result_ for(size_t k = 0; k < n_order; k++) { for(size_t i = 0; i < ny; i++) r_result_[k].data()[i] = py[ i * n_order + k ]; } // ------------------------------------------------------------------- // initialize r_arg_ as zero for(size_t k = 0; k < n_order; k++) r_arg_[k] = matrix::Zero(nr, nr); // ------------------------------------------------------------------- // matrix reverse mode calculation // for(size_t k1 = n_order; k1 > 1; k1--) { size_t k = k1 - 1; // bar{R}_0 = bar{R}_0 + bar{R}_k (A_0 R_k)^T r_result_[0] += r_result_[k] * f_result_[k].transpose() * f_arg_[0].transpose(); // for(size_t ell = 1; ell <= k; ell++) { // bar{A}_l = bar{A}_l - R_0^T bar{R}_k R_{k-l}^T r_arg_[ell] -= f_result_[0].transpose() * r_result_[k] * f_result_[k-ell].transpose(); // bar{R}_{k-l} = bar{R}_{k-1} - (R_0 A_l)^T bar{R}_k r_result_[k-ell] -= f_arg_[ell].transpose() * f_result_[0].transpose() * r_result_[k]; } } r_arg_[0] -= f_result_[0].transpose() * r_result_[0] * f_result_[0].transpose(); // ------------------------------------------------------------------- // pack r_arg into px for(size_t k = 0; k < n_order; k++) { for(size_t i = 0; i < ny; i++) px[ (1 + i) * n_order + k ] = r_arg_[k].data()[i]; } // return true; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of atomic_eigen_mat_inv class } // END_EMPTY_NAMESPACE /* %$$ $$ $comment end nospell$$ $end */ # endif cppad-20170000.3/cppad/example/eigen_mat_mul.hpp0000644000175200017650000005226213057470467020506 0ustar coincoin-web// $Id$ # ifndef CPPAD_EXAMPLE_EIGEN_MAT_MUL_HPP # define CPPAD_EXAMPLE_EIGEN_MAT_MUL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_eigen_mat_mul.hpp$$ $spell Eigen Taylor nr nc $$ $section Atomic Eigen Matrix Multiply Class$$ $head See Also$$ $cref atomic_mat_mul.hpp$$ $head Purpose$$ Construct an atomic operation that computes the matrix product, $latex R = A \times B$$ for any positive integers $latex r$$, $latex m$$, $latex c$$, and any $latex A \in \B{R}^{r \times m}$$, $latex B \in \B{R}^{m \times c}$$. $head Matrix Dimensions$$ This example puts the matrix dimensions in the atomic function arguments, instead of the $cref/constructor/atomic_ctor/$$, so that they can be different for different calls to the atomic function. These dimensions are: $table $icode nr_left$$ $cnext number of rows in the left matrix; i.e, $latex r$$ $rend $icode n_middle$$ $cnext rows in the left matrix and columns in right; i.e, $latex m$$ $rend $icode nc_right$$ $cnext number of columns in the right matrix; i.e., $latex c$$ $tend $head Theory$$ $subhead Forward$$ For $latex k = 0 , \ldots $$, the $th k$$ order Taylor coefficient $latex R_k$$ is given by $latex \[ R_k = \sum_{\ell = 0}^{k} A_\ell B_{k-\ell} \] $$ $subhead Product of Two Matrices$$ Suppose $latex \bar{E}$$ is the derivative of the scalar value function $latex s(E)$$ with respect to $latex E$$; i.e., $latex \[ \bar{E}_{i,j} = \frac{ \partial s } { \partial E_{i,j} } \] $$ Also suppose that $latex t$$ is a scalar valued argument and $latex \[ E(t) = C(t) D(t) \] $$ It follows that $latex \[ E'(t) = C'(t) D(t) + C(t) D'(t) \] $$ $latex \[ (s \circ E)'(t) = \R{tr} [ \bar{E}^\R{T} E'(t) ] \] $$ $latex \[ = \R{tr} [ \bar{E}^\R{T} C'(t) D(t) ] + \R{tr} [ \bar{E}^\R{T} C(t) D'(t) ] \] $$ $latex \[ = \R{tr} [ D(t) \bar{E}^\R{T} C'(t) ] + \R{tr} [ \bar{E}^\R{T} C(t) D'(t) ] \] $$ $latex \[ \bar{C} = \bar{E} D^\R{T} \W{,} \bar{D} = C^\R{T} \bar{E} \] $$ $subhead Reverse$$ Reverse mode eliminates $latex R_k$$ as follows: for $latex \ell = 0, \ldots , k-1$$, $latex \[ \bar{A}_\ell = \bar{A}_\ell + \bar{R}_k B_{k-\ell}^\R{T} \] $$ $latex \[ \bar{B}_{k-\ell} = \bar{B}_{k-\ell} + A_\ell^\R{T} \bar{R}_k \] $$ $nospell $head Start Class Definition$$ $srccode%cpp% */ # include # include /* %$$ $head Public$$ $subhead Types$$ $srccode%cpp% */ namespace { // BEGIN_EMPTY_NAMESPACE template class atomic_eigen_mat_mul : public CppAD::atomic_base { public: // ----------------------------------------------------------- // type of elements during calculation of derivatives typedef Base scalar; // type of elements during taping typedef CppAD::AD ad_scalar; // type of matrix during calculation of derivatives typedef Eigen::Matrix< scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> matrix; // type of matrix during taping typedef Eigen::Matrix< ad_scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > ad_matrix; /* %$$ $subhead Constructor$$ $srccode%cpp% */ // constructor atomic_eigen_mat_mul(void) : CppAD::atomic_base( "atom_eigen_mat_mul" , CppAD::atomic_base::set_sparsity_enum ) { } /* %$$ $subhead op$$ $srccode%cpp% */ // use atomic operation to multiply two AD matrices ad_matrix op( const ad_matrix& left , const ad_matrix& right ) { size_t nr_left = size_t( left.rows() ); size_t n_middle = size_t( left.cols() ); size_t nc_right = size_t( right.cols() ); assert( n_middle == size_t( right.rows() ) ); # ifndef NDEBUG size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t ny = nr_left * nc_right; # endif size_t n_left = nr_left * n_middle; size_t n_right = n_middle * nc_right; size_t n_result = nr_left * nc_right; // assert( 3 + n_left + n_right == nx ); assert( n_result == ny ); // ----------------------------------------------------------------- // packed version of left and right CPPAD_TESTVECTOR(ad_scalar) packed_arg(nx); // packed_arg[0] = ad_scalar( nr_left ); packed_arg[1] = ad_scalar( n_middle ); packed_arg[2] = ad_scalar( nc_right ); for(size_t i = 0; i < n_left; i++) packed_arg[3 + i] = left.data()[i]; for(size_t i = 0; i < n_right; i++) packed_arg[ 3 + n_left + i ] = right.data()[i]; // ------------------------------------------------------------------ // Packed version of result = left * right. // This as an atomic_base funciton call that CppAD uses // to store the atomic operation on the tape. CPPAD_TESTVECTOR(ad_scalar) packed_result(ny); (*this)(packed_arg, packed_result); // ------------------------------------------------------------------ // unpack result matrix ad_matrix result(nr_left, nc_right); for(size_t i = 0; i < n_result; i++) result.data()[i] = packed_result[ i ]; // return result; } /* %$$ $head Private$$ $subhead Variables$$ $srccode%cpp% */ private: // ------------------------------------------------------------- // one forward mode vector of matrices for left, right, and result CppAD::vector f_left_, f_right_, f_result_; // one reverse mode vector of matrices for left, right, and result CppAD::vector r_left_, r_right_, r_result_; // ------------------------------------------------------------- /* %$$ $subhead forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( // lowest order Taylor coefficient we are evaluating size_t p , // highest order Taylor coefficient we are evaluating size_t q , // which components of x are variables const CppAD::vector& vx , // which components of y are variables CppAD::vector& vy , // tx [ 3 + j * (q+1) + k ] is x_j^k const CppAD::vector& tx , // ty [ i * (q+1) + k ] is y_i^k CppAD::vector& ty ) { size_t n_order = q + 1; size_t nr_left = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) ); size_t n_middle = size_t( CppAD::Integer( tx[ 1 * n_order + 0 ] ) ); size_t nc_right = size_t( CppAD::Integer( tx[ 2 * n_order + 0 ] ) ); # ifndef NDEBUG size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t ny = nr_left * nc_right; # endif // assert( vx.size() == 0 || nx == vx.size() ); assert( vx.size() == 0 || ny == vy.size() ); assert( nx * n_order == tx.size() ); assert( ny * n_order == ty.size() ); // size_t n_left = nr_left * n_middle; size_t n_right = n_middle * nc_right; size_t n_result = nr_left * nc_right; assert( 3 + n_left + n_right == nx ); assert( n_result == ny ); // // ------------------------------------------------------------------- // make sure f_left_, f_right_, and f_result_ are large enough assert( f_left_.size() == f_right_.size() ); assert( f_left_.size() == f_result_.size() ); if( f_left_.size() < n_order ) { f_left_.resize(n_order); f_right_.resize(n_order); f_result_.resize(n_order); // for(size_t k = 0; k < n_order; k++) { f_left_[k].resize(nr_left, n_middle); f_right_[k].resize(n_middle, nc_right); f_result_[k].resize(nr_left, nc_right); } } // ------------------------------------------------------------------- // unpack tx into f_left and f_right for(size_t k = 0; k < n_order; k++) { // unpack left values for this order for(size_t i = 0; i < n_left; i++) f_left_[k].data()[i] = tx[ (3 + i) * n_order + k ]; // // unpack right values for this order for(size_t i = 0; i < n_right; i++) f_right_[k].data()[i] = tx[ ( 3 + n_left + i) * n_order + k ]; } // ------------------------------------------------------------------- // result for each order // (we could avoid recalculting f_result_[k] for k=0,...,p-1) for(size_t k = 0; k < n_order; k++) { // result[k] = sum_ell left[ell] * right[k-ell] f_result_[k] = matrix::Zero(nr_left, nc_right); for(size_t ell = 0; ell <= k; ell++) f_result_[k] += f_left_[ell] * f_right_[k-ell]; } // ------------------------------------------------------------------- // pack result_ into ty for(size_t k = 0; k < n_order; k++) { for(size_t i = 0; i < n_result; i++) ty[ i * n_order + k ] = f_result_[k].data()[i]; } // ------------------------------------------------------------------ // check if we are computing vy if( vx.size() == 0 ) return true; // ------------------------------------------------------------------ // compute variable information for y; i.e., vy // (note that the constant zero times a variable is a constant) scalar zero(0.0); assert( n_order == 1 ); for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { bool var = false; for(size_t ell = 0; ell < n_middle; ell++) { // left information size_t index = 3 + i * n_middle + ell; bool var_left = vx[index]; bool nz_left = var_left | (f_left_[0](i, ell) != zero); // right information index = 3 + n_left + ell * nc_right + j; bool var_right = vx[index]; bool nz_right = var_right | (f_right_[0](ell, j) != zero); // effect of result var |= var_left & nz_right; var |= nz_left & var_right; } size_t index = i * nc_right + j; vy[index] = var; } } return true; } /* %$$ $subhead reverse$$ $srccode%cpp% */ // reverse mode routine called by CppAD virtual bool reverse( // highest order Taylor coefficient that we are computing derivative of size_t q , // forward mode Taylor coefficients for x variables const CppAD::vector& tx , // forward mode Taylor coefficients for y variables const CppAD::vector& ty , // upon return, derivative of G[ F[ {x_j^k} ] ] w.r.t {x_j^k} CppAD::vector& px , // derivative of G[ {y_i^k} ] w.r.t. {y_i^k} const CppAD::vector& py ) { size_t n_order = q + 1; size_t nr_left = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) ); size_t n_middle = size_t( CppAD::Integer( tx[ 1 * n_order + 0 ] ) ); size_t nc_right = size_t( CppAD::Integer( tx[ 2 * n_order + 0 ] ) ); # ifndef NDEBUG size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t ny = nr_left * nc_right; # endif // assert( nx * n_order == tx.size() ); assert( ny * n_order == ty.size() ); assert( px.size() == tx.size() ); assert( py.size() == ty.size() ); // size_t n_left = nr_left * n_middle; size_t n_right = n_middle * nc_right; size_t n_result = nr_left * nc_right; assert( 3 + n_left + n_right == nx ); assert( n_result == ny ); // ------------------------------------------------------------------- // make sure f_left_, f_right_ are large enough assert( f_left_.size() == f_right_.size() ); assert( f_left_.size() == f_result_.size() ); // must have previous run forward with order >= n_order assert( f_left_.size() >= n_order ); // ------------------------------------------------------------------- // make sure r_left_, r_right_, and r_result_ are large enough assert( r_left_.size() == r_right_.size() ); assert( r_left_.size() == r_result_.size() ); if( r_left_.size() < n_order ) { r_left_.resize(n_order); r_right_.resize(n_order); r_result_.resize(n_order); // for(size_t k = 0; k < n_order; k++) { r_left_[k].resize(nr_left, n_middle); r_right_[k].resize(n_middle, nc_right); r_result_[k].resize(nr_left, nc_right); } } // ------------------------------------------------------------------- // unpack tx into f_left and f_right for(size_t k = 0; k < n_order; k++) { // unpack left values for this order for(size_t i = 0; i < n_left; i++) f_left_[k].data()[i] = tx[ (3 + i) * n_order + k ]; // // unpack right values for this order for(size_t i = 0; i < n_right; i++) f_right_[k].data()[i] = tx[ (3 + n_left + i) * n_order + k ]; } // ------------------------------------------------------------------- // unpack py into r_result_ for(size_t k = 0; k < n_order; k++) { for(size_t i = 0; i < n_result; i++) r_result_[k].data()[i] = py[ i * n_order + k ]; } // ------------------------------------------------------------------- // initialize r_left_ and r_right_ as zero for(size_t k = 0; k < n_order; k++) { r_left_[k] = matrix::Zero(nr_left, n_middle); r_right_[k] = matrix::Zero(n_middle, nc_right); } // ------------------------------------------------------------------- // matrix reverse mode calculation for(size_t k1 = n_order; k1 > 0; k1--) { size_t k = k1 - 1; for(size_t ell = 0; ell <= k; ell++) { // nr x nm = nr x nc * nc * nm r_left_[ell] += r_result_[k] * f_right_[k-ell].transpose(); // nm x nc = nm x nr * nr * nc r_right_[k-ell] += f_left_[ell].transpose() * r_result_[k]; } } // ------------------------------------------------------------------- // pack r_left and r_right int px for(size_t k = 0; k < n_order; k++) { // dimensions are integer constants px[ 0 * n_order + k ] = 0.0; px[ 1 * n_order + k ] = 0.0; px[ 2 * n_order + k ] = 0.0; // // pack left values for this order for(size_t i = 0; i < n_left; i++) px[ (3 + i) * n_order + k ] = r_left_[k].data()[i]; // // pack right values for this order for(size_t i = 0; i < n_right; i++) px[ (3 + i + n_left) * n_order + k] = r_right_[k].data()[i]; } // return true; } /* %$$ $subhead for_sparse_jac$$ $srccode%cpp% */ // forward Jacobian sparsity routine called by CppAD virtual bool for_sparse_jac( // number of columns in the matrix R size_t q , // sparsity pattern for the matrix R const CppAD::vector< std::set >& r , // sparsity pattern for the matrix S = f'(x) * R CppAD::vector< std::set >& s , const CppAD::vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); # ifndef NDEBUG size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t ny = nr_left * nc_right; # endif // assert( nx == r.size() ); assert( ny == s.size() ); // size_t n_left = nr_left * n_middle; for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { // pack index for entry (i, j) in result size_t i_result = i * nc_right + j; s[i_result].clear(); for(size_t ell = 0; ell < n_middle; ell++) { // pack index for entry (i, ell) in left size_t i_left = 3 + i * n_middle + ell; // pack index for entry (ell, j) in right size_t i_right = 3 + n_left + ell * nc_right + j; // s[i_result] = CppAD::set_union(s[i_result], r[i_left] ); s[i_result] = CppAD::set_union(s[i_result], r[i_right] ); } } } return true; } /* %$$ $subhead rev_sparse_jac$$ $srccode%cpp% */ // reverse Jacobian sparsity routine called by CppAD virtual bool rev_sparse_jac( // number of columns in the matrix R^T size_t q , // sparsity pattern for the matrix R^T const CppAD::vector< std::set >& rt , // sparsoity pattern for the matrix S^T = f'(x)^T * R^T CppAD::vector< std::set >& st , const CppAD::vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); size_t nx = 3 + (nr_left + nc_right) * n_middle; # ifndef NDEBUG size_t ny = nr_left * nc_right; # endif // assert( nx == st.size() ); assert( ny == rt.size() ); // // initialize S^T as empty for(size_t i = 0; i < nx; i++) st[i].clear(); // sparsity for S(x)^T = f'(x)^T * R^T size_t n_left = nr_left * n_middle; for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { // pack index for entry (i, j) in result size_t i_result = i * nc_right + j; st[i_result].clear(); for(size_t ell = 0; ell < n_middle; ell++) { // pack index for entry (i, ell) in left size_t i_left = 3 + i * n_middle + ell; // pack index for entry (ell, j) in right size_t i_right = 3 + n_left + ell * nc_right + j; // st[i_left] = CppAD::set_union(st[i_left], rt[i_result]); st[i_right] = CppAD::set_union(st[i_right], rt[i_result]); } } } return true; } /* %$$ $subhead for_sparse_hes$$ $srccode%cpp% */ virtual bool for_sparse_hes( // which components of x are variables for this call const CppAD::vector& vx, // sparsity pattern for the diagonal of R const CppAD::vector& r , // sparsity pattern for the vector S const CppAD::vector& s , // sparsity patternfor the Hessian H(x) CppAD::vector< std::set >& h , const CppAD::vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); size_t nx = 3 + (nr_left + nc_right) * n_middle; # ifndef NDEBUG size_t ny = nr_left * nc_right; # endif // assert( vx.size() == nx ); assert( r.size() == nx ); assert( s.size() == ny ); assert( h.size() == nx ); // // initilize h as empty for(size_t i = 0; i < nx; i++) h[i].clear(); // size_t n_left = nr_left * n_middle; for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { // pack index for entry (i, j) in result size_t i_result = i * nc_right + j; if( s[i_result] ) { for(size_t ell = 0; ell < n_middle; ell++) { // pack index for entry (i, ell) in left size_t i_left = 3 + i * n_middle + ell; // pack index for entry (ell, j) in right size_t i_right = 3 + n_left + ell * nc_right + j; if( r[i_left] & r[i_right] ) { h[i_left].insert(i_right); h[i_right].insert(i_left); } } } } } return true; } /* %$$ $subhead rev_sparse_hes$$ $srccode%cpp% */ // reverse Hessian sparsity routine called by CppAD virtual bool rev_sparse_hes( // which components of x are variables for this call const CppAD::vector& vx, // sparsity pattern for S(x) = g'[f(x)] const CppAD::vector& s , // sparsity pattern for d/dx g[f(x)] = S(x) * f'(x) CppAD::vector& t , // number of columns in R, U(x), and V(x) size_t q , // sparsity pattern for R const CppAD::vector< std::set >& r , // sparsity pattern for U(x) = g^{(2)} [ f(x) ] * f'(x) * R const CppAD::vector< std::set >& u , // sparsity pattern for // V(x) = f'(x)^T * U(x) + sum_{i=0}^{m-1} S_i(x) f_i^{(2)} (x) * R CppAD::vector< std::set >& v , // parameters as integers const CppAD::vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); size_t nx = 3 + (nr_left + nc_right) * n_middle; # ifndef NDEBUG size_t ny = nr_left * nc_right; # endif // assert( vx.size() == nx ); assert( s.size() == ny ); assert( t.size() == nx ); assert( r.size() == nx ); assert( v.size() == nx ); // // initilaize return sparsity patterns as false for(size_t j = 0; j < nx; j++) { t[j] = false; v[j].clear(); } // size_t n_left = nr_left * n_middle; for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { // pack index for entry (i, j) in result size_t i_result = i * nc_right + j; for(size_t ell = 0; ell < n_middle; ell++) { // pack index for entry (i, ell) in left size_t i_left = 3 + i * n_middle + ell; // pack index for entry (ell, j) in right size_t i_right = 3 + n_left + ell * nc_right + j; // // back propagate T(x) = S(x) * f'(x). t[i_left] |= bool( s[i_result] ); t[i_right] |= bool( s[i_result] ); // // V(x) = f'(x)^T * U(x) + sum_i S_i(x) * f_i''(x) * R // U(x) = g''[ f(x) ] * f'(x) * R // S_i(x) = g_i'[ f(x) ] // // back propagate f'(x)^T * U(x) v[i_left] = CppAD::set_union(v[i_left], u[i_result] ); v[i_right] = CppAD::set_union(v[i_right], u[i_result] ); // // back propagate S_i(x) * f_i''(x) * R // (here is where we use vx to check for cross terms) if( s[i_result] & vx[i_left] & vx[i_right] ) { v[i_left] = CppAD::set_union(v[i_left], r[i_right] ); v[i_right] = CppAD::set_union(v[i_right], r[i_left] ); } } } } return true; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of atomic_eigen_mat_mul class } // END_EMPTY_NAMESPACE /* %$$ $$ $comment end nospell$$ $end */ # endif cppad-20170000.3/cppad/example/eigen_plugin.hpp0000644000175200017650000000163013057470467020337 0ustar coincoin-web// $Id: eigen_plugin.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_EXAMPLE_EIGEN_PLUGIN_HPP # define CPPAD_EXAMPLE_EIGEN_PLUGIN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /*$ $begin eigen_plugin.hpp$$ $spell eigen_plugin.hpp typedef $$ $section Source Code for eigen_plugin.hpp$$ $srccode%cpp% */ // Declaration needed so an Eigen vector is a simple vector typedef Scalar value_type; /* %$$ $end */ # endif cppad-20170000.3/cppad/example/eigen_cholesky.hpp0000644000175200017650000003002513057470467020662 0ustar coincoin-web// $Id$ # ifndef CPPAD_EXAMPLE_EIGEN_CHOLESKY_HPP # define CPPAD_EXAMPLE_EIGEN_CHOLESKY_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_eigen_cholesky.hpp$$ $spell Eigen Taylor Cholesky op $$ $section Atomic Eigen Cholesky Factorization Class$$ $head Purpose$$ Construct an atomic operation that computes a lower triangular matrix $latex L $$ such that $latex L L^\R{T} = A$$ for any positive integer $latex p$$ and symmetric positive definite matrix $latex A \in \B{R}^{p \times p}$$. $head Start Class Definition$$ $srccode%cpp% */ # include # include /* %$$ $head Public$$ $subhead Types$$ $srccode%cpp% */ namespace { // BEGIN_EMPTY_NAMESPACE template class atomic_eigen_cholesky : public CppAD::atomic_base { public: // ----------------------------------------------------------- // type of elements during calculation of derivatives typedef Base scalar; // type of elements during taping typedef CppAD::AD ad_scalar; // // type of matrix during calculation of derivatives typedef Eigen::Matrix< scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> matrix; // type of matrix during taping typedef Eigen::Matrix< ad_scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > ad_matrix; // // lower triangular scalar matrix typedef Eigen::TriangularView lower_view; /* %$$ $subhead Constructor$$ $srccode%cpp% */ // constructor atomic_eigen_cholesky(void) : CppAD::atomic_base( "atom_eigen_cholesky" , CppAD::atomic_base::set_sparsity_enum ) { } /* %$$ $subhead op$$ $srccode%cpp% */ // use atomic operation to invert an AD matrix ad_matrix op(const ad_matrix& arg) { size_t nr = size_t( arg.rows() ); size_t ny = ( (nr + 1 ) * nr ) / 2; size_t nx = 1 + ny; assert( nr == size_t( arg.cols() ) ); // ------------------------------------------------------------------- // packed version of arg CPPAD_TESTVECTOR(ad_scalar) packed_arg(nx); size_t index = 0; packed_arg[index++] = ad_scalar( nr ); // lower triangle of symmetric matrix A for(size_t i = 0; i < nr; i++) { for(size_t j = 0; j <= i; j++) packed_arg[index++] = arg(i, j); } assert( index == nx ); // ------------------------------------------------------------------- // packed version of result = arg^{-1}. // This is an atomic_base function call that CppAD uses to // store the atomic operation on the tape. CPPAD_TESTVECTOR(ad_scalar) packed_result(ny); (*this)(packed_arg, packed_result); // ------------------------------------------------------------------- // unpack result matrix L ad_matrix result = ad_matrix::Zero(nr, nr); index = 0; for(size_t i = 0; i < nr; i++) { for(size_t j = 0; j <= i; j++) result(i, j) = packed_result[index++]; } return result; } /* %$$ $head Private$$ $subhead Variables$$ $srccode%cpp% */ private: // ------------------------------------------------------------- // one forward mode vector of matrices for argument and result CppAD::vector f_arg_, f_result_; // one reverse mode vector of matrices for argument and result CppAD::vector r_arg_, r_result_; // ------------------------------------------------------------- /* %$$ $subhead forward$$ $srccode%cpp% */ // forward mode routine called by CppAD virtual bool forward( // lowest order Taylor coefficient we are evaluating size_t p , // highest order Taylor coefficient we are evaluating size_t q , // which components of x are variables const CppAD::vector& vx , // which components of y are variables CppAD::vector& vy , // tx [ j * (q+1) + k ] is x_j^k const CppAD::vector& tx , // ty [ i * (q+1) + k ] is y_i^k CppAD::vector& ty ) { size_t n_order = q + 1; size_t nr = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) ); size_t ny = ((nr + 1) * nr) / 2; size_t nx = 1 + ny; assert( vx.size() == 0 || nx == vx.size() ); assert( vx.size() == 0 || ny == vy.size() ); assert( nx * n_order == tx.size() ); assert( ny * n_order == ty.size() ); // // ------------------------------------------------------------------- // make sure f_arg_ and f_result_ are large enough assert( f_arg_.size() == f_result_.size() ); if( f_arg_.size() < n_order ) { f_arg_.resize(n_order); f_result_.resize(n_order); // for(size_t k = 0; k < n_order; k++) { f_arg_[k].resize(nr, nr); f_result_[k].resize(nr, nr); } } // ------------------------------------------------------------------- // unpack tx into f_arg_ for(size_t k = 0; k < n_order; k++) { size_t index = 1; // unpack arg values for this order for(size_t i = 0; i < nr; i++) { for(size_t j = 0; j <= i; j++) { f_arg_[k](i, j) = tx[ index * n_order + k ]; f_arg_[k](j, i) = f_arg_[k](i, j); index++; } } } // ------------------------------------------------------------------- // result for each order // (we could avoid recalculting f_result_[k] for k=0,...,p-1) // Eigen::LLT cholesky(f_arg_[0]); f_result_[0] = cholesky.matrixL(); lower_view L_0 = f_result_[0].template triangularView(); for(size_t k = 1; k < n_order; k++) { // initialize sum as A_k matrix f_sum = f_arg_[k]; // compute A_k - B_k for(size_t ell = 1; ell < k; ell++) f_sum -= f_result_[ell] * f_result_[k-ell].transpose(); // compute L_0^{-1} * (A_k - B_k) * L_0^{-T} matrix temp = L_0.template solve(f_sum); temp = L_0.transpose().template solve(temp); // divide the diagonal by 2 for(size_t i = 0; i < nr; i++) temp(i, i) /= scalar(2.0); // L_k = L_0 * low[ L_0^{-1} * (A_k - B_k) * L_0^{-T} ] lower_view view = temp.template triangularView(); f_result_[k] = f_result_[0] * view; } // ------------------------------------------------------------------- // pack result_ into ty for(size_t k = 0; k < n_order; k++) { size_t index = 0; for(size_t i = 0; i < nr; i++) { for(size_t j = 0; j <= i; j++) { ty[ index * n_order + k ] = f_result_[k](i, j); index++; } } } // ------------------------------------------------------------------- // check if we are computing vy if( vx.size() == 0 ) return true; // ------------------------------------------------------------------ // This is a very dumb algorithm that over estimates which // elements of the inverse are variables (which is not efficient). bool var = false; for(size_t i = 0; i < ny; i++) var |= vx[1 + i]; for(size_t i = 0; i < ny; i++) vy[i] = var; // return true; } /* %$$ $subhead reverse$$ $srccode%cpp% */ // reverse mode routine called by CppAD virtual bool reverse( // highest order Taylor coefficient that we are computing derivative of size_t q , // forward mode Taylor coefficients for x variables const CppAD::vector& tx , // forward mode Taylor coefficients for y variables const CppAD::vector& ty , // upon return, derivative of G[ F[ {x_j^k} ] ] w.r.t {x_j^k} CppAD::vector& px , // derivative of G[ {y_i^k} ] w.r.t. {y_i^k} const CppAD::vector& py ) { size_t n_order = q + 1; size_t nr = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) ); size_t ny = ( (nr + 1 ) * nr ) / 2; size_t nx = 1 + ny; // assert( nx * n_order == tx.size() ); assert( ny * n_order == ty.size() ); assert( px.size() == tx.size() ); assert( py.size() == ty.size() ); // ------------------------------------------------------------------- // make sure f_arg_ is large enough assert( f_arg_.size() == f_result_.size() ); // must have previous run forward with order >= n_order assert( f_arg_.size() >= n_order ); // ------------------------------------------------------------------- // make sure r_arg_, r_result_ are large enough assert( r_arg_.size() == r_result_.size() ); if( r_arg_.size() < n_order ) { r_arg_.resize(n_order); r_result_.resize(n_order); // for(size_t k = 0; k < n_order; k++) { r_arg_[k].resize(nr, nr); r_result_[k].resize(nr, nr); } } // ------------------------------------------------------------------- // unpack tx into f_arg_ for(size_t k = 0; k < n_order; k++) { size_t index = 1; // unpack arg values for this order for(size_t i = 0; i < nr; i++) { for(size_t j = 0; j <= i; j++) { f_arg_[k](i, j) = tx[ index * n_order + k ]; f_arg_[k](j, i) = f_arg_[k](i, j); index++; } } } // ------------------------------------------------------------------- // unpack py into r_result_ for(size_t k = 0; k < n_order; k++) { r_result_[k] = matrix::Zero(nr, nr); size_t index = 0; for(size_t i = 0; i < nr; i++) { for(size_t j = 0; j <= i; j++) { r_result_[k](i, j) = py[ index * n_order + k ]; index++; } } } // ------------------------------------------------------------------- // initialize r_arg_ as zero for(size_t k = 0; k < n_order; k++) r_arg_[k] = matrix::Zero(nr, nr); // ------------------------------------------------------------------- // matrix reverse mode calculation lower_view L_0 = f_result_[0].template triangularView(); // for(size_t k1 = n_order; k1 > 1; k1--) { size_t k = k1 - 1; // // L_0^T * bar{L}_k matrix tmp1 = L_0.transpose() * r_result_[k]; // //low[ L_0^T * bar{L}_k ] for(size_t i = 0; i < nr; i++) tmp1(i, i) /= scalar(2.0); matrix tmp2 = tmp1.template triangularView(); // // L_0^{-T} low[ L_0^T * bar{L}_k ] tmp1 = L_0.transpose().template solve( tmp2 ); // // M_k = L_0^{-T} * low[ L_0^T * bar{L}_k ]^{T} L_0^{-1} matrix M_k = L_0.transpose().template solve( tmp1.transpose() ); // // remove L_k and compute bar{B}_k matrix barB_k = scalar(0.5) * ( M_k + M_k.transpose() ); r_arg_[k] += barB_k; barB_k = scalar(-1.0) * barB_k; // // 2.0 * lower( bar{B}_k L_k ) matrix temp = scalar(2.0) * barB_k * f_result_[k]; temp = temp.template triangularView(); // // remove C_k r_result_[0] += temp; // // remove B_k for(size_t ell = 1; ell < k; ell++) { // bar{L}_ell = 2 * lower( \bar{B}_k * L_{k-ell} ) temp = scalar(2.0) * barB_k * f_result_[k-ell]; r_result_[ell] += temp.template triangularView(); } } // M_0 = L_0^{-T} * low[ L_0^T * bar{L}_0 ]^{T} L_0^{-1} matrix M_0 = L_0.transpose() * r_result_[0]; for(size_t i = 0; i < nr; i++) M_0(i, i) /= scalar(2.0); M_0 = M_0.template triangularView(); M_0 = L_0.template solve( M_0 ); M_0 = L_0.transpose().template solve( M_0 ); // remove L_0 r_arg_[0] += scalar(0.5) * ( M_0 + M_0.transpose() ); // ------------------------------------------------------------------- // pack r_arg into px // note that only the lower triangle of barA_k is stored in px for(size_t k = 0; k < n_order; k++) { size_t index = 0; px[ index * n_order + k ] = 0.0; index++; for(size_t i = 0; i < nr; i++) { for(size_t j = 0; j < i; j++) { px[ index * n_order + k ] = 2.0 * r_arg_[k](i, j); index++; } px[ index * n_order + k] = r_arg_[k](i, i); index++; } } // ------------------------------------------------------------------- return true; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of atomic_eigen_cholesky class } // END_EMPTY_NAMESPACE /* %$$ $end */ # endif cppad-20170000.3/cppad/example/base_adolc.hpp0000644000175200017650000002230513057470467017750 0ustar coincoin-web// $Id: base_adolc.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_EXAMPLE_BASE_ADOLC_HPP # define CPPAD_EXAMPLE_BASE_ADOLC_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_adolc.hpp$$ $spell stringstream struct string setprecision str valgrind azmul expm1 atanh acosh asinh erf ifndef define endif Rel codassign eps std abs_geq fabs cppad.hpp undef Lt Le Eq Ge Gt namespace cassert condassign hpp bool const Adolc adouble CondExpOp inline enum CppAD pow acos asin atan cos cosh exp sqrt $$ $section Enable use of AD where Base is Adolc's adouble Type$$ $head Syntax$$ $codei%# include %$$ $children% example/mul_level_adolc.cpp %$$ $head Example$$ The file $cref mul_level_adolc.cpp$$ contains an example use of Adolc's $code adouble$$ type for a CppAD $icode Base$$ type. It returns true if it succeeds and false otherwise. The file $cref mul_level_adolc_ode.cpp$$ contains a more realistic (and complex) example. $head Include Files$$ This file $code base_adolc.hpp$$ requires $code adouble$$ to be defined. In addition, it is included before $code $$, but it needs to include parts of CppAD that are used by this file. This is done with the following include commands: $srccode%cpp% */ # include # include /* %$$ $head CondExpOp$$ The type $code adouble$$ supports a conditional assignment function with the syntax $codei% condassign(%a%, %b%, %c%, %d%) %$$ which evaluates to $codei% %a% = (%b% > 0) ? %c% : %d%; %$$ This enables one to include conditionals in the recording of $code adouble$$ operations and later evaluation for different values of the independent variables (in the same spirit as the CppAD $cref CondExp$$ function). $srccode%cpp% */ namespace CppAD { inline adouble CondExpOp( enum CppAD::CompareOp cop , const adouble &left , const adouble &right , const adouble &trueCase , const adouble &falseCase ) { adouble result; switch( cop ) { case CompareLt: // left < right condassign(result, right - left, trueCase, falseCase); break; case CompareLe: // left <= right condassign(result, left - right, falseCase, trueCase); break; case CompareEq: // left == right condassign(result, left - right, falseCase, trueCase); condassign(result, right - left, falseCase, result); break; case CompareGe: // left >= right condassign(result, right - left, falseCase, trueCase); break; case CompareGt: // left > right condassign(result, left - right, trueCase, falseCase); break; default: CppAD::ErrorHandler::Call( true , __LINE__ , __FILE__ , "CppAD::CondExp", "Error: for unknown reason." ); result = trueCase; } return result; } } /* %$$ $head CondExpRel$$ The $cref/CPPAD_COND_EXP_REL/base_cond_exp/CondExpRel/$$ macro invocation $srccode%cpp% */ namespace CppAD { CPPAD_COND_EXP_REL(adouble) } /* %$$ $head EqualOpSeq$$ The Adolc user interface does not specify a way to determine if two $code adouble$$ variables correspond to the same operations sequence. Make $code EqualOpSeq$$ an error if it gets used: $srccode%cpp% */ namespace CppAD { inline bool EqualOpSeq(const adouble &x, const adouble &y) { CppAD::ErrorHandler::Call( true , __LINE__ , __FILE__ , "CppAD::EqualOpSeq(x, y)", "Error: adouble does not support EqualOpSeq." ); return false; } } /* %$$ $head Identical$$ The Adolc user interface does not specify a way to determine if an $code adouble$$ depends on the independent variables. To be safe (but slow) return $code false$$ in all the cases below. $srccode%cpp% */ namespace CppAD { inline bool IdenticalPar(const adouble &x) { return false; } inline bool IdenticalZero(const adouble &x) { return false; } inline bool IdenticalOne(const adouble &x) { return false; } inline bool IdenticalEqualPar(const adouble &x, const adouble &y) { return false; } } /* %$$ $head Integer$$ $srccode%cpp% */ inline int Integer(const adouble &x) { return static_cast( x.getValue() ); } /* %$$ $head azmul$$ $srccode%cpp% */ namespace CppAD { CPPAD_AZMUL( adouble ) } /* %$$ $head Ordered$$ $srccode%cpp% */ namespace CppAD { inline bool GreaterThanZero(const adouble &x) { return (x > 0); } inline bool GreaterThanOrZero(const adouble &x) { return (x >= 0); } inline bool LessThanZero(const adouble &x) { return (x < 0); } inline bool LessThanOrZero(const adouble &x) { return (x <= 0); } inline bool abs_geq(const adouble& x, const adouble& y) { return fabs(x) >= fabs(y); } } /* %$$ $head Unary Standard Math$$ The following $cref/required/base_require/$$ functions are defined by the Adolc package for the $code adouble$$ base case: $pre $$ $code acos$$, $code asin$$, $code atan$$, $code cos$$, $code cosh$$, $code exp$$, $code fabs$$, $code log$$, $code sin$$, $code sinh$$, $code sqrt$$, $code tan$$. $head erf, asinh, acosh, atanh, expm1, log1p$$ If the $cref/erf, asinh, acosh, atanh, expm1, log1p /base_std_math /erf, asinh, acosh, atanh, expm1, log1p /$$, functions are supported by the compiler, they must also be supported by a $icode Base$$ type; The adolc package does not support these functions so make their use an error: $srccode%cpp% */ namespace CppAD { # define CPPAD_BASE_ADOLC_NO_SUPPORT(fun) \ inline adouble fun(const adouble& x) \ { CPPAD_ASSERT_KNOWN( \ false, \ #fun ": adolc does not support this function" \ ); \ return 0.0; \ } # if CPPAD_USE_CPLUSPLUS_2011 CPPAD_BASE_ADOLC_NO_SUPPORT(erf) CPPAD_BASE_ADOLC_NO_SUPPORT(asinh) CPPAD_BASE_ADOLC_NO_SUPPORT(acosh) CPPAD_BASE_ADOLC_NO_SUPPORT(atanh) CPPAD_BASE_ADOLC_NO_SUPPORT(expm1) CPPAD_BASE_ADOLC_NO_SUPPORT(log1p) # endif # undef CPPAD_BASE_ADOLC_NO_SUPPORT } /* %$$ $head sign$$ This $cref/required/base_require/$$ function is defined using the $code codassign$$ function so that its $code adouble$$ operation sequence does not depend on the value of $icode x$$. $srccode%cpp% */ namespace CppAD { inline adouble sign(const adouble& x) { adouble s_plus, s_minus, half(.5); // set s_plus to sign(x)/2, except for case x == 0, s_plus = -.5 condassign(s_plus, +x, -half, +half); // set s_minus to -sign(x)/2, except for case x == 0, s_minus = -.5 condassign(s_minus, -x, -half, +half); // set s to sign(x) return s_plus - s_minus; } } /* %$$ $head abs$$ This $cref/required/base_require/$$ function uses the adolc $code fabs$$ function: $srccode%cpp% */ namespace CppAD { inline adouble abs(const adouble& x) { return fabs(x); } } /* %$$ $head pow$$ This $cref/required/base_require/$$ function is defined by the Adolc package for the $code adouble$$ base case. $head numeric_limits$$ The following defines the CppAD $cref numeric_limits$$ for the type $code adouble$$: $srccode%cpp% */ namespace CppAD { CPPAD_NUMERIC_LIMITS(double, adouble) } /* %$$ $head to_string$$ The following defines the CppAD $cref to_string$$ function for the type $code adouble$$: $srccode%cpp% */ namespace CppAD { template <> struct to_string_struct { std::string operator()(const adouble& x) { std::stringstream os; double epsilon = std::numeric_limits::epsilon(); double log10 = std::log( epsilon ) / std::log(10.); size_t n_digits = 1 - Integer( log10 ); os << std::setprecision(n_digits); os << x.value(); return os.str(); } }; } /* %$$ $head hash_code$$ It appears that an $code adouble$$ object can have fields that are not initialized. This results in a $code valgrind$$ error when these fields are used by the $cref/default/base_hash/Default/$$ hashing function. For this reason, the $code adouble$$ class overrides the default definition. $srccode|cpp| */ namespace CppAD { inline unsigned short hash_code(const adouble& x) { unsigned short code = 0; double value = x.value(); if( value == 0.0 ) return code; double log_x = std::log( abs( value ) ); // assume log( std::numeric_limits::max() ) is near 700 code = static_cast( (CPPAD_HASH_TABLE_SIZE / 700 + 1) * log_x ); code = code % CPPAD_HASH_TABLE_SIZE; return code; } } /* |$$ Note that after the hash codes match, the $cref/Identical/base_adolc.hpp/Identical/$$ function will be used to make sure two values are the same and one can replace the other. A more sophisticated implementation of the $code Identical$$ function would detect which $code adouble$$ values depend on the $code adouble$$ independent variables (and hence can change). $end */ # endif cppad-20170000.3/cppad/example/cppad_eigen.hpp0000644000175200017650000001113413057470467020130 0ustar coincoin-web// $Id: cppad_eigen.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_EXAMPLE_CPPAD_EIGEN_HPP # define CPPAD_EXAMPLE_CPPAD_EIGEN_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin cppad_eigen.hpp$$ $spell impl typename Real Real inline neg eps plugin atan Num acos asin CppAD std::numeric enum Mul Eigen cppad.hpp namespace struct typedef const imag sqrt exp cos $$ $section Enable Use of Eigen Linear Algebra Package with CppAD$$ $head Syntax$$ $codei%# include %$$ $children% cppad/example/eigen_plugin.hpp% example/eigen_array.cpp% example/eigen_det.cpp %$$ $head Purpose$$ Enables the use of the $href%http://eigen.tuxfamily.org%eigen%$$ linear algebra package with the type $icode%AD<%Base%>%$$. $head Example$$ The files $cref eigen_array.cpp$$ and $cref eigen_det.cpp$$ contain an example and test of this include file. It returns true if it succeeds and false otherwise. $head Include Files$$ The file $code cppad_eigen.hpp$$ includes both $code $$ and $code $$. In addition, The file $cref eigen_plugin.hpp$$ is used to define $code value_type$$ in the Eigen matrix class definition so its vectors are $cref/simple vectors/SimpleVector/$$. $srccode%cpp% */ # define EIGEN_MATRIXBASE_PLUGIN # include # include /* %$$ $head Eigen NumTraits$$ Eigen needs the following definitions to work properly with $codei%AD<%Base%>%$$ scalars: $srccode%cpp% */ namespace Eigen { template struct NumTraits< CppAD::AD > { // type that corresponds to the real part of an AD value typedef CppAD::AD Real; // type for AD operations that result in non-integer values typedef CppAD::AD NonInteger; // type for nested value inside an AD expression tree typedef CppAD::AD Nested; enum { // does not support complex Base types IsComplex = 0 , // does not support integer Base types IsInteger = 0 , // only support signed Base types IsSigned = 1 , // must initialize an AD object RequireInitialization = 1 , // computational cost of the corresponding operations ReadCost = 1 , AddCost = 2 , MulCost = 2 }; // machine epsilon with type of real part of x // (use assumption that Base is not complex) static CppAD::AD epsilon(void) { return CppAD::numeric_limits< CppAD::AD >::epsilon(); } // relaxed version of machine epsilon for comparison of different // operations that should result in the same value static CppAD::AD dummy_precision(void) { return 100. * CppAD::numeric_limits< CppAD::AD >::epsilon(); } // minimum normalized positive value static CppAD::AD lowest(void) { return CppAD::numeric_limits< CppAD::AD >::min(); } // maximum finite value static CppAD::AD highest(void) { return CppAD::numeric_limits< CppAD::AD >::max(); } }; } /* %$$ $head CppAD Namespace$$ Eigen also needs the following definitions to work properly with $codei%AD<%Base%>%$$ scalars: $srccode%cpp% */ namespace CppAD { // functions that return references template const AD& conj(const AD& x) { return x; } template const AD& real(const AD& x) { return x; } // functions that return values (note abs is defined by cppad.hpp) template AD imag(const AD& x) { return CppAD::AD(0.); } template AD abs2(const AD& x) { return x * x; } } namespace Eigen { namespace internal { template struct significant_decimals_default_impl< CppAD::AD, false> { typedef CppAD::AD Scalar; typedef typename NumTraits::Real RealScalar; static inline int run() { Scalar neg_log_eps = - log( NumTraits::epsilon() ); int ceil_neg_log_eps = Integer( neg_log_eps ); if( Scalar(ceil_neg_log_eps) < neg_log_eps ) ceil_neg_log_eps++; return ceil_neg_log_eps; } }; } } /* %$$ $end */ # endif cppad-20170000.3/cppad/example/mat_mul.hpp0000644000175200017650000004755413057470467017347 0ustar coincoin-web// $Id$ # ifndef CPPAD_EXAMPLE_MAT_MUL_HPP # define CPPAD_EXAMPLE_MAT_MUL_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin atomic_mat_mul.hpp$$ $spell Taylor ty px CppAD jac hes nr nc $$ $section Matrix Multiply as an Atomic Operation$$ $head See Also$$ $cref atomic_eigen_mat_mul.hpp$$ $head Matrix Dimensions$$ This example puts the matrix dimensions in the atomic function arguments, instead of the $cref/constructor/atomic_ctor/$$, so that they can be different for different calls to the atomic function. These dimensions are: $table $icode nr_left$$ $cnext number of rows in the left matrix $rend $icode n_middle$$ $cnext rows in the left matrix and columns in right $rend $icode nc_right$$ $cnext number of columns in the right matrix $tend $head Start Class Definition$$ $srccode%cpp% */ # include namespace { // Begin empty namespace using CppAD::vector; // using CppAD::set_union; // // matrix result = left * right class atomic_mat_mul : public CppAD::atomic_base { /* %$$ $head Constructor$$ $srccode%cpp% */ public: // --------------------------------------------------------------------- // constructor atomic_mat_mul(void) : CppAD::atomic_base("mat_mul") { } private: /* %$$ $head Left Operand Element Index$$ Index in the Taylor coefficient matrix $icode tx$$ of a left matrix element. $srccode%cpp% */ size_t left( size_t i , // left matrix row index size_t j , // left matrix column index size_t k , // Taylor coeffocient order size_t nk , // number of Taylor coefficients in tx size_t nr_left , // rows in left matrix size_t n_middle , // rows in left and columns in right size_t nc_right ) // columns in right matrix { assert( i < nr_left ); assert( j < n_middle ); return (3 + i * n_middle + j) * nk + k; } /* %$$ $head Right Operand Element Index$$ Index in the Taylor coefficient matrix $icode tx$$ of a right matrix element. $srccode%cpp% */ size_t right( size_t i , // right matrix row index size_t j , // right matrix column index size_t k , // Taylor coeffocient order size_t nk , // number of Taylor coefficients in tx size_t nr_left , // rows in left matrix size_t n_middle , // rows in left and columns in right size_t nc_right ) // columns in right matrix { assert( i < n_middle ); assert( j < nc_right ); size_t offset = 3 + nr_left * n_middle; return (offset + i * nc_right + j) * nk + k; } /* %$$ $head Result Element Index$$ Index in the Taylor coefficient matrix $icode ty$$ of a result matrix element. $srccode%cpp% */ size_t result( size_t i , // result matrix row index size_t j , // result matrix column index size_t k , // Taylor coeffocient order size_t nk , // number of Taylor coefficients in ty size_t nr_left , // rows in left matrix size_t n_middle , // rows in left and columns in right size_t nc_right ) // columns in right matrix { assert( i < nr_left ); assert( j < nc_right ); return (i * nc_right + j) * nk + k; } /* %$$ $head Forward Matrix Multiply$$ Forward mode multiply Taylor coefficients in $icode tx$$ and sum into $icode ty$$ (for one pair of left and right orders) $srccode%cpp% */ void forward_multiply( size_t k_left , // order for left coefficients size_t k_right , // order for right coefficients const vector& tx , // domain space Taylor coefficients vector& ty , // range space Taylor coefficients size_t nr_left , // rows in left matrix size_t n_middle , // rows in left and columns in right size_t nc_right ) // columns in right matrix { size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t nk = tx.size() / nx; # ifndef NDEBUG size_t ny = nr_left * nc_right; assert( nk == ty.size() / ny ); # endif // size_t k_result = k_left + k_right; assert( k_result < nk ); // for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { double sum = 0.0; for(size_t ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k_left, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k_right, nk, nr_left, n_middle, nc_right ); sum += tx[i_left] * tx[i_right]; } size_t i_result = result( i, j, k_result, nk, nr_left, n_middle, nc_right ); ty[i_result] += sum; } } } /* %$$ $head Reverse Matrix Multiply$$ Reverse mode partials of Taylor coefficients and sum into $icode px$$ (for one pair of left and right orders) $srccode%cpp% */ void reverse_multiply( size_t k_left , // order for left coefficients size_t k_right , // order for right coefficients const vector& tx , // domain space Taylor coefficients const vector& ty , // range space Taylor coefficients vector& px , // partials w.r.t. tx const vector& py , // partials w.r.t. ty size_t nr_left , // rows in left matrix size_t n_middle , // rows in left and columns in right size_t nc_right ) // columns in right matrix { size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t nk = tx.size() / nx; # ifndef NDEBUG size_t ny = nr_left * nc_right; assert( nk == ty.size() / ny ); # endif assert( tx.size() == px.size() ); assert( ty.size() == py.size() ); // size_t k_result = k_left + k_right; assert( k_result < nk ); // for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { size_t i_result = result( i, j, k_result, nk, nr_left, n_middle, nc_right ); for(size_t ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k_left, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k_right, nk, nr_left, n_middle, nc_right ); // sum += tx[i_left] * tx[i_right]; px[i_left] += tx[i_right] * py[i_result]; px[i_right] += tx[i_left] * py[i_result]; } } } return; } /* %$$ $head forward$$ Routine called by CppAD during $cref Forward$$ mode. $srccode%cpp% */ virtual bool forward( size_t q , size_t p , const vector& vx , vector& vy , const vector& tx , vector& ty ) { size_t n_order = p + 1; size_t nr_left = size_t( tx[ 0 * n_order + 0 ] ); size_t n_middle = size_t( tx[ 1 * n_order + 0 ] ); size_t nc_right = size_t( tx[ 2 * n_order + 0 ] ); # ifndef NDEBUG size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t ny = nr_left * nc_right; # endif assert( vx.size() == 0 || nx == vx.size() ); assert( vx.size() == 0 || ny == vy.size() ); assert( nx * n_order == tx.size() ); assert( ny * n_order == ty.size() ); size_t i, j, ell; // check if we are computing vy information if( vx.size() > 0 ) { size_t nk = 1; size_t k = 0; for(i = 0; i < nr_left; i++) { for(j = 0; j < nc_right; j++) { bool var = false; for(ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k, nk, nr_left, n_middle, nc_right ); bool nz_left = vx[i_left] |(tx[i_left] != 0.); bool nz_right = vx[i_right]|(tx[i_right] != 0.); // if not multiplying by the constant zero if( nz_left & nz_right ) var |= bool(vx[i_left]) | bool(vx[i_right]); } size_t i_result = result( i, j, k, nk, nr_left, n_middle, nc_right ); vy[i_result] = var; } } } // initialize result as zero size_t k; for(i = 0; i < nr_left; i++) { for(j = 0; j < nc_right; j++) { for(k = q; k <= p; k++) { size_t i_result = result( i, j, k, n_order, nr_left, n_middle, nc_right ); ty[i_result] = 0.0; } } } for(k = q; k <= p; k++) { // sum the produces that result in order k for(ell = 0; ell <= k; ell++) forward_multiply( ell, k - ell, tx, ty, nr_left, n_middle, nc_right ); } // all orders are implented, so always return true return true; } /* %$$ $head reverse$$ Routine called by CppAD during $cref Reverse$$ mode. $srccode%cpp% */ virtual bool reverse( size_t p , const vector& tx , const vector& ty , vector& px , const vector& py ) { size_t n_order = p + 1; size_t nr_left = size_t( tx[ 0 * n_order + 0 ] ); size_t n_middle = size_t( tx[ 1 * n_order + 0 ] ); size_t nc_right = size_t( tx[ 2 * n_order + 0 ] ); # ifndef NDEBUG size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t ny = nr_left * nc_right; # endif assert( nx * n_order == tx.size() ); assert( ny * n_order == ty.size() ); assert( px.size() == tx.size() ); assert( py.size() == ty.size() ); // initialize summation for(size_t i = 0; i < px.size(); i++) px[i] = 0.0; // number of orders to differentiate size_t k = n_order; while(k--) { // differentiate the produces that result in order k for(size_t ell = 0; ell <= k; ell++) reverse_multiply( ell, k - ell, tx, ty, px, py, nr_left, n_middle, nc_right ); } // all orders are implented, so always return true return true; } /* %$$ $head for_sparse_jac$$ Routines called by CppAD during $cref ForSparseJac$$. $srccode%cpp% */ // boolean sparsity patterns virtual bool for_sparse_jac( size_t q , const vector& r , vector& s , const vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); # ifndef NDEBUG size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t ny = nr_left * nc_right; # endif assert( nx == x.size() ); assert( nx * q == r.size() ); assert( ny * q == s.size() ); size_t p; // sparsity for S(x) = f'(x) * R size_t nk = 1; size_t k = 0; for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { size_t i_result = result( i, j, k, nk, nr_left, n_middle, nc_right ); for(p = 0; p < q; p++) s[i_result * q + p] = false; for(size_t ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k, nk, nr_left, n_middle, nc_right ); for(p = 0; p < q; p++) { // cast avoids Microsoft warning (should not be needed) s[i_result * q + p] |= bool( r[i_left * q + p ] ); s[i_result * q + p] |= bool( r[i_right * q + p ] ); } } } } return true; } // set sparsity patterns virtual bool for_sparse_jac( size_t q , const vector< std::set >& r , vector< std::set >& s , const vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); # ifndef NDEBUG size_t nx = 3 + (nr_left + nc_right) * n_middle; size_t ny = nr_left * nc_right; # endif assert( nx == x.size() ); assert( nx == r.size() ); assert( ny == s.size() ); // sparsity for S(x) = f'(x) * R size_t nk = 1; size_t k = 0; for(size_t i = 0; i < nr_left; i++) { for(size_t j = 0; j < nc_right; j++) { size_t i_result = result( i, j, k, nk, nr_left, n_middle, nc_right ); s[i_result].clear(); for(size_t ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k, nk, nr_left, n_middle, nc_right ); // s[i_result] = set_union(s[i_result], r[i_left] ); s[i_result] = set_union(s[i_result], r[i_right] ); } } } return true; } /* %$$ $head rev_sparse_jac$$ Routines called by CppAD during $cref RevSparseJac$$. $srccode%cpp% */ // boolean sparsity patterns virtual bool rev_sparse_jac( size_t q , const vector& rt , vector& st , const vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); size_t nx = 3 + (nr_left + nc_right) * n_middle; # ifndef NDEBUG size_t ny = nr_left * nc_right; # endif assert( nx == x.size() ); assert( nx * q == st.size() ); assert( ny * q == rt.size() ); size_t i, j, p; // initialize for(i = 0; i < nx; i++) { for(p = 0; p < q; p++) st[ i * q + p ] = false; } // sparsity for S(x)^T = f'(x)^T * R^T size_t nk = 1; size_t k = 0; for(i = 0; i < nr_left; i++) { for(j = 0; j < nc_right; j++) { size_t i_result = result( i, j, k, nk, nr_left, n_middle, nc_right ); for(size_t ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k, nk, nr_left, n_middle, nc_right ); for(p = 0; p < q; p++) { st[i_left * q + p] |= bool( rt[i_result * q + p] ); st[i_right* q + p] |= bool( rt[i_result * q + p] ); } } } } return true; } // set sparsity patterns virtual bool rev_sparse_jac( size_t q , const vector< std::set >& rt , vector< std::set >& st , const vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); size_t nx = 3 + (nr_left + nc_right) * n_middle; # ifndef NDEBUG size_t ny = nr_left * nc_right; # endif assert( nx == x.size() ); assert( nx == st.size() ); assert( ny == rt.size() ); size_t i, j; // initialize for(i = 0; i < nx; i++) st[i].clear(); // sparsity for S(x)^T = f'(x)^T * R^T size_t nk = 1; size_t k = 0; for(i = 0; i < nr_left; i++) { for(j = 0; j < nc_right; j++) { size_t i_result = result( i, j, k, nk, nr_left, n_middle, nc_right ); for(size_t ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k, nk, nr_left, n_middle, nc_right ); // st[i_left] = set_union(st[i_left], rt[i_result]); st[i_right] = set_union(st[i_right], rt[i_result]); } } } return true; } /* %$$ $head rev_sparse_hes$$ Routines called by $cref RevSparseHes$$. $srccode%cpp% */ // set sparsity patterns virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t q , const vector< std::set >& r , const vector< std::set >& u , vector< std::set >& v , const vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); size_t nx = 3 + (nr_left + nc_right) * n_middle; # ifndef NDEBUG size_t ny = nr_left * nc_right; # endif assert( x.size() == nx ); assert( vx.size() == nx ); assert( t.size() == nx ); assert( r.size() == nx ); assert( v.size() == nx ); assert( s.size() == ny ); assert( u.size() == ny ); // size_t i, j; // // initilaize sparsity patterns as false for(j = 0; j < nx; j++) { t[j] = false; v[j].clear(); } size_t nk = 1; size_t k = 0; for(i = 0; i < nr_left; i++) { for(j = 0; j < nc_right; j++) { size_t i_result = result( i, j, k, nk, nr_left, n_middle, nc_right ); for(size_t ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k, nk, nr_left, n_middle, nc_right ); // // Compute sparsity for T(x) = S(x) * f'(x). // We need not use vx with f'(x) back propagation. t[i_left] |= bool( s[i_result] ); t[i_right] |= bool( s[i_result] ); // V(x) = f'(x)^T * U(x) + S(x) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate f'(x)^T * U(x) // (no need to use vx with f'(x) propogation) v[i_left] = set_union(v[i_left], u[i_result] ); v[i_right] = set_union(v[i_right], u[i_result] ); // back propagate S(x) * f''(x) * R // (here is where we must check for cross terms) if( s[i_result] & vx[i_left] & vx[i_right] ) { v[i_left] = set_union(v[i_left], r[i_right] ); v[i_right] = set_union(v[i_right], r[i_left] ); } } } } return true; } // bool sparsity virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t q , const vector& r , const vector& u , vector& v , const vector& x ) { size_t nr_left = size_t( CppAD::Integer( x[0] ) ); size_t n_middle = size_t( CppAD::Integer( x[1] ) ); size_t nc_right = size_t( CppAD::Integer( x[2] ) ); size_t nx = 3 + (nr_left + nc_right) * n_middle; # ifndef NDEBUG size_t ny = nr_left * nc_right; # endif assert( x.size() == nx ); assert( vx.size() == nx ); assert( t.size() == nx ); assert( r.size() == nx * q ); assert( v.size() == nx * q ); assert( s.size() == ny ); assert( u.size() == ny * q ); size_t i, j, p; // // initilaize sparsity patterns as false for(j = 0; j < nx; j++) { t[j] = false; for(p = 0; p < q; p++) v[j * q + p] = false; } size_t nk = 1; size_t k = 0; for(i = 0; i < nr_left; i++) { for(j = 0; j < nc_right; j++) { size_t i_result = result( i, j, k, nk, nr_left, n_middle, nc_right ); for(size_t ell = 0; ell < n_middle; ell++) { size_t i_left = left( i, ell, k, nk, nr_left, n_middle, nc_right ); size_t i_right = right( ell, j, k, nk, nr_left, n_middle, nc_right ); // // Compute sparsity for T(x) = S(x) * f'(x). // We so not need to use vx with f'(x) propagation. t[i_left] |= bool( s[i_result] ); t[i_right] |= bool( s[i_result] ); // V(x) = f'(x)^T * U(x) + S(x) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate f'(x)^T * U(x) // (no need to use vx with f'(x) propogation) for(p = 0; p < q; p++) { v[ i_left * q + p] |= bool( u[ i_result * q + p] ); v[ i_right * q + p] |= bool( u[ i_result * q + p] ); } // back propagate S(x) * f''(x) * R // (here is where we must check for cross terms) if( s[i_result] & vx[i_left] & vx[i_right] ) { for(p = 0; p < q; p++) { v[i_left * q + p] |= bool( r[i_right * q + p] ); v[i_right * q + p] |= bool( r[i_left * q + p] ); } } } } } return true; } /* %$$ $head End Class Definition$$ $srccode%cpp% */ }; // End of mat_mul class } // End empty namespace /* %$$ $comment end nospell$$ $end */ # endif cppad-20170000.3/cppad/ipopt/0002755000175200017650000000000013057470467014663 5ustar coincoin-webcppad-20170000.3/cppad/ipopt/solve_callback.hpp0000644000175200017650000010260413057470467020341 0ustar coincoin-web// $Id: solve_callback.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_IPOPT_SOLVE_CALLBACK_HPP # define CPPAD_IPOPT_SOLVE_CALLBACK_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE namespace ipopt { /*! \file solve_callback.hpp \brief Class that connects ipopt::solve to Ipopt */ /*! Class that Ipopt uses for obtaining information about this problem. \section Evaluation_Methods Evaluation Methods The set of evaluation methods for this class is \verbatim { eval_f, eval_grad_f, eval_g, eval_jac_g, eval_h } \endverbatim Note that the bool return flag for the evaluations methods does not appear in the Ipopt documentation. Looking at the code, it seems to be a flag telling Ipopt to abort when the flag is false. */ template class solve_callback : public Ipopt::TNLP { private: // ------------------------------------------------------------------ // Types used by this class // ------------------------------------------------------------------ /// A Scalar value used by Ipopt typedef Ipopt::Number Number; /// An index value used by Ipopt typedef Ipopt::Index Index; /// Indexing style used in Ipopt sparsity structure typedef Ipopt::TNLP::IndexStyleEnum IndexStyleEnum; // ------------------------------------------------------------------ // Values directly passed in to constuctor // ------------------------------------------------------------------ /// dimension of the range space for f(x). /// The objective is sum_i f_i (x). /// Note that, at this point, there is no advantage having nf_ > 1. const size_t nf_; /// dimension of the domain space for f(x) and g(x) const size_t nx_; /// dimension of the range space for g(x) const size_t ng_; /// initial value for x const Dvector& xi_; /// lower limit for x const Dvector& xl_; /// upper limit for x const Dvector& xu_; /// lower limit for g(x) const Dvector& gl_; /// upper limit for g(x) const Dvector& gu_; /// object that evaluates f(x) and g(x) FG_eval& fg_eval_; /// should operation sequence be retaped for each new x. bool retape_; /// Should sparse methods be used to compute Jacobians and Hessians /// with forward mode used for Jacobian. bool sparse_forward_; /// Should sparse methods be used to compute Jacobians and Hessians /// with reverse mode used for Jacobian. bool sparse_reverse_; /// final results are returned to this structure solve_result& solution_; // ------------------------------------------------------------------ // Values that are initilaized by the constructor // ------------------------------------------------------------------ /// AD function object that evaluates x -> [ f(x) , g(x) ] /// If retape is false, this object is initialzed by constructor /// otherwise it is set by cache_new_x each time it is called. CppAD::ADFun adfun_; /// value of x corresponding to previous new_x Dvector x0_; /// value of fg corresponding to previous new_x Dvector fg0_; // ---------------------------------------------------------------------- // Jacobian information // ---------------------------------------------------------------------- /// Sparsity pattern for Jacobian of [f(x), g(x) ]. /// If sparse is true, this pattern set by constructor and does not change. /// Otherwise this vector has size zero. CppAD::vectorBool pattern_jac_; /// Row indices of [f(x), g(x)] for Jacobian of g(x) in row order. /// (Set by constructor and not changed.) CppAD::vector row_jac_; /// Column indices for Jacobian of g(x), same order as row_jac_. /// (Set by constructor and not changed.) CppAD::vector col_jac_; /// col_order_jac_ sorts row_jac_ and col_jac_ in column order. /// (Set by constructor and not changed.) CppAD::vector col_order_jac_; /// Work vector used by SparseJacobian, stored here to avoid recalculation. CppAD::sparse_jacobian_work work_jac_; // ---------------------------------------------------------------------- // Hessian information // ---------------------------------------------------------------------- /// Sparsity pattern for Hessian of Lagragian /// \f[ L(x) = \sigma \sum_i f_i (x) + \sum_i \lambda_i g_i (x) \f] /// If sparse is true, this pattern set by constructor and does not change. /// Otherwise this vector has size zero. CppAD::vectorBool pattern_hes_; /// Row indices of Hessian lower left triangle in row order. /// (Set by constructor and not changed.) CppAD::vector row_hes_; /// Column indices of Hessian left triangle in same order as row_hes_. /// (Set by constructor and not changed.) CppAD::vector col_hes_; /// Work vector used by SparseJacobian, stored here to avoid recalculation. CppAD::sparse_hessian_work work_hes_; // ------------------------------------------------------------------ // Private member functions // ------------------------------------------------------------------ /*! Cache information for a new value of x. \param x is the new value for x. \par x0_ the elements of this vector are set to the new value for x. \par fg0_ the elements of this vector are set to the new value for [f(x), g(x)] \par adfun_ If retape is true, the operation sequence for this function is changes to correspond to the argument x. If retape is false, the operation sequence is not changed. The zero order Taylor coefficients for this function are set so they correspond to the argument x. */ void cache_new_x(const Number* x) { size_t i; if( retape_ ) { // make adfun_, as well as x0_ and fg0_ correspond to this x ADvector a_x(nx_), a_fg(nf_ + ng_); for(i = 0; i < nx_; i++) { x0_[i] = x[i]; a_x[i] = x[i]; } CppAD::Independent(a_x); fg_eval_(a_fg, a_x); adfun_.Dependent(a_x, a_fg); } else { // make x0_ and fg0_ correspond to this x for(i = 0; i < nx_; i++) x0_[i] = x[i]; } fg0_ = adfun_.Forward(0, x0_); } public: // ---------------------------------------------------------------------- /*! Constructor for the interface between ipopt::solve and Ipopt \param nf dimension of the range space for f(x) \param nx dimension of the domain space for f(x) and g(x). \param ng dimension of the range space for g(x) \param xi initial value of x during the optimization procedure (size nx). \param xl lower limit for x (size nx). \param xu upper limit for x (size nx). \param gl lower limit for g(x) (size ng). \param gu upper limit for g(x) (size ng). \param fg_eval function object that evaluations f(x) and g(x) using fg_eval(fg, x) \param retape should the operation sequence be retaped for each argument value. \param sparse_forward should sparse matrix computations be used for Jacobians and Hessians with forward mode for Jacobian. \param sparse_reverse should sparse matrix computations be used for Jacobians and Hessians with reverse mode for Jacobian. (sparse_forward and sparse_reverse cannot both be true). \param solution object where final results are stored. */ solve_callback( size_t nf , size_t nx , size_t ng , const Dvector& xi , const Dvector& xl , const Dvector& xu , const Dvector& gl , const Dvector& gu , FG_eval& fg_eval , bool retape , bool sparse_forward , bool sparse_reverse , solve_result& solution ) : nf_ ( nf ), nx_ ( nx ), ng_ ( ng ), xi_ ( xi ), xl_ ( xl ), xu_ ( xu ), gl_ ( gl ), gu_ ( gu ), fg_eval_ ( fg_eval ), retape_ ( retape ), sparse_forward_ ( sparse_forward ), sparse_reverse_ ( sparse_reverse ), solution_ ( solution ) { CPPAD_ASSERT_UNKNOWN( ! ( sparse_forward_ & sparse_reverse_ ) ); size_t i, j; size_t nfg = nf_ + ng_; // initialize x0_ and fg0_ wih proper dimensions and value nan x0_.resize(nx); fg0_.resize(nfg); for(i = 0; i < nx_; i++) x0_[i] = CppAD::nan(0.0); for(i = 0; i < nfg; i++) fg0_[i] = CppAD::nan(0.0); if( ! retape_ ) { // make adfun_ correspond to x -> [ f(x), g(x) ] ADvector a_x(nx_), a_fg(nfg); for(i = 0; i < nx_; i++) a_x[i] = xi_[i]; CppAD::Independent(a_x); fg_eval_(a_fg, a_x); adfun_.Dependent(a_x, a_fg); // optimize because we will make repeated use of this tape adfun_.optimize(); } if( sparse_forward_ | sparse_reverse_ ) { CPPAD_ASSERT_UNKNOWN( ! retape ); size_t m = nf_ + ng_; // // ----------------------------------------------------------- // Jacobian pattern_jac_.resize( m * nx_ ); if( nx_ <= m ) { // use forward mode to compute sparsity // number of bits that are packed into one unit in vectorBool size_t n_column = vectorBool::bit_per_unit(); // sparsity patterns for current columns vectorBool r(nx_ * n_column), s(m * n_column); // compute the sparsity pattern n_column columns at a time size_t n_loop = (nx_ - 1) / n_column + 1; for(size_t i_loop = 0; i_loop < n_loop; i_loop++) { // starting column index for this iteration size_t i_column = i_loop * n_column; // pattern that picks out the appropriate columns for(i = 0; i < nx_; i++) { for(j = 0; j < n_column; j++) r[i * n_column + j] = (i == i_column + j); } s = adfun_.ForSparseJac(n_column, r); // fill in the corresponding columns of total_sparsity for(i = 0; i < m; i++) { for(j = 0; j < n_column; j++) { if( i_column + j < nx_ ) pattern_jac_[i * nx_ + i_column + j] = s[i * n_column + j]; } } } } else { // use reverse mode to compute sparsity // number of bits that are packed into one unit in vectorBool size_t n_row = vectorBool::bit_per_unit(); // sparsity patterns for current rows vectorBool r(n_row * m), s(n_row * nx_); // compute the sparsity pattern n_row row at a time size_t n_loop = (m - 1) / n_row + 1; for(size_t i_loop = 0; i_loop < n_loop; i_loop++) { // starting row index for this iteration size_t i_row = i_loop * n_row; // pattern that picks out the appropriate rows for(i = 0; i < n_row; i++) { for(j = 0; j < m; j++) r[i * m + j] = (i_row + i == j); } s = adfun_.RevSparseJac(n_row, r); // fill in correspoding rows of total sparsity for(i = 0; i < n_row; i++) { for(j = 0; j < nx_; j++) if( i_row + i < m ) pattern_jac_[ (i_row + i) * nx_ + j ] = s[ i * nx_ + j]; } } } /* { // use reverse mode to compute sparsity CppAD::vectorBool s(m * m); for(i = 0; i < m; i++) { for(j = 0; j < m; j++) s[i * m + j] = (i == j); } pattern_jac_ = adfun_.RevSparseJac(m, s); } */ // Set row and column indices in Jacoian of [f(x), g(x)] // for Jacobian of g(x). These indices are in row major order. for(i = nf_; i < nfg; i++) { for(j = 0; j < nx_; j++) { if( pattern_jac_[ i * nx_ + j ] ) { row_jac_.push_back(i); col_jac_.push_back(j); } } } // Set row and column indices in Jacoian of [f(x), g(x)] // for Jacobian of g(x). These indices are in row major order. // ----------------------------------------------------------- // Hessian pattern_hes_.resize(nx_ * nx_); // number of bits that are packed into one unit in vectorBool size_t n_column = vectorBool::bit_per_unit(); // sparsity patterns for current columns vectorBool r(nx_ * n_column), h(nx_ * n_column); // sparsity pattern for range space of function vectorBool s(m); for(i = 0; i < m; i++) s[i] = true; // compute the sparsity pattern n_column columns at a time size_t n_loop = (nx_ - 1) / n_column + 1; for(size_t i_loop = 0; i_loop < n_loop; i_loop++) { // starting column index for this iteration size_t i_column = i_loop * n_column; // pattern that picks out the appropriate columns for(i = 0; i < nx_; i++) { for(j = 0; j < n_column; j++) r[i * n_column + j] = (i == i_column + j); } adfun_.ForSparseJac(n_column, r); // sparsity pattern corresponding to paritls w.r.t. (theta, u) // of partial w.r.t. the selected columns bool transpose = true; h = adfun_.RevSparseHes(n_column, s, transpose); // fill in the corresponding columns of total_sparsity for(i = 0; i < nx_; i++) { for(j = 0; j < n_column; j++) { if( i_column + j < nx_ ) pattern_hes_[i * nx_ + i_column + j] = h[i * n_column + j]; } } } // Set row and column indices for Lower triangle of Hessian // of Lagragian. These indices are in row major order. for(i = 0; i < nx_; i++) { for(j = 0; j < nx_; j++) { if( pattern_hes_[ i * nx_ + j ] ) if( j <= i ) { row_hes_.push_back(i); col_hes_.push_back(j); } } } } else { // Set row and column indices in Jacoian of [f(x), g(x)] // for Jacobian of g(x). These indices are in row major order. for(i = nf_; i < nfg; i++) { for(j = 0; j < nx_; j++) { row_jac_.push_back(i); col_jac_.push_back(j); } } // Set row and column indices for lower triangle of Hessian. // These indices are in row major order. for(i = 0; i < nx_; i++) { for(j = 0; j <= i; j++) { row_hes_.push_back(i); col_hes_.push_back(j); } } } // Column order indirect sort of the Jacobian indices col_order_jac_.resize( col_jac_.size() ); index_sort( col_jac_, col_order_jac_ ); } // ----------------------------------------------------------------------- /*! Return dimension information about optimization problem. \param[out] n is set to the value nx_. \param[out] m is set to the value ng_. \param[out] nnz_jac_g is set to ng_ * nx_ (sparsity not yet implemented) \param[out] nnz_h_lag is set to nx_*(nx_+1)/2 (sparsity not yet implemented) \param[out] index_style is set to C_STYLE; i.e., zeoro based indexing is used in the information passed to Ipopt. */ virtual bool get_nlp_info( Index& n , Index& m , Index& nnz_jac_g , Index& nnz_h_lag , IndexStyleEnum& index_style ) { n = static_cast(nx_); m = static_cast(ng_); nnz_jac_g = static_cast(row_jac_.size()); nnz_h_lag = static_cast(row_hes_.size()); # ifndef NDEBUG if( ! (sparse_forward_ | sparse_reverse_) ) { size_t nnz = static_cast(nnz_jac_g); CPPAD_ASSERT_UNKNOWN( nnz == ng_ * nx_); // nnz = static_cast(nnz_h_lag); CPPAD_ASSERT_UNKNOWN( nnz == (nx_ * (nx_ + 1)) / 2 ); } # endif // use the fortran index style for row/col entries index_style = C_STYLE; return true; } // ----------------------------------------------------------------------- /*! Return bound information about optimization problem. \param[in] n is the dimension of the domain space for f(x) and g(x); i.e., it must be equal to nx_. \param[out] x_l is a vector of size nx_. The input value of its elements does not matter. On output, it is a copy of the lower bound for \f$ x \f$; i.e., xl_. \param[out] x_u is a vector of size nx_. The input value of its elements does not matter. On output, it is a copy of the upper bound for \f$ x \f$; i.e., xu_. \param[in] m is the dimension of the range space for g(x). i.e., it must be equal to ng_. \param[out] g_l is a vector of size ng_. The input value of its elements does not matter. On output, it is a copy of the lower bound for \f$ g(x) \f$; i.e., gl_. \param[out] g_u is a vector of size ng_. The input value of its elements does not matter. On output, it is a copy of the upper bound for \f$ g(x) \f$; i.e, gu_. */ virtual bool get_bounds_info( Index n , Number* x_l , Number* x_u , Index m , Number* g_l , Number* g_u ) { size_t i; // here, the n and m we gave IPOPT in get_nlp_info are passed back CPPAD_ASSERT_UNKNOWN(static_cast(n) == nx_); CPPAD_ASSERT_UNKNOWN(static_cast(m) == ng_); // pass back bounds for(i = 0; i < nx_; i++) { x_l[i] = xl_[i]; x_u[i] = xu_[i]; } for(i = 0; i < ng_; i++) { g_l[i] = gl_[i]; g_u[i] = gu_[i]; } return true; } // ----------------------------------------------------------------------- /*! Return initial x value where optimiation is started. \param[in] n must be equal to the domain dimension for f(x) and g(x); i.e., it must be equal to nx_. \param[in] init_x must be equal to true. \param[out] x is a vector of size nx_. The input value of its elements does not matter. On output, it is a copy of the initial value for \f$ x \f$; i.e. xi_. \param[in] init_z must be equal to false. \param z_L is not used. \param z_U is not used. \param[in] m must be equal to the domain dimension for f(x) and g(x); i.e., it must be equal to ng_. \param init_lambda must be equal to false. \param lambda is not used. */ virtual bool get_starting_point( Index n , bool init_x , Number* x , bool init_z , Number* z_L , Number* z_U , Index m , bool init_lambda , Number* lambda ) { size_t j; CPPAD_ASSERT_UNKNOWN(static_cast(n) == nx_ ); CPPAD_ASSERT_UNKNOWN(static_cast(m) == ng_ ); CPPAD_ASSERT_UNKNOWN(init_x == true); CPPAD_ASSERT_UNKNOWN(init_z == false); CPPAD_ASSERT_UNKNOWN(init_lambda == false); for(j = 0; j < nx_; j++) x[j] = xi_[j]; return true; } // ----------------------------------------------------------------------- /*! Evaluate the objective fucntion f(x). \param[in] n is the dimension of the argument space for f(x); i.e., must be equal nx_. \param[in] x is a vector of size nx_ containing the point at which to evaluate the function sum_i f_i (x). \param[in] new_x is false if the previous call to any one of the \ref Evaluation_Methods used the same value for x. \param[out] obj_value is the value of the objective sum_i f_i (x) at this value of x. \return The return value is always true; see \ref Evaluation_Methods. */ virtual bool eval_f( Index n , const Number* x , bool new_x , Number& obj_value ) { size_t i; if( new_x ) cache_new_x(x); // double sum = 0.0; for(i = 0; i < nf_; i++) sum += fg0_[i]; obj_value = static_cast(sum); return true; } // ----------------------------------------------------------------------- /*! Evaluate the gradient of f(x). \param[in] n is the dimension of the argument space for f(x); i.e., must be equal nx_. \param[in] x has a vector of size nx_ containing the point at which to evaluate the gradient of f(x). \param[in] new_x is false if the previous call to any one of the \ref Evaluation_Methods used the same value for x. \param[out] grad_f is a vector of size nx_. The input value of its elements does not matter. The output value of its elements is the gradient of f(x) at this value of. \return The return value is always true; see \ref Evaluation_Methods. */ virtual bool eval_grad_f( Index n , const Number* x , bool new_x , Number* grad_f ) { size_t i; if( new_x ) cache_new_x(x); // Dvector w(nf_ + ng_), dw(nx_); for(i = 0; i < nf_; i++) w[i] = 1.0; for(i = 0; i < ng_; i++) w[nf_ + i] = 0.0; dw = adfun_.Reverse(1, w); for(i = 0; i < nx_; i++) grad_f[i] = dw[i]; return true; } // ----------------------------------------------------------------------- /*! Evaluate the function g(x). \param[in] n is the dimension of the argument space for g(x); i.e., must be equal nx_. \param[in] x has a vector of size n containing the point at which to evaluate the gradient of g(x). \param[in] new_x is false if the previous call to any one of the \ref Evaluation_Methods used the same value for x. \param[in] m is the dimension of the range space for g(x); i.e., must be equal to ng_. \param[out] g is a vector of size ng_. The input value of its elements does not matter. The output value of its elements is the value of the function g(x) at this value of x. \return The return value is always true; see \ref Evaluation_Methods. */ virtual bool eval_g( Index n , const Number* x , bool new_x , Index m , Number* g ) { size_t i; if( new_x ) cache_new_x(x); // for(i = 0; i < ng_; i++) g[i] = fg0_[nf_ + i]; return true; } // ----------------------------------------------------------------------- /*! Evaluate the Jacobian of g(x). \param[in] n is the dimension of the argument space for g(x); i.e., must be equal nx_. \param x If values is not NULL, x is a vector of size nx_ containing the point at which to evaluate the gradient of g(x). \param[in] new_x is false if the previous call to any one of the \ref Evaluation_Methods used the same value for x. \param[in] m is the dimension of the range space for g(x); i.e., must be equal to ng_. \param[in] nele_jac is the number of possibly non-zero elements in the Jacobian of g(x); i.e., must be equal to ng_ * nx_. \param iRow if values is not NULL, iRow is not defined. if values is NULL, iRow is a vector with size nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, iRow[k] is the base zero row index for the k-th possibly non-zero entry in the Jacobian of g(x). \param jCol if values is not NULL, jCol is not defined. if values is NULL, jCol is a vector with size nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, jCol[k] is the base zero column index for the k-th possibly non-zero entry in the Jacobian of g(x). \param values if \c values is not \c NULL, \c values is a vector with size \c nele_jac. The input value of its elements does not matter. On output, For k = 0 , ... , nele_jac-1, values[k] is the value for the k-th possibly non-zero entry in the Jacobian of g(x). \return The return value is always true; see \ref Evaluation_Methods. */ virtual bool eval_jac_g( Index n, const Number* x, bool new_x, Index m, Index nele_jac, Index* iRow, Index *jCol, Number* values) { size_t i, j, k, ell; CPPAD_ASSERT_UNKNOWN(static_cast(m) == ng_ ); CPPAD_ASSERT_UNKNOWN(static_cast(n) == nx_ ); // size_t nk = row_jac_.size(); CPPAD_ASSERT_UNKNOWN( static_cast(nele_jac) == nk ); // if( new_x ) cache_new_x(x); if( values == NULL ) { for(k = 0; k < nk; k++) { i = row_jac_[k]; j = col_jac_[k]; CPPAD_ASSERT_UNKNOWN( i >= nf_ ); iRow[k] = static_cast(i - nf_); jCol[k] = static_cast(j); } return true; } // if( nk == 0 ) return true; // if( sparse_forward_ ) { Dvector jac(nk); adfun_.SparseJacobianForward( x0_ , pattern_jac_, row_jac_, col_jac_, jac, work_jac_ ); for(k = 0; k < nk; k++) values[k] = jac[k]; } else if( sparse_reverse_ ) { Dvector jac(nk); adfun_.SparseJacobianReverse( x0_ , pattern_jac_, row_jac_, col_jac_, jac, work_jac_ ); for(k = 0; k < nk; k++) values[k] = jac[k]; } else if( nx_ < ng_ ) { // use forward mode Dvector x1(nx_), fg1(nf_ + ng_); for(j = 0; j < nx_; j++) x1[j] = 0.0; // index in col_order_jac_ of next entry ell = 0; k = col_order_jac_[ell]; for(j = 0; j < nx_; j++) { // compute j-th column of Jacobian of g(x) x1[j] = 1.0; fg1 = adfun_.Forward(1, x1); while( ell < nk && col_jac_[k] <= j ) { CPPAD_ASSERT_UNKNOWN( col_jac_[k] == j ); i = row_jac_[k]; CPPAD_ASSERT_UNKNOWN( i >= nf_ ) values[k] = fg1[i]; ell++; if( ell < nk ) k = col_order_jac_[ell]; } x1[j] = 0.0; } } else { // user reverse mode size_t nfg = nf_ + ng_; // user reverse mode Dvector w(nfg), dw(nx_); for(i = 0; i < nfg; i++) w[i] = 0.0; // index in row_jac_ of next entry k = 0; for(i = nf_; i < nfg; i++) { // compute i-th row of Jacobian of g(x) w[i] = 1.0; dw = adfun_.Reverse(1, w); while( k < nk && row_jac_[k] <= i ) { CPPAD_ASSERT_UNKNOWN( row_jac_[k] == i ); j = col_jac_[k]; values[k] = dw[j]; k++; } w[i] = 0.0; } } return true; } // ----------------------------------------------------------------------- /*! Evaluate the Hessian of the Lagragian \section The_Hessian_of_the_Lagragian The Hessian of the Lagragian The Hessian of the Lagragian is defined as \f[ H(x, \sigma, \lambda ) = \sigma \nabla^2 f(x) + \sum_{i=0}^{m-1} \lambda_i \nabla^2 g(x)_i \f] \param[in] n is the dimension of the argument space for g(x); i.e., must be equal nx_. \param x if values is not NULL, x is a vector of size nx_ containing the point at which to evaluate the Hessian of the Lagragian. \param[in] new_x is false if the previous call to any one of the \ref Evaluation_Methods used the same value for x. \param[in] obj_factor the value \f$ \sigma \f$ multiplying the Hessian of f(x) in the expression for \ref The_Hessian_of_the_Lagragian. \param[in] m is the dimension of the range space for g(x); i.e., must be equal to ng_. \param[in] lambda if values is not NULL, lambda is a vector of size ng_ specifing the value of \f$ \lambda \f$ in the expression for \ref The_Hessian_of_the_Lagragian. \param[in] new_lambda is true if the previous call to eval_h had the same value for lambda and false otherwise. (Not currently used.) \param[in] nele_hess is the number of possibly non-zero elements in the Hessian of the Lagragian; i.e., must be equal to nx_*(nx_+1)/2. \param iRow if values is not NULL, iRow is not defined. if values is NULL, iRow is a vector with size nele_hess. The input value of its elements does not matter. On output, For k = 0 , ... , nele_hess-1, iRow[k] is the base zero row index for the k-th possibly non-zero entry in the Hessian fo the Lagragian. \param jCol if values is not NULL, jCol is not defined. if values is NULL, jCol is a vector with size nele_hess. The input value of its elements does not matter. On output, For k = 0 , ... , nele_hess-1, jCol[k] is the base zero column index for the k-th possibly non-zero entry in the Hessian of the Lagragian. \param values if values is not NULL, it is a vector with size nele_hess. The input value of its elements does not matter. On output, For k = 0 , ... , nele_hess-1, values[k] is the value for the k-th possibly non-zero entry in the Hessian of the Lagragian. \return The return value is always true; see \ref Evaluation_Methods. */ virtual bool eval_h( Index n , const Number* x , bool new_x , Number obj_factor , Index m , const Number* lambda , bool new_lambda , Index nele_hess , Index* iRow , Index* jCol , Number* values ) { size_t i, j, k; CPPAD_ASSERT_UNKNOWN(static_cast(m) == ng_ ); CPPAD_ASSERT_UNKNOWN(static_cast(n) == nx_ ); // size_t nk = row_hes_.size(); CPPAD_ASSERT_UNKNOWN( static_cast(nele_hess) == nk ); // if( new_x ) cache_new_x(x); // if( values == NULL ) { for(k = 0; k < nk; k++) { i = row_hes_[k]; j = col_hes_[k]; iRow[k] = static_cast(i); jCol[k] = static_cast(j); } return true; } // if( nk == 0 ) return true; // weigting vector for Lagragian Dvector w(nf_ + ng_); for(i = 0; i < nf_; i++) w[i] = obj_factor; for(i = 0; i < ng_; i++) w[i + nf_] = lambda[i]; // if( sparse_forward_ | sparse_reverse_ ) { Dvector hes(nk); adfun_.SparseHessian( x0_, w, pattern_hes_, row_hes_, col_hes_, hes, work_hes_ ); for(k = 0; k < nk; k++) values[k] = hes[k]; } else { Dvector hes(nx_ * nx_); hes = adfun_.Hessian(x0_, w); for(k = 0; k < nk; k++) { i = row_hes_[k]; j = col_hes_[k]; values[k] = hes[i * nx_ + j]; } } return true; } // ---------------------------------------------------------------------- /*! Pass solution information from Ipopt to users solution structure. \param[in] status is value that the Ipopt solution status which gets mapped to a correponding value for \n solution_.status \param[in] n is the dimension of the domain space for f(x) and g(x); i.e., it must be equal to nx_. \param[in] x is a vector with size nx_ specifing the final solution. This is the output value for \n solution_.x \param[in] z_L is a vector with size nx_ specifing the Lagragian multipliers for the constraint \f$ x^l \leq x \f$. This is the output value for \n solution_.zl \param[in] z_U is a vector with size nx_ specifing the Lagragian multipliers for the constraint \f$ x \leq x^u \f$. This is the output value for \n solution_.zu \param[in] m is the dimension of the range space for g(x). i.e., it must be equal to ng_. \param[in] g is a vector with size ng_ containing the value of the constraint function g(x) at the final solution x. This is the output value for \n solution_.g \param[in] lambda is a vector with size ng_ specifing the Lagragian multipliers for the constraints \f$ g^l \leq g(x) \leq g^u \f$. This is the output value for \n solution_.lambda \param[in] obj_value is the value of the objective function f(x) at the final solution x. This is the output value for \n solution_.obj_value \param[in] ip_data is unspecified (by Ipopt) and hence not used. \param[in] ip_cq is unspecified (by Ipopt) and hence not used. \par solution_[out] this is a reference to the solution argument in the constructor for solve_callback. The results are stored here (see documentation above). */ virtual void finalize_solution( Ipopt::SolverReturn status , Index n , const Number* x , const Number* z_L , const Number* z_U , Index m , const Number* g , const Number* lambda , Number obj_value , const Ipopt::IpoptData* ip_data , Ipopt::IpoptCalculatedQuantities* ip_cq ) { size_t i, j; CPPAD_ASSERT_UNKNOWN(static_cast(n) == nx_ ); CPPAD_ASSERT_UNKNOWN(static_cast(m) == ng_ ); switch(status) { // convert status from Ipopt enum to solve_result enum case Ipopt::SUCCESS: solution_.status = solve_result::success; break; case Ipopt::MAXITER_EXCEEDED: solution_.status = solve_result::maxiter_exceeded; break; case Ipopt::STOP_AT_TINY_STEP: solution_.status = solve_result::stop_at_tiny_step; break; case Ipopt::STOP_AT_ACCEPTABLE_POINT: solution_.status = solve_result::stop_at_acceptable_point; break; case Ipopt::LOCAL_INFEASIBILITY: solution_.status = solve_result::local_infeasibility; break; case Ipopt::USER_REQUESTED_STOP: solution_.status = solve_result::user_requested_stop; break; case Ipopt::DIVERGING_ITERATES: solution_.status = solve_result::diverging_iterates; break; case Ipopt::RESTORATION_FAILURE: solution_.status = solve_result::restoration_failure; break; case Ipopt::ERROR_IN_STEP_COMPUTATION: solution_.status = solve_result::error_in_step_computation; break; case Ipopt::INVALID_NUMBER_DETECTED: solution_.status = solve_result::invalid_number_detected; break; case Ipopt::INTERNAL_ERROR: solution_.status = solve_result::internal_error; break; default: solution_.status = solve_result::unknown; } solution_.x.resize(nx_); solution_.zl.resize(nx_); solution_.zu.resize(nx_); for(j = 0; j < nx_; j++) { solution_.x[j] = x[j]; solution_.zl[j] = z_L[j]; solution_.zu[j] = z_U[j]; } solution_.g.resize(ng_); solution_.lambda.resize(ng_); for(i = 0; i < ng_; i++) { solution_.g[i] = g[i]; solution_.lambda[i] = lambda[i]; } solution_.obj_value = obj_value; return; } }; } // end namespace ipopt } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/ipopt/solve_result.hpp0000644000175200017650000000367213057470467020130 0ustar coincoin-web// $Id: solve_result.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_IPOPT_SOLVE_RESULT_HPP # define CPPAD_IPOPT_SOLVE_RESULT_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ namespace CppAD { // BEGIN_CPPAD_NAMESPACE namespace ipopt { /*! \file solve_result.hpp Class that contains information about solve problem result */ /*! Class that contains information about solve problem result \tparam Dvector a simple vector with elements of type double */ template class solve_result { public: /// possible values for the result status enum status_type { not_defined, success, maxiter_exceeded, stop_at_tiny_step, stop_at_acceptable_point, local_infeasibility, user_requested_stop, feasible_point_found, diverging_iterates, restoration_failure, error_in_step_computation, invalid_number_detected, too_few_degrees_of_freedom, internal_error, unknown }; /// possible values for solution status status_type status; /// the approximation solution Dvector x; /// Lagrange multipliers corresponding to lower bounds on x Dvector zl; /// Lagrange multipliers corresponding to upper bounds on x Dvector zu; /// value of g(x) Dvector g; /// Lagrange multipliers correspondiing constraints on g(x) Dvector lambda; /// value of f(x) double obj_value; /// constructor initializes solution status as not yet defined solve_result(void) { status = not_defined; } }; } // end namespace ipopt } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/ipopt/solve.hpp0000644000175200017650000004112513057470467016525 0ustar coincoin-web// $Id: solve.hpp 3804 2016-03-20 15:08:46Z bradbell $ # ifndef CPPAD_IPOPT_SOLVE_HPP # define CPPAD_IPOPT_SOLVE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin ipopt_solve$$ $spell Jacobian Jacobians retape Bvector bool infeasibility const cpp cppad doesn't ADvector eval fg gl gu hpp inf ipopt maxiter naninf nf ng nx obj optimizer std xi xl xu zl zu $$ $section Use Ipopt to Solve a Nonlinear Programming Problem$$ $head Syntax$$ $codei%# include %$$ $codei%ipopt::solve( %options%, %xi%, %xl%, %xu%, %gl%, %gu%, %fg_eval%, %solution% )%$$ $head Purpose$$ The function $code ipopt::solve$$ solves nonlinear programming problems of the form $latex \[ \begin{array}{rll} {\rm minimize} & f (x) \\ {\rm subject \; to} & gl \leq g(x) \leq gu \\ & xl \leq x \leq xu \end{array} \] $$ This is done using $href% http://www.coin-or.org/projects/Ipopt.xml% Ipopt %$$ optimizer and CppAD for the derivative and sparsity calculations. $head Include File$$ Currently, this routine $cref/ipopt::solve/ipopt_solve/$$ is not included by the command $codei% # include %$$ (Doing so would require the ipopt library to link the corresponding program (even if $code ipopt::solve$$) was not used.) For this reason, if you are using $code ipopt::solve$$ you should use $codei% # include %$$ which in turn will also include $code $$. $head Bvector$$ The type $icode Bvector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code bool$$. $head Dvector$$ The type $icode DVector$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code double$$. $head options$$ The argument $icode options$$ has prototype $codei% const std::string %options% %$$ It contains a list of options. Each option, including the last option, is terminated by the $code '\n'$$ character. Each line consists of two or three tokens separated by one or more spaces. $subhead Retape$$ You can set the retape flag with the following syntax: $codei% Retape %value% %$$ If the value is $code true$$, $code ipopt::solve$$ with retape the $cref/operation sequence/glossary/Operation/Sequence/$$ for each new value of $icode x$$. If the value is $code false$$, $code ipopt::solve$$ will tape the operation sequence at the value of $icode xi$$ and use that sequence for the entire optimization process. The default value is $code false$$. $subhead Sparse$$ You can set the sparse Jacobian and Hessian flag with the following syntax: $codei% Sparse %value% %direction% %$$ If the value is $code true$$, $code ipopt::solve$$ will use a sparse matrix representation for the computation of Jacobians and Hessians. Otherwise, it will use a full matrix representation for these calculations. The default for $icode value$$ is $code false$$. If sparse is true, retape must be false. $pre $$ It is unclear if $cref sparse_jacobian$$ would be faster user forward or reverse mode so you are able to choose the direction. If $codei% %value% == true && %direction% == forward %$$ the Jacobians will be calculated using $code SparseJacobianForward$$. If $codei% %value% == true && %direction% == reverse %$$ the Jacobians will be calculated using $code SparseJacobianReverse$$. $subhead String$$ You can set any Ipopt string option using a line with the following syntax: $codei% String %name% %value% %$$ Here $icode name$$ is any valid Ipopt string option and $icode value$$ is its setting. $subhead Numeric$$ You can set any Ipopt numeric option using a line with the following syntax: $codei% Numeric %name% %value% %$$ Here $icode name$$ is any valid Ipopt numeric option and $icode value$$ is its setting. $subhead Integer$$ You can set any Ipopt integer option using a line with the following syntax: $codei% Integer %name% %value% %$$ Here $icode name$$ is any valid Ipopt integer option and $icode value$$ is its setting. $head xi$$ The argument $icode xi$$ has prototype $codei% const %Vector%& %xi% %$$ and its size is equal to $icode nx$$. It specifies the initial point where Ipopt starts the optimization process. $head xl$$ The argument $icode xl$$ has prototype $codei% const %Vector%& %xl% %$$ and its size is equal to $icode nx$$. It specifies the lower limits for the argument in the optimization problem. $head xu$$ The argument $icode xu$$ has prototype $codei% const %Vector%& %xu% %$$ and its size is equal to $icode nx$$. It specifies the upper limits for the argument in the optimization problem. $head gl$$ The argument $icode gl$$ has prototype $codei% const %Vector%& %gl% %$$ and its size is equal to $icode ng$$. It specifies the lower limits for the constraints in the optimization problem. $head gu$$ The argument $icode gu$$ has prototype $codei% const %Vector%& %gu% %$$ and its size is equal to $icode ng$$. It specifies the upper limits for the constraints in the optimization problem. $head fg_eval$$ The argument $icode fg_eval$$ has prototype $codei% %FG_eval% %fg_eval% %$$ where the class $icode FG_eval$$ is unspecified except for the fact that it supports the syntax $codei% %FG_eval%::ADvector %fg_eval%(%fg%, %x%) %$$ The type $icode ADvector$$ and the arguments to $icode fg$$, $icode x$$ have the following meaning: $subhead ADvector$$ The type $icode%FG_eval%::ADvector%$$ must be a $cref SimpleVector$$ class with $cref/elements of type/SimpleVector/Elements of Specified Type/$$ $code AD$$. $subhead x$$ The $icode fg_eval$$ argument $icode x$$ has prototype $codei% const %ADvector%& %x% %$$ where $icode%nx% = %x%.size()%$$. $subhead fg$$ The $icode fg_eval$$ argument $icode fg$$ has prototype $codei% %ADvector%& %fg% %$$ where $codei%1 + %ng% = %fg%.size()%$$. The input value of the elements of $icode fg$$ does not matter. Upon return from $icode fg_eval$$, $codei% %fg%[0] =%$$ $latex f (x)$$ $codei% %$$ and for $latex i = 0, \ldots , ng-1$$, $codei% %fg%[1 + %i%] =%$$ $latex g_i (x)$$ $head solution$$ The argument $icode solution$$ has prototype $codei% ipopt::solve_result<%Dvector%>& %solution% %$$ After the optimization process is completed, $icode solution$$ contains the following information: $subhead status$$ The $icode status$$ field of $icode solution$$ has prototype $codei% ipopt::solve_result<%Dvector%>::status_type %solution%.status %$$ It is the final Ipopt status for the optimizer. Here is a list of the possible values for the status: $table $icode status$$ $cnext Meaning $rnext not_defined $cnext The optimizer did not return a final status for this problem. $rnext unknown $cnext The status returned by the optimizer is not defined in the Ipopt documentation for $code finalize_solution$$. $rnext success $cnext Algorithm terminated successfully at a point satisfying the convergence tolerances (see Ipopt options). $rnext maxiter_exceeded $cnext The maximum number of iterations was exceeded (see Ipopt options). $rnext stop_at_tiny_step $cnext Algorithm terminated because progress was very slow. $rnext stop_at_acceptable_point $cnext Algorithm stopped at a point that was converged, not to the 'desired' tolerances, but to 'acceptable' tolerances (see Ipopt options). $rnext local_infeasibility $cnext Algorithm converged to a non-feasible point (problem may have no solution). $rnext user_requested_stop $cnext This return value should not happen. $rnext diverging_iterates $cnext It the iterates are diverging. $rnext restoration_failure $cnext Restoration phase failed, algorithm doesn't know how to proceed. $rnext error_in_step_computation $cnext An unrecoverable error occurred while Ipopt tried to compute the search direction. $rnext invalid_number_detected $cnext Algorithm received an invalid number (such as $code nan$$ or $code inf$$) from the users function $icode%fg_info%.eval%$$ or from the CppAD evaluations of its derivatives (see the Ipopt option $code check_derivatives_for_naninf$$). $rnext internal_error $cnext An unknown Ipopt internal error occurred. Contact the Ipopt authors through the mailing list. $tend $subhead x$$ The $code x$$ field of $icode solution$$ has prototype $codei% %Vector% %solution%.x %$$ and its size is equal to $icode nx$$. It is the final $latex x$$ value for the optimizer. $subhead zl$$ The $code zl$$ field of $icode solution$$ has prototype $codei% %Vector% %solution%.zl %$$ and its size is equal to $icode nx$$. It is the final Lagrange multipliers for the lower bounds on $latex x$$. $subhead zu$$ The $code zu$$ field of $icode solution$$ has prototype $codei% %Vector% %solution%.zu %$$ and its size is equal to $icode nx$$. It is the final Lagrange multipliers for the upper bounds on $latex x$$. $subhead g$$ The $code g$$ field of $icode solution$$ has prototype $codei% %Vector% %solution%.g %$$ and its size is equal to $icode ng$$. It is the final value for the constraint function $latex g(x)$$. $subhead lambda$$ The $code lambda$$ field of $icode solution$$ has prototype $codei% %Vector%> %solution%.lambda %$$ and its size is equal to $icode ng$$. It is the final value for the Lagrange multipliers corresponding to the constraint function. $subhead obj_value$$ The $code obj_value$$ field of $icode solution$$ has prototype $codei% double %solution%.obj_value %$$ It is the final value of the objective function $latex f(x)$$. $children% example/ipopt_solve/get_started.cpp% example/ipopt_solve/retape.cpp% example/ipopt_solve/ode_inverse.cpp %$$ $head Example$$ All the examples return true if it succeeds and false otherwise. $subhead get_started$$ The file $cref%example/ipopt_solve/get_started.cpp%ipopt_solve_get_started.cpp%$$ is an example and test of $code ipopt::solve$$ taken from the Ipopt manual. $subhead retape$$ The file $cref%example/ipopt_solve/retape.cpp%ipopt_solve_retape.cpp%$$ demonstrates when it is necessary to specify $cref/retape/ipopt_solve/options/Retape/$$ as true. $subhead ode_inverse$$ The file $cref%example/ipopt_solve/ode_inverse.cpp%ipopt_solve_ode_inverse.cpp%$$ demonstrates using Ipopt to solve for parameters in an ODE model. $end ------------------------------------------------------------------------------- */ # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE namespace ipopt { /*! \file solve.hpp \brief Implement the ipopt::solve Nonlinear Programming Solver */ /*! Use Ipopt to Solve a Nonlinear Programming Problem \tparam Bvector simple vector class with elements of type bool. \tparam Dvector simple vector class with elements of type double. \tparam FG_eval function object used to evaluate f(x) and g(x); see fg_eval below. It must also support \code FG_eval::ADvector \endcode to dentify the type used for the arguments to fg_eval. \param options list of options, one for each line. Ipopt options (are optional) and have one of the following forms \code String name value Numeric name value Integer name value \endcode The following other possible options are listed below: \code Retape value \endcode \param xi initial argument value to start optimization procedure at. \param xl lower limit for argument during optimization \param xu upper limit for argument during optimization \param gl lower limit for g(x) during optimization. \param gu upper limit for g(x) during optimization. \param fg_eval function that evaluates the objective and constraints using the syntax \code fg_eval(fg, x) \endcode \param solution structure that holds the solution of the optimization. */ template void solve( const std::string& options , const Dvector& xi , const Dvector& xl , const Dvector& xu , const Dvector& gl , const Dvector& gu , FG_eval& fg_eval , ipopt::solve_result& solution ) { bool ok = true; typedef typename FG_eval::ADvector ADvector; CPPAD_ASSERT_KNOWN( xi.size() == xl.size() && xi.size() == xu.size() , "ipopt::solve: size of xi, xl, and xu are not all equal." ); CPPAD_ASSERT_KNOWN( gl.size() == gu.size() , "ipopt::solve: size of gl and gu are not equal." ); size_t nx = xi.size(); size_t ng = gl.size(); // Create an IpoptApplication using Ipopt::IpoptApplication; Ipopt::SmartPtr app = new IpoptApplication(); // process the options argument size_t begin_1, end_1, begin_2, end_2, begin_3, end_3; begin_1 = 0; bool retape = false; bool sparse_forward = false; bool sparse_reverse = false; while( begin_1 < options.size() ) { // split this line into tokens while( options[begin_1] == ' ') begin_1++; end_1 = options.find_first_of(" \n", begin_1); begin_2 = end_1; while( options[begin_2] == ' ') begin_2++; end_2 = options.find_first_of(" \n", begin_2); begin_3 = end_2; while( options[begin_3] == ' ') begin_3++; end_3 = options.find_first_of(" \n", begin_3); // check for errors CPPAD_ASSERT_KNOWN( (end_1 != std::string::npos) & (end_2 != std::string::npos) & (end_3 != std::string::npos) , "ipopt::solve: missing '\\n' at end of an option line" ); CPPAD_ASSERT_KNOWN( (end_1 > begin_1) & (end_2 > begin_2) , "ipopt::solve: an option line does not have two tokens" ); // get first two tokens std::string tok_1 = options.substr(begin_1, end_1 - begin_1); std::string tok_2 = options.substr(begin_2, end_2 - begin_2); // get third token std::string tok_3; bool three_tok = false; three_tok |= tok_1 == "Sparse"; three_tok |= tok_1 == "String"; three_tok |= tok_1 == "Numeric"; three_tok |= tok_1 == "Integer"; if( three_tok ) { CPPAD_ASSERT_KNOWN( (end_3 > begin_3) , "ipopt::solve: a Sparse, String, Numeric, or Integer\n" "option line does not have three tokens." ); tok_3 = options.substr(begin_3, end_3 - begin_3); } // switch on option type if( tok_1 == "Retape" ) { CPPAD_ASSERT_KNOWN( (tok_2 == "true") | (tok_2 == "false") , "ipopt::solve: Retape value is not true or false" ); retape = (tok_2 == "true"); } else if( tok_1 == "Sparse" ) { CPPAD_ASSERT_KNOWN( (tok_2 == "true") | (tok_2 == "false") , "ipopt::solve: Sparse value is not true or false" ); CPPAD_ASSERT_KNOWN( (tok_3 == "forward") | (tok_3 == "reverse") , "ipopt::solve: Sparse direction is not forward or reverse" ); if( tok_2 == "false" ) { sparse_forward = false; sparse_reverse = false; } else { sparse_forward = tok_3 == "forward"; sparse_reverse = tok_3 == "reverse"; } } else if ( tok_1 == "String" ) app->Options()->SetStringValue(tok_2.c_str(), tok_3.c_str()); else if ( tok_1 == "Numeric" ) { Ipopt::Number value = std::atof( tok_3.c_str() ); app->Options()->SetNumericValue(tok_2.c_str(), value); } else if ( tok_1 == "Integer" ) { Ipopt::Index value = std::atoi( tok_3.c_str() ); app->Options()->SetIntegerValue(tok_2.c_str(), value); } else CPPAD_ASSERT_KNOWN( false, "ipopt::solve: First token is not one of\n" "Retape, Sparse, String, Numeric, Integer" ); begin_1 = end_3; while( options[begin_1] == ' ') begin_1++; if( options[begin_1] != '\n' ) CPPAD_ASSERT_KNOWN( false, "ipopt::solve: either more than three tokens " "or no '\\n' at end of a line" ); begin_1++; } CPPAD_ASSERT_KNOWN( ! ( retape & (sparse_forward | sparse_reverse) ) , "ipopt::solve: retape and sparse both true is not supported." ); // Initialize the IpoptApplication and process the options Ipopt::ApplicationReturnStatus status = app->Initialize(); ok &= status == Ipopt::Solve_Succeeded; if( ! ok ) { solution.status = solve_result::unknown; return; } // Create an interface from Ipopt to this specific problem. // Note the assumption here that ADvector is same as cppd_ipopt::ADvector size_t nf = 1; Ipopt::SmartPtr cppad_nlp = new CppAD::ipopt::solve_callback( nf, nx, ng, xi, xl, xu, gl, gu, fg_eval, retape, sparse_forward, sparse_reverse, solution ); // Run the IpoptApplication app->OptimizeTNLP(cppad_nlp); return; } } // end ipopt namespace } // END_CPPAD_NAMESPACE # endif cppad-20170000.3/cppad/base_require.hpp0000644000175200017650000001065613057470467016715 0ustar coincoin-web// $Id: base_require.hpp 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_BASE_REQUIRE_HPP # define CPPAD_BASE_REQUIRE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin base_require$$ $spell azmul ostream alloc eps std Lt Le Eq Ge Gt cppad.hpp namespace optimizations bool const CppAD enum Lt Le Eq Ge Gt inline Op std CondExp $$ $section AD Requirements for a CppAD Base Type$$ $head Syntax$$ $code # include $$ $head Purpose$$ This section lists the requirements for the type $icode Base$$ so that the type $codei%AD<%Base%>%$$ can be used. $head API Warning$$ Defining a CppAD $icode Base$$ type is an advanced use of CppAD. This part of the CppAD API changes with time. The most common change is adding more requirements. Search for $code base_require$$ in the current $cref whats_new$$ section for these changes. $head Standard Base Types$$ In the case where $icode Base$$ is $code float$$, $code double$$, $code std::complex$$, $code std::complex$$, or $codei%AD<%Other%>%$$, these requirements are provided by including the file $code cppad/cppad.hpp$$. $head Include Order$$ If you are linking a non-standard base type to CppAD, you must first include the file $code cppad/base_require.hpp$$, then provide the specifications below, and then include the file $code cppad/cppad.hpp$$. $head Numeric Type$$ The type $icode Base$$ must support all the operations for a $cref NumericType$$. $head Output Operator$$ The type $icode Base$$ must support the syntax $codei% %os% << %x% %$$ where $icode os$$ is an $code std::ostream&$$ and $icode x$$ is a $code const base_alloc&$$. For example, see $cref/base_alloc/base_alloc.hpp/Output Operator/$$. $head Integer$$ The type $icode Base$$ must support the syntax $codei% %i% = CppAD::Integer(%x%) %$$ which converts $icode x$$ to an $code int$$. The argument $icode x$$ has prototype $codei% const %Base%& %x% %$$ and the return value $icode i$$ has prototype $codei% int %i% %$$ $subhead Suggestion$$ In many cases, the $icode Base$$ version of the $code Integer$$ function can be defined by $codei% namespace CppAD { inline int Integer(const %Base%& x) { return static_cast(x); } } %$$ For example, see $cref/base_float/base_float.hpp/Integer/$$ and $cref/base_alloc/base_alloc.hpp/Integer/$$. $head Absolute Zero, azmul$$ The type $icode Base$$ must support the syntax $codei% %z% = azmul(%x%, %y%) %$$ see; $cref azmul$$. The following preprocessor macro invocation suffices (for most $icode Base$$ types): $codei% namespace CppAD { CPPAD_AZMUL(%Base%) } %$$ where the macro is defined by $srccode%cpp% */ # define CPPAD_AZMUL(Base) \ inline Base azmul(const Base& x, const Base& y) \ { Base zero(0.0); \ if( x == zero ) \ return zero; \ return x * y; \ } /* %$$ $childtable% omh/base_require/base_member.omh% cppad/core/base_cond_exp.hpp% omh/base_require/base_identical.omh% omh/base_require/base_ordered.omh% cppad/core/base_std_math.hpp% cppad/core/base_limits.hpp% cppad/core/base_to_string.hpp% cppad/core/base_hash.hpp% omh/base_require/base_example.omh %$$ $end */ // definitions that must come before base implementations # include # include # include # include // grouping documentation by feature # include # include # include # include # include // must define template class numeric_limits before the base cases # include # include // deprecated // base cases that come with CppAD # include # include # include // deprecated base type # include # endif cppad-20170000.3/cppad/configure.hpp.in0000644000175200017650000001351413057470467016631 0ustar coincoin-web// $Id: configure.hpp.in 3845 2016-11-19 01:50:47Z bradbell $ # ifndef CPPAD_CONFIGURE_HPP # define CPPAD_CONFIGURE_HPP /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin configure$$ $spell CppAD $$ $section Configuration Preprocessor Symbols Used by CppAD$$ $head Preprocessor Symbols$$ All of the preprocessor symbols used by CppAD begin with $code CPPAD_$$ (there are some deprecated symbols that begin with $code CppAD$$). $end */ /*! \file configure.hpp Replacement for config.h so that all preprocessor symbols begin with CPPAD_ */ /*! \def CPPAD_DISABLE_SOME_MICROSOFT_COMPILER_WARNINGS This macro is only used to document the pragmas that disables the follow warnings: \li C4100 unreferenced formal parameter. \li C4127 conditional expression is constant. */ # define CPPAD_DISABLE_SOME_MICROSOFT_COMPILER_WARNINGS 1 # if _MSC_VER # pragma warning( disable : 4100 ) # pragma warning( disable : 4127 ) # endif # undef CPPAD_DISABLE_SOME_MICROSOFT_COMPILER_WARNINGS /*! \def CPPAD_USE_CPLUSPLUS_2011 Should CppAD use C++11 features. This will be true if the current compiler flags request C++11 features and the install procedure determined that all the necessary features are avaiable. */ # if _MSC_VER # define CPPAD_USE_CPLUSPLUS_2011 @cppad_cplusplus_201100_ok@ # else // # if __cplusplus >= 201100 # define CPPAD_USE_CPLUSPLUS_2011 @cppad_cplusplus_201100_ok@ # else // # define CPPAD_USE_CPLUSPLUS_2011 0 # endif // # endif // /*! \def CPPAD_PACKAGE_STRING cppad-yyyymmdd as a C string where yyyy is year, mm is month, and dd is day. */ # define CPPAD_PACKAGE_STRING "cppad-@cppad_version@" /*! def CPPAD_HAS_COLPACK Was a colpack_prefix specified on the cmake command line. */ # define CPPAD_HAS_COLPACK @cppad_has_colpack@ /*! \def CPPAD_DEPRECATED If this symbol is one, an implicit constor of AD is defined where the argument has any type. Otherwise this constructor is explicit. */ # define CPPAD_DEPRECATED @cppad_deprecated@ /*! \def CPPAD_BOOSTVECTOR If this symbol is one, and _MSC_VER is not defined, we are using boost vector for CPPAD_TESTVECTOR. It this symbol is zero, we are not using boost vector for CPPAD_TESTVECTOR. */ # define CPPAD_BOOSTVECTOR @cppad_boostvector@ /*! \def CPPAD_CPPADVECTOR If this symbol is one, we are using CppAD vector for CPPAD_TESTVECTOR. It this symbol is zero, we are not using CppAD vector for CPPAD_TESTVECTOR. */ # define CPPAD_CPPADVECTOR @cppad_cppadvector@ /*! \def CPPAD_STDVECTOR If this symbol is one, we are using standard vector for CPPAD_TESTVECTOR. It this symbol is zero, we are not using standard vector for CPPAD_TESTVECTOR. */ # define CPPAD_STDVECTOR @cppad_stdvector@ /*! \def CPPAD_EIGENVECTOR If this symbol is one, we are using Eigen vector for CPPAD_TESTVECTOR. If this symbol is zero, we are not using Eigen vector for CPPAD_TESTVECTOR. */ # define CPPAD_EIGENVECTOR @cppad_eigenvector@ /*! \def CPPAD_HAS_GETTIMEOFDAY If this symbol is one, and _MSC_VER is not defined, this system supports the gettimeofday funcgtion. Otherwise, this smybol should be zero. */ # define CPPAD_HAS_GETTIMEOFDAY @cppad_has_gettimeofday@ /*! \def CPPAD_SIZE_T_NOT_UNSIGNED_INT If this symbol is zero, the type size_t is the same as the type unsigned int, otherwise this symbol is one. */ # define CPPAD_SIZE_T_NOT_UNSIGNED_INT @cppad_size_t_not_unsigned_int@ /*! \def CPPAD_TAPE_ADDR_TYPE Is the type used to store address on the tape. If not size_t, then sizeof(CPPAD_TAPE_ADDR_TYPE) <= sizeof( size_t ) to conserve memory. This type must support \c std::numeric_limits, the \c <= operator, and conversion to \c size_t. Make sure that the type chosen returns true for is_pod in pod_vector.hpp. This type is later defined as \c addr_t in the CppAD namespace. */ # define CPPAD_TAPE_ADDR_TYPE @cppad_tape_addr_type@ /*! \def CPPAD_TAPE_ID_TYPE Is the type used to store tape identifiers. If not size_t, then sizeof(CPPAD_TAPE_ID_TYPE) <= sizeof( size_t ) to conserve memory. This type must support \c std::numeric_limits, the \c <= operator, and conversion to \c size_t. Make sure that the type chosen returns true for is_pod in pod_vector.hpp. This type is later defined as \c tape_id_t in the CppAD namespace. */ # define CPPAD_TAPE_ID_TYPE @cppad_tape_id_type@ /*! \def CPPAD_MAX_NUM_THREADS Specifies the maximum number of threads that CppAD can support (must be greater than or equal four). The user may define CPPAD_MAX_NUM_THREADS before including any of the CppAD header files. 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Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # automake input file # See ./CMakeLists.txt for specifications. # BUILT_SOURCES = det_by_minor_c.c det_by_minor_cpp.cpp det_by_minor_c.c: det_by_minor.c cp $(srcdir)/det_by_minor.c det_by_minor_c.c det_by_minor_cpp.cpp: det_by_minor.c cp $(srcdir)/det_by_minor.c det_by_minor_cpp.cpp # EXTRA_DIST = \ det_by_minor.c # # erase configures choice of flags DEFS = # # AM_CXXFLAGS = -g # AM_CFLAGS = -g # AM_CXXFLAGS = -O2 -DNDEBUG AM_CFLAGS = -O2 -DNDEBUG # check_PROGRAMS = det_by_minor_c det_by_minor_cpp # det_by_minor_c_SOURCES = det_by_minor_c.c det_by_minor_cpp_SOURCES = det_by_minor_cpp.cpp # test: det_by_minor_c det_by_minor_cpp echo "Running version compiled using C compiler" ./det_by_minor_c echo "Running version compiled using C++ compiler" ./det_by_minor_cpp cppad-20170000.3/compare_c/det_by_minor.c0000644000175200017650000003472413057470467017217 0ustar coincoin-web/* $Id: */ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ # include # include # include # include # include // In the case of plain C, we defined the type bool together with ture, false # ifndef __cplusplus # define bool int # define true 1 # define false 0 # endif /* ------------------------------------------------------------------------------- $begin det_of_minor_c$$ $spell det const $$ $section Determinant of a Minor$$ $head Syntax$$ $icode%d% = det_of_minor(%a%, %m%, %n%, %r%, %c%)%$$ $head Purpose$$ returns the determinant of a minor of the matrix $latex A$$ using expansion by minors. The elements of the $latex n \times n$$ minor $latex M$$ of the matrix $latex A$$ are defined, for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , n-1$$, by $latex \[ M_{i,j} = A_{R(i), C(j)} \]$$ where the functions $latex R(i)$$ is defined by the $cref/argument r/det_of_minor/r/$$ and $latex C(j)$$ is defined by the $cref/argument c/det_of_minor/c/$$. $pre $$ This function is for example and testing purposes only. Expansion by minors is chosen as an example because it uses a lot of floating point operations yet does not require much source code (on the order of $icode m$$ factorial floating point operations and about 70 lines of source code including comments). This is not an efficient method for computing a determinant; for example, using an LU factorization would be better. $head Determinant of A$$ If the following conditions hold, the minor is the entire matrix $latex A$$ and hence $code det_of_minor$$ will return the determinant of $latex A$$: $list number$$ $latex n = m$$. $lnext for $latex i = 0 , \ldots , m-1$$, $latex r[i] = i+1$$, and $latex r[m] = 0$$. $lnext for $latex j = 0 , \ldots , m-1$$, $latex c[j] = j+1$$, and $latex c[m] = 0$$. $lend $head a$$ The argument $icode a$$ has prototype $codei% const double* %a% %$$ and is a vector with size $latex m * m$$. The elements of the $latex m \times m$$ matrix $latex A$$ are defined, for $latex i = 0 , \ldots , m-1$$ and $latex j = 0 , \ldots , m-1$$, by $latex \[ A_{i,j} = a[ i * m + j] \] $$ $head m$$ The argument $icode m$$ has prototype $codei% size_t %m% %$$ and is the size of the square matrix $latex A$$. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ and is the size of the square minor $latex M$$. $head r$$ The argument $icode r$$ has prototype $codei% size_t* %r% %$$ and is a vector with $latex m + 1$$ elements. This vector defines the function $latex R(i)$$ which specifies the rows of the minor $latex M$$. To be specific, the function $latex R(i)$$ for $latex i = 0, \ldots , n-1$$ is defined by $latex \[ \begin{array}{rcl} R(0) & = & r[m] \\ R(i+1) & = & r[ R(i) ] \end{array} \] $$ All the elements of $icode r$$ must have value less than or equal $icode m$$. The elements of vector $icode r$$ are modified during the computation, and restored to their original value before the return from $code det_of_minor$$. $head c$$ The argument $icode c$$ has prototype $codei% size_t* %c% %$$ and is a vector with $latex m + 1$$ elements This vector defines the function $latex C(i)$$ which specifies the rows of the minor $latex M$$. To be specific, the function $latex C(i)$$ for $latex j = 0, \ldots , n-1$$ is defined by $latex \[ \begin{array}{rcl} C(0) & = & c[m] \\ C(j+1) & = & c[ C(j) ] \end{array} \] $$ All the elements of $icode c$$ must have value less than or equal $icode m$$. The elements of vector $icode c$$ are modified during the computation, and restored to their original value before the return from $code det_of_minor$$. $head d$$ The result $icode d$$ has prototype $codei% double %d% %$$ and is equal to the determinant of the minor $latex M$$. $spell Cj $$ $head Source Code$$ $srccode%cpp% */ double det_of_minor( const double* a , size_t m , size_t n , size_t* r , size_t* c ) { size_t R0, Cj, Cj1, j; double detM, M0j, detS; int s; R0 = r[m]; /* R(0) */ Cj = c[m]; /* C(j) (case j = 0) */ Cj1 = m; /* C(j-1) (case j = 0) */ /* check for 1 by 1 case */ if( n == 1 ) return a[ R0 * m + Cj ]; /* initialize determinant of the minor M */ detM = 0.; /* initialize sign of factor for neat sub-minor */ s = 1; /* remove row with index 0 in M from all the sub-minors of M */ r[m] = r[R0]; /* for each column of M */ for(j = 0; j < n; j++) { /* element with index (0,j) in the minor M */ M0j = a[ R0 * m + Cj ]; /* remove column with index j in M to form next sub-minor S of M */ c[Cj1] = c[Cj]; /* compute determinant of the current sub-minor S */ detS = det_of_minor(a, m, n - 1, r, c); /* restore column Cj to representation of M as a minor of A */ c[Cj1] = Cj; /* include this sub-minor term in the summation */ if( s > 0 ) detM = detM + M0j * detS; else detM = detM - M0j * detS; /* advance to neat column of M */ Cj1 = Cj; Cj = c[Cj]; s = - s; } /* restore row zero to the minor representation for M */ r[m] = R0; /* return the determinant of the minor M */ return detM; } /* %$$ $end ------------------------------------------------------------------------------- $begin det_by_minor_c$$ $spell det const $$ $section Compute Determinant using Expansion by Minors$$ $head Syntax$$ $icode%d% = det_by_minor(%a%, %n%)%$$ $head Purpose$$ returns the determinant of the matrix $latex A$$ using expansion by minors. The elements of the $latex n \times n$$ minor $latex M$$ of the matrix $latex A$$ are defined, for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , n-1$$, by $latex \[ M_{i,j} = A_{i, j} \]$$ $head a$$ The argument $icode a$$ has prototype $codei% const double* %a% %$$ and is a vector with size $latex m * m$$. The elements of the $latex m \times m$$ matrix $latex A$$ are defined, for $latex i = 0 , \ldots , m-1$$ and $latex j = 0 , \ldots , m-1$$, by $latex \[ A_{i,j} = a[ i * m + j] \] $$ $head m$$ The argument $icode m$$ has prototype $codei% size_t %m% %$$ and is the number of rows (and columns) in the square matrix $latex A$$. $hilitecmd%codep%$$ $hiliteseq% %det_of_minor%(%det_of_minor_c %$$ $spell det malloc sizeof $$ $head Source Code$$ $srccode%cpp% */ double det_by_minor(double* a, size_t m) { size_t *r, *c, i; double value; r = (size_t*) malloc( (m+1) * sizeof(size_t) ); c = (size_t*) malloc( (m+1) * sizeof(size_t) ); assert(m <= 100); for(i = 0; i < m; i++) { r[i] = i+1; c[i] = i+1; } r[m] = 0; c[m] = 0; value = det_of_minor(a, m, m, r, c); free(r); free(c); return value; } /* %$$ $end -------------------------------------------------------------------------- $begin uniform_01_c$$ $section Simulate a [0,1] Uniform Random Variate$$ $head Syntax$$ $codei%random_seed(%seed%) %$$ $codei%uniform_01(%n%, %a%)%$$ $head Purpose$$ This routine is used to create random values for speed testing purposes. $head seed$$ The argument $icode seed$$ has prototype $codei% size_t %seed% %$$ It specifies a seed for the uniform random number generator. $head n$$ The argument $icode n$$ has prototype $codei% size_t %n% %$$ It specifies the number of elements in the random vector $icode a$$. $head a$$ The argument $icode a$$ has prototype $codei% double* %a% %$$. The input value of the elements of $icode a$$ does not matter. Upon return, the elements of $icode a$$ are set to values randomly sampled over the interval [0,1]. $hilitecmd%codep%$$ $hiliteseq% %elapsed_seconds%(%elapsed_seconds_c% %repeat_det_by_minor%(%elapsed_seconds_c %$$ $spell srand $$ $head Source Code$$ $srccode%cpp% */ void random_seed(size_t seed) { srand(seed); } void uniform_01(unsigned n, double* a) { static double factor = 1. / (double) RAND_MAX; while(n--) a[n] = rand() * factor; } /* %$$ $end ------------------------------------------------------------------------------ $begin correct_det_by_minor_c$$ $spell det bool $$ $section Correctness Test of det_by_minor Routine$$ $head Syntax$$ $icode%flag% = correct_det_by_minor()%$$ $head flag$$ The return value has prototype $codei% bool %flag% %$$ It value is $code 1$$ if the test passes and $code 0$$ otherwise. $hilitecmd%codep%$$ $hiliteseq% %random_seed%(%uniform_01_c% %uniform_01%(%uniform_01_c %$$ $spell fabs $$ $head Source Code$$ $srccode%cpp% */ bool correct_det_by_minor(void) { double a[9], det, check; random_seed(123); uniform_01(9, a); /* compute determinant using expansion by minors */ det = det_by_minor(a, 3); /* use expansion by minors to hand code the determinant */ check = 0.; check += a[0] * ( a[4] * a[8] - a[5] * a[7] ); check -= a[1] * ( a[3] * a[8] - a[5] * a[6] ); check += a[2] * ( a[3] * a[7] - a[4] * a[6] ); if( fabs(det / check - 1.0) < 1e-10 ) return true; return false; } /* %$$ $end ------------------------------------------------------------------------------ $begin repeat_det_by_minor_c$$ $spell det $$ $section Repeat det_by_minor Routine A Specified Number of Times$$ $head Syntax$$ $codei%repeat_det_by_minor(%repeat%, %size%)%$$ $head repeat$$ The argument has prototype $codei% size_t %repeat% %$$ It specifies the number of times to repeat the calculation. $head size$$ The argument has prototype $codei% size_t %size% %$$ It specifies the number of rows (and columns) in the square matrix we are computing the determinant of. $hilitecmd%codep%$$ $hiliteseq% %uniform_01%(%uniform_01_c% %det_by_minor%(%det_by_minor_c %$$ $spell malloc sizeof $$ $head Source Code$$ $srccode%cpp% */ void repeat_det_by_minor(size_t repeat, size_t size) { double *a; a = (double*) malloc( (size * size) * sizeof(double) ); while(repeat--) { uniform_01(size * size, a); det_by_minor(a, size); } free(a); return; } /* %$$ $end ------------------------------------------------------------------------------ $begin elapsed_seconds_c$$ $spell gettimeofday $$ $section Returns Elapsed Number of Seconds$$ $head Syntax$$ $icode%s% = elapsed_seconds()%$$ $head Purpose$$ This routine is accurate to within .02 seconds It does not necessary work for time intervals that are greater than a day. $head s$$ is a $code double$$ equal to the number of seconds since the first call to $code elapsed_seconds$$. $spell Microsoft cassert milli sys endif usec diff bool struct timeval $$ $head Source Code$$ $srccode%cpp% */ # if _MSC_VER // --------------------------------------------------------------------------- // Microsoft version of timer # include # include double elapsed_seconds(void) { static bool first_ = true; static SYSTEMTIME st_; double hour, minute, second, milli, diff; SYSTEMTIME st; if( first_ ) { GetSystemTime(&st_); first_ = false; return 0.; } GetSystemTime(&st); hour = (double) st.wHour - (double) st_.wHour; minute = (double) st.wMinute - (double) st_.wMinute; second = (double) st.wSecond - (double) st_.wSecond; milli = (double) st.wMilliseconds - (double) st_.wMilliseconds; diff = 1e-3*milli + second + 60.*minute + 3600.*hour; if( diff < 0. ) diff += 3600.*24.; assert( 0 <= diff && diff < 3600.*24. ); return diff; } # else // --------------------------------------------------------------------------- // Unix version of timer # include double elapsed_seconds(void) { double sec, usec, diff; static bool first_ = true; static struct timeval tv_first; struct timeval tv; if( first_ ) { gettimeofday(&tv_first, NULL); first_ = false; return 0.; } gettimeofday(&tv, NULL); assert( tv.tv_sec >= tv_first.tv_sec ); sec = (double)(tv.tv_sec - tv_first.tv_sec); usec = (double)tv.tv_usec - (double)tv_first.tv_usec; diff = sec + 1e-6*usec; return diff; } # endif /* %$$ $end ----------------------------------------------------------------------------- $begin time_det_by_minor_c$$ $spell det $$ $section Determine Amount of Time to Execute det_by_minor$$ $head Syntax$$ $icode%time% = time_test(%size%, %time_min%)%$$ $head Purpose$$ reports the amount of wall clock time for $code det_by_minor$$ to compute the determinant of a square matrix. The $icode size$$ has prototype $codei% size_t %size% %$$ It specifies the number of rows (and columns) in the square matrix that the determinant is being calculated for. $head time_min$$ The argument $icode time_min$$ has prototype $codei% double %time_min% %$$ It specifies the minimum amount of time in seconds that the $icode test$$ routine should take. The calculations is repeated the necessary number of times so that this amount of execution time (or more) is reached. $head time$$ The return value $icode time$$ has prototype $codei% double %time% %$$ and is the number of wall clock seconds that it took for $code det_by_minor$$ to compute its determinant (plus overhead which includes choosing a random matrix). $hilitecmd%codep%$$ $hiliteseq% %elapsed_seconds%(%elapsed_seconds_c% %repeat_det_by_minor%(%elapsed_seconds_c %$$ $spell det $$ $head Source Code$$ $srccode%cpp% */ double time_det_by_minor(size_t size, double time_min) { size_t repeat; double s0, s1, time; repeat = 0; s0 = elapsed_seconds(); s1 = s0; while( s1 - s0 < time_min ) { if( repeat == 0 ) repeat = 1; else repeat = 2 * repeat; s0 = elapsed_seconds(); repeat_det_by_minor(repeat, size); s1 = elapsed_seconds(); } time = (s1 - s0) / (double) repeat; return time; } /* %$$ $end ------------------------------------------------------------------------------ $begin main_compare_c$$ $section Main Program For Comparing C and C++ Speed$$ $hilitecmd%codep%$$ $hiliteseq% %correct_det_by_minor%(%correct_det_by_minor_c% %random_seed%(%uniform_01_c %$$ $spell bool printf det $$ $head Source Code$$ $srccode|cpp| */ int main(void) { bool flag; size_t i; random_seed(123); printf("correct_det_by_minor: "); flag = correct_det_by_minor(); if( flag ) printf("OK\n"); else printf("Error\n"); for(i = 0; i < 5; i++) { double time_min = 1.0; size_t size = 2 + i * 2; int i_size = (int) size; printf("time_det_minor for %d x %d matrix = ", i_size, i_size); printf("%g\n", time_det_by_minor(size, time_min) ); } if( flag ) return 0; return 1; } /* |$$ $end */ cppad-20170000.3/compare_c/CMakeLists.txt0000644000175200017650000000465313057470467017137 0ustar coincoin-web# $Id: CMakeLists.txt 3857 2016-12-23 13:08:43Z bradbell $ # ----------------------------------------------------------------------------- # CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell # # CppAD is distributed under multiple licenses. This distribution is under # the terms of the # GNU General Public License Version 3. # # A copy of this license is included in the COPYING file of this distribution. # Please visit http://www.coin-or.org/CppAD/ for information on other licenses. # ----------------------------------------------------------------------------- # $begin compare_c$$ $newlinech #$$ # $spell # det # cpp # $$ # # $section Compare Speed of C and C++$$ # $index compare, speed C and C++$$ # $index speed, compare C and C++$$ # $index C, compare speed with C++$$ # $index C++, compare speed with C$$ # # $head Syntax$$ # $codei%compare_c/det_by_minor_c # %$$ # $codei compare_c/det_by_minor_cpp$$ # # $head Purpose$$ # Compares the speed of the exact same source code compiled # using C versus C++. # # $childtable% # compare_c/det_by_minor.c # %$$ # # $end # ----------------------------------------------------------------------------- # Specifies build type for this directory. Possible values are # empty, Debug, Release, RelWithDebInfo and MinSizeRel SET(CMAKE_BUILD_TYPE RELEASE) # Loop though the C and C++ compilers FOREACH( com c cpp ) # Copy a file to another location and modify its contents. # configure_file(InputFile OutputFile [COPYONLY] [ESCAPE_QUOTES] [@ONLY]) SET( source det_by_minor_${com}.${com} ) CONFIGURE_FILE( ${CMAKE_CURRENT_SOURCE_DIR}/det_by_minor.c ${CMAKE_CURRENT_BINARY_DIR}/${source} COPYONLY ) ADD_EXECUTABLE( det_by_minor_${com} EXCLUDE_FROM_ALL ${source}) # IF( ${com} STREQUAL cpp ) # These are C++ compiler flags (may not be valid for C) add_cppad_cxx_flags(det_by_minor_${com}) ENDIF( ${com} STREQUAL cpp ) # # Add target the executes this program ADD_CUSTOM_TARGET(check_det_by_minor_${com} det_by_minor_${com} DEPENDS det_by_minor_${com} ) MESSAGE(STATUS "make check_det_by_minor_${com}: available") ENDFOREACH(com) # check_compare_c target ADD_CUSTOM_TARGET( check_compare_c DEPENDS check_det_by_minor_c check_det_by_minor_cpp ) MESSAGE(STATUS "make check_compare_c: available") # Add check_compare_c to check depends in parent environment add_to_list(check_depends check_compare_c) SET(check_depends "${check_depends}" PARENT_SCOPE) cppad-20170000.3/gpl-3.0.txt0000644000175200017650000010451313057470467014264 0ustar coincoin-web GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. 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Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see . The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . cppad-20170000.3/doc.omh0000644000175200017650000001670613057470467013723 0ustar coincoin-web/* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin CppAD$$ $comment default navigate command for all of CppAD documentation$$ $navigate% Prev%Prev% Next%Next% Across%Index% Up%Up% Down_up_3%_up_3% Down_up_2%_up_2% Down_up_1%_up_1% Down_up_0%_up_0% Current%Headings %$$ $comment ------------------------------------------------------------- default automatic indexing command for all CppAD documentaiton $$ $aindex section head subhead$$ $comment ------------------------------------------------------------- Latex used throughout the CppAD documentation $$ $latex \newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} } $$ $comment ------------------------------------------------------------- hilite commands used throughout the CppAD documentation $$ $hilitecmd% verbatim% codep %$$ $hiliteseq% CppAD::%AD%<% AD % %AD%<% AD %CppAD::%ADFun%<% FunConstruct % %ADFun%<% FunConstruct % %CPPAD_TESTVECTOR%(% testvector %.%Forward%(% Forward %CppAD::%Independent%(% Independent % %Independent%(% Independent %.%Jacobian%(% Jacobian %CppAD::%NearEqual%(% NearEqual % %NearEqual%(% NearEqual %.%Reverse%(% Reverse %$$ $spell Jax cppad.hpp cppad namespaces std templated const CppADvector multiplicative Microsoft bool Det namespace Cpp Var Diff initializes $$ , $comment bin/version assumes that : follows cppad version number here$$ $section cppad-20170000.3: A Package for Differentiation of C++ Algorithms $$ $mindex AD algorithmic differentiation automatic C++ algorithm derivative CppAD version cppad.hpp$$ $comment This comment is used to remove the table below$$ $table $cnext One section per web page $pre $$ $cnext All sections in one web page $rnext $cnext (fast to load) $pre $$ $cnext (slow to load) $rnext Math displayed using MathJax $pre $$ $cnext $href%cppad.htm%$$ $pre $$ $cnext $href%_printable.htm%$$ $rnext Math displayed using MathML $pre $$ $cnext $href%cppad.xml%$$ $pre $$ $cnext $href%_printable.xml%$$ $tend $head Syntax$$ $code # include $$ $head Introduction$$ We refer to the step by step conversion from an algorithm that computes function values to an algorithm that computes derivative values as $italic Algorithmic Differentiation$$ (often referred to as $italic Automatic Differentiation$$.) Given a C++ algorithm that computes function values, CppAD generates an algorithm that computes its derivative values. A brief introduction to Algorithmic Differentiation can be found in $href%http://en.wikipedia.org/wiki/Automatic_differentiation%wikipedia%$$. The web site $href%http://www.autodiff.org%autodiff.org%$$ is dedicated to research about, and promoting the use of, AD. $list number$$ $href%http://www.coin-or.org/CppAD/%CppAD%$$ uses operator overloading to compute derivatives of algorithms defined in C++. It is distributed by the $href%http://www.coin-or.org/foundation.html%COIN-OR Foundation%$$ with the Eclipse Public License $href%http://www.opensource.org/licenses/EPL-1.0%EPL-1.0%$$ or the GNU General Public License $href%http://www.opensource.org/licenses/AGPL-3.0%GPL-3.0%$$. Testing and installation is supported for Unix, Microsoft, and Apple operating systems. Extensive user and developer documentation is included. $lnext An AD of $italic Base$$ $xref/glossary/Operation/Sequence/operation sequence/1/$$ is stored as an $xref/ADFun//AD function object/$$ which can evaluate function values and derivatives. Arbitrary order $xref/Forward//forward/$$ and $xref/Reverse//reverse/$$ mode derivative calculations can be preformed on the operation sequence. Logical comparisons can be included in an operation sequence using AD $xref/CondExp//conditional expressions/$$. Evaluation of user defined unary $xref/Discrete//discrete functions/$$ can also be included in the sequence of operations; i.e., functions that depend on the $cref/independent variables/glossary/Tape/Independent Variable/$$ but which have identically zero derivatives (e.g., a step function). $lnext Derivatives of functions that are defined in terms of other derivatives can be computed using multiple levels of AD; see $cref/mul_level.cpp/$$ for a simple example and $cref/mul_level_ode.cpp/$$ for a more realistic example. To this end, CppAD can also be used with other AD types; for example see $cref/mul_level_adolc_ode.cpp/$$. $lnext A set of programs for doing $cref/speed/$$ comparisons between $href%https://projects.coin-or.org/ADOL-C%Adolc%$$, CppAD, $href%http://www.fadbad.com/%Fadbad%$$, and $href%http://trilinos.sandia.gov/packages/sacado/%Sacado%$$ are included. $lnext Includes a set of C++ $cref/utilities/utility/$$ that are useful for general operator overloaded numerical method. Allows for replacement of the $cref/testvector/$$ template vector class which is used for extensive testing; for example, you can do your testing with the $href%http://www.boost.org/libs/numeric/ublas/doc/index.htm%uBlas%$$ template vector class. $lnext See $xref/whats_new/$$ for a list of recent extensions and bug fixes. $lend You can find out about other algorithmic differentiation tools and about algorithmic differentiation in general at the following web sites: $href%http://en.wikipedia.org/wiki/Automatic_differentiation%wikipedia%$$, $href%http://www.autodiff.org%autodiff.org%$$. $head Example$$ The file $xref/get_started.cpp/$$ contains an example and test of using CppAD to compute the derivative of a polynomial. There are many other $xref/Example//examples/$$. $head Include File$$ The following include directive $syntax% # include %$$ includes the CppAD package for the rest of the current compilation unit. $head Preprocessor Symbols$$ All the $cref preprocessor$$ symbols used by CppAD begin with eight $code CppAD$$ or $code CPPAD_$$. $head Namespace$$ All of the functions and objects defined by CppAD are in the $code CppAD$$ namespace; for example, you can access the $xref/AD/$$ types as $syntax% size_t n = 2; CppAD::vector< CppAD::AD<%Base%> > %x%(%n%) %$$ You can abbreviate access to one object or function a $code using$$ command of the form $syntax% using CppAD::AD CppAD::vector< AD<%Base%> > %x%(%n%) %$$ You can abbreviate access to all CppAD objects and functions with a command of the form $syntax% using namespace CppAD vector< AD<%Base%> > %x%(%n%) %$$ If you include other namespaces in a similar manner, this can cause naming conflicts. $childtable% omh/install/install.omh% omh/introduction.omh% cppad/core/user_ad.hpp% cppad/core/ad_fun.hpp% omh/preprocessor.omh% omh/multi_thread.omh% omh/utility.omh% cppad/ipopt/solve.hpp% omh/example.omh% omh/speed/speed.omh% omh/appendix.omh %$$ $end cppad-20170000.3/doc/0002755000175200017650000000000013057470543013201 5ustar coincoin-webcppad-20170000.3/doc/_external.xml0000644000175200017650000005560313057470513015710 0ustar coincoin-web External Internet References
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External Internet References
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http://cscapes.cs.purdue.edu/dox/ColPack/html/get_colpack.sh#Purpose
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http://eigen.tuxfamily.orgauto_tools#eigen_dir
http://eigen.tuxfamily.orgcppad_eigen.hpp#Purpose
http://eigen.tuxfamily.orgwhats_new_13#04-28
http://eigen.tuxfamily.orgwhats_new_12#06-16
http://eigen.tuxfamily.org/dox/TopicCustomizingEigen.htmlwhats_new_12#07-01
http://en.wikipedia.org/wiki/Automatic_differentiationCppAD#Introduction
http://en.wikipedia.org/wiki/Automatic_differentiationCppAD#Introduction
http://list.coin-or.org/mailman/listinfo/cppadFaq#Bugs
http://list.coin-or.org/pipermail/cppad/2006-February/000020.htmlwhats_new_06#02-21
http://list.coin-or.org/pipermail/cppad/2006q4/000076.htmlwhats_new_06#12-07
http://list.coin-or.org/pipermail/cppad/2010q2/000166.htmlwhats_new_10#06-01
http://lists.fedoraproject.org/pipermail/devel/2011-January/147915.htmlwhats_new_11#01-19
http://moby.ihme.washington.edu/bradbell/cppad_mixedaddon#Name
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http://projects.coin-or.org/CppAD/browserwhats_new_05#12-05
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http://www.boost.org/libs/numeric/ublas/doc/index.htmCppAD#Introduction
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http://www.coin-or.org/CppAD/whats_new_05#12-06
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http://www.coin-or.org/download/source/CppAD/download#Monthly Versions
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http://www.fadbad.com/speed#Purpose
http://www.microsoft.com/en-us/download/confirmation.aspx?id=44914download#Windows File Extraction and Testing
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http://www.opensource.org/licenses/AGPL-3.0CppAD#Introduction
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http://www.rpm.org/max-rpm/ch-rpm-file-format.htmlwhats_new_06#11-30
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mailto:Jean-Pierre.Dussault@Usherbrooke.cawhats_new_05#02-24
mailto:magister@u.washington.eduwhats_new_04#04-19
mailto:magister@u.washington.eduwhats_new_03#10-05
cppad-20170000.3/doc/_search.xml.js0000644000175200017650000022660513057470504015750 0ustar coincoin-web// ------------------------------------------------------------ // Copyright (C) Bradley M. Bell 1998-2015, All rights reserved // ------------------------------------------------------------ Keyword = [ 'CppAD cppad-20170000.3: A Package for Differentiation of C++ Algorithms ',' algorithmic automatic derivative version cppad.hpp syntax introduction example include file preprocessor symbols namespace ', 'Install CppAD Download, Test, and Install Instructions ',' step 1: 2: cmake 3: check 4: installation ', 'download Download The CppAD Source Code ',' purpose distribution directory compressed archives current version subversion git release versions coin github monthly daily windows file extraction testing install instructions no documentation building ', 'cmake Using CMake to Configure CppAD ',' makefile install prefix postfix include directories lib datadir documentation package compile flags profile maximum number threads sparsity internal structure vector sets memory usage tape implicit explicit the program command build directory check cmake_verbose_makefile generator cppad_prefix cppad_postfix cmake_install_includedirs cmake_install_libdirs cmake_install_datadir cmake_install_docdir package_prefix cppad_cxx_flags c++11 cppad_profile_flag eigen fadbad cppad_testvector cppad_max_num_threads cppad_tape_id_type cstdint cppad_tape_addr_type cppad_deprecated ', 'adolc_prefix Including the ADOL-C Examples and Tests ',' get purpose speed unix cygwin get_adolc ', 'get_adolc.sh Download and Install Adolc in Build Directory ',' syntax purpose requirements distribution external prefix reuse ', 'colpack_prefix Including the ColPack Sparsity Calculations ',' get purpose cppad_lib example get_colpack ', 'colpack_jac.cpp Using ColPack: Example and Test ',' jacobian sparse ', 'colpack_hes.cpp Using ColPack: Example and Test ',' hessian sparse ', 'get_colpack.sh Download and Install ColPack in Build Directory ',' syntax purpose distribution external prefix reuse ', 'eigen_prefix Including the Eigen Examples and Tests ',' get purpose vector get_eigen ', 'get_eigen.sh Download and Install Eigen in Build Directory ',' syntax purpose distribution external prefix reuse ', 'fadbad_prefix Including the FADBAD Speed Tests ',' get purpose get_fadbad ', 'get_fadbad.sh Download and Install Fadbad in Build Directory ',' syntax purpose distribution external prefix ', 'ipopt_prefix Including the cppad_ipopt Library and Tests ',' get purpose examples get_ipopt ', 'get_ipopt.sh Download and Install Ipopt in Build Directory ',' syntax purpose distribution external prefix reuse ', 'sacado_prefix Including the Sacado Speed Tests ',' get purpose get_sacado ', 'get_sacado.sh Download and Install Sacado in Build Directory ',' syntax purpose distribution external prefix reuse ', 'cppad_testvector Choosing the CppAD Test Vector Template Class ',' purpose std boost eigen ', 'cmake_check Checking the CppAD Examples and Tests ',' purpose all windows subsets ', 'pkgconfig CppAD pkg-config Files ',' pc purpose usage defined fields configuration ', 'auto_tools Auto Tools Unix Test and Installation ',' speed profile prefix std vector boost eigen sparse internal sets implicit explicit compile flags openmp postfix adolc fadbad ipopt sacado memory usage tape deprecated 2012-12-26 distribution directory work configure make examples tests profiling cppad prefix_dir --with-documentation --with-testvector --with-deprecated max_num_threads cxx_flags openmp_flags postfix_dir adolc_dir linux cygwin boost_dir eigen_dir fadbad_dir ipopt_dir sacado_dir tape_addr_type tape_id_type ', 'Introduction An Introduction by Example to Algorithmic Differentiation ',' ad automatic purpose preface forward mode reverse operation count efficiency outline reference ', 'get_started.cpp Getting Started Using CppAD to Compute Derivatives ',' simple example purpose function value poly exercises program output running ', 'exp_2 Second Order Exponential Approximation ',' example algorithm syntax purpose mathematical form include type implementation test exercises ', 'exp_2.hpp exp_2: Implementation ',' ', 'exp_2.cpp exp_2: Test ',' ', 'exp_2_for0 exp_2: Operation Sequence and Zero Order Forward Mode ',' example mathematical form expansion index code sweep return value verification exercises ', 'exp_2_for1 exp_2: First Order Forward Mode ',' expansion purpose mathematical form operation sequence index zero derivative sweep return value verification exercises ', 'exp_2_rev1 exp_2: First Order Reverse Mode ',' purpose mathematical form f_5 index 5: f_4 4: f_3 3: f_2 f_1 verification exercises ', 'exp_2_for2 exp_2: Second Order Forward Mode ',' expansion purpose mathematical form operation sequence index zero first derivative sweep return value verification exercises ', 'exp_2_rev2 exp_2: Second Order Reverse Mode ',' purpose mathematical form f_5 index 5: f_4 4: f_3 3: f_2 f_1 verification exercises ', 'exp_2_for0.cpp exp_2: Verify Zero Order Forward Sweep ',' ', 'exp_2_for1.cpp exp_2: Verify First Order Forward Sweep ',' ', 'exp_2_rev1.cpp exp_2: Verify First Order Reverse Sweep ',' mode ', 'exp_2_for2.cpp exp_2: Verify Second Order Forward Sweep ',' ', 'exp_2_rev2.cpp exp_2: Verify Second Order Reverse Sweep ',' mode ', 'exp_2_cppad exp_2: CppAD Forward and Reverse Sweeps ',' purpose exercises ', 'exp_eps An Epsilon Accurate Exponential Approximation ',' example algorithm syntax purpose mathematical function include type implementation test exercises ', 'exp_eps.hpp exp_eps: Implementation ',' ', 'exp_eps.cpp exp_eps: Test of exp_eps ',' ', 'exp_eps_for0 exp_eps: Operation Sequence and Zero Order Forward Sweep ',' example mathematical form variable parameter index code return value comparisons verification exercises ', 'exp_eps_for1 exp_eps: First Order Forward Sweep ',' expansion mathematical form operation sequence index zero derivative return value verification exercises ', 'exp_eps_rev1 exp_eps: First Order Reverse Sweep ',' mode purpose mathematical form epsilon f_7 index 7: f_6 6: f_5 5: f_4 4: f_3 3: f_2 2: f_1 verification exercises ', 'exp_eps_for2 exp_eps: Second Order Forward Mode ',' expansion purpose mathematical form operation sequence index zero first derivative sweep return value verification exercises ', 'exp_eps_rev2 exp_eps: Second Order Reverse Sweep ',' purpose mathematical form epsilon f_7 index 7: f_6 6: f_5 5: f_4 4: f_3 3: f_2 2: f_1 verification exercises ', 'exp_eps_for0.cpp exp_eps: Verify Zero Order Forward Sweep ',' ', 'exp_eps_for1.cpp exp_eps: Verify First Order Forward Sweep ',' exp_2 ', 'exp_eps_rev1.cpp exp_eps: Verify First Order Reverse Sweep ',' ', 'exp_eps_for2.cpp exp_eps: Verify Second Order Forward Sweep ',' first exp_2 ', 'exp_eps_rev2.cpp exp_eps: Verify Second Order Reverse Sweep ',' ', 'exp_eps_cppad exp_eps: CppAD Forward and Reverse Sweeps ',' purpose exercises ', 'exp_apx_main.cpp Correctness Tests For Exponential Approximation in Introduction ',' run running ', 'AD AD Objects ',' require purpose base type requirements ', 'ad_ctor AD Constructors ',' convert base vecad syntax purpose implicit explicit deprecated 2013-12-31 example ', 'ad_ctor.cpp AD Constructors: Example and Test ',' object ', 'ad_assign AD Assignment Operator ',' base vecad syntax purpose example ', 'ad_assign.cpp AD Assignment: Example and Test ',' object ', 'Convert Conversion and I/O of AD Objects ',' from ', 'Value Convert From an AD Type to its Base Type ',' syntax see also purpose operation sequence restriction example ', 'value.cpp Convert From AD to its Base Type: Example and Test ',' record ', 'Integer Convert From AD to Integer ',' syntax purpose real types complex operation sequence example ', 'integer.cpp Convert From AD to Integer: Example and Test ',' ', 'ad_to_string Convert An AD or Base Type to String ',' syntax see also value example ', 'ad_input AD Output Stream Operator ',' >> write syntax purpose is result operation sequence example ', 'ad_output AD Output Stream Operator ',' << syntax purpose assumption result operation sequence example ', 'ad_input.cpp AD Output Operator: Example and Test ',' << ', 'ad_output.cpp AD Output Operator: Example and Test ',' << ', 'PrintFor Printing AD Values During Forward Mode ',' text output debug syntax purpose f.forward(0 x) before var after redirecting discussion alternative example ', 'print_for_cout.cpp Printing During Forward Mode: Example and Test ',' running source code output ', 'print_for_string.cpp Print During Zero Order Forward Mode: Example and Test ',' ', 'Var2Par Convert an AD Variable to a Parameter ',' from value_ obtain during taping syntax see also purpose example ', 'var2par.cpp Convert an AD Variable to a Parameter: Example and Test ',' value during taping ', 'ADValued AD Valued Operations and Functions ',' ', 'Arithmetic AD Arithmetic Operators and Computed Assignments ',' ', 'UnaryPlus AD Unary Plus Operator ',' + syntax purpose operation sequence derivative example ', 'unary_plus.cpp AD Unary Plus Operator: Example and Test ',' ', 'UnaryMinus AD Unary Minus Operator ',' - syntax purpose base operation sequence derivative example ', 'unary_minus.cpp AD Unary Minus Operator: Example and Test ',' ', 'ad_binary AD Binary Arithmetic Operators ',' + add plus - subtract minus * multiply times / divide syntax purpose base z operation sequence example derivative addition subtraction multiplication division ', 'add.cpp AD Binary Addition: Example and Test ',' + plus ', 'sub.cpp AD Binary Subtraction: Example and Test ',' - minus ', 'mul.cpp AD Binary Multiplication: Example and Test ',' * multiply times ', 'div.cpp AD Binary Division: Example and Test ',' / divide quotient ', 'compute_assign AD Computed Assignment Operators ',' + add plus - subtract minus * multiply times / divide multiple syntax purpose base result operation sequence example derivative addition subtraction multiplication division ', 'AddEq.cpp AD Computed Assignment Addition: Example and Test ',' += plus ', 'sub_eq.cpp AD Computed Assignment Subtraction: Example and Test ',' -= plus add ', 'mul_eq.cpp AD Computed Assignment Multiplication: Example and Test ',' *= multiply plus add ', 'div_eq.cpp AD Computed Assignment Division: Example and Test ',' /= divide plus add ', 'unary_standard_math The Unary Standard Math Functions ',' syntax purpose possible types base ad vecad ', 'binary_math The Binary Math Functions ',' ', 'acos Inverse Sine Function: acos ',' syntax atomic derivative example ', 'asin Inverse Sine Function: asin ',' syntax atomic derivative example ', 'atan Inverse Tangent Function: atan ',' syntax atomic derivative example ', 'cos The Cosine Function: cos ',' syntax atomic derivative example ', 'cosh The Hyperbolic Cosine Function: cosh ',' syntax atomic derivative example ', 'exp The Exponential Function: exp ',' syntax atomic derivative example ', 'log The Exponential Function: log ',' syntax atomic derivative example ', 'log10 The Base 10 Logarithm Function: log10 ',' syntax method example ', 'sin The Sine Function: sin ',' syntax atomic derivative example ', 'sinh The Hyperbolic Sine Function: sinh ',' syntax atomic derivative example ', 'sqrt The Square Root Function: sqrt ',' syntax atomic derivative example ', 'tan The Tangent Function: tan ',' syntax atomic derivative example ', 'tanh The Hyperbolic Tangent Function: tanh ',' syntax atomic derivative example ', 'acos.cpp The AD acos Function: Example and Test ',' ', 'asin.cpp The AD asin Function: Example and Test ',' ', 'atan.cpp The AD atan Function: Example and Test ',' ', 'cos.cpp The AD cos Function: Example and Test ',' ', 'cosh.cpp The AD cosh Function: Example and Test ',' ', 'exp.cpp The AD exp Function: Example and Test ',' ', 'log.cpp The AD log Function: Example and Test ',' ', 'log10.cpp The AD log10 Function: Example and Test ',' ', 'sin.cpp The AD sin Function: Example and Test ',' ', 'sinh.cpp The AD sinh Function: Example and Test ',' ', 'sqrt.cpp The AD sqrt Function: Example and Test ',' ', 'tan.cpp The AD tan Function: Example and Test ',' ', 'tanh.cpp The AD tanh Function: Example and Test ',' ', 'abs AD Absolute Value Functions: abs, fabs ',' syntax atomic complex types derivative example ', 'abs.cpp AD Absolute Value Function: Example and Test ',' fabs ', 'acosh The Inverse Hyperbolic Cosine Function: acosh ',' syntax description cppad_use_cplusplus_2011 true false example ', 'acosh.cpp The AD acosh Function: Example and Test ',' ', 'asinh The Inverse Hyperbolic Sine Function: asinh ',' syntax description cppad_use_cplusplus_2011 true false example ', 'asinh.cpp The AD asinh Function: Example and Test ',' ', 'atanh The Inverse Hyperbolic Tangent Function: atanh ',' syntax description cppad_use_cplusplus_2011 true false example ', 'atanh.cpp The AD atanh Function: Example and Test ',' ', 'erf The Error Function ',' syntax description cppad_use_cplusplus_2011 true false example ', 'erf.cpp The AD erf Function: Example and Test ',' ', 'expm1 The Exponential Function Minus One: expm1 ',' syntax description cppad_use_cplusplus_2011 true false example ', 'expm1.cpp The AD exp Function: Example and Test ',' ', 'log1p The Logarithm of One Plus Argument: log1p ',' syntax description cppad_use_cplusplus_2011 true false example ', 'log1p.cpp The AD log1p Function: Example and Test ',' ', 'sign The Sign: sign ',' syntax description atomic derivative example ', 'sign.cpp Sign Function: Example and Test ',' ', 'atan2 AD Two Argument Inverse Tangent Function ',' syntax purpose theta operation sequence example ', 'atan2.cpp The AD atan2 Function: Example and Test ',' ', 'pow The AD Power Function ',' exponent syntax see also purpose z operation sequence example ', 'pow.cpp The AD Power Function: Example and Test ',' ', 'azmul Absolute Zero Multiplication ',' syntax purpose base ad vecad example ', 'azmul.cpp AD Absolute Zero Multiplication: Example and Test ',' ', 'CondExp AD Conditional Expressions ',' assign syntax purpose rel type left right if_true if_false result optimize deprecate 2005-08-07 operation sequence example test atan2 ', 'cond_exp.cpp Conditional Expressions: Example and Test ',' see also description ', 'Discrete Discrete AD Functions ',' cppad_discrete_function syntax purpose base name ay create version operation sequence derivatives parallel mode example cppadcreatediscrete deprecated 2007-07-28 ', 'tape_index.cpp Taping Array Index Operation: Example and Test ',' ', 'interp_onetape.cpp Interpolation With Out Retaping: Example and Test ',' interpolate retape see also ', 'interp_retape.cpp Interpolation With Retaping: Example and Test ',' interpolate see also ', 'numeric_limits Numeric Limits For an AD and Base Types ',' syntax cppad::numeric_limits std::numeric_limits float epsilon min max quiet_nan example ', 'num_limits.cpp Numeric Limits: Example and Test ',' ', 'atomic Atomic AD Functions ',' operation ', 'checkpoint Checkpointing Functions ',' syntax see also purpose reduce memory faster recording repeating forward restriction multiple level ad method constructor base advector name ay sparsity optimize size_var option algo atom_fun clear example ', 'checkpoint.cpp Simple Checkpointing: Example and Test ',' purpose ', 'atomic_mul_level.cpp Atomic Operations and Multiple-Levels of AD: Example and Test ',' discussion ', 'checkpoint_ode.cpp Checkpointing an ODE Solver: Example and Test ',' see also purpose problem solution ', 'checkpoint_extended_ode.cpp Checkpointing an Extended ODE Solver: Example and Test ',' mul_level see also discussion problem solution ', 'atomic_base User Defined Atomic AD Functions ',' syntax purpose virtual examples getting started scalar vector range hessian sparsity patterns general case ', 'atomic_ctor Atomic Function Constructor ',' syntax atomic_user ctor_arg_list afun implementation atomic_base restrictions name sparsity example define ', 'atomic_option Set Atomic Function Options ',' syntax atomic_sparsity pack_sparsity_enum bool_sparsity_enum set_sparsity_enum ', 'atomic_afun Using AD Version of Atomic Function ',' syntax purpose advector ay examples ', 'atomic_forward Atomic Forward Mode ',' callback virtual syntax purpose implementation q vx vy tx ty ok discussion examples ', 'atomic_reverse Atomic Reverse Mode ',' syntax purpose implementation q tx ty f g h py px ok examples ', 'atomic_for_sparse_jac Atomic Forward Jacobian Sparsity Patterns ',' syntax deprecated 2016-06-27 purpose implementation q ok examples ', 'atomic_rev_sparse_jac Atomic Reverse Jacobian Sparsity Patterns ',' syntax deprecated 2016-06-27 purpose implementation q rt st ok examples ', 'atomic_for_sparse_hes Atomic Forward Hessian Sparsity Patterns ',' syntax deprecated 2016-06-27 purpose implementation vx examples ', 'atomic_rev_sparse_hes Atomic Reverse Hessian Sparsity Patterns ',' syntax deprecated 2016-06-27 purpose implementation vx q examples ', 'atomic_base_clear Free Static Variables ',' syntax purpose future use restriction ', 'atomic_forward.cpp Atomic Forward: Example and Test ',' purpose function start class definition constructor use ', 'atomic_reverse.cpp Atomic Reverse: Example and Test ',' purpose function start class definition constructor forward use ', 'atomic_for_sparse_jac.cpp Atomic Forward Jacobian Sparsity: Example and Test ',' purpose function start class definition constructor use with x_1 both variable parameter ', 'atomic_rev_sparse_jac.cpp Atomic Reverse Jacobian Sparsity: Example and Test ',' purpose function start class definition constructor forward use with x_1 both variable parameter ', 'atomic_for_sparse_hes.cpp Atomic Forward Hessian Sparsity: Example and Test ',' purpose function start class definition constructor for_sparse_jac rev_sparse_jac use with x_1 both variable parameter ', 'atomic_rev_sparse_hes.cpp Atomic Reverse Hessian Sparsity: Example and Test ',' purpose function start class definition constructor forward for_sparse_jac rev_sparse_jac use with x_1 both variable parameter ', 'atomic_get_started.cpp Getting Started with Atomic Operations: Example and Test ',' purpose class definition constructor forward end use function recording ', 'atomic_norm_sq.cpp Atomic Euclidean Norm Squared: Example and Test ',' bool_sparsity_enum theory start class definition constructor forward reverse for_sparse_jac rev_sparse_jac rev_sparse_hes end use function recording ', 'atomic_reciprocal.cpp Reciprocal as an Atomic Operation: Example and Test ',' set_sparsity_enum theory start class definition constructor forward reverse for_sparse_jac rev_sparse_jac rev_sparse_hes end use function recording ', 'atomic_set_sparsity.cpp Atomic Sparsity with Set Patterns: Example and Test ',' function set_sparsity_enum start class definition constructor forward for_sparse_jac rev_sparse_jac for_sparse_hes rev_sparse_hes end recording result ', 'atomic_tangent.cpp Tan and Tanh as User Atomic Operations: Example and Test ',' theory sparsity start class definition constructor forward reverse for_sparse_jac rev_sparse_jac rev_sparse_hes end function recording large values ', 'atomic_eigen_mat_mul.cpp Atomic Eigen Matrix Multiply: Example and Test ',' description class definition use function constructor ', 'atomic_eigen_mat_mul.hpp Atomic Eigen Matrix Multiply Class ',' see also purpose dimensions theory forward product two matrices reverse start definition public types constructor op private variables for_sparse_jac rev_sparse_jac for_sparse_hes rev_sparse_hes end ', 'atomic_eigen_mat_inv.cpp Atomic Eigen Matrix Inverse: Example and Test ',' description class definition use function constructor ', 'atomic_eigen_mat_inv.hpp Atomic Eigen Matrix Inversion Class ',' purpose dimensions theory forward product three matrices reverse start definition public types constructor op private variables end ', 'atomic_eigen_cholesky.cpp Atomic Eigen Cholesky Factorization: Example and Test ',' description use function constructor ', 'cholesky_theory AD Theory for Cholesky Factorization ',' reference notation taylor coefficient lower triangular part forward mode lemma 1 proof 2 reverse case = 0 > ', 'atomic_eigen_cholesky.hpp Atomic Eigen Cholesky Factorization Class ',' purpose start definition public types constructor op private variables forward reverse end ', 'atomic_mat_mul.cpp User Atomic Matrix Multiply: Example and Test ',' see also class definition function constructor recording forward reverse option for_sparse_jac rev_sparse_jac rev_sparse_hes ', 'atomic_mat_mul.hpp Matrix Multiply as an Atomic Operation ',' see also dimensions start class definition constructor left operand element index right result forward reverse for_sparse_jac rev_sparse_jac rev_sparse_hes end ', 'BoolValued Bool Valued Operations and Functions with AD Arguments ',' ', 'Compare AD Binary Comparison Operators ',' < <= > >= == != syntax purpose operation sequence assumptions example ', 'compare.cpp AD Binary Comparison Operators: Example and Test ',' < <= > >= == != ', 'NearEqualExt Compare AD and Base Objects for Nearly Equal ',' with syntax purpose type operation sequence example ', 'near_equal_ext.cpp Compare AD with Base Objects: Example and Test ',' nearequalext ', 'BoolFun AD Boolean Functions ',' cppad_bool_unary cppad_bool_binary syntax purpose unary_name create binary_name v operation sequence example deprecated 2007-07-31 ', 'bool_fun.cpp AD Boolean Functions: Example and Test ',' ', 'ParVar Is an AD Object a Parameter or Variable ',' syntax purpose operation sequence example ', 'par_var.cpp AD Parameter and Variable Functions: Example and Test ',' ', 'EqualOpSeq Check if Two Value are Identically Equal ',' operation sequence syntax purpose motivation b example ', 'equal_op_seq.cpp EqualOpSeq: Example and Test ',' ', 'VecAD AD Vectors that Record Index Operations ',' tape reference vecad syntax purpose alternatives vecad::reference exceptions constructor size size_t indexing example speed memory ', 'vec_ad.cpp AD Vectors that Record Index Operations: Example and Test ',' vecad ', 'base_require AD Requirements for a CppAD Base Type ',' syntax purpose api warning standard types include order numeric output operator integer suggestion absolute zero azmul ', 'base_member Required Base Class Member Functions ',' notation default constructor double copy unary operators assignment binary bool example ', 'base_cond_exp Base Type Requirements for Conditional Expressions ',' condexp cppad_cond_exp_rel purpose compareop condexptemplate ordered not condexprel ', 'base_identical Base Type Requirements for Identically Equal Comparisons ',' equalopseq the simple case more complicated cases identicalpar prototypes functions examples ', 'base_ordered Base Type Requirements for Ordered Comparisons ',' purpose not ', 'base_std_math Base Type Requirements for Standard Math Functions ',' purpose unary cppad_standard_math_unary erf asinh acosh atanh expm1 log1p sign pow isnan ', 'base_limits Base Type Requirements for Numeric Limits ',' cppad::numeric_limits cppad_numeric_limits ', 'base_to_string Extending to_string To Another Floating Point Type ',' requirement cppad_to_string ', 'base_hash Base Type Requirements for Hash Coding Values ',' syntax purpose default code inline example ', 'base_example Example AD Base Types That are not AD ',' ', 'base_alloc.hpp Example AD Where Base Constructor Allocates Memory ',' purpose include file computed assignment macro binary operator boolean class definition condexpop condexprel equalopseq identical output integer azmul ordered unary standard math erf asinh acosh atanh expm1 log1p pow numeric_limits to_string hash_code ', 'base_require.cpp Using a User Defined AD Base Type: Example and Test ',' purpose ', 'base_adolc.hpp Enable use of AD where Base is Adolc\'s adouble Type ',' syntax example include files condexpop condexprel equalopseq identical integer azmul ordered unary standard math erf asinh acosh atanh expm1 log1p sign abs pow numeric_limits to_string hash_code ', 'mul_level_adolc.cpp Using Adolc with Multiple Levels of Taping: Example and Test ',' purpose memory management configuration requirement source ', 'base_float.hpp Enable use of AD where Base is float ',' condexpop condexprel equalopseq identical integer azmul ordered unary standard math sign pow numeric_limits to_string ', 'base_double.hpp Enable use of AD where Base is double ',' condexpop condexprel equalopseq identical integer azmul ordered unary standard math sign pow numeric_limits to_string ', 'base_complex.hpp Enable use of AD where Base is std::complex ',' example include order condexpop condexprel equalopseq identical ordered integer azmul isnan valid unary math invalid pow numeric_limits to_string ', 'complex_poly.cpp Complex Polynomial: Example and Test ',' ', 'ADFun ADFun Objects ',' purpose ', 'Independent Declare Independent Variables and Start Recording ',' syntax purpose stop abort_op_index vectorad parallel mode example ', 'independent.cpp Independent and ADFun Constructor: Example and Test ',' ', 'FunConstruct Construct an ADFun Object and Stop Recording ',' tape syntax purpose vectorad default constructor sequence copy assignment operator taylor coefficients sparsity patterns parallel mode example ', 'fun_assign.cpp ADFun Assignment: Example and Test ',' ', 'Dependent Stop Recording and Store Operation Sequence ',' adfun tape syntax purpose advector taping forward parallel mode example ', 'abort_recording Abort Recording of an Operation Sequence ',' tape syntax purpose example ', 'abort_recording.cpp Abort Current Recording: Example and Test ',' ', 'seq_property ADFun Sequence Properties ',' syntax see also purpose domain range parameter size_var size_par size_op size_op_arg size_text size_vecad size_op_seq example ', 'seq_property.cpp ADFun Sequence Properties: Example and Test ',' domain range parameter size_var size_par size_op_arg size_vecad ', 'FunEval Evaluate ADFun Functions, Derivatives, and Sparsity Patterns ',' ', 'Forward Forward Mode ',' ', 'forward_zero Zero Order Forward Mode: Function Values ',' syntax purpose x0 y0 vector example special case ', 'forward_one First Order Forward Mode: Derivative Values ',' syntax purpose x0 x1 vector example special case ', 'forward_two Second Order Forward Mode: Derivative Values ',' syntax purpose x0 x1 x2 y2 vector example special case ', 'forward_order Multiple Order Forward Mode ',' any syntax purpose function values derivative notation one q xq orders restrictions x(t) y(t) yq vector zero first second example ', 'forward.cpp Forward Mode: Example and Test ',' ', 'forward_order.cpp Forward Mode: Example and Test of Multiple Orders ',' ', 'forward_dir Multiple Directions Forward Mode ',' syntax purpose reverse notation q xq zero order non-zero lower orders x(t) y(t) yq vector example ', 'forward_dir.cpp Forward Mode: Example and Test of Multiple Directions ',' orders ', 'size_order Number Taylor Coefficient Orders Currently Stored ',' syntax see also purpose constructor forward capacity_order example ', 'compare_change Comparison Changes Between Taping and Zero Order Forward ',' adfun syntax purpose count speed number discussion op_index example ', 'compare_change.cpp CompareChange and Re-Tape: Example and Test ',' ', 'capacity_order Controlling Taylor Coefficients Memory Allocation ',' forward syntax see also purpose pre-allocating freeing original state example ', 'capacity_order.cpp Controlling Taylor Coefficient Memory Allocation: Example and Test ',' ', 'number_skip Number of Variables that Can be Skipped ',' syntax see also purpose example ', 'number_skip.cpp Number of Variables That Can be Skipped: Example and Test ',' optimize conditional expression ', 'Reverse Reverse Mode ',' multiple directions ', 'reverse_one First Order Reverse Mode ',' derivative syntax purpose w dw vector example ', 'reverse_one.cpp First Order Reverse Mode: Example and Test ',' ', 'reverse_two Second Order Reverse Mode ',' derivative syntax purpose x^(k) f dw first partials vector hessian times direction example ', 'reverse_two.cpp Second Order Reverse ModeExample and Test ',' ', 'hes_times_dir.cpp Hessian Times Direction: Example and Test ',' ', 'reverse_any Any Order Reverse Mode ',' derivative syntax purpose notation u^(k) x(t u) y(t w^(k) w(u) f q dw first second vector example ', 'reverse_three.cpp Third Order Reverse Mode: Example and Test ',' taylor coefficients ', 'reverse_checkpoint.cpp Reverse Mode General Case (Checkpointing): Example and Test ',' see also purpose processing steps ', 'Sparse Calculating Sparsity Patterns ',' ', 'ForSparseJac Jacobian Sparsity Pattern: Forward Mode ',' syntax purpose size_forward_bool size_forward_set q transpose dependency false true vectorset entire example ', 'for_sparse_jac.cpp Forward Mode Jacobian Sparsity: Example and Test ',' forsparsejac ', 'RevSparseJac Jacobian Sparsity Pattern: Reverse Mode ',' syntax purpose f q transpose dependency false true vectorset entire example ', 'rev_sparse_jac.cpp Reverse Mode Jacobian Sparsity: Example and Test ',' revsparsejac ', 'dependency.cpp Computing Dependency: Example and Test ',' discussion pattern ', 'RevSparseHes Hessian Sparsity Pattern: Reverse Mode ',' syntax purpose f q transpose false true vectorset entire example ', 'rev_sparse_hes.cpp Reverse Mode Hessian Sparsity: Example and Test ',' revsparsehes ', 'sparsity_sub.cpp Sparsity Patterns For a Subset of Variables: Example and Test ',' see also forsparsejac revsparsehes ', 'ForSparseHes Hessian Sparsity Pattern: Forward Mode ',' syntax purpose vectorset algorithm example ', 'for_sparse_hes.cpp Forward Mode Hessian Sparsity: Example and Test ',' forsparsehes ', 'bool_sparsity.cpp Using vectorBool Sparsity To Conserve Memory: Example and Test ',' purpose ', 'Drivers First and Second Derivatives: Easy Drivers ',' forward reverse ', 'Jacobian Jacobian: Driver Routine ',' first derivative syntax purpose vector forward reverse example ', 'jacobian.cpp Jacobian: Example and Test ',' ', 'ForOne First Order Partial Derivative: Driver Routine ',' easy syntax purpose j dy vector uses forward example ', 'for_one.cpp First Order Partial Driver: Example and Test ',' ', 'RevOne First Order Derivative: Driver Routine ',' easy syntax purpose dw vector uses forward example ', 'rev_one.cpp First Order Derivative Driver: Example and Test ',' ', 'Hessian Hessian: Easy Driver ',' second derivative syntax purpose f l w vector uses forward example ', 'hessian.cpp Hessian: Example and Test ',' ', 'hes_lagrangian.cpp Hessian of Lagrangian and ADFun Default Constructor: Example and Test ',' heslagrangian ', 'ForTwo Forward Mode Second Partial Derivative Driver ',' order easy syntax purpose j k ddy vectorbase vectorsize_t uses examples ', 'for_two.cpp Subset of Second Order Partials: Example and Test ',' ', 'RevTwo Reverse Mode Second Partial Derivative Driver ',' order easy syntax purpose f j ddw vectorbase vectorsize_t uses forward examples ', 'rev_two.cpp Second Partials Reverse Driver: Example and Test ',' ', 'sparse_jacobian Sparse Jacobian: Easy Driver ',' sparsejacobian syntax purpose f row col work color_method n_sweep vectorbase vectorset restrictions vectorsize uses forward example ', 'sparse_jacobian.cpp Sparse Jacobian: Example and Test ',' spare ', 'sparse_hessian Sparse Hessian: Easy Driver ',' sparsehessian syntax purpose f w work column subset row color_method n_sweep vectorbase vectorset restrictions vectorsize uses forward example ', 'sparse_hessian.cpp Sparse Hessian: Example and Test ',' spare ', 'sub_sparse_hes.cpp Computing Sparse Hessian for a Subset of Variables ',' purpose see also function example ', 'sparse_sub_hes.cpp Sparse Hessian on Subset of Variables: Example and Test ',' purpose see also ', 'FunCheck Check an ADFun Sequence of Operations ',' syntax purpose g ok vector uses forward discussion example ', 'fun_check.cpp ADFun Check and Re-Tape: Example and Test ',' funcheck dependent ', 'optimize Optimize an ADFun Object Tape ',' sequence operations speed memory ndebug syntax purpose options no_conditional_skip no_compare_op no_print_for_op examples efficiency testing atomic functions rev_sparse_jac nan checking optimization ', 'optimize_forward_active.cpp Example Optimization and Forward Activity Analysis ',' ', 'optimize_reverse_active.cpp Example Optimization and Reverse Activity Analysis ',' ', 'optimize_compare_op.cpp Example Optimization and Comparison Operators ',' see also ', 'optimize_print_for.cpp Example Optimization and Print Forward Operators ',' ', 'optimize_conditional_skip.cpp Example Optimization and Conditional Expressions ',' see also ', 'optimize_nest_conditional.cpp Example Optimization and Nested Conditional Expressions ',' see also ', 'optimize_cumulative_sum.cpp Example Optimization and Cumulative Sum Operations ',' ', 'check_for_nan Check an ADFun Object For Nan Results ',' syntax debugging default error message vector_size file_name index get_check_for_nan example ', 'check_for_nan.cpp ADFun Checking For Nan: Example and Test ',' ', 'preprocessor CppAD API Preprocessor Symbols ',' cppad_ null pointer purpose documented here cppad_null cppad_package_string cppad_use_cplusplus_2011 elsewhere deprecated ', 'multi_thread Using CppAD in a Multi-Threading Environment ',' mode execution maximum number purpose cppad_max_num_threads parallel_setup hold_memory initialization same prohibited ', 'parallel_ad Enable AD Calculations During Parallel Mode ',' syntax purpose discussion checksimplevector example restriction ', 'thread_test.cpp Run Multi-Threading Examples and Speed Tests ',' openmp pthread bthread syntax running purpose a11c simple_ad team_example harmonic test_time max_threads mega_sum multi_newton num_zero num_sub num_sum use_ad implementations source ', 'a11c_openmp.cpp A Simple OpenMP Example and Test ',' a.1.1c thread purpose source code ', 'a11c_bthread.cpp A Simple Boost Thread Example and Test ',' a.1.1c purpose source code ', 'a11c_pthread.cpp A Simple Parallel Pthread Example and Test ',' openmp a.1.1c purpose source code ', 'simple_ad_openmp.cpp A Simple OpenMP AD: Example and Test ',' purpose source code ', 'simple_ad_bthread.cpp A Simple Boost Threading AD: Example and Test ',' purpose source code ', 'simple_ad_pthread.cpp A Simple pthread AD: Example and Test ',' purpose source code ', 'team_example.cpp Using a Team of AD Threads: Example and Test ',' purpose thread_team source code ', 'harmonic.cpp Multi-Threaded Implementation of Summation of 1/i ',' multi_thread syntax ok num_sum num_threads source ', 'harmonic_time.cpp Timing Test of Multi-Threaded Summation of 1/i ',' multi_thread speed syntax purpose ok time_out test_time num_threads mega_sum source ', 'harmonic_work.cpp Multi-threading Sum of 1/i Utility Routines ',' setup worker combine syntax purpose harmonic_setup num_sum num_threads harmonic_worker harmonic_combine source ', 'multi_newton.cpp A Multi-Threaded Newton\'s Method ',' threading multi-threading syntax purpose ok xout fun num_sub xlow xup epsilon max_itr num_threads source ', 'multi_newton_time.cpp Timing Test of Multi-Threaded Newton Method ',' multi_thread speed syntax purpose ok time_out test_time num_threads num_zero num_sub num_sum use_ad source ', 'multi_newton_work.cpp Multi-threading Newton Method Utility Routines ',' setup worker combine syntax purpose multi_newton_setup fun num_sub xlow xup epsilon max_itr num_threads multi_newton_worker multi_newton_combine xout source ', 'team_thread.hpp Specifications for A Team of AD Threads ',' syntax purpose restrictions team_create team_work team_destroy team_name ok example use implementation speed test source ', 'team_openmp.cpp OpenMP Implementation of a Team of AD Threads ',' ', 'team_bthread.cpp Boost Thread Implementation of a Team of AD Threads ',' ', 'team_pthread.cpp Pthread Implementation of a Team of AD Threads ',' pthread_exit bug cygwin ', 'utility Some General Purpose Utilities ',' testing c++ concepts numerical routines miscellaneous error handler simple vector template class multi-threading memory allocation sorting indices to_string set_union ', 'ErrorHandler Replacing the CppAD Error Handler ',' replace assert exception syntax constructor parallel mode call info known line file exp msg example ', 'error_handler.cpp Replacing The CppAD Error Handler: Example and Test ',' ', 'cppad_assert CppAD Assertions During Execution ',' macro cppad_assert_known cppad_assert_unknown syntax purpose ndebug restriction exp msg error handler ', 'NearEqual Determine if Two Values Are Nearly Equal ',' absolute difference relative syntax purpose type include files example exercise ', 'near_equal.cpp NearEqual Function: Example and Test ',' file name ', 'speed_test Run One Speed Test and Return Results ',' syntax purpose motivation include vector size repeat size_vec time_min rate_vec timing example ', 'SpeedTest Run One Speed Test and Print Results ',' syntax purpose motivation include size repeat name first last rate errors example ', 'speed_test.cpp speed_test: Example and test ',' ', 'speed_program.cpp Example Use of SpeedTest ',' running this output ', 'time_test Determine Amount of Time to Execute a Test ',' speed syntax purpose motivation include size repeat time_min test_size timing example ', 'elapsed_seconds Returns Elapsed Number of Seconds ',' time syntax purpose microsoft systems example ', 'elapsed_seconds.cpp Elapsed Seconds: Example and Test ',' timer ', 'time_test.cpp time_test: Example and test ',' ', 'NumericType Definition of a Numeric Type ',' int requirements default constructor from integer copy assignment operators example exercise ', 'numeric_type.cpp The NumericType: Example and Test ',' ', 'CheckNumericType Check NumericType Class Concept ',' syntax purpose include parallel mode example ', 'check_numeric_type.cpp The CheckNumericType Function: Example and Test ',' ', 'SimpleVector Definition of a Simple Vector ',' value_type [] ndebug template class requirements elements specified default constructor sizing copy destructor assignment size resize access using example exercise ', 'simple_vector.cpp Simple Vector Template Class: Example and Test ',' ', 'CheckSimpleVector Check Simple Vector Concept ',' syntax purpose restrictions include parallel mode example ', 'check_simple_vector.cpp The CheckSimpleVector Function: Example and Test ',' ', 'nan Obtain Nan or Determine if a Value is Nan ',' syntax purpose include macros isnan hasnan nan(zero) deprecated 2015-10-04 scalar vector example ', 'nan.cpp nan: Example and Test ',' ', 'pow_int The Integer Power Function ',' exponent syntax see also purpose include z type operation sequence example ', 'pow_int.cpp The Pow Integer Exponent: Example and Test ',' ', 'Poly Evaluate a Polynomial or its Derivative ',' template syntax description include k z type operations vector sequence example source ', 'poly.cpp Polynomial Evaluation: Example and Test ',' ', 'poly.hpp Source: Poly ',' ', 'LuDetAndSolve Compute Determinants and Solve Equations by LU Factorization ',' matrix linear ', 'LuSolve Compute Determinant and Solve Linear Equations ',' syntax description include factor invert matrix storage signdet b logdet float floatvector leqzero absgeq example source ', 'lu_solve.cpp LuSolve With Complex Arguments: Example and Test ',' ', 'lu_solve.hpp Source: LuSolve ',' ', 'LuFactor LU Factorization of A Square Matrix ',' linear equation solve syntax description include storage sign jp determinant sizevector floatvector absgeq example source ', 'lu_factor.cpp LuFactor: Example and Test ',' ', 'lu_factor.hpp Source: LuFactor ',' ', 'LuInvert Invert an LU Factored Equation ',' linear syntax description include matrix storage jp example source ', 'lu_invert.cpp LuInvert: Example and Test ',' ', 'lu_invert.hpp Source: LuInvert ',' ', 'RombergOne One DimensionalRomberg Integration ',' integrate syntax description include f float example source code ', 'romberg_one.cpp One Dimensional Romberg Integration: Example and Test ',' ', 'RombergMul Multi-dimensional Romberg Integration ',' integrate syntax description include f float floatvector example source code ', 'Rombergmul.cpp One Dimensional Romberg Integration: Example and Test ',' ', 'Runge45 An Embedded 4th and 5th Order Runge-Kutta ODE Solver ',' differential equation syntax purpose operation sequence include xf fun warning tf xi scalar fabs vector parallel mode example source code ', 'runge45_1.cpp Runge45: Example and Test ',' ', 'runge45_2.cpp Runge45: Example and Test ',' ', 'Rosen34 A 3rd and 4th Order Rosenbrock ODE Solver ',' stiff differential equation syntax description include xf fun f_t f_x nan warning optimization tf xi scalar vector parallel mode example source code ', 'rosen_34.cpp Rosen34: Example and Test ',' ', 'OdeErrControl An Error Controller for ODE Solvers ',' differential equation syntax description include notation xf method step nan order tf xi smin smax scur eabs erel ef maxabs nstep criteria discussion scalar vector example theory source code ', 'ode_err_control.cpp OdeErrControl: Example and Test ',' nan ', 'ode_err_maxabs.cpp OdeErrControl: Example and Test Using Maxabs Argument ',' ', 'OdeGear An Arbitrary Order Gear Method ',' stiff differential equation syntax purpose include fun f_x warning scalar vector example source code theory gear\'s ', 'ode_gear.cpp OdeGear: Example and Test ',' ', 'OdeGearControl An Error Controller for Gear\'s Ode Solvers ',' differential equation syntax purpose include notation xf fun f_x warning m tf xi smin smax sini eabs erel ef maxabs nstep criteria discussion scalar vector example theory source code ', 'ode_gear_control.cpp OdeGearControl: Example and Test ',' ', 'CppAD_vector The CppAD::vector Template Class ',' [] push thread_alloc syntax description include capacity assignment check size return reference move semantics element access push_back push_vector output resize clear data vectorbool memory bit_per_unit type parallel mode example exercise ', 'cppad_vector.cpp CppAD::vector Template Class: Example and Test ',' ', 'vector_bool.cpp CppAD::vectorBool Class: Example and Test ',' ', 'thread_alloc A Fast Multi-Threading Memory Allocator ',' allocation syntax purpose include ', 'thread_alloc.cpp Fast Multi-Threading Memory Allocator: Example and Test ',' openmp allocation pthread boost ', 'ta_parallel_setup Setup thread_alloc For Use in Multi-Threading Environment ',' initialize syntax purpose speed num_threads in_parallel thread_num restrictions example ', 'ta_num_threads Get Number of Threads ',' syntax purpose example ', 'ta_in_parallel Is The Current Execution in Parallel Mode ',' sequential syntax purpose flag example ', 'ta_thread_num Get the Current Thread Number ',' syntax purpose example ', 'ta_get_memory Get At Least A Specified Amount of Memory ',' allocate syntax purpose min_bytes cap_bytes v_ptr allocation speed alignment example ', 'ta_return_memory Return Memory to thread_alloc ',' available syntax purpose v_ptr ndebug example ', 'ta_free_available Free Memory Currently Available for Quick Use by a Thread ',' syntax purpose extra example ', 'ta_hold_memory Control When Thread Alloc Retains Memory For Future Use ',' syntax purpose value free_available ', 'ta_inuse Amount of Memory a Thread is Currently Using ',' syntax purpose num_bytes example ', 'ta_available Amount of Memory Available for Quick Use by a Thread ',' syntax purpose num_bytes example ', 'ta_create_array Allocate An Array and Call Default Constructor for its Elements ',' syntax purpose type size_min size_out delta alignment example ', 'ta_delete_array Deallocate An Array and Call Destructor for its Elements ',' syntax purpose type thread delta example ', 'ta_free_all Free All Memory That Was Allocated for Use by thread_alloc ',' syntax purpose ok restrictions example ', 'index_sort Returns Indices that Sort a Vector ',' syntax keys input example ', 'index_sort.cpp Index Sort: Example and Test ',' ', 'to_string Convert Certain Types to a String ',' syntax see also purpose value integer float example ', 'to_string.cpp to_string: Example and Test ',' ', 'set_union Union of Standard Sets ',' syntax purpose element left right result example ', 'set_union.cpp Set Union: Example and Test ',' ', 'ipopt_solve Use Ipopt to Solve a Nonlinear Programming Problem ',' syntax purpose include file bvector dvector options retape sparse string numeric integer xi xl xu gl gu fg_eval advector solution status zl zu lambda obj_value example get_started ode_inverse ', 'ipopt_solve_get_started.cpp Nonlinear Programming Using CppAD and Ipopt: Example and Test ',' purpose configuration requirement ', 'ipopt_solve_retape.cpp Nonlinear Programming Retaping: Example and Test ',' purpose ', 'ipopt_solve_ode_inverse.cpp ODE Inverse Problem Definitions: Source Code ',' example purpose forward measurements simulation analytic solution parameter values simulated trapezoidal approximation method ', 'Example Examples ',' introduction running the cppad test vector template class ', 'General General Examples ',' realistic description ', 'ExampleUtility Utility Routines used by CppAD Examples ',' ', 'ListAllExamples List of All the CppAD Examples ',' ', 'ad_fun.cpp Creating Your Own Interface to an ADFun Object ',' example test ', 'ad_in_c.cpp Example and Test Linking CppAD to Languages Other than C++ ',' algorithmic differentiation automatic ', 'conj_grad.cpp Differentiate Conjugate Gradient Algorithm: Example and Test ',' purpose ', 'cppad_eigen.hpp Enable Use of Eigen Linear Algebra Package with CppAD ',' syntax purpose example include files numtraits namespace ', 'eigen_plugin.hpp Source Code for eigen_plugin.hpp ',' ', 'eigen_array.cpp Using Eigen Arrays: Example and Test ',' ', 'eigen_det.cpp Using Eigen To Compute Determinant: Example and Test ',' ', 'hes_minor_det.cpp Gradient of Determinant Using Expansion by Minors: Example and Test ',' ', 'hes_lu_det.cpp Gradient of Determinant Using LU Factorization: Example and Test ',' ', 'interface2c.cpp Interfacing to C: Example and Test ',' difference central ', 'jac_minor_det.cpp Gradient of Determinant Using Expansion by Minors: Example and Test ',' ', 'jac_lu_det.cpp Gradient of Determinant Using Lu Factorization: Example and Test ',' ', 'mul_level Using Multiple Levels of AD ',' background motivation procedure first start ad recording inner function second outer derivatives example ', 'mul_level.cpp Multiple Level of AD: Example and Test ',' purpose source ', 'change_param.cpp Computing a Jacobian With Constants that Change ',' multiple ad level purpose ', 'ode_stiff.cpp A Stiff Ode: Example and Test ',' ', 'mul_level_ode.cpp Taylor\'s Ode Solver: A Multi-Level AD Example and Test ',' purpose solution derivative method using source ', 'mul_level_adolc_ode.cpp Taylor\'s Ode Solver: A Multi-Level Adolc Example and Test ',' purpose solution derivative method using base_adolc.hpp memory management configuration requirement source ', 'ode_taylor.cpp Taylor\'s Ode Solver: An Example and Test ',' purpose solution forward mode ', 'stack_machine.cpp Example Differentiating a Stack Machine Interpreter ',' test ', 'example.cpp CppAD Examples and Tests ',' running ', 'speed_example.cpp Run the Speed Examples ',' program running tests ', 'lu_vec_ad.cpp Lu Factor and Solve with Recorded Pivoting ',' luvecad linear equation determinant syntax purpose storage convention matrix rhs result logdet example ', 'lu_vec_ad_ok.cpp Lu Factor and Solve With Recorded Pivoting: Example and Test ',' ', 'testvector Using The CppAD Test Vector Template Class ',' cppad_testvector syntax introduction cppad::vector std::vector boost::numeric::ublas::vector eigen vectors ', 'speed Speed Test an Operator Overloading AD Package ',' purpose ', 'speed_main Running the Speed Test Program ',' cppad uniform_01 syntax purpose package double profile correct seed global options onetape optimize atomic memory sparsity boolsparsity revsparsity colpack correctness results n_sweep link functions ', 'link_det_lu Speed Testing Gradient of Determinant Using Lu Factorization ',' prototype purpose method return value size repeat matrix double ', 'link_det_minor Speed Testing Gradient of Determinant by Minor Expansion ',' prototype purpose method return value size repeat matrix double ', 'link_mat_mul Speed Testing Derivative of Matrix Multiply ',' multiple prototype purpose return value repeat z dz ', 'link_ode Speed Testing the Jacobian of Ode Solution ',' prototype purpose method return value size repeat x double ', 'link_poly Speed Testing Second Derivative of a Polynomial ',' prototype purpose method return value size repeat ddp double ', 'link_sparse_hessian Speed Testing Sparse Hessian ',' prototype method size repeat x row col n_sweep double ', 'link_sparse_jacobian Speed Testing Sparse Jacobian ',' prototype method size repeat row col x n_sweep double ', 'microsoft_timer Microsoft Version of Elapsed Number of Seconds ',' syntax purpose linking ', 'speed_utility Speed Testing Utilities ',' main program routines library source code ', 'det_by_lu Determinant Using Expansion by Lu Factorization ',' syntax inclusion constructor scalar vector example source code ', 'det_by_lu.cpp Determinant Using Lu Factorization: Example and Test ',' minors ', 'det_by_lu.hpp Source: det_by_lu ',' ', 'det_of_minor Determinant of a Minor ',' matrix syntax inclusion purpose scalar example source code ', 'det_of_minor.cpp Determinant of a Minor: Example and Test ',' ', 'det_of_minor.hpp Source: det_of_minor ',' ', 'det_by_minor Determinant Using Expansion by Minors ',' syntax inclusion constructor scalar vector example source code ', 'det_by_minor.cpp Determinant Using Expansion by Minors: Example and Test ',' ', 'det_by_minor.hpp Source: det_by_minor ',' ', 'det_33 Check Determinant of 3 by 3 matrix ',' correct syntax purpose inclusion vector ok source code ', 'det_33.hpp Source: det_33 ',' ', 'det_grad_33 Check Gradient of Determinant of 3 by 3 matrix ',' correct syntax purpose inclusion vector ok source code ', 'det_grad_33.hpp Source: det_grad_33 ',' ', 'mat_sum_sq Sum Elements of a Matrix Times Itself ',' multiply speed test syntax purpose inclusion z vector example source code ', 'mat_sum_sq.cpp Sum of the Elements of the Square of a Matrix: Example and Test ',' ', 'mat_sum_sq.hpp Source: mat_sum_sq ',' ', 'ode_evaluate Evaluate a Function Defined in Terms of an ODE ',' syntax purpose inclusion float operation sequence fabs == 0 1 fp gradient example source code ', 'ode_evaluate.cpp ode_evaluate: Example and test ',' ', 'ode_evaluate.hpp Source: ode_evaluate ',' ', 'sparse_jac_fun Evaluate a Function That Has a Sparse Jacobian ',' syntax purpose inclusion float floatvector m row col fp example source code ', 'sparse_jac_fun.cpp sparse_jac_fun: Example and test ',' ', 'sparse_jac_fun.hpp Source: sparse_jac_fun ',' ', 'sparse_hes_fun Evaluate a Function That Has a Sparse Hessian ',' syntax purpose inclusion float floatvector row col fp example source code ', 'sparse_hes_fun.cpp sparse_hes_fun: Example and test ',' ', 'sparse_hes_fun.hpp Source: sparse_hes_fun ',' ', 'uniform_01 Simulate a [0,1] Uniform Random Variate ',' [01] syntax purpose inclusion seed vector source code ', 'uniform_01.hpp Source: uniform_01 ',' ', 'speed_double Speed Test of Functions in Double ',' purpose running tests ', 'double_det_minor.cpp Double Speed: Determinant by Minor Expansion ',' link_det_minor specifications implementation ', 'double_det_lu.cpp Double Speed: Determinant Using Lu Factorization ',' link_det_lu matrix specifications implementation ', 'double_mat_mul.cpp CppAD Speed: Matrix Multiplication (Double Version) ',' multiply link_mat_mul specifications implementation ', 'double_ode.cpp Double Speed: Ode Solution ',' link_ode specifications implementation ', 'double_poly.cpp Double Speed: Evaluate a Polynomial ',' link_poly specifications implementation ', 'double_sparse_hessian.cpp Double Speed: Sparse Hessian ',' link_sparse_hessian specifications implementation ', 'double_sparse_jacobian.cpp Double Speed: Sparse Jacobian ',' link_sparse_jacobian specifications implementation ', 'speed_adolc Speed Test of Derivatives Using Adolc ',' purpose adolc_prefix running tests ', 'adolc_det_minor.cpp Adolc Speed: Gradient of Determinant by Minor Expansion ',' link_det_minor specifications implementation ', 'adolc_det_lu.cpp Adolc Speed: Gradient of Determinant Using Lu Factorization ',' link_det_lu matrix specifications implementation ', 'adolc_mat_mul.cpp Adolc Speed: Matrix Multiplication ',' link_mat_mul multiply specifications implementation ', 'adolc_ode.cpp Adolc Speed: Ode ',' link_ode specifications implementation ', 'adolc_poly.cpp Adolc Speed: Second Derivative of a Polynomial ',' link_poly specifications implementation ', 'adolc_sparse_hessian.cpp Adolc Speed: Sparse Hessian ',' link_sparse_hessian specifications implementation ', 'adolc_sparse_jacobian.cpp adolc Speed: Sparse Jacobian ',' link_sparse_jacobian specifications implementation ', 'adolc_alloc_mat Adolc Test Utility: Allocate and Free Memory For a Matrix ',' syntax purpose ', 'speed_cppad Speed Test Derivatives Using CppAD ',' purpose running tests ', 'cppad_det_minor.cpp CppAD Speed: Gradient of Determinant by Minor Expansion ',' link_det_minor specifications implementation ', 'cppad_det_lu.cpp CppAD Speed: Gradient of Determinant Using Lu Factorization ',' link_det_lu matrix specifications implementation ', 'cppad_mat_mul.cpp CppAD Speed, Matrix Multiplication ',' link_mat_mul multiply specifications implementation ', 'cppad_ode.cpp CppAD Speed: Gradient of Ode Solution ',' link_ode specifications implementation ', 'cppad_poly.cpp CppAD Speed: Second Derivative of a Polynomial ',' link_poly specifications implementation ', 'cppad_sparse_hessian.cpp CppAD Speed: Sparse Hessian ',' link_sparse_hessian specifications implementation ', 'cppad_sparse_jacobian.cpp CppAD Speed: Sparse Jacobian ',' link_sparse_jacobian specifications implementation ', 'speed_fadbad Speed Test Derivatives Using Fadbad ',' purpose fadbad_prefix running tests ', 'fadbad_det_minor.cpp Fadbad Speed: Gradient of Determinant by Minor Expansion ',' link_det_minor specifications implementation ', 'fadbad_det_lu.cpp Fadbad Speed: Gradient of Determinant Using Lu Factorization ',' link_det_lu matrix specifications implementation ', 'fadbad_mat_mul.cpp Fadbad Speed: Matrix Multiplication ',' link_mat_mul multiply specifications implementation ', 'fadbad_ode.cpp Fadbad Speed: Ode ',' link_ode specifications implementation ', 'fadbad_poly.cpp Fadbad Speed: Second Derivative of a Polynomial ',' link_poly specifications implementation ', 'fadbad_sparse_hessian.cpp Fadbad Speed: Sparse Hessian ',' ', 'fadbad_sparse_jacobian.cpp fadbad Speed: sparse_jacobian ',' ', 'speed_sacado Speed Test Derivatives Using Sacado ',' purpose sacado_prefix running tests ', 'sacado_det_minor.cpp Sacado Speed: Gradient of Determinant by Minor Expansion ',' link_det_minor specifications implementation ', 'sacado_det_lu.cpp Sacado Speed: Gradient of Determinant Using Lu Factorization ',' link_det_lu matrix specifications implementation ', 'sacado_mat_mul.cpp Sacado Speed: Matrix Multiplication ',' link_mat_mul multiply specifications implementation ', 'sacado_ode.cpp Sacado Speed: Gradient of Ode Solution ',' link_ode specifications implementation ', 'sacado_poly.cpp Sacado Speed: Second Derivative of a Polynomial ',' link_poly specifications implementation ', 'sacado_sparse_hessian.cpp Sacado Speed: Sparse Hessian ',' ', 'sacado_sparse_jacobian.cpp sacado Speed: sparse_jacobian ',' ', 'Appendix Appendix ',' ', 'Faq Frequently Asked Questions and Answers ',' operator reporting errorhandler avoid record taping mode cppad_testvector standard math function storage assignment independent bugs comparechange complex types exceptions variables matrix inverse mode: forward reverse namespace preprocessor symbol using speed ndebug optimize memory allocation tape storage: disk ', 'Theory The Theory of Derivative Calculations ',' ', 'ForwardTheory The Theory of Forward Mode ',' taylor notation binary operators addition subtraction multiplication division standard math functions differential equation coefficients recursion formula cases that apply above special ', 'exp_forward Exponential Function Forward Mode Theory ',' expm1 derivatives taylor coefficients recursion ', 'log_forward Logarithm Function Forward Mode Theory ',' log1p derivatives taylor coefficients recursion ', 'sqrt_forward Square Root Function Forward Mode Theory ',' ', 'sin_cos_forward Trigonometric and Hyperbolic Sine and Cosine Forward Theory ',' sinh cosh differential equation ', 'atan_forward Inverse Tangent and Hyperbolic Tangent Forward Mode Theory ',' atanh derivatives taylor coefficients recursion ', 'asin_forward Inverse Sine and Hyperbolic Sine Forward Mode Theory ',' asinh derivatives taylor coefficients recursion ', 'acos_forward Inverse Cosine and Hyperbolic Cosine Forward Mode Theory ',' acosh derivatives taylor coefficients recursion ', 'tan_forward Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory ',' derivatives coefficients recursion ', 'erf_forward Error Function Forward Taylor Polynomial Theory ',' derivatives coefficients recursion ', 'ReverseTheory The Theory of Reverse Mode ',' taylor notation binary operators addition subtraction multiplication division standard math functions ', 'exp_reverse Exponential Function Reverse Mode Theory ',' expm1 ', 'log_reverse Logarithm Function Reverse Mode Theory ',' log1p ', 'sqrt_reverse Square Root Function Reverse Mode Theory ',' ', 'sin_cos_reverse Trigonometric and Hyperbolic Sine and Cosine Reverse Theory ',' sinh cosh ', 'atan_reverse Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory ',' ', 'asin_reverse Inverse Sine and Hyperbolic Sine Reverse Mode Theory ',' asinh ', 'acos_reverse Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory ',' acosh ', 'tan_reverse Tangent and Hyperbolic Tangent Reverse Mode Theory ',' notation eliminating y(t) positive orders z(t) zero ', 'erf_reverse Error Function Reverse Mode Theory ',' notation positive orders z(t) zero ', 'reverse_identity An Important Reverse Mode Identity ',' notation sweep theorem proof ', 'glossary Glossary ',' efficient ad function base type above elementary vector operation atomic sequence dependent independent parameter sparsity pattern boolean sets tape active inactive variable variables taylor coefficient ', 'Bib Bibliography ',' abramowitz stegun the c++ programming language evaluating derivatives numerical recipes shampine l.f. ', 'wish_list The CppAD Wish List ',' optimization taping special operators checkpoint retape testing sparsity patterns check_finite compilation speed base requirements adolc forward mode recomputation iterator interface operation sequence software guidelines tracing atan2 benderquad ', 'whats_new Changes and Additions to CppAD ',' introduction this year previous years ', 'whats_new_16 Changes and Additions to CppAD During 2016 ',' introduction 12-23 12-20 12-18 12-13 12-11 12-09 11-18 11-14 11-13 10-27 10-12 09-29 09-27 09-26 09-16 09-13 08-30 08-25 07-17 07-14 06-30 06-29 06-27 06-25 06-10 05-05 04-17 03-27 03-26 03-25 03-24 03-23 03-22 03-21 03-20 03-19 03-17 03-12 03-05 03-01 02-29 02-28 02-27 02-26 02-25 02-23 01-21 01-20 01-18 ', 'whats_new_15 CppAD Changes and Additions During 2015 ',' introduction 12-31 12-29 12-28 12-08 12-01 11-30 11-25 11-24 11-14 11-08 11-06 10-21 10-16 10-06 10-04 10-03 10-02 09-28 09-27 09-25 09-24 09-23 09-21 09-20 09-19 09-16 09-03 09-02 08-31 08-30 08-29 08-28 08-26 08-25 08-20 08-17 08-16 08-09 08-06 07-31 06-16 06-11 06-09 06-07 05-26 cond_exp_1 cond_exp_2 05-11 05-10 05-09 05-08 05-07 05-05 04-18 03-13 03-06 02-28 02-18 02-16 02-14 02-11 02-10 02-09 02-07 02-06 02-04 02-03 02-02 01-30 01-29 01-26 01-23 01-21 01-20 01-09 01-07 01-02 ', 'whats_new_14 CppAD Changes and Additions During 2014 ',' introduction 12-30 12-29 12-28 12-27 12-26 12-25 12-23 12-22 12-17 12-16 12-15 11-28 11-27 09-28 09-27 09-25 09-21 05-28 05-27 05-23 05-22 05-20 05-19 05-16 05-14 03-18 03-17 03-09 03-05 03-02 03-01 02-28 02-27 02-26 02-23 02-22 02-17 02-15 01-26 01-21 01-10 ', 'whats_new_13 CppAD Changes and Additions During 2013 ',' introduction 12-29 12-27 12-26 12-24 11-27 11-13 11-12 10-29 10-23 10-22 10-16 10-15 10-14 10-13 10-12 09-20 09-19 09-18 09-07 08-12 08-11 08-06 07-26 05-28 05-21 05-17 05-15 05-14 05-12 05-11 05-04 04-28 04-27 04-26 ', 'whats_new_12 CppAD Changes and Additions During 2012 ',' introduction 12-30 12-29 12-28 12-27 12-26 12-23 12-22 12-20 12-19 12-17 12-15 12-14 12-13 11-28 11-21 11-20 11-17 11-16 11-14 11-09 11-06 11-04 10-31 10-30 10-25 10-24 10-12 10-04 10-03 10-02 09-24 09-11 08-05 07-30 07-08 07-07 07-05 07-04 07-03 07-02 07-01 06-17 06-16 06-15 06-12 06-10 06-09 06-08 06-07 06-05 06-04 06-03 06-02 06-01 05-31 05-30 05-29 05-27 05-24 04-19 04-18 04-17 04-10 04-06 04-05 04-01 03-27 03-26 03-23 03-21 03-17 03-11 03-03 03-02 02-11 02-10 02-09 01-30 01-27 01-24 01-23 01-20 01-19 01-16 01-15 01-12 01-07 01-02 ', 'whats_new_11 Changes and Additions to CppAD During 2011 ',' introduction 12-30 12-28 12-21 12-20 11-29 11-27 11-24 11-21 11-20 11-18 11-17 11-09 11-07 11-06 11-04 11-01 10-30 10-29 10-14 10-12 09-06 09-05 09-02 09-01 08-31 08-30 08-25 08-23 08-21 08-11 08-10 08-09 08-08 08-07 08-06 08-04 08-03 08-02 07-31 07-29 07-28 07-27 07-25 07-18 07-17 07-14 07-13 07-11 openmp/run.sh 07-10 07-09 07-07 06-23 06-21 06-18 05-29 05-28 05-26 05-22 05-11 05-03 04-29 04-20 04-19 03-19 03-11 03-05 02-22 02-19 02-17 02-15 02-09 02-06 02-02 02-01 01-19 01-16 01-09 ', 'whats_new_10 Changes and Additions to CppAD During 2010 ',' introduction 12-31 11-27 09-26 09-22 08-21 07-14 07-11 06-01 04-28 04-26 04-24 04-01 03-11 03-10 03-09 03-03 02-11 02-08 02-06 02-05 02-03 01-26 01-24 01-23 01-20 01-18 01-04 ', 'whats_new_09 Changes and Additions to CppAD During 2009 ',' introduction 12-23 12-22 12-18 12-12 12-04 12-02 11-28 11-27 11-26 10-30 10-29 10-28 10-27 10-24 10-23 10-21 10-16 10-14 10-03 09-30 09-29 09-28 09-26 09-20 09-19 09-18 08-25 08-14 08_13 08-13 08-11 08-10 08-09 08-06 08-02 08-01 07-31 07-26 07-25 07-24 07-23 07-06 07-04 07-03 07-02 07-01 06-30 06-29 06-28 06-25 06-22 06-21 06-20 06-06 05-20 03-24 02-20 02-15 02-01 01-31 01-18 01-06 ', 'whats_new_08 Changes and Additions to CppAD During 2008 ',' erf ipopt_cppad_nlp introduction 12-19 12-14 12-04 11-22 11-21 11-20 10-27 10-17 10-16 09-30 09-26 09-18 09-17 09-16 09-12 09-10 09-09 09-07 09-06 09-05 09-04 09-03 09-01 08-29 08-19 08-08 07-02 06-18 06-15 06-11 06-10 05-08 05-03 04-20 04-18 04-10 04-06 04-04 03-27 02-05 02-03 01-26 01-24 01-21 01-20 01-11 01-08 ', 'whats_new_07 Changes and Additions to CppAD During 2007 ',' introduction 12-29 12-25 12-21 12-08 12-05 12-04 12-03 12-02 11-29 11-23 11-18 11-06 11-05 11-04 11-03 11-02 11-01 10-30 10-27 10-23 10-22 10-16 10-13 10-05 10-02 09-06 08-09 08-07 07-30 07-29 07-28 07-26 07-25 07-23 07-22 07-21 07-20 07-19 07-18 07-14 07-13 06-22 06-20 06-14 05-26 05-25 05-24 05-22 05-08 05-05 04-19 04-17 04-14 04-11 04-10 04-07 04-06 04-05 03-31 03-30 03-29 03-20 03-15 03-14 03-13 03-09 03-28 02-27 02-22 02-17 02-16 02-15 02-06 02-04 02-03 02-02 02-01 01-29 ', 'whats_new_06 Changes and Additions to CppAD During 2006 ',' aclocal introduction 12-24 12-23 12-22 12-21 12-19 12-18 12-17 12-15 12-13 12-12 12-11 12-10 12-09 12-07 12-05 12-03 12-02 12-01 11-30 11-29 11-28 11-23 11-18 11-12 11-08 11-06 11-05 11-04 11-02 11-01 10-31 10-29 10-28 10-27 10-26 10-25 10-18 10-16 10-10 09-30 08-17 07-14 07-12 06-29 06-22 06-19 06-17 06-18 06-15 06-09 06-07 06-05 06-02 05-31 05-29 05-27 05-03 04-29 04-28 04-26 04-25 04-19 04-18 04-17 04-15 04-14 04-13 04-08 04-06 04-05 04-04 04-03 04-02 04-01 03-31 03-30 03-29 03-28 03-27 03-26 03-24 03-23 03-22 03-18 03-17 03-16 03-15 03-11 03-10 03-09 03-07 03-05 02-28 02-25 02-24 02-23 02-21 02-15 02-14 02-13 02-11 02-10 02-04 01-20 01-18 01-08 01-07 01-02 01-05 ', 'whats_new_05 Changes and Additions to CppAD During 2005 ',' 12-24 12-23 12-22 12-20 12-19 12-16 12-15 12-14 12-11 12-08 12-07 12-06 12-05 12-03 12-02 12-01 11-23 11-22 11-20 11-19 11-15 11-12 11-09 11-07 11-06 11-01 10-20 10-18 10-14 10-12 10-06 09-29 09-27 09-24 09-20 09-14 09-09 09-07 08-30 08-24 08-20 08-19 08-15 08-14 08-13 08-07 07-21 07-19 07-15 07-11 07-08 07-05 07-04 07-03 07-02 07-01 06-25 06-24 06-18 06-14 06-13 06-06 05-19 05-18 05-16 05-12 05-06 05-01 04-21 04-20 04-19 03-26 03-23 03-22 03-09 03-04 03-01 02-24 01-08 ', 'whats_new_04 Changes and Additions to CppAD During 2004 ',' introduction 12-11 12-09 12-03 11-17 11-16 11-15 11-14 11-13 11-12 11-10 11-04 11-02 11-01 10-29 10-28 10-27 10-21 10-19 10-16 10-06 09-29 09-26 09-23 09-21 09-13 09-10 09-09 09-07 09-04 09-02 08-27 08-25 08-24 08-12 07-31 07-08 07-07 07-03 07-02 06-29 06-25 06-12 06-04 06-03 06-01 05-30 05-29 05-26 05-25 05-14 05-12 05-09 05-07 05-04 05-03 04-29 04-28 04-25 04-24 04-22 04-21 04-20 04-19 04-09 04-08 04-07 04-03 04-02 04-01 03-30 03-28 03-25 03-18 03-17 03-15 03-12 03-11 03-09 03-07 03-06 03-05 03-04 03-03 03-01 02-29 02-28 02-21 02-20 02-17 02-16 02-15 02-12 02-01 01-29 01-28 01-22 ', 'whats_new_03 Changes and Additions to CppAD During 2003 ',' introduction 12-24 12-22 12-14 12-13 12-12 12-10 12-05 12-01 11-21 11-20 11-16 11-15 11-14 11-12 11-11 11-06 11-04 11-02 10-21 10-16 10-14 10-10 10-06 10-05 09-30 09-20 09-19 09-18 09-15 09-14 09-13 09-06 09-05 09-04 09-03 08-23 08-22 08-19 08-17 08-16 08-11 08-10 08-07 08-06 08-05 08-04 08-03 08-01 07-30 07-29 07-26 07-22 07-20 07-18 07-16 07-14 ', 'deprecated CppAD Deprecated API Features ',' atomic functions ', 'include_deprecated Deprecated Include Files ',' 2015-11-30 2006-12-17 linking new to commands ', 'FunDeprecated ADFun Object Deprecated Member Functions ',' syntax purpose dependent 2007-08-07 order 2006-03-31 memory size 2006-04-03 taylor_size 2006-06-17 use_vecad 2006-04-08 size_taylor 2014-03-18 capacity_taylor ', 'CompareChange Comparison Changes During Zero Order Forward Mode ',' adfun syntax deprecated 2015-01-20 purpose discussion ', 'omp_max_thread OpenMP Parallel Setup ',' deprecated 2011-06-23 syntax purpose number independent restriction ', 'TrackNewDel Routines That Track Use of New and Delete ',' memory ndebug cppad_track_new_vec cppadtracknewvec cppad_track_del_vec cppadtrackdelvec cppad_track_extend cppadtrackextend cppad_track_count thread multi deprecated 2007-07-23 syntax purpose include file line oldptr newlen head newptr ncopy macro previously trackcount multi-threading example ', 'TrackNewDel.cpp Tracking Use of New and Delete: Example and Test ',' ', 'omp_alloc A Quick OpenMP Memory Allocator Used by CppAD ',' multi-threading allocation syntax purpose include deprecated 2011-08-23 ', 'omp_max_num_threads Set and Get Maximum Number of Threads for omp_alloc Allocator ',' deprecated 2011-08-31 syntax purpose set_max_num_threads get_max_num_threads restrictions ', 'omp_in_parallel Is The Current Execution in OpenMP Parallel Mode ',' deprecated 2011-08-31 syntax purpose flag example ', 'omp_get_thread_num Get the Current OpenMP Thread Number ',' deprecated 2011-08-31 syntax purpose example ', 'omp_get_memory Get At Least A Specified Amount of Memory ',' deprecated 2011-08-31 syntax purpose min_bytes cap_bytes v_ptr allocation speed example ', 'omp_return_memory Return Memory to omp_alloc ',' deprecated 2011-08-31 syntax purpose v_ptr thread ndebug example ', 'omp_free_available Free Memory Currently Available for Quick Use by a Thread ',' deprecated 2011-08-31 syntax purpose example ', 'omp_inuse Amount of Memory a Thread is Currently Using ',' deprecated 2011-08-31 syntax purpose num_bytes example ', 'omp_available Amount of Memory Available for Quick Use by a Thread ',' deprecated 2011-08-31 syntax purpose num_bytes example ', 'omp_create_array Allocate Memory and Create A Raw Array ',' deprecated 2011-08-31 syntax purpose type size_min size_out delta example ', 'omp_delete_array Return A Raw Array to The Available Memory for a Thread ',' deprecated 2011-08-31 syntax purpose type delta example ', 'omp_efficient Check If A Memory Allocation is Efficient for Another Use ',' removed syntax purpose v_ptr num_bytes flag thread ndebug ', 'old_max_num_threads Set Maximum Number of Threads for omp_alloc Allocator ',' removed syntax purpose restrictions ', 'omp_alloc.cpp OpenMP Memory Allocator: Example and Test ',' allocation multi thread deprecated 2011-08-31 ', 'memory_leak Memory Leak Detection ',' check static deprecated 2012-04-06 syntax purpose thread add_static flag inuse available track_count error message ', 'epsilon Machine Epsilon For AD Types ',' deprecated 2012-06-17 syntax purpose float ', 'test_vector Choosing The Vector Testing Template Class ',' cppad_test_vector deprecated 2012-07-03 syntax introduction ms windows cppad::vector std::vector boost::numeric::ublas::vector cppadvector 2007-07-28 ', 'cppad_ipopt_nlp Nonlinear Programming Using the CppAD Interface to Ipopt ',' deprecated 2012-11-28 syntax purpose namespace ipopt_library_paths fg(x) index vector projection injection representation simple sizevector numbervector adnumber advector x_i x_l x_u g_l g_u fg_info fg_info.number_functions fg_info.eval_r fg_info.retape fg_info.domain_size fg_info.range_size fg_info.number_terms fg_info.index solution status z_l z_u lambda obj_value example wish list ', 'ipopt_nlp_get_started.cpp Nonlinear Programming Using CppAD and Ipopt: Example and Test ',' purpose configuration requirement ', 'ipopt_nlp_ode Example Simultaneous Solution of Forward and Inverse Problem ',' ', 'ipopt_nlp_ode_problem An ODE Inverse Problem Example ',' notation forward measurements simulation analytic solution parameter values simulated trapezoidal approximation time grid black box method two levels iteration derivatives simultaneous source ', 'ipopt_nlp_ode_simple ODE Fitting Using Simple Representation ',' cppad_ipopt_nlp purpose argument vector objective function initial condition constraint trapezoidal approximation source ', 'ipopt_nlp_ode_fast ODE Fitting Using Fast Representation ',' purpose objective function range indices i(k0) domain j(k0) initial condition trapezoidal approximation source ', 'ipopt_nlp_ode_problem.hpp ODE Inverse Problem Definitions: Source Code ',' example ', 'ipopt_nlp_ode_simple.hpp ODE Fitting Using Simple Representation ',' cppad_ipopt_nlp example source ', 'ipopt_nlp_ode_fast.hpp ODE Fitting Using Fast Representation ',' cppad_ipopt_nlp example source ', 'ipopt_nlp_ode_run.hpp Driver for Running the Ipopt ODE Example ',' ', 'ipopt_nlp_ode_check.cpp Correctness Check for Both Simple and Fast Representations ',' ', 'ipopt_ode_speed.cpp Speed Test for Both Simple and Fast Representations ',' ', 'old_atomic User Defined Atomic AD Functions ',' operation deprecated 2013-05-27 syntax callback routines free static memory purpose partial implementation cppad_user_atomic tvector base ok id tx ty forward reverse afun ay parallel mode usage vx vy py px for_jac_sparse q rev_jac_sparse rev_hes_sparse clear restriction example simple tangent matrix multiplication ', 'old_reciprocal.cpp Old Atomic Operation Reciprocal: Example and Test ',' deprecated 2013-05-27 theory ', 'old_usead_1.cpp Using AD to Compute Atomic Function Derivatives ',' inside user checkpoint deprecated 2013-05-27 purpose simple case ', 'old_usead_2.cpp Using AD to Compute Atomic Function Derivatives ',' inside user checkpoint deprecated 2013-05-27 purpose ', 'old_tan.cpp Old Tan and Tanh as User Atomic Operations: Example and Test ',' deprecated 2013-05-27 theory ', 'old_mat_mul.cpp Old Matrix Multiply as a User Atomic Operation: Example and Test ',' deprecated 2013-05-27 include file ', 'old_mat_mul.hpp Define Matrix Multiply as a User Atomic Operation ',' old_atomic test syntax example begin source extra call information indexing one reverse partials order set union cppad callback functions declare ', 'zdouble zdouble: An AD Base Type With Absolute Zero ',' deprecated 2015-09-26 syntax constructor assignment comparison operators arithmetic standard math nan motivation general cppad requirements example ', 'zdouble.cpp zdouble: Example and Test ',' ', 'compare_c Compare Speed of C and C++ ',' with syntax purpose ', 'det_of_minor_c Determinant of a Minor ',' syntax purpose source code ', 'det_by_minor_c Compute Determinant using Expansion by Minors ',' syntax purpose source code ', 'uniform_01_c Simulate a [0,1] Uniform Random Variate ',' [01] syntax purpose seed source code ', 'correct_det_by_minor_c Correctness Test of det_by_minor Routine ',' syntax flag source code ', 'repeat_det_by_minor_c Repeat det_by_minor Routine A Specified Number of Times ',' syntax size source code ', 'elapsed_seconds_c Returns Elapsed Number of Seconds ',' syntax purpose source code ', 'time_det_by_minor_c Determine Amount of Time to Execute det_by_minor ',' syntax purpose time_min source code ', 'main_compare_c Main Program For Comparing C and C++ Speed ',' source code ', 'numeric_ad Some Numerical AD Utilities ',' ', 'BenderQuad Computing Jacobian and Hessian of Bender\'s Reduced Objective ',' syntax see also problem purpose fun fun.f fun.h fun.dy gx gxx bavector advector example ', 'bender_quad.cpp BenderQuad: Example and Test ',' ', 'opt_val_hes Jacobian and Hessian of Optimal Values ',' syntax see also reference purpose basevector fun fun::ad_vector fun.ell fun.s fun.sy signdet example ', 'opt_val_hes.cpp opt_val_hes: Example and Test ',' ', 'LuRatio LU Factorization of A Square Matrix and Stability Calculation ',' linear equation solve syntax description include storage sign jp determinant purpose sizevector advector example ', 'lu_ratio.cpp LuRatio: Example and Test ',' ', 'addon CppAD Addons ',' name include files library preprocessor symbols namespace ', 'License Your License for the CppAD Software ',' ' ] var MaxList = 100; var Nstring = -1; var Nkeyword = Keyword.length / 2; Initialize(); function Initialize() { UpdateList(); document.search.keywords.focus(); } function UpdateList(event) { key = 0; if( window.event ) key = window.event.keyCode; else if( event ) key = event.which; if( key == 13 ) { Goto(); return; } var string = document.search.keywords.value; if( Nstring == string.length ) return; Nstring = string.length; var word = string.match(/\S+/g); var nword = 0; if(word != null ) nword = word.length; var pattern = new Array(nword); for(var j = 0; j < nword; j++) pattern[j] = new RegExp(word[j], 'i'); var nlist = 0; var list = ''; for(i = 0; (i < Nkeyword) && (nlist < MaxList) ; i++) { var match = true; for(j = 0; j < nword; j++) { var flag = pattern[j].test(Keyword[2*i]); flag = flag || pattern[j].test(Keyword[2*i+1]); match = match && flag; } if( match ) { line = Keyword[2*i].split(/\s+/); line = line.join(' '); list = list + line + '\n'; nlist = nlist + 1; } } document.search.list.value = list; } function Choose(textarea) { var start_select = textarea.value.substring(0, textarea.selectionStart); var start_pos = Math.max(0, start_select.lastIndexOf('\n') ); var length = textarea.value.length; var end_select = textarea.value.substring(textarea.selectionEnd, length); var end_pos = end_select.indexOf('\n'); if( end_pos >= 0 ) { end_pos = textarea.selectionEnd + end_pos; } else { end_pos = length; } // highlight the selected line textarea.selectionStart = start_pos; textarea.selectionEnd = end_pos; // get the choice from the beginning of the line var line = textarea.value.substring(start_pos, length); var end_choice = line.indexOf(' '); if( end_choice >= 0 ) { var choice = line.substring(0, end_choice); document.search.choice.value = choice.toLowerCase(); } return true; } function Goto() { parent.location = document.search.choice.value + '.xml'; } cppad-20170000.3/doc/_image.gif0000644000175200017650000000210613057470467015113 0ustar coincoin-webGIF89a."÷€€€€€€€€€ÀÀÀÀÜÀ¦ÊðÿÿÌÌ™fÿf3Bš§7<™ÿ33f€ÿfÌ™f™fÌ"""ÌÌÿ™™ÿffÌ3ÿ™3f™Ì3333f3™3Ì3ÿff3fff™fÌfÿ™™3™f™™™ÌÌÌ3ÌfÌ™ÌÌÌÿÿ3ÿfÿ™ÿÌ3333f3™3Ì3ÿ3333333™33Ì33ÿ3f3f33ff3f™3fÌ3fÿ3™3™33™f3™™3™Ì3™ÿ3Ì3Ì33Ìf3Ì™3ÌÌ3Ìÿ3ÿ3ÿ33ÿf3ÿÌ3ÿÿff3fff™fÌfÿf3f33f3ff3™f3Ìf3ÿffff3fffff™ffÿf™f™3f™ff™™f™Ìf™ÿfÌfÌ3fÌffÌ™fÌÌfÌÿfÿfÿ3fÿffÿ™fÿÌfÿÿ™™3™™™Ì™ÿ™3™33™3f™3™™3Ì™3ÿ™f™f3™ff™f™™fÿ™™™™3™™f™™™™™Ì™Ì™Ì3™Ìf™Ì™™ÌÌ™Ìÿ™ÿ™ÿ3™ÿf™ÿ™™ÿÌ™ÿÿÌÌ3ÌfÌ™ÌÌÌÿÌ3Ì33Ì3fÌ3™Ì3ÌÌ3ÿÌfÌf3ÌffÌf™ÌfÌÌfÿ̙̙3Ì™™Ì™ÌÌ™ÿÌÌÌÌ3ÌÌfÌÌ™ÌÿÌÿ3ÌÿfÌÿ™ÌÿÌÌÿÿÿ3ÿfÿ™ÿÌÿ3ÿ33ÿ3fÿ3™ÿ3Ìÿ3ÿÿfÿffÿf™ÿfÿÿ™ÿ™3ÿ™fÿ™™ÿ™Ìÿ™ÿÿÌÿÌ3ÿÌfÿÌ™ÿÌÌÿÌÿÿÿ3ÿÿfÿÿ™æ“¦ä·šä¼¤ÛžÁεÉä˜ÀâµÆÖÅ›×Å´æÉ“éÉ°ùèÌÌÌÍÊÒÏÒåÛâÝÜáîñÙÇäÚäõäÔüüûHy%Èù¨¶ÀÿÿÌÿûð  ¤€€€ÿÿÿÿÿÿÿÿÿÿÿÿ,."þH° Áƒ*\HÐÂJ\èð‚Å !NÜhЂ AfŒÈ±¤G BbY’ãÉ RŠ|H²%×+c†|ÁæÍVž”‰bOŸqz\º2$ÄšHž„¸´jS§P‘NZu)„*³ú,Z¡«Y*À„p4ê@FV‹ÂeêÀFn;29÷%Û¼zO‚Äg•­Ø¼q1ôýøpÁ¸wã^8ì¶pd¦“)ûlР*ÛË'/0jà>;{\°€i ø˜– Ø4jøX³f°`6gÔœ9;N¼¸q›&?Žp¹@çÌ B‡}àtë–gOž;õÛ·,?·~@ûxçß%^/OÞ<ûðé®GϾ>w·óÛO¾åúòÝÙ·ŸxÕ¹;cppad-20170000.3/doc/install.xml0000644000175200017650000001104013057470504015360 0ustar coincoin-web CppAD Download, Test, and Install Instructions
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CppAD Download, Test, and Install Instructions

Instructions

Step 1: Download
Use the download instructions to obtain a copy or CppAD.

Step 2: Cmake
Use the cmake instructions to configure CppAD.

Step 3: Check
Use the cmake_check instructions to check the CppAD examples and tests.

Step 4: Installation
Use the command 
 
     make install
to install CppAD. If you created nmake makefiles, you will have to use 
 
     nmake install
see the generator option for the cmake command.

Contents
downloadDownload The CppAD Source Code
cmakeUsing CMake to Configure CppAD
cmake_checkChecking the CppAD Examples and Tests
pkgconfigCppAD pkg-config Files
auto_toolsAuto Tools Unix Test and Installation
Input File: omh/install/install.omh cppad-20170000.3/doc/download.xml0000644000175200017650000005200513057470504015527 0ustar coincoin-web Download The CppAD Source Code
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Download The CppAD Source Code

Purpose
CppAD is an include file library and you therefore need the source code to use it. This section discusses how to download the different versions of CppAD.

Distribution Directory
We refer to the CppAD source directory created by the download instruction below as the distribution directory. To be specific, the distribution directory contains the file cppad/cppad.hpp.

Compressed Archives
These files have been archived using tar and compressed using gzip. We use version to denote the year, month, and day, corresponding to a version of the CppAD API. For example 20160101 corresponds to January 1, 2016. We use rel to denote the release number. Higher release numbers corresponding to more bug fixes. We use lic to denote the licence corresponding to a compressed archive which can be either epl or gpl (gpl denotes the GNU General Public License and epl denotes the Eclipse Public License). The compressed archives names have one of the following formats:
     cppad-version.rel.lic.tgz
     cppad-version.rel.tgz
     cppad-version.lic.tgz
 In Unix, you can extract these compressed archives using tar. For example,
     tar -xzf cppad-version.rel.lic.tgz
 No matter what the format of the name, the corresponding distribution directory is cppad-version . To see that the extraction has been done correctly, check for the following file:
     cppad-version/cppad/cppad.hpp
Current Version

Compressed Archives
version    license    link
current EPL cppad-20170000.3.epl.tgz
current GPL cppad-20170000.3.gpl.tgz

Subversion
The archives above correspond to the current subversion trunk . You can obtain a subversion copy of the current version using the command
     svn checkout https://projects.coin-or.org/svn/CppAD/trunk cppad.svn/trunk
 This procedure requires that the subversion program is installed on your system.

Git
The archives above correspond to the current git master . You can a git clone of the current version using the command
    git clone https://github.com/coin-or/CppAD.git cppad.git
 This procedure requires that the git is installed on your system.

Release Versions

Coin
Release versions have the rel field in the compressed archive name. The release version on the Coin download page have the format
     cppad-version.rel.lic.tgz
github
The release versions on the github download page have the format
     cppad-version.rel.tgz
Monthly Versions
Monthly versions of the compressed tar files are available on the Coin download page . These are kept until the end of the current year, when the next release is created. The monthly versions have the form
     cppad-yyyy0101.lic.tgz
 where the license code lic is gpl or epl and yyyy is the current year.

Daily Versions
You can use the git version of the repository to obtain the version corresponding to a specific day as follows:
     git clone https://github.com/coin-or/CppAD.git cppad.git
     cd cppad.git
     git checkout --quiet hash_id
 where hash_id is the SHA-1 hash code for the version of the repository for the day of interest. Note that a list of these hash_id values can be found at the CppAD github commits/master . page.

Windows File Extraction and Testing
If you know how to extract the distribution directory from the tar file, just do so. Otherwise, below is one way you can do it. (Note that if 7z.exe, cmake.exe, and nmake.exe are you your execution path, you will not need to specify their paths below.)
  1. Download and install the open source program http://www.7-zip.org .
  2. Download and install the Visual Studio Express; for example Visual Studio 2013
  3. In a command window, execute the following commands:
         set PATH=    path_to_7_zip;%PATH%
         set PATH=    path_to_cmake;%PATH%
         set VCDIR=    path_to_vcdir;%PATH%
         call "%VCDIR%\vcvarsall.bat" x86
     For example, on one machine these paths had the following values:
             path_to_7_zip=C:\Program Files\7-zip
             path_to_cmake=C:\Program Files (x86)\CMake\bin
             path_to_vcdir=C:\Program Files (x86)\Microsoft Visual Studio 14.0\VC
  4. Use the following commands to extract the distribution from the compressed archive:
         7z x cppad-    version.lic.tgz
         7z x cppad-    version.lic.tar
  5. To see if this has been done correctly, check for the following file:
         cppad-    version\cppad\cppad.hpp
  6. The commands below are optional. They run the CppAD tests using the default cmake settings (except for the generator option)
         mkdir build
         cd build
         cmake -G "NMake Makefiles" ..
         nmake check

Install Instructions
The install instructions on this web site correspond to the current version of CppAD. If you are using an old version of CppAD these instructions may work. If you have trouble (or just to be careful), you should follow the instructions in the doc subdirectory of the distribution directory. If there is no such documentation, you can build it; see building documentation .

No Documentation
Some of the download methods do not include documentation. To be specific, the subversion method, git method, daily version method, and the github release version method. In addition, these methods only provide the EPL licensed version of CppAD.

Building Documentation
If you are using one of these download methods, you can build the documentation to get the corresponding install instructions. The documentation for CppAD is built from the source code files using OMhelp . You will need to install the omhelp command so that 
 
     which omhelp
shows it is in your path. Once you have done this, in the distribution directory execute the following command:
     bin/run_omhelp.sh htm
 You will then be able to follow the install instructions in the doc subdirectory of the distribution directory.
Input File: omh/install/download.omh cppad-20170000.3/doc/cmake.xml0000644000175200017650000010145313057470504015002 0ustar coincoin-web Using CMake to Configure CppAD
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Using CMake to Configure CppAD

The CMake Program
The cmake program enables one to create a single set of scripts, called CMakeLists.txt, that can be used to test and install a program on Unix, Microsoft, or Apple operating systems. For example, one can use it to automatically generate Microsoft project files.

CMake Command
The command below assumes that cmake is in your execution path with version greater than or equal 2.8. If not, you can put the path to the version of cmake in font the command. Only the cmake command and the path to the distribution directory (.. at the end of the command below) are required. In other words, the first and last lines below are required and all of the other lines are optional.

Build Directory
Create a build subdirectory of the distribution directory , change into the build directory, and execute the following command:
cmake                                                                      \
    -D CMAKE_VERBOSE_MAKEFILE=cmake_verbose_makefile                       \
    -G generator                                                           \
     \
    -D cppad_prefix=cppad_prefix                                           \
    -D cppad_postfix=cppad_postfix                                         \
     \
    -D cmake_install_includedirs=cmake_install_includedirs                 \
    -D cmake_install_libdirs=cmake_install_libdirs                         \
     \
    -D cmake_install_datadir=cmake_install_datadir                         \
    -D cmake_install_docdir=cmake_install_docdir                           \
    \
    -D adolc_prefix=adolc_prefix                                           \
    -D colpack_prefix=colpack_prefix                                       \
    -D eigen_prefix=eigen_prefix                                           \
    -D fadbad_prefix=fadbad_prefix                                         \
    -D ipopt_prefix=ipopt_prefix                                           \
    -D sacado_prefix=sacado_prefix                                         \
    \
    -D cppad_cxx_flags=cppad_cxx_flags                                     \
    -D cppad_profile_flag=cppad_profile_flag                               \
    \
    -D cppad_testvector=cppad_testvector                                   \
    -D cppad_max_num_threads=cppad_max_num_threads                         \
    -D cppad_tape_id_type=cppad_tape_id_type                               \
    -D cppad_tape_addr_type=cppad_tape_addr_type                           \
    -D cppad_deprecated=cppad_deprecated \
    \
    ..
make check
Important information about the CppAD configuration is output by this command. If you have the grep program, and store the output in cmake.log, you can get a list of all the test options with the command: 
 
     grep 'make check' cmake.log

cmake_verbose_makefile
This value should be either YES or NO. The default value, when it is not present, is NO. If it is YES, then the output of the make commands will include all of the files and flags used to run the compiler and linker. This can be useful for seeing how to compile and link your own applications.

generator
The CMake program is capable of generating different kinds of files. Below is a table with a few of the possible files
generator Description
"Unix Makefiles" make files for unix operating system
"NMake Makefiles" make files for Visual Studio
Other generator choices are available; see the cmake generators documentation.

cppad_prefix
This is the top level absolute path below which all of the CppAD files are installed by the command
     make install
 For example, if cppad_prefix is /usr, cmake_install_includedirs is include, and cppad_postfix is not specified, the file cppad.hpp is installed in the location
     /usr/include/cppad/cppad.hpp
 The default value for cppad_prefix is /usr.

cppad_postfix
This is the bottom level relative path below which all of the CppAD files are installed. For example, if cppad_prefix is /usr, cmake_install_includedirs is include, and cppad_postfix is coin, the file cppad.hpp is installed in the location
     /usr/include/coin/cppad/cppad.hpp
 The default value for cppad_postfix is empty; i.e, there is no bottom level relative directory for the installed files.

cmake_install_includedirs
This is one directory, or a list of directories separated by spaces or by semi-colons. This first entry in the list is the middle level relative path below which the CppAD include files are installed. The entire list is used for searching for include files. For example, if cppad_prefix is /usr, cmake_install_includedirs is include, and cppad_postfix is not specified, the file cppad.hpp is installed in the location
     /usr/include/cppad/cppad.hpp
 The default value for this directory list is include.

cmake_install_libdirs
This is one directory, or a list of directories separated by spaces or by semi-colons. This first entry in the list is the middle level relative path below which the CppAD library files are installed. The entire list is used for searching for library files. For example, if cppad_prefix is /usr, cmake_install_libdirs is lib, cppad_postfix is not specified, and ipopt_prefix is specified, the file libcppad_ipopt.a is installed in the location
     /usr/lib/libcppad_ipopt.a
 The default value for this directory list is lib.

cmake_install_datadir
This is the middle level relative path below which the CppAD data files are installed. For example, if cppad_prefix is /usr, cmake_install_datadir is share, and cppad_postfix is not specified, the pkgconfig file cppad.pc is installed in the location
     /usr/share/pkgconfig/cppad.pc
 The default value for cmake_install_datadir is share.

cmake_install_docdir
This is the middle level relative path below which the CppAD documentation files are installed. For example, if cppad_prefix is /usr, cmake_install_docdir is share/doc, and cppad_postfix is not specified, the file cppad.xml is installed in the location
     /usr/share/doc/cppad/cppad.xml
 There is no default value for cmake_install_docdir . If it is not specified, the documentation files are not installed.

package_prefix
Each of these packages corresponds to optional CppAD examples, that can be compiled and tested if the corresponding prefix is provided:
adolc_prefix Including the ADOL-C Examples and Tests
colpack_prefix Including the ColPack Sparsity Calculations
eigen_prefix Including the Eigen Examples and Tests
fadbad_prefix Including the FADBAD Speed Tests
ipopt_prefix Including the cppad_ipopt Library and Tests
sacado_prefix Including the Sacado Speed Tests

cppad_cxx_flags
This specifies the addition compiler flags, besides the debug and release flags, that are used when compiling the CppAD examples and tests. The default value for these flags is the empty string "". These flags must be valid for the C++ compiler on your system. For example, if you are using g++ you could specify 
 
     -D cppad_cxx_flags="-Wall -ansi -pedantic-errors -std=c++11 -Wshadow"

C++11
In order for the compiler to take advantage of features that are new in C++11, the cppad_cxx_flags must enable these features. The compiler may still be used with a flag that disables the new features (unless it is a Microsoft compiler; i.e., _MSC_VER is defined).

cppad_profile_flag
This specifies an addition compiler and link flag that is used for profiling the speed tests. A profile version of the speed test is only build when this argument is present.

Eigen and Fadbad
The packages eigen and fadbad currently generate a lot of shadowed variable warnings. If the -Wshadow flag is present, it is automatically removed when compiling examples and test that use these packages.

cppad_testvector
See Choosing the CppAD Test Vector Template Class.

cppad_max_num_threads
The value cppad_max_num_threads must be greater than or equal to four; i.e., max_num_threads >= 4 . The current default value for cppad_max_num_threads is 48, but it may change in future versions of CppAD. The value cppad_max_num_threads in turn specifies the default value for the preprocessor symbol CPPAD_MAX_NUM_THREADS .

cppad_tape_id_type
The type cppad_tape_id_type is used for identifying different tapes. The valid values for this type are unsigned char, unsigned short int, unsigned int, and size_t. The smaller the value of sizeof(cppad_tape_id_type) , the less memory is used. On the other hand, the value
     std::numeric_limits<cppad_tape_id_type>::max()
 must be larger than the maximum number of tapes used by one thread times CPPAD_MAX_NUM_THREADS .

cstdint
If all of the following cstdint types are defined, they can also be used as the value of cppad_tape_addr_type : uint8_t, uint16_t, uint32_t, uint64_t.

cppad_tape_addr_type
The type cppad_tape_addr_type is used for address in the AD recordings (tapes). The valid values for this argument are unsigned char, unsigned short int, unsigned int, size_t. The smaller the value of sizeof(cppad_tape_addr_type) , the less memory is used. On the other hand, the value
     std::numeric_limits<cppad_tape_addr_type>::max()
 must be larger than any of the following: size_op , size_op_arg , size_par , size_par , size_par .

cstdint
If all of the following cstdint types are defined, they can also be used as the value of cppad_tape_addr_type : uint8_t, uint16_t, uint32_t, uint64_t.

cppad_deprecated
The default value for cppad_deprecated is NO. If it is YES, then all the CppAD deprecated features are included in the installation . Otherwise, some of the deprecated features may be excluded from the installation. (The intention here is to exclude more deprecated features as time marches on.)
Input File: omh/install/cmake.omh cppad-20170000.3/doc/get_adolc.sh.xml0000644000175200017650000001137413057470504016256 0ustar coincoin-web Download and Install Adolc in Build Directory
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Download and Install Adolc in Build Directory

Syntax
bin/get_adolc.sh

Purpose
If you are using Unix, this command will download and install ADOL-C in the CppAD build directory.

Requirements
You must first use get_colpack.sh to download and install ColPack (coloring algorithms used for sparse matrix derivatives).

Distribution Directory
This command must be executed in the distribution directory .

External Directory
The Adolc source code is downloaded into the sub-directory build/external below the distribution directory.

Prefix Directory
The Adolc include files are installed in the sub-directory build/prefix/include/adolc below the distribution directory.

Reuse
The files build/external/ADOL-C-version.tgz and the directory build/external/ADOL-C-version will be reused if they exist. Delete this file and directory to get a complete rebuild.
Input File: bin/get_adolc.sh cppad-20170000.3/doc/colpack_prefix.xml0000644000175200017650000001416313057470504016714 0ustar coincoin-web Including the ColPack Sparsity Calculations
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Including the ColPack Sparsity Calculations

Purpose
If you specify a colpack_prefix on the cmake command line, the CppAD sparse_jacobian calculations use the ColPack package.

colpack_prefix
If ColPack is installed on your system, you can specify a value for its install colpack_prefix on the cmake command line. The value of colpack_prefix must be such that, for one of the directories dir in cmake_install_includedirs ,
     colpack_prefix/dir/ColPack/ColPackHeaders.h
 is a valid way to reference to the include file ColPackHeaders.h.

cppad_lib
The ColPack header files has a
     using namespace std
 at the global level. For this reason, CppAD does not include these files. It is therefore necessary to link the object library cppad_lib when using ColPack.

Example
The file colpack_jac.cpp (colpack_hes.cpp ) contains an example and test of using ColPack to compute the coloring for sparse Jacobians (Hessians). It returns true, if it succeeds and false otherwise.

get_colpack
If you are using Unix, you can download and install a copy of ColPack using get_colpack.sh . The corresponding colpack_prefix would be build/prefix.
Input File: omh/install/colpack_prefix.omh cppad-20170000.3/doc/colpack_jac.cpp.xml0000644000175200017650000005350113057470504016734 0ustar coincoin-web Using ColPack: Example and Test
Prev Next colpack_jac.cpp Headings

Using ColPack: Example and Test

# include <cppad/cppad.hpp>
bool colpack_jac(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
     typedef CPPAD_TESTVECTOR(double)     d_vector;
     typedef CppAD::vector<size_t>        i_vector;
     size_t i, j, k, ell;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 4;
     a_vector  a_x(n);
     for(j = 0; j < n; j++)
          a_x[j] = AD<double> (0);

     // declare independent variables and starting recording
     CppAD::Independent(a_x);

     size_t m = 3;
     a_vector  a_y(m);
     a_y[0] = a_x[0] + a_x[1];
     a_y[1] = a_x[2] + a_x[3];
     a_y[2] = a_x[0] + a_x[1] + a_x[2] + a_x[3] * a_x[3] / 2.;

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(a_x, a_y);

     // new value for the independent variable vector
     d_vector x(n);
     for(j = 0; j < n; j++)
          x[j] = double(j);

     /*
           [ 1 1 0 0  ]
     jac = [ 0 0 1 1  ]
           [ 1 1 1 x_3]
     */
     d_vector check(m * n);
     check[0] = 1.; check[1] = 1.; check[2]  = 0.; check[3]  = 0.;
     check[4] = 0.; check[5] = 0.; check[6]  = 1.; check[7]  = 1.;
     check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3];

     // Normally one would use f.ForSparseJac or f.RevSparseJac to compute
     // sparsity pattern, but for this example we extract it from check.
     std::vector< std::set<size_t> >  p(m);

     // using row and column indices to compute non-zero in rows 1 and 2
     i_vector row, col;
     for(i = 0; i < m; i++)
     {     for(j = 0; j < n; j++)
          {     ell = i * n + j;
               if( check[ell] != 0. )
               {     row.push_back(i);
                    col.push_back(j);
                    p[i].insert(j);
               }
          }
     }
     size_t K = row.size();
     d_vector jac(K);

     // empty work structure
     CppAD::sparse_jacobian_work work;
     ok &= work.color_method == "cppad";

     // choose to use ColPack
     work.color_method = "colpack";

     // forward mode
     size_t n_sweep = f.SparseJacobianForward(x, p, row, col, jac, work);
     for(k = 0; k < K; k++)
     {     ell = row[k] * n + col[k];
          ok &= NearEqual(check[ell], jac[k], eps, eps);
     }
     ok &= n_sweep == 4;

     // reverse mode
     work.clear();
     work.color_method = "colpack";
     n_sweep = f.SparseJacobianReverse(x, p, row, col, jac, work);
     for(k = 0; k < K; k++)
     {     ell = row[k] * n + col[k];
          ok &= NearEqual(check[ell], jac[k], eps, eps);
     }
     ok &= n_sweep == 2;

     return ok;
}
Input File: example/colpack_jac.cpp cppad-20170000.3/doc/colpack_hes.cpp.xml0000644000175200017650000006147513057470504016767 0ustar coincoin-web Using ColPack: Example and Test
Prev Next colpack_hes.cpp Headings

Using ColPack: Example and Test

# include <cppad/cppad.hpp>
bool colpack_hes(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
     typedef CPPAD_TESTVECTOR(double)     d_vector;
     typedef CppAD::vector<size_t>        i_vector;
     size_t i, j, k, ell;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 5;
     a_vector  a_x(n);
     for(j = 0; j < n; j++)
          a_x[j] = AD<double> (0);

     // declare independent variables and starting recording
     CppAD::Independent(a_x);

     // colpack example case where hessian is a spear head
     // i.e, H(i, j) non zero implies i = 0, j = 0, or i = j
     AD<double> sum = 0.0;
     // partial_0 partial_j = x[j]
     // partial_j partial_j = x[0]
     for(j = 1; j < n; j++)
          sum += a_x[0] * a_x[j] * a_x[j] / 2.0;
     //
     // partial_i partial_i = 2 * x[i]
     for(i = 0; i < n; i++)
          sum += a_x[i] * a_x[i] * a_x[i] / 3.0;

     // declare dependent variables
     size_t m = 1;
     a_vector  a_y(m);
     a_y[0] = sum;

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(a_x, a_y);

     // new value for the independent variable vector
     d_vector x(n);
     for(j = 0; j < n; j++)
          x[j] = double(j + 1);

     /*
           [ 2  2  3  4  5 ]
     hes = [ 2  5  0  0  0 ]
           [ 3  0  7  0  0 ]
           [ 4  0  0  9  0 ]
           [ 5  0  0  0 11 ]
     */
     d_vector check(n * n);
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     size_t index = i * n + j;
               check[index] = 0.0;
               if( i == 0 && 1 <= j )
                    check[index] += x[j];
               if( 1 <= i && j == 0 )
                    check[index] += x[i];
               if( i == j )
               {     check[index] += 2.0 * x[i];
                    if( i != 0 )
                         check[index] += x[0];
               }
          }
     }
     // Normally one would use f.RevSparseHes to compute
     // sparsity pattern, but for this example we extract it from check.
     std::vector< std::set<size_t> >  p(n);
     i_vector row, col;
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     ell = i * n + j;
               if( check[ell] != 0. )
               {     // insert this non-zero entry in sparsity pattern
                    p[i].insert(j);

                    // the Hessian is symmetric, so only upper lower triangle
                    if( j <= i )
                    {     row.push_back(i);
                         col.push_back(j);
                    }
               }
          }
     }
     size_t K = row.size();
     d_vector hes(K);

     // contrast and check results using both cppad and colpack
     CppAD::sparse_hessian_work work;
     for(size_t i_method = 0; i_method < 3; i_method++)
     {     // empty work structure
          ok &= work.color_method == "cppad.symmetric";
          if( i_method == 2 )
               work.color_method = "colpack.star";

          // compute Hessian
          d_vector w(m);
          w[0] = 1.0;
          size_t n_sweep = f.SparseHessian(x, w, p, row, col, hes, work);

          // check result
          for(k = 0; k < K; k++)
          {     ell = row[k] * n + col[k];
               ok &= NearEqual(check[ell], hes[k], eps, eps);
          }
          if( work.color_method != "cppad.general" )
               ok &= n_sweep == 2;
          else
               ok &= n_sweep == 5;
          //
          // check that clear resets color_method to cppad.symmetric
          work.clear();
          ok &= work.color_method == "cppad.symmetric";
     }

     return ok;
}
Input File: example/colpack_hes.cpp cppad-20170000.3/doc/get_colpack.sh.xml0000644000175200017650000001074313057470504016607 0ustar coincoin-web Download and Install ColPack in Build Directory
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Download and Install ColPack in Build Directory

Syntax
bin/get_colpack.sh

Purpose
If you are using Unix, this command will download and install ColPack in the CppAD build directory.

Distribution Directory
This command must be executed in the distribution directory .

External Directory
The ColPack source code is downloaded into the sub-directory build/external below the distribution directory.

Prefix Directory
The ColPack include files are installed in the sub-directory build/prefix/include/ColPack below the distribution directory.

Reuse
The file build/external/ColPack-version.tar.gz and the directory build/external/ColPack-version will be reused if they exist. Delete this file and directory to get a complete rebuild.
Input File: bin/get_colpack.sh cppad-20170000.3/doc/eigen_prefix.xml0000644000175200017650000001631613057470504016371 0ustar coincoin-web Including the Eigen Examples and Tests
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Including the Eigen Examples and Tests

Purpose
CppAD can include the following examples and tests that use the linear algebra package Eigen :
eigen_plugin.hpp Source Code for eigen_plugin.hpp
cppad_eigen.hpp Enable Use of Eigen Linear Algebra Package with CppAD
eigen_array.cpp Using Eigen Arrays: Example and Test
eigen_det.cpp Using Eigen To Compute Determinant: Example and Test
atomic_eigen_mat_mul.hpp Atomic Eigen Matrix Multiply Class
atomic_eigen_mat_inv.hpp Atomic Eigen Matrix Inversion Class

eigen_prefix
If Eigen is installed on your system, you can specify a value for its install eigen_prefix on the cmake command line. The value of eigen_prefix must be such that, for one of the directories dir in cmake_install_includedirs ,
     eigen_prefix/dir/Eigen/Core
 is a valid way to reference to the include file Core;

Examples
If you include eigen_prefix on the cmake command line, you will be able to run the Eigen examples list above by executing the following commands starting in the distribution directory :
     cd build/example
     make check_example
 If you do this, you will see an indication that the examples eigen_array and eigen_det have passed their correctness check. options to this program.

Test Vector
If you have specified eigen_prefix you can choose
     -D cppad_testvector=eigen
 on the cmake command line. This we set the CppAD testvector to use Eigen vectors.

get_eigen
If you are using Unix, you can download and install a copy of Eigen using get_eigen.sh . The corresponding eigen_prefix would be build/prefix.
Input File: omh/install/eigen_prefix.omh cppad-20170000.3/doc/get_eigen.sh.xml0000644000175200017650000001055713057470504016265 0ustar coincoin-web Download and Install Eigen in Build Directory
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Download and Install Eigen in Build Directory

Syntax
bin/get_eigen.sh

Purpose
If you are using Unix, this command will download and install Eigen in the CppAD build directory.

Distribution Directory
This command must be executed in the distribution directory .

External Directory
The Eigen source code is downloaded into the sub-directory build/external below the distribution directory.

Prefix Directory
The Eigen include files are installed in the sub-directory build/prefix/include/Eigen below the distribution directory.

Reuse
The file build/external/eigen-version.tar.gz and the directory build/external/eigen-version will be reused if they exist. Delete this file and directory to get a complete rebuild.
Input File: bin/get_eigen.sh cppad-20170000.3/doc/fadbad_prefix.xml0000644000175200017650000001357313057470504016505 0ustar coincoin-web Including the FADBAD Speed Tests
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Including the FADBAD Speed Tests

Purpose
CppAD includes speed comparisons for the AD package FADBAD ; see speed_fadbad .

fadbad_prefix
If FADBAD is installed on your system, you can specify a value for its install fadbad_prefix on the cmake command line. The value of fadbad_prefix must be such that, for one of the directories dir in cmake_install_includedirs ,
     fadbad_prefix/dir/FADBAD++/badiff.h
 is a valid way to reference to the include file badiff.h;

Speed Tests
If you include fadbad_prefix on the cmake command line, you will be able to run the FADBAD speed correctness tests by executing the following commands starting in the distribution directory :
     cd build/speed/fadbad
     make check_speed_fadbad
 After executing make check, you can run a specific FADBAD speed test by executing the command ./speed_fadbad; see speed_main for the meaning of the command line options to this program.

get_fadbad
If you are using Unix, you can download and install a copy of Fadbad using get_fadbad.sh . The corresponding fadbad_prefix would be build/prefix.
Input File: omh/install/fadbad_prefix.omh cppad-20170000.3/doc/get_fadbad.sh.xml0000644000175200017650000000734413057470504016377 0ustar coincoin-web Download and Install Fadbad in Build Directory
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Download and Install Fadbad in Build Directory

Syntax
bin/get_fadbad.sh

Purpose
If you are using Unix, this command will download and install Fadbad in the CppAD build directory.

Distribution Directory
This command must be executed in the distribution directory .

External Directory
The Fadbad source code is downloaded into the sub-directory build/external below the distribution directory.

Prefix Directory
The Fadbad include files are installed in the sub-directory build/prefix/include/FADBAD++ below the distribution directory.
Input File: bin/get_fadbad.sh cppad-20170000.3/doc/ipopt_prefix.xml0000644000175200017650000001335013057470504016430 0ustar coincoin-web Including the cppad_ipopt Library and Tests
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Including the cppad_ipopt Library and Tests

Purpose
Includes the cppad_ipopt_nlp example and tests as well as installing the cppad_ipopt library during the make install step.

ipopt_prefix
If you have Ipopt installed on your system, you can specify the value for ipopt_prefix on the cmake command line. The value of ipopt_prefix must be such that, for one of the directories dir in cmake_install_includedirs ,
     ipopt_prefix/dir/coin/IpIpoptApplication.hpp
 is a valid way to reference to the include file IpIpoptApplication.hpp.

Examples and Tests
If you include ipopt_prefix on the cmake command line, you will be able to run the Ipopt examples and tests by executing the following commands starting in the distribution directory :
     cd cppad_ipopt
     make check_ipopt
get_ipopt
If you are using Unix, you can download and install a copy of Ipopt using get_ipopt.sh . The corresponding ipopt_prefix would be build/prefix.
Input File: omh/install/ipopt_prefix.omh cppad-20170000.3/doc/get_ipopt.sh.xml0000644000175200017650000001060613057470504016324 0ustar coincoin-web Download and Install Ipopt in Build Directory
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Download and Install Ipopt in Build Directory

Syntax
bin/get_ipopt.sh

Purpose
If you are using Unix, this command will download and install Ipopt in the CppAD build directory.

Distribution Directory
This command must be executed in the distribution directory .

External Directory
The Ipopt source code is downloaded and compiled in the sub-directory build/external below the distribution directory.

Prefix Directory
The Ipopt libraries and include files are installed in the sub-directory build/prefix below the distribution directory.

Reuse
The file build/external/Ipopt-version.tgz and the directory build/external/Ipopt-version will be reused if they exist. Delete this file and directory to get a complete rebuild.
Input File: bin/get_ipopt.sh cppad-20170000.3/doc/sacado_prefix.xml0000644000175200017650000001363113057470504016531 0ustar coincoin-web Including the Sacado Speed Tests
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Including the Sacado Speed Tests

Purpose
CppAD includes speed comparisons for the AD package Sacado ; see speed_sacado .

sacado_prefix
If Sacado is installed on your system, you can specify a value for its install sacado_prefix on the cmake command line. The value of sacado_prefix must be such that, for one of the directories dir in cmake_install_includedirs ,
     sacado_prefix/dir/Sacado.hpp
 is a valid way to reference to the include file Sacado.hpp;

Speed Tests
If you include sacado_prefix on the cmake command line, you will be able to run the Sacado speed correctness tests by executing the following commands starting in the distribution directory :
     cd build/speed/sacado
     make check_speed_sacado
 After executing make check_speed_sacado, you can run a specific Sacado speed test by executing the command ./speed_sacado; see speed_main for the meaning of the command line options to this program.

get_sacado
If you are using Unix, you can download and install a copy of Sacado using get_sacado.sh . The corresponding sacado_prefix would be build/prefix.
Input File: omh/install/sacado_prefix.omh cppad-20170000.3/doc/get_sacado.sh.xml0000644000175200017650000001075113057470504016424 0ustar coincoin-web Download and Install Sacado in Build Directory
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Download and Install Sacado in Build Directory

Syntax
bin/get_sacado.sh

Purpose
If you are using Unix, this command will download and install Sacado in the CppAD build directory.

Distribution Directory
This command must be executed in the distribution directory .

External Directory
The Sacado source code is downloaded into the sub-directory build/external below the distribution directory.

Prefix Directory
The Sacado libraries and include files are installed in the sub-directory build/prefix below the distribution directory.

Reuse
The file build/external/trilinos-version-Source.tar.gz and the directory build/external/trilinos-version-Source will be reused if they exist. Delete this file and directory to get a complete rebuild.
Input File: bin/get_sacado.sh cppad-20170000.3/doc/cppad_testvector.xml0000644000175200017650000001317013057470504017271 0ustar coincoin-web Choosing the CppAD Test Vector Template Class
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Choosing the CppAD Test Vector Template Class

Purpose
The value cppad_testvector in the cmake command must be one of the following: boost, cppad, eigen, or std. It specifies which type of vector is corresponds to the template class CPPAD_TESTVECTOR which is used for many of the CppAD examples and tests.

std
If cppad_testvector is std , the std::vector template class is used to define CPPAD_TESTVECTOR.

cppad
If cppad_testvector is cppad , the cppad_vector template class is used to define CPPAD_TESTVECTOR.

boost
If cppad_testvector is boost , boost ublas vector template class is used to define CPPAD_TESTVECTOR. In this case, the cmake FindBoost module must be able to automatically figure out where Boost is installed.

eigen
If cppad_testvector is eigen , one of the eigen template classes is used to define CPPAD_TESTVECTOR. In this case, eigen_prefix must be specified on the cmake command line.
Input File: omh/install/testvector.omh cppad-20170000.3/doc/cmake_check.xml0000644000175200017650000001371613057470504016143 0ustar coincoin-web Checking the CppAD Examples and Tests
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Checking the CppAD Examples and Tests

Purpose
After you configure your system with the cmake command you can run the CppAD example and tests to make sure that CppAD functions properly on your system.

Check All
In the build subdirectory of the distribution directory execute the command 
 
     make check
This will build and run all of the tests that are support by your system and the cmake command options.

Windows
If you created nmake makefiles, you will have to use nmake instead of make in the commands above and below; see windows file extraction and testing .

Subsets
It is possible to build and run the following subsets of the examples and tests:
Command Description
make check_compare_c Compare Speed of C and C++
make check_introduction the programs in the Introduction
make check_example most of the Example programs
make check_print_for the PrintFor command
make check_test_more correctness tests that are not examples
make check_multi_thread multi_thread tests (run correctness only)
make check_speed single threading speed tests (run correctness only)
make check_cppad_ipopt the cppad_ipopt_nlp speed and correctness tests
Input File: omh/install/cmake_check.omh cppad-20170000.3/doc/pkgconfig.xml0000644000175200017650000001766413057470504015703 0ustar coincoin-web CppAD pkg-config Files
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CppAD pkg-config Files

Purpose
The pkg-config package helps with the use of installed libraries; see its guide for more information.

Usage
The necessary flags for compiling code that includes CppAD can be obtained with the command 
 
     pkg-config --cflags cppad
Note that this command assumes cppad.pc is in the search path PKG_CONFIG_PATH. If ipopt_prefix is specified, the necessary flags for linking cppad_ipopt can be obtained with the commands 
 
     pkg-config --libs cppad
Note that this command assumes ipopt.pc is in the search path PKG_CONFIG_PATH.

Defined Fields
Name A human-readable name for the CppAD package.
Description A brief description of the CppAD package.
URL A URL where people can get more information about the CppAD package.
Version A string specifically defining the version of the CppAD package.
Cflags The necessary flags for using any of the CppAD include files.
Libs If ipopt_prefix is specified, the necessary flags for using the cppad_ipopt library
Requires If ipopt_prefix is specified, the packages required to use the cppad_ipopt library

CppAD Configuration Files
In the table below, builddir is the build directory; i.e., the directory where the CppAD cmake command is executed. The directory prefix is the value of cppad_prefix during configuration. The directory datadir is the value of cmake_install_datadir . The following configuration files contain the information above
File Description
prefix/datadir/pkgconfig/cppad.pc for use after make install
builddir/pkgconfig/cppad-uninstalled.pc for testing before make install
Input File: omh/install/pkgconfig.omh cppad-20170000.3/doc/_pkgconfig_xml.js0000644000175200017650000000303613057470504016522 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'install.xml', 'pkgconfig.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'download.xml', 'cmake.xml', 'cmake_check.xml', 'pkgconfig.xml', 'auto_tools.xml' ]; var list_current0 = [ 'pkgconfig.xml#Purpose', 'pkgconfig.xml#Usage', 'pkgconfig.xml#Defined Fields', 'pkgconfig.xml#CppAD Configuration Files' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/introduction.xml0000644000175200017650000002070513057470504016443 0ustar coincoin-web An Introduction by Example to Algorithmic Differentiation
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An Introduction by Example to Algorithmic Differentiation

Purpose
This is an introduction by example to Algorithmic Differentiation. Its purpose is to aid in understand what AD calculates, how the calculations are preformed, and the amount of computation and memory required for a forward or reverse sweep.

Preface

Algorithmic Differentiation
Algorithmic Differentiation (often referred to as Automatic Differentiation or just AD) uses the software representation of a function to obtain an efficient method for calculating its derivatives. These derivatives can be of arbitrary order and are analytic in nature (do not have any truncation error).

Forward Mode
A forward mode sweep computes the partial derivative of all the dependent variables with respect to one independent variable (or independent variable direction).

Reverse Mode
A reverse mode sweep computes the derivative of one dependent variable (or one dependent variable direction) with respect to all the independent variables.

Operation Count
The number of floating point operations for either a forward or reverse mode sweep is a small multiple of the number required to evaluate the original function. Thus, using reverse mode, you can evaluate the derivative of a scalar valued function with respect to thousands of variables in a small multiple of the work to evaluate the original function.

Efficiency
AD automatically takes advantage of the speed of your algorithmic representation of a function. For example, if you calculate a determinant using LU factorization, AD will use the LU representation for the derivative of the determinant (which is faster than using the definition of the determinant).

Outline
  1. Demonstrate the use of CppAD to calculate derivatives of a polynomial: get_started.cpp .
  2. Present two algorithms that approximate the exponential function. The first algorithm exp_2.hpp is simpler and does not include any logical variables or loops. The second algorithm exp_eps.hpp includes logical operations and a while loop. For each of these algorithms, do the following:
    1. Define the mathematical function corresponding to the algorithm (exp_2 and exp_eps ).
    2. Write out the floating point operation sequence, and corresponding values, that correspond to executing the algorithm for a specific input (exp_2_for0 and exp_eps_for0 ).
    3. Compute a forward sweep derivative of the operation sequence (exp_2_for1 and exp_eps_for1 ).
    4. Compute a reverse sweep derivative of the operation sequence (exp_2_rev1 and exp_eps_rev1 ).
    5. Use CppAD to compute both a forward and reverse sweep of the operation sequence (exp_2_cppad and exp_eps_cppad ).
  3. The program exp_apx_main.cpp runs all of the test routines that validate the calculations in the exp_2 and exp_eps presentation.


Reference
An in-depth review of AD theory and methods can be found in the book Evaluating Derivatives:
Principles and Techniques of Algorithmic Differentiation
 , Andreas Griewank, SIAM Frontiers in Applied Mathematics, 2000.

Contents
get_started.cppGetting Started Using CppAD to Compute Derivatives
exp_2Second Order Exponential Approximation
exp_epsAn Epsilon Accurate Exponential Approximation
exp_apx_main.cppCorrectness Tests For Exponential Approximation in Introduction
Input File: omh/introduction.omh cppad-20170000.3/doc/get_started.cpp.xml0000644000175200017650000005566213057470504017022 0ustar coincoin-web Getting Started Using CppAD to Compute Derivatives
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Getting Started Using CppAD to Compute Derivatives

Purpose
Demonstrate the use of CppAD by computing the derivative of a simple example function.

Function
The example function f : R → R is defined by f ( x ) = a 0 + a 1 * x 1 + ⋯ + a k -1 * x k -1 where a is a fixed vector of length k .

Derivative
The derivative of f ( x ) is given by f ' ( x ) = a 1 + 2 * a 2 * x + ⋯ + ( k -1 ) * a k -1 * x k -2
Value
For the particular case in this example, k is equal to 5, a = ( 1 , 1 , 1 , 1 , 1 ) , and x = 3 . If follows that f ' ( 3 ) = 1 + 2 * 3 + 3 * 3 2 + 4 * 3 3 = 142
Poly
The routine Poly is defined below for this particular application. A general purpose polynomial evaluation routine is documented and distributed with CppAD (see Poly ).

Exercises
Modify the program below to accomplish the following tasks using CppAD:
  1. Compute and print the derivative of f ( x ) = 1 + x + x 2 + x 3 + x 4 at the point x = 2 .
  2. Compute and print the derivative of f ( x ) = 1 + x + x 2 / 2 at the point x = .5 .
  3. Compute and print the derivative of f ( x ) = exp ( x ) - 1 - x - x 2 / 2 at the point x = .5 .


Program 
#include <iostream>      // standard input/output
#include <vector>        // standard vector
#include <cppad/cppad.hpp> // the CppAD package http://www.coin-or.org/CppAD/

namespace {
      // define y(x) = Poly(a, x) in the empty namespace
      template <class Type>
      Type Poly(const std::vector<double> &a, const Type &x)
      {     size_t k  = a.size();
            Type y   = 0.;  // initialize summation
            Type x_i = 1.;  // initialize x^i
            size_t i;
            for(i = 0; i < k; i++)
            {     y   += a[i] * x_i;  // y   = y + a_i * x^i
                  x_i *= x;           // x_i = x_i * x
            }
            return y;
      }
}
// main program
int main(void)
{     using CppAD::AD;           // use AD as abbreviation for CppAD::AD
      using std::vector;         // use vector as abbreviation for std::vector
      size_t i;                  // a temporary index

      // vector of polynomial coefficients
      size_t k = 5;              // number of polynomial coefficients
      vector<double> a(k);       // vector of polynomial coefficients
      for(i = 0; i < k; i++)
            a[i] = 1.;           // value of polynomial coefficients

      // domain space vector
      size_t n = 1;              // number of domain space variables
      vector< AD<double> > X(n); // vector of domain space variables
      X[0] = 3.;                 // value corresponding to operation sequence

      // declare independent variables and start recording operation sequence
      CppAD::Independent(X);

      // range space vector
      size_t m = 1;              // number of ranges space variables
      vector< AD<double> > Y(m); // vector of ranges space variables
      Y[0] = Poly(a, X[0]);      // value during recording of operations

      // store operation sequence in f: X -> Y and stop recording
      CppAD::ADFun<double> f(X, Y);

      // compute derivative using operation sequence stored in f
      vector<double> jac(m * n); // Jacobian of f (m by n matrix)
      vector<double> x(n);       // domain space vector
      x[0] = 3.;                 // argument value for derivative
      jac  = f.Jacobian(x);      // Jacobian for operation sequence

      // print the results
      std::cout << "f'(3) computed by CppAD = " << jac[0] << std::endl;

      // check if the derivative is correct
      int error_code;
      if( jac[0] == 142. )
            error_code = 0;      // return code for correct case
      else  error_code = 1;      // return code for incorrect case

      return error_code;
}

Output
Executing the program above will generate the following output: 
 
     f'(3) computed by CppAD = 142

Running
To build and run this program see cmake_check .
Input File: introduction/get_started/get_started.cpp cppad-20170000.3/doc/exp_2.xml0000644000175200017650000003461513057470504014744 0ustar coincoin-web Second Order Exponential Approximation
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Second Order Exponential Approximation

Syntax
# include "exp_2.hpp"
y = exp_2(x)

Purpose
This is a simple example algorithm that is used to demonstrate Algorithmic Differentiation (see exp_eps for a more complex example).

Mathematical Form
The exponential function can be defined by exp ( x ) = 1 + x 1 / 1 ! + x 2 / 2 ! + ⋯ The second order approximation for the exponential function is exp _ 2 ( x ) = 1 + x + x 2 / 2
include
The include command in the syntax is relative to
     cppad-yyyymmdd/introduction/exp_apx
 where cppad-yyyymmdd is the distribution directory created during the beginning steps of the installation of CppAD.

x
The argument x has prototype
     const Type &x
 (see Type below). It specifies the point at which to evaluate the approximation for the second order exponential approximation.

y
The result y has prototype
     Type y
 It is the value of the exponential function approximation defined above.

Type
If u and v are Type objects and i is an int:
Operation Result Type Description
Type(i) Type construct object with value equal to i
Type u = v Type construct u with value equal to v
u * v Type result is value of u * v
u / v Type result is value of u / v
u + v Type result is value of u + v

Contents
exp_2.hppexp_2: Implementation
exp_2.cppexp_2: Test
exp_2_for0exp_2: Operation Sequence and Zero Order Forward Mode
exp_2_for1exp_2: First Order Forward Mode
exp_2_rev1exp_2: First Order Reverse Mode
exp_2_for2exp_2: Second Order Forward Mode
exp_2_rev2exp_2: Second Order Reverse Mode
exp_2_cppadexp_2: CppAD Forward and Reverse Sweeps

Implementation
The file exp_2.hpp contains a C++ implementation of this function.

Test
The file exp_2.cpp contains a test of this implementation. It returns true for success and false for failure.

Exercises
  1. Suppose that we make the call 
     
     double x = .1;
     double y = exp_2(x);
    What is the value assigned to v1, v2, ... ,v5 in exp_2.hpp ?
  2. Extend the routine exp_2.hpp to a routine exp_3.hpp that computes 1 + x 2 / 2 ! + x 3 / 3 ! Do this in a way that only assigns one value to each variable (as exp_2 does).
  3. Suppose that we make the call 
     
     double x = .5;
     double y = exp_3(x);
    using exp_3 created in the previous problem. What is the value assigned to the new variables in exp_3 (variables that are in exp_3 and not in exp_2) ?
Input File: introduction/exp_apx/exp_2.hpp cppad-20170000.3/doc/_exp_2_xml.js0000644000175200017650000000345013057470504015570 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'introduction.xml', 'exp_2.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'get_started.cpp.xml', 'exp_2.xml', 'exp_eps.xml', 'exp_apx_main.cpp.xml' ]; var list_down0 = [ 'exp_2.hpp.xml', 'exp_2.cpp.xml', 'exp_2_for0.xml', 'exp_2_for1.xml', 'exp_2_rev1.xml', 'exp_2_for2.xml', 'exp_2_rev2.xml', 'exp_2_cppad.xml' ]; var list_current0 = [ 'exp_2.xml#Syntax', 'exp_2.xml#Purpose', 'exp_2.xml#Mathematical Form', 'exp_2.xml#include', 'exp_2.xml#x', 'exp_2.xml#y', 'exp_2.xml#Type', 'exp_2.xml#Contents', 'exp_2.xml#Implementation', 'exp_2.xml#Test', 'exp_2.xml#Exercises' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/exp_2.hpp.xml0000644000175200017650000001171113057470504015522 0ustar coincoin-web exp_2: Implementation
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exp_2: Implementation
template <class Type>
Type exp_2(const Type &x)
{       Type v1  = x;                // v1 = x
        Type v2  = Type(1) + v1;     // v2 = 1 + x
        Type v3  = v1 * v1;          // v3 = x^2
        Type v4  = v3 / Type(2);     // v4 = x^2 / 2
        Type v5  = v2 + v4;          // v5 = 1 + x + x^2 / 2
        return v5;                   // exp_2(x) = 1 + x + x^2 / 2
}
Input File: introduction/exp_apx/exp_2.omh cppad-20170000.3/doc/exp_2.cpp.xml0000644000175200017650000001062413057470504015517 0ustar coincoin-web exp_2: Test
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exp_2: Test
# include <cmath>           // define fabs function
# include "exp_2.hpp"       // definition of exp_2 algorithm
bool exp_2(void)
{     double x     = .5;
     double check = 1 + x + x * x / 2.;
     bool   ok    = std::fabs( exp_2(x) - check ) <= 1e-10;
     return ok;
}
Input File: introduction/exp_apx/exp_2.omh cppad-20170000.3/doc/exp_2_for0.xml0000644000175200017650000004152313057470504015666 0ustar coincoin-web exp_2: Operation Sequence and Zero Order Forward Mode
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exp_2: Operation Sequence and Zero Order Forward Mode

Mathematical Form
The operation sequence (see below) corresponding to the algorithm exp_2.hpp is the same for all values of x . The mathematical form for the corresponding function is f ( x ) = 1 + x + x 2 / 2 An algorithmic differentiation package does not operate on the mathematical function f ( x ) but rather on the particular algorithm used to compute the function (in this case exp_2.hpp ).

Zero Order Expansion
In general, a zero order forward sweep is given a vector x ( 0 ) ∈ R n and it returns the corresponding vector y ( 0 ) ∈ R m given by y ( 0 ) = f ( x ( 0 ) ) The superscript ( 0 ) denotes zero order derivative; i.e., it is equal to the value of the corresponding variable. For the example we are considering here, both n and m are equal to one.

Operation Sequence
An atomic Type operation is an operation that has a Type result and is not made up of other more basic operations. A sequence of atomic Type operations is called a Type operation sequence. Given an C++ algorithm and its inputs, there is a corresponding Type operation sequence for each type. If Type is clear from the context, we drop it and just refer to the operation sequence.

We consider the case where exp_2.hpp is executed with x ( 0 ) = .5 . The table below contains the corresponding operation sequence and the results of a zero order sweep.

Index
The Index column contains the index in the operation sequence of the corresponding atomic operation and variable. A Forward sweep starts with the first operation and ends with the last.

Code
The Code column contains the C++ source code corresponding to the corresponding atomic operation in the sequence.

Operation
The Operation column contains the mathematical function corresponding to each atomic operation in the sequence.

Zero Order
The Zero Order column contains the zero order derivative for the corresponding variable in the operation sequence. Forward mode refers to the fact that these coefficients are computed in the same order as the original algorithm; i.e, in order of increasing index in the operation sequence.

Sweep
Index    Code    Operation    Zero Order
1    Type v1 = x; v 1 = x v 1 ( 0 ) = 0.5
2    Type v2 = Type(1) + v1; v 2 = 1 + v 1 v 2 ( 0 ) = 1.5
3    Type v3 = v1 * v1; v 3 = v 1 * v 1 v 3 ( 0 ) = 0.25
4    Type v4 = v3 / Type(2); v 4 = v 3 / 2 v 4 ( 0 ) = 0.125
5    Type v5 = v2 + v4; v 5 = v 2 + v 4 v 5 ( 0 ) = 1.625
Return Value
The return value for this case is 1.625 = v 5 ( 0 ) = f ( x ( 0 ) )
Verification
The file exp_2_for0.cpp contains a routine that verifies the values computed above. It returns true for success and false for failure.

Exercises
  1. Suppose that x ( 0 ) = .2 , what is the result of a zero order forward sweep for the operation sequence above; i.e., what are the corresponding values for v 1 ( 0 ) , v 2 ( 0 ) , ⋯ , v 5 ( 0 )
  2. Create a modified version of exp_2_for0.cpp that verifies the values you obtained for the previous exercise.
  3. Create and run a main program that reports the result of calling the modified version of exp_2_for0.cpp in the previous exercise.
Input File: introduction/exp_apx/exp_2.omh cppad-20170000.3/doc/exp_2_for0.cpp.xml0000644000175200017650000002231513057470504016445 0ustar coincoin-web exp_2: Verify Zero Order Forward Sweep
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exp_2: Verify Zero Order Forward Sweep
# include <cmath>            // for fabs function
bool exp_2_for0(double *v0)  // double v0[6]
{     bool  ok = true;
     double x = .5;

     v0[1] = x;                                  // v1 = x
     ok  &= std::fabs( v0[1] - 0.5) < 1e-10;

     v0[2] = 1. + v0[1];                         // v2 = 1 + v1
     ok  &= std::fabs( v0[2] - 1.5) < 1e-10;

     v0[3] = v0[1] * v0[1];                      // v3 = v1 * v1
     ok  &= std::fabs( v0[3] - 0.25) < 1e-10;

     v0[4] = v0[3] / 2.;                         // v4 = v3 / 2
     ok  &= std::fabs( v0[4] - 0.125) < 1e-10;

     v0[5] = v0[2] + v0[4];                      // v5  = v2 + v4
     ok  &= std::fabs( v0[5] - 1.625) < 1e-10;

     return ok;
}
bool exp_2_for0(void)
{     double v0[6];
     return exp_2_for0(v0);
}
Input File: introduction/exp_apx/exp_2_for0.cpp cppad-20170000.3/doc/exp_2_for1.cpp.xml0000644000175200017650000002451513057470504016452 0ustar coincoin-web exp_2: Verify First Order Forward Sweep
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exp_2: Verify First Order Forward Sweep
# include <cmath>                   // prototype for fabs
extern bool exp_2_for0(double *v0); // computes zero order forward sweep
bool exp_2_for1(double *v1)         // double v1[6]
{     bool ok = true;
     double v0[6];

     // set the value of v0[j] for j = 1 , ... , 5
     ok &= exp_2_for0(v0);

     v1[1] = 1.;                                     // v1 = x
     ok    &= std::fabs( v1[1] - 1. ) <= 1e-10;

     v1[2] = v1[1];                                  // v2 = 1 + v1
     ok    &= std::fabs( v1[2] - 1. ) <= 1e-10;

     v1[3] = v1[1] * v0[1] + v0[1] * v1[1];          // v3 = v1 * v1
     ok    &= std::fabs( v1[3] - 1. ) <= 1e-10;

     v1[4] = v1[3] / 2.;                             // v4 = v3 / 2
     ok    &= std::fabs( v1[4] - 0.5) <= 1e-10;

     v1[5] = v1[2] + v1[4];                          // v5 = v2 + v4
     ok    &= std::fabs( v1[5] - 1.5) <= 1e-10;

     return ok;
}
bool exp_2_for1(void)
{     double v1[6];
     return exp_2_for1(v1);
}
Input File: introduction/exp_apx/exp_2_for1.cpp cppad-20170000.3/doc/exp_2_rev1.cpp.xml0000644000175200017650000002774513057470504016470 0ustar coincoin-web exp_2: Verify First Order Reverse Sweep
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exp_2: Verify First Order Reverse Sweep
# include <cstddef>                 // define size_t
# include <cmath>                   // prototype for fabs
extern bool exp_2_for0(double *v0); // computes zero order forward sweep
bool exp_2_rev1(void)
{     bool ok = true;

     // set the value of v0[j] for j = 1 , ... , 5
     double v0[6];
     ok &= exp_2_for0(v0);

     // initial all partial derivatives as zero
     double f_v[6];
     size_t j;
     for(j = 0; j < 6; j++)
          f_v[j] = 0.;

     // set partial derivative for f5
     f_v[5] = 1.;
     ok &= std::fabs( f_v[5] - 1. ) <= 1e-10; // f5_v5

     // f4 = f5( v1 , v2 , v3 , v4 , v2 + v4 )
     f_v[2] += f_v[5] * 1.;
     f_v[4] += f_v[5] * 1.;
     ok &= std::fabs( f_v[2] - 1. ) <= 1e-10; // f4_v2
     ok &= std::fabs( f_v[4] - 1. ) <= 1e-10; // f4_v4

     // f3 = f4( v1 , v2 , v3 , v3 / 2 )
     f_v[3] += f_v[4] / 2.;
     ok &= std::fabs( f_v[3] - 0.5) <= 1e-10; // f3_v3

     // f2 = f3( v1 , v2 , v1 * v1 )
     f_v[1] += f_v[3] * 2. * v0[1];
     ok &= std::fabs( f_v[1] - 0.5) <= 1e-10; // f2_v1

     // f1 = f2( v1 , 1 + v1 )
     f_v[1] += f_v[2] * 1.;
     ok &= std::fabs( f_v[1] - 1.5) <= 1e-10; // f1_v1

     return ok;
}
Input File: introduction/exp_apx/exp_2_rev1.cpp cppad-20170000.3/doc/exp_2_for2.cpp.xml0000644000175200017650000002472613057470504016457 0ustar coincoin-web exp_2: Verify Second Order Forward Sweep
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exp_2: Verify Second Order Forward Sweep
# include <cmath>                   // prototype for fabs
extern bool exp_2_for0(double *v0); // computes zero order forward sweep
extern bool exp_2_for1(double *v1); // computes first order forward sweep
bool exp_2_for2(void)
{     bool ok = true;
     double v0[6], v1[6], v2[6];

     // set the value of v0[j], v1[j], for j = 1 , ... , 5
     ok &= exp_2_for0(v0);
     ok &= exp_2_for1(v1);

     v2[1] = 0.;                                     // v1 = x
     ok    &= std::fabs( v2[1] - 0. ) <= 1e-10;

     v2[2] = v2[1];                                  // v2 = 1 + v1
     ok    &= std::fabs( v2[2] - 0. ) <= 1e-10;

     v2[3] = 2.*(v0[1]*v2[1] + v1[1]*v1[1]);         // v3 = v1 * v1
     ok    &= std::fabs( v2[3] - 2. ) <= 1e-10;

     v2[4] = v2[3] / 2.;                             // v4 = v3 / 2
     ok    &= std::fabs( v2[4] - 1. ) <= 1e-10;

     v2[5] = v2[2] + v2[4];                          // v5 = v2 + v4
     ok    &= std::fabs( v2[5] - 1. ) <= 1e-10;

     return ok;
}
Input File: introduction/exp_apx/exp_2_for2.cpp cppad-20170000.3/doc/exp_2_rev2.cpp.xml0000644000175200017650000004665213057470504016467 0ustar coincoin-web exp_2: Verify Second Order Reverse Sweep
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exp_2: Verify Second Order Reverse Sweep
# include <cstddef>                 // define size_t
# include <cmath>                   // prototype for fabs
extern bool exp_2_for0(double *v0); // computes zero order forward sweep
extern bool exp_2_for1(double *v1); // computes first order forward sweep
bool exp_2_rev2(void)
{     bool ok = true;

     // set the value of v0[j], v1[j] for j = 1 , ... , 5
     double v0[6], v1[6];
     ok &= exp_2_for0(v0);
     ok &= exp_2_for1(v1);

     // initial all partial derivatives as zero
     double f_v0[6], f_v1[6];
     size_t j;
     for(j = 0; j < 6; j++)
     {     f_v0[j] = 0.;
          f_v1[j] = 0.;
     }

     // set partial derivative for f_5
     f_v1[5] = 1.;
     ok &= std::fabs( f_v1[5] - 1. ) <= 1e-10; // partial f_5 w.r.t v_5^1

     // f_4 = f_5( v_1^0 , ... , v_4^1 , v_2^0 + v_4^0 , v_2^1 + v_4^1 )
     f_v0[2] += f_v0[5] * 1.;
     f_v0[4] += f_v0[5] * 1.;
     f_v1[2] += f_v1[5] * 1.;
     f_v1[4] += f_v1[5] * 1.;
     ok &= std::fabs( f_v0[2] - 0. ) <= 1e-10; // partial f_4 w.r.t. v_2^0
     ok &= std::fabs( f_v0[4] - 0. ) <= 1e-10; // partial f_4 w.r.t. v_4^0
     ok &= std::fabs( f_v1[2] - 1. ) <= 1e-10; // partial f_4 w.r.t. v_2^1
     ok &= std::fabs( f_v1[4] - 1. ) <= 1e-10; // partial f_4 w.r.t. v_4^1

     // f_3 = f_4( v_1^0 , ... , v_3^1, v_3^0 / 2 , v_3^1 / 2 )
     f_v0[3] += f_v0[4] / 2.;
     f_v1[3] += f_v1[4] / 2.;
     ok &= std::fabs( f_v0[3] - 0.  ) <= 1e-10; // partial f_3 w.r.t. v_3^0
     ok &= std::fabs( f_v1[3] - 0.5 ) <= 1e-10; // partial f_3 w.r.t. v_3^1

     // f_2 = f_3(  v_1^0 , ... , v_2^1, v_1^0 * v_1^0 , 2 * v_1^0 * v_1^1 )
     f_v0[1] += f_v0[3] * 2. * v0[1];
     f_v0[1] += f_v1[3] * 2. * v1[1];
     f_v1[1] += f_v1[3] * 2. * v0[1];
     ok &= std::fabs( f_v0[1] - 1.  ) <= 1e-10; // partial f_2 w.r.t. v_1^0
     ok &= std::fabs( f_v1[1] - 0.5 ) <= 1e-10; // partial f_2 w.r.t. v_1^1

     // f_1 = f_2( v_1^0 , v_1^1 , 1 + v_1^0 , v_1^1 )
     f_v0[1] += f_v0[2] * 1.;
     f_v1[1] += f_v1[2] * 1.;
     ok &= std::fabs( f_v0[1] - 1. ) <= 1e-10; // partial f_1 w.r.t. v_1^0
     ok &= std::fabs( f_v1[1] - 1.5) <= 1e-10; // partial f_1 w.r.t. v_1^1

     return ok;
}
Input File: introduction/exp_apx/exp_2_rev2.cpp cppad-20170000.3/doc/exp_2_for1.xml0000644000175200017650000006100513057470504015664 0ustar coincoin-web exp_2: First Order Forward Mode
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exp_2: First Order Forward Mode

First Order Expansion
We define x ( t ) near t = 0 by the first order expansion x ( t ) = x ( 0 ) + x ( 1 ) * t it follows that x ( 0 ) is the zero, and x ( 1 ) the first, order derivative of x ( t ) at t = 0 .

Purpose
In general, a first order forward sweep is given the zero order derivative for all of the variables in an operation sequence, and the first order derivatives for the independent variables. It uses these to compute the first order derivatives, and thereby obtain the first order expansion, for all the other variables in the operation sequence.

Mathematical Form
Suppose that we use the algorithm exp_2.hpp to compute f ( x ) = 1 + x + x 2 / 2 The corresponding derivative function is ∂ x f ( x ) = 1 + x An algorithmic differentiation package does not operate on the mathematical form of the function, or its derivative, but rather on the operation sequence for the for the algorithm that is used to evaluate the function.

Operation Sequence
We consider the case where exp_2.hpp is executed with x = .5 . The corresponding operation sequence and zero order forward mode values (see zero order sweep ) are inputs and are used by a first order forward sweep.

Index
The Index column contains the index in the operation sequence of the corresponding atomic operation. A Forward sweep starts with the first operation and ends with the last.

Operation
The Operation column contains the mathematical function corresponding to each atomic operation in the sequence.

Zero Order
The Zero Order column contains the zero order derivatives for the corresponding variable in the operation sequence (see zero order sweep ).

Derivative
The Derivative column contains the mathematical function corresponding to the derivative with respect to t , at t = 0 , for each variable in the sequence.

First Order
The First Order column contains the first order derivatives for the corresponding variable in the operation sequence; i.e., v j ( t ) = v j ( 0 ) + v j ( 1 ) t We use x ( 1 ) = 1 so that differentiation with respect to t , at t = 0 , is the same as partial differentiation with respect to x at x = x ( 0 ) .

Sweep
Index    Operation    Zero Order    Derivative    First Order
1    v 1 = x 0.5 v 1 ( 1 ) = x ( 1 ) v 1 ( 1 ) = 1
2    v 2 = 1 + v 1 1.5 v 2 ( 1 ) = v 1 ( 1 ) v 2 ( 1 ) = 1
3    v 3 = v 1 * v 1 0.25 v 3 ( 1 ) = 2 * v 1 ( 0 ) * v 1 ( 1 ) v 3 ( 1 ) = 1
4    v 4 = v 3 / 2 0.125 v 4 ( 1 ) = v 3 ( 1 ) / 2 v 4 ( 1 ) = 0.5
5   v 5 = v 2 + v 4 1.625 v 5 ( 1 ) = v 2 ( 1 ) + v 4 ( 1 ) v 5 ( 1 ) = 1.5
Return Value
The derivative of the return value for this case is 1.5 = v 5 ( 1 ) = [∂ v 5 ∂ t ] t = 0 = [∂ ∂ t f ( x ( 0 ) + x ( 1 ) t ) ] t = 0 = f ( 1 ) ( x ( 0 ) ) * x ( 1 ) = f ( 1 ) ( x ( 0 ) ) (We have used the fact that x ( 1 ) = 1 .)

Verification
The file exp_2_for1.cpp contains a routine which verifies the values computed above. It returns true for success and false for failure.

Exercises
  1. Which statement in the routine defined by exp_2_for1.cpp uses the values that are calculated by the routine defined by exp_2_for0.cpp ?
  2. Suppose that x = .1 , what are the results of a zero and first order forward sweep for the operation sequence above; i.e., what are the corresponding values for v 1 ( 0 ) , v 2 ( 0 ) , ⋯ , v 5 ( 0 ) and v 1 ( 1 ) , v 2 ( 1 ) , ⋯ , v 5 ( 1 ) ?
  3. Create a modified version of exp_2_for1.cpp that verifies the derivative values from the previous exercise. Also create and run a main program that reports the result of calling the modified version of exp_2_for1.cpp .
Input File: introduction/exp_apx/exp_2.omh cppad-20170000.3/doc/exp_2_rev1.xml0000644000175200017650000006465613057470504015711 0ustar coincoin-web exp_2: First Order Reverse Mode
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exp_2: First Order Reverse Mode

Purpose
First order reverse mode uses the operation sequence , and zero order forward sweep values, to compute the first order derivative of one dependent variable with respect to all the independent variables. The computations are done in reverse of the order of the computations in the original algorithm.

Mathematical Form
Suppose that we use the algorithm exp_2.hpp to compute f ( x ) = 1 + x + x 2 / 2 The corresponding derivative function is ∂ x f ( x ) = 1 + x
f_5
For our example, we chose to compute the derivative of the value returned by exp_2.hpp which is equal to the symbol v 5 in the exp_2 operation sequence . We begin with the function f 5 where v 5 is both an argument and the value of the function; i.e., f 5 ( v 1 , v 2 , v 3 , v 4 , v 5 ) = v 5 ∂ f 5 ∂ v 5 = 1 All the other partial derivatives of f 5 are zero.

Index 5: f_4
Reverse mode starts with the last operation in the sequence. For the case in question, this is the operation with index 5, v 5 = v 2 + v 4 We define the function f 4 ( v 1 , v 2 , v 3 , v 4 ) as equal to f 5 except that v 5 is eliminated using this operation; i.e. f 4 = f 5 [ v 1 , v 2 , v 3 , v 4 , v 5 ( v 2 , v 4 ) ] It follows that ∂ f 4 ∂ v 2 = ∂ f 5 ∂ v 2 + ∂ f 5 ∂ v 5 * ∂ v 5 ∂ v 2 = 1 ∂ f 4 ∂ v 4 = ∂ f 5 ∂ v 4 + ∂ f 5 ∂ v 5 * ∂ v 5 ∂ v 4 = 1 All the other partial derivatives of f 4 are zero.

Index 4: f_3
The next operation has index 4, v 4 = v 3 / 2 We define the function f 3 ( v 1 , v 2 , v 3 ) as equal to f 4 except that v 4 is eliminated using this operation; i.e., f 3 = f 4 [ v 1 , v 2 , v 3 , v 4 ( v 3 ) ] It follows that ∂ f 3 ∂ v 1 = ∂ f 4 ∂ v 1 = 0 ∂ f 3 ∂ v 2 = ∂ f 4 ∂ v 2 = 1 ∂ f 3 ∂ v 3 = ∂ f 4 ∂ v 3 + ∂ f 4 ∂ v 4 * ∂ v 4 ∂ v 3 = 0.5
Index 3: f_2
The next operation has index 3, v 3 = v 1 * v 1 We define the function f 2 ( v 1 , v 2 ) as equal to f 3 except that v 3 is eliminated using this operation; i.e., f 2 = f 3 [ v 1 , v 2 , v 3 ( v 1 ) ] Note that the value of v 1 is equal to x which is .5 for this evaluation. It follows that ∂ f 2 ∂ v 1 = ∂ f 3 ∂ v 1 + ∂ f 3 ∂ v 3 * ∂ v 3 ∂ v 1 = 0.5 ∂ f 2 ∂ v 2 = ∂ f 3 ∂ v 2 = 1
Index 2: f_1
The next operation has index 2, v 2 = 1 + v 1 We define the function f 1 ( v 1 ) as equal to f 2 except that v 2 is eliminated using this operation; i.e., f 1 = f 2 [ v 1 , v 2 ( v 1 ) ] It follows that ∂ f 1 ∂ v 1 = ∂ f 2 ∂ v 1 + ∂ f 2 ∂ v 2 * ∂ v 2 ∂ v 1 = 1.5 Note that v 1 is equal to x , so the derivative of this is the derivative of the function defined by exp_2.hpp at x = .5 .

Verification
The file exp_2_rev1.cpp contains a routine which verifies the values computed above. It returns true for success and false for failure. It only tests the partial derivatives of f j that might not be equal to the corresponding partials of f j + 1 ; i.e., the other partials of f j must be equal to the corresponding partials of f j + 1 .

Exercises
  1. Which statement in the routine defined by exp_2_rev1.cpp uses the values that are calculated by the routine defined by exp_2_for0.cpp ?
  2. Consider the case where x = .1 and we first preform a zero order forward sweep for the operation sequence used above. What are the results of a first order reverse sweep; i.e., what are the corresponding derivatives of f 5 , f 4 , … , f 1 .
  3. Create a modified version of exp_2_rev1.cpp that verifies the values you obtained for the previous exercise. Also create and run a main program that reports the result of calling the modified version of exp_2_rev1.cpp .
Input File: introduction/exp_apx/exp_2.omh cppad-20170000.3/doc/exp_2_for2.xml0000644000175200017650000006773513057470504015705 0ustar coincoin-web exp_2: Second Order Forward Mode
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exp_2: Second Order Forward Mode

Second Order Expansion
We define x ( t ) near t = 0 by the second order expansion x ( t ) = x ( 0 ) + x ( 1 ) * t + x ( 2 ) * t 2 / 2 It follows that for k = 0 , 1 , 2 , x ( k ) = d k d t k x ( 0 )
Purpose
In general, a second order forward sweep is given the first order expansion for all of the variables in an operation sequence, and the second order derivatives for the independent variables. It uses these to compute the second order derivative, and thereby obtain the second order expansion, for all the variables in the operation sequence.

Mathematical Form
Suppose that we use the algorithm exp_2.hpp to compute f ( x ) = 1 + x + x 2 / 2 The corresponding second derivative function is ∂ 2 ∂ x 2 f ( x ) = 1
Operation Sequence
We consider the case where exp_2.hpp is executed with x = .5 . The corresponding operation sequence, zero order forward sweep values, and first order forward sweep values are inputs and are used by a second order forward sweep.

Index
The Index column contains the index in the operation sequence of the corresponding atomic operation. A Forward sweep starts with the first operation and ends with the last.

Zero
The Zero column contains the zero order sweep results for the corresponding variable in the operation sequence (see zero order sweep ).

Operation
The Operation column contains the first order sweep operation for this variable.

First
The First column contains the first order sweep results for the corresponding variable in the operation sequence (see first order sweep ).

Derivative
The Derivative column contains the mathematical function corresponding to the second derivative with respect to t , at t = 0 , for each variable in the sequence.

Second
The Second column contains the second order derivatives for the corresponding variable in the operation sequence; i.e., the second order expansion for the i-th variable is given by v i ( t ) = v i ( 0 ) + v i ( 1 ) * t + v i ( 2 ) * t 2 / 2 We use x ( 0 ) = 1 , and x ( 2 ) = 0 so that second order differentiation with respect to t , at t = 0 , is the same as the second partial differentiation with respect to x at x = x ( 0 ) .

Sweep
Index    Zero    Operation    First    Derivative    Second
1 0.5    v 1 ( 1 ) = x ( 1 ) 1 v 1 ( 2 ) = x ( 2 ) v 1 ( 2 ) = 0
2 1.5    v 2 ( 1 ) = v 1 ( 1 ) 1 v 2 ( 2 ) = v 1 ( 2 ) v 2 ( 2 ) = 0
3 0.25    v 3 ( 1 ) = 2 * v 1 ( 0 ) * v 1 ( 1 ) 1 v 3 ( 2 ) = 2 * ( v 1 ( 1 ) * v 1 ( 1 ) + v 1 ( 0 ) * v 1 ( 2 ) ) v 3 ( 2 ) = 2
4 0.125    v 4 ( 1 ) = v 3 ( 1 ) / 2 .5 v 4 ( 2 ) = v 3 ( 2 ) / 2 v 4 ( 2 ) = 1
5 1.625   v 5 ( 1 ) = v 2 ( 1 ) + v 4 ( 1 ) 1.5 v 5 ( 2 ) = v 2 ( 2 ) + v 4 ( 2 ) v 5 ( 2 ) = 1
Return Value
The second derivative of the return value for this case is 1 = v 5 ( 2 ) = [∂ 2 ∂ t 2 v 5 ] t = 0 = [∂ 2 ∂ t 2 f ( x ( 0 ) + x ( 1 ) * t ) ] t = 0 = x ( 1 ) * ∂ 2 ∂ x 2 f ( x ( 0 ) ) * x ( 1 ) = ∂ 2 ∂ x 2 f ( x ( 0 ) ) (We have used the fact that x ( 1 ) = 1 and x ( 2 ) = 0 .)

Verification
The file exp_2_for2.cpp contains a routine which verifies the values computed above. It returns true for success and false for failure.

Exercises
  1. Which statement in the routine defined by exp_2_for2.cpp uses the values that are calculated by the routine defined by exp_2_for1.cpp ?
  2. Suppose that x = .1 , what are the results of a zero, first, and second order forward sweep for the operation sequence above; i.e., what are the corresponding values for v i ( k ) for i = 1 , … , 5 and k = 0 , 1 , 2 .
  3. Create a modified version of exp_2_for2.cpp that verifies the derivative values from the previous exercise. Also create and run a main program that reports the result of calling the modified version of exp_2_for2.cpp .
Input File: introduction/exp_apx/exp_2.omh cppad-20170000.3/doc/exp_2_rev2.xml0000644000175200017650000013423113057470504015675 0ustar coincoin-web exp_2: Second Order Reverse Mode
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exp_2: Second Order Reverse Mode

Purpose
In general, a second order reverse sweep is given the first order expansion for all of the variables in an operation sequence. Given a choice of a particular variable, it computes the derivative, of that variables first order expansion coefficient, with respect to all of the independent variables.

Mathematical Form
Suppose that we use the algorithm exp_2.hpp to compute f ( x ) = 1 + x + x 2 / 2 The corresponding second derivative is ∂ 2 ∂ x 2 f ( x ) = 1
f_5
For our example, we chose to compute the derivative of v 5 ( 1 ) with respect to all the independent variable. For the case computed for the first order sweep , v 5 ( 1 ) is the derivative of the value returned by exp_2.hpp . This the value computed will be the second derivative of the value returned by exp_2.hpp . We begin with the function f 5 where v 5 ( 1 ) is both an argument and the value of the function; i.e., f 5 (v 1 ( 0 ) , v 1 ( 1 ) , … , v 5 ( 0 ) , v 5 ( 1 ) ) = v 5 ( 1 ) ∂ f 5 ∂ v 5 ( 1 ) = 1 All the other partial derivatives of f 5 are zero.

Index 5: f_4
Second order reverse mode starts with the last operation in the sequence. For the case in question, this is the operation with index 5. The zero and first order sweep representations of this operation are v 5 ( 0 ) = v 2 ( 0 ) + v 4 ( 0 ) v 5 ( 1 ) = v 2 ( 1 ) + v 4 ( 1 ) We define the function f 4 (v 1 ( 0 ) , … , v 4 ( 1 ) ) as equal to f 5 except that v 5 ( 0 ) and v 5 ( 1 ) are eliminated using this operation; i.e. f 4 = f 5 [v 1 ( 0 ) , … , v 4 ( 1 ) , v 5 ( 0 ) (v 2 ( 0 ) , v 4 ( 0 ) ) , v 5 ( 1 ) (v 2 ( 1 ) , v 4 ( 1 ) ) ] It follows that ∂ f 4 ∂ v 2 ( 1 ) = ∂ f 5 ∂ v 2 ( 1 ) + ∂ f 5 ∂ v 5 ( 1 ) * ∂ v 5 ( 1 ) ∂ v 2 ( 1 ) = 1 ∂ f 4 ∂ v 4 ( 1 ) = ∂ f 5 ∂ v 4 ( 1 ) + ∂ f 5 ∂ v 5 ( 1 ) * ∂ v 5 ∂ v 4 ( 1 ) = 1 All the other partial derivatives of f 4 are zero.

Index 4: f_3
The next operation has index 4, v 4 ( 0 ) = v 3 ( 0 ) / 2 v 4 ( 1 ) = v 3 ( 1 ) / 2 We define the function f 3 (v 1 ( 0 ) , … , v 3 ( 1 ) ) as equal to f 4 except that v 4 ( 0 ) and v 4 ( 1 ) are eliminated using this operation; i.e., f 3 = f 4 [v 1 ( 0 ) , … , v 3 ( 1 ) , v 4 ( 0 ) (v 3 ( 0 ) ) , v 4 ( 1 ) (v 3 ( 1 ) ) ] It follows that ∂ f 3 ∂ v 2 ( 1 ) = ∂ f 4 ∂ v 2 ( 1 ) = 1 ∂ f 3 ∂ v 3 ( 1 ) = ∂ f 4 ∂ v 3 ( 1 ) + ∂ f 4 ∂ v 4 ( 1 ) * ∂ v 4 ( 1 ) ∂ v 3 ( 1 ) = 0.5 All the other partial derivatives of f 3 are zero.

Index 3: f_2
The next operation has index 3, v 3 ( 0 ) = v 1 ( 0 ) * v 1 ( 0 ) v 3 ( 1 ) = 2 * v 1 ( 0 ) * v 1 ( 1 ) We define the function f 2 (v 1 ( 0 ) , … , v 2 ( 1 ) ) as equal to f 3 except that v 3 ( 0 ) and v 3 ( 1 ) are eliminated using this operation; i.e., f 2 = f 3 [v 1 ( 0 ) , … , v 2 ( 1 ) , v 3 ( 0 ) ( v 1 ( 0 ) ) , v 3 ( 1 ) ( v 1 ( 0 ) , v 1 ( 1 ) ) ] Note that, from the first order forward sweep , the value of v 1 ( 0 ) is equal to .5 and v 1 ( 1 ) is equal 1. It follows that ∂ f 2 ∂ v 1 ( 0 ) = ∂ f 3 ∂ v 1 ( 0 ) + ∂ f 3 ∂ v 3 ( 0 ) * ∂ v 3 ( 0 ) ∂ v 1 ( 0 ) + ∂ f 3 ∂ v 3 ( 1 ) * ∂ v 3 ( 1 ) ∂ v 1 ( 0 ) = 1 ∂ f 2 ∂ v 1 ( 1 ) = ∂ f 3 ∂ v 1 ( 1 ) + ∂ f 3 ∂ v 3 ( 1 ) * ∂ v 3 ( 1 ) ∂ v 1 ( 1 ) = 0.5 ∂ f 2 ∂ v 2 ( 0 ) = ∂ f 3 ∂ v 2 ( 0 ) = 0 ∂ f 2 ∂ v 2 ( 1 ) = ∂ f 3 ∂ v 2 ( 1 ) = 1
Index 2: f_1
The next operation has index 2, v 2 ( 0 ) = 1 + v 1 ( 0 ) v 2 ( 1 ) = v 1 ( 1 ) We define the function f 1 ( v 1 ( 0 ) , v 1 ( 1 ) ) as equal to f 2 except that v 2 ( 0 ) and v 2 ( 1 ) are eliminated using this operation; i.e., f 1 = f 2 [v 1 ( 0 ) , v 1 ( 1 ) , v 2 ( 0 ) ( v 1 ( 0 ) ) , v 2 ( 1 ) ( v 1 ( 1 ) ) ] It follows that ∂ f 1 ∂ v 1 ( 0 ) = ∂ f 2 ∂ v 1 ( 0 ) + ∂ f 2 ∂ v 2 ( 0 ) * ∂ v 2 ( 0 ) ∂ v 1 ( 0 ) = 1 ∂ f 1 ∂ v 1 ( 1 ) = ∂ f 2 ∂ v 1 ( 1 ) + ∂ f 2 ∂ v 2 ( 1 ) * ∂ v 2 ( 1 ) ∂ v 1 ( 1 ) = 1.5 Note that v 1 is equal to x , so the second derivative of the function defined by exp_2.hpp at x = .5 is given by ∂ 2 ∂ x 2 v 5 ( 0 ) = ∂ v 5 ( 1 ) ∂ x = ∂ v 5 ( 1 ) ∂ v 1 ( 0 ) = ∂ f 1 ∂ v 1 ( 0 ) = 1 There is a theorem about Algorithmic Differentiation that explains why the other partial of f 1 is equal to the first derivative of the function defined by exp_2.hpp at x = .5 .

Verification
The file exp_2_rev2.cpp contains a routine which verifies the values computed above. It returns true for success and false for failure. It only tests the partial derivatives of f j that might not be equal to the corresponding partials of f j + 1 ; i.e., the other partials of f j must be equal to the corresponding partials of f j + 1 .

Exercises
  1. Which statement in the routine defined by exp_2_rev2.cpp uses the values that are calculated by the routine defined by exp_2_for0.cpp ? Which statements use values that are calculate by the routine defined in exp_2_for1.cpp ?
  2. Consider the case where x = .1 and we first preform a zero order forward sweep, then a first order sweep, for the operation sequence used above. What are the results of a second order reverse sweep; i.e., what are the corresponding derivatives of f 5 , f 4 , … , f 1 .
  3. Create a modified version of exp_2_rev2.cpp that verifies the values you obtained for the previous exercise. Also create and run a main program that reports the result of calling the modified version of exp_2_rev2.cpp .
Input File: introduction/exp_apx/exp_2.omh cppad-20170000.3/doc/exp_2_cppad.xml0000644000175200017650000004662313057470504016115 0ustar coincoin-web exp_2: CppAD Forward and Reverse Sweeps
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exp_2: CppAD Forward and Reverse Sweeps
.

Purpose
Use CppAD forward and reverse modes to compute the partial derivative with respect to x , at the point x = .5 , of the function
     exp_2(x)
 as defined by the exp_2.hpp include file.

Exercises
  1. Create and test a modified version of the routine below that computes the same order derivatives with respect to x , at the point x = .1 of the function
         exp_2(    x)
  2. Create a routine called
         exp_3(    x)
     that evaluates the function f ( x ) = 1 + x 2 / 2 + x 3 / 6 Test a modified version of the routine below that computes the derivative of f ( x ) at the point x = .5 . 

# include <cppad/cppad.hpp>  // http://www.coin-or.org/CppAD/
# include "exp_2.hpp"        // second order exponential approximation
bool exp_2_cppad(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::vector;    // can use any simple vector template class
     using CppAD::NearEqual; // checks if values are nearly equal

     // domain space vector
     size_t n = 1; // dimension of the domain space
     vector< AD<double> > X(n);
     X[0] = .5;    // value of x for this operation sequence

     // declare independent variables and start recording operation sequence
     CppAD::Independent(X);

     // evaluate our exponential approximation
     AD<double> x   = X[0];
     AD<double> apx = exp_2(x);

     // range space vector
     size_t m = 1;  // dimension of the range space
     vector< AD<double> > Y(m);
     Y[0] = apx;    // variable that represents only range space component

     // Create f: X -> Y corresponding to this operation sequence
     // and stop recording. This also executes a zero order forward
     // sweep using values in X for x.
     CppAD::ADFun<double> f(X, Y);

     // first order forward sweep that computes
     // partial of exp_2(x) with respect to x
     vector<double> dx(n);  // differential in domain space
     vector<double> dy(m);  // differential in range space
     dx[0] = 1.;            // direction for partial derivative
     dy    = f.Forward(1, dx);
     double check = 1.5;
     ok   &= NearEqual(dy[0], check, 1e-10, 1e-10);

     // first order reverse sweep that computes the derivative
     vector<double>  w(m);   // weights for components of the range
     vector<double> dw(n);   // derivative of the weighted function
     w[0] = 1.;              // there is only one weight
     dw   = f.Reverse(1, w); // derivative of w[0] * exp_2(x)
     check = 1.5;            // partial of exp_2(x) with respect to x
     ok   &= NearEqual(dw[0], check, 1e-10, 1e-10);

     // second order forward sweep that computes
     // second partial of exp_2(x) with respect to x
     vector<double> x2(n);     // second order Taylor coefficients
     vector<double> y2(m);
     x2[0] = 0.;               // evaluate second partial .w.r.t. x
     y2    = f.Forward(2, x2);
     check = 0.5 * 1.;         // Taylor coef is 1/2 second derivative
     ok   &= NearEqual(y2[0], check, 1e-10, 1e-10);

     // second order reverse sweep that computes
     // derivative of partial of exp_2(x) w.r.t. x
     dw.resize(2 * n);         // space for first and second derivatives
     dw    = f.Reverse(2, w);
     check = 1.;               // result should be second derivative
     ok   &= NearEqual(dw[0*2+1], check, 1e-10, 1e-10);

     return ok;
}
Input File: introduction/exp_apx/exp_2_cppad.cpp cppad-20170000.3/doc/exp_eps.xml0000644000175200017650000005005113057470504015362 0ustar coincoin-web An Epsilon Accurate Exponential Approximation
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An Epsilon Accurate Exponential Approximation

Syntax
# include "exp_eps.hpp"
y = exp_eps(x, epsilon)

Purpose
This is a an example algorithm that is used to demonstrate how Algorithmic Differentiation works with loops and boolean decision variables (see exp_2 for a simpler example).

Mathematical Function
The exponential function can be defined by exp ( x ) = 1 + x 1 / 1 ! + x 2 / 2 ! + ⋯ We define k ( x , ε ) as the smallest non-negative integer such that ε ≥ x k / k ! ; i.e., k ( x , ε ) = min { k ∈ Z + | ε ≥ x k / k ! } The mathematical form for our approximation of the exponential function is exp _ eps ( x , ε ) = { 1 exp _ eps ( - x , ε ) if x < 0 1 + x 1 / 1 ! + ⋯ + x k ( x , ε ) / k ( x , ε ) ! otherwise
include
The include command in the syntax is relative to
     cppad-yyyymmdd/introduction/exp_apx
 where cppad-yyyymmdd is the distribution directory created during the beginning steps of the installation of CppAD.

x
The argument x has prototype
     const Type &x
 (see Type below). It specifies the point at which to evaluate the approximation for the exponential function.

epsilon
The argument epsilon has prototype
     const Type &epsilon
 It specifies the accuracy with which to approximate the exponential function value; i.e., it is the value of ε in the exponential function approximation defined above.

y
The result y has prototype
     Type y
 It is the value of the exponential function approximation defined above.

Type
If u and v are Type objects and i is an int:
Operation Result Type Description
Type(i) Type object with value equal to i
Type u = v Type construct u with value equal to v
u > v bool true, if u greater than v , an false otherwise
u = v Type new u (and result) is value of v
u * v Type result is value of u * v
u / v Type result is value of u / v
u + v Type result is value of u + v
-u Type result is value of - u

Implementation
The file exp_eps.hpp contains a C++ implementation of this function.

Test
The file exp_eps.cpp contains a test of this implementation. It returns true for success and false for failure.

Exercises
  1. Using the definition of k ( x , ε ) above, what is the value of k ( .5 , 1 ) , k ( .5 , .1 ) , and k ( .5 , .01 ) ?
  2. Suppose that we make the following call to exp_eps: 
     
     double x       = 1.;
     double epsilon = .01;
     double y = exp_eps(x, epsilon);
    What is the value assigned to k, temp, term, and sum the first time through the while loop in exp_eps.hpp ?
  3. Continuing the previous exercise, what is the value assigned to k, temp, term, and sum the second time through the while loop in exp_eps.hpp ?
Input File: introduction/exp_apx/exp_eps.hpp cppad-20170000.3/doc/exp_eps.hpp.xml0000644000175200017650000001645513057470504016162 0ustar coincoin-web exp_eps: Implementation
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exp_eps: Implementation
template <class Type>
Type exp_eps(const Type &x, const Type &epsilon)
{     // abs_x = |x|
     Type abs_x = x;
     if( Type(0) > x )
          abs_x = - x;
     // initialize
     int  k    = 0;          // initial order
     Type term = 1.;         // term = |x|^k / k !
     Type sum  = term;       // initial sum
     while(term > epsilon)
     {     k         = k + 1;          // order for next term
          Type temp = term * abs_x;   // term = |x|^k / (k-1)!
          term      = temp / Type(k); // term = |x|^k / k !
          sum       = sum + term;     // sum  = 1 + ... + |x|^k / k !
     }
     // In the case where x is negative, use exp(x) = 1 / exp(-|x|)
     if( Type(0) > x )
          sum = Type(1) / sum;
     return sum;
}
Input File: introduction/exp_apx/exp_eps.omh cppad-20170000.3/doc/exp_eps.cpp.xml0000644000175200017650000001157413057470504016152 0ustar coincoin-web exp_eps: Test of exp_eps
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exp_eps: Test of exp_eps
# include <cmath>             // for fabs function
# include "exp_eps.hpp"       // definition of exp_eps algorithm
bool exp_eps(void)
{     double x       = .5;
     double epsilon = .2;
     double check   = 1 + .5 + .125; // include 1 term less than epsilon
     bool   ok      = std::fabs( exp_eps(x, epsilon) - check ) <= 1e-10;
     return ok;
}
Input File: introduction/exp_apx/exp_eps.omh cppad-20170000.3/doc/exp_eps_for0.xml0000644000175200017650000004541713057470504016322 0ustar coincoin-web exp_eps: Operation Sequence and Zero Order Forward Sweep
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exp_eps: Operation Sequence and Zero Order Forward Sweep

Mathematical Form
Suppose that we use the algorithm exp_eps.hpp to compute exp_eps(x, epsilon) with x is equal to .5 and epsilon is equal to .2. For this case, the mathematical form for the operation sequence corresponding to the exp_eps is f ( x , ε ) = 1 + x + x 2 / 2 Note that, for these particular values of x and epsilon , this is the same as the mathematical form for exp_2 .

Operation Sequence
We consider the operation sequence corresponding to the algorithm exp_eps.hpp with the argument x is equal to .5 and epsilon is equal to .2.

Variable
We refer to values that depend on the input variables x and epsilon as variables.

Parameter
We refer to values that do not depend on the input variables x or epsilon as parameters. Operations where the result is a parameter are not included in the zero order sweep below.

Index
The Index column contains the index in the operation sequence of the corresponding atomic operation and variable. A Forward sweep starts with the first operation and ends with the last.

Code
The Code column contains the C++ source code corresponding to the corresponding atomic operation in the sequence.

Operation
The Operation column contains the mathematical function corresponding to each atomic operation in the sequence.

Zero Order
The Zero Order column contains the zero order derivative for the corresponding variable in the operation sequence. Forward mode refers to the fact that these coefficients are computed in the same order as the original algorithm; i.e., in order of increasing index.

Sweep
Index    Code    Operation    Zero Order
1    abs_x = x; v 1 = x v 1 ( 0 ) = 0.5
2    temp = term * abs_x; v 2 = 1 * v 1 v 2 ( 0 ) = 0.5
3    term = temp / Type(k); v 3 = v 2 / 1 v 3 ( 0 ) = 0.5
4    sum = sum + term; v 4 = 1 + v 3 v 4 ( 0 ) = 1.5
5    temp = term * abs_x; v 5 = v 3 * v 1 v 5 ( 0 ) = 0.25
6    term = temp / Type(k); v 6 = v 5 / 2 v 6 ( 0 ) = 0.125
7    sum = sum + term; v 7 = v 4 + v 6 v 7 ( 0 ) = 1.625
Return Value
The return value for this case is 1.625 = v 7 ( 0 ) = f ( x ( 0 ) , ε ( 0 ) )
Comparisons
If x were negative, or if epsilon were a much smaller or much larger value, the results of the following comparisons could be different: 
 
     if( Type(0) > x )
     while(term > epsilon)
This in turn would result in a different operation sequence. Thus the operation sequence above only corresponds to exp_eps.hpp for values of x and epsilon within a certain range. Note that there is a neighborhood of x = 0.5 for which the comparisons would have the same result and hence the operation sequence would be the same.

Verification
The file exp_eps_for0.cpp contains a routine that verifies the values computed above. It returns true for success and false for failure.

Exercises
  1. Suppose that x ( 0 ) = .1 , what is the result of a zero order forward sweep for the operation sequence above; i.e., what are the corresponding values for v 1 ( 0 ) , v 2 ( 0 ) , … , v 7 ( 0 ) .
  2. Create a modified version of exp_eps_for0.cpp that verifies the values you obtained for the previous exercise.
  3. Create and run a main program that reports the result of calling the modified version of exp_eps_for0.cpp in the previous exercise.
Input File: introduction/exp_apx/exp_eps.omh cppad-20170000.3/doc/exp_eps_for0.cpp.xml0000644000175200017650000002660713057470504017103 0ustar coincoin-web exp_eps: Verify Zero Order Forward Sweep
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exp_eps: Verify Zero Order Forward Sweep
# include <cmath>                // for fabs function
bool exp_eps_for0(double *v0)    // double v0[8]
{     bool  ok = true;
     double x = .5;

     v0[1] = x;                                  // abs_x = x;
     ok  &= std::fabs( v0[1] - 0.5) < 1e-10;

     v0[2] = 1. * v0[1];                         // temp = term * abs_x;
     ok  &= std::fabs( v0[2] - 0.5) < 1e-10;

     v0[3] = v0[2] / 1.;                         // term = temp / Type(k);
     ok  &= std::fabs( v0[3] - 0.5) < 1e-10;

     v0[4] = 1. + v0[3];                         // sum = sum + term;
     ok  &= std::fabs( v0[4] - 1.5) < 1e-10;

     v0[5] = v0[3] * v0[1];                      // temp = term * abs_x;
     ok  &= std::fabs( v0[5] - 0.25) < 1e-10;

     v0[6] = v0[5] / 2.;                         // term = temp / Type(k);
     ok  &= std::fabs( v0[6] - 0.125) < 1e-10;

     v0[7] = v0[4] + v0[6];                      // sum = sum + term;
     ok  &= std::fabs( v0[7] - 1.625) < 1e-10;

     return ok;
}
bool exp_eps_for0(void)
{     double v0[8];
     return exp_eps_for0(v0);
}
Input File: introduction/exp_apx/exp_eps_for0.cpp cppad-20170000.3/doc/exp_eps_for1.cpp.xml0000644000175200017650000003105413057470504017074 0ustar coincoin-web exp_eps: Verify First Order Forward Sweep
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exp_eps: Verify First Order Forward Sweep
# include <cmath>                     // for fabs function
extern bool exp_eps_for0(double *v0); // computes zero order forward sweep
bool exp_eps_for1(double *v1)         // double v[8]
{     bool ok = true;
     double v0[8];

     // set the value of v0[j] for j = 1 , ... , 7
     ok &= exp_eps_for0(v0);

     v1[1] = 1.;                                      // v1 = x
     ok    &= std::fabs( v1[1] - 1. ) <= 1e-10;

     v1[2] = 1. * v1[1];                              // v2 = 1 * v1
     ok    &= std::fabs( v1[2] - 1. ) <= 1e-10;

     v1[3] = v1[2] / 1.;                              // v3 = v2 / 1
     ok    &= std::fabs( v1[3] - 1. ) <= 1e-10;

     v1[4] = v1[3];                                   // v4 = 1 + v3
     ok    &= std::fabs( v1[4] - 1. ) <= 1e-10;

     v1[5] = v1[3] * v0[1] + v0[3] * v1[1];           // v5 = v3 * v1
     ok    &= std::fabs( v1[5] - 1. ) <= 1e-10;

     v1[6] = v1[5] / 2.;                              // v6 = v5 / 2
     ok    &= std::fabs( v1[6] - 0.5 ) <= 1e-10;

     v1[7] = v1[4] + v1[6];                           // v7 = v4 + v6
     ok    &= std::fabs( v1[7] - 1.5 ) <= 1e-10;

     return ok;
}
bool exp_eps_for1(void)
{     double v1[8];
     return exp_eps_for1(v1);
}
Input File: introduction/exp_apx/exp_eps_for1.cpp cppad-20170000.3/doc/exp_eps_rev1.cpp.xml0000644000175200017650000003633613057470504017112 0ustar coincoin-web exp_eps: Verify First Order Reverse Sweep
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exp_eps: Verify First Order Reverse Sweep
# include <cstddef>                     // define size_t
# include <cmath>                       // for fabs function
extern bool exp_eps_for0(double *v0);   // computes zero order forward sweep
bool exp_eps_rev1(void)
{     bool ok = true;

     // set the value of v0[j] for j = 1 , ... , 7
     double v0[8];
     ok &= exp_eps_for0(v0);

     // initial all partial derivatives as zero
     double f_v[8];
     size_t j;
     for(j = 0; j < 8; j++)
          f_v[j] = 0.;

     // set partial derivative for f7
     f_v[7] = 1.;
     ok    &= std::fabs( f_v[7] - 1. ) <= 1e-10;     // f7_v7

     // f6( v1 , v2 , v3 , v4 , v5 , v6 )
     f_v[4] += f_v[7] * 1.;
     f_v[6] += f_v[7] * 1.;
     ok     &= std::fabs( f_v[4] - 1.  ) <= 1e-10;   // f6_v4
     ok     &= std::fabs( f_v[6] - 1.  ) <= 1e-10;   // f6_v6

     // f5( v1 , v2 , v3 , v4 , v5 )
     f_v[5] += f_v[6] / 2.;
     ok     &= std::fabs( f_v[5] - 0.5 ) <= 1e-10;   // f5_v5

     // f4( v1 , v2 , v3 , v4 )
     f_v[1] += f_v[5] * v0[3];
     f_v[3] += f_v[5] * v0[1];
     ok     &= std::fabs( f_v[1] - 0.25) <= 1e-10;   // f4_v1
     ok     &= std::fabs( f_v[3] - 0.25) <= 1e-10;   // f4_v3

     // f3( v1 , v2 , v3 )
     f_v[3] += f_v[4] * 1.;
     ok     &= std::fabs( f_v[3] - 1.25) <= 1e-10;   // f3_v3

     // f2( v1 , v2 )
     f_v[2] += f_v[3] / 1.;
     ok     &= std::fabs( f_v[2] - 1.25) <= 1e-10;   // f2_v2

     // f1( v1 )
     f_v[1] += f_v[2] * 1.;
     ok     &= std::fabs( f_v[1] - 1.5 ) <= 1e-10;   // f1_v2

     return ok;
}
Input File: introduction/exp_apx/exp_eps_rev1.cpp cppad-20170000.3/doc/exp_eps_for2.cpp.xml0000644000175200017650000003214113057470504017073 0ustar coincoin-web exp_eps: Verify Second Order Forward Sweep
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exp_eps: Verify Second Order Forward Sweep
# include <cmath>                     // for fabs function
extern bool exp_eps_for0(double *v0); // computes zero order forward sweep
extern bool exp_eps_for1(double *v1); // computes first order forward sweep
bool exp_eps_for2(void)
{     bool ok = true;
     double v0[8], v1[8], v2[8];

     // set the value of v0[j], v1[j] for j = 1 , ... , 7
     ok &= exp_eps_for0(v0);
     ok &= exp_eps_for1(v1);

     v2[1] = 0.;                                      // v1 = x
     ok    &= std::fabs( v2[1] - 0. ) <= 1e-10;

     v2[2] = 1. * v2[1];                              // v2 = 1 * v1
     ok    &= std::fabs( v2[2] - 0. ) <= 1e-10;

     v2[3] = v2[2] / 1.;                              // v3 = v2 / 1
     ok    &= std::fabs( v2[3] - 0. ) <= 1e-10;

     v2[4] = v2[3];                                   // v4 = 1 + v3
     ok    &= std::fabs( v2[4] - 0. ) <= 1e-10;

     v2[5] = v2[3] * v0[1] + 2. * v1[3] * v1[1]       // v5 = v3 * v1
           + v0[3] * v2[1];
     ok    &= std::fabs( v2[5] - 2. ) <= 1e-10;

     v2[6] = v2[5] / 2.;                              // v6 = v5 / 2
     ok    &= std::fabs( v2[6] - 1. ) <= 1e-10;

     v2[7] = v2[4] + v2[6];                           // v7 = v4 + v6
     ok    &= std::fabs( v2[7] - 1. ) <= 1e-10;

     return ok;
}
Input File: introduction/exp_apx/exp_eps_for2.cpp cppad-20170000.3/doc/exp_eps_rev2.cpp.xml0000644000175200017650000006153113057470504017106 0ustar coincoin-web exp_eps: Verify Second Order Reverse Sweep
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exp_eps: Verify Second Order Reverse Sweep
# include <cstddef>                     // define size_t
# include <cmath>                       // for fabs function
extern bool exp_eps_for0(double *v0);   // computes zero order forward sweep
extern bool exp_eps_for1(double *v1);   // computes first order forward sweep
bool exp_eps_rev2(void)
{     bool ok = true;

     // set the value of v0[j], v1[j] for j = 1 , ... , 7
     double v0[8], v1[8];
     ok &= exp_eps_for0(v0);
     ok &= exp_eps_for1(v1);

     // initial all partial derivatives as zero
     double f_v0[8], f_v1[8];
     size_t j;
     for(j = 0; j < 8; j++)
     {     f_v0[j] = 0.;
          f_v1[j] = 0.;
     }

     // set partial derivative for f_7
     f_v1[7] = 1.;
     ok &= std::fabs( f_v1[7] - 1.  ) <= 1e-10; // partial f_7 w.r.t. v_7^1

     // f_6 = f_7( v_1^0 , ... , v_6^1 , v_4^0 + v_6^0, v_4^1 , v_6^1 )
     f_v0[4] += f_v0[7];
     f_v0[6] += f_v0[7];
     f_v1[4] += f_v1[7];
     f_v1[6] += f_v1[7];
     ok &= std::fabs( f_v0[4] - 0.  ) <= 1e-10; // partial f_6 w.r.t. v_4^0
     ok &= std::fabs( f_v0[6] - 0.  ) <= 1e-10; // partial f_6 w.r.t. v_6^0
     ok &= std::fabs( f_v1[4] - 1.  ) <= 1e-10; // partial f_6 w.r.t. v_4^1
     ok &= std::fabs( f_v1[6] - 1.  ) <= 1e-10; // partial f_6 w.r.t. v_6^1

     // f_5 = f_6( v_1^0 , ... , v_5^1 , v_5^0 / 2 , v_5^1 / 2 )
     f_v0[5] += f_v0[6] / 2.;
     f_v1[5] += f_v1[6] / 2.;
     ok &= std::fabs( f_v0[5] - 0.  ) <= 1e-10; // partial f_5 w.r.t. v_5^0
     ok &= std::fabs( f_v1[5] - 0.5 ) <= 1e-10; // partial f_5 w.r.t. v_5^1

     // f_4 = f_5( v_1^0 , ... , v_4^1 , v_3^0 * v_1^0 ,
     //            v_3^1 * v_1^0 + v_3^0 * v_1^1 )
     f_v0[1] += f_v0[5] * v0[3] + f_v1[5] * v1[3];
     f_v0[3] += f_v0[5] * v0[1] + f_v1[5] * v1[1];
     f_v1[1] += f_v1[5] * v0[3];
     f_v1[3] += f_v1[5] * v0[1];
     ok &= std::fabs( f_v0[1] - 0.5  ) <= 1e-10; // partial f_4 w.r.t. v_1^0
     ok &= std::fabs( f_v0[3] - 0.5  ) <= 1e-10; // partial f_4 w.r.t. v_3^0
     ok &= std::fabs( f_v1[1] - 0.25 ) <= 1e-10; // partial f_4 w.r.t. v_1^1
     ok &= std::fabs( f_v1[3] - 0.25 ) <= 1e-10; // partial f_4 w.r.t. v_3^1

     // f_3 = f_4(  v_1^0 , ... , v_3^1 , 1 + v_3^0 , v_3^1 )
     f_v0[3] += f_v0[4];
     f_v1[3] += f_v1[4];
     ok &= std::fabs( f_v0[3] - 0.5 ) <= 1e-10;  // partial f_3 w.r.t. v_3^0
     ok &= std::fabs( f_v1[3] - 1.25) <= 1e-10;  // partial f_3 w.r.t. v_3^1

     // f_2 = f_3( v_1^0 , ... , v_2^1 , v_2^0 , v_2^1 )
     f_v0[2] += f_v0[3];
     f_v1[2] += f_v1[3];
     ok &= std::fabs( f_v0[2] - 0.5 ) <= 1e-10;  // partial f_2 w.r.t. v_2^0
     ok &= std::fabs( f_v1[2] - 1.25) <= 1e-10;  // partial f_2 w.r.t. v_2^1

     // f_1 = f_2 ( v_1^0 , v_2^0 , v_1^0 , v_2^0 )
     f_v0[1] += f_v0[2];
     f_v1[1] += f_v1[2];
     ok &= std::fabs( f_v0[1] - 1.  ) <= 1e-10;  // partial f_1 w.r.t. v_1^0
     ok &= std::fabs( f_v1[1] - 1.5 ) <= 1e-10;  // partial f_1 w.r.t. v_1^1

     return ok;
}
Input File: introduction/exp_apx/exp_eps_rev2.cpp cppad-20170000.3/doc/exp_eps_for1.xml0000644000175200017650000007515013057470504016320 0ustar coincoin-web exp_eps: First Order Forward Sweep
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exp_eps: First Order Forward Sweep

First Order Expansion
We define x ( t ) and ε ( t ) ] near t = 0 by the first order expansions x ( t ) = x ( 0 ) + x ( 1 ) * t ε ( t ) = ε ( 0 ) + ε ( 1 ) * t It follows that x ( 0 ) ( ε ( 0 ) ) is the zero, and x ( 1 ) ( ε ( 1 ) ) the first, order derivative of x ( t ) at t = 0 ( ε ( t ) ) at t = 0 .

Mathematical Form
Suppose that we use the algorithm exp_eps.hpp to compute exp_eps(x, epsilon) with x is equal to .5 and epsilon is equal to .2. For this case, the mathematical function for the operation sequence corresponding to exp_eps is f ( x , ε ) = 1 + x + x 2 / 2 The corresponding partial derivative with respect to x , and the value of the derivative, are ∂ x f ( x , ε ) = 1 + x = 1.5
Operation Sequence

Index
The Index column contains the index in the operation sequence of the corresponding atomic operation. A Forward sweep starts with the first operation and ends with the last.

Operation
The Operation column contains the mathematical function corresponding to each atomic operation in the sequence.

Zero Order
The Zero Order column contains the zero order derivatives for the corresponding variable in the operation sequence (see zero order sweep ).

Derivative
The Derivative column contains the mathematical function corresponding to the derivative with respect to t , at t = 0 , for each variable in the sequence.

First Order
The First Order column contains the first order derivatives for the corresponding variable in the operation sequence; i.e., v j ( t ) = v j ( 0 ) + v j ( 1 ) t We use x ( 1 ) = 1 and ε ( 1 ) = 0 , so that differentiation with respect to t , at t = 0 , is the same partial differentiation with respect to x at x = x ( 0 ) .

Sweep
Index    Operation    Zero Order    Derivative    First Order
1    v 1 = x 0.5 v 1 ( 1 ) = x ( 1 ) v 1 ( 1 ) = 1
2    v 2 = 1 * v 1 0.5 v 2 ( 1 ) = 1 * v 1 ( 1 ) v 2 ( 1 ) = 1
3    v 3 = v 2 / 1 0.5 v 3 ( 1 ) = v 2 ( 1 ) / 1 v 3 ( 1 ) = 1
4    v 4 = 1 + v 3 1.5 v 4 ( 1 ) = v 3 ( 1 ) v 4 ( 1 ) = 1
5    v 5 = v 3 * v 1 0.25 v 5 ( 1 ) = v 3 ( 1 ) * v 1 ( 0 ) + v 3 ( 0 ) * v 1 ( 1 ) v 5 ( 1 ) = 1
6    v 6 = v 5 / 2 0.125 v 6 ( 1 ) = v 5 ( 1 ) / 2 v 6 ( 1 ) = 0.5
7    v 7 = v 4 + v 6 1.625 v 7 ( 1 ) = v 4 ( 1 ) + v 6 ( 1 ) v 7 ( 1 ) = 1.5
Return Value
The derivative of the return value for this case is 1.5 = v 7 ( 1 ) = [∂ v 7 ∂ t ] t = 0 = [∂ ∂ t f ( x ( 0 ) + x ( 1 ) * t , ε ( 0 ) ) ] t = 0 = ∂ x f ( x ( 0 ) , ε ( 0 ) ) * x ( 1 ) = ∂ x f ( x ( 0 ) , ε ( 0 ) ) (We have used the fact that x ( 1 ) = 1 and ε ( 1 ) = 0 .)

Verification
The file exp_eps_for1.cpp contains a routine that verifies the values computed above. It returns true for success and false for failure.

Exercises
  1. Suppose that x = .1 , what are the results of a zero and first order forward mode sweep for the operation sequence above; i.e., what are the corresponding values for v 1 ( 0 ) , v 2 ( 0 ) , ⋯ , v 7 ( 0 ) and v 1 ( 1 ) , v 2 ( 1 ) , ⋯ , v 7 ( 1 ) ?
  2. Create a modified version of exp_eps_for1.cpp that verifies the derivative values from the previous exercise. Also create and run a main program that reports the result of calling the modified version of exp_eps_for1.cpp .
  3. Suppose that x = .1 and ∈ = .2 , what is the operation sequence corresponding to
         exp_eps(    x, epsilon)
Input File: introduction/exp_apx/exp_eps.omh cppad-20170000.3/doc/exp_eps_rev1.xml0000644000175200017650000012114313057470504016320 0ustar coincoin-web exp_eps: First Order Reverse Sweep
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exp_eps: First Order Reverse Sweep

Purpose
First order reverse mode uses the operation sequence , and zero order forward sweep values, to compute the first order derivative of one dependent variable with respect to all the independent variables. The computations are done in reverse of the order of the computations in the original algorithm.

Mathematical Form
Suppose that we use the algorithm exp_eps.hpp to compute exp_eps(x, epsilon) with x is equal to .5 and epsilon is equal to .2. For this case, the mathematical function for the operation sequence corresponding to exp_eps is f ( x , ε ) = 1 + x + x 2 / 2 The corresponding partial derivatives, and the value of the derivatives, are ∂ x f ( x , ε ) = 1 + x = 1.5 ∂ ε f ( x , ε ) = 0
epsilon
Since ε is an independent variable, it could included as an argument to all of the f j functions below. The result would be that all the partials with respect to ε would be zero and hence we drop it to simplify the presentation.

f_7
In reverse mode we choose one dependent variable and compute its derivative with respect to all the independent variables. For our example, we chose the value returned by exp_eps.hpp which is v 7 . We begin with the function f 7 where v 7 is both an argument and the value of the function; i.e., f 7 ( v 1 , v 2 , v 3 , v 4 , v 5 , v 6 , v 7 ) = v 7 ∂ f 7 ∂ v 7 = 1 All the other partial derivatives of f 7 are zero.

Index 7: f_6
The last operation has index 7, v 7 = v 4 + v 6 We define the function f 6 ( v 1 , v 2 , v 3 , v 4 , v 5 , v 6 ) as equal to f 7 except that v 7 is eliminated using this operation; i.e. f 6 = f 7 [ v 1 , v 2 , v 3 , v 4 , v 5 , v 6 , v 7 ( v 4 , v 6 ) ] It follows that ∂ f 6 ∂ v 4 = ∂ f 7 ∂ v 4 + ∂ f 7 ∂ v 7 * ∂ v 7 ∂ v 4 = 1 ∂ f 6 ∂ v 6 = ∂ f 7 ∂ v 6 + ∂ f 7 ∂ v 7 * ∂ v 7 ∂ v 6 = 1 All the other partial derivatives of f 6 are zero.

Index 6: f_5
The previous operation has index 6, v 6 = v 5 / 2 We define the function f 5 ( v 1 , v 2 , v 3 , v 4 , v 5 ) as equal to f 6 except that v 6 is eliminated using this operation; i.e., f 5 = f 6 [ v 1 , v 2 , v 3 , v 4 , v 5 , v 6 ( v 5 ) ] It follows that ∂ f 5 ∂ v 4 = ∂ f 6 ∂ v 4 = 1 ∂ f 5 ∂ v 5 = ∂ f 6 ∂ v 5 + ∂ f 6 ∂ v 6 * ∂ v 6 ∂ v 5 = 0.5 All the other partial derivatives of f 5 are zero.

Index 5: f_4
The previous operation has index 5, v 5 = v 3 * v 1 We define the function f 4 ( v 1 , v 2 , v 3 , v 4 ) as equal to f 5 except that v 5 is eliminated using this operation; i.e., f 4 = f 5 [ v 1 , v 2 , v 3 , v 4 , v 5 ( v 3 , v 1 ) ] Given the information from the forward sweep, we have v 3 = 0.5 and v 1 = 0.5 . It follows that ∂ f 4 ∂ v 1 = ∂ f 5 ∂ v 1 + ∂ f 5 ∂ v 5 * ∂ v 5 ∂ v 1 = 0.25 ∂ f 4 ∂ v 2 = ∂ f 5 ∂ v 2 = 0 ∂ f 4 ∂ v 3 = ∂ f 5 ∂ v 3 + ∂ f 5 ∂ v 5 * ∂ v 5 ∂ v 3 = 0.25 ∂ f 4 ∂ v 4 = ∂ f 5 ∂ v 4 = 1
Index 4: f_3
The previous operation has index 4, v 4 = 1 + v 3 We define the function f 3 ( v 1 , v 2 , v 3 ) as equal to f 4 except that v 4 is eliminated using this operation; i.e., f 3 = f 4 [ v 1 , v 2 , v 3 , v 4 ( v 3 ) ] It follows that ∂ f 3 ∂ v 1 = ∂ f 4 ∂ v 1 = 0.25 ∂ f 3 ∂ v 2 = ∂ f 4 ∂ v 2 = 0 ∂ f 3 ∂ v 3 = ∂ f 4 ∂ v 3 + ∂ f 4 ∂ v 4 * ∂ v 4 ∂ v 3 = 1.25
Index 3: f_2
The previous operation has index 3, v 3 = v 2 / 1 We define the function f 2 ( v 1 , v 2 ) as equal to f 3 except that v 3 is eliminated using this operation; i.e., f 2 = f 4 [ v 1 , v 2 , v 3 ( v 2 ) ] It follows that ∂ f 2 ∂ v 1 = ∂ f 3 ∂ v 1 = 0.25 ∂ f 2 ∂ v 2 = ∂ f 3 ∂ v 2 + ∂ f 3 ∂ v 3 * ∂ v 3 ∂ v 2 = 1.25
Index 2: f_1
The previous operation has index 1, v 2 = 1 * v 1 We define the function f 1 ( v 1 ) as equal to f 2 except that v 2 is eliminated using this operation; i.e., f 1 = f 2 [ v 1 , v 2 ( v 1 ) ] It follows that ∂ f 1 ∂ v 1 = ∂ f 2 ∂ v 1 + ∂ f 2 ∂ v 2 * ∂ v 2 ∂ v 1 = 1.5 Note that v 1 is equal to x , so the derivative of exp_eps(x, epsilon) at x equal to .5 and epsilon equal .2 is 1.5 in the x direction and zero in the epsilon direction. We also note that forward forward mode gave the same result for the partial in the x direction.

Verification
The file exp_eps_rev1.cpp contains a routine that verifies the values computed above. It returns true for success and false for failure. It only tests the partial derivatives of f j that might not be equal to the corresponding partials of f j + 1 ; i.e., the other partials of f j must be equal to the corresponding partials of f j + 1 .

Exercises
  1. Consider the case where x = .1 and we first preform a zero order forward mode sweep for the operation sequence used above (in reverse order). What are the results of a first order reverse mode sweep; i.e., what are the corresponding values for ∂ f j ∂ v k for all j , k such that ∂ f j ∂ v k ≠ 0 .
  2. Create a modified version of exp_eps_rev1.cpp that verifies the values you obtained for the previous exercise. Also create and run a main program that reports the result of calling the modified version of exp_eps_rev1.cpp .
Input File: introduction/exp_apx/exp_eps.omh cppad-20170000.3/doc/exp_eps_for2.xml0000644000175200017650000010361113057470504016313 0ustar coincoin-web exp_eps: Second Order Forward Mode
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exp_eps: Second Order Forward Mode

Second Order Expansion
We define x ( t ) and ε ( t ) ] near t = 0 by the second order expansions x ( t ) = x ( 0 ) + x ( 1 ) * t + x ( 2 ) * t 2 / 2 ε ( t ) = ε ( 0 ) + ε ( 1 ) * t + ε ( 2 ) * t 2 / 2 It follows that for k = 0 , 1 , 2 , x ( k ) = d k d t k x ( 0 ) ε ( k ) = d k d t k ε ( 0 )
Purpose
In general, a second order forward sweep is given the first order expansion for all of the variables in an operation sequence, and the second order derivatives for the independent variables. It uses these to compute the second order derivative, and thereby obtain the second order expansion, for all the variables in the operation sequence.

Mathematical Form
Suppose that we use the algorithm exp_eps.hpp to compute exp_eps(x, epsilon) with x is equal to .5 and epsilon is equal to .2. For this case, the mathematical function for the operation sequence corresponding to exp_eps is f ( x , ε ) = 1 + x + x 2 / 2 The corresponding second partial derivative with respect to x , and the value of the derivative, are ∂ 2 ∂ x 2 f ( x , ε ) = 1.
Operation Sequence

Index
The Index column contains the index in the operation sequence of the corresponding atomic operation. A Forward sweep starts with the first operation and ends with the last.

Zero
The Zero column contains the zero order sweep results for the corresponding variable in the operation sequence (see zero order sweep ).

Operation
The Operation column contains the first order sweep operation for this variable.

First
The First column contains the first order sweep results for the corresponding variable in the operation sequence (see first order sweep ).

Derivative
The Derivative column contains the mathematical function corresponding to the second derivative with respect to t , at t = 0 , for each variable in the sequence.

Second
The Second column contains the second order derivatives for the corresponding variable in the operation sequence; i.e., the second order expansion for the i-th variable is given by v i ( t ) = v i ( 0 ) + v i ( 1 ) * t + v i ( 2 ) * t 2 / 2 We use x ( 1 ) = 1 , x ( 2 ) = 0 , use ε ( 1 ) = 1 , and ε ( 2 ) = 0 so that second order differentiation with respect to t , at t = 0 , is the same as the second partial differentiation with respect to x at x = x ( 0 ) .

Sweep
Index    Zero    Operation    First    Derivative    Second
1 0.5 v 1 ( 1 ) = x ( 1 ) 1 v 2 ( 2 ) = x ( 2 ) 0
2 0.5 v 2 ( 1 ) = 1 * v 1 ( 1 ) 1 v 2 ( 2 ) = 1 * v 1 ( 2 ) 0
3 0.5 v 3 ( 1 ) = v 2 ( 1 ) / 1 1 v 3 ( 2 ) = v 2 ( 2 ) / 1 0
4 1.5 v 4 ( 1 ) = v 3 ( 1 ) 1 v 4 ( 2 ) = v 3 ( 2 ) 0
5 0.25 v 5 ( 1 ) = v 3 ( 1 ) * v 1 ( 0 ) + v 3 ( 0 ) * v 1 ( 1 ) 1 v 5 ( 2 ) = v 3 ( 2 ) * v 1 ( 0 ) + 2 * v 3 ( 1 ) * v 1 ( 1 ) + v 3 ( 0 ) * v 1 ( 2 ) 2
6 0.125 v 6 ( 1 ) = v 5 ( 1 ) / 2 0.5 v 6 ( 2 ) = v 5 ( 2 ) / 2 1
7 1.625 v 7 ( 1 ) = v 4 ( 1 ) + v 6 ( 1 ) 1.5 v 7 ( 2 ) = v 4 ( 2 ) + v 6 ( 2 ) 1
Return Value
The second derivative of the return value for this case is 1 = v 7 ( 2 ) = [∂ 2 ∂ t 2 v 7 ] t = 0 = [∂ 2 ∂ t 2 f ( x ( 0 ) + x ( 1 ) * t , ε ( 0 ) ) ] t = 0 = x ( 1 ) * ∂ 2 ∂ x 2 f ( x ( 0 ) , ε ( 0 ) ) * x ( 1 ) = ∂ 2 ∂ x 2 f ( x ( 0 ) , ε ( 0 ) ) (We have used the fact that x ( 1 ) = 1 , x ( 2 ) = 0 , ε ( 1 ) = 1 , and ε ( 2 ) = 0 .)

Verification
The file exp_eps_for2.cpp contains a routine which verifies the values computed above. It returns true for success and false for failure.

Exercises
  1. Which statement in the routine defined by exp_eps_for2.cpp uses the values that are calculated by the routine defined by exp_eps_for1.cpp ?
  2. Suppose that x = .1 , what are the results of a zero, first, and second order forward sweep for the operation sequence above; i.e., what are the corresponding values for v i ( k ) for i = 1 , … , 7 and k = 0 , 1 , 2 .
  3. Create a modified version of exp_eps_for2.cpp that verifies the derivative values from the previous exercise. Also create and run a main program that reports the result of calling the modified version of exp_eps_for2.cpp .
Input File: introduction/exp_apx/exp_eps.omh cppad-20170000.3/doc/exp_eps_rev2.xml0000644000175200017650000021543013057470504016324 0ustar coincoin-web exp_eps: Second Order Reverse Sweep
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exp_eps: Second Order Reverse Sweep

Purpose
In general, a second order reverse sweep is given the first order expansion for all of the variables in an operation sequence. Given a choice of a particular variable, it computes the derivative, of that variables first order expansion coefficient, with respect to all of the independent variables.

Mathematical Form
Suppose that we use the algorithm exp_eps.hpp to compute exp_eps(x, epsilon) with x is equal to .5 and epsilon is equal to .2. For this case, the mathematical function for the operation sequence corresponding to exp_eps is f ( x , ε ) = 1 + x + x 2 / 2 The corresponding derivative of the partial derivative with respect to x is ∂ 2 ∂ x 2 f ( x , ε ) = 1 ∂ ε ∂ x f ( x , ε ) = 0
epsilon
Since ε is an independent variable, it could included as an argument to all of the f j functions below. The result would be that all the partials with respect to ε would be zero and hence we drop it to simplify the presentation.

f_7
In reverse mode we choose one dependent variable and compute its derivative with respect to all the independent variables. For our example, we chose the value returned by exp_eps.hpp which is v 7 . We begin with the function f 7 where v 7 is both an argument and the value of the function; i.e., f 7 (v 1 ( 0 ) , v 1 ( 1 ) , … , v 7 ( 0 ) , v 7 ( 1 ) ) = v 7 ( 1 ) ∂ f 7 ∂ v 7 ( 1 ) = 1 All the other partial derivatives of f 7 are zero.

Index 7: f_6
The last operation has index 7, v 7 ( 0 ) = v 4 ( 0 ) + v 6 ( 0 ) v 7 ( 1 ) = v 4 ( 1 ) + v 6 ( 1 ) We define the function f 6 (v 1 ( 0 ) , … , v 6 ( 1 ) ) as equal to f 7 except that v 7 ( 0 ) and v 7 ( 1 ) are eliminated using this operation; i.e. f 6 = f 7 [v 1 ( 0 ) , … , v 6 ( 1 ) , v 7 ( 0 ) (v 4 ( 0 ) , v 6 ( 0 ) ) , v 7 ( 1 ) (v 4 ( 1 ) , v 6 ( 1 ) ) ] It follows that ∂ f 6 ∂ v 4 ( 1 ) = ∂ f 7 ∂ v 4 ( 1 ) + ∂ f 7 ∂ v 7 ( 1 ) * ∂ v 7 ( 1 ) ∂ v 4 ( 1 ) = 1 ∂ f 6 ∂ v 6 ( 1 ) = ∂ f 7 ∂ v 6 ( 1 ) + ∂ f 7 ∂ v 7 ( 1 ) * ∂ v 7 ( 1 ) ∂ v 6 ( 1 ) = 1 All the other partial derivatives of f 6 are zero.

Index 6: f_5
The previous operation has index 6, v 6 ( 0 ) = v 5 ( 0 ) / 2 v 6 ( 1 ) = v 5 ( 1 ) / 2 We define the function f 5 (v 1 ( 0 ) , … , v 5 ( 1 ) ) as equal to f 6 except that v 6 ( 0 ) and v 6 ( 1 ) are eliminated using this operation; i.e. f 5 = f 6 [v 1 ( 0 ) , … , v 5 ( 1 ) , v 6 ( 0 ) (v 5 ( 0 ) ) , v 6 ( 1 ) (v 5 ( 1 ) ) ] It follows that ∂ f 5 ∂ v 4 ( 1 ) = ∂ f 6 ∂ v 4 ( 1 ) = 1 ∂ f 5 ∂ v 5 ( 1 ) = ∂ f 6 ∂ v 5 + ∂ f 6 ∂ v 6 ( 1 ) * ∂ v 6 ( 1 ) ∂ v 5 ( 1 ) = 0.5 All the other partial derivatives of f 5 are zero.

Index 5: f_4
The previous operation has index 5, v 5 ( 0 ) = v 3 ( 0 ) * v 1 ( 0 ) v 5 ( 1 ) = v 3 ( 1 ) * v 1 ( 0 ) + v 3 ( 0 ) * v 1 ( 1 ) We define the function f 4 (v 1 ( 0 ) , … , v 4 ( 1 ) ) as equal to f 5 except that v 5 ( 0 ) and v 5 ( 1 ) are eliminated using this operation; i.e. f 4 = f 5 [v 1 ( 0 ) , … , v 4 ( 1 ) , v 5 ( 0 ) (v 1 ( 0 ) , v 3 ( 0 ) ) , v 5 ( 1 ) (v 1 ( 0 ) , v 1 ( 1 ) , v 3 ( 0 ) , v 3 ( 1 ) ) , ] Given the information from the forward sweep, we have v 1 ( 0 ) = 0.5 , v 3 ( 0 ) = 0.5 , v 1 ( 1 ) = 1 , v 3 ( 1 ) = 1 , and the fact that the partial of f 5 with respect to v 5 ( 0 ) is zero, we have ∂ f 4 ∂ v 1 ( 0 ) = ∂ f 5 ∂ v 1 ( 0 ) + ∂ f 5 ∂ v 5 ( 1 ) * ∂ v 5 ( 1 ) ∂ v 1 ( 0 ) = 0.5 ∂ f 4 ∂ v 1 ( 1 ) = ∂ f 5 ∂ v 1 ( 1 ) + ∂ f 5 ∂ v 5 ( 1 ) * ∂ v 5 ( 1 ) ∂ v 1 ( 1 ) = 0.25 ∂ f 4 ∂ v 3 ( 0 ) = ∂ f 5 ∂ v 3 ( 0 ) + ∂ f 5 ∂ v 5 ( 1 ) * ∂ v 5 ( 1 ) ∂ v 3 ( 0 ) = 0.5 ∂ f 4 ∂ v 3 ( 1 ) = ∂ f 3 ∂ v 1 ( 1 ) + ∂ f 5 ∂ v 5 ( 1 ) * ∂ v 5 ( 1 ) ∂ v 3 ( 1 ) = 0.25 ∂ f 4 ∂ v 4 ( 1 ) = ∂ f 5 ∂ v 4 ( 1 ) = 1 All the other partial derivatives of f 5 are zero.

Index 4: f_3
The previous operation has index 4, v 4 ( 0 ) = 1 + v 3 ( 0 ) v 4 ( 1 ) = v 3 ( 1 ) We define the function f 3 (v 1 ( 0 ) , … , v 3 ( 1 ) ) as equal to f 4 except that v 4 ( 0 ) and v 4 ( 1 ) are eliminated using this operation; i.e. f 3 = f 4 [v 1 ( 0 ) , … , v 3 ( 1 ) , v 4 ( 0 ) (v 3 ( 0 ) ) , v 4 ( 1 ) (v 3 ( 1 ) ) ] It follows that ∂ f 3 ∂ v 1 ( 0 ) = ∂ f 4 ∂ v 1 ( 0 ) = 0.5 ∂ f 3 ∂ v 1 ( 1 ) = ∂ f 4 ∂ v 1 ( 1 ) = 0.25 ∂ f 3 ∂ v 2 ( 0 ) = ∂ f 4 ∂ v 2 ( 0 ) = 0 ∂ f 3 ∂ v 2 ( 1 ) = ∂ f 4 ∂ v 2 ( 1 ) = 0 ∂ f 3 ∂ v 3 ( 0 ) = ∂ f 4 ∂ v 3 ( 0 ) + ∂ f 4 ∂ v 4 ( 0 ) * ∂ v 4 ( 0 ) ∂ v 3 ( 0 ) = 0.5 ∂ f 3 ∂ v 3 ( 1 ) = ∂ f 4 ∂ v 3 ( 1 ) + ∂ f 4 ∂ v 4 ( 1 ) * ∂ v 4 ( 1 ) ∂ v 3 ( 1 ) = 1.25
Index 3: f_2
The previous operation has index 3, v 3 ( 0 ) = v 2 ( 0 ) / 1 v 3 ( 1 ) = v 2 ( 1 ) / 1 We define the function f 2 (v 1 ( 0 ) , … , v 2 ( 1 ) ) as equal to f 3 except that v 3 ( 0 ) and v 3 ( 1 ) are eliminated using this operation; i.e. f 2 = f 3 [v 1 ( 0 ) , … , v 2 ( 1 ) , v 3 ( 0 ) (v 2 ( 0 ) ) , v 3 ( 1 ) (v 2 ( 1 ) ) ] It follows that ∂ f 2 ∂ v 1 ( 0 ) = ∂ f 3 ∂ v 1 ( 0 ) = 0.5 ∂ f 2 ∂ v 1 ( 1 ) = ∂ f 3 ∂ v 1 ( 1 ) = 0.25 ∂ f 2 ∂ v 2 ( 0 ) = ∂ f 3 ∂ v 2 ( 0 ) + ∂ f 3 ∂ v 3 ( 0 ) * ∂ v 3 ( 0 ) ∂ v 2 ( 0 ) = 0.5 ∂ f 2 ∂ v 2 ( 1 ) = ∂ f 3 ∂ v 2 ( 1 ) + ∂ f 3 ∂ v 3 ( 1 ) * ∂ v 3 ( 1 ) ∂ v 2 ( 0 ) = 1.25
Index 2: f_1
The previous operation has index 1, v 2 ( 0 ) = 1 * v 1 ( 0 ) v 2 ( 1 ) = 1 * v 1 ( 1 ) We define the function f 1 (v 1 ( 0 ) , v 1 ( 1 ) ) as equal to f 2 except that v 2 ( 0 ) and v 2 ( 1 ) are eliminated using this operation; i.e. f 1 = f 2 [v 1 ( 0 ) , v 1 ( 1 ) , v 2 ( 0 ) (v 1 ( 0 ) ) , v 2 ( 1 ) (v 1 ( 1 ) ) ] It follows that ∂ f 1 ∂ v 1 ( 0 ) = ∂ f 2 ∂ v 1 ( 0 ) + ∂ f 2 ∂ v 2 ( 0 ) * ∂ v 2 ( 0 ) ∂ v 1 ( 0 ) = 1 ∂ f 1 ∂ v 1 ( 1 ) = ∂ f 2 ∂ v 1 ( 1 ) + ∂ f 2 ∂ v 2 ( 1 ) * ∂ v 2 ( 1 ) ∂ v 1 ( 1 ) = 1.5 Note that v 1 is equal to x , so the second partial derivative of exp_eps(x, epsilon) at x equal to .5 and epsilon equal .2 is ∂ 2 ∂ x 2 v 7 ( 0 ) = ∂ v 7 ( 1 ) ∂ x = ∂ f 1 ∂ v 1 ( 0 ) = 1 There is a theorem about algorithmic differentiation that explains why the other partial of f 1 is equal to the first partial of exp_eps(x, epsilon) with respect to x .

Verification
The file exp_eps_rev2.cpp contains a routine that verifies the values computed above. It returns true for success and false for failure. It only tests the partial derivatives of f j that might not be equal to the corresponding partials of f j + 1 ; i.e., the other partials of f j must be equal to the corresponding partials of f j + 1 .

Exercises
  1. Consider the case where x = .1 and we first preform a zero order forward mode sweep for the operation sequence used above (in reverse order). What are the results of a first order reverse mode sweep; i.e., what are the corresponding values for ∂ f j ∂ v k for all j , k such that ∂ f j ∂ v k ≠ 0 .
  2. Create a modified version of exp_eps_rev2.cpp that verifies the values you obtained for the previous exercise. Also create and run a main program that reports the result of calling the modified version of exp_eps_rev2.cpp .
Input File: introduction/exp_apx/exp_eps.omh cppad-20170000.3/doc/exp_eps_cppad.xml0000644000175200017650000005452113057470504016537 0ustar coincoin-web exp_eps: CppAD Forward and Reverse Sweeps
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exp_eps: CppAD Forward and Reverse Sweeps
.

Purpose
Use CppAD forward and reverse modes to compute the partial derivative with respect to x , at the point x = .5 and ε = .2 , of the function
     exp_eps(x, epsilon)
 as defined by the exp_eps.hpp include file.

Exercises
  1. Create and test a modified version of the routine below that computes the same order derivatives with respect to x , at the point x = .1 and ε = .2 , of the function
         exp_eps(    x, epsilon)
  2. Create and test a modified version of the routine below that computes partial derivative with respect to x , at the point x = .1 and ε = .2 , of the function corresponding to the operation sequence for x = .5 and ε = .2 . Hint: you could define a vector u with two components and use
             f.Forward(0, u)
     to run zero order forward mode at a point different form the point where the operation sequence corresponding to f was recorded. 
# include <cppad/cppad.hpp>  // http://www.coin-or.org/CppAD/
# include "exp_eps.hpp"      // our example exponential function approximation
bool exp_eps_cppad(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::vector;    // can use any simple vector template class
     using CppAD::NearEqual; // checks if values are nearly equal

     // domain space vector
     size_t n = 2; // dimension of the domain space
     vector< AD<double> > U(n);
     U[0] = .5;    // value of x for this operation sequence
     U[1] = .2;    // value of e for this operation sequence

     // declare independent variables and start recording operation sequence
     CppAD::Independent(U);

     // evaluate our exponential approximation
     AD<double> x       = U[0];
     AD<double> epsilon = U[1];
     AD<double> apx = exp_eps(x, epsilon);

     // range space vector
     size_t m = 1;  // dimension of the range space
     vector< AD<double> > Y(m);
     Y[0] = apx;    // variable that represents only range space component

     // Create f: U -> Y corresponding to this operation sequence
     // and stop recording. This also executes a zero order forward
     // mode sweep using values in U for x and e.
     CppAD::ADFun<double> f(U, Y);

     // first order forward mode sweep that computes partial w.r.t x
     vector<double> du(n);      // differential in domain space
     vector<double> dy(m);      // differential in range space
     du[0] = 1.;                // x direction in domain space
     du[1] = 0.;
     dy    = f.Forward(1, du);  // partial w.r.t. x
     double check = 1.5;
     ok   &= NearEqual(dy[0], check, 1e-10, 1e-10);

     // first order reverse mode sweep that computes the derivative
     vector<double>  w(m);     // weights for components of the range
     vector<double> dw(n);     // derivative of the weighted function
     w[0] = 1.;                // there is only one weight
     dw   = f.Reverse(1, w);   // derivative of w[0] * exp_eps(x, epsilon)
     check = 1.5;              // partial w.r.t. x
     ok   &= NearEqual(dw[0], check, 1e-10, 1e-10);
     check = 0.;               // partial w.r.t. epsilon
     ok   &= NearEqual(dw[1], check, 1e-10, 1e-10);

     // second order forward sweep that computes
     // second partial of exp_eps(x, epsilon) w.r.t. x
     vector<double> x2(n);     // second order Taylor coefficients
     vector<double> y2(m);
     x2[0] = 0.;               // evaluate partial w.r.t x
     x2[1] = 0.;
     y2    = f.Forward(2, x2);
     check = 0.5 * 1.;         // Taylor coef is 1/2 second derivative
     ok   &= NearEqual(y2[0], check, 1e-10, 1e-10);

     // second order reverse sweep that computes
     // derivative of partial of exp_eps(x, epsilon) w.r.t. x
     dw.resize(2 * n);         // space for first and second derivative
     dw    = f.Reverse(2, w);
     check = 1.;               // result should be second derivative
     ok   &= NearEqual(dw[0*2+1], check, 1e-10, 1e-10);

     return ok;
}
Input File: introduction/exp_apx/exp_eps_cppad.cpp cppad-20170000.3/doc/exp_apx_main.cpp.xml0000644000175200017650000004517213057470504017160 0ustar coincoin-web Correctness Tests For Exponential Approximation in Introduction
Prev Next exp_apx_main.cpp

Correctness Tests For Exponential Approximation in Introduction

Running Tests
To build this program and run its correctness tests see cmake_check .

main.cpp 


// system include files used for I/O
# include <iostream>

// external complied tests
extern bool exp_2(void);
extern bool exp_2_cppad(void);
extern bool exp_2_for1(void);
extern bool exp_2_for2(void);
extern bool exp_2_rev1(void);
extern bool exp_2_rev2(void);
extern bool exp_2_for0(void);
extern bool exp_eps(void);
extern bool exp_eps_cppad(void);
extern bool exp_eps_for1(void);
extern bool exp_eps_for2(void);
extern bool exp_eps_for0(void);
extern bool exp_eps_rev1(void);
extern bool exp_eps_rev2(void);

namespace {
     static size_t Run_ok_count    = 0;
     static size_t Run_error_count = 0;
     bool Run(bool TestOk(void), std::string name)
     {     bool ok               = true;
          std::streamsize width =  20;
          std::cout.width( width );
          std::cout.setf( std::ios_base::left );
          std::cout << name.c_str();
          //
          ok &= name.size() < size_t(width);
          ok &= TestOk();
          if( ok )
          {     std::cout << "OK" << std::endl;
               Run_ok_count++;
          }
          else
          {     std::cout << "Error" << std::endl;
               Run_error_count++;
          }
          return ok;
     }
}

// main program that runs all the tests
int main(void)
{     bool ok = true;
     using namespace std;

     // This comment is used by OneTest

     // external compiled tests
     ok &= Run( exp_2,           "exp_2"          );
     ok &= Run( exp_2_cppad,     "exp_2_cppad"    );
     ok &= Run( exp_2_for0,      "exp_2_for0"     );
     ok &= Run( exp_2_for1,      "exp_2_for1"     );
     ok &= Run( exp_2_for2,      "exp_2_for2"     );
     ok &= Run( exp_2_rev1,      "exp_2_rev1"     );
     ok &= Run( exp_2_rev2,      "exp_2_rev2"     );
     ok &= Run( exp_eps,         "exp_eps"        );
     ok &= Run( exp_eps_cppad,   "exp_eps_cppad"  );
     ok &= Run( exp_eps_for0,    "exp_eps_for0"   );
     ok &= Run( exp_eps_for1,    "exp_eps_for1"   );
     ok &= Run( exp_eps_for2,    "exp_eps_for2"   );
     ok &= Run( exp_eps_rev1,    "exp_eps_rev1"   );
     ok &= Run( exp_eps_rev2,    "exp_eps_rev2"   );
     if( ok )
          cout << "All " << int(Run_ok_count) << " tests passed." << endl;
     else     cout << int(Run_error_count) << " tests failed." << endl;

     return static_cast<int>( ! ok );
}
Input File: introduction/exp_apx/main.cpp cppad-20170000.3/doc/ad.xml0000644000175200017650000001114713057470504014306 0ustar coincoin-web AD Objects
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AD Objects

Purpose
The sections listed below describe the operations that are available to AD of Base objects. These objects are used to tape an AD of Base operation sequence . This operation sequence can be transferred to an ADFun object where it can be used to evaluate the corresponding function and derivative values.

Base Type Requirements
The Base requirements are provided by the CppAD package for the following base types: float, double, std::complex<float>, std::complex<double>. Otherwise, see base_require .

Contents
ad_ctorAD Constructors
ad_assignAD Assignment Operator
ConvertConversion and I/O of AD Objects
ADValuedAD Valued Operations and Functions
BoolValuedBool Valued Operations and Functions with AD Arguments
VecADAD Vectors that Record Index Operations
base_requireAD<Base> Requirements for a CppAD Base Type
Input File: cppad/core/user_ad.hpp cppad-20170000.3/doc/ad_ctor.xml0000644000175200017650000002030713057470504015333 0ustar coincoin-web AD Constructors
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AD Constructors

Syntax
AD<Base> y()
 AD<Base> y(x)
Purpose
creates a new AD<Base> object y and initializes its value as equal to x .

x

implicit
There is an implicit constructor where x has one of the following prototypes:
     const Base&        x
     const VecAD<Base>& x
explicit
There is an explicit constructor where x has prototype
     const Type&        x
 for any type that has an explicit constructor of the form Base(x) .

Deprecated 2013-12-31
If you set cppad_deprecated to be YES during the install procedure, you will get an implicit constructor with prototype
     const Type&        x
 for any type that has an explicit constructor of the form Base(x) .

y
The target y has prototype
     AD<Base> y
Example
The files ad_ctor.cpp contain examples and tests of these operations. It test returns true if it succeeds and false otherwise.
Input File: cppad/core/ad_ctor.hpp cppad-20170000.3/doc/ad_ctor.cpp.xml0000644000175200017650000001514713057470504016122 0ustar coincoin-web AD Constructors: Example and Test
Prev Next ad_ctor.cpp Headings

AD Constructors: Example and Test

# include <cppad/cppad.hpp>

bool ad_ctor(void)
{     bool ok = true;   // initialize test result flag
     using CppAD::AD;  // so can use AD in place of CppAD::AD

     // default constructor
     AD<double> a;
     a = 0.;
     ok &= a == 0.;

     // constructor from base type
     AD<double> b(1.);
     ok &= b == 1.;

     // constructor from another type that converts to the base type
     AD<double> c(2);
     ok &= c == 2.;

     // constructor from AD<Base>
     AD<double> d(c);
     ok &= d == 2.;

     // constructor from a VecAD<Base> element
     CppAD::VecAD<double> v(1);
     v[0] = 3.;
     AD<double> e( v[0] );
     ok &= e == 3.;

     return ok;
}
Input File: example/ad_ctor.cpp cppad-20170000.3/doc/ad_assign.xml0000644000175200017650000001300513057470504015645 0ustar coincoin-web AD Assignment Operator
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AD Assignment Operator

Syntax
y = x

Purpose
Assigns the value in x to the object y . In either case,

x
The argument x has prototype
     const Type &x
 where Type is VecAD<Base>::reference , AD<Base> , Base , or any type that has an implicit constructor of the form Base(x) .

y
The target y has prototype
     AD<Base> y
Example
The file ad_assign.cpp contain examples and tests of these operations. It test returns true if it succeeds and false otherwise.
Input File: cppad/core/ad_assign.hpp cppad-20170000.3/doc/ad_assign.cpp.xml0000644000175200017650000001365113057470504016435 0ustar coincoin-web AD Assignment: Example and Test
Prev Next ad_assign.cpp Headings

AD Assignment: Example and Test

# include <cppad/cppad.hpp>

bool ad_assign(void)
{     bool ok = true;   // initialize test result flag
     using CppAD::AD;  // so can use AD in place of CppAD::AD

     // assignment to base value
     AD<double> a;
     a = 1.;
     ok &= a == 1.;

     // assignment to a value that converts to the base type
     a = 2;
     ok &= a == 2.;

     // assignment to an AD<Base>
     AD<double> b(3.);
     a = b;
     ok &= a == 3.;

     // assignment to an VecAD<Base> element
     CppAD::VecAD<double> v(1);
     v[0] = 4.;
     a = v[0];
     ok &= a == 4.;

     return ok;
}
Input File: example/ad_assign.cpp cppad-20170000.3/doc/convert.xml0000644000175200017650000000566213057470504015407 0ustar coincoin-web Conversion and I/O of AD Objects
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Conversion and I/O of AD Objects
Value Convert From an AD Type to its Base Type
Integer Convert From AD to Integer
ad_output AD Output Stream Operator
PrintFor Printing AD Values During Forward Mode
Var2Par Convert an AD Variable to a Parameter
Input File: cppad/core/convert.hpp cppad-20170000.3/doc/value.xml0000644000175200017650000001456413057470504015044 0ustar coincoin-web Convert From an AD Type to its Base Type
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Convert From an AD Type to its Base Type

Syntax
b = Value(x)

See Also
var2par

Purpose
Converts from an AD type to the corresponding base type .

x
The argument x has prototype
     const AD<Base> &x
b
The return value b has prototype
     Base b
Operation Sequence
The result of this operation is not an AD of Base object. Thus it will not be recorded as part of an AD of Base operation sequence .

Restriction
If the argument x is a variable its dependency information would not be included in the Value result (see above). For this reason, the argument x must be a parameter ; i.e., it cannot depend on the current independent variables .

Example
The file value.cpp contains an example and test of this operation.
Input File: cppad/core/value.hpp cppad-20170000.3/doc/value.cpp.xml0000644000175200017650000002265213057470504015622 0ustar coincoin-web Convert From AD to its Base Type: Example and Test
Prev Next value.cpp Headings

Convert From AD to its Base Type: Example and Test

# include <cppad/cppad.hpp>

bool Value(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::Value;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0] = 3.;
     x[1] = 4.;

     // check value before recording
     ok &= (Value(x[0]) == 3.);
     ok &= (Value(x[1]) == 4.);

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = - x[1];

     // cannot call Value(x[j]) or Value(y[0]) here (currently variables)
     AD<double> p = 5.;        // p is a parameter (does not depend on x)
     ok &= (Value(p) == 5.);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // can call Value(x[j]) or Value(y[0]) here (currently parameters)
     ok &= (Value(x[0]) ==  3.);
     ok &= (Value(x[1]) ==  4.);
     ok &= (Value(y[0]) == -4.);

     return ok;
}
Input File: example/value.cpp cppad-20170000.3/doc/integer.xml0000644000175200017650000002330413057470504015355 0ustar coincoin-web Convert From AD to Integer
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Convert From AD to Integer

Syntax
i = Integer(x)

Purpose
Converts from an AD type to the corresponding integer value.

i
The result i has prototype
     int i
x

Real Types
If the argument x has either of the following prototypes:
     const float                  &x
     const double                 &x
 the fractional part is dropped to form the integer value. For example, if x is 1.5, i is 1. In general, if x ≥ 0 , i is the greatest integer less than or equal x . If x ≤ 0 , i is the smallest integer greater than or equal x .

Complex Types
If the argument x has either of the following prototypes:
     const std::complex<float>    &x
     const std::complex<double>   &x
 The result i is given by
     i = Integer(x.real())
AD Types
If the argument x has either of the following prototypes:
     const AD<Base>               &x
     const VecAD<Base>::reference &x
 Base must support the Integer function and the conversion has the same meaning as for Base .

Operation Sequence
The result of this operation is not an AD of Base object. Thus it will not be recorded as part of an AD of Base operation sequence .

Example
The file integer.cpp contains an example and test of this operation.
Input File: cppad/core/integer.hpp cppad-20170000.3/doc/integer.cpp.xml0000644000175200017650000002561613057470504016146 0ustar coincoin-web Convert From AD to Integer: Example and Test
Prev Next integer.cpp Headings

Convert From AD to Integer: Example and Test

# include <cppad/cppad.hpp>

bool Integer(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::Integer;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0] = 3.5;
     x[1] = 4.5;

     // check integer before recording
     ok &= (Integer(x[0]) == 3);
     ok &= (Integer(x[1]) == 4);

     // start recording

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // check integer during recording
     ok &= (Integer(x[0]) == 3);
     ok &= (Integer(x[1]) == 4);

     // check integer for VecAD element
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = 2;
     ok &= (Integer(v[zero]) == 2);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = - x[1];

     // create f: x -> y and stop recording
     CppAD::ADFun<double> f(x, y);

     // check integer after recording
     ok &= (Integer(x[0]) ==  3.);
     ok &= (Integer(x[1]) ==  4.);
     ok &= (Integer(y[0]) == -4.);

     return ok;
}
Input File: example/integer.cpp cppad-20170000.3/doc/ad_to_string.xml0000644000175200017650000001316413057470504016377 0ustar coincoin-web Convert An AD or Base Type to String
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Convert An AD or Base Type to String

Syntax
s = to_string(value) .

See Also
to_string , base_to_string

value
The argument value has prototype
     const AD<Base>& value
     const Base&     value
 where Base is a type that supports the base_to_string type requirement.

s
The return value has prototype
     std::string s
 and contains a representation of the specified value . If value is an AD type, the result has the same precision as for the Base type.

Example
The file to_string.cpp includes an example and test of to_string with AD types. It returns true if it succeeds and false otherwise.
Input File: cppad/core/ad_to_string.hpp cppad-20170000.3/doc/ad_input.xml0000644000175200017650000002031513057470504015522 0ustar coincoin-web AD Output Stream Operator
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AD Output Stream Operator

Syntax
is >> x

Purpose
Sets x to a parameter with value b corresponding to
     is >> b
 where b is a Base object. It is assumed that this Base input operation returns a reference to is .

is
The operand is has prototype
     std::istream& is
x
The operand x has one of the following prototypes
     AD<Base>&               x
Result
The result of this operation can be used as a reference to is . For example, if the operand y has prototype
     AD<Base> y
 then the syntax
     is >> x >> y
 will first read the Base value of x from is , and then read the Base value to y .

Operation Sequence
The result of this operation is not an AD of Base object. Thus it will not be recorded as part of an AD of Base operation sequence .

Example
The file ad_input.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/ad_io.hpp cppad-20170000.3/doc/ad_input.cpp.xml0000644000175200017650000001725513057470504016314 0ustar coincoin-web AD Output Operator: Example and Test
Prev Next ad_input.cpp Headings

AD Output Operator: Example and Test

# include <cppad/cppad.hpp>

# include <sstream>  // std::istringstream
# include <string>   // std::string

bool ad_input(void)
{     bool ok = true;

     // create the input string stream is.
     std::string str ("123 456");
     std::istringstream is(str);

     // start and AD<double> recording
     CPPAD_TESTVECTOR( CppAD::AD<double> ) x(1), y(1);
     x[0] = 1.0;
     CppAD::Independent(x);
     CppAD::AD<double> z = x[0];
     ok &= Variable(z);

     // read first number into z and second into y[0]
     is >> z >> y[0];
     ok   &= Parameter(z);
     ok   &= (z == 123.);
     ok   &= Parameter(y[0]);
     ok   &= (y[0] == 456.);
     //
     // terminate recording starting by call to Independent
     CppAD::ADFun<double> f(x, y);

     return ok;
}
Input File: example/ad_input.cpp cppad-20170000.3/doc/_acos_xml.js0000644000175200017650000000375113057470505015505 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'acos.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'acos.cpp.xml' ]; var list_current0 = [ 'acos.xml#Syntax', 'acos.xml#x, y', 'acos.xml#Atomic', 'acos.xml#Derivative', 'acos.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/ad_output.xml0000644000175200017650000002047613057470504015733 0ustar coincoin-web AD Output Stream Operator
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AD Output Stream Operator

Syntax
os << x

Purpose
Writes the Base value, corresponding to x , to the output stream os .

Assumption
If b is a Base object,
     os << b
 returns a reference to os .

os
The operand os has prototype
     std::ostream& os
x
The operand x has one of the following prototypes
     const AD<Base>&               x
     const VecAD<Base>::reference& x
Result
The result of this operation can be used as a reference to os . For example, if the operand y has prototype
     AD<Base> y
 then the syntax
     os << x << y
 will output the value corresponding to x followed by the value corresponding to y .

Operation Sequence
The result of this operation is not an AD of Base object. Thus it will not be recorded as part of an AD of Base operation sequence .

Example
The file ad_output.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/ad_io.hpp cppad-20170000.3/doc/printfor.xml0000644000175200017650000003262113057470504015565 0ustar coincoin-web Printing AD Values During Forward Mode
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Printing AD Values During Forward Mode

Syntax
f.Forward(0, x)
 PrintFor(before, var)
 PrintFor(pos, before, var, after)
Purpose
The zero order forward mode command
     f.Forward(0, x)
 assigns the independent variable vector equal to x . It then computes a value for all of the dependent variables in the operation sequence corresponding to f . Putting a PrintFor in the operation sequence will cause the value of var , corresponding to x , to be printed during zero order forward operations.

f.Forward(0, x)
The objects f , x , and the purpose for this operation, are documented in Forward .

pos
If present, the argument pos has one of the following prototypes
     const AD<Base>&               pos
     const VecAD<Base>::reference& pos
 In this case the text and var will be printed if and only if pos is not greater than zero and a finite number.

before
The argument before has prototype
     const char* before
 This text is written to std::cout before var .

var
The argument var has one of the following prototypes
     const AD<Base>&               var
     const VecAD<Base>::reference& var
 The value of var , that corresponds to x , is written to std::cout during the execution of
     f.Forward(0, x)
 Note that var may be a variable or parameter . (A parameters value does not depend on the value of the independent variable vector x .)

after
The argument after has prototype
     const char* after
 This text is written to std::cout after var .

Redirecting Output
You can redirect this output to any standard output stream; see the s in the forward mode documentation.

Discussion
This is helpful for understanding why tape evaluations have trouble. For example, if one of the operations in f is log(var) and var <= 0 , the corresponding result will be nan .

Alternative
The ad_output section describes the normal printing of values; i.e., printing when the corresponding code is executed.

Example
The program print_for_cout.cpp is an example and test that prints to standard output. The output of this program states the conditions for passing and failing the test. The function print_for_string.cpp is an example and test that prints to an standard string stream. This function automatically check for correct output.
Input File: cppad/core/print_for.hpp cppad-20170000.3/doc/print_for_cout.cpp.xml0000644000175200017650000004504013057470504017536 0ustar coincoin-web Printing During Forward Mode: Example and Test
Prev Next print_for_cout.cpp

Printing During Forward Mode: Example and Test

Running
To build this program and run its correctness test see cmake_check .

Source Code 
# include <cppad/cppad.hpp>

namespace {
     using std::cout;
     using std::endl;
     using CppAD::AD;

     // use of PrintFor to check for invalid function arguments
     AD<double> check_log(const AD<double>& y)
     {     // check during recording
          if( y <= 0. )
               cout << "check_log: y = " << y << " is <= 0" << endl;

          // check during zero order forward calculation
          PrintFor(y, "check_log: y == ", y , " which is <= 0\n");

          return log(y);
     }
}

void print_for(void)
{     using CppAD::PrintFor;

     // independent variable vector
     size_t n = 1;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 1.;
     Independent(ax);

     // print a VecAD<double>::reference object that is a parameter
     CppAD::VecAD<double> av(1);
     AD<double> Zero(0);
     av[Zero] = 0.;
     PrintFor("v[0] = ", av[Zero]);

     // Print a newline to separate this from previous output,
     // then print an AD<double> object that is a variable.
     PrintFor("\nv[0] + x[0] = ", av[0] + ax[0]);

     // A conditional print that will not generate output when x[0] = 2.
     PrintFor(ax[0], "\n  2. + x[0] = ",   2. + ax[0], "\n");

     // A conditional print that will generate output when x[0] = 2.
     PrintFor(ax[0] - 2., "\n  3. + x[0] = ",   3. + ax[0], "\n");

     // A log evaluations that will result in an error message when x[0] = 2.
     AD<double> var     = 2. - ax[0];
     AD<double> log_var = check_log(var);

     // dependent variable vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = av[Zero] + ax[0];

     // define f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // zero order forward with x[0] = 2
     CPPAD_TESTVECTOR(double) x(n);
     x[0] = 2.;

     cout << "v[0] = 0" << endl;
     cout << "v[0] + x[0] = 2" << endl;
     cout << "  3. + x[0] = 5" << endl;
     cout << "check_log: y == 0 which is <= 0" << endl;
     // ./makefile.am expects "Test passes" at beginning of next output line
     cout << "Test passes if four lines above repeat below:" << endl;
     f.Forward(0, x);

     return;
}
int main(void)
{     bool ok = true;
     print_for();

     size_t thread;
     for(thread = 0; thread < 2; thread++)
     {     ok &= CppAD::omp_alloc::inuse(thread) == 0;
          ok &= CppAD::omp_alloc::available(thread) == 0;
     }
     if( ! ok )
          return 1;
     return 0;
}

Output
Executing the program above generates the following output: 
 
     v[0] = 0
     v[0] + x[0] = 2
     Test passes if two lines above repeat below:
     v[0] = 0
     v[0] + x[0] = 2
Input File: print_for/print_for.cpp cppad-20170000.3/doc/print_for_string.cpp.xml0000644000175200017650000002717013057470504020076 0ustar coincoin-web Print During Zero Order Forward Mode: Example and Test
Prev Next print_for_string.cpp Headings

Print During Zero Order Forward Mode: Example and Test
# include <cppad/cppad.hpp>

namespace {
     using std::endl;
     using CppAD::AD;

     // use of PrintFor to check for invalid function arguments
     AD<double> check_log(const AD<double>& y, std::ostream& s_out)
     {     // check AD<double> value during recording
          if( y <= 0 )
               s_out << "check_log: y == " << y << " which is <= 0\n";

          // check double value during zero order forward calculation
          PrintFor(y, "check_log: y == ", y , " which is <= 0\n");

          return log(y);
     }
}

bool print_for(void)
{     bool ok = true;
     using CppAD::PrintFor;
     std::stringstream stream_out;

     // independent variable vector
     size_t n = 1;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 1.;         // value of the independent variable during recording
     Independent(ax);

     // A log evaluations that is OK when x[0] = 1 but not when x[0] = 2.
     AD<double> var     = 2. - ax[0];
     AD<double> log_var = check_log(var, stream_out);
     ok &= stream_out.str() == "";

     // dependent variable vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0]    = log_var;

     // define f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // zero order forward with x[0] = 2
     CPPAD_TESTVECTOR(double) x(n);
     x[0] = 2.;
     f.Forward(0, x, stream_out);

     std::string string_out = stream_out.str();
     ok &= stream_out.str() == "check_log: y == 0 which is <= 0\n";

     return ok;
}
Input File: example/print_for.cpp cppad-20170000.3/doc/var2par.xml0000644000175200017650000001245413057470504015301 0ustar coincoin-web Convert an AD Variable to a Parameter
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Convert an AD Variable to a Parameter

Syntax
y = Var2Par(x)

See Also
value

Purpose
Returns a parameter y with the same value as the variable x .

x
The argument x has prototype
     const AD<Base> &x
 The argument x may be a variable or parameter.

y
The result y has prototype
     AD<Base> &y
 The return value y will be a parameter.

Example
The file var2par.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/var2par.hpp cppad-20170000.3/doc/var2par.cpp.xml0000644000175200017650000003105413057470504016057 0ustar coincoin-web Convert an AD Variable to a Parameter: Example and Test
Prev Next var2par.cpp Headings

Convert an AD Variable to a Parameter: Example and Test

# include <cppad/cppad.hpp>


bool Var2Par(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::Value;
     using CppAD::Var2Par;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0] = 3.;
     x[1] = 4.;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = - x[1] * Var2Par(x[0]);    // same as y[0] = -x[1] * 3.;

     // cannot call Value(x[j]) or Value(y[0]) here (currently variables)
     ok &= ( Value( Var2Par(x[0]) ) == 3. );
     ok &= ( Value( Var2Par(x[1]) ) == 4. );
     ok &= ( Value( Var2Par(y[0]) ) == -12. );

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // can call Value(x[j]) or Value(y[0]) here (currently parameters)
     ok &= (Value(x[0]) ==  3.);
     ok &= (Value(x[1]) ==  4.);
     ok &= (Value(y[0]) == -12.);

     // evaluate derivative of y w.r.t x
     CPPAD_TESTVECTOR(double) w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0] = 1.;
     dw   = f.Reverse(1, w);
     ok  &= (dw[0] == 0.);  // derivative of y[0] w.r.t x[0] is zero
     ok  &= (dw[1] == -3.); // derivative of y[0] w.r.t x[1] is 3

     return ok;
}
Input File: example/var2par.cpp cppad-20170000.3/doc/advalued.xml0000644000175200017650000000665713057470504015521 0ustar coincoin-web AD Valued Operations and Functions
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AD Valued Operations and Functions

Contents
ArithmeticAD Arithmetic Operators and Computed Assignments
unary_standard_mathThe Unary Standard Math Functions
binary_mathThe Binary Math Functions
CondExpAD Conditional Expressions
DiscreteDiscrete AD Functions
numeric_limitsNumeric Limits For an AD and Base Types
atomicAtomic AD Functions
Input File: cppad/core/ad_valued.hpp cppad-20170000.3/doc/arithmetic.xml0000644000175200017650000000646213057470504016057 0ustar coincoin-web AD Arithmetic Operators and Computed Assignments
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AD Arithmetic Operators and Computed Assignments

Contents
UnaryPlusAD Unary Plus Operator
UnaryMinusAD Unary Minus Operator
ad_binaryAD Binary Arithmetic Operators
compute_assignAD Computed Assignment Operators
Input File: cppad/core/arithmetic.hpp cppad-20170000.3/doc/unaryplus.xml0000644000175200017650000001566013057470504015770 0ustar coincoin-web AD Unary Plus Operator
Prev Next

AD Unary Plus Operator

Syntax
y = + x

Purpose
Performs the unary plus operation (the result y is equal to the operand x ).

x
The operand x has one of the following prototypes
     const AD<Base>               &x
     const VecAD<Base>::reference &x
y
The result y has type
     AD<Base> y
 It is equal to the operand x .

Operation Sequence
This is an AD of Base atomic operation and hence is part of the current AD of Base operation sequence .

Derivative
If f is a Base function , ∂ [ + f ( x ) ] ∂ x = ∂ f ( x ) ∂ x
Example
The file unary_plus.cpp contains an example and test of this operation.
Input File: cppad/core/unary_plus.hpp cppad-20170000.3/doc/unary_plus.cpp.xml0000644000175200017650000002655113057470504016711 0ustar coincoin-web AD Unary Plus Operator: Example and Test
Prev Next unary_plus.cpp Headings

AD Unary Plus Operator: Example and Test

# include <cppad/cppad.hpp>

bool UnaryPlus(void)
{     bool ok = true;
     using CppAD::AD;


     // domain space vector
     size_t n = 1;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = 3.;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = + x[0];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check values
     ok &= ( y[0] == 3. );

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     size_t p = 1;
     dx[0]    = 1.;
     dy       = f.Forward(p, dx);
     ok      &= ( dy[0] == 1. );   // dy[0] / dx[0]

     // reverse computation of dertivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0] = 1.;
     dw   = f.Reverse(p, w);
     ok &= ( dw[0] == 1. );       // dy[0] / dx[0]

     // use a VecAD<Base>::reference object with unary plus
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = x[0];
     AD<double> result = + v[zero];
     ok     &= (result == y[0]);

     return ok;
}
Input File: example/unary_plus.cpp cppad-20170000.3/doc/unaryminus.xml0000644000175200017650000001625713057470504016143 0ustar coincoin-web AD Unary Minus Operator
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AD Unary Minus Operator

Syntax
y = - x

Purpose
Computes the negative of x .

Base
The operation in the syntax above must be supported for the case where the operand is a const Base object.

x
The operand x has one of the following prototypes
     const AD<Base>               &x
     const VecAD<Base>::reference &x
y
The result y has type
     AD<Base> y
 It is equal to the negative of the operand x .

Operation Sequence
This is an AD of Base atomic operation and hence is part of the current AD of Base operation sequence .

Derivative
If f is a Base function , ∂ [ - f ( x ) ] ∂ x = - ∂ f ( x ) ∂ x
Example
The file unary_minus.cpp contains an example and test of this operation.
Input File: cppad/core/unary_minus.hpp cppad-20170000.3/doc/unary_minus.cpp.xml0000644000175200017650000002674513057470504017066 0ustar coincoin-web AD Unary Minus Operator: Example and Test
Prev Next unary_minus.cpp Headings

AD Unary Minus Operator: Example and Test

# include <cppad/cppad.hpp>

bool UnaryMinus(void)
{     bool ok = true;
     using CppAD::AD;


     // domain space vector
     size_t n = 1;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = 3.;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = - x[0];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check values
     ok &= ( y[0] == -3. );

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     size_t p = 1;
     dx[0]    = 1.;
     dy       = f.Forward(p, dx);
     ok      &= ( dy[0] == -1. );   // dy[0] / dx[0]

     // reverse computation of dertivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0] = 1.;
     dw   = f.Reverse(p, w);
     ok &= ( dw[0] == -1. );       // dy[0] / dx[0]

     // use a VecAD<Base>::reference object with unary minus
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = x[0];
     AD<double> result = - v[zero];
     ok     &= (result == y[0]);

     return ok;
}
Input File: example/unary_minus.cpp cppad-20170000.3/doc/ad_binary.xml0000644000175200017650000004410013057470504015645 0ustar coincoin-web AD Binary Arithmetic Operators
Prev Next

AD Binary Arithmetic Operators

Syntax
z = x Op y

Purpose
Performs arithmetic operations where either x or y has type AD<Base> or VecAD<Base>::reference .

Op
The operator Op is one of the following
Op Meaning
+ z is x plus y
- z is x minus y
* z is x times y
/ z is x divided by y

Base
The type Base is determined by the operand that has type AD<Base> or VecAD<Base>::reference .

x
The operand x has the following prototype
     const Type &x
 where Type is VecAD<Base>::reference , AD<Base> , Base , or double.

y
The operand y has the following prototype
     const Type &y
 where Type is VecAD<Base>::reference , AD<Base> , Base , or double.

z
The result z has the following prototype
     Type z
 where Type is AD<Base> .

Operation Sequence
This is an atomic AD of Base operation and hence it is part of the current AD of Base operation sequence .

Example
The following files contain examples and tests of these functions. Each test returns true if it succeeds and false otherwise.
add.cpp AD Binary Addition: Example and Test
sub.cpp AD Binary Subtraction: Example and Test
mul.cpp AD Binary Multiplication: Example and Test
div.cpp AD Binary Division: Example and Test

Derivative
If f and g are Base functions

Addition ∂ [ f ( x ) + g ( x ) ] ∂ x = ∂ f ( x ) ∂ x + ∂ g ( x ) ∂ x
Subtraction ∂ [ f ( x ) - g ( x ) ] ∂ x = ∂ f ( x ) ∂ x - ∂ g ( x ) ∂ x
Multiplication ∂ [ f ( x ) * g ( x ) ] ∂ x = g ( x ) * ∂ f ( x ) ∂ x + f ( x ) * ∂ g ( x ) ∂ x
Division ∂ [ f ( x ) / g ( x ) ] ∂ x = [ 1 / g ( x ) ] * ∂ f ( x ) ∂ x - [ f ( x ) / g ( x ) 2 ] * ∂ g ( x ) ∂ x
Input File: cppad/core/ad_binary.hpp cppad-20170000.3/doc/add.cpp.xml0000644000175200017650000003360113057470504015232 0ustar coincoin-web AD Binary Addition: Example and Test
Prev Next add.cpp Headings

AD Binary Addition: Example and Test
# include <cppad/cppad.hpp>

bool Add(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // some binary addition operations
     AD<double> a = x[0] + 1.; // AD<double> + double
     AD<double> b = a    + 2;  // AD<double> + int
     AD<double> c = 3.   + b;  // double     + AD<double>
     AD<double> d = 4    + c;  // int        + AD<double>

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = d + x[0];          // AD<double> + AD<double>

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , 2. * x0 + 10, eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 2., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 2., eps99, eps99);

     // use a VecAD<Base>::reference object with addition
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = a;
     AD<double> result = v[zero] + 2;
     ok     &= (result == b);

     return ok;
}
Input File: example/add.cpp cppad-20170000.3/doc/sub.cpp.xml0000644000175200017650000003442613057470504015301 0ustar coincoin-web AD Binary Subtraction: Example and Test
Prev Next sub.cpp Headings

AD Binary Subtraction: Example and Test
# include <cppad/cppad.hpp>

bool Sub(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t  n =  1;
     double x0 = .5;
     CPPAD_TESTVECTOR(AD<double>) x(1);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     AD<double> a = 2. * x[0] - 1.; // AD<double> - double
     AD<double> b = a  - 2;         // AD<double> - int
     AD<double> c = 3. - b;         // double     - AD<double>
     AD<double> d = 4  - c;         // int        - AD<double>

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = x[0] - d;              // AD<double> - AD<double>

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0], x0-4.+3.+2.-2.*x0+1., eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], -1., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], -1., eps99, eps99);

     // use a VecAD<Base>::reference object with subtraction
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = b;
     AD<double> result = 3. - v[zero];
     ok     &= (result == c);

     return ok;
}
Input File: example/sub.cpp cppad-20170000.3/doc/mul.cpp.xml0000644000175200017650000003513113057470504015277 0ustar coincoin-web AD Binary Multiplication: Example and Test
Prev Next mul.cpp Headings

AD Binary Multiplication: Example and Test
# include <cppad/cppad.hpp>

bool Mul(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;

     // domain space vector
     size_t n  = 1;
     double x0 = .5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // some binary multiplication operations
     AD<double> a = x[0] * 1.; // AD<double> * double
     AD<double> b = a    * 2;  // AD<double> * int
     AD<double> c = 3.   * b;  // double     * AD<double>
     AD<double> d = 4    * c;  // int        * AD<double>

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = x[0] * d;          // AD<double> * AD<double>

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0*(4.*3.*2.*1.)*x0,  1e-10 , 1e-10);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10);

     // use a VecAD<Base>::reference object with multiplication
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = c;
     AD<double> result = 4 * v[zero];
     ok     &= (result == d);

     return ok;
}
Input File: example/mul.cpp cppad-20170000.3/doc/div.cpp.xml0000644000175200017650000003576213057470505015277 0ustar coincoin-web AD Binary Division: Example and Test
Prev Next div.cpp Headings

AD Binary Division: Example and Test
# include <cppad/cppad.hpp>

bool Div(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();


     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // some binary division operations
     AD<double> a = x[0] / 1.; // AD<double> / double
     AD<double> b = a  / 2;    // AD<double> / int
     AD<double> c = 3. / b;    // double     / AD<double>
     AD<double> d = 4  / c;    // int        / AD<double>

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = (x[0] * x[0]) / d;   // AD<double> / AD<double>

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0], x0*x0*3.*2.*1./(4.*x0), eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 3.*2.*1./4., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 3.*2.*1./4., eps99, eps99);

     // use a VecAD<Base>::reference object with division
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = d;
     AD<double> result = (x[0] * x[0]) / v[zero];
     ok     &= (result == y[0]);

     return ok;
}
Input File: example/div.cpp cppad-20170000.3/doc/compute_assign.xml0000644000175200017650000004305613057470505016747 0ustar coincoin-web AD Computed Assignment Operators
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AD Computed Assignment Operators

Syntax
x Op y

Purpose
Performs computed assignment operations where either x has type AD<Base> .

Op
The operator Op is one of the following
Op Meaning
+= x is assigned x plus y
-= x is assigned x minus y
*= x is assigned x times y
/= x is assigned x divided by y

Base
The type Base is determined by the operand x .

x
The operand x has the following prototype
     AD<Base> &x
y
The operand y has the following prototype
     const Type &y
 where Type is VecAD<Base>::reference , AD<Base> , Base , or double.

Result
The result of this assignment can be used as a reference to x . For example, if z has the following type
     AD<Base> z
 then the syntax
     z = x += y
 will compute x plus y and then assign this value to both x and z .

Operation Sequence
This is an atomic AD of Base operation and hence it is part of the current AD of Base operation sequence .

Example
The following files contain examples and tests of these functions. Each test returns true if it succeeds and false otherwise.
AddEq.cpp AD Computed Assignment Addition: Example and Test
sub_eq.cpp AD Computed Assignment Subtraction: Example and Test
mul_eq.cpp AD Computed Assignment Multiplication: Example and Test
div_eq.cpp AD Computed Assignment Division: Example and Test

Derivative
If f and g are Base functions

Addition ∂ [ f ( x ) + g ( x ) ] ∂ x = ∂ f ( x ) ∂ x + ∂ g ( x ) ∂ x
Subtraction ∂ [ f ( x ) - g ( x ) ] ∂ x = ∂ f ( x ) ∂ x - ∂ g ( x ) ∂ x
Multiplication ∂ [ f ( x ) * g ( x ) ] ∂ x = g ( x ) * ∂ f ( x ) ∂ x + f ( x ) * ∂ g ( x ) ∂ x
Division ∂ [ f ( x ) / g ( x ) ] ∂ x = [ 1 / g ( x ) ] * ∂ f ( x ) ∂ x - [ f ( x ) / g ( x ) 2 ] * ∂ g ( x ) ∂ x
Input File: cppad/core/compute_assign.hpp cppad-20170000.3/doc/addeq.cpp.xml0000644000175200017650000003564713057470505015575 0ustar coincoin-web AD Computed Assignment Addition: Example and Test
Prev Next AddEq.cpp Headings

AD Computed Assignment Addition: Example and Test
# include <cppad/cppad.hpp>

bool AddEq(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t  n = 1;
     double x0 = .5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = x[0];         // initial value
     y[0] += 2;           // AD<double> += int
     y[0] += 4.;          // AD<double> += double
     y[1] = y[0] += x[0]; // use the result of a computed assignment

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0+2.+4.+x0, eps99, eps99);
     ok &= NearEqual(y[1] ,        y[0], eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 2., eps99, eps99);
     ok   &= NearEqual(dy[1], 2., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     w[1]  = 0.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 2., eps99, eps99);

     // use a VecAD<Base>::reference object with computed addition
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     AD<double> result = 1;
     v[zero] = 2;
     result += v[zero];
     ok     &= (result == 3);

     return ok;
}
Input File: example/add_eq.cpp cppad-20170000.3/doc/sub_eq.cpp.xml0000644000175200017650000003624013057470505015763 0ustar coincoin-web AD Computed Assignment Subtraction: Example and Test
Prev Next sub_eq.cpp Headings

AD Computed Assignment Subtraction: Example and Test
# include <cppad/cppad.hpp>

bool SubEq(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t  n = 1;
     double x0 = .5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = 3. * x[0];    // initial value
     y[0] -= 2;           // AD<double> -= int
     y[0] -= 4.;          // AD<double> -= double
     y[1] = y[0] -= x[0]; // use the result of a computed assignment

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , 3.*x0-(2.+4.+x0), eps99, eps99);
     ok &= NearEqual(y[1] ,             y[0], eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 2., eps99, eps99);
     ok   &= NearEqual(dy[1], 2., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     w[1]  = 0.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 2., eps99, eps99);

     // use a VecAD<Base>::reference object with computed subtraction
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     AD<double> result = 1;
     v[zero] = 2;
     result -= v[zero];
     ok     &= (result == -1);

     return ok;
}
Input File: example/sub_eq.cpp cppad-20170000.3/doc/mul_eq.cpp.xml0000644000175200017650000003644313057470505015774 0ustar coincoin-web AD Computed Assignment Multiplication: Example and Test
Prev Next mul_eq.cpp Headings

AD Computed Assignment Multiplication: Example and Test
# include <cppad/cppad.hpp>

bool MulEq(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t  n = 1;
     double x0 = .5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = x[0];         // initial value
     y[0] *= 2;           // AD<double> *= int
     y[0] *= 4.;          // AD<double> *= double
     y[1] = y[0] *= x[0]; // use the result of a computed assignment

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0*2.*4.*x0, eps99, eps99);
     ok &= NearEqual(y[1] ,        y[0], eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 8.*2.*x0, eps99, eps99);
     ok   &= NearEqual(dy[1], 8.*2.*x0, eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     w[1]  = 0.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 8.*2.*x0, eps99, eps99);

     // use a VecAD<Base>::reference object with computed multiplication
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     AD<double> result = 1;
     v[zero] = 2;
     result *= v[zero];
     ok     &= (result == 2);

     return ok;
}
Input File: example/mul_eq.cpp cppad-20170000.3/doc/div_eq.cpp.xml0000644000175200017650000003652513057470505015762 0ustar coincoin-web AD Computed Assignment Division: Example and Test
Prev Next div_eq.cpp Headings

AD Computed Assignment Division: Example and Test
# include <cppad/cppad.hpp>

bool DivEq(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t  n = 1;
     double x0 = .5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = x[0] * x[0];  // initial value
     y[0] /= 2;           // AD<double> /= int
     y[0] /= 4.;          // AD<double> /= double
     y[1] = y[0] /= x[0]; // use the result of a computed assignment

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0*x0/(2.*4.*x0), eps99, eps99);
     ok &= NearEqual(y[1] ,             y[0], eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1./8., eps99, eps99);
     ok   &= NearEqual(dy[1], 1./8., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     w[1]  = 0.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1./8., eps99, eps99);

     // use a VecAD<Base>::reference object with computed division
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     AD<double> result = 2;
     v[zero] = 1;
     result /= v[zero];
     ok     &= (result == 2);

     return ok;
}
Input File: example/div_eq.cpp cppad-20170000.3/doc/unary_standard_math.xml0000644000175200017650000003204613057470505017753 0ustar coincoin-web The Unary Standard Math Functions
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The Unary Standard Math Functions

Syntax
y = fun(x)

Purpose
Evaluates the standard math function fun .

Possible Types

Base
If Base satisfies the base type requirements and argument x has prototype
     const Base& x
 then the result y has prototype
     Base y
AD<Base>
If the argument x has prototype
     const AD<Base>& x
 then the result y has prototype
     AD<Base> y
VecAD<Base>
If the argument x has prototype
     const VecAD<Base>::reference& x
 then the result y has prototype
     AD<Base> y
fun
The possible values for fun are
 fun    Description
abs AD Absolute Value Functions: abs, fabs
acos Inverse Sine Function: acos
acosh The Inverse Hyperbolic Cosine Function: acosh
asin Inverse Sine Function: asin
asinh The Inverse Hyperbolic Sine Function: asinh
atan Inverse Tangent Function: atan
atanh The Inverse Hyperbolic Tangent Function: atanh
cos The Cosine Function: cos
cosh The Hyperbolic Cosine Function: cosh
erf The Error Function
exp The Exponential Function: exp
expm1 The Exponential Function Minus One: expm1
fabs AD Absolute Value Functions: abs, fabs
log10 The Base 10 Logarithm Function: log10
log1p The Logarithm of One Plus Argument: log1p
log The Exponential Function: log
sign The Sign: sign
sin The Sine Function: sin
sinh The Hyperbolic Sine Function: sinh
sqrt The Square Root Function: sqrt
tan The Tangent Function: tan
tanh The Hyperbolic Tangent Function: tanh
Input File: cppad/core/standard_math.hpp cppad-20170000.3/doc/acos.xml0000644000175200017650000001162613057470505014652 0ustar coincoin-web Inverse Sine Function: acos
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Inverse Sine Function: acos

Syntax
y = acos(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative acos ( 1 ) ( x ) = - ( 1 - x * x ) -1 / 2
Example
The file acos.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/atan2.xml0000644000175200017650000002057013057470505014730 0ustar coincoin-web AD Two Argument Inverse Tangent Function
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AD Two Argument Inverse Tangent Function

Syntax
theta = atan2(y, x)

Purpose
Determines an angle θ ∈ [ - π , + π ] such that sin ( θ ) = y / x 2 + y 2 cos ( θ ) = x / x 2 + y 2
y
The argument y has one of the following prototypes
     const AD<Base>               &y
     const VecAD<Base>::reference &y
x
The argument x has one of the following prototypes
     const AD<Base>               &x
     const VecAD<Base>::reference &x
theta
The result theta has prototype
     AD<Base> theta
Operation Sequence
The AD of Base operation sequence used to calculate theta is independent of x and y .

Example
The file atan2.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/atan2.hpp cppad-20170000.3/doc/atan2.cpp.xml0000644000175200017650000003316613057470505015516 0ustar coincoin-web The AD atan2 Function: Example and Test
Prev Next atan2.cpp Headings

The AD atan2 Function: Example and Test

# include <cppad/cppad.hpp>

bool atan2(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> sin_of_x0 = CppAD::sin(x[0]);
     AD<double> cos_of_x0 = CppAD::cos(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::atan2(sin_of_x0, cos_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps99, eps99);

     // use a VecAD<Base>::reference object with atan2
     CppAD::VecAD<double> v(2);
     AD<double> zero(0);
     AD<double> one(1);
     v[zero]           = sin_of_x0;
     v[one]            = cos_of_x0;
     AD<double> result = CppAD::atan2(v[zero], v[one]);
     ok               &= NearEqual(result, x0, eps99, eps99);

     return ok;
}
Input File: example/atan2.cpp cppad-20170000.3/doc/acos.cpp.xml0000644000175200017650000003230613057470505015431 0ustar coincoin-web The AD acos Function: Example and Test
Prev Next acos.cpp Headings

The AD acos Function: Example and Test

# include <cppad/cppad.hpp>

bool acos(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> cos_of_x0 = CppAD::cos(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::acos(cos_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps, eps);

     // use a VecAD<Base>::reference object with acos
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = cos_of_x0;
     AD<double> result = CppAD::acos(v[zero]);
     ok     &= NearEqual(result, x0, eps, eps);

     return ok;
}
Input File: example/acos.cpp cppad-20170000.3/doc/asin.cpp.xml0000644000175200017650000003230313057470505015433 0ustar coincoin-web The AD asin Function: Example and Test
Prev Next asin.cpp Headings

The AD asin Function: Example and Test

# include <cppad/cppad.hpp>

bool asin(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> sin_of_x0 = CppAD::sin(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::asin(sin_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps, eps);

     // use a VecAD<Base>::reference object with asin
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = sin_of_x0;
     AD<double> result = CppAD::asin(v[zero]);
     ok     &= NearEqual(result, x0, eps, eps);

     return ok;
}
Input File: example/asin.cpp cppad-20170000.3/doc/atan.cpp.xml0000644000175200017650000003210213057470505015421 0ustar coincoin-web The AD atan Function: Example and Test
Prev Next atan.cpp Headings

The AD atan Function: Example and Test

# include <cppad/cppad.hpp>

bool atan(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> tan_of_x0 = CppAD::tan(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::atan(tan_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps99, eps99);

     // use a VecAD<Base>::reference object with atan
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = tan_of_x0;
     AD<double> result = CppAD::atan(v[zero]);
     ok     &= NearEqual(result, x0, eps99, eps99);

     return ok;
}
Input File: example/atan.cpp cppad-20170000.3/doc/cos.cpp.xml0000644000175200017650000003302313057470505015265 0ustar coincoin-web The AD cos Function: Example and Test
Prev Next cos.cpp Headings

The AD cos Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool Cos(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::cos(x[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     double check = std::cos(x0);
     ok &= NearEqual(y[0] , check, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     check = - std::sin(x0);
     ok   &= NearEqual(dy[0], check, eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check, eps99, eps99);

     // use a VecAD<Base>::reference object with cos
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::cos(v[zero]);
     check = std::cos(x0);
     ok   &= NearEqual(result, check, eps99, eps99);

     return ok;
}
Input File: example/cos.cpp cppad-20170000.3/doc/cosh.cpp.xml0000644000175200017650000003277713057470505015454 0ustar coincoin-web The AD cosh Function: Example and Test
Prev Next cosh.cpp Headings

The AD cosh Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool Cosh(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::cosh(x[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     double check = std::cosh(x0);
     ok &= NearEqual(y[0] , check, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     check = std::sinh(x0);
     ok   &= NearEqual(dy[0], check, eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check, eps99, eps99);

     // use a VecAD<Base>::reference object with cosh
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::cosh(v[zero]);
     check = std::cosh(x0);
     ok   &= NearEqual(result, check, eps99, eps99);

     return ok;
}
Input File: example/cosh.cpp cppad-20170000.3/doc/exp.cpp.xml0000644000175200017650000003176513057470505015310 0ustar coincoin-web The AD exp Function: Example and Test
Prev Next exp.cpp Headings

The AD exp Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool exp(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = CppAD::exp(ax[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // check value
     double check = std::exp(x0);
     ok &= NearEqual(ay[0], check,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], check, eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check, eps, eps);

     // use a VecAD<Base>::reference object with exp
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::exp(v[zero]);
     ok   &= NearEqual(result, check, eps, eps);

     return ok;
}
Input File: example/exp.cpp cppad-20170000.3/doc/log.cpp.xml0000644000175200017650000003207413057470505015267 0ustar coincoin-web The AD log Function: Example and Test
Prev Next log.cpp Headings

The AD log Function: Example and Test

# include <cppad/cppad.hpp>

bool log(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> exp_of_x0 = CppAD::exp(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::log(exp_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps99, eps99);

     // use a VecAD<Base>::reference object with log
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = exp_of_x0;
     AD<double> result = CppAD::log(v[zero]);
     ok   &= NearEqual(result, x0, eps99, eps99);

     return ok;
}
Input File: example/log.cpp cppad-20170000.3/doc/log10.cpp.xml0000644000175200017650000003247513057470505015435 0ustar coincoin-web The AD log10 Function: Example and Test
Prev Next log10.cpp Headings

The AD log10 Function: Example and Test

# include <cppad/cppad.hpp>

bool log10(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // ten raised to the x0 power
     AD<double> ten = 10.;
     AD<double> pow_10_x0 = CppAD::pow(ten, x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::log10(pow_10_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps99, eps99);

     // use a VecAD<Base>::reference object with log10
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = pow_10_x0;
     AD<double> result = CppAD::log10(v[zero]);
     ok   &= NearEqual(result, x0, eps99, eps99);

     return ok;
}
Input File: example/log10.cpp cppad-20170000.3/doc/sin.cpp.xml0000644000175200017650000003275513057470505015305 0ustar coincoin-web The AD sin Function: Example and Test
Prev Next sin.cpp Headings

The AD sin Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool Sin(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::sin(x[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     double check = std::sin(x0);
     ok &= NearEqual(y[0] , check, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     check = std::cos(x0);
     ok   &= NearEqual(dy[0], check, eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check, eps99, eps99);

     // use a VecAD<Base>::reference object with sin
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::sin(v[zero]);
     check = std::sin(x0);
     ok   &= NearEqual(result, check, eps99, eps99);

     return ok;
}
Input File: example/sin.cpp cppad-20170000.3/doc/sinh.cpp.xml0000644000175200017650000003300013057470505015435 0ustar coincoin-web The AD sinh Function: Example and Test
Prev Next sinh.cpp Headings

The AD sinh Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool Sinh(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::sinh(x[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     double check = std::sinh(x0);
     ok &= NearEqual(y[0] , check, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     check = std::cosh(x0);
     ok   &= NearEqual(dy[0], check, eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check, eps99, eps99);

     // use a VecAD<Base>::reference object with sinh
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::sinh(v[zero]);
     check = std::sinh(x0);
     ok   &= NearEqual(result, check, eps99, eps99);

     return ok;
}
Input File: example/sinh.cpp cppad-20170000.3/doc/sqrt.cpp.xml0000644000175200017650000003345413057470505015502 0ustar coincoin-web The AD sqrt Function: Example and Test
Prev Next sqrt.cpp Headings

The AD sqrt Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool Sqrt(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::sqrt(x[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     double check = std::sqrt(x0);
     ok &= NearEqual(y[0] , check, eps99, eps99);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     check = 1. / (2. * std::sqrt(x0) );
     ok   &= NearEqual(dy[0], check, eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check, eps99, eps99);

     // use a VecAD<Base>::reference object with sqrt
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::sqrt(v[zero]);
     check = std::sqrt(x0);
     ok   &= NearEqual(result, check, eps99, eps99);

     return ok;
}
Input File: example/sqrt.cpp cppad-20170000.3/doc/tan.cpp.xml0000644000175200017650000003374213057470505015273 0ustar coincoin-web The AD tan Function: Example and Test
Prev Next tan.cpp Headings

The AD tan Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>
# include <limits>

bool Tan(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::tan(x[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     double check = std::tan(x0);
     ok &= NearEqual(y[0] , check,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     check = 1. + std::tan(x0) * std::tan(x0);
     ok   &= NearEqual(dy[0], check, eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check, eps, eps);

     // use a VecAD<Base>::reference object with tan
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::tan(v[zero]);
     check = std::tan(x0);
     ok   &= NearEqual(result, check, eps, eps);

     return ok;
}
Input File: example/tan.cpp cppad-20170000.3/doc/tanh.cpp.xml0000644000175200017650000003376613057470505015451 0ustar coincoin-web The AD tanh Function: Example and Test
Prev Next tanh.cpp Headings

The AD tanh Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>
# include <limits>

bool Tanh(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::tanh(x[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     double check = std::tanh(x0);
     ok &= NearEqual(y[0] , check,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     check = 1. - std::tanh(x0) * std::tanh(x0);
     ok   &= NearEqual(dy[0], check, eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check, eps, eps);

     // use a VecAD<Base>::reference object with tan
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::tanh(v[zero]);
     check = std::tanh(x0);
     ok   &= NearEqual(result, check, eps, eps);

     return ok;
}
Input File: example/tanh.cpp cppad-20170000.3/doc/asin.xml0000644000175200017650000001156213057470505014656 0ustar coincoin-web Inverse Sine Function: asin
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Inverse Sine Function: asin

Syntax
y = asin(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative asin ( 1 ) ( x ) = ( 1 - x * x ) -1 / 2
Example
The file asin.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/atan.xml0000644000175200017650000001141313057470505014642 0ustar coincoin-web Inverse Tangent Function: atan
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Inverse Tangent Function: atan

Syntax
y = atan(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative atan ( 1 ) ( x ) = 1 1 + x 2
Example
The file atan.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/cos.xml0000644000175200017650000001132413057470505014504 0ustar coincoin-web The Cosine Function: cos
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The Cosine Function: cos

Syntax
y = cos(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative cos ( 1 ) ( x ) = - sin ( x )
Example
The file cos.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/cosh.xml0000644000175200017650000001136113057470505014655 0ustar coincoin-web The Hyperbolic Cosine Function: cosh
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The Hyperbolic Cosine Function: cosh

Syntax
y = cosh(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative cosh ( 1 ) ( x ) = sinh ( x )
Example
The file cosh.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/exp.xml0000644000175200017650000001131413057470505014513 0ustar coincoin-web The Exponential Function: exp
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The Exponential Function: exp

Syntax
y = exp(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative exp ( 1 ) ( x ) = exp ( x )
Example
The file exp.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/log.xml0000644000175200017650000001127513057470505014506 0ustar coincoin-web The Exponential Function: log
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The Exponential Function: log

Syntax
y = log(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative log ( 1 ) ( x ) = 1 x
Example
The file log.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/log10.xml0000644000175200017650000001106213057470505014641 0ustar coincoin-web The Base 10 Logarithm Function: log10
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The Base 10 Logarithm Function: log10

Syntax
y = log10(x)

x, y
See the possible types for a unary standard math function.

Method
CppAD uses the representation log 10 ( x ) = log ( x ) / log ( 10 )
Example
The file log10.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/sin.xml0000644000175200017650000001126113057470505014511 0ustar coincoin-web The Sine Function: sin
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The Sine Function: sin

Syntax
y = sin(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative sin ( 1 ) ( x ) = cos ( x )
Example
The file sin.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/sinh.xml0000644000175200017650000001135113057470505014661 0ustar coincoin-web The Hyperbolic Sine Function: sinh
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The Hyperbolic Sine Function: sinh

Syntax
y = sinh(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative sinh ( 1 ) ( x ) = cosh ( x )
Example
The file sinh.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/sqrt.xml0000644000175200017650000001154513057470505014716 0ustar coincoin-web The Square Root Function: sqrt
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The Square Root Function: sqrt

Syntax
y = sqrt(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative sqrt ( 1 ) ( x ) = 1 2 sqrt ( x )
Example
The file sqrt.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/tan.xml0000644000175200017650000001137413057470505014507 0ustar coincoin-web The Tangent Function: tan
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The Tangent Function: tan

Syntax
y = tan(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative tan ( 1 ) ( x ) = 1 + tan ( x ) 2
Example
The file tan.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/tanh.xml0000644000175200017650000001146513057470505014660 0ustar coincoin-web The Hyperbolic Tangent Function: tanh
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The Hyperbolic Tangent Function: tanh

Syntax
y = tanh(x)

x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative tanh ( 1 ) ( x ) = 1 - tanh ( x ) 2
Example
The file tanh.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/std_math_98.hpp cppad-20170000.3/doc/abs.xml0000644000175200017650000001623113057470505014467 0ustar coincoin-web AD Absolute Value Functions: abs, fabs
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AD Absolute Value Functions: abs, fabs

Syntax
y = abs(x)
 y = fabs(x)

x, y
See the possible types for a unary standard math function.

Atomic
In the case where x is an AD type, this is an atomic operation .

Complex Types
The functions abs and fabs are not defined for the base types std::complex<float> or std::complex<double> because the complex abs function is not complex differentiable (see complex types faq ).

Derivative
CppAD defines the derivative of the abs function is the sign function; i.e., abs ( 1 ) ( x ) = sign ( x ) = { + 1 if x > 0 0 if x = 0 -1 if x < 0 The result for x == 0 used to be a directional derivative.

Example
The file abs.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/abs.hpp cppad-20170000.3/doc/abs.cpp.xml0000644000175200017650000006317713057470505015263 0ustar coincoin-web AD Absolute Value Function: Example and Test
Prev Next abs.cpp Headings

AD Absolute Value Function: Example and Test

# include <cppad/cppad.hpp>

bool abs(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 1;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]     = 0.;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 6;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0]     = abs(x[0] - 1.);
     y[1]     = abs(x[0]);
     y[2]     = abs(x[0] + 1.);
     //
     y[3]     = fabs(x[0] - 1.);
     y[4]     = fabs(x[0]);
     y[5]     = fabs(x[0] + 1.);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check values
     ok &= (y[0] == 1.);
     ok &= (y[1] == 0.);
     ok &= (y[2] == 1.);
     //
     ok &= (y[3] == 1.);
     ok &= (y[4] == 0.);
     ok &= (y[5] == 1.);

     // forward computation of partials w.r.t. a positive x[0] direction
     size_t p = 1;
     CPPAD_TESTVECTOR(double) dx(n), dy(m);
     dx[0] = 1.;
     dy    = f.Forward(p, dx);
     ok  &= (dy[0] == - dx[0]);
     ok  &= (dy[1] ==   0.   ); // used to be (dy[1] == + dx[0]);
     ok  &= (dy[2] == + dx[0]);
     //
     ok  &= (dy[3] == - dx[0]);
     ok  &= (dy[4] ==   0.   ); // used to be (dy[1] == + dx[0]);
     ok  &= (dy[5] == + dx[0]);

     // forward computation of partials w.r.t. a negative x[0] direction
     dx[0] = -1.;
     dy    = f.Forward(p, dx);
     ok  &= (dy[0] == - dx[0]);
     ok  &= (dy[1] ==   0.   ); // used to be (dy[1] == - dx[0]);
     ok  &= (dy[2] == + dx[0]);
     //
     ok  &= (dy[3] == - dx[0]);
     ok  &= (dy[4] ==   0.   ); // used to be (dy[1] == - dx[0]);
     ok  &= (dy[5] == + dx[0]);

     // reverse computation of derivative of y[0]
     p    = 1;
     CPPAD_TESTVECTOR(double)  w(m), dw(n);
     w[0] = 1.; w[1] = 0.; w[2] = 0.; w[3] = 0.; w[4] = 0.; w[5] = 0.;
     dw   = f.Reverse(p, w);
     ok  &= (dw[0] == -1.);

     // reverse computation of derivative of y[1]
     w[0] = 0.; w[1] = 1.;
     dw   = f.Reverse(p, w);
     ok  &= (dw[0] == 0.);

     // reverse computation of derivative of y[5]
     w[1] = 0.; w[5] = 1.;
     dw   = f.Reverse(p, w);
     ok  &= (dw[0] == 1.);

     // use a VecAD<Base>::reference object with abs and fabs
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = -1;
     AD<double> result = abs(v[zero]);
     ok    &= NearEqual(result, 1., eps99, eps99);
     result = fabs(v[zero]);
     ok    &= NearEqual(result, 1., eps99, eps99);

     return ok;
}
Input File: example/abs.cpp cppad-20170000.3/doc/acosh.xml0000644000175200017650000001350213057470505015015 0ustar coincoin-web The Inverse Hyperbolic Cosine Function: acosh
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The Inverse Hyperbolic Cosine Function: acosh

Syntax
y = acosh(x)

Description
The inverse hyperbolic cosine function is defined by x == cosh(y) .

x, y
See the possible types for a unary standard math function.

CPPAD_USE_CPLUSPLUS_2011

true
If this preprocessor symbol is true (1), and x is an AD type, this is an atomic operation .

false
If this preprocessor symbol is false (0), CppAD uses the representation acosh ( x ) = log (x + x 2 - 1 ) to compute this function.

Example
The file acosh.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/acosh.hpp cppad-20170000.3/doc/acosh.cpp.xml0000644000175200017650000003233313057470505015601 0ustar coincoin-web The AD acosh Function: Example and Test
Prev Next acosh.cpp Headings

The AD acosh Function: Example and Test

# include <cppad/cppad.hpp>

bool acosh(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> cosh_of_x0 = CppAD::cosh(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::acosh(cosh_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps, eps);

     // use a VecAD<Base>::reference object with acosh
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = cosh_of_x0;
     AD<double> result = CppAD::acosh(v[zero]);
     ok     &= NearEqual(result, x0, eps, eps);

     return ok;
}
Input File: example/acosh.cpp cppad-20170000.3/doc/asinh.xml0000644000175200017650000001347213057470505015030 0ustar coincoin-web The Inverse Hyperbolic Sine Function: asinh
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The Inverse Hyperbolic Sine Function: asinh

Syntax
y = asinh(x)

Description
The inverse hyperbolic sine function is defined by x == sinh(y) .

x, y
See the possible types for a unary standard math function.

CPPAD_USE_CPLUSPLUS_2011

true
If this preprocessor symbol is true (1), and x is an AD type, this is an atomic operation .

false
If this preprocessor symbol is false (0), CppAD uses the representation asinh ( x ) = log (x + 1 + x 2 ) to compute this function.

Example
The file asinh.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/asinh.hpp cppad-20170000.3/doc/asinh.cpp.xml0000644000175200017650000003233313057470505015606 0ustar coincoin-web The AD asinh Function: Example and Test
Prev Next asinh.cpp Headings

The AD asinh Function: Example and Test

# include <cppad/cppad.hpp>

bool asinh(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> sinh_of_x0 = CppAD::sinh(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::asinh(sinh_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps, eps);

     // use a VecAD<Base>::reference object with asinh
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = sinh_of_x0;
     AD<double> result = CppAD::asinh(v[zero]);
     ok     &= NearEqual(result, x0, eps, eps);

     return ok;
}
Input File: example/asinh.cpp cppad-20170000.3/doc/atanh.xml0000644000175200017650000001361313057470505015016 0ustar coincoin-web The Inverse Hyperbolic Tangent Function: atanh
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The Inverse Hyperbolic Tangent Function: atanh

Syntax
y = atanh(x)

Description
The inverse hyperbolic tangent function is defined by x == tanh(y) .

x, y
See the possible types for a unary standard math function.

CPPAD_USE_CPLUSPLUS_2011

true
If this preprocessor symbol is true (1), and x is an AD type, this is an atomic operation .

false
If this preprocessor symbol is false (0), CppAD uses the representation atanh ( x ) = 1 2 log (1 + x 1 - x ) to compute this function.

Example
The file atanh.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/atanh.hpp cppad-20170000.3/doc/atanh.cpp.xml0000644000175200017650000003233113057470505015575 0ustar coincoin-web The AD atanh Function: Example and Test
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The AD atanh Function: Example and Test

# include <cppad/cppad.hpp>

bool atanh(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> tanh_of_x0 = CppAD::tanh(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::atanh(tanh_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps, eps);

     // use a VecAD<Base>::reference object with atanh
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = tanh_of_x0;
     AD<double> result = CppAD::atanh(v[zero]);
     ok     &= NearEqual(result, x0, eps, eps);

     return ok;
}
Input File: example/atanh.cpp cppad-20170000.3/doc/erf.xml0000644000175200017650000001416413057470505014501 0ustar coincoin-web The Error Function
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The Error Function

Syntax
y = erf(x)

Description
Returns the value of the error function which is defined by erf ( x ) = 2 π ∫ 0 x exp ( - t * t ) d t
x, y
See the possible types for a unary standard math function.

CPPAD_USE_CPLUSPLUS_2011

true
If this preprocessor symbol is true (1), and x is an AD type, this is an atomic operation .

false
If this preprocessor symbol is false (0), CppAD uses a fast approximation (few numerical operations) with relative error bound 4 × 10 -4 ; see Vedder, J.D., Simple approximations for the error function and its inverse , American Journal of Physics, v 55, n 8, 1987, p 762-3.

Example
The file erf.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/erf.hpp cppad-20170000.3/doc/erf.cpp.xml0000644000175200017650000004307513057470505015265 0ustar coincoin-web The AD erf Function: Example and Test
Prev Next erf.cpp Headings

The AD erf Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>
# include <limits>

bool Erf(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = CppAD::erf(ax[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // check relative erorr
     double erf_x0 = 0.5204998778130465;
     ok &= NearEqual(ay[0] , erf_x0,  0.,    4e-4);
# if CPPAD_USE_CPLUSPLUS_2011
     double tmp = std::max(1e-15, eps);
     ok &= NearEqual(ay[0] , erf_x0,  0.,    tmp);
# endif

     // value of derivative of erf at x0
     double pi     = 4. * std::atan(1.);
     double factor = 2. / sqrt(pi);
     double check  = factor * std::exp(-x0 * x0);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], check,  0.,  1e-3);
# if CPPAD_USE_CPLUSPLUS_2011
     ok   &= NearEqual(dy[0], check,  0.,  eps);
# endif

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], check,  0., 1e-1);
# if CPPAD_USE_CPLUSPLUS_2011
     ok   &= NearEqual(dw[0], check,  0., eps);
# endif

     // use a VecAD<Base>::reference object with erf
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::erf(v[zero]);
     ok   &= NearEqual(result, ay[0], eps, eps);

     // use a double with erf
     ok   &= NearEqual(CppAD::erf(x0), ay[0], eps, eps);

     return ok;
}
Input File: example/erf.cpp cppad-20170000.3/doc/expm1.xml0000644000175200017650000001332613057470505014756 0ustar coincoin-web The Exponential Function Minus One: expm1
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The Exponential Function Minus One: expm1

Syntax
y = expm1(x)

Description
Returns the value of the exponential function minus one which is defined by y == exp(x) - 1 .

x, y
See the possible types for a unary standard math function.

CPPAD_USE_CPLUSPLUS_2011

true
If this preprocessor symbol is true (1), and x is an AD type, this is an atomic operation .

false
If this preprocessor symbol is false (0), CppAD uses the representation expm 1 ( x ) = exp ( x ) - 1 to compute this function.

Example
The file expm1.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/expm1.hpp cppad-20170000.3/doc/expm1.cpp.xml0000644000175200017650000003225013057470505015534 0ustar coincoin-web The AD exp Function: Example and Test
Prev Next expm1.cpp Headings

The AD exp Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool expm1(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = CppAD::expm1(ax[0]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // expx0 value
     double expx0 = std::exp(x0);
     ok &= NearEqual(ay[0], expx0-1.0,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], expx0, eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], expx0, eps, eps);

     // use a VecAD<Base>::reference object with exp
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = x0;
     AD<double> result = CppAD::expm1(v[zero]);
     ok   &= NearEqual(result, expx0-1.0, eps, eps);

     return ok;
}
Input File: example/expm1.cpp cppad-20170000.3/doc/log1p.xml0000644000175200017650000001336413057470505014750 0ustar coincoin-web The Logarithm of One Plus Argument: log1p
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The Logarithm of One Plus Argument: log1p

Syntax
y = log1p(x)

Description
Returns the value of the logarithm of one plus argument which is defined by y == log(1 + x) .

x, y
See the possible types for a unary standard math function.

CPPAD_USE_CPLUSPLUS_2011

true
If this preprocessor symbol is true (1), and x is an AD type, this is an atomic operation .

false
If this preprocessor symbol is false (0), CppAD uses the representation log 1 p ( x ) = log ( 1 + x ) to compute this function.

Example
The file log1p.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/log1p.hpp cppad-20170000.3/doc/log1p.cpp.xml0000644000175200017650000003233613057470505015531 0ustar coincoin-web The AD log1p Function: Example and Test
Prev Next log1p.cpp Headings

The AD log1p Function: Example and Test

# include <cppad/cppad.hpp>

bool log1p(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> expm1_of_x0 = CppAD::expm1(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::log1p(expm1_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps, eps);

     // use a VecAD<Base>::reference object with log1p
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = expm1_of_x0;
     AD<double> result = CppAD::log1p(v[zero]);
     ok     &= NearEqual(result, x0, eps, eps);

     return ok;
}
Input File: example/log1p.cpp cppad-20170000.3/doc/sign.xml0000644000175200017650000001476313057470505014672 0ustar coincoin-web The Sign: sign
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The Sign: sign

Syntax
y = sign(x)

Description
Evaluates the sign function which is defined by sign ( x ) = { + 1 if x > 0 0 if x = 0 -1 if x < 0
x, y
See the possible types for a unary standard math function.

Atomic
This is an atomic operation .

Derivative
CppAD computes the derivative of the sign function as zero for all argument values x . The correct mathematical derivative is different and is given by sign ( 1 ) ( x ) = 2 δ ( x ) where δ ( x ) is the Dirac Delta function.

Example
The file sign.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/sign.hpp cppad-20170000.3/doc/sign.cpp.xml0000644000175200017650000003755413057470505015456 0ustar coincoin-web Sign Function: Example and Test
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Sign Function: Example and Test

# include <cppad/cppad.hpp>

bool sign(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // create f: x -> y where f(x) = sign(x)
     size_t n = 1;
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ax(n), ay(m);
     ax[0]     = 0.;
     CppAD::Independent(ax);
     ay[0]     = sign(ax[0]);
     CppAD::ADFun<double> f(ax, ay);

     // check value during recording
     ok &= (ay[0] == 0.);

     // use f(x) to evaluate the sign function and its derivatives
     CPPAD_TESTVECTOR(double) x(n), y(m), dx(n), dy(m), w(m), dw(n);
     dx[0] = 1.;
     w[0] = 1.;
     //
     x[0]  = 2.;
     y     = f.Forward(0, x);
     ok   &= (y[0] == 1.);
     dy    = f.Forward(1, dx);
     ok   &= (dy[0] == 0.);
     dw   = f.Reverse(1, w);
     ok  &= (dw[0] == 0.);
     //
     x[0]  = 0.;
     y     = f.Forward(0, x);
     ok   &= (y[0] == 0.);
     dy    = f.Forward(1, dx);
     ok   &= (dy[0] == 0.);
     dw   = f.Reverse(1, w);
     ok  &= (dw[0] == 0.);
     //
     x[0]  = -2.;
     y     = f.Forward(0, x);
     ok   &= (y[0] == -1.);
     dy    = f.Forward(1, dx);
     ok   &= (dy[0] == 0.);
     dw   = f.Reverse(1, w);
     ok  &= (dw[0] == 0.);

     // use a VecAD<Base>::reference object with sign
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = 2.;
     AD<double> result = sign(v[zero]);
     ok   &= (result == 1.);

     return ok;
}
Input File: example/sign.cpp cppad-20170000.3/doc/_atan2_xml.js0000644000175200017650000000347213057470505015565 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'binary_math.xml', 'atan2.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'atan2.xml', 'pow.xml', 'azmul.xml' ]; var list_down0 = [ 'atan2.cpp.xml' ]; var list_current0 = [ 'atan2.xml#Syntax', 'atan2.xml#Purpose', 'atan2.xml#y', 'atan2.xml#x', 'atan2.xml#theta', 'atan2.xml#Operation Sequence', 'atan2.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/pow.xml0000644000175200017650000002310213057470505014522 0ustar coincoin-web The AD Power Function
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The AD Power Function

Syntax
z = pow(x, y)

See Also
pow_int

Purpose
Determines the value of the power function which is defined by pow ( x , y ) = x y This version of the pow function may use logarithms and exponentiation to compute derivatives. This will not work if x is less than or equal zero. If the value of y is an integer, the pow_int function is used to compute this value using only multiplication (and division if y is negative). (This will work even if x is less than or equal zero.)

x
The argument x has one of the following prototypes
     const Base&                    x
     const AD<Base>&                x
     const VecAD<Base>::reference&  x
y
The argument y has one of the following prototypes
     const Base&                    y
     const AD<Base>&                y
     const VecAD<Base>::reference&  y
z
If both x and y are Base objects, the result z is also a Base object. Otherwise, it has prototype
     AD<Base> z
Operation Sequence
This is an AD of Base atomic operation and hence is part of the current AD of Base operation sequence .

Example
The file pow.cpp is an examples and tests of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/pow.hpp cppad-20170000.3/doc/_pow_xml.js0000644000175200017650000000347013057470505015363 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'binary_math.xml', 'pow.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'atan2.xml', 'pow.xml', 'azmul.xml' ]; var list_down0 = [ 'pow.cpp.xml' ]; var list_current0 = [ 'pow.xml#Syntax', 'pow.xml#See Also', 'pow.xml#Purpose', 'pow.xml#x', 'pow.xml#y', 'pow.xml#z', 'pow.xml#Operation Sequence', 'pow.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/pow.cpp.xml0000644000175200017650000005317313057470505015316 0ustar coincoin-web The AD Power Function: Example and Test
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The AD Power Function: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool pow(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 2;
     double x = 0.5;
     double y = 2.;
     CPPAD_TESTVECTOR(AD<double>) axy(n);
     axy[0]      = x;
     axy[1]      = y;

     // declare independent variables and start tape recording
     CppAD::Independent(axy);

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>) az(m);
     az[0] = CppAD::pow(axy[0], axy[1]); // pow(variable, variable)
     az[1] = CppAD::pow(axy[0], y);      // pow(variable, parameter)
     az[2] = CppAD::pow(x,     axy[1]);  // pow(parameter, variable)

     // create f: axy -> az and stop tape recording
     CppAD::ADFun<double> f(axy, az);

     // check value
     double check = std::pow(x, y);
     size_t i;
     for(i = 0; i < m; i++)
          ok &= NearEqual(az[i] , check,  eps, eps);

     // forward computation of first partial w.r.t. x
     CPPAD_TESTVECTOR(double) dxy(n);
     CPPAD_TESTVECTOR(double) dz(m);
     dxy[0] = 1.;
     dxy[1] = 0.;
     dz    = f.Forward(1, dxy);
     check = y * std::pow(x, y-1.);
     ok   &= NearEqual(dz[0], check, eps, eps);
     ok   &= NearEqual(dz[1], check, eps, eps);
     ok   &= NearEqual(dz[2],    0., eps, eps);

     // forward computation of first partial w.r.t. y
     dxy[0] = 0.;
     dxy[1] = 1.;
     dz    = f.Forward(1, dxy);
     check = std::log(x) * std::pow(x, y);
     ok   &= NearEqual(dz[0], check, eps, eps);
     ok   &= NearEqual(dz[1],    0., eps, eps);
     ok   &= NearEqual(dz[2], check, eps, eps);

     // reverse computation of derivative of z[0] + z[1] + z[2]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     w[1]  = 1.;
     w[2]  = 1.;
     dw    = f.Reverse(1, w);
     check = y * std::pow(x, y-1.);
     ok   &= NearEqual(dw[0], 2. * check, eps, eps);
     check = std::log(x) * std::pow(x, y);
     ok   &= NearEqual(dw[1], 2. * check, eps, eps);

     // use a VecAD<Base>::reference object with pow
     CppAD::VecAD<double> v(2);
     AD<double> zero(0);
     AD<double> one(1);
     v[zero]           = axy[0];
     v[one]            = axy[1];
     AD<double> result = CppAD::pow(v[zero], v[one]);
     ok               &= NearEqual(result, az[0], eps, eps);

     return ok;
}
Input File: example/pow.cpp cppad-20170000.3/doc/azmul.xml0000644000175200017650000002344313057470505015055 0ustar coincoin-web Absolute Zero Multiplication
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Absolute Zero Multiplication

Syntax
z = azmul(x, y)

Purpose
Evaluates multiplication with an absolute zero for any of the possible types listed below. The result is given by z = { 0 if x = 0 x · y otherwise Note if x is zero and y is infinity, ieee multiplication would result in not a number whereas z would be zero.

Base
If Base satisfies the base type requirements and arguments x , y have prototypes
     const Base& x
     const Base& y
 then the result z has prototype
     Base z
AD<Base>
If the arguments x , y have prototype
     const AD<Base>& x
     const AD<Base>& y
 then the result z has prototype
     AD<Base> z
VecAD<Base>
If the arguments x , y have prototype
     const VecAD<Base>::reference& x
     const VecAD<Base>::reference& y
 then the result z has prototype
     AD<Base> z
Example
The file azmul.cpp is an examples and tests of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/azmul.hpp cppad-20170000.3/doc/azmul.cpp.xml0000644000175200017650000003576513057470505015650 0ustar coincoin-web AD Absolute Zero Multiplication: Example and Test
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AD Absolute Zero Multiplication: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool azmul(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double inf = std::numeric_limits<double>::infinity();
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 2;
     double x = 0.5;
     double y = 2.0;
     CPPAD_TESTVECTOR(AD<double>) axy(n);
     axy[0]      = x;
     axy[1]      = y;

     // declare independent variables and start tape recording
     CppAD::Independent(axy);

     // range space vector
     size_t m = 5;
     CPPAD_TESTVECTOR(AD<double>) az(m);
     az[0] = CppAD::azmul(axy[0], axy[1]); // azmul(variable, variable)
     az[1] = CppAD::azmul(axy[0], inf);    // azmul(variable, parameter=inf)
     az[2] = CppAD::azmul(axy[0], 3.0);    // azmul(variable, parameter=3.0)
     az[3] = CppAD::azmul(0.0, axy[1]);    // azmul(parameter=0.0, variable)
     az[4] = CppAD::azmul(4.0, axy[1]);    // azmul(parameter=4.0, variable)

     // create f: axy -> az and stop tape recording
     CppAD::ADFun<double> f(axy, az);

     // check value when x is not zero
     ok &= NearEqual(az[0] , x * y,  eps, eps);
     ok &= az[1] == inf;
     ok &= NearEqual(az[2] , x * 3.0,  eps, eps);
     ok &= az[3] == 0.0;
     ok &= NearEqual(az[4] , 4.0 * y,  eps, eps);


     // check value x is zero and y is infinity
     CPPAD_TESTVECTOR(double) xy(n), z(m);
     xy[0] = 0.0;
     xy[1] = inf;
     z     = f.Forward(0, xy);
     ok &= z[0] == 0.0;
     ok &= z[1] == 0.0;
     ok &= z[2] == 0.0;
     ok &= z[3] == 0.0;
     ok &= z[4] == inf;

     return ok;
}
Input File: example/azmul.cpp cppad-20170000.3/doc/condexp.xml0000644000175200017650000005231613057470505015366 0ustar coincoin-web AD Conditional Expressions
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AD Conditional Expressions

Syntax
result = CondExpRel(left, right, if_true, if_false)

Purpose
Record, as part of an AD of Base operation sequence , the conditional result
     if( left Cop right )
          result = if_true
     else result = if_false
 The relational Rel and comparison operator Cop above have the following correspondence:
     Rel   Lt   Le   Eq   Ge   Gt
     Cop    <   <=   ==   >=   >
 If f is the ADFun object corresponding to the AD operation sequence, the assignment choice for result in an AD conditional expression is made each time f.Forward is used to evaluate the zero order Taylor coefficients with new values for the independent variables . This is in contrast to the AD comparison operators which are boolean valued and not included in the AD operation sequence.

Rel
In the syntax above, the relation Rel represents one of the following two characters: Lt, Le, Eq, Ge, Gt. As in the table above, Rel determines which comparison operator Cop is used when comparing left and right .

Type
These functions are defined in the CppAD namespace for arguments of Type is float , double, or any type of the form AD<Base> . (Note that all four arguments must have the same type.)

left
The argument left has prototype
     const Type& left
 It specifies the value for the left side of the comparison operator.

right
The argument right has prototype
     const Type& right
 It specifies the value for the right side of the comparison operator.

if_true
The argument if_true has prototype
     const Type& if_true
 It specifies the return value if the result of the comparison is true.

if_false
The argument if_false has prototype
     const Type& if_false
 It specifies the return value if the result of the comparison is false.

result
The result has prototype
     Type& if_false
Optimize
The optimize method will optimize conditional expressions in the following way: During zero order forward mode , once the value of the left and right have been determined, it is known if the true or false case is required. From this point on, values corresponding to the case that is not required are not computed. This optimization is done for the rest of zero order forward mode as well as forward and reverse derivatives calculations.

Deprecate 2005-08-07
Previous versions of CppAD used
     CondExp(flag, if_true, if_false)
 for the same meaning as
     CondExpGt(flag, Type(0), if_true, if_false)
 Use of CondExp is deprecated, but continues to be supported.

Operation Sequence
This is an AD of Base atomic operation and hence is part of the current AD of Base operation sequence .

Example

Test
The file cond_exp.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.

Atan2
The following implementation of the AD atan2 function is a more complex example of using conditional expressions: 
template <class Base>
AD<Base> atan2 (const AD<Base> &y, const AD<Base> &x)
{     AD<Base> alpha;
     AD<Base> beta;
     AD<Base> theta;

     AD<Base> zero(0.);
     AD<Base> pi2(2. * atan(1.));
     AD<Base> pi(2. * pi2);

     AD<Base> ax = abs(x);
     AD<Base> ay = abs(y);

     // if( ax > ay )
     //     theta = atan(ay / ax);
     // else     theta = pi2 - atan(ax / ay);
     alpha = atan(ay / ax);
     beta  = pi2 - atan(ax / ay);
     theta = CondExpGt(ax, ay, alpha, beta);         // use of CondExp

     // if( x <= 0 )
     //     theta = pi - theta;
     theta = CondExpLe(x, zero, pi - theta, theta);  // use of CondExp

     // if( y <= 0 )
     //     theta = - theta;
     theta = CondExpLe(y, zero, -theta, theta);      // use of CondExp

     return theta;
}
Input File: cppad/core/cond_exp.hpp cppad-20170000.3/doc/discrete.xml0000644000175200017650000003441213057470505015525 0ustar coincoin-web Discrete AD Functions
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Discrete AD Functions

Syntax
CPPAD_DISCRETE_FUNCTION(Base, name)
 y  = name(x)
 ay = name(ax)
Purpose
Record the evaluation of a discrete function as part of an AD<Base> operation sequence . The value of a discrete function can depend on the independent variables , but its derivative is identically zero. For example, suppose that the integer part of a variable x is the index into an array of values.

Base
This is the base type corresponding to the operations sequence; i.e., use of the name with arguments of type AD<Base> can be recorded in an operation sequence.

name
This is the name of the function (as it is used in the source code). The user must provide a version of name where the argument has type Base . CppAD uses this to create a version of name where the argument has type AD<Base> .

x
The argument x has prototype
     const Base& x
 It is the value at which the user provided version of name is to be evaluated.

y
The result y has prototype
     Base y
 It is the return value for the user provided version of name .

ax
The argument ax has prototype
     const AD<Base>& ax
 It is the value at which the CppAD provided version of name is to be evaluated.

ay
The result ay has prototype
     AD<Base> ay
 It is the return value for the CppAD provided version of name .

Create AD Version
The preprocessor macro invocation
     CPPAD_DISCRETE_FUNCTION(Base, name)
 defines the AD<Base> version of name . This can be with in a namespace (not the CppAD namespace) but must be outside of any routine.

Operation Sequence
This is an AD of Base atomic operation and hence is part of the current AD of Base operation sequence .

Derivatives
During a zero order Forward operation, an ADFun object will compute the value of name using the user provided Base version of this routine. All the derivatives of name will be evaluated as zero.

Parallel Mode
The first call to
     ay = name(ax)
 must not be in parallel execution mode.

Example
The file tape_index.cpp contains an example and test that uses a discrete function to vary an array index during Forward mode calculations. The file interp_onetape.cpp contains an example and test that uses discrete functions to avoid retaping a calculation that requires interpolation. (The file interp_retape.cpp shows how interpolation can be done with retaping.)

CppADCreateDiscrete Deprecated 2007-07-28
The preprocessor symbol CppADCreateDiscrete is defined to be the same as CPPAD_DISCRETE_FUNCTION but its use is deprecated.
Input File: cppad/core/discrete.hpp cppad-20170000.3/doc/_discrete_xml.js0000644000175200017650000000432213057470505016355 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'discrete.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down1 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down0 = [ 'tape_index.cpp.xml', 'interp_onetape.cpp.xml', 'interp_retape.cpp.xml' ]; var list_current0 = [ 'discrete.xml#Syntax', 'discrete.xml#Purpose', 'discrete.xml#Base', 'discrete.xml#name', 'discrete.xml#x', 'discrete.xml#y', 'discrete.xml#ax', 'discrete.xml#ay', 'discrete.xml#Create AD Version', 'discrete.xml#Operation Sequence', 'discrete.xml#Derivatives', 'discrete.xml#Parallel Mode', 'discrete.xml#Example', 'discrete.xml#CppADCreateDiscrete Deprecated 2007-07-28' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/atomic.xml0000644000175200017650000000561213057470505015177 0ustar coincoin-web Atomic AD Functions
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Atomic AD Functions

Contents
checkpointCheckpointing Functions
atomic_baseUser Defined Atomic AD Functions
Input File: omh/atomic.omh cppad-20170000.3/doc/compare.xml0000644000175200017650000003260513057470505015353 0ustar coincoin-web AD Binary Comparison Operators
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AD Binary Comparison Operators

Syntax
b = x Op y

Purpose
Compares two operands where one of the operands is an AD<Base> object. The comparison has the same interpretation as for the Base type.

Op
The operator Op is one of the following:
Op   Meaning
< is x less than y
<= is x less than or equal y
> is x greater than y
>= is x greater than or equal y
== is x equal to y
!= is x not equal to y

x
The operand x has prototype
     const Type &x
 where Type is AD<Base> , Base , or int.

y
The operand y has prototype
     const Type &y
 where Type is AD<Base> , Base , or int.

b
The result b has type
     bool b
Operation Sequence
The result of this operation is a bool value (not an AD of Base object). Thus it will not be recorded as part of an AD of Base operation sequence .

For example, suppose x and y are AD<Base> objects, the tape corresponding to AD<Base> is recording, b is true, and the subsequent code is
     if( b )
          y = cos(x);
     else y = sin(x);
 only the assignment y = cos(x) is recorded on the tape (if x is a parameter , nothing is recorded). The CompareChange function can yield some information about changes in comparison operation results. You can use CondExp to obtain comparison operations that depends on the independent variable values with out re-taping the AD sequence of operations.

Assumptions
If one of the Op operators listed above is used with an AD<Base> object, it is assumed that the same operator is supported by the base type Base .

Example
The file compare.cpp contains an example and test of these operations. It returns true if it succeeds and false otherwise.
Input File: cppad/core/compare.hpp cppad-20170000.3/doc/interp_retape.cpp.xml0000644000175200017650000006367413057470505017361 0ustar coincoin-web Interpolation With Retaping: Example and Test
Prev Next interp_retape.cpp

Interpolation With Retaping: Example and Test

See Also
interp_onetape.cpp 

# include <cppad/cppad.hpp>
# include <cassert>
# include <cmath>

namespace {
     double ArgumentValue[] = {
          .0 ,
          .2 ,
          .4 ,
          .8 ,
          1.
     };
     double FunctionValue[] = {
          std::sin( ArgumentValue[0] ) ,
          std::sin( ArgumentValue[1] ) ,
          std::sin( ArgumentValue[2] ) ,
          std::sin( ArgumentValue[3] ) ,
          std::sin( ArgumentValue[4] )
     };
     size_t TableLength = 5;

     size_t Index(const CppAD::AD<double> &x)
     {     // determine the index j such that x is between
          // ArgumentValue[j] and ArgumentValue[j+1]
          static size_t j = 0;
          while ( x < ArgumentValue[j] && j > 0 )
               j--;
          while ( x > ArgumentValue[j+1] && j < TableLength - 2)
               j++;
          // assert conditions that must be true given logic above
          assert( j >= 0 && j < TableLength - 1 );
          return j;
     }
     double Argument(const CppAD::AD<double> &x)
     {     size_t j = Index(x);
          return ArgumentValue[j];
     }
     double Function(const CppAD::AD<double> &x)
     {     size_t j = Index(x);
          return FunctionValue[j];
     }
     double Slope(const CppAD::AD<double> &x)
     {     size_t j  = Index(x);
          double dx = ArgumentValue[j+1] - ArgumentValue[j];
          double dy = FunctionValue[j+1] - FunctionValue[j];
          return dy / dx;
     }
}

bool interp_retape(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 1;
     CPPAD_TESTVECTOR(AD<double>) X(n);

     // loop over argument values
     size_t k;
     for(k = 0; k < TableLength - 1; k++)
     {
          X[0] = .4 * ArgumentValue[k] + .6 * ArgumentValue[k+1];

          // declare independent variables and start tape recording
          // (use a different tape for each argument value)
          CppAD::Independent(X);

          // evaluate piecewise linear interpolant at X[0]
          AD<double> A = Argument(X[0]);
          AD<double> F = Function(X[0]);
          AD<double> S = Slope(X[0]);
          AD<double> I = F + (X[0] - A) * S;

          // range space vector
          size_t m = 1;
          CPPAD_TESTVECTOR(AD<double>) Y(m);
          Y[0] = I;

          // create f: X -> Y and stop tape recording
          CppAD::ADFun<double> f(X, Y);

          // vectors for arguments to the function object f
          CPPAD_TESTVECTOR(double) x(n);   // argument values
          CPPAD_TESTVECTOR(double) y(m);   // function values
          CPPAD_TESTVECTOR(double) dx(n);  // differentials in x space
          CPPAD_TESTVECTOR(double) dy(m);  // differentials in y space

          // to check function value we use the fact that X[0] is between
          // ArgumentValue[k] and ArgumentValue[k+1]
          double delta, check;
          x[0]   = Value(X[0]);
          delta  = ArgumentValue[k+1] - ArgumentValue[k];
          check  = FunctionValue[k+1] * (x[0]-ArgumentValue[k]) / delta
                    + FunctionValue[k] * (ArgumentValue[k+1]-x[0]) / delta;
          ok    &= NearEqual(Y[0], check, eps99, eps99);

          // evaluate partials w.r.t. x[0]
          dx[0] = 1.;
          dy    = f.Forward(1, dx);

          // check that the derivative is the slope
          check = (FunctionValue[k+1] - FunctionValue[k])
                / (ArgumentValue[k+1] - ArgumentValue[k]);
          ok   &= NearEqual(dy[0], check, eps99, eps99);
     }
     return ok;
}
Input File: example/interp_retape.cpp cppad-20170000.3/doc/_interp_retape.cpp_xml.js0000644000175200017650000000332413057470505020176 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'discrete.xml', 'interp_retape.cpp.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'tape_index.cpp.xml', 'interp_onetape.cpp.xml', 'interp_retape.cpp.xml' ]; var list_current0 = [ 'interp_retape.cpp.xml#See Also' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/numeric_limits.xml0000644000175200017650000003523613057470505016753 0ustar coincoin-web Numeric Limits For an AD and Base Types
Prev Next

Numeric Limits For an AD and Base Types

Syntax
eps = numeric_limits<Float>::epsilon()
 min = numeric_limits<Float>::min()
 max = numeric_limits<Float>::max()
 nan = numeric_limits<Float>::quiet_NaN()
CppAD::numeric_limits
These functions and have the prototype
     static Float CppAD::numeric_limits<Float>::fun(void)
 where fun is epsilon, min, max, and quiet_NaN.

std::numeric_limits
CppAD does not use a specialization of std::numeric_limits because this would be to restrictive. The C++ standard specifies that Non-fundamental standard types, such as std::complex<double> shall not have specializations of std::numeric_limits; see Section 18.2 of ISO/IEC 14882:1998(E). In addition, since C++11, a only literal types can have a specialization of std::numeric_limits.

Float
These functions are defined for all AD<Base> , and for all corresponding Base types; see Base type base_limits .

epsilon
The result eps is equal to machine epsilon and has prototype
     Float eps
 The file num_limits.cpp tests the value eps by checking that the following are true
     1 != 1 + eps
     1 == 1 + eps / 2
 where all the values, and calculations, are done with the precision corresponding to Float .

min
The result min is equal to the minimum positive normalized value and has prototype
     Float min
 The file num_limits.cpp tests the value min by checking that the following are true
     abs( ((min / 100) * 100) / min - 1 ) > 3 * eps
     abs( ((min * 100) / 100) / min - 1 ) < 3 * eps
 where all the values, and calculations, are done with the precision corresponding to Float .

max
The result max is equal to the maximum finite value and has prototype
     Float max
 The file num_limits.cpp tests the value max by checking that the following are true
     abs( ((max * 100) / 100) / max - 1 ) > 3 * eps
     abs( ((max / 100) * 100) / max - 1 ) < 3 * eps
 where all the values, and calculations, are done with the precision corresponding to Float .

quiet_NaN
The result nan is not a number and has prototype
     Float nan
 The file num_limits.cpp tests the value nan by checking that the following is true
     nan != nan
Example
The file num_limits.cpp contains an example and test of these functions.
Input File: cppad/core/numeric_limits.hpp cppad-20170000.3/doc/num_limits.cpp.xml0000644000175200017650000003704213057470505016666 0ustar coincoin-web Numeric Limits: Example and Test
Prev Next num_limits.cpp Headings

Numeric Limits: Example and Test

# ifdef _MSC_VER
// Supress Microsoft compiler warning about possible loss of precision,
// in the constructors (when converting to std::complex<float>)
//     Float one = 1
//     Float two = 2
// 1 and 2 are small enough so no loss of precision when converting to float.
# pragma warning(disable:4244)
# endif

# include <cppad/cppad.hpp>
# include <complex>

namespace {
     typedef CppAD::AD<double> Float;
     //
     // -----------------------------------------------------------------
     bool check_epsilon(void)
     {     bool ok    = true;
          Float eps   = CppAD::numeric_limits<Float>::epsilon();
          Float eps2  = eps / 2.0;
          Float check = 1.0 + eps;
          ok         &= 1.0 !=  check;
          check       = 1.0 + eps2;
          ok         &= 1.0 == check;
          return ok;
     }
     // -----------------------------------------------------------------
     bool check_min(void)
     {     bool ok     = true;
          Float min   = CppAD::numeric_limits<Float>::min();
          Float eps   = CppAD::numeric_limits<Float>::epsilon();
          //
          Float match = (min / 100.) * 100.;
          ok         &= abs(match / min - 1.0)  > 3.0 * eps;
          //
          match       = (min * 100.) / 100.;
          ok         &= abs(match / min - 1.0)  < 3.0 * eps;
          return ok;
     }
     // -----------------------------------------------------------------
     bool check_max(void)
     {     bool ok     = true;
          Float max   = CppAD::numeric_limits<Float>::max();
          Float eps   = CppAD::numeric_limits<Float>::epsilon();
          //
          Float match = (max * 100.) / 100.;
          ok         &= abs(match / max - 1.0) > 3.0 * eps;
          //
          match       = (max / 100.) * 100.;
          ok         &= abs(match / max - 1.0) < 3.0 * eps;
          return ok;
     }
     // -----------------------------------------------------------------
     bool check_nan(void)
     {     bool ok     = true;
          Float nan   = CppAD::numeric_limits<Float>::quiet_NaN();
          ok         &= nan != nan;
          return ok;
     }
}

bool num_limits(void)
{     bool ok = true;

     ok &= check_epsilon();
     ok &= check_min();
     ok &= check_max();
     ok &= check_nan();

     return ok;
}
Input File: example/num_limits.cpp cppad-20170000.3/doc/_atomic_xml.js0000644000175200017650000000351713057470505016034 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'atomic.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down1 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down0 = [ 'checkpoint.xml', 'atomic_base.xml' ]; var list_current0 = [ 'atomic.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/checkpoint.cpp.xml0000644000175200017650000011612713057470505016637 0ustar coincoin-web Simple Checkpointing: Example and Test
Prev Next checkpoint.cpp

Simple Checkpointing: Example and Test

Purpose
Break a large computation into pieces and only store values at the interface of the pieces. In actual applications, there may be many functions, but for this example there are only two. The functions F : R 2 → R 2 and G : R 2 → R 2 defined by F ( y ) = ( y 0 + y 0 + y 0 y 1 + y 1 + y 1 ) , G ( x ) = ( x 0 · x 0 · x 0 x 1 · x 1 · x 1 ) 

# include <cppad/cppad.hpp>

namespace {
     using CppAD::AD;
     typedef CPPAD_TESTVECTOR(AD<double>)            ADVector;
     typedef CppAD::atomic_base<double>::option_enum option_enum;

     void f_algo(const ADVector& y, ADVector& z)
     {     z[0] = 0.0;
          z[1] = 0.0;
          for(size_t k = 0; k < 3; k++)
          {     z[0] += y[0];
               z[1] += y[1];
          }
          return;
     }
     void g_algo(const ADVector& x, ADVector& y)
     {     y[0] = 1.0;
          y[1] = 1.0;
          for(size_t k = 0; k < 3; k++)
          {     y[0] *= x[0];
               y[1] *= x[1];
          }
          return;
     }
     bool test_case(
          option_enum f_sparsity, option_enum g_sparsity, bool optimize )
     {     bool ok = true;
          using CppAD::checkpoint;
          using CppAD::ADFun;
          using CppAD::NearEqual;
          size_t i, j, k, n = 2, m = n;
          double eps = 10. * std::numeric_limits<double>::epsilon();

          // checkpoint version of the function F(x)
          ADVector ax(n), ay(n), az(m);
          for(j = 0; j < n; j++)
               ax[j] = double(j + 1);
          // could also use bool_sparsity_enum or set_sparsity_enum
          checkpoint<double> atom_f("atom_f", f_algo, ax, ay, f_sparsity);
          checkpoint<double> atom_g("atom_g", g_algo, ay, az, g_sparsity);

          // Record a version of z = g[f(x)] without checkpointing
          Independent(ax);
          f_algo(ax, ay);
          g_algo(ay, az);
          ADFun<double> check_not(ax, az);

          // Record a version of z = g[f(x)] with checkpointing
          Independent(ax);
          atom_f(ax, ay);
          atom_g(ay, az);
          ADFun<double> check_yes(ax, az);

          // checkpointing should use fewer operations
          ok &= check_yes.size_var() < check_not.size_var();

          // this does not really save space because f and g are only used once
          ok &= check_not.size_var() <=
               check_yes.size_var() + atom_f.size_var() + atom_g.size_var();

          // compare forward mode results for orders 0, 1, 2
          size_t q = 2;
          CPPAD_TESTVECTOR(double) x_q(n*(q+1)), z_not(m*(q+1)), z_yes(m*(q+1));
          for(j = 0; j < n; j++)
          {     for(k = 0; k <= q; k++)
                    x_q[ j * (q+1) + k ] = 1.0 / (q + 1 - k);
          }
          z_not = check_not.Forward(q, x_q);
          z_yes = check_yes.Forward(q, x_q);
          for(i = 0; i < m; i++)
          {     for(k = 0; k <= q; k++)
               {     double zik_not = z_not[ i * (q+1) + k];
                    double zik_yes = z_yes[ i * (q+1) + k];
                    ok &= NearEqual(zik_not, zik_yes, eps, eps);
               }
          }

          // compare reverse mode results
          CPPAD_TESTVECTOR(double) w(m*(q+1)), dw_not(n*(q+1)), dw_yes(n*(q+1));
          dw_not = check_not.Reverse(q+1, w);
          dw_yes = check_yes.Reverse(q+1, w);
          for(j = 0; j < n; j++)
          {     for(k = 0; k <= q; k++)
               {     double dwjk_not = dw_not[ j * (q+1) + k];
                    double dwjk_yes = dw_yes[ j * (q+1) + k];
                    ok &= NearEqual(dwjk_not, dwjk_yes, eps, eps);
               }
          }

          // compare forward mode Jacobian sparsity patterns
          CppAD::vector< std::set<size_t> > r(n), s_not(m), s_yes(m);
          for(j = 0; j < n; j++)
               r[j].insert(j);
          s_not = check_not.ForSparseJac(n, r);
          s_yes = check_yes.ForSparseJac(n, r);
          for(i = 0; i < m; i++)
               ok &= s_not[i] == s_yes[i];

          // compare reverse mode Jacobian sparsity patterns
          CppAD::vector< std::set<size_t> > s(m), r_not(m), r_yes(m);
          for(i = 0; i < m; i++)
               s[i].insert(i);
          r_not = check_not.RevSparseJac(m, s);
          r_yes = check_yes.RevSparseJac(m, s);
          for(i = 0; i < m; i++)
               ok &= s_not[i] == s_yes[i];


          // compare reverse mode Hessian sparsity patterns
          CppAD::vector< std::set<size_t> > s_one(1), h_not(n), h_yes(n);
          for(i = 0; i < m; i++)
               s_one[0].insert(i);
          h_not = check_not.RevSparseHes(n, s_one);
          h_yes = check_yes.RevSparseHes(n, s_one);
          for(i = 0; i < n; i++)
               ok &= h_not[i] == h_yes[i];

          return ok;
     }
}

bool checkpoint(void)
{     bool ok = true;

     // different types of sparsity
     option_enum pack_sparsity = CppAD::atomic_base<double>::pack_sparsity_enum;
     option_enum bool_sparsity = CppAD::atomic_base<double>::bool_sparsity_enum;
     option_enum set_sparsity  = CppAD::atomic_base<double>::set_sparsity_enum;

     // test some different cases
     ok &= test_case(pack_sparsity, pack_sparsity, true);
     ok &= test_case(pack_sparsity, bool_sparsity, false);
     ok &= test_case(bool_sparsity, set_sparsity,  true);
     ok &= test_case(set_sparsity,  set_sparsity,  false);

     return ok;
}
Input File: example/atomic/checkpoint.cpp cppad-20170000.3/doc/checkpoint_ode.cpp.xml0000644000175200017650000020174113057470505017463 0ustar coincoin-web Checkpointing an ODE Solver: Example and Test
Prev Next checkpoint_ode.cpp

Checkpointing an ODE Solver: Example and Test

See Also
checkpoint_extended_ode.cpp ,

Purpose
In this example we checkpoint one step of an ODE solver.

Problem
We consider the initial value problem with parameter x defined by, z ( 0 , x ) = z 0 ( x ) , ∂ t z ( t , x ) = h [ x , z ( t , x ) ] Note that if t needs to be in the equation, one can define the first component of z ( t , x ) to be equal to t .

ODE Solver
For this example, we consider the Fourth order Runge-Kutta ODE solver. Given an approximation solution at time t k denoted by z ˜ k ( x ) , and Δ t = t k + 1 - t k , it defines the approximation solution z ˜ k + 1 ( x ) at time t k + 1 by h 1 = h [ x , z ˜ k ( x ) ] h 2 = h [ x , z ˜ k ( x ) + Δ t h 1 / 2 ] h 3 = h [ x , z ˜ k ( x ) + Δ t h 2 / 2 ] h 4 = h [ x , z ˜ k ( x ) + Δ t h 3 ] z ˜ k + 1 ( x ) = z ˜ k ( x ) + Δ t ( h 1 + 2 h 2 + 2 h 3 + h 4 ) / 6 If z ˜ k ( x ) = z k ( x ) , z ˜ k + 1 ( x ) = z k + 1 ( x ) + O ( Δ t 5 ) . Other ODE solvers can use a similar method to the one used below.

ODE
For this example the ODE is defined by z ( 0 , x ) = 0 and h [ x , z ( t , x ) ] = ( x 0 x 1 z 0 ( t , x ) ⋮ x n -1 z n -2 ( t , x ) ) = ( ∂ t z 0 ( t , x ) ∂ t z 1 ( t , x ) ⋮ ∂ t z n -1 ( t , x ) )
Solution
The solution of the ODE for this example, which is used to check the results, can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain z ( t , x ) = ( x 0 t x 1 x 0 t 2 / 2 ⋮ x n -1 x n -2 … x 0 t n / n ! ) 

# include <cppad/cppad.hpp>

namespace {
     using CppAD::AD;
     typedef AD<double>                     a1double;
     typedef AD<a1double>                   a2double;
     //
     typedef CPPAD_TESTVECTOR(   double )   a0vector;
     typedef CPPAD_TESTVECTOR( a1double )   a1vector;
     typedef CPPAD_TESTVECTOR( a2double )   a2vector;
     //
     // set once by main and kept that way
     double delta_t_ = std::numeric_limits<double>::quiet_NaN();
     size_t n_       = 0;
     //
     // The function h( x , y)
     template <class FloatVector>
     FloatVector h(const FloatVector& x, const FloatVector& y)
     {     assert( size_t( x.size() ) == n_ );
          assert( size_t( y.size() ) == n_ );
          FloatVector result(n_);
          result[0] = x[0];
          for(size_t i = 1; i < n_; i++)
               result[i] = x[i] * y[i-1];
          return result;
     }

     // The 4-th Order Runge-Kutta Step
     template <class FloatVector>
     FloatVector Runge4(const FloatVector& x, const FloatVector& z0
     )
     {     assert( size_t( x.size() ) == n_ );
          assert( size_t( z0.size() ) == n_ );
          //
          typedef typename FloatVector::value_type Float;
          //
          Float  dt = Float(delta_t_);
          size_t m  = z0.size();
          //
          FloatVector h1(m), h2(m), h3(m), h4(m), result(m);
          h1 = h( x, z0 );
          //
          for(size_t i = 0; i < m; i++)
               h2[i] = z0[i] + dt * h1[i] / 2.0;
          h2 = h( x, h2 );
          //
          for(size_t i = 0; i < m; i++)
               h3[i] = z0[i] + dt * h2[i] / 2.0;
          h3 = h( x, h3 );
          //
          for(size_t i = 0; i < m; i++)
               h4[i] = z0[i] + dt * h3[i];
          h4 = h( x, h4 );
          //
          for(size_t i = 0; i < m; i++)
          {     Float dz = dt * ( h1[i] + 2.0*h2[i] + 2.0*h3[i] + h4[i] ) / 6.0;
               result[i] = z0[i] + dz;
          }
          return result;
     }

     // pack x and z into an ode_info vector
     template <class FloatVector>
     void pack(
          FloatVector&         ode_info ,
          const FloatVector&   x        ,
          const FloatVector&   z        )
     {     assert( size_t( ode_info.size() ) == n_ + n_ );
          assert( size_t( x.size()        ) == n_      );
          assert( size_t( z.size()        ) == n_      );
          //
          size_t offset = 0;
          for(size_t i = 0; i < n_; i++)
               ode_info[offset + i] = x[i];
          offset += n_;
          for(size_t i = 0; i < n_; i++)
               ode_info[offset + i] = z[i];
     }

     // unpack an ode_info vector
     template <class FloatVector>
     void unpack(
          const FloatVector&         ode_info ,
          FloatVector&               x        ,
          FloatVector&               z        )
     {     assert( size_t( ode_info.size() ) == n_ + n_ );
          assert( size_t( x.size()        ) == n_      );
          assert( size_t( z.size()        ) == n_      );
          //
          size_t offset = 0;
          for(size_t i = 0; i < n_; i++)
               x[i] = ode_info[offset + i];
          offset += n_;
          for(size_t i = 0; i < n_; i++)
               z[i] = ode_info[offset + i];
     }

     // Algorithm that z(t, x)
     void ode_algo(const a1vector& ode_info_in, a1vector& ode_info_out)
     {     assert( size_t( ode_info_in.size()  ) == n_ + n_ );
          assert( size_t( ode_info_out.size() ) == n_ + n_ );
          //
          // initial ode information
          a1vector x(n_), z0(n_);
          unpack(ode_info_in, x, z0);
          //
          // advance z(t, x)
          a1vector z1 = Runge4(x, z0);
          //
          // final ode information
          pack(ode_info_out, x, z1);
          //
          return;
     }
}
//
bool ode(void)
{     bool ok = true;
     using CppAD::NearEqual;
     double eps = std::numeric_limits<double>::epsilon();
     //
     // number of terms in the differential equation
     n_ = 6;
     //
     // step size for the differentiail equation
     size_t n_step = 10;
     double T      = 1.0;
     delta_t_ = T / double(n_step);
     //
     // set parameter value and initial value of the ode
     a1vector ax(n_), az0(n_);
     for(size_t i = 0; i < n_; i++)
     {     ax[i]  = a1double(i + 1);
          az0[i] = a1double(0);
     }
     //
     // pack ode information input vector
     a1vector ode_info_in(2 * n_);
     pack(ode_info_in, ax, az0);
     //
     // create checkpoint version of the algorithm
     a1vector ode_info_out(2 * n_);
     CppAD::checkpoint<double> ode_check(
          "ode", ode_algo, ode_info_in, ode_info_out
     );
     //
     // set the independent variables for recording
     CppAD::Independent( ax );
     //
     // repack to get dependence on ax
     pack(ode_info_in, ax, az0);
     //
     // Now run the checkpoint algorithm n_step times
     for(size_t k = 0; k < n_step; k++)
     {     ode_check(ode_info_in, ode_info_out);
          ode_info_in = ode_info_out;
     }
     //
     // Unpack the results (must use ax1 so do not overwrite ax)
     a1vector ax1(n_), az1(n_);
     unpack(ode_info_out, ax1, az1);
     //
     // We could record a complicated funciton of x and z(T, x) in f,
     // but make this example simpler we record x -> z(T, x).
     CppAD::ADFun<double> f(ax, az1);
     //
     // check function values
     a0vector x(n_), z1(n_);
     for(size_t j = 0; j < n_; j++)
          x[j] = double(j + 1);
     z1 = f.Forward(0, x);
     //
     // separate calculation of z(t, x)
     a0vector check_z1(n_);
     check_z1[0] = x[0] * T;
     for(size_t i = 1; i < n_; i++)
          check_z1[i] = x[i] * T * check_z1[i-1] / double(i+1);
     //
     // expected accuracy for each component of of z(t, x)
     a0vector acc(n_);
     for(size_t i = 0; i < n_; i++)
     {     if( i < 4 )
          {     // Runge-Kutta methos is exact for this case
               acc[i] = 10. * eps;
          }
          else
          {     acc[i] = 1.0;
               for(size_t k = 0; k < 5; k++)
                         acc[i] *= x[k] * delta_t_;
          }
     }
     // check z1(T, x)
     for(size_t i = 0; i < n_; i++)
          ok &= NearEqual(z1[i] , check_z1[i], acc[i], acc[i]);
     //
     // Now use f to compute a derivative. For this 'simple' example it is
     // the derivative of z_{n-1} (T, x) respect to x of the
     a0vector w(n_), dw(n_);
     for(size_t i = 0; i < n_; i++)
     {     w[i] = 0.0;
          if( i == n_ - 1 )
               w[i] = 1.0;
     }
     dw = f.Reverse(1, w);
     for(size_t j = 0; j < n_; j++)
     {     double check = z1[n_ - 1] / x[j];
          ok &= NearEqual(dw[j] , check, 100.*eps, 100.*eps);
     }
     //
     return ok;
}
Input File: example/atomic/ode.cpp cppad-20170000.3/doc/checkpoint_extended_ode.cpp.xml0000644000175200017650000026214513057470505021350 0ustar coincoin-web Checkpointing an Extended ODE Solver: Example and Test
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Checkpointing an Extended ODE Solver: Example and Test

See Also
checkpoint_ode.cpp , atomic_mul_level.cpp .

Discussion
Suppose that we wish to extend an ODE to include derivatives with respect to some parameter in the ODE. In addition, suppose we wish to differentiate a function that depends on these derivatives. Applying checkpointing to at the second level of AD would not work; see atomic_mul_level.cpp In this example we show how one can do this by checkpointing an extended ODE solver.

Problem
We consider the initial value problem with parameter x defined by, z ( 0 , x ) = z 0 ( x ) , ∂ t z ( t , x ) = h [ x , z ( t , x ) ] Note that if t needs to be in the equation, one can define the first component of z ( t , x ) to be equal to t .

ODE Solver
For this example, we consider the Fourth order Runge-Kutta ODE solver. Given an approximation solution at time t k denoted by z ˜ k ( x ) , and Δ t = t k + 1 - t k , it defines the approximation solution z ˜ k + 1 ( x ) at time t k + 1 by h 1 = h [ x , z ˜ k ( x ) ] h 2 = h [ x , z ˜ k ( x ) + Δ t h 1 / 2 ] h 3 = h [ x , z ˜ k ( x ) + Δ t h 2 / 2 ] h 4 = h [ x , z ˜ k ( x ) + Δ t h 3 ] z ˜ k + 1 ( x ) = z ˜ k ( x ) + Δ t ( h 1 + 2 h 2 + 2 h 3 + h 4 ) / 6 If z ˜ k ( x ) = z k ( x ) , then z ˜ k + 1 ( x ) = z k + 1 ( x ) + O ( Δ t 5 ) , then Other ODE solvers can use a similar method to the one used below.

ODE
For this example the ODE is defined by z ( 0 , x ) = 0 and h [ x , z ( t , x ) ] = ( x 0 x 1 z 0 ( t , x ) ⋮ x n -1 z n -2 ( t , x ) ) = ( ∂ t z 0 ( t , x ) ∂ t z 1 ( t , x ) ⋮ ∂ t z n -1 ( t , x ) )
Solution
The solution of the ODE for this example, which is used to check the results, can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain z ( t , x ) = ( x 0 t x 1 x 0 t 2 / 2 ⋮ x n -1 x n -2 … x 0 t n / n ! ) 

# include <cppad/cppad.hpp>

namespace {
     using CppAD::AD;
     typedef AD<double>                     a1double;
     typedef AD<a1double>                   a2double;
     //
     typedef CPPAD_TESTVECTOR(   double )   a0vector;
     typedef CPPAD_TESTVECTOR( a1double )   a1vector;
     typedef CPPAD_TESTVECTOR( a2double )   a2vector;
     //
     // set once by main and kept that way
     double delta_t_ = std::numeric_limits<double>::quiet_NaN();
     size_t n_       = 0;
     //
     // The function h( x , y)
     template <class FloatVector>
     FloatVector h(const FloatVector& x, const FloatVector& y)
     {     assert( size_t( x.size() ) == n_ );
          assert( size_t( y.size() ) == n_ );
          FloatVector result(n_);
          result[0] = x[0];
          for(size_t i = 1; i < n_; i++)
               result[i] = x[i] * y[i-1];
          return result;
     }

     // The 4-th Order Runge-Kutta Step
     template <class FloatVector>
     FloatVector Runge4(const FloatVector& x, const FloatVector& z0
     )
     {     assert( size_t( x.size() ) == n_ );
          assert( size_t( z0.size() ) == n_ );
          //
          typedef typename FloatVector::value_type Float;
          //
          Float  dt = Float(delta_t_);
          size_t m  = z0.size();
          //
          FloatVector h1(m), h2(m), h3(m), h4(m), result(m);
          h1 = h( x, z0 );
          //
          for(size_t i = 0; i < m; i++)
               h2[i] = z0[i] + dt * h1[i] / 2.0;
          h2 = h( x, h2 );
          //
          for(size_t i = 0; i < m; i++)
               h3[i] = z0[i] + dt * h2[i] / 2.0;
          h3 = h( x, h3 );
          //
          for(size_t i = 0; i < m; i++)
               h4[i] = z0[i] + dt * h3[i];
          h4 = h( x, h4 );
          //
          for(size_t i = 0; i < m; i++)
          {     Float dz = dt * ( h1[i] + 2.0*h2[i] + 2.0*h3[i] + h4[i] ) / 6.0;
               result[i] = z0[i] + dz;
          }
          return result;
     }

     // Derivative of 4-th Order Runge-Kutta Step w.r.t x
     a1vector Runge4_x(const a1vector& x, const a1vector& z0)
     {     assert( size_t( x.size() ) == n_ );
          assert( size_t( z0.size() ) == n_ );
          //
          a2vector ax(n_);
          for(size_t j = 0; j < n_; j++)
               ax[j] = x[j];
          //
          a2vector az0(n_);
          for(size_t i = 0; i < n_; i++)
               az0[i] = z0[i];
          //
          CppAD::Independent(ax);
          a2vector az(n_);
          az = Runge4(ax, az0);
          CppAD::ADFun<a1double> f(ax, az);
          //
          a1vector result =  f.Jacobian(x);
          //
          return result;
     }

     // Derivative of 4-th Order Runge-Kutta Step w.r.t z0
     a1vector Runge4_z0(const a1vector& x, const a1vector& z0)
     {     assert( size_t( x.size()  ) == n_ );
          assert( size_t( z0.size() ) == n_ );
          //
          a2vector ax(n_);
          for(size_t j = 0; j < n_; j++)
               ax[j] = x[j];
          //
          a2vector az0(n_);
          for(size_t i = 0; i < n_; i++)
               az0[i] = z0[i];
          //
          CppAD::Independent(az0);
          a2vector az(n_);
          az = Runge4(ax, az0);
          CppAD::ADFun<a1double> f(az0, az);
          //
          a1vector result =  f.Jacobian(z0);
          //
          return result;
     }

     // pack an extended ode vector
     template <class FloatVector>
     void pack(
          FloatVector&         extended_ode ,
          const FloatVector&   x            ,
          const FloatVector&   z            ,
          const FloatVector&   z_x          )
     {     assert( size_t( extended_ode.size() ) == n_ + n_ + n_ * n_ );
          assert( size_t( x.size()            ) == n_                );
          assert( size_t( z.size()            ) == n_                );
          assert( size_t( z_x.size()          ) == n_ * n_           );
          //
          size_t offset = 0;
          for(size_t i = 0; i < n_; i++)
               extended_ode[offset + i] = x[i];
          offset += n_;
          for(size_t i = 0; i < n_; i++)
               extended_ode[offset + i] = z[i];
          offset += n_;
          for(size_t i = 0; i < n_; i++)
          {     for(size_t j = 0; j < n_; j++)
               {     // partial of z_i (t , x ) w.r.t x_j
                    extended_ode[offset + i * n_ + j] = z_x[i * n_ + j];
               }
          }
     }

     // unpack an extended ode vector
     template <class FloatVector>
     void unpack(
          const FloatVector&         extended_ode ,
          FloatVector&               x            ,
          FloatVector&               z            ,
          FloatVector&               z_x          )
     {     assert( size_t( extended_ode.size() ) == n_ + n_ + n_ * n_ );
          assert( size_t( x.size()            ) == n_                );
          assert( size_t( z.size()            ) == n_                );
          assert( size_t( z_x.size()          ) == n_ * n_           );
          //
          size_t offset = 0;
          for(size_t i = 0; i < n_; i++)
               x[i] = extended_ode[offset + i];
          offset += n_;
          for(size_t i = 0; i < n_; i++)
               z[i] = extended_ode[offset + i];
          offset += n_;
          for(size_t i = 0; i < n_; i++)
          {     for(size_t j = 0; j < n_; j++)
               {     // partial of z_i (t , x ) w.r.t x_j
                    z_x[i * n_ + j] = extended_ode[offset + i * n_ + j];
               }
          }
     }

     // Algorithm that advances the partial of z(t, x) w.r.t x
     void ext_ode_algo(const a1vector& ext_ode_in, a1vector& ext_ode_out)
     {     assert( size_t( ext_ode_in.size()  ) == n_ + n_ + n_ * n_ );
          assert( size_t( ext_ode_out.size() ) == n_ + n_ + n_ * n_ );
          //
          // initial extended ode information
          a1vector x(n_), z0(n_), z0_x(n_ * n_);
          unpack(ext_ode_in, x, z0, z0_x);
          //
          // advance z(t, x)
          a1vector z1 = Runge4(x, z0);
          //
          // partial of z1 w.r.t. x
          a1vector z1_x = Runge4_x(x, z0);
          //
          // partial of z1 w.r.t. z0
          a1vector z1_z0 = Runge4_z0(x, z0);
          //
          // total derivative of z1 w.r.t x
          for(size_t i = 0; i < n_; i++)
          {     for(size_t j = 0; j < n_; j++)
               {     a1double sum = 0.0;
                    for(size_t k = 0; k < n_; k++)
                         sum += z1_z0 [ i * n_ + k ] * z0_x [ k * n_ + j ];
                    z1_x[ i * n_ + j] += sum;
               }
          }
          //
          // final extended ode information
          pack(ext_ode_out, x, z1, z1_x);
          //
          return;
     }
}
//
bool extended_ode(void)
{     bool ok = true;
     using CppAD::NearEqual;
     double eps = std::numeric_limits<double>::epsilon();
     //
     // number of terms in the differential equation
     n_ = 6;
     //
     // step size for the differentiail equation
     size_t n_step = 10;
     double T      = 1.0;
     delta_t_ = T / double(n_step);
     //
     // set parameter value and initial value of the extended ode
     a1vector ax(n_), az0(n_), az0_x(n_ * n_);
     for(size_t i = 0; i < n_; i++)
     {     ax[i]  = a1double(i + 1);
          az0[i] = a1double(0);
          for(size_t j = 0; j < n_; j++)
               az0_x[ i * n_ + j ] = 0.0;
     }
     //
     // pack into extended ode information input vector
     size_t n_ext = n_ + n_ + n_ * n_;
     a1vector aext_ode_in(n_ext);
     pack(aext_ode_in, ax, az0, az0_x);
     //
     // create checkpoint version of the algorithm
     a1vector aext_ode_out(n_ext);
     CppAD::checkpoint<double> ext_ode_check(
          "ext_ode", ext_ode_algo, aext_ode_in, aext_ode_out
     );
     //
     // set the independent variables for recording
     CppAD::Independent( ax );
     //
     // repack to get dependence on ax
     pack(aext_ode_in, ax, az0, az0_x);
     //
     // Now run the checkpoint algorithm n_step times
     for(size_t k = 0; k < n_step; k++)
     {     ext_ode_check(aext_ode_in, aext_ode_out);
          aext_ode_in = aext_ode_out;
     }
     //
     // Unpack the results (must use ax1 so do not overwrite ax)
     a1vector ax1(n_), az1(n_), az1_x(n_ * n_);
     unpack(aext_ode_out, ax1, az1, az1_x);
     //
     // We could record a complicated funciton of x and z_x(T, x) in f,
     // but make this example simpler we record x -> z_x(T, x).
     CppAD::ADFun<double> f(ax, az1_x);
     //
     // check function values
     a0vector x(n_), z1(n_), z1_x(n_ * n_);
     for(size_t j = 0; j < n_; j++)
          x[j] = double(j + 1);
     z1_x = f.Forward(0, x);
     //
     // use z(t, x) for checking solution
     z1[0] = x[0] * T;
     for(size_t i = 1; i < n_; i++)
          z1[i] = x[i] * T * z1[i-1] / double(i+1);
     //
     // expected accuracy for each component of of z(t, x)
     a0vector acc(n_);
     for(size_t i = 0; i < n_; i++)
     {     if( i < 4 )
          {     // Runge-Kutta methos is exact for this case
               acc[i] = 10. * eps;
          }
          else
          {     acc[i] = 1.0;
               for(size_t k = 0; k < 5; k++)
                         acc[i] *= x[k] * delta_t_;
          }
     }
     // check z1(T, x)
     for(size_t i = 0; i < n_; i++)
     {     for(size_t j = 0; j < n_; j++)
          {     // check partial of z1_i w.r.t x_j
               double check = 0.0;
               if( j <= i )
                    check = z1[i] / x[j];
               ok &= NearEqual(z1_x[ i * n_ + j ] , check, acc[i], acc[i]);
          }
     }
     //
     // Now use f to compute a derivative. For this 'simple' example it is
     // the derivative with respect to x of the
     // parital with respect to x[n-1] of z_{n-1} (t , x)
     a0vector w(n_ * n_), dw(n_);
     for(size_t i = 0; i < n_; i++)
     {     for(size_t j = 0; j < n_; j++)
          {     w[ i * n_ + j ] = 0.0;
               if( i == n_ - 1 && j == n_ - 1 )
                    w[ i * n_ + j ] = 1.0;
          }
     }
     dw = f.Reverse(1, w);
     for(size_t j = 0; j < n_; j++)
     {     double check = 0.0;
          if( j < n_ - 1 )
               check = z1[n_ - 1] / ( x[n_ - 1] * x[j] );
          ok &= NearEqual(dw[j] , check, acc[n_-1], acc[n_-1]);
     }
     //
     return ok;
}
Input File: example/atomic/extended_ode.cpp cppad-20170000.3/doc/atomic_base.xml0000644000175200017650000004731113057470505016173 0ustar coincoin-web User Defined Atomic AD Functions
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User Defined Atomic AD Functions

Syntax

atomic_user afun(ctor_arg_list)
afun(ax, ay)
ok = afun.forward(p, q, vx, vy, tx, ty)
ok = afun.reverse(q, tx, ty, px, py)
ok = afun.for_sparse_jac(q, r, s)
ok = afun.rev_sparse_jac(q, r, s)
ok = afun.for_sparse_hes(vx, r, s, h)
ok = afun.rev_sparse_hes(vx, s, t, q, r, u, v)
atomic_base<Base>::clear()

Purpose
In some cases, the user knows how to compute derivatives of a function y = f ( x ) where f : B n → B m more efficiently than by coding it using AD<Base> atomic operations and letting CppAD do the rest. In this case atomic_base<Base> can use the user code for f ( x ) , and its derivatives, as AD<Base> atomic operations.

Virtual Functions
User defined derivatives are implemented by defining the following virtual functions in the base_atomic class: forward , reverse , for_sparse_jac , rev_sparse_jac , and rev_sparse_hes . These virtual functions have a default implementation that returns ok == false . The forward function, for the case q == 0 , must be implemented. Otherwise, only those functions required by the your calculations need to be implemented. For example, forward for the case q == 2 can just return ok == false unless you require forward mode calculation of second derivatives.

Contents
atomic_ctorAtomic Function Constructor
atomic_optionSet Atomic Function Options
atomic_afunUsing AD Version of Atomic Function
atomic_forwardAtomic Forward Mode
atomic_reverseAtomic Reverse Mode
atomic_for_sparse_jacAtomic Forward Jacobian Sparsity Patterns
atomic_rev_sparse_jacAtomic Reverse Jacobian Sparsity Patterns
atomic_for_sparse_hesAtomic Forward Hessian Sparsity Patterns
atomic_rev_sparse_hesAtomic Reverse Hessian Sparsity Patterns
atomic_base_clearFree Static Variables
atomic_get_started.cppGetting Started with Atomic Operations: Example and Test
atomic_norm_sq.cppAtomic Euclidean Norm Squared: Example and Test
atomic_reciprocal.cppReciprocal as an Atomic Operation: Example and Test
atomic_set_sparsity.cppAtomic Sparsity with Set Patterns: Example and Test
atomic_tangent.cppTan and Tanh as User Atomic Operations: Example and Test
atomic_eigen_mat_mul.cppAtomic Eigen Matrix Multiply: Example and Test
atomic_eigen_mat_inv.cppAtomic Eigen Matrix Inverse: Example and Test
atomic_eigen_cholesky.cppAtomic Eigen Cholesky Factorization: Example and Test
atomic_mat_mul.cppUser Atomic Matrix Multiply: Example and Test

Examples

Getting Started
The file atomic_get_started.cpp contains an example and test that shows the minimal amount of information required to create a user defined atomic operation.

Scalar Function
The file atomic_reciprocal.cpp contains an example and test where the user provides the code for computing derivatives. This example is simple because the domain and range are scalars.

Vector Range
The file atomic_tangent.cpp contains another example where the user provides the code for computing derivatives. This example is more complex because the range has two components.

Hessian Sparsity Patterns
The file atomic_rev_sparse_hes.cpp contains an minimal example where the user provides the code for computing Hessian sparsity patterns.

General Case
The file atomic_mat_mul.cpp contains a more general example where the user provides the code for computing derivatives. This example is more complex because both the domain and range dimensions are arbitrary.
Input File: omh/atomic_base.omh cppad-20170000.3/doc/_atomic_base_xml.js0000644000175200017650000000500113057470505017014 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'atomic.xml', 'atomic_base.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'checkpoint.xml', 'atomic_base.xml' ]; var list_down0 = [ 'atomic_ctor.xml', 'atomic_option.xml', 'atomic_afun.xml', 'atomic_forward.xml', 'atomic_reverse.xml', 'atomic_for_sparse_jac.xml', 'atomic_rev_sparse_jac.xml', 'atomic_for_sparse_hes.xml', 'atomic_rev_sparse_hes.xml', 'atomic_base_clear.xml', 'atomic_get_started.cpp.xml', 'atomic_norm_sq.cpp.xml', 'atomic_reciprocal.cpp.xml', 'atomic_set_sparsity.cpp.xml', 'atomic_tangent.cpp.xml', 'atomic_eigen_mat_mul.cpp.xml', 'atomic_eigen_mat_inv.cpp.xml', 'atomic_eigen_cholesky.cpp.xml', 'atomic_mat_mul.cpp.xml' ]; var list_current0 = [ 'atomic_base.xml#Syntax', 'atomic_base.xml#Purpose', 'atomic_base.xml#Virtual Functions', 'atomic_base.xml#Contents', 'atomic_base.xml#Examples', 'atomic_base.xml#Examples.Getting Started', 'atomic_base.xml#Examples.Scalar Function', 'atomic_base.xml#Examples.Vector Range', 'atomic_base.xml#Examples.Hessian Sparsity Patterns', 'atomic_base.xml#General Case' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/atomic_ctor.xml0000644000175200017650000003233613057470505016231 0ustar coincoin-web Atomic Function Constructor
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Atomic Function Constructor

Syntax
atomic_user afun(ctor_arg_list)
 atomic_base<Base>(name, sparsity)
atomic_user

ctor_arg_list
Is a list of arguments for the atomic_user constructor.

afun
The object afun must stay in scope for as long as the corresponding atomic function is used. This includes use by any ADFun<Base> that has this atomic_user operation in its operation sequence .

Implementation
The user defined atomic_user class is a publicly derived class of atomic_base<Base> . It should be declared as follows:
     class atomic_user : public CppAD::atomic_base<Base> {
     public:
          atomic_user(ctor_arg_list) : atomic_base<Base>(name, sparsity)
     ...
     };
 where ... denotes the rest of the implementation of the derived class. This includes completing the constructor and all the virtual functions that have their atomic_base implementations replaced by atomic_user implementations.

atomic_base

Restrictions
The atomic_base constructor cannot be called in parallel mode.

Base
The template parameter determines the Base type for this AD<Base> atomic operation.

name
This atomic_base constructor argument has the following prototype
     const std::string& name
 It is the name for this atomic function and is used for error reporting. The suggested value for name is afun or atomic_user , i.e., the name of the corresponding atomic object or class.

sparsity
This atomic_base constructor argument has prototype
     atomic_base<Base>::option_enum sparsity
 The current sparsity for an atomic_base object determines which type of sparsity patterns it uses and its value is one of the following:
sparsity sparsity patterns
atomic_base<Base>::pack_sparsity_enum    vectorBool
atomic_base<Base>::bool_sparsity_enum    vector <bool>
atomic_base<Base>::set_sparsity_enum    vector <std::set<std::size_t> >
There is a default value for sparsity if it is not included in the constructor (which may be either the bool or set option).

Example

Define Constructor
The following is an example of a user atomic function constructor definitions: get_started.cpp .

Use Constructor
The following is an example using a user atomic function constructor: get_started.cpp .
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_option.xml0000644000175200017650000002515313057470505016571 0ustar coincoin-web Set Atomic Function Options
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Set Atomic Function Options

Syntax
afun.option(option_value) These settings do not apply to individual afun calls, but rather all subsequent uses of the corresponding atomic operation in an ADFun object.

atomic_sparsity
Note that, if you use optimize , these sparsity patterns are used to determine the dependency relationship between argument and result variables.

pack_sparsity_enum
If option_value is atomic_base<Base>::pack_sparsity_enum , then the type used by afun for sparsity patterns , (after the option is set) will be
     typedef CppAD::vectorBool atomic_sparsity
 If r is a sparsity pattern for a matrix R ∈ B p × q : r.size() == p * q .

bool_sparsity_enum
If option_value is atomic_base<Base>::bool_sparsity_enum , then the type used by afun for sparsity patterns , (after the option is set) will be
     typedef CppAD::vector<bool> atomic_sparsity
 If r is a sparsity pattern for a matrix R ∈ B p × q : r.size() == p * q .

set_sparsity_enum
If option_value is atomic_base<Base>::set_sparsity_enum , then the type used by afun for sparsity patterns , (after the option is set) will be
     typedef CppAD::vector< std::set<size_t> > atomic_sparsity
 If r is a sparsity pattern for a matrix R ∈ B p × q : r.size() == p , and for i = 0 , … , p -1 , the elements of r[i] are between zero and q -1 inclusive.
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_afun.xml0000644000175200017650000002206713057470505016213 0ustar coincoin-web Using AD Version of Atomic Function
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Using AD Version of Atomic Function

Syntax
afun(ax, ay)

Purpose
Given ax , this call computes the corresponding value of ay . If AD<Base> operations are being recorded, it enters the computation as an atomic operation in the recording; see start recording .

ADVector
The type ADVector must be a simple vector class with elements of type AD<Base> ; see Base .

afun
is a atomic_user object and this afun function call is implemented by the atomic_base class.

ax
This argument has prototype
     const ADVector& ax
 and size must be equal to n . It specifies vector x ∈ B n at which an AD<Base> version of y = f ( x ) is to be evaluated; see Base .

ay
This argument has prototype
     ADVector& ay
 and size must be equal to m . The input values of its elements are not specified (must not matter). Upon return, it is an AD<Base> version of y = f ( x ) .

Examples
The following files contain example uses of the AD version of atomic functions during recording: get_started.cpp , norm_sq.cpp , reciprocal.cpp , tangent.cpp , mat_mul.cpp .
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_forward.xml0000644000175200017650000010327313057470505016725 0ustar coincoin-web Atomic Forward Mode
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Atomic Forward Mode

Syntax
ok = afun.forward(p, q, vx, vy, tx, ty)

Purpose
This virtual function is used by atomic_afun to evaluate function values. It is also used buy forward to compute function vales and derivatives.

Implementation
This virtual function must be defined by the atomic_user class. It can just return ok == false (and not compute anything) for values of q > 0 that are greater than those used by your forward mode calculations.

p
The argument p has prototype
     size_t p
 It specifies the lowest order Taylor coefficient that we are evaluating. During calls to atomic_afun , p == 0 .

q
The argument q has prototype
     size_t q
 It specifies the highest order Taylor coefficient that we are evaluating. During calls to atomic_afun , q == 0 .

vx
The forward argument vx has prototype
     const CppAD::vector<bool>& vx
 The case vx.size() > 0 only occurs while evaluating a call to atomic_afun . In this case, p == q == 0 , vx.size() == n , and for j = 0 , … , n -1 , vx[j] is true if and only if ax[j] is a variable in the corresponding call to
     afun(ax, ay)
 If vx.size() == 0 , then vy.size() == 0 and neither of these vectors should be used.

vy
The forward argument vy has prototype
     CppAD::vector<bool>& vy
 If vy.size() == 0 , it should not be used. Otherwise, q == 0 and vy.size() == m . The input values of the elements of vy are not specified (must not matter). Upon return, for j = 0 , … , m -1 , vy[i] is true if and only if ay[i] is a variable (CppAD uses vy to reduce the necessary computations).

tx
The argument tx has prototype
     const CppAD::vector<Base>& tx
 and tx.size() == (q+1)*n . For j = 0 , … , n -1 and k = 0 , … , q , we use the Taylor coefficient notation x j k = tx [ j * ( q + 1 ) + k ] X j ( t ) = x j 0 + x j 1 t 1 + ⋯ + x j q t q Note that superscripts represent an index for x j k and an exponent for t k . Also note that the Taylor coefficients for X ( t ) correspond to the derivatives of X ( t ) at t = 0 in the following way: x j k = 1 k ! X j ( k ) ( 0 )
ty
The argument ty has prototype
     CppAD::vector<Base>& ty
 and tx.size() == (q+1)*m . Upon return, For i = 0 , … , m -1 and k = 0 , … , q , Y i ( t ) = f i [ X ( t ) ] Y i ( t ) = y i 0 + y i 1 t 1 + ⋯ + y i q t q + o ( t q ) ty [ i * ( q + 1 ) + k ] = y i k where o ( t q ) / t q → 0 as t → 0 . Note that superscripts represent an index for y j k and an exponent for t k . Also note that the Taylor coefficients for Y ( t ) correspond to the derivatives of Y ( t ) at t = 0 in the following way: y j k = 1 k ! Y j ( k ) ( 0 ) If p > 0 , for i = 0 , … , m -1 and k = 0 , … , p -1 , the input of ty satisfies ty [ i * ( q + 1 ) + k ] = y i k and hence the corresponding elements need not be recalculated.

ok
If the required results are calculated, ok should be true. Otherwise, it should be false.

Discussion
For example, suppose that q == 2 , and you know how to compute the function f ( x ) , its first derivative f ( 1 ) ( x ) , and it component wise Hessian f i ( 2 ) ( x ) . Then you can compute ty using the following formulas: y i 0 = Y ( 0 ) = f i ( x 0 ) y i 1 = Y ( 1 ) ( 0 ) = f i ( 1 ) ( x 0 ) X ( 1 ) ( 0 ) = f i ( 1 ) ( x 0 ) x 1 y i 2 = 1 2 ! Y ( 2 ) ( 0 ) = 1 2 X ( 1 ) ( 0 ) T f i ( 2 ) ( x 0 ) X ( 1 ) ( 0 ) + 1 2 f i ( 1 ) ( x 0 ) X ( 2 ) ( 0 ) = 1 2 ( x 1 ) T f i ( 2 ) ( x 0 ) x 1 + f i ( 1 ) ( x 0 ) x 2 For i = 0 , … , m -1 , and k = 0 , 1 , 2 , ty [ i * ( q + 1 ) + k ] = y i k
Examples
The file atomic_forward.cpp contains an example and test that uses this routine. It returns true if the test passes and false if it fails.
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_forward.cpp.xml0000644000175200017650000015625413057470505017515 0ustar coincoin-web Atomic Forward: Example and Test
Prev Next atomic_forward.cpp

Atomic Forward: Example and Test

Purpose
This example demonstrates forward mode derivative calculation using an atomic operation.

function
For this example, the atomic function f : R 3 → R 2 is defined by f ( x ) = ( x 2 * x 2 x 0 * x 1 ) The corresponding Jacobian is f ( 1 ) ( x ) = ( 0 0 2 x 2 x 1 x 0 0 ) The Hessians of the component functions are f 0 ( 2 ) ( x ) = ( 0 0 0 0 0 0 0 0 2 ) , f 1 ( 2 ) ( x ) = ( 0 1 0 1 0 0 0 0 0 )
Start Class Definition 
# include <cppad/cppad.hpp>
namespace {          // isolate items below to this file
using CppAD::vector; // abbreviate as vector
//
class atomic_forward : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_forward(const std::string& name) :
     // this example does not use sparsity patterns
     CppAD::atomic_base<double>(name)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {
          size_t q1 = q + 1;
# ifndef NDEBUG
          size_t n = tx.size() / q1;
          size_t m = ty.size() / q1;
# endif
          assert( n == 3 );
          assert( m == 2 );
          assert( p <= q );

          // this example only implements up to second order forward mode
          bool ok = q <= 2;
          if( ! ok )
               return ok;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
          {     vy[0] = vx[2];
               vy[1] = vx[0] || vx[1];
          }
          // ------------------------------------------------------------------
          // Zero forward mode.
          // This case must always be implemented
          // f(x) = [ x_2 * x_2 ]
          //        [ x_0 * x_1 ]
          // y^0  = f( x^0 )
          if( p <= 0 )
          {     // y_0^0 = x_2^0 * x_2^0
               ty[0 * q1 + 0] = tx[2 * q1 + 0] * tx[2 * q1 + 0];
               // y_1^0 = x_0^0 * x_1^0
               ty[1 * q1 + 0] = tx[0 * q1 + 0] * tx[1 * q1 + 0];
          }
          if( q <= 0 )
               return ok;
          // ------------------------------------------------------------------
          // First order one forward mode.
          // This case is needed if first order forward mode is used.
          // f'(x) = [   0,   0, 2 * x_2 ]
          //         [ x_1, x_0,       0 ]
          // y^1 =  f'(x^0) * x^1
          if( p <= 1 )
          {     // y_0^1 = 2 * x_2^0 * x_2^1
               ty[0 * q1 + 1] = 2.0 * tx[2 * q1 + 0] * tx[2 * q1 + 1];
               // y_1^1 = x_1^0 * x_0^1 + x_0^0 * x_1^1
               ty[1 * q1 + 1]  = tx[1 * q1 + 0] * tx[0 * q1 + 1];
               ty[1 * q1 + 1] += tx[0 * q1 + 0] * tx[1 * q1 + 1];
          }
          if( q <= 1 )
               return ok;
          // ------------------------------------------------------------------
          // Second order forward mode.
          // This case is neede if second order forwrd mode is used.
          // f'(x) = [   0,   0, 2 x_2 ]
          //         [ x_1, x_0,     0 ]
          //
          //            [ 0 , 0 , 0 ]                  [ 0 , 1 , 0 ]
          // f_0''(x) = [ 0 , 0 , 0 ]  f_1^{(2)} (x) = [ 1 , 0 , 0 ]
          //            [ 0 , 0 , 2 ]                  [ 0 , 0 , 0 ]
          //
          //  y_0^2 = x^1 * f_0''( x^0 ) x^1 / 2! + f_0'( x^0 ) x^2
          //        = ( x_2^1 * 2.0 * x_2^1 ) / 2!
          //        + 2.0 * x_2^0 * x_2^2
          ty[0 * q1 + 2]  = tx[2 * q1 + 1] * tx[2 * q1 + 1];
          ty[0 * q1 + 2] += 2.0 * tx[2 * q + 0] * tx[2 * q1 + 2];
          //
          //  y_1^2 = x^1 * f_1''( x^0 ) x^1 / 2! + f_1'( x^0 ) x^2
          //        = ( x_1^1 * x_0^1 + x_0^1 * x_1^1) / 2
          //        + x_1^0 * x_0^2 + x_0^0 + x_1^2
          ty[1 * q1 + 2]  = tx[1 * q1 + 1] * tx[0 * q1 + 1];
          ty[1 * q1 + 2] += tx[1 * q1 + 0] * tx[0 * q1 + 2];
          ty[1 * q1 + 2] += tx[0 * q1 + 0] * tx[1 * q1 + 2];
          // ------------------------------------------------------------------
          return ok;
     }
};
}  // End empty namespace

Use Atomic Function 
bool forward(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     //
     // Create the atomic_forward object
     atomic_forward afun("atomic_forward");
     //
     // Create the function f(u)
     //
     // domain space vector
     size_t n  = 3;
     double x_0 = 1.00;
     double x_1 = 2.00;
     double x_2 = 3.00;
     vector< AD<double> > au(n);
     au[0] = x_0;
     au[1] = x_1;
     au[2] = x_2;

     // declare independent variables and start tape recording
     CppAD::Independent(au);

     // range space vector
     size_t m = 2;
     vector< AD<double> > ay(m);

     // call user function
     vector< AD<double> > ax = au;
     afun(ax, ay);

     // create f: u -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (au, ay);  // y = f(u)
     //
     // check function value
     double check = x_2 * x_2;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual( Value(ay[1]) , check,  eps, eps);

     // --------------------------------------------------------------------
     // zero order forward
     //
     vector<double> x0(n), y0(m);
     x0[0] = x_0;
     x0[1] = x_1;
     x0[2] = x_2;
     y0   = f.Forward(0, x0);
     check = x_2 * x_2;
     ok &= NearEqual(y0[0] , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual(y0[1] , check,  eps, eps);
     // --------------------------------------------------------------------
     // first order forward
     //
     // value of Jacobian of f
     double check_jac[] = {
          0.0, 0.0, 2.0 * x_2,
          x_1, x_0,       0.0
     };
     vector<double> x1(n), y1(m);
     // check first order forward mode
     for(size_t j = 0; j < n; j++)
          x1[j] = 0.0;
     for(size_t j = 0; j < n; j++)
     {     // compute partial in j-th component direction
          x1[j] = 1.0;
          y1    = f.Forward(1, x1);
          x1[j] = 0.0;
          // check this direction
          for(size_t i = 0; i < m; i++)
               ok &= NearEqual(y1[i], check_jac[i * n + j], eps, eps);
     }
     // --------------------------------------------------------------------
     // second order forward
     //
     // value of Hessian of f_0
     double check_hes_0[] = {
          0.0, 0.0, 0.0,
          0.0, 0.0, 0.0,
          0.0, 0.0, 2.0
     };
     //
     // value of Hessian of f_1
     double check_hes_1[] = {
          0.0, 1.0, 0.0,
          1.0, 0.0, 0.0,
          0.0, 0.0, 0.0
     };
     vector<double> x2(n), y2(m);
     for(size_t j = 0; j < n; j++)
          x2[j] = 0.0;
     // compute diagonal elements of the Hessian
     for(size_t j = 0; j < n; j++)
     {     // first order forward in j-th direction
          x1[j] = 1.0;
          f.Forward(1, x1);
          y2 = f.Forward(2, x2);
          // check this element of Hessian diagonal
          ok &= NearEqual(y2[0], check_hes_0[j * n + j] / 2.0, eps, eps);
          ok &= NearEqual(y2[1], check_hes_1[j * n + j] / 2.0, eps, eps);
          //
          for(size_t k = 0; k < n; k++) if( k != j )
          {     x1[k] = 1.0;
               f.Forward(1, x1);
               y2 = f.Forward(2, x2);
               //
               // y2 = (H_jj + H_kk + H_jk + H_kj) / 2.0
               // y2 = (H_jj + H_kk) / 2.0 + H_jk
               //
               double H_jj = check_hes_0[j * n + j];
               double H_kk = check_hes_0[k * n + k];
               double H_jk = y2[0] - (H_kk + H_jj) / 2.0;
               ok &= NearEqual(H_jk, check_hes_0[j * n + k], eps, eps);
               //
               H_jj = check_hes_1[j * n + j];
               H_kk = check_hes_1[k * n + k];
               H_jk = y2[1] - (H_kk + H_jj) / 2.0;
               ok &= NearEqual(H_jk, check_hes_1[j * n + k], eps, eps);
               //
               x1[k] = 0.0;
          }
          x1[j] = 0.0;
     }
     // --------------------------------------------------------------------
     return ok;
}
Input File: example/atomic/forward.cpp cppad-20170000.3/doc/atomic_for_sparse_jac.cpp.xml0000644000175200017650000012064313057470505021022 0ustar coincoin-web Atomic Forward Jacobian Sparsity: Example and Test
Prev Next atomic_for_sparse_jac.cpp

Atomic Forward Jacobian Sparsity: Example and Test

Purpose
This example demonstrates calculation of the forward Jacobian sparsity pattern for an atomic operation.

function
For this example, the atomic function f : R 3 → R 2 is defined by f ( x ) = ( x 2 * x 2 x 0 * x 1 ) The corresponding Jacobian is f ( 1 ) ( x ) = ( 0 0 2 x 2 x 1 x 0 0 )
Start Class Definition 
# include <cppad/cppad.hpp>
namespace {          // isolate items below to this file
using CppAD::vector; // abbreviate as vector
//
class atomic_for_sparse_jac : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_for_sparse_jac(const std::string& name) :
     // this example only uses pack sparsty patterns
     CppAD::atomic_base<double>(name, pack_sparsity_enum)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( n == 3 );
          assert( m == 2 );

          // return flag
          bool ok = q == 0;
          if( ! ok )
               return ok;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
          {     vy[0] = vx[2];
               vy[1] = vx[0] || vx[1];
          }

          // Order zero forward mode.
          // This case must always be implemented
          // f(x) = [ x_2 * x_2 ]
          //        [ x_0 * x_1 ]
          assert( p <= 0 );
          if( p <= 0 )
          {     ty[0] = tx[2] * tx[2];
               ty[1] = tx[0] * tx[1];
          }
          return ok;
     }

for_sparse_jac 
     // forward Jacobian sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          size_t                     q ,
          const CppAD::vectorBool&   r ,
          CppAD::vectorBool&         s ,
          const vector<double>&      x )
     {     // This function needed because we are using ForSparseJac
          // with afun.option( CppAD::atomic_base<double>::pack_sparsity_enum )
# ifndef NDEBUG
          size_t n = r.size() / q;
          size_t m = s.size() / q;
# endif
          assert( x.size() == n );
          assert( n == 3 );
          assert( m == 2 );

          // f'(x) = [   0,   0, 2 x_2 ]
          //         [ x_1, x_0,     0 ]

          // sparsity for first row of S(x) = f'(x) * R
          size_t i = 0;
          for(size_t j = 0; j < q; j++)
               s[ i * q + j ] = r[ 2 * q + j ];

          // sparsity for second row of S(x) = f'(x) * R
          i = 1;
          for(size_t j = 0; j < q; j++)
               s[ i * q + j ] = r[ 0 * q + j ] | r[ 1 * q + j];

          return true;
     }
}; // End of atomic_for_sparse_jac class
Use Atomic Function 
bool use_atomic_for_sparse_jac(bool x_1_variable)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     //
     // Create the atomic for_sparse_jac object
     atomic_for_sparse_jac afun("atomic_for_sparse_jac");
     //
     // Create the function f(u)
     //
     // domain space vector
     size_t n  = 3;
     double x_0 = 1.00;
     double x_1 = 2.00;
     double x_2 = 3.00;
     vector< AD<double> > au(n);
     au[0] = x_0;
     au[1] = x_1;
     au[2] = x_2;

     // declare independent variables and start tape recording
     CppAD::Independent(au);

     // range space vector
     size_t m = 2;
     vector< AD<double> > ay(m);

     // call user function
     vector< AD<double> > ax(n);
     ax[0] = au[0];
     ax[2] = au[2];
     if( x_1_variable )
          ax[1] = au[1];
     else
          ax[1] = x_1;
     afun(ax, ay);          // y = [ x_2 * x_2 ,  x_0 * x_1 ]^T

     // create f: u -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (au, ay);  // f(u) = y
     //
     // check function value
     double check = x_2 * x_2;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual( Value(ay[1]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> xq(n), yq(m);
     q     = 0;
     xq[0] = x_0;
     xq[1] = x_1;
     xq[2] = x_2;
     yq    = f.Forward(q, xq);
     check = x_2 * x_2;
     ok &= NearEqual(yq[0] , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual(yq[1] , check,  eps, eps);

     // forward sparse Jacobian
     CppAD::vectorBool r(n * n), s(m * n);
     // r = identity matrix
     for(size_t i = 0; i < n; i++)
          for(size_t j = 0; j < n; j++)
               r[ i * n + j] = i == j;
     s = f.ForSparseJac(n, r);

     // check result
     CppAD::vectorBool check_s(m * n);
     check_s[ 0 * n + 0 ] = false;
     check_s[ 0 * n + 1 ] = false;
     check_s[ 0 * n + 2 ] = true;
     check_s[ 1 * n + 0 ] = true;
     check_s[ 1 * n + 1 ] = x_1_variable;
     check_s[ 1 * n + 2 ] = false;
     //
     for(size_t i = 0; i < m * n; i++)
          ok &= s[ i ] == check_s[ i ];
     //
     return ok;
}
}  // End empty namespace

Test with x_1 Both a Variable and a Parameter 
bool for_sparse_jac(void)
{     bool ok = true;
     // test with x_1 a variable
     ok     &= use_atomic_for_sparse_jac(true);
     // test with x_1 a parameter
     ok     &= use_atomic_for_sparse_jac(false);
     return ok;
}
Input File: example/atomic/for_sparse_jac.cpp cppad-20170000.3/doc/atomic_rev_sparse_jac.cpp.xml0000644000175200017650000012260213057470505021025 0ustar coincoin-web Atomic Reverse Jacobian Sparsity: Example and Test
Prev Next atomic_rev_sparse_jac.cpp

Atomic Reverse Jacobian Sparsity: Example and Test

Purpose
This example demonstrates calculation of the reverse Jacobians sparsity pattern for an atomic operation.

function
For this example, the atomic function f : R 3 → R 2 is defined by f ( x ) = ( x 2 * x 2 x 0 * x 1 ) The corresponding Jacobian is f ( 1 ) ( x ) = ( 0 0 2 x 2 x 1 x 0 0 )
Start Class Definition 
# include <cppad/cppad.hpp>
namespace {          // isolate items below to this file
using CppAD::vector; // abbreviate as vector
//
class atomic_rev_sparse_jac : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_rev_sparse_jac(const std::string& name) :
     // this example only uses pack sparsity patterns
     CppAD::atomic_base<double>(name, pack_sparsity_enum)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( n == 3 );
          assert( m == 2 );

          // return flag
          bool ok = q == 0;
          if( ! ok )
               return ok;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
          {     vy[0] = vx[0];
               vy[1] = vx[0] || vy[0];
          }

          // Order zero forward mode.
          // This case must always be implemented
          // f(x) = [ x_0 * x_0 ]
          //        [ x_0 * x_1 ]
          assert( p <= 0 );
          if( p <= 0 )
          {     ty[0] = tx[2] * tx[2];
               ty[1] = tx[0] * tx[1];
          }
          return ok;
     }

rev_sparse_jac 
     // reverse Jacobian sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          size_t                     q  ,
          const CppAD::vectorBool&   rt ,
          CppAD::vectorBool&         st ,
          const vector<double>&      x  )
     {     // This function needed because we are using RevSparseHes
          // with afun.option( CppAD::atomic_base<double>::pack_sparsity_enum )
# ifndef NDEBUG
          size_t m = rt.size() / q;
          size_t n = st.size() / q;
# endif
          assert( n == x.size() );
          assert( n == 3 );
          assert( m == 2 );

          //           [     0,  x_1 ]
          // f'(x)^T = [     0,  x_0 ]
          //           [ 2 x_2,    0 ]

          // sparsity for first row of S(x)^T = f'(x)^T * R^T
          size_t i = 0;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 1 * q + j ];

          // sparsity for second row of S(x)^T = f'(x)^T * R^T
          i = 1;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 1 * q + j ];

          // sparsity for third row of S(x)^T = f'(x)^T * R^T
          i = 2;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 0 * q + j ];

          return true;
     }
}; // End of atomic_rev_sparse_jac class
Use Atomic Function 
bool use_atomic_rev_sparse_jac(bool x_1_variable)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     //
     // Create the atomic rev_sparse_jac object
     atomic_rev_sparse_jac afun("atomic_rev_sparse_jac");
     //
     // Create the function f(u)
     //
     // domain space vector
     size_t n  = 3;
     double x_0 = 1.00;
     double x_1 = 2.00;
     double x_2 = 3.00;
     vector< AD<double> > au(n);
     au[0] = x_0;
     au[1] = x_1;
     au[2] = x_2;

     // declare independent variables and start tape recording
     CppAD::Independent(au);

     // range space vector
     size_t m = 2;
     vector< AD<double> > ay(m);

     // call user function
     vector< AD<double> > ax(n);
     ax[0] = au[0];
     ax[2] = au[2];
     if( x_1_variable )
          ax[1] = au[1];
     else
          ax[1] = x_1;
     afun(ax, ay);          // y = [ x_2 * x_2 ,  x_0 * x_1 ]^T

     // create f: u -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (au, ay);  // f(u) = y
     //
     // check function value
     double check = x_2 * x_2;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual( Value(ay[1]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> xq(n), yq(m);
     q     = 0;
     xq[0] = x_0;
     xq[1] = x_1;
     xq[2] = x_2;
     yq    = f.Forward(q, xq);
     check = x_2 * x_2;
     ok &= NearEqual(yq[0] , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual(yq[1] , check,  eps, eps);

     // forward sparse Jacobian
     CppAD::vectorBool r(m * m), s(m * n);
     // r = identity matrix
     for(size_t i = 0; i < m; i++)
          for(size_t j = 0; j < m; j++)
               r[ i * m + j] = i == j;
     s = f.RevSparseJac(m, r);

     // check result
     CppAD::vectorBool check_s(m * n);
     check_s[ 0 * n + 0 ] = false;
     check_s[ 0 * n + 1 ] = false;
     check_s[ 0 * n + 2 ] = true;
     check_s[ 1 * n + 0 ] = true;
     check_s[ 1 * n + 1 ] = x_1_variable;
     check_s[ 1 * n + 2 ] = false;
     //
     for(size_t i = 0; i < m * n; i++)
          ok &= s[ i ] == check_s[ i ];
     //
     return ok;
}
}  // End empty namespace

Test with x_1 Both a Variable and a Parameter 
bool rev_sparse_jac(void)
{     bool ok = true;
     // test with x_1 a variable
     ok     &= use_atomic_rev_sparse_jac(true);
     // test with x_1 a parameter
     ok     &= use_atomic_rev_sparse_jac(false);
     return ok;
}
Input File: example/atomic/rev_sparse_jac.cpp cppad-20170000.3/doc/atomic_for_sparse_hes.cpp.xml0000644000175200017650000015752113057470505021051 0ustar coincoin-web Atomic Forward Hessian Sparsity: Example and Test
Prev Next atomic_for_sparse_hes.cpp

Atomic Forward Hessian Sparsity: Example and Test

Purpose
This example demonstrates calculation of the forward Hessian sparsity pattern for an atomic operation.

function
For this example, the atomic function f : R 3 → R 2 is defined by f ( x ) = ( x 2 * x 2 x 0 * x 1 ) The Hessians of the component functions are f 0 ( 2 ) ( x ) = ( 0 0 0 0 0 0 0 0 2 ) , f 1 ( 2 ) ( x ) = ( 0 1 0 1 0 0 0 0 0 )
Start Class Definition 
# include <cppad/cppad.hpp>
namespace {          // isolate items below to this file
using CppAD::vector; // abbreviate as vector
//
class atomic_for_sparse_hes : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_for_sparse_hes(const std::string& name) :
     // this example only uses pack sparsity patterns
     CppAD::atomic_base<double>(name, pack_sparsity_enum)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( n == 3 );
          assert( m == 2 );

          // return flag
          bool ok = q == 0;
          if( ! ok )
               return ok;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
          {     vy[0] = vx[0];
               vy[1] = vx[0] || vy[0];
          }

          // Order zero forward mode.
          // This case must always be implemented
          // f(x) = [ x_0 * x_0 ]
          //        [ x_0 * x_1 ]
          assert( p <= 0 );
          if( p <= 0 )
          {     ty[0] = tx[2] * tx[2];
               ty[1] = tx[0] * tx[1];
          }
          return ok;
     }

for_sparse_jac 
     // forward Jacobian sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          size_t                     q ,
          const CppAD::vectorBool&   r ,
          CppAD::vectorBool&         s ,
          const vector<double>&      x )
     {     // This function needed because we are using ForSparseHes
          // with afun.option( CppAD::atomic_base<double>::pack_sparsity_enum )
# ifndef NDEBUG
          size_t n = r.size() / q;
          size_t m = s.size() / q;
# endif
          assert( x.size() == n );
          assert( n == 3 );
          assert( m == 2 );


          // f'(x) = [   0,   0, 2 x_2 ]
          //         [ x_1, x_0,     0 ]

          // sparsity for first row of S(x) = f'(x) * R
          size_t i = 0;
          for(size_t j = 0; j < q; j++)
               s[ i * q + j ] = r[ 2 * q + j ];

          // sparsity for second row of S(x) = f'(x) * R
          i = 1;
          for(size_t j = 0; j < q; j++)
               s[ i * q + j ] = r[ 0 * q + j ] | r[ 1 * q + j];

          return true;
     }

rev_sparse_jac 
     // reverse Jacobian sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          size_t                     q  ,
          const CppAD::vectorBool&   rt ,
          CppAD::vectorBool&         st ,
          const vector<double>&      x  )
     {     // This function needed because we are using ForSparseHes
          // with afun.option( CppAD::atomic_base<double>::pack_sparsity_enum )
# ifndef NDEBUG
          size_t m = rt.size() / q;
          size_t n = st.size() / q;
# endif
          assert( x.size() == n );
          assert( n == 3 );
          assert( m == 2 );

          //           [     0,  x_1 ]
          // f'(x)^T = [     0,  x_0 ]
          //           [ 2 x_2,    0 ]

          // sparsity for first row of S(x)^T = f'(x)^T * R^T
          size_t i = 0;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 1 * q + j ];

          // sparsity for second row of S(x)^T = f'(x)^T * R^T
          i = 1;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 1 * q + j ];

          // sparsity for third row of S(x)^T = f'(x)^T * R^T
          i = 2;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 0 * q + j ];

          return true;
     }

for_sparse_hes 
     // forward Hessian sparsity routine called by CppAD
     virtual bool for_sparse_hes(
          const vector<bool>&   vx,
          const vector<bool>&   r ,
          const vector<bool>&   s ,
          CppAD::vectorBool&    h ,
          const vector<double>& x )
     {     // This function needed because we are using RevSparseHes
          // with afun.option( CppAD::atomic_base<double>::pack_sparsity_enum )
          size_t n = r.size();
# ifndef NDEBUG
          size_t m = s.size();
# endif
          assert( x.size() == n );
          assert( n == 3 );
          assert( m == 2 );
          assert( h.size() == n * n );

          //            [ 0 , 0 , 0 ]                  [ 0 , 1 , 0 ]
          // f_0''(x) = [ 0 , 0 , 0 ]  f_1^{(2)} (x) = [ 1 , 0 , 0 ]
          //            [ 0 , 0 , 2 ]                  [ 0 , 0 , 0 ]

          // initial entire matrix as false
          for(size_t i = 0; i < n * n; i++)
               h[i] = false;

          // component (2, 2)
          h[ 2 * n + 2 ] = s[0] & r[2];

          // components (1, 0) and (0, 1)
          h[ 1 * n + 0 ] = s[1] & r[0] & r[1];
          h[ 0 * n + 1 ] = s[1] & r[0] & r[1];

          return true;
     }
}; // End of atomic_for_sparse_hes class
Use Atomic Function 
bool use_atomic_for_sparse_hes(bool x_1_variable)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     //
     // Create the atomic for_sparse_hes object
     atomic_for_sparse_hes afun("atomic_for_sparse_hes");
     //
     // Create the function f(u)
     //
     // domain space vector
     size_t n  = 3;
     double x_0 = 1.00;
     double x_1 = 2.00;
     double x_2 = 3.00;
     vector< AD<double> > au(n);
     au[0] = x_0;
     au[1] = x_1;
     au[2] = x_2;

     // declare independent variables and start tape recording
     CppAD::Independent(au);

     // range space vector
     size_t m = 2;
     vector< AD<double> > ay(m);

     // call user function
     vector< AD<double> > ax(n);
     ax[0] = au[0];
     ax[2] = au[2];
     if( x_1_variable )
          ax[1] = au[1];
     else
          ax[1] = x_1;
     afun(ax, ay);          // y = [ x_2 * x_2 ,  x_0 * x_1 ]^T

     // create f: u -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (au, ay);  // f(u) = y
     //
     // check function value
     double check = x_2 * x_2;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual( Value(ay[1]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> xq(n), yq(m);
     q     = 0;
     xq[0] = x_0;
     xq[1] = x_1;
     xq[2] = x_2;
     yq    = f.Forward(q, xq);
     check = x_2 * x_2;
     ok &= NearEqual(yq[0] , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual(yq[1] , check,  eps, eps);

     // forward sparse Hessian
     CppAD::vectorBool r(n), s(m), h(n * n);
     for(size_t j = 0; j < n; j++)
          r[j] = true;
     for(size_t i = 0; i < m; i++)
          s[i] = true;
     h = f.ForSparseHes(r, s);

     // check result
     CppAD::vectorBool check_h(n * n);
     for(size_t i = 0; i < n * n; i++)
          check_h[i] = false;
     check_h[ 2 * n + 2 ] = true;
     if( x_1_variable )
     {     check_h[0 * n + 1] = true;
          check_h[1 * n + 0] = true;
     }
     for(size_t i = 0; i < n * n; i++)
          ok &= h[ i ] == check_h[ i ];
     //
     return ok;
}
}  // End empty namespace

Test with x_1 Both a Variable and a Parameter 
bool for_sparse_hes(void)
{     bool ok = true;
     // test with x_1 a variable
     ok     &= use_atomic_for_sparse_hes(true);
     // test with x_1 a parameter
     ok     &= use_atomic_for_sparse_hes(false);
     return ok;
}
Input File: example/atomic/for_sparse_hes.cpp cppad-20170000.3/doc/atomic_rev_sparse_hes.cpp.xml0000644000175200017650000017722213057470505021057 0ustar coincoin-web Atomic Reverse Hessian Sparsity: Example and Test
Prev Next atomic_rev_sparse_hes.cpp

Atomic Reverse Hessian Sparsity: Example and Test

Purpose
This example demonstrates calculation of the reverse Hessian sparsity pattern for an atomic operation.

function
For this example, the atomic function f : R 3 → R 2 is defined by f ( x ) = ( x 2 * x 2 x 0 * x 1 ) The Hessians of the component functions are f 0 ( 2 ) ( x ) = ( 0 0 0 0 0 0 0 0 2 ) , f 1 ( 2 ) ( x ) = ( 0 1 0 1 0 0 0 0 0 )
Start Class Definition 
# include <cppad/cppad.hpp>
namespace {          // isolate items below to this file
using CppAD::vector; // abbreviate as vector
//
class atomic_rev_sparse_hes : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_rev_sparse_hes(const std::string& name) :
     // this example only uses pack sparsity patterns
     CppAD::atomic_base<double>(name, pack_sparsity_enum)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( n == 3 );
          assert( m == 2 );

          // return flag
          bool ok = q == 0;
          if( ! ok )
               return ok;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
          {     vy[0] = vx[0];
               vy[1] = vx[0] || vy[0];
          }

          // Order zero forward mode.
          // This case must always be implemented
          // f(x) = [ x_0 * x_0 ]
          //        [ x_0 * x_1 ]
          assert( p <= 0 );
          if( p <= 0 )
          {     ty[0] = tx[2] * tx[2];
               ty[1] = tx[0] * tx[1];
          }
          return ok;
     }

for_sparse_jac 
     // forward Jacobian sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          size_t                     q ,
          const CppAD::vectorBool&   r ,
          CppAD::vectorBool&         s ,
          const vector<double>&      x )
     {     // This function needed because we are using ForSparseHes
          // with afun.option( CppAD::atomic_base<double>::pack_sparsity_enum )
# ifndef NDEBUG
          size_t n = r.size() / q;
          size_t m = s.size() / q;
# endif
          assert( n == x.size() );
          assert( n == 3 );
          assert( m == 2 );


          // f'(x) = [   0,   0, 2 x_2 ]
          //         [ x_1, x_0,     0 ]

          // sparsity for first row of S(x) = f'(x) * R
          size_t i = 0;
          for(size_t j = 0; j < q; j++)
               s[ i * q + j ] = r[ 2 * q + j ];

          // sparsity for second row of S(x) = f'(x) * R
          i = 1;
          for(size_t j = 0; j < q; j++)
               s[ i * q + j ] = r[ 0 * q + j ] | r[ 1 * q + j];

          return true;
     }

rev_sparse_jac 
     // reverse Jacobian sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          size_t                     q  ,
          const CppAD::vectorBool&   rt ,
          CppAD::vectorBool&         st ,
          const vector<double>&      x  )
     {     // This function needed because we are using ForSparseHes
          // with afun.option( CppAD::atomic_base<double>::pack_sparsity_enum )
# ifndef NDEBUG
          size_t m = rt.size() / q;
          size_t n = st.size() / q;
# endif
          assert( n == x.size() );
          assert( n == 3 );
          assert( m == 2 );

          //           [     0,  x_1 ]
          // f'(x)^T = [     0,  x_0 ]
          //           [ 2 x_2,    0 ]

          // sparsity for first row of S(x)^T = f'(x)^T * R^T
          size_t i = 0;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 1 * q + j ];

          // sparsity for second row of S(x)^T = f'(x)^T * R^T
          i = 1;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 1 * q + j ];

          // sparsity for third row of S(x)^T = f'(x)^T * R^T
          i = 2;
          for(size_t j = 0; j < q; j++)
               st[ i * q + j ] = rt[ 0 * q + j ];

          return true;
     }

rev_sparse_hes 
     // reverse Hessian sparsity routine called by CppAD
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
          vector<bool>&                         t ,
          size_t                                q ,
          const CppAD::vectorBool&              r ,
          const CppAD::vectorBool&              u ,
          CppAD::vectorBool&                    v ,
          const vector<double>&                 x )
     {     // This function needed because we are using RevSparseHes
          // with afun.option( CppAD::atomic_base<double>::pack_sparsity_enum )
# ifndef NDEBUG
          size_t m = s.size();
          size_t n = t.size();
# endif
          assert( x.size() == n );
          assert( r.size() == n * q );
          assert( u.size() == m * q );
          assert( v.size() == n * q );
          assert( n == 3 );
          assert( m == 2 );
          //
          // f'(x) = [   0,   0, 2 x_2 ]
          //         [ x_1, x_0,     0 ]
          //
          //            [ 0 , 0 , 0 ]                  [ 0 , 1 , 0 ]
          // f_0''(x) = [ 0 , 0 , 0 ]  f_1^{(2)} (x) = [ 1 , 0 , 0 ]
          //            [ 0 , 0 , 2 ]                  [ 0 , 0 , 0 ]
          // ------------------------------------------------------------------
          // sparsity pattern for row vector T(x) = S(x) * f'(x)
          t[0] = s[1];
          t[1] = s[1];
          t[2] = s[0];
          // ------------------------------------------------------------------
          // sparsity pattern for W(x) = f'(x)^T * U(x)
          for(size_t j = 0; j < q; j++)
          {     v[ 0 * q + j ] = u[ 1 * q + j ];
               v[ 1 * q + j ] = u[ 1 * q + j ];
               v[ 2 * q + j ] = u[ 0 * q + j ];
          }
          // ------------------------------------------------------------------
          // sparsity pattern for Q(x) = W(x) + S_0 (x) * f_0^{(2)} (x) * R
          if( s[0] )
          {     for(size_t j = 0; j < q; j++)
               {     // cannot use |= with vectorBool
                    v[ 2 * q + j ] = bool(v[ 2 * q + j ]) | bool(r[ 2 * q + j ]);
               }
          }
          // ------------------------------------------------------------------
          // sparsity pattern for V(x) = Q(x) + S_1 (x) * f_1^{(2)} (x) * R
          if( s[1] )
          {     for(size_t j = 0; j < q; j++)
               {     // cannot use |= with vectorBool
                    v[ 0 * q + j ] = bool(v[ 0 * q + j ]) | bool(r[ 1 * q + j ]);
                    v[ 1 * q + j ] = bool(v[ 1 * q + j ]) | bool(r[ 0 * q + j ]);
               }
          }
          return true;
     }
}; // End of atomic_rev_sparse_hes class
Use Atomic Function 
bool use_atomic_rev_sparse_hes(bool x_1_variable)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     //
     // Create the atomic rev_sparse_hes object
     atomic_rev_sparse_hes afun("atomic_rev_sparse_hes");
     //
     // Create the function f(u)
     //
     // domain space vector
     size_t n  = 3;
     double x_0 = 1.00;
     double x_1 = 2.00;
     double x_2 = 3.00;
     vector< AD<double> > au(n);
     au[0] = x_0;
     au[1] = x_1;
     au[2] = x_2;

     // declare independent variables and start tape recording
     CppAD::Independent(au);

     // range space vector
     size_t m = 2;
     vector< AD<double> > ay(m);

     // call user function
     vector< AD<double> > ax(n);
     ax[0] = au[0];
     ax[2] = au[2];
     if( x_1_variable )
          ax[1] = au[1];
     else
          ax[1] = x_1;
     afun(ax, ay);          // y = [ x_2 * x_2 ,  x_0 * x_1 ]^T

     // create f: u -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (au, ay);  // f(u) = y
     //
     // check function value
     double check = x_2 * x_2;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual( Value(ay[1]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> xq(n), yq(m);
     q     = 0;
     xq[0] = x_0;
     xq[1] = x_1;
     xq[2] = x_2;
     yq    = f.Forward(q, xq);
     check = x_2 * x_2;
     ok &= NearEqual(yq[0] , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual(yq[1] , check,  eps, eps);

     // reverse sparse Hessian
     CppAD::vectorBool r(n * n), s(m), h(n * n);
     for(size_t i = 0; i < n; i++)
     {     for(size_t j = 0; j < n; j++)
               r[i * n + j] = i == j;
     }
     for(size_t i = 0; i < m; i++)
          s[i] = true;
     f.ForSparseJac(n, r);
     h = f.RevSparseHes(n, s);

     // check result
     CppAD::vectorBool check_h(n * n);
     for(size_t i = 0; i < n * n; i++)
          check_h[i] = false;
     check_h[ 2 * n + 2 ] = true;
     if( x_1_variable )
     {     check_h[0 * n + 1] = true;
          check_h[1 * n + 0] = true;
     }
     for(size_t i = 0; i < n * n; i++)
          ok &= h[ i ] == check_h[ i ];
     //
     return ok;
}
}  // End empty namespace

Test with x_1 Both a Variable and a Parameter 
bool rev_sparse_hes(void)
{     bool ok = true;
     // test with x_1 a variable
     ok     &= use_atomic_rev_sparse_hes(true);
     // test with x_1 a parameter
     ok     &= use_atomic_rev_sparse_hes(false);
     return ok;
}
Input File: example/atomic/rev_sparse_hes.cpp cppad-20170000.3/doc/atomic_get_started.cpp.xml0000644000175200017650000005161313057470505020347 0ustar coincoin-web Getting Started with Atomic Operations: Example and Test
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Getting Started with Atomic Operations: Example and Test

Purpose
This example demonstrates the minimal amount of information necessary for a atomic_base operation.

Start Class Definition 
# include <cppad/cppad.hpp>
namespace {          // isolate items below to this file
using CppAD::vector; // abbreviate as vector
class atomic_get_started : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_get_started(const std::string& name) :
     // this example does not use any sparsity patterns
     CppAD::atomic_base<double>(name)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
                vector<bool>&      vy ,
          const vector<double>&    tx ,
                vector<double>&    ty
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( n == 1 );
          assert( m == 1 );

          // return flag
          bool ok = q == 0;
          if( ! ok )
               return ok;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
               vy[0] = vx[0];

          // Order zero forward mode.
          // This case must always be implemented
          // y^0 = f( x^0 ) = 1 / x^0
          double f = 1. / tx[0];
          if( p <= 0 )
               ty[0] = f;
          return ok;
     }

End Class Definition 

}; // End of atomic_get_started class
}  // End empty namespace
Use Atomic Function 
bool get_started(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

Constructor 

     // Create the atomic get_started object
     atomic_get_started afun("atomic_get_started");

Recording 
     // Create the function f(x)
     //
     // domain space vector
     size_t n  = 1;
     double  x0 = 0.5;
     vector< AD<double> > ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     vector< AD<double> > ay(m);

     // call user function and store get_started(x) in au[0]
     vector< AD<double> > au(m);
     afun(ax, au);        // u = 1 / x

     // now use AD division to invert to invert the operation
     ay[0] = 1.0 / au[0]; // y = 1 / u = x

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (ax, ay);  // f(x) = x

forward 
     // check function value
     double check = x0;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> x_q(n), y_q(m);
     q      = 0;
     x_q[0] = x0;
     y_q    = f.Forward(q, x_q);
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     return ok;
}
Input File: example/atomic/get_started.cpp cppad-20170000.3/doc/_vecad_xml.js0000644000175200017650000000366413057470506015646 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'vecad.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down0 = [ 'vec_ad.cpp.xml' ]; var list_current0 = [ 'vecad.xml#Syntax', 'vecad.xml#Purpose', 'vecad.xml#Alternatives', 'vecad.xml#VecAD<Base>::reference', 'vecad.xml#VecAD<Base>::reference.Exceptions', 'vecad.xml#Constructor', 'vecad.xml#Constructor.v', 'vecad.xml#n', 'vecad.xml#size', 'vecad.xml#size_t Indexing', 'vecad.xml#size_t Indexing.i', 'vecad.xml#size_t Indexing.b', 'vecad.xml#AD Indexing', 'vecad.xml#AD Indexing.x', 'vecad.xml#AD Indexing.r', 'vecad.xml#Example', 'vecad.xml#Speed and Memory' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/atomic_reverse.xml0000644000175200017650000010550513057470505016734 0ustar coincoin-web Atomic Reverse Mode
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Atomic Reverse Mode

Syntax
ok = afun.reverse(q, tx, ty, px, py)

Purpose
This function is used by reverse to compute derivatives.

Implementation
If you are using reverse mode, this virtual function must be defined by the atomic_user class. It can just return ok == false (and not compute anything) for values of q that are greater than those used by your reverse mode calculations.

q
The argument q has prototype
     size_t q
 It specifies the highest order Taylor coefficient that computing the derivative of.

tx
The argument tx has prototype
     const CppAD::vector<Base>& tx
 and tx.size() == (q+1)*n . For j = 0 , … , n -1 and k = 0 , … , q , we use the Taylor coefficient notation x j k = tx [ j * ( q + 1 ) + k ] X j ( t ) = x j 0 + x j 1 t 1 + ⋯ + x j q t q Note that superscripts represent an index for x j k and an exponent for t k . Also note that the Taylor coefficients for X ( t ) correspond to the derivatives of X ( t ) at t = 0 in the following way: x j k = 1 k ! X j ( k ) ( 0 )
ty
The argument ty has prototype
     const CppAD::vector<Base>& ty
 and tx.size() == (q+1)*m . For i = 0 , … , m -1 and k = 0 , … , q , we use the Taylor coefficient notation Y i ( t ) = f i [ X ( t ) ] Y i ( t ) = y i 0 + y i 1 t 1 + ⋯ + y i q t q + o ( t q ) y i k = ty [ i * ( q + 1 ) + k ] where o ( t q ) / t q → 0 as t → 0 . Note that superscripts represent an index for y j k and an exponent for t k . Also note that the Taylor coefficients for Y ( t ) correspond to the derivatives of Y ( t ) at t = 0 in the following way: y j k = 1 k ! Y j ( k ) ( 0 )
F
We use the notation { x j k } ∈ B n × ( q + 1 ) for { x j k : j = 0 , … , n -1 , k = 0 , … , q } We use the notation { y i k } ∈ B m × ( q + 1 ) for { y i k : i = 0 , … , m -1 , k = 0 , … , q } We define the function F : B n × ( q + 1 ) → B m × ( q + 1 ) by y i k = F i k [ { x j k } ] Note that F i 0 ( { x j k } ) = f i ( X ( 0 ) ) = f i ( x 0 ) We also note that F i ℓ ( { x j k } ) is a function of x 0 , … , x ℓ and is determined by the derivatives of f i ( x ) up to order ℓ .

G, H
We use G : B m × ( q + 1 ) → B to denote an arbitrary scalar valued function of { y i k } . We use H : B n × ( q + 1 ) → B defined by H ( { x j k } ) = G [ F ( { x j k } ) ]
py
The argument py has prototype
     const CppAD::vector<Base>& py
 and py.size() == m * (q+1) . For i = 0 , … , m -1 , k = 0 , … , q , py [ i * ( q + 1 ) + k ] = ∂ G / ∂ y i k
px
The px has prototype
     CppAD::vector<Base>& px
 and px.size() == n * (q+1) . The input values of the elements of px are not specified (must not matter). Upon return, for j = 0 , … , n -1 and ℓ = 0 , … , q , px [ j * ( q + 1 ) + ℓ ] = ∂ H / ∂ x j ℓ = ( ∂ G / ∂ { y i k } ) · ( ∂ { y i k } / ∂ x j ℓ ) = ∑ k = 0 q ∑ i = 0 m -1 ( ∂ G / ∂ y i k ) ( ∂ y i k / ∂ x j ℓ ) = ∑ k = ℓ q ∑ i = 0 m -1 py [ i * ( q + 1 ) + k ] ( ∂ F i k / ∂ x j ℓ ) Note that we have used the fact that for k < ℓ , ∂ F i k / ∂ x j ℓ = 0 .

ok
The return value ok has prototype
     bool ok
 If it is true, the corresponding evaluation succeeded, otherwise it failed.

Examples
The file atomic_forward.cpp contains an example and test that uses this routine. It returns true if the test passes and false if it fails.
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_for_sparse_jac.xml0000644000175200017650000003632313057470505020242 0ustar coincoin-web Atomic Forward Jacobian Sparsity Patterns
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Atomic Forward Jacobian Sparsity Patterns

Syntax
ok = afun.for_sparse_jac(q, r, s, x)
Deprecated 2016-06-27
ok = afun.for_sparse_jac(q, r, s)
Purpose
This function is used by ForSparseJac to compute Jacobian sparsity patterns. For a fixed matrix R ∈ B n × q , the Jacobian of f ( x + R * u ) with respect to u ∈ B q is S ( x ) = f ( 1 ) ( x ) * R Given a sparsity pattern for R , for_sparse_jac computes a sparsity pattern for S ( x ) .

Implementation
If you are using ForSparseJac , ForSparseHes , or RevSparseHes , one of the versions of this virtual function must be defined by the atomic_user class.

q
The argument q has prototype
     size_t q
 It specifies the number of columns in R ∈ B n × q and the Jacobian S ( x ) ∈ B m × q .

r
This argument has prototype
     const atomic_sparsity& r
 and is a atomic_sparsity pattern for R ∈ B n × q .

s
This argument has prototype
     atomic_sparsity& s
 The input values of its elements are not specified (must not matter). Upon return, s is a atomic_sparsity pattern for S ( x ) ∈ B m × q .

x
The argument has prototype
     const CppAD::vector<Base>& x
 and size is equal to the n . This is the Value value corresponding to the parameters in the vector ax (when the atomic function was called). To be specific, if
     if( Parameter(ax[i]) == true )
          x[i] = Value( ax[i] );
     else
          x[i] = CppAD::numeric_limits<Base>::quiet_NaN();
 The version of this function with out the x argument is deprecated; i.e., you should include the argument even if you do not use it.

ok
The return value ok has prototype
     bool ok
 If it is true, the corresponding evaluation succeeded, otherwise it failed.

Examples
The file atomic_for_sparse_jac.cpp contains an example and test that uses this routine. It returns true if the test passes and false if it fails.
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_rev_sparse_jac.xml0000644000175200017650000003713413057470505020251 0ustar coincoin-web Atomic Reverse Jacobian Sparsity Patterns
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Atomic Reverse Jacobian Sparsity Patterns

Syntax
ok = afun.rev_sparse_jac(q, rt, st, x)
Deprecated 2016-06-27
ok = afun.rev_sparse_jac(q, rt, st)
Purpose
This function is used by RevSparseJac to compute Jacobian sparsity patterns. If you are using RevSparseJac , one of the versions of this virtual function must be defined by the atomic_user class.

For a fixed matrix R ∈ B q × m , the Jacobian of R * f ( x ) with respect to x ∈ B n is S ( x ) = R * f ( 1 ) ( x ) Given a sparsity pattern for R , rev_sparse_jac computes a sparsity pattern for S ( x ) .

Implementation
If you are using RevSparseJac or ForSparseHes , this virtual function must be defined by the atomic_user class.

q
The argument q has prototype
     size_t q
 It specifies the number of rows in R ∈ B q × m and the Jacobian S ( x ) ∈ B q × n .

rt
This argument has prototype
     const atomic_sparsity& rt
 and is a atomic_sparsity pattern for R T ∈ B m × q .

st
This argument has prototype
     atomic_sparsity& st
 The input value of its elements are not specified (must not matter). Upon return, s is a atomic_sparsity pattern for S ( x ) T ∈ B n × q .

x
The argument has prototype
     const CppAD::vector<Base>& x
 and size is equal to the n . This is the Value corresponding to the parameters in the vector ax (when the atomic function was called). To be specific, if
     if( Parameter(ax[i]) == true )
          x[i] = Value( ax[i] );
     else
          x[i] = CppAD::numeric_limits<Base>::quiet_NaN();
 The version of this function with out the x argument is deprecated; i.e., you should include the argument even if you do not use it.

ok
The return value ok has prototype
     bool ok
 If it is true, the corresponding evaluation succeeded, otherwise it failed.

Examples
The file atomic_rev_sparse_jac.cpp contains an example and test that uses this routine. It returns true if the test passes and false if it fails.
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_for_sparse_hes.xml0000644000175200017650000004127013057470505020261 0ustar coincoin-web Atomic Forward Hessian Sparsity Patterns
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Atomic Forward Hessian Sparsity Patterns

Syntax
ok = afun.for_sparse_hes(vx, r, s, h, x)

Deprecated 2016-06-27
ok = afun.for_sparse_hes(vx, r, s, h)

Purpose
This function is used by ForSparseHes to compute Hessian sparsity patterns. If you are using ForSparseHes , one of the versions of this virtual function must be defined by the atomic_user class.

Given a sparsity pattern for a diagonal matrix R ∈ B n × n , and a row vector S ∈ B 1 × m , this routine computes the sparsity pattern for H ( x ) = R T · ( S · f ) ( 2 ) ( x ) · R
Implementation
If you are using and ForSparseHes , this virtual function must be defined by the atomic_user class.

vx
The argument vx has prototype
     const CppAD:vector<bool>& vx
 vx.size() == n , and for j = 0 , … , n -1 , vx[j] is true if and only if ax[j] is a variable in the corresponding call to
     afun(ax, ay)
r
This argument has prototype
     const CppAD:vector<bool>& r
 and is a atomic_sparsity pattern for the diagonal of R ∈ B n × n .

s
The argument s has prototype
     const CppAD:vector<bool>& s
 and its size is m . It is a sparsity pattern for S ∈ B 1 × m .

h
This argument has prototype
     atomic_sparsity& h
 The input value of its elements are not specified (must not matter). Upon return, h is a atomic_sparsity pattern for H ( x ) ∈ B n × n which is defined above.

x
The argument has prototype
     const CppAD::vector<Base>& x
 and size is equal to the n . This is the Value value corresponding to the parameters in the vector ax (when the atomic function was called). To be specific, if
     if( Parameter(ax[i]) == true )
          x[i] = Value( ax[i] );
     else
          x[i] = CppAD::numeric_limits<Base>::quiet_NaN();
 The version of this function with out the x argument is deprecated; i.e., you should include the argument even if you do not use it.

Examples
The file atomic_for_sparse_hes.cpp contains an example and test that uses this routine. It returns true if the test passes and false if it fails.
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_rev_sparse_hes.xml0000644000175200017650000007645513057470505020304 0ustar coincoin-web Atomic Reverse Hessian Sparsity Patterns
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Atomic Reverse Hessian Sparsity Patterns

Syntax
ok = afun.rev_sparse_hes(vx, s, t, q, r, u, v, x)

Deprecated 2016-06-27
ok = afun.rev_sparse_hes(vx, s, t, q, r, u, v)

Purpose
This function is used by RevSparseHes to compute Hessian sparsity patterns. If you are using RevSparseHes to compute one of the versions of this virtual function muse be defined by the atomic_user class.

There is an unspecified scalar valued function g : B m → B . Given a sparsity pattern for R ∈ B n × q , and information about the function z = g ( y ) , this routine computes the sparsity pattern for V ( x ) = ( g ∘ f ) ( 2 ) ( x ) R
Implementation
If you are using and RevSparseHes , this virtual function must be defined by the atomic_user class.

vx
The argument vx has prototype
     const CppAD:vector<bool>& vx
 vx.size() == n , and for j = 0 , … , n -1 , vx[j] is true if and only if ax[j] is a variable in the corresponding call to
     afun(ax, ay)
s
The argument s has prototype
     const CppAD:vector<bool>& s
 and its size is m . It is a sparsity pattern for S ( x ) = g ( 1 ) [ f ( x ) ] ∈ B 1 × m .

t
This argument has prototype
     CppAD:vector<bool>& t
 and its size is m . The input values of its elements are not specified (must not matter). Upon return, t is a sparsity pattern for T ( x ) ∈ B 1 × n where T ( x ) = ( g ∘ f ) ( 1 ) ( x ) = S ( x ) * f ( 1 ) ( x )
q
The argument q has prototype
     size_t q
 It specifies the number of columns in R ∈ B n × q , U ( x ) ∈ B m × q , and V ( x ) ∈ B n × q .

r
This argument has prototype
     const atomic_sparsity& r
 and is a atomic_sparsity pattern for R ∈ B n × q .

u
This argument has prototype
     const atomic_sparsity& u
 and is a atomic_sparsity pattern for U ( x ) ∈ B m × q which is defined by U ( x ) = { ∂ u { ∂ y g [ y + f ( 1 ) ( x ) R u ] } y = f ( x ) } u = 0 = ∂ u { g ( 1 ) [ f ( x ) + f ( 1 ) ( x ) R u ] } u = 0 = g ( 2 ) [ f ( x ) ] f ( 1 ) ( x ) R
v
This argument has prototype
     atomic_sparsity& v
 The input value of its elements are not specified (must not matter). Upon return, v is a atomic_sparsity pattern for V ( x ) ∈ B n × q which is defined by V ( x ) = ∂ u [ ∂ x ( g ∘ f ) ( x + R u ) ] u = 0 = ∂ u [ ( g ∘ f ) ( 1 ) ( x + R u ) ] u = 0 = ( g ∘ f ) ( 2 ) ( x ) R = f ( 1 ) ( x ) T g ( 2 ) [ f ( x ) ] f ( 1 ) ( x ) R + ∑ i = 1 m g i ( 1 ) [ f ( x ) ] f i ( 2 ) ( x ) R = f ( 1 ) ( x ) T U ( x ) + ∑ i = 1 m S i ( x ) f i ( 2 ) ( x ) R
x
The argument has prototype
     const CppAD::vector<Base>& x
 and size is equal to the n . This is the Value value corresponding to the parameters in the vector ax (when the atomic function was called). To be specific, if
     if( Parameter(ax[i]) == true )
          x[i] = Value( ax[i] );
     else
          x[i] = CppAD::numeric_limits<Base>::quiet_NaN();
 The version of this function with out the x argument is deprecated; i.e., you should include the argument even if you do not use it.

Examples
The file atomic_rev_sparse_hes.cpp contains an example and test that uses this routine. It returns true if the test passes and false if it fails.
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_base_clear.xml0000644000175200017650000001143713057470505017341 0ustar coincoin-web Free Static Variables
Prev Next atomic_base_clear

Free Static Variables

Syntax
atomic_base<Base>::clear()

Purpose
Each atomic_base objects holds onto work space in order to avoid repeated memory allocation calls and thereby increase speed (until it is deleted). If an the atomic_base object is global or static because, the it does not get deleted. This is a problem when using thread_alloc free_all to check that all allocated memory has been freed. Calling this clear function will free all the memory currently being held onto by the atomic_base<Base> class.

Future Use
If there is future use of an atomic_base object, after a call to clear, the work space will be reallocated and held onto.

Restriction
This routine cannot be called while in parallel execution mode.
Input File: cppad/core/atomic_base.hpp cppad-20170000.3/doc/atomic_norm_sq.cpp.xml0000644000175200017650000021247213057470505017522 0ustar coincoin-web Atomic Euclidean Norm Squared: Example and Test
Prev Next atomic_norm_sq.cpp

Atomic Euclidean Norm Squared: Example and Test

Theory
This example demonstrates using atomic_base to define the operation f : R n → R m where n = 2 , m = 1 , where f ( x ) = x 0 2 + x 1 2
sparsity
This example only uses bool sparsity patterns.

Start Class Definition 
# include <cppad/cppad.hpp>
namespace {           // isolate items below to this file
using CppAD::vector;  // abbreviate as vector
//
class atomic_norm_sq : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_norm_sq(const std::string& name) :
     // this example only uses boolean sparsity patterns
     CppAD::atomic_base<double>(name, atomic_base<double>::bool_sparsity_enum)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
                vector<bool>&      vy ,
          const vector<double>&    tx ,
                vector<double>&    ty
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q+1);
          size_t m = ty.size() / (q+1);
# endif
          assert( n == 2 );
          assert( m == 1 );
          assert( p <= q );

          // return flag
          bool ok = q <= 1;

          // Variable information must always be implemented.
          // y_0 is a variable if and only if x_0 or x_1 is a variable.
          if( vx.size() > 0 )
               vy[0] = vx[0] | vx[1];

          // Order zero forward mode must always be implemented.
          // y^0 = f( x^0 )
          double x_00 = tx[ 0*(q+1) + 0];        // x_0^0
          double x_10 = tx[ 1*(q+1) + 0];        // x_10
          double f = x_00 * x_00 + x_10 * x_10;  // f( x^0 )
          if( p <= 0 )
               ty[0] = f;   // y_0^0
          if( q <= 0 )
               return ok;
          assert( vx.size() == 0 );

          // Order one forward mode.
          // This case needed if first order forward mode is used.
          // y^1 = f'( x^0 ) x^1
          double x_01 = tx[ 0*(q+1) + 1];   // x_0^1
          double x_11 = tx[ 1*(q+1) + 1];   // x_1^1
          double fp_0 = 2.0 * x_00;         // partial f w.r.t x_0^0
          double fp_1 = 2.0 * x_10;         // partial f w.r.t x_1^0
          if( p <= 1 )
               ty[1] = fp_0 * x_01 + fp_1 * x_11; // f'( x^0 ) * x^1
          if( q <= 1 )
               return ok;

          // Assume we are not using forward mode with order > 1
          assert( ! ok );
          return ok;
     }

reverse 
     // reverse mode routine called by CppAD
     virtual bool reverse(
          size_t                    q ,
          const vector<double>&    tx ,
          const vector<double>&    ty ,
                vector<double>&    px ,
          const vector<double>&    py
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q+1);
          size_t m = ty.size() / (q+1);
# endif
          assert( px.size() == n * (q+1) );
          assert( py.size() == m * (q+1) );
          assert( n == 2 );
          assert( m == 1 );
          bool ok = q <= 1;

          double fp_0, fp_1;
          switch(q)
          {     case 0:
               // This case needed if first order reverse mode is used
               // F ( {x} ) = f( x^0 ) = y^0
               fp_0  =  2.0 * tx[0];  // partial F w.r.t. x_0^0
               fp_1  =  2.0 * tx[1];  // partial F w.r.t. x_0^1
               px[0] = py[0] * fp_0;; // partial G w.r.t. x_0^0
               px[1] = py[0] * fp_1;; // partial G w.r.t. x_0^1
               assert(ok);
               break;

               default:
               // Assume we are not using reverse with order > 1 (q > 0)
               assert(!ok);
          }
          return ok;
     }

for_sparse_jac 
     // forward Jacobian bool sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          size_t                                p ,
          const vector<bool>&                   r ,
                vector<bool>&                   s ,
          const vector<double>&                 x )
     {     // This function needed if using f.ForSparseJac
          size_t n = r.size() / p;
# ifndef NDEBUG
          size_t m = s.size() / p;
# endif
          assert( n == x.size() );
          assert( n == 2 );
          assert( m == 1 );

          // sparsity for S(x) = f'(x) * R
          // where f'(x) = 2 * [ x_0, x_1 ]
          for(size_t j = 0; j < p; j++)
          {     s[j] = false;
               for(size_t i = 0; i < n; i++)
               {     // Visual Studio 2013 generates warning without bool below
                    s[j] |= bool( r[i * p + j] );
               }
          }
          return true;
     }

rev_sparse_jac 
     // reverse Jacobian bool sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          size_t                                p  ,
          const vector<bool>&                   rt ,
                vector<bool>&                   st ,
          const vector<double>&                 x  )
     {     // This function needed if using RevSparseJac or optimize
          size_t n = st.size() / p;
# ifndef NDEBUG
          size_t m = rt.size() / p;
# endif
          assert( n == x.size() );
          assert( n == 2 );
          assert( m == 1 );

          // sparsity for S(x)^T = f'(x)^T * R^T
          // where f'(x)^T = 2 * [ x_0, x_1]^T
          for(size_t j = 0; j < p; j++)
               for(size_t i = 0; i < n; i++)
                    st[i * p + j] = rt[j];

          return true;
     }

rev_sparse_hes 
     // reverse Hessian bool sparsity routine called by CppAD
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
                vector<bool>&                   t ,
          size_t                                p ,
          const vector<bool>&                   r ,
          const vector<bool>&                   u ,
                vector<bool>&                   v ,
          const vector<double>&                 x )
     {     // This function needed if using RevSparseHes
# ifndef NDEBUG
          size_t m = s.size();
# endif
          size_t n = t.size();
          assert( x.size() == n );
          assert( r.size() == n * p );
          assert( u.size() == m * p );
          assert( v.size() == n * p );
          assert( n == 2 );
          assert( m == 1 );

          // There are no cross term second derivatives for this case,
          // so it is not necessary to use vx.

          // sparsity for T(x) = S(x) * f'(x)
          t[0] = s[0];
          t[1] = s[0];

          // V(x) = f'(x)^T * g''(y) * f'(x) * R  +  g'(y) * f''(x) * R
          // U(x) = g''(y) * f'(x) * R
          // S(x) = g'(y)

          // back propagate the sparsity for U
          size_t j;
          for(j = 0; j < p; j++)
               for(size_t i = 0; i < n; i++)
                    v[ i * p + j] = u[j];

          // include forward Jacobian sparsity in Hessian sparsity
          // sparsity for g'(y) * f''(x) * R  (Note f''(x) has same sparsity
          // as the identity matrix)
          if( s[0] )
          {     for(j = 0; j < p; j++)
                    for(size_t i = 0; i < n; i++)
                    {     // Visual Studio 2013 generates warning without bool below
                         v[ i * p + j] |= bool( r[ i * p + j] );
                    }
          }

          return true;
     }

End Class Definition 

}; // End of atomic_norm_sq class
}  // End empty namespace
Use Atomic Function 
bool norm_sq(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

Constructor 

     // --------------------------------------------------------------------
     // Create the atomic reciprocal object
     atomic_norm_sq afun("atomic_norm_sq");

Recording 
     // Create the function f(x)
     //
     // domain space vector
     size_t  n  = 2;
     double  x0 = 0.25;
     double  x1 = 0.75;
     vector< AD<double> > ax(n);
     ax[0]      = x0;
     ax[1]      = x1;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     vector< AD<double> > ay(m);

     // call user function and store norm_sq(x) in au[0]
     afun(ax, ay);        // y_0 = x_0 * x_0 + x_1 * x_1

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (ax, ay);

forward 
     // check function value
     double check = x0 * x0 + x1 * x1;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> x_q(n), y_q(m);
     q      = 0;
     x_q[0] = x0;
     x_q[1] = x1;
     y_q    = f.Forward(q, x_q);
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // check first order forward mode
     q      = 1;
     x_q[0] = 0.3;
     x_q[1] = 0.7;
     y_q    = f.Forward(q, x_q);
     check  = 2.0 * x0 * x_q[0] + 2.0 * x1 * x_q[1];
     ok &= NearEqual(y_q[0] , check,  eps, eps);
reverse 
     // first order reverse mode
     q     = 1;
     vector<double> w(m), dw(n * q);
     w[0]  = 1.;
     dw    = f.Reverse(q, w);
     check = 2.0 * x0;
     ok &= NearEqual(dw[0] , check,  eps, eps);
     check = 2.0 * x1;
     ok &= NearEqual(dw[1] , check,  eps, eps);

for_sparse_jac 
     // forward mode sparstiy pattern
     size_t p = n;
     CppAD::vectorBool r1(n * p), s1(m * p);
     r1[0] = true;  r1[1] = false; // sparsity pattern identity
     r1[2] = false; r1[3] = true;
     //
     s1    = f.ForSparseJac(p, r1);
     ok  &= s1[0] == true;  // f[0] depends on x[0]
     ok  &= s1[1] == true;  // f[0] depends on x[1]

rev_sparse_jac 
     // reverse mode sparstiy pattern
     q = m;
     CppAD::vectorBool s2(q * m), r2(q * n);
     s2[0] = true;          // compute sparsity pattern for f[0]
     //
     r2    = f.RevSparseJac(q, s2);
     ok  &= r2[0] == true;  // f[0] depends on x[0]
     ok  &= r2[1] == true;  // f[0] depends on x[1]

rev_sparse_hes 
     // Hessian sparsity (using previous ForSparseJac call)
     CppAD::vectorBool s3(m), h(p * n);
     s3[0] = true;        // compute sparsity pattern for f[0]
     //
     h     = f.RevSparseHes(p, s3);
     ok  &= h[0] == true;  // partial of f[0] w.r.t. x[0],x[0] is non-zero
     ok  &= h[1] == false; // partial of f[0] w.r.t. x[0],x[1] is zero
     ok  &= h[2] == false; // partial of f[0] w.r.t. x[1],x[0] is zero
     ok  &= h[3] == true;  // partial of f[0] w.r.t. x[1],x[1] is non-zero
     //
     return ok;
}
Input File: example/atomic/norm_sq.cpp cppad-20170000.3/doc/atomic_reciprocal.cpp.xml0000644000175200017650000021357413057470505020173 0ustar coincoin-web Reciprocal as an Atomic Operation: Example and Test
Prev Next atomic_reciprocal.cpp

Reciprocal as an Atomic Operation: Example and Test

Theory
This example demonstrates using atomic_base to define the operation f : R n → R m where n = 1 , m = 1 , and f ( x ) = 1 / x .

sparsity
This example only uses set sparsity patterns.

Start Class Definition 
# include <cppad/cppad.hpp>
namespace {           // isolate items below to this file
using CppAD::vector;  // abbreviate as vector
//
// a utility to compute the union of two sets.
using CppAD::set_union;
//
class atomic_reciprocal : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_reciprocal(const std::string& name) :
     // this exmaple only uses set sparsity patterns
     CppAD::atomic_base<double>(name, atomic_base<double>::set_sparsity_enum)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
                vector<bool>&      vy ,
          const vector<double>&    tx ,
                vector<double>&    ty
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( n == 1 );
          assert( m == 1 );
          assert( p <= q );

          // return flag
          bool ok = q <= 2;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
               vy[0] = vx[0];

          // Order zero forward mode.
          // This case must always be implemented
          // y^0 = f( x^0 ) = 1 / x^0
          double f = 1. / tx[0];
          if( p <= 0 )
               ty[0] = f;
          if( q <= 0 )
               return ok;
          assert( vx.size() == 0 );

          // Order one forward mode.
          // This case needed if first order forward mode is used.
          // y^1 = f'( x^0 ) x^1
          double fp = - f / tx[0];
          if( p <= 1 )
               ty[1] = fp * tx[1];
          if( q <= 1 )
               return ok;

          // Order two forward mode.
          // This case needed if second order forward mode is used.
          // Y''(t) = X'(t)^\R{T} f''[X(t)] X'(t) + f'[X(t)] X''(t)
          // 2 y^2  = x^1 * f''( x^0 ) x^1 + 2 f'( x^0 ) x^2
          double fpp  = - 2.0 * fp / tx[0];
          ty[2] = tx[1] * fpp * tx[1] / 2.0 + fp * tx[2];
          if( q <= 2 )
               return ok;

          // Assume we are not using forward mode with order > 2
          assert( ! ok );
          return ok;
     }

reverse 
     // reverse mode routine called by CppAD
     virtual bool reverse(
          size_t                    q ,
          const vector<double>&    tx ,
          const vector<double>&    ty ,
                vector<double>&    px ,
          const vector<double>&    py
     )
     {
# ifndef NDEBUG
          size_t n = tx.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
# endif
          assert( px.size() == n * (q + 1) );
          assert( py.size() == m * (q + 1) );
          assert( n == 1 );
          assert( m == 1 );
          bool ok = q <= 2;

          double f, fp, fpp, fppp;
          switch(q)
          {     case 0:
               // This case needed if first order reverse mode is used
               // reverse: F^0 ( tx ) = y^0 = f( x^0 )
               f     = ty[0];
               fp    = - f / tx[0];
               px[0] = py[0] * fp;;
               assert(ok);
               break;

               case 1:
               // This case needed if second order reverse mode is used
               // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1
               f      = ty[0];
               fp     = - f / tx[0];
               fpp    = - 2.0 * fp / tx[0];
               px[1]  = py[1] * fp;
               px[0]  = py[1] * fpp * tx[1];
               // reverse: F^0 ( tx ) = y^0 = f( x^0 );
               px[0] += py[0] * fp;
               assert(ok);
               break;

               case 2:
               // This needed if third order reverse mode is used
               // reverse: F^2 ( tx ) = y^2 =
               //          = x^1 * f''( x^0 ) x^1 / 2 + f'( x^0 ) x^2
               f      = ty[0];
               fp     = - f / tx[0];
               fpp    = - 2.0 * fp / tx[0];
               fppp   = - 3.0 * fpp / tx[0];
               px[2]  = py[2] * fp;
               px[1]  = py[2] * fpp * tx[1];
               px[0]  = py[2] * tx[1] * fppp * tx[1] / 2.0 + fpp * tx[2];
               // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1
               px[1] += py[1] * fp;
               px[0] += py[1] * fpp * tx[1];
               // reverse: F^0 ( tx ) = y^0 = f( x^0 );
               px[0] += py[0] * fp;
               assert(ok);
               break;

               default:
               assert(!ok);
          }
          return ok;
     }

for_sparse_jac 
     // forward Jacobian set sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
                vector< std::set<size_t> >&     s ,
          const vector<double>&                 x )
     {     // This function needed if using f.ForSparseJac
# ifndef NDEBUG
          size_t n = r.size();
          size_t m = s.size();
# endif
          assert( n == x.size() );
          assert( n == 1 );
          assert( m == 1 );

          // sparsity for S(x) = f'(x) * R is same as sparsity for R
          s[0] = r[0];

          return true;
     }

rev_sparse_jac 
     // reverse Jacobian set sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          size_t                                p  ,
          const vector< std::set<size_t> >&     rt ,
                vector< std::set<size_t> >&     st ,
          const vector<double>&                 x  )
     {     // This function needed if using RevSparseJac or optimize
# ifndef NDEBUG
          size_t n = st.size();
          size_t m = rt.size();
# endif
          assert( n == x.size() );
          assert( n == 1 );
          assert( m == 1 );

          // sparsity for S(x)^T = f'(x)^T * R^T is same as sparsity for R^T
          st[0] = rt[0];

          return true;
     }

rev_sparse_hes 
     // reverse Hessian set sparsity routine called by CppAD
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
                vector<bool>&                   t ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          const vector< std::set<size_t> >&     u ,
                vector< std::set<size_t> >&     v ,
          const vector<double>&                 x )
     {     // This function needed if using RevSparseHes
# ifndef NDEBUG
          size_t n = vx.size();
          size_t m = s.size();
# endif
          assert( x.size() == n );
          assert( t.size() == n );
          assert( r.size() == n );
          assert( u.size() == m );
          assert( v.size() == n );
          assert( n == 1 );
          assert( m == 1 );

          // There are no cross term second derivatives for this case,
          // so it is not necessary to vx.

          // sparsity for T(x) = S(x) * f'(x) is same as sparsity for S
          t[0] = s[0];

          // V(x) = f'(x)^T * g''(y) * f'(x) * R  +  g'(y) * f''(x) * R
          // U(x) = g''(y) * f'(x) * R
          // S(x) = g'(y)

          // back propagate the sparsity for U, note f'(x) may be non-zero;
          v[0] = u[0];

          // include forward Jacobian sparsity in Hessian sparsity
          // (note sparsty for f''(x) * R same as for R)
          if( s[0] )
               v[0] = set_union(v[0], r[0] );

          return true;
     }

End Class Definition 

}; // End of atomic_reciprocal class
}  // End empty namespace
Use Atomic Function 
bool reciprocal(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

Constructor 

     // --------------------------------------------------------------------
     // Create the atomic reciprocal object
     atomic_reciprocal afun("atomic_reciprocal");

Recording 
     // Create the function f(x)
     //
     // domain space vector
     size_t n  = 1;
     double  x0 = 0.5;
     vector< AD<double> > ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     vector< AD<double> > ay(m);

     // call user function and store reciprocal(x) in au[0]
     vector< AD<double> > au(m);
     afun(ax, au);        // u = 1 / x

     // now use AD division to invert to invert the operation
     ay[0] = 1.0 / au[0]; // y = 1 / u = x

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (ax, ay);  // f(x) = x

forward 
     // check function value
     double check = x0;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> x_q(n), y_q(m);
     q      = 0;
     x_q[0] = x0;
     y_q    = f.Forward(q, x_q);
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // check first order forward mode
     q      = 1;
     x_q[0] = 1;
     y_q    = f.Forward(q, x_q);
     check  = 1.;
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // check second order forward mode
     q      = 2;
     x_q[0] = 0;
     y_q    = f.Forward(q, x_q);
     check  = 0.;
     ok &= NearEqual(y_q[0] , check,  eps, eps);

reverse 
     // third order reverse mode
     q     = 3;
     vector<double> w(m), dw(n * q);
     w[0]  = 1.;
     dw    = f.Reverse(q, w);
     check = 1.;
     ok &= NearEqual(dw[0] , check,  eps, eps);
     check = 0.;
     ok &= NearEqual(dw[1] , check,  eps, eps);
     ok &= NearEqual(dw[2] , check,  eps, eps);

for_sparse_jac 
     // forward mode sparstiy pattern
     size_t p = n;
     CppAD::vectorBool r1(n * p), s1(m * p);
     r1[0] = true;          // compute sparsity pattern for x[0]
     //
     s1    = f.ForSparseJac(p, r1);
     ok  &= s1[0] == true;  // f[0] depends on x[0]

rev_sparse_jac 
     // reverse mode sparstiy pattern
     q = m;
     CppAD::vectorBool s2(q * m), r2(q * n);
     s2[0] = true;          // compute sparsity pattern for f[0]
     //
     r2    = f.RevSparseJac(q, s2);
     ok  &= r2[0] == true;  // f[0] depends on x[0]

rev_sparse_hes 
     // Hessian sparsity (using previous ForSparseJac call)
     CppAD::vectorBool s3(m), h(p * n);
     s3[0] = true;        // compute sparsity pattern for f[0]
     //
     h     = f.RevSparseHes(p, s3);
     ok  &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero
     //
     return ok;
}
Input File: example/atomic/reciprocal.cpp cppad-20170000.3/doc/atomic_set_sparsity.cpp.xml0000644000175200017650000016576413057470505020610 0ustar coincoin-web Atomic Sparsity with Set Patterns: Example and Test
Prev Next atomic_set_sparsity.cpp

Atomic Sparsity with Set Patterns: Example and Test

function
For this example, the atomic function f : R 3 → R 2 is defined by f ( x ) = ( x 2 x 0 * x 1 )
set_sparsity_enum
This example only uses set sparsity patterns.

Start Class Definition 
# include <cppad/cppad.hpp>
namespace {   // isolate items below to this file
using   CppAD::vector;                          // vector
typedef vector< std::set<size_t> > set_vector;  // atomic_sparsity
//
// a utility to compute the union of two sets.
using CppAD::set_union;
//
class atomic_set_sparsity : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor
     atomic_set_sparsity(const std::string& name) :
     // this exampel only uses set sparsity patterns
     CppAD::atomic_base<double>(name, set_sparsity_enum )
     { }
private:

forward 
     // forward
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {
          size_t n = tx.size() / (q + 1);
# ifndef NDEBUG
          size_t m = ty.size() / (q + 1);
# endif
          assert( n == 3 );
          assert( m == 2 );

          // only order zero
          bool ok = q == 0;
          if( ! ok )
               return ok;

          // check for defining variable information
          if( vx.size() > 0 )
          {     ok   &= vx.size() == n;
               vy[0] = vx[2];
               vy[1] = vx[0] || vx[1];
          }

          // Order zero forward mode.
          // y[0] = x[2], y[1] = x[0] * x[1]
          if( p <= 0 )
          {     ty[0] = tx[2];
               ty[1] = tx[0] * tx[1];
          }
          return ok;
     }

for_sparse_jac 
     // for_sparse_jac
     virtual bool for_sparse_jac(
          size_t                          p ,
          const set_vector&               r ,
          set_vector&                     s ,
          const vector<double>&           x )
     {     // This function needed if using f.ForSparseJac
# ifndef NDEBUG
          size_t n = r.size();
          size_t m = s.size();
# endif
          assert( n == x.size() );
          assert( n == 3 );
          assert( m == 2 );

          // sparsity for S(x) = f'(x) * R  = [ 0,   0, 1 ] * R
          s[0] = r[2];
          // s[1] = union(r[0], r[1])
          s[1] = set_union(r[0], r[1]);
          //
          return true;
     }

rev_sparse_jac 
     virtual bool rev_sparse_jac(
          size_t                                p  ,
          const set_vector&                     rt ,
          set_vector&                           st ,
          const vector<double>&                 x  )
     {     // This function needed if using RevSparseJac or optimize
# ifndef NDEBUG
          size_t n = st.size();
          size_t m = rt.size();
# endif
          assert( n == x.size() );
          assert( n == 3 );
          assert( m == 2 );

          //                                       [ 0, x1 ]
          // sparsity for S(x)^T = f'(x)^T * R^T = [ 0, x0 ] * R^T
          //                                       [ 1, 0  ]
          st[0] = rt[1];
          st[1] = rt[1];
          st[2] = rt[0];
          return true;
     }

for_sparse_hes 
     virtual bool for_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   r ,
          const vector<bool>&                   s ,
          set_vector&                           h ,
          const vector<double>&                 x )
     {
          size_t n = r.size();
# ifndef NDEBUG
          size_t m = s.size();
# endif
          assert( x.size() == n );
          assert( h.size() == n );
          assert( n == 3 );
          assert( m == 2 );

          // initialize h as empty
          for(size_t i = 0; i < n; i++)
               h[i].clear();

          // only f_1 has a non-zero hessian
          if( ! s[1] )
               return true;

          // only the cross term between x[0] and x[1] is non-zero
          if( ! ( r[0] & r[1] ) )
               return true;

          // set the possibly non-zero terms in the hessian
          h[0].insert(1);
          h[1].insert(0);

          return true;
     }

rev_sparse_hes 
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
          vector<bool>&                         t ,
          size_t                                p ,
          const set_vector&                     r ,
          const set_vector&                     u ,
          set_vector&                           v ,
          const vector<double>&                 x )
     {     // This function needed if using RevSparseHes
# ifndef NDEBUG
          size_t m = s.size();
          size_t n = t.size();
# endif
          assert( x.size() == n );
          assert( r.size() == n );
          assert( u.size() == m );
          assert( v.size() == n );
          assert( n == 3 );
          assert( m == 2 );

          // sparsity for T(x) = S(x) * f'(x) = S(x) * [  0,  0,  1 ]
          //                                           [ x1, x0,  0 ]
          t[0] = s[1];
          t[1] = s[1];
          t[2] = s[0];

          // V(x) = f'(x)^T * g''(y) * f'(x) * R  +  g'(y) * f''(x) * R
          // U(x) = g''(y) * f'(x) * R
          // S(x) = g'(y)

          //                                      [ 0, x1 ]
          // sparsity for W(x) = f'(x)^T * U(x) = [ 0, x0 ] * U(x)
          //                                      [ 1, 0  ]
          v[0] = u[1];
          v[1] = u[1];
          v[2] = u[0];
          //
          //                                      [ 0, 1, 0 ]
          // sparsity for V(x) = W(x) + S_1 (x) * [ 1, 0, 0 ] * R
          //                                      [ 0, 0, 0 ]
          if( s[1] )
          {     // v[0] = union( v[0], r[1] )
               v[0] = set_union(v[0], r[1]);
               // v[1] = union( v[1], r[0] )
               v[1] = set_union(v[1], r[0]);
          }
          return true;
     }

End Class Definition 

}; // End of atomic_set_sparsity class
}  // End empty namespace
Test Atomic Function 
bool set_sparsity(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();

Constructor 

     // Create the atomic get_started object
     atomic_set_sparsity afun("atomic_set_sparsity");

Recording 
     size_t n = 3;
     size_t m = 2;
     vector< AD<double> > ax(n), ay(m);
     for(size_t j = 0; j < n; j++)
          ax[j] = double(j + 1);

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // call user function
     afun(ax, ay);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (ax, ay);  // f(x) = x

     // check function value
     ok &= NearEqual(ay[0] , ax[2],  eps, eps);
     ok &= NearEqual(ay[1] , ax[0] * ax[1],  eps, eps);
for_sparse_jac 
     // correct Jacobian result
     set_vector check_s(m);
     check_s[0].insert(2);
     check_s[1].insert(0);
     check_s[1].insert(1);
     // compute and test forward mode
     {     set_vector r(n), s(m);
          for(size_t i = 0; i < n; i++)
               r[i].insert(i);
          s = f.ForSparseJac(n, r);
          for(size_t i = 0; i < m; i++)
               ok &= s[i] == check_s[i];
     }

rev_sparse_jac 
     // compute and test reverse mode
     {     set_vector r(m), s(m);
          for(size_t i = 0; i < m; i++)
               r[i].insert(i);
          s = f.RevSparseJac(m, r);
          for(size_t i = 0; i < m; i++)
               ok &= s[i] == check_s[i];
     }

for_sparse_hes 
     // correct Hessian result
     set_vector check_h(n);
     check_h[0].insert(1);
     check_h[1].insert(0);
     // compute and test forward mode
     {     set_vector r(1), s(1), h(n);
          for(size_t i = 0; i < m; i++)
               s[0].insert(i);
          for(size_t j = 0; j < n; j++)
               r[0].insert(j);
          h = f.ForSparseHes(r, s);
          for(size_t i = 0; i < n; i++)
               ok &= h[i] == check_h[i];
     }

rev_sparse_hes
Note the previous call to ForSparseJac above stored its results in f . 
     // compute and test reverse mode
     {     set_vector s(1), h(n);
          for(size_t i = 0; i < m; i++)
               s[0].insert(i);
          h = f.RevSparseHes(n, s);
          for(size_t i = 0; i < n; i++)
               ok &= h[i] == check_h[i];
     }

Test Result 

     return ok;
}
Input File: example/atomic/set_sparsity.cpp cppad-20170000.3/doc/atomic_tangent.cpp.xml0000644000175200017650000030623013057470505017500 0ustar coincoin-web Tan and Tanh as User Atomic Operations: Example and Test
Prev Next atomic_tangent.cpp

Tan and Tanh as User Atomic Operations: Example and Test

Theory
The code below uses the tan_forward and tan_reverse to implement the tangent and hyperbolic tangent functions as user atomic operations.

sparsity
This atomic operation can use both set and bool sparsity patterns.

Start Class Definition 
# include <cppad/cppad.hpp>
namespace { // Begin empty namespace
using CppAD::vector;
//
// a utility to compute the union of two sets.
using CppAD::set_union;
//
class atomic_tangent : public CppAD::atomic_base<float> {

Constructor 
private:
     const bool hyperbolic_; // is this hyperbolic tangent
public:
     // constructor
     atomic_tangent(const char* name, bool hyperbolic)
     : CppAD::atomic_base<float>(name),
     hyperbolic_(hyperbolic)
     { }
private:

forward 
     // forward mode routine called by CppAD
     bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
                vector<bool>&     vzy ,
          const vector<float>&     tx ,
                vector<float>&    tzy
     )
     {     size_t q1 = q + 1;
# ifndef NDEBUG
          size_t n  = tx.size()  / q1;
          size_t m  = tzy.size() / q1;
# endif
          assert( n == 1 );
          assert( m == 2 );
          assert( p <= q );
          size_t j, k;

          // check if this is during the call to old_tan(id, ax, ay)
          if( vx.size() > 0 )
          {     // set variable flag for both y an z
               vzy[0] = vx[0];
               vzy[1] = vx[0];
          }

          if( p == 0 )
          {     // z^{(0)} = tan( x^{(0)} ) or tanh( x^{(0)} )
               if( hyperbolic_ )
                    tzy[0] = tanh( tx[0] );
               else     tzy[0] = tan( tx[0] );

               // y^{(0)} = z^{(0)} * z^{(0)}
               tzy[q1 + 0] = tzy[0] * tzy[0];

               p++;
          }
          for(j = p; j <= q; j++)
          {     float j_inv = 1.f / float(j);
               if( hyperbolic_ )
                    j_inv = - j_inv;

               // z^{(j)} = x^{(j)} +- sum_{k=1}^j k x^{(k)} y^{(j-k)} / j
               tzy[j] = tx[j];
               for(k = 1; k <= j; k++)
                    tzy[j] += tx[k] * tzy[q1 + j-k] * k * j_inv;

               // y^{(j)} = sum_{k=0}^j z^{(k)} z^{(j-k)}
               tzy[q1 + j] = 0.;
               for(k = 0; k <= j; k++)
                    tzy[q1 + j] += tzy[k] * tzy[j-k];
          }

          // All orders are implemented and there are no possible errors
          return true;
     }

reverse 
     // reverse mode routine called by CppAD
     virtual bool reverse(
          size_t                    q ,
          const vector<float>&     tx ,
          const vector<float>&    tzy ,
                vector<float>&     px ,
          const vector<float>&    pzy
     )
     {     size_t q1 = q + 1;
# ifndef NDEBUG
          size_t n  = tx.size()  / q1;
          size_t m  = tzy.size() / q1;
# endif
          assert( px.size()  == n * q1 );
          assert( pzy.size() == m * q1 );
          assert( n == 1 );
          assert( m == 2 );

          size_t j, k;

          // copy because partials w.r.t. y and z need to change
          vector<float> qzy = pzy;

          // initialize accumultion of reverse mode partials
          for(k = 0; k < q1; k++)
               px[k] = 0.;

          // eliminate positive orders
          for(j = q; j > 0; j--)
          {     float j_inv = 1.f / float(j);
               if( hyperbolic_ )
                    j_inv = - j_inv;

               // H_{x^{(k)}} += delta(j-k) +- H_{z^{(j)} y^{(j-k)} * k / j
               px[j] += qzy[j];
               for(k = 1; k <= j; k++)
                    px[k] += qzy[j] * tzy[q1 + j-k] * k * j_inv;

               // H_{y^{j-k)} += +- H_{z^{(j)} x^{(k)} * k / j
               for(k = 1; k <= j; k++)
                    qzy[q1 + j-k] += qzy[j] * tx[k] * k * j_inv;

               // H_{z^{(k)}} += H_{y^{(j-1)}} * z^{(j-k-1)} * 2.
               for(k = 0; k < j; k++)
                    qzy[k] += qzy[q1 + j-1] * tzy[j-k-1] * 2.f;
          }

          // eliminate order zero
          if( hyperbolic_ )
               px[0] += qzy[0] * (1.f - tzy[q1 + 0]);
          else
               px[0] += qzy[0] * (1.f + tzy[q1 + 0]);

          return true;
     }

for_sparse_jac 
     // forward Jacobian sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          size_t                                p ,
          const vector<bool>&                   r ,
                vector<bool>&                   s ,
          const vector<float>&                  x )
     {
# ifndef NDEBUG
          size_t n = r.size() / p;
          size_t m = s.size() / p;
# endif
          assert( n == x.size() );
          assert( n == 1 );
          assert( m == 2 );

          // sparsity for S(x) = f'(x) * R
          for(size_t j = 0; j < p; j++)
          {     s[0 * p + j] = r[j];
               s[1 * p + j] = r[j];
          }

          return true;
     }
     // forward Jacobian sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
                vector< std::set<size_t> >&     s ,
          const vector<float>&                  x )
     {
# ifndef NDEBUG
          size_t n = r.size();
          size_t m = s.size();
# endif
          assert( n == x.size() );
          assert( n == 1 );
          assert( m == 2 );

          // sparsity for S(x) = f'(x) * R
          s[0] = r[0];
          s[1] = r[0];

          return true;
     }

rev_sparse_jac 
     // reverse Jacobian sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          size_t                                p ,
          const vector<bool>&                  rt ,
                vector<bool>&                  st ,
          const vector<float>&                  x )
     {
# ifndef NDEBUG
          size_t n = st.size() / p;
          size_t m = rt.size() / p;
# endif
          assert( n == 1 );
          assert( m == 2 );
          assert( n == x.size() );

          // sparsity for S(x)^T = f'(x)^T * R^T
          for(size_t j = 0; j < p; j++)
               st[j] = rt[0 * p + j] | rt[1 * p + j];

          return true;
     }
     // reverse Jacobian sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          size_t                                p ,
          const vector< std::set<size_t> >&    rt ,
                vector< std::set<size_t> >&    st ,
          const vector<float>&                  x )
     {
# ifndef NDEBUG
          size_t n = st.size();
          size_t m = rt.size();
# endif
          assert( n == 1 );
          assert( m == 2 );
          assert( n == x.size() );

          // sparsity for S(x)^T = f'(x)^T * R^T
          st[0] = set_union(rt[0], rt[1]);
          return true;
     }

rev_sparse_hes 
     // reverse Hessian sparsity routine called by CppAD
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
                vector<bool>&                   t ,
          size_t                                p ,
          const vector<bool>&                   r ,
          const vector<bool>&                   u ,
                vector<bool>&                   v ,
          const vector<float>&                  x )
     {
# ifndef NDEBUG
          size_t m = s.size();
          size_t n = t.size();
# endif
          assert( x.size() == n );
          assert( r.size() == n * p );
          assert( u.size() == m * p );
          assert( v.size() == n * p );
          assert( n == 1 );
          assert( m == 2 );

          // There are no cross term second derivatives for this case,
          // so it is not necessary to vx.

          // sparsity for T(x) = S(x) * f'(x)
          t[0] =  s[0] | s[1];

          // V(x) = f'(x)^T * g''(y) * f'(x) * R  +  g'(y) * f''(x) * R
          // U(x) = g''(y) * f'(x) * R
          // S(x) = g'(y)

          // back propagate the sparsity for U, note both components
          // of f'(x) may be non-zero;
          size_t j;
          for(j = 0; j < p; j++)
               v[j] = u[ 0 * p + j ] | u[ 1 * p + j ];

          // include forward Jacobian sparsity in Hessian sparsity
          // (note sparsty for f''(x) * R same as for R)
          if( s[0] | s[1] )
          {     for(j = 0; j < p; j++)
               {     // Visual Studio 2013 generates warning without bool below
                    v[j] |= bool( r[j] );
               }
          }

          return true;
     }
     // reverse Hessian sparsity routine called by CppAD
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
                vector<bool>&                   t ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          const vector< std::set<size_t> >&     u ,
                vector< std::set<size_t> >&     v ,
          const vector<float>&                  x )
     {
# ifndef NDEBUG
          size_t m = s.size();
          size_t n = t.size();
# endif
          assert( x.size() == n );
          assert( r.size() == n );
          assert( u.size() == m );
          assert( v.size() == n );
          assert( n == 1 );
          assert( m == 2 );

          // There are no cross term second derivatives for this case,
          // so it is not necessary to vx.

          // sparsity for T(x) = S(x) * f'(x)
          t[0] =  s[0] | s[1];

          // V(x) = f'(x)^T * g''(y) * f'(x) * R  +  g'(y) * f''(x) * R
          // U(x) = g''(y) * f'(x) * R
          // S(x) = g'(y)

          // back propagate the sparsity for U, note both components
          // of f'(x) may be non-zero;
          v[0] = set_union(u[0], u[1]);

          // include forward Jacobian sparsity in Hessian sparsity
          // (note sparsty for f''(x) * R same as for R)
          if( s[0] | s[1] )
               v[0] = set_union(v[0], r[0]);

          return true;
     }

End Class Definition 

}; // End of atomic_tangent class
}  // End empty namespace
Use Atomic Function 
bool tangent(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     float eps = 10.f * CppAD::numeric_limits<float>::epsilon();

Constructor 

     // --------------------------------------------------------------------
     // Creater a tan and tanh object
     atomic_tangent my_tan("my_tan", false), my_tanh("my_tanh", true);

Recording 
     // domain space vector
     size_t n  = 1;
     float  x0 = 0.5;
     CppAD::vector< AD<float> > ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 3;
     CppAD::vector< AD<float> > af(m);

     // temporary vector for computations
     // (my_tan and my_tanh computes tan or tanh and its square)
     CppAD::vector< AD<float> > az(2);

     // call atomic tan function and store tan(x) in f[0] (ignore tan(x)^2)
     my_tan(ax, az);
     af[0] = az[0];

     // call atomic tanh function and store tanh(x) in f[1] (ignore tanh(x)^2)
     my_tanh(ax, az);
     af[1] = az[0];

     // put a constant in f[2] = tanh(1.) (for sparsity pattern testing)
     CppAD::vector< AD<float> > one(1);
     one[0] = 1.;
     my_tanh(one, az);
     af[2] = az[0];

     // create f: x -> f and stop tape recording
     CppAD::ADFun<float> F;
     F.Dependent(ax, af);

forward 
     // check function value
     float tan = std::tan(x0);
     ok &= NearEqual(af[0] , tan,  eps, eps);
     float tanh = std::tanh(x0);
     ok &= NearEqual(af[1] , tanh,  eps, eps);

     // check zero order forward
     CppAD::vector<float> x(n), f(m);
     x[0] = x0;
     f    = F.Forward(0, x);
     ok &= NearEqual(f[0] , tan,  eps, eps);
     ok &= NearEqual(f[1] , tanh,  eps, eps);

     // compute first partial of f w.r.t. x[0] using forward mode
     CppAD::vector<float> dx(n), df(m);
     dx[0] = 1.;
     df    = F.Forward(1, dx);

reverse 
     // compute derivative of tan - tanh using reverse mode
     CppAD::vector<float> w(m), dw(n);
     w[0]  = 1.;
     w[1]  = 1.;
     w[2]  = 0.;
     dw    = F.Reverse(1, w);

     // tan'(x)   = 1 + tan(x)  * tan(x)
     // tanh'(x)  = 1 - tanh(x) * tanh(x)
     float tanp  = 1.f + tan * tan;
     float tanhp = 1.f - tanh * tanh;
     ok   &= NearEqual(df[0], tanp, eps, eps);
     ok   &= NearEqual(df[1], tanhp, eps, eps);
     ok   &= NearEqual(dw[0], w[0]*tanp + w[1]*tanhp, eps, eps);

     // compute second partial of f w.r.t. x[0] using forward mode
     CppAD::vector<float> ddx(n), ddf(m);
     ddx[0] = 0.;
     ddf    = F.Forward(2, ddx);

     // compute second derivative of tan - tanh using reverse mode
     CppAD::vector<float> ddw(2);
     ddw   = F.Reverse(2, w);

     // tan''(x)   = 2 *  tan(x) * tan'(x)
     // tanh''(x)  = - 2 * tanh(x) * tanh'(x)
     // Note that second order Taylor coefficient for u half the
     // corresponding second derivative.
     float two    = 2;
     float tanpp  =   two * tan * tanp;
     float tanhpp = - two * tanh * tanhp;
     ok   &= NearEqual(two * ddf[0], tanpp, eps, eps);
     ok   &= NearEqual(two * ddf[1], tanhpp, eps, eps);
     ok   &= NearEqual(ddw[0], w[0]*tanp  + w[1]*tanhp , eps, eps);
     ok   &= NearEqual(ddw[1], w[0]*tanpp + w[1]*tanhpp, eps, eps);

for_sparse_jac 
     // Forward mode computation of sparsity pattern for F.
     size_t p = n;
     // user vectorBool because m and n are small
     CppAD::vectorBool r1(p), s1(m * p);
     r1[0] = true;            // propagate sparsity for x[0]
     s1    = F.ForSparseJac(p, r1);
     ok  &= (s1[0] == true);  // f[0] depends on x[0]
     ok  &= (s1[1] == true);  // f[1] depends on x[0]
     ok  &= (s1[2] == false); // f[2] does not depend on x[0]

rev_sparse_jac 
     // Reverse mode computation of sparsity pattern for F.
     size_t q = m;
     CppAD::vectorBool s2(q * m), r2(q * n);
     // Sparsity pattern for identity matrix
     size_t i, j;
     for(i = 0; i < q; i++)
     {     for(j = 0; j < m; j++)
               s2[i * q + j] = (i == j);
     }
     r2   = F.RevSparseJac(q, s2);
     ok  &= (r2[0] == true);  // f[0] depends on x[0]
     ok  &= (r2[1] == true);  // f[1] depends on x[0]
     ok  &= (r2[2] == false); // f[2] does not depend on x[0]

rev_sparse_hes 
     // Hessian sparsity for f[0]
     CppAD::vectorBool s3(m), h(p * n);
     s3[0] = true;
     s3[1] = false;
     s3[2] = false;
     h    = F.RevSparseHes(p, s3);
     ok  &= (h[0] == true);  // Hessian is non-zero

     // Hessian sparsity for f[2]
     s3[0] = false;
     s3[2] = true;
     h    = F.RevSparseHes(p, s3);
     ok  &= (h[0] == false);  // Hessian is zero

Large x Values 
     // check tanh results for a large value of x
     x[0]  = std::numeric_limits<float>::max() / two;
     f     = F.Forward(0, x);
     tanh  = 1.;
     ok   &= NearEqual(f[1], tanh, eps, eps);
     df    = F.Forward(1, dx);
     tanhp = 0.;
     ok   &= NearEqual(df[1], tanhp, eps, eps);

     return ok;
}
Input File: example/atomic/tangent.cpp cppad-20170000.3/doc/atomic_eigen_mat_mul.cpp.xml0000644000175200017650000015355213057470505020654 0ustar coincoin-web Atomic Eigen Matrix Multiply: Example and Test
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Atomic Eigen Matrix Multiply: Example and Test

Description
The ADFun function object f for this example is f ( x ) = ( 0 0 1 2 x 0 x 1 ) ( x 0 x 1 ) = ( 0 x 0 + 2 x 1 x 0 x 0 + x 1 x 1 ) )
Class Definition
This example uses the file atomic_eigen_mat_mul.hpp which defines matrix multiply as a atomic_base operation.

Use Atomic Function 
# include <cppad/cppad.hpp>
# include <cppad/example/eigen_mat_mul.hpp>

bool eigen_mat_mul(void)
{     //
     typedef double                                            scalar;
     typedef CppAD::AD<scalar>                                 ad_scalar;
     typedef typename atomic_eigen_mat_mul<scalar>::ad_matrix  ad_matrix;
     //
     bool ok    = true;
     scalar eps = 10. * std::numeric_limits<scalar>::epsilon();
     using CppAD::NearEqual;
     //

Constructor 
     // -------------------------------------------------------------------
     // object that multiplies arbitrary matrices
     atomic_eigen_mat_mul<scalar> mat_mul;
     // -------------------------------------------------------------------
     // declare independent variable vector x
     size_t n = 2;
     CPPAD_TESTVECTOR(ad_scalar) ad_x(n);
     for(size_t j = 0; j < n; j++)
          ad_x[j] = ad_scalar(j);
     CppAD::Independent(ad_x);
     // -------------------------------------------------------------------
     //        [ 0     0    ]
     // left = [ 1     2    ]
     //        [ x[0]  x[1] ]
     size_t nr_left  = 3;
     size_t n_middle   = 2;
     ad_matrix ad_left(nr_left, n_middle);
     ad_left(0, 0) = ad_scalar(0.0);
     ad_left(0, 1) = ad_scalar(0.0);
     ad_left(1, 0) = ad_scalar(1.0);
     ad_left(1, 1) = ad_scalar(2.0);
     ad_left(2, 0) = ad_x[0];
     ad_left(2, 1) = ad_x[1];
     // -------------------------------------------------------------------
     // right = [ x[0] , x[1] ]^T
     size_t nc_right = 1;
     ad_matrix ad_right(n_middle, nc_right);
     ad_right(0, 0) = ad_x[0];
     ad_right(1, 0) = ad_x[1];
     // -------------------------------------------------------------------
     // use atomic operation to multiply left * right
     ad_matrix ad_result = mat_mul.op(ad_left, ad_right);
     // -------------------------------------------------------------------
     // check that first component of result is a parameter
     // and the other components are varaibles.
     ok &= Parameter( ad_result(0, 0) );
     ok &= Variable(  ad_result(1, 0) );
     ok &= Variable(  ad_result(2, 0) );
     // -------------------------------------------------------------------
     // declare the dependent variable vector y
     size_t m = 3;
     CPPAD_TESTVECTOR(ad_scalar) ad_y(m);
     for(size_t i = 0; i < m; i++)
          ad_y[i] = ad_result(i, 0);
     CppAD::ADFun<scalar> f(ad_x, ad_y);
     // -------------------------------------------------------------------
     // check zero order forward mode
     CPPAD_TESTVECTOR(scalar) x(n), y(m);
     for(size_t i = 0; i < n; i++)
          x[i] = scalar(i + 2);
     y   = f.Forward(0, x);
     ok &= NearEqual(y[0], 0.0,                       eps, eps);
     ok &= NearEqual(y[1], x[0] + 2.0 * x[1],         eps, eps);
     ok &= NearEqual(y[2], x[0] * x[0] + x[1] * x[1], eps, eps);
     // -------------------------------------------------------------------
     // check first order forward mode
     CPPAD_TESTVECTOR(scalar) x1(n), y1(m);
     x1[0] = 1.0;
     x1[1] = 0.0;
     y1    = f.Forward(1, x1);
     ok   &= NearEqual(y1[0], 0.0,        eps, eps);
     ok   &= NearEqual(y1[1], 1.0,        eps, eps);
     ok   &= NearEqual(y1[2], 2.0 * x[0], eps, eps);
     x1[0] = 0.0;
     x1[1] = 1.0;
     y1    = f.Forward(1, x1);
     ok   &= NearEqual(y1[0], 0.0,        eps, eps);
     ok   &= NearEqual(y1[1], 2.0,        eps, eps);
     ok   &= NearEqual(y1[2], 2.0 * x[1], eps, eps);
     // -------------------------------------------------------------------
     // check second order forward mode
     CPPAD_TESTVECTOR(scalar) x2(n), y2(m);
     x2[0] = 0.0;
     x2[1] = 0.0;
     y2    = f.Forward(2, x2);
     ok   &= NearEqual(y2[0], 0.0, eps, eps);
     ok   &= NearEqual(y2[1], 0.0, eps, eps);
     ok   &= NearEqual(y2[2], 1.0, eps, eps); // 1/2 * f_1''(x)
     // -------------------------------------------------------------------
     // check first order reverse mode
     CPPAD_TESTVECTOR(scalar) w(m), d1w(n);
     w[0]  = 0.0;
     w[1]  = 1.0;
     w[2]  = 0.0;
     d1w   = f.Reverse(1, w);
     ok   &= NearEqual(d1w[0], 1.0, eps, eps);
     ok   &= NearEqual(d1w[1], 2.0, eps, eps);
     w[0]  = 0.0;
     w[1]  = 0.0;
     w[2]  = 1.0;
     d1w   = f.Reverse(1, w);
     ok   &= NearEqual(d1w[0], 2.0 * x[0], eps, eps);
     ok   &= NearEqual(d1w[1], 2.0 * x[1], eps, eps);
     // -------------------------------------------------------------------
     // check second order reverse mode
     CPPAD_TESTVECTOR(scalar) d2w(2 * n);
     d2w   = f.Reverse(2, w);
     // partial f_2 w.r.t. x_0
     ok   &= NearEqual(d2w[0 * 2 + 0], 2.0 * x[0], eps, eps);
     // partial f_2 w.r.t  x_1
     ok   &= NearEqual(d2w[1 * 2 + 0], 2.0 * x[1], eps, eps);
     // partial f_2 w.r.t x_1, x_0
     ok   &= NearEqual(d2w[0 * 2 + 1], 0.0,        eps, eps);
     // partial f_2 w.r.t x_1, x_1
     ok   &= NearEqual(d2w[1 * 2 + 1], 2.0,        eps, eps);
     // -------------------------------------------------------------------
     // check forward Jacobian sparsity
     CPPAD_TESTVECTOR( std::set<size_t> ) r(n), s(m);
     std::set<size_t> check_set;
     for(size_t j = 0; j < n; j++)
          r[j].insert(j);
     s      = f.ForSparseJac(n, r);
     check_set.clear();
     ok    &= s[0] == check_set;
     check_set.insert(0);
     check_set.insert(1);
     ok    &= s[1] == check_set;
     ok    &= s[2] == check_set;
     // -------------------------------------------------------------------
     // check reverse Jacobian sparsity
     r.resize(m);
     for(size_t i = 0; i < m; i++)
          r[i].insert(i);
     s  = f.RevSparseJac(m, r);
     check_set.clear();
     ok    &= s[0] == check_set;
     check_set.insert(0);
     check_set.insert(1);
     ok    &= s[1] == check_set;
     ok    &= s[2] == check_set;
     // -------------------------------------------------------------------
     // check forward Hessian sparsity for f_2 (x)
     CPPAD_TESTVECTOR( std::set<size_t> ) r2(1), s2(1), h(n);
     for(size_t j = 0; j < n; j++)
          r2[0].insert(j);
     s2[0].clear();
     s2[0].insert(2);
     h = f.ForSparseHes(r2, s2);
     check_set.clear();
     check_set.insert(0);
     ok &= h[0] == check_set;
     check_set.clear();
     check_set.insert(1);
     ok &= h[1] == check_set;
     // -------------------------------------------------------------------
     // check reverse Hessian sparsity for f_2 (x)
     CPPAD_TESTVECTOR( std::set<size_t> ) s3(1);
     s3[0].clear();
     s3[0].insert(2);
     h = f.RevSparseHes(n, s3);
     check_set.clear();
     check_set.insert(0);
     ok &= h[0] == check_set;
     check_set.clear();
     check_set.insert(1);
     ok &= h[1] == check_set;
     // -------------------------------------------------------------------
     return ok;
}
Input File: example/atomic/eigen_mat_mul.cpp cppad-20170000.3/doc/atomic_eigen_mat_mul.hpp.xml0000644000175200017650000042644213057470505020662 0ustar coincoin-web Atomic Eigen Matrix Multiply Class
Prev Next atomic_eigen_mat_mul.hpp

Atomic Eigen Matrix Multiply Class

See Also
atomic_mat_mul.hpp

Purpose
Construct an atomic operation that computes the matrix product, R = A × B for any positive integers r , m , c , and any A ∈ R r × m , B ∈ R m × c .

Matrix Dimensions
This example puts the matrix dimensions in the atomic function arguments, instead of the constructor , so that they can be different for different calls to the atomic function. These dimensions are:
nr_left number of rows in the left matrix; i.e, r
n_middle rows in the left matrix and columns in right; i.e, m
nc_right number of columns in the right matrix; i.e., c

Theory

Forward
For k = 0 , … , the k-th order Taylor coefficient R k is given by R k = ∑ ℓ = 0 k A ℓ B k - ℓ
Product of Two Matrices
Suppose E ¯ is the derivative of the scalar value function s ( E ) with respect to E ; i.e., E ¯ i , j = ∂ s ∂ E i , j Also suppose that t is a scalar valued argument and E ( t ) = C ( t ) D ( t ) It follows that E ' ( t ) = C ' ( t ) D ( t ) + C ( t ) D ' ( t ) ( s ∘ E ) ' ( t ) = tr [ E ¯ T E ' ( t ) ] = tr [ E ¯ T C ' ( t ) D ( t ) ] + tr [ E ¯ T C ( t ) D ' ( t ) ] = tr [ D ( t ) E ¯ T C ' ( t ) ] + tr [ E ¯ T C ( t ) D ' ( t ) ] C ¯ = E ¯ D T , D ¯ = C T E ¯
Reverse
Reverse mode eliminates R k as follows: for ℓ = 0 , … , k -1 , A ¯ ℓ = A ¯ ℓ + R ¯ k B k - ℓ T B ¯ k - ℓ = B ¯ k - ℓ + A ℓ T R ¯ k
Start Class Definition 
# include <cppad/cppad.hpp>
# include <Eigen/Core>
Public

Types 
namespace { // BEGIN_EMPTY_NAMESPACE

template <class Base>
class atomic_eigen_mat_mul : public CppAD::atomic_base<Base> {
public:
     // -----------------------------------------------------------
     // type of elements during calculation of derivatives
     typedef Base              scalar;
     // type of elements during taping
     typedef CppAD::AD<scalar> ad_scalar;
     // type of matrix during calculation of derivatives
     typedef Eigen::Matrix<
          scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>     matrix;
     // type of matrix during taping
     typedef Eigen::Matrix<
          ad_scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > ad_matrix;

Constructor 
     // constructor
     atomic_eigen_mat_mul(void) : CppAD::atomic_base<Base>(
          "atom_eigen_mat_mul"                             ,
          CppAD::atomic_base<Base>::set_sparsity_enum
     )
     { }

op 
     // use atomic operation to multiply two AD matrices
     ad_matrix op(
          const ad_matrix&              left    ,
          const ad_matrix&              right   )
     {     size_t  nr_left   = size_t( left.rows() );
          size_t  n_middle  = size_t( left.cols() );
          size_t  nc_right  = size_t( right.cols() );
          assert( n_middle  == size_t( right.rows() )  );
# ifndef NDEBUG
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
          size_t  ny        = nr_left * nc_right;
# endif
          size_t n_left   = nr_left * n_middle;
          size_t n_right  = n_middle * nc_right;
          size_t n_result = nr_left * nc_right;
          //
          assert( 3 + n_left + n_right == nx );
          assert( n_result == ny );
          // -----------------------------------------------------------------
          // packed version of left and right
          CPPAD_TESTVECTOR(ad_scalar) packed_arg(nx);
          //
          packed_arg[0] = ad_scalar( nr_left );
          packed_arg[1] = ad_scalar( n_middle );
          packed_arg[2] = ad_scalar( nc_right );
          for(size_t i = 0; i < n_left; i++)
               packed_arg[3 + i] = left.data()[i];
          for(size_t i = 0; i < n_right; i++)
               packed_arg[ 3 + n_left + i ] = right.data()[i];
          // ------------------------------------------------------------------
          // Packed version of result = left * right.
          // This as an atomic_base funciton call that CppAD uses
          // to store the atomic operation on the tape.
          CPPAD_TESTVECTOR(ad_scalar) packed_result(ny);
          (*this)(packed_arg, packed_result);
          // ------------------------------------------------------------------
          // unpack result matrix
          ad_matrix result(nr_left, nc_right);
          for(size_t i = 0; i < n_result; i++)
               result.data()[i] = packed_result[ i ];
          //
          return result;
     }

Private

Variables 
private:
     // -------------------------------------------------------------
     // one forward mode vector of matrices for left, right, and result
     CppAD::vector<matrix> f_left_, f_right_, f_result_;
     // one reverse mode vector of matrices for left, right, and result
     CppAD::vector<matrix> r_left_, r_right_, r_result_;
     // -------------------------------------------------------------

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          // lowest order Taylor coefficient we are evaluating
          size_t                          p ,
          // highest order Taylor coefficient we are evaluating
          size_t                          q ,
          // which components of x are variables
          const CppAD::vector<bool>&      vx ,
          // which components of y are variables
          CppAD::vector<bool>&            vy ,
          // tx [ 3 + j * (q+1) + k ] is x_j^k
          const CppAD::vector<scalar>&    tx ,
          // ty [ i * (q+1) + k ] is y_i^k
          CppAD::vector<scalar>&          ty
     )
     {     size_t n_order  = q + 1;
          size_t nr_left  = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) );
          size_t n_middle = size_t( CppAD::Integer( tx[ 1 * n_order + 0 ] ) );
          size_t nc_right = size_t( CppAD::Integer( tx[ 2 * n_order + 0 ] ) );
# ifndef NDEBUG
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
          size_t  ny        = nr_left * nc_right;
# endif
          //
          assert( vx.size() == 0 || nx == vx.size() );
          assert( vx.size() == 0 || ny == vy.size() );
          assert( nx * n_order == tx.size() );
          assert( ny * n_order == ty.size() );
          //
          size_t n_left   = nr_left * n_middle;
          size_t n_right  = n_middle * nc_right;
          size_t n_result = nr_left * nc_right;
          assert( 3 + n_left + n_right == nx );
          assert( n_result == ny );
          //
          // -------------------------------------------------------------------
          // make sure f_left_, f_right_, and f_result_ are large enough
          assert( f_left_.size() == f_right_.size() );
          assert( f_left_.size() == f_result_.size() );
          if( f_left_.size() < n_order )
          {     f_left_.resize(n_order);
               f_right_.resize(n_order);
               f_result_.resize(n_order);
               //
               for(size_t k = 0; k < n_order; k++)
               {     f_left_[k].resize(nr_left, n_middle);
                    f_right_[k].resize(n_middle, nc_right);
                    f_result_[k].resize(nr_left, nc_right);
               }
          }
          // -------------------------------------------------------------------
          // unpack tx into f_left and f_right
          for(size_t k = 0; k < n_order; k++)
          {     // unpack left values for this order
               for(size_t i = 0; i < n_left; i++)
                    f_left_[k].data()[i] = tx[ (3 + i) * n_order + k ];
               //
               // unpack right values for this order
               for(size_t i = 0; i < n_right; i++)
                    f_right_[k].data()[i] = tx[ ( 3 + n_left + i) * n_order + k ];
          }
          // -------------------------------------------------------------------
          // result for each order
          // (we could avoid recalculting f_result_[k] for k=0,...,p-1)
          for(size_t k = 0; k < n_order; k++)
          {     // result[k] = sum_ell left[ell] * right[k-ell]
               f_result_[k] = matrix::Zero(nr_left, nc_right);
               for(size_t ell = 0; ell <= k; ell++)
                    f_result_[k] += f_left_[ell] * f_right_[k-ell];
          }
          // -------------------------------------------------------------------
          // pack result_ into ty
          for(size_t k = 0; k < n_order; k++)
          {     for(size_t i = 0; i < n_result; i++)
                    ty[ i * n_order + k ] = f_result_[k].data()[i];
          }
          // ------------------------------------------------------------------
          // check if we are computing vy
          if( vx.size() == 0 )
               return true;
          // ------------------------------------------------------------------
          // compute variable information for y; i.e., vy
          // (note that the constant zero times a variable is a constant)
          scalar zero(0.0);
          assert( n_order == 1 );
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     bool var = false;
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     // left information
                         size_t index   = 3 + i * n_middle + ell;
                         bool var_left  = vx[index];
                         bool nz_left   = var_left | (f_left_[0](i, ell) != zero);
                         // right information
                         index          = 3 + n_left + ell * nc_right + j;
                         bool var_right = vx[index];
                         bool nz_right  = var_right | (f_right_[0](ell, j) != zero);
                         // effect of result
                         var |= var_left & nz_right;
                         var |= nz_left  & var_right;
                    }
                    size_t index = i * nc_right + j;
                    vy[index]    = var;
               }
          }
          return true;
     }

reverse 
     // reverse mode routine called by CppAD
     virtual bool reverse(
          // highest order Taylor coefficient that we are computing derivative of
          size_t                     q ,
          // forward mode Taylor coefficients for x variables
          const CppAD::vector<double>&     tx ,
          // forward mode Taylor coefficients for y variables
          const CppAD::vector<double>&     ty ,
          // upon return, derivative of G[ F[ {x_j^k} ] ] w.r.t {x_j^k}
          CppAD::vector<double>&           px ,
          // derivative of G[ {y_i^k} ] w.r.t. {y_i^k}
          const CppAD::vector<double>&     py
     )
     {     size_t n_order  = q + 1;
          size_t nr_left  = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) );
          size_t n_middle = size_t( CppAD::Integer( tx[ 1 * n_order + 0 ] ) );
          size_t nc_right = size_t( CppAD::Integer( tx[ 2 * n_order + 0 ] ) );
# ifndef NDEBUG
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
          size_t  ny        = nr_left * nc_right;
# endif
          //
          assert( nx * n_order == tx.size() );
          assert( ny * n_order == ty.size() );
          assert( px.size() == tx.size() );
          assert( py.size() == ty.size() );
          //
          size_t n_left   = nr_left * n_middle;
          size_t n_right  = n_middle * nc_right;
          size_t n_result = nr_left * nc_right;
          assert( 3 + n_left + n_right == nx );
          assert( n_result == ny );
          // -------------------------------------------------------------------
          // make sure f_left_, f_right_ are large enough
          assert( f_left_.size() == f_right_.size() );
          assert( f_left_.size() == f_result_.size() );
          // must have previous run forward with order >= n_order
          assert( f_left_.size() >= n_order );
          // -------------------------------------------------------------------
          // make sure r_left_, r_right_, and r_result_ are large enough
          assert( r_left_.size() == r_right_.size() );
          assert( r_left_.size() == r_result_.size() );
          if( r_left_.size() < n_order )
          {     r_left_.resize(n_order);
               r_right_.resize(n_order);
               r_result_.resize(n_order);
               //
               for(size_t k = 0; k < n_order; k++)
               {     r_left_[k].resize(nr_left, n_middle);
                    r_right_[k].resize(n_middle, nc_right);
                    r_result_[k].resize(nr_left, nc_right);
               }
          }
          // -------------------------------------------------------------------
          // unpack tx into f_left and f_right
          for(size_t k = 0; k < n_order; k++)
          {     // unpack left values for this order
               for(size_t i = 0; i < n_left; i++)
                    f_left_[k].data()[i] = tx[ (3 + i) * n_order + k ];
               //
               // unpack right values for this order
               for(size_t i = 0; i < n_right; i++)
                    f_right_[k].data()[i] = tx[ (3 + n_left + i) * n_order + k ];
          }
          // -------------------------------------------------------------------
          // unpack py into r_result_
          for(size_t k = 0; k < n_order; k++)
          {     for(size_t i = 0; i < n_result; i++)
                    r_result_[k].data()[i] = py[ i * n_order + k ];
          }
          // -------------------------------------------------------------------
          // initialize r_left_ and r_right_ as zero
          for(size_t k = 0; k < n_order; k++)
          {     r_left_[k]   = matrix::Zero(nr_left, n_middle);
               r_right_[k]  = matrix::Zero(n_middle, nc_right);
          }
          // -------------------------------------------------------------------
          // matrix reverse mode calculation
          for(size_t k1 = n_order; k1 > 0; k1--)
          {     size_t k = k1 - 1;
               for(size_t ell = 0; ell <= k; ell++)
               {     // nr x nm       = nr x nc      * nc * nm
                    r_left_[ell]    += r_result_[k] * f_right_[k-ell].transpose();
                    // nm x nc       = nm x nr * nr * nc
                    r_right_[k-ell] += f_left_[ell].transpose() * r_result_[k];
               }
          }
          // -------------------------------------------------------------------
          // pack r_left and r_right int px
          for(size_t k = 0; k < n_order; k++)
          {     // dimensions are integer constants
               px[ 0 * n_order + k ] = 0.0;
               px[ 1 * n_order + k ] = 0.0;
               px[ 2 * n_order + k ] = 0.0;
               //
               // pack left values for this order
               for(size_t i = 0; i < n_left; i++)
                    px[ (3 + i) * n_order + k ] = r_left_[k].data()[i];
               //
               // pack right values for this order
               for(size_t i = 0; i < n_right; i++)
                    px[ (3 + i + n_left) * n_order + k] = r_right_[k].data()[i];
          }
          //
          return true;
     }

for_sparse_jac 
     // forward Jacobian sparsity routine called by CppAD
     virtual bool for_sparse_jac(
          // number of columns in the matrix R
          size_t                                       q ,
          // sparsity pattern for the matrix R
          const CppAD::vector< std::set<size_t> >&     r ,
          // sparsity pattern for the matrix S = f'(x) * R
          CppAD::vector< std::set<size_t> >&           s ,
          const CppAD::vector<Base>&                   x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
# ifndef NDEBUG
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
          size_t  ny        = nr_left * nc_right;
# endif
          //
          assert( nx == r.size() );
          assert( ny == s.size() );
          //
          size_t n_left = nr_left * n_middle;
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     // pack index for entry (i, j) in result
                    size_t i_result = i * nc_right + j;
                    s[i_result].clear();
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     // pack index for entry (i, ell) in left
                         size_t i_left  = 3 + i * n_middle + ell;
                         // pack index for entry (ell, j) in right
                         size_t i_right = 3 + n_left + ell * nc_right + j;
                         //
                         s[i_result] = CppAD::set_union(s[i_result], r[i_left] );
                         s[i_result] = CppAD::set_union(s[i_result], r[i_right] );
                    }
               }
          }
          return true;
     }

rev_sparse_jac 
     // reverse Jacobian sparsity routine called by CppAD
     virtual bool rev_sparse_jac(
          // number of columns in the matrix R^T
          size_t                                      q  ,
          // sparsity pattern for the matrix R^T
          const CppAD::vector< std::set<size_t> >&    rt ,
          // sparsoity pattern for the matrix S^T = f'(x)^T * R^T
          CppAD::vector< std::set<size_t> >&          st ,
          const CppAD::vector<Base>&                   x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
# ifndef NDEBUG
          size_t  ny        = nr_left * nc_right;
# endif
          //
          assert( nx == st.size() );
          assert( ny == rt.size() );
          //
          // initialize S^T as empty
          for(size_t i = 0; i < nx; i++)
               st[i].clear();

          // sparsity for S(x)^T = f'(x)^T * R^T
          size_t n_left = nr_left * n_middle;
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     // pack index for entry (i, j) in result
                    size_t i_result = i * nc_right + j;
                    st[i_result].clear();
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     // pack index for entry (i, ell) in left
                         size_t i_left  = 3 + i * n_middle + ell;
                         // pack index for entry (ell, j) in right
                         size_t i_right = 3 + n_left + ell * nc_right + j;
                         //
                         st[i_left]  = CppAD::set_union(st[i_left],  rt[i_result]);
                         st[i_right] = CppAD::set_union(st[i_right], rt[i_result]);
                    }
               }
          }
          return true;
     }

for_sparse_hes 
     virtual bool for_sparse_hes(
          // which components of x are variables for this call
          const CppAD::vector<bool>&                   vx,
          // sparsity pattern for the diagonal of R
          const CppAD::vector<bool>&                   r ,
          // sparsity pattern for the vector S
          const CppAD::vector<bool>&                   s ,
          // sparsity patternfor the Hessian H(x)
          CppAD::vector< std::set<size_t> >&           h ,
          const CppAD::vector<Base>&                   x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
# ifndef NDEBUG
          size_t  ny        = nr_left * nc_right;
# endif
          //
          assert( vx.size() == nx );
          assert( r.size()  == nx );
          assert( s.size()  == ny );
          assert( h.size()  == nx );
          //
          // initilize h as empty
          for(size_t i = 0; i < nx; i++)
               h[i].clear();
          //
          size_t n_left = nr_left * n_middle;
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     // pack index for entry (i, j) in result
                    size_t i_result = i * nc_right + j;
                    if( s[i_result] )
                    {     for(size_t ell = 0; ell < n_middle; ell++)
                         {     // pack index for entry (i, ell) in left
                              size_t i_left  = 3 + i * n_middle + ell;
                              // pack index for entry (ell, j) in right
                              size_t i_right = 3 + n_left + ell * nc_right + j;
                              if( r[i_left] & r[i_right] )
                              {     h[i_left].insert(i_right);
                                   h[i_right].insert(i_left);
                              }
                         }
                    }
               }
          }
          return true;
     }

rev_sparse_hes 
     // reverse Hessian sparsity routine called by CppAD
     virtual bool rev_sparse_hes(
          // which components of x are variables for this call
          const CppAD::vector<bool>&                   vx,
          // sparsity pattern for S(x) = g'[f(x)]
          const CppAD::vector<bool>&                   s ,
          // sparsity pattern for d/dx g[f(x)] = S(x) * f'(x)
          CppAD::vector<bool>&                         t ,
          // number of columns in R, U(x), and V(x)
          size_t                                       q ,
          // sparsity pattern for R
          const CppAD::vector< std::set<size_t> >&     r ,
          // sparsity pattern for U(x) = g^{(2)} [ f(x) ] * f'(x) * R
          const CppAD::vector< std::set<size_t> >&     u ,
          // sparsity pattern for
          // V(x) = f'(x)^T * U(x) + sum_{i=0}^{m-1} S_i(x) f_i^{(2)} (x) * R
          CppAD::vector< std::set<size_t> >&           v ,
          // parameters as integers
          const CppAD::vector<Base>&                   x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
# ifndef NDEBUG
          size_t  ny        = nr_left * nc_right;
# endif
          //
          assert( vx.size() == nx );
          assert( s.size()  == ny );
          assert( t.size()  == nx );
          assert( r.size()  == nx );
          assert( v.size()  == nx );
          //
          // initilaize return sparsity patterns as false
          for(size_t j = 0; j < nx; j++)
          {     t[j] = false;
               v[j].clear();
          }
          //
          size_t n_left = nr_left * n_middle;
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     // pack index for entry (i, j) in result
                    size_t i_result = i * nc_right + j;
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     // pack index for entry (i, ell) in left
                         size_t i_left  = 3 + i * n_middle + ell;
                         // pack index for entry (ell, j) in right
                         size_t i_right = 3 + n_left + ell * nc_right + j;
                         //
                         // back propagate T(x) = S(x) * f'(x).
                         t[i_left]  |= bool( s[i_result] );
                         t[i_right] |= bool( s[i_result] );
                         //
                         // V(x) = f'(x)^T * U(x) +  sum_i S_i(x) * f_i''(x) * R
                         // U(x)   = g''[ f(x) ] * f'(x) * R
                         // S_i(x) = g_i'[ f(x) ]
                         //
                         // back propagate f'(x)^T * U(x)
                         v[i_left]  = CppAD::set_union(v[i_left],  u[i_result] );
                         v[i_right] = CppAD::set_union(v[i_right], u[i_result] );
                         //
                         // back propagate S_i(x) * f_i''(x) * R
                         // (here is where we use vx to check for cross terms)
                         if( s[i_result] & vx[i_left] & vx[i_right] )
                         {     v[i_left]  = CppAD::set_union(v[i_left],  r[i_right] );
                              v[i_right] = CppAD::set_union(v[i_right], r[i_left]  );
                         }
                    }
               }
          }
          return true;
     }

End Class Definition 

}; // End of atomic_eigen_mat_mul class

}  // END_EMPTY_NAMESPACE
Input File: cppad/example/eigen_mat_mul.hpp cppad-20170000.3/doc/atomic_eigen_mat_inv.cpp.xml0000644000175200017650000012502513057470505020645 0ustar coincoin-web Atomic Eigen Matrix Inverse: Example and Test
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Atomic Eigen Matrix Inverse: Example and Test

Description
The ADFun function object f for this example is f ( x ) = ( x 0 0 0 x 1 ) -1 ( 0 x 2 ) = ( 0 x 2 / x 1 ) )
Class Definition
This example uses the file atomic_eigen_mat_inv.hpp which defines matrix multiply as a atomic_base operation.

Use Atomic Function 
# include <cppad/cppad.hpp>
# include <cppad/example/eigen_mat_inv.hpp>
# include <cppad/example/eigen_mat_mul.hpp>


bool eigen_mat_inv(void)
{
     typedef double                                            scalar;
     typedef CppAD::AD<scalar>                                 ad_scalar;
     typedef typename atomic_eigen_mat_inv<scalar>::ad_matrix  ad_matrix;
     //
     bool ok    = true;
     scalar eps = 10. * std::numeric_limits<scalar>::epsilon();
     using CppAD::NearEqual;
     //

Constructor 
     // -------------------------------------------------------------------
     // object that multiplies matrices
     atomic_eigen_mat_mul<scalar> mat_mul;
     // -------------------------------------------------------------------
     // object that computes inverse of a square matrix
     atomic_eigen_mat_inv<scalar> mat_inv;
     // -------------------------------------------------------------------
     // declare independent variable vector x
     size_t n = 3;
     CPPAD_TESTVECTOR(ad_scalar) ad_x(n);
     for(size_t j = 0; j < n; j++)
          ad_x[j] = ad_scalar(j + 1);
     CppAD::Independent(ad_x);
     // -------------------------------------------------------------------
     // left = [ x[0]  0    ]
     //        [ 0     x[1] ]
     size_t nr_left  = 2;
     ad_matrix ad_left(nr_left, nr_left);
     ad_left(0, 0) = ad_x[0];
     ad_left(0, 1) = ad_scalar(0.0);
     ad_left(1, 0) = ad_scalar(0.0);
     ad_left(1, 1) = ad_x[1];
     // -------------------------------------------------------------------
     // right = [ 0 , x[2] ]^T
     size_t nc_right = 1;
     ad_matrix ad_right(nr_left, nc_right);
     ad_right(0, 0) = ad_scalar(0.0);
     ad_right(1, 0) = ad_x[2];
     // -------------------------------------------------------------------
     // use atomic operation to compute left^{-1}
     ad_matrix ad_left_inv = mat_inv.op(ad_left);
     // use atomic operation to multiply left^{-1} * right
     ad_matrix ad_result   = mat_mul.op(ad_left_inv, ad_right);
     // -------------------------------------------------------------------
     // declare the dependent variable vector y
     size_t m = 2;
     CPPAD_TESTVECTOR(ad_scalar) ad_y(2);
     for(size_t i = 0; i < m; i++)
          ad_y[i] = ad_result(i, 0);
     CppAD::ADFun<scalar> f(ad_x, ad_y);
     // -------------------------------------------------------------------
     // check zero order forward mode
     CPPAD_TESTVECTOR(scalar) x(n), y(m);
     for(size_t i = 0; i < n; i++)
          x[i] = scalar(i + 2);
     y   = f.Forward(0, x);
     ok &= NearEqual(y[0], 0.0,          eps, eps);
     ok &= NearEqual(y[1], x[2] / x[1],  eps, eps);
     // -------------------------------------------------------------------
     // check first order forward mode
     CPPAD_TESTVECTOR(scalar) x1(n), y1(m);
     x1[0] = 1.0;
     x1[1] = 0.0;
     x1[2] = 0.0;
     y1    = f.Forward(1, x1);
     ok   &= NearEqual(y1[0], 0.0,        eps, eps);
     ok   &= NearEqual(y1[1], 0.0,        eps, eps);
     x1[0] = 0.0;
     x1[1] = 0.0;
     x1[2] = 1.0;
     y1    = f.Forward(1, x1);
     ok   &= NearEqual(y1[0], 0.0,        eps, eps);
     ok   &= NearEqual(y1[1], 1.0 / x[1], eps, eps);
     x1[0] = 0.0;
     x1[1] = 1.0;
     x1[2] = 0.0;
     y1    = f.Forward(1, x1);
     ok   &= NearEqual(y1[0], 0.0,                  eps, eps);
     ok   &= NearEqual(y1[1], - x[2] / (x[1]*x[1]), eps, eps);
     // -------------------------------------------------------------------
     // check second order forward mode
     CPPAD_TESTVECTOR(scalar) x2(n), y2(m);
     x2[0] = 0.0;
     x2[1] = 0.0;
     x2[2] = 0.0;
     scalar  f1_x1_x1 = 2.0 * x[2] / (x[1] * x[1] * x[1] );
     y2    = f.Forward(2, x2);
     ok   &= NearEqual(y2[0], 0.0,            eps, eps);
     ok   &= NearEqual(y2[1], f1_x1_x1 / 2.0, eps, eps);
     // -------------------------------------------------------------------
     // check first order reverse
     CPPAD_TESTVECTOR(scalar) w(m), d1w(n);
     w[0] = 1.0;
     w[1] = 0.0;
     d1w  = f.Reverse(1, w);
     ok  &= NearEqual(d1w[0], 0.0, eps, eps);
     ok  &= NearEqual(d1w[1], 0.0, eps, eps);
     ok  &= NearEqual(d1w[2], 0.0, eps, eps);
     w[0] = 0.0;
     w[1] = 1.0;
     d1w  = f.Reverse(1, w);
     ok  &= NearEqual(d1w[0], 0.0,                  eps, eps);
     ok  &= NearEqual(d1w[1], - x[2] / (x[1]*x[1]), eps, eps);
     ok  &= NearEqual(d1w[2], 1.0 / x[1],           eps, eps);
     // -------------------------------------------------------------------
     // check second order reverse
     CPPAD_TESTVECTOR(scalar) d2w(2 * n);
     d2w  = f.Reverse(2, w);
     // partial f_1 w.r.t x_0
     ok  &= NearEqual(d2w[0 * 2 + 0], 0.0,                  eps, eps);
     // partial f_1 w.r.t x_1
     ok  &= NearEqual(d2w[1 * 2 + 0], - x[2] / (x[1]*x[1]), eps, eps);
     // partial f_1 w.r.t x_2
     ok  &= NearEqual(d2w[2 * 2 + 0], 1.0 / x[1],           eps, eps);
     // partial f_1 w.r.t x_1, x_0
     ok  &= NearEqual(d2w[0 * 2 + 1], 0.0,                  eps, eps);
     // partial f_1 w.r.t x_1, x_1
     ok  &= NearEqual(d2w[1 * 2 + 1], f1_x1_x1,             eps, eps);
     // partial f_1 w.r.t x_1, x_2
     ok  &= NearEqual(d2w[2 * 2 + 1], - 1.0 / (x[1]*x[1]),  eps, eps);
     // -------------------------------------------------------------------
     return ok;
}
Input File: example/atomic/eigen_mat_inv.cpp cppad-20170000.3/doc/atomic_eigen_mat_inv.hpp.xml0000644000175200017650000024113613057470505020654 0ustar coincoin-web Atomic Eigen Matrix Inversion Class
Prev Next atomic_eigen_mat_inv.hpp

Atomic Eigen Matrix Inversion Class

Purpose
Construct an atomic operation that computes the matrix inverse R = A -1 for any positive integer p and invertible matrix A ∈ R p × p .

Matrix Dimensions
This example puts the matrix dimension p in the atomic function arguments, instead of the constructor , so it can be different for different calls to the atomic function.

Theory

Forward
The zero order forward mode Taylor coefficient is give by R 0 = A 0 -1 For k = 1 , … , the k-th order Taylor coefficient of A R is given by 0 = ∑ ℓ = 0 k A ℓ R k - ℓ Solving for R k in terms of the coefficients for A and the lower order coefficients for R we have R k = - R 0 (∑ ℓ = 1 k A ℓ R k - ℓ ) Furthermore, once we have R k we can compute the sum using A 0 R k = - (∑ ℓ = 1 k A ℓ R k - ℓ )
Product of Three Matrices
Suppose E ¯ is the derivative of the scalar value function s ( E ) with respect to E ; i.e., E ¯ i , j = ∂ s ∂ E i , j Also suppose that t is a scalar valued argument and E ( t ) = B ( t ) C ( t ) D ( t ) It follows that E ' ( t ) = B ' ( t ) C ( t ) D ( t ) + B ( t ) C ' ( t ) D ( t ) + B ( t ) C ( t ) D ' ( t ) ( s ∘ E ) ' ( t ) = tr [ E ¯ T E ' ( t ) ] = tr [ E ¯ T B ' ( t ) C ( t ) D ( t ) ] + tr [ E ¯ T B ( t ) C ' ( t ) D ( t ) ] + tr [ E ¯ T B ( t ) C ( t ) D ' ( t ) ] = tr [ B ( t ) D ( t ) E ¯ T B ' ( t ) ] + tr [ D ( t ) E ¯ T B ( t ) C ' ( t ) ] + tr [ E ¯ T B ( t ) C ( t ) D ' ( t ) ] B ¯ = E ¯ ( C D ) T , C ¯ = B T E ¯ D T , D ¯ = ( B C ) T E ¯
Reverse
For k > 0 , reverse mode eliminates R k and expresses the function values s in terms of the coefficients of A and the lower order coefficients of R . The effect on R ¯ 0 (of eliminating R k ) is R ¯ 0 = R ¯ 0 - R ¯ k (∑ ℓ = 1 k A ℓ R k - ℓ ) T = R ¯ 0 + R ¯ k ( A 0 R k ) T For ℓ = 1 , … , k , the effect on R ¯ k - ℓ and A ℓ (of eliminating R k ) is A ¯ ℓ = A ¯ ℓ - R 0 T R ¯ k R k - ℓ T R ¯ k - ℓ = R ¯ k - ℓ - ( R 0 A ℓ ) T R ¯ k We note that R 0 ' ( t ) A 0 ( t ) + R 0 ( t ) A 0 ' ( t ) = 0 R 0 ' ( t ) = - R 0 ( t ) A 0 ' ( t ) R 0 ( t ) The reverse mode formula that eliminates R 0 is A ¯ 0 = A ¯ 0 - R 0 T R ¯ 0 R 0 T
Start Class Definition 
# include <cppad/cppad.hpp>
# include <Eigen/Core>
# include <Eigen/LU>
Public

Types 
namespace { // BEGIN_EMPTY_NAMESPACE

template <class Base>
class atomic_eigen_mat_inv : public CppAD::atomic_base<Base> {
public:
     // -----------------------------------------------------------
     // type of elements during calculation of derivatives
     typedef Base              scalar;
     // type of elements during taping
     typedef CppAD::AD<scalar> ad_scalar;
     // type of matrix during calculation of derivatives
     typedef Eigen::Matrix<
          scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>     matrix;
     // type of matrix during taping
     typedef Eigen::Matrix<
          ad_scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > ad_matrix;

Constructor 
     // constructor
     atomic_eigen_mat_inv(void) : CppAD::atomic_base<Base>(
          "atom_eigen_mat_inv"                             ,
          CppAD::atomic_base<Base>::set_sparsity_enum
     )
     { }

op 
     // use atomic operation to invert an AD matrix
     ad_matrix op(const ad_matrix& arg)
     {     size_t nr = size_t( arg.rows() );
          size_t ny = nr * nr;
          size_t nx = 1 + ny;
          assert( nr == size_t( arg.cols() ) );
          // -------------------------------------------------------------------
          // packed version of arg
          CPPAD_TESTVECTOR(ad_scalar) packed_arg(nx);
          packed_arg[0] = ad_scalar( nr );
          for(size_t i = 0; i < ny; i++)
               packed_arg[1 + i] = arg.data()[i];
          // -------------------------------------------------------------------
          // packed version of result = arg^{-1}.
          // This is an atomic_base function call that CppAD uses to
          // store the atomic operation on the tape.
          CPPAD_TESTVECTOR(ad_scalar) packed_result(ny);
          (*this)(packed_arg, packed_result);
          // -------------------------------------------------------------------
          // unpack result matrix
          ad_matrix result(nr, nr);
          for(size_t i = 0; i < ny; i++)
               result.data()[i] = packed_result[i];
          return result;
     }

Private

Variables 
private:
     // -------------------------------------------------------------
     // one forward mode vector of matrices for argument and result
     CppAD::vector<matrix> f_arg_, f_result_;
     // one reverse mode vector of matrices for argument and result
     CppAD::vector<matrix> r_arg_, r_result_;
     // -------------------------------------------------------------

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          // lowest order Taylor coefficient we are evaluating
          size_t                          p ,
          // highest order Taylor coefficient we are evaluating
          size_t                          q ,
          // which components of x are variables
          const CppAD::vector<bool>&      vx ,
          // which components of y are variables
          CppAD::vector<bool>&            vy ,
          // tx [ j * (q+1) + k ] is x_j^k
          const CppAD::vector<scalar>&    tx ,
          // ty [ i * (q+1) + k ] is y_i^k
          CppAD::vector<scalar>&          ty
     )
     {     size_t n_order = q + 1;
          size_t nr      = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) );
          size_t ny      = nr * nr;
          size_t nx      = 1 + ny;
          assert( vx.size() == 0 || nx == vx.size() );
          assert( vx.size() == 0 || ny == vy.size() );
          assert( nx * n_order == tx.size() );
          assert( ny * n_order == ty.size() );
          //
          // -------------------------------------------------------------------
          // make sure f_arg_ and f_result_ are large enough
          assert( f_arg_.size() == f_result_.size() );
          if( f_arg_.size() < n_order )
          {     f_arg_.resize(n_order);
               f_result_.resize(n_order);
               //
               for(size_t k = 0; k < n_order; k++)
               {     f_arg_[k].resize(nr, nr);
                    f_result_[k].resize(nr, nr);
               }
          }
          // -------------------------------------------------------------------
          // unpack tx into f_arg_
          for(size_t k = 0; k < n_order; k++)
          {     // unpack arg values for this order
               for(size_t i = 0; i < ny; i++)
                    f_arg_[k].data()[i] = tx[ (1 + i) * n_order + k ];
          }
          // -------------------------------------------------------------------
          // result for each order
          // (we could avoid recalculting f_result_[k] for k=0,...,p-1)
          //
          f_result_[0] = f_arg_[0].inverse();
          for(size_t k = 1; k < n_order; k++)
          {     // initialize sum
               matrix f_sum = matrix::Zero(nr, nr);
               // compute sum
               for(size_t ell = 1; ell <= k; ell++)
                    f_sum -= f_arg_[ell] * f_result_[k-ell];
               // result_[k] = arg_[0]^{-1} * sum_
               f_result_[k] = f_result_[0] * f_sum;
          }
          // -------------------------------------------------------------------
          // pack result_ into ty
          for(size_t k = 0; k < n_order; k++)
          {     for(size_t i = 0; i < ny; i++)
                    ty[ i * n_order + k ] = f_result_[k].data()[i];
          }
          // -------------------------------------------------------------------
          // check if we are computing vy
          if( vx.size() == 0 )
               return true;
          // ------------------------------------------------------------------
          // This is a very dumb algorithm that over estimates which
          // elements of the inverse are variables (which is not efficient).
          bool var = false;
          for(size_t i = 0; i < ny; i++)
               var |= vx[1 + i];
          for(size_t i = 0; i < ny; i++)
               vy[i] = var;
          return true;
     }

reverse 
     // reverse mode routine called by CppAD
     virtual bool reverse(
          // highest order Taylor coefficient that we are computing derivative of
          size_t                     q ,
          // forward mode Taylor coefficients for x variables
          const CppAD::vector<double>&     tx ,
          // forward mode Taylor coefficients for y variables
          const CppAD::vector<double>&     ty ,
          // upon return, derivative of G[ F[ {x_j^k} ] ] w.r.t {x_j^k}
          CppAD::vector<double>&           px ,
          // derivative of G[ {y_i^k} ] w.r.t. {y_i^k}
          const CppAD::vector<double>&     py
     )
     {     size_t n_order = q + 1;
          size_t nr      = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) );
          size_t ny      = nr * nr;
          size_t nx      = 1 + ny;
          //
          assert( nx * n_order == tx.size() );
          assert( ny * n_order == ty.size() );
          assert( px.size()    == tx.size() );
          assert( py.size()    == ty.size() );
          // -------------------------------------------------------------------
          // make sure f_arg_ is large enough
          assert( f_arg_.size() == f_result_.size() );
          // must have previous run forward with order >= n_order
          assert( f_arg_.size() >= n_order );
          // -------------------------------------------------------------------
          // make sure r_arg_, r_result_ are large enough
          assert( r_arg_.size() == r_result_.size() );
          if( r_arg_.size() < n_order )
          {     r_arg_.resize(n_order);
               r_result_.resize(n_order);
               //
               for(size_t k = 0; k < n_order; k++)
               {     r_arg_[k].resize(nr, nr);
                    r_result_[k].resize(nr, nr);
               }
          }
          // -------------------------------------------------------------------
          // unpack tx into f_arg_
          for(size_t k = 0; k < n_order; k++)
          {     // unpack arg values for this order
               for(size_t i = 0; i < ny; i++)
                    f_arg_[k].data()[i] = tx[ (1 + i) * n_order + k ];
          }
          // -------------------------------------------------------------------
          // unpack py into r_result_
          for(size_t k = 0; k < n_order; k++)
          {     for(size_t i = 0; i < ny; i++)
                    r_result_[k].data()[i] = py[ i * n_order + k ];
          }
          // -------------------------------------------------------------------
          // initialize r_arg_ as zero
          for(size_t k = 0; k < n_order; k++)
               r_arg_[k]   = matrix::Zero(nr, nr);
          // -------------------------------------------------------------------
          // matrix reverse mode calculation
          //
          for(size_t k1 = n_order; k1 > 1; k1--)
          {     size_t k = k1 - 1;
               // bar{R}_0 = bar{R}_0 + bar{R}_k (A_0 R_k)^T
               r_result_[0] +=
               r_result_[k] * f_result_[k].transpose() * f_arg_[0].transpose();
               //
               for(size_t ell = 1; ell <= k; ell++)
               {     // bar{A}_l = bar{A}_l - R_0^T bar{R}_k R_{k-l}^T
                    r_arg_[ell] -= f_result_[0].transpose()
                         * r_result_[k] * f_result_[k-ell].transpose();
                    // bar{R}_{k-l} = bar{R}_{k-1} - (R_0 A_l)^T bar{R}_k
                    r_result_[k-ell] -= f_arg_[ell].transpose()
                         * f_result_[0].transpose() * r_result_[k];
               }
          }
          r_arg_[0] -=
          f_result_[0].transpose() * r_result_[0] * f_result_[0].transpose();
          // -------------------------------------------------------------------
          // pack r_arg into px
          for(size_t k = 0; k < n_order; k++)
          {     for(size_t i = 0; i < ny; i++)
                    px[ (1 + i) * n_order + k ] = r_arg_[k].data()[i];
          }
          //
          return true;
     }

End Class Definition 

}; // End of atomic_eigen_mat_inv class

}  // END_EMPTY_NAMESPACE
Input File: cppad/example/eigen_mat_inv.hpp cppad-20170000.3/doc/atomic_eigen_cholesky.cpp.xml0000644000175200017650000017306013057470505021033 0ustar coincoin-web Atomic Eigen Cholesky Factorization: Example and Test
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Atomic Eigen Cholesky Factorization: Example and Test

Description
The ADFun function object f for this example is f ( x ) = chol ( x 0 x 1 x 1 x 2 ) = 1 x 0 ( x 0 0 x 1 x 0 x 2 - x 1 x 1 ) where the matrix is positive definite; i.e., x 0 > 0 , x 2 > 0 and x 0 x 2 - x 1 x 1 > 0 .

Contents
cholesky_theoryAD Theory for Cholesky Factorization
atomic_eigen_cholesky.hppAtomic Eigen Cholesky Factorization Class

Use Atomic Function 
# include <cppad/cppad.hpp>
# include <cppad/example/eigen_cholesky.hpp>


bool eigen_cholesky(void)
{
     typedef double scalar;
     typedef typename atomic_eigen_cholesky<scalar>::ad_scalar ad_scalar;
     typedef typename atomic_eigen_cholesky<scalar>::ad_matrix ad_matrix;
     //
     bool ok    = true;
     scalar eps = 10. * std::numeric_limits<scalar>::epsilon();
     using CppAD::NearEqual;
     //

Constructor 
     // -------------------------------------------------------------------
     // object that computes cholesky factor of a matrix
     atomic_eigen_cholesky<scalar> cholesky;
     // -------------------------------------------------------------------
     // declare independent variable vector x
     size_t n = 3;
     CPPAD_TESTVECTOR(ad_scalar) ad_x(n);
     ad_x[0] = 2.0;
     ad_x[1] = 0.5;
     ad_x[2] = 3.0;
     CppAD::Independent(ad_x);
     // -------------------------------------------------------------------
     // A = [ x[0]  x[1] ]
     //     [ x[1]  x[2] ]
     size_t nr  = 2;
     ad_matrix ad_A(nr, nr);
     ad_A(0, 0) = ad_x[0];
     ad_A(1, 0) = ad_x[1];
     ad_A(0, 1) = ad_x[1];
     ad_A(1, 1) = ad_x[2];
     // -------------------------------------------------------------------
     // use atomic operation to L such that A = L * L^T
     ad_matrix ad_L = cholesky.op(ad_A);
     // -------------------------------------------------------------------
     // declare the dependent variable vector y
     size_t m = 3;
     CPPAD_TESTVECTOR(ad_scalar) ad_y(m);
     ad_y[0] = ad_L(0, 0);
     ad_y[1] = ad_L(1, 0);
     ad_y[2] = ad_L(1, 1);
     CppAD::ADFun<scalar> f(ad_x, ad_y);
     // -------------------------------------------------------------------
     // check zero order forward mode
     CPPAD_TESTVECTOR(scalar) x(n), y(m);
     x[0] = 2.0;
     x[1] = 0.5;
     x[2] = 5.0;
     y   = f.Forward(0, x);
     scalar check;
     check = std::sqrt( x[0] );
     ok   &= NearEqual(y[0], check, eps, eps);
     check = x[1] / std::sqrt( x[0] );
     ok   &= NearEqual(y[1], check, eps, eps);
     check = std::sqrt( x[2] - x[1] * x[1] / x[0] );
     ok   &= NearEqual(y[2], check, eps, eps);
     // -------------------------------------------------------------------
     // check first order forward mode
     CPPAD_TESTVECTOR(scalar) x1(n), y1(m);
     //
     // partial w.r.t. x[0]
     x1[0] = 1.0;
     x1[1] = 0.0;
     x1[2] = 0.0;
     //
     y1    = f.Forward(1, x1);
     check = 1.0 / (2.0 * std::sqrt( x[0] ) );
     ok   &= NearEqual(y1[0], check, eps, eps);
     //
     check = - x[1] / (2.0 * x[0] * std::sqrt( x[0] ) );
     ok   &= NearEqual(y1[1], check, eps, eps);
     //
     check = std::sqrt( x[2] - x[1] * x[1] / x[0] );
     check = x[1] * x[1] / (x[0] * x[0] * 2.0 * check);
     ok   &= NearEqual(y1[2], check, eps, eps);
     //
     // partial w.r.t. x[1]
     x1[0] = 0.0;
     x1[1] = 1.0;
     x1[2] = 0.0;
     //
     y1    = f.Forward(1, x1);
     ok   &= NearEqual(y1[0], 0.0, eps, eps);
     //
     check = 1.0 / std::sqrt( x[0] );
     ok   &= NearEqual(y1[1], check, eps, eps);
     //
     check = std::sqrt( x[2] - x[1] * x[1] / x[0] );
     check = - 2.0 * x[1] / (2.0 * check * x[0] );
     ok   &= NearEqual(y1[2], check, eps, eps);
     //
     // partial w.r.t. x[2]
     x1[0] = 0.0;
     x1[1] = 0.0;
     x1[2] = 1.0;
     //
     y1    = f.Forward(1, x1);
     ok   &= NearEqual(y1[0], 0.0, eps, eps);
     ok   &= NearEqual(y1[1], 0.0, eps, eps);
     //
     check = std::sqrt( x[2] - x[1] * x[1] / x[0] );
     check = 1.0 / (2.0 * check);
     ok   &= NearEqual(y1[2], check, eps, eps);
     // -------------------------------------------------------------------
     // check second order forward mode
     CPPAD_TESTVECTOR(scalar) x2(n), y2(m);
     //
     // second partial w.r.t x[2]
     x2[0] = 0.0;
     x2[1] = 0.0;
     x2[2] = 0.0;
     y2    = f.Forward(2, x2);
     ok   &= NearEqual(y2[0], 0.0, eps, eps);
     ok   &= NearEqual(y2[1], 0.0, eps, eps);
     //
     check = std::sqrt( x[2] - x[1] * x[1] / x[0] );  // funciton value
     check = - 1.0 / ( 4.0 * check * check * check ); // second derivative
     check = 0.5 * check;                             // taylor coefficient
     ok   &= NearEqual(y2[2], check, eps, eps);
     // -------------------------------------------------------------------
     // check first order reverse mode
     CPPAD_TESTVECTOR(scalar) w(m), d1w(n);
     w[0] = 0.0;
     w[1] = 0.0;
     w[2] = 1.0;
     d1w  = f.Reverse(1, w);
     //
     // partial of f[2] w.r.t x[0]
     scalar f2    = std::sqrt( x[2] - x[1] * x[1] / x[0] );
     scalar f2_x0 = x[1] * x[1] / (2.0 * f2 * x[0] * x[0] );
     ok          &= NearEqual(d1w[0], f2_x0, eps, eps);
     //
     // partial of f[2] w.r.t x[1]
     scalar f2_x1 = - x[1] / (f2 * x[0] );
     ok          &= NearEqual(d1w[1], f2_x1, eps, eps);
     //
     // partial of f[2] w.r.t x[2]
     scalar f2_x2 = 1.0 / (2.0 * f2 );
     ok          &= NearEqual(d1w[2], f2_x2, eps, eps);
     // -------------------------------------------------------------------
     // check second order reverse mode
     CPPAD_TESTVECTOR(scalar) d2w(2 * n);
     d2w  = f.Reverse(2, w);
     //
     // check first order results
     ok &= NearEqual(d2w[0 * 2 + 0], f2_x0, eps, eps);
     ok &= NearEqual(d2w[1 * 2 + 0], f2_x1, eps, eps);
     ok &= NearEqual(d2w[2 * 2 + 0], f2_x2, eps, eps);
     //
     // check second order results
     scalar f2_x2_x0 = - 0.5 * f2_x0 / (f2 * f2 );
     ok             &= NearEqual(d2w[0 * 2 + 1], f2_x2_x0, eps, eps);
     scalar f2_x2_x1 = - 0.5 * f2_x1 / (f2 * f2 );
     ok             &= NearEqual(d2w[1 * 2 + 1], f2_x2_x1, eps, eps);
     scalar f2_x2_x2 = - 0.5 * f2_x2 / (f2 * f2 );
     ok             &= NearEqual(d2w[2 * 2 + 1], f2_x2_x2, eps, eps);
     // -------------------------------------------------------------------
     // check third order reverse mode
     CPPAD_TESTVECTOR(scalar) d3w(3 * n);
     d3w  = f.Reverse(3, w);
     //
     // check first order results
     ok &= NearEqual(d3w[0 * 3 + 0], f2_x0, eps, eps);
     ok &= NearEqual(d3w[1 * 3 + 0], f2_x1, eps, eps);
     ok &= NearEqual(d3w[2 * 3 + 0], f2_x2, eps, eps);
     //
     // check second order results
     ok             &= NearEqual(d3w[0 * 3 + 1], f2_x2_x0, eps, eps);
     ok             &= NearEqual(d3w[1 * 3 + 1], f2_x2_x1, eps, eps);
     ok             &= NearEqual(d3w[2 * 3 + 1], f2_x2_x2, eps, eps);
     // -------------------------------------------------------------------
     scalar f2_x2_x2_x0 = - 0.5 * f2_x2_x0 / (f2 * f2);
     f2_x2_x2_x0 += f2_x2 * f2_x0 / (f2 * f2 * f2);
     ok          &= NearEqual(d3w[0 * 3 + 2], 0.5 * f2_x2_x2_x0, eps, eps);
     scalar f2_x2_x2_x1 = - 0.5 * f2_x2_x1 / (f2 * f2);
     f2_x2_x2_x1 += f2_x2 * f2_x1 / (f2 * f2 * f2);
     ok          &= NearEqual(d3w[1 * 3 + 2], 0.5 * f2_x2_x2_x1, eps, eps);
     scalar f2_x2_x2_x2 = - 0.5 * f2_x2_x2 / (f2 * f2);
     f2_x2_x2_x2 += f2_x2 * f2_x2 / (f2 * f2 * f2);
     ok          &= NearEqual(d3w[2 * 3 + 2], 0.5 * f2_x2_x2_x2, eps, eps);
     return ok;
}
Input File: example/atomic/eigen_cholesky.cpp cppad-20170000.3/doc/cholesky_theory.xml0000644000175200017650000022407313057470505017142 0ustar coincoin-web AD Theory for Cholesky Factorization
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AD Theory for Cholesky Factorization

Reference
See section 3.6 of Sebastian F. Walter's Ph.D. thesis, Structured Higher-Order Algorithmic Differentiation in the Forward and Reverse Mode with Application in Optimum Experimental Design , Humboldt-Universitat zu Berlin, 2011.

Notation

Cholesky Factor
We are given a positive definite symmetric matrix A ∈ R n × n and a Cholesky factorization A = L L T where L ∈ R n × n is lower triangular.

Taylor Coefficient
The matrix A is a function of a scalar argument t . For k = 0 , … , K , we use A k for the corresponding Taylor coefficients; i.e., A ( t ) = o ( t K ) + ∑ k = 0 K A k t k where o ( t K ) / t K → 0 as t → 0 . We use a similar notation for L ( t ) .

Lower Triangular Part
For a square matrix C , lower ( C ) is the lower triangular part of C , diag ( C ) is the diagonal matrix with the same diagonal as C and low ( C ) = lower ( C ) - 1 2 diag ( C )
Forward Mode
For Taylor coefficient order k = 0 , … , K the coefficients A k ∈ R n × n , and satisfy the equation A k = ∑ ℓ = 0 k L ℓ L k - ℓ T In the case where k = 0 , the A 0 = L 0 L 0 T The value of L 0 can be computed using the Cholesky factorization. In the case where k > 0 , A k = L k L 0 T + L 0 L k T + B k where B k = ∑ ℓ = 1 k -1 L ℓ L k - ℓ T Note that B k is defined in terms of Taylor coefficients of L ( t ) that have order less than k . We also note that L 0 -1 ( A k - B k ) L 0 - T = L 0 -1 L k + L k T L 0 - T The first matrix on the right hand side is lower triangular, the second is upper triangular, and the diagonals are equal. It follows that L 0 -1 L k = low [ L 0 -1 ( A k - B k ) L 0 - T ] L k = L 0 low [ L 0 -1 ( A k - B k ) L 0 - T ] This expresses L k in term of the Taylor coefficients of A ( t ) and the lower order coefficients of L ( t ) .

Lemma 1
We use the notation C ˙ for the derivative of a matrix valued function C ( s ) with respect to a scalar argument s . We use the notation S ¯ and L ¯ for the partial derivative of a scalar value function F ¯ ( S , L ) with respect to a symmetric matrix S and an lower triangular matrix L . Define the scalar valued function F ^ ( C ) = F ¯ [ S , L ^ ( S ) ] We use S ^ for the total derivative of F ^ with respect to S . Suppose that L ^ ( S ) is such that L ˙ = L 0 low ( L 0 -1 S ˙ L 0 - T ) for any S ( s ) . It follows that S ^ = S ¯ + 1 2 ( M + M T ) where M = L 0 - T low ( L 0 T L ¯ ) T L 0 -1
Proof ∂ s F ^ [ S ( s ) , L ( s ) ] = tr ( S ¯ T S ˙ ) + tr ( L ¯ T L ˙ ) tr ( L ¯ T L ˙ ) = tr [ L ¯ T L 0 low ( L 0 -1 S ˙ L 0 - T ) ] = tr [ low ( L 0 -1 S ˙ L 0 - T ) T L 0 T L ¯ ] = tr [ L 0 -1 S ˙ L 0 - T low ( L 0 T L ¯ ) ] = tr [ L 0 - T low ( L 0 T L ¯ ) L 0 -1 S ˙ ] ∂ s F ^ [ S ( s ) , L ( s ) ] = tr ( S ¯ T S ˙ ) + tr [ L 0 - T low ( L 0 T L ¯ ) L 0 -1 S ˙ ] We now consider the ( i , j ) component function, for a symmetric matrix S ( s ) , defined by S k , ℓ ( s ) = { 1 if k = i and ℓ = j 1 if k = j and ℓ = i 0 otherwise } This shows that the formula in the lemma is correct for S ^ i , j and S ^ j , i . This completes the proof because the component ( i , j ) was arbitrary.

Lemma 2
We use the same assumptions as in Lemma 1 except that the matrix S is lower triangular (instead of symmetric). It follows that S ^ = S ¯ + lower ( M ) where M = L 0 - T low ( L 0 T L ¯ ) T L 0 -1 The proof of this lemma is identical to Lemma 2 except that component function is defined by S k , ℓ ( s ) = { 1 if k = i and ℓ = j 0 otherwise }
Reverse Mode

Case k = 0
For the case k = 0 , A ˙ 0 = L ˙ 0 L 0 T + L 0 L ˙ 0 T L 0 -1 A ˙ 0 L 0 - T = L 0 -1 L ˙ 0 + L ˙ 0 T L 0 - T low ( L 0 -1 A ˙ 0 L 0 - T ) = L 0 -1 L ˙ 0 L ˙ 0 = L 0 low ( L 0 -1 A ˙ 0 L 0 - T ) It follows from Lemma 1 that A ¯ 0 = + 1 2 ( M + M T ) where M = L 0 - T low ( L 0 T L ¯ 0 ) T L 0 -1 and A ¯ 0 is the partial before and after is before and after L 0 is removed from the scalar function dependency.

Case k > 0
In the case where k > 0 , A k = L k L 0 T + L 0 L k T + B k where B k is defined in terms of Taylor coefficients of L ( t ) that have order less than k . It follows that L ˙ k L 0 T + L 0 L ˙ k T = A ˙ k - B ˙ k - L ˙ 0 L k T - L k L ˙ 0 T L 0 -1 L ˙ k + L ˙ k T L 0 - T = L 0 -1 ( A ˙ k - B ˙ k - L ˙ 0 L k T - L k L ˙ 0 T ) L 0 - T L 0 -1 L ˙ k = low [ L 0 -1 ( A ˙ k - B ˙ k - L ˙ 0 L k T - L k L ˙ 0 T ) L 0 - T ] L ˙ k = L 0 low [ L 0 -1 ( A ˙ k - B ˙ k - L ˙ 0 L k T - L k L ˙ 0 T ) L 0 - T ] The matrix A k is symmetric, it follows that A ¯ k = + 1 2 ( M k + M k T ) where M k = L 0 - T low ( L 0 T L ¯ k ) T L 0 -1 The matrix B k is also symmetric, hence B ¯ k = - 1 2 ( M k + M k T ) We define the symmetric matrix C k ( s ) by C ˙ k = L ˙ 0 L k T + L k L ˙ 0 T and remove the dependency on C k with tr ( C ¯ k T C ˙ k ) = tr ( B ¯ k T C ˙ k ) = tr ( B ¯ k T L ˙ 0 L k T ) + tr ( B ¯ k T L k L ˙ 0 T ) = tr ( L k T B ¯ k T L ˙ 0 ) + tr ( L k T B ¯ k L ˙ 0 ) = tr [ L k T ( B ¯ k + B ¯ k T ) L ˙ 0 ] Thus, removing C k from the dependency results in the following update to L ¯ 0 : L ¯ 0 = + lower [ ( B ¯ k + B ¯ k T ) L k ] which is the same as L ¯ 0 = + 2 lower [ B ¯ k L k ] We still need to remove B k from the dependency. It follows from its definition that B ˙ k = ∑ ℓ = 1 k -1 L ˙ ℓ L k - ℓ T + L ℓ L ˙ k - ℓ T tr ( B ¯ k T B ˙ k ) = ∑ ℓ = 1 k -1 tr ( B ¯ k T L ˙ ℓ L k - ℓ T ) + tr ( B ¯ k T L ℓ L ˙ k - ℓ T ) = ∑ ℓ = 1 k -1 tr ( L k - ℓ T B ¯ k T L ˙ ℓ ) + ∑ ℓ = 1 k -1 tr ( L ℓ T B ¯ k L ˙ k - ℓ ) We now use the fact that B ¯ k is symmetric to conclude tr ( B ¯ k T B ˙ k ) = 2 ∑ ℓ = 1 k -1 tr ( L k - ℓ T B ¯ k T L ˙ ℓ ) Each of the L ˙ ℓ matrices is lower triangular. Thus, removing B k from the dependency results in the following update for ℓ = 1 , … , k -1 : L ¯ ℓ = + 2 lower ( B ¯ k L k - ℓ )
Input File: omh/theory/cholesky.omh cppad-20170000.3/doc/atomic_eigen_cholesky.hpp.xml0000644000175200017650000023012113057470505021030 0ustar coincoin-web Atomic Eigen Cholesky Factorization Class
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Atomic Eigen Cholesky Factorization Class

Purpose
Construct an atomic operation that computes a lower triangular matrix L such that L L T = A for any positive integer p and symmetric positive definite matrix A ∈ R p × p .

Start Class Definition 
# include <cppad/cppad.hpp>
# include <Eigen/Dense>
Public

Types 
namespace { // BEGIN_EMPTY_NAMESPACE

template <class Base>
class atomic_eigen_cholesky : public CppAD::atomic_base<Base> {
public:
     // -----------------------------------------------------------
     // type of elements during calculation of derivatives
     typedef Base              scalar;
     // type of elements during taping
     typedef CppAD::AD<scalar> ad_scalar;
     //
     // type of matrix during calculation of derivatives
     typedef Eigen::Matrix<
          scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>        matrix;
     // type of matrix during taping
     typedef Eigen::Matrix<
          ad_scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > ad_matrix;
     //
     // lower triangular scalar matrix
     typedef Eigen::TriangularView<matrix, Eigen::Lower>             lower_view;

Constructor 
     // constructor
     atomic_eigen_cholesky(void) : CppAD::atomic_base<Base>(
          "atom_eigen_cholesky"                             ,
          CppAD::atomic_base<Base>::set_sparsity_enum
     )
     { }

op 
     // use atomic operation to invert an AD matrix
     ad_matrix op(const ad_matrix& arg)
     {     size_t nr = size_t( arg.rows() );
          size_t ny = ( (nr + 1 ) * nr ) / 2;
          size_t nx = 1 + ny;
          assert( nr == size_t( arg.cols() ) );
          // -------------------------------------------------------------------
          // packed version of arg
          CPPAD_TESTVECTOR(ad_scalar) packed_arg(nx);
          size_t index = 0;
          packed_arg[index++] = ad_scalar( nr );
          // lower triangle of symmetric matrix A
          for(size_t i = 0; i < nr; i++)
          {     for(size_t j = 0; j <= i; j++)
                    packed_arg[index++] = arg(i, j);
          }
          assert( index == nx );
          // -------------------------------------------------------------------
          // packed version of result = arg^{-1}.
          // This is an atomic_base function call that CppAD uses to
          // store the atomic operation on the tape.
          CPPAD_TESTVECTOR(ad_scalar) packed_result(ny);
          (*this)(packed_arg, packed_result);
          // -------------------------------------------------------------------
          // unpack result matrix L
          ad_matrix result = ad_matrix::Zero(nr, nr);
          index = 0;
          for(size_t i = 0; i < nr; i++)
          {     for(size_t j = 0; j <= i; j++)
                    result(i, j) = packed_result[index++];
          }
          return result;
     }

Private

Variables 
private:
     // -------------------------------------------------------------
     // one forward mode vector of matrices for argument and result
     CppAD::vector<matrix> f_arg_, f_result_;
     // one reverse mode vector of matrices for argument and result
     CppAD::vector<matrix> r_arg_, r_result_;
     // -------------------------------------------------------------

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          // lowest order Taylor coefficient we are evaluating
          size_t                          p ,
          // highest order Taylor coefficient we are evaluating
          size_t                          q ,
          // which components of x are variables
          const CppAD::vector<bool>&      vx ,
          // which components of y are variables
          CppAD::vector<bool>&            vy ,
          // tx [ j * (q+1) + k ] is x_j^k
          const CppAD::vector<scalar>&    tx ,
          // ty [ i * (q+1) + k ] is y_i^k
          CppAD::vector<scalar>&          ty
     )
     {     size_t n_order = q + 1;
          size_t nr      = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) );
          size_t ny      = ((nr + 1) * nr) / 2;
          size_t nx      = 1 + ny;
          assert( vx.size() == 0 || nx == vx.size() );
          assert( vx.size() == 0 || ny == vy.size() );
          assert( nx * n_order == tx.size() );
          assert( ny * n_order == ty.size() );
          //
          // -------------------------------------------------------------------
          // make sure f_arg_ and f_result_ are large enough
          assert( f_arg_.size() == f_result_.size() );
          if( f_arg_.size() < n_order )
          {     f_arg_.resize(n_order);
               f_result_.resize(n_order);
               //
               for(size_t k = 0; k < n_order; k++)
               {     f_arg_[k].resize(nr, nr);
                    f_result_[k].resize(nr, nr);
               }
          }
          // -------------------------------------------------------------------
          // unpack tx into f_arg_
          for(size_t k = 0; k < n_order; k++)
          {     size_t index = 1;
               // unpack arg values for this order
               for(size_t i = 0; i < nr; i++)
               {     for(size_t j = 0; j <= i; j++)
                    {     f_arg_[k](i, j) = tx[ index * n_order + k ];
                         f_arg_[k](j, i) = f_arg_[k](i, j);
                         index++;
                    }
               }
          }
          // -------------------------------------------------------------------
          // result for each order
          // (we could avoid recalculting f_result_[k] for k=0,...,p-1)
          //
          Eigen::LLT<matrix> cholesky(f_arg_[0]);
          f_result_[0]   = cholesky.matrixL();
          lower_view L_0 = f_result_[0].template triangularView<Eigen::Lower>();
          for(size_t k = 1; k < n_order; k++)
          {     // initialize sum as A_k
               matrix f_sum = f_arg_[k];
               // compute A_k - B_k
               for(size_t ell = 1; ell < k; ell++)
                    f_sum -= f_result_[ell] * f_result_[k-ell].transpose();
               // compute L_0^{-1} * (A_k - B_k) * L_0^{-T}
               matrix temp = L_0.template solve<Eigen::OnTheLeft>(f_sum);
               temp   = L_0.transpose().template solve<Eigen::OnTheRight>(temp);
               // divide the diagonal by 2
               for(size_t i = 0; i < nr; i++)
                    temp(i, i) /= scalar(2.0);
               // L_k = L_0 * low[ L_0^{-1} * (A_k - B_k) * L_0^{-T} ]
               lower_view view = temp.template triangularView<Eigen::Lower>();
               f_result_[k] = f_result_[0] * view;
          }
          // -------------------------------------------------------------------
          // pack result_ into ty
          for(size_t k = 0; k < n_order; k++)
          {     size_t index = 0;
               for(size_t i = 0; i < nr; i++)
               {     for(size_t j = 0; j <= i; j++)
                    {     ty[ index * n_order + k ] = f_result_[k](i, j);
                         index++;
                    }
               }
          }
          // -------------------------------------------------------------------
          // check if we are computing vy
          if( vx.size() == 0 )
               return true;
          // ------------------------------------------------------------------
          // This is a very dumb algorithm that over estimates which
          // elements of the inverse are variables (which is not efficient).
          bool var = false;
          for(size_t i = 0; i < ny; i++)
               var |= vx[1 + i];
          for(size_t i = 0; i < ny; i++)
               vy[i] = var;
          //
          return true;
     }

reverse 
     // reverse mode routine called by CppAD
     virtual bool reverse(
          // highest order Taylor coefficient that we are computing derivative of
          size_t                     q ,
          // forward mode Taylor coefficients for x variables
          const CppAD::vector<double>&     tx ,
          // forward mode Taylor coefficients for y variables
          const CppAD::vector<double>&     ty ,
          // upon return, derivative of G[ F[ {x_j^k} ] ] w.r.t {x_j^k}
          CppAD::vector<double>&           px ,
          // derivative of G[ {y_i^k} ] w.r.t. {y_i^k}
          const CppAD::vector<double>&     py
     )
     {     size_t n_order = q + 1;
          size_t nr = size_t( CppAD::Integer( tx[ 0 * n_order + 0 ] ) );
          size_t ny = ( (nr + 1 ) * nr ) / 2;
          size_t nx = 1 + ny;
          //
          assert( nx * n_order == tx.size() );
          assert( ny * n_order == ty.size() );
          assert( px.size()    == tx.size() );
          assert( py.size()    == ty.size() );
          // -------------------------------------------------------------------
          // make sure f_arg_ is large enough
          assert( f_arg_.size() == f_result_.size() );
          // must have previous run forward with order >= n_order
          assert( f_arg_.size() >= n_order );
          // -------------------------------------------------------------------
          // make sure r_arg_, r_result_ are large enough
          assert( r_arg_.size() == r_result_.size() );
          if( r_arg_.size() < n_order )
          {     r_arg_.resize(n_order);
               r_result_.resize(n_order);
               //
               for(size_t k = 0; k < n_order; k++)
               {     r_arg_[k].resize(nr, nr);
                    r_result_[k].resize(nr, nr);
               }
          }
          // -------------------------------------------------------------------
          // unpack tx into f_arg_
          for(size_t k = 0; k < n_order; k++)
          {     size_t index = 1;
               // unpack arg values for this order
               for(size_t i = 0; i < nr; i++)
               {     for(size_t j = 0; j <= i; j++)
                    {     f_arg_[k](i, j) = tx[ index * n_order + k ];
                         f_arg_[k](j, i) = f_arg_[k](i, j);
                         index++;
                    }
               }
          }
          // -------------------------------------------------------------------
          // unpack py into r_result_
          for(size_t k = 0; k < n_order; k++)
          {     r_result_[k] = matrix::Zero(nr, nr);
               size_t index = 0;
               for(size_t i = 0; i < nr; i++)
               {     for(size_t j = 0; j <= i; j++)
                    {     r_result_[k](i, j) = py[ index * n_order + k ];
                         index++;
                    }
               }
          }
          // -------------------------------------------------------------------
          // initialize r_arg_ as zero
          for(size_t k = 0; k < n_order; k++)
               r_arg_[k]   = matrix::Zero(nr, nr);
          // -------------------------------------------------------------------
          // matrix reverse mode calculation
          lower_view L_0 = f_result_[0].template triangularView<Eigen::Lower>();
          //
          for(size_t k1 = n_order; k1 > 1; k1--)
          {     size_t k = k1 - 1;
               //
               // L_0^T * bar{L}_k
               matrix tmp1 = L_0.transpose() * r_result_[k];
               //
               //low[ L_0^T * bar{L}_k ]
               for(size_t i = 0; i < nr; i++)
                    tmp1(i, i) /= scalar(2.0);
               matrix tmp2 = tmp1.template triangularView<Eigen::Lower>();
               //
               // L_0^{-T} low[ L_0^T * bar{L}_k ]
               tmp1 = L_0.transpose().template solve<Eigen::OnTheLeft>( tmp2 );
               //
               // M_k = L_0^{-T} * low[ L_0^T * bar{L}_k ]^{T} L_0^{-1}
               matrix M_k = L_0.transpose().template
                    solve<Eigen::OnTheLeft>( tmp1.transpose() );
               //
               // remove L_k and compute bar{B}_k
               matrix barB_k = scalar(0.5) * ( M_k + M_k.transpose() );
               r_arg_[k]    += barB_k;
               barB_k        = scalar(-1.0) * barB_k;
               //
               // 2.0 * lower( bar{B}_k L_k )
               matrix temp = scalar(2.0) * barB_k * f_result_[k];
               temp        = temp.template triangularView<Eigen::Lower>();
               //
               // remove C_k
               r_result_[0] += temp;
               //
               // remove B_k
               for(size_t ell = 1; ell < k; ell++)
               {     // bar{L}_ell = 2 * lower( \bar{B}_k * L_{k-ell} )
                    temp = scalar(2.0) * barB_k * f_result_[k-ell];
                    r_result_[ell] += temp.template triangularView<Eigen::Lower>();
               }
          }
          // M_0 = L_0^{-T} * low[ L_0^T * bar{L}_0 ]^{T} L_0^{-1}
          matrix M_0 = L_0.transpose() * r_result_[0];
          for(size_t i = 0; i < nr; i++)
               M_0(i, i) /= scalar(2.0);
          M_0 = M_0.template triangularView<Eigen::Lower>();
          M_0 = L_0.template solve<Eigen::OnTheRight>( M_0 );
          M_0 = L_0.transpose().template solve<Eigen::OnTheLeft>( M_0 );
          // remove L_0
          r_arg_[0] += scalar(0.5) * ( M_0 + M_0.transpose() );
          // -------------------------------------------------------------------
          // pack r_arg into px
          // note that only the lower triangle of barA_k is stored in px
          for(size_t k = 0; k < n_order; k++)
          {     size_t index = 0;
               px[ index * n_order + k ] = 0.0;
               index++;
               for(size_t i = 0; i < nr; i++)
               {     for(size_t j = 0; j < i; j++)
                    {     px[ index * n_order + k ] = 2.0 * r_arg_[k](i, j);
                         index++;
                    }
                    px[ index * n_order + k] = r_arg_[k](i, i);
                    index++;
               }
          }
          // -------------------------------------------------------------------
          return true;
     }

End Class Definition 

}; // End of atomic_eigen_cholesky class

}  // END_EMPTY_NAMESPACE
Input File: cppad/example/eigen_cholesky.hpp cppad-20170000.3/doc/atomic_mat_mul.cpp.xml0000644000175200017650000017714113057470505017505 0ustar coincoin-web User Atomic Matrix Multiply: Example and Test
Prev Next

User Atomic Matrix Multiply: Example and Test

See Also
atomic_eigen_mat_mul.cpp

Class Definition
This example uses the file atomic_mat_mul.hpp which defines matrix multiply as a atomic_base operation.

Use Atomic Function 
# include <cppad/cppad.hpp>
# include <cppad/example/mat_mul.hpp>

bool mat_mul(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::vector;
     size_t i, j;

Constructor 

     // -------------------------------------------------------------------
     // object that multiplies  2 x 2  matrices
     atomic_mat_mul afun;

Recording 
     // start recording with four independent varables
     size_t n = 4;
     vector<double> x(n);
     vector< AD<double> > ax(n);
     for(j = 0; j < n; j++)
          ax[j] = x[j] = j + 1;
     CppAD::Independent(ax);

     // ------------------------------------------------------------------
     size_t nr_left = 2;
     size_t n_middle  = 2;
     size_t nc_right = 2;
     vector< AD<double> > atom_x(3 + (nr_left + nc_right) * n_middle );

     // matrix dimensions
     atom_x[0] = AD<double>( nr_left );
     atom_x[1] = AD<double>( n_middle );
     atom_x[2] = AD<double>( nc_right );

     // left matrix
     atom_x[3] = ax[0];  // left[0, 0] = x0
     atom_x[4] = ax[1];  // left[0, 1] = x1
     atom_x[5] = 5.;     // left[1, 0] = 5
     atom_x[6] = 6.;     // left[1, 1] = 6

     // right matix
     atom_x[7] = ax[2];  // right[0, 0] = x2
     atom_x[8] = 7.;     // right[0, 1] = 7
     atom_x[9] = ax[3];  // right[1, 0] = x3
     atom_x[10] = 8.;     // right[1, 1] = 8
     // ------------------------------------------------------------------
     /*
     [ x0 , x1 ] * [ x2 , 7 ] = [ x0*x2 + x1*x3 , x0*7 + x1*8 ]
     [ 5  , 6  ]   [ x3 , 8 ]   [  5*x2 +  6*x3 ,  5*7 +  6*8 ]
     */
     vector< AD<double> > atom_y(nr_left * nc_right);
     afun(atom_x, atom_y);

     ok &= (atom_y[0] == x[0]*x[2] + x[1]*x[3]) & Variable(atom_y[0]);
     ok &= (atom_y[1] == x[0]*7.   + x[1]*8.  ) & Variable(atom_y[1]);
     ok &= (atom_y[2] ==   5.*x[2] +   6.*x[3]) & Variable(atom_y[2]);
     ok &= (atom_y[3] ==   5.*7.   +   6.*8.  ) & Parameter(atom_y[3]);

     // ------------------------------------------------------------------
     // define the function g : x -> atom_y
     // g(x) = [ x0*x2 + x1*x3 , x0*7 + x1*8 , 5*x2  + 6*x3  , 5*7 + 6*8 ]^T
     CppAD::ADFun<double> g(ax, atom_y);

forward 
     // Test zero order forward mode evaluation of g(x)
     size_t m = atom_y.size();
     vector<double> y(m);
     for(j = 0; j <  n; j++)
          x[j] = j + 2;
     y = g.Forward(0, x);
     ok &= y[0] == x[0] * x[2] + x[1] * x[3];
     ok &= y[1] == x[0] * 7.   + x[1] * 8.;
     ok &= y[2] == 5. * x[2]   + 6. * x[3];
     ok &= y[3] == 5. * 7.     + 6. * 8.;

     //----------------------------------------------------------------------
     // Test first order forward mode evaluation of g'(x) * [1, 2, 3, 4]^T
     // g'(x) = [ x2, x3, x0, x1 ]
     //         [ 7 ,  8,  0, 0  ]
     //         [ 0 ,  0,  5, 6  ]
     //         [ 0 ,  0,  0, 0  ]
     CppAD::vector<double> dx(n), dy(m);
     for(j = 0; j <  n; j++)
          dx[j] = j + 1;
     dy = g.Forward(1, dx);
     ok &= dy[0] == 1. * x[2] + 2. * x[3] + 3. * x[0] + 4. * x[1];
     ok &= dy[1] == 1. * 7.   + 2. * 8.   + 3. * 0.   + 4. * 0.;
     ok &= dy[2] == 1. * 0.   + 2. * 0.   + 3. * 5.   + 4. * 6.;
     ok &= dy[3] == 1. * 0.   + 2. * 0.   + 3. * 0.   + 4. * 0.;

     //----------------------------------------------------------------------
     // Test second order forward mode
     // g_0^2 (x) = [ 0, 0, 1, 0 ], g_0^2 (x) * [1] = [3]
     //             [ 0, 0, 0, 1 ]              [2]   [4]
     //             [ 1, 0, 0, 0 ]              [3]   [1]
     //             [ 0, 1, 0, 0 ]              [4]   [2]
     CppAD::vector<double> ddx(n), ddy(m);
     for(j = 0; j <  n; j++)
          ddx[j] = 0.;
     ddy = g.Forward(2, ddx);

     // [1, 2, 3, 4] * g_0^2 (x) * [1, 2, 3, 4]^T = 1*3 + 2*4 + 3*1 + 4*2
     ok &= 2. * ddy[0] == 1. * 3. + 2. * 4. + 3. * 1. + 4. * 2.;

     // for i > 0, [1, 2, 3, 4] * g_i^2 (x) * [1, 2, 3, 4]^T = 0
     ok &= ddy[1] == 0.;
     ok &= ddy[2] == 0.;
     ok &= ddy[3] == 0.;

reverse 
     // Test second order reverse mode
     CppAD::vector<double> w(m), dw(2 * n);
     for(i = 0; i < m; i++)
          w[i] = 0.;
     w[0] = 1.;
     dw = g.Reverse(2, w);

     // g_0'(x) = [ x2, x3, x0, x1 ]
     ok &= dw[0*2 + 0] == x[2];
     ok &= dw[1*2 + 0] == x[3];
     ok &= dw[2*2 + 0] == x[0];
     ok &= dw[3*2 + 0] == x[1];

     // g_0'(x)   * [1, 2, 3, 4]  = 1 * x2 + 2 * x3 + 3 * x0 + 4 * x1
     // g_0^2 (x) * [1, 2, 3, 4]  = [3, 4, 1, 2]
     ok &= dw[0*2 + 1] == 3.;
     ok &= dw[1*2 + 1] == 4.;
     ok &= dw[2*2 + 1] == 1.;
     ok &= dw[3*2 + 1] == 2.;

option 
     //----------------------------------------------------------------------
     // Test both the boolean and set sparsity at the atomic level
     for(size_t sparse_index = 0; sparse_index < 2; sparse_index++)
     {     if( sparse_index == 0 )
               afun.option( CppAD::atomic_base<double>::bool_sparsity_enum );
          else     afun.option( CppAD::atomic_base<double>::set_sparsity_enum );

for_sparse_jac 
     // Test forward Jacobian sparsity pattern
     /*
     g(x) = [ x0*x2 + x1*x3 , x0*7 + x1*8 , 5*x2  + 6*x3  , 5*7 + 6*8 ]^T
     so the sparsity pattern should be
     s[0] = {0, 1, 2, 3}
     s[1] = {0, 1}
     s[2] = {2, 3}
     s[3] = {}
     */
     CppAD::vector< std::set<size_t> > r(n), s(m);
     for(j = 0; j <  n; j++)
     {     assert( r[j].empty() );
          r[j].insert(j);
     }
     s = g.ForSparseJac(n, r);
     for(j = 0; j <  n; j++)
     {     // s[0] = {0, 1, 2, 3}
          ok &= s[0].find(j) != s[0].end();
          // s[1] = {0, 1}
          if( j == 0 || j == 1 )
               ok &= s[1].find(j) != s[1].end();
          else     ok &= s[1].find(j) == s[1].end();
          // s[2] = {2, 3}
          if( j == 2 || j == 3 )
               ok &= s[2].find(j) != s[2].end();
          else     ok &= s[2].find(j) == s[2].end();
     }
     // s[3] == {}
     ok &= s[3].empty();

rev_sparse_jac 
     // Test reverse Jacobian sparsity pattern
     for(i = 0; i <  m; i++)
     {     s[i].clear();
          s[i].insert(i);
     }
     r = g.RevSparseJac(m, s);
     for(j = 0; j <  n ; j++)
     {     // r[0] = {0, 1, 2, 3}
          ok &= r[0].find(j) != r[0].end();
          // r[1] = {0, 1}
          if( j == 0 || j == 1 )
               ok &= r[1].find(j) != r[1].end();
          else     ok &= r[1].find(j) == r[1].end();
          // r[2] = {2, 3}
          if( j == 2 || j == 3 )
               ok &= r[2].find(j) != r[2].end();
          else     ok &= r[2].find(j) == r[2].end();
     }
     // r[3] == {}
     ok &= r[3].empty();

rev_sparse_hes 
     /* Test reverse Hessian sparsity pattern
     g_0^2 (x) = [ 0, 0, 1, 0 ] and for i > 0, g_i^2 = 0
                 [ 0, 0, 0, 1 ]
                 [ 1, 0, 0, 0 ]
                 [ 0, 1, 0, 0 ]
     so for the sparsity pattern for the first component of g is
     h[0] = {2}
     h[1] = {3}
     h[2] = {0}
     h[3] = {1}
     */
     CppAD::vector< std::set<size_t> > h(n), t(1);
     t[0].clear();
     t[0].insert(0);
     h = g.RevSparseHes(n, t);
     size_t check[] = {2, 3, 0, 1};
     for(j = 0; j <  n; j++)
     {     // h[j] = { check[j] }
          for(i = 0; i < n; i++)
          {     if( i == check[j] )
                    ok &= h[j].find(i) != h[j].end();
               else     ok &= h[j].find(i) == h[j].end();
          }
     }
     t[0].clear();
     for( j = 1; j < n; j++)
               t[0].insert(j);
     h = g.RevSparseHes(n, t);
     for(j = 0; j <  n; j++)
     {     // h[j] = { }
          for(i = 0; i < n; i++)
               ok &= h[j].find(i) == h[j].end();
     }

     //-----------------------------------------------------------------
     } // end for(size_t sparse_index  ...
     //-----------------------------------------------------------------

     return ok;
}
Input File: example/atomic/mat_mul.cpp cppad-20170000.3/doc/atomic_mat_mul.hpp.xml0000644000175200017650000042642113057470505017510 0ustar coincoin-web Matrix Multiply as an Atomic Operation
Prev Next atomic_mat_mul.hpp

Matrix Multiply as an Atomic Operation

See Also
atomic_eigen_mat_mul.hpp

Matrix Dimensions
This example puts the matrix dimensions in the atomic function arguments, instead of the constructor , so that they can be different for different calls to the atomic function. These dimensions are:
nr_left number of rows in the left matrix
n_middle rows in the left matrix and columns in right
nc_right number of columns in the right matrix

Start Class Definition 
# include <cppad/cppad.hpp>
namespace { // Begin empty namespace
using CppAD::vector;
//
using CppAD::set_union;
//
// matrix result = left * right
class atomic_mat_mul : public CppAD::atomic_base<double> {

Constructor 
public:
     // ---------------------------------------------------------------------
     // constructor
     atomic_mat_mul(void) : CppAD::atomic_base<double>("mat_mul")
     { }
private:

Left Operand Element Index
Index in the Taylor coefficient matrix tx of a left matrix element. 
     size_t left(
          size_t i        , // left matrix row index
          size_t j        , // left matrix column index
          size_t k        , // Taylor coeffocient order
          size_t nk       , // number of Taylor coefficients in tx
          size_t nr_left  , // rows in left matrix
          size_t n_middle , // rows in left and columns in right
          size_t nc_right ) // columns in right matrix
     {     assert( i < nr_left );
          assert( j < n_middle );
          return (3 + i * n_middle + j) * nk + k;
     }

Right Operand Element Index
Index in the Taylor coefficient matrix tx of a right matrix element. 
     size_t right(
          size_t i        , // right matrix row index
          size_t j        , // right matrix column index
          size_t k        , // Taylor coeffocient order
          size_t nk       , // number of Taylor coefficients in tx
          size_t nr_left  , // rows in left matrix
          size_t n_middle , // rows in left and columns in right
          size_t nc_right ) // columns in right matrix
     {     assert( i < n_middle );
          assert( j < nc_right );
          size_t offset = 3 + nr_left * n_middle;
          return (offset + i * nc_right + j) * nk + k;
     }

Result Element Index
Index in the Taylor coefficient matrix ty of a result matrix element. 
     size_t result(
          size_t i        , // result matrix row index
          size_t j        , // result matrix column index
          size_t k        , // Taylor coeffocient order
          size_t nk       , // number of Taylor coefficients in ty
          size_t nr_left  , // rows in left matrix
          size_t n_middle , // rows in left and columns in right
          size_t nc_right ) // columns in right matrix
     {     assert( i < nr_left  );
          assert( j < nc_right );
          return (i * nc_right + j) * nk + k;
     }

Forward Matrix Multiply
Forward mode multiply Taylor coefficients in tx and sum into ty (for one pair of left and right orders) 
     void forward_multiply(
          size_t                 k_left   , // order for left coefficients
          size_t                 k_right  , // order for right coefficients
          const vector<double>&  tx       , // domain space Taylor coefficients
                vector<double>&  ty       , // range space Taylor coefficients
          size_t                 nr_left  , // rows in left matrix
          size_t                 n_middle , // rows in left and columns in right
          size_t                 nc_right ) // columns in right matrix
     {
          size_t nx       = 3 + (nr_left + nc_right) * n_middle;
          size_t nk       = tx.size() / nx;
# ifndef NDEBUG
          size_t ny       = nr_left * nc_right;
          assert( nk == ty.size() / ny );
# endif
          //
          size_t k_result = k_left + k_right;
          assert( k_result < nk );
          //
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     double sum = 0.0;
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     size_t i_left  = left(
                              i, ell, k_left, nk, nr_left, n_middle, nc_right
                         );
                         size_t i_right = right(
                              ell, j,  k_right, nk, nr_left, n_middle, nc_right
                         );
                         sum           += tx[i_left] * tx[i_right];
                    }
                    size_t i_result = result(
                         i, j, k_result, nk, nr_left, n_middle, nc_right
                    );
                    ty[i_result]   += sum;
               }
          }
     }

Reverse Matrix Multiply
Reverse mode partials of Taylor coefficients and sum into px (for one pair of left and right orders) 
     void reverse_multiply(
          size_t                 k_left  , // order for left coefficients
          size_t                 k_right , // order for right coefficients
          const vector<double>&  tx      , // domain space Taylor coefficients
          const vector<double>&  ty      , // range space Taylor coefficients
                vector<double>&  px      , // partials w.r.t. tx
          const vector<double>&  py      , // partials w.r.t. ty
          size_t                 nr_left  , // rows in left matrix
          size_t                 n_middle , // rows in left and columns in right
          size_t                 nc_right ) // columns in right matrix
     {
          size_t nx       = 3 + (nr_left + nc_right) * n_middle;
          size_t nk       = tx.size() / nx;
# ifndef NDEBUG
          size_t ny       = nr_left * nc_right;
          assert( nk == ty.size() / ny );
# endif
          assert( tx.size() == px.size() );
          assert( ty.size() == py.size() );
          //
          size_t k_result = k_left + k_right;
          assert( k_result < nk );
          //
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     size_t i_result = result(
                         i, j, k_result, nk, nr_left, n_middle, nc_right
                    );
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     size_t i_left  = left(
                              i, ell, k_left, nk, nr_left, n_middle, nc_right
                         );
                         size_t i_right = right(
                              ell, j,  k_right, nk, nr_left, n_middle, nc_right
                         );
                         // sum        += tx[i_left] * tx[i_right];
                         px[i_left]    += tx[i_right] * py[i_result];
                         px[i_right]   += tx[i_left]  * py[i_result];
                    }
               }
          }
          return;
     }

forward
Routine called by CppAD during Forward mode. 
     virtual bool forward(
          size_t                    q ,
          size_t                    p ,
          const vector<bool>&      vx ,
                vector<bool>&      vy ,
          const vector<double>&    tx ,
                vector<double>&    ty
     )
     {     size_t n_order  = p + 1;
          size_t nr_left  = size_t( tx[ 0 * n_order + 0 ] );
          size_t n_middle = size_t( tx[ 1 * n_order + 0 ] );
          size_t nc_right = size_t( tx[ 2 * n_order + 0 ] );
# ifndef NDEBUG
          size_t nx       = 3 + (nr_left + nc_right) * n_middle;
          size_t ny       = nr_left * nc_right;
# endif
          assert( vx.size() == 0 || nx == vx.size() );
          assert( vx.size() == 0 || ny == vy.size() );
          assert( nx * n_order == tx.size() );
          assert( ny * n_order == ty.size() );
          size_t i, j, ell;

          // check if we are computing vy information
          if( vx.size() > 0 )
          {     size_t nk = 1;
               size_t k  = 0;
               for(i = 0; i < nr_left; i++)
               {     for(j = 0; j < nc_right; j++)
                    {     bool var = false;
                         for(ell = 0; ell < n_middle; ell++)
                         {     size_t i_left  = left(
                                   i, ell, k, nk, nr_left, n_middle, nc_right
                              );
                              size_t i_right = right(
                                   ell, j, k, nk, nr_left, n_middle, nc_right
                              );
                              bool   nz_left = vx[i_left] |(tx[i_left]  != 0.);
                              bool  nz_right = vx[i_right]|(tx[i_right] != 0.);
                              // if not multiplying by the constant zero
                              if( nz_left & nz_right )
                                        var |= bool(vx[i_left]) | bool(vx[i_right]);
                         }
                         size_t i_result = result(
                              i, j, k, nk, nr_left, n_middle, nc_right
                         );
                         vy[i_result] = var;
                    }
               }
          }

          // initialize result as zero
          size_t k;
          for(i = 0; i < nr_left; i++)
          {     for(j = 0; j < nc_right; j++)
               {     for(k = q; k <= p; k++)
                    {     size_t i_result = result(
                              i, j, k, n_order, nr_left, n_middle, nc_right
                         );
                         ty[i_result] = 0.0;
                    }
               }
          }
          for(k = q; k <= p; k++)
          {     // sum the produces that result in order k
               for(ell = 0; ell <= k; ell++)
                    forward_multiply(
                         ell, k - ell, tx, ty, nr_left, n_middle, nc_right
                    );
          }

          // all orders are implented, so always return true
          return true;
     }

reverse
Routine called by CppAD during Reverse mode. 
     virtual bool reverse(
          size_t                     p ,
          const vector<double>&     tx ,
          const vector<double>&     ty ,
                vector<double>&     px ,
          const vector<double>&     py
     )
     {     size_t n_order  = p + 1;
          size_t nr_left  = size_t( tx[ 0 * n_order + 0 ] );
          size_t n_middle = size_t( tx[ 1 * n_order + 0 ] );
          size_t nc_right = size_t( tx[ 2 * n_order + 0 ] );
# ifndef NDEBUG
          size_t nx       = 3 + (nr_left + nc_right) * n_middle;
          size_t ny       = nr_left * nc_right;
# endif
          assert( nx * n_order == tx.size() );
          assert( ny * n_order == ty.size() );
          assert( px.size() == tx.size() );
          assert( py.size() == ty.size() );

          // initialize summation
          for(size_t i = 0; i < px.size(); i++)
               px[i] = 0.0;

          // number of orders to differentiate
          size_t k = n_order;
          while(k--)
          {     // differentiate the produces that result in order k
               for(size_t ell = 0; ell <= k; ell++)
                    reverse_multiply(
                         ell, k - ell, tx, ty, px, py, nr_left, n_middle, nc_right
                    );
          }

          // all orders are implented, so always return true
          return true;
     }

for_sparse_jac
Routines called by CppAD during ForSparseJac . 
     // boolean sparsity patterns
     virtual bool for_sparse_jac(
          size_t                                q ,
          const vector<bool>&                   r ,
                vector<bool>&                   s ,
          const vector<double>&                 x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
# ifndef NDEBUG
          size_t  nx      = 3 + (nr_left + nc_right) * n_middle;
          size_t  ny      = nr_left * nc_right;
# endif
          assert( nx     == x.size() );
          assert( nx * q == r.size() );
          assert( ny * q == s.size() );
          size_t p;

          // sparsity for S(x) = f'(x) * R
          size_t nk = 1;
          size_t k  = 0;
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     size_t i_result = result(
                         i, j, k, nk, nr_left, n_middle, nc_right
                    );
                    for(p = 0; p < q; p++)
                         s[i_result * q + p] = false;
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     size_t i_left  = left(
                              i, ell, k, nk, nr_left, n_middle, nc_right
                         );
                         size_t i_right = right(
                              ell, j, k, nk, nr_left, n_middle, nc_right
                         );
                         for(p = 0; p < q; p++)
                         {     // cast avoids Microsoft warning (should not be needed)
                              s[i_result * q + p] |= bool( r[i_left * q + p ] );
                              s[i_result * q + p] |= bool( r[i_right * q + p ] );
                         }
                    }
               }
          }
          return true;
     }
     // set sparsity patterns
     virtual bool for_sparse_jac(
          size_t                                q ,
          const vector< std::set<size_t> >&     r ,
                vector< std::set<size_t> >&     s ,
          const vector<double>&                 x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
# ifndef NDEBUG
          size_t  nx      = 3 + (nr_left + nc_right) * n_middle;
          size_t  ny      = nr_left * nc_right;
# endif
          assert( nx == x.size() );
          assert( nx == r.size() );
          assert( ny == s.size() );

          // sparsity for S(x) = f'(x) * R
          size_t nk = 1;
          size_t k  = 0;
          for(size_t i = 0; i < nr_left; i++)
          {     for(size_t j = 0; j < nc_right; j++)
               {     size_t i_result = result(
                         i, j, k, nk, nr_left, n_middle, nc_right
                    );
                    s[i_result].clear();
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     size_t i_left  = left(
                              i, ell, k, nk, nr_left, n_middle, nc_right
                         );
                         size_t i_right = right(
                              ell, j, k, nk, nr_left, n_middle, nc_right
                         );
                         //
                         s[i_result] = set_union(s[i_result], r[i_left] );
                         s[i_result] = set_union(s[i_result], r[i_right] );
                    }
               }
          }
          return true;
     }

rev_sparse_jac
Routines called by CppAD during RevSparseJac . 
     // boolean sparsity patterns
     virtual bool rev_sparse_jac(
          size_t                                q ,
          const vector<bool>&                  rt ,
                vector<bool>&                  st ,
          const vector<double>&                 x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
          size_t  nx      = 3 + (nr_left + nc_right) * n_middle;
# ifndef NDEBUG
          size_t  ny      = nr_left * nc_right;
# endif
          assert( nx     == x.size() );
          assert( nx * q == st.size() );
          assert( ny * q == rt.size() );
          size_t i, j, p;

          // initialize
          for(i = 0; i < nx; i++)
          {     for(p = 0; p < q; p++)
                    st[ i * q + p ] = false;
          }

          // sparsity for S(x)^T = f'(x)^T * R^T
          size_t nk = 1;
          size_t k  = 0;
          for(i = 0; i < nr_left; i++)
          {     for(j = 0; j < nc_right; j++)
               {     size_t i_result = result(
                         i, j, k, nk, nr_left, n_middle, nc_right
                    );
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     size_t i_left  = left(
                              i, ell, k, nk, nr_left, n_middle, nc_right
                         );
                         size_t i_right = right(
                              ell, j, k, nk, nr_left, n_middle, nc_right
                         );
                         for(p = 0; p < q; p++)
                         {     st[i_left * q + p] |= bool( rt[i_result * q + p] );
                              st[i_right* q + p] |= bool( rt[i_result * q + p] );
                         }
                    }
               }
          }
          return true;
     }
     // set sparsity patterns
     virtual bool rev_sparse_jac(
          size_t                                q ,
          const vector< std::set<size_t> >&    rt ,
                vector< std::set<size_t> >&    st ,
          const vector<double>&                 x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
          size_t  nx      = 3 + (nr_left + nc_right) * n_middle;
# ifndef NDEBUG
          size_t  ny        = nr_left * nc_right;
# endif
          assert( nx == x.size() );
          assert( nx == st.size() );
          assert( ny == rt.size() );
          size_t i, j;

          // initialize
          for(i = 0; i < nx; i++)
               st[i].clear();

          // sparsity for S(x)^T = f'(x)^T * R^T
          size_t nk = 1;
          size_t k  = 0;
          for(i = 0; i < nr_left; i++)
          {     for(j = 0; j < nc_right; j++)
               {     size_t i_result = result(
                         i, j, k, nk, nr_left, n_middle, nc_right
                    );
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     size_t i_left  = left(
                              i, ell, k, nk, nr_left, n_middle, nc_right
                         );
                         size_t i_right = right(
                              ell, j, k, nk, nr_left, n_middle, nc_right
                         );
                         //
                         st[i_left]  = set_union(st[i_left],  rt[i_result]);
                         st[i_right] = set_union(st[i_right], rt[i_result]);
                    }
               }
          }
          return true;
     }

rev_sparse_hes
Routines called by RevSparseHes . 
     // set sparsity patterns
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
                vector<bool>&                   t ,
          size_t                                q ,
          const vector< std::set<size_t> >&     r ,
          const vector< std::set<size_t> >&     u ,
                vector< std::set<size_t> >&     v ,
          const vector<double>&                 x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
# ifndef NDEBUG
          size_t  ny        = nr_left * nc_right;
# endif
          assert( x.size()  == nx );
          assert( vx.size() == nx );
          assert( t.size()  == nx );
          assert( r.size()  == nx );
          assert( v.size()  == nx );
          assert( s.size()  == ny );
          assert( u.size()  == ny );
          //
          size_t i, j;
          //
          // initilaize sparsity patterns as false
          for(j = 0; j < nx; j++)
          {     t[j] = false;
               v[j].clear();
          }
          size_t nk = 1;
          size_t k  = 0;
          for(i = 0; i < nr_left; i++)
          {     for(j = 0; j < nc_right; j++)
               {     size_t i_result = result(
                         i, j, k, nk, nr_left, n_middle, nc_right
                    );
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     size_t i_left  = left(
                              i, ell, k, nk, nr_left, n_middle, nc_right
                         );
                         size_t i_right = right(
                              ell, j, k, nk, nr_left, n_middle, nc_right
                         );
                         //
                         // Compute sparsity for T(x) = S(x) * f'(x).
                         // We need not use vx with f'(x) back propagation.
                         t[i_left]  |= bool( s[i_result] );
                         t[i_right] |= bool( s[i_result] );

                         // V(x) = f'(x)^T * U(x) +  S(x) * f''(x) * R
                         // U(x) = g''(y) * f'(x) * R
                         // S(x) = g'(y)

                         // back propagate f'(x)^T * U(x)
                         // (no need to use vx with f'(x) propogation)
                         v[i_left]  = set_union(v[i_left],  u[i_result] );
                         v[i_right] = set_union(v[i_right], u[i_result] );

                         // back propagate S(x) * f''(x) * R
                         // (here is where we must check for cross terms)
                         if( s[i_result] & vx[i_left] & vx[i_right] )
                         {     v[i_left]  = set_union(v[i_left],  r[i_right] );
                              v[i_right] = set_union(v[i_right], r[i_left]  );
                         }
                    }
               }
          }
          return true;
     }
     // bool sparsity
     virtual bool rev_sparse_hes(
          const vector<bool>&                   vx,
          const vector<bool>&                   s ,
                vector<bool>&                   t ,
          size_t                                q ,
          const vector<bool>&                   r ,
          const vector<bool>&                   u ,
                vector<bool>&                   v ,
          const vector<double>&                 x )
     {
          size_t nr_left  = size_t( CppAD::Integer( x[0] ) );
          size_t n_middle = size_t( CppAD::Integer( x[1] ) );
          size_t nc_right = size_t( CppAD::Integer( x[2] ) );
          size_t  nx        = 3 + (nr_left + nc_right) * n_middle;
# ifndef NDEBUG
          size_t  ny        = nr_left * nc_right;
# endif
          assert( x.size()  == nx );
          assert( vx.size() == nx );
          assert( t.size()  == nx );
          assert( r.size()  == nx * q );
          assert( v.size()  == nx * q );
          assert( s.size()  == ny );
          assert( u.size()  == ny * q );
          size_t i, j, p;
          //
          // initilaize sparsity patterns as false
          for(j = 0; j < nx; j++)
          {     t[j] = false;
               for(p = 0; p < q; p++)
                    v[j * q + p] = false;
          }
          size_t nk = 1;
          size_t k  = 0;
          for(i = 0; i < nr_left; i++)
          {     for(j = 0; j < nc_right; j++)
               {     size_t i_result = result(
                         i, j, k, nk, nr_left, n_middle, nc_right
                    );
                    for(size_t ell = 0; ell < n_middle; ell++)
                    {     size_t i_left  = left(
                              i, ell, k, nk, nr_left, n_middle, nc_right
                         );
                         size_t i_right = right(
                              ell, j, k, nk, nr_left, n_middle, nc_right
                         );
                         //
                         // Compute sparsity for T(x) = S(x) * f'(x).
                         // We so not need to use vx with f'(x) propagation.
                         t[i_left]  |= bool( s[i_result] );
                         t[i_right] |= bool( s[i_result] );

                         // V(x) = f'(x)^T * U(x) +  S(x) * f''(x) * R
                         // U(x) = g''(y) * f'(x) * R
                         // S(x) = g'(y)

                         // back propagate f'(x)^T * U(x)
                         // (no need to use vx with f'(x) propogation)
                         for(p = 0; p < q; p++)
                         {     v[ i_left  * q + p] |= bool( u[ i_result * q + p] );
                              v[ i_right * q + p] |= bool( u[ i_result * q + p] );
                         }

                         // back propagate S(x) * f''(x) * R
                         // (here is where we must check for cross terms)
                         if( s[i_result] & vx[i_left] & vx[i_right] )
                         {     for(p = 0; p < q; p++)
                              {     v[i_left * q + p]  |= bool( r[i_right * q + p] );
                                   v[i_right * q + p] |= bool( r[i_left * q + p] );
                              }
                         }
                    }
               }
          }
          return true;
     }

End Class Definition 

}; // End of mat_mul class
}  // End empty namespace
Input File: cppad/example/mat_mul.hpp cppad-20170000.3/doc/boolvalued.xml0000644000175200017650000000576513057470505016070 0ustar coincoin-web Bool Valued Operations and Functions with AD Arguments
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Bool Valued Operations and Functions with AD Arguments
Compare AD Binary Comparison Operators
NearEqualExt Compare AD and Base Objects for Nearly Equal
BoolFun AD Boolean Functions
ParVar Is an AD Object a Parameter or Variable
EqualOpSeq Check if Two Value are Identically Equal
Input File: cppad/core/bool_valued.hpp cppad-20170000.3/doc/_compare_xml.js0000644000175200017650000000367613057470505016214 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'boolvalued.xml', 'compare.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down1 = [ 'compare.xml', 'nearequalext.xml', 'boolfun.xml', 'parvar.xml', 'equalopseq.xml' ]; var list_down0 = [ 'compare.cpp.xml' ]; var list_current0 = [ 'compare.xml#Syntax', 'compare.xml#Purpose', 'compare.xml#Op', 'compare.xml#x', 'compare.xml#y', 'compare.xml#b', 'compare.xml#Operation Sequence', 'compare.xml#Assumptions', 'compare.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/compare.cpp.xml0000644000175200017650000004714613057470505016142 0ustar coincoin-web AD Binary Comparison Operators: Example and Test
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AD Binary Comparison Operators: Example and Test
# include <cppad/cppad.hpp>

bool Compare(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // declare independent variables and start tape recording
     size_t n  = 2;
     double x0 = 0.5;
     double x1 = 1.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;
     x[1]      = x1;
     CppAD::Independent(x);

     // some binary comparision operations
     AD<double> p;
     if( x[0] < x[1] )
          p = x[0];   // values in x choose this case
     else     p = x[1];
     if( x[0] <= x[1] )
          p *= x[0];  // values in x choose this case
     else     p *= x[1];
     if( x[0] >  x[1] )
          p *= x[0];
     else     p *= x[1];  // values in x choose this case
     if( x[0] >= x[1] )
          p *= x[0];
     else     p *= x[1];  // values in x choose this case
     if( x[0] == x[1] )
          p *= x[0];
     else     p *= x[1];  // values in x choose this case
     if( x[0] != x[1] )
          p *= x[0];  // values in x choose this case
     else     p *= x[1];

     // dependent variable vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = p;

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0*x0*x1*x1*x1*x0, eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dx[1] = 0.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 3.*x0*x0*x1*x1*x1, eps99, eps99);

     // forward computation of partials w.r.t. x[1]
     dx[0] = 0.;
     dx[1] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 3.*x0*x0*x1*x1*x0, eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 3.*x0*x0*x1*x1*x1, eps99, eps99);
     ok   &= NearEqual(dw[1], 3.*x0*x0*x1*x1*x0, eps99, eps99);

     return ok;
}
Input File: example/compare.cpp cppad-20170000.3/doc/nearequalext.xml0000644000175200017650000003211213057470505016414 0ustar coincoin-web Compare AD and Base Objects for Nearly Equal
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Compare AD and Base Objects for Nearly Equal

Syntax
b = NearEqual(x, y, r, a)

Purpose
The routine NearEqual determines if two objects of the same type are nearly. This routine is extended to the case where one object can have type Type while the other can have type AD<Type> or AD< std::complex<Type> > .

x
The arguments x has one of the following possible prototypes:
     const Type                     &x
     const AD<Type>                 &x
     const AD< std::complex<Type> > &x
y
The arguments y has one of the following possible prototypes:
     const Type                     &y
     const AD<Type>                 &y
     const AD< std::complex<Type> > &x
r
The relative error criteria r has prototype
     const Type &r
 It must be greater than or equal to zero. The relative error condition is defined as: | x - y | | x | + | y | ≤ r
a
The absolute error criteria a has prototype
     const Type &a
 It must be greater than or equal to zero. The absolute error condition is defined as: | x - y | ≤ a
b
The return value b has prototype
     bool b
 If either x or y is infinite or not a number, the return value is false. Otherwise, if either the relative or absolute error condition (defined above) is satisfied, the return value is true. Otherwise, the return value is false.

Type
The type Type must be a NumericType . The routine CheckNumericType will generate an error message if this is not the case. If a and b have type Type , the following operation must be defined
Operation Description
a <= b less that or equal operator (returns a bool object)

Operation Sequence
The result of this operation is not an AD of Base object. Thus it will not be recorded as part of an AD of Base operation sequence .

Example
The file near_equal_ext.cpp contains an example and test of this extension of NearEqual . It return true if it succeeds and false otherwise.
Input File: cppad/core/near_equal_ext.hpp cppad-20170000.3/doc/near_equal_ext.cpp.xml0000644000175200017650000002132513057470505017477 0ustar coincoin-web Compare AD with Base Objects: Example and Test
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Compare AD with Base Objects: Example and Test

# include <cppad/cppad.hpp>
# include <complex>

bool NearEqualExt(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;

     // double
     double x    = 1.00000;
     double y    = 1.00001;
     double a    =  .00005;
     double r    =  .00005;
     double zero = 0.;

     // AD<double>
     AD<double> ax(x);
     AD<double> ay(y);

     ok &= NearEqual(ax, ay, zero, a);
     ok &= NearEqual(ax, y,  r, zero);
     ok &= NearEqual(x, ay,  r,    a);

     // std::complex<double>
     AD<double> cx(x);
     AD<double> cy(y);

     // AD< std::complex<double> >
     AD<double> acx(x);
     AD<double> acy(y);

     ok &= NearEqual(acx, acy, zero, a);
     ok &= NearEqual(acx,  cy, r, zero);
     ok &= NearEqual(acx,   y, r,    a);
     ok &= NearEqual( cx, acy, r,    a);
     ok &= NearEqual(  x, acy, r,    a);

     return ok;
}
Input File: example/near_equal_ext.cpp cppad-20170000.3/doc/boolfun.xml0000644000175200017650000003662613057470505015400 0ustar coincoin-web AD Boolean Functions
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AD Boolean Functions

Syntax
CPPAD_BOOL_UNARY(Base, unary_name)
 b = unary_name(u)
 b = unary_name(x)
 CPPAD_BOOL_BINARY(Base, binary_name)
 b = binary_name(u, v)
 b = binary_name(x, y)

Purpose
Create a bool valued function that has AD<Base> arguments.

unary_name
This is the name of the bool valued function with one argument (as it is used in the source code). The user must provide a version of unary_name where the argument has type Base . CppAD uses this to create a version of unary_name where the argument has type AD<Base> .

u
The argument u has prototype
     const Base &u
 It is the value at which the user provided version of unary_name is to be evaluated. It is also used for the first argument to the user provided version of binary_name .

x
The argument x has prototype
     const AD<Base> &x
 It is the value at which the CppAD provided version of unary_name is to be evaluated. It is also used for the first argument to the CppAD provided version of binary_name .

b
The result b has prototype
     bool b
Create Unary
The preprocessor macro invocation
     CPPAD_BOOL_UNARY(Base, unary_name)
 defines the version of unary_name with a AD<Base> argument. This can with in a namespace (not the CppAD namespace) but must be outside of any routine.

binary_name
This is the name of the bool valued function with two arguments (as it is used in the source code). The user must provide a version of binary_name where the arguments have type Base . CppAD uses this to create a version of binary_name where the arguments have type AD<Base> .

v
The argument v has prototype
     const Base &v
 It is the second argument to the user provided version of binary_name .

y
The argument x has prototype
     const AD<Base> &y
 It is the second argument to the CppAD provided version of binary_name .

Create Binary
The preprocessor macro invocation
     CPPAD_BOOL_BINARY(Base, binary_name)
 defines the version of binary_name with AD<Base> arguments. This can with in a namespace (not the CppAD namespace) but must be outside of any routine.

Operation Sequence
The result of this operation is not an AD of Base object. Thus it will not be recorded as part of an AD of Base operation sequence .

Example
The file bool_fun.cpp contains an example and test of these operations. It returns true if it succeeds and false otherwise.

Deprecated 2007-07-31
The preprocessor symbols CppADCreateUnaryBool and CppADCreateBinaryBool are defined to be the same as CPPAD_BOOL_UNARY and CPPAD_BOOL_BINARY respectively (but their use is deprecated).
Input File: cppad/core/bool_fun.hpp cppad-20170000.3/doc/bool_fun.cpp.xml0000644000175200017650000002303413057470505016305 0ustar coincoin-web AD Boolean Functions: Example and Test
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AD Boolean Functions: Example and Test

# include <cppad/cppad.hpp>
# include <complex>


// define abbreviation for double precision complex
typedef std::complex<double> Complex;

namespace {
     // a unary bool function with Complex argument
     static bool IsReal(const Complex &x)
     {     return x.imag() == 0.; }

     // a binary bool function with Complex arguments
     static bool AbsGeq(const Complex &x, const Complex &y)
     {     double axsq = x.real() * x.real() + x.imag() * x.imag();
          double aysq = y.real() * y.real() + y.imag() * y.imag();

          return axsq >= aysq;
     }

     // Create version of IsReal with AD<Complex> argument
     // inside of namespace and outside of any other function.
     CPPAD_BOOL_UNARY(Complex, IsReal)

     // Create version of AbsGeq with AD<Complex> arguments
     // inside of namespace and outside of any other function.
     CPPAD_BOOL_BINARY(Complex, AbsGeq)

}
bool BoolFun(void)
{     bool ok = true;

     CppAD::AD<Complex> x = Complex(1.,  0.);
     CppAD::AD<Complex> y = Complex(1.,  1.);

     ok &= IsReal(x);
     ok &= ! AbsGeq(x, y);

     return ok;
}
Input File: example/bool_fun.cpp cppad-20170000.3/doc/parvar.xml0000644000175200017650000001505413057470505015217 0ustar coincoin-web Is an AD Object a Parameter or Variable
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Is an AD Object a Parameter or Variable

Syntax
b = Parameter(x)
b = Variable(x)

Purpose
Determine if x is a parameter or variable .

x
The argument x has prototype
     const AD<Base>    &x
     const VecAD<Base> &x
b
The return value b has prototype
     bool b
 The return value for Parameter (Variable) is true if and only if x is a parameter (variable). Note that a VecAD<Base> object is a variable if any element of the vector depends on the independent variables.

Operation Sequence
The result of this operation is not an AD of Base object. Thus it will not be recorded as part of an AD of Base operation sequence .

Example
The file par_var.cpp contains an example and test of these functions. It returns true if it succeeds and false otherwise.
Input File: cppad/core/par_var.hpp cppad-20170000.3/doc/par_var.cpp.xml0000644000175200017650000002777013057470505016147 0ustar coincoin-web AD Parameter and Variable Functions: Example and Test
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AD Parameter and Variable Functions: Example and Test

# include <cppad/cppad.hpp>

bool ParVar(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::VecAD;
     using CppAD::Parameter;
     using CppAD::Variable;

     // declare independent variables and start tape recording
     size_t n = 1;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]     = 0.;
     ok &= Parameter(x[0]);     // x[0] is a paraemter here
     CppAD::Independent(x);
     ok &= Variable(x[0]);      // now x[0] is a variable

     // dependent variable vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = 2.;
     ok  &= Parameter(y[0]);    // y[0] does not depend on x[0]
     y[1] = abs(x[0]);
     ok  &= Variable(y[1]);     // y[1] does depends on x[0]

     // VecAD objects
     VecAD<double> z(2);
     z[0] = 0.;
     z[1] = 1.;
     ok  &= Parameter(z);      // z does not depend on x[0]
     z[x[0]] = 2.;
     ok  &= Variable(z);       // z depends on x[0]


     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check that now all AD<double> objects are parameters
     ok &= Parameter(x[0]); ok &= ! Variable(x[0]);
     ok &= Parameter(y[0]); ok &= ! Variable(y[0]);
     ok &= Parameter(y[1]); ok &= ! Variable(y[1]);

     // check that the VecAD<double> object is a parameter
     ok &= Parameter(z);

     return ok;
}
Input File: example/par_var.cpp cppad-20170000.3/doc/equalopseq.xml0000644000175200017650000002153413057470506016104 0ustar coincoin-web Check if Two Value are Identically Equal
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Check if Two Value are Identically Equal

Syntax
b = EqualOpSeq(x, y)

Purpose
Determine if two x and y are identically equal; i.e., not only is x == y true, but if they are variables , they correspond have the same operation sequence .

Motivation
Sometimes it is useful to cache information and only recalculate when a function's arguments change. In the case of AD variables, it may be important not only when the argument values are equal, but when they are related to the independent variables by the same operation sequence. After the assignment
     y = x
 these two AD objects would not only have equal values, but would also correspond to the same operation sequence.

x
The argument x has prototype
     const AD<Base> &x
y
The argument y has prototype
     const AD<Base> &y
b
The result b has prototype
     bool b
 The result is true if and only if one of the following cases holds:
  1. Both x and y are variables and correspond to the same operation sequence.
  2. Both x and y are parameters, Base is an AD type, and EqualOpSeq( Value(x) , Value(y) ) is true.
  3. Both x and y are parameters, Base is not an AD type, and x == y is true.


Example
The file equal_op_seq.cpp contains an example and test of EqualOpSeq. It returns true if it succeeds and false otherwise.
Input File: cppad/core/equal_op_seq.hpp cppad-20170000.3/doc/equal_op_seq.cpp.xml0000644000175200017650000002100113057470506017150 0ustar coincoin-web EqualOpSeq: Example and Test
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EqualOpSeq: Example and Test
# include <cppad/cppad.hpp>

bool EqualOpSeq(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::EqualOpSeq;

     // domain space vector
     size_t n  = 1;
     double x0 = 1.;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     AD<double> a = 1. + x[0];  // this variable is 1 + x0
     AD<double> b = 2. * x[0];  // this variable is 2 * x0

     // both a and b are variables
     ok &= (a == b);            // 1 + 1     == 2 * 1
     ok &= ! EqualOpSeq(a, b);  // 1 + x[0]  != 2 * x[0]

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = a;

     // both y[0] and a are variables
     EqualOpSeq(y[0], a);       // 2 * x[0] == 2 * x[0]

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // both a and b are parameters (after the creation of f above)
     ok &= EqualOpSeq(a, b);    // 1 + 1 == 2 * 1

     return ok;
}
Input File: example/equal_op_seq.cpp cppad-20170000.3/doc/vecad.xml0000644000175200017650000007324613057470506015016 0ustar coincoin-web AD Vectors that Record Index Operations
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AD Vectors that Record Index Operations

Syntax
VecAD<Base> v(n)
v.size()
b = v[i]
r = v[x]

Purpose
If either v or x is a variable , the indexing operation
     r = v[x]
 is recorded in the corresponding AD of Base operation sequence and transferred to the corresponding ADFun object f . Such an index can change each time zero order f.Forward is used; i.e., f is evaluated with new value for the independent variables . Note that the value of y depends on the value of x in a discrete fashion and CppAD computes its partial derivative with respect to x as zero.

Alternatives
If only the values in the vector, and not the indices, depend on the independent variables, the class Vector< AD<Base> > is much more efficient for storing AD values where Vector is any SimpleVector template class, If only the indices, and not the values in the vector, depend on the independent variables, The Discrete functions are a much more efficient way to represent these vectors.

VecAD<Base>::reference
The result r has type
     VecAD<Base>::reference
 which is very much like the AD<Base> type with some notable exceptions:

Exceptions
  1. The object r cannot be used with the Value function to compute the corresponding Base value. If v and i are not variables
             b = v[i]
     can be used to compute the corresponding Base value.
  2. The object r cannot be used with the computed assignments operators +=, -=, *=, or /=. For example, the following syntax is not valid:
             v[x] += z;
     no matter what the types of z .
  3. Assignment to r returns a void. For example, the following syntax is not valid:
             z = v[x] = u;
     no matter what the types of z , and u .
  4. The CondExp functions do not accept VecAD<Base>::reference arguments. For example, the following syntax is not valid:
         CondExpGt(    v[x], z, u, v)
     no matter what the types of z , u , and v .
  5. The Parameter and Variable functions cannot be used with VecAD<Base>::reference arguments like r , use the entire VecAD<Base> vector instead; i.e. v .
  6. The vectors passed to Independent must have elements of type AD<Base> ; i.e., VecAD vectors cannot be passed to Independent.
  7. If one uses this type in a AD of Base operation sequence , sparsity pattern calculations (Sparse ) are less efficient because the dependence of different elements of the vector cannot be separated.


Constructor

v
The syntax
     VecAD<Base> v(n)
 creates an VecAD object v with n elements. The initial value of the elements of v is unspecified.

n
The argument n has prototype
     size_t n
size
The syntax
     v.size()
 returns the number of elements in the vector v ; i.e., the value of n when it was constructed.

size_t Indexing
We refer to the syntax
     b = v[i]
 as size_t indexing of a VecAD object. This indexing is only valid if the vector v is a parameter ; i.e., it does not depend on the independent variables.

i
The operand i has prototype
     size_t i
 It must be greater than or equal zero and less than n ; i.e., less than the number of elements in v .

b
The result b has prototype
     Base b
 and is a reference to the i-th element in the vector v . It can be used to change the element value; for example,
     v[i] = c
 is valid where c is a Base object. The reference b is no longer valid once the destructor for v is called; for example, when v falls out of scope.

AD Indexing
We refer to the syntax
     r = v[x]
 as AD indexing of a VecAD object.

x
The argument x has prototype
     const AD<Base> &x
 The value of x must be greater than or equal zero and less than n ; i.e., less than the number of elements in v .

r
The result r has prototype
     VecAD<Base>::reference r
 The object r has an AD type and its operations are recorded as part of the same AD of Base operation sequence as for AD<Base> objects. It acts as a reference to the element with index floor ( x ) in the vector v ( floor ( x ) is the greatest integer less than or equal x ). Because it is a reference, it can be used to change the element value; for example,
     v[x] = z
 is valid where z is an VecAD<Base>::reference object. As a reference, r is no longer valid once the destructor for v is called; for example, when v falls out of scope.

Example
The file vec_ad.cpp contains an example and test using VecAD vectors. It returns true if it succeeds and false otherwise.

Speed and Memory
The VecAD vector type is inefficient because every time an element of a vector is accessed, a new CppAD variable is created on the tape using either the Ldp or Ldv operation (unless all of the elements of the vector are parameters ). The effect of this can be seen by executing the following steps:
  1. In the file cppad/local/forward1sweep.h, change the definition of CPPAD_FORWARD1SWEEP_TRACE to 
     
     # define CPPAD_FORWARD1SWEEP_TRACE 1
  2. In the Example directory, execute the command 
     
     ./test_one.sh lu_vec_ad_ok.cpp lu_vec_ad.cpp -DNDEBUG > lu_vec_ad_ok.log
    This will write a trace of all the forward tape operations, for the test case lu_vec_ad_ok.cpp , to the file lu_vec_ad_ok.log.
  3. In the Example directory execute the commands 
     
     grep "op="           lu_vec_ad_ok.log | wc -l
     grep "op=Ld[vp]"     lu_vec_ad_ok.log | wc -l
     grep "op=St[vp][vp]" lu_vec_ad_ok.log | wc -l
    The first command counts the number of operators in the tracing, the second counts the number of VecAD load operations, and the third counts the number of VecAD store operations. (For CppAD version 05-11-20 these counts were 956, 348, and 118 respectively.)
Input File: cppad/core/vec_ad.hpp cppad-20170000.3/doc/vec_ad.cpp.xml0000644000175200017650000012450613057470506015732 0ustar coincoin-web AD Vectors that Record Index Operations: Example and Test
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AD Vectors that Record Index Operations: Example and Test

# include <cppad/cppad.hpp>
# include <cassert>

namespace {
     // return the vector x that solves the following linear system
     //     a[0] * x[0] + a[1] * x[1] = b[0]
     //     a[2] * x[0] + a[3] * x[1] = b[1]
     // in a way that will record pivot operations on the AD<double> tape
     typedef CPPAD_TESTVECTOR(CppAD::AD<double>) Vector;
     Vector Solve(const Vector &a , const Vector &b)
     {     using namespace CppAD;
          assert(a.size() == 4 && b.size() == 2);

          // copy the vector b into the VecAD object B
          VecAD<double> B(2);
          AD<double>    u;
          for(u = 0; u < 2; u += 1.)
               B[u] = b[ Integer(u) ];

          // copy the matrix a into the VecAD object A
          VecAD<double> A(4);
          for(u = 0; u < 4; u += 1.)
               A[u] = a [ Integer(u) ];

          // tape AD operation sequence that determines the row of A
          // with maximum absolute element in column zero
          AD<double> zero(0), one(1);
          AD<double> rmax = CondExpGt(abs(a[0]), abs(a[2]), zero, one);

          // divide row rmax by A(rmax, 0)
          A[rmax * 2 + 1]  = A[rmax * 2 + 1] / A[rmax * 2 + 0];
          B[rmax]          = B[rmax]         / A[rmax * 2 + 0];
          A[rmax * 2 + 0]  = one;

          // subtract A(other,0) times row A(rmax, *) from row A(other,*)
          AD<double> other   = one - rmax;
          A[other * 2 + 1]   = A[other * 2 + 1]
                             - A[other * 2 + 0] * A[rmax * 2 + 1];
          B[other]           = B[other]
                             - A[other * 2 + 0] * B[rmax];
          A[other * 2 + 0] = zero;

          // back substitute to compute the solution vector x.
          // Note that the columns of A correspond to rows of x.
          // Also note that A[rmax * 2 + 0] is equal to one.
          CPPAD_TESTVECTOR(AD<double>) x(2);
          x[1] = B[other] / A[other * 2 + 1];
          x[0] = B[rmax] - A[rmax * 2 + 1] * x[1];

          return x;
     }
}

bool vec_ad(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 4;
     CPPAD_TESTVECTOR(double)       x(n);
     CPPAD_TESTVECTOR(AD<double>) X(n);
     // 2 * identity matrix (rmax in Solve will be 0)
     X[0] = x[0] = 2.; X[1] = x[1] = 0.;
     X[2] = x[2] = 0.; X[3] = x[3] = 2.;

     // declare independent variables and start tape recording
     CppAD::Independent(X);

     // define the vector b
     CPPAD_TESTVECTOR(double)       b(2);
     CPPAD_TESTVECTOR(AD<double>) B(2);
     B[0] = b[0] = 0.;
     B[1] = b[1] = 1.;

     // range space vector solves X * Y = b
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y = Solve(X, B);

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // By Cramer's rule:
     // y[0] = [ b[0] * x[3] - x[1] * b[1] ] / [ x[0] * x[3] - x[1] * x[2] ]
     // y[1] = [ x[0] * b[1] - b[0] * x[2] ] / [ x[0] * x[3] - x[1] * x[2] ]

     double den   = x[0] * x[3] - x[1] * x[2];
     double dsq   = den * den;
     double num0  = b[0] * x[3] - x[1] * b[1];
     double num1  = x[0] * b[1] - b[0] * x[2];

     // check value
     ok &= NearEqual(Y[0] , num0 / den, eps99, eps99);
     ok &= NearEqual(Y[1] , num1 / den, eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.; dx[1] = 0.;
     dx[2] = 0.; dx[3] = 0.;
     dy    = f.Forward(1, dx);
     ok &= NearEqual(dy[0], 0.         - num0 * x[3] / dsq, eps99, eps99);
     ok &= NearEqual(dy[1], b[1] / den - num1 * x[3] / dsq, eps99, eps99);

     // compute the solution for a new x matrix such that pivioting
     // on the original rmax row would divide by zero
     CPPAD_TESTVECTOR(double) y(m);
     x[0] = 0.; x[1] = 2.;
     x[2] = 2.; x[3] = 0.;

     // new values for Cramer's rule
     den   = x[0] * x[3] - x[1] * x[2];
     dsq   = den * den;
     num0  = b[0] * x[3] - x[1] * b[1];
     num1  = x[0] * b[1] - b[0] * x[2];

     // check values
     y    = f.Forward(0, x);
     ok &= NearEqual(y[0] , num0 / den, eps99, eps99);
     ok &= NearEqual(y[1] , num1 / den, eps99, eps99);

     // forward computation of partials w.r.t. x[1]
     dx[0] = 0.; dx[1] = 1.;
     dx[2] = 0.; dx[3] = 0.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0],-b[1] / den + num0 * x[2] / dsq, eps99, eps99);
     ok   &= NearEqual(dy[1], 0.         + num1 * x[2] / dsq, eps99, eps99);

     // reverse computation of derivative of y[0] w.r.t x
     CPPAD_TESTVECTOR(double) w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0] = 1.; w[1] = 0.;
     dw   = f.Reverse(1, w);
     ok  &= NearEqual(dw[0], 0.         - num0 * x[3] / dsq, eps99, eps99);
     ok  &= NearEqual(dw[1],-b[1] / den + num0 * x[2] / dsq, eps99, eps99);
     ok  &= NearEqual(dw[2], 0.         + num0 * x[1] / dsq, eps99, eps99);
     ok  &= NearEqual(dw[3], b[0] / den - num0 * x[0] / dsq, eps99, eps99);

     return ok;
}
Input File: example/vec_ad.cpp cppad-20170000.3/doc/base_require.xml0000644000175200017650000003427113057470506016375 0ustar coincoin-web AD<Base> Requirements for a CppAD Base Type
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AD<Base> Requirements for a CppAD Base Type

Syntax
# include <cppad/base_require.hpp>

Purpose
This section lists the requirements for the type Base so that the type AD<Base> can be used.

API Warning
Defining a CppAD Base type is an advanced use of CppAD. This part of the CppAD API changes with time. The most common change is adding more requirements. Search for base_require in the current whats_new section for these changes.

Standard Base Types
In the case where Base is float, double, std::complex<float>, std::complex<double>, or AD<Other> , these requirements are provided by including the file cppad/cppad.hpp.

Include Order
If you are linking a non-standard base type to CppAD, you must first include the file cppad/base_require.hpp, then provide the specifications below, and then include the file cppad/cppad.hpp.

Numeric Type
The type Base must support all the operations for a NumericType .

Output Operator
The type Base must support the syntax
     os << x
 where os is an std::ostream& and x is a const base_alloc&. For example, see base_alloc .

Integer
The type Base must support the syntax
     i = CppAD::Integer(x)
 which converts x to an int. The argument x has prototype
     const Base& x
 and the return value i has prototype
     int i
Suggestion
In many cases, the Base version of the Integer function can be defined by
namespace CppAD {
     inline int Integer(const Base& x)
     {    return static_cast<int>(x); }
}
 For example, see base_float and base_alloc .

Absolute Zero, azmul
The type Base must support the syntax
     z = azmul(x, y)
 see; azmul . The following preprocessor macro invocation suffices (for most Base types):
namespace CppAD {
     CPPAD_AZMUL(Base)
}
 where the macro is defined by 
# define CPPAD_AZMUL(Base) \
    inline Base azmul(const Base& x, const Base& y) \
    {   Base zero(0.0);   \
        if( x == zero ) \
            return zero;  \
        return x * y;     \
    }

Contents
base_memberRequired Base Class Member Functions
base_cond_expBase Type Requirements for Conditional Expressions
base_identicalBase Type Requirements for Identically Equal Comparisons
base_orderedBase Type Requirements for Ordered Comparisons
base_std_mathBase Type Requirements for Standard Math Functions
base_limitsBase Type Requirements for Numeric Limits
base_to_stringExtending to_string To Another Floating Point Type
base_hashBase Type Requirements for Hash Coding Values
base_exampleExample AD Base Types That are not AD<OtherBase>
Input File: cppad/base_require.hpp cppad-20170000.3/doc/base_member.xml0000644000175200017650000002456713057470506016177 0ustar coincoin-web Required Base Class Member Functions
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Required Base Class Member Functions

Notation
Symbol Meaning
Base The base type corresponding to AD<Base>
b An object of type bool
d An object of type double
x An object of type const Base&
y An object of type const Base&
z An object of type Base

Default Constructor
Base z

Double Constructor
Base z(d)

Copy Constructor
Base z(x)

Unary Operators
For op equal to +, - the following operation must be supported:
     z = op x

Assignment Operators
For op equal to = , +=, -=, *=, and /= the following operation must be supported:
     z op x

Binary Operators
For op equal to +, -, *, and / the following operation must be supported:
     z = x op y

Bool Operators
For op equal to ==, !=, <=, the following operation must be supported:
     b = x op y

Example
See the heading Class Definition in base_alloc .
Input File: omh/base_require/base_member.omh cppad-20170000.3/doc/base_cond_exp.xml0000644000175200017650000004312313057470506016514 0ustar coincoin-web Base Type Requirements for Conditional Expressions
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Base Type Requirements for Conditional Expressions

Purpose
These definitions are required by the user's code to support the AD<Base> type for CondExp operations:

CompareOp
The following enum type is used in the specifications below: 
 
namespace CppAD {
     // The conditional expression operator enum type
     enum CompareOp
     {    CompareLt, // less than
          CompareLe, // less than or equal
          CompareEq, // equal
          CompareGe, // greater than or equal
          CompareGt, // greater than
          CompareNe  // not equal
     };
}

CondExpTemplate
The type Base must support the syntax
     result = CppAD::CondExpOp(
          cop, left, right, exp_if_true, exp_if_false
     )
 which computes implements the corresponding CondExp function when the result has prototype
     Base result
 The argument cop has prototype
     enum CppAD::CompareOp cop
 The other arguments have the prototype
     const Base&  left
     const Base&  right
     const Base&  exp_if_true
     const Base&  exp_if_false
Ordered Type
If Base is a relatively simple type that supports <, <=, ==, >=, and > operators its CondExpOp function can be defined by
namespace CppAD {
     inline Base CondExpOp(
     enum CppAD::CompareOp  cop            ,
     const Base           &left          ,
     const Base           &right         ,
     const Base           &exp_if_true   ,
     const Base           &exp_if_false  )
     {    return CondExpTemplate(
               cop, left, right, trueCase, falseCase);
     }
}
 For example, see double CondExpOp . For an example of and implementation of CondExpOp with a more involved Base type see adolc CondExpOp .

Not Ordered
If the type Base does not support ordering, the CondExpOp function does not make sense. In this case one might (but need not) define CondExpOp as follows:
namespace CppAD {
     inline Base CondExpOp(
     enum CompareOp cop           ,
     const Base   &left         ,
     const Base   &right        ,
     const Base   &exp_if_true  ,
     const Base   &exp_if_false )
     {    // attempt to use CondExp with a Base argument
          assert(0);
          return Base(0);
     }
}
 For example, see complex CondExpOp .

CondExpRel
The macro invocation
     CPPAD_COND_EXP_REL(Base)
 uses CondExpOp above to define the following functions
     CondExpLt(left, right, exp_if_true, exp_if_false)
     CondExpLe(left, right, exp_if_true, exp_if_false)
     CondExpEq(left, right, exp_if_true, exp_if_false)
     CondExpGe(left, right, exp_if_true, exp_if_false)
     CondExpGt(left, right, exp_if_true, exp_if_false)
 where the arguments have type Base . This should be done inside of the CppAD namespace. For example, see base_alloc .
Input File: cppad/core/base_cond_exp.hpp cppad-20170000.3/doc/base_identical.xml0000644000175200017650000004070513057470506016654 0ustar coincoin-web Base Type Requirements for Identically Equal Comparisons
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Base Type Requirements for Identically Equal Comparisons

EqualOpSeq
If function EqualOpSeq is used with arguments of type AD<Base> , the type Base must support the syntax
     b = CppAD::EqualOpSeq(u, v)
 This should return true if and only if u is identically equal to v and it makes no different which one is used. The arguments u and v have prototype
     const Base& u
     const Base& v
 The return value b has prototype
     bool b
The Simple Case
If Base is a relatively simple type, the EqualOpSeq function can be defined by
namespace CppAD {
     inline Base EqualOpSeq(const Base& u, const Base& v)
     {    return u == v; }
}
 For example, see base_alloc .

More Complicated Cases
The variables u and v are not identically equal in the following case (which CppAD automatically defines EqualOpSeq for): The type Base is AD<double> , x[0] = x[1] = 1. , then independent is used to make x the independent variable vector, and then u = x[0] , v = x[1] , Note that during a future Forward calculation, u and v could correspond to different values. For example, see adolc EqualOpSeq .

Identical

IdenticalPar
A Base is a parameter when used in an AD<Base> operation sequence. It is however still possible for a parameter to change its value. For example, the Base value u is not identically a parameter equal in the following case (which CppAD automatically defines IdenticalPar for): The type Base is AD<double> , x[0] = 1. , then independent is used to make x the independent variable vector, and then u = x[0] , Note that during a future Forward calculation, u could correspond to different values.

Prototypes
The argument u has prototype
     const Base u
 If it is present, the argument v has prototype
     const Base v
 The result b has prototype
     bool b
Identical Functions
The type Base must support the following functions (in the CppAD namespace):
Syntax Result
b = IdenticalPar(u)    the Base value will always be the same
b = IdenticalZero(u)    u equals zero and IdenticalPar(u)
b = IdenticalOne(u)    u equals one and IdenticalPar(u)
b = IdenticalEqualPar(u, v)    u equals v , IdenticalPar(u) and IdenticalPar(v)

Examples
See base_alloc .
Input File: omh/base_require/base_identical.omh cppad-20170000.3/doc/base_ordered.xml0000644000175200017650000002431713057470506016345 0ustar coincoin-web Base Type Requirements for Ordered Comparisons
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Base Type Requirements for Ordered Comparisons

Purpose
The following operations (in the CppAD namespace) are required to use the type AD<Base> :
Syntax Result
b = GreaterThanZero(x)    x > 0
b = GreaterThanOrZero(x)    x ≥ 0
b = LessThanZero(x)    x < 0
b = LessThanOrZero(x)    x ≤ 0
b = abs_geq(x, y)    | x | ≥ | y | .
where the arguments and return value have the prototypes
     const Base& x
     const Base& y
     bool        b
Ordered Type
If the type Base supports ordered operations, these functions should have their corresponding definitions. For example,
namespace CppAD {
     inline bool GreaterThanZero(const Base &x)
     {    return (x > 0);
     }
}
 The other functions would replace > by the corresponding operator. For example, see base_alloc .

Not Ordered
If the type Base does not support ordering, one might (but need not) define GreaterThanZero as follows:
namespace CppAD {
     inline bool GreaterThanZero(const Base &x)
     {    // attempt to use GreaterThanZero with a Base argument
          assert(0);
          return x;
     }
}
 The other functions would have the corresponding definition. For example, see complex Ordered .
Input File: omh/base_require/base_ordered.omh cppad-20170000.3/doc/base_std_math.xml0000644000175200017650000005276113057470506016530 0ustar coincoin-web Base Type Requirements for Standard Math Functions
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Base Type Requirements for Standard Math Functions

Purpose
These definitions are required for the user's code to use the type AD<Base> :

Unary Standard Math
The type Base must support the following functions unary standard math functions (in the CppAD namespace):
Syntax Result
y = abs(x) absolute value
y = acos(x) inverse cosine
y = asin(x) inverse sine
y = atan(x) inverse tangent
y = cos(x) cosine
y = cosh(x) hyperbolic cosine
y = exp(x) exponential
y = fabs(x) absolute value
y = log(x) natural logarithm
y = sin(x) sine
y = sinh(x) hyperbolic sine
y = sqrt(x) square root
y = tan(x) tangent
where the arguments and return value have the prototypes
     const Base& x
     Base        y
 For example, base_alloc ,

CPPAD_STANDARD_MATH_UNARY
The macro invocation, within the CppAD namespace,
     CPPAD_STANDARD_MATH_UNARY(Base, Fun)
 defines the syntax
     y = CppAD::Fun(x)
 This macro uses the functions std::Fun which must be defined and have the same prototype as CppAD::Fun . For example, float .

erf, asinh, acosh, atanh, expm1, log1p
If this preprocessor symbol CPPAD_USE_CPLUSPLUS_2011 is true (1), when compiling for c++11, the type double is supported for the functions listed below. In this case, the type Base must also support these functions:
Syntax Result
y = erf(x) error function
y = asinh(x) inverse hyperbolic sin
y = acosh(x) inverse hyperbolic cosine
y = atanh(x) inverse hyperbolic tangent
y = expm1(x) exponential of x minus one
y = log1p(x) logarithm of one plus x
where the arguments and return value have the prototypes
     const Base& x
     Base        y
sign
The type Base must support the syntax
     y = CppAD::sign(x)
 which computes y = { + 1 if x > 0 0 if x = 0 -1 if x < 0 where x and y have the same prototype as above. For example, see base_alloc . Note that, if ordered comparisons are not defined for the type Base , the code sign function should generate an assert if it is used; see complex invalid unary math .

pow
The type Base must support the syntax
     z = CppAD::pow(x, y)
 which computes z = x y . The arguments x and y have prototypes
     const Base& x
     const Base& y
 and the return value z has prototype
     Base z
 For example, see base_alloc .

isnan
If Base defines the isnan function, you may also have to provide a definition in the CppAD namespace (to avoid a function ambiguity). For example, see base_complex .
Input File: cppad/core/base_std_math.hpp cppad-20170000.3/doc/base_limits.xml0000644000175200017650000002443513057470506016223 0ustar coincoin-web Base Type Requirements for Numeric Limits
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Base Type Requirements for Numeric Limits

CppAD::numeric_limits
A specialization for CppAD::numeric_limits must be defined in order to use the type AD<Base> . CppAD does not use a specialization of std::numeric_limits<Base> . Since C++11, using a specialization of std::numeric_limits<Base> would require that Base be a literal type.

CPPAD_NUMERIC_LIMITS
In most cases, this macro can be used to define the specialization where the numeric limits for the type Base are the same as the standard numeric limits for the type Other . For most Base types, there is a choice of Other , for which the following preprocessor macro invocation suffices:
     namespace CppAD {
          CPPAD_NUMERIC_LIMITS(Other, Base)
     }
 where the macro is defined by 
# define CPPAD_NUMERIC_LIMITS(Other, Base) \
template <> class numeric_limits<Base>\
{\
     public:\
     static Base min(void) \
     {     return static_cast<Base>( std::numeric_limits<Other>::min() ); }\
     static Base max(void) \
     {     return static_cast<Base>( std::numeric_limits<Other>::max() ); }\
     static Base epsilon(void) \
     {     return static_cast<Base>( std::numeric_limits<Other>::epsilon() ); }\
     static Base quiet_NaN(void) \
     {     return static_cast<Base>( std::numeric_limits<Other>::quiet_NaN() ); }\
};
Input File: cppad/core/base_limits.hpp cppad-20170000.3/doc/base_to_string.xml0000644000175200017650000001720413057470506016726 0ustar coincoin-web Extending to_string To Another Floating Point Type
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Extending to_string To Another Floating Point Type

Base Requirement
If the function to_string is used by an AD type above Base , A specialization for the template structure CppAD::to_string_struct must be defined.

CPPAD_TO_STRING
For most Base types, the following can be used to define the specialization:
     namespace CppAD {
          CPPAD_TO_STRING(Base)
     }
 Note that the CPPAD_TO_STRING macro assumes that the base_limits and base_std_math have already been defined for this type. This macro is defined as follows: 
# define CPPAD_TO_STRING(Base) \
template <> struct to_string_struct<Base>\
{     std::string operator()(const Base& value) \
     {     std::stringstream os;\
          Base epsilon    = CppAD::numeric_limits<Base>::epsilon();\
          Base log10      = CppAD::log( epsilon ) / CppAD::log(Base(10.));\
          size_t n_digits = 1 - Integer( log10 );\
          os << std::setprecision(n_digits);\
          os << value;\
          return os.str();\
     }\
};
Input File: cppad/core/base_to_string.hpp cppad-20170000.3/doc/base_hash.xml0000644000175200017650000001537713057470506015652 0ustar coincoin-web Base Type Requirements for Hash Coding Values
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Base Type Requirements for Hash Coding Values

Syntax
code = hash_code(x)

Purpose
CppAD uses a table of Base type values when recording AD<Base> operations. A hashing function is used to reduce number of values stored in this table; for example, it is not necessary to store the value 3.0 every time it is used as a parameter .

Default
The default hashing function works with the set of bits that correspond to a Base value. In most cases this works well, but in some cases it does not. For example, in the base_adolc.hpp case, an adouble value can have fields that are not initialized and valgrind reported an error when these are used to form the hash code.

x
This argument has prototype
     const Base& x
 It is the value we are forming a hash code for.

code
The return value code has prototype
     unsigned short code
 It is the hash code corresponding to x . This intention is the commonly used values will have different hash codes. The hash code must satisfy
     code < CPPAD_HASH_TABLE_SIZE
 so that it is a valid index into the hash code table.

inline
If you define this function, it should declare it to be inline, so that you do not get multiple definitions from different compilation units.

Example
See the base_alloc hash_code and the adouble hash_code .
Input File: cppad/core/base_hash.hpp cppad-20170000.3/doc/base_example.xml0000644000175200017650000000761713057470506016360 0ustar coincoin-web Example AD Base Types That are not AD<OtherBase>
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Example AD Base Types That are not AD<OtherBase>

Contents
Input File: omh/base_require/base_example.omh cppad-20170000.3/doc/base_alloc.hpp.xml0000644000175200017650000015152013057470506016576 0ustar coincoin-web Example AD<Base> Where Base Constructor Allocates Memory
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Example AD<Base> Where Base Constructor Allocates Memory

Purpose
Demonstrate use of AD<Base> where memory is allocated for each element of the type Base . In addition, this is a complete example where all the required Base type operations are defined (as apposed to other examples where some of the operations for the Base type are already defined).

Include File
This file uses some of the definitions in base_require and thread_alloc . 

# include <cppad/base_require.hpp>
# include <cppad/utility/thread_alloc.hpp>

Computed Assignment Macro
This macro is used for the base_alloc computed assignment operators; to be specific, used with op  equal to +=, -=, *=, /=. 

# define BASE_ALLOC_ASSIGN_OPERATOR(op) \
     void operator op (const base_alloc& x) \
     {     *ptrdbl_ op *x.ptrdbl_; }

Binary Operator Macro
This macro is used for the base_alloc binary operators (as member functions); to be specific, used with op  equal to +, -, *, /. 
# define BASE_ALLOC_BINARY_OPERATOR(op) const \
     base_alloc operator op (const base_alloc& x) const \
     {     base_alloc result; \
          double   dbl = *ptrdbl_; \
          double x_dbl = *x.ptrdbl_; \
          *result.ptrdbl_ = dbl op x_dbl; \
          return result; \
     }

Boolean Operator Macro
This macro can be used for the base_alloc binary operators that have a bool result; to be specific, used with op  equal to ==, !=, <, <=, >=, and >, 
# define BASE_ALLOC_BOOL_OPERATOR(op) const \
     bool operator op (const base_alloc& x) const \
     {     double   dbl = *ptrdbl_; \
          double x_dbl = *x.ptrdbl_; \
          return dbl op x_dbl; \
     }

Class Definition
The following example class defines the necessary base_member functions. It is made more complicated by storing a pointer to a double instead of the double value itself. 

class base_alloc {
public:
     double* ptrdbl_;

     base_alloc(void)
     {     size_t cap;
          void* v  = CppAD::thread_alloc::get_memory(sizeof(double), cap);
          ptrdbl_  = static_cast<double*>(v);
     }
     base_alloc(double dbl)
     {     size_t cap;
          void *v  = CppAD::thread_alloc::get_memory(sizeof(double), cap);
          ptrdbl_  = static_cast<double*>(v);
          *ptrdbl_ = dbl;
     }
     base_alloc(const base_alloc& x)
     {     size_t cap;
          void *v  = CppAD::thread_alloc::get_memory(sizeof(double), cap);
          ptrdbl_  = static_cast<double*>(v);
          *ptrdbl_ = *x.ptrdbl_;
     }
     ~base_alloc(void)
     {     void* v  = static_cast<void*>(ptrdbl_);
          CppAD::thread_alloc::return_memory(v);
     }
     base_alloc operator-(void) const
     {     base_alloc result;
          *result.ptrdbl_ = - *ptrdbl_;
          return result;
     }
     base_alloc operator+(void) const
     {     return *this; }
     void operator=(const base_alloc& x)
     {     *ptrdbl_ = *x.ptrdbl_; }
     BASE_ALLOC_ASSIGN_OPERATOR(+=)
     BASE_ALLOC_ASSIGN_OPERATOR(-=)
     BASE_ALLOC_ASSIGN_OPERATOR(*=)
     BASE_ALLOC_ASSIGN_OPERATOR(/=)
     BASE_ALLOC_BINARY_OPERATOR(+)
     BASE_ALLOC_BINARY_OPERATOR(-)
     BASE_ALLOC_BINARY_OPERATOR(*)
     BASE_ALLOC_BINARY_OPERATOR(/)
     BASE_ALLOC_BOOL_OPERATOR(==)
     BASE_ALLOC_BOOL_OPERATOR(!=)
     // The <= operator is not necessary for the base type requirements
     // (needed so we can use NearEqual with base_alloc arguments).
     BASE_ALLOC_BOOL_OPERATOR(<=)
};

CondExpOp
The type base_alloc does not use CondExp operations. Hence its CondExpOp function is defined by 
namespace CppAD {
     inline base_alloc CondExpOp(
          enum CompareOp     cop          ,
          const base_alloc&       left         ,
          const base_alloc&       right        ,
          const base_alloc&       exp_if_true  ,
          const base_alloc&       exp_if_false )
     {     // not used
          assert(false);

          // to void compiler error
          return base_alloc();
     }
}

CondExpRel
The CPPAD_COND_EXP_REL macro invocation 

namespace CppAD {
     CPPAD_COND_EXP_REL(base_alloc)
}
uses CondExpOp above to define CondExpRel for base_alloc arguments and Rel equal to Lt, Le, Eq, Ge, and Gt.

EqualOpSeq
The type base_alloc is simple (in this respect) and so we define 
namespace CppAD {
     inline bool EqualOpSeq(const base_alloc& x, const base_alloc& y)
     {     return *x.ptrdbl_ == *y.ptrdbl_; }
}

Identical
The type base_alloc is simple (in this respect) and so we define 
namespace CppAD {
     inline bool IdenticalPar(const base_alloc& x)
     {     return true; }
     inline bool IdenticalZero(const base_alloc& x)
     {     return (*x.ptrdbl_ == 0.0); }
     inline bool IdenticalOne(const base_alloc& x)
     {     return (*x.ptrdbl_ == 1.0); }
     inline bool IdenticalEqualPar(const base_alloc& x, const base_alloc& y)
     {     return (*x.ptrdbl_ == *y.ptrdbl_); }
}

Output Operator 
namespace CppAD {
     std::ostream& operator << (std::ostream &os, const base_alloc& x)
     {     os << *x.ptrdbl_;
          return os;
     }
}

Integer 
namespace CppAD {
     inline int Integer(const base_alloc& x)
     {     return static_cast<int>(*x.ptrdbl_); }
}

azmul 

namespace CppAD {
     CPPAD_AZMUL( base_alloc )
}

Ordered
The base_alloc type supports ordered comparisons 
namespace CppAD {
     inline bool GreaterThanZero(const base_alloc& x)
     {     return *x.ptrdbl_ > 0.0; }
     inline bool GreaterThanOrZero(const base_alloc& x)
     {     return *x.ptrdbl_ >= 0.0; }
     inline bool LessThanZero(const base_alloc& x)
     {     return *x.ptrdbl_ < 0.0; }
     inline bool LessThanOrZero(const base_alloc& x)
     {     return *x.ptrdbl_ <= 0.f; }
     inline bool abs_geq(const base_alloc& x, const base_alloc& y)
     {     return std::fabs(*x.ptrdbl_) >= std::fabs(*y.ptrdbl_); }
}

Unary Standard Math
The macro CPPAD_STANDARD_MATH_UNARY would not work with the type base_alloc so we define a special macro for this type: 

# define BASE_ALLOC_STD_MATH(fun) \
     inline base_alloc fun (const base_alloc& x) \
     { return   std::fun(*x.ptrdbl_); }
The following invocations of the macro above define the unary standard math functions (except for abs): 
namespace CppAD {
     BASE_ALLOC_STD_MATH(acos)
     BASE_ALLOC_STD_MATH(asin)
     BASE_ALLOC_STD_MATH(atan)
     BASE_ALLOC_STD_MATH(cos)
     BASE_ALLOC_STD_MATH(cosh)
     BASE_ALLOC_STD_MATH(exp)
     BASE_ALLOC_STD_MATH(log)
     BASE_ALLOC_STD_MATH(log10)
     BASE_ALLOC_STD_MATH(sin)
     BASE_ALLOC_STD_MATH(sinh)
     BASE_ALLOC_STD_MATH(sqrt)
     BASE_ALLOC_STD_MATH(tan)
     BASE_ALLOC_STD_MATH(tanh)
}
The absolute value function is special because its std name is fabs 
namespace CppAD {
     inline base_alloc abs(const base_alloc& x)
     {     return std::fabs(*x.ptrdbl_); }
}

erf, asinh, acosh, atanh, expm1, log1p
The following defines the erf, asinh, acosh, atanh, expm1, log1p functions required by AD<base_alloc>: 
# if CPPAD_USE_CPLUSPLUS_2011
     BASE_ALLOC_STD_MATH(erf)
     BASE_ALLOC_STD_MATH(asinh)
     BASE_ALLOC_STD_MATH(acosh)
     BASE_ALLOC_STD_MATH(atanh)
     BASE_ALLOC_STD_MATH(expm1)
     BASE_ALLOC_STD_MATH(log1p)
# endif

sign
The following defines the CppAD::sign function that is required to use AD<base_alloc>: 
namespace CppAD {
     inline base_alloc sign(const base_alloc& x)
     {     if( *x.ptrdbl_ > 0.0 )
               return 1.0;
          if( *x.ptrdbl_ == 0.0 )
               return 0.0;
          return -1.0;
     }
}

pow
The following defines a CppAD::pow function that is required to use AD<base_alloc>: 
namespace CppAD {
     inline base_alloc pow(const base_alloc& x, const base_alloc& y)
     { return std::pow(*x.ptrdbl_, *y.ptrdbl_); }
}

numeric_limits
The following defines the CppAD numeric_limits for the type base_alloc: 

namespace CppAD {
     CPPAD_NUMERIC_LIMITS(double, base_alloc)
}

to_string
The following defines the CppAD to_string function for the type base_alloc: 

namespace CppAD {
     CPPAD_TO_STRING(base_alloc)
}

hash_code
The default hashing function does not work well for this case because two different pointers can have the same value. 
namespace CppAD {
     inline unsigned short hash_code(const base_alloc& x)
     {     unsigned short code = 0;
          if( *x.ptrdbl_ == 0.0 )
               return code;
          double log_x = log( abs( *x.ptrdbl_ ) );
          // assume log( std::numeric_limits<double>::max() ) is near 700
          code = static_cast<unsigned short>(
               (CPPAD_HASH_TABLE_SIZE / 700 + 1) * log_x
          );
          code = code % CPPAD_HASH_TABLE_SIZE;
          return code;
     }
}
Input File: example/base_alloc.hpp cppad-20170000.3/doc/base_require.cpp.xml0000644000175200017650000002702113057470506017151 0ustar coincoin-web Using a User Defined AD Base Type: Example and Test
Prev Next base_require.cpp

Using a User Defined AD Base Type: Example and Test
# include "base_alloc.hpp"
# include <cppad/cppad.hpp>

bool base_require(void)
{     bool ok = true;
     using CppAD::thread_alloc;
     typedef CppAD::AD<base_alloc> ad_base_alloc;

     // check the amount of memory inuse by this thread (thread zero)
     size_t thread = thread_alloc::thread_num();
     ok &= thread == 0;

     // y = x^2
     size_t n = 1, m = 1;
     CPPAD_TESTVECTOR(ad_base_alloc) a_x(n), a_y(m);
     a_x[0] = ad_base_alloc(1.);
     CppAD::Independent(a_x);
     a_y[0] = a_x[0] * a_x[0];
     CppAD::ADFun<base_alloc> f(a_x, a_y);

     // check function value f(x) = x^2
     CPPAD_TESTVECTOR(base_alloc) x(n), y(m);
     base_alloc eps =
          base_alloc(100.) * CppAD::numeric_limits<base_alloc>::epsilon();
     x[0] = base_alloc(3.);
     y    = f.Forward(0, x);
     ok  &= CppAD::NearEqual(y[0], x[0] * x[0], eps, eps);

     // check derivative value f'(x) = 2 * x
     CPPAD_TESTVECTOR(base_alloc) dy(m * n);
     dy   = f.Jacobian(x);
     ok  &= CppAD::NearEqual(dy[0], base_alloc(2.) * x[0], eps, eps);

     return ok;
}
Purpose
The type base_alloc, defined in base_alloc.hpp , meets the requirements specified by base_require for Base in AD<Base> . The program below is an example use of AD<base_alloc> .
Input File: example/base_require.cpp cppad-20170000.3/doc/base_adolc.hpp.xml0000644000175200017650000012745113057470506016574 0ustar coincoin-web Enable use of AD<Base> where Base is Adolc's adouble Type
Prev Next

Enable use of AD<Base> where Base is Adolc's adouble Type

Syntax
# include <cppad/example/base_adolc.hpp>
Example
The file mul_level_adolc.cpp contains an example use of Adolc's adouble type for a CppAD Base type. It returns true if it succeeds and false otherwise. The file mul_level_adolc_ode.cpp contains a more realistic (and complex) example.

Include Files
This file base_adolc.hpp requires adouble to be defined. In addition, it is included before <cppad/cppad.hpp>, but it needs to include parts of CppAD that are used by this file. This is done with the following include commands: 

# include <adolc/adolc.h>
# include <cppad/base_require.hpp>

CondExpOp
The type adouble supports a conditional assignment function with the syntax
     condassign(a, b, c, d)
 which evaluates to
     a = (b > 0) ? c : d;
 This enables one to include conditionals in the recording of adouble operations and later evaluation for different values of the independent variables (in the same spirit as the CppAD CondExp function). 
namespace CppAD {
     inline adouble CondExpOp(
          enum  CppAD::CompareOp     cop ,
          const adouble            &left ,
          const adouble           &right ,
          const adouble        &trueCase ,
          const adouble       &falseCase )
     {     adouble result;
          switch( cop )
          {
               case CompareLt: // left < right
               condassign(result, right - left, trueCase, falseCase);
               break;

               case CompareLe: // left <= right
               condassign(result, left - right, falseCase, trueCase);
               break;

               case CompareEq: // left == right
               condassign(result, left - right, falseCase, trueCase);
               condassign(result, right - left, falseCase, result);
               break;

               case CompareGe: // left >= right
               condassign(result, right - left, falseCase, trueCase);
               break;

               case CompareGt: // left > right
               condassign(result, left - right, trueCase, falseCase);
               break;
               default:
               CppAD::ErrorHandler::Call(
                    true     , __LINE__ , __FILE__ ,
                    "CppAD::CondExp",
                    "Error: for unknown reason."
               );
               result = trueCase;
          }
          return result;
     }
}

CondExpRel
The CPPAD_COND_EXP_REL macro invocation 

namespace CppAD {
     CPPAD_COND_EXP_REL(adouble)
}

EqualOpSeq
The Adolc user interface does not specify a way to determine if two adouble variables correspond to the same operations sequence. Make EqualOpSeq an error if it gets used: 
namespace CppAD {
     inline bool EqualOpSeq(const adouble &x, const adouble &y)
     {     CppAD::ErrorHandler::Call(
               true     , __LINE__ , __FILE__ ,
               "CppAD::EqualOpSeq(x, y)",
               "Error: adouble does not support EqualOpSeq."
          );
          return false;
     }
}

Identical
The Adolc user interface does not specify a way to determine if an adouble depends on the independent variables. To be safe (but slow) return false in all the cases below. 
namespace CppAD {
     inline bool IdenticalPar(const adouble &x)
     {     return false; }
     inline bool IdenticalZero(const adouble &x)
     {     return false; }
     inline bool IdenticalOne(const adouble &x)
     {     return false; }
     inline bool IdenticalEqualPar(const adouble &x, const adouble &y)
     {     return false; }
}

Integer 

     inline int Integer(const adouble &x)
     {    return static_cast<int>( x.getValue() ); }

azmul 

namespace CppAD {
     CPPAD_AZMUL( adouble )
}

Ordered 
namespace CppAD {
     inline bool GreaterThanZero(const adouble &x)
     {    return (x > 0); }
     inline bool GreaterThanOrZero(const adouble &x)
     {    return (x >= 0); }
     inline bool LessThanZero(const adouble &x)
     {    return (x < 0); }
     inline bool LessThanOrZero(const adouble &x)
     {    return (x <= 0); }
     inline bool abs_geq(const adouble& x, const adouble& y)
     {     return fabs(x) >= fabs(y); }
}

Unary Standard Math
The following required functions are defined by the Adolc package for the adouble base case:
acos, asin, atan, cos, cosh, exp, fabs, log, sin, sinh, sqrt, tan.

erf, asinh, acosh, atanh, expm1, log1p
If the erf, asinh, acosh, atanh, expm1, log1p , functions are supported by the compiler, they must also be supported by a Base type; The adolc package does not support these functions so make their use an error: 
namespace CppAD {
# define CPPAD_BASE_ADOLC_NO_SUPPORT(fun)                         \
    inline adouble fun(const adouble& x)                          \
    {   CPPAD_ASSERT_KNOWN(                                       \
            false,                                                \
            #fun ": adolc does not support this function"         \
        );                                                        \
        return 0.0;                                               \
    }
# if CPPAD_USE_CPLUSPLUS_2011
     CPPAD_BASE_ADOLC_NO_SUPPORT(erf)
     CPPAD_BASE_ADOLC_NO_SUPPORT(asinh)
     CPPAD_BASE_ADOLC_NO_SUPPORT(acosh)
     CPPAD_BASE_ADOLC_NO_SUPPORT(atanh)
     CPPAD_BASE_ADOLC_NO_SUPPORT(expm1)
     CPPAD_BASE_ADOLC_NO_SUPPORT(log1p)
# endif
# undef CPPAD_BASE_ADOLC_NO_SUPPORT
}

sign
This required function is defined using the codassign function so that its adouble operation sequence does not depend on the value of x . 
namespace CppAD {
     inline adouble sign(const adouble& x)
     {     adouble s_plus, s_minus, half(.5);
          // set s_plus to sign(x)/2,  except for case x == 0, s_plus = -.5
          condassign(s_plus,  +x, -half, +half);
          // set s_minus to -sign(x)/2, except for case x == 0, s_minus = -.5
          condassign(s_minus, -x, -half, +half);
          // set s to sign(x)
          return s_plus - s_minus;
     }
}

abs
This required function uses the adolc fabs function: 
namespace CppAD {
     inline adouble abs(const adouble& x)
     {     return fabs(x); }
}

pow
This required function is defined by the Adolc package for the adouble base case.

numeric_limits
The following defines the CppAD numeric_limits for the type adouble: 

namespace CppAD {
     CPPAD_NUMERIC_LIMITS(double, adouble)
}

to_string
The following defines the CppAD to_string function for the type adouble: 
namespace CppAD {
     template <> struct to_string_struct<adouble>
     {     std::string operator()(const adouble& x)
          {     std::stringstream os;
               double epsilon    = std::numeric_limits<double>::epsilon();
               double log10      = std::log( epsilon ) / std::log(10.);
               size_t n_digits   = 1 - Integer( log10 );
               os << std::setprecision(n_digits);
               os << x.value();
               return os.str();
          }
     };
}

hash_code
It appears that an adouble object can have fields that are not initialized. This results in a valgrind error when these fields are used by the default hashing function. For this reason, the adouble class overrides the default definition. 
namespace CppAD {
     inline unsigned short hash_code(const adouble& x)
     {     unsigned short code = 0;
          double value = x.value();
          if( value == 0.0 )
               return code;
          double log_x = std::log( abs( value ) );
          // assume log( std::numeric_limits<double>::max() ) is near 700
          code = static_cast<unsigned short>(
               (CPPAD_HASH_TABLE_SIZE / 700 + 1) * log_x
          );
          code = code % CPPAD_HASH_TABLE_SIZE;
          return code;
     }
}
Note that after the hash codes match, the Identical function will be used to make sure two values are the same and one can replace the other. A more sophisticated implementation of the Identical function would detect which adouble values depend on the adouble independent variables (and hence can change).
Input File: cppad/example/base_adolc.hpp cppad-20170000.3/doc/mul_level_adolc.cpp.xml0000644000175200017650000006357013057470506017642 0ustar coincoin-web Using Adolc with Multiple Levels of Taping: Example and Test
Prev Next mul_level_adolc.cpp

Using Adolc with Multiple Levels of Taping: Example and Test

Purpose
In this example, we use AD< adouble> > (level two taping), the compute values of the function f : R n → R where f ( x ) = 1 2 (x 0 2 + ⋯ + x n -1 2 ) We then use Adolc's adouble (level one taping) to compute the directional derivative f ( 1 ) ( x ) * v = x 0 v 0 + ⋯ + x n -1 v n -1 . where v ∈ R n . We then use double (no taping) to compute d dx [f ( 1 ) ( x ) * v ] = v This is only meant as an example of multiple levels of taping. The example hes_times_dir.cpp computes the same value more efficiently by using the identity: d dx [f ( 1 ) ( x ) * v ] = f ( 2 ) ( x ) * v The example mul_level.cpp computes the same values using AD< AD<double> > and AD<double>.

Memory Management
Adolc uses raw memory arrays that depend on the number of dependent and independent variables. The memory management utility thread_alloc is used to manage this memory allocation.

Configuration Requirement
This example will be compiled and tested provided that the value adolc_prefix is specified on the cmake command line.

Source 

# include <adolc/adouble.h>
# include <adolc/taping.h>
# include <adolc/interfaces.h>

// adouble definitions not in Adolc distribution and
// required in order to use CppAD::AD<adouble>
# include <cppad/example/base_adolc.hpp>

# include <cppad/cppad.hpp>

namespace {
     // f(x) = |x|^2 / 2 = .5 * ( x[0]^2 + ... + x[n-1]^2 )
     template <class Type>
     Type f(const CPPAD_TESTVECTOR(Type)& x)
     {     Type sum;

          sum  = 0.;
          size_t i = size_t(x.size());
          for(i = 0; i < size_t(x.size()); i++)
               sum += x[i] * x[i];

          return .5 * sum;
     }
}

bool mul_level_adolc(void)
{     bool ok = true;                // initialize test result
     using CppAD::thread_alloc;        // The CppAD memory allocator

     typedef adouble           a1type;  // for first level of taping
     typedef CppAD::AD<a1type> a2type; // for second level of taping
     size_t n = 5;                          // number independent variables
     size_t j;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     CPPAD_TESTVECTOR(double) x(n);
     CPPAD_TESTVECTOR(a1type) a1x(n);
     CPPAD_TESTVECTOR(a2type) a2x(n);

     // Values for the independent variables while taping the function f(x)
     for(j = 0; j < n; j++)
          a2x[j] = double(j);
     // Declare the independent variable for taping f(x)
     CppAD::Independent(a2x);

     // Use AD<adouble> to tape the evaluation of f(x)
     CPPAD_TESTVECTOR(a2type) a2y(1);
     a2y[0] = f(a2x);

     // Declare a1f as the corresponding ADFun<adouble> function f(x)
     // (make sure we do not run zero order forward during constructor)
     CppAD::ADFun<a1type> a1f;
     a1f.Dependent(a2x, a2y);

     // Value of the independent variables whitle taping f'(x) * v
     int tag = 0;
     int keep = 1;
     trace_on(tag, keep);
     for(j = 0; j < n; j++)
          a1x[j] <<= double(j);

     // set the argument value x for computing f'(x) * v
     a1f.Forward(0, a1x);

     // compute f'(x) * v
     CPPAD_TESTVECTOR(a1type) a1v(n);
     CPPAD_TESTVECTOR(a1type) a1df(1);
     for(j = 0; j < n; j++)
          a1v[j] = double(n - j);
     a1df = a1f.Forward(1, a1v);

     // declare Adolc function corresponding to f'(x) * v
     double df;
     a1df[0] >>= df;
     trace_off();

     // compute the d/dx of f'(x) * v = f''(x) * v
     size_t m      = 1;                     // # dependent in f'(x) * v

     // w = new double[capacity] where capacity >= m
     size_t capacity;
     double* w  = thread_alloc::create_array<double>(m, capacity);

     // dw = new double[capacity] where capacity >= n
     double* dw = thread_alloc::create_array<double>(n, capacity);

     w[0]  = 1.;
     fos_reverse(tag, int(m), int(n), w, dw);

     for(j = 0; j < n; j++)
     {     double vj = a1v[j].value();
          ok &= CppAD::NearEqual(dw[j], vj, eps, eps);
     }

     // make memory avaialble for other use by this thread
     thread_alloc::delete_array(w);
     thread_alloc::delete_array(dw);
     return ok;
}
Input File: example/mul_level_adolc.cpp cppad-20170000.3/doc/base_float.hpp.xml0000644000175200017650000006731013057470506016614 0ustar coincoin-web Enable use of AD<Base> where Base is float
Prev Next base_float.hpp

Enable use of AD<Base> where Base is float

CondExpOp
The type float is a relatively simple type that supports <, <=, ==, >=, and > operators; see ordered type . Hence its CondExpOp function is defined by 
namespace CppAD {
     inline float CondExpOp(
          enum CompareOp     cop          ,
          const float&       left         ,
          const float&       right        ,
          const float&       exp_if_true  ,
          const float&       exp_if_false )
     {     return CondExpTemplate(cop, left, right, exp_if_true, exp_if_false);
     }
}

CondExpRel
The CPPAD_COND_EXP_REL macro invocation 

namespace CppAD {
     CPPAD_COND_EXP_REL(float)
}
uses CondExpOp above to define CondExpRel for float arguments and Rel equal to Lt, Le, Eq, Ge, and Gt.

EqualOpSeq
The type float is simple (in this respect) and so we define 
namespace CppAD {
     inline bool EqualOpSeq(const float& x, const float& y)
     {     return x == y; }
}

Identical
The type float is simple (in this respect) and so we define 
namespace CppAD {
     inline bool IdenticalPar(const float& x)
     {     return true; }
     inline bool IdenticalZero(const float& x)
     {     return (x == 0.f); }
     inline bool IdenticalOne(const float& x)
     {     return (x == 1.f); }
     inline bool IdenticalEqualPar(const float& x, const float& y)
     {     return (x == y); }
}

Integer 
namespace CppAD {
     inline int Integer(const float& x)
     {     return static_cast<int>(x); }
}

azmul 

namespace CppAD {
     CPPAD_AZMUL( float )
}

Ordered
The float type supports ordered comparisons 
namespace CppAD {
     inline bool GreaterThanZero(const float& x)
     {     return x > 0.f; }
     inline bool GreaterThanOrZero(const float& x)
     {     return x >= 0.f; }
     inline bool LessThanZero(const float& x)
     {     return x < 0.f; }
     inline bool LessThanOrZero(const float& x)
     {     return x <= 0.f; }
     inline bool abs_geq(const float& x, const float& y)
     {     return std::fabs(x) >= std::fabs(y); }
}

Unary Standard Math
The following macro invocations import the float versions of the unary standard math functions into the CppAD namespace. Importing avoids ambiguity errors when using both the CppAD and std namespaces. Note this also defines the double versions of these functions. 
namespace CppAD {
     using std::acos;
     using std::asin;
     using std::atan;
     using std::cos;
     using std::cosh;
     using std::exp;
     using std::fabs;
     using std::log;
     using std::log10;
     using std::sin;
     using std::sinh;
     using std::sqrt;
     using std::tan;
     using std::tanh;
# if CPPAD_USE_CPLUSPLUS_2011
     using std::erf;
     using std::asinh;
     using std::acosh;
     using std::atanh;
     using std::expm1;
     using std::log1p;
# endif
}
The absolute value function is special because its std name is fabs 
namespace CppAD {
     inline float abs(const float& x)
     {     return std::fabs(x); }
}

sign
The following defines the CppAD::sign function that is required to use AD<float>: 
namespace CppAD {
     inline float sign(const float& x)
     {     if( x > 0.f )
               return 1.f;
          if( x == 0.f )
               return 0.f;
          return -1.f;
     }
}

pow
The following defines a CppAD::pow function that is required to use AD<float>. As with the unary standard math functions, this has the exact same signature as std::pow, so use it instead of defining another function. 

namespace CppAD {
     using std::pow;
}

numeric_limits
The following defines the CppAD numeric_limits for the type float: 

namespace CppAD {
     CPPAD_NUMERIC_LIMITS(float, float)
}

to_string
There is no need to define to_string for float because it is defined by including cppad/utility/to_string.hpp; see to_string . See base_complex.hpp for an example where it is necessary to define to_string for a Base type.
Input File: cppad/core/base_float.hpp cppad-20170000.3/doc/base_double.hpp.xml0000644000175200017650000006664313057470506016771 0ustar coincoin-web Enable use of AD<Base> where Base is double
Prev Next base_double.hpp

Enable use of AD<Base> where Base is double

CondExpOp
The type double is a relatively simple type that supports <, <=, ==, >=, and > operators; see ordered type . Hence its CondExpOp function is defined by 
namespace CppAD {
     inline double CondExpOp(
          enum CompareOp     cop          ,
          const double&       left         ,
          const double&       right        ,
          const double&       exp_if_true  ,
          const double&       exp_if_false )
     {     return CondExpTemplate(cop, left, right, exp_if_true, exp_if_false);
     }
}

CondExpRel
The CPPAD_COND_EXP_REL macro invocation 

namespace CppAD {
     CPPAD_COND_EXP_REL(double)
}
uses CondExpOp above to define CondExpRel for double arguments and Rel equal to Lt, Le, Eq, Ge, and Gt.

EqualOpSeq
The type double is simple (in this respect) and so we define 
namespace CppAD {
     inline bool EqualOpSeq(const double& x, const double& y)
     {     return x == y; }
}

Identical
The type double is simple (in this respect) and so we define 
namespace CppAD {
     inline bool IdenticalPar(const double& x)
     {     return true; }
     inline bool IdenticalZero(const double& x)
     {     return (x == 0.); }
     inline bool IdenticalOne(const double& x)
     {     return (x == 1.); }
     inline bool IdenticalEqualPar(const double& x, const double& y)
     {     return (x == y); }
}

Integer 
namespace CppAD {
     inline int Integer(const double& x)
     {     return static_cast<int>(x); }
}

azmul 

namespace CppAD {
     CPPAD_AZMUL( double )
}

Ordered
The double type supports ordered comparisons 
namespace CppAD {
     inline bool GreaterThanZero(const double& x)
     {     return x > 0.; }
     inline bool GreaterThanOrZero(const double& x)
     {     return x >= 0.; }
     inline bool LessThanZero(const double& x)
     {     return x < 0.; }
     inline bool LessThanOrZero(const double& x)
     {     return x <= 0.; }
     inline bool abs_geq(const double& x, const double& y)
     {     return std::fabs(x) >= std::fabs(y); }
}

Unary Standard Math
The following macro invocations import the double versions of the unary standard math functions into the CppAD namespace. Importing avoids ambiguity errors when using both the CppAD and std namespaces. Note this also defines the float versions of these functions. 
namespace CppAD {
     using std::acos;
     using std::asin;
     using std::atan;
     using std::cos;
     using std::cosh;
     using std::exp;
     using std::fabs;
     using std::log;
     using std::log10;
     using std::sin;
     using std::sinh;
     using std::sqrt;
     using std::tan;
     using std::tanh;
# if CPPAD_USE_CPLUSPLUS_2011
     using std::erf;
     using std::asinh;
     using std::acosh;
     using std::atanh;
     using std::expm1;
     using std::log1p;
# endif
}
The absolute value function is special because its std name is fabs 
namespace CppAD {
     inline double abs(const double& x)
     {     return std::fabs(x); }
}

sign
The following defines the CppAD::sign function that is required to use AD<double>: 
namespace CppAD {
     inline double sign(const double& x)
     {     if( x > 0. )
               return 1.;
          if( x == 0. )
               return 0.;
          return -1.;
     }
}

pow
The following defines a CppAD::pow function that is required to use AD<double>. As with the unary standard math functions, this has the exact same signature as std::pow, so use it instead of defining another function. 

namespace CppAD {
     using std::pow;
}

numeric_limits
The following defines the CppAD numeric_limits for the type double: 

namespace CppAD {
     CPPAD_NUMERIC_LIMITS(double, double)
}

to_string
There is no need to define to_string for double because it is defined by including cppad/utility/to_string.hpp; see to_string . See base_complex.hpp for an example where it is necessary to define to_string for a Base type.
Input File: cppad/core/base_double.hpp cppad-20170000.3/doc/base_complex.hpp.xml0000644000175200017650000010704413057470506017155 0ustar coincoin-web Enable use of AD<Base> where Base is std::complex<double>
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Enable use of AD<Base> where Base is std::complex<double>

Example
The file complex_poly.cpp contains an example use of std::complex<double> type for a CppAD Base type. It returns true if it succeeds and false otherwise.

Include Order
This file is included before <cppad/cppad.hpp> so it is necessary to define the error handler in addition to including base_require.hpp 
# include <limits>
# include <complex>
# include <cppad/base_require.hpp>
# include <cppad/core/cppad_assert.hpp>
CondExpOp
The type std::complex<double> does not supports the <, <=, ==, >=, and > operators; see not ordered . Hence its CondExpOp function is defined by 
namespace CppAD {
     inline std::complex<double> CondExpOp(
          enum CppAD::CompareOp      cop        ,
          const std::complex<double> &left      ,
          const std::complex<double> &right     ,
          const std::complex<double> &trueCase  ,
          const std::complex<double> &falseCase )
     {     CppAD::ErrorHandler::Call(
               true     , __LINE__ , __FILE__ ,
               "std::complex<float> CondExpOp(...)",
               "Error: cannot use CondExp with a complex type"
          );
          return std::complex<double>(0);
     }
}

CondExpRel
The CPPAD_COND_EXP_REL macro invocation 

namespace CppAD {
     CPPAD_COND_EXP_REL( std::complex<double> )
}
used CondExpOp above to define CondExpRel for std::complex<double> arguments and Rel equal to Lt, Le, Eq, Ge, and Gt.

EqualOpSeq
Complex numbers do not carry operation sequence information. Thus they are equal in this sense if and only if there values are equal. 
namespace CppAD {
     inline bool EqualOpSeq(
          const std::complex<double> &x ,
          const std::complex<double> &y )
     {     return x == y;
     }
}

Identical
Complex numbers do not carry operation sequence information. Thus they are all parameters so the identical functions just check values. 
namespace CppAD {
     inline bool IdenticalPar(const std::complex<double> &x)
     {     return true; }
     inline bool IdenticalZero(const std::complex<double> &x)
     {     return (x == std::complex<double>(0., 0.) ); }
     inline bool IdenticalOne(const std::complex<double> &x)
     {     return (x == std::complex<double>(1., 0.) ); }
     inline bool IdenticalEqualPar(
          const std::complex<double> &x, const std::complex<double> &y)
     {     return (x == y); }
}

Ordered
Complex types do not support comparison operators, 
# undef  CPPAD_USER_MACRO
# define CPPAD_USER_MACRO(Fun)                                     \
inline bool Fun(const std::complex<double>& x)                     \
{      CppAD::ErrorHandler::Call(                                  \
               true     , __LINE__ , __FILE__ ,                    \
               #Fun"(x)",                                          \
               "Error: cannot use " #Fun " with x complex<double> " \
       );                                                          \
       return false;                                               \
}
namespace CppAD {
     CPPAD_USER_MACRO(LessThanZero)
     CPPAD_USER_MACRO(LessThanOrZero)
     CPPAD_USER_MACRO(GreaterThanOrZero)
     CPPAD_USER_MACRO(GreaterThanZero)
     inline bool abs_geq(
          const std::complex<double>& x ,
          const std::complex<double>& y )
     {     return std::abs(x) >= std::abs(y); }
}

Integer
The implementation of this function must agree with the CppAD user specifications for complex arguments to the Integer function: 
namespace CppAD {
     inline int Integer(const std::complex<double> &x)
     {     return static_cast<int>( x.real() ); }
}

azmul 

namespace CppAD {
     CPPAD_AZMUL( std::complex<double> )
}

isnan
The gcc 4.1.1 complier defines the function
     int std::complex<double>::isnan( std::complex<double> z )
 (which is not specified in the C++ 1998 standard ISO/IEC 14882). This causes an ambiguity between the function above and the CppAD isnan template function. We avoid this ambiguity by defining a non-template version of this function in the CppAD namespace. 
namespace CppAD {
     inline bool isnan(const std::complex<double>& z)
     {     return (z != z);
     }
}

Valid Unary Math
The following macro invocations define the standard unary math functions that are valid with complex arguments and are required to use AD< std::complex<double> >. 
namespace CppAD {
     CPPAD_STANDARD_MATH_UNARY(std::complex<double>, cos)
     CPPAD_STANDARD_MATH_UNARY(std::complex<double>, cosh)
     CPPAD_STANDARD_MATH_UNARY(std::complex<double>, exp)
     CPPAD_STANDARD_MATH_UNARY(std::complex<double>, log)
     CPPAD_STANDARD_MATH_UNARY(std::complex<double>, sin)
     CPPAD_STANDARD_MATH_UNARY(std::complex<double>, sinh)
     CPPAD_STANDARD_MATH_UNARY(std::complex<double>, sqrt)
}

Invalid Unary Math
The following macro definition and invocations define the standard unary math functions that are invalid with complex arguments and are required to use AD< std::complex<double> >. 
# undef  CPPAD_USER_MACRO
# define CPPAD_USER_MACRO(Fun)                                     \
inline std::complex<double> Fun(const std::complex<double>& x)     \
{      CppAD::ErrorHandler::Call(                                  \
               true     , __LINE__ , __FILE__ ,                    \
               #Fun"(x)",                                          \
               "Error: cannot use " #Fun " with x complex<double> " \
       );                                                          \
       return std::complex<double>(0);                             \
}
namespace CppAD {
     CPPAD_USER_MACRO(abs)
     CPPAD_USER_MACRO(acos)
     CPPAD_USER_MACRO(asin)
     CPPAD_USER_MACRO(atan)
     CPPAD_USER_MACRO(sign)
# if CPPAD_USE_CPLUSPLUS_2011
     CPPAD_USER_MACRO(erf)
     CPPAD_USER_MACRO(asinh)
     CPPAD_USER_MACRO(acosh)
     CPPAD_USER_MACRO(atanh)
     CPPAD_USER_MACRO(expm1)
     CPPAD_USER_MACRO(log1p)
# endif
}

pow
The following defines a CppAD::pow function that is required to use AD< std::complex<double> >: 
namespace CppAD {
     inline std::complex<double> pow(
          const std::complex<double> &x ,
          const std::complex<double> &y )
     {     return std::pow(x, y); }
}

numeric_limits
The following defines the CppAD numeric_limits for the type std::complex<double>: 

namespace CppAD {
     CPPAD_NUMERIC_LIMITS(double, std::complex<double>)
}

to_string
The following defines the function CppAD to_string for the type std::complex<double>: 

namespace CppAD {
     CPPAD_TO_STRING(std::complex<double>)
}
Input File: cppad/core/base_complex.hpp cppad-20170000.3/doc/complex_poly.cpp.xml0000644000175200017650000003127013057470506017216 0ustar coincoin-web Complex Polynomial: Example and Test
Prev Next complex_poly.cpp

Complex Polynomial: Example and Test

Poly
Select this link to view specifications for Poly : 

# include <cppad/cppad.hpp>
# include <complex>

bool complex_poly(void)
{     bool ok    = true;
     size_t deg = 4;

     using CppAD::AD;
     using CppAD::Poly;
     typedef std::complex<double> Complex;

     // polynomial coefficients
     CPPAD_TESTVECTOR( Complex )     a   (deg + 1); // coefficients for p(z)
     CPPAD_TESTVECTOR(AD<Complex>) A   (deg + 1);
     size_t i;
     for(i = 0; i <= deg; i++)
          A[i] = a[i] = Complex(i, i);

     // independent variable vector
     CPPAD_TESTVECTOR(AD<Complex>) Z(1);
     Complex z = Complex(1., 2.);
     Z[0]      = z;
     Independent(Z);

     // dependent variable vector and indices
     CPPAD_TESTVECTOR(AD<Complex>) P(1);

     // dependent variable values
     P[0] = Poly(0, A, Z[0]);

     // create f: Z -> P and vectors used for derivative calculations
     CppAD::ADFun<Complex> f(Z, P);
     CPPAD_TESTVECTOR(Complex) v( f.Domain() );
     CPPAD_TESTVECTOR(Complex) w( f.Range() );

     // check first derivative w.r.t z
     v[0]      = 1.;
     w         = f.Forward(1, v);
     Complex p = Poly(1, a, z);
     ok &= ( w[0]  == p );

     // second derivative w.r.t z is 2 times its second order Taylor coeff
     v[0] = 0.;
     w    = f.Forward(2, v);
     p    = Poly(2, a, z);
     ok &= ( 2. * w[0]  == p );

     return ok;
}
Input File: example/complex_poly.cpp cppad-20170000.3/doc/adfun.xml0000644000175200017650000001054713057470506015024 0ustar coincoin-web ADFun Objects
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ADFun Objects

Purpose
An AD of Base operation sequence is stored in an ADFun object by its FunConstruct . The ADFun object can then be used to calculate function values, derivative values, and other values related to the corresponding function.

Contents
IndependentDeclare Independent Variables and Start Recording
FunConstructConstruct an ADFun Object and Stop Recording
DependentStop Recording and Store Operation Sequence
abort_recordingAbort Recording of an Operation Sequence
seq_propertyADFun Sequence Properties
FunEvalEvaluate ADFun Functions, Derivatives, and Sparsity Patterns
DriversFirst and Second Derivatives: Easy Drivers
FunCheckCheck an ADFun Sequence of Operations
optimizeOptimize an ADFun Object Tape
check_for_nanCheck an ADFun Object For Nan Results
Input File: cppad/core/ad_fun.hpp cppad-20170000.3/doc/_adfun_xml.js0000644000175200017650000000260213057470506015650 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml' ]; var list_down1 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down0 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_current0 = [ 'adfun.xml#Purpose', 'adfun.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/independent.cpp.xml0000644000175200017650000004641613057470506017011 0ustar coincoin-web Independent and ADFun Constructor: Example and Test
Prev Next independent.cpp Headings

Independent and ADFun Constructor: Example and Test
# include <cppad/cppad.hpp>

namespace { // --------------------------------------------------------
// define the template function Test<VectorAD>(void) in empty namespace
template <class VectorAD>
bool Test(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;

     // domain space vector
     size_t  n  = 2;
     VectorAD X(n);  // VectorAD is the template parameter in call to Test
     X[0] = 0.;
     X[1] = 1.;

     // declare independent variables and start recording
     // use the template parameter VectorAD for the vector type
     CppAD::Independent(X);

     AD<double> a = X[0] + X[1];      // first AD operation
     AD<double> b = X[0] * X[1];      // second AD operation

     // range space vector
     size_t m = 2;
     VectorAD Y(m);  // VectorAD is the template paraemter in call to Test
     Y[0] = a;
     Y[1] = b;

     // create f: X -> Y and stop tape recording
     // use the template parameter VectorAD for the vector type
     CppAD::ADFun<double> f(X, Y);

     // check value
     ok &= NearEqual(Y[0] , 1.,  1e-10 , 1e-10);
     ok &= NearEqual(Y[1] , 0.,  1e-10 , 1e-10);

     // compute f(1, 2)
     CPPAD_TESTVECTOR(double) x(n);
     CPPAD_TESTVECTOR(double) y(m);
     x[0] = 1.;
     x[1] = 2.;
     y    = f.Forward(0, x);
     ok &= NearEqual(y[0] , 3.,  1e-10 , 1e-10);
     ok &= NearEqual(y[1] , 2.,  1e-10 , 1e-10);

     // compute partial of f w.r.t x[0] at (1, 2)
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dx[1] = 0.;
     dy    = f.Forward(1, dx);
     ok &= NearEqual(dy[0] ,   1.,  1e-10 , 1e-10);
     ok &= NearEqual(dy[1] , x[1],  1e-10 , 1e-10);

     // compute partial of f w.r.t x[1] at (1, 2)
     dx[0] = 0.;
     dx[1] = 1.;
     dy    = f.Forward(1, dx);
     ok &= NearEqual(dy[0] ,   1.,  1e-10 , 1e-10);
     ok &= NearEqual(dy[1] , x[0],  1e-10 , 1e-10);

     return ok;
}
} // End of empty namespace -------------------------------------------

# include <vector>
# include <valarray>
bool Independent(void)
{     bool ok = true;
     typedef CppAD::AD<double> ADdouble;
     // Run with VectorAD equal to three different cases
     // all of which are Simple Vectors with elements of type AD<double>.
     ok &= Test< CppAD::vector  <ADdouble> >();
     ok &= Test< std::vector    <ADdouble> >();
     ok &= Test< std::valarray  <ADdouble> >();
     return ok;
}
Input File: example/independent.cpp cppad-20170000.3/doc/funconstruct.xml0000644000175200017650000006015413057470506016463 0ustar coincoin-web Construct an ADFun Object and Stop Recording
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Construct an ADFun Object and Stop Recording

Syntax
ADFun<Base> f, g
 ADFun<Base> f(x, y)
 g = f
Purpose
The AD<Base> object f can store an AD of Base operation sequence . It can then be used to calculate derivatives of the corresponding AD function F : B n → B m where B is the space corresponding to objects of type Base .

x
If the argument x is present, it has prototype
     const VectorAD &x
 It must be the vector argument in the previous call to Independent . Neither its size, or any of its values, are allowed to change between calling
     Independent(x)
 and
     ADFun<Base> f(x, y)
y
If the argument y is present, it has prototype
     const VectorAD &y
 The sequence of operations that map x to y are stored in the ADFun object f .

VectorAD
The type VectorAD must be a SimpleVector class with elements of type AD<Base> . The routine CheckSimpleVector will generate an error message if this is not the case.

Default Constructor
The default constructor
     ADFun<Base> f
 creates an AD<Base> object with no corresponding operation sequence; i.e.,
     f.size_var()
 returns the value zero (see size_var ).

Sequence Constructor
The sequence constructor
     ADFun<Base> f(x, y)
 creates the AD<Base> object f , stops the recording of AD of Base operations corresponding to the call
     Independent(x)
 and stores the corresponding operation sequence in the object f . It then stores the zero order Taylor coefficients (corresponding to the value of x ) in f . This is equivalent to the following steps using the default constructor:
  1. Create f with the default constructor
         ADFun<    Base> f;
  2. Stop the tape and storing the operation sequence using
             f.Dependent(x, y);
     (see Dependent ).
  3. Calculate the zero order Taylor coefficients for all the variables in the operation sequence using
             f.Forward(p, x_p)
     with p equal to zero and the elements of x_p equal to the corresponding elements of x (see Forward ).


Copy Constructor
It is an error to attempt to use the ADFun<Base> copy constructor; i.e., the following syntax is not allowed:
     ADFun<Base> g(f)
 where f is an ADFun<Base> object. Use its default constructor instead and its assignment operator.

Assignment Operator
The ADFun<Base> assignment operation
     g = f
 makes a copy of the operation sequence currently stored in f in the object g . The object f is not affected by this operation and can be const. All of information (state) stored in f is copied to g and any information originally in g is lost.

Taylor Coefficients
The Taylor coefficient information currently stored in f (computed by f.Forward ) is copied to g . Hence, directly after this operation
     g.size_order() == f.size_order()
Sparsity Patterns
The forward Jacobian sparsity pattern currently stored in f (computed by f.ForSparseJac ) is copied to g . Hence, directly after this operation
     g.size_forward_bool() == f.size_forward_bool()
     g.size_forward_set()  == f.size_forward_set()
Parallel Mode
The call to Independent, and the corresponding call to
     ADFun<Base> f( x, y)
 or
     f.Dependent( x, y)
 or abort_recording , must be preformed by the same thread; i.e., thread_alloc::thread_num must be the same.

Example

Sequence Constructor
The file independent.cpp contains an example and test of the sequence constructor. It returns true if it succeeds and false otherwise.

Default Constructor
The files fun_check.cpp and hes_lagrangian.cpp contain an examples and tests using the default constructor. They return true if they succeed and false otherwise.

Assignment Operator
The file fun_assign.cpp contains an example and test of the ADFun<Base> assignment operator. It returns true if it succeeds and false otherwise.
Input File: cppad/core/fun_construct.hpp cppad-20170000.3/doc/fun_assign.cpp.xml0000644000175200017650000005715713057470506016654 0ustar coincoin-web ADFun Assignment: Example and Test
Prev Next fun_assign.cpp Headings

ADFun Assignment: Example and Test
# include <cppad/cppad.hpp>
# include <limits>

bool fun_assign(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     size_t i, j;

     // ten times machine percision
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // two ADFun<double> objects
     CppAD::ADFun<double> g;

     // domain space vector
     size_t n  = 3;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     for(j = 0; j < n; j++)
          x[j] = AD<double>(j + 2);

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = x[0] + x[0] * x[1];
     y[1] = x[1] * x[2] + x[2];

     // Store operation sequence, and order zero forward results, in f.
     CppAD::ADFun<double> f(x, y);

     // sparsity pattern for the identity matrix
     CPPAD_TESTVECTOR(std::set<size_t>) r(n);
     for(j = 0; j < n; j++)
          r[j].insert(j);

     // Store forward mode sparsity pattern in f
     f.ForSparseJac(n, r);

     // make a copy in g
     g = f;

     // check values that should be equal
     ok &= ( g.size_order()       == f.size_order() );
     ok &= ( g.size_forward_bool() == f.size_forward_bool() );
     ok &= ( g.size_forward_set()  == f.size_forward_set() );

     // Use zero order Taylor coefficient from f for first order
     // calculation using g.
     CPPAD_TESTVECTOR(double) dx(n), dy(m);
     for(i = 0; i < n; i++)
          dx[i] = 0.;
     dx[1] = 1;
     dy    = g.Forward(1, dx);
     ok &= NearEqual(dy[0], x[0], eps, eps); // partial y[0] w.r.t x[1]
     ok &= NearEqual(dy[1], x[2], eps, eps); // partial y[1] w.r.t x[1]

     // Use forward Jacobian sparsity pattern from f to calculate
     // Hessian sparsity pattern using g.
     CPPAD_TESTVECTOR(std::set<size_t>) s(1), h(n);
     s[0].insert(0); // Compute sparsity pattern for Hessian of y[0]
     h =  f.RevSparseHes(n, s);

     // check sparsity pattern for Hessian of y[0] = x[0] + x[0] * x[1]
     ok  &= ( h[0].find(0) == h[0].end() ); // zero     w.r.t x[0], x[0]
     ok  &= ( h[0].find(1) != h[0].end() ); // non-zero w.r.t x[0], x[1]
     ok  &= ( h[0].find(2) == h[0].end() ); // zero     w.r.t x[0], x[2]

     ok  &= ( h[1].find(0) != h[1].end() ); // non-zero w.r.t x[1], x[0]
     ok  &= ( h[1].find(1) == h[1].end() ); // zero     w.r.t x[1], x[1]
     ok  &= ( h[1].find(2) == h[1].end() ); // zero     w.r.t x[1], x[2]

     ok  &= ( h[2].find(0) == h[2].end() ); // zero     w.r.t x[2], x[0]
     ok  &= ( h[2].find(1) == h[2].end() ); // zero     w.r.t x[2], x[1]
     ok  &= ( h[2].find(2) == h[2].end() ); // zero     w.r.t x[2], x[2]

     return ok;
}
Input File: example/fun_assign.cpp cppad-20170000.3/doc/dependent.xml0000644000175200017650000003134613057470506015675 0ustar coincoin-web Stop Recording and Store Operation Sequence
Prev Next Dependent

Stop Recording and Store Operation Sequence

Syntax
f.Dependent(x, y)

Purpose
Stop recording and the AD of Base operation sequence that started with the call
     Independent(x)
 and store the operation sequence in f . The operation sequence defines an AD function F : B n → B m where B is the space corresponding to objects of type Base . The value n is the dimension of the domain space for the operation sequence. The value m is the dimension of the range space for the operation sequence (which is determined by the size of y ).

f
The object f has prototype
     ADFun<Base> f
 The AD of Base operation sequence is stored in f ; i.e., it becomes the operation sequence corresponding to f . If a previous operation sequence was stored in f , it is deleted.

x
The argument x must be the vector argument in a previous call to Independent . Neither its size, or any of its values, are allowed to change between calling
     Independent(x)
 and
     f.Dependent(x, y)
 .

y
The vector y has prototype
     const ADvector &y
 (see ADvector below). The length of y must be greater than zero and is the dimension of the range space for f .

ADvector
The type ADvector must be a SimpleVector class with elements of type AD<Base> . The routine CheckSimpleVector will generate an error message if this is not the case.

Taping
The tape, that was created when Independent(x) was called, will stop recording. The AD operation sequence will be transferred from the tape to the object f and the tape will then be deleted.

Forward
No Forward calculation is preformed during this operation. Thus, directly after this operation,
     f.size_order()
 is zero (see size_order ).

Parallel Mode
The call to Independent, and the corresponding call to
     ADFun<Base> f( x, y)
 or
     f.Dependent( x, y)
 or abort_recording , must be preformed by the same thread; i.e., thread_alloc::thread_num must be the same.

Example
The file fun_check.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/dependent.hpp cppad-20170000.3/doc/_dependent_xml.js0000644000175200017650000000336113057470506016524 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'dependent.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_current0 = [ 'dependent.xml#Syntax', 'dependent.xml#Purpose', 'dependent.xml#f', 'dependent.xml#x', 'dependent.xml#y', 'dependent.xml#ADvector', 'dependent.xml#Taping', 'dependent.xml#Forward', 'dependent.xml#Parallel Mode', 'dependent.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/abort_recording.cpp.xml0000644000175200017650000002742213057470506017653 0ustar coincoin-web Abort Current Recording: Example and Test
Prev Next abort_recording.cpp Headings

Abort Current Recording: Example and Test

# include <cppad/cppad.hpp>
# include <limits>

bool abort_recording(void)
{     bool ok = true;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     using CppAD::AD;

     try
     {     // domain space vector
          size_t n = 1;
          CPPAD_TESTVECTOR(AD<double>) x(n);
          x[0]     = 0.;

          // declare independent variables and start tape recording
          CppAD::Independent(x);

          // simulate an error during calculation of y and the execution
          // stream was aborted
          throw 1;
     }
     catch (int e)
     {     ok &= (e == 1);

          // do this incase throw occured after the call to Independent
          // (for case above this is known, but in general it is unknown)
          AD<double>::abort_recording();
     }
     /*
     Now make sure that we can start another recording
     */

     // declare independent variables and start tape recording
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;
     CppAD::Independent(x);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = 2 * x[0];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= CppAD::NearEqual(dy[0], 2., eps, eps);

     return ok;
}
Input File: example/abort_recording.cpp cppad-20170000.3/doc/seq_property.xml0000644000175200017650000005675113057470506016472 0ustar coincoin-web ADFun Sequence Properties
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ADFun Sequence Properties

Syntax
n = f.Domain()
 m = f.Range()
 p = f.Parameter(i)
 s = f.size_var()
 s = f.size_par()
 s = f.size_op()
 s = f.size_op_arg()
 s = f.size_text()
 s = f.size_VecAD()
 s = f.size_op_seq()
See Also
size_order , capacity_order , number_skip .

Purpose
The operations above return properties of the AD of Base operation sequence stored in the ADFun object f . (If there is no operation sequence stored in f , size_var returns zero.)

f
The object f has prototype
     const ADFun<Base> f
 (see ADFun<Base> constructor ).

Domain
The result n has prototype
     size_t n
 and is the dimension of the domain space corresponding to f . This is equal to the size of the vector x in the call
     Independent(x)
 that starting recording the operation sequence currently stored in f (see FunConstruct and Dependent ).

Range
The result m has prototype
     size_t m
 and is the dimension of the range space corresponding to f . This is equal to the size of the vector y in syntax
     ADFun<Base> f(x, y)
 or
     f.Dependent(y)
 depending on which stored the operation sequence currently in f (see FunConstruct and Dependent ).

Parameter
The argument i has prototype
     size_t i
 and 0 ≤ i < m . The result p has prototype
     bool p
 It is true if the i-th component of range space for F corresponds to a parameter in the operation sequence. In this case, the i-th component of F is constant and ∂ F i ∂ x j ( x ) = 0 for j = 0 , … , n -1 and all x ∈ B n .

size_var
The result s has prototype
     size_t s
 and is the number of variables in the operation sequence plus the following: one for a phantom variable with tape address zero, one for each component of the range that is a parameter. The amount of work and memory necessary for computing function values and derivatives using f is roughly proportional to s . (The function call f.size_order() returns the number of Taylor coefficient orders, per variable,direction, currently stored in f .)

If there is no operation sequence stored in f , size_var returns zero (see default constructor ).

size_par
The result s has prototype
     size_t s
 and is the number of parameters in the operation sequence. Parameters differ from variables in that only values (and not derivatives) need to be stored for each parameter. These parameters are considered part of the operation sequence, as opposed to the Taylor coefficients which are considered extra data in the function object f . Note that one Base value is required for each parameter.

size_op
The result s has prototype
     size_t s
 and is the number of operations in the operation sequence. Some operators, like comparison operators, do not correspond to a variable. Other operators, like the sine operator, correspond to two variables. Thus, this value will be different from size_var . Note that one enum value is required for each operator.

size_op_arg
The result s has prototype
     size_t s
 and is the total number of operator arguments in the operation sequence. For example, Binary operators (e.g. addition) have two arguments. Note that one integer index is stored in the operation sequence for each argument. Also note that, as of 2013-10-20, there is an extra phantom argument with index 0 that is not used.

size_text
The result s has prototype
     size_t s
 and is the total characters used in the PrintFor commands in this operation sequence.

size_VecAD
The result s has prototype
     size_t s
 and is the number of VecAD vectors, plus the number of elements in the vectors. Only VecAD vectors that depend on the independent variables are stored in the operation sequence.

size_op_seq
The result s has prototype
     size_t s
 and is the amount of memory required to store the operation sequence (not counting a small amount of memory required for every operation sequence). For the current version of CppAD, this is given by
     s = f.size_op()     * sizeof(CppAD::local::OpCode)
         + f.size_op_arg() * sizeof(tape_addr_type)
         + f.size_par()    * sizeof(Base)
         + f.size_text()   * sizeof(char)
         + f.size_VecAD()  * sizeof(tape_addr_type)
 see tape_addr_type . Note that this is the minimal amount of memory that can hold the information corresponding to an operation sequence. The actual amount of memory allocated (inuse ) for the operations sequence may be larger.

Example
The file seq_property.cpp contains an example and test of these operations. It returns true if it succeeds and false otherwise.
Input File: omh/seq_property.omh cppad-20170000.3/doc/seq_property.cpp.xml0000644000175200017650000005307613057470506017250 0ustar coincoin-web ADFun Sequence Properties: Example and Test
Prev Next seq_property.cpp Headings

ADFun Sequence Properties: Example and Test

# include <cppad/cppad.hpp>

bool seq_property(void)
{     bool ok = true;
     using CppAD::AD;

     // Use nvar to track the number of variables in the operation sequence.
     // Start with one for the phantom variable at tape address zero.
     size_t nvar = 1;

     // Use npar to track the number of parameters in the operation sequence.
     size_t npar = 0;

     // Start with one for operator corresponding to phantom variable
     size_t nop  = 1;

     // Start with one for operator corresponding to phantom argument
     size_t narg = 1;

     // Use ntext to track the number of characters used to label
     // output generated using PrintFor commands.
     size_t ntext = 0;

     // Use nvecad to track the number of VecAD vectors, plus the number
     // of VecAD vector elements, in the operation sequence.
     size_t nvecad = 0;

     // a VecAD vector
     CppAD::VecAD<double> v(2);
     v[0]     = 0; // requires the parameter 0, when becomes a variable
     v[1]     = 1; // requires the parameter 1, when becomes a variable

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]     = 0.;
     x[1]     = 1.;

     // declare independent variables and start tape recording
     CppAD::Independent(x);
     nvar    += n;
     nop     += n;

     // a computation that adds to the operation sequence
     AD<double> I = 0;
     v[I]         = x[0];
     nvecad      +=   3;  // one for vector, two for its elements
     npar        +=   2;  // need parameters 0 and 1 for initial v
     nop         +=   1;  // operator for storing in a VecAD object
     narg        +=   3;  // the three arguments are v, I, and x[0]

     // some operations that do not add to the operation sequence
     AD<double> u = x[0];  // use same variable as x[0]
     AD<double> w = x[1];  // use same variable as x[1]

     // a computation that adds to the operation sequence
     w      = w * (u + w);
     nop   += 2;   // requires two new operators, an add and a multiply
     nvar  += 2;   // each operator results in its own variable
     narg  += 4;   // each operator has two arguments

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>) y(m);

     // operations that do not add to the operation sequence
     y[0]   = 1.;  // re-use the parameter 1
     y[1]   = u;   // use same variable as u

     // a computation that adds to the operation sequence
     y[2]   = w + 2.;
     nop   += 1;   // requires a new add operator
     npar  += 1;   // new parameter 2 is new, so it must be included
     nvar  += 1;   // variable corresponding to the result
     narg  += 2;   // operator has two arguments

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);
     nop   += 1;   // special operator for y[0] because it is a parameter
     nvar  += 1;   // special variable for y[0] because it is a parameter
     narg  += 1;   // identifies which parameter corresponds to y[0]
     nop   += 1;   // special operator at the end of operation sequence

     // check the sequence property functions
     ok &= f.Domain()      == n;
     ok &= f.Range()       == m;
     ok &= f.Parameter(0)  == true;
     ok &= f.Parameter(1)  == false;
     ok &= f.Parameter(2)  == false;
     ok &= f.size_var()    == nvar;
     ok &= f.size_op()     == nop;
     ok &= f.size_op_arg() == narg;
     ok &= f.size_par()    == npar;
     ok &= f.size_text()   == ntext;
     ok &= f.size_VecAD()  == nvecad;
     size_t sum = 0;
     sum += nop    * sizeof(CppAD::local::OpCode);
     sum += narg   * sizeof(CPPAD_TAPE_ADDR_TYPE);
     sum += npar   * sizeof(double);
     sum += ntext  * sizeof(char);
     sum += nvecad * sizeof(CPPAD_TAPE_ADDR_TYPE);
     ok &= f.size_op_seq() == sum;

     return ok;
}
Input File: example/seq_property.cpp cppad-20170000.3/doc/funeval.xml0000644000175200017650000000562713057470506015372 0ustar coincoin-web Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
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Evaluate ADFun Functions, Derivatives, and Sparsity Patterns

Contents
ForwardForward Mode
ReverseReverse Mode
SparseCalculating Sparsity Patterns
Input File: cppad/core/fun_eval.hpp cppad-20170000.3/doc/_funeval_xml.js0000644000175200017650000000313313057470506016213 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_current0 = [ 'funeval.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/forward.xml0000644000175200017650000001017013057470506015363 0ustar coincoin-web Forward Mode
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Forward Mode

Contents
forward_zeroZero Order Forward Mode: Function Values
forward_oneFirst Order Forward Mode: Derivative Values
forward_twoSecond Order Forward Mode: Derivative Values
forward_orderMultiple Order Forward Mode
forward_dirMultiple Directions Forward Mode
size_orderNumber Taylor Coefficient Orders Currently Stored
compare_changeComparison Changes Between Taping and Zero Order Forward
capacity_orderControlling Taylor Coefficients Memory Allocation
number_skipNumber of Variables that Can be Skipped
Input File: omh/forward/forward.omh cppad-20170000.3/doc/forward_one.xml0000644000175200017650000004306513057470506016235 0ustar coincoin-web First Order Forward Mode: Derivative Values
Prev Next forward_one

First Order Forward Mode: Derivative Values

Syntax
y1 = f.Forward(1, x1)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The result of the syntax above is y 1 = F ( 1 ) ( x 0 ) * x 1 where F ( 1 ) ( x 0 ) is the Jacobian of F evaluated at x0 .

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const. Before this call to Forward, the value returned by
     f.size_order()
 must be greater than or equal one. After this call it will be will be two (see size_order ).

x0
The vector x0 in the formula y 1 = F ( 1 ) ( x 0 ) * x 1 corresponds to the previous call to forward_zero using this ADFun object f ; i.e.,
     f.Forward(0, x0)
 If there is no previous call with the first argument zero, the value of the independent variables during the recording of the AD sequence of operations is used for x0 .

x1
The argument x1 has prototype
     const Vector& x1
 (see Vector below) and its size must be equal to n , the dimension of the domain space for f .

Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file forward.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.

Special Case
This is special case of forward_order where Y ( t ) = F [ X ( t ) ] X ( t ) = x ( 0 ) t 0 + x ( 1 ) * t 1 + ⋯ , + x ( q ) * t q + o ( t q ) Y ( t ) = y ( 0 ) t 0 + y ( 1 ) * t 1 + ⋯ , + y ( q ) * t q + o ( t q ) and o ( t q ) * t - q → 0 as t → 0 . For this special case, q = 1 , x ( 0 ) = x0 , x ( 1 ) = x1 , X ( t ) = x ( 0 ) + x ( 1 ) t , and y ( 0 ) + y ( 1 ) t = F [ x ( 0 ) + x ( 1 ) t ] + o ( t ) Taking the derivative with respect to t , at t = 0 , we obtain y ( 1 ) = F ( 1 ) [ x ( 0 ) ] x ( 1 ) which agrees with the specifications for y1 in the purpose above.
Input File: omh/forward/forward_one.omh cppad-20170000.3/doc/forward_two.xml0000644000175200017650000006304213057470506016262 0ustar coincoin-web Second Order Forward Mode: Derivative Values
Prev Next forward_two

Second Order Forward Mode: Derivative Values

Syntax
y2 = f.Forward(1, x2)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The result of the syntax above is that for i = 0 , ... , m-1 ,
     y2[i] = F i ( 1 ) ( x 0 ) * x 2 + 1 2 x 1 T * F i ( 2 ) ( x 0 ) * x 1
where F ( 1 ) ( x 0 ) is the Jacobian of F , and F i ( 2 ) ( x 0 ) is the Hessian of th i-th component of F , evaluated at x0 .

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const. Before this call to Forward, the value returned by
     f.size_order()
 must be greater than or equal two. After this call it will be will be three (see size_order ).

x0
The vector x0 in the formula for y2[i] corresponds to the previous call to forward_zero using this ADFun object f ; i.e.,
     f.Forward(0, x0)
 If there is no previous call with the first argument zero, the value of the independent variables during the recording of the AD sequence of operations is used for x0 .

x1
The vector x1 in the formula for y2[i] corresponds to the previous call to forward_one using this ADFun object f ; i.e.,
     f.Forward(1, x1)
x2
The argument x2 has prototype
     const Vector& x2
 (see Vector below) and its size must be equal to n , the dimension of the domain space for f .

y2
The result y2 has prototype
     Vector y2
 (see Vector below) The size of y1 is equal to m , the dimension of the range space for f . Its value is given element-wise by the formula in the purpose above.

Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file forward.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.

Special Case
This is special case of forward_order where Y ( t ) = F [ X ( t ) ] X ( t ) = x ( 0 ) t 0 + x ( 1 ) * t 1 + ⋯ , + x ( q ) * t q + o ( t q ) Y ( t ) = y ( 0 ) t 0 + y ( 1 ) * t 1 + ⋯ , + y ( q ) * t q + o ( t q ) and o ( t q ) * t - q → 0 as t → 0 . For this special case, q = 2 , x ( 0 ) = x0 , x ( 1 ) = x1 , X ( t ) = x ( 0 ) + x ( 1 ) t + x ( 2 ) t 2 , and y ( 0 ) + y ( 1 ) t + y ( 2 ) t 2 = F [ x ( 0 ) + x ( 1 ) t + x ( 2 ) t 2 ] + o ( t 2 ) Restricting our attention to the i-th component, and taking the derivative with respect to t , we obtain y i ( 1 ) + 2 y i ( 2 ) t = F i ( 1 ) [ x ( 0 ) + x ( 1 ) t + x ( 2 ) t 2 ] [ x ( 1 ) + 2 x ( 2 ) t ] + o ( t ) Taking a second derivative with respect to t , and evaluating at t = 0 , we obtain 2 y i ( 2 ) = [ x ( 1 ) ] T F i ( 2 ) [ x ( 0 ) ] x ( 1 ) + F i ( 1 ) [ x ( 0 ) ] 2 x ( 2 ) which agrees with the specification for y2[i] in the purpose above.
Input File: omh/forward/forward_two.omh cppad-20170000.3/doc/forward_order.xml0000644000175200017650000010643113057470506016564 0ustar coincoin-web Multiple Order Forward Mode
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Multiple Order Forward Mode

Syntax
yq = f.Forward(q, xq )
 yq = f.Forward(q, xq, s)
Purpose
We use F : B n → B m to denote the AD function corresponding to f . Given a function X : B → B n , defined by its Taylor coefficients , forward mode computes the Taylor coefficients for the function Y ( t ) = F [ X ( t ) ]
Function Values
If you are using forward mode to compute values for F ( x ) , forward_zero is simpler to understand than this explanation of the general case.

Derivative Values
If you are using forward mode to compute values for F ( 1 ) ( x ) * dx , forward_one is simpler to understand than this explanation of the general case.

Notation

n
We use n to denote the dimension of the domain space for f .

m
We use m to denote the dimension of the range space for f .

f
The ADFun object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const. After this call we will have
     f.size_order()     == q + 1
     f.size_direction() == 1
One Order
If xq.size() == n , then we are only computing one order. In this case, before this call we must have
     f.size_order()     >= q
     f.size_direction() == 1
q
The argument q has prototype
     size_t q
 and specifies the highest order of the Taylor coefficients to be calculated.

xq
The argument xq has prototype
     const Vector& xq
 (see Vector below). As above, we use n to denote the dimension of the domain space for f . The size of xq must be either n or n*(q+1) . After this call we will have
     f.size_order()     == q + 1
One Order
If xq.size() == n , the q-th order Taylor coefficient for X ( t ) is defined by
      x ( q ) = xq . For k = 0 , … , q -1 , the Taylor coefficient x ( k ) is defined by xk in the previous call to
     f.Forward(k, xk)
Multiple Orders
If xq.size() == n*(q+1) , For k = 0 , … , q , j = 0 , … , n -1 , the j-th component of the k-th order Taylor coefficient for X ( t ) is defined by
      x j ( k ) = xq[ (q+1) * j + k ]

Restrictions
Note if f uses old_atomic functions, the size of xq must be n .

s
If the argument s is not present, std::cout is used in its place. Otherwise, this argument has prototype
     std::ostream& s
 If order zero is begin calculated, s specifies where the output corresponding to PrintFor will be written. If order zero is not being calculated, s is not used

X(t)
The function X : B → B n is defined using the Taylor coefficients x ( k ) ∈ B n : X ( t ) = x ( 0 ) * t 0 + x ( 1 ) * t 1 + ⋯ + x ( q ) * t q Note that for k = 0 , … , q , the k-th derivative of X ( t ) is related to the Taylor coefficients by the equation x ( k ) = 1 k ! X ( k ) ( 0 )
Y(t)
The function Y : B → B m is defined by Y ( t ) = F [ X ( t ) ] . We use y ( k ) ∈ B m to denote the k-th order Taylor coefficient of Y ( t ) ; i.e., Y ( t ) = y ( 0 ) * t 0 + y ( 1 ) * t 1 + ⋯ + y ( q ) * t q + o ( t q ) where o ( t q ) * t - q → 0 as t → 0 . Note that y ( k ) is related to the k-th derivative of Y ( t ) by the equation y ( k ) = 1 k ! Y ( k ) ( 0 )
yq
The return value yq has prototype
     Vector yq
 (see Vector below).

One Order
If xq.size() == n , the vector yq has size m . The q-th order Taylor coefficient for Y ( t ) is returned as
     yq = y ( q ) .

Multiple Orders
If xq.size() == n*(q+1) , the vector yq has size m*(q+1) . For k = 0 , … , q , for i = 0 , … , m -1 , the i-th component of the k-th order Taylor coefficient for Y ( t ) is returned as
     yq[ (q+1) * i + k ] = y i ( k )

Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Zero Order
The case where q = 0 and xq.size() == n , corresponds to the zero order special case .

First Order
The case where q = 1 and xq.size() == n , corresponds to the first order special case .

Second Order
The case where q = 2 and xq.size() == n , corresponds to the second order special case .

Example
The file forward.cpp ( forward_order.cpp ) contains an example and test using one order (multiple orders). They return true if they succeed and false otherwise.
Input File: omh/forward/forward_order.omh cppad-20170000.3/doc/forward.cpp.xml0000644000175200017650000004444513057470506016160 0ustar coincoin-web Forward Mode: Example and Test
Prev Next forward.cpp Headings

Forward Mode: Example and Test
# include <limits>
# include <cppad/cppad.hpp>
namespace { // --------------------------------------------------------
// define the template function ForwardCases<Vector> in empty namespace
template <class Vector>
bool ForwardCases(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;

     // declare independent variables and starting recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = ax[0] * ax[0] * ax[1];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // initially, the variable values during taping are stored in f
     ok &= f.size_order() == 1;

     // zero order forward mode using notation in forward_zero
     // use the template parameter Vector for the vector type
     Vector x0(n), y0(m);
     x0[0] = 3.;
     x0[1] = 4.;
     y0    = f.Forward(0, x0);
     ok  &= NearEqual(y0[0] , x0[0]*x0[0]*x0[1], eps, eps);
     ok  &= f.size_order() == 1;

     // first order forward mode using notation in forward_one
     // X(t)           = x0 + x1 * t
     // Y(t) = F[X(t)] = y0 + y1 * t + o(t)
     Vector x1(n), y1(m);
     x1[0] = 1.;
     x1[1] = 0.;
     y1    = f.Forward(1, x1); // partial F w.r.t. x_0
     ok   &= NearEqual(y1[0] , 2.*x0[0]*x0[1], eps, eps);
     ok   &= f.size_order() == 2;

     // second order forward mode using notation in forward_order
     // X(t) =           x0 + x1 * t + x2 * t^2
     // Y(t) = F[X(t)] = y0 + y1 * t + y2 * t^2 + o(t^3)
     Vector x2(n), y2(m);
     x2[0]      = 0.;
     x2[1]      = 0.;
     y2         = f.Forward(2, x2);
     double F_00 = 2. * y2[0]; // second partial F w.r.t. x_0, x_0
     ok         &= NearEqual(F_00, 2.*x0[1], eps, eps);
     ok         &= f.size_order() == 3;

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool Forward(void)
{     bool ok = true;
     // Run with Vector equal to three different cases
     // all of which are Simple Vectors with elements of type double.
     ok &= ForwardCases< CppAD::vector  <double> >();
     ok &= ForwardCases< std::vector    <double> >();
     ok &= ForwardCases< std::valarray  <double> >();
     return ok;
}
Input File: example/forward.cpp cppad-20170000.3/doc/forward_order.cpp.xml0000644000175200017650000004162613057470506017351 0ustar coincoin-web Forward Mode: Example and Test of Multiple Orders
Prev Next forward_order.cpp Headings

Forward Mode: Example and Test of Multiple Orders
# include <limits>
# include <cppad/cppad.hpp>
bool forward_order(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;

     // declare independent variables and starting recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = ax[0] * ax[0] * ax[1];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // initially, the variable values during taping are stored in f
     ok &= f.size_order() == 1;

     // Compute three forward orders at one
     size_t q = 2, q1 = q+1;
     CPPAD_TESTVECTOR(double) xq(n*q1), yq;
     xq[q1*0 + 0] = 3.;    xq[q1*1 + 0] = 4.; // x^0 (order zero)
     xq[q1*0 + 1] = 1.;    xq[q1*1 + 1] = 0.; // x^1 (order one)
     xq[q1*0 + 2] = 0.;    xq[q1*1 + 2] = 0.; // x^2 (order two)
     // X(t) =   x^0 + x^1 * t + x^2 * t^2
     //      = [ 3 + t, 4 ]
     yq  = f.Forward(q, xq);
     ok &= size_t( yq.size() ) == m*q1;
     // Y(t) = F[X(t)]
     //      = (3 + t) * (3 + t) * 4
     //      = y^0 + y^1 * t + y^2 * t^2 + o(t^3)
     //
     // check y^0 (order zero)
     CPPAD_TESTVECTOR(double) x0(n);
     x0[0] = xq[q1*0 + 0];
     x0[1] = xq[q1*1 + 0];
     ok  &= NearEqual(yq[q1*0 + 0] , x0[0]*x0[0]*x0[1], eps, eps);
     //
     // check y^1 (order one)
     ok  &= NearEqual(yq[q1*0 + 1] , 2.*x0[0]*x0[1], eps, eps);
     //
     // check y^2 (order two)
     double F_00 = 2. * yq[q1*0 + 2]; // second partial F w.r.t. x_0, x_0
     ok   &= NearEqual(F_00, 2.*x0[1], eps, eps);

     // check number of orders per variable
     ok   &= f.size_order() == 3;

     return ok;
}
Input File: example/forward_order.cpp cppad-20170000.3/doc/forward_dir.xml0000644000175200017650000010130513057470506016222 0ustar coincoin-web Multiple Directions Forward Mode
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Multiple Directions Forward Mode

Syntax
yq = f.Forward(q, r, xq)
Purpose
We use F : B n → B m to denote the AD function corresponding to f . Given a function X : B → B n , defined by its Taylor coefficients , forward mode computes the Taylor coefficients for the function Y ( t ) = F [ X ( t ) ] This version of forward mode computes multiple directions as the same time (reducing the number of passes through the tape). This requires more memory, but might be faster in some cases.

Reverse Mode
Reverse mode for multiple directions has not yet been implemented. If you have speed tests that indicate that multiple direction forward mode is faster, and you want to try multiple direction reverse mode, contact the CppAD project manager.

Notation

n
We use n to denote the dimension of the domain space for f .

m
We use m to denote the dimension of the range space for f .

f
The ADFun object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const. After this call we will have
     f.size_order()     == q + 1
     f.size_direction() == r
q
This argument has prototype
     size_t q
 It specifies the order of Taylor Coefficient that we are calculating and must be greater than zero. The zero order coefficients can only have one direction computed and stored in f so use forward_zero to compute the zero order coefficients.

r
This argument has prototype
     size_t r
 It specifies the number of directions that are computed together. If ( r == 1 ), you are only using one direction and forward_order is simpler, and should be faster, than this more general case.

xq
The argument xq has prototype
     const Vector& xq
 and its size must be n*r (see Vector below). For ℓ = 0 , … , r -1 , j = 0 , … , n -1 , the j-th component of the q-th order Taylor coefficient for X ℓ ( t ) is defined by
      x j ( q ) , ℓ = xq[ r * j + ell ]

Zero Order
For j = 0 , … , n -1 , the j-th component of the zero order Taylor coefficient for X ℓ ( t ) is defined by
      x j ( 0 ) = xk[ j ] where xk corresponds to the previous call
     f.Forward(k, xk)
 with k = 0 .

Non-Zero Lower Orders
For ℓ = 0 , … , r -1 , j = 0 , … , n -1 , k = 1 , … , q -1 , the j-th component of the k-th order Taylor coefficient for X ℓ ( t ) is defined by
      x j ( k ) , ℓ = xk[ r * j + ell ] where xk corresponds to the previous call
     f.Forward(k, r, xk)
 Note that r must have the same value in this previous call.

X(t)
For ℓ = 0 , … , r -1 , the function X ℓ : B → B n is defined using the Taylor coefficients x ( k ) , ℓ ∈ B n : X ℓ ( t ) = x ( 0 ) + x ( 1 ) , ℓ * t 1 + ⋯ + x ( q ) , ℓ t q Note that the k-th derivative of X ℓ ( t ) is related to its Taylor coefficients by x ( 0 ) = X ℓ ( 0 ) x ( k ) , ℓ = 1 k ! X ℓ ( k ) ( 0 ) for k = 1 , … , q .

Y(t)
For ℓ = 0 , … , r -1 , the function Y ℓ : B → B m is defined by Y ℓ ( t ) = F [ X ℓ ( t ) ] . We use y ( 0 ) for the zero order coefficient and y ( k ) , ℓ ∈ B m to denote the hight order coefficients; i.e., Y ℓ ( t ) = y ( 0 ) + y ( 1 ) , ℓ * t 1 + ⋯ + y ( q ) , ℓ * t q + o ( t q ) where o ( t q ) * t - q → 0 as t → 0 . Note that the k-th derivative of Y ℓ ( t ) is related to its Taylor coefficients by y ( 0 ) = Y ℓ ( 0 ) y ( k ) , ℓ = 1 k ! Y ℓ ( k ) ( 0 ) for k = 1 , … , q .

yq
The argument yq has prototype
     Vector yq
 and its size is m*r (see Vector below). For ℓ = 0 , … , r -1 , i = 0 , … , m -1 , the i-th component of the q-th order Taylor coefficient for Y ℓ ( t ) is given by
      y i ( q ) , ℓ = yq[ r * i + ell ]

Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file forward_dir.cpp contains an example and test using one order (multiple orders). They return true if they succeed and false otherwise.
Input File: omh/forward/forward_dir.omh cppad-20170000.3/doc/forward_dir.cpp.xml0000644000175200017650000005532713057470506017017 0ustar coincoin-web Forward Mode: Example and Test of Multiple Directions
Prev Next forward_dir.cpp Headings

Forward Mode: Example and Test of Multiple Directions
# include <limits>
# include <cppad/cppad.hpp>
bool forward_dir(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();
     size_t j;

     // domain space vector
     size_t n = 3;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;
     ax[2] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = ax[0] * ax[1] * ax[2];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // initially, the variable values during taping are stored in f
     ok &= f.size_order() == 1;

     // zero order Taylor coefficients
     CPPAD_TESTVECTOR(double) x0(n), y0;
     for(j = 0; j < n; j++)
          x0[j] = double(j+1);
     y0          = f.Forward(0, x0);
     ok         &= size_t( y0.size() ) == m;
     double y_0  = 1.*2.*3.;
     ok         &= NearEqual(y0[0], y_0, eps, eps);

     // first order Taylor coefficients
     size_t r = 2, ell;
     CPPAD_TESTVECTOR(double) x1(r*n), y1;
     for(ell = 0; ell < r; ell++)
     {     for(j = 0; j < n; j++)
               x1[ r * j + ell ] = double(j + 1 + ell);
     }
     y1  = f.Forward(1, r, x1);
     ok &= size_t( y1.size() ) == r*m;

     // secondorder Taylor coefficients
     CPPAD_TESTVECTOR(double) x2(r*n), y2;
     for(ell = 0; ell < r; ell++)
     {     for(j = 0; j < n; j++)
               x2[ r * j + ell ] = 0.0;
     }
     y2  = f.Forward(2, r, x2);
     ok &= size_t( y2.size() ) == r*m;
     //
     // Y_0 (t)     = F[X_0(t)]
     //             =  (1 + 1t)(2 + 2t)(3 + 3t)
     double y_1_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
     double y_2_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
     //
     // Y_1 (t)     = F[X_1(t)]
     //             =  (1 + 2t)(2 + 3t)(3 + 4t)
     double y_1_1   = 2.*2.*3. + 3.*1.*3. + 4.*1.*2.;
     double y_2_1   = 1.*3.*4. + 2.*2.*4. + 3.*2.*3.;
     //
     ok  &= NearEqual(y1[0] , y_1_0, eps, eps);
     ok  &= NearEqual(y1[1] , y_1_1, eps, eps);
     ok  &= NearEqual(y2[0] , y_2_0, eps, eps);
     ok  &= NearEqual(y2[1] , y_2_1, eps, eps);
     //
     // check number of orders
     ok   &= f.size_order() == 3;
     //
     // check number of directions
     ok   &= f.size_direction() == 2;
     //
     return ok;
}
Input File: example/forward_dir.cpp cppad-20170000.3/doc/size_order.xml0000644000175200017650000002465713057470506016103 0ustar coincoin-web Number Taylor Coefficient Orders Currently Stored
Prev Next size_order

Number Taylor Coefficient Orders Currently Stored

Syntax
s = f.size_order()

See Also
seq_property

Purpose
Determine the number of Taylor coefficient orders, per variable,direction, currently calculated and stored in the ADFun object f . See the discussion under Constructor , Forward , and capacity_order for a description of when this value can change.

f
The object f has prototype
     const ADFun<Base> f
s
The result s has prototype
     size_t s
 and is the number of Taylor coefficient orders, per variable,direction in the AD operation sequence, currently calculated and stored in the ADFun object f .

Constructor
Directly after the FunConstruct syntax
     ADFun<Base> f(x, y)
 the value of s returned by size_order is one. This is because there is an implicit call to Forward that computes the zero order Taylor coefficients during this constructor.

Forward
After a call to Forward with the syntax
        f.Forward(q, x_q)
 the value of s returned by size_order would be q + 1 . The call to Forward above uses the lower order Taylor coefficients to compute and store the q-th order Taylor coefficients for all the variables in the operation sequence corresponding to f . Thus there are q + 1 (order zero through q ) Taylor coefficients per variable,direction. (You can determine the number of variables in the operation sequence using the size_var function.)

capacity_order
If the number of Taylor coefficient orders currently stored in f is less than or equal c , a call to capacity_order with the syntax
     f.capacity_order(c)
 does not affect the value s returned by size_order. Otherwise, the value s returned by size_order is equal to c (only Taylor coefficients of order zero through c -1 have been retained).

Example
The file forward.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: omh/forward/size_order.omh cppad-20170000.3/doc/compare_change.xml0000644000175200017650000004347213057470506016665 0ustar coincoin-web Comparison Changes Between Taping and Zero Order Forward
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Comparison Changes Between Taping and Zero Order Forward

Syntax
f.compare_change_count(count)
 number = f.compare_change_number()
 op_index = f.compare_change_op_index()

 See Also FunCheck

Purpose
We use F : B n → B m to denote the AD function corresponding to f ; i.e, given x ∈ B n , F ( x ) is defined by
     F(x) = f.Forward(0, x)
 see forward_zero . If x is such that all the algorithm comparison operations have the same result as when the algorithm was taped, The function F ( x ) and the algorithm will have the same values. (This is a sufficient, but not necessary condition).

f
In the compare_change_number and compare_change_op_index syntax, the object f has prototype
     const ADFun<Base> f
 In the compare_change_count syntax, the object f has prototype
     ADFun<Base> f
count
The argument count has prototype
     size_t count
 It specifies which comparison change should correspond to the information stored in f during subsequent calls to forward_zero ; i.e.,
     f.Forward(0, x)
 For example, if count == 1 , the operator index corresponding to the first comparison change will be stored. This is the default value used if count is not specified.

Speed
The special case where count == 0 , should be faster because the comparisons are not checked during
     f.Forward(0, x)
number
The return value number has prototype
     size_t number
 If count is non-zero, number is the number of AD<Base> comparison operations, corresponding to the previous call to
     f.Forward(0, x)
 that have a different result for this value of x than the value used when f was created by taping an algorithm. If count is zero, or if no calls to f.Forward(0, x) follow the previous setting of count , number is zero.

Discussion
If count and number are non-zero, you may want to re-tape the algorithm with the independent variables equal to the values in x , so the AD operation sequence properly represents the algorithm for this value of independent variables. On the other hand, re-taping the AD operation sequence usually takes significantly more time than evaluation using forward_zero . If the functions values have not changed (see FunCheck ) it may not be worth re-taping a new AD operation sequence.

op_index
The return value op_index has prototype
     size_t op_index
 If count is non-zero, op_index is the operator index corresponding the count -th comparison change during the previous call to
     f.Forward(0, x)
 If count is greater than the corresponding number , there is no such comparison change and op_index will also be zero. If count is zero, if the function f has been optimized , or if no calls to f.Forward(0, x) follow the previous setting of count , op_index is zero.

Purpose
The operator index can be used to generate an error during the taping process so that the corresponding algorithm can be inspected. In some cases, it is possible to re-design this part of the algorithm to avoid the particular comparison operation. For example, using an conditional expression may be appropriate in some cases. See abort_op_index in the syntax
     Independent(x, abort_op_index)
Example
compare_change.cpp contains an example and test of this operation. It returns true if they succeed and false otherwise.
Input File: omh/forward/compare_change.omh cppad-20170000.3/doc/compare_change.cpp.xml0000644000175200017650000007633013057470506017445 0ustar coincoin-web CompareChange and Re-Tape: Example and Test
Prev Next compare_change.cpp Headings

CompareChange and Re-Tape: Example and Test

# include <cppad/cppad.hpp>

namespace { // put this function in the empty namespace
     template <typename Type>
     Type Minimum(const Type &x, const Type &y)
     {     // Use a comparision to compute the min(x, y)
          // (note that CondExp would never require retaping).
          if( x < y )
               return x;
          return y;
     }
     struct error_info {
          bool known;
          int  line;
          std::string file;
          std::string exp;
          std::string msg;
     };
     void error_handler(
          bool        known       ,
          int         line        ,
          const char *file        ,
          const char *exp         ,
          const char *msg         )
     {     // error handler must not return, so throw an exception
          error_info info;
          info.known = known;
          info.line  = line;
          info.file  = file;
          info.exp   = exp;
          info.msg   = msg;
          throw info;
     }

}

bool compare_change(void)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 3.;
     ax[1] = 4.;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = Minimum(ax[0], ax[1]);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // set count to one (not necessry because is its default value)
     f.compare_change_count(1);

     // evaluate zero mode Forward where comparison has the same result
     // as during taping; i.e., x[0] < x[1].
     CPPAD_TESTVECTOR(double) x(n), y(m);
     x[0] = 2.;
     x[1] = 3.;
     y    = f.Forward(0, x);
     ok  &= (y[0] == x[0]);
     ok  &= (y[0] == Minimum(x[0], x[1]));
     ok  &= (f.compare_change_number() == 0);
     ok  &= (f.compare_change_op_index() == 0);

     // evaluate zero mode Forward where comparison has different result
     // as during taping; i.e., x[0] >= x[1].
     x[0] = 3.;
     x[1] = 2.;
     y    = f.Forward(0, x);
     ok  &= (y[0] == x[0]);
     ok  &= (y[0] != Minimum(x[0], x[1]));
     ok  &= (f.compare_change_number() == 1);
     ok  &= (f.compare_change_op_index() > 0 );
     size_t op_index = f.compare_change_op_index();

     // Local block during which default CppAD error handler is replaced.
     // If you do not replace the default CppAD error handler,
     // and you run in the debugger, you will be able to inspect the
     // call stack and see that 'if( x < y )' is where the comparison is.
     bool missed_error = true;
     {     CppAD::ErrorHandler local_error_handler(error_handler);

          std::string check_msg =
               "Operator index equals abort_op_index in Independent";
          try {
               // determine the operation index where the change occurred
               CppAD::Independent(ax, op_index);
               ay[0] = Minimum(ax[0], ax[1]);
# ifdef NDEBUG
               // CppAD does not spend time checking operator index when
               // NDEBUG is defined
               missed_error = false;
               AD<double>::abort_recording();
# endif
          }
          catch( error_info info )
          {     missed_error = false;
               ok          &= info.known;
               ok          &= info.msg == check_msg;
               // Must abort the recording so we can start a new one
               // (and to avoid a memory leak).
               AD<double>::abort_recording();
          }
     }
     ok &= ! missed_error;


     // set count to zero to demonstrate case where comparisons are not checked
     f.compare_change_count(0);
     y    = f.Forward(0, x);
     ok  &= (y[0] == x[0]);
     ok  &= (y[0] != Minimum(x[0], x[1]));
     ok  &= (f.compare_change_number()   == 0);
     ok  &= (f.compare_change_op_index() == 0);

     // now demonstrate that compare_change_number works for an optimized
     // tape (note that compare_change_op_index is always zero after optimize)
     f.optimize();
     f.compare_change_count(1);
     y    = f.Forward(0, x);
     ok  &= (y[0] == x[0]);
     ok  &= (y[0] != Minimum(x[0], x[1]));
     ok  &= (f.compare_change_number()   == 1);
     ok  &= (f.compare_change_op_index() == 0);

     // now retape to get the a tape that agrees with the algorithm
     ax[0] = x[0];
     ax[1] = x[1];
     Independent(ax);
     ay[0] = Minimum(ax[0], ax[1]);
     f.Dependent(ax, ay);
     y    = f.Forward(0, x);
     ok  &= (y[0] == x[1]);
     ok  &= (y[0] == Minimum(x[0], x[1]));
     ok  &= (f.compare_change_number()   == 0);
     ok  &= (f.compare_change_op_index() == 0);

     return ok;
}
Input File: example/compare_change.cpp cppad-20170000.3/doc/capacity_order.xml0000644000175200017650000002742213057470506016717 0ustar coincoin-web Controlling Taylor Coefficients Memory Allocation
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Controlling Taylor Coefficients Memory Allocation

Syntax
f.capacity_order(c)

See Also
seq_property

Purpose
The Taylor coefficients calculated by Forward mode calculations are retained in an ADFun object for subsequent use during Reverse mode and higher order Forward mode calculations. For example, a call to Forward with the syntax
        yq = f.Forward(q, xq)
 where q > 0 and %xq%.size() == %f%.Domain()%, uses the lower order Taylor coefficients and computes the q-th order Taylor coefficients for all the variables in the operation sequence corresponding to f . The capacity_order operation allows you to control that amount of memory that is retained by an AD function object (to hold Forward results for subsequent calculations).

f
The object f has prototype
     ADFun<Base> f
c
The argument c has prototype
     size_t c
 It specifies the number of Taylor coefficient orders that are allocated in the AD operation sequence corresponding to f .

Pre-Allocating Memory
If you plan to make calls to Forward with the maximum value of q equal to Q , it should be faster to pre-allocate memory for these calls using
     f.capacity_order(c)
 with c equal to Q + 1 . If you do no do this, Forward will automatically allocate memory and will copy the results to a larger buffer, when necessary.

Note that each call to Dependent frees the old memory connected to the function object and sets the corresponding taylor capacity to zero.

Freeing Memory
If you no longer need the Taylor coefficients of order q and higher (that are stored in f ), you can reduce the memory allocated to f using
     f.capacity_order(c)
 with c equal to q . Note that, if ta_hold_memory is true, this memory is not actually returned to the system, but rather held for future use by the same thread.

Original State
If f is constructed with the syntax
     ADFun<Base> f(x, y)
 , there is an implicit call to forward_zero with xq equal to the value of the independent variables when the AD operation sequence was recorded. This corresponds to c == 1 .

Example
The file capacity_order.cpp contains an example and test of these operations. It returns true if it succeeds and false otherwise.
Input File: cppad/core/capacity_order.hpp cppad-20170000.3/doc/capacity_order.cpp.xml0000644000175200017650000005007313057470506017476 0ustar coincoin-web Controlling Taylor Coefficient Memory Allocation: Example and Test
Prev Next capacity_order.cpp Headings

Controlling Taylor Coefficient Memory Allocation: Example and Test
# include <cppad/cppad.hpp>

namespace {
     bool test(void)
     {     bool ok = true;
          using CppAD::AD;
          using CppAD::NearEqual;
          using CppAD::thread_alloc;

          // domain space vector
          size_t n(1), m(1);
          CPPAD_TESTVECTOR(AD<double>) ax(n), ay(n);

          // declare independent variables and start tape recording
          ax[0]  = 1.0;
          CppAD::Independent(ax);

          // Set y = x^3, use enough variables so more that the minimal amount
          // of memory is allocated for Taylor coefficients
          ay[0] = 0.;
          for( size_t i = 0; i < 10; i++)
               ay[0] += ax[0] * ax[0] * ax[0];
          ay[0] = ay[0] / 10.;

          // create f: x -> y and stop tape recording
          // (without running zero order forward mode).
          CppAD::ADFun<double> f;
          f.Dependent(ax, ay);

          // check that this is master thread
          size_t thread = thread_alloc::thread_num();
          ok           &= thread == 0; // this should be master thread

          // The highest order forward mode calculation below is first order.
          // This corresponds to two Taylor coefficient per variable,direction
          // (orders zero and one). Preallocate memory for speed.
          size_t inuse  = thread_alloc::inuse(thread);
          f.capacity_order(2);
          ok &= thread_alloc::inuse(thread) > inuse;

          // zero order forward mode
          CPPAD_TESTVECTOR(double) x(n), y(m);
          x[0] = 0.5;
          y    = f.Forward(0, x);
          double eps = 10. * CppAD::numeric_limits<double>::epsilon();
          ok  &= NearEqual(y[0], x[0] * x[0] * x[0], eps, eps);

          // forward computation of partials w.r.t. x
          CPPAD_TESTVECTOR(double) dx(n), dy(m);
          dx[0] = 1.;
          dy    = f.Forward(1, dx);
          ok   &= NearEqual(dy[0], 3. * x[0] * x[0], eps, eps);

          // Suppose we no longer need the first order Taylor coefficients.
          inuse = thread_alloc::inuse(thread);
          f.capacity_order(1); // just keep zero order coefficients
          ok   &= thread_alloc::inuse(thread) < inuse;

          // Suppose we no longer need the zero order Taylor coefficients
          // (could have done this first and not used f.capacity_order(1)).
          inuse = thread_alloc::inuse(thread);
          f.capacity_order(0);
          ok   &= thread_alloc::inuse(thread) < inuse;

          // turn off memory holding
          thread_alloc::hold_memory(false);

          return ok;
     }
}
bool capacity_order(void)
{     bool ok = true;
     using CppAD::thread_alloc;

     // original amount of memory inuse
     size_t thread = thread_alloc::thread_num();
     ok           &= thread == 0; // this should be master thread
     size_t inuse  = thread_alloc::inuse(thread);

     // do test in separate routine so all objects are destroyed
     ok &= test();

     // check that the amount of memroy inuse has not changed
     ok &= thread_alloc::inuse(thread) == inuse;

     // Test above uses hold_memory, so return available memory
     thread_alloc::free_available(thread);

     return ok;
}
Input File: example/capacity_order.cpp cppad-20170000.3/doc/number_skip.xml0000644000175200017650000001270013057470506016236 0ustar coincoin-web Number of Variables that Can be Skipped
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Number of Variables that Can be Skipped

Syntax
n = f.number_skip()

See Also
seq_property

Purpose
The conditional expressions use either the if_true or if_false . Hence, some terms only need to be evaluated depending on the value of the comparison in the conditional expression. The optimize option is capable of detecting some of these case and determining variables that can be skipped. This routine returns the number such variables.

n
The return value n has type size_t is the number of variables that the optimizer has determined can be skipped (given the independent variable values specified by the previous call to f.Forward for order zero).

f
The object f has prototype
     ADFun<Base> f
Example
The file number_skip.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/num_skip.hpp cppad-20170000.3/doc/number_skip.cpp.xml0000644000175200017650000003033113057470506017017 0ustar coincoin-web Number of Variables That Can be Skipped: Example and Test
Prev Next number_skip.cpp Headings

Number of Variables That Can be Skipped: Example and Test
# include <cppad/cppad.hpp>
bool number_skip(void)
{     bool ok = true;
     using CppAD::AD;

     // independent variable vector
     CppAD::vector< AD<double> > ax(2);
     ax[0] = 0.;
     ax[1] = 1.;
     Independent(ax);

     // Use a conditional expression
     CppAD::vector< AD<double> > ay(1);

     // variable that gets optimized out
     AD<double> az = ax[0] * ax[0];


     // conditional expression
     ay[0] = CondExpLt(ax[0], ax[1], ax[0] + ax[1], ax[0] - ax[1]);

     // create function object F : x -> ay
     CppAD::ADFun<double> f;
     f.Dependent(ax, ay);

     // use zero order to evaluate F[ (3, 4) ]
     CppAD::vector<double>  x( f.Domain() );
     CppAD::vector<double>  y( f.Range() );
     x[0]    = 3.;
     x[1]    = 4.;
     y   = f.Forward(0, x);
     ok &= (y[0] == x[0] + x[1]);

     // before call to optimize
     ok &= f.number_skip() == 0;
     size_t n_var = f.size_var();

     // now optimize the operation sequence
     f.optimize();

     // after optimize, check forward mode result
     x[0]    = 4.;
     x[1]    = 3.;
     y   = f.Forward(0, x);
     ok &= (y[0] == x[0] - x[1]);

     // after optimize, check amount of optimization
     ok &= f.size_var() == n_var - 1;
     ok &= f.number_skip() == 1;

     return ok;
}
Input File: example/number_skip.cpp cppad-20170000.3/doc/reverse.xml0000644000175200017650000000746313057470506015405 0ustar coincoin-web Reverse Mode
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Reverse Mode

Multiple Directions
Reverse mode after Forward(q, r, xq) with number of directions r != 1 is not yet supported. There is one exception, reverse_one is allowed because there is only one zero order forward direction. After such an operation, only the zero order forward results are retained (the higher order forward results are lost).

Contents
reverse_oneFirst Order Reverse Mode
reverse_twoSecond Order Reverse Mode
reverse_anyAny Order Reverse Mode
Input File: omh/reverse/reverse.omh cppad-20170000.3/doc/_reverse_xml.js0000644000175200017650000000356713057470506016241 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'reverse.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down0 = [ 'reverse_one.xml', 'reverse_two.xml', 'reverse_any.xml' ]; var list_current0 = [ 'reverse.xml#Multiple Directions', 'reverse.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/reverse_one.cpp.xml0000644000175200017650000004123013057470506017015 0ustar coincoin-web First Order Reverse Mode: Example and Test
Prev Next reverse_one.cpp Headings

First Order Reverse Mode: Example and Test
# include <cppad/cppad.hpp>
namespace { // ----------------------------------------------------------
// define the template function reverse_one_cases<Vector> in empty namespace
template <typename Vector>
bool reverse_one_cases(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) X(n);
     X[0] = 0.;
     X[1] = 1.;

     // declare independent variables and start recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y[0] = X[0] * X[0] * X[1];

     // create f : X -> Y and stop recording
     CppAD::ADFun<double> f(X, Y);

     // use first order reverse mode to evaluate derivative of y[0]
     // and use the values in X for the independent variables.
     CPPAD_TESTVECTOR(double) w(m), dw(n);
     w[0] = 1.;
     dw   = f.Reverse(1, w);
     ok  &= NearEqual(dw[0] , 2.*X[0]*X[1], eps99, eps99);
     ok  &= NearEqual(dw[1] ,    X[0]*X[0], eps99, eps99);

     // use zero order forward mode to evaluate y at x = (3, 4)
     // and use the template parameter Vector for the vector type
     Vector x(n), y(m);
     x[0]    = 3.;
     x[1]    = 4.;
     y       = f.Forward(0, x);
     ok     &= NearEqual(y[0] , x[0]*x[0]*x[1], eps99, eps99);

     // use first order reverse mode to evaluate derivative of y[0]
     // and using the values in x for the independent variables.
     w[0] = 1.;
     dw   = f.Reverse(1, w);
     ok  &= NearEqual(dw[0] , 2.*x[0]*x[1], eps99, eps99);
     ok  &= NearEqual(dw[1] ,    x[0]*x[0], eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool reverse_one(void)
{     bool ok = true;
     // Run with Vector equal to three different cases
     // all of which are Simple Vectors with elements of type double.
     ok &= reverse_one_cases< CppAD::vector  <double> >();
     ok &= reverse_one_cases< std::vector    <double> >();
     ok &= reverse_one_cases< std::valarray  <double> >();
     return ok;
}
Input File: example/reverse_one.cpp cppad-20170000.3/doc/reverse_two.xml0000644000175200017650000007305113057470506016272 0ustar coincoin-web Second Order Reverse Mode
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Second Order Reverse Mode

Syntax
dw = f.Reverse(2, w)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . Reverse mode computes the derivative of the Forward mode Taylor coefficients with respect to the domain variable x .

x^(k)
For k = 0 , 1 , the vector x ( k ) ∈ B n is defined as the value of x_k in the previous call (counting this call) of the form
     f.Forward(k, x_k)
 If there is no previous call with k = 0 , x ( 0 ) is the value of the independent variables when the corresponding AD of Base operation sequence was recorded.

W
The functions W 0 : B n → B and W 1 : B n → B are defined by W 0 ( u ) = w 0 * F 0 ( u ) + ⋯ + w m -1 * F m -1 ( u ) W 1 ( u ) = w 0 * F 0 ( 1 ) ( u ) * x ( 1 ) + ⋯ + w m -1 * F m -1 ( 1 ) ( u ) * x ( 1 ) This operation computes the derivatives W 0 ( 1 ) ( u ) = w 0 * F 0 ( 1 ) ( u ) + ⋯ + w m -1 * F m -1 ( 1 ) ( u ) W 1 ( 1 ) ( u ) = w 0 * (x ( 1 ) ) T * F 0 ( 2 ) ( u ) + ⋯ + w m -1 * (x ( 1 ) ) T F m -1 ( 2 ) ( u ) at u = x ( 0 ) .

f
The object f has prototype
     const ADFun<Base> f
 Before this call to Reverse, the value returned by
     f.size_order()
 must be greater than or equal two (see size_order ).

w
The argument w has prototype
     const Vector &w
 (see Vector below) and its size must be equal to m , the dimension of the range space for f .

dw
The result dw has prototype
     Vector dw
 (see Vector below). It contains both the derivative W ( 1 ) ( x ) and the derivative U ( 1 ) ( x ) . The size of dw is equal to n × 2 , where n is the dimension of the domain space for f .

First Order Partials
For j = 0 , … , n - 1 , dw [ j * 2 + 0 ] = ∂ W 0 ∂ u j (x ( 0 ) ) = w 0 * ∂ F 0 ∂ u j (x ( 0 ) ) + ⋯ + w m -1 * ∂ F m -1 ∂ u j (x ( 0 ) ) This part of dw contains the same values as are returned by reverse_one .

Second Order Partials
For j = 0 , … , n - 1 , dw [ j * 2 + 1 ] = ∂ W 1 ∂ u j (x ( 0 ) ) = ∑ ℓ = 0 n -1 x ℓ ( 1 ) [w 0 * ∂ 2 F 0 ∂ u ℓ ∂ u j (x ( 0 ) ) + ⋯ + w m -1 * ∂ 2 F m -1 ∂ u ℓ ∂ u j (x ( 0 ) ) ]
Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Hessian Times Direction
Suppose that w is the i-th elementary vector. It follows that for j = 0 , … , n -1 dw [ j * 2 + 1 ] = w i ∑ ℓ = 0 n -1 ∂ 2 F i ∂ u j ∂ u ℓ (x ( 0 ) ) x ℓ ( 1 ) = [F i ( 2 ) (x ( 0 ) ) * x ( 1 ) ] j Thus the vector ( dw [ 1 ] , dw [ 3 ] , … , dw [ n * q - 1 ] ) is equal to the Hessian of F i ( x ) times the direction x ( 1 ) . In the special case where x ( 1 ) is the l-th elementary vector , dw [ j * 2 + 1 ] = ∂ 2 F i ∂ x j ∂ x ℓ (x ( 0 ) )
Example
The files reverse_two.cpp and hes_times_dir.cpp contain a examples and tests of reverse mode calculations. They return true if they succeed and false otherwise.
Input File: omh/reverse/reverse_two.omh cppad-20170000.3/doc/reverse_two.cpp.xml0000644000175200017650000004707613057470506017063 0ustar coincoin-web Second Order Reverse ModeExample and Test
Prev Next reverse_two.cpp Headings

Second Order Reverse ModeExample and Test
# include <cppad/cppad.hpp>
namespace { // ----------------------------------------------------------
// define the template function reverse_two_cases<Vector> in empty namespace
template <typename Vector>
bool reverse_two_cases(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) X(n);
     X[0] = 0.;
     X[1] = 1.;

     // declare independent variables and start recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y[0] = X[0] * X[0] * X[1];

     // create f : X -> Y and stop recording
     CppAD::ADFun<double> f(X, Y);

     // use zero order forward mode to evaluate y at x = (3, 4)
     // use the template parameter Vector for the vector type
     Vector x(n), y(m);
     x[0]  = 3.;
     x[1]  = 4.;
     y     = f.Forward(0, x);
     ok    &= NearEqual(y[0] , x[0]*x[0]*x[1], eps99, eps99);

     // use first order forward mode in x[0] direction
     // (all second order partials below involve x[0])
     Vector dx(n), dy(m);
     dx[0] = 1.;
     dx[1] = 1.;
     dy    = f.Forward(1, dx);
     double check = 2.*x[0]*x[1]*dx[0] + x[0]*x[0]*dx[1];
     ok   &= NearEqual(dy[0], check, eps99, eps99);

     // use second order reverse mode to evalaute second partials of y[0]
     // with respect to (x[0], x[0]) and with respect to (x[0], x[1])
     Vector w(m), dw( n * 2 );
     w[0]  = 1.;
     dw    = f.Reverse(2, w);

     // check derivative of f
     ok   &= NearEqual(dw[0*2+0] , 2.*x[0]*x[1], eps99, eps99);
     ok   &= NearEqual(dw[1*2+0] ,    x[0]*x[0], eps99, eps99);

     // check derivative of f^{(1)} (x) * dx
     check = 2.*x[1]*dx[1] + 2.*x[0]*dx[1];
     ok   &= NearEqual(dw[0*2+1] , check, eps99, eps99);
     check = 2.*x[0]*dx[1];
     ok   &= NearEqual(dw[1*2+1] , check, eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool reverse_two(void)
{     bool ok = true;
     ok &= reverse_two_cases< CppAD::vector  <double> >();
     ok &= reverse_two_cases< std::vector    <double> >();
     ok &= reverse_two_cases< std::valarray  <double> >();
     return ok;
}
Input File: example/reverse_two.cpp cppad-20170000.3/doc/hes_times_dir.cpp.xml0000644000175200017650000003402613057470506017324 0ustar coincoin-web Hessian Times Direction: Example and Test
Prev Next hes_times_dir.cpp Headings

Hessian Times Direction: Example and Test
// Example and test of computing the Hessian times a direction; i.e.,
// given F : R^n -> R and a direction dx in R^n, we compute F''(x) * dx

# include <cppad/cppad.hpp>

namespace { // put this function in the empty namespace
     // F(x) = |x|^2 = x[0]^2 + ... + x[n-1]^2
     template <class Type>
     Type F(CPPAD_TESTVECTOR(Type) &x)
     {     Type sum = 0;
          size_t i = x.size();
          while(i--)
               sum += x[i] * x[i];
          return sum;
     }
}

bool HesTimesDir(void)
{     bool ok = true;                   // initialize test result
     size_t j;                         // a domain variable variable

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 5;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     for(j = 0; j < n; j++)
          X[j] = AD<double>(j);

     // declare independent variables and start recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y[0] = F(X);

     // create f : X -> Y and stop recording
     CppAD::ADFun<double> f(X, Y);

     // choose a direction dx and compute dy(x) = F'(x) * dx
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     for(j = 0; j < n; j++)
          dx[j] = double(n - j);
     dy = f.Forward(1, dx);

     // compute ddw = F''(x) * dx
     CPPAD_TESTVECTOR(double) w(m);
     CPPAD_TESTVECTOR(double) ddw(2 * n);
     w[0] = 1.;
     ddw  = f.Reverse(2, w);

     // F(x)        = x[0]^2 + x[1]^2 + ... + x[n-1]^2
     // F''(x)      = 2 * Identity_Matrix
     // F''(x) * dx = 2 * dx
     for(j = 0; j < n; j++)
          ok &= NearEqual(ddw[j * 2 + 1], 2.*dx[j], eps99, eps99);

     return ok;
}
Input File: example/hes_times_dir.cpp cppad-20170000.3/doc/reverse_any.xml0000644000175200017650000011350413057470506016246 0ustar coincoin-web Any Order Reverse Mode
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Any Order Reverse Mode

Syntax
dw = f.Reverse(q, w)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . Reverse mode computes the derivative of the Forward mode Taylor coefficients with respect to the domain variable x . To be specific, it computes the derivative W ( 1 ) ( u ) at u = x which is specified by the following notation:

Notation

u^(k)
For k = 0 , … , q -1 , the vector u ( k ) ∈ B n is defined as the value of x_k in the previous calls of the form
     f.Forward(k, x_k)
 If there is no previous call with k = 0 , u ( 0 ) is the value of the independent variables when the corresponding AD of Base operation sequence was recorded.

X(t, u)
The function X : B × B n × q → B n is defined by X ( t , u ) = u ( 0 ) + u ( 1 ) * t + ⋯ + u ( q -1 ) * t q -1 Note that for k = 0 , … , q -1 , u ( k ) is related to the k-th partial of X ( t , u ) with respect to t by u ( k ) = 1 k ! ∂ k ∂ t k X ( 0 , u )
Y(t, u)
The function Y : B × B n × q → B m is defined by Y ( t , u ) = F [ X ( t , u ) ]
w^(k)
If the argument w has size m * q , for k = 0 , … , q -1 and i = 0 , … , m -1 , w i ( k ) = w [ i * q + k ] If the argument w has size m , for k = 0 , … , q -1 and i = 0 , … , m -1 , w i ( k ) = { w [ i ] if k = q -1 0 otherwise
W(u)
The function W : B n × q → B is defined by W ( u ) = ∑ k = 0 q -1 ( w ( k ) ) T 1 k ! ∂ k ∂ t k Y ( 0 , u )
f
The object f has prototype
     const ADFun<Base> f
 Before this call to Reverse, the value returned by
     f.size_order()
 must be greater than or equal q (see size_order ).

q
The argument q has prototype
     size_t q
 and specifies the number of Taylor coefficient orders to be differentiated (for each variable).

w
The argument w has prototype
     const Vector &w
 (see Vector below) and its size must be equal to m or m * q , It specifies the weighting vector w in the definition of W(u) .

dw
The return value dw has prototype
     Vector dw
 (see Vector below). It is a vector with size n × q . For j = 0 , … , n -1 and k = 0 , … , q -1 If the argument w has size m * q , dw [ j * q + k ] = W ( 1 ) ( x ) j , k where u = x is value of the Taylor coefficients where the derivative is evaluated.

If the argument w has size m , dw [ j * q + q - k - 1 ] = W ( 1 ) ( x ) j , k where u = x is value of the Taylor coefficients where the derivative is evaluated. Note the reverse order in which the order indices are stored. This is an unfortunate consequence of keeping Reverse backward compatible.

First Order
We consider the case where q = 1 and w.size() == m . In this case W ( u ) = w 0 Y 0 ( 0 , u ) + ⋯ + w m Y m ( 0 , u ) W ( u ) = w 0 F 0 [ X ( 0 , u ) ] + ⋯ + w m F m [ X ( 0 , u ) ] W ( 1 ) ( x ) = w 0 F 0 ( 1 ) ( x ( 0 ) ) + ⋯ + w m F m ( 1 ) ( x ( 0 ) ) This is the same as the result documented in reverse_one .

Second Order
We consider the case where q = 2 and w.size() == m . In this case W ( u ) = w 0 ∂ t Y 0 ( 0 , u ) + ⋯ + w m ∂ t Y m ( 0 , u ) W ( u ) = w 0 ∂ t { F 0 [ X ( t , u ) ] } t = 0 + ⋯ + w m ∂ t { F m [ X ( t , u ) ] } t = 0 W ( u ) = w 0 F 0 ( 1 ) ( u ( 0 ) ) u ( 1 ) + ⋯ + w 0 F m ( 1 ) ( u ( 0 ) ) u ( 1 ) ∂ u ( 0 ) W ( x ) = w 0 ( x ( 1 ) ) T F 0 ( 2 ) ( x ( 0 ) ) + ⋯ + w m ( x ( 1 ) ) T F m ( 2 ) ( x ( 0 ) ) ∂ u ( 1 ) W ( x ) = w 0 F 0 ( 1 ) ( x ( 0 ) ) + ⋯ + w m F m ( 1 ) ( x ( 0 ) ) where ∂ u ( 0 ) denotes partial with respect to u ( 0 ) . These are the same as the result documented in reverse_two .

Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
  1. The file reverse_three.cpp contains an example and test of using reverse mode to compute third order derivatives.
  2. The file reverse_checkpoint.cpp contains an example and test of the general reverse mode case.
Input File: omh/reverse/reverse_any.omh cppad-20170000.3/doc/reverse_three.cpp.xml0000644000175200017650000007076313057470506017360 0ustar coincoin-web Third Order Reverse Mode: Example and Test
Prev Next reverse_three.cpp

Third Order Reverse Mode: Example and Test

Taylor Coefficients X ( t ) = x ( 0 ) + x ( 1 ) t + x ( 2 ) t 2 X ( 1 ) ( t ) = x ( 1 ) + 2 x ( 2 ) t X ( 2 ) ( t ) = 2 x ( 2 ) Thus, we need to be careful to properly account for the fact that X ( 2 ) ( 0 ) = 2 x ( 2 ) (and similarly Y ( 2 ) ( 0 ) = 2 y ( 2 ) ). 
# include <cppad/cppad.hpp>
namespace { // ----------------------------------------------------------
// define the template function cases<Vector> in empty namespace
template <typename Vector>
bool cases(void)
{     bool ok    = true;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     using CppAD::AD;
     using CppAD::NearEqual;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) X(n);
     X[0] = 0.;
     X[1] = 1.;

     // declare independent variables and start recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y[0] = X[0] * X[1];

     // create f : X -> Y and stop recording
     CppAD::ADFun<double> f(X, Y);

     // define x^0 and compute y^0 using user zero order forward
     Vector x0(n), y0(m);
     x0[0]    = 2.;
     x0[1]    = 3.;
     y0       = f.Forward(0, x0);

     // y^0 = F(x^0)
     double check;
     check    =  x0[0] * x0[1];
     ok      &= NearEqual(y0[0] , check, eps, eps);

     // define x^1 and compute y^1 using first order forward mode
     Vector x1(n), y1(m);
     x1[0] = 4.;
     x1[1] = 5.;
     y1    = f.Forward(1, x1);

     // Y^1 (x) = partial_t F( x^0 + x^1 * t )
     // y^1     = Y^1 (0)
     check = x1[0] * x0[1] + x0[0] * x1[1];
     ok   &= NearEqual(y1[0], check, eps, eps);

     // define x^2 and compute y^2 using second order forward mode
     Vector x2(n), y2(m);
     x2[0] = 6.;
     x2[1] = 7.;
     y2    = f.Forward(2, x2);

     // Y^2 (x) = partial_tt F( x^0 + x^1 * t + x^2 * t^2 )
     // y^2     = (1/2) *  Y^2 (0)
     check  = x2[0] * x0[1] + x1[0] * x1[1] + x0[0] * x2[1];
     ok    &= NearEqual(y2[0], check, eps, eps);

     // W(x)  = Y^0 (x) + 2 * Y^1 (x) + 3 * (1/2) * Y^2 (x)
     size_t p = 3;
     Vector dw(n*p), w(m*p);
     w[0] = 1.;
     w[1] = 2.;
     w[2] = 3.;
     dw   = f.Reverse(p, w);

     // check partial w.r.t x^0_0 of W(x)
     check = x0[1] + 2. * x1[1] + 3. * x2[1];
     ok   &= NearEqual(dw[0*p+0], check, eps, eps);

     // check partial w.r.t x^0_1 of W(x)
     check = x0[0] + 2. * x1[0] + 3. * x2[0];
     ok   &= NearEqual(dw[1*p+0], check, eps, eps);

     // check partial w.r.t x^1_0 of W(x)
     check = 2. * x0[1] + 3. * x1[1];
     ok   &= NearEqual(dw[0*p+1], check, eps, eps);

     // check partial w.r.t x^1_1 of W(x)
     check = 2. * x0[0] + 3. * x1[0];
     ok   &= NearEqual(dw[1*p+1], check, eps, eps);

     // check partial w.r.t x^2_0 of W(x)
     check = 3. * x0[1];
     ok   &= NearEqual(dw[0*p+2], check, eps, eps);

     // check partial w.r.t x^2_1 of W(x)
     check = 3. * x0[0];
     ok   &= NearEqual(dw[1*p+2], check, eps, eps);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool reverse_three(void)
{     bool ok = true;
     ok &= cases< CppAD::vector  <double> >();
     ok &= cases< std::vector    <double> >();
     ok &= cases< std::valarray  <double> >();
     return ok;
}
Input File: example/reverse_three.cpp cppad-20170000.3/doc/reverse_checkpoint.cpp.xml0000644000175200017650000016672413057470506020403 0ustar coincoin-web Reverse Mode General Case (Checkpointing): Example and Test
Prev Next reverse_checkpoint.cpp

Reverse Mode General Case (Checkpointing): Example and Test

See Also
checkpoint

Purpose
Break a large computation into pieces and only store values at the interface of the pieces (this is much easier to do using checkpoint ). In actual applications, there may be many functions, but for this example there are only two. The functions F : R 2 → R 2 and G : R 2 → R 2 defined by F ( x ) = ( x 0 x 1 x 1 - x 0 ) , G ( y ) = ( y 0 - y 1 y 1 y 0 )
Processing Steps
We apply reverse mode to compute the derivative of H : R 2 → R is defined by H ( x ) = G 0 [ F ( x ) ] + G 1 [ F ( x ) ] = x 0 x 1 - ( x 1 - x 0 ) + x 0 x 1 ( x 1 - x 0 ) = x 0 x 1 ( 1 - x 0 + x 1 ) - x 1 + x 0 Given the zero and first order Taylor coefficients x ( 0 ) and x ( 1 ) , we use X ( t ) , Y ( t ) and Z ( t ) for the corresponding functions; i.e., X ( t ) = x ( 0 ) + x ( 1 ) t Y ( t ) = F [ X ( t ) ] = y ( 0 ) + y ( 1 ) t + O ( t 2 ) Z ( t ) = G { F [ X ( t ) ] } = z ( 0 ) + z ( 1 ) t + O ( t 2 ) h ( 0 ) = z 0 ( 0 ) + z 1 ( 0 ) h ( 1 ) = z 0 ( 1 ) + z 1 ( 1 ) Here are the processing steps:
  1. Use forward mode on F ( x ) to compute y ( 0 ) and y ( 1 ) .
  2. Free some, or all, of the memory corresponding to F ( x ) .
  3. Use forward mode on G ( y ) to compute z ( 0 ) and z ( 1 )
  4. Use reverse mode on G ( y ) to compute the derivative of h ( 1 ) with respect to y ( 0 ) and y ( 1 ) .
  5. Free all the memory corresponding to G ( y ) .
  6. Use reverse mode on F ( x ) to compute the derivative of h ( 1 ) with respect to x ( 0 ) and x ( 1 ) .
This uses the following relations: ∂ x ( 0 ) h ( 1 ) [ x ( 0 ) , x ( 1 ) ] = ∂ y ( 0 ) h ( 1 ) [ y ( 0 ) , y ( 1 ) ] ∂ x ( 0 ) y ( 0 ) [ x ( 0 ) , x ( 1 ) ] + ∂ y ( 1 ) h ( 1 ) [ y ( 0 ) , y ( 1 ) ] ∂ x ( 0 ) y ( 1 ) [ x ( 0 ) , x ( 1 ) ] ∂ x ( 1 ) h ( 1 ) [ x ( 0 ) , x ( 1 ) ] = ∂ y ( 0 ) h ( 1 ) [ y ( 0 ) , y ( 1 ) ] ∂ x ( 1 ) y ( 0 ) [ x ( 0 ) , x ( 1 ) ] + ∂ y ( 1 ) h ( 1 ) [ y ( 0 ) , y ( 1 ) ] ∂ x ( 1 ) y ( 1 ) [ x ( 0 ) , x ( 1 ) ] where ∂ x ( 0 ) denotes the partial with respect to x ( 0 ) . 

# include <cppad/cppad.hpp>

namespace {
     template <class Vector>
     Vector F(const Vector& x)
     {     Vector y(2);
          y[0] = x[0] * x[1];
          y[1] = x[1] - x[0];
          return y;
     }
     template <class Vector>
     Vector G(const Vector& y)
     {     Vector z(2);
          z[0] = y[0] - y[1];
          z[1] = y[1] * y[0];
          return z;
     }
}

namespace {
     bool reverse_any_case(bool free_all)
     {     bool ok = true;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

          using CppAD::AD;
          using CppAD::NearEqual;
          CppAD::ADFun<double> f, g, empty;

          // specify the Taylor coefficients for X(t)
          size_t n    = 2;
          CPPAD_TESTVECTOR(double) x0(n), x1(n);
          x0[0] = 1.; x0[1] = 2.;
          x1[0] = 3.; x1[1] = 4.;

          // record the function F(x)
          CPPAD_TESTVECTOR(AD<double>) X(n), Y(n);
          size_t i;
          for(i = 0; i < n; i++)
               X[i] = x0[i];
          CppAD::Independent(X);
          Y = F(X);
          f.Dependent(X, Y);

          // a fucntion object with an almost empty operation sequence
          CppAD::Independent(X);
          empty.Dependent(X, X);

          // compute the Taylor coefficients for Y(t)
          CPPAD_TESTVECTOR(double) y0(n), y1(n);
          y0 = f.Forward(0, x0);
          y1 = f.Forward(1, x1);
          if( free_all )
               f = empty;
          else
          {     // free all the Taylor coefficients stored in f
               f.capacity_order(0);
          }

          // record the function G(x)
          CPPAD_TESTVECTOR(AD<double>) Z(n);
          CppAD::Independent(Y);
          Z = G(Y);
          g.Dependent(Y, Z);

          // compute the Taylor coefficients for Z(t)
          CPPAD_TESTVECTOR(double) z0(n), z1(n);
          z0 = g.Forward(0, y0);
          z1 = g.Forward(1, y1);

          // check zero order Taylor coefficient for h^0 = z_0^0 + z_1^0
          double check = x0[0] * x0[1] * (1. - x0[0] + x0[1]) - x0[1] + x0[0];
          double h0    = z0[0] + z0[1];
          ok          &= NearEqual(h0, check, eps, eps);

          // check first order Taylor coefficient h^1
          check     = x0[0] * x0[1] * (- x1[0] + x1[1]) - x1[1] + x1[0];
          check    += x1[0] * x0[1] * (1. - x0[0] + x0[1]);
          check    += x0[0] * x1[1] * (1. - x0[0] + x0[1]);
          double h1 = z1[0] + z1[1];
          ok       &= NearEqual(h1, check, eps, eps);

          // compute the derivative with respect to y^0 and y^0 of h^1
          size_t p = 2;
          CPPAD_TESTVECTOR(double) w(n*p), dw(n*p);
          w[0*p+0] = 0.; // coefficient for z_0^0
          w[0*p+1] = 1.; // coefficient for z_0^1
          w[1*p+0] = 0.; // coefficient for z_1^0
          w[1*p+1] = 1.; // coefficient for z_1^1
          dw       = g.Reverse(p, w);

          // We are done using g, so we can free its memory.
          g = empty;
          // We need to use f next.
          if( free_all )
          {     // we must again record the operation sequence for F(x)
               CppAD::Independent(X);
               Y = F(X);
               f.Dependent(X, Y);
          }
          // now recompute the Taylor coefficients corresponding to F(x)
          // (we already know the result; i.e., y0 and y1).
          f.Forward(0, x0);
          f.Forward(1, x1);

          // compute the derivative with respect to x^0 and x^0 of
          //     h^1 = z_0^1 + z_1^1
          CPPAD_TESTVECTOR(double) dv(n*p);
          dv   = f.Reverse(p, dw);

          // check partial of h^1 w.r.t x^0_0
          check  = x0[1] * (- x1[0] + x1[1]);
          check -= x1[0] * x0[1];
          check += x1[1] * (1. - x0[0] + x0[1]) - x0[0] * x1[1];
          ok    &= NearEqual(dv[0*p+0], check, eps, eps);

          // check partial of h^1 w.r.t x^0_1
          check  = x0[0] * (- x1[0] + x1[1]);
          check += x1[0] * (1. - x0[0] + x0[1]) + x1[0] * x0[1];
          check += x0[0] * x1[1];
          ok    &= NearEqual(dv[1*p+0], check, eps, eps);

          // check partial of h^1 w.r.t x^1_0
          check  = 1. - x0[0] * x0[1];
          check += x0[1] * (1. - x0[0] + x0[1]);
          ok    &= NearEqual(dv[0*p+1], check, eps, eps);

          // check partial of h^1 w.r.t x^1_1
          check  = x0[0] * x0[1] - 1.;
          check += x0[0] * (1. - x0[0] + x0[1]);
          ok    &= NearEqual(dv[1*p+1], check, eps, eps);

          return ok;
     }
}
bool reverse_any(void)
{     bool ok = true;
     ok     &= reverse_any_case(true);
     ok     &= reverse_any_case(false);
     return ok;
}
Input File: example/reverse_checkpoint.cpp cppad-20170000.3/doc/sparse.xml0000644000175200017650000000730013057470506015215 0ustar coincoin-web Calculating Sparsity Patterns
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Calculating Sparsity Patterns

Contents
ForSparseJacJacobian Sparsity Pattern: Forward Mode
RevSparseJacJacobian Sparsity Pattern: Reverse Mode
dependency.cppComputing Dependency: Example and Test
RevSparseHesHessian Sparsity Pattern: Reverse Mode
ForSparseHesHessian Sparsity Pattern: Forward Mode
bool_sparsity.cppUsing vectorBool Sparsity To Conserve Memory: Example and Test
Input File: cppad/core/sparse.hpp cppad-20170000.3/doc/_sparse_xml.js0000644000175200017650000000363013057470506016052 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'sparse.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down0 = [ 'forsparsejac.xml', 'revsparsejac.xml', 'dependency.cpp.xml', 'revsparsehes.xml', 'forsparsehes.xml', 'bool_sparsity.cpp.xml' ]; var list_current0 = [ 'sparse.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/for_sparse_jac.cpp.xml0000644000175200017650000013236313057470506017471 0ustar coincoin-web Forward Mode Jacobian Sparsity: Example and Test
Prev Next for_sparse_jac.cpp Headings

Forward Mode Jacobian Sparsity: Example and Test

# include <set>
# include <cppad/cppad.hpp>

namespace { // -------------------------------------------------------------
// define the template function BoolCases<Vector>
template <typename Vector>  // vector class, elements of type bool
bool BoolCases(void)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) X(n);
     X[0] = 0.;
     X[1] = 1.;

     // declare independent variables and start recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y[0] = X[0];
     Y[1] = X[0] * X[1];
     Y[2] = X[1];

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // sparsity pattern for the identity matrix
     Vector r(n * n);
     size_t i, j;
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
               r[ i * n + j ] = (i == j);
     }

     // sparsity pattern for F'(x)
     Vector s(m * n);
     s = f.ForSparseJac(n, r);

     // check values
     ok &= (s[ 0 * n + 0 ] == true);  // Y[0] does     depend on X[0]
     ok &= (s[ 0 * n + 1 ] == false); // Y[0] does not depend on X[1]
     ok &= (s[ 1 * n + 0 ] == true);  // Y[1] does     depend on X[0]
     ok &= (s[ 1 * n + 1 ] == true);  // Y[1] does     depend on X[1]
     ok &= (s[ 2 * n + 0 ] == false); // Y[2] does not depend on X[0]
     ok &= (s[ 2 * n + 1 ] == true);  // Y[2] does     depend on X[1]

     // check that values are stored
     ok &= (f.size_forward_bool() > 0);
     ok &= (f.size_forward_set() == 0);

     // sparsity pattern for F'(x)^T, note R is the identity, so R^T = R
     bool transpose = true;
     Vector st(n * m);
     st = f.ForSparseJac(n, r, transpose);

     // check values
     ok &= (st[ 0 * m + 0 ] == true);  // Y[0] does     depend on X[0]
     ok &= (st[ 1 * m + 0 ] == false); // Y[0] does not depend on X[1]
     ok &= (st[ 0 * m + 1 ] == true);  // Y[1] does     depend on X[0]
     ok &= (st[ 1 * m + 1 ] == true);  // Y[1] does     depend on X[1]
     ok &= (st[ 0 * m + 2 ] == false); // Y[2] does not depend on X[0]
     ok &= (st[ 1 * m + 2 ] == true);  // Y[2] does     depend on X[1]

     // check that values are stored
     ok &= (f.size_forward_bool() > 0);
     ok &= (f.size_forward_set() == 0);

     // free values from forward calculation
     f.size_forward_bool(0);
     ok &= (f.size_forward_bool() == 0);

     return ok;
}
// define the template function SetCases<Vector>
template <typename Vector>  // vector class, elements of type std::set<size_t>
bool SetCases(void)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) X(n);
     X[0] = 0.;
     X[1] = 1.;

     // declare independent variables and start recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y[0] = X[0];
     Y[1] = X[0] * X[1];
     Y[2] = X[1];

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // sparsity pattern for the identity matrix
     Vector r(n);
     size_t i;
     for(i = 0; i < n; i++)
     {     assert( r[i].empty() );
          r[i].insert(i);
     }

     // sparsity pattern for F'(x)
     Vector s(m);
     s = f.ForSparseJac(n, r);

     // an interator to a standard set
     std::set<size_t>::iterator itr;
     bool found;

     // Y[0] does     depend on X[0]
     found = s[0].find(0) != s[0].end();  ok &= ( found == true );
     // Y[0] does not depend on X[1]
     found = s[0].find(1) != s[0].end();  ok &= ( found == false );
     // Y[1] does     depend on X[0]
     found = s[1].find(0) != s[1].end();  ok &= ( found == true );
     // Y[1] does     depend on X[1]
     found = s[1].find(1) != s[1].end();  ok &= ( found == true );
     // Y[2] does not depend on X[0]
     found = s[2].find(0) != s[2].end();  ok &= ( found == false );
     // Y[2] does     depend on X[1]
     found = s[2].find(1) != s[2].end();  ok &= ( found == true );

     // check that values are stored
     ok &= (f.size_forward_set() > 0);
     ok &= (f.size_forward_bool() == 0);


     // sparsity pattern for F'(x)^T
     bool transpose = true;
     Vector st(n);
     st = f.ForSparseJac(n, r, transpose);

     // Y[0] does     depend on X[0]
     found = st[0].find(0) != st[0].end();  ok &= ( found == true );
     // Y[0] does not depend on X[1]
     found = st[1].find(0) != st[1].end();  ok &= ( found == false );
     // Y[1] does     depend on X[0]
     found = st[0].find(1) != st[0].end();  ok &= ( found == true );
     // Y[1] does     depend on X[1]
     found = st[1].find(1) != st[1].end();  ok &= ( found == true );
     // Y[2] does not depend on X[0]
     found = st[0].find(2) != st[0].end();  ok &= ( found == false );
     // Y[2] does     depend on X[1]
     found = st[1].find(2) != st[1].end();  ok &= ( found == true );

     // check that values are stored
     ok &= (f.size_forward_set() > 0);
     ok &= (f.size_forward_bool() == 0);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool ForSparseJac(void)
{     bool ok = true;
     // Run with Vector equal to four different cases
     // all of which are Simple Vectors with elements of type bool.
     ok &= BoolCases< CppAD::vectorBool     >();
     ok &= BoolCases< CppAD::vector  <bool> >();
     ok &= BoolCases< std::vector    <bool> >();
     ok &= BoolCases< std::valarray  <bool> >();

     // Run with Vector equal to two different cases both of which are
     // Simple Vectors with elements of type std::set<size_t>
     typedef std::set<size_t> set;
     ok &= SetCases< CppAD::vector  <set> >();
     // ok &= SetCases< std::vector    <set> >();

     // Do not use valarray because its element access in the const case
     // returns a copy instead of a reference
     // ok &= SetCases< std::valarray  <set> >();

     return ok;
}
Input File: example/for_sparse_jac.cpp cppad-20170000.3/doc/revsparsejac.xml0000644000175200017650000005024413057470506016415 0ustar coincoin-web Jacobian Sparsity Pattern: Reverse Mode
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Jacobian Sparsity Pattern: Reverse Mode

Syntax
s = f.RevSparseJac(q, r)
 s = f.RevSparseJac(q, r, transpose, dependency)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . For a fixed matrix R ∈ B q × m , the Jacobian of R * F ( x ) with respect to x is S ( x ) = R * F ( 1 ) ( x ) Given a sparsity pattern for R , RevSparseJac returns a sparsity pattern for the S ( x ) .

f
The object f has prototype
     ADFun<Base> f
x
If the operation sequence in f is independent of the independent variables in x ∈ B n , the sparsity pattern is valid for all values of (even if it has CondExp or VecAD operations).

q
The argument q has prototype
     size_t q
 It specifies the number of rows in R ∈ B q × m and the Jacobian S ( x ) ∈ B q × n .

transpose
The argument transpose has prototype
     bool transpose
 The default value false is used when transpose is not present.

dependency
The argument dependency has prototype
     bool dependency
 If dependency is true, the dependency pattern (instead of sparsity pattern) is computed.

r
The argument s has prototype
     const VectorSet& r
 see VectorSet below.

transpose false
If r has elements of type bool, its size is q * m . If it has elements of type std::set<size_t>, its size is q and all its set elements are between zero and m - 1 . It specifies a sparsity pattern for the matrix R ∈ B q × m .

transpose true
If r has elements of type bool, its size is m * q . If it has elements of type std::set<size_t>, its size is m and all its set elements are between zero and q - 1 . It specifies a sparsity pattern for the matrix R T ∈ B m × q .

s
The return value s has prototype
     VectorSet s
 see VectorSet below.

transpose false
If it has elements of type bool, its size is q * n . If it has elements of type std::set<size_t>, its size is q and all its set elements are between zero and n - 1 . It specifies a sparsity pattern for the matrix S ( x ) ∈ q × n .

transpose true
If it has elements of type bool, its size is n * q . If it has elements of type std::set<size_t>, its size is n and all its set elements are between zero and q - 1 . It specifies a sparsity pattern for the matrix S ( x ) T ∈ n × q .

VectorSet
The type VectorSet must be a SimpleVector class with elements of type bool or std::set<size_t>; see sparsity pattern for a discussion of the difference.

Entire Sparsity Pattern
Suppose that q = m and R is the m × m identity matrix. In this case, the corresponding value for s is a sparsity pattern for the Jacobian S ( x ) = F ( 1 ) ( x ) .

Example
The file rev_sparse_jac.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/rev_sparse_jac.hpp cppad-20170000.3/doc/rev_sparse_jac.cpp.xml0000644000175200017650000012167113057470506017477 0ustar coincoin-web Reverse Mode Jacobian Sparsity: Example and Test
Prev Next rev_sparse_jac.cpp Headings

Reverse Mode Jacobian Sparsity: Example and Test

# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------------
// define the template function BoolCases<Vector>
template <typename Vector>  // vector class, elements of type bool
bool BoolCases(void)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;

     // declare independent variables and start recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = ax[0];
     ay[1] = ax[0] * ax[1];
     ay[2] = ax[1];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // sparsity pattern for the identity matrix
     Vector r(m * m);
     size_t i, j;
     for(i = 0; i < m; i++)
     {     for(j = 0; j < m; j++)
               r[ i * m + j ] = (i == j);
     }

     // sparsity pattern for F'(x)
     Vector s(m * n);
     s = f.RevSparseJac(m, r);

     // check values
     ok &= (s[ 0 * n + 0 ] == true);  // y[0] does     depend on x[0]
     ok &= (s[ 0 * n + 1 ] == false); // y[0] does not depend on x[1]
     ok &= (s[ 1 * n + 0 ] == true);  // y[1] does     depend on x[0]
     ok &= (s[ 1 * n + 1 ] == true);  // y[1] does     depend on x[1]
     ok &= (s[ 2 * n + 0 ] == false); // y[2] does not depend on x[0]
     ok &= (s[ 2 * n + 1 ] == true);  // y[2] does     depend on x[1]

     // sparsity pattern for F'(x)^T, note R is the identity, so R^T = R
     bool transpose = true;
     Vector st(n * m);
     st = f.RevSparseJac(m, r, transpose);

     // check values
     ok &= (st[ 0 * m + 0 ] == true);  // y[0] does     depend on x[0]
     ok &= (st[ 1 * m + 0 ] == false); // y[0] does not depend on x[1]
     ok &= (st[ 0 * m + 1 ] == true);  // y[1] does     depend on x[0]
     ok &= (st[ 1 * m + 1 ] == true);  // y[1] does     depend on x[1]
     ok &= (st[ 0 * m + 2 ] == false); // y[2] does not depend on x[0]
     ok &= (st[ 1 * m + 2 ] == true);  // y[2] does     depend on x[1]

     return ok;
}
// define the template function SetCases<Vector>
template <typename Vector>  // vector class, elements of type std::set<size_t>
bool SetCases(void)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;

     // declare independent variables and start recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = ax[0];
     ay[1] = ax[0] * ax[1];
     ay[2] = ax[1];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // sparsity pattern for the identity matrix
     Vector r(m);
     size_t i;
     for(i = 0; i < m; i++)
     {     assert( r[i].empty() );
          r[i].insert(i);
     }

     // sparsity pattern for F'(x)
     Vector s(m);
     s = f.RevSparseJac(m, r);

     // check values
     bool found;

     // y[0] does     depend on x[0]
     found = s[0].find(0) != s[0].end();  ok &= (found == true);
     // y[0] does not depend on x[1]
     found = s[0].find(1) != s[0].end();  ok &= (found == false);
     // y[1] does     depend on x[0]
     found = s[1].find(0) != s[1].end();  ok &= (found == true);
     // y[1] does     depend on x[1]
     found = s[1].find(1) != s[1].end();  ok &= (found == true);
     // y[2] does not depend on x[0]
     found = s[2].find(0) != s[2].end();  ok &= (found == false);
     // y[2] does     depend on x[1]
     found = s[2].find(1) != s[2].end();  ok &= (found == true);

     // sparsity pattern for F'(x)^T
     bool transpose = true;
     Vector st(n);
     st = f.RevSparseJac(m, r, transpose);

     // y[0] does     depend on x[0]
     found = st[0].find(0) != st[0].end();  ok &= (found == true);
     // y[0] does not depend on x[1]
     found = st[1].find(0) != st[1].end();  ok &= (found == false);
     // y[1] does     depend on x[0]
     found = st[0].find(1) != st[0].end();  ok &= (found == true);
     // y[1] does     depend on x[1]
     found = st[1].find(1) != st[1].end();  ok &= (found == true);
     // y[2] does not depend on x[0]
     found = st[0].find(2) != st[0].end();  ok &= (found == false);
     // y[2] does     depend on x[1]
     found = st[1].find(2) != st[1].end();  ok &= (found == true);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool RevSparseJac(void)
{     bool ok = true;
     // Run with Vector equal to four different cases
     // all of which are Simple Vectors with elements of type bool.
     ok &= BoolCases< CppAD::vectorBool     >();
     ok &= BoolCases< CppAD::vector  <bool> >();
     ok &= BoolCases< std::vector    <bool> >();
     ok &= BoolCases< std::valarray  <bool> >();


     // Run with Vector equal to two different cases both of which are
     // Simple Vectors with elements of type std::set<size_t>
     typedef std::set<size_t> set;
     ok &= SetCases< CppAD::vector  <set> >();
     ok &= SetCases< std::vector    <set> >();

     // Do not use valarray because its element access in the const case
     // returns a copy instead of a reference
     // ok &= SetCases< std::valarray  <set> >();

     return ok;
}
Input File: example/rev_sparse_jac.cpp cppad-20170000.3/doc/dependency.cpp.xml0000644000175200017650000006344113057470506016627 0ustar coincoin-web Computing Dependency: Example and Test
Prev Next dependency.cpp

Computing Dependency: Example and Test

Discussion
The partial of an dependent variable with respect to an independent variable might always be zero even though the dependent variable depends on the value of the dependent variable. Consider the following case f ( x ) = sign ( x ) = { + 1 if x > 0 0 if x = 0 -1 if x < 0 In this case the value of f ( x ) depends on the value of x but CppAD always returns zero for the derivative of the sign function.

Dependency Pattern
If the i-th dependent variables depends on the value of the j-th independent variable, the corresponding entry in the dependency pattern is non-zero (true). Otherwise it is zero (false). CppAD uses sparsity patterns to represent dependency matrices. The dependency argument to ForSparseJac and RevSparseJac is a flag that signals that the dependency pattern (instead of the sparsity pattern) is computed. 
# include <cppad/cppad.hpp>
namespace {
     double heavyside(const double& x)
     {     if( x <= 0.0 )
               return 0.0;
          return 1.0;
     }
     CPPAD_DISCRETE_FUNCTION(double, heavyside)
}

bool dependency(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;

     // VecAD object for use later
     CppAD::VecAD<double> vec_ad(2);
     vec_ad[0] = 0.0;
     vec_ad[1] = 1.0;

     // domain space vector
     size_t n  = 5;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     for(size_t j = 0; j < n; j++)
          ax[j] = AD<double>(j + 1);

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // some AD constants
     AD<double> azero(0.0), aone(1.0);

     // range space vector
     size_t m  = n;
     size_t m1 = n - 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[m1-0] = sign( ax[0] );
     ay[m1-1] = CondExpLe( ax[1], azero, azero, aone);
     ay[m1-2] = CondExpLe( azero, ax[2], azero, aone);
     ay[m1-3] = heavyside( ax[3] );
     ay[m1-4] = vec_ad[ ax[4] - AD<double>(4.0) ];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // -----------------------------------------------------------
     // ForSparseJac and bool dependency
     bool transpose  = false;
     bool dependency;
     // could replace CppAD::vectorBooll by CPPAD_TEST_VECTOR<bool>
     CppAD::vectorBool eye_bool(n * n), depend_bool(m * n);
     for(size_t i = 0; i < n; i++)
     {     for(size_t j = 0; j < n; j++)
               eye_bool[i * n + j] = (i == j);
     }
     dependency = true;
     depend_bool = f.ForSparseJac(n, eye_bool, transpose, dependency);
     for(size_t i = 0; i < m; i++)
     {     for(size_t j = 0; j < n; j++)
               ok &= depend_bool[i * n + j] == (i == (m1-j));
     }
     dependency = false;
     depend_bool = f.ForSparseJac(n, eye_bool, transpose, dependency);
     for(size_t i = 0; i < m; i++)
     {     for(size_t j = 0; j < n; j++)
               ok &= depend_bool[i * n + j] == false;
     }

     // -----------------------------------------------------------
     // RevSparseJac and set dependency
     CppAD::vector<    std::set<size_t> > eye_set(m), depend_set(m);
     for(size_t i = 0; i < m; i++)
     {     ok &= eye_set[i].empty();
          eye_set[i].insert(i);
     }
     dependency = true;
     depend_set = f.RevSparseJac(n, eye_set, transpose, dependency);
     for(size_t i = 0; i < m; i++)
     {     std::set<size_t> check;
          check.insert(m1 - i);
          ok &= depend_set[i] == check;
     }
     dependency = false;
     depend_set = f.RevSparseJac(n, eye_set, transpose, dependency);
     for(size_t i = 0; i < m; i++)
          ok &= depend_set[i].empty();
     return ok;
}
Input File: example/dependency.cpp cppad-20170000.3/doc/revsparsehes.xml0000644000175200017650000006056013057470506016441 0ustar coincoin-web Hessian Sparsity Pattern: Reverse Mode
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Hessian Sparsity Pattern: Reverse Mode

Syntax
h = f.RevSparseHes(q, s)
 h = f.RevSparseHes(q, s, transpose)

Purpose
We use F : R n → R m to denote the AD function corresponding to f . For a fixed matrix R ∈ R n × q and a fixed vector S ∈ R 1 × m , we define H ( x ) = ∂ x [∂ u S * F [ x + R * u ] ] u = 0 = R T * ( S * F ) ( 2 ) ( x ) H ( x ) T = ( S * F ) ( 2 ) ( x ) * R Given a sparsity pattern for the matrix R and the vector S , RevSparseHes returns a sparsity pattern for the H ( x ) .

f
The object f has prototype
     const ADFun<Base> f
x
If the operation sequence in f is independent of the independent variables in x ∈ B n , the sparsity pattern is valid for all values of (even if it has CondExp or VecAD operations).

q
The argument q has prototype
     size_t q
 It specifies the number of columns in R ∈ R n × q and the number of rows in H ( x ) ∈ R q × n . It must be the same value as in the previous ForSparseJac call
     f.ForSparseJac(q, r, r_transpose)
 Note that if r_transpose is true, r in the call above corresponding to R T ∈ R q × n

transpose
The argument transpose has prototype
     bool transpose
 The default value false is used when transpose is not present.

r
The matrix R is specified by the previous call
     f.ForSparseJac(q, r, transpose)
 see r . The type of the elements of VectorSet must be the same as the type of the elements of r .

s
The argument s has prototype
     const VectorSet& s
 (see VectorSet below) If it has elements of type bool, its size is m . If it has elements of type std::set<size_t>, its size is one and all the elements of s[0] are between zero and m - 1 . It specifies a sparsity pattern for the vector S .

h
The result h has prototype
     VectorSet& h
 (see VectorSet below).

transpose false
If h has elements of type bool, its size is q * n . If it has elements of type std::set<size_t>, its size is q and all the set elements are between zero and n-1 inclusive. It specifies a sparsity pattern for the matrix H ( x ) .

transpose true
If h has elements of type bool, its size is n * q . If it has elements of type std::set<size_t>, its size is n and all the set elements are between zero and q-1 inclusive. It specifies a sparsity pattern for the matrix H ( x ) T .

VectorSet
The type VectorSet must be a SimpleVector class with elements of type bool or std::set<size_t>; see sparsity pattern for a discussion of the difference. The type of the elements of VectorSet must be the same as the type of the elements of r .

Entire Sparsity Pattern
Suppose that q = n and R ∈ R n × n is the n × n identity matrix. Further suppose that the S is the k-th elementary vector ; i.e. S j = { 1 if j = k 0 otherwise In this case, the corresponding value h is a sparsity pattern for the Hessian matrix F k ( 2 ) ( x ) ∈ R n × n .

Example
The file rev_sparse_hes.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise. The file sparsity_sub.cpp contains an example and test of using RevSparseHes to compute the sparsity pattern for a subset of the Hessian.
Input File: cppad/core/rev_sparse_hes.hpp cppad-20170000.3/doc/rev_sparse_hes.cpp.xml0000644000175200017650000012061213057470506017513 0ustar coincoin-web Reverse Mode Hessian Sparsity: Example and Test
Prev Next rev_sparse_hes.cpp Headings

Reverse Mode Hessian Sparsity: Example and Test

# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------------

// expected sparsity pattern
bool check_f0[] = {
     false, false, false,  // partials w.r.t x0 and (x0, x1, x2)
     false, false, false,  // partials w.r.t x1 and (x0, x1, x2)
     false, false, true    // partials w.r.t x2 and (x0, x1, x2)
};
bool check_f1[] = {
     false,  true, false,  // partials w.r.t x0 and (x0, x1, x2)
     true,  false, false,  // partials w.r.t x1 and (x0, x1, x2)
     false, false, false   // partials w.r.t x2 and (x0, x1, x2)
};

// define the template function BoolCases<Vector> in empty namespace
template <typename Vector> // vector class, elements of type bool
bool BoolCases(void)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 3;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;
     ax[2] = 2.;

     // declare independent variables and start recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = sin( ax[2] );
     ay[1] = ax[0] * ax[1];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // sparsity pattern for the identity matrix
     Vector r(n * n);
     size_t i, j;
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
               r[ i * n + j ] = (i == j);
     }

     // compute sparsity pattern for J(x) = F^{(1)} (x)
     f.ForSparseJac(n, r);

     // compute sparsity pattern for H(x) = F_0^{(2)} (x)
     Vector s(m);
     for(i = 0; i < m; i++)
          s[i] = false;
     s[0] = true;
     Vector h(n * n);
     h    = f.RevSparseHes(n, s);

     // check values
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               ok &= (h[ i * n + j ] == check_f0[ i * n + j ] );

     // compute sparsity pattern for H(x) = F_1^{(2)} (x)
     for(i = 0; i < m; i++)
          s[i] = false;
     s[1] = true;
     h    = f.RevSparseHes(n, s);

     // check values
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               ok &= (h[ i * n + j ] == check_f1[ i * n + j ] );

     // call that transposed the result
     bool transpose = true;
     h    = f.RevSparseHes(n, s, transpose);

     // This h is symmetric, because R is symmetric, not really testing here
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               ok &= (h[ j * n + i ] == check_f1[ i * n + j ] );

     return ok;
}
// define the template function SetCases<Vector> in empty namespace
template <typename Vector> // vector class, elements of type std::set<size_t>
bool SetCases(void)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 3;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;
     ax[2] = 2.;

     // declare independent variables and start recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = sin( ax[2] );
     ay[1] = ax[0] * ax[1];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // sparsity pattern for the identity matrix
     Vector r(n);
     size_t i;
     for(i = 0; i < n; i++)
     {     assert( r[i].empty() );
          r[i].insert(i);
     }

     // compute sparsity pattern for J(x) = F^{(1)} (x)
     f.ForSparseJac(n, r);

     // compute sparsity pattern for H(x) = F_0^{(2)} (x)
     Vector s(1);
     assert( s[0].empty() );
     s[0].insert(0);
     Vector h(n);
     h    = f.RevSparseHes(n, s);

     // check values
     std::set<size_t>::iterator itr;
     size_t j;
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     bool found = h[i].find(j) != h[i].end();
               ok        &= (found == check_f0[i * n + j]);
          }
     }

     // compute sparsity pattern for H(x) = F_1^{(2)} (x)
     s[0].clear();
     assert( s[0].empty() );
     s[0].insert(1);
     h    = f.RevSparseHes(n, s);

     // check values
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     bool found = h[i].find(j) != h[i].end();
               ok        &= (found == check_f1[i * n + j]);
          }
     }

     // call that transposed the result
     bool transpose = true;
     h    = f.RevSparseHes(n, s, transpose);

     // This h is symmetric, because R is symmetric, not really testing here
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     bool found = h[j].find(i) != h[j].end();
               ok        &= (found == check_f1[i * n + j]);
          }
     }

     return ok;
}
} // End empty namespace

# include <vector>
# include <valarray>
bool rev_sparse_hes(void)
{     bool ok = true;
     // Run with Vector equal to four different cases
     // all of which are Simple Vectors with elements of type bool.
     ok &= BoolCases< CppAD::vector  <bool> >();
     ok &= BoolCases< CppAD::vectorBool     >();
     ok &= BoolCases< std::vector    <bool> >();
     ok &= BoolCases< std::valarray  <bool> >();

     // Run with Vector equal to two different cases both of which are
     // Simple Vectors with elements of type std::set<size_t>
     typedef std::set<size_t> set;
     ok &= SetCases< CppAD::vector  <set> >();
     ok &= SetCases< std::vector    <set> >();

     // Do not use valarray because its element access in the const case
     // returns a copy instead of a reference
     // ok &= SetCases< std::valarray  <set> >();

     return ok;
}
Input File: example/rev_sparse_hes.cpp cppad-20170000.3/doc/sparsity_sub.cpp.xml0000644000175200017650000004343413057470506017240 0ustar coincoin-web Sparsity Patterns For a Subset of Variables: Example and Test
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Sparsity Patterns For a Subset of Variables: Example and Test

See Also
sparse_sub_hes.cpp , sub_sparse_hes.cpp .

ForSparseJac
The routine ForSparseJac is used to compute the sparsity for both the full Jacobian (see s ) and a subset of the Jacobian (see s2 ).

RevSparseHes
The routine RevSparseHes is used to compute both sparsity for both the full Hessian (see h ) and a subset of the Hessian (see h2 ). 
# include <cppad/cppad.hpp>

bool sparsity_sub(void)
{     // C++ source code
     bool ok = true;
     //
     using std::cout;
     using CppAD::vector;
     using CppAD::AD;
     using CppAD::vectorBool;

     size_t n = 4;
     size_t m = n-1;
     vector< AD<double> > ax(n), ay(m);
     for(size_t j = 0; j < n; j++)
          ax[j] = double(j+1);
     CppAD::Independent(ax);
     for(size_t i = 0; i < m; i++)
          ay[i] = (ax[i+1] - ax[i]) * (ax[i+1] - ax[i]);
     CppAD::ADFun<double> f(ax, ay);

     // Evaluate the full Jacobian sparsity pattern for f
     vectorBool r(n * n), s(m * n);
     for(size_t j = 0 ; j < n; j++)
     {     for(size_t i = 0; i < n; i++)
               r[i * n + j] = (i == j);
     }
     s = f.ForSparseJac(n, r);

     // evaluate the sparsity for the Hessian of f_0 + ... + f_{m-1}
     vectorBool t(m), h(n * n);
     for(size_t i = 0; i < m; i++)
          t[i] = true;
     h = f.RevSparseHes(n, t);

     // evaluate the Jacobian sparsity pattern for first n/2 components of x
     size_t n2 = n / 2;
     vectorBool r2(n * n2), s2(m * n2);
     for(size_t j = 0 ; j < n2; j++)
     {     for(size_t i = 0; i < n; i++)
               r2[i * n2 + j] = (i == j);
     }
     s2 = f.ForSparseJac(n2, r2);

     // evaluate the sparsity for the subset of Hessian of
     // f_0 + ... + f_{m-1} where first partial has only first n/2 components
     vectorBool h2(n2 * n);
     h2 = f.RevSparseHes(n2, t);

     // check sparsity pattern for Jacobian
     for(size_t i = 0; i < m; i++)
     {     for(size_t j = 0; j < n2; j++)
               ok &= s2[i * n2 + j] == s[i * n + j];
     }

     // check sparsity pattern for Hessian
     for(size_t i = 0; i < n2; i++)
     {     for(size_t j = 0; j < n; j++)
               ok &= h2[i * n + j] == h[i * n + j];
     }
     return ok;
}
Input File: example/sparsity_sub.cpp cppad-20170000.3/doc/forsparsehes.xml0000644000175200017650000004034213057470506016427 0ustar coincoin-web Hessian Sparsity Pattern: Forward Mode
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Hessian Sparsity Pattern: Forward Mode

Syntax
h = f.ForSparseHes(r, s)
Purpose
We use F : R n → R m to denote the AD function corresponding to f . we define H ( x ) = ∂ x [∂ u S · F [ x + R · u ] ] u = 0 = R T · ( S · F ) ( 2 ) ( x ) · R Where R ∈ R n × n is a diagonal matrix and S ∈ R 1 × m is a row vector. Given a sparsity pattern for the diagonal of R and the vector S , ForSparseHes returns a sparsity pattern for the H ( x ) .

f
The object f has prototype
     const ADFun<Base> f
x
If the operation sequence in f is independent of the independent variables in x ∈ B n , the sparsity pattern is valid for all values of (even if it has CondExp or VecAD operations).

r
The argument r has prototype
     const VectorSet& r
 (see VectorSet below) If it has elements of type bool, its size is n . If it has elements of type std::set<size_t>, its size is one and all the elements of s[0] are between zero and n - 1 . It specifies a sparsity pattern for the diagonal of R . The fewer non-zero elements in this sparsity pattern, the faster the calculation should be and the more sparse H ( x ) should be.

s
The argument s has prototype
     const VectorSet& s
 (see VectorSet below) If it has elements of type bool, its size is m . If it has elements of type std::set<size_t>, its size is one and all the elements of s[0] are between zero and m - 1 . It specifies a sparsity pattern for the vector S . The fewer non-zero elements in this sparsity pattern, the faster the calculation should be and the more sparse H ( x ) should be.

h
The result h has prototype
     VectorSet& h
 (see VectorSet below). If h has elements of type bool, its size is n * n . If it has elements of type std::set<size_t>, its size is n and all the set elements are between zero and n-1 inclusive. It specifies a sparsity pattern for the matrix H ( x ) .

VectorSet
The type VectorSet must be a SimpleVector class with elements of type bool or std::set<size_t>; see sparsity pattern for a discussion of the difference. The type of the elements of VectorSet must be the same as the type of the elements of r .

Algorithm
See Algorithm II in Computing sparse Hessians with automatic differentiation by Andrea Walther. Note that s provides the information so that 'dead ends' are not included in the sparsity pattern.

Example
The file for_sparse_hes.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/for_sparse_hes.hpp cppad-20170000.3/doc/for_sparse_hes.cpp.xml0000644000175200017650000011057413057470506017513 0ustar coincoin-web Forward Mode Hessian Sparsity: Example and Test
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Forward Mode Hessian Sparsity: Example and Test

# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------------

// expected sparsity pattern
bool check_f0[] = {
     false, false, false,  // partials w.r.t x0 and (x0, x1, x2)
     false, false, false,  // partials w.r.t x1 and (x0, x1, x2)
     false, false, true    // partials w.r.t x2 and (x0, x1, x2)
};
bool check_f1[] = {
     false,  true, false,  // partials w.r.t x0 and (x0, x1, x2)
     true,  false, false,  // partials w.r.t x1 and (x0, x1, x2)
     false, false, false   // partials w.r.t x2 and (x0, x1, x2)
};

// define the template function BoolCases<Vector> in empty namespace
template <typename Vector> // vector class, elements of type bool
bool BoolCases(bool optimize)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 3;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;
     ax[2] = 2.;

     // declare independent variables and start recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = sin( ax[2] ) + ax[0] + ax[1] + ax[2];
     ay[1] = ax[0] * ax[1];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);
     if( optimize )
          f.optimize();

     // sparsity pattern for diagonal of identity matrix
     Vector r(n);
     size_t i, j;
     for(i = 0; i < n; i++)
          r[ i ] = true;

     // compute sparsity pattern for H(x) = F_0^{(2)} (x)
     Vector s(m);
     for(i = 0; i < m; i++)
          s[i] = false;
     s[0] = true;
     Vector h(n * n);
     h    = f.ForSparseHes(r, s);

     // check values
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               ok &= (h[ i * n + j ] == check_f0[ i * n + j ] );

     // compute sparsity pattern for H(x) = F_1^{(2)} (x)
     for(i = 0; i < m; i++)
          s[i] = false;
     s[1] = true;
     h    = f.ForSparseHes(r, s);

     // check values
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               ok &= (h[ i * n + j ] == check_f1[ i * n + j ] );

     return ok;
}
// define the template function SetCases<Vector> in empty namespace
template <typename Vector> // vector class, elements of type std::set<size_t>
bool SetCases(bool optimize)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 3;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;
     ax[2] = 2.;

     // declare independent variables and start recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 2;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = sin( ax[2] );
     ay[1] = ax[0] * ax[1];

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);
     if( optimize )
          f.optimize();

     // sparsity pattern for the diagonal of the identity matrix
     Vector r(1);
     size_t i;
     for(i = 0; i < n; i++)
          r[0].insert(i);

     // compute sparsity pattern for H(x) = F_0^{(2)} (x)
     Vector s(1);
     assert( s[0].empty() );
     s[0].insert(0);
     Vector h(n);
     h    = f.ForSparseHes(r, s);

     // check values
     std::set<size_t>::iterator itr;
     size_t j;
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     bool found = h[i].find(j) != h[i].end();
               ok        &= (found == check_f0[i * n + j]);
          }
     }

     // compute sparsity pattern for H(x) = F_1^{(2)} (x)
     s[0].clear();
     assert( s[0].empty() );
     s[0].insert(1);
     h    = f.ForSparseHes(r, s);

     // check values
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     bool found = h[i].find(j) != h[i].end();
               ok        &= (found == check_f1[i * n + j]);
          }
     }

     return ok;
}
} // End empty namespace

# include <vector>
# include <valarray>
bool for_sparse_hes(void)
{     bool ok = true;
     for(size_t k = 0; k < 2; k++)
     {     bool optimize = bool(k);

          // Run with Vector equal to four different cases
          // all of which are Simple Vectors with elements of type bool.
          ok &= BoolCases< CppAD::vector  <bool> >(optimize);
          ok &= BoolCases< CppAD::vectorBool     >(optimize);
          ok &= BoolCases< std::vector    <bool> >(optimize);
          ok &= BoolCases< std::valarray  <bool> >(optimize);

          // Run with Vector equal to two different cases both of which are
          // Simple Vectors with elements of type std::set<size_t>
          typedef std::set<size_t> set;
          ok &= SetCases< CppAD::vector  <set> >(optimize);
          ok &= SetCases< std::vector    <set> >(optimize);

          // Do not use valarray because its element access in the const case
          // returns a copy instead of a reference
          // ok &= SetCases< std::valarray  <set> >(optimize);
     }
     return ok;
}
Input File: example/for_sparse_hes.cpp cppad-20170000.3/doc/bool_sparsity.cpp.xml0000644000175200017650000012223513057470506017377 0ustar coincoin-web Using vectorBool Sparsity To Conserve Memory: Example and Test
Prev Next bool_sparsity.cpp

Using vectorBool Sparsity To Conserve Memory: Example and Test

Purpose
This example show how to conserve memory when computing sparsity patterns. 
# include <cppad/cppad.hpp>
namespace {
     using CppAD::vector;
     using std::cout;
     using CppAD::vectorBool;
     using CppAD::AD;
     using CppAD::ADFun;

     // function f(x) that we are computing sparsity patterns for
     template <class Float>
     vector<Float> fun(const vector<Float>& x)
     {     size_t n  = x.size();
          vector<Float> ret(n + 1);
          for(size_t j = 0; j < n; j++)
          {     size_t k = (j + 1) % n;
               ret[j] = x[j] * x[j] * x[k];
          }
          ret[n] = 0.0;
          return ret;
     }
     // check sparsity pattern for f(x)
     bool check_jac(const vectorBool& pattern, size_t n)
     {     bool ok = true;
          for(size_t i = 0; i < n; i++)
          {     size_t k = (i + 1) % n;
               for(size_t j = 0; j < n; j++)
               {     bool non_zero = (i == j) || (j == k);
                    ok &= pattern[ i * n + j] == non_zero;
               }
          }
          for(size_t j = 0; j < n; j++)
               ok &= pattern[ n * n + j] == false;
          return ok;
     }
     // check sparsity pattern for the Hessian of sum_i f_i(x)
     bool check_hes(const vectorBool& pattern, size_t n)
     {     bool ok = true;
          for(size_t i = 0; i < n; i++)
          {     size_t k1 = (i + 1) % n;
               size_t k2 = (n + i - 1) % n;
               for(size_t j = 0; j < n; j++)
               {     bool non_zero = (i == j) || (j == k1) || (j == k2);
                    ok &= pattern[ i * n + j] == non_zero;
               }
          }
          return ok;
     }
     // compute sparsity for Jacobian of f(x) using forward mode
     bool for_sparse_jac(ADFun<double>& f)
     {     bool ok = true;
          size_t n = f.Domain();
          size_t m = f.Range();
          //
          // number of columns of the sparsity patter to compute at a time
          size_t n_col = vectorBool::bit_per_unit();
          vectorBool pattern(m * n), s(m * n_col), r(n * n_col);
          //
          size_t n_loop = (n - 1) / n_col + 1;
          for(size_t i_loop = 0; i_loop < n_loop; i_loop++)
          {     size_t j_col = i_loop * n_col;

               for(size_t i = 0; i < n; i++)
               {     for(size_t j = 0; j < n_col; j++)
                         r[i * n_col + j] = (i == j_col + j);
               }
               s = f.ForSparseJac(n_col, r);
               for(size_t i = 0; i < m; i++)
               {     for(size_t j = 0; j < n_col; j++)
                         if( j_col + j < n )
                              pattern[ i * n + j_col + j ] = s[ i * n_col + j];
               }
          }
          ok &= check_jac(pattern, n);
          //
          return ok;
     }
     // compute sparsity for Jacobian of f(x) using reverse mode
     bool rev_sparse_jac(ADFun<double>& f)
     {     bool ok = true;
          size_t n = f.Domain();
          size_t m = f.Range();
          //
          // number of rows of the sparsity patter to compute at a time
          size_t n_row = vectorBool::bit_per_unit();
          vectorBool pattern(m * n), s(n_row * n), r(n_row * m);
          //
          size_t n_loop = (m - 1) / n_row + 1;
          for(size_t i_loop = 0; i_loop < n_loop; i_loop++)
          {     size_t i_row = i_loop * n_row;

               for(size_t i = 0; i < n_row; i++)
               {     for(size_t j = 0; j < m; j++)
                         r[i * m + j] = (i_row + i == j);
               }
               s = f.RevSparseJac(n_row, r);
               for(size_t i = 0; i < n_row; i++)
               {     for(size_t j = 0; j < n; j++)
                         if( i_row + i < m )
                              pattern[ (i_row + i) * n + j ] = s[ i * n + j];
               }
          }
          ok &= check_jac(pattern, n);
          //
          return ok;
     }
     // compute sparsity for Hessian of sum_i f_i (x)
     bool rev_sparse_hes(ADFun<double>& f)
     {     bool ok = true;
          size_t n = f.Domain();
          size_t m = f.Range();
          //
          // number of columns of the sparsity patter to compute at a time
          size_t n_col = vectorBool::bit_per_unit();
          vectorBool pattern(n * n), r(n * n_col), h(n * n_col);

          // consider case where Hessian for sum of f_i(x) w.r.t i
          vectorBool s(m);
          for(size_t i = 0; i < m; i++)
               s[i] = true;
          //
          size_t n_loop = (n - 1) / n_col + 1;
          for(size_t i_loop = 0; i_loop < n_loop; i_loop++)
          {     size_t j_col = i_loop * n_col;

               for(size_t i = 0; i < n; i++)
               {     for(size_t j = 0; j < n_col; j++)
                         r[i * n_col + j] = (i == j_col + j);
               }
               //
               f.ForSparseJac(n_col, r);
               bool transpose = true;
               h = f.RevSparseHes(n_col, s, transpose);
               //
               for(size_t i = 0; i < n; i++)
               {     for(size_t j = 0; j < n_col; j++)
                         if( j_col + j < n )
                              pattern[ i * n + j_col + j ] = h[ i * n_col + j];
               }
          }
          ok &= check_hes(pattern, n);
          //
          return ok;
     }
}
// driver for all of the cases above
bool bool_sparsity(void)
{     bool ok = true;
     //
     // record the funcion
     size_t n = 100;
     size_t m = n + 1;
     vector< AD<double> > x(n), y(m);
     for(size_t j = 0; j < n; j++)
          x[j] = AD<double>(j+1);
     CppAD::Independent(x);
     y = fun(x);
     ADFun<double> f(x, y);
     //
     // run the three example / tests
     ok &= for_sparse_jac(f);
     ok &= rev_sparse_jac(f);
     ok &= rev_sparse_hes(f);
     return ok;
}
Input File: example/bool_sparsity.cpp cppad-20170000.3/doc/drivers.xml0000644000175200017650000000732113057470506015401 0ustar coincoin-web First and Second Derivatives: Easy Drivers
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First and Second Derivatives: Easy Drivers

Contents
JacobianJacobian: Driver Routine
ForOneFirst Order Partial Derivative: Driver Routine
RevOneFirst Order Derivative: Driver Routine
HessianHessian: Easy Driver
ForTwoForward Mode Second Partial Derivative Driver
RevTwoReverse Mode Second Partial Derivative Driver
sparse_jacobianSparse Jacobian: Easy Driver
sparse_hessianSparse Hessian: Easy Driver
Input File: cppad/core/drivers.hpp cppad-20170000.3/doc/_drivers_xml.js0000644000175200017650000000326313057470506016235 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_current0 = [ 'drivers.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/jacobian.xml0000644000175200017650000002714013057470506015472 0ustar coincoin-web Jacobian: Driver Routine
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Jacobian: Driver Routine

Syntax
jac = f.Jacobian(x)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The syntax above sets jac to the Jacobian of F evaluated at x ; i.e., jac = F ( 1 ) ( x )
f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see Forward or Reverse below).

x
The argument x has prototype
     const Vector &x
 (see Vector below) and its size must be equal to n , the dimension of the domain space for f . It specifies that point at which to evaluate the Jacobian.

jac
The result jac has prototype
     Vector jac
 (see Vector below) and its size is m * n ; i.e., the product of the domain and range dimensions for f . For i = 0 , … , m - 1 and j = 0 , … , n - 1 . jac [ i * n + j ] = ∂ F i ∂ x j ( x )
Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Forward or Reverse
This will use order zero Forward mode and either order one Forward or order one Reverse to compute the Jacobian (depending on which it estimates will require less work). After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to Jacobian, the zero order Taylor coefficients correspond to f.Forward(0, x) and the other coefficients are unspecified.

Example
The routine Jacobian is both an example and test. It returns true, if it succeeds and false otherwise.
Input File: cppad/core/jacobian.hpp cppad-20170000.3/doc/forone.xml0000644000175200017650000003314613057470506015217 0ustar coincoin-web First Order Partial Derivative: Driver Routine
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First Order Partial Derivative: Driver Routine

Syntax
dy = f.ForOne(x, j)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The syntax above sets dy to the partial of F with respect to x j ; i.e., dy = ∂ F ∂ x j ( x ) = [∂ F 0 ∂ x j ( x ) , ⋯ , ∂ F m -1 ∂ x j ( x ) ]
f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see ForOne Uses Forward below).

x
The argument x has prototype
     const Vector &x
 (see Vector below) and its size must be equal to n , the dimension of the domain space for f . It specifies that point at which to evaluate the partial derivative.

j
The argument j has prototype
     size_t j
 an is less than n , domain space for f . It specifies the component of F for which we are computing the partial derivative.

dy
The result dy has prototype
     Vector dy
 (see Vector below) and its size is m , the dimension of the range space for f . The value of dy is the partial of F with respect to x j evaluated at x ; i.e., for i = 0 , … , m - 1 . dy [ i ] = ∂ F i ∂ x j ( x )
Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

ForOne Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to ForOne, the zero order Taylor coefficients correspond to f.Forward(0,x) and the other coefficients are unspecified.

Example
The routine ForOne is both an example and test. It returns true, if it succeeds and false otherwise.
Input File: cppad/core/for_one.hpp cppad-20170000.3/doc/_forone_xml.js0000644000175200017650000000404613057470506016047 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'forone.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down0 = [ 'for_one.cpp.xml' ]; var list_current0 = [ 'forone.xml#Syntax', 'forone.xml#Purpose', 'forone.xml#f', 'forone.xml#x', 'forone.xml#j', 'forone.xml#dy', 'forone.xml#Vector', 'forone.xml#ForOne Uses Forward', 'forone.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/revone.xml0000644000175200017650000003266413057470506015231 0ustar coincoin-web First Order Derivative: Driver Routine
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First Order Derivative: Driver Routine

Syntax
dw = f.RevOne(x, i)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The syntax above sets dw to the derivative of F i with respect to x ; i.e., dw = F i ( 1 ) ( x ) = [∂ F i ∂ x 0 ( x ) , ⋯ , ∂ F i ∂ x n -1 ( x ) ]
f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see RevOne Uses Forward below).

x
The argument x has prototype
     const Vector &x
 (see Vector below) and its size must be equal to n , the dimension of the domain space for f . It specifies that point at which to evaluate the derivative.

i
The index i has prototype
     size_t i
 and is less than m , the dimension of the range space for f . It specifies the component of F that we are computing the derivative of.

dw
The result dw has prototype
     Vector dw
 (see Vector below) and its size is n , the dimension of the domain space for f . The value of dw is the derivative of F i evaluated at x ; i.e., for j = 0 , … , n - 1 . dw [ j ] = ∂ F i ∂ x j ( x )
Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

RevOne Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to RevOne, the zero order Taylor coefficients correspond to f.Forward(0, x) and the other coefficients are unspecified.

Example
The routine RevOne is both an example and test. It returns true, if it succeeds and false otherwise.
Input File: cppad/core/rev_one.hpp cppad-20170000.3/doc/_revone_xml.js0000644000175200017650000000404613057470506016055 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'revone.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down0 = [ 'rev_one.cpp.xml' ]; var list_current0 = [ 'revone.xml#Syntax', 'revone.xml#Purpose', 'revone.xml#f', 'revone.xml#x', 'revone.xml#i', 'revone.xml#dw', 'revone.xml#Vector', 'revone.xml#RevOne Uses Forward', 'revone.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/hessian.xml0000644000175200017650000003737313057470506015367 0ustar coincoin-web Hessian: Easy Driver
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Hessian: Easy Driver

Syntax
hes = f.Hessian(x, w)
 hes = f.Hessian(x, l)
Purpose
We use F : B n → B m to denote the AD function corresponding to f . The syntax above sets hes to the Hessian The syntax above sets h to the Hessian hes = d 2 d x 2 ∑ i = 1 m w i F i ( x ) The routine sparse_hessian may be faster in the case where the Hessian is sparse.

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see Hessian Uses Forward below).

x
The argument x has prototype
     const Vector &x
 (see Vector below) and its size must be equal to n , the dimension of the domain space for f . It specifies that point at which to evaluate the Hessian.

l
If the argument l is present, it has prototype
     size_t l
 and is less than m , the dimension of the range space for f . It specifies the component of F for which we are evaluating the Hessian. To be specific, in the case where the argument l is present, w i = { 1 i = l 0 otherwise
w
If the argument w is present, it has prototype
     const Vector &w
 and size m . It specifies the value of w i in the expression for h .

hes
The result hes has prototype
     Vector hes
 (see Vector below) and its size is n * n . For j = 0 , … , n - 1 and ℓ = 0 , … , n - 1 hes [ j * n + ℓ ] = ∂ 2 w T F ∂ x j ∂ x ℓ ( x )
Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Hessian Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to Hessian, the zero order Taylor coefficients correspond to f.Forward(0, x) and the other coefficients are unspecified.

Example
The routines hessian.cpp and hes_lagrangian.cpp are examples and tests of Hessian. They return true, if they succeed and false otherwise.
Input File: cppad/core/hessian.hpp cppad-20170000.3/doc/_hessian_xml.js0000644000175200017650000000413513057470506016210 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'hessian.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down0 = [ 'hessian.cpp.xml', 'hes_lagrangian.cpp.xml' ]; var list_current0 = [ 'hessian.xml#Syntax', 'hessian.xml#Purpose', 'hessian.xml#f', 'hessian.xml#x', 'hessian.xml#l', 'hessian.xml#w', 'hessian.xml#hes', 'hessian.xml#Vector', 'hessian.xml#Hessian Uses Forward', 'hessian.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/hes_lagrangian.cpp.xml0000644000175200017650000012370013057470506017446 0ustar coincoin-web Hessian of Lagrangian and ADFun Default Constructor: Example and Test
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Hessian of Lagrangian and ADFun Default Constructor: Example and Test

# include <cppad/cppad.hpp>
# include <cassert>

namespace {
     CppAD::AD<double> Lagragian(
          const CppAD::vector< CppAD::AD<double> > &xyz )
     {     using CppAD::AD;
          assert( xyz.size() == 6 );

          AD<double> x0 = xyz[0];
          AD<double> x1 = xyz[1];
          AD<double> x2 = xyz[2];
          AD<double> y0 = xyz[3];
          AD<double> y1 = xyz[4];
          AD<double> z  = xyz[5];

          // compute objective function
          AD<double> f = x0 * x0;
          // compute constraint functions
          AD<double> g0 = 1. + 2.*x1 + 3.*x2;
          AD<double> g1 = log( x0 * x2 );
          // compute the Lagragian
          AD<double> L = y0 * g0 + y1 * g1 + z * f;

          return L;

     }
     CppAD::vector< CppAD::AD<double> > fg(
          const CppAD::vector< CppAD::AD<double> > &x )
     {     using CppAD::AD;
          using CppAD::vector;
          assert( x.size() == 3 );

          vector< AD<double> > fg(3);
          fg[0] = x[0] * x[0];
          fg[1] = 1. + 2. * x[1] + 3. * x[2];
          fg[2] = log( x[0] * x[2] );

          return fg;
     }
     bool CheckHessian(
     CppAD::vector<double> H ,
     double x0, double x1, double x2, double y0, double y1, double z )
     {     using CppAD::NearEqual;
          double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
          bool ok  = true;
          size_t n = 3;
          assert( H.size() == n * n );
          /*
          L   =    z*x0*x0 + y0*(1 + 2*x1 + 3*x2) + y1*log(x0*x2)

          L_0 = 2 * z * x0 + y1 / x0
          L_1 = y0 * 2
          L_2 = y0 * 3 + y1 / x2
          */
          // L_00 = 2 * z - y1 / ( x0 * x0 )
          double check = 2. * z - y1 / (x0 * x0);
          ok &= NearEqual(H[0 * n + 0], check, eps99, eps99);
          // L_01 = L_10 = 0
          ok &= NearEqual(H[0 * n + 1], 0., eps99, eps99);
          ok &= NearEqual(H[1 * n + 0], 0., eps99, eps99);
          // L_02 = L_20 = 0
          ok &= NearEqual(H[0 * n + 2], 0., eps99, eps99);
          ok &= NearEqual(H[2 * n + 0], 0., eps99, eps99);
          // L_11 = 0
          ok &= NearEqual(H[1 * n + 1], 0., eps99, eps99);
          // L_12 = L_21 = 0
          ok &= NearEqual(H[1 * n + 2], 0., eps99, eps99);
          ok &= NearEqual(H[2 * n + 1], 0., eps99, eps99);
          // L_22 = - y1 / (x2 * x2)
          check = - y1 / (x2 * x2);
          ok &= NearEqual(H[2 * n + 2], check, eps99, eps99);

          return ok;
     }
     bool UseL()
     {     using CppAD::AD;
          using CppAD::vector;

          // double values corresponding to XYZ vector
          double x0(.5), x1(1e3), x2(1), y0(2.), y1(3.), z(4.);

          // domain space vector
          size_t n = 3;
          vector< AD<double> >  XYZ(n);
          XYZ[0] = x0;
          XYZ[1] = x1;
          XYZ[2] = x2;

          // declare X as independent variable vector and start recording
          CppAD::Independent(XYZ);

          // add the Lagragian multipliers to XYZ
          // (note that this modifies the vector XYZ)
          XYZ.push_back(y0);
          XYZ.push_back(y1);
          XYZ.push_back(z);

          // range space vector
          size_t m = 1;
          vector< AD<double> >  L(m);
          L[0] = Lagragian(XYZ);

          // create K: X -> L and stop tape recording
          // We cannot use the ADFun sequence constructor because XYZ has
          // changed between the call to Independent and here.
          CppAD::ADFun<double> K;
          K.Dependent(L);

          // Operation sequence corresponding to K does depends on
          // value of y0, y1, and z. Must redo calculations above when
          // y0, y1, or z changes.

          // declare independent variable vector and Hessian
          vector<double> x(n);
          vector<double> H( n * n );

          // point at which we are computing the Hessian
          // (must redo calculations below each time x changes)
          x[0] = x0;
          x[1] = x1;
          x[2] = x2;
          H = K.Hessian(x, 0);

          // check this Hessian calculation
          return CheckHessian(H, x0, x1, x2, y0, y1, z);
     }
     bool Usefg()
     {     using CppAD::AD;
          using CppAD::vector;

          // parameters defining problem
          double x0(.5), x1(1e3), x2(1), y0(2.), y1(3.), z(4.);

          // domain space vector
          size_t n = 3;
          vector< AD<double> >  X(n);
          X[0] = x0;
          X[1] = x1;
          X[2] = x2;

          // declare X as independent variable vector and start recording
          CppAD::Independent(X);

          // range space vector
          size_t m = 3;
          vector< AD<double> >  FG(m);
          FG = fg(X);

          // create K: X -> FG and stop tape recording
          CppAD::ADFun<double> K;
          K.Dependent(FG);

          // Operation sequence corresponding to K does not depend on
          // value of x0, x1, x2, y0, y1, or z.

          // forward and reverse mode arguments and results
          vector<double> x(n);
          vector<double> H( n * n );
          vector<double>  dx(n);
          vector<double>   w(m);
          vector<double>  dw(2*n);

          // compute Hessian at this value of x
          // (must redo calculations below each time x changes)
          x[0] = x0;
          x[1] = x1;
          x[2] = x2;
          K.Forward(0, x);

          // set weights to Lagrange multiplier values
          // (must redo calculations below each time y0, y1, or z changes)
          w[0] = z;
          w[1] = y0;
          w[2] = y1;

          // initialize dx as zero
          size_t i, j;
          for(i = 0; i < n; i++)
               dx[i] = 0.;
          // loop over components of x
          for(i = 0; i < n; i++)
          {     dx[i] = 1.;             // dx is i-th elementary vector
               K.Forward(1, dx);       // partial w.r.t dx
               dw = K.Reverse(2, w);   // deritavtive of partial
               for(j = 0; j < n; j++)
                    H[ i * n + j ] = dw[ j * 2 + 1 ];
               dx[i] = 0.;             // dx is zero vector
          }

          // check this Hessian calculation
          return CheckHessian(H, x0, x1, x2, y0, y1, z);
     }
}

bool HesLagrangian(void)
{     bool ok = true;

     // UseL is simpler, but must retape every time that y of z changes
     ok     &= UseL();

     // Usefg does not need to retape unless operation sequence changes
     ok     &= Usefg();
     return ok;
}
Input File: example/hes_lagrangian.cpp cppad-20170000.3/doc/fortwo.xml0000644000175200017650000004256413057470506015253 0ustar coincoin-web Forward Mode Second Partial Derivative Driver
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Forward Mode Second Partial Derivative Driver

Syntax
ddy = f.ForTwo(x, j, k)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The syntax above sets ddy [ i * p + ℓ ] = ∂ 2 F i ∂ x j [ ℓ ] ∂ x k [ ℓ ] ( x ) for i = 0 , … , m -1 and ℓ = 0 , … , p , where p is the size of the vectors j and k .

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see ForTwo Uses Forward below).

x
The argument x has prototype
     const VectorBase &x
 (see VectorBase below) and its size must be equal to n , the dimension of the domain space for f . It specifies that point at which to evaluate the partial derivatives listed above.

j
The argument j has prototype
     const VectorSize_t &j
 (see VectorSize_t below) We use p to denote the size of the vector j . All of the indices in j must be less than n ; i.e., for ℓ = 0 , … , p -1 , j [ ℓ ] < n .

k
The argument k has prototype
     const VectorSize_t &k
 (see VectorSize_t below) and its size must be equal to p , the size of the vector j . All of the indices in k must be less than n ; i.e., for ℓ = 0 , … , p -1 , k [ ℓ ] < n .

ddy
The result ddy has prototype
     VectorBase ddy
 (see VectorBase below) and its size is m * p . It contains the requested partial derivatives; to be specific, for i = 0 , … , m - 1 and ℓ = 0 , … , p - 1 ddy [ i * p + ℓ ] = ∂ 2 F i ∂ x j [ ℓ ] ∂ x k [ ℓ ] ( x )
VectorBase
The type VectorBase must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

VectorSize_t
The type VectorSize_t must be a SimpleVector class with elements of type size_t . The routine CheckSimpleVector will generate an error message if this is not the case.

ForTwo Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to ForTwo, the zero order Taylor coefficients correspond to f.Forward(0, x) and the other coefficients are unspecified.

Examples
The routine ForTwo is both an example and test. It returns true, if it succeeds and false otherwise.
Input File: cppad/core/for_two.hpp cppad-20170000.3/doc/_fortwo_xml.js0000644000175200017650000000412713057470506016077 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'fortwo.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down0 = [ 'for_two.cpp.xml' ]; var list_current0 = [ 'fortwo.xml#Syntax', 'fortwo.xml#Purpose', 'fortwo.xml#f', 'fortwo.xml#x', 'fortwo.xml#j', 'fortwo.xml#k', 'fortwo.xml#ddy', 'fortwo.xml#VectorBase', 'fortwo.xml#VectorSize_t', 'fortwo.xml#ForTwo Uses Forward', 'fortwo.xml#Examples' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/revtwo.xml0000644000175200017650000004312413057470506015252 0ustar coincoin-web Reverse Mode Second Partial Derivative Driver
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Reverse Mode Second Partial Derivative Driver

Syntax
ddw = f.RevTwo(x, i, j)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The syntax above sets ddw [ k * p + ℓ ] = ∂ 2 F i [ ℓ ] ∂ x j [ ℓ ] ∂ x k ( x ) for k = 0 , … , n -1 and ℓ = 0 , … , p , where p is the size of the vectors i and j .

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see RevTwo Uses Forward below).

x
The argument x has prototype
     const VectorBase &x
 (see VectorBase below) and its size must be equal to n , the dimension of the domain space for f . It specifies that point at which to evaluate the partial derivatives listed above.

i
The argument i has prototype
     const VectorSize_t &i
 (see VectorSize_t below) We use p to denote the size of the vector i . All of the indices in i must be less than m , the dimension of the range space for f ; i.e., for ℓ = 0 , … , p -1 , i [ ℓ ] < m .

j
The argument j has prototype
     const VectorSize_t &j
 (see VectorSize_t below) and its size must be equal to p , the size of the vector i . All of the indices in j must be less than n ; i.e., for ℓ = 0 , … , p -1 , j [ ℓ ] < n .

ddw
The result ddw has prototype
     VectorBase ddw
 (see VectorBase below) and its size is n * p . It contains the requested partial derivatives; to be specific, for k = 0 , … , n - 1 and ℓ = 0 , … , p - 1 ddw [ k * p + ℓ ] = ∂ 2 F i [ ℓ ] ∂ x j [ ℓ ] ∂ x k ( x )
VectorBase
The type VectorBase must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

VectorSize_t
The type VectorSize_t must be a SimpleVector class with elements of type size_t . The routine CheckSimpleVector will generate an error message if this is not the case.

RevTwo Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to RevTwo, the zero order Taylor coefficients correspond to f.Forward(0, x) and the other coefficients are unspecified.

Examples
The routine RevTwo is both an example and test. It returns true, if it succeeds and false otherwise.
Input File: cppad/core/rev_two.hpp cppad-20170000.3/doc/_revtwo_xml.js0000644000175200017650000000412713057470506016105 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'revtwo.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down0 = [ 'rev_two.cpp.xml' ]; var list_current0 = [ 'revtwo.xml#Syntax', 'revtwo.xml#Purpose', 'revtwo.xml#f', 'revtwo.xml#x', 'revtwo.xml#i', 'revtwo.xml#j', 'revtwo.xml#ddw', 'revtwo.xml#VectorBase', 'revtwo.xml#VectorSize_t', 'revtwo.xml#RevTwo Uses Forward', 'revtwo.xml#Examples' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/sparse_jacobian.xml0000644000175200017650000010000513057470506017037 0ustar coincoin-web Sparse Jacobian: Easy Driver
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Sparse Jacobian: Easy Driver

Syntax
jac = f.SparseJacobian(x)
jac = f.SparseJacobian(x, p)
n_sweep = f.SparseJacobianForward(x, p, row, col, jac, work)
n_sweep = f.SparseJacobianReverse(x, p, row, col, jac, work)
Purpose
We use n for the domain size, and m for the range size of f . We use F : R n → R m do denote the AD function corresponding to f . The syntax above sets jac to the Jacobian jac = F ( 1 ) ( x ) This routine takes advantage of the sparsity of the Jacobian in order to reduce the amount of computation necessary. If row and col are present, it also takes advantage of the reduced set of elements of the Jacobian that need to be computed. One can use speed tests (e.g. speed_test ) to verify that results are computed faster than when using the routine Jacobian .

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see Uses Forward below).

x
The argument x has prototype
     const VectorBase& x
 (see VectorBase below) and its size must be equal to n , the dimension of the domain space for f . It specifies that point at which to evaluate the Jacobian.

p
The argument p is optional and has prototype
     const VectorSet& p
 (see VectorSet below). If it has elements of type bool, its size is m * n . If it has elements of type std::set<size_t>, its size is m and all its set elements are between zero and n - 1 . It specifies a sparsity pattern for the Jacobian F ( 1 ) ( x ) .

If this sparsity pattern does not change between calls to SparseJacobian , it should be faster to calculate p once (using ForSparseJac or RevSparseJac ) and then pass p to SparseJacobian . Furthermore, if you specify work in the calling sequence, it is not necessary to keep the sparsity pattern; see the heading p under the work description.

In addition, if you specify p , CppAD will use the same type of sparsity representation (vectors of bool or vectors of std::set<size_t>) for its internal calculations. Otherwise, the representation for the internal calculations is unspecified.

row, col
The arguments row and col are optional and have prototype
     const VectorSize& row
     const VectorSize& col
 (see VectorSize below). They specify which rows and columns of F ( 1 ) ( x ) are computes and in what order. Not all the non-zero entries in F ( 1 ) ( x ) need be computed, but all the entries specified by row and col must be possibly non-zero in the sparsity pattern. We use K to denote the value jac.size() which must also equal the size of row and col . Furthermore, for k = 0 , … , K -1 , it must hold that row [ k ] < m and col [ k ] < n .

jac
The result jac has prototype
     VectorBase& jac
 In the case where the arguments row and col are not present, the size of jac is m * n and for i = 0 , … , m -1 , j = 0 , … , n -1 , jac [ i * n + j ] = ∂ F i ∂ x j ( x )

In the case where the arguments row and col are present, we use K to denote the size of jac . The input value of its elements does not matter. Upon return, for k = 0 , … , K - 1 , jac [ k ] = ∂ F i ∂ x j ( x ) , where i = row [ k ] and j = col [ k ]
work
If this argument is present, it has prototype
     sparse_jacobian_work& work
 This object can only be used with the routines SparseJacobianForward and SparseJacobianReverse. During its the first use, information is stored in work . This is used to reduce the work done by future calls to the same mode (forward or reverse), the same f , p , row , and col . If a future call is for a different mode, or any of these values have changed, you must first call work.clear() to inform CppAD that this information needs to be recomputed.

color_method
The coloring algorithm determines which columns (forward mode) or rows (reverse mode) can be computed during the same sweep. This field has prototype 
 
     std::string %work%.color_method
and its default value (after a constructor or clear()) is "cppad". If colpack_prefix is specified on the cmake command line, you can set this method to "colpack". This value only matters on the first call to sparse_jacobian that follows the work constructor or a call to work.clear() .

p
If work is present, and it is not the first call after its construction or a clear, the sparsity pattern p is not used. This enables one to free the sparsity pattern and still compute corresponding sparse Jacobians.

n_sweep
The return value n_sweep has prototype
     size_t n_sweep
 If SparseJacobianForward (SparseJacobianReverse) is used, n_sweep is the number of first order forward (reverse) sweeps used to compute the requested Jacobian values. (This is also the number of colors determined by the coloring method mentioned above). This is proportional to the total work that SparseJacobian does, not counting the zero order forward sweep, or the work to combine multiple columns (rows) into a single sweep.

VectorBase
The type VectorBase must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

VectorSet
The type VectorSet must be a SimpleVector class with elements of type bool or std::set<size_t>; see sparsity pattern for a discussion of the difference. The routine CheckSimpleVector will generate an error message if this is not the case.

Restrictions
If VectorSet has elements of std::set<size_t>, then p[i] must return a reference (not a copy) to the corresponding set. According to section 26.3.2.3 of the 1998 C++ standard, std::valarray< std::set<size_t> > does not satisfy this condition.

VectorSize
The type VectorSize must be a SimpleVector class with elements of type size_t. The routine CheckSimpleVector will generate an error message if this is not the case.

Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to any of the sparse Jacobian routines, the zero order Taylor coefficients correspond to f.Forward(0, x) and the other coefficients are unspecified. After SparseJacobian, the previous calls to Forward are undefined.

Example
The routine sparse_jacobian.cpp is examples and tests of sparse_jacobian. It return true, if it succeeds and false otherwise.
Input File: cppad/core/sparse_jacobian.hpp cppad-20170000.3/doc/sparse_jacobian.cpp.xml0000644000175200017650000016324513057470506017637 0ustar coincoin-web Sparse Jacobian: Example and Test
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Sparse Jacobian: Example and Test

# include <cppad/cppad.hpp>
namespace { // ---------------------------------------------------------
bool reverse()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
     typedef CPPAD_TESTVECTOR(double)       d_vector;
     typedef CPPAD_TESTVECTOR(size_t)       i_vector;
     size_t i, j, k, ell;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 4;
     a_vector  a_x(n);
     for(j = 0; j < n; j++)
          a_x[j] = AD<double> (0);

     // declare independent variables and starting recording
     CppAD::Independent(a_x);

     size_t m = 3;
     a_vector  a_y(m);
     a_y[0] = a_x[0] + a_x[1];
     a_y[1] = a_x[2] + a_x[3];
     a_y[2] = a_x[0] + a_x[1] + a_x[2] + a_x[3] * a_x[3] / 2.;

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(a_x, a_y);

     // new value for the independent variable vector
     d_vector x(n);
     for(j = 0; j < n; j++)
          x[j] = double(j);

     // Jacobian of y without sparsity pattern
     d_vector jac(m * n);
     jac = f.SparseJacobian(x);
     /*
           [ 1 1 0 0  ]
     jac = [ 0 0 1 1  ]
           [ 1 1 1 x_3]
     */
     d_vector check(m * n);
     check[0] = 1.; check[1] = 1.; check[2]  = 0.; check[3]  = 0.;
     check[4] = 0.; check[5] = 0.; check[6]  = 1.; check[7]  = 1.;
     check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3];
     for(ell = 0; ell < size_t(check.size()); ell++)
          ok &=  NearEqual(check[ell], jac[ell], eps, eps );

     // using packed boolean sparsity patterns
     CppAD::vectorBool s_b(m * m), p_b(m * n);
     for(i = 0; i < m; i++)
     {     for(ell = 0; ell < m; ell++)
               s_b[i * m + ell] = false;
          s_b[i * m + i] = true;
     }
     p_b   = f.RevSparseJac(m, s_b);
     jac   = f.SparseJacobian(x, p_b);
     for(ell = 0; ell < size_t(check.size()); ell++)
          ok &=  NearEqual(check[ell], jac[ell], eps, eps );

     // using vector of sets sparsity patterns
     std::vector< std::set<size_t> > s_s(m),  p_s(m);
     for(i = 0; i < m; i++)
          s_s[i].insert(i);
     p_s   = f.RevSparseJac(m, s_s);
     jac   = f.SparseJacobian(x, p_s);
     for(ell = 0; ell < size_t(check.size()); ell++)
          ok &=  NearEqual(check[ell], jac[ell], eps, eps );

     // using row and column indices to compute non-zero in rows 1 and 2
     // (skip row 0).
     size_t K = 6;
     i_vector row(K), col(K);
     jac.resize(K);
     k = 0;
     for(j = 0; j < n; j++)
     {     for(i = 1; i < m; i++)
          {     ell = i * n + j;
               if( p_b[ell] )
               {     ok &= check[ell] != 0.;
                    row[k] = i;
                    col[k] = j;
                    k++;
               }
          }
     }
     ok &= k == K;

     // empty work structure
     CppAD::sparse_jacobian_work work;

     // could use p_b
     size_t n_sweep = f.SparseJacobianReverse(x, p_s, row, col, jac, work);
     for(k = 0; k < K; k++)
     {     ell = row[k] * n + col[k];
          ok &= NearEqual(check[ell], jac[k], eps, eps);
     }
     ok &= n_sweep == 2;

     // now recompute at a different x value (using work from previous call)
     check[11] = x[3] = 10.;
     std::vector< std::set<size_t> > not_used;
     n_sweep = f.SparseJacobianReverse(x, not_used, row, col, jac, work);
     for(k = 0; k < K; k++)
     {     ell = row[k] * n + col[k];
          ok &= NearEqual(check[ell], jac[k], eps, eps);
     }
     ok &= n_sweep == 2;

     return ok;
}

bool forward()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
     typedef CPPAD_TESTVECTOR(double)       d_vector;
     typedef CPPAD_TESTVECTOR(size_t)       i_vector;
     size_t i, j, k, ell;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 3;
     a_vector  a_x(n);
     for(j = 0; j < n; j++)
          a_x[j] = AD<double> (0);

     // declare independent variables and starting recording
     CppAD::Independent(a_x);

     size_t m = 4;
     a_vector  a_y(m);
     a_y[0] = a_x[0] + a_x[2];
     a_y[1] = a_x[0] + a_x[2];
     a_y[2] = a_x[1] + a_x[2];
     a_y[3] = a_x[1] + a_x[2] * a_x[2] / 2.;

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(a_x, a_y);

     // new value for the independent variable vector
     d_vector x(n);
     for(j = 0; j < n; j++)
          x[j] = double(j);

     // Jacobian of y without sparsity pattern
     d_vector jac(m * n);
     jac = f.SparseJacobian(x);
     /*
           [ 1 0 1   ]
     jac = [ 1 0 1   ]
           [ 0 1 1   ]
           [ 0 1 x_2 ]
     */
     d_vector check(m * n);
     check[0] = 1.; check[1]  = 0.; check[2]  = 1.;
     check[3] = 1.; check[4]  = 0.; check[5]  = 1.;
     check[6] = 0.; check[7]  = 1.; check[8]  = 1.;
     check[9] = 0.; check[10] = 1.; check[11] = x[2];
     for(ell = 0; ell < size_t(check.size()); ell++)
          ok &=  NearEqual(check[ell], jac[ell], eps, eps );

     // test using packed boolean vectors for sparsity pattern
     CppAD::vectorBool r_b(n * n), p_b(m * n);
     for(j = 0; j < n; j++)
     {     for(ell = 0; ell < n; ell++)
               r_b[j * n + ell] = false;
          r_b[j * n + j] = true;
     }
     p_b = f.ForSparseJac(n, r_b);
     jac = f.SparseJacobian(x, p_b);
     for(ell = 0; ell < size_t(check.size()); ell++)
          ok &=  NearEqual(check[ell], jac[ell], eps, eps );

     // test using vector of sets for sparsity pattern
     std::vector< std::set<size_t> > r_s(n), p_s(m);
     for(j = 0; j < n; j++)
          r_s[j].insert(j);
     p_s = f.ForSparseJac(n, r_s);
     jac = f.SparseJacobian(x, p_s);
     for(ell = 0; ell < size_t(check.size()); ell++)
          ok &=  NearEqual(check[ell], jac[ell], eps, eps );

     // using row and column indices to compute non-zero elements excluding
     // row 0 and column 0.
     size_t K = 5;
     i_vector row(K), col(K);
     jac.resize(K);
     k = 0;
     for(i = 1; i < m; i++)
     {     for(j = 1; j < n; j++)
          {     ell = i * n + j;
               if( p_b[ell] )
               {     ok &= check[ell] != 0.;
                    row[k] = i;
                    col[k] = j;
                    k++;
               }
          }
     }
     ok &= k == K;

     // empty work structure
     CppAD::sparse_jacobian_work work;

     // could use p_s
     size_t n_sweep = f.SparseJacobianForward(x, p_b, row, col, jac, work);
     for(k = 0; k < K; k++)
     {    ell = row[k] * n + col[k];
          ok &= NearEqual(check[ell], jac[k], eps, eps);
     }
     ok &= n_sweep == 2;

     // now recompute at a different x value (using work from previous call)
     check[11] = x[2] = 10.;
     n_sweep = f.SparseJacobianForward(x, p_s, row, col, jac, work);
     for(k = 0; k < K; k++)
     {    ell = row[k] * n + col[k];
          ok &= NearEqual(check[ell], jac[k], eps, eps);
     }
     ok &= n_sweep == 2;

     return ok;
}
} // End empty namespace

bool sparse_jacobian(void)
{     bool ok = true;
     ok &= forward();
     ok &= reverse();

     return ok;
}
Input File: example/sparse_jacobian.cpp cppad-20170000.3/doc/sparse_hessian.xml0000644000175200017650000011036013057470506016730 0ustar coincoin-web Sparse Hessian: Easy Driver
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Sparse Hessian: Easy Driver

Syntax
hes = f.SparseHessian(x, w)
hes = f.SparseHessian(x, w, p)
n_sweep = f.SparseHessian(x, w, p, row, col, hes, work)
Purpose
We use n for the domain size, and m for the range size of f . We use F : R n → R m do denote the AD function corresponding to f . The syntax above sets hes to the Hessian H ( x ) = d 2 d x 2 ∑ i = 1 m w i F i ( x ) This routine takes advantage of the sparsity of the Hessian in order to reduce the amount of computation necessary. If row and col are present, it also takes advantage of the reduced set of elements of the Hessian that need to be computed. One can use speed tests (e.g. speed_test ) to verify that results are computed faster than when using the routine Hessian .

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see Uses Forward below).

x
The argument x has prototype
     const VectorBase& x
 (see VectorBase below) and its size must be equal to n , the dimension of the domain space for f . It specifies that point at which to evaluate the Hessian.

w
The argument w has prototype
     const VectorBase& w
 and size m . It specifies the value of w i in the expression for hes . The more components of w that are identically zero, the more sparse the resulting Hessian may be (and hence the more efficient the calculation of hes may be).

p
The argument p is optional and has prototype
     const VectorSet& p
 (see VectorSet below) If it has elements of type bool, its size is n * n . If it has elements of type std::set<size_t>, its size is n and all its set elements are between zero and n - 1 . It specifies a sparsity pattern for the Hessian H ( x ) .

Purpose
If this sparsity pattern does not change between calls to SparseHessian , it should be faster to calculate p once and pass this argument to SparseHessian . If you specify p , CppAD will use the same type of sparsity representation (vectors of bool or vectors of std::set<size_t>) for its internal calculations. Otherwise, the representation for the internal calculations is unspecified.

work
If you specify work in the calling sequence, it is not necessary to keep the sparsity pattern; see the heading p under the work description.

Column Subset
If the arguments row and col are present, and color_method is cppad.general or cppad.symmetric, it is not necessary to compute the entire sparsity pattern. Only the following subset of column values will matter:
     { col[k] : k = 0 , ... , K-1 }
 .

row, col
The arguments row and col are optional and have prototype
     const VectorSize& row
     const VectorSize& col
 (see VectorSize below). They specify which rows and columns of H ( x ) are returned and in what order. We use K to denote the value hes.size() which must also equal the size of row and col . Furthermore, for k = 0 , … , K -1 , it must hold that row [ k ] < n and col [ k ] < n . In addition, all of the ( row [ k ] , col [ k ] ) pairs must correspond to a true value in the sparsity pattern p .

hes
The result hes has prototype
     VectorBase hes
 In the case where row and col are not present, the size of hes is n * n and its size is n * n . In this case, for i = 0 , … , n - 1 and ell = 0 , … , n - 1 hes [ j * n + ℓ ] = ∂ 2 w T F ∂ x j ∂ x ℓ ( x )

In the case where the arguments row and col are present, we use K to denote the size of hes . The input value of its elements does not matter. Upon return, for k = 0 , … , K - 1 , hes [ k ] = ∂ 2 w T F ∂ x j ∂ x ℓ ( x ) , where j = row [ k ] and ℓ = col [ k ]
work
If this argument is present, it has prototype
     sparse_hessian_work& work
 This object can only be used with the routines SparseHessian. During its the first use, information is stored in work . This is used to reduce the work done by future calls to SparseHessian with the same f , p , row , and col . If a future call is made where any of these values have changed, you must first call work.clear() to inform CppAD that this information needs to be recomputed.

color_method
The coloring algorithm determines which rows and columns can be computed during the same sweep. This field has prototype
     std::string work.color_method
 This value only matters on the first call to sparse_hessian that follows the work constructor or a call to work.clear() .

"cppad.symmetric"
 This is the default coloring method (after a constructor or clear()). It takes advantage of the fact that the Hessian matrix is symmetric to find a coloring that requires fewer sweeps .

"cppad.general"
 This is the same as the "cppad" method for the sparse_jacobian calculation.

"colpack.star"
 This method requires that colpack_prefix was specified on the cmake command line. It also takes advantage of the fact that the Hessian matrix is symmetric.

p
If work is present, and it is not the first call after its construction or a clear, the sparsity pattern p is not used. This enables one to free the sparsity pattern and still compute corresponding sparse Hessians.

n_sweep
The return value n_sweep has prototype
     size_t n_sweep
 It is the number of first order forward sweeps used to compute the requested Hessian values. Each first forward sweep is followed by a second order reverse sweep so it is also the number of reverse sweeps. This is proportional to the total work that SparseHessian does, not counting the zero order forward sweep, or the work to combine multiple columns into a single forward-reverse sweep pair.

VectorBase
The type VectorBase must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

VectorSet
The type VectorSet must be a SimpleVector class with elements of type bool or std::set<size_t>; see sparsity pattern for a discussion of the difference. The routine CheckSimpleVector will generate an error message if this is not the case.

Restrictions
If VectorSet has elements of std::set<size_t>, then p[i] must return a reference (not a copy) to the corresponding set. According to section 26.3.2.3 of the 1998 C++ standard, std::valarray< std::set<size_t> > does not satisfy this condition.

VectorSize
The type VectorSize must be a SimpleVector class with elements of type size_t. The routine CheckSimpleVector will generate an error message if this is not the case.

Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After a call to any of the sparse Hessian routines, the zero order Taylor coefficients correspond to f.Forward(0, x) and the other coefficients are unspecified.

Example
The routine sparse_hessian.cpp is examples and tests of sparse_hessian. It return true, if it succeeds and false otherwise.

Subset Hessian
The routines sub_sparse_hes.cpp and sparse_sub_hes.cpp are examples and tests that compute a sparse Hessian for a subset of the variables. They return true, if they succeed and false otherwise.
Input File: cppad/core/sparse_hessian.hpp cppad-20170000.3/doc/sparse_hessian.cpp.xml0000644000175200017650000010235313057470506017514 0ustar coincoin-web Sparse Hessian: Example and Test
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Sparse Hessian: Example and Test
# include <cppad/cppad.hpp>
bool sparse_hessian(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     size_t i, j, k, ell;
     typedef CPPAD_TESTVECTOR(AD<double>)               a_vector;
     typedef CPPAD_TESTVECTOR(double)                     d_vector;
     typedef CPPAD_TESTVECTOR(size_t)                     i_vector;
     typedef CPPAD_TESTVECTOR(bool)                       b_vector;
     typedef CPPAD_TESTVECTOR(std::set<size_t>)         s_vector;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 12;  // must be greater than or equal 3; see n_sweep below
     a_vector a_x(n);
     for(j = 0; j < n; j++)
          a_x[j] = AD<double> (0);

     // declare independent variables and starting recording
     CppAD::Independent(a_x);

     // range space vector
     size_t m = 1;
     a_vector a_y(m);
     a_y[0] = a_x[0]*a_x[1];
     for(j = 0; j < n; j++)
          a_y[0] += a_x[j] * a_x[j] * a_x[j];

     // create f: x -> y and stop tape recording
     // (without executing zero order forward calculation)
     CppAD::ADFun<double> f;
     f.Dependent(a_x, a_y);

     // new value for the independent variable vector, and weighting vector
     d_vector w(m), x(n);
     for(j = 0; j < n; j++)
          x[j] = double(j);
     w[0] = 1.0;

     // vector used to check the value of the hessian
     d_vector check(n * n);
     for(ell = 0; ell < n * n; ell++)
          check[ell] = 0.0;
     ell        = 0 * n + 1;
     check[ell] = 1.0;
     ell        = 1 * n + 0;
     check[ell] = 1.0 ;
     for(j = 0; j < n; j++)
     {     ell = j * n + j;
          check[ell] = 6.0 * x[j];
     }

     // -------------------------------------------------------------------
     // second derivative of y[0] w.r.t x
     d_vector hes(n * n);
     hes = f.SparseHessian(x, w);
     for(ell = 0; ell < n * n; ell++)
          ok &=  NearEqual(w[0] * check[ell], hes[ell], eps, eps );

     // --------------------------------------------------------------------
     // example using vectors of bools to compute sparsity pattern for Hessian
     b_vector r_bool(n * n);
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
               r_bool[i * n + j] = false;
          r_bool[i * n + i] = true;
     }
     f.ForSparseJac(n, r_bool);
     //
     b_vector s_bool(m);
     for(i = 0; i < m; i++)
          s_bool[i] = w[i] != 0;
     b_vector p_bool = f.RevSparseHes(n, s_bool);

     hes = f.SparseHessian(x, w, p_bool);
     for(ell = 0; ell < n * n; ell++)
          ok &=  NearEqual(w[0] * check[ell], hes[ell], eps, eps );

     // --------------------------------------------------------------------
     // example using vectors of sets to compute sparsity pattern for Hessian
     s_vector r_set(n);
     for(i = 0; i < n; i++)
          r_set[i].insert(i);
     f.ForSparseJac(n, r_set);
     //
     s_vector s_set(m);
     for(i = 0; i < m; i++)
          if( w[i] != 0. )
               s_set[0].insert(i);
     s_vector p_set = f.RevSparseHes(n, s_set);

     // example passing sparsity pattern to SparseHessian
     hes = f.SparseHessian(x, w, p_set);
     for(ell = 0; ell < n * n; ell++)
          ok &=  NearEqual(w[0] * check[ell], hes[ell], eps, eps );

     // --------------------------------------------------------------------
     // use row and column indices to specify upper triangle of
     // non-zero elements of Hessian
     size_t K = n + 1;
     i_vector row(K), col(K);
     hes.resize(K);
     k = 0;
     for(j = 0; j < n; j++)
     {     // diagonal of Hessian
          row[k] = j;
          col[k] = j;
          k++;
     }
     // only off diagonal non-zero elemenet in upper triangle
     row[k] = 0;
     col[k] = 1;
     k++;
     ok &= k == K;
     CppAD::sparse_hessian_work work;

     // can use p_set or p_bool.
     size_t n_sweep = f.SparseHessian(x, w, p_set, row, col, hes, work);
     for(k = 0; k < K; k++)
     {     ell = row[k] * n + col[k];
          ok &=  NearEqual(w[0] * check[ell], hes[k], eps, eps );
     }
     ok &= n_sweep == 2;

     // now recompute at a different x and w (using work from previous call
     w[0]       = 2.0;
     x[1]       = 0.5;
     ell        = 1 * n + 1;
     check[ell] = 6.0 * x[1];
     s_vector   not_used;
     n_sweep    = f.SparseHessian(x, w, not_used, row, col, hes, work);
     for(k = 0; k < K; k++)
     {     ell = row[k] * n + col[k];
          ok &=  NearEqual(w[0] * check[ell], hes[k], eps, eps );
     }
     ok &= n_sweep == 2;



     return ok;
}
Input File: example/sparse_hessian.cpp cppad-20170000.3/doc/sub_sparse_hes.cpp.xml0000644000175200017650000007113113057470506017511 0ustar coincoin-web Computing Sparse Hessian for a Subset of Variables
Prev Next sub_sparse_hes.cpp

Computing Sparse Hessian for a Subset of Variables

Purpose
This example uses multiple levels of AD to compute the Hessian for a subset of the variables without having to compute the sparsity pattern for the entire function.

See Also
sparse_sub_hes.cpp , sparsity_sub.cpp ,

Function
We consider the function f : R nu × R nv → R defined by f ( u , v ) = (∑ j = 0 nu -1 u j 3 ) (∑ j = 0 nv -1 v j )
Subset
Suppose that we are only interested computing the function H ( u , v ) = ∂ u ∂ u f ( u , v ) where this Hessian is sparse.

Example
The following code shows one way to compute this subset of the Hessian of f . 
# include <cppad/cppad.hpp>

namespace {
     using CppAD::vector;
     template <class Scalar>
     Scalar f(const vector<Scalar>& u,const vector<Scalar>& v)
     {     size_t i;
          Scalar sum_v = Scalar(0);
          for(i = 0; i < v.size(); i++)
               sum_v += v[i];
          Scalar sum_cube_u = Scalar(0);
          for(i = 0; i < u.size(); i++)
               sum_cube_u += u[i] * u[i] * u[i] / 6.0;
          return sum_v * sum_cube_u;
     }
}

bool sub_sparse_hes(void)
{     bool ok = true;
     using CppAD::AD;
     typedef AD<double>   adouble;
     typedef AD<adouble> a2double;
     typedef vector< std::set<size_t> > pattern;
     double eps = 10. * std::numeric_limits<double>::epsilon();
     size_t i, j;

     // start recording with x = (u , v)
     size_t nu = 10;
     size_t nv = 5;
     size_t n  = nu + nv;
     vector<adouble> ax(n);
     for(j = 0; j < n; j++)
          ax[j] = adouble(j + 2);
     CppAD::Independent(ax);

     // extract u as independent variables
     vector<a2double> a2u(nu);
     for(j = 0; j < nu; j++)
          a2u[j] = a2double(j + 2);
     CppAD::Independent(a2u);

     // extract v as parameters
     vector<a2double> a2v(nv);
     for(j = 0; j < nv; j++)
          a2v[j] = ax[nu+j];

     // record g(u)
     vector<a2double> a2y(1);
     a2y[0] = f(a2u, a2v);
     CppAD::ADFun<adouble> g;
     g.Dependent(a2u, a2y);

     // compue sparsity pattern for Hessian of g(u)
     pattern r(nu), s(1);
     for(j = 0; j < nu; j++)
          r[j].insert(j);
     g.ForSparseJac(nu, r);
     s[0].insert(0);
     pattern p = g.RevSparseHes(nu, s);

     // Row and column indices for non-zeros in lower triangle of Hessian
     vector<size_t> row, col;
     for(i = 0; i < nu; i++)
     {     std::set<size_t>::const_iterator itr;
          for(itr = p[i].begin(); itr != p[i].end(); itr++)
          {     j = *itr;
               if( j <= i )
               {     row.push_back(i);
                    col.push_back(j);
               }
          }
     }
     size_t K = row.size();
     CppAD::sparse_hessian_work work;
     vector<adouble> au(nu), ahes(K), aw(1);
     aw[0] = 1.0;
     for(j = 0; j < nu; j++)
          au[j] = ax[j];
     size_t n_sweep = g.SparseHessian(au, aw, p, row, col, ahes, work);

     // The Hessian w.r.t u is diagonal
     ok &= n_sweep == 1;

     // record H(u, v) = Hessian of f w.r.t u
     CppAD::ADFun<double> H(ax, ahes);

     // remove unecessary operations
     H.optimize();

     // Now evaluate the Hessian at a particular value for u, v
     vector<double> u(nu), v(nv), x(n);
     for(j = 0; j < n; j++)
          x[j] = double(j + 2);
     vector<double> hes = H.Forward(0, x);

     // Now check the Hessian
     double sum_v = 0.0;
     for(j = 0; j < nv; j++)
          sum_v += x[nu + j];
     for(size_t k = 0; k < K; k++)
     {     i     = row[k];
          j     = col[k];
          ok   &= i == j;
          double check = sum_v * x[i];
          ok &= CppAD::NearEqual(hes[k], check, eps, eps);
     }
     return ok;
}
Input File: example/sub_sparse_hes.cpp cppad-20170000.3/doc/sparse_sub_hes.cpp.xml0000644000175200017650000011665413057470506017523 0ustar coincoin-web Sparse Hessian on Subset of Variables: Example and Test
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Sparse Hessian on Subset of Variables: Example and Test

Purpose
This example uses a column subset of the sparsity pattern to compute the Hessian for a subset of the variables. The values in the rest of the sparsity pattern do not matter.

See Also
sub_sparse_hes.cpp 
# include <cppad/cppad.hpp>
namespace { // BEGIN_EMPTY_NAMESPACE

// --------------------------------------------------------------------------
CppAD::ADFun<double> record_function(size_t n)
{     // must be greater than or equal 3; see n_sweep below
     assert( n >= 3 );
     //
     using CppAD::AD;
     typedef CppAD::vector< AD<double> >     a_vector;
     //
     // domain space vector
     a_vector a_x(n);
     for(size_t j = 0; j < n; j++)
          a_x[j] = AD<double> (0);

     // declare independent variables and starting recording
     CppAD::Independent(a_x);

     // range space vector
     size_t m = 1;
     a_vector a_y(m);
     a_y[0] = 0.0;
     for(size_t j = 1; j < n; j++)
          a_y[0] += a_x[j-1] * a_x[j] * a_x[j];

     // create f: x -> y and stop tape recording
     // (without executing zero order forward calculation)
     CppAD::ADFun<double> f;
     f.Dependent(a_x, a_y);
     //
     return f;
}
// --------------------------------------------------------------------------
bool test_set(const char* color_method)
{     bool ok = true;
     //
     typedef CppAD::vector< double >                   d_vector;
     typedef CppAD::vector<size_t>                     i_vector;
     typedef CppAD::vector< std::set<size_t> >         s_vector;
     //
     size_t n = 12;
     CppAD::ADFun<double> f = record_function(n);
     //
     // sparsity patteren for the sub-set of variables we are computing
     // the hessian w.r.t.
     size_t n_sub = 4;
     s_vector r(n);
     for(size_t j = 0; j < n_sub; j++)
     {     assert(  r[j].empty() );
          r[j].insert(j);
     }

     // store forward sparsity for J(x) = F^{(1)} (x) * R
     f.ForSparseJac(n_sub, r);

     // compute sparsity pattern for H(x) = (S * F)^{(2)} ( x ) * R
     s_vector s(1);
     assert(  s[0].empty() );
     s[0].insert(0);
     bool transpose = true;
     s_vector h = f.RevSparseHes(n_sub, s, transpose);

     // set the row and column indices that correspond to lower triangle
     i_vector row, col;
     for(size_t i = 0; i < n_sub; i++)
     {     if( i > 0 )
          {     // diagonal element
               row.push_back(i);
               col.push_back(i);
               // lower diagonal element
               row.push_back(i);
               col.push_back(i-1);
          }
     }

     // weighting for the Hessian
     d_vector w(1);
     w[0] = 1.0;

     // compute Hessian
     CppAD::sparse_hessian_work work;
     work.color_method = color_method;
     d_vector x(n), hes( row.size() );
     for(size_t j = 0; j < n; j++)
          x[j] = double(j+1);
     f.SparseHessian(x, w, h, row, col, hes, work);

     // check the values in the sparse hessian
     for(size_t ell = 0; ell < row.size(); ell++)
     {     size_t i = row[ell];
          size_t j = col[ell];
          if( i == j )
               ok &= hes[ell] == 2.0 * x[i-1];
          else
          {     ok &= j+1 == i;
               ok &= hes[ell] == 2.0 * x[i];
          }
          ell++;
     }
     return ok;
}
// --------------------------------------------------------------------------
bool test_bool(const char* color_method)
{     bool ok = true;
     //
     typedef CppAD::vector< double >    d_vector;
     typedef CppAD::vector<size_t>      i_vector;
     typedef CppAD::vector<bool>        s_vector;
     //
     size_t n = 12;
     CppAD::ADFun<double> f = record_function(n);
     //
     // sparsity patteren for the sub-set of variables we are computing
     // the hessian w.r.t.
     size_t n_sub = 4;
     s_vector r(n * n_sub);
     for(size_t i = 0; i < n; i++)
     {     for(size_t j = 0; j < n_sub; j++)
               r[ i * n_sub + j ] = (i == j);
     }

     // store forward sparsity for J(x) = F^{(1)} (x) * R
     f.ForSparseJac(n_sub, r);

     // compute sparsity pattern for H(x) = (S * F)^{(2)} ( x ) * R
     s_vector s(1);
     s[0] = true;
     bool transpose = true;
     s_vector h = f.RevSparseHes(n_sub, s, transpose);

     // set the row and column indices that correspond to lower triangle
     i_vector row, col;
     for(size_t i = 0; i < n_sub; i++)
     {     if( i > 0 )
          {     // diagonal element
               row.push_back(i);
               col.push_back(i);
               // lower diagonal element
               row.push_back(i);
               col.push_back(i-1);
          }
     }

     // weighting for the Hessian
     d_vector w(1);
     w[0] = 1.0;

     // extend sparsity pattern (values in extended columns do not matter)
     s_vector h_extended(n * n);
     for(size_t i = 0; i < n; i++)
     {     for(size_t j = 0; j < n_sub; j++)
               h_extended[ i * n + j ] = h[ i * n_sub + j ];
          for(size_t j = n_sub; j < n; j++)
               h_extended[ i * n + j ] = false;
     }
     // compute Hessian
     CppAD::sparse_hessian_work work;
     work.color_method = color_method;
     d_vector x(n), hes( row.size() );
     for(size_t j = 0; j < n; j++)
          x[j] = double(j+1);
     f.SparseHessian(x, w, h_extended, row, col, hes, work);

     // check the values in the sparse hessian
     for(size_t ell = 0; ell < row.size(); ell++)
     {     size_t i = row[ell];
          size_t j = col[ell];
          if( i == j )
               ok &= hes[ell] == 2.0 * x[i-1];
          else
          {     ok &= j+1 == i;
               ok &= hes[ell] == 2.0 * x[i];
          }
          ell++;
     }
     return ok;
}
} // END_EMPTY_NAMESPACE

bool sparse_sub_hes(void)
{     bool ok = true;
     ok &= test_set("cppad.symmetric");
     ok &= test_set("cppad.general");
     //
     ok &= test_bool("cppad.symmetric");
     ok &= test_bool("cppad.general");
     return ok;
}
Input File: example/sparse_sub_hes.cpp cppad-20170000.3/doc/funcheck.xml0000644000175200017650000005670113057470506015517 0ustar coincoin-web Check an ADFun Sequence of Operations
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Check an ADFun Sequence of Operations

Syntax
ok = FunCheck(f, g, x, r, a)
See Also CompareChange

Purpose
We use F : B n → B m to denote the AD function corresponding to f . We use G : B n → B m to denote the function corresponding to the C++ function object g . This routine check if F ( x ) = G ( x ) If F ( x ) ≠ G ( x ) , the operation sequence corresponding to f does not represents the algorithm used by g to calculate values for G (see Discussion below).

f
The FunCheck argument f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const (see Forward below).

g
The FunCheck argument g has prototype
     Fun &g
 ( Fun is defined the properties of g ). The C++ function object g supports the syntax
     y = g(x)
 which computes y = G ( x ) .

x
The g argument x has prototype
     const Vector &x
 (see Vector below) and its size must be equal to n , the dimension of the domain space for f .

y
The g result y has prototype
     Vector y
 and its value is G ( x ) . The size of y is equal to m , the dimension of the range space for f .

x
The FunCheck argument x has prototype
     const Vector &x
 and its size must be equal to n , the dimension of the domain space for f . This specifies that point at which to compare the values calculated by f and G .

r
The FunCheck argument r has prototype
     const Base &r
 It specifies the relative error the element by element comparison of the value of F ( x ) and G ( x ) .

a
The FunCheck argument a has prototype
     const Base &a
 It specifies the absolute error the element by element comparison of the value of F ( x ) and G ( x ) .

ok
The FunCheck result ok has prototype
     bool ok
 It is true, if for i = 0 , … , m -1 either the relative error bound is satisfied | F i ( x ) - G i ( x ) | ≤ r ( | F i ( x ) | + | G i ( x ) | ) or the absolute error bound is satisfied | F i ( x ) - G i ( x ) | ≤ a It is false if for some ( i , j ) neither of these bounds is satisfied.

Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

FunCheck Uses Forward
After each call to Forward , the object f contains the corresponding Taylor coefficients . After FunCheck, the previous calls to Forward are undefined.

Discussion
Suppose that the algorithm corresponding to g contains
     if( x >= 0 )
          y = exp(x)
     else y = exp(-x)
 where x and y are AD<double> objects. It follows that the AD of double operation sequence depends on the value of x . If the sequence of operations stored in f corresponds to g with x ≥ 0 , the function values computed using f when x < 0 will not agree with the function values computed by g . This is because the operation sequence corresponding to g changed (and hence the object f does not represent the function G for this value of x ). In this case, you probably want to re-tape the calculations performed by g with the independent variables equal to the values in x (so AD operation sequence properly represents the algorithm for this value of independent variables).

Example
The file fun_check.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/core/fun_check.hpp cppad-20170000.3/doc/_funcheck_xml.js0000644000175200017650000000353713057470506016351 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funcheck.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'fun_check.cpp.xml' ]; var list_current0 = [ 'funcheck.xml#Syntax', 'funcheck.xml#Purpose', 'funcheck.xml#f', 'funcheck.xml#g', 'funcheck.xml#g.x', 'funcheck.xml#y', 'funcheck.xml#x', 'funcheck.xml#r', 'funcheck.xml#a', 'funcheck.xml#ok', 'funcheck.xml#Vector', 'funcheck.xml#FunCheck Uses Forward', 'funcheck.xml#Discussion', 'funcheck.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/optimize.xml0000644000175200017650000004222613057470506015566 0ustar coincoin-web Optimize an ADFun Object Tape
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Optimize an ADFun Object Tape

Syntax
f.optimize()
 f.optimize(options)
Purpose
The operation sequence corresponding to an ADFun object can be very large and involve many operations; see the size functions in seq_property . The f.optimize procedure reduces the number of operations, and thereby the time and the memory, required to compute function and derivative values.

f
The object f has prototype
     ADFun<Base> f
options
This argument has prototype
     const std::string& options
 The default for options is the empty string. If it is present, it must consist of one or more of the options below separated by a single space character.

no_conditional_skip
The optimize function can create conditional skip operators to improve the speed of conditional expressions; see optimize . If the sub-string no_conditional_skip appears in options , conditional skip operations are not be generated. This may make the optimize routine use significantly less memory and take less time to optimize f . If conditional skip operations are generated, it may save a significant amount of time when using f for forward or reverse mode calculations; see number_skip .

no_compare_op
If the sub-string no_compare_op appears in options , comparison operators will be removed from the optimized function. These operators are necessary for the compare_change functions to be meaningful. On the other hand, they are not necessary, and take extra time, when the compare_change functions are not used.

no_print_for_op
If the sub-string no_compare_op appears in options , PrintFor operations will be removed form the optimized function. These operators are useful for reporting problems evaluating derivatives at independent variable values different from those used to record a function.

Examples
forward_active.cpp Example Optimization and Forward Activity Analysis
reverse_active.cpp Example Optimization and Reverse Activity Analysis
compare_op.cpp Example Optimization and Comparison Operators
print_for_op.cpp Example Optimization and Print Forward Operators
conditional_skip.cpp Example Optimization and Conditional Expressions
nest_conditional.cpp Example Optimization and Nested Conditional Expressions
cumulative_sum.cpp Example Optimization and Cumulative Sum Operations

Efficiency
If a zero order forward calculation is done during the construction of f , it will require more memory and time than required after the optimization procedure. In addition, it will need to be redone. For this reason, it is more efficient to use
     ADFun<Base> f;
     f.Dependent(x, y);
     f.optimize();
 instead of
     ADFun<Base> f(x, y)
     f.optimize();
 See the discussion about sequence constructors .

Speed Testing
You can run the CppAD speed tests and see the corresponding changes in number of variables and execution time. Note that there is an interaction between using optimize and onetape . If onetape is true and optimize is true, the optimized tape will be reused many times. If onetape is false and optimize is true, the tape will be re-optimized for each test.

Atomic Functions
There are some subtitle issue with optimized atomic functions v = g ( u ) :

rev_sparse_jac
The atomic_rev_sparse_jac function is be used to determine which components of u affect the dependent variables of f . For each atomic operation, the current atomic_sparsity setting is used to determine if pack_sparsity_enum, bool_sparsity_enum, or set_sparsity_enum is used to determine dependency relations between argument and result variables.

nan
If u[i] does not affect the value of the dependent variables for f , the value of u[i] is set to nan .

Checking Optimization
If NDEBUG is not defined, and f.size_order() is greater than zero, a forward_zero calculation is done using the optimized version of f and the results are checked to see that they are the same as before. If they are not the same, the ErrorHandler is called with a known error message related to f.optimize() .
Input File: cppad/core/optimize.hpp cppad-20170000.3/doc/_optimize_xml.js0000644000175200017650000000431113057470506016412 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'optimize.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'optimize_forward_active.cpp.xml', 'optimize_reverse_active.cpp.xml', 'optimize_compare_op.cpp.xml', 'optimize_print_for.cpp.xml', 'optimize_conditional_skip.cpp.xml', 'optimize_nest_conditional.cpp.xml', 'optimize_cumulative_sum.cpp.xml' ]; var list_current0 = [ 'optimize.xml#Syntax', 'optimize.xml#Purpose', 'optimize.xml#f', 'optimize.xml#options', 'optimize.xml#options.no_conditional_skip', 'optimize.xml#options.no_compare_op', 'optimize.xml#options.no_print_for_op', 'optimize.xml#Examples', 'optimize.xml#Efficiency', 'optimize.xml#Speed Testing', 'optimize.xml#Atomic Functions', 'optimize.xml#Atomic Functions.rev_sparse_jac', 'optimize.xml#Atomic Functions.nan', 'optimize.xml#Checking Optimization' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/optimize_reverse_active.cpp.xml0000644000175200017650000005153313057470506021436 0ustar coincoin-web Example Optimization and Reverse Activity Analysis
Prev Next optimize_reverse_active.cpp Headings

Example Optimization and Reverse Activity Analysis
# include <cppad/cppad.hpp>
namespace {
     struct tape_size { size_t n_var; size_t n_op; };

     template <class Vector> void fun(
          const Vector& x, Vector& y, tape_size& before, tape_size& after
     )
     {     typedef typename Vector::value_type scalar;

          // phantom variable with index 0 and independent variables
          // begin operator, independent variable operators and end operator
          before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
          after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

          // initilized product of even and odd variables
          scalar prod_even = x[0];
          scalar prod_odd  = x[1];
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;
          //
          // compute product of even and odd variables
          for(size_t i = 2; i < x.size(); i++)
          {     if( i % 2 == 0 )
               {     // prod_even will affect dependent variable
                    prod_even = prod_even * x[i];
                    before.n_var += 1; before.n_op += 1;
                    after.n_var  += 1; after.n_op  += 1;
               }
               else
               {     // prod_odd will not affect dependent variable
                    prod_odd  = prod_odd * x[i];
                    before.n_var += 1; before.n_op += 1;
                    after.n_var  += 0; after.n_op  += 0;
               }
          }

          // dependent variable for this operation sequence
          y[0] = prod_even;
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;
     }
}

bool reverse_active(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 6;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     for(size_t i = 0; i < n; i++)
          ax[i] = AD<double>(i + 1);

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     tape_size before, after;
     fun(ax, ay, before, after);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);
     ok &= f.size_var() == before.n_var;
     ok &= f.size_op()  == before.n_op;

     // Optimize the operation sequence
     f.optimize();
     ok &= f.size_var() == after.n_var;
     ok &= f.size_op()  == after.n_op;

     // check zero order forward with different argument value
     CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
     for(size_t i = 0; i < n; i++)
          x[i] = double(i + 2);
     y    = f.Forward(0, x);
     fun(x, check, before, after);
     ok &= NearEqual(y[0], check[0], eps10, eps10);

     return ok;
}
Input File: example/optimize/reverse_active.cpp cppad-20170000.3/doc/optimize_compare_op.cpp.xml0000644000175200017650000006564513057470506020565 0ustar coincoin-web Example Optimization and Comparison Operators
Prev Next optimize_compare_op.cpp

Example Optimization and Comparison Operators

See Also
cond_exp.cpp 
# include <cppad/cppad.hpp>
namespace {
     struct tape_size { size_t n_var; size_t n_op; };

     template <class Vector> void fun(
          const std::string& options ,
          const Vector& x, Vector& y, tape_size& before, tape_size& after
     )
     {     typedef typename Vector::value_type scalar;

          // phantom variable with index 0 and independent variables
          // begin operator, independent variable operators and end operator
          before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
          after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

          // Create a variable that is is only used in the comparision operation
          // It is not used when the comparison operator is not included
          scalar one = 1. / x[0];
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 0; after.n_op  += 0;
          // If we keep comparision operators, we must compute their operands
          if( options.find("no_compare_op") == std::string::npos )
          {     after.n_var += 1;  after.n_op += 1;
          }

          // Create a variable that is used by the result
          scalar two = x[0] * 5.;
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op += 1;

          // Only one variable created for this comparison operation
          // but the value depends on which branch is taken.
          scalar three;
          if( one < x[0] )        // comparison operator
               three = two / 2.0;  // division operator
          else
               three = 2.0 * two;  // multiplication operator
          // comparison and either division of multiplication operator
          before.n_var += 1; before.n_op += 2;
          // comparison operator depends on optimization options
          after.n_var += 1;  after.n_op += 1;
          // check if we are keeping the comparison operator
          if( options.find("no_compare_op") == std::string::npos )
               after.n_op += 1;

          // results for this operation sequence
          y[0] = three;
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;
     }
}

bool compare_op(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.5;

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);

     for(size_t k = 0; k < 2; k++)
     {     // optimization options
          std::string options = "";
          if( k == 0 )
               options = "no_compare_op";

          // declare independent variables and start tape recording
          CppAD::Independent(ax);

          // compute function value
          tape_size before, after;
          fun(options, ax, ay, before, after);

          // create f: x -> y and stop tape recording
          CppAD::ADFun<double> f(ax, ay);
          ok &= f.size_var() == before.n_var;
          ok &= f.size_op() == before.n_op;

          // Optimize the operation sequence
          f.optimize(options);
          ok &= f.size_var() == after.n_var;
          ok &= f.size_op() == after.n_op;

          // Check result for a zero order calculation for a different x,
          // where the result of the comparison is he same.
          CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
          x[0] = 0.75;
          y    = f.Forward(0, x);
          if ( options == "" )
               ok  &= f.CompareChange() == 0;
          fun(options, x, check, before, after);
          ok &= NearEqual(y[0], check[0], eps10, eps10);

          // Check case where result of the comparision is differnent
          // (hence one needs to re-tape to get correct result)
          x[0] = 2.0;
          y    = f.Forward(0, x);
          if ( options == "" )
               ok  &= f.CompareChange() == 1;
          fun(options, x, check, before, after);
          ok  &= std::fabs(y[0] - check[0]) > 0.5;
     }
     return ok;
}
Input File: example/optimize/compare_op.cpp cppad-20170000.3/doc/optimize_print_for.cpp.xml0000644000175200017650000005447313057470506020440 0ustar coincoin-web Example Optimization and Print Forward Operators
Prev Next optimize_print_for.cpp Headings

Example Optimization and Print Forward Operators
# include <cppad/cppad.hpp>

namespace {
     struct tape_size { size_t n_var; size_t n_op; };

     void PrintFor(
          double pos, const char* before, double var, const char* after
     )
     {     if( pos <= 0.0 )
               std::cout << before << var << after;
          return;
     }
     template <class Vector> void fun(
          const std::string& options ,
          const Vector& x, Vector& y, tape_size& before, tape_size& after
     )
     {     typedef typename Vector::value_type scalar;

          // phantom variable with index 0 and independent variables
          // begin operator, independent variable operators and end operator
          before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
          after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

          // Argument to PrintFor is only needed
          // if we are keeping print forward operators
          scalar minus_one = x[0] - 1.0;
          before.n_var += 1; before.n_op += 1;
          if( options.find("no_print_for_op") == std::string::npos )
          {     after.n_var += 1;  after.n_op += 1;
          }

          // print argument to log function minus one, if it is <= 0
          PrintFor(minus_one, "minus_one == ", minus_one , " is <=  0\n");
          before.n_var += 0; before.n_op += 1;
          if( options.find("no_print_for_op") == std::string::npos )
          {     after.n_var += 0;  after.n_op += 1;
          }

          // now compute log
          y[0] = log( x[0] );
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;
     }
}

bool print_for(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 1.5;

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);

     for(size_t k = 0; k < 2; k++)
     {     // optimization options
          std::string options = "";
          if( k == 0 )
               options = "no_print_for_op";

          // declare independent variables and start tape recording
          CppAD::Independent(ax);

          // compute function value
          tape_size before, after;
          fun(options, ax, ay, before, after);

          // create f: x -> y and stop tape recording
          CppAD::ADFun<double> f(ax, ay);
          ok &= f.size_var() == before.n_var;
          ok &= f.size_op() == before.n_op;

          // Optimize the operation sequence
          f.optimize(options);
          ok &= f.size_var() == after.n_var;
          ok &= f.size_op() == after.n_op;

          // Check result for a zero order calculation for a different x
          CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
          x[0] = 2.75;
          y    = f.Forward(0, x);
          fun(options, x, check, before, after);
          ok &= NearEqual(y[0], check[0], eps10, eps10);
     }
     return ok;
}
Input File: example/optimize/print_for.cpp cppad-20170000.3/doc/optimize_conditional_skip.cpp.xml0000644000175200017650000007053113057470506021760 0ustar coincoin-web Example Optimization and Conditional Expressions
Prev Next optimize_conditional_skip.cpp

Example Optimization and Conditional Expressions

See Also
cond_exp.cpp 
# include <cppad/cppad.hpp>
namespace {
     struct tape_size { size_t n_var; size_t n_op; };

     template <class Vector> void fun(
          const std::string& options ,
          const Vector& x, Vector& y, tape_size& before, tape_size& after
     )
     {     typedef typename Vector::value_type scalar;


          // phantom variable with index 0 and independent variables
          // begin operator, independent variable operators and end operator
          before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
          after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

          // Create a variable that is is only used as left operand
          // in the comparision operation
          scalar left = 1. / x[0];
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;

          // right operand in comparison operation
          scalar right  = x[0];
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;

          // Note that the left and right operand in the CondExpLt comparison
          // are determined at this point. Hence the conditional skip operator
          // will be inserted here so that the operations mentioned below can
          // also be skipped during zero order foward mode.
          if( options.find("no_conditional_skip") == std::string::npos )
               after.n_op += 1; // for conditional skip operation

          // Create a variable that is only used when comparison result is true
          // (can be skipped when the comparison result is false)
          scalar if_true = x[0] * 5.0;
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;

          // Create two variables only used when the comparison result is false
          // (can be skipped when the comparison result is true)
          scalar temp      = 5.0 + x[0];
          scalar if_false  = temp * 3.0;
          before.n_var += 2; before.n_op += 2;
          after.n_var  += 2; after.n_op  += 2;

          // conditional comparision is 1 / x[0] < x[0]
          scalar value = CppAD::CondExpLt(left, right, if_true, if_false);
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;

          // results for this operation sequence
          y[0] = value;
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;
     }
}

bool conditional_skip(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.5;

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);

     for(size_t k = 0; k < 2; k++)
     {     // optimization options
          std::string options = "";
          if( k == 0 )
               options = "no_conditional_skip";

          // declare independent variables and start tape recording
          CppAD::Independent(ax);

          // compute function computation
          tape_size before, after;
          fun(options, ax, ay, before, after);

          // create f: x -> y and stop tape recording
          CppAD::ADFun<double> f(ax, ay);
          ok &= f.size_var() == before.n_var;
          ok &= f.size_op()  == before.n_op;

          // Optimize the operation sequence
          f.optimize(options);
          ok &= f.size_var() == after.n_var;
          ok &= f.size_op()  == after.n_op;

          // Check case where result of the comparison is true (x[0] > 1.0).
          CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
          x[0] = 1.75;
          y    = f.Forward(0, x);
          fun(options, x, check, before, after);
          ok &= NearEqual(y[0], check[0], eps10, eps10);
          if( options == "" )
               ok  &= f.number_skip() == 2;
          else
               ok &= f.number_skip() == 0;

          // Check case where result of the comparision is false (x[0] <= 1.0)
          x[0] = 0.5;
          y    = f.Forward(0, x);
          fun(options, x, check, before, after);
          ok &= NearEqual(y[0], check[0], eps10, eps10);
          if( options == "" )
               ok  &= f.number_skip() == 1;
          else
               ok &= f.number_skip() == 0;
     }
     return ok;
}
Input File: example/optimize/conditional_skip.cpp cppad-20170000.3/doc/optimize_nest_conditional.cpp.xml0000644000175200017650000010742213057470506021763 0ustar coincoin-web Example Optimization and Nested Conditional Expressions
Prev Next optimize_nest_conditional.cpp

Example Optimization and Nested Conditional Expressions

See Also
cond_exp.cpp 
# include <cppad/cppad.hpp>
namespace {
     struct tape_size { size_t n_var; size_t n_op; };

     template <class Vector> void fun(
          const std::string& options ,
          const Vector& x, Vector& y, tape_size& before, tape_size& after
     )
     {     typedef typename Vector::value_type scalar;

          // phantom variable with index 0 and independent variables
          // begin operator, independent variable operators and end operator
          before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
          after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

          // Create a variable that is is only used in the second comparision
          scalar two = 1. + x[0];
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;

          // Conditional skip for second comparison will be inserted here.
          if( options.find("no_conditional_skip") == std::string::npos )
               after.n_op += 1; // for conditional skip operation

          // Create a variable that is is only used in the first comparision
          // (can be skipped when second comparison result is false)
          scalar one = 1. / x[0];
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;

          // Conditional skip for first comparison will be inserted here.
          if( options.find("no_conditional_skip") == std::string::npos )
               after.n_op += 1; // for conditional skip operation

          // value when first comparison if false
          scalar one_false = 5.0;

          // Create a variable that is only used when second comparison is true
          // (can be skipped when it is false)
          scalar one_true = x[0] / 5.0;
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;

          // value when second comparison is false
          scalar two_false = 3.0;

          // First conditional compaison is 1 / x[0] < x[0]
          // is only used when second conditional expression is true
          // (can be skipped when it is false)
          scalar two_true  = CppAD::CondExpLt(one, x[0], one_true, one_false);
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;

          // Second conditional compaison is 1 + x[0] < x[1]
          scalar two_value = CppAD::CondExpLt(two, x[1], two_true, two_false);
          before.n_var += 1; before.n_op += 1;
          after.n_var  += 1; after.n_op  += 1;

          // results for this operation sequence
          y[0] = two_value;
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;
     }
}

bool nest_conditional(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.5;
     ax[1] = 0.5;

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);

     for(size_t k = 0; k < 2; k++)
     {     // optimization options
          std::string options = "";
          if( k == 0 )
               options = "no_conditional_skip";

          // declare independent variables and start tape recording
          CppAD::Independent(ax);

          // compute function computation
          tape_size before, after;
          fun(options, ax, ay, before, after);

          // create f: x -> y and stop tape recording
          CppAD::ADFun<double> f(ax, ay);
          ok &= f.size_var() == before.n_var;
          ok &= f.size_op()  == before.n_op;

          // Optimize the operation sequence
          f.optimize(options);
          ok &= f.size_var() == after.n_var;
          ok &= f.size_op()  == after.n_op;

          // Check case where result of the second comparison is true
          // and first comparison is true
          CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
          x[0] = 1.75;
          x[1] = 4.0;
          y    = f.Forward(0, x);
          fun(options, x, check, before, after);
          ok &= NearEqual(y[0], check[0], eps10, eps10);
          ok  &= f.number_skip() == 0;

          // Check case where result of the second comparison is true
          // and first comparison is false
          x[0] = 0.5;
          x[1] = 4.0;
          y    = f.Forward(0, x);
          fun(options, x, check, before, after);
          ok &= NearEqual(y[0], check[0], eps10, eps10);
          if( options == "" )
               ok  &= f.number_skip() == 1;
          else
               ok &= f.number_skip() == 0;

          // Check case where result of the second comparison is false
          // and first comparison is true
          x[0] = 1.75;
          x[1] = 0.0;
          y    = f.Forward(0, x);
          fun(options, x, check, before, after);
          ok &= NearEqual(y[0], check[0], eps10, eps10);
          if( options == "" )
               ok  &= f.number_skip() == 3;
          else
               ok &= f.number_skip() == 0;

          // Check case where result of the second comparison is false
          // and first comparison is false
          x[0] = 0.5;
          x[1] = 0.0;
          y    = f.Forward(0, x);
          fun(options, x, check, before, after);
          ok &= NearEqual(y[0], check[0], eps10, eps10);
          if( options == "" )
               ok  &= f.number_skip() == 3;
          else
               ok &= f.number_skip() == 0;
     }
     return ok;
}
Input File: example/optimize/nest_conditional.cpp cppad-20170000.3/doc/optimize_cumulative_sum.cpp.xml0000644000175200017650000004762513057470506021501 0ustar coincoin-web Example Optimization and Cumulative Sum Operations
Prev Next optimize_cumulative_sum.cpp Headings

Example Optimization and Cumulative Sum Operations
# include <cppad/cppad.hpp>

namespace {
     struct tape_size { size_t n_var; size_t n_op; };

     template <class Vector> void fun(
          const Vector& x, Vector& y, tape_size& before, tape_size& after
     )
     {     typedef typename Vector::value_type scalar;

          // phantom variable with index 0 and independent variables
          // begin operator, independent variable operators and end operator
          before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
          after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

          // operators that are identical, and that will be made part of the
          // cummulative summation. Make sure do not replace second variable
          // using the first and then remove the first as part of the
          // cumulative summation.
          scalar first  = x[0] + x[1];
          scalar second = x[0] + x[1];
          before.n_var += 2; before.n_op  += 2;
          after.n_var  += 0; after.n_op   += 0;

          // test that subtractions are also included in cumulative summations
          scalar third = x[1] - 2.0;
          before.n_var += 1; before.n_op  += 1;
          after.n_var  += 0; after.n_op   += 0;

          // the finial summation is converted to a cumulative summation
          // the other is removed.
          scalar csum = first + second + third;
          before.n_var += 2; before.n_op  += 2;
          after.n_var  += 1; after.n_op   += 1;

          // results for this operation sequence
          y[0] = csum;
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;
     }
}
bool cumulative_sum(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.5;
     ax[1] = 1.5;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     tape_size before, after;
     fun(ax, ay, before, after);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);
     ok &= f.size_var() == before.n_var;
     ok &= f.size_op()  == before.n_op;

     // Optimize the operation sequence
     f.optimize();
     ok &= f.size_var() == after.n_var;
     ok &= f.size_op()  == after.n_op;

     // Check result for a zero order calculation for a different x,
     CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
     x[0] = 0.75;
     x[1] = 2.25;
     y    = f.Forward(0, x);
     fun(x, check, before, after);
     ok  &= CppAD::NearEqual(y[0], check[0], eps10, eps10);

     return ok;
}
Input File: example/optimize/cumulative_sum.cpp cppad-20170000.3/doc/check_for_nan.xml0000644000175200017650000003033313057470506016501 0ustar coincoin-web Check an ADFun Object For Nan Results
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Check an ADFun Object For Nan Results

Syntax
f.check_for_nan(b)
 b = f.check_for_nan()
 get_check_for_nan(vec, file)
Debugging
If NDEBUG is not defined, and the result of a forward or reverse calculation contains a nan , CppAD can halt with an error message.

f
For the syntax where b is an argument, f has prototype
     ADFun<Base> f
 (see ADFun<Base> constructor ). For the syntax where b is the result, f has prototype
     const ADFun<Base> f
b
This argument or result has prototype
     bool b
 Future calls to f.Forward will (will not) check for nan. depending on if b is true (false).

Default
The value for this setting after construction of f ) is true. The value of this setting is not affected by calling Dependent for this function object.

Error Message
If this error is detected during zero order forward mode, the values of the independent variables that resulted in the nan are written to a temporary binary file. This is so that you can run the original source code with those values to see what is causing the nan.

vector_size
The error message with contain the text vector_size = vector_size followed the newline character '\n'. The value of vector_size is the number of elements in the independent vector.

file_name
The error message with contain the text file_name = file_name followed the newline character '\n'. The value of file_name is the name of the temporary file that contains the dependent variable values.

index
The error message will contain the text index = index followed by the newline character '\n'. The value of index is the lowest dependent variable index that has the value nan.

get_check_for_nan
This routine can be used to get the independent variable values that result in a nan.

vec
This argument has prototype
     CppAD::vector<Base>& vec
 It size must be equal to the corresponding value of vector_size in the corresponding error message. The input value of its elements does not matter. Upon return, it will contain the values for the independent variables, in the corresponding call to Independent , that resulted in the nan. (Note that the call to Independent uses an vector with elements of type AD<Base> and vec has elements of type Base .)

file
This argument has prototype
     const std::string& file
 It must be the value of file_name in the corresponding error message.

Example
The file check_for_nan.cpp contains an example and test of these operations. It returns true if it succeeds and false otherwise.
Input File: cppad/core/check_for_nan.hpp cppad-20170000.3/doc/_check_for_nan_xml.js0000644000175200017650000000377713057470506017350 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'check_for_nan.cpp.xml' ]; var list_current0 = [ 'check_for_nan.xml#Syntax', 'check_for_nan.xml#Debugging', 'check_for_nan.xml#f', 'check_for_nan.xml#b', 'check_for_nan.xml#Default', 'check_for_nan.xml#Error Message', 'check_for_nan.xml#Error Message.vector_size', 'check_for_nan.xml#Error Message.file_name', 'check_for_nan.xml#Error Message.index', 'check_for_nan.xml#get_check_for_nan', 'check_for_nan.xml#get_check_for_nan.vec', 'check_for_nan.xml#get_check_for_nan.file', 'check_for_nan.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/check_for_nan.cpp.xml0000644000175200017650000005100113057470506017255 0ustar coincoin-web ADFun Checking For Nan: Example and Test
Prev Next check_for_nan.cpp Headings

ADFun Checking For Nan: Example and Test
# include <cppad/cppad.hpp>
# include <cctype>

namespace {
     void myhandler(
          bool known       ,
          int  line        ,
          const char *file ,
          const char *exp  ,
          const char *msg  )
     {     // error handler must not return, so throw an exception
          std::string message = msg;
          throw message;
     }
}

bool check_for_nan(void)
{     bool ok = true;
     using CppAD::AD;
     using std::string;
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // replace the default CppAD error handler
     CppAD::ErrorHandler info(myhandler);

     CPPAD_TESTVECTOR(AD<double>) ax(2), ay(2);
     ax[0] = 2.0;
     ax[1] = 1.0;
     CppAD::Independent(ax);
     ay[0] = sqrt( ax[0] );
     ay[1] = sqrt( ax[1] );
     CppAD::ADFun<double> f(ax, ay);

     CPPAD_TESTVECTOR(double) x(2), y(2);
     x[0] = 2.0;
     x[1] = -1.0;

     // use try / catch because this causes an exception
     // (assuming that NDEBUG is not defined)
     f.check_for_nan(true);
     try {
          y = f.Forward(0, x);

# ifndef NDEBUG
          // When compiled with NDEBUG defined,
          // CppAD does not spend time checking for nan.
          ok = false;
# endif
     }
     catch(std::string msg)
     {
          // get and check size of the independent variable vector
          string pattern = "vector_size = ";
          size_t start   = msg.find(pattern) + pattern.size();
          string number;
          for(size_t i = start; msg[i] != '\n'; i++)
               number += msg[i];
          size_t vector_size = std::atoi(number.c_str());
          ok &= vector_size == 2;

          // get and check first dependent variable index that is nan
          pattern = "index = ";
          start   = msg.find(pattern) + pattern.size();
          number  = "";
          for(size_t i = start; msg[i] != '\n'; i++)
               number += msg[i];
          size_t index = std::atoi(number.c_str());
          ok &= index == 1;

          // get the name of the file
          pattern = "file_name = ";
          start   = msg.find(pattern) + pattern.size();
          string file_name;
          for(size_t i = start; msg[i] != '\n'; i++)
               file_name += msg[i];

          // get and check independent variable vector that resulted in the nan
          CppAD::vector<double> vec(vector_size);
          CppAD::get_check_for_nan(vec, file_name);
          for(size_t i = 0; i < vector_size; i++)
               ok &= vec[i] == x[i];
     }

     // now do calculation without an exception
     f.check_for_nan(false);
     y = f.Forward(0, x);
     ok &= CppAD::NearEqual(y[0], std::sqrt(x[0]), eps, eps);
     ok &= CppAD::isnan( y[1] );

     return ok;
}
Input File: example/check_for_nan.cpp cppad-20170000.3/doc/preprocessor.xml0000644000175200017650000001674713057470506016465 0ustar coincoin-web CppAD API Preprocessor Symbols
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CppAD API Preprocessor Symbols

Purpose
The CppAD include files define preprocessor symbols all of which begin with CPPAD_. Note that there are some old, deprecated preprocessor symbols that begin with CppAD. In this section we list all of the CppAD preprocessor symbols that are part of the CppAD Application Interface (API).

Documented Here

CPPAD_NULL
Is a null pointer used by CppAD, instead of just using the value zero which was often done in C++98, which has been replaced by the value nullptr in C++11.

CPPAD_PACKAGE_STRING
Is a const char* representation of this version of CppAD.

CPPAD_USE_CPLUSPLUS_2011
This preprocessor symbol has the value has the value 1 if C++11 features are being used by CppAD. Otherwise it has the value zero.

Documented Elsewhere
CPPAD_BOOL_BINARY
CPPAD_BOOL_UNARY
CPPAD_DISCRETE_FUNCTION
CPPAD_MAX_NUM_THREADS
CPPAD_NUMERIC_LIMITS
CPPAD_STANDARD_MATH_UNARY
CPPAD_TAPE_ADDR_TYPE
CPPAD_TAPE_ID_TYPE
CPPAD_TESTVECTOR
CPPAD_TO_STRING

Deprecated
CppADCreateDiscrete
CppADvector
CPPAD_TEST_VECTOR
CPPAD_TRACK_NEW_VEC
CPPAD_TRACK_DEL_VEC
CPPAD_TRACK_EXTEND
CPPAD_TRACK_COUNT
CPPAD_USER_ATOMIC
CppADTrackNewVec
CppADTrackDelVec
CppADTrackExtend
CppADTrackCount
Input File: omh/preprocessor.omh cppad-20170000.3/doc/multi_thread.xml0000644000175200017650000001625313057470506016410 0ustar coincoin-web Using CppAD in a Multi-Threading Environment
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Using CppAD in a Multi-Threading Environment

Purpose
Extra steps and care must be taken to use CppAD in parallel execution mode. This section collects this information in one place.

CPPAD_MAX_NUM_THREADS
The value CPPAD_MAX_NUM_THREADS is an absolute maximum for the number of threads that CppAD should support. If this preprocessor symbol is defined before including any CppAD header files, it must be an integer greater than or equal to one. Otherwise, cppad_max_num_threads is used to define this preprocessor symbol. Note that the minimum allowable value for cppad_max_num_threads is 4; i.e., you can only get smaller values for CPPAD_MAX_NUM_THREADS by defining it before including the CppAD header files.

parallel_setup
Using any of the following routines in a multi-threading environment requires that thread_alloc::parallel_setup has been completed: CppAD::vector , CheckSimpleVector , CheckNumericType , parallel_ad .

hold_memory
Memory allocation should be much faster after calling hold_memory with value equal to true. This may even be true if there is only one thread.


One must first call thread_alloc::parallel_setup and then call parallel_ad before using AD types in parallel execution mode.

Initialization
The following routines must be called at least once before being used in parallel mode: CheckSimpleVector , CheckNumericType , discrete functions , Rosen34 , Runge45 .

Same Thread
Some operations must be preformed by the same thread: ADFun , Independent , Dependent .

Parallel Prohibited
The following routine cannot be called in parallel mode: ErrorHandler constructor .

Contents
parallel_adEnable AD Calculations During Parallel Mode
thread_test.cppRun Multi-Threading Examples and Speed Tests
Input File: omh/multi_thread.omh cppad-20170000.3/doc/parallel_ad.xml0000644000175200017650000001516413057470506016167 0ustar coincoin-web Enable AD Calculations During Parallel Mode
Prev Next parallel_ad

Enable AD Calculations During Parallel Mode

Syntax
parallel_ad<Base>()

Purpose
The function parallel_ad<Base>() must be called before any AD<Base> objects are used in parallel mode. In addition, if this routine is called after one is done using parallel mode, it will free extra memory used to keep track of the multiple AD<Base> tapes required for parallel execution.

Discussion
By default, for each AD<Base> class there is only one tape that records AD of Base operations. This tape is a global variable and hence it cannot be used by multiple threads at the same time. The parallel_setup function informs CppAD of the maximum number of threads that can be active in parallel mode. This routine does extra setup (and teardown) for the particular Base type.

CheckSimpleVector
This routine has the side effect of calling the routines
     CheckSimpleVector< Type, CppAD::vector<Type> >()
 where Type is Base and AD<Base> .

Example
The files team_openmp.cpp , team_bthread.cpp , and team_pthread.cpp , contain examples and tests that implement this function.

Restriction
This routine cannot be called in parallel mode or while there is a tape recording AD<Base> operations.
Input File: cppad/core/parallel_ad.hpp cppad-20170000.3/doc/thread_test.cpp.xml0000644000175200017650000015765613057470506017033 0ustar coincoin-web Run Multi-Threading Examples and Speed Tests
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Run Multi-Threading Examples and Speed Tests

Syntax
./multi_thread_threading a11c
./multi_thread_threading simple_ad
./multi_thread_threading team_example
./multi_thread_threading harmonic test_time max_threads mega_sum
./multi_thread_threading multi_newton test_time max_threads \
     num_zero num_sub num_sum use_ad
Running Tests
You can build this program and run the default version of its test parameters by executing the following commands:
     cd multi_thread
     make test
 After this operation you can run the syntax above for the different valid values of threading :

threading
If the cmake command output indicates that openmp is supported by your system, you can execute the syntax above with threading equal to openmp.

If the cmake command output indicates that pthreads with barriers is supported by your system, you can execute the syntax above with threading equal to pthread.

If the cmake command output indicates that boost threads is supported is by your system, you can execute the syntax above with threading equal to bthread.

Purpose
Runs the CppAD multi-threading examples and timing tests:

a11c
The examples a11c_openmp.cpp , a11c_bthread.cpp , and a11c_pthread.cpp demonstrate simple multi-threading, without algorithmic differentiation.

simple_ad
The examples simple_ad_openmp.cpp , simple_ad_bthread.cpp , and simple_ad_pthread.cpp demonstrate simple multi-threading, with algorithmic differentiation, using OpenMP, boost threads and pthreads respectively.

team_example
The team_example.cpp routine demonstrates simple multi-threading with algorithmic differentiation and using a team of threads .

harmonic
The harmonic_time.cpp routine preforms a timing test for a multi-threading example without algorithmic differentiation using a team of threads.

test_time
Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported time is the total wall clock time divided by the number of repeats.

max_threads
If the argument max_threads is a non-negative integer specifying the maximum number of threads to use for the test. The specified test is run with the following number of threads:
     num_threads = 0 , ... , max_threads
 The value of zero corresponds to not using the multi-threading system.

mega_sum
The command line argument mega_sum is an integer greater than or equal one and has the same meaning as in harmonic_time.cpp .

multi_newton
The multi_newton_time.cpp routine preforms a timing test for a multi-threading example with algorithmic differentiation using a team of threads.

test_time
Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported time is the total wall clock time divided by the number of repeats.

max_threads
If the argument max_threads is a non-negative integer specifying the maximum number of threads to use for the test. The specified test is run with the following number of threads:
     num_threads = 0 , ... , max_threads
 The value of zero corresponds to not using the multi-threading system.

num_zero
The command line argument num_zero is an integer greater than or equal two and has the same meaning as in multi_newton_time.cpp .

num_sub
The command line argument num_sub is an integer greater than or equal one and has the same meaning as in multi_newton_time.cpp .

num_sum
The command line argument num_sum is an integer greater than or equal one and has the same meaning as in multi_newton_time.cpp .

use_ad
The command line argument use_ad is either true or false and has the same meaning as in multi_newton_time.cpp .

Team Implementations
The following routines are used to implement the specific threading systems through the common interface team_thread.hpp :
team_openmp.cpp OpenMP Implementation of a Team of AD Threads
team_bthread.cpp Boost Thread Implementation of a Team of AD Threads
team_pthread.cpp Pthread Implementation of a Team of AD Threads

Source 


# include <cppad/cppad.hpp>
# include <cmath>
# include <cstring>
# include <ctime>
# include "team_thread.hpp"
# include "team_example.hpp"
# include "harmonic_time.hpp"
# include "multi_newton_time.hpp"

extern bool a11c(void);
extern bool simple_ad(void);

namespace {
     size_t arg2size_t(
          const char* arg       ,
          int limit             ,
          const char* error_msg )
     {     int i = std::atoi(arg);
          if( i >= limit )
               return size_t(i);
          std::cerr << "value = " << i << std::endl;
          std::cerr << error_msg << std::endl;
          exit(1);
     }
     double arg2double(
          const char* arg       ,
          double limit          ,
          const char* error_msg )
     {     double d = std::atof(arg);
          if( d >= limit )
               return d;
          std::cerr << "value = " << d << std::endl;
          std::cerr << error_msg << std::endl;
          exit(1);
     }
}

int main(int argc, char *argv[])
{     using CppAD::thread_alloc;
     bool ok         = true;
     using std::cout;
     using std::endl;

     // commnd line usage message
     const char* usage =
     "./<thread>_test a11c\n"
     "./<thread>_test simple_ad\n"
     "./<thread>_test team_example\n"
     "./<thread>_test harmonic    test_time max_threads mega_sum\n"
     "./<thread>_test multi_newton test_time max_threads\\\n"
     "     num_zero num_sub num_sum use_ad\\\n"
     "where <thread> is bthread, openmp, or pthread";

     // command line argument values (assign values to avoid compiler warnings)
     size_t num_zero=0, num_sub=0, num_sum=0;
     bool use_ad=true;

     // put the date and time in the output file
     std::time_t rawtime;
     std::time( &rawtime );
     const char* gmt = std::asctime( std::gmtime( &rawtime ) );
     size_t len = size_t( std::strlen(gmt) );
     cout << "gmtime        = '";
     for(size_t i = 0; i < len; i++)
          if( gmt[i] != '\n' ) cout << gmt[i];
     cout << "';" << endl;

     // CppAD version number
     cout << "cppad_version = '" << CPPAD_PACKAGE_STRING << "';" << endl;

     // put the team name in the output file
     cout << "team_name     = '" << team_name() << "';" << endl;

     // print command line as valid matlab/octave
     cout << "command       = '" << argv[0];
     for(int i = 1; i < argc; i++)
          cout << " " << argv[i];
     cout << "';" << endl;

     ok = false;
     const char* test_name = "";
     if( argc > 1 )
          test_name = *++argv;
     bool run_a11c         = std::strcmp(test_name, "a11c")         == 0;
     bool run_simple_ad    = std::strcmp(test_name, "simple_ad")    == 0;
     bool run_team_example = std::strcmp(test_name, "team_example") == 0;
     bool run_harmonic     = std::strcmp(test_name, "harmonic")     == 0;
     bool run_multi_newton = std::strcmp(test_name, "multi_newton") == 0;
     if( run_a11c || run_simple_ad || run_team_example )
          ok = (argc == 2);
     else if( run_harmonic )
          ok = (argc == 5);
     else if( run_multi_newton )
          ok = (argc == 8);
     if( ! ok )
     {     std::cerr << "test_name     = " << test_name << endl;
          std::cerr << "argc          = " << argc      << endl;
          std::cerr << usage << endl;
          exit(1);
     }
     if( run_a11c || run_simple_ad || run_team_example )
     {     if( run_a11c )
               ok        = a11c();
          else if( run_simple_ad )
               ok        = simple_ad();
          else     ok        = team_example();
          if( thread_alloc::free_all() )
               cout << "free_all      = true;"  << endl;
          else
          {     ok = false;
               cout << "free_all      = false;" << endl;
          }
          if( ok )
               cout << "OK            = true;"  << endl;
          else cout << "OK            = false;" << endl;
          return ! ok;
     }

     // test_time
     double test_time = arg2double( *++argv, 0.,
          "run: test_time is less than zero"
     );

     // max_threads
     size_t max_threads = arg2size_t( *++argv, 0,
          "run: max_threads is less than zero"
     );

     size_t mega_sum = 0; // assignment to avoid compiler warning
     if( run_harmonic )
     {     // mega_sum
          mega_sum = arg2size_t( *++argv, 1,
               "run: mega_sum is less than one"
          );
     }
     else
     {     ok &= run_multi_newton;

          // num_zero
          num_zero = arg2size_t( *++argv, 2,
               "run: num_zero is less than two"
          );

          // num_sub
          num_sub = arg2size_t( *++argv, 1,
               "run: num_sub is less than one"
          );

          // num_sum
          num_sum = arg2size_t( *++argv, 1,
               "run: num_sum is less than one"
          );

          // use_ad
          ++argv;
          if( std::strcmp(*argv, "true") == 0 )
               use_ad = true;
          else if( std::strcmp(*argv, "false") == 0 )
               use_ad = false;
          else
          {     std::cerr << "run: use_ad = '" << *argv;
               std::cerr << "' is not true or false" << endl;
               exit(1);
          }
     }

     // run the test for each number of threads
     size_t num_threads, inuse_this_thread = 0;
     cout << "time_all  = [" << endl;
     for(num_threads = 0; num_threads <= max_threads; num_threads++)
     {     double time_out;

          // set the number of threads
          if( num_threads > 0 )
               ok &= team_create(num_threads);

          // ammount of memory initialy inuse by thread zero
          ok &= 0 == thread_alloc::thread_num();
          inuse_this_thread = thread_alloc::inuse(0);

          // run the requested test
          if( run_harmonic ) ok &=
               harmonic_time(time_out, test_time, num_threads, mega_sum);
          else
          {     ok &= run_multi_newton;
               ok &= multi_newton_time(
                    time_out                ,
                    test_time               ,
                    num_threads             ,
                    num_zero                ,
                    num_sub                 ,
                    num_sum                 ,
                    use_ad
               );
          }

          // set back to one thread and fee all avaialable memory
          if( num_threads > 0 )
               ok &= team_destroy();
          size_t thread;
          for(thread = 0; thread < num_threads; thread++)
          {     thread_alloc::free_available(thread);
               if( thread == 0 )
                    ok &= thread_alloc::inuse(thread) == inuse_this_thread;
               else     ok &= thread_alloc::inuse(thread) == 0;
          }
          cout << "\t" << time_out << " % ";
          if( num_threads == 0 )
               cout << "no threading" << endl;
          else     cout << num_threads << " threads" << endl;
     }
     cout << "];" << endl;
     //
     if( thread_alloc::free_all() )
          cout << "free_all      = true;"  << endl;
     else
     {     ok = false;
          cout << "free_all      = false;" << endl;
     }
     if( ok )
          cout << "OK            = true;"  << endl;
     else cout << "OK            = false;" << endl;

     return  ! ok;
}
Input File: multi_thread/thread_test.cpp cppad-20170000.3/doc/a11c_openmp.cpp.xml0000644000175200017650000002772613057470506016622 0ustar coincoin-web A Simple OpenMP Example and Test
Prev Next a11c_openmp.cpp

A Simple OpenMP Example and Test

Purpose
This example just demonstrates OpenMP and does not use CppAD at all.

Source Code 

# include <omp.h>
# include <limits>
# include <cmath>
# include <cassert>
# define NUMBER_THREADS 4

namespace {
     // Beginning of Example A.1.1.1c of OpenMP 2.5 standard document ---------
     void a1(int n, float *a, float *b)
     {     int i;
     # pragma omp parallel for
          for(i = 1; i < n; i++) /* i is private by default */
          {     assert( omp_get_num_threads() == NUMBER_THREADS );
               b[i] = (a[i] + a[i-1]) / float(2);
          }
     }
     // End of Example A.1.1.1c of OpenMP 2.5 standard document ---------------
}
bool a11c(void)
{     bool ok = true;

     // Test setup
     int i, n = 1000;
     float *a = new float[n];
     float *b = new float[n];
     for(i = 0; i < n; i++)
          a[i] = float(i);

     int n_thread = NUMBER_THREADS;   // number of threads in parallel regions
     omp_set_dynamic(0);              // off dynamic thread adjust
     omp_set_num_threads(n_thread);   // set the number of threads

     a1(n, a, b);

     // check the result
     float eps = float(100) * std::numeric_limits<float>::epsilon();
     for(i = 1; i < n ; i++)
          ok &= std::fabs( (float(2) * b[i] - a[i] - a[i-1]) / b[i] ) <= eps;

     delete [] a;
     delete [] b;

     return ok;
}
Input File: multi_thread/openmp/a11c_openmp.cpp cppad-20170000.3/doc/a11c_bthread.cpp.xml0000644000175200017650000004503213057470506016723 0ustar coincoin-web A Simple Boost Thread Example and Test
Prev Next a11c_bthread.cpp

A Simple Boost Thread Example and Test

Purpose
This example just demonstrates Boost threads and does not use CppAD at all.

Source Code 

# include <boost/thread.hpp>
# include <limits>
# include <cmath>
# include <cassert>
# define NUMBER_THREADS 4

namespace { // Begin empty namespace
     class worker_t
     {
     private:
          int    n_;
          float* a_;
          float* b_;
     public:
          void setup(size_t n, float* a, float* b)
          {     n_ = static_cast<int>(n);
               a_ = a;
               b_ = b;
          }
          // Beginning of Example A.1.1.1c of OpenMP 2.5 standard document
          void a1(int n, float *a, float *b)
          {     int i;
               // for some reason this function is missing on some systems
               // assert( bthread_is_multithreaded_np() > 0 );
               for(i = 1; i < n; i++)
                    b[i] = (a[i] + a[i-1]) / 2.0;
               return;
          }
          // End of Example A.1.1.1c of OpenMP 2.5 standard document
          void operator()()
          {     a1(n_, a_, b_); }
     };
}

bool a11c(void)
{     bool ok = true;

     // Test setup
     size_t i, j, n_total = 10;
     float *a = new float[n_total];
     float *b = new float[n_total];
     for(i = 0; i < n_total; i++)
          a[i] = float(i);

     // number of threads
     size_t number_threads = NUMBER_THREADS;

     // set of workers
     worker_t worker[NUMBER_THREADS];
     // threads for each worker
     boost::thread* bthread[NUMBER_THREADS];

     // Break the work up into sub work for each thread
     size_t  n     = n_total / number_threads;
     size_t  n_tmp = n;
     float*  a_tmp = a;
     float*  b_tmp = b;
     worker[0].setup(n_tmp, a_tmp, b_tmp);
     for(j = 1; j < number_threads; j++)
     {     n_tmp = n + 1;
          a_tmp = a_tmp + n - 1;
          b_tmp = b_tmp + n - 1;
          if( j == (number_threads - 1) )
               n_tmp = n_total - j * n + 1;

          worker[j].setup(n_tmp, a_tmp, b_tmp);

          // create this thread
          bthread[j] = new boost::thread(worker[j]);
     }

     // do this threads protion of the work
     worker[0]();

     // wait for other threads to finish
     for(j = 1; j < number_threads; j++)
     {     bthread[j]->join();
          delete bthread[j];
     }

     // check the result
     float eps = 100. * std::numeric_limits<float>::epsilon();
     for(i = 1; i < n ; i++)
          ok &= std::fabs( (2. * b[i] - a[i] - a[i-1]) / b[i] ) <= eps;

     delete [] a;
     delete [] b;

     return ok;
}
Input File: multi_thread/bthread/a11c_bthread.cpp cppad-20170000.3/doc/a11c_pthread.cpp.xml0000644000175200017650000005411713057470506016745 0ustar coincoin-web A Simple Parallel Pthread Example and Test
Prev Next a11c_pthread.cpp

A Simple Parallel Pthread Example and Test

Purpose
This example just demonstrates pthreads and does not use CppAD at all.

Source Code 

# include <pthread.h>
# include <limits>
# include <cmath>
# include <cassert>

// define CPPAD_NULPTR
# include <cppad/configure.hpp>
# if CPPAD_USE_CPLUSPLUS_2011
# define CPPAD_NULL nullptr
# else
# define CPPAD_NULL 0
# endif
//
# define NUMBER_THREADS 4

# ifdef NDEBUG
# define CHECK_ZERO(expression) expression
# else
# define CHECK_ZERO(expression) assert( expression == 0 );
# endif
namespace {
     // Beginning of Example A.1.1.1c of OpenMP 2.5 standard document ---------
     void a1(int n, float *a, float *b)
     {     int i;
          // for some reason this function is missing on some systems
          // assert( pthread_is_multithreaded_np() > 0 );
          for(i = 1; i < n; i++)
               b[i] = (a[i] + a[i-1]) / 2.0;
          return;
     }
     // End of Example A.1.1.1c of OpenMP 2.5 standard document ---------------
     struct start_arg { int  n; float* a; float* b; };
     void* start_routine(void* arg_vptr)
     {     start_arg* arg = static_cast<start_arg*>( arg_vptr );
          a1(arg->n, arg->a, arg->b);

          void* no_status = CPPAD_NULL;
          pthread_exit(no_status);

          return no_status;
     }
}

bool a11c(void)
{     bool ok = true;

     // Test setup
     int i, j, n_total = 10;
     float *a = new float[n_total];
     float *b = new float[n_total];
     for(i = 0; i < n_total; i++)
          a[i] = float(i);

     // number of threads
     int n_thread = NUMBER_THREADS;
     // the threads
     pthread_t thread[NUMBER_THREADS];
     // arguments to start_routine
     struct start_arg arg[NUMBER_THREADS];
     // attr
     pthread_attr_t attr;
     CHECK_ZERO( pthread_attr_init( &attr ) );
     CHECK_ZERO( pthread_attr_setdetachstate(&attr, PTHREAD_CREATE_JOINABLE) );
     //
     // Break the work up into sub work for each thread
     int n = n_total / n_thread;
     arg[0].n = n;
     arg[0].a = a;
     arg[0].b = b;
     for(j = 1; j < n_thread; j++)
     {     arg[j].n = n + 1;
          arg[j].a = arg[j-1].a + n - 1;
          arg[j].b = arg[j-1].b + n - 1;
          if( j == (n_thread - 1) )
               arg[j].n = n_total - j * n + 1;
     }
     for(j = 0; j < n_thread; j++)
     {     // inform each thread of which block it is working on
          void* arg_vptr = static_cast<void*>( &arg[j] );
          CHECK_ZERO( pthread_create(
               &thread[j], &attr, start_routine, arg_vptr
          ) );
     }
     for(j = 0; j < n_thread; j++)
     {     void* no_status = CPPAD_NULL;
          CHECK_ZERO( pthread_join(thread[j], &no_status) );
     }

     // check the result
     float eps = 100. * std::numeric_limits<float>::epsilon();
     for(i = 1; i < n ; i++)
          ok &= std::fabs( (2. * b[i] - a[i] - a[i-1]) / b[i] ) <= eps;

     delete [] a;
     delete [] b;

     return ok;
}
Input File: multi_thread/pthread/a11c_pthread.cpp cppad-20170000.3/doc/simple_ad_openmp.cpp.xml0000644000175200017650000007175113057470506020027 0ustar coincoin-web A Simple OpenMP AD: Example and Test
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A Simple OpenMP AD: Example and Test

Purpose
This example demonstrates how CppAD can be used in a OpenMP multi-threading environment.

Source Code 

# include <cppad/cppad.hpp>
# include <omp.h>
# define NUMBER_THREADS  4

namespace {
     // structure with problem specific information
     typedef struct {
          // function argument (worker input)
          double          x;
          // This structure would also have return information in it,
          // but this example only returns the ok flag
     } problem_specific;
     // =====================================================================
     // General purpose code you can copy to your application
     // =====================================================================
     using CppAD::thread_alloc;
     // ------------------------------------------------------------------
     // used to inform CppAD when we are in parallel execution mode
     bool in_parallel(void)
     {     return omp_in_parallel() != 0; }
     // ------------------------------------------------------------------
     // used to inform CppAD of the current thread number
     size_t thread_number(void)
     {     return static_cast<size_t>( omp_get_thread_num() ); }
     // ------------------------------------------------------------------
     // structure with information for one thread
     typedef struct {
          // false if an error occurs, true otherwise (worker output)
          bool               ok;
     } thread_one_t;
     // vector with information for all threads
     thread_one_t thread_all_[NUMBER_THREADS];
     // ------------------------------------------------------------------
     // function that calls all the workers
     bool worker(problem_specific* info);
     bool run_all_workers(size_t num_threads, problem_specific* info_all[])
     {     bool ok = true;

          // initialize thread_all_
          int thread_num, int_num_threads = int(num_threads);
          for(thread_num = 0; thread_num < int_num_threads; thread_num++)
          {     // initialize as false to make sure gets called for all threads
               thread_all_[thread_num].ok         = false;
          }

          // turn off dynamic thread adjustment
          omp_set_dynamic(0);

          // set the number of OpenMP threads
          omp_set_num_threads( int_num_threads );

          // setup for using CppAD::AD<double> in parallel
          thread_alloc::parallel_setup(
               num_threads, in_parallel, thread_number
          );
          thread_alloc::hold_memory(true);
          CppAD::parallel_ad<double>();

          // execute worker in parallel
# pragma omp parallel for
     for(thread_num = 0; thread_num < int_num_threads; thread_num++)
          thread_all_[thread_num].ok = worker(info_all[thread_num]);
// end omp parallel for

          // set the number of OpenMP threads to one
          omp_set_num_threads(1);

          // now inform CppAD that there is only one thread
          thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL);
          thread_alloc::hold_memory(false);
          CppAD::parallel_ad<double>();

          // check to ok flag returned by during calls to work by other threads
          for(thread_num = 1; thread_num < int_num_threads; thread_num++)
               ok &= thread_all_[thread_num].ok;

          return ok;
     }
     // =====================================================================
     // End of General purpose code
     // =====================================================================
     // function that does the work for one thread
     bool worker(problem_specific* info)
     {     using CppAD::NearEqual;
          using CppAD::AD;
          bool ok = true;

          // CppAD::vector uses the CppAD fast multi-threading allocator
          CppAD::vector< AD<double> > ax(1), ay(1);
          ax[0] = info->x;
          Independent(ax);
          ay[0] = sqrt( ax[0] * ax[0] );
          CppAD::ADFun<double> f(ax, ay);

          // Check function value corresponds to the identity
          double eps = 10. * CppAD::numeric_limits<double>::epsilon();
          ok        &= NearEqual(ay[0], ax[0], eps, eps);

          // Check derivative value corresponds to the identity.
          CppAD::vector<double> d_x(1), d_y(1);
          d_x[0] = 1.;
          d_y    = f.Forward(1, d_x);
          ok    &= NearEqual(d_x[0], 1., eps, eps);

          return ok;
     }
}
bool simple_ad(void)
{     bool ok = true;
     size_t num_threads = NUMBER_THREADS;

     // Check that no memory is in use or avialable at start
     // (using thread_alloc in sequential mode)
     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     ok &= thread_alloc::inuse(thread_num) == 0;
          ok &= thread_alloc::available(thread_num) == 0;
     }

     // initialize info_all
     problem_specific *info, *info_all[NUMBER_THREADS];
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     // problem specific information
          size_t min_bytes(sizeof(info)), cap_bytes;
          void*  v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes);
          info         = static_cast<problem_specific*>(v_ptr);
          info->x      = double(thread_num) + 1.;
          info_all[thread_num] = info;
     }

     ok &= run_all_workers(num_threads, info_all);

     // go down so that free memory for other threads before memory for master
     thread_num = num_threads;
     while(thread_num--)
     {     // delete problem specific information
          void* v_ptr = static_cast<void*>( info_all[thread_num] );
          thread_alloc::return_memory( v_ptr );
          // check that there is no longer any memory inuse by this thread
          ok &= thread_alloc::inuse(thread_num) == 0;
          // return all memory being held for future use by this thread
          thread_alloc::free_available(thread_num);
     }

     return ok;
}
Input File: multi_thread/openmp/simple_ad_openmp.cpp cppad-20170000.3/doc/simple_ad_bthread.cpp.xml0000644000175200017650000011367613057470506020145 0ustar coincoin-web A Simple Boost Threading AD: Example and Test
Prev Next simple_ad_bthread.cpp

A Simple Boost Threading AD: Example and Test

Purpose
This example demonstrates how CppAD can be used in a boost multi-threading environment.

Source Code 

# include <cppad/cppad.hpp>
# include <boost/thread.hpp>
# define NUMBER_THREADS  4

namespace {
     // structure with problem specific information
     typedef struct {
          // function argument (worker input)
          double          x;
          // This structure would also have return information in it,
          // but this example only returns the ok flag
     } problem_specific;
     // =====================================================================
     // General purpose code you can copy to your application
     // =====================================================================
     using CppAD::thread_alloc;
     // ------------------------------------------------------------------
     // thread specific point to the thread number (initialize as null)
     void cleanup(size_t*)
     {     return; }
     boost::thread_specific_ptr<size_t> thread_num_ptr_(cleanup);

     // Are we in sequential mode; i.e., other threads are waiting for
     // master thread to set up next job ?
     bool sequential_execution_ = true;

     // used to inform CppAD when we are in parallel execution mode
     bool in_parallel(void)
     {     return ! sequential_execution_; }

     // used to inform CppAD of current thread number thread_number()
     size_t thread_number(void)
     {     // return thread_all_[thread_num].thread_num
          return *thread_num_ptr_.get();
     }
     // ---------------------------------------------------------------------
     // structure with information for one thread
     typedef struct {
          // number for this thread (thread specific points here)
          size_t            thread_num;
          // pointer to this boost thread
          boost::thread*    bthread;
          // false if an error occurs, true otherwise
          bool              ok;
          // pointer to problem specific information
          problem_specific* info;
     } thread_one_t;
     // vector with information for all threads
     thread_one_t thread_all_[NUMBER_THREADS];
     // --------------------------------------------------------------------
     // function that initializes the thread and then calls actual worker
     bool worker(size_t thread_num, problem_specific* info);
     void run_one_worker(size_t thread_num)
     {     bool ok = true;

          // The master thread should call worker directly
          ok &= thread_num != 0;

          // This is not the master thread, so thread specific infromation
          // has not yet been set. We use it to inform other routines
          // of this threads number.
          // We must do this before calling thread_alloc::thread_num().
          thread_num_ptr_.reset(& thread_all_[thread_num].thread_num);

          // Check the value of thread_alloc::thread_num().
          ok = thread_num == thread_alloc::thread_num();

          // Now do the work
          ok &= worker(thread_num, thread_all_[thread_num].info);

          // pass back ok information for this thread
          thread_all_[thread_num].ok = ok;

          // no return value
          return;
     }
     // ----------------------------------------------------------------------
     // function that calls all the workers
     bool run_all_workers(size_t num_threads, problem_specific* info_all[])
     {     bool ok = true;

          // initialize thread_all_ (execpt for pthread_id)
          size_t thread_num;
          for(thread_num = 0; thread_num < num_threads; thread_num++)
          {     // pointed to by thread specific info for this thread
               thread_all_[thread_num].thread_num = thread_num;
               // initialize as false to make sure worker gets called by other
               // threads. Note that thread_all_[0].ok does not get used
               thread_all_[thread_num].ok         = false;
               // problem specific information
               thread_all_[thread_num].info       = info_all[thread_num];
          }

          // master bthread number
          thread_num_ptr_.reset(& thread_all_[0].thread_num);

          // Now thread_number() has necessary information for this thread
          // (number zero), and while still in sequential mode,
          // call setup for using CppAD::AD<double> in parallel mode.
          thread_alloc::parallel_setup(
               num_threads, in_parallel, thread_number
          );
          thread_alloc::hold_memory(true);
          CppAD::parallel_ad<double>();

          // inform CppAD that we now may be in parallel execution mode
          sequential_execution_ = false;

          // This master thread is already running, we need to create
          // num_threads - 1 more threads
          thread_all_[0].bthread = CPPAD_NULL;
          for(thread_num = 1; thread_num < num_threads; thread_num++)
          {     // Create the thread with thread number equal to thread_num
               thread_all_[thread_num].bthread =
                    new boost::thread(run_one_worker, thread_num);
          }

          // now call worker for the master thread
          thread_num = thread_alloc::thread_num();
          ok &= thread_num == 0;
          ok &= worker(thread_num, thread_all_[thread_num].info);

          // now wait for the other threads to finish
          for(thread_num = 1; thread_num < num_threads; thread_num++)
          {     thread_all_[thread_num].bthread->join();
               delete thread_all_[thread_num].bthread;
               thread_all_[thread_num].bthread = CPPAD_NULL;
          }

          // Inform CppAD that we now are definately back to sequential mode
          sequential_execution_ = true;

          // now inform CppAD that there is only one thread
          thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL);
          thread_alloc::hold_memory(false);
          CppAD::parallel_ad<double>();

          // check to ok flag returned by during calls to work by other threads
          for(thread_num = 1; thread_num < num_threads; thread_num++)
               ok &= thread_all_[thread_num].ok;

          return ok;
     }
     // =====================================================================
     // End of General purpose code
     // =====================================================================
     // function that does the work for one thread
     bool worker(size_t thread_num, problem_specific* info)
     {     bool ok = true;

          // CppAD::vector uses the CppAD fast multi-threading allocator
          CppAD::vector< CppAD::AD<double> > ax(1), ay(1);
          ax[0] = info->x;
          Independent(ax);
          ay[0] = sqrt( ax[0] * ax[0] );
          CppAD::ADFun<double> f(ax, ay);

          // Check function value corresponds to the identity
          double eps = 10. * CppAD::numeric_limits<double>::epsilon();
          ok        &= CppAD::NearEqual(ay[0], ax[0], eps, eps);

          // Check derivative value corresponds to the identity.
          CppAD::vector<double> d_x(1), d_y(1);
          d_x[0] = 1.;
          d_y    = f.Forward(1, d_x);
          ok    &= CppAD::NearEqual(d_x[0], 1., eps, eps);

          return ok;
     }
}
bool simple_ad(void)
{     bool ok = true;
     size_t num_threads = NUMBER_THREADS;

     // Check that no memory is in use or avialable at start
     // (using thread_alloc in sequential mode)
     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     ok &= thread_alloc::inuse(thread_num) == 0;
          ok &= thread_alloc::available(thread_num) == 0;
     }

     // initialize info_all
     problem_specific *info, *info_all[NUMBER_THREADS];
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     // problem specific information
          size_t min_bytes(sizeof(info)), cap_bytes;
          void*  v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes);
          info         = static_cast<problem_specific*>(v_ptr);
          info->x      = double(thread_num) + 1.;
          info_all[thread_num] = info;
     }

     ok &= run_all_workers(num_threads, info_all);

     // go down so that free memory for other threads before memory for master
     thread_num = num_threads;
     while(thread_num--)
     {     // delete problem specific information
          void* v_ptr = static_cast<void*>( info_all[thread_num] );
          thread_alloc::return_memory( v_ptr );
          // check that there is no longer any memory inuse by this thread
          ok &= thread_alloc::inuse(thread_num) == 0;
          // return all memory being held for future use by this thread
          thread_alloc::free_available(thread_num);
     }

     return ok;
}
Input File: multi_thread/bthread/simple_ad_bthread.cpp cppad-20170000.3/doc/simple_ad_pthread.cpp.xml0000644000175200017650000012640413057470506020154 0ustar coincoin-web A Simple pthread AD: Example and Test
Prev Next simple_ad_pthread.cpp

A Simple pthread AD: Example and Test

Purpose
This example demonstrates how CppAD can be used in a pthread multi-threading environment.

Source Code 

# include <cppad/cppad.hpp>
# include <pthread.h>
# define NUMBER_THREADS  4

namespace {
     // structure with problem specific information
     typedef struct {
          // function argument (worker input)
          double          x;
          // This structure would also have return information in it,
          // but this example only returns the ok flag
     } problem_specific;
     // =====================================================================
     // General purpose code you can copy to your application
     // =====================================================================
     using CppAD::thread_alloc;
     // ------------------------------------------------------------------
     // key for accessing thread specific information
     pthread_key_t thread_specific_key_;

     // no need to destroy thread specific information
     void thread_specific_destructor(void* thread_num_vptr)
     {     return; }

     // Are we in sequential mode; i.e., other threads are waiting for
     // master thread to set up next job ?
     bool sequential_execution_ = true;

     // used to inform CppAD when we are in parallel execution mode
     bool in_parallel(void)
     {     return ! sequential_execution_; }

     // used to inform CppAD of current thread number thread_number()
     size_t thread_number(void)
     {     // get thread specific information
          void*   thread_num_vptr = pthread_getspecific(thread_specific_key_);
          size_t* thread_num_ptr  = static_cast<size_t*>(thread_num_vptr);
          size_t  thread_num      = *thread_num_ptr;
          return thread_num;
     }
     // ---------------------------------------------------------------------
     // structure with information for one thread
     typedef struct {
          // number for this thread (thread specific points here)
          size_t            thread_num;
          // pthread unique identifier for this thread
          pthread_t         pthread_id;
          // false if an error occurs, true otherwise
          bool              ok;
          // pointer to problem specific information
          problem_specific* info;
     } thread_one_t;
     // vector with information for all threads
     thread_one_t thread_all_[NUMBER_THREADS];
     // --------------------------------------------------------------------
     // function that initializes the thread and then calls the actual worker
     bool worker(size_t thread_num, problem_specific* info);
     void* run_one_worker(void* thread_num_vptr)
     {     bool ok = true;

          // thread_num for this thread
          size_t thread_num = *static_cast<size_t*>(thread_num_vptr);

          // The master thread should call worker directly
          ok &= thread_num != 0;

          // This is not the master thread, so thread specific infromation
          // has not yet been set. We use it to inform other routines
          // of this threads number.
          // We must do this before calling thread_alloc::thread_num().
          int rc = pthread_setspecific(
               thread_specific_key_,
               thread_num_vptr
          );
          ok &= rc == 0;

          // check the value of thread_alloc::thread_num().
          ok = thread_num == thread_alloc::thread_num();

          // Now do the work
          ok &= worker(thread_num, thread_all_[thread_num].info);

          // pass back ok information for this thread
          thread_all_[thread_num].ok = ok;

          // no return value
          return CPPAD_NULL;
     }
     // --------------------------------------------------------------------
     // function that calls all the workers
     bool run_all_workers(size_t num_threads, problem_specific* info_all[])
     {     bool ok = true;

          // initialize thread_all_ (execpt for pthread_id)
          size_t thread_num;
          for(thread_num = 0; thread_num < num_threads; thread_num++)
          {     // pointed to by thread specific info for this thread
               thread_all_[thread_num].thread_num = thread_num;
               // initialize as false to make sure worker gets called by other
               // threads. Note that thread_all_[0].ok does not get used
               thread_all_[thread_num].ok         = false;
               // problem specific information
               thread_all_[thread_num].info       = info_all[thread_num];
          }

          // master pthread_id
          thread_all_[0].pthread_id = pthread_self();

          // error flag for calls to pthread library
          int rc;

          // create a key for thread specific information
          rc = pthread_key_create(
               &thread_specific_key_, thread_specific_destructor
          );
          ok &= (rc == 0);

          // set thread specific information for this (master thread)
          void* thread_num_vptr = static_cast<void*>(
               &(thread_all_[0].thread_num)
          );
          rc = pthread_setspecific(thread_specific_key_, thread_num_vptr);
          ok &= (rc == 0);

          // Now thread_number() has necessary information for this thread
          // (number zero), and while still in sequential mode,
          // call setup for using CppAD::AD<double> in parallel mode.
          thread_alloc::parallel_setup(
               num_threads, in_parallel, thread_number
          );
          thread_alloc::hold_memory(true);
          CppAD::parallel_ad<double>();

          // inform CppAD that we now may be in parallel execution mode
          sequential_execution_ = false;

          // structure used to create the threads
          pthread_t       pthread_id;
          // default for pthread_attr_setdetachstate is PTHREAD_CREATE_JOINABLE
          pthread_attr_t* no_attr= CPPAD_NULL;

          // This master thread is already running, we need to create
          // num_threads - 1 more threads
          for(thread_num = 1; thread_num < num_threads; thread_num++)
          {     // Create the thread with thread number equal to thread_num
               thread_num_vptr = static_cast<void*> (
                    &(thread_all_[thread_num].thread_num)
               );
               rc = pthread_create(
                         &pthread_id ,
                         no_attr     ,
                         run_one_worker,
                         thread_num_vptr
               );
               thread_all_[thread_num].pthread_id = pthread_id;
               ok &= (rc == 0);
          }

          // now call worker for the master thread
          thread_num = thread_alloc::thread_num();
          ok &= thread_num == 0;
          ok &= worker(thread_num, thread_all_[thread_num].info);

          // now wait for the other threads to finish
          for(thread_num = 1; thread_num < num_threads; thread_num++)
          {     void* no_status = CPPAD_NULL;
               rc      = pthread_join(
                    thread_all_[thread_num].pthread_id, &no_status
               );
               ok &= (rc == 0);
          }

          // Inform CppAD that we now are definately back to sequential mode
          sequential_execution_ = true;

          // now inform CppAD that there is only one thread
          thread_alloc::parallel_setup(1, CPPAD_NULL, CPPAD_NULL);
          thread_alloc::hold_memory(false);
          CppAD::parallel_ad<double>();

          // destroy the key for thread specific data
          pthread_key_delete(thread_specific_key_);

          // check to ok flag returned by during calls to work by other threads
          for(thread_num = 1; thread_num < num_threads; thread_num++)
               ok &= thread_all_[thread_num].ok;

          return ok;
     }
     // =====================================================================
     // End of General purpose code
     // =====================================================================
     // function that does the work for one thread
     bool worker(size_t thread_num, problem_specific* info)
     {     bool ok = true;

          // CppAD::vector uses the CppAD fast multi-threading allocator
          CppAD::vector< CppAD::AD<double> > ax(1), ay(1);
          ax[0] = info->x;
          Independent(ax);
          ay[0] = sqrt( ax[0] * ax[0] );
          CppAD::ADFun<double> f(ax, ay);

          // Check function value corresponds to the identity
          double eps = 10. * CppAD::numeric_limits<double>::epsilon();
          ok        &= CppAD::NearEqual(ay[0], ax[0], eps, eps);

          // Check derivative value corresponds to the identity.
          CppAD::vector<double> d_x(1), d_y(1);
          d_x[0] = 1.;
          d_y    = f.Forward(1, d_x);
          ok    &= CppAD::NearEqual(d_x[0], 1., eps, eps);

          return ok;
     }
}
bool simple_ad(void)
{     bool ok = true;
     size_t num_threads = NUMBER_THREADS;

     // Check that no memory is in use or avialable at start
     // (using thread_alloc in sequential mode)
     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     ok &= thread_alloc::inuse(thread_num) == 0;
          ok &= thread_alloc::available(thread_num) == 0;
     }

     // initialize info_all
     problem_specific *info, *info_all[NUMBER_THREADS];
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     // problem specific information
          size_t min_bytes(sizeof(info)), cap_bytes;
          void*  v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes);
          info         = static_cast<problem_specific*>(v_ptr);
          info->x      = double(thread_num) + 1.;
          info_all[thread_num] = info;
     }

     ok &= run_all_workers(num_threads, info_all);

     // go down so that free memory for other threads before memory for master
     thread_num = num_threads;
     while(thread_num--)
     {     // delete problem specific information
          void* v_ptr = static_cast<void*>( info_all[thread_num] );
          thread_alloc::return_memory( v_ptr );
          // check that there is no longer any memory inuse by this thread
          ok &= thread_alloc::inuse(thread_num) == 0;
          // return all memory being held for future use by this thread
          thread_alloc::free_available(thread_num);
     }

     return ok;
}
Input File: multi_thread/pthread/simple_ad_pthread.cpp cppad-20170000.3/doc/team_example.cpp.xml0000644000175200017650000005135113057470506017147 0ustar coincoin-web Using a Team of AD Threads: Example and Test
Prev Next team_example.cpp

Using a Team of AD Threads: Example and Test

Purpose
This example demonstrates how use a team threads with CppAD.

thread_team
The following three implementations of the team_thread.hpp specifications are included:
team_openmp.cpp OpenMP Implementation of a Team of AD Threads
team_bthread.cpp Boost Thread Implementation of a Team of AD Threads
team_pthread.cpp Pthread Implementation of a Team of AD Threads

Source Code 

# include <cppad/cppad.hpp>
# include "team_thread.hpp"
# define NUMBER_THREADS  4

namespace {
     using CppAD::thread_alloc;

     // structure with information for one thread
     typedef struct {
          // function argument (worker input)
          double          x;
          // false if an error occurs, true otherwise (worker output)
          bool            ok;
     } work_one_t;
     // vector with information for all threads
     // (use pointers instead of values to avoid false sharing)
     work_one_t* work_all_[NUMBER_THREADS];
     // --------------------------------------------------------------------
     // function that does the work for one thread
     void worker(void)
     {     using CppAD::NearEqual;
          using CppAD::AD;
          bool ok = true;
          size_t thread_num = thread_alloc::thread_num();

          // CppAD::vector uses the CppAD fast multi-threading allocator
          CppAD::vector< AD<double> > ax(1), ay(1);
          ax[0] = work_all_[thread_num]->x;
          Independent(ax);
          ay[0] = sqrt( ax[0] * ax[0] );
          CppAD::ADFun<double> f(ax, ay);

          // Check function value corresponds to the identity
          double eps = 10. * CppAD::numeric_limits<double>::epsilon();
          ok        &= NearEqual(ay[0], ax[0], eps, eps);

          // Check derivative value corresponds to the identity.
          CppAD::vector<double> d_x(1), d_y(1);
          d_x[0] = 1.;
          d_y    = f.Forward(1, d_x);
          ok    &= NearEqual(d_x[0], 1., eps, eps);

          // pass back ok information for this thread
          work_all_[thread_num]->ok = ok;
     }
}

// This test routine is only called by the master thread (thread_num = 0).
bool team_example(void)
{     bool ok = true;

     size_t num_threads = NUMBER_THREADS;

     // Check that no memory is in use or avialable at start
     // (using thread_alloc in sequential mode)
     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     ok &= thread_alloc::inuse(thread_num) == 0;
          ok &= thread_alloc::available(thread_num) == 0;
     }

     // initialize work_all_
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     // allocate separate memory for this thread to avoid false sharing
          size_t min_bytes(sizeof(work_one_t)), cap_bytes;
          void*  v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes);
          work_all_[thread_num]     = static_cast<work_one_t*>(v_ptr);
          // incase this thread's worker does not get called
          work_all_[thread_num]->ok = false;
          // parameter that defines the work for this thread
          work_all_[thread_num]->x  = double(thread_num) + 1.;
     }

     ok &= team_create(num_threads);
     ok &= team_work(worker);
     ok &= team_destroy();

     // go down so that free memrory for other threads before memory for master
     thread_num = num_threads;
     while(thread_num--)
     {     // check that this thread was ok with the work it did
          ok &= work_all_[thread_num]->ok;
          // delete problem specific information
          void* v_ptr = static_cast<void*>( work_all_[thread_num] );
          thread_alloc::return_memory( v_ptr );
          // check that there is no longer any memory inuse by this thread
          // (for general applications, the master might still be using memory)
          ok &= thread_alloc::inuse(thread_num) == 0;
          // return all memory being held for future use by this thread
          thread_alloc::free_available(thread_num);
     }
     return ok;
}
Input File: multi_thread/team_example.cpp cppad-20170000.3/doc/harmonic.cpp.xml0000644000175200017650000002403613057470506016306 0ustar coincoin-web Multi-Threaded Implementation of Summation of 1/i
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Multi-Threaded Implementation of Summation of 1/i

Syntax
ok = harmonic(sum, num_sum, num_threads)

Summation
Multi-threaded computation of the summation that defines the harmonic series s = 1 + 1 / 2 + 1 / 3 + . . . + 1 / n
ok
This return value has prototype
     bool ok
 If this return value is false, an error occurred during harmonic.

sum
This argument has prototype
     double& sum
 The input value of the argument does not matter. Upon return it is the value of the summation; i.e. s .

num_sum
This argument has prototype
     size_t num_sum
 It specifies the number of terms in the summation; i.e. n .

num_threads
This argument has prototype
     size_t num_threads
 It specifies the number of threads that are available for this test. If it is zero, the test is run without a multi-threading environment.

Contents
harmonic_time.cppTiming Test of Multi-Threaded Summation of 1/i
harmonic_work.cppMulti-threading Sum of 1/i Utility Routines

Source 

// general purpose multi-threading interface
# include "team_thread.hpp"
// special utilities for the harmonic problem
# include "harmonic_work.hpp"

bool harmonic(double& sum, size_t num_sum, size_t num_threads)
{     // sum = 1/num_sum + 1/(num_sum-1) + ... + 1
     bool ok = true;

     // setup the work for num_threads_ threads
     ok &= harmonic_setup(num_sum, num_threads);

     // now do the work for each thread
     if( num_threads > 0 )
          team_work( harmonic_worker );
     else     harmonic_worker();

     // now combine the result for all the threads
     ok &= harmonic_combine(sum);

     return ok;
}
Input File: multi_thread/harmonic.cpp cppad-20170000.3/doc/harmonic_time.cpp.xml0000644000175200017650000004575013057470506017332 0ustar coincoin-web Timing Test of Multi-Threaded Summation of 1/i
Prev Next harmonic_time.cpp

Timing Test of Multi-Threaded Summation of 1/i

Syntax
ok = harmonic_time(time_out, num_threads, mega_sum)

Purpose
Runs a correctness and timing test for a multi-threaded computation of the summation that defines the harmonic series 1 + 1 / 2 + 1 / 3 + . . . + 1 / n This routine must be called in sequential execution mode, even though in_parallel may return true.

ok
This return value has prototype
     bool ok
 If it is true, harmonic_time passed the correctness test. Otherwise it is false.

time_out
This argument has prototype
     double& time_out
 The input value of the argument does not matter. Upon return it is the number of wall clock seconds required for to compute the summation .

test_time
Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported time_out is the total wall clock time divided by the number of repeats.

num_threads
This argument has prototype
     size_t num_threads
 It specifies the number of threads that are available for this test. If it is zero, the test is run without the multi-threading environment and
     1 == CppAD::thread_alloc::num_threads()
 when harmonic_time is called. If it is non-zero, the test is run with the multi-threading and
     num_threads = CppAD::thread_alloc::num_threads()
 when harmonic_time is called.

mega_sum
This argument has prototype
     size_t& mega_sum
 and is greater than zero. The value n in the summation . is equal to 10 6 times mega_sum .

Source 

# include <omp.h>
# include <cstring>
# include <limits>
# include <vector>
# include <iostream>
# include <cstdlib>
# include <algorithm>

// Note there is no mention of parallel mode in the documentation for
// speed_test (so it is safe to use without special consideration).
# include <cppad/utility/time_test.hpp>
# include "harmonic.hpp"

namespace { // empty namespace

     // value of num_threads in previous call to harmonic_time.
     size_t num_threads_;

     // value of mega_sum in previous call to harmonic_time.
     size_t mega_sum_;

     // value of sum resulting from most recent call to test_once
     double sum_ = 0.;

     void test_once(void)
     {     if( mega_sum_ < 1 )
          {     std::cerr << "harmonic_time: mega_sum < 1" << std::endl;
               exit(1);
          }
          size_t num_sum = mega_sum_ * 1000000;
          bool ok = harmonic(sum_, num_sum, num_threads_);
          if( ! ok )
          {     std::cerr << "harmonic: error" << std::endl;
               exit(1);
          }
          return;
     }

     void test_repeat(size_t repeat)
     {     size_t i;
          for(i = 0; i < repeat; i++)
               test_once();
          return;
     }
} // end empty namespace

bool harmonic_time(
     double& time_out, double test_time, size_t num_threads, size_t mega_sum)
{     bool ok  = true;
     using std::vector;

     // arguments passed to harmonic_time
     num_threads_ = num_threads;
     mega_sum_    = mega_sum;

     // convert zero to actual number of threads
     num_threads  = std::max(num_threads_, size_t(1));

     // expect number of threads to already be set up
     ok &= num_threads == CppAD::thread_alloc::num_threads();

     // run the test case and set the time return value
     time_out = CppAD::time_test(test_repeat, test_time);

     // Correctness check
     double eps   = mega_sum_ * 1e3 * std::numeric_limits<double>::epsilon();
     size_t i     = mega_sum_ * 1000000;
     double check = 0.;
     while(i)
          check += 1. / double(i--);
     ok &= std::fabs(sum_ - check) <= eps;

     return ok;
}
Input File: multi_thread/harmonic_time.cpp cppad-20170000.3/doc/harmonic_work.cpp.xml0000644000175200017650000006014313057470506017347 0ustar coincoin-web Multi-threading Sum of 1/i Utility Routines
Prev Next harmonic_work.cpp

Multi-threading Sum of 1/i Utility Routines

Syntax
ok = harmonic_setup(num_sum, num_threads)
 harmonic_worker()
 ok = harmonic_combine(sum)
Purpose
These routines aid in the multi-threading computation of the summation that defines the harmonic series 1 + 1 / 2 + 1 / 3 + . . . + 1 / n
harmonic_setup
Calling this function splits up the computation of the summation into different parts for each thread.

num_sum
The argument num_sum has prototype
     size_t num_sum
 It specifies the value of n in the summation.

num_threads
The argument num_threads has prototype
     size_t num_threads
 It specifies the number of threads that will be used for the summation. In the special case where num_thread is zero, the summation should be done by one thread, but without the overhead of the multi_threading system.

harmonic_worker
Calling this function does the computation for one thread. Following a call to harmonic_setup, this function should be called by each of the num_threads threads.

harmonic_combine
After the num_threads threads have completed their calls to harmonic_worker, this function call will combine the results and return the final summation.

Source 

# include <cppad/cppad.hpp>
# include "harmonic_work.hpp"
# define MAX_NUMBER_THREADS 48

namespace {
     using CppAD::thread_alloc;

     // number of threads specified by previous call to harmonic_setup
     size_t num_threads_ = 0;

     // structure with information for one thread
     typedef struct {
          // index to start summation at (worker input)
          size_t start;
          // index to end summation at (worker input)
          size_t stop;
          // summation for this thread (worker output)
          double sum;
          // false if an error occurs, true otherwise (worker output)
          bool   ok;
     } work_one_t;
     // vector with information for all threads
     // (use pointers instead of values to avoid false sharing)
     work_one_t* work_all_[MAX_NUMBER_THREADS];
}
// -----------------------------------------------------------------------
// do the work for one thread
void harmonic_worker(void)
{     // sum =  1/(stop-1) + 1/(stop-2) + ... + 1/start
     size_t thread_num  = thread_alloc::thread_num();
     size_t num_threads = std::max(num_threads_, size_t(1));
     bool   ok          = thread_num < num_threads;
     size_t start       = work_all_[thread_num]->start;
     size_t stop        = work_all_[thread_num]->stop;
     double sum         = 0.;

     ok &= stop > start;
     size_t i = stop;
     while( i > start )
     {     i--;
          sum += 1. / double(i);
     }

     work_all_[thread_num]->sum = sum;
     work_all_[thread_num]->ok  = ok;
}
// -----------------------------------------------------------------------
// setup the work up for multiple threads
bool harmonic_setup(size_t num_sum, size_t num_threads)
{     // sum = 1/num_sum + 1/(num_sum-1) + ... + 1
     num_threads_ = num_threads;
     num_threads  = std::max(num_threads_, size_t(1));
     bool ok      = num_threads == thread_alloc::num_threads();
     ok          &= num_sum >= num_threads;

     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     // allocate separate memory for this thread to avoid false sharing
          size_t min_bytes(sizeof(work_one_t)), cap_bytes;
          void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes);
          work_all_[thread_num] = static_cast<work_one_t*>(v_ptr);
          // in case this thread's worker does not get called
          work_all_[thread_num]->ok = false;
          // parameters that define the work for this and previous thread
          if( thread_num == 0 )
               work_all_[0]->start = 1;
          else
          {     size_t index  = (num_sum * thread_num) / num_threads;
               work_all_[thread_num-1]->stop = index;
               work_all_[thread_num]->start  = index;
          }
     }
     work_all_[num_threads-1]->stop = num_sum + 1;
     return ok;
}
// -----------------------------------------------------------------------
// get the result of the work
bool harmonic_combine(double& sum)
{     // sum = 1/num_sum + 1/(num_sum-1) + ... + 1
     bool ok            = true;
     size_t num_threads = std::max(num_threads_, size_t(1));
     sum                = 0.;

     // go down so that free memory for other threads before memory for master
     size_t thread_num = num_threads;
     while(thread_num--)
     {     // check that this tread was ok with the work it did
          ok  &= work_all_[thread_num]->ok;
          // add this threads contribution to the sum
          sum += work_all_[thread_num]->sum;
          // delete problem specific information
          void* v_ptr = static_cast<void*>( work_all_[thread_num] );
          thread_alloc::return_memory( v_ptr );
          // check that there is no longer any memory inuse by this thread
          // (for general applications, the master might still be using memory)
          ok &= thread_alloc::inuse(thread_num) == 0;
          // return all memory being held for future use by this thread
          thread_alloc::free_available(thread_num);
     }
     return ok;
}
Input File: multi_thread/harmonic_work.cpp cppad-20170000.3/doc/multi_newton.cpp.xml0000644000175200017650000005774613057470506017250 0ustar coincoin-web A Multi-Threaded Newton's Method
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A Multi-Threaded Newton's Method

Syntax
ok = multi_newton(xout,
     fun, num_sub, xlow, xup, epsilon, max_itr, num_threads
)

Purpose
Multi-threaded determination of the argument values x , in the interval [ a , b ] (where a < b ), such that f ( x ) = 0 .

Method
For i = 0 , … , n , we define the i-th grid point g i by g i = a n - i n + b i n For i = 0 , … , n -1 , we define the i-th sub-interval of [ a , b ] by I i = [ g i , g i + 1 ] Newton's method is applied starting at the center of each of the sub-intervals I i for i = 0 , … , n -1 and at most one zero is found for each sub-interval.

ok
The return value ok has prototype
     bool ok
 If an error occurs, it is false, otherwise it is true.

xout
The argument xout has the prototype
     CppAD::vector<double>& xout
 The input size and value of the elements of xout do not matter. Upon return from multi_newton, the size of xout is less than or equal the number of sub-intervals n and | f ( xout [ i ] ) | ≤ epsilon for each valid index 0 <= i < xout.size() . Two x solutions are considered equal (and joined as one) if the absolute difference between the solutions is less than ( b - a ) / n .

fun
The argument fun has prototype
     void fun (double x, double& f, double& df)
 This function must evaluate f ( x ) , and its derivative f ( 1 ) ( x ) , using the syntax
     fun(x, f, df)
 where the arguments to fun have the prototypes
     double    x
     double&   f
     double&   df
 . The input values of f and df do not matter. Upon return they are f ( x ) and f ( 1 ) ( x ) respectively.

num_sub
The argument num_sub has prototype
     size_t num_sub
 It specifies the number of sub-intervals; i.e., n .

xlow
The argument xlow has prototype
     double xlow
 It specifies the lower limit for the entire search interval; i.e., a .

xup
The argument xup has prototype
     double xup
 It specifies the upper limit for the entire search interval; i.e., b .

epsilon
The argument epsilon has prototype
     double epsilon
 It specifies the convergence criteria for Newton's method in terms of how small the function value must be.

max_itr
The argument max_itr has prototype
     size_t max_itr
 It specifies the maximum number of iterations of Newton's method to try before giving up on convergence (on each sub-interval).

num_threads
This argument has prototype
     size_t num_threads
 It specifies the number of threads that are available for this test. If it is zero, the test is run without the multi-threading environment.

Contents
multi_newton_time.cppTiming Test of Multi-Threaded Newton Method
multi_newton_work.cppMulti-threading Newton Method Utility Routines

Source 

// general purpose multi-threading interface
# include "team_thread.hpp"
// special utilities for the multi_newton problem
# include "multi_newton_work.hpp"

bool multi_newton(
     CppAD::vector<double> &xout                ,
     void fun(double x, double& f, double& df)  ,
     size_t num_sub                             ,
     double xlow                                ,
     double xup                                 ,
     double epsilon                             ,
     size_t max_itr                             ,
     size_t num_threads                         )
{
     bool ok = true;
     using CppAD::AD;
     using CppAD::vector;

     // setup the work for num_threads threads
     ok &= multi_newton_setup(
          fun, num_sub, xlow, xup, epsilon, max_itr, num_threads
     );

     // now do the work for each thread
     if( num_threads > 0 )
          team_work( multi_newton_worker );
     else     multi_newton_worker();

     // now combine the result for all the threads
     ok &= multi_newton_combine(xout);

     return ok;
}
Input File: multi_thread/multi_newton.cpp cppad-20170000.3/doc/multi_newton_time.cpp.xml0000644000175200017650000011303113057470506020242 0ustar coincoin-web Timing Test of Multi-Threaded Newton Method
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.
Timing Test of Multi-Threaded Newton Method

Syntax
ok = multi_newton_time(time_out, num_threads,
     num_zero, num_sub, num_sum, use_ad
)

Purpose
Runs correctness and timing test for a multi-threaded Newton method. This test uses Newton's method to determine all the zeros of the sine function on an interval. CppAD, or hand coded derivatives, can be used to calculate the derivatives used by Newton's method. The calculation can be done in parallel on the different sub-intervals. In addition, the calculation can be done without multi-threading.

ok
This return value has prototype
     bool ok
 If it is true, multi_newton_time passed the correctness test. Otherwise it is false.

time_out
This argument has prototype
     double& time_out
 The input value of the argument does not matter. Upon return it is the number of wall clock seconds required for the multi-threaded Newton method can compute all the zeros.

test_time
Is the minimum amount of wall clock time that the test should take. The number of repeats for the test will be increased until this time is reached. The reported time_out is the total wall clock time divided by the number of repeats.

num_threads
This argument has prototype
     size_t num_threads
 It specifies the number of threads that are available for this test. If it is zero, the test is run without multi-threading and
     1 == CppAD::thread_alloc::num_threads()
 when multi_newton_time is called. If it is non-zero, the test is run with multi-threading and
     num_threads == CppAD::thread_alloc::num_threads()
 when multi_newton_time is called.

num_zero
This argument has prototype
     size_t num_zero
 and it must be greater than one. It specifies the actual number of zeros in the test function sin ( x ) . To be specific, multi_newton_time will attempt to determine all of the values of x for which sin ( x ) = 0 and x is in the interval
     [ 0 , (num_zero - 1) * pi ]
 .

num_sub
This argument has prototype
     size_t num_sub
 It specifies the number of sub-intervals to divide the total interval into. It must be greater than zero and should probably be greater than two times num_zero .

num_sum
This argument has prototype
     size_t num_sum
 and must be greater than zero. The actual function used by the Newton method is f ( x ) = 1 n ∑ i = 1 n sin ( x ) where n is equal to num_sum . Larger values of num_sum simulate a case where the evaluation of the function f ( x ) takes more time.

use_ad
This argument has prototype
     bool user_ad
 If use_ad is true, then derivatives will be computed using CppAD. Note that this derivative computation includes re-taping the function for each value of x (even though re-taping is not necessary).

If use_ad is false, derivatives will be computed using a hand coded routine.

Source 

# include <cppad/cppad.hpp>
# include <cppad/utility/time_test.hpp>
# include <cmath>
# include <cstring>
# include "multi_newton.hpp"

namespace { // empty namespace

     // values correspond to arguments in previous call to multi_newton_time
     size_t num_threads_;// value passed to multi_newton_time
     size_t num_zero_;   // number of zeros of f(x) in the total interval
     size_t num_sub_;    // number of sub-intervals to split calculation into
     size_t num_sum_;    // larger values make f(x) take longer to calculate

     // value of xout corresponding to most recent call to test_once
     CppAD::vector<double> xout_;

     // either fun_ad or fun_no depending on value of use_ad
     void (*fun_)(double x, double& f, double& df) = 0;

     // A version of the sine function that can be made as slow as we like
     template <class Float>
     Float f_eval(Float x)
     {     Float sum = 0.;
          size_t i;
          for(i = 0; i < num_sum_; i++)
               sum += sin(x);

          return sum / Float(num_sum_);
     }

     // Direct calculation of derivative with same number of floating point
     // operations as for f_eval.
     double df_direct(double x)
     {     double sum = 0.;
          size_t i;
          for(i = 0; i < num_sum_; i++)
               sum += cos(x);

          return sum / double(num_sum_);
     }

     // AD calculation of detivative
     void fun_ad(double x, double& f, double& df)
     {     // use CppAD::vector because it uses fast multi-threaded memory alloc
          using CppAD::vector;
          using CppAD::AD;
          vector< AD<double> > X(1), Y(1);
          X[0] = x;
          CppAD::Independent(X);
          Y[0] = f_eval(X[0]);
          CppAD::ADFun<double> F(X, Y);
          vector<double> dx(1), dy(1);
          dx[0] = 1.;
          dy    = F.Forward(1, dx);
          f     = Value( Y[0] );
          df    = dy[0];
          return;
     }

     // evaulate the function and its derivative
     void fun_no(double x, double& f, double& df)
     {     f  = f_eval(x);
          df = df_direct(x);
          return;
     }


     // Run computation of all the zeros once
     void test_once(void)
     {     if(  num_zero_ == 0 )
          {     std::cerr << "multi_newton_time: num_zero == 0" << std::endl;
               exit(1);
          }
          double pi      = 4. * std::atan(1.);
          double xlow    = 0.;
          double xup     = (num_zero_ - 1) * pi;
          double eps     =
               xup * 100. * CppAD::numeric_limits<double>::epsilon();
          size_t max_itr = 20;

          bool ok = multi_newton(
               xout_       ,
               fun_        ,
               num_sub_    ,
               xlow        ,
               xup         ,
               eps         ,
               max_itr     ,
               num_threads_
          );
          if( ! ok )
          {     std::cerr << "multi_newton: error" << std::endl;
               exit(1);
          }
          return;
     }

     // Repeat computation of all the zeros a specied number of times
     void test_repeat(size_t repeat)
     {     size_t i;
          for(i = 0; i < repeat; i++)
               test_once();
          return;
     }
} // end empty namespace

bool multi_newton_time(
     double& time_out      ,
     double  test_time     ,
     size_t  num_threads   ,
     size_t  num_zero      ,
     size_t  num_sub       ,
     size_t  num_sum       ,
     bool    use_ad
)
{     bool ok = true;
     using CppAD::thread_alloc;

     // Set local namespace environment variables
     num_threads_  = num_threads;
     num_zero_     = num_zero;
     num_sub_      = num_sub;
     num_sum_      = num_sum;
     if( use_ad )
          fun_ = fun_ad;
     else     fun_ = fun_no;

     // expect number of threads to already be set up
     if( num_threads > 0 )
          ok &= num_threads == CppAD::thread_alloc::num_threads();
     else     ok &= 1           == CppAD::thread_alloc::num_threads();

     // run the test case and set time return value
     time_out = CppAD::time_test(test_repeat, test_time);

     // Call test_once for a correctness check
     double pi      = 4. * std::atan(1.);
     double xup     = (num_zero_ - 1) * pi;
     double eps     = xup * 100. * CppAD::numeric_limits<double>::epsilon();
     ok        &= (xout_.size() == num_zero);
     size_t i   = 0;
     for(i = 0; i < num_zero; i++)
          ok &= std::fabs( xout_[i] - pi * i) <= 2 * eps;

     // xout_ is a static variable, so clear it to free its memory
     xout_.clear();

     // return correctness check result
     return  ok;
}
Input File: multi_thread/multi_newton_time.cpp cppad-20170000.3/doc/multi_newton_work.cpp.xml0000644000175200017650000017530013057470506020275 0ustar coincoin-web Multi-threading Newton Method Utility Routines
Prev Next multi_newton_work.cpp

Multi-threading Newton Method Utility Routines

Syntax
ok = multi_newton_setup(
     fun, num_sub, xlow, xup, epsilon, max_itr, num_threads
) multi_newton_worker()
 ok = multi_newton_combine(xout)
Purpose
These routines aid in the computation of multiple zeros of a function f : [ a , b ] → R .

multi_newton_setup
Calling this functions splits up the computation of the zeros into different sub-intervals for each thread.

fun
The argument fun has prototype
     void fun (double x, double& f, double& df)
 This argument must evaluate the function f ( x ) , and its derivative f ( 1 ) ( x ) , using the syntax
     fun(x, f, df)
 where the arguments have the prototypes
     double    x
     double&   f
     double&   df
 . The input values of f and df do not matter. Upon return they are f ( x ) and f ( 1 ) ( x ) respectively.

num_sub
The argument num_sub has prototype
     size_t num_sub
 It specifies the number of sub-intervals; i.e., n in to split the calculation into.

xlow
The argument xlow has prototype
     double xlow
 It specifies the lower limit for the entire search; i.e., a .

xup
The argument xup has prototype
     double xup
 It specifies the upper limit for the entire search; i.e., b .

epsilon
The argument epsilon has prototype
     double epsilon
 It specifies the convergence criteria for Newton's method in terms of how small the function value | f ( x ) | ≤ ε .

max_itr
The argument max_itr has prototype
     size_t max_itr
 It specifies the maximum number of iterations of Newton's method to try before giving up on convergence.

num_threads
This argument has prototype
     size_t num_threads
 It specifies the number of threads that are available for this test. If it is zero, the test is run without multi-threading.

multi_newton_worker
Calling this function does the computation for one thread. Following a call to multi_newton_setup, this function should be called by each of the num_threads threads.

multi_newton_combine
After the num_threads threads have completed their calls to multi_newton_worker, this function call will combine the results and return the final set of approximate zeros for f ( x ) .

xout
The argument xout has the prototype
     CppAD::vector<double>& xout
 The input size and value of the elements of xout do not matter. Upon return from multi_newton_combine, the size of xout is less than or equal n and
     | f( xout[i] ) | <= epsilon
 for each valid index i . In addition, the elements of xout are in ascending order and
     xout[i+1] - xout[i] >=  0.5 * (xup - xlow) / num_sub
Source 

# include <cppad/cppad.hpp>
# include "multi_newton_work.hpp"

# define USE_THREAD_ALLOC_FOR_WORK_ALL 1

namespace {
     using CppAD::thread_alloc;

     // This vector template class frees all memory when resized to zero.
     // In addition, its memory allocation works well during multi-threading.
     using CppAD::vector;

     // number of threads in previous call to multi_newton_setup
     size_t num_threads_ = 0;
     // convergence criteria in previous call to multi_newton_setup
     double epsilon_ = 0.;
     // maximum number of iterations in previous call to multi_newton_setup
     size_t max_itr_ = 0;
     // length for all sub-intervals
     double sub_length_ = 0.;
     // function we are finding zeros of in previous call to multi_newton_setup
     void (*fun_)(double x, double& f, double& df) = 0;

     // structure with information for one thread
     typedef struct {
          // number of sub intervals (worker input)
          size_t num_sub;
          // beginning of interval (worker input)
          double xlow;
          // end of interval (worker input)
          double xup;
          // vector of zero candidates (worker output)
          // after call to multi_newton_setup:   x.size() == 0
          // after call to multi_newton_work:    x.size() is number of zeros
          // after call to multi_newton_combine: x.size() == 0
          vector<double> x;
          // false if an error occurs, true otherwise (worker output)
          bool   ok;
     } work_one_t;
     // vector with information for all threads
     // after call to multi_newton_setup:   work_all.size() == num_threads
     // after call to multi_newton_combine: work_all.size() == 0
     // (use pointers instead of values to avoid false sharing)
     vector<work_one_t*> work_all_;
}
// -----------------------------------------------------------------------
// do the work for one thread
void multi_newton_worker(void)
{     using CppAD::vector;

     // Split [xlow, xup] into num_sub intervales and
     // look for one zero in each sub-interval.
     size_t thread_num    = thread_alloc::thread_num();
     size_t num_threads   = std::max(num_threads_, size_t(1));
     bool   ok            = thread_num < num_threads;
     size_t num_sub       = work_all_[thread_num]->num_sub;
     double xlow          = work_all_[thread_num]->xlow;
     double xup           = work_all_[thread_num]->xup;
     vector<double>& x    = work_all_[thread_num]->x;

     // check arguments
     ok &= max_itr_ > 0;
     ok &= num_sub > 0;
     ok &= xlow < xup;
     ok &= x.size() == 0;

     // check for special case where there is nothing for this thread to do
     if( num_sub == 0 )
     {     work_all_[thread_num]->ok = ok;
          return;
     }

     // check for a zero on each sub-interval
     size_t i;
     double xlast = xlow - 2 * sub_length_; // over sub_length_ away from x_low
     double flast = 2 * epsilon_;           // any value > epsilon_ would do
     for(i = 0; i < num_sub; i++)
     {
          // note that when i == 0, xlow_i == xlow (exactly)
          double xlow_i = xlow + i * sub_length_;

          // note that when i == num_sub - 1, xup_i = xup (exactly)
          double xup_i  = xup  - (num_sub - i - 1) * sub_length_;

          // initial point for Newton iterations
          double xcur = (xup_i + xlow_i) / 2.;

          // Newton iterations
          bool more_itr = true;
          size_t itr    = 0;
          // initialize these values to avoid MSC C++ warning
          double fcur=0.0, dfcur=0.0;
          while( more_itr )
          {     fun_(xcur, fcur, dfcur);

               // check end of iterations
               if( fabs(fcur) <= epsilon_ )
                    more_itr = false;
               if( (xcur == xlow_i ) & (fcur * dfcur > 0.) )
                    more_itr = false;
               if( (xcur == xup_i)   & (fcur * dfcur < 0.) )
                    more_itr = false;

               // next Newton iterate
               if( more_itr )
               {     xcur = xcur - fcur / dfcur;
                    // keep in bounds
                    xcur = std::max(xcur, xlow_i);
                    xcur = std::min(xcur, xup_i);

                    more_itr = ++itr < max_itr_;
               }
          }
          if( fabs( fcur ) <= epsilon_ )
          {     // check for case where xcur is lower bound for this
               // sub-interval and upper bound for previous sub-interval
               if( fabs(xcur - xlast) >= sub_length_ )
               {     x.push_back( xcur );
                    xlast = xcur;
                    flast = fcur;
               }
               else if( fabs(fcur) < fabs(flast) )
               {     x[ x.size() - 1] = xcur;
                    xlast            = xcur;
                    flast            = fcur;
               }
          }
     }
     work_all_[thread_num]->ok = ok;
}
// -----------------------------------------------------------------------
// setup the work up for multiple threads
bool multi_newton_setup(
     void (fun)(double x, double& f, double& df) ,
     size_t num_sub                              ,
     double xlow                                 ,
     double xup                                  ,
     double epsilon                              ,
     size_t max_itr                              ,
     size_t num_threads                          )
{
     num_threads_ = num_threads;
     num_threads  = std::max(num_threads_, size_t(1));
     bool ok      = num_threads == thread_alloc::num_threads();

     // inputs that are same for all threads
     epsilon_ = epsilon;
     max_itr_ = max_itr;
     fun_     = fun;

     // resize the work vector to accomidate the number of threads
     ok &= work_all_.size() == 0;
     work_all_.resize(num_threads);

     // length of each sub interval
     sub_length_ = (xup - xlow) / double(num_sub);

     // determine values that are specific to each thread
     size_t num_min   = num_sub / num_threads; // minimum num_sub
     size_t num_more  = num_sub % num_threads; // number that have one more
     size_t sum_num   = 0;  // sum with respect to thread of num_sub
     size_t thread_num, num_sub_thread;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {
# if  USE_THREAD_ALLOC_FOR_WORK_ALL
          // allocate separate memory for this thread to avoid false sharing
          size_t min_bytes(sizeof(work_one_t)), cap_bytes;
          void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes);
          work_all_[thread_num] = static_cast<work_one_t*>(v_ptr);

          // thread_alloc is a raw memory allocator; i.e., it does not call
          // the constructor for the objects it creates. The CppAD::vector
          // class requires it's constructor to be called so we do it here
          new(& (work_all_[thread_num]->x) ) vector<double>();
# else
          work_all_[thread_num] = new work_one_t;
# endif

          // number of sub-intervalse for this thread
          if( thread_num < num_more  )
               num_sub_thread = num_min + 1;
          else     num_sub_thread = num_min;

          // when thread_num == 0, xlow_thread == xlow
          double xlow_thread = xlow + sum_num * sub_length_;

          // when thread_num == num_threads - 1, xup_thread = xup
          double xup_thread = xlow + (sum_num + num_sub_thread) * sub_length_;
          if( thread_num == num_threads - 1 )
               xup_thread = xup;

          // update sum_num for next time through loop
          sum_num += num_sub_thread;

          // input information specific to this thread
          work_all_[thread_num]->num_sub = num_sub_thread;
          work_all_[thread_num]->xlow    = xlow_thread;
          work_all_[thread_num]->xup     = xup_thread;
          ok &= work_all_[thread_num]->x.size() == 0;

          // in case this thread does not get called
          work_all_[thread_num]->ok = false;
     }
     ok &= sum_num == num_sub;
     return ok;
}
// -----------------------------------------------------------------------
// get the result of the work
bool multi_newton_combine(CppAD::vector<double>& xout)
{     // number of threads in the calculation
     size_t num_threads  = std::max(num_threads_, size_t(1));

     // remove duplicates and points that are not solutions
     xout.resize(0);
     bool   ok = true;
     size_t thread_num;

     // initialize as more that sub_lenght_ / 2 from any possible solution
     double xlast = - sub_length_;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     vector<double>& x = work_all_[thread_num]->x;

          size_t i;
          for(i = 0; i < x.size(); i++)
          {     // check for case where this point is lower limit for this
               // thread and upper limit for previous thread
               if( fabs(x[i] - xlast) >= sub_length_ )
               {     xout.push_back( x[i] );
                    xlast = x[i];
               }
               else
               {     double fcur, flast, df;
                    fun_(x[i],   fcur, df);
                    fun_(xlast, flast, df);
                    if( fabs(fcur) < fabs(flast) )
                    {     xout[ xout.size() - 1] = x[i];
                         xlast                  = x[i];
                    }
               }
          }
          ok &= work_all_[thread_num]->ok;
     }

     // go down so free memory for other threads before memory for master
     thread_num = num_threads;
     while(thread_num--)
     {
# if USE_THREAD_ALLOC_FOR_WORK_ALL
          // call the destructor for CppAD::vector destructor
          work_all_[thread_num]->x.~vector<double>();
          // delete the raw memory allocation
          void* v_ptr = static_cast<void*>( work_all_[thread_num] );
          thread_alloc::return_memory( v_ptr );
# else
          delete work_all_[thread_num];
# endif
          // Note that xout corresponds to memroy that is inuse by master
          // (so we can only chech have freed all their memory).
          if( thread_num > 0 )
          {     // check that there is no longer any memory inuse by this thread
               ok &= thread_alloc::inuse(thread_num) == 0;
               // return all memory being held for future use by this thread
               thread_alloc::free_available(thread_num);
          }
     }
     // now we are done with the work_all_ vector so free its memory
     // (because it is a static variable)
     work_all_.clear();

     return ok;
}
Input File: multi_thread/multi_newton_work.cpp cppad-20170000.3/doc/team_thread.hpp.xml0000644000175200017650000003124613057470506016771 0ustar coincoin-web Specifications for A Team of AD Threads
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Specifications for A Team of AD Threads

Syntax
include "team_thread.hpp"
ok   = team_create(num_threads)
ok   = team_work(worker)
ok   = team_destroy()
name = team_name()
Purpose
These routines start, use, and stop a team of threads that can be used with the CppAD type AD<double>. For example, these could be OpenMP threads, pthreads, or Boost threads to name a few.

Restrictions
Calls to the routines team_create, team_work, and team_destroy, must all be done by the master thread; i.e., thread_num must be zero. In addition, they must all be done in sequential execution mode; i.e., when the master thread is the only thread that is running (in_parallel must be false).

team_create
The argument num_threads > 0 has type size_t and specifies the number of threads in this team. This initializes both AD<double> and team_work to be used with num_threads . If num_threads > 1 , num_threads - 1 new threads are created and put in a waiting state until team_work is called.

team_work
This routine may be called one or more times between the call to team_create and team_destroy. The argument worker has type bool worker(void) . Each call to team_work runs num_threads versions of worker with the corresponding value of thread_num between zero and num_threads - 1 and different for each thread,

team_destroy
This routine terminates all the other threads except for thread number zero; i.e., it terminates the threads corresponding to
     thread_num = 1 , ... , num_threads-1
team_name
This routines returns a name that identifies this thread_team. The return value has prototype
     const char* name
 and is a statically allocated '\0' terminated C string.

ok
The return value ok has type bool. It is false if an error is detected during the corresponding call. Otherwise it is true.

Example Use
Example use of these specifications can be found in the file team_example.cpp .

Example Implementation
Example implementations of these specifications can be found in the files:
team_openmp.cpp OpenMP Implementation of a Team of AD Threads
team_bthread.cpp Boost Thread Implementation of a Team of AD Threads
team_pthread.cpp Pthread Implementation of a Team of AD Threads

Speed Test of Implementation
Speed tests of using CppAD with the team implementations above can be found in:
harmonic.cpp Multi-Threaded Implementation of Summation of 1/i
multi_newton.cpp A Multi-Threaded Newton's Method

Source 
# include <cstddef> // for size_t

extern bool team_create(size_t num_threads);
extern bool team_work(void worker(void));
extern bool team_destroy(void);
extern const char* team_name(void);
Input File: multi_thread/team_thread.hpp cppad-20170000.3/doc/team_openmp.cpp.xml0000644000175200017650000003354313057470506017015 0ustar coincoin-web OpenMP Implementation of a Team of AD Threads
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OpenMP Implementation of a Team of AD Threads
See team_thread.hpp for this routines specifications. 
# include <omp.h>
# include <cppad/cppad.hpp>
# include "../team_thread.hpp"

namespace {
     using CppAD::thread_alloc;

     // number of threads in this team
     size_t num_threads_;

     // used to inform CppAD when we are in parallel execution mode
     bool in_parallel(void)
     {     return omp_in_parallel() != 0; }

     // used to inform CppAD of the current thread number
     size_t thread_num(void)
     {     return static_cast<size_t>( omp_get_thread_num() ); }
}

bool team_create(size_t num_threads)
{
     bool ok = ! in_parallel();
     ok     &= thread_num() == 0;;
     ok     &= num_threads > 0;

     // Turn off dynamic thread adjustment
     omp_set_dynamic(0);

     // Set the number of OpenMP threads
     omp_set_num_threads( int(num_threads) );

     // setup for using CppAD::AD<double> in parallel
     thread_alloc::parallel_setup(num_threads, in_parallel, thread_num);
     thread_alloc::hold_memory(true);
     CppAD::parallel_ad<double>();

     // inform team_work of number of threads
     num_threads_ = num_threads;

     return ok;
}

bool team_work(void worker(void))
{     bool ok = ! in_parallel();
     ok     &= thread_num() == 0;;
     ok     &= num_threads_ > 0;

     int number_threads = int(num_threads_);
     int thread_num;
# pragma omp parallel for
     for(thread_num = 0; thread_num < number_threads; thread_num++)
          worker();
// end omp parallel for

     return ok;
}

bool team_destroy(void)
{     bool ok = ! in_parallel();
     ok     &= thread_num() == 0;;
     ok     &= num_threads_ > 0;

     // inform team_work of number of threads
     num_threads_ = 1;

     // Set the number of OpenMP threads to one
     omp_set_num_threads(num_threads_);

     // inform CppAD no longer in multi-threading mode
     thread_alloc::parallel_setup(num_threads_, CPPAD_NULL, CPPAD_NULL);
     thread_alloc::hold_memory(false);
     CppAD::parallel_ad<double>();

     return ok;
}

const char* team_name(void)
{     return "openmp"; }
Input File: multi_thread/openmp/team_openmp.cpp cppad-20170000.3/doc/team_bthread.cpp.xml0000644000175200017650000010645713057470506017135 0ustar coincoin-web Boost Thread Implementation of a Team of AD Threads
Prev Next team_bthread.cpp Headings

Boost Thread Implementation of a Team of AD Threads
See team_thread.hpp for this routines specifications. 
# include <boost/thread.hpp>
# include <cppad/cppad.hpp>
# include "../team_thread.hpp"
# define MAX_NUMBER_THREADS 48

namespace {
     using CppAD::thread_alloc;

     // number of threads in the team
     size_t num_threads_ = 1;

     // no need to cleanup up thread specific data
     void cleanup(size_t*)
     {     return; }

     // thread specific pointer the thread number (initialize as null)
     boost::thread_specific_ptr<size_t> thread_num_ptr_(cleanup);

     // type of the job currently being done by each thread
     enum thread_job_t { init_enum, work_enum, join_enum } thread_job_;

     // barrier used to wait for other threads to finish work
     boost::barrier* wait_for_work_ = CPPAD_NULL;

     // barrier used to wait for master thread to set next job
     boost::barrier* wait_for_job_ = CPPAD_NULL;

     // Are we in sequential mode; i.e., other threads are waiting for
     // master thread to set up next job ?
     bool sequential_execution_ = true;

     // structure with information for one thread
     typedef struct {
          // The thread
          boost::thread*       bthread;
          // CppAD thread number as global (pointed to by thread_num_ptr_)
          size_t               thread_num;
          // true if no error for this thread, false otherwise.
          bool                 ok;
     } thread_one_t;

     // vector with information for all threads
     thread_one_t thread_all_[MAX_NUMBER_THREADS];

     // pointer to function that does the work for one thread
     void (* worker_)(void) = CPPAD_NULL;

     // ---------------------------------------------------------------------
     // in_parallel()
     bool in_parallel(void)
     {     return ! sequential_execution_; }

     // ---------------------------------------------------------------------
     // thread_number()
     size_t thread_number(void)
     {     // return thread_all_[thread_num].thread_num
          return *thread_num_ptr_.get();
     }
     // --------------------------------------------------------------------
     // function that gets called by boost thread constructor
     void thread_work(size_t thread_num)
     {     bool ok = wait_for_work_ != CPPAD_NULL;
          ok     &= wait_for_job_  != CPPAD_NULL;
          ok     &= thread_num     != 0;

          // thread specific storage of thread number for this thread
          thread_num_ptr_.reset(& thread_all_[thread_num].thread_num );

          while( true )
          {
               // Use wait_for_jog_ to give master time in sequential mode
               // (so it can change global information like thread_job_)
               wait_for_job_->wait();

               // case where we are terminating this thread (no more work)
               if( thread_job_ == join_enum)
                    break;

               // only other case once wait_for_job_ has been completed (so far)
               ok &= thread_job_ == work_enum;
               worker_();

               // Use wait_for_work_ to inform master that our work is done and
               // that this thread will not use global infromation until
               // passing its barrier wait_for_job_ above.
               wait_for_work_->wait();

          }
          thread_all_[thread_num].ok &= ok;
          return;
     }
}

bool team_create(size_t num_threads)
{     bool ok = true;;

     if( num_threads > MAX_NUMBER_THREADS )
     {     std::cerr << "team_create: num_threads greater than ";
          std::cerr << MAX_NUMBER_THREADS << std::endl;
          exit(1);
     }
     // check that we currently do not have multiple threads running
     ok  = num_threads_ == 1;
     ok &= wait_for_work_ == CPPAD_NULL;
     ok &= wait_for_job_  == CPPAD_NULL;
     ok &= sequential_execution_;

     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     // Each thread gets a pointer to its version of this thread_num
          // so it knows which section of thread_all it is working with
          thread_all_[thread_num].thread_num = thread_num;

          // initialize
          thread_all_[thread_num].ok = true;
          thread_all_[0].bthread     = CPPAD_NULL;
     }
     // Finish setup of thread_all_ for this thread
     thread_num_ptr_.reset(& thread_all_[0].thread_num);

     // Now that thread_number() has necessary information for the case
     // num_threads_ == 1, and while still in sequential mode,
     // call setup for using CppAD::AD<double> in parallel mode.
     thread_alloc::parallel_setup(num_threads, in_parallel, thread_number);
     thread_alloc::hold_memory(true);
     CppAD::parallel_ad<double>();

     // now change num_threads_ to its final value.
     num_threads_ = num_threads;

     // initialize two barriers, one for work done, one for new job ready
     wait_for_work_ = new boost::barrier(num_threads);
     wait_for_job_  = new boost::barrier(num_threads);

     // initial job for the threads
     thread_job_           = init_enum;
     if( num_threads > 1 )
          sequential_execution_ = false;

     // This master thread is already running, we need to create
     // num_threads - 1 more threads
     for(thread_num = 1; thread_num < num_threads; thread_num++)
     {     // Create the thread with thread number equal to thread_num
          thread_all_[thread_num].bthread =
               new boost::thread(thread_work, thread_num);
     }

     // Current state is other threads are at wait_for_job_.
     // This master thread (thread zero) has not completed wait_for_job_
     sequential_execution_ = true;
     return ok;
}

bool team_work(void worker(void))
{
     // Current state is other threads are at wait_for_job_.
     // This master thread (thread zero) has not completed wait_for_job_
     bool ok = sequential_execution_;
     ok     &= thread_number() == 0;
     ok     &= wait_for_work_  != CPPAD_NULL;
     ok     &= wait_for_job_   != CPPAD_NULL;

     // set global version of this work routine
     worker_ = worker;

     // set the new job that other threads are waiting for
     thread_job_ = work_enum;

     // Enter parallel exectuion when master thread calls wait_for_job_
     if( num_threads_ > 1 )
          sequential_execution_ = false;
     wait_for_job_->wait();

     // Now do the work in this thread and then wait
     // until all threads have completed wait_for_work_
     worker();
     wait_for_work_->wait();

     // Current state is other threads are at wait_for_job_.
     // This master thread (thread zero) has not completed wait_for_job_
     sequential_execution_ = true;

     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads_; thread_num++)
          ok &= thread_all_[thread_num].ok;
     return ok;
}

bool team_destroy(void)
{     // Current state is other threads are at wait_for_job_.
     // This master thread (thread zero) has not completed wait_for_job_
     bool ok = sequential_execution_;
     ok     &= thread_number() == 0;
     ok     &= wait_for_work_ != CPPAD_NULL;
     ok     &= wait_for_job_  != CPPAD_NULL;

     // set the new job that other threads are waiting for
     thread_job_ = join_enum;

     // enter parallel exectuion soon as master thread completes wait_for_job_
     if( num_threads_ > 1 )
               sequential_execution_ = false;
     wait_for_job_->wait();

     // now wait for the other threads to be destroyed
     size_t thread_num;
     ok &= thread_all_[0].bthread == CPPAD_NULL;
     for(thread_num = 1; thread_num < num_threads_; thread_num++)
     {     thread_all_[thread_num].bthread->join();
          delete thread_all_[thread_num].bthread;
          thread_all_[thread_num].bthread = CPPAD_NULL;
     }
     // now we are down to just the master thread (thread zero)
     sequential_execution_ = true;

     // destroy wait_for_work_
     delete wait_for_work_;
     wait_for_work_ = CPPAD_NULL;

     // destroy wait_for_job_
     delete wait_for_job_;
     wait_for_job_ = CPPAD_NULL;

     // check ok before changing num_threads_
     for(thread_num = 0; thread_num < num_threads_; thread_num++)
          ok &= thread_all_[thread_num].ok;

     // now inform CppAD that there is only one thread
     num_threads_ = 1;
     thread_alloc::parallel_setup(num_threads_, CPPAD_NULL, CPPAD_NULL);
     thread_alloc::hold_memory(false);
     CppAD::parallel_ad<double>();

     return ok;
}

const char* team_name(void)
{     return "bthread"; }
Input File: multi_thread/bthread/team_bthread.cpp cppad-20170000.3/doc/team_pthread.cpp.xml0000644000175200017650000013145713057470507017152 0ustar coincoin-web Pthread Implementation of a Team of AD Threads
Prev Next team_pthread.cpp

Pthread Implementation of a Team of AD Threads
See team_thread.hpp for this routines specifications.

Bug in Cygwin
There is a bug in pthread_exit, using cygwin 5.1 and g++ version 4.3.4, whereby calling pthread_exit is not the same as returning from the corresponding routine. To be specific, destructors for the vectors are not called and a memory leaks result. Set the following preprocessor symbol to 1 to demonstrate this bug: 

# define DEMONSTRATE_BUG_IN_CYGWIN 0

# include <pthread.h>
# include <cppad/cppad.hpp>
# include "../team_thread.hpp"
# define MAX_NUMBER_THREADS 48

// It seems that when a barrier is passed, its counter is automatically reset
// to its original value and it can be used again, but where is this
// stated in the pthreads speicifcations ?
namespace {
     using CppAD::thread_alloc;

     // number of threads in the team
     size_t num_threads_ = 1;

     // key for accessing thread specific information
     pthread_key_t thread_specific_key_;

     // no need to destroy thread specific information
     void thread_specific_destructor(void* thread_num_vptr)
     {     return; }

     // type of the job currently being done by each thread
     enum thread_job_t { init_enum, work_enum, join_enum } thread_job_;

     // barrier used to wait for other threads to finish work
     pthread_barrier_t wait_for_work_;

     // barrier used to wait for master thread to set next job
     pthread_barrier_t wait_for_job_;

     // Are we in sequential mode; i.e., other threads are waiting for
     // master thread to set up next job ?
     bool sequential_execution_ = true;

     // structure with information for one thread
     typedef struct {
          // cppad unique identifier for thread that uses this struct
          size_t          thread_num;
          // pthread unique identifier for thread that uses this struct
          pthread_t       pthread_id;
          // true if no error for this thread, false otherwise.
          bool            ok;
     } thread_one_t;

     // vector with information for all threads
     thread_one_t thread_all_[MAX_NUMBER_THREADS];

     // pointer to function that does the work for one thread
     void (* worker_)(void) = CPPAD_NULL;

     // ---------------------------------------------------------------------
     // in_parallel()
     bool in_parallel(void)
     {     return ! sequential_execution_; }

     // ---------------------------------------------------------------------
     // thread_number()
     size_t thread_number(void)
     {     // get thread specific information
          void*   thread_num_vptr = pthread_getspecific(thread_specific_key_);
          size_t* thread_num_ptr  = static_cast<size_t*>(thread_num_vptr);
          size_t  thread_num      = *thread_num_ptr;
          if( thread_num >= num_threads_ )
          {     std::cerr << "thread_number: program error" << std::endl;
               exit(1);
          }
          return thread_num;
     }
     // --------------------------------------------------------------------
     // function that gets called by pthread_create
     void* thread_work(void* thread_num_vptr)
     {     int rc;
          bool ok = true;

          // Set thread specific data where other routines can access it
          rc = pthread_setspecific(thread_specific_key_, thread_num_vptr);
          ok &= rc == 0;

          // thread_num to problem specific information for this thread
          size_t thread_num = *static_cast<size_t*>(thread_num_vptr);

          // master thread does not use this routine
          ok &= thread_num > 0;

          while( true )
          {
               // Use wait_for_job_ to give master time in sequential mode
               // (so it can change global infromation like thread_job_)
               rc = pthread_barrier_wait(&wait_for_job_);
               ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD);

               // case where we are terminating this thread (no more work)
               if( thread_job_ == join_enum )
                    break;

               // only other case once wait_for_job_ barrier is passed (so far)
               ok &= thread_job_ == work_enum;
               worker_();

               // Use wait_for_work_ to inform master that our work is done and
               // that this thread will not use global information until
               // passing its barrier wait_for_job_ above.
               rc = pthread_barrier_wait(&wait_for_work_);
               ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD);
          }
          thread_all_[thread_num].ok = ok;
# if DEMONSTRATE_BUG_IN_CYGWIN
          // Terminate this thread
          void* no_status = CPPAD_NULL;
          pthread_exit(no_status);
# endif
          return CPPAD_NULL;
     }
}

bool team_create(size_t num_threads)
{     bool ok = true;;
     int rc;

     if( num_threads > MAX_NUMBER_THREADS )
     {     std::cerr << "team_create: num_threads greater than ";
          std::cerr << MAX_NUMBER_THREADS << std::endl;
          exit(1);
     }
     // check that we currently do not have multiple threads running
     ok  = num_threads_ == 1;
     ok &= sequential_execution_;

     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads; thread_num++)
     {     // Each thread gets a pointer to its version of this thread_num
          // so it knows which section of thread_all_ it is working with
          thread_all_[thread_num].thread_num = thread_num;

          // initialize
          thread_all_[thread_num].ok         = true;
     }
     // Finish setup of thread_all_ for this thread
     thread_all_[0].pthread_id = pthread_self();

     // create a key for thread specific information
     rc = pthread_key_create(&thread_specific_key_,thread_specific_destructor);
     ok &= (rc == 0);

     // set thread specific information for this (master thread)
     void* thread_num_vptr = static_cast<void*>(&(thread_all_[0].thread_num));
     rc = pthread_setspecific(thread_specific_key_, thread_num_vptr);
     ok &= (rc == 0);

     // Now that thread_number() has necessary information for this thread
     // (number zero), and while still in sequential mode,
     // call setup for using CppAD::AD<double> in parallel mode.
     thread_alloc::parallel_setup(num_threads, in_parallel, thread_number);
     thread_alloc::hold_memory(true);
     CppAD::parallel_ad<double>();

     // Now change num_threads_ to its final value. Waiting till now allows
     // calls to thread_number during parallel_setup to check thread_num == 0.
     num_threads_ = num_threads;

     // initialize two barriers, one for work done, one for new job ready
     pthread_barrierattr_t* no_barrierattr = CPPAD_NULL;
     rc = pthread_barrier_init(
          &wait_for_work_, no_barrierattr, num_threads
     );
     ok &= (rc == 0);
     rc  = pthread_barrier_init(
          &wait_for_job_, no_barrierattr, num_threads
     );
     ok &= (rc == 0);

     // structure used to create the threads
     pthread_t       pthread_id;
     // default for pthread_attr_setdetachstate is PTHREAD_CREATE_JOINABLE
     pthread_attr_t* no_attr= CPPAD_NULL;

     // initial job for the threads
     thread_job_           = init_enum;
     if( num_threads > 1 )
          sequential_execution_ = false;

     // This master thread is already running, we need to create
     // num_threads - 1 more threads
     for(thread_num = 1; thread_num < num_threads; thread_num++)
     {
          // Create the thread with thread number equal to thread_num
          thread_num_vptr = static_cast<void*> (
               &(thread_all_[thread_num].thread_num)
          );
          rc = pthread_create(
                    &pthread_id ,
                    no_attr     ,
                    thread_work ,
                    thread_num_vptr
          );
          thread_all_[thread_num].pthread_id = pthread_id;
          ok &= (rc == 0);
     }

     // Current state is other threads are at wait_for_job_.
     // This master thread (thread zero) has not completed wait_for_job_
     sequential_execution_ = true;
     return ok;
}

bool team_work(void worker(void))
{     int rc;

     // Current state is other threads are at wait_for_job_.
     // This master thread (thread zero) has not completed wait_for_job_
     bool ok = sequential_execution_;
     ok     &= thread_number() == 0;

     // set global version of this work routine
     worker_ = worker;


     // set the new job that other threads are waiting for
     thread_job_ = work_enum;

     // enter parallel execution soon as master thread completes wait_for_job_
     if( num_threads_ > 1 )
          sequential_execution_ = false;

     // wait until all threads have completed wait_for_job_
     rc  = pthread_barrier_wait(&wait_for_job_);
     ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD);

     // Now do the work in this thread and then wait
     // until all threads have completed wait_for_work_
     worker();
     rc = pthread_barrier_wait(&wait_for_work_);
     ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD);

     // Current state is other threads are at wait_for_job_.
     // This master thread (thread zero) has not completed wait_for_job_
     sequential_execution_ = true;

     size_t thread_num;
     for(thread_num = 0; thread_num < num_threads_; thread_num++)
          ok &= thread_all_[thread_num].ok;
     return ok;
}

bool team_destroy(void)
{     int rc;

     // Current state is other threads are at wait_for_job_.
     // This master thread (thread zero) has not completed wait_for_job_
     bool ok = sequential_execution_;
     ok     &= thread_number() == 0;

     // set the new job that other threads are waiting for
     thread_job_ = join_enum;

     // Enter parallel exectuion soon as master thread completes wait_for_job_
     if( num_threads_ > 1 )
               sequential_execution_ = false;
     rc  = pthread_barrier_wait(&wait_for_job_);
     ok &= (rc == 0 || rc == PTHREAD_BARRIER_SERIAL_THREAD);

     // now wait for the other threads to exit
     size_t thread_num;
     for(thread_num = 1; thread_num < num_threads_; thread_num++)
     {     void* no_status = CPPAD_NULL;
          rc      = pthread_join(
               thread_all_[thread_num].pthread_id, &no_status
          );
          ok &= (rc == 0);
     }

     // now we are down to just the master thread (thread zero)
     sequential_execution_ = true;

     // destroy the key for thread specific data
     pthread_key_delete(thread_specific_key_);

     // destroy wait_for_work_
     rc  = pthread_barrier_destroy(&wait_for_work_);
     ok &= (rc == 0);

     // destroy wait_for_job_
     rc  = pthread_barrier_destroy(&wait_for_job_);
     ok &= (rc == 0);

     // check ok before changing num_threads_
     for(thread_num = 0; thread_num < num_threads_; thread_num++)
          ok &= thread_all_[thread_num].ok;

     // now inform CppAD that there is only one thread
     num_threads_ = 1;
     thread_alloc::parallel_setup(num_threads_, CPPAD_NULL, CPPAD_NULL);
     thread_alloc::hold_memory(false);
     CppAD::parallel_ad<double>();

     return ok;
}

const char* team_name(void)
{     return "pthread"; }
Input File: multi_thread/pthread/team_pthread.cpp cppad-20170000.3/doc/utility.xml0000644000175200017650000002174713057470507015437 0ustar coincoin-web Some General Purpose Utilities
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Some General Purpose Utilities
These routines can be include individually; for example, 
 
     # include <cppad/utility/vector.hpp>
only includes the definitions necessary for the CppAD::vector class. They can also be included as a group, separate from the rest of CppAD, using 
 
     # include <cppad/utility.hpp>
They will also be included, along with the rest of CppAD, using 
 
     # include <cppad/cppad.hpp>

Testing
The routines listed below support numerical correctness and speed testing:
NearEqual Determine if Two Values Are Nearly Equal
time_test Determine Amount of Time to Execute a Test
speed_test Run One Speed Test and Return Results
SpeedTest Run One Speed Test and Print Results

C++ Concepts
We refer to a the set of classes that satisfy certain conditions as a C++ concept. The following concepts are used by the CppAD Template library:
NumericType Definition of a Numeric Type
CheckNumericType Check NumericType Class Concept
SimpleVector Definition of a Simple Vector
CheckSimpleVector Check Simple Vector Concept

General Numerical Routines
The routines listed below are general purpose numerical routines written with the floating point type a C++ template parameter. This enables them to be used with algorithmic differentiation types, as well as for other purposes.
nan Obtain Nan or Determine if a Value is Nan
pow_int The Integer Power Function
Poly Evaluate a Polynomial or its Derivative
LuDetAndSolve Compute Determinants and Solve Equations by LU Factorization
RombergOne One DimensionalRomberg Integration
RombergMul Multi-dimensional Romberg Integration
Runge45 An Embedded 4th and 5th Order Runge-Kutta ODE Solver
Rosen34 A 3rd and 4th Order Rosenbrock ODE Solver
OdeErrControl An Error Controller for ODE Solvers
OdeGear An Arbitrary Order Gear Method
OdeGearControl An Error Controller for Gear's Ode Solvers

Miscellaneous

Error Handler
All of the routines in the CppAD namespace use the following general purpose error handler:
ErrorHandler Replacing the CppAD Error Handler

Simple Vector Template Class
A simple implementation of a template vector class (that is easy to view in a C++ debugger):
CppAD_vector The CppAD::vector Template Class

Multi-Threading Memory Allocation
thread_alloc A Fast Multi-Threading Memory Allocator

Sorting Indices
index_sort Returns Indices that Sort a Vector

to_string
to_string Convert Certain Types to a String

set_union
set_union Union of Standard Sets
Input File: omh/utility.omh cppad-20170000.3/doc/errorhandler.xml0000644000175200017650000003003113057470507016405 0ustar coincoin-web Replacing the CppAD Error Handler
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Replacing the CppAD Error Handler

Syntax
# include <cppad/utility/error_handler.hpp>
 ErrorHandler info(handler)
 ErrorHandler::Call(known, line, file, exp, msg)
Constructor
When you construct a ErrorHandler object, the current CppAD error handler is replaced by handler . When the object is destructed, the previous CppAD error handler is restored.

Parallel Mode
The ErrorHandler constructor and destructor cannot be called in parallel execution mode. Furthermore, this rule is not abided by, a raw C++ assert, instead of one that uses this error handler, will be generated.

Call
When ErrorHandler::Call is called, the current CppAD error handler is used to report an error. This starts out as a default error handler and can be replaced using the ErrorHandler constructor.

info
The object info is used to store information that is necessary to restore the previous CppAD error handler. This is done when the destructor for info is called.

handler
The argument handler has prototype
     void (*handler)
          (bool, int, const char *, const char *, const char *);
 When an error is detected, it is called with the syntax
     handler (known, line, file, exp, msg)
 This routine should not return; i.e., upon detection of the error, the routine calling handler does not know how to proceed.

known
The handler argument known has prototype
     bool known
 If it is true, the error being reported is from a know problem.

line
The handler argument line has prototype
     int line
 It reports the source code line number where the error is detected.

file
The handler argument file has prototype
     const char *file
 and is a '\0' terminated character vector. It reports the source code file where the error is detected.

exp
The handler argument exp has prototype
     const char *exp
 and is a '\0' terminated character vector. It is a source code boolean expression that should have been true, but is false, and thereby causes this call to handler .

msg
The handler argument msg has prototype
     const char *msg
 and is a '\0' terminated character vector. It reports the meaning of the error from the C++ programmers point of view.

Example
The file error_handler.cpp contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise.
Input File: cppad/utility/error_handler.hpp cppad-20170000.3/doc/error_handler.cpp.xml0000644000175200017650000002173513057470507017340 0ustar coincoin-web Replacing The CppAD Error Handler: Example and Test
Prev Next error_handler.cpp Headings

Replacing The CppAD Error Handler: Example and Test

# include <cppad/utility/error_handler.hpp>
# include <cstring>

namespace {
     void myhandler(
          bool known       ,
          int  line        ,
          const char *file ,
          const char *exp  ,
          const char *msg  )
     {     // error handler must not return, so throw an exception
          throw line;
     }
}


bool ErrorHandler(void)
{     using CppAD::ErrorHandler;

     int lineMinusFive = 0;

     // replace the default CppAD error handler
     ErrorHandler info(myhandler);

     // set ok to false unless catch block is executed
     bool ok = false;

     // use try / catch because handler throws an exception
     try {
          // set the static variable Line to next source code line
          lineMinusFive = __LINE__;

          // can call myhandler anywhere that ErrorHandler is defined
          ErrorHandler::Call(
               true     , // reason for the error is known
               __LINE__ , // current source code line number
               __FILE__ , // current source code file name
               "1 > 0"  , // an intentional error condition
               "Testing ErrorHandler"     // reason for error
          );
     }
     catch ( int line )
     {     // check value of the line number that was passed to handler
          ok = (line == lineMinusFive + 5);
     }

     // info drops out of scope and the default CppAD error handler
     // is restored when this routine returns.
     return ok;
}
Input File: example/error_handler.cpp cppad-20170000.3/doc/cppad_assert.xml0000644000175200017650000001563113057470507016377 0ustar coincoin-web CppAD Assertions During Execution
Prev Next cppad_assert

CppAD Assertions During Execution

Syntax
CPPAD_ASSERT_KNOWN(exp, msg)
 CPPAD_ASSERT_UNKNOWN(exp)

Purpose
These CppAD macros are used to detect and report errors. They are documented here because they correspond to the C++ source code that the error is reported at.

NDEBUG
If the preprocessor symbol NDEBUG is defined, these macros do nothing; i.e., they are optimized out.

Restriction
The CppAD user should not uses these macros. You can however write your own macros that do not begin with CPPAD and that call the CppAD error handler .

Known
The CPPAD_ASSERT_KNOWN macro is used to check for an error with a known cause. For example, many CppAD routines uses these macros to make sure their arguments conform to their specifications.

Unknown
The CPPAD_ASSERT_UNKNOWN macro is used to check that the CppAD internal data structures conform as expected. If this is not the case, CppAD does not know why the error has occurred; for example, the user may have written past the end of an allocated array.

Exp
The argument exp is a C++ source code expression that results in a bool value that should be true. If it is false, an error has occurred. This expression may be execute any number of times (including zero times) so it must have not side effects.

Msg
The argument msg has prototype
     const char *msg
 and contains a '\0' terminated character string. This string is a description of the error corresponding to exp being false.

Error Handler
These macros use the CppAD error handler to report errors. This error handler can be replaced by the user.
Input File: cppad/core/cppad_assert.hpp cppad-20170000.3/doc/nearequal.xml0000644000175200017650000003056113057470507015703 0ustar coincoin-web Determine if Two Values Are Nearly Equal
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Determine if Two Values Are Nearly Equal

Syntax
# include <cppad/utility/near_equal.hpp>
 b = NearEqual(x, y, r, a)

Purpose
Returns true, if x and y are nearly equal, and false otherwise.

x
The argument x has one of the following possible prototypes
     const Type               &x,
     const std::complex<Type> &x,
y
The argument y has one of the following possible prototypes
     const Type               &y,
     const std::complex<Type> &y,
r
The relative error criteria r has prototype
     const Type &r
 It must be greater than or equal to zero. The relative error condition is defined as: | x - y | ≤ r ( | x | + | y | )
a
The absolute error criteria a has prototype
     const Type &a
 It must be greater than or equal to zero. The absolute error condition is defined as: | x - y | ≤ a
b
The return value b has prototype
     bool b
 If either x or y is infinite or not a number, the return value is false. Otherwise, if either the relative or absolute error condition (defined above) is satisfied, the return value is true. Otherwise, the return value is false.

Type
The type Type must be a NumericType . The routine CheckNumericType will generate an error message if this is not the case. In addition, the following operations must be defined objects a and b of type Type :
Operation Description
a <= b less that or equal operator (returns a bool object)

Include Files
The file cppad/near_equal.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Example
The file near_equal.cpp contains an example and test of NearEqual. It return true if it succeeds and false otherwise.

Exercise
Create and run a program that contains the following code: 
 
     using std::complex;
     using std::cout;
     using std::endl;

     complex<double> one(1., 0), i(0., 1);
     complex<double> x = one / i;
     complex<double> y = - i;
     double          r = 1e-12;
     double          a = 0;
     bool           ok = CppAD::NearEqual(x, y, r, a);
     if( ok )
          cout << "Ok"    << endl;
     else cout << "Error" << endl;
Input File: cppad/utility/near_equal.hpp cppad-20170000.3/doc/near_equal.cpp.xml0000644000175200017650000003076113057470507016625 0ustar coincoin-web NearEqual Function: Example and Test
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NearEqual Function: Example and Test

File Name
This file is called near_equal.cpp instead of NearEqual.cpp to avoid a name conflict with ../lib/NearEqual.cpp in the corresponding Microsoft project file. 

# include <cppad/utility/near_equal.hpp>

# include <complex>

bool Near_Equal(void)
{     bool ok = true;
     typedef std::complex<double> Complex;
     using CppAD::NearEqual;

     // double
     double x    = 1.00000;
     double y    = 1.00001;
     double a    =  .00003;
     double r    =  .00003;
     double zero = 0.;
     double inf  = 1. / zero;
     double nan  = 0. / zero;

     ok &= NearEqual(x, y, zero, a);
     ok &= NearEqual(x, y, r, zero);
     ok &= NearEqual(x, y, r, a);

     ok &= ! NearEqual(x, y, r / 10., a / 10.);
     ok &= ! NearEqual(inf, inf, r, a);
     ok &= ! NearEqual(-inf, -inf, r, a);
     ok &= ! NearEqual(nan, nan, r, a);

     // complex
     Complex X(x, x / 2.);
     Complex Y(y, y / 2.);
     Complex Inf(inf, zero);
     Complex Nan(zero, nan);

     ok &= NearEqual(X, Y, zero, a);
     ok &= NearEqual(X, Y, r, zero);
     ok &= NearEqual(X, Y, r, a);

     ok &= ! NearEqual(X, Y, r / 10., a / 10.);
     ok &= ! NearEqual(Inf, Inf, r, a);
     ok &= ! NearEqual(-Inf, -inf, r, a);
     ok &= ! NearEqual(Nan, Nan, r, a);

     return ok;
}
Input File: example/near_equal.cpp cppad-20170000.3/doc/speed_test.xml0000644000175200017650000003037613057470507016071 0ustar coincoin-web Run One Speed Test and Return Results
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Run One Speed Test and Return Results

Syntax
# include <cppad/utility/speed_test.hpp>
 rate_vec = speed_test(test, size_vec, time_min)

Purpose
The speed_test function executes a speed test for various sized problems and reports the rate of execution.

Motivation
It is important to separate small calculation units and test them individually. This way individual changes can be tested in the context of the routine that they are in. On many machines, accurate timing of a very short execution sequences is not possible. In addition, there may be set up and tear down time for a test that we do not really want included in the timing. For this reason speed_test automatically determines how many times to repeat the section of the test that we wish to time.

Include
The file cppad/speed_test.hpp defines the speed_test function. This file is included by cppad/cppad.hpp and it can also be included separately with out the rest of the CppAD routines.

Vector
We use Vector to denote a simple vector class with elements of type size_t.

test
The speed_test argument test is a function with the syntax
     test(size, repeat)
 and its return value is void.

size
The test argument size has prototype
     size_t size
 It specifies the size for this test.

repeat
The test argument repeat has prototype
     size_t repeat
 It specifies the number of times to repeat the test.

size_vec
The speed_test argument size_vec has prototype
     const Vector& size_vec
 This vector determines the size for each of the tests problems.

time_min
The argument time_min has prototype
     double time_min
 It specifies the minimum amount of time in seconds that the test routine should take. The repeat argument to test is increased until this amount of execution time is reached.

rate_vec
The return value rate_vec has prototype
     Vector& rate_vec
 We use n to denote its size which is the same as the vector size_vec . For i = 0 , … , n -1 ,
     rate_vec[i]
 is the ratio of repeat divided by time in seconds for the problem with size size_vec[i] .

Timing
If your system supports the unix gettimeofday function, it will be used to measure time. Otherwise, time is measured by the difference in 
 
     (double) clock() / (double) CLOCKS_PER_SEC
in the context of the standard <ctime> definitions.

Example
The routine speed_test.cpp is an example and test of speed_test.
Input File: cppad/utility/speed_test.hpp cppad-20170000.3/doc/speed_test.cpp.xml0000644000175200017650000003246313057470507016651 0ustar coincoin-web speed_test: Example and test
Prev Next speed_test.cpp Headings

speed_test: Example and test
# include <cppad/utility/speed_test.hpp>
# include <cppad/utility/vector.hpp>

namespace { // empty namespace
     using CppAD::vector;
     vector<double> a, b, c;
     void test(size_t size, size_t repeat)
     {     // setup
          a.resize(size);
          b.resize(size);
          c.resize(size);
          size_t i  = size;;
          while(i)
          {     --i;
               a[i] = i;
               b[i] = 2 * i;
               c[i] = 0.0;
          }
          // operations we are timing
          while(repeat--)
          {     i = size;;
               while(i)
               {     --i;
                    c[i] += std::sqrt(a[i] * a[i] + b[i] * b[i]);
               }
          }
     }
}
bool speed_test(void)
{     bool ok = true;

     // size of the test cases
     vector<size_t> size_vec(2);
     size_vec[0] = 40;
     size_vec[1] = 80;

     // minimum amount of time to run test
     double time_min = 0.5;

     // run the test cases
     vector<size_t> rate_vec(2);
     rate_vec = CppAD::speed_test(test, size_vec, time_min);

     // time per repeat loop (note counting setup or teardown)
     double time_0 = 1. / double(rate_vec[0]);
     double time_1 = 1. / double(rate_vec[1]);

     // for this case, time should be linear w.r.t size
     double check    = double(size_vec[1]) * time_0 / double(size_vec[0]);
     double rel_diff = (check - time_1) / time_1;
     ok             &= (std::fabs(rel_diff) <= .1);
     if( ! ok )
          std::cout << std::endl << "rel_diff = " << rel_diff << std::endl;

     a.clear();
     b.clear();
     c.clear();
     return ok;
}
Input File: speed/example/speed_test.cpp cppad-20170000.3/doc/speed_program.cpp.xml0000644000175200017650000002277013057470507017341 0ustar coincoin-web Example Use of SpeedTest
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Example Use of SpeedTest

Running This Program
On a Unix system that includes the g++ compiler, you can compile and run this program by changing into the speed/example directory and executing the following commands 
 
     g++ -I../.. speed_program.cpp -o speed_program.exe
     ./speed_program.exe

Program 
# include <cppad/utility/speed_test.hpp>

std::string Test(size_t size, size_t repeat)
{     // setup
     double *a = new double[size];
     double *b = new double[size];
     double *c = new double[size];
     size_t i  = size;;
     while(i)
     {     --i;
          a[i] = i;
          b[i] = 2 * i;
     }
     // operations we are timing
     while(repeat--)
     {     i = size;;
          while(i)
          {     --i;
               c[i] = a[i] + b[i];
          }
     }
     // teardown
     delete [] a;
     delete [] b;
     delete [] c;

     // return a test name that is valid for all sizes and repeats
     return "double: c[*] = a[*] + b[*]";
}
int main(void)
{
     CppAD::SpeedTest(Test, 10, 10, 100);
     return 0;
}
Output
Executing of the program above generated the following output (the rates will be different for each particular system): 
 
     double: c[*] = a[*] + b[*]
     size = 10  rate = 14,122,236
     size = 20  rate = 7,157,515
     size = 30  rate = 4,972,500
     size = 40  rate = 3,887,214
     size = 50  rate = 3,123,086
     size = 60  rate = 2,685,214
     size = 70  rate = 2,314,737
     size = 80  rate = 2,032,124
     size = 90  rate = 1,814,145
     size = 100 rate = 1,657,828
Input File: speed/example/speed_program.cpp cppad-20170000.3/doc/speedtest.xml0000644000175200017650000003377413057470507015737 0ustar coincoin-web Run One Speed Test and Print Results
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Run One Speed Test and Print Results

Syntax
# include <cppad/utility/speed_test.hpp>
 SpeedTest(Test, first, inc, last)

Purpose
The SpeedTest function executes a speed test for various sized problems and reports the results on standard output; i.e. std::cout. The size of each test problem is included in its report (unless first is equal to last ).

Motivation
It is important to separate small calculation units and test them individually. This way individual changes can be tested in the context of the routine that they are in. On many machines, accurate timing of a very short execution sequences is not possible. In addition, there may be set up time for a test that we do not really want included in the timing. For this reason SpeedTest automatically determines how many times to repeat the section of the test that we wish to time.

Include
The file speed_test.hpp contains the SpeedTest function. This file is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Test
The SpeedTest argument Test is a function with the syntax
     name = Test(size, repeat)
size
The Test argument size has prototype
     size_t size
 It specifies the size for this test.

repeat
The Test argument repeat has prototype
     size_t repeat
 It specifies the number of times to repeat the test.

name
The Test result name has prototype
     std::string name
 The results for this test are reported on std::cout with name as an identifier for the test. It is assumed that, for the duration of this call to SpeedTest, Test will always return the same value for name . If name is the empty string, no test name is reported by SpeedTest.

first
The SpeedTest argument first has prototype
     size_t first
 It specifies the size of the first test problem reported by this call to SpeedTest.

last
The SpeedTest argument last has prototype
     size_t last
 It specifies the size of the last test problem reported by this call to SpeedTest.

inc
The SpeedTest argument inc has prototype
     int inc
 It specifies the increment between problem sizes; i.e., all values of size in calls to Test are given by
     size = first + j * inc
 where j is a positive integer. The increment can be positive or negative but it cannot be zero. The values first , last and inc must satisfy the relation inc * ( last - first ) ≥ 0
rate
The value displayed in the rate column on std::cout is defined as the value of repeat divided by the corresponding elapsed execution time in seconds. The elapsed execution time is measured by the difference in 
 
     (double) clock() / (double) CLOCKS_PER_SEC
in the context of the standard <ctime> definitions.

Errors
If one of the restrictions above is violated, the CppAD error handler is used to report the error. You can redefine this action using the instructions in ErrorHandler

Example
The program speed_program.cpp is an example usage of SpeedTest.
Input File: cppad/utility/speed_test.hpp cppad-20170000.3/doc/time_test.xml0000644000175200017650000002762013057470507015725 0ustar coincoin-web Determine Amount of Time to Execute a Test
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Determine Amount of Time to Execute a Test

Syntax
# include <cppad/utility/time_test.hpp>
 time = time_test(test, time_min)
 time = time_test(test, time_min, test_size)

Purpose
The time_test function executes a timing test and reports the amount of wall clock time for execution.

Motivation
It is important to separate small calculation units and test them individually. This way individual changes can be tested in the context of the routine that they are in. On many machines, accurate timing of a very short execution sequences is not possible. In addition, there may be set up and tear down time for a test that we do not really want included in the timing. For this reason time_test automatically determines how many times to repeat the section of the test that we wish to time.

Include
The file cppad/time_test.hpp defines the time_test function. This file is included by cppad/cppad.hpp and it can also be included separately with out the rest of the CppAD routines.

test
The time_test argument test is a function, or function object. In the case where test_size is not present, test supports the syntax
     test(repeat)
 In the case where test_size is present, test supports the syntax
     test(size, repeat)
 In either case, the return value for test is void.

size
If the argument size is present, it has prototype
     size_t size
 and is equal to the test_size argument to time_test.

repeat
The test argument repeat has prototype
     size_t repeat
 It will be equal to the size argument to time_test.

time_min
The argument time_min has prototype
     double time_min
 It specifies the minimum amount of time in seconds that the test routine should take. The repeat argument to test is increased until this amount of execution time (or more) is reached.

test_size
This argument has prototype
     size_t test_size
 It specifies the size argument to test .

time
The return value time has prototype
     double time
 and is the number of wall clock seconds that it took to execute test divided by the value used for repeat .

Timing
The routine elapsed_seconds will be used to determine the amount of time it took to execute the test.

Example
The routine time_test.cpp is an example and test of time_test.
Input File: cppad/utility/time_test.hpp cppad-20170000.3/doc/elapsed_seconds.xml0000644000175200017650000001227513057470507017063 0ustar coincoin-web Returns Elapsed Number of Seconds
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Returns Elapsed Number of Seconds

Syntax
# include <cppad/utility/elapsed_seconds.hpp>
 s = elapsed_seconds()

Purpose
This routine is accurate to within .02 seconds (see elapsed_seconds.cpp ). It does not necessary work for time intervals that are greater than a day.
  1. If the C++11 std::chrono::steady_clock is available, it will be used for timing.
  2. Otherwise, if running under the Microsoft compiler, ::GetSystemTime will be used for timing.
  3. Otherwise, if gettimeofday is available, it is used for timing.
  4. Otherwise, std::clock() will be used for timing.


s
is a double equal to the number of seconds since the first call to elapsed_seconds.

Microsoft Systems
It you are using ::GetSystemTime, you will need to link in the external routine called microsoft_timer .

Example
The routine elapsed_seconds.cpp is an example and test of this routine.
Input File: cppad/utility/elapsed_seconds.hpp cppad-20170000.3/doc/elapsed_seconds.cpp.xml0000644000175200017650000001555313057470507017646 0ustar coincoin-web Elapsed Seconds: Example and Test
Prev Next elapsed_seconds.cpp Headings

Elapsed Seconds: Example and Test
# include <cppad/utility/elapsed_seconds.hpp>

# include <iostream>
# include <algorithm>
# include <cmath>

# define CPPAD_DEBUG_ELAPSED_SECONDS 0

bool elapsed_seconds(void)
{     bool ok = true;

     double max_diff = 0.;
     double s0 = CppAD::elapsed_seconds();
     double s1 = CppAD::elapsed_seconds();
     double s2 = CppAD::elapsed_seconds();
     while(s2 - s0 < 1.)
     {     max_diff = std::max(s2 - s1, max_diff);
          s1 = s2;
          s2 = CppAD::elapsed_seconds();

     }
# if CPPAD_DEBUG_ELAPSED_SECONDS
     std::cout << "max_diff = " << max_diff << std::endl;
# endif
     ok &= 0. < max_diff && max_diff < .04;
     return ok;
}
Input File: speed/example/elapsed_seconds.cpp cppad-20170000.3/doc/time_test.cpp.xml0000644000175200017650000002771613057470507016514 0ustar coincoin-web time_test: Example and test
Prev Next time_test.cpp Headings

time_test: Example and test
# include <cppad/utility/time_test.hpp>
# include <cppad/utility/vector.hpp>

namespace { // empty namespace
     using CppAD::vector;

     // size for the test
     size_t size_;

     vector<double> a, b, c;
     void test(size_t repeat)
     {     // setup
          a.resize(size_);
          b.resize(size_);
          c.resize(size_);
          size_t i  = size_;;
          while(i)
          {     --i;
               a[i] = i;
               b[i] = 2 * i;
               c[i] = 0.0;
          }
          // operations we are timing
          while(repeat--)
          {     i = size_;;
               while(i)
               {     --i;
                    c[i] += std::sqrt(a[i] * a[i] + b[i] * b[i]);
               }
          }
     }

}
bool time_test(void)
{     bool ok = true;

     // minimum amount of time to run test
     double time_min = 0.5;

     // size of first test case
     size_ = 20;

     // run the first test case
     double time_first = CppAD::time_test(test, time_min);

     // size of second test case is twice as large
     size_ = 2 * size_;

     // run the second test case
     double time_second = CppAD::time_test(test, time_min);

     // for this case, time should be linear w.r.t size
     double rel_diff = 1. - 2. * time_first / time_second;
     ok             &= (std::fabs(rel_diff) <= .1);
     if( ! ok )
          std::cout << std::endl << "rel_diff = " << rel_diff  << std::endl;

     a.clear();
     b.clear();
     c.clear();
     return ok;
}
Input File: speed/example/time_test.cpp cppad-20170000.3/doc/numerictype.xml0000644000175200017650000003724013057470507016273 0ustar coincoin-web Definition of a Numeric Type
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Definition of a Numeric Type

Type Requirements
A NumericType is any type that satisfies the requirements below. The following is a list of some numeric types: int, float, double, AD<double>, AD< AD<double> >. The routine CheckNumericType can be used to check that a type satisfies these conditions.

Default Constructor
The syntax
     NumericType x;
 creates a NumericType object with an unspecified value.

Constructor From Integer
If i is an int, the syntax
     NumericType x(i);
 creates a NumericType object with a value equal to i where i can be const.

Copy Constructor
If x is a NumericType object the syntax
     NumericType y(x);
 creates a NumericType object y with the same value as x where x can be const.

Assignment
If x and y are NumericType objects, the syntax
     x = y
 sets the value of x equal to the value of y where y can be const. The expression corresponding to this operation is unspecified; i.e., it could be void and hence
     x = y = z
 may not be legal.

Operators
Suppose x , y and z NumericType objects where x and y may be const. In the result type column, NumericType can be replaced by any type that can be used just like a NumericType object.
Operation Description Result Type
+x unary plus NumericType
-x unary minus NumericType
x +  y binary addition NumericType
x -  y binary subtraction NumericType
x *  y binary multiplication NumericType
x /  y binary division NumericType
z += y computed assignment addition unspecified
z -= y computed assignment subtraction unspecified
z *= y computed assignment multiplication unspecified
z /= y computed assignment division unspecified

Example
The file numeric_type.cpp contains an example and test of using numeric types. It returns true if it succeeds and false otherwise. (It is easy to modify to test additional numeric types.)

Exercise
  1. List three operators that are not supported by every numeric type but that are supported by the numeric types int, float, double.
  2. Which of the following are numeric types: std::complex<double>, std::valarray<double>, std::vector<double> ?
Input File: omh/numeric_type.omh cppad-20170000.3/doc/numeric_type.cpp.xml0000644000175200017650000004465313057470507017221 0ustar coincoin-web The NumericType: Example and Test
Prev Next numeric_type.cpp Headings

The NumericType: Example and Test

# include <cppad/cppad.hpp>

namespace { // Empty namespace

     // -------------------------------------------------------------------
     class MyType {
     private:
          double d;
     public:
          // constructor from void
          MyType(void) : d(0.)
          { }
          // constructor from an int
          MyType(int d_) : d(d_)
          { }
          // copy constructor
          MyType(const MyType &x)
          {     d = x.d; }
          // assignment operator
          void operator = (const MyType &x)
          {     d = x.d; }
          // member function that converts to double
          double Double(void) const
          {     return d; }
          // unary plus
          MyType operator + (void) const
          {     MyType x;
               x.d =  d;
               return x;
          }
          // unary plus
          MyType operator - (void) const
          {     MyType x;
               x.d = - d;
               return x;
          }
          // binary addition
          MyType operator + (const MyType &x) const
          {     MyType y;
               y.d = d + x.d ;
               return y;
          }
          // binary subtraction
          MyType operator - (const MyType &x) const
          {     MyType y;
               y.d = d - x.d ;
               return y;
          }
          // binary multiplication
          MyType operator * (const MyType &x) const
          {     MyType y;
               y.d = d * x.d ;
               return y;
          }
          // binary division
          MyType operator / (const MyType &x) const
          {     MyType y;
               y.d = d / x.d ;
               return y;
          }
          // computed assignment addition
          void operator += (const MyType &x)
          {     d += x.d; }
          // computed assignment subtraction
          void operator -= (const MyType &x)
          {     d -= x.d; }
          // computed assignment multiplication
          void operator *= (const MyType &x)
          {     d *= x.d; }
          // computed assignment division
          void operator /= (const MyType &x)
          {     d /= x.d; }
     };
}
bool NumericType(void)
{     bool ok  = true;
     using CppAD::AD;
     using CppAD::CheckNumericType;

     CheckNumericType<MyType>            ();

     CheckNumericType<int>               ();
     CheckNumericType<double>            ();
     CheckNumericType< AD<double> >      ();
     CheckNumericType< AD< AD<double> > >();

     return ok;
}
Input File: example/numeric_type.cpp cppad-20170000.3/doc/checknumerictype.xml0000644000175200017650000001253713057470507017273 0ustar coincoin-web Check NumericType Class Concept
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Check NumericType Class Concept

Syntax
# include <cppad/utility/check_numeric_type.hpp>
 CheckNumericType<NumericType>()

Purpose
The syntax
     CheckNumericType<NumericType>()
 preforms compile and run time checks that the type specified by NumericType satisfies all the requirements for a NumericType class. If a requirement is not satisfied, a an error message makes it clear what condition is not satisfied.

Include
The file cppad/check_numeric_type.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest if the CppAD include files.

Parallel Mode
The routine thread_alloc::parallel_setup must be called before it can be used in parallel mode.

Example
The file check_numeric_type.cpp contains an example and test of this function. It returns true, if it succeeds an false otherwise. The comments in this example suggest a way to change the example so an error message occurs.
Input File: cppad/utility/check_numeric_type.hpp cppad-20170000.3/doc/check_numeric_type.cpp.xml0000644000175200017650000010304113057470507020341 0ustar coincoin-web The CheckNumericType Function: Example and Test
Prev Next check_numeric_type.cpp Headings

The CheckNumericType Function: Example and Test

# include <cppad/utility/check_numeric_type.hpp>
# include <cppad/utility/near_equal.hpp>


// Chosing a value between 1 and 10 selects a numeric class properity to be
// omitted and result in an error message being generated
# define CppADMyTypeOmit 0

namespace { // Empty namespace

     // -------------------------------------------------------------------
     class MyType {
     private:
          double d;
     public:
          // constructor from void
          MyType(void) : d(0.)
          { }
          // constructor from an int
          MyType(int d_) : d(d_)
          { }
          // copy constuctor
          MyType(const MyType &x)
          {     d = x.d; }
          // assignment operator
          void operator = (const MyType &x)
          {     d = x.d; }
          // member function that converts to double
          double Double(void) const
          {     return d; }
# if CppADMyTypeOmit != 1
          // unary plus
          MyType operator + (void) const
          {     MyType x;
               x.d =  d;
               return x;
          }
# endif
# if CppADMyTypeOmit != 2
          // unary plus
          MyType operator - (void) const
          {     MyType x;
               x.d = - d;
               return x;
          }
# endif
# if CppADMyTypeOmit != 3
          // binary addition
          MyType operator + (const MyType &x) const
          {     MyType y;
               y.d = d + x.d ;
               return y;
          }
# endif
# if CppADMyTypeOmit != 4
          // binary subtraction
          MyType operator - (const MyType &x) const
          {     MyType y;
               y.d = d - x.d ;
               return y;
          }
# endif
# if CppADMyTypeOmit != 5
          // binary multiplication
          MyType operator * (const MyType &x) const
          {     MyType y;
               y.d = d * x.d ;
               return y;
          }
# endif
# if CppADMyTypeOmit != 6
          // binary division
          MyType operator / (const MyType &x) const
          {     MyType y;
               y.d = d / x.d ;
               return y;
          }
# endif
# if CppADMyTypeOmit != 7
          // computed assignment addition
          void operator += (const MyType &x)
          {     d += x.d; }
# endif
# if CppADMyTypeOmit != 8
          // computed assignment subtraction
          void operator -= (const MyType &x)
          {     d -= x.d; }
# endif
# if CppADMyTypeOmit != 9
          // computed assignment multiplication
          void operator *= (const MyType &x)
          {     d *= x.d; }
# endif
# if CppADMyTypeOmit != 10
          // computed assignment division
          void operator /= (const MyType &x)
          {     d /= x.d; }
# endif
     };
     // -------------------------------------------------------------------
     /*
     Solve: A[0] * x[0] + A[1] * x[1] = b[0]
            A[2] * x[0] + A[3] * x[1] = b[1]
     */
     template <class NumericType>
     void Solve(NumericType *A, NumericType *x, NumericType *b)
     {
          // make sure NumericType satisfies its conditions
          CppAD::CheckNumericType<NumericType>();

          // copy b to x
          x[0] = b[0];
          x[1] = b[1];

          // copy A to work space
          NumericType W[4];
          W[0] = A[0];
          W[1] = A[1];
          W[2] = A[2];
          W[3] = A[3];

          // divide first row by W(1,1)
          W[1] /= W[0];
          x[0] /= W[0];
          W[0] = NumericType(1);

          // subtract W(2,1) times first row from second row
          W[3] -= W[2] * W[1];
          x[1] -= W[2] * x[0];
          W[2] = NumericType(0);

          // divide second row by W(2, 2)
          x[1] /= W[3];
          W[3]  = NumericType(1);

          // use first row to solve for x[0]
          x[0] -= W[1] * x[1];
     }
} // End Empty namespace

bool CheckNumericType(void)
{     bool ok  = true;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     MyType A[4];
     A[0] = MyType(1); A[1] = MyType(2);
     A[2] = MyType(3); A[3] = MyType(4);

     MyType b[2];
     b[0] = MyType(1);
     b[1] = MyType(2);

     MyType x[2];
     Solve(A, x, b);

     MyType sum;
     sum = A[0] * x[0] + A[1] * x[1];
     ok &= NearEqual(sum.Double(), b[0].Double(), eps99, eps99);

     sum = A[2] * x[0] + A[3] * x[1];
     ok &= NearEqual(sum.Double(), b[1].Double(), eps99, eps99);

     return ok;
}
Input File: example/check_numeric_type.cpp cppad-20170000.3/doc/simplevector.xml0000644000175200017650000006321013057470507016437 0ustar coincoin-web Definition of a Simple Vector
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Definition of a Simple Vector

Template Class Requirements
A simple vector template class SimpleVector , is any template class that satisfies the requirements below. The following is a list of some simple vector template classes:
Name Documentation
std::vector Section 16.3 of The C++ Programming Language
std::valarray Section 22.4 of The C++ Programming Language
CppAD::vector The CppAD::vector Template Class

Elements of Specified Type
A simple vector class with elements of type Scalar , is any class that satisfies the requirements for a class of the form
     SimpleVector<Scalar>
 The routine CheckSimpleVector can be used to check that a class is a simple vector class with a specified element type.

Default Constructor
The syntax
     SimpleVector<Scalar> x;
 creates an empty vector x ( x.size() is zero) that can later contain elements of the specified type (see resize below).

Sizing Constructor
If n has type size_t,
     SimpleVector<Scalar> x(n)
 creates a vector x with n elements each of the specified type.

Copy Constructor
If x is a SimpleVector<Scalar> object,
     SimpleVector<Scalar> y(x)
 creates a vector with the same type and number of elements as x . The Scalar assignment operator ( = ) is used to set each element of y equal to the corresponding element of x . This is a `deep copy' in that the values of the elements of x and y can be set independently after the copy. The argument x is passed by reference and may be const.

Element Constructor and Destructor
The default constructor for type Scalar is called for every element in a vector when the vector element is created. The Scalar destructor is called when it is removed from the vector (this includes when the vector is destroyed).

Assignment
If x and y are SimpleVector<Scalar> objects,
     y = x
 uses the Scalar assignment operator ( = ) to set each element of y equal to the corresponding element of x . This is a `deep assignment' in that the values of the elements of x and y can be set independently after the assignment. The vectors x and y must have the same number of elements. The argument x is passed by reference and may be const.

The type returned by this assignment is unspecified; for example, it might be void in which case the syntax
     z = y = x
 would not be valid.

Size
If x is a SimpleVector<Scalar> object and n has type size_t,
     n = size_t( x.size() )
 sets n to the number of elements in the vector x . The object x may be const.

Resize
If x is a SimpleVector<Scalar> object and n has type size_t,
     x.resize(n)
 changes the number of elements contained in the vector x to be n . The value of the elements of x are not specified after this operation; i.e., any values previously stored in x are lost. (The object x can not be const.)

Value Type
If Vector is any simple vector class, the syntax
     Vector::value_type
 is the type of the elements corresponding to the vector class; i.e.,
     SimpleVector<Scalar>::value_type
 is equal to Scalar .

Element Access
If x is a SimpleVector<Scalar> object and i has type size_t,
     x[i]
 returns an object of an unspecified type, referred to here as elementType .

Using Value
If elementType is not the same as Scalar , the conversion operator
     static_cast<Scalar>(x[i])
 is used implicitly when x[i] is used in an expression with values of type Scalar . For this type of usage, the object x may be const.

Assignment
If y is an object of type Scalar ,
     x[i] = y
 assigns the i-th element of x to have value y . For this type of usage, the object x can not be const. The type returned by this assignment is unspecified; for example, it might be void in which case the syntax
     z = x[i] = y
 would not be valid.

Example
The file simple_vector.cpp contains an example and test of a Simple template class. It returns true if it succeeds and false otherwise. (It is easy to modify to test additional simple vector template classes.)

Exercise
  1. If Vector is a simple vector template class, the following code may not be valid:
             Vector<double> x(2);
         x[2] = 1.;
     Create and run a program that executes the code segment above where Vector is each of the following cases: std::vector, CppAD::vector. Do this both where the compiler option -DNDEBUG is and is not present on the compilation command line.
  2. If Vector is a simple vector template class, the following code may not be valid:
             Vector<int> x(2);
             Vector<int> y(1);
         x[0] = 0;
         x[1] = 1;
         y    = x;
     Create and run a program that executes the code segment above where Vector is each of the following cases: std::valarray, CppAD::vector. Do this both where the compiler option -DNDEBUG is and is not present on the compilation command line.
Input File: omh/simple_vector.omh cppad-20170000.3/doc/simple_vector.cpp.xml0000644000175200017650000003736713057470507017375 0ustar coincoin-web Simple Vector Template Class: Example and Test
Prev Next simple_vector.cpp Headings

Simple Vector Template Class: Example and Test
# include <iostream>                   // std::cout and std::endl

# include <vector>                     // std::vector
# include <valarray>                   // std::valarray
# include <cppad/utility/vector.hpp>       // CppAD::vector
# include <cppad/utility/check_simple_vector.hpp>  // CppAD::CheckSimpleVector
namespace {
     template <typename Vector>
     bool Ok(void)
     {     // type corresponding to elements of Vector
          typedef typename Vector::value_type Scalar;

          bool ok = true;             // initialize testing flag

          Vector x;                   // use the default constructor
          ok &= (x.size() == 0);      // test size for an empty vector
          Vector y(2);                // use the sizing constructor
          ok &= (y.size() == 2);      // size for an vector with elements

          // non-const access to the elements of y
          size_t i;
          for(i = 0; i < 2; i++)
               y[i] = Scalar(i);

          const Vector z(y);          // copy constructor
          x.resize(2);                // resize
          x = z;                      // vector assignment

          // use the const access to the elements of x
          // and test the values of elements of x, y, z
          for(i = 0; i < 2; i++)
          {     ok &= (x[i] == Scalar(i));
               ok &= (y[i] == Scalar(i));
               ok &= (z[i] == Scalar(i));
          }
          return ok;
     }
}
bool SimpleVector (void)
{     bool ok = true;

     // use routine above to check these cases
     ok &= Ok< std::vector<double> >();
     ok &= Ok< std::valarray<float> >();
     ok &= Ok< CppAD::vector<int> >();
# ifndef _MSC_VER
     // Avoid Microsoft following compiler warning:  'size_t' :
     // forcing value to bool 'true' or 'false' (performance warning)
     ok &= Ok< std::vector<bool> >();
     ok &= Ok< CppAD::vector<bool> >();
# endif
     // use CheckSimpleVector for more extensive testing
     CppAD::CheckSimpleVector<double, std::vector<double>  >();
     CppAD::CheckSimpleVector<float,  std::valarray<float> >();
     CppAD::CheckSimpleVector<int,    CppAD::vector<int>   >();
     CppAD::CheckSimpleVector<bool,   std::vector<bool>    >();
     CppAD::CheckSimpleVector<bool,   CppAD::vector<bool>  >();

     return ok;
}
Input File: example/simple_vector.cpp cppad-20170000.3/doc/checksimplevector.xml0000644000175200017650000002510513057470507017436 0ustar coincoin-web Check Simple Vector Concept
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Check Simple Vector Concept

Syntax
# include <cppad/utility/check_simple_vector.hpp>
 CheckSimpleVector<Scalar, Vector>()
CheckSimpleVector<Scalar, Vector>(x, y)

Purpose
Preforms compile and run time checks that the type specified by Vector satisfies all the requirements for a SimpleVector class with elements of type Scalar . If a requirement is not satisfied, a an error message makes it clear what condition is not satisfied.

x, y
If the arguments x and y are present, they have prototype
     const Scalar& x
     const Scalar& y
 In addition, the check
     x == x
 will return the boolean value true, and
     x == y
 will return false.

Restrictions
If the arguments x and y are not present, the following extra assumption is made by CheckSimpleVector: If x is a Scalar object
     x = 0
     y = 1
 assigns values to the objects x and y . In addition, x == x would return the boolean value true and x == y would return false.

Include
The file cppad/check_simple_vector.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest if the CppAD include files.

Parallel Mode
The routine thread_alloc::parallel_setup must be called before it can be used in parallel mode.

Example
The file check_simple_vector.cpp contains an example and test of this function where S is the same as T . It returns true, if it succeeds an false otherwise. The comments in this example suggest a way to change the example so S is not the same as T .
Input File: cppad/utility/check_simple_vector.hpp cppad-20170000.3/doc/check_simple_vector.cpp.xml0000644000175200017650000007032613057470507020522 0ustar coincoin-web The CheckSimpleVector Function: Example and Test
Prev Next check_simple_vector.cpp Headings

The CheckSimpleVector Function: Example and Test

# include <cppad/utility/vector.hpp>
# include <cppad/utility/check_simple_vector.hpp>
# include <iostream>


// Chosing a value between 1 and 9 selects a simple vector properity to be
// omitted and result in an error message being generated
# define CppADMyVectorOmit 0

// -------------------------------------------------------------------------

// example class used for non-constant elements (different from Scalar)
template <class Scalar>
class MyElement {
private:
     Scalar *element;
public:
     // element constructor
     MyElement(Scalar *e)
     {     element = e; }
     // an example element assignment that returns void
     void operator = (const Scalar &s)
     {     *element = s; }
     // conversion to Scalar
     operator Scalar() const
     {     return *element; }
};


// example simple vector class
template <class Scalar>
class MyVector {
private:
     size_t length;
     Scalar * data;
public:

# if CppADMyVectorOmit != 1
     // type of the elements in the vector
     typedef Scalar value_type;
# endif
# if CppADMyVectorOmit != 2
     // default constructor
     inline MyVector(void) : length(0) , data(0)
     { }
# endif
# if CppADMyVectorOmit != 3
     // constructor with a specified size
     inline MyVector(size_t n) : length(n)
     {     if( length == 0 )
               data = 0;
          else     data = new Scalar[length];
     }
# endif
# if CppADMyVectorOmit != 4
     // copy constructor
     inline MyVector(const MyVector &x) : length(x.length)
     {     size_t i;
          if( length == 0 )
               data = 0;
          else     data = new Scalar[length];

          for(i = 0; i < length; i++)
               data[i] = x.data[i];
     }
# endif
# if CppADMyVectorOmit != 4
# if CppADMyVectorOmit != 7
     // destructor (it is not safe to delete the pointer in cases 4 and 7)
     ~MyVector(void)
     {     delete [] data; }
# endif
# endif
# if CppADMyVectorOmit != 5
     // size function
     inline size_t size(void) const
     {     return length; }
# endif
# if CppADMyVectorOmit != 6
     // resize function
     inline void resize(size_t n)
     {     if( length > 0 )
               delete [] data;
          length = n;
          if( length > 0 )
               data = new Scalar[length];
          else     data = 0;
     }
# endif
# if CppADMyVectorOmit != 7
     // assignment operator
     inline MyVector & operator=(const MyVector &x)
     {     size_t i;
          for(i = 0; i < length; i++)
               data[i] = x.data[i];
          return *this;
     }
# endif
# if CppADMyVectorOmit != 8
     // non-constant element access
     MyElement<Scalar> operator[](size_t i)
     {     return data + i; }
# endif
# if CppADMyVectorOmit != 9
     // constant element access
     const Scalar & operator[](size_t i) const
     {     return data[i]; }
# endif
};
// -------------------------------------------------------------------------

/*
Compute r = a * v, where a is a scalar with same type as the elements of
the Simple Vector v. This routine uses the CheckSimpleVector function to ensure that
the types agree.
*/
namespace { // Empty namespace
     template <class Scalar, class Vector>
     Vector Sscal(const Scalar &a, const Vector &v)
     {
          // invoke CheckSimpleVector function
          CppAD::CheckSimpleVector<Scalar, Vector>();

          size_t n = v.size();
          Vector r(n);

          size_t i;
          for(i = 0; i < n; i++)
               r[i] = a * v[i];

          return r;
     }
}

bool CheckSimpleVector(void)
{     bool ok  = true;
     using CppAD::vector;

     // --------------------------------------------------------
     // If you change double to float in the next statement,
     // CheckSimpleVector will generate an error message at compile time.
     double a = 3.;
     // --------------------------------------------------------

     size_t n = 2;
     MyVector<double> v(n);
     v[0]     = 1.;
     v[1]     = 2.;
     MyVector<double> r = Sscal(a, v);
     ok      &= (r[0] == 3.);
     ok      &= (r[1] == 6.);

     return ok;
}
Input File: example/check_simple_vector.cpp cppad-20170000.3/doc/nan.xml0000644000175200017650000003327213057470507014504 0ustar coincoin-web Obtain Nan or Determine if a Value is Nan
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Obtain Nan or Determine if a Value is Nan

Syntax
# include <cppad/utility/nan.hpp>
 b = isnan(s)
 b = hasnan(v)

Purpose
It obtain and check for the value not a number nan. The IEEE standard specifies that a floating point value a is nan if and only if the following returns true
     a != a
Include
The file cppad/nan.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Macros
Some C++ compilers use preprocessor symbols called nan and isnan. These preprocessor symbols will no longer be defined after this file is included.

isnan
This routine determines if a scalar value is nan.

s
The argument s has prototype
     const Scalar s
b
The return value b has prototype
     bool b
 It is true if the value s is nan.

hasnan
This routine determines if a SimpleVector has an element that is nan.

v
The argument v has prototype
     const Vector &v
 (see Vector for the definition of Vector ).

b
The return value b has prototype
     bool b
 It is true if the vector v has a nan.

nan(zero)

Deprecated 2015-10-04
This routine has been deprecated, use CppAD numeric limits quiet_NaN in its place.

Syntax
s = nan(z)
z
The argument z has prototype
     const Scalar &z
 and its value is zero (see Scalar for the definition of Scalar ).

s
The return value s has prototype
     Scalar s
 It is the value nan for this floating point type.

Scalar
The type Scalar must support the following operations;
Operation Description
a / b division operator (returns a Scalar object)
a == b equality operator (returns a bool object)
a != b not equality operator (returns a bool object)
Note that the division operator will be used with a and b equal to zero. For some types (e.g. int) this may generate an exception. No attempt is made to catch any such exception.

Vector
The type Vector must be a SimpleVector class with elements of type Scalar .

Example
The file nan.cpp contains an example and test of this routine. It returns true if it succeeds and false otherwise.
Input File: cppad/utility/nan.hpp cppad-20170000.3/doc/nan.cpp.xml0000644000175200017650000001600113057470507015254 0ustar coincoin-web nan: Example and Test
Prev Next nan.cpp Headings

nan: Example and Test
# include <cppad/utility/nan.hpp>
# include <vector>
# include <limits>

bool nan(void)
{     bool ok = true;

     // get a nan
     double double_zero = 0.;
     double double_nan = std::numeric_limits<double>::quiet_NaN();

     // create a simple vector with no nans
     std::vector<double> v(2);
     v[0] = double_zero;
     v[1] = double_zero;

     // check that zero is not nan
     ok &= ! CppAD::isnan(double_zero);
     ok &= ! CppAD::hasnan(v);

     // check that nan is a nan
     v[1] = double_nan;
     ok &= CppAD::isnan(double_nan);
     ok &= CppAD::hasnan(v);

     // check that nan is not equal to itself
     ok &= (double_nan != double_nan);

     return ok;
}
Input File: example/nan.cpp cppad-20170000.3/doc/pow_int.xml0000644000175200017650000002534713057470507015413 0ustar coincoin-web The Integer Power Function
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The Integer Power Function

Syntax
# include <cppad/utility/pow_int.hpp>
 z = pow(x, y)

See Also
pow

Purpose
Determines the value of the power function pow ( x , y ) = x y for integer exponents n using multiplication and possibly division to compute the value. The other CppAD pow function may use logarithms and exponentiation to compute derivatives of the same value (which will not work if x is less than or equal zero).

Include
The file cppad/pow_int.h is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines. Including this file defines this version of the pow within the CppAD namespace.

x
The argument x has prototype
     const Type& x
y
The argument y has prototype
     const int& y
z
The result z has prototype
     Type z
Type
The type Type must support the following operations where a and b are Type objects and i is an int:
Operation    Description Result Type
Type a(i) construction of a Type object from an int Type
a * b binary multiplication of Type objects Type
a / b binary division of Type objects Type

Operation Sequence
The Type operation sequence used to calculate z is independent of x .

Example
The file pow_int.cpp is an example and test of this function. It returns true if it succeeds and false otherwise.
Input File: cppad/utility/pow_int.hpp cppad-20170000.3/doc/pow_int.cpp.xml0000644000175200017650000003773213057470507016175 0ustar coincoin-web The Pow Integer Exponent: Example and Test
Prev Next pow_int.cpp Headings

The Pow Integer Exponent: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool pow_int(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // declare independent variables and start tape recording
     size_t n  = 1;
     double x0 = -0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;
     CppAD::Independent(x);

     // dependent variable vector
     size_t m = 7;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     int i;
     for(i = 0; i < int(m); i++)
          y[i] = CppAD::pow(x[0], i - 3);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     double check;
     for(i = 0; i < int(m); i++)
     {     check = std::pow(x0, double(i - 3));
          ok &= NearEqual(y[i] , check,  1e-10 , 1e-10);
     }

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     for(i = 0; i < int(m); i++)
     {     check = double(i-3) * std::pow(x0, double(i - 4));
          ok &= NearEqual(dy[i] , check,  1e-10 , 1e-10);
     }

     // reverse computation of derivative of y[i]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     for(i = 0; i < int(m); i++)
          w[i] = 0.;
     for(i = 0; i < int(m); i++)
     {     w[i] = 1.;
          dw    = f.Reverse(1, w);
          check = double(i-3) * std::pow(x0, double(i - 4));
          ok &= NearEqual(dw[0] , check,  1e-10 , 1e-10);
          w[i] = 0.;
     }

     return ok;
}
Input File: example/pow_int.cpp cppad-20170000.3/doc/poly.xml0000644000175200017650000003627513057470507014721 0ustar coincoin-web Evaluate a Polynomial or its Derivative
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Evaluate a Polynomial or its Derivative

Syntax
# include <cppad/utility/poly.hpp>
 p = Poly(k, a, z)

Description
Computes the k-th derivative of the polynomial P ( z ) = a 0 + a 1 z 1 + ⋯ + a d z d If k is equal to zero, the return value is P ( z ) .

Include
The file cppad/poly.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines. Including this file defines Poly within the CppAD namespace.

k
The argument k has prototype
     size_t k
 It specifies the order of the derivative to calculate.

a
The argument a has prototype
     const Vector &a
 (see Vector below). It specifies the vector corresponding to the polynomial P ( z ) .

z
The argument z has prototype
     const Type &z
 (see Type below). It specifies the point at which to evaluate the polynomial

p
The result p has prototype
     Type p
 (see Type below) and it is equal to the k-th derivative of P ( z ) ; i.e., p = k ! 0 ! a k + ( k + 1 ) ! 1 ! a k + 1 z 1 + … + d ! ( d - k ) ! a d z d - k If k > d , p = Type(0) .

Type
The type Type is determined by the argument z . It is assumed that multiplication and addition of Type objects are commutative.

Operations
The following operations must be supported where x and y are objects of type Type and i is an int:
x  = i assignment
x  = y assignment
x *= y multiplication computed assignment
x += y addition computed assignment

Vector
The type Vector must be a SimpleVector class with elements of type Type . The routine CheckSimpleVector will generate an error message if this is not the case.

Operation Sequence
The Type operation sequence used to calculate p is independent of z and the elements of a (it does depend on the size of the vector a ).

Example
The file poly.cpp contains an example and test of this routine. It returns true if it succeeds and false otherwise.

Source
The file poly.hpp contains the current source code that implements these specifications.
Input File: cppad/utility/poly.hpp cppad-20170000.3/doc/poly.cpp.xml0000644000175200017650000001665513057470507015502 0ustar coincoin-web Polynomial Evaluation: Example and Test
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Polynomial Evaluation: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool Poly(void)
{     bool ok = true;

     // degree of the polynomial
     size_t deg = 3;

     // set the polynomial coefficients
     CPPAD_TESTVECTOR(double)   a(deg + 1);
     size_t i;
     for(i = 0; i <= deg; i++)
          a[i] = 1.;

     // evaluate this polynomial
     size_t k = 0;
     double z = 2.;
     double p = CppAD::Poly(k, a, z);
     ok      &= (p == 1. + z + z*z + z*z*z);

     // evaluate derivative
     k = 1;
     p = CppAD::Poly(k, a, z);
     ok &= (p == 1 + 2.*z + 3.*z*z);

     return ok;
}
Input File: example/poly.cpp cppad-20170000.3/doc/poly.hpp.xml0000644000175200017650000002505213057470507015476 0ustar coincoin-web Source: Poly
Prev Next poly.hpp Headings

Source: Poly
# ifndef CPPAD_POLY_HPP
# define CPPAD_POLY_HPP 
# include <cstddef>  // used to defined size_t
# include <cppad/utility/check_simple_vector.hpp>

namespace CppAD {    // BEGIN CppAD namespace

template <class Type, class Vector>
Type Poly(size_t k, const Vector &a, const Type &z)
{     size_t i;
     size_t d = a.size() - 1;

     Type tmp;

     // check Vector is Simple Vector class with Type elements
     CheckSimpleVector<Type, Vector>();

     // case where derivative order greater than degree of polynomial
     if( k > d )
     {     tmp = 0;
          return tmp;
     }
     // case where we are evaluating a derivative
     if( k > 0 )
     {     // initialize factor as (k-1) !
          size_t factor = 1;
          for(i = 2; i < k; i++)
               factor *= i;

          // set b to coefficient vector corresponding to derivative
          Vector b(d - k + 1);
          for(i = k; i <= d; i++)
          {     factor   *= i;
               tmp       = factor;
               b[i - k]  = a[i] * tmp;
               factor   /= (i - k + 1);
          }
          // value of derivative polynomial
          return Poly(0, b, z);
     }
     // case where we are evaluating the original polynomial
     Type sum = a[d];
     i        = d;
     while(i > 0)
     {     sum *= z;
          sum += a[--i];
     }
     return sum;
}
} // END CppAD namespace
# endif
Input File: omh/poly_hpp.omh cppad-20170000.3/doc/ludetandsolve.xml0000644000175200017650000000672713057470507016606 0ustar coincoin-web Compute Determinants and Solve Equations by LU Factorization
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Compute Determinants and Solve Equations by LU Factorization

Contents
LuSolveCompute Determinant and Solve Linear Equations
LuFactorLU Factorization of A Square Matrix
LuInvertInvert an LU Factored Equation
Input File: omh/lu_det_and_solve.omh cppad-20170000.3/doc/lusolve.xml0000644000175200017650000006351513057470507015424 0ustar coincoin-web Compute Determinant and Solve Linear Equations
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Compute Determinant and Solve Linear Equations

Syntax
 include <cppad/utility/lu_solve.hpp>
 signdet = LuSolve(n, m, A, B, X, logdet)

Description
Use an LU factorization of the matrix A to compute its determinant and solve for X in the linear of equation A * X = B where A is an n by n matrix, X is an n by m matrix, and B is an n x m matrix.

Include
The file cppad/lu_solve.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Factor and Invert
This routine is an easy to user interface to LuFactor and LuInvert for computing determinants and solutions of linear equations. These separate routines should be used if one right hand side B depends on the solution corresponding to another right hand side (with the same value of A ). In this case only one call to LuFactor is required but there will be multiple calls to LuInvert.

Matrix Storage
All matrices are stored in row major order. To be specific, if Y is a vector that contains a p by q matrix, the size of Y must be equal to p * q and for i = 0 , … , p -1 , j = 0 , … , q -1 , Y i , j = Y [ i * q + j ]
signdet
The return value signdet is a int value that specifies the sign factor for the determinant of A . This determinant of A is zero if and only if signdet is zero.

n
The argument n has type size_t and specifies the number of rows in the matrices A , X , and B . The number of columns in A is also equal to n .

m
The argument m has type size_t and specifies the number of columns in the matrices X and B . If m is zero, only the determinant of A is computed and the matrices X and B are not used.

A
The argument A has the prototype
     const FloatVector &A
 and the size of A must equal n * n (see description of FloatVector below). This is the n by n matrix that we are computing the determinant of and that defines the linear equation.

B
The argument B has the prototype
     const FloatVector &B
 and the size of B must equal n * m (see description of FloatVector below). This is the n by m matrix that defines the right hand side of the linear equations. If m is zero, B is not used.

X
The argument X has the prototype
     FloatVector &X
 and the size of X must equal n * m (see description of FloatVector below). The input value of X does not matter. On output, the elements of X contain the solution of the equation we wish to solve (unless signdet is equal to zero). If m is zero, X is not used.

logdet
The argument logdet has prototype
     Float &logdet
 On input, the value of logdet does not matter. On output, it has been set to the log of the determinant of A (but not quite). To be more specific, the determinant of A is given by the formula
     det = signdet * exp( logdet )
 This enables LuSolve to use logs of absolute values in the case where Float corresponds to a real number.

Float
The type Float must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case. In addition, the following operations must be defined for any pair of Float objects x and y :
Operation Description
log(x) returns the logarithm of x as a Float object

FloatVector
The type FloatVector must be a SimpleVector class with elements of type Float . The routine CheckSimpleVector will generate an error message if this is not the case.

LeqZero
Including the file lu_solve.hpp defines the template function
     template <typename Float>
     bool LeqZero<Float>(const Float &x)
 in the CppAD namespace. This function returns true if x is less than or equal to zero and false otherwise. It is used by LuSolve to avoid taking the log of zero (or a negative number if Float corresponds to real numbers). This template function definition assumes that the operator <= is defined for Float objects. If this operator is not defined for your use of Float , you will need to specialize this template so that it works for your use of LuSolve.

Complex numbers do not have the operation or <= defined. In addition, in the complex case, one can take the log of a negative number. The specializations
     bool LeqZero< std::complex<float> > (const std::complex<float> &x)
     bool LeqZero< std::complex<double> >(const std::complex<double> &x)
 are defined by including lu_solve.hpp. These return true if x is zero and false otherwise.

AbsGeq
Including the file lu_solve.hpp defines the template function
     template <typename Float>
     bool AbsGeq<Float>(const Float &x, const Float &y)
 If the type Float does not support the <= operation and it is not std::complex<float> or std::complex<double>, see the documentation for AbsGeq in LuFactor .

Example
The file lu_solve.cpp contains an example and test of using this routine. It returns true if it succeeds and false otherwise.

Source
The file lu_solve.hpp contains the current source code that implements these specifications.
Input File: cppad/utility/lu_solve.hpp cppad-20170000.3/doc/lu_solve.cpp.xml0000644000175200017650000003735613057470507016350 0ustar coincoin-web LuSolve With Complex Arguments: Example and Test
Prev Next lu_solve.cpp Headings

LuSolve With Complex Arguments: Example and Test

# include <cppad/utility/lu_solve.hpp>       // for CppAD::LuSolve
# include <cppad/utility/near_equal.hpp>     // for CppAD::NearEqual
# include <cppad/utility/vector.hpp>  // for CppAD::vector
# include <complex>               // for std::complex

typedef std::complex<double> Complex;    // define the Complex type
bool LuSolve(void)
{     bool  ok = true;
     using namespace CppAD;

     size_t   n = 3;           // number rows in A and B
     size_t   m = 2;           // number columns in B, X and S

     // A is an n by n matrix, B, X, and S are n by m matrices
     CppAD::vector<Complex> A(n * n), B(n * m), X(n * m) , S(n * m);

     Complex  logdet;          // log of determinant of A
     int      signdet;         // zero if A is singular
     Complex  det;             // determinant of A
     size_t   i, j, k;         // some temporary indices

     // set A equal to the n by n Hilbert Matrix
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               A[i * n + j] = 1. / (double) (i + j + 1);

     // set S to the solution of the equation we will solve
     for(j = 0; j < n; j++)
          for(k = 0; k < m; k++)
               S[ j * m + k ] = Complex(j, j + k);

     // set B = A * S
     size_t ik;
     Complex sum;
     for(k = 0; k < m; k++)
     {     for(i = 0; i < n; i++)
          {     sum = 0.;
               for(j = 0; j < n; j++)
                    sum += A[i * n + j] * S[j * m + k];
               B[i * m + k] = sum;
          }
     }

     // solve the equation A * X = B and compute determinant of A
     signdet = CppAD::LuSolve(n, m, A, B, X, logdet);
     det     = Complex( signdet ) * exp( logdet );

     double cond  = 4.62963e-4;       // condition number of A when n = 3
     double determinant = 1. / 2160.; // determinant of A when n = 3
     double delta = 1e-14 / cond;     // accuracy expected in X

     // check determinant
     ok &= CppAD::NearEqual(det, determinant, delta, delta);

     // check solution
     for(ik = 0; ik < n * m; ik++)
          ok &= CppAD::NearEqual(X[ik], S[ik], delta, delta);

     return ok;
}
Input File: example/lu_solve.cpp cppad-20170000.3/doc/lu_solve.hpp.xml0000644000175200017650000004500213057470507016340 0ustar coincoin-web Source: LuSolve
Prev Next lu_solve.hpp Headings

Source: LuSolve
# ifndef CPPAD_LU_SOLVE_HPP
# define CPPAD_LU_SOLVE_HPP 
# include <complex>
# include <vector>

// link exp for float and double cases
# include <cppad/base_require.hpp>

# include <cppad/core/cppad_assert.hpp>
# include <cppad/utility/check_simple_vector.hpp>
# include <cppad/utility/check_numeric_type.hpp>
# include <cppad/utility/lu_factor.hpp>
# include <cppad/utility/lu_invert.hpp>

namespace CppAD { // BEGIN CppAD namespace

// LeqZero
template <typename Float>
inline bool LeqZero(const Float &x)
{     return x <= Float(0); }
inline bool LeqZero( const std::complex<double> &x )
{     return x == std::complex<double>(0); }
inline bool LeqZero( const std::complex<float> &x )
{     return x == std::complex<float>(0); }

// LuSolve
template <typename Float, typename FloatVector>
int LuSolve(
     size_t             n      ,
     size_t             m      ,
     const FloatVector &A      ,
     const FloatVector &B      ,
     FloatVector       &X      ,
     Float        &logdet      )
{
     // check numeric type specifications
     CheckNumericType<Float>();

     // check simple vector class specifications
     CheckSimpleVector<Float, FloatVector>();

     size_t        p;       // index of pivot element (diagonal of L)
     int     signdet;       // sign of the determinant
     Float     pivot;       // pivot element

     // the value zero
     const Float zero(0);

     // pivot row and column order in the matrix
     std::vector<size_t> ip(n);
     std::vector<size_t> jp(n);

     // -------------------------------------------------------
     CPPAD_ASSERT_KNOWN(
          size_t(A.size()) == n * n,
          "Error in LuSolve: A must have size equal to n * n"
     );
     CPPAD_ASSERT_KNOWN(
          size_t(B.size()) == n * m,
          "Error in LuSolve: B must have size equal to n * m"
     );
     CPPAD_ASSERT_KNOWN(
          size_t(X.size()) == n * m,
          "Error in LuSolve: X must have size equal to n * m"
     );
     // -------------------------------------------------------

     // copy A so that it does not change
     FloatVector Lu(A);

     // copy B so that it does not change
     X = B;

     // Lu factor the matrix A
     signdet = LuFactor(ip, jp, Lu);

     // compute the log of the determinant
     logdet  = Float(0);
     for(p = 0; p < n; p++)
     {     // pivot using the max absolute element
          pivot   = Lu[ ip[p] * n + jp[p] ];

          // check for determinant equal to zero
          if( pivot == zero )
          {     // abort the mission
               logdet = Float(0);
               return   0;
          }

          // update the determinant
          if( LeqZero ( pivot ) )
          {     logdet += log( - pivot );
               signdet = - signdet;
          }
          else     logdet += log( pivot );

     }

     // solve the linear equations
     LuInvert(ip, jp, Lu, X);

     // return the sign factor for the determinant
     return signdet;
}
} // END CppAD namespace
# endif
Input File: omh/lu_solve_hpp.omh cppad-20170000.3/doc/lufactor.xml0000644000175200017650000007366313057470507015557 0ustar coincoin-web LU Factorization of A Square Matrix
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LU Factorization of A Square Matrix

Syntax
 include <cppad/utility/lu_factor.hpp>
 sign = LuFactor(ip, jp, LU)

Description
Computes an LU factorization of the matrix A where A is a square matrix.

Include
The file cppad/lu_factor.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Matrix Storage
All matrices are stored in row major order. To be specific, if Y is a vector that contains a p by q matrix, the size of Y must be equal to p * q and for i = 0 , … , p -1 , j = 0 , … , q -1 , Y i , j = Y [ i * q + j ]
sign
The return value sign has prototype
     int sign
 If A is invertible, sign is plus or minus one and is the sign of the permutation corresponding to the row ordering ip and column ordering jp . If A is not invertible, sign is zero.

ip
The argument ip has prototype
     SizeVector &ip
 (see description of SizeVector below). The size of ip is referred to as n in the specifications below. The input value of the elements of ip does not matter. The output value of the elements of ip determine the order of the rows in the permuted matrix.

jp
The argument jp has prototype
     SizeVector &jp
 (see description of SizeVector below). The size of jp must be equal to n . The input value of the elements of jp does not matter. The output value of the elements of jp determine the order of the columns in the permuted matrix.

LU
The argument LU has the prototype
     FloatVector &LU
 and the size of LU must equal n * n (see description of FloatVector below).

A
We define A as the matrix corresponding to the input value of LU .

P
We define the permuted matrix P in terms of A by
     P(i, j) = A[ ip[i] * n + jp[j] ]
L
We define the lower triangular matrix L in terms of the output value of LU . The matrix L is zero above the diagonal and the rest of the elements are defined by
     L(i, j) = LU[ ip[i] * n + jp[j] ]
 for i = 0 , … , n -1 and j = 0 , … , i .

U
We define the upper triangular matrix U in terms of the output value of LU . The matrix U is zero below the diagonal, one on the diagonal, and the rest of the elements are defined by
     U(i, j) = LU[ ip[i] * n + jp[j] ]
 for i = 0 , … , n -2 and j = i + 1 , … , n -1 .

Factor
If the return value sign is non-zero,
     L * U = P
 If the return value of sign is zero, the contents of L and U are not defined.

Determinant
If the return value sign is zero, the determinant of A is zero. If sign is non-zero, using the output value of LU the determinant of the matrix A is equal to
sign * LU[ip[0], jp[0]] * ... * LU[ip[n-1], jp[n-1]]
SizeVector
The type SizeVector must be a SimpleVector class with elements of type size_t . The routine CheckSimpleVector will generate an error message if this is not the case.

FloatVector
The type FloatVector must be a simple vector class . The routine CheckSimpleVector will generate an error message if this is not the case.

Float
This notation is used to denote the type corresponding to the elements of a FloatVector . The type Float must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case. In addition, the following operations must be defined for any pair of Float objects x and y :
Operation Description
log(x) returns the logarithm of x as a Float object

AbsGeq
Including the file lu_factor.hpp defines the template function
     template <typename Float>
     bool AbsGeq<Float>(const Float &x, const Float &y)
 in the CppAD namespace. This function returns true if the absolute value of x is greater than or equal the absolute value of y . It is used by LuFactor to choose the pivot elements. This template function definition uses the operator <= to obtain the absolute value for Float objects. If this operator is not defined for your use of Float , you will need to specialize this template so that it works for your use of LuFactor.

Complex numbers do not have the operation <= defined. The specializations
bool AbsGeq< std::complex<float> >
     (const std::complex<float> &x, const std::complex<float> &y)
bool AbsGeq< std::complex<double> >
     (const std::complex<double> &x, const std::complex<double> &y)
 are define by including lu_factor.hpp These return true if the sum of the square of the real and imaginary parts of x is greater than or equal the sum of the square of the real and imaginary parts of y .

Example
The file lu_factor.cpp contains an example and test of using LuFactor by itself. It returns true if it succeeds and false otherwise.

The file lu_solve.hpp provides a useful example usage of LuFactor with LuInvert.

Source
The file lu_factor.hpp contains the current source code that implements these specifications.
Input File: cppad/utility/lu_factor.hpp cppad-20170000.3/doc/lu_factor.cpp.xml0000644000175200017650000005040613057470507016465 0ustar coincoin-web LuFactor: Example and Test
Prev Next lu_factor.cpp Headings

LuFactor: Example and Test
# include <cstdlib>               // for rand function
# include <cppad/utility/lu_factor.hpp>      // for CppAD::LuFactor
# include <cppad/utility/near_equal.hpp>     // for CppAD::NearEqual
# include <cppad/utility/vector.hpp>  // for CppAD::vector

bool LuFactor(void)
{     bool  ok = true;

# ifndef _MSC_VER
     using std::rand;
     using std::srand;
# endif
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     size_t  n = 5;                        // number rows in A
     double  rand_max = double(RAND_MAX);  // maximum rand value
     double  sum;                          // element of L * U
     double  pij;                          // element of permuted A
     size_t  i, j, k;                      // temporary indices

     // A is an n by n matrix
     CppAD::vector<double> A(n*n), LU(n*n), L(n*n), U(n*n);

     // set A equal to an n by n random matrix
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               A[i * n + j] = rand() / rand_max;

     // pivot vectors
     CppAD::vector<size_t> ip(n);
     CppAD::vector<size_t> jp(n);

     // factor the matrix A
     LU       = A;
     CppAD::LuFactor(ip, jp, LU);

     // check that ip and jp are permutations of the indices 0, ... , n-1
     for(i = 0; i < n; i++)
     {     ok &= (ip[i] < n);
          ok &= (jp[i] < n);
          for(j = 0; j < n; j++)
          {     if( i != j )
               {     ok &= (ip[i] != ip[j]);
                    ok &= (jp[i] != jp[j]);
               }
          }
     }

     // Extract L from LU
     for(i = 0; i < n; i++)
     {     // elements along and below the diagonal
          for(j = 0; j <= i; j++)
               L[i * n + j] = LU[ ip[i] * n + jp[j] ];
          // elements above the diagonal
          for(j = i+1; j < n; j++)
               L[i * n + j] = 0.;
     }

     // Extract U from LU
     for(i = 0; i < n; i++)
     {     // elements below the diagonal
          for(j = 0; j < i; j++)
               U[i * n + j] = 0.;
          // elements along the diagonal
          U[i * n + i] = 1.;
          // elements above the diagonal
          for(j = i+1; j < n; j++)
               U[i * n + j] = LU[ ip[i] * n + jp[j] ];
     }

     // Compute L * U
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     // compute element (i,j) entry in L * U
               sum = 0.;
               for(k = 0; k < n; k++)
                    sum += L[i * n + k] * U[k * n + j];
               // element (i,j) in permuted version of A
               pij  = A[ ip[i] * n + jp[j] ];
               // compare
               ok  &= NearEqual(pij, sum, eps99, eps99);
          }
     }

     return ok;
}
Input File: example/lu_factor.cpp cppad-20170000.3/doc/lu_factor.hpp.xml0000644000175200017650000007714713057470507016505 0ustar coincoin-web Source: LuFactor
Prev Next lu_factor.hpp Headings

Source: LuFactor
# ifndef CPPAD_LU_FACTOR_HPP
# define CPPAD_LU_FACTOR_HPP 

# include <complex>
# include <vector>

# include <cppad/core/cppad_assert.hpp>
# include <cppad/utility/check_simple_vector.hpp>
# include <cppad/utility/check_numeric_type.hpp>

namespace CppAD { // BEGIN CppAD namespace

// AbsGeq
template <typename Float>
inline bool AbsGeq(const Float &x, const Float &y)
{     Float xabs = x;
     if( xabs <= Float(0) )
          xabs = - xabs;
     Float yabs = y;
     if( yabs <= Float(0) )
          yabs = - yabs;
     return xabs >= yabs;
}
inline bool AbsGeq(
     const std::complex<double> &x,
     const std::complex<double> &y)
{     double xsq = x.real() * x.real() + x.imag() * x.imag();
     double ysq = y.real() * y.real() + y.imag() * y.imag();

     return xsq >= ysq;
}
inline bool AbsGeq(
     const std::complex<float> &x,
     const std::complex<float> &y)
{     float xsq = x.real() * x.real() + x.imag() * x.imag();
     float ysq = y.real() * y.real() + y.imag() * y.imag();

     return xsq >= ysq;
}

// Lines that are different from code in cppad/core/lu_ratio.hpp end with //
template <class SizeVector, class FloatVector>                          //
int LuFactor(SizeVector &ip, SizeVector &jp, FloatVector &LU)           //
{
     // type of the elements of LU                                   //
     typedef typename FloatVector::value_type Float;                 //

     // check numeric type specifications
     CheckNumericType<Float>();

     // check simple vector class specifications
     CheckSimpleVector<Float, FloatVector>();
     CheckSimpleVector<size_t, SizeVector>();

     size_t  i, j;          // some temporary indices
     const Float zero( 0 ); // the value zero as a Float object
     size_t  imax;          // row index of maximum element
     size_t  jmax;          // column indx of maximum element
     Float    emax;         // maximum absolute value
     size_t  p;             // count pivots
     int     sign;          // sign of the permutation
     Float   etmp;          // temporary element
     Float   pivot;         // pivot element

     // -------------------------------------------------------
     size_t n = ip.size();
     CPPAD_ASSERT_KNOWN(
          size_t(jp.size()) == n,
          "Error in LuFactor: jp must have size equal to n"
     );
     CPPAD_ASSERT_KNOWN(
          size_t(LU.size()) == n * n,
          "Error in LuFactor: LU must have size equal to n * m"
     );
     // -------------------------------------------------------

     // initialize row and column order in matrix not yet pivoted
     for(i = 0; i < n; i++)
     {     ip[i] = i;
          jp[i] = i;
     }
     // initialize the sign of the permutation
     sign = 1;
     // ---------------------------------------------------------

     // Reduce the matrix P to L * U using n pivots
     for(p = 0; p < n; p++)
     {     // determine row and column corresponding to element of
          // maximum absolute value in remaining part of P
          imax = jmax = n;
          emax = zero;
          for(i = p; i < n; i++)
          {     for(j = p; j < n; j++)
               {     CPPAD_ASSERT_UNKNOWN(
                         (ip[i] < n) & (jp[j] < n)
                    );
                    etmp = LU[ ip[i] * n + jp[j] ];

                    // check if maximum absolute value so far
                    if( AbsGeq (etmp, emax) )
                    {     imax = i;
                         jmax = j;
                         emax = etmp;
                    }
               }
          }
          CPPAD_ASSERT_KNOWN(
          (imax < n) & (jmax < n) ,
          "LuFactor can't determine an element with "
          "maximum absolute value.\n"
          "Perhaps original matrix contains not a number or infinity.\n"
          "Perhaps your specialization of AbsGeq is not correct."
          );
          if( imax != p )
          {     // switch rows so max absolute element is in row p
               i        = ip[p];
               ip[p]    = ip[imax];
               ip[imax] = i;
               sign     = -sign;
          }
          if( jmax != p )
          {     // switch columns so max absolute element is in column p
               j        = jp[p];
               jp[p]    = jp[jmax];
               jp[jmax] = j;
               sign     = -sign;
          }
          // pivot using the max absolute element
          pivot   = LU[ ip[p] * n + jp[p] ];

          // check for determinant equal to zero
          if( pivot == zero )
          {     // abort the mission
               return   0;
          }

          // Reduce U by the elementary transformations that maps
          // LU( ip[p], jp[p] ) to one.  Only need transform elements
          // above the diagonal in U and LU( ip[p] , jp[p] ) is
          // corresponding value below diagonal in L.
          for(j = p+1; j < n; j++)
               LU[ ip[p] * n + jp[j] ] /= pivot;

          // Reduce U by the elementary transformations that maps
          // LU( ip[i], jp[p] ) to zero. Only need transform elements
          // above the diagonal in U and LU( ip[i], jp[p] ) is
          // corresponding value below diagonal in L.
          for(i = p+1; i < n; i++ )
          {     etmp = LU[ ip[i] * n + jp[p] ];
               for(j = p+1; j < n; j++)
               {     LU[ ip[i] * n + jp[j] ] -=
                         etmp * LU[ ip[p] * n + jp[j] ];
               }
          }
     }
     return sign;
}
} // END CppAD namespace
# endif
Input File: omh/lu_factor_hpp.omh cppad-20170000.3/doc/luinvert.xml0000644000175200017650000005232713057470507015602 0ustar coincoin-web Invert an LU Factored Equation
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Invert an LU Factored Equation

Syntax
 include <cppad/utility/lu_invert.hpp>
 LuInvert(ip, jp, LU, X)

Description
Solves the matrix equation A * X = B using an LU factorization computed by LuFactor .

Include
The file cppad/lu_invert.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Matrix Storage
All matrices are stored in row major order. To be specific, if Y is a vector that contains a p by q matrix, the size of Y must be equal to p * q and for i = 0 , … , p -1 , j = 0 , … , q -1 , Y i , j = Y [ i * q + j ]
ip
The argument ip has prototype
     const SizeVector &ip
 (see description for SizeVector in LuFactor specifications). The size of ip is referred to as n in the specifications below. The elements of ip determine the order of the rows in the permuted matrix.

jp
The argument jp has prototype
     const SizeVector &jp
 (see description for SizeVector in LuFactor specifications). The size of jp must be equal to n . The elements of jp determine the order of the columns in the permuted matrix.

LU
The argument LU has the prototype
     const FloatVector &LU
 and the size of LU must equal n * n (see description for FloatVector in LuFactor specifications).

L
We define the lower triangular matrix L in terms of LU . The matrix L is zero above the diagonal and the rest of the elements are defined by
     L(i, j) = LU[ ip[i] * n + jp[j] ]
 for i = 0 , … , n -1 and j = 0 , … , i .

U
We define the upper triangular matrix U in terms of LU . The matrix U is zero below the diagonal, one on the diagonal, and the rest of the elements are defined by
     U(i, j) = LU[ ip[i] * n + jp[j] ]
 for i = 0 , … , n -2 and j = i + 1 , … , n -1 .

P
We define the permuted matrix P in terms of the matrix L and the matrix U by P = L * U .

A
The matrix A , which defines the linear equations that we are solving, is given by
     P(i, j) = A[ ip[i] * n + jp[j] ]
 (Hence LU contains a permuted factorization of the matrix A .)

X
The argument X has prototype
     FloatVector &X
 (see description for FloatVector in LuFactor specifications). The matrix X must have the same number of rows as the matrix A . The input value of X is the matrix B and the output value solves the matrix equation A * X = B .

Example
The file lu_solve.hpp is a good example usage of LuFactor with LuInvert. The file lu_invert.cpp contains an example and test of using LuInvert by itself. It returns true if it succeeds and false otherwise.

Source
The file lu_invert.hpp contains the current source code that implements these specifications.
Input File: cppad/utility/lu_invert.hpp cppad-20170000.3/doc/lu_invert.cpp.xml0000644000175200017650000006105213057470507016515 0ustar coincoin-web LuInvert: Example and Test
Prev Next lu_invert.cpp Headings

LuInvert: Example and Test
# include <cstdlib>               // for rand function
# include <cppad/utility/lu_invert.hpp>      // for CppAD::LuInvert
# include <cppad/utility/near_equal.hpp>     // for CppAD::NearEqual
# include <cppad/utility/vector.hpp>  // for CppAD::vector

bool LuInvert(void)
{     bool  ok = true;

# ifndef _MSC_VER
     using std::rand;
     using std::srand;
# endif

     size_t  n = 7;                        // number rows in A
     size_t  m = 3;                        // number columns in B
     double  rand_max = double(RAND_MAX);  // maximum rand value
     double  sum;                          // element of L * U
     size_t  i, j, k;                      // temporary indices

     // dimension matrices
     CppAD::vector<double>
          A(n*n), X(n*m), B(n*m), LU(n*n), L(n*n), U(n*n);

     // seed the random number generator
     srand(123);

     // pivot vectors
     CppAD::vector<size_t> ip(n);
     CppAD::vector<size_t> jp(n);

     // set pivot vectors
     for(i = 0; i < n; i++)
     {     ip[i] = (i + 2) % n;      // ip = 2 , 3, ... , n-1, 0, 1
          jp[i] = (n + 2 - i) % n;  // jp = 2 , 1, n-1, n-2, ... , 3
     }

     // chose L, a random lower triangular matrix
     for(i = 0; i < n; i++)
     {     for(j = 0; j <= i; j++)
               L [i * n + j]  = rand() / rand_max;
          for(j = i+1; j < n; j++)
               L [i * n + j]  = 0.;
     }
     // chose U, a random upper triangular matrix with ones on diagonal
     for(i = 0; i < n; i++)
     {     for(j = 0; j < i; j++)
               U [i * n + j]  = 0.;
          U[ i * n + i ] = 1.;
          for(j = i+1; j < n; j++)
               U [i * n + j]  = rand() / rand_max;
     }
     // chose X, a random matrix
     for(i = 0; i < n; i++)
     {     for(k = 0; k < m; k++)
               X[i * m + k] = rand() / rand_max;
     }
     // set LU to a permuted combination of both L and U
     for(i = 0; i < n; i++)
     {     for(j = 0; j <= i; j++)
               LU [ ip[i] * n + jp[j] ]  = L[i * n + j];
          for(j = i+1; j < n; j++)
               LU [ ip[i] * n + jp[j] ]  = U[i * n + j];
     }
     // set A to a permuted version of L * U
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     // compute (i,j) entry in permuted matrix
               sum = 0.;
               for(k = 0; k < n; k++)
                    sum += L[i * n + k] * U[k * n + j];
               A[ ip[i] * n + jp[j] ] = sum;
          }
     }
     // set B to A * X
     for(i = 0; i < n; i++)
     {     for(k = 0; k < m; k++)
          {     // compute (i,k) entry of B
               sum = 0.;
               for(j = 0; j < n; j++)
                    sum += A[i * n + j] * X[j * m + k];
               B[i * m + k] = sum;
          }
     }
     // solve for X
     CppAD::LuInvert(ip, jp, LU, B);

     // check result
     for(i = 0; i < n; i++)
     {     for(k = 0; k < m; k++)
          {     ok &= CppAD::NearEqual(
                    X[i * m + k], B[i * m + k], 1e-10, 1e-10
               );
          }
     }
     return ok;
}
Input File: example/lu_invert.cpp cppad-20170000.3/doc/lu_invert.hpp.xml0000644000175200017650000004021213057470507016515 0ustar coincoin-web Source: LuInvert
Prev Next lu_invert.hpp Headings

Source: LuInvert
# ifndef CPPAD_LU_INVERT_HPP
# define CPPAD_LU_INVERT_HPP 
# include <cppad/core/cppad_assert.hpp>
# include <cppad/utility/check_simple_vector.hpp>
# include <cppad/utility/check_numeric_type.hpp>

namespace CppAD { // BEGIN CppAD namespace

// LuInvert
template <typename SizeVector, typename FloatVector>
void LuInvert(
     const SizeVector  &ip,
     const SizeVector  &jp,
     const FloatVector &LU,
     FloatVector       &B )
{     size_t k; // column index in X
     size_t p; // index along diagonal in LU
     size_t i; // row index in LU and X

     typedef typename FloatVector::value_type Float;

     // check numeric type specifications
     CheckNumericType<Float>();

     // check simple vector class specifications
     CheckSimpleVector<Float, FloatVector>();
     CheckSimpleVector<size_t, SizeVector>();

     Float etmp;

     size_t n = ip.size();
     CPPAD_ASSERT_KNOWN(
          size_t(jp.size()) == n,
          "Error in LuInvert: jp must have size equal to n * n"
     );
     CPPAD_ASSERT_KNOWN(
          size_t(LU.size()) == n * n,
          "Error in LuInvert: Lu must have size equal to n * m"
     );
     size_t m = size_t(B.size()) / n;
     CPPAD_ASSERT_KNOWN(
          size_t(B.size()) == n * m,
          "Error in LuSolve: B must have size equal to a multiple of n"
     );

     // temporary storage for reordered solution
     FloatVector x(n);

     // loop over equations
     for(k = 0; k < m; k++)
     {     // invert the equation c = L * b
          for(p = 0; p < n; p++)
          {     // solve for c[p]
               etmp = B[ ip[p] * m + k ] / LU[ ip[p] * n + jp[p] ];
               B[ ip[p] * m + k ] = etmp;
               // subtract off effect on other variables
               for(i = p+1; i < n; i++)
                    B[ ip[i] * m + k ] -=
                         etmp * LU[ ip[i] * n + jp[p] ];
          }

          // invert the equation x = U * c
          p = n;
          while( p > 0 )
          {     --p;
               etmp       = B[ ip[p] * m + k ];
               x[ jp[p] ] = etmp;
               for(i = 0; i < p; i++ )
                    B[ ip[i] * m + k ] -=
                         etmp * LU[ ip[i] * n + jp[p] ];
          }

          // copy reordered solution into B
          for(i = 0; i < n; i++)
               B[i * m + k] = x[i];
     }
     return;
}
} // END CppAD namespace
# endif
Input File: omh/lu_invert_hpp.omh cppad-20170000.3/doc/rombergone.xml0000644000175200017650000003734413057470507016073 0ustar coincoin-web One DimensionalRomberg Integration
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One DimensionalRomberg Integration

Syntax
# include <cppad/utility/romberg_one.hpp>
 r = RombergOne(F, a, b, n, e)

Description
Returns the Romberg integration estimate r for a one dimensional integral r = ∫ a b F ( x ) d x + O [( b - a ) / 2 n -1 ] 2 ( p + 1 )
Include
The file cppad/romberg_one.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

r
The return value r has prototype
     Float r
 It is the estimate computed by RombergOne for the integral above.

F
The object F can be of any type, but it must support the operation
     F(x)
 The argument x to F has prototype
     const Float &x
 The return value of F is a Float object (see description of Float below).

a
The argument a has prototype
     const Float &a
 It specifies the lower limit for the integration.

b
The argument b has prototype
     const Float &b
 It specifies the upper limit for the integration.

n
The argument n has prototype
     size_t n
 A total number of 2 n -1 + 1 evaluations of F(x) are used to estimate the integral.

p
The argument p has prototype
     size_t p
 It must be less than or equal n and determines the accuracy order in the approximation for the integral that is returned by RombergOne. To be specific r = ∫ a b F ( x ) d x + O [( b - a ) / 2 n -1 ] 2 ( p + 1 )
e
The argument e has prototype
     Float &e
 The input value of e does not matter and its output value is an approximation for the error in the integral estimates; i.e., e ≈ |r - ∫ a b F ( x ) d x |
Float
The type Float must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case. In addition, if x and y are Float objects,
     x < y
 returns the bool value true if x is less than y and false otherwise.

Example
The file romberg_one.cpp contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise.

Source Code
The source code for this routine is in the file cppad/romberg_one.hpp.
Input File: cppad/utility/romberg_one.hpp cppad-20170000.3/doc/romberg_one.cpp.xml0000644000175200017650000003167013057470507017007 0ustar coincoin-web One Dimensional Romberg Integration: Example and Test
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One Dimensional Romberg Integration: Example and Test

# include <cppad/utility/romberg_one.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/utility/near_equal.hpp>

namespace {
     class Fun {
     private:
          const size_t degree;
     public:
          // constructor
          Fun(size_t degree_) : degree(degree_)
          { }

          // function F(x) = x^degree
          template <class Type>
          Type operator () (const Type &x)
          {     size_t i;
               Type   f = 1;
               for(i = 0; i < degree; i++)
                    f *= x;
               return f;
          }
     };
}

bool RombergOne(void)
{     bool ok = true;
     size_t i;

     size_t degree = 4;
     Fun F(degree);

     // arguments to RombergOne
     double a = 0.;
     double b = 1.;
     size_t n = 4;
     size_t p;
     double r, e;

     // int_a^b F(x) dx = [ b^(degree+1) - a^(degree+1) ] / (degree+1)
     double bpow = 1.;
     double apow = 1.;
     for(i = 0; i <= degree; i++)
     {     bpow *= b;
          apow *= a;
     }
     double check = (bpow - apow) / (degree+1);

     // step size corresponding to r
     double step = (b - a) / exp(log(2.)*(n-1));
     // step size corresponding to error estimate
     step *= 2.;
     // step size raised to a power
     double spow = 1;

     for(p = 0; p < n; p++)
     {     spow = spow * step * step;

          r = CppAD::RombergOne(F, a, b, n, p, e);

          ok  &= e < (degree+1) * spow;
          ok  &= CppAD::NearEqual(check, r, 0., e);
     }

     return ok;
}
Input File: example/romberg_one.cpp cppad-20170000.3/doc/rombergmul.xml0000644000175200017650000005034213057470507016100 0ustar coincoin-web Multi-dimensional Romberg Integration
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Multi-dimensional Romberg Integration

Syntax
# include <cppad/utility/romberg_mul.hpp>
 RombergMul<Fun, SizeVector, FloatVector, m> R
r = R(F, a, b, n, p, e)

Description
Returns the Romberg integration estimate r for the multi-dimensional integral r = ∫ a [ 0 ] b [ 0 ] ⋯ ∫ a [ m -1 ] b [ m -1 ] F ( x ) d x 0 ⋯ d x m -1 + ∑ i = 0 m -1 O [( b [ i ] - a [ i ] ) / 2 n [ i ] -1 ] 2 ( p [ i ] + 1 )
Include
The file cppad/romberg_mul.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

m
The template parameter m must be convertible to a size_t object with a value that can be determined at compile time; for example 2. It determines the dimension of the domain space for the integration.

r
The return value r has prototype
     Float r
 It is the estimate computed by RombergMul for the integral above (see description of Float below).

F
The object F has the prototype
     Fun &F
 It must support the operation
     F(x)
 The argument x to F has prototype
     const Float &x
 The return value of F is a Float object

a
The argument a has prototype
     const FloatVector &a
 It specifies the lower limit for the integration (see description of FloatVector below).

b
The argument b has prototype
     const FloatVector &b
 It specifies the upper limit for the integration.

n
The argument n has prototype
     const SizeVector &n
 A total number of 2 n [ i ] -1 + 1 evaluations of F(x) are used to estimate the integral with respect to d x i .

p
The argument p has prototype
     const SizeVector &p
 For i = 0 , … , m -1 , n [ i ] determines the accuracy order in the approximation for the integral that is returned by RombergMul. The values in p must be less than or equal n ; i.e., p[i] <= n[i] .

e
The argument e has prototype
     Float &e
 The input value of e does not matter and its output value is an approximation for the absolute error in the integral estimate.

Float
The type Float is defined as the type of the elements of FloatVector . The type Float must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case. In addition, if x and y are Float objects,
     x < y
 returns the bool value true if x is less than y and false otherwise.

FloatVector
The type FloatVector must be a SimpleVector class. The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file Rombergmul.cpp contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise.

Source Code
The source code for this routine is in the file cppad/romberg_mul.hpp.
Input File: cppad/utility/romberg_mul.hpp cppad-20170000.3/doc/rombergmul.cpp.xml0000644000175200017650000004713413057470507016666 0ustar coincoin-web One Dimensional Romberg Integration: Example and Test
Prev Next Rombergmul.cpp Headings

One Dimensional Romberg Integration: Example and Test

# include <cppad/utility/romberg_mul.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/utility/near_equal.hpp>


namespace {

     class TestFun {
     private:
          const CppAD::vector<size_t> deg;
     public:
          // constructor
          TestFun(const CppAD::vector<size_t> deg_)
          : deg(deg_)
          { }

          // function F(x) = x[0]^deg[0] * x[1]^deg[1]
          double operator () (const CppAD::vector<double> &x)
          {     size_t i;
               double   f = 1;
               for(i = 0; i < deg[0]; i++)
                    f *= x[0];
               for(i = 0; i < deg[1]; i++)
                    f *= x[1];
               return f;
          }
     };

}

bool RombergMul(void)
{     bool ok = true;
     size_t i;
     size_t k;

     CppAD::vector<size_t> deg(2);
     deg[0] = 5;
     deg[1] = 3;
     TestFun F(deg);

     CppAD::RombergMul<
          TestFun              ,
          CppAD::vector<size_t>,
          CppAD::vector<double>,
          2                    > RombergMulTest;

     // arugments to RombergMul
     CppAD::vector<double> a(2);
     CppAD::vector<double> b(2);
     CppAD::vector<size_t> n(2);
     CppAD::vector<size_t> p(2);
     for(i = 0; i < 2; i++)
     {     a[i] = 0.;
          b[i] = 1.;
     }
     n[0] = 4;
     n[1] = 3;
     double r, e;

     // int_a1^b1 dx1 int_a0^b0 F(x0,x1) dx0
     //     = [ b0^(deg[0]+1) - a0^(deg[0]+1) ] / (deg[0]+1)
     //     * [ b1^(deg[1]+1) - a1^(deg[1]+1) ] / (deg[1]+1)
     double bpow = 1.;
     double apow = 1.;
     for(i = 0; i <= deg[0]; i++)
     {     bpow *= b[0];
          apow *= a[0];
     }
     double check = (bpow - apow) / (deg[0]+1);
     bpow = 1.;
     apow = 1.;
     for(i = 0; i <= deg[1]; i++)
     {     bpow *= b[1];
          apow *= a[1];
     }
     check *= (bpow - apow) / (deg[1]+1);

     double step = (b[1] - a[1]) / exp(log(2.)*(n[1]-1));
     double spow = 1;
     for(k = 0; k <= n[1]; k++)
     {     spow = spow * step * step;
          double bnd = 3 * (deg[1] + 1) * spow;

          for(i = 0; i < 2; i++)
               p[i] = k;
          r    = RombergMulTest(F, a, b, n, p, e);

          ok  &= e < bnd;
          ok  &= CppAD::NearEqual(check, r, 0., e);

     }

     return ok;
}
Input File: example/romberg_mul.cpp cppad-20170000.3/doc/runge45.xml0000644000175200017650000007354113057470507015224 0ustar coincoin-web An Embedded 4th and 5th Order Runge-Kutta ODE Solver
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An Embedded 4th and 5th Order Runge-Kutta ODE Solver

Syntax
# include <cppad/utility/runge_45.hpp>
 xf = Runge45(F, M, ti, tf, xi)
 xf = Runge45(F, M, ti, tf, xi, e)
Purpose
This is an implementation of the Cash-Karp embedded 4th and 5th order Runge-Kutta ODE solver described in Section 16.2 of Numerical Recipes . We use n for the size of the vector xi . Let R denote the real numbers and let F : R × R n → R n be a smooth function. The return value xf contains a 5th order approximation for the value X ( tf ) where X : [ ti , tf ] → R n is defined by the following initial value problem: X ( ti ) = xi X ' ( t ) = F [ t , X ( t ) ] If your set of ordinary differential equations are stiff, an implicit method may be better (perhaps Rosen34 .)

Operation Sequence
The operation sequence for Runge does not depend on any of its Scalar input values provided that the operation sequence for
     F.Ode(t, x, f)
 does not on any of its Scalar inputs (see below).

Include
The file cppad/runge_45.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

xf
The return value xf has the prototype
     Vector xf
 and the size of xf is equal to n (see description of Vector below). X ( tf ) = xf + O ( h 6 ) where h = ( tf - ti ) / M is the step size. If xf contains not a number nan , see the discussion for f .

Fun
The class Fun and the object F satisfy the prototype
     Fun &F
 The object F (and the class Fun ) must have a member function named Ode that supports the syntax
     F.Ode(t, x, f)
t
The argument t to F.Ode has prototype
     const Scalar &t
 (see description of Scalar below).

x
The argument x to F.Ode has prototype
     const Vector &x
 and has size n (see description of Vector below).

f
The argument f to F.Ode has prototype
     Vector &f
 On input and output, f is a vector of size n and the input values of the elements of f do not matter. On output, f is set equal to F ( t , x ) in the differential equation. If any of the elements of f have the value not a number nan the routine Runge45 returns with all the elements of xf and e equal to nan.

Warning
The argument f to F.Ode must have a call by reference in its prototype; i.e., do not forget the & in the prototype for f .

M
The argument M has prototype
     size_t M
 It specifies the number of steps to use when solving the differential equation. This must be greater than or equal one. The step size is given by h = ( tf - ti ) / M , thus the larger M , the more accurate the return value xf is as an approximation for X ( tf ) .

ti
The argument ti has prototype
     const Scalar &ti
 (see description of Scalar below). It specifies the initial time for t in the differential equation; i.e., the time corresponding to the value xi .

tf
The argument tf has prototype
     const Scalar &tf
 It specifies the final time for t in the differential equation; i.e., the time corresponding to the value xf .

xi
The argument xi has the prototype
     const Vector &xi
 and the size of xi is equal to n . It specifies the value of X ( ti )

e
The argument e is optional and has the prototype
     Vector &e
 If e is present, the size of e must be equal to n . The input value of the elements of e does not matter. On output it contains an element by element estimated bound for the absolute value of the error in xf e = O ( h 5 ) where h = ( tf - ti ) / M is the step size. If on output, e contains not a number nan, see the discussion for f .

Scalar
The type Scalar must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case.

fabs
In addition, the following function must be defined for Scalar objects a and b
     a = fabs(b)
 Note that this operation is only used for computing e ; hence the operation sequence for xf can still be independent of the arguments to Runge45 even if
     fabs(b) = std::max(-b, b)
 .

Vector
The type Vector must be a SimpleVector class with elements of type Scalar . The routine CheckSimpleVector will generate an error message if this is not the case.

Parallel Mode
For each set of types Scalar , Vector , and Fun , the first call to Runge45 must not be parallel execution mode.

Example
The file runge45_1.cpp contains a simple example and test of Runge45. It returns true if it succeeds and false otherwise.

The file runge45_2.cpp contains an example using Runge45 in the context of algorithmic differentiation. It also returns true if it succeeds and false otherwise.

Source Code
The source code for this routine is in the file cppad/runge_45.hpp.
Input File: cppad/utility/runge_45.hpp cppad-20170000.3/doc/runge45_1.cpp.xml0000644000175200017650000005125413057470507016222 0ustar coincoin-web Runge45: Example and Test
Prev Next runge45_1.cpp Headings

Runge45: Example and Test
Define X : R → R n by X i ( t ) = t i + 1 for i = 1 , … , n -1 . It follows that X i ( 0 ) = 0 for all i X i ' ( t ) = 1 if i = 0 X i ' ( t ) = ( i + 1 ) t i = ( i + 1 ) X i -1 ( t ) if i > 0 The example tests Runge45 using the relations above: 

# include <cstddef>                 // for size_t
# include <cppad/utility/near_equal.hpp>    // for CppAD::NearEqual
# include <cppad/utility/vector.hpp>        // for CppAD::vector
# include <cppad/utility/runge_45.hpp>      // for CppAD::Runge45

// Runge45 requires fabs to be defined (not std::fabs)
// <cppad/cppad.hpp> defines this for doubles, but runge_45.hpp does not.
# include <math.h>      // for fabs without std in front

namespace {
     class Fun {
     public:
          // constructor
          Fun(bool use_x_) : use_x(use_x_)
          { }

          // set f = x'(t)
          void Ode(
               const double                &t,
               const CppAD::vector<double> &x,
               CppAD::vector<double>       &f)
          {     size_t n  = x.size();
               double ti = 1.;
               f[0]      = 1.;
               size_t i;
               for(i = 1; i < n; i++)
               {     ti *= t;
                    if( use_x )
                         f[i] = (i+1) * x[i-1];
                    else     f[i] = (i+1) * ti;
               }
          }
     private:
          const bool use_x;

     };
}

bool runge_45_1(void)
{     bool ok = true;     // initial return value
     size_t i;           // temporary indices

     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     size_t  n = 5;      // number components in X(t) and order of method
     size_t  M = 2;      // number of Runge45 steps in [ti, tf]
     double ti = 0.;     // initial time
     double tf = 2.;     // final time

     // xi = X(0)
     CppAD::vector<double> xi(n);
     for(i = 0; i <n; i++)
          xi[i] = 0.;

     size_t use_x;
     for( use_x = 0; use_x < 2; use_x++)
     {     // function object depends on value of use_x
          Fun F(use_x > 0);

          // compute Runge45 approximation for X(tf)
          CppAD::vector<double> xf(n), e(n);
          xf = CppAD::Runge45(F, M, ti, tf, xi, e);

          double check = tf;
          for(i = 0; i < n; i++)
          {     // check that error is always positive
               ok    &= (e[i] >= 0.);
               // 5th order method is exact for i < 5
               if( i < 5 ) ok &=
                    NearEqual(xf[i], check, eps99, eps99);
               // 4th order method is exact for i < 4
               if( i < 4 )
                    ok &= (e[i] <= 1e-10);

               // check value for next i
               check *= tf;
          }
     }
     return ok;
}
Input File: example/runge45_1.cpp cppad-20170000.3/doc/runge45_2.cpp.xml0000644000175200017650000006375213057470507016231 0ustar coincoin-web Runge45: Example and Test
Prev Next runge45_2.cpp Headings

Runge45: Example and Test
Define X : R × R → R n by X j ( b , t ) = b (∑ k = 0 j t k / k ! ) for j = 0 , … , n -1 . It follows that X j ( b , 0 ) = b ∂ t X j ( b , t ) = b (∑ k = 0 j -1 t k / k ! ) ∂ t X j ( b , t ) = { 0 if j = 0 X j -1 ( b , t ) otherwise For a fixed t f , we can use Runge45 to define f : R → R n as an approximation for f ( b ) = X ( b , t f ) . We can then compute f ( 1 ) ( b ) which is an approximation for ∂ b X ( b , t f ) = ∑ k = 0 j t f k / k ! 

# include <cstddef>              // for size_t
# include <limits>               // for machine epsilon
# include <cppad/cppad.hpp>      // for all of CppAD

namespace {

     template <class Scalar>
     class Fun {
     public:
          // constructor
          Fun(void)
          { }

          // set return value to X'(t)
          void Ode(
               const Scalar                    &t,
               const CPPAD_TESTVECTOR(Scalar) &x,
               CPPAD_TESTVECTOR(Scalar)       &f)
          {     size_t n  = x.size();
               f[0]      = 0.;
               for(size_t k = 1; k < n; k++)
                    f[k] = x[k-1];
          }
     };
}

bool runge_45_2(void)
{     typedef CppAD::AD<double> Scalar;
     using CppAD::NearEqual;

     bool ok = true;     // initial return value
     size_t j;           // temporary indices

     size_t     n = 5;   // number components in X(t) and order of method
     size_t     M = 2;   // number of Runge45 steps in [ti, tf]
     Scalar ad_ti = 0.;  // initial time
     Scalar ad_tf = 2.;  // final time

     // value of independent variable at which to record operations
     CPPAD_TESTVECTOR(Scalar) ad_b(1);
     ad_b[0] = 1.;

     // declare b to be the independent variable
     Independent(ad_b);

     // object to evaluate ODE
     Fun<Scalar> ad_F;

     // xi = X(0)
     CPPAD_TESTVECTOR(Scalar) ad_xi(n);
     for(j = 0; j < n; j++)
          ad_xi[j] = ad_b[0];

     // compute Runge45 approximation for X(tf)
     CPPAD_TESTVECTOR(Scalar) ad_xf(n), ad_e(n);
     ad_xf = CppAD::Runge45(ad_F, M, ad_ti, ad_tf, ad_xi, ad_e);

     // stop recording and use it to create f : b -> xf
     CppAD::ADFun<double> f(ad_b, ad_xf);

     // evaluate f(b)
     CPPAD_TESTVECTOR(double)  b(1);
     CPPAD_TESTVECTOR(double) xf(n);
     b[0] = 1.;
     xf   = f.Forward(0, b);

     // check that f(b) = X(b, tf)
     double tf    = Value(ad_tf);
     double term  = 1;
     double sum   = 0;
     double eps   = 10. * CppAD::numeric_limits<double>::epsilon();
     for(j = 0; j < n; j++)
     {     sum += term;
          ok &= NearEqual(xf[j], b[0] * sum, eps, eps);
          term *= tf;
          term /= double(j+1);
     }

     // evalute f'(b)
     CPPAD_TESTVECTOR(double) d_xf(n);
     d_xf = f.Jacobian(b);

     // check that f'(b) = partial of X(b, tf) w.r.t b
     term  = 1;
     sum   = 0;
     for(j = 0; j < n; j++)
     {     sum += term;
          ok &= NearEqual(d_xf[j], sum, eps, eps);
          term *= tf;
          term /= double(j+1);
     }

     return ok;
}
Input File: example/runge45_2.cpp cppad-20170000.3/doc/rosen34.xml0000644000175200017650000010607013057470507015222 0ustar coincoin-web A 3rd and 4th Order Rosenbrock ODE Solver
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A 3rd and 4th Order Rosenbrock ODE Solver

Syntax
# include <cppad/utility/rosen_34.hpp>
 xf = Rosen34(F, M, ti, tf, xi)
 xf = Rosen34(F, M, ti, tf, xi, e)
Description
This is an embedded 3rd and 4th order Rosenbrock ODE solver (see Section 16.6 of Numerical Recipes for a description of Rosenbrock ODE solvers). In particular, we use the formulas taken from page 100 of Shampine, L.F. (except that the fraction 98/108 has been correction to be 97/108).

We use n for the size of the vector xi . Let R denote the real numbers and let F : R × R n → R n be a smooth function. The return value xf contains a 5th order approximation for the value X ( tf ) where X : [ ti , tf ] → R n is defined by the following initial value problem: X ( ti ) = xi X ' ( t ) = F [ t , X ( t ) ] If your set of ordinary differential equations are not stiff an explicit method may be better (perhaps Runge45 .)

Include
The file cppad/rosen_34.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

xf
The return value xf has the prototype
     Vector xf
 and the size of xf is equal to n (see description of Vector below). X ( tf ) = xf + O ( h 5 ) where h = ( tf - ti ) / M is the step size. If xf contains not a number nan , see the discussion of f .

Fun
The class Fun and the object F satisfy the prototype
     Fun &F
 This must support the following set of calls
     F.Ode(t, x, f)
     F.Ode_ind(t, x, f_t)
     F.Ode_dep(t, x, f_x)
t
In all three cases, the argument t has prototype
     const Scalar &t
 (see description of Scalar below).

x
In all three cases, the argument x has prototype
     const Vector &x
 and has size n (see description of Vector below).

f
The argument f to F.Ode has prototype
     Vector &f
 On input and output, f is a vector of size n and the input values of the elements of f do not matter. On output, f is set equal to F ( t , x ) (see F(t, x) in Description ).

f_t
The argument f_t to F.Ode_ind has prototype
     Vector &f_t
 On input and output, f_t is a vector of size n and the input values of the elements of f_t do not matter. On output, the i-th element of f_t is set equal to ∂ t F i ( t , x ) (see F(t, x) in Description ).

f_x
The argument f_x to F.Ode_dep has prototype
     Vector &f_x
 On input and output, f_x is a vector of size n*n and the input values of the elements of f_x do not matter. On output, the [ i*n+j ] element of f_x is set equal to ∂ x ( j ) F i ( t , x ) (see F(t, x) in Description ).

Nan
If any of the elements of f , f_t , or f_x have the value not a number nan, the routine Rosen34 returns with all the elements of xf and e equal to nan.

Warning
The arguments f , f_t , and f_x must have a call by reference in their prototypes; i.e., do not forget the & in the prototype for f , f_t and f_x .

Optimization
Every call of the form
     F.Ode_ind(t, x, f_t)
 is directly followed by a call of the form
     F.Ode_dep(t, x, f_x)
 where the arguments t and x have not changed between calls. In many cases it is faster to compute the values of f_t and f_x together and then pass them back one at a time.

M
The argument M has prototype
     size_t M
 It specifies the number of steps to use when solving the differential equation. This must be greater than or equal one. The step size is given by h = ( tf - ti ) / M , thus the larger M , the more accurate the return value xf is as an approximation for X ( tf ) .

ti
The argument ti has prototype
     const Scalar &ti
 (see description of Scalar below). It specifies the initial time for t in the differential equation; i.e., the time corresponding to the value xi .

tf
The argument tf has prototype
     const Scalar &tf
 It specifies the final time for t in the differential equation; i.e., the time corresponding to the value xf .

xi
The argument xi has the prototype
     const Vector &xi
 and the size of xi is equal to n . It specifies the value of X ( ti )

e
The argument e is optional and has the prototype
     Vector &e
 If e is present, the size of e must be equal to n . The input value of the elements of e does not matter. On output it contains an element by element estimated bound for the absolute value of the error in xf e = O ( h 4 ) where h = ( tf - ti ) / M is the step size.

Scalar
The type Scalar must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case. In addition, the following operations must be defined for Scalar objects a and b :
Operation Description
a < b less than operator (returns a bool object)

Vector
The type Vector must be a SimpleVector class with elements of type Scalar . The routine CheckSimpleVector will generate an error message if this is not the case.

Parallel Mode
For each set of types Scalar , Vector , and Fun , the first call to Rosen34 must not be parallel execution mode.

Example
The file rosen_34.cpp contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise.

Source Code
The source code for this routine is in the file cppad/rosen_34.hpp.
Input File: cppad/utility/rosen_34.hpp cppad-20170000.3/doc/rosen_34.cpp.xml0000644000175200017650000010663313057470507016147 0ustar coincoin-web Rosen34: Example and Test
Prev Next rosen_34.cpp Headings

Rosen34: Example and Test
Define X : R → R n by X i ( t ) = t i + 1 for i = 1 , … , n -1 . It follows that X i ( 0 ) = 0 for all i X i ' ( t ) = 1 if i = 0 X i ' ( t ) = ( i + 1 ) t i = ( i + 1 ) X i -1 ( t ) if i > 0 The example tests Rosen34 using the relations above: 

# include <cppad/cppad.hpp>        // For automatic differentiation

namespace {
     class Fun {
     public:
          // constructor
          Fun(bool use_x_) : use_x(use_x_)
          { }

          // compute f(t, x) both for double and AD<double>
          template <typename Scalar>
          void Ode(
               const Scalar                    &t,
               const CPPAD_TESTVECTOR(Scalar) &x,
               CPPAD_TESTVECTOR(Scalar)       &f)
          {     size_t n  = x.size();
               Scalar ti(1);
               f[0]   = Scalar(1);
               size_t i;
               for(i = 1; i < n; i++)
               {     ti *= t;
                    // convert int(size_t) to avoid warning
                    // on _MSC_VER systems
                    if( use_x )
                         f[i] = int(i+1) * x[i-1];
                    else     f[i] = int(i+1) * ti;
               }
          }

          // compute partial of f(t, x) w.r.t. t using AD
          void Ode_ind(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f_t)
          {     using namespace CppAD;

               size_t n  = x.size();
               CPPAD_TESTVECTOR(AD<double>) T(1);
               CPPAD_TESTVECTOR(AD<double>) X(n);
               CPPAD_TESTVECTOR(AD<double>) F(n);

               // set argument values
               T[0] = t;
               size_t i;
               for(i = 0; i < n; i++)
                    X[i] = x[i];

               // declare independent variables
               Independent(T);

               // compute f(t, x)
               this->Ode(T[0], X, F);

               // define AD function object
               ADFun<double> fun(T, F);

               // compute partial of f w.r.t t
               CPPAD_TESTVECTOR(double) dt(1);
               dt[0] = 1.;
               f_t = fun.Forward(1, dt);
          }

          // compute partial of f(t, x) w.r.t. x using AD
          void Ode_dep(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f_x)
          {     using namespace CppAD;

               size_t n  = x.size();
               CPPAD_TESTVECTOR(AD<double>) T(1);
               CPPAD_TESTVECTOR(AD<double>) X(n);
               CPPAD_TESTVECTOR(AD<double>) F(n);

               // set argument values
               T[0] = t;
               size_t i, j;
               for(i = 0; i < n; i++)
                    X[i] = x[i];

               // declare independent variables
               Independent(X);

               // compute f(t, x)
               this->Ode(T[0], X, F);

               // define AD function object
               ADFun<double> fun(X, F);

               // compute partial of f w.r.t x
               CPPAD_TESTVECTOR(double) dx(n);
               CPPAD_TESTVECTOR(double) df(n);
               for(j = 0; j < n; j++)
                    dx[j] = 0.;
               for(j = 0; j < n; j++)
               {     dx[j] = 1.;
                    df = fun.Forward(1, dx);
                    for(i = 0; i < n; i++)
                         f_x [i * n + j] = df[i];
                    dx[j] = 0.;
               }
          }

     private:
          const bool use_x;

     };
}

bool Rosen34(void)
{     bool ok = true;     // initial return value
     size_t i;           // temporary indices

     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     size_t  n = 4;      // number components in X(t) and order of method
     size_t  M = 2;      // number of Rosen34 steps in [ti, tf]
     double ti = 0.;     // initial time
     double tf = 2.;     // final time

     // xi = X(0)
     CPPAD_TESTVECTOR(double) xi(n);
     for(i = 0; i <n; i++)
          xi[i] = 0.;

     size_t use_x;
     for( use_x = 0; use_x < 2; use_x++)
     {     // function object depends on value of use_x
          Fun F(use_x > 0);

          // compute Rosen34 approximation for X(tf)
          CPPAD_TESTVECTOR(double) xf(n), e(n);
          xf = CppAD::Rosen34(F, M, ti, tf, xi, e);

          double check = tf;
          for(i = 0; i < n; i++)
          {     // check that error is always positive
               ok    &= (e[i] >= 0.);
               // 4th order method is exact for i < 4
               if( i < 4 ) ok &=
                    NearEqual(xf[i], check, eps99, eps99);
               // 3rd order method is exact for i < 3
               if( i < 3 )
                    ok &= (e[i] <= 1e-10);

               // check value for next i
               check *= tf;
          }
     }
     return ok;
}
Input File: example/rosen_34.cpp cppad-20170000.3/doc/odeerrcontrol.xml0000644000175200017650000014546413057470507016620 0ustar coincoin-web An Error Controller for ODE Solvers
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An Error Controller for ODE Solvers

Syntax
# include <cppad/utility/ode_err_control.hpp>
 xf = OdeErrControl(method, ti, tf, xi,
     smin, smax, scur, eabs, erel, ef , maxabs, nstep )

Description
Let R denote the real numbers and let F : R × R n → R n be a smooth function. We define X : [ ti , tf ] → R n by the following initial value problem: X ( ti ) = xi X ' ( t ) = F [ t , X ( t ) ] The routine OdeErrControl can be used to adjust the step size used an arbitrary integration methods in order to be as fast as possible and still with in a requested error bound.

Include
The file cppad/ode_err_control.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Notation
The template parameter types Scalar and Vector are documented below.

xf
The return value xf has the prototype
     Vector xf
 (see description of Vector below). and the size of xf is equal to n . If xf contains not a number nan , see the discussion of step .

Method
The class Method and the object method satisfy the following syntax
     Method &method
 The object method must support step and order member functions defined below:

step
The syntax
     method.step(ta, tb, xa, xb, eb)
 executes one step of the integration method.

ta
 The argument ta has prototype
     const Scalar &ta
 It specifies the initial time for this step in the ODE integration. (see description of Scalar below).

tb
 The argument tb has prototype
     const Scalar &tb
 It specifies the final time for this step in the ODE integration.

xa
 The argument xa has prototype
     const Vector &xa
 and size n . It specifies the value of X ( ta ) . (see description of Vector below).

xb
 The argument value xb has prototype
     Vector &xb
 and size n . The input value of its elements does not matter. On output, it contains the approximation for X ( tb ) that the method obtains.

eb
 The argument value eb has prototype
     Vector &eb
 and size n . The input value of its elements does not matter. On output, it contains an estimate for the error in the approximation xb . It is assumed (locally) that the error bound in this approximation nearly equal to K ( tb - ta ) m where K is a fixed constant and m is the corresponding argument to CodeControl.

Nan
If any element of the vector eb or xb are not a number nan, the current step is considered to large. If this happens with the current step size equal to smin , OdeErrControl returns with xf and ef as vectors of nan.

order
If m is size_t, the object method must also support the following syntax
     m = method.order()
 The return value m is the order of the error estimate; i.e., there is a constant K such that if ti ≤ ta ≤ tb ≤ tf , | eb ( tb ) | ≤ K | tb - ta | m where ta , tb , and eb are as in method.step(ta, tb, xa, xb, eb)

ti
The argument ti has prototype
     const Scalar &ti
 It specifies the initial time for the integration of the differential equation.

tf
The argument tf has prototype
     const Scalar &tf
 It specifies the final time for the integration of the differential equation.

xi
The argument xi has prototype
     const Vector &xi
 and size n . It specifies value of X ( ti ) .

smin
The argument smin has prototype
     const Scalar &smin
 The step size during a call to method is defined as the corresponding value of tb - ta . If tf - ti ≤ smin , the integration will be done in one step of size tf - ti . Otherwise, the minimum value of tb - ta will be smin except for the last two calls to method where it may be as small as smin / 2 .

smax
The argument smax has prototype
     const Scalar &smax
 It specifies the maximum step size to use during the integration; i.e., the maximum value for tb - ta in a call to method . The value of smax must be greater than or equal smin .

scur
The argument scur has prototype
     Scalar &scur
 The value of scur is the suggested next step size, based on error criteria, to try in the next call to method . On input it corresponds to the first call to method , in this call to OdeErrControl (where ta = ti ). On output it corresponds to the next call to method , in a subsequent call to OdeErrControl (where ta = tf ).

eabs
The argument eabs has prototype
     const Vector &eabs
 and size n . Each of the elements of eabs must be greater than or equal zero. It specifies a bound for the absolute error in the return value xf as an approximation for X ( tf ) . (see the error criteria discussion below).

erel
The argument erel has prototype
     const Scalar &erel
 and is greater than or equal zero. It specifies a bound for the relative error in the return value xf as an approximation for X ( tf ) (see the error criteria discussion below).

ef
The argument value ef has prototype
     Vector &ef
 and size n . The input value of its elements does not matter. On output, it contains an estimated bound for the absolute error in the approximation xf ; i.e., ef i > | X ( tf ) i - xf i | If on output ef contains not a number nan, see the discussion of step .

maxabs
The argument maxabs is optional in the call to OdeErrControl. If it is present, it has the prototype
     Vector &maxabs
 and size n . The input value of its elements does not matter. On output, it contains an estimate for the maximum absolute value of X ( t ) ; i.e., maxabs [ i ] ≈ max {| X ( t ) i | : t ∈ [ ti , tf ] }
nstep
The argument nstep is optional in the call to OdeErrControl. If it is present, it has the prototype
     size_t &nstep
 Its input value does not matter and its output value is the number of calls to method.step used by OdeErrControl.

Error Criteria Discussion
The relative error criteria erel and absolute error criteria eabs are enforced during each step of the integration of the ordinary differential equations. In addition, they are inversely scaled by the step size so that the total error bound is less than the sum of the error bounds. To be specific, if X ˜ ( t ) is the approximate solution at time t , ta is the initial step time, and tb is the final step time, |X ˜ ( tb ) j - X ( tb ) j | ≤ tf - ti tb - ta [eabs [ j ] + erel | X ˜ ( tb ) j | ] If X ( tb ) j is near zero for some tb ∈ [ ti , tf ] , and one uses an absolute error criteria eabs [ j ] of zero, the error criteria above will force OdeErrControl to use step sizes equal to smin for steps ending near tb . In this case, the error relative to maxabs can be judged after OdeErrControl returns. If ef is to large relative to maxabs , OdeErrControl can be called again with a smaller value of smin .

Scalar
The type Scalar must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case. In addition, the following operations must be defined for Scalar objects a and b :
Operation Description
a <= b returns true (false) if a is less than or equal (greater than) b .
a == b returns true (false) if a is equal to b .
log(a) returns a Scalar equal to the logarithm of a
exp(a) returns a Scalar equal to the exponential of a

Vector
The type Vector must be a SimpleVector class with elements of type Scalar . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The files ode_err_control.cpp and ode_err_maxabs.cpp contain examples and tests of using this routine. They return true if they succeed and false otherwise.

Theory
Let e ( s ) be the error as a function of the step size s and suppose that there is a constant K such that e ( s ) = K s m . Let a be our error bound. Given the value of e ( s ) , a step of size λ s would be ok provided that a ≥ e ( λ s ) ( tf - ti ) / ( λ s ) a ≥ K λ m s m ( tf - ti ) / ( λ s ) a ≥ λ m -1 s m -1 ( tf - ti ) e ( s ) / s m a ≥ λ m -1 ( tf - ti ) e ( s ) / s λ m -1 ≤ a e ( s ) s tf - ti Thus if the right hand side of the last inequality is greater than or equal to one, the step of size s is ok.

Source Code
The source code for this routine is in the file cppad/ode_err_control.hpp.
Input File: cppad/utility/ode_err_control.hpp cppad-20170000.3/doc/ode_err_control.cpp.xml0000644000175200017650000006274613057470507017700 0ustar coincoin-web OdeErrControl: Example and Test
Prev Next ode_err_control.cpp

OdeErrControl: Example and Test
Define X : R → R 2 by X 0 ( 0 ) = 1 X 1 ( 0 ) = 0 X 0 ( 1 ) ( t ) = - α X 0 ( t ) X 1 ( 1 ) ( t ) = 1 / X 0 ( t ) It follows that X 0 ( t ) = exp ( - α t ) X 1 ( t ) = [ exp ( α t ) - 1 ] / α This example tests OdeErrControl using the relations above.

Nan
Note that X 0 ( t ) > 0 for all t and that the ODE goes through a singularity between X 0 ( t ) > 0 and X 0 ( t ) < 0 . If X 0 ( t ) < 0 , we return nan in order to inform OdeErrControl that its is taking to large a step. 

# include <limits>                      // for quiet_NaN
# include <cstddef>                     // for size_t
# include <cmath>                       // for exp
# include <cppad/utility/ode_err_control.hpp>   // CppAD::OdeErrControl
# include <cppad/utility/near_equal.hpp>        // CppAD::NearEqual
# include <cppad/utility/vector.hpp>            // CppAD::vector
# include <cppad/utility/runge_45.hpp>          // CppAD::Runge45

namespace {
     // --------------------------------------------------------------
     class Fun {
     private:
          const double alpha_;
     public:
          // constructor
          Fun(double alpha) : alpha_(alpha)
          { }

          // set f = x'(t)
          void Ode(
               const double                &t,
               const CppAD::vector<double> &x,
               CppAD::vector<double>       &f)
          {     f[0] = - alpha_ * x[0];
               f[1] = 1. / x[0];
               // case where ODE does not make sense
               if( x[0] < 0. )
                    f[1] = std::numeric_limits<double>::quiet_NaN();
          }

     };

     // --------------------------------------------------------------
     class Method {
     private:
          Fun F;
     public:
          // constructor
          Method(double alpha) : F(alpha)
          { }
          void step(
               double ta,
               double tb,
               CppAD::vector<double> &xa ,
               CppAD::vector<double> &xb ,
               CppAD::vector<double> &eb )
          {     xb = CppAD::Runge45(F, 1, ta, tb, xa, eb);
          }
          size_t order(void)
          {     return 4; }
     };
}

bool OdeErrControl(void)
{     bool ok = true;     // initial return value

     double alpha = 10.;
     Method method(alpha);

     CppAD::vector<double> xi(2);
     xi[0] = 1.;
     xi[1] = 0.;

     CppAD::vector<double> eabs(2);
     eabs[0] = 1e-4;
     eabs[1] = 1e-4;

     // inputs
     double ti   = 0.;
     double tf   = 1.;
     double smin = 1e-4;
     double smax = 1.;
     double scur = 1.;
     double erel = 0.;

     // outputs
     CppAD::vector<double> ef(2);
     CppAD::vector<double> xf(2);
     CppAD::vector<double> maxabs(2);
     size_t nstep;


     xf = OdeErrControl(method,
          ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);

     double x0 = exp(-alpha*tf);
     ok &= CppAD::NearEqual(x0, xf[0], 1e-4, 1e-4);
     ok &= CppAD::NearEqual(0., ef[0], 1e-4, 1e-4);

     double x1 = (exp(alpha*tf) - 1) / alpha;
     ok &= CppAD::NearEqual(x1, xf[1], 1e-4, 1e-4);
     ok &= CppAD::NearEqual(0., ef[1], 1e-4, 1e-4);

     return ok;
}
Input File: example/ode_err_control.cpp cppad-20170000.3/doc/ode_err_maxabs.cpp.xml0000644000175200017650000006702013057470507017461 0ustar coincoin-web OdeErrControl: Example and Test Using Maxabs Argument
Prev Next ode_err_maxabs.cpp Headings

OdeErrControl: Example and Test Using Maxabs Argument
Define X : R → R 2 by X 0 ( t ) = - exp ( - w 0 t ) X 1 ( t ) = w 0 w 1 - w 0 [ exp ( - w 0 t ) - exp ( - w 1 t ) ] It follows that X 0 ( 0 ) = 1 , X 1 ( 0 ) = 0 and X 0 ( 1 ) ( t ) = - w 0 X 0 ( t ) X 1 ( 1 ) ( t ) = + w 0 X 0 ( t ) - w 1 X 1 ( t ) Note that X 1 ( 0 ) is zero an if w 0 t is large, X 0 ( t ) is near zero. This example tests OdeErrControl using the maxabs argument. 

# include <cstddef>              // for size_t
# include <cmath>                // for exp
# include <cppad/utility/ode_err_control.hpp>   // CppAD::OdeErrControl
# include <cppad/utility/near_equal.hpp>    // CppAD::NearEqual
# include <cppad/utility/vector.hpp> // CppAD::vector
# include <cppad/utility/runge_45.hpp>      // CppAD::Runge45

namespace {
     // --------------------------------------------------------------
     class Fun {
     private:
           CppAD::vector<double> w;
     public:
          // constructor
          Fun(const CppAD::vector<double> &w_) : w(w_)
          { }

          // set f = x'(t)
          void Ode(
               const double                &t,
               const CppAD::vector<double> &x,
               CppAD::vector<double>       &f)
          {     f[0] = - w[0] * x[0];
               f[1] = + w[0] * x[0] - w[1] * x[1];
          }
     };

     // --------------------------------------------------------------
     class Method {
     private:
          Fun F;
     public:
          // constructor
          Method(const CppAD::vector<double> &w_) : F(w_)
          { }
          void step(
               double ta,
               double tb,
               CppAD::vector<double> &xa ,
               CppAD::vector<double> &xb ,
               CppAD::vector<double> &eb )
          {     xb = CppAD::Runge45(F, 1, ta, tb, xa, eb);
          }
          size_t order(void)
          {     return 4; }
     };
}

bool OdeErrMaxabs(void)
{     bool ok = true;     // initial return value

     CppAD::vector<double> w(2);
     w[0] = 10.;
     w[1] = 1.;
     Method method(w);

     CppAD::vector<double> xi(2);
     xi[0] = 1.;
     xi[1] = 0.;

     CppAD::vector<double> eabs(2);
     eabs[0] = 0.;
     eabs[1] = 0.;

     CppAD::vector<double> ef(2);
     CppAD::vector<double> xf(2);
     CppAD::vector<double> maxabs(2);

     double ti   = 0.;
     double tf   = 1.;
     double smin = .5;
     double smax = 1.;
     double scur = .5;
     double erel = 1e-4;

     bool accurate = false;
     while( ! accurate )
     {     xf = OdeErrControl(method,
               ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs);
          accurate = true;
          size_t i;
          for(i = 0; i < 2; i++)
               accurate &= ef[i] <= erel * maxabs[i];
          if( ! accurate )
               smin = smin / 2;
     }

     double x0 = exp(-w[0]*tf);
     ok &= CppAD::NearEqual(x0, xf[0], erel, 0.);
     ok &= CppAD::NearEqual(0., ef[0], erel, erel);

     double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]);
     ok &= CppAD::NearEqual(x1, xf[1], erel, 0.);
     ok &= CppAD::NearEqual(0., ef[1], erel, erel);

     return ok;
}
Input File: example/ode_err_maxabs.cpp cppad-20170000.3/doc/odegear.xml0000644000175200017650000015333013057470507015334 0ustar coincoin-web An Arbitrary Order Gear Method
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An Arbitrary Order Gear Method

Syntax
# include <cppad/utility/ode_gear.hpp>
 OdeGear(F, m, n, T, X, e)

Purpose
This routine applies Gear's Method to solve an explicit set of ordinary differential equations. We are given f : R × R n → R n be a smooth function. This routine solves the following initial value problem x ( t m -1 ) = x 0 x ′ ( t ) = f [ t , x ( t ) ] for the value of x ( t m ) . If your set of ordinary differential equations are not stiff an explicit method may be better (perhaps Runge45 .)

Include
The file cppad/ode_gear.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Fun
The class Fun and the object F satisfy the prototype
     Fun &F
 This must support the following set of calls
     F.Ode(t, x, f)
     F.Ode_dep(t, x, f_x)
t
The argument t has prototype
     const Scalar &t
 (see description of Scalar below).

x
The argument x has prototype
     const Vector &x
 and has size n (see description of Vector below).

f
The argument f to F.Ode has prototype
     Vector &f
 On input and output, f is a vector of size n and the input values of the elements of f do not matter. On output, f is set equal to f ( t , x ) (see f(t, x) in Purpose ).

f_x
The argument f_x has prototype
     Vector &f_x
 On input and output, f_x is a vector of size n * n and the input values of the elements of f_x do not matter. On output, f _ x [ i * n + j ] = ∂ x ( j ) f i ( t , x )
Warning
The arguments f , and f_x must have a call by reference in their prototypes; i.e., do not forget the & in the prototype for f and f_x .

m
The argument m has prototype
     size_t m
 It specifies the order (highest power of t ) used to represent the function x ( t ) in the multi-step method. Upon return from OdeGear, the i-th component of the polynomial is defined by p i ( t j ) = X [ j * n + i ] for j = 0 , … , m (where 0 ≤ i < n ). The value of m must be greater than or equal one.

n
The argument n has prototype
     size_t n
 It specifies the range space dimension of the vector valued function x ( t ) .

T
The argument T has prototype
     const Vector &T
 and size greater than or equal to m + 1 . For j = 0 , … m , T [ j ] is the time corresponding to time corresponding to a previous point in the multi-step method. The value T [ m ] is the time of the next point in the multi-step method. The array T must be monotone increasing; i.e., T [ j ] < T [ j + 1 ] . Above and below we often use the shorthand t j for T [ j ] .

X
The argument X has the prototype
     Vector &X
 and size greater than or equal to ( m + 1 ) * n . On input to OdeGear, for j = 0 , … , m -1 , and i = 0 , … , n -1 X [ j * n + i ] = x i ( t j ) Upon return from OdeGear, for i = 0 , … , n -1 X [ m * n + i ] ≈ x i ( t m )
e
The vector e is an approximate error bound for the result; i.e., e [ i ] ≥ | X [ m * n + i ] - x i ( t m ) | The order of this approximation is one less than the order of the solution; i.e., e = O ( h m ) where h is the maximum of t j + 1 - t j .

Scalar
The type Scalar must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case. In addition, the following operations must be defined for Scalar objects a and b :
Operation Description
a < b less than operator (returns a bool object)

Vector
The type Vector must be a SimpleVector class with elements of type Scalar . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file ode_gear.cpp contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise.

Source Code
The source code for this routine is in the file cppad/ode_gear.hpp.

Theory
For this discussion we use the shorthand x j for the value x ( t j ) ∈ R n which is not to be confused with x i ( t ) ∈ R in the notation above. The interpolating polynomial p ( t ) is given by p ( t ) = ∑ j = 0 m x j ∏ i ≠ j ( t - t i ) ∏ i ≠ j ( t j - t i ) The derivative p ′ ( t ) is given by p ′ ( t ) = ∑ j = 0 m x j ∑ i ≠ j ∏ k ≠ i , j ( t - t k ) ∏ k ≠ j ( t j - t k ) Evaluating the derivative at the point t ℓ we have p ′ ( t ℓ ) = x ℓ ∑ i ≠ ℓ ∏ k ≠ i , ℓ ( t ℓ - t k ) ∏ k ≠ ℓ ( t ℓ - t k ) + ∑ j ≠ ℓ x j ∑ i ≠ j ∏ k ≠ i , j ( t ℓ - t k ) ∏ k ≠ j ( t j - t k ) = x ℓ ∑ i ≠ ℓ 1 t ℓ - t i + ∑ j ≠ ℓ x j ∏ k ≠ ℓ , j ( t ℓ - t k ) ∏ k ≠ j ( t j - t k ) = x ℓ ∑ k ≠ ℓ ( t ℓ - t k ) -1 + ∑ j ≠ ℓ x j ( t j - t ℓ ) -1 ∏ k ≠ ℓ , j ( t ℓ - t k ) / ( t j - t k ) We define the vector α ∈ R m + 1 by α j = { ∑ k ≠ m ( t m - t k ) -1 if j = m ( t j - t m ) -1 ∏ k ≠ m , j ( t m - t k ) / ( t j - t k ) otherwise It follows that p ′ ( t m ) = α 0 x 0 + ⋯ + α m x m Gear's method determines x m by solving the following nonlinear equation f ( t m , x m ) = α 0 x 0 + ⋯ + α m x m Newton's method for solving this equation determines iterates, which we denote by x m k , by solving the following affine approximation of the equation above f ( t m , x m k -1 ) + ∂ x f ( t m , x m k -1 ) ( x m k - x m k -1 ) = α 0 x 0 k + α 1 x 1 + ⋯ + α m x m [α m I - ∂ x f ( t m , x m k -1 ) ] x m = [f ( t m , x m k -1 ) - ∂ x f ( t m , x m k -1 ) x m k -1 - α 0 x 0 - ⋯ - α m -1 x m -1 ] In order to initialize Newton's method; i.e. choose x m 0 we define the vector β ∈ R m + 1 by β j = { ∑ k ≠ m -1 ( t m -1 - t k ) -1 if j = m -1 ( t j - t m -1 ) -1 ∏ k ≠ m -1 , j ( t m -1 - t k ) / ( t j - t k ) otherwise It follows that p ′ ( t m -1 ) = β 0 x 0 + ⋯ + β m x m We solve the following approximation of the equation above to determine x m 0 : f ( t m -1 , x m -1 ) = β 0 x 0 + ⋯ + β m -1 x m -1 + β m x m 0
Gear's Method
C. W. Gear, ``Simultaneous Numerical Solution of Differential-Algebraic Equations,'' IEEE Transactions on Circuit Theory, vol. 18, no. 1, pp. 89-95, Jan. 1971.
Input File: cppad/utility/ode_gear.hpp cppad-20170000.3/doc/ode_gear.cpp.xml0000644000175200017650000007601313057470507016256 0ustar coincoin-web OdeGear: Example and Test
Prev Next ode_gear.cpp Headings

OdeGear: Example and Test
Define x : R → R n by x i ( t ) = t i + 1 for i = 1 , … , n -1 . It follows that x i ( 0 ) = 0 for all i x i ' ( t ) = 1 if i = 0 x i ' ( t ) = ( i + 1 ) t i = ( i + 1 ) x i -1 ( t ) if i > 0 The example tests OdeGear using the relations above: 

# include <cppad/utility/ode_gear.hpp>
# include <cppad/cppad.hpp>        // For automatic differentiation

namespace {
     class Fun {
     public:
          // constructor
          Fun(bool use_x_) : use_x(use_x_)
          { }

          // compute f(t, x) both for double and AD<double>
          template <typename Scalar>
          void Ode(
               const Scalar                    &t,
               const CPPAD_TESTVECTOR(Scalar) &x,
               CPPAD_TESTVECTOR(Scalar)       &f)
          {     size_t n  = x.size();
               Scalar ti(1);
               f[0]   = Scalar(1);
               size_t i;
               for(i = 1; i < n; i++)
               {     ti *= t;
                    // convert int(size_t) to avoid warning
                    // on _MSC_VER systems
                    if( use_x )
                         f[i] = int(i+1) * x[i-1];
                    else     f[i] = int(i+1) * ti;
               }
          }

          void Ode_dep(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f_x)
          {     using namespace CppAD;

               size_t n  = x.size();
               CPPAD_TESTVECTOR(AD<double>) T(1);
               CPPAD_TESTVECTOR(AD<double>) X(n);
               CPPAD_TESTVECTOR(AD<double>) F(n);

               // set argument values
               T[0] = t;
               size_t i, j;
               for(i = 0; i < n; i++)
                    X[i] = x[i];

               // declare independent variables
               Independent(X);

               // compute f(t, x)
               this->Ode(T[0], X, F);

               // define AD function object
               ADFun<double> fun(X, F);

               // compute partial of f w.r.t x
               CPPAD_TESTVECTOR(double) dx(n);
               CPPAD_TESTVECTOR(double) df(n);
               for(j = 0; j < n; j++)
                    dx[j] = 0.;
               for(j = 0; j < n; j++)
               {     dx[j] = 1.;
                    df = fun.Forward(1, dx);
                    for(i = 0; i < n; i++)
                         f_x [i * n + j] = df[i];
                    dx[j] = 0.;
               }
          }

     private:
          const bool use_x;

     };
}

bool OdeGear(void)
{     bool ok = true; // initial return value
     size_t i, j;    // temporary indices

     size_t  m = 4;  // index of next value in X
     size_t  n = m;  // number of components in x(t)

     // vector of times
     CPPAD_TESTVECTOR(double) T(m+1);
     double step = .1;
     T[0]        = 0.;
     for(j = 1; j <= m; j++)
     {     T[j] = T[j-1] + step;
          step = 2. * step;
     }

     // initial values for x( T[m-j] )
     CPPAD_TESTVECTOR(double) X((m+1) * n);
     for(j = 0; j < m; j++)
     {     double ti = T[j];
          for(i = 0; i < n; i++)
          {     X[ j * n + i ] = ti;
               ti *= T[j];
          }
     }

     // error bound
     CPPAD_TESTVECTOR(double) e(n);

     size_t use_x;
     for( use_x = 0; use_x < 2; use_x++)
     {     // function object depends on value of use_x
          Fun F(use_x > 0);

          // compute OdeGear approximation for x( T[m] )
          CppAD::OdeGear(F, m, n, T, X, e);

          double check = T[m];
          for(i = 0; i < n; i++)
          {     // method is exact up to order m and x[i] = t^{i+1}
               if( i + 1 <= m ) ok &= CppAD::NearEqual(
                    X[m * n + i], check, 1e-10, 1e-10
               );
               // error bound should be zero up to order m-1
               if( i + 1 < m ) ok &= CppAD::NearEqual(
                    e[i], 0., 1e-10, 1e-10
               );
               // check value for next i
               check *= T[m];
          }
     }
     return ok;
}
Input File: example/ode_gear.cpp cppad-20170000.3/doc/odegearcontrol.xml0000644000175200017650000013450313057470507016736 0ustar coincoin-web An Error Controller for Gear's Ode Solvers
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An Error Controller for Gear's Ode Solvers

Syntax
# include <cppad/utility/ode_gear_control.hpp>
 xf = OdeGearControl(F, M, ti, tf, xi,
     smin, smax, sini, eabs, erel, ef , maxabs, nstep )

Purpose
Let R denote the real numbers and let f : R × R n → R n be a smooth function. We define X : [ ti , tf ] → R n by the following initial value problem: X ( ti ) = xi X ' ( t ) = f [ t , X ( t ) ] The routine OdeGear is a stiff multi-step method that can be used to approximate the solution to this equation. The routine OdeGearControl sets up this multi-step method and controls the error during such an approximation.

Include
The file cppad/ode_gear_control.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.

Notation
The template parameter types Scalar and Vector are documented below.

xf
The return value xf has the prototype
     Vector xf
 and the size of xf is equal to n (see description of Vector below). It is the approximation for X ( tf ) .

Fun
The class Fun and the object F satisfy the prototype
     Fun &F
 This must support the following set of calls
     F.Ode(t, x, f)
     F.Ode_dep(t, x, f_x)
t
The argument t has prototype
     const Scalar &t
 (see description of Scalar below).

x
The argument x has prototype
     const Vector &x
 and has size N (see description of Vector below).

f
The argument f to F.Ode has prototype
     Vector &f
 On input and output, f is a vector of size N and the input values of the elements of f do not matter. On output, f is set equal to f ( t , x ) (see f(t, x) in Purpose ).

f_x
The argument f_x has prototype
     Vector &f_x
 On input and output, f_x is a vector of size N * N and the input values of the elements of f_x do not matter. On output, f _ x [ i * n + j ] = ∂ x ( j ) f i ( t , x )
Warning
The arguments f , and f_x must have a call by reference in their prototypes; i.e., do not forget the & in the prototype for f and f_x .

M
The argument M has prototype
     size_t M
 It specifies the order of the multi-step method; i.e., the order of the approximating polynomial (after the initialization process). The argument M must greater than or equal one.

ti
The argument ti has prototype
     const Scalar &ti
 It specifies the initial time for the integration of the differential equation.

tf
The argument tf has prototype
     const Scalar &tf
 It specifies the final time for the integration of the differential equation.

xi
The argument xi has prototype
     const Vector &xi
 and size n . It specifies value of X ( ti ) .

smin
The argument smin has prototype
     const Scalar &smin
 The minimum value of T [ M ] - T [ M -1 ] in a call to OdeGear will be smin except for the last two calls where it may be as small as smin / 2 . The value of smin must be less than or equal smax .

smax
The argument smax has prototype
     const Scalar &smax
 It specifies the maximum step size to use during the integration; i.e., the maximum value for T [ M ] - T [ M -1 ] in a call to OdeGear.

sini
The argument sini has prototype
     Scalar &sini
 The value of sini is the minimum step size to use during initialization of the multi-step method; i.e., for calls to OdeGear where m < M . The value of sini must be less than or equal smax (and can also be less than smin ).

eabs
The argument eabs has prototype
     const Vector &eabs
 and size n . Each of the elements of eabs must be greater than or equal zero. It specifies a bound for the absolute error in the return value xf as an approximation for X ( tf ) . (see the error criteria discussion below).

erel
The argument erel has prototype
     const Scalar &erel
 and is greater than or equal zero. It specifies a bound for the relative error in the return value xf as an approximation for X ( tf ) (see the error criteria discussion below).

ef
The argument value ef has prototype
     Vector &ef
 and size n . The input value of its elements does not matter. On output, it contains an estimated bound for the absolute error in the approximation xf ; i.e., ef i > | X ( tf ) i - xf i |
maxabs
The argument maxabs is optional in the call to OdeGearControl. If it is present, it has the prototype
     Vector &maxabs
 and size n . The input value of its elements does not matter. On output, it contains an estimate for the maximum absolute value of X ( t ) ; i.e., maxabs [ i ] ≈ max {| X ( t ) i | : t ∈ [ ti , tf ] }
nstep
The argument nstep has the prototype
     size_t &nstep
 Its input value does not matter and its output value is the number of calls to OdeGear used by OdeGearControl.

Error Criteria Discussion
The relative error criteria erel and absolute error criteria eabs are enforced during each step of the integration of the ordinary differential equations. In addition, they are inversely scaled by the step size so that the total error bound is less than the sum of the error bounds. To be specific, if X ˜ ( t ) is the approximate solution at time t , ta is the initial step time, and tb is the final step time, |X ˜ ( tb ) j - X ( tb ) j | ≤ tf - ti tb - ta [eabs [ j ] + erel | X ˜ ( tb ) j | ] If X ( tb ) j is near zero for some tb ∈ [ ti , tf ] , and one uses an absolute error criteria eabs [ j ] of zero, the error criteria above will force OdeGearControl to use step sizes equal to smin for steps ending near tb . In this case, the error relative to maxabs can be judged after OdeGearControl returns. If ef is to large relative to maxabs , OdeGearControl can be called again with a smaller value of smin .

Scalar
The type Scalar must satisfy the conditions for a NumericType type. The routine CheckNumericType will generate an error message if this is not the case. In addition, the following operations must be defined for Scalar objects a and b :
Operation Description
a <= b returns true (false) if a is less than or equal (greater than) b .
a == b returns true (false) if a is equal to b .
log(a) returns a Scalar equal to the logarithm of a
exp(a) returns a Scalar equal to the exponential of a

Vector
The type Vector must be a SimpleVector class with elements of type Scalar . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file ode_gear_control.cpp contains an example and test a test of using this routine. It returns true if it succeeds and false otherwise.

Theory
Let e ( s ) be the error as a function of the step size s and suppose that there is a constant K such that e ( s ) = K s m . Let a be our error bound. Given the value of e ( s ) , a step of size λ s would be ok provided that a ≥ e ( λ s ) ( tf - ti ) / ( λ s ) a ≥ K λ m s m ( tf - ti ) / ( λ s ) a ≥ λ m -1 s m -1 ( tf - ti ) e ( s ) / s m a ≥ λ m -1 ( tf - ti ) e ( s ) / s λ m -1 ≤ a e ( s ) s tf - ti Thus if the right hand side of the last inequality is greater than or equal to one, the step of size s is ok.

Source Code
The source code for this routine is in the file cppad/ode_gear_control.hpp.
Input File: cppad/utility/ode_gear_control.hpp cppad-20170000.3/doc/ode_gear_control.cpp.xml0000644000175200017650000007535513057470507020026 0ustar coincoin-web OdeGearControl: Example and Test
Prev Next ode_gear_control.cpp Headings

OdeGearControl: Example and Test
Define X : R → R 2 by X 0 ( t ) = - exp ( - w 0 t ) X 1 ( t ) = w 0 w 1 - w 0 [ exp ( - w 0 t ) - exp ( - w 1 t ) ] It follows that X 0 ( 0 ) = 1 , X 1 ( 0 ) = 0 and X 0 ( 1 ) ( t ) = - w 0 X 0 ( t ) X 1 ( 1 ) ( t ) = + w 0 X 0 ( t ) - w 1 X 1 ( t ) The example tests OdeGearControl using the relations above: 

# include <cppad/cppad.hpp>
# include <cppad/utility/ode_gear_control.hpp>   // CppAD::OdeGearControl

namespace {
     // --------------------------------------------------------------
     class Fun {
     private:
           CPPAD_TESTVECTOR(double) w;
     public:
          // constructor
          Fun(const CPPAD_TESTVECTOR(double) &w_) : w(w_)
          { }

          // set f = x'(t)
          template <typename Scalar>
          void Ode(
               const Scalar                    &t,
               const CPPAD_TESTVECTOR(Scalar) &x,
               CPPAD_TESTVECTOR(Scalar)       &f)
          {     f[0] = - w[0] * x[0];
               f[1] = + w[0] * x[0] - w[1] * x[1];
          }

          void Ode_dep(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f_x)
          {     using namespace CppAD;

               size_t n  = x.size();
               CPPAD_TESTVECTOR(AD<double>) T(1);
               CPPAD_TESTVECTOR(AD<double>) X(n);
               CPPAD_TESTVECTOR(AD<double>) F(n);

               // set argument values
               T[0] = t;
               size_t i, j;
               for(i = 0; i < n; i++)
                    X[i] = x[i];

               // declare independent variables
               Independent(X);

               // compute f(t, x)
               this->Ode(T[0], X, F);

               // define AD function object
               ADFun<double> fun(X, F);

               // compute partial of f w.r.t x
               CPPAD_TESTVECTOR(double) dx(n);
               CPPAD_TESTVECTOR(double) df(n);
               for(j = 0; j < n; j++)
                    dx[j] = 0.;
               for(j = 0; j < n; j++)
               {     dx[j] = 1.;
                    df = fun.Forward(1, dx);
                    for(i = 0; i < n; i++)
                         f_x [i * n + j] = df[i];
                    dx[j] = 0.;
               }
          }
     };
}

bool OdeGearControl(void)
{     bool ok = true;     // initial return value
     using CppAD::NearEqual;

     CPPAD_TESTVECTOR(double) w(2);
     w[0] = 10.;
     w[1] = 1.;
     Fun F(w);

     CPPAD_TESTVECTOR(double) xi(2);
     xi[0] = 1.;
     xi[1] = 0.;

     CPPAD_TESTVECTOR(double) eabs(2);
     eabs[0] = 1e-4;
     eabs[1] = 1e-4;

     // return values
     CPPAD_TESTVECTOR(double) ef(2);
     CPPAD_TESTVECTOR(double) maxabs(2);
     CPPAD_TESTVECTOR(double) xf(2);
     size_t                nstep;

     // input values
     size_t  M   = 5;
     double ti   = 0.;
     double tf   = 1.;
     double smin = 1e-8;
     double smax = 1.;
     double sini = 1e-10;
     double erel = 0.;

     xf = CppAD::OdeGearControl(F, M,
          ti, tf, xi, smin, smax, sini, eabs, erel, ef, maxabs, nstep);

     double x0 = exp(-w[0]*tf);
     ok &= NearEqual(x0, xf[0], 1e-4, 1e-4);
     ok &= NearEqual(0., ef[0], 1e-4, 1e-4);

     double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]);
     ok &= NearEqual(x1, xf[1], 1e-4, 1e-4);
     ok &= NearEqual(0., ef[1], 1e-4, 1e-4);

     return ok;
}
Input File: example/ode_gear_control.cpp cppad-20170000.3/doc/cppad_vector.xml0000644000175200017650000010167613057470507016405 0ustar coincoin-web The CppAD::vector Template Class
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The CppAD::vector Template Class

Syntax
%# include <cppad/utility/vector.hpp>

Description
The include file cppad/vector.hpp defines the vector template class CppAD::vector. This is a SimpleVector template class and in addition it has the features listed below:

Include
The file cppad/vector.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD include files.

capacity
If x is a CppAD::vector<Scalar> , and cap is a size_t object,
     cap = x.capacity()
 set cap to the number of Scalar objects that could fit in the memory currently allocated for x . Note that
     x.size() <= x.capacity()
Assignment
If x and y are CppAD::vector<Scalar> objects,
     y = x
 has all the properties listed for a simple vector assignment plus the following:

Check Size
The CppAD::vector template class will check that the size of x is either zero or the size of y before doing the assignment. If this is not the case, CppAD::vector will use ErrorHandler to generate an appropriate error report. Allowing for assignment to a vector with size zero makes the following code work:
     CppAD::vector<Scalar> y;
     y = x;
Return Reference
A reference to the vector y is returned. An example use of this reference is in multiple assignments of the form
     z = y = x
Move Semantics
If the C++ compiler supports move semantic rvalues using the && syntax, then it will be used during the vector assignment statement. This means that return values and other temporaries are not be copied, but rather pointers are transferred.

Element Access
If x is a CppAD::vector<Scalar> object and i has type size_t,
     x[i]
 has all the properties listed for a simple vector element access plus the following:

The object x[i] has type Scalar (is not possibly a different type that can be converted to Scalar ).

If i is not less than the size of the x , CppAD::vector will use ErrorHandler to generate an appropriate error report.

push_back
If x is a CppAD::vector<Scalar> object with size equal to n and s has type Scalar ,
     x.push_back(s)
 extends the vector x so that its new size is n plus one and x[n] is equal to s (equal in the sense of the Scalar assignment operator).

push_vector
If x is a CppAD::vector<Scalar> object with size equal to n and v is a simple vector with elements of type Scalar and size m ,
     x.push_vector(v)
 extends the vector x so that its new size is n+m and x[n + i] is equal to v[i] for i = 1 , ... , m-1 (equal in the sense of the Scalar assignment operator).

Output
If x is a CppAD::vector<Scalar> object and os is an std::ostream, and the operation
     os << x
 will output the vector x to the standard output stream os . The elements of x are enclosed at the beginning by a { character, they are separated by , characters, and they are enclosed at the end by } character. It is assumed by this operation that if e is an object with type Scalar ,
     os << e
 will output the value e to the standard output stream os .

resize
The call x.resize(n) set the size of x equal to n . If n <= x.capacity() , no memory is freed or allocated, the capacity of x does not change, and the data in x is preserved. If n > x.capacity() , new memory is allocated and the data in x is lost (not copied to the new memory location).

clear
All memory allocated for the vector is freed and both its size and capacity are set to zero. This can be useful when using very large vectors and when checking for memory leaks (and there are global vectors) see the memory discussion.

data
If x is a CppAD::vector<Scalar> object
     x.data()
 returns a pointer to a Scalar object such that for 0 <= i < x.size() , x[i] and x.data()[i] are the same Scalar object. If x is const, the pointer is const. If x.capacity() is zero, the value of the pointer is not defined. The pointer may no longer be valid after the following operations on x : its destructor, clear, resize, push_back, push_vector, assignment to another vector when original size of x is zero.

vectorBool
The file <cppad/vector.hpp> also defines the class CppAD::vectorBool. This has the same specifications as CppAD::vector<bool> with the following exceptions:

Memory
The class vectorBool conserves on memory (on the other hand, CppAD::vector<bool> is expected to be faster than vectorBool).

bit_per_unit
The static function call
     s = vectorBool::bit_per_unit()
 returns the size_t value s which is equal to the number of boolean values (bits) that are packed into one operational unit. For example, a logical or acts on this many boolean values with one operation.

data
The data function is not supported by vectorBool.

Output
The CppAD::vectorBool output operator prints each boolean value as a 0 for false, a 1 for true, and does not print any other output; i.e., the vector is written a long sequence of zeros and ones with no surrounding {, } and with no separating commas or spaces.

Element Type
If x has type vectorBool and i has type size_t, the element access value x[i] has an unspecified type, referred to here as elementType , that supports the following operations:
  1. elementType can be converted to bool; e.g. the following syntax is supported:
         static_cast<bool>(     x[i] )
  2. elementType supports the assignment operator = where the right hand side is a bool or an elementType object; e.g., if y has type bool, the following syntax is supported:
             x[i] = y
  3. The result of an assignment to an elementType also has type elementType . Thus, if z has type bool, the following syntax is supported:
             z = x[i] = y

Memory and Parallel Mode
These vectors use the multi-threaded fast memory allocator thread_alloc :
  1. The routine parallel_setup must be called before these vectors can be used in parallel .
  2. Using these vectors affects the amount of memory in_use and available .
  3. Calling clear , makes the corresponding memory available (though thread_alloc) to the current thread.
  4. Available memory can then be completely freed using free_available .


Example
The files cppad_vector.cpp and vector_bool.cpp each contain an example and test of this template class. They return true if they succeed and false otherwise.

Exercise
Create and run a program that contains the following code: 
 
     CppAD::vector<double> x(3);
     size_t i;
     for(i = 0; i < 3; i++)
          x[i] = 4. - i;
     std::cout << "x = " << x << std::endl;
Input File: cppad/utility/vector.hpp cppad-20170000.3/doc/cppad_vector.cpp.xml0000644000175200017650000005712313057470507017163 0ustar coincoin-web CppAD::vector Template Class: Example and Test
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CppAD::vector Template Class: Example and Test

# include <cppad/utility/vector.hpp>
# include <cppad/utility/check_simple_vector.hpp>
# include <sstream> // sstream and string are used to test output operation
# include <string>

bool CppAD_vector(void)
{     bool ok = true;
     using CppAD::vector;     // so can use vector instead of CppAD::vector
     typedef double Type;     // change double to test other types

     // check Simple Vector specifications
     CppAD::CheckSimpleVector< Type, vector<Type> >();

     vector<Type> x;          // default constructor
     ok &= (x.size() == 0);

     x.resize(2);             // resize and set element assignment
     ok &= (x.size() == 2);
     x[0] = Type(1);
     x[1] = Type(2);

     vector<Type> y(2);       // sizing constructor
     ok &= (y.size() == 2);

     const vector<Type> z(x); // copy constructor and const element access
     ok &= (z.size() == 2);
     ok &= ( (z[0] == Type(1)) && (z[1] == Type(2)) );

     x[0] = Type(2);          // modify, assignment changes x
     ok &= (x[0] == Type(2));

     x = y = z;               // vector assignment
     ok &= ( (x[0] == Type(1)) && (x[1] == Type(2)) );
     ok &= ( (y[0] == Type(1)) && (y[1] == Type(2)) );
     ok &= ( (z[0] == Type(1)) && (z[1] == Type(2)) );

     // test of output
     std::string        correct= "{ 1, 2 }";
     std::string        str;
     std::ostringstream buf;
     buf << z;
     str = buf.str();
     ok &= (str == correct);

     // test resize(1), resize(0), capacity, and clear
     size_t i = x.capacity();
     ok      &= i >= 2;
     x.resize(1);
     ok      &= x[0] == Type(1);
     ok      &= i == x.capacity();
     x.resize(0);
     ok      &= i == x.capacity();
     x.clear();
     ok      &= 0 == x.capacity();

     // test of push_back scalar and capacity
     size_t N = 100;
     for(i = 0; i < N; i++)
     {     size_t old_capacity = x.capacity();
          x.push_back( Type(i) );
          ok &= (i+1) == x.size();
          ok &= i < x.capacity();
          ok &= (i == old_capacity) || old_capacity == x.capacity();
     }
     for(i = 0; i < N; i++)
          ok &= ( x[i] == Type(i) );

     // test of data
     Type* data = x.data();
     for(i = 0; i < N; i++)
     {     ok &= data[i] == Type(i);
          data[i] = Type(N - i);
          ok &= x[i] == Type(N - i);
     }

     // test of push_vector
     x.push_vector(x);
     ok &= (x.size() == 2 * N);
     for(i = 0; i < N; i++)
     {     ok &= x[i] == Type(N - i);
          ok &= x[i+N] == Type(N - i);
     }


     return ok;
}
Input File: example/cppad_vector.cpp cppad-20170000.3/doc/vector_bool.cpp.xml0000644000175200017650000005237613057470507017034 0ustar coincoin-web CppAD::vectorBool Class: Example and Test
Prev Next vector_bool.cpp Headings

CppAD::vectorBool Class: Example and Test

# include <cppad/utility/vector.hpp>
# include <cppad/utility/check_simple_vector.hpp>
# include <sstream> // sstream and string are used to test output operation
# include <string>

bool vectorBool(void)
{     bool ok = true;
     using CppAD::vectorBool;

     vectorBool x;          // default constructor
     ok &= (x.size() == 0);

     x.resize(2);             // resize and set element assignment to bool
     ok &= (x.size() == 2);
     x[0] = false;
     x[1] = true;

     vectorBool y(2);       // sizing constructor
     ok &= (y.size() == 2);

     const vectorBool z(x); // copy constructor and const element access
     ok &= (z.size() == 2);
     ok &= ( (z[0] == false) && (z[1] == true) );

     x[0] = true;           // modify, assignment changes x
     ok &= (x[0] == true);

     // resize x to zero and check that vector assignment works for both
     // size zero and mathching sizes
     x.resize(0);
     ok &= (x.size() == 0);
     ok &= (y.size() == z.size());
     //
     x = y = z;
     ok &= ( (x[0] == false) && (x[1] == true) );
     ok &= ( (y[0] == false) && (y[1] == true) );
     ok &= ( (z[0] == false) && (z[1] == true) );

     // test of push_vector
     y.push_vector(z);
     ok &= y.size() == 4;
     ok &= ( (y[0] == false) && (y[1] == true) );
     ok &= ( (y[2] == false) && (y[3] == true) );

     y[1] = false;           // element assignment to another element
     x[0] = y[1];
     ok &= (x[0] == false);

     // test of output
     std::string        correct= "01";
     std::string        str;
     std::ostringstream buf;
     buf << z;
     str = buf.str();
     ok &= (str == correct);

     // test resize(0), capacity, and clear
     size_t i = x.capacity();
     ok      &= i > 0;
     x.resize(0);
     ok      &= i == x.capacity();
     x.clear();
     ok      &= 0 == x.capacity();

     // test of push_back element
     for(i = 0; i < 100; i++)
          x.push_back( (i % 3) != 0 );
     ok &= (x.size() == 100);
     for(i = 0; i < 100; i++)
          ok &= ( x[i] == ((i % 3) != 0) );

     // is that boolvector is
     // a simple vector class with elements of type bool
     CppAD::CheckSimpleVector< bool, vectorBool >();

     return ok;
}
Input File: example/vector_bool.cpp cppad-20170000.3/doc/thread_alloc.xml0000644000175200017650000001613213057470507016345 0ustar coincoin-web A Fast Multi-Threading Memory Allocator
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A Fast Multi-Threading Memory Allocator

Syntax
# include <cppad/thread_alloc.hpp>

Purpose
The C++ new and delete operators are thread safe, but this means that a thread may have to wait for a lock on these operations. Once memory is obtained for a thread, the thread_alloc memory allocator keeps that memory available for the thread so that it can be re-used without waiting for a lock. All the CppAD memory allocations use this utility. The free_available function should be used to return memory to the system (once it is no longer required by a thread).

Include
The routines in sections below are defined by cppad/thread_alloc.hpp. This file is included by cppad/cppad.hpp, but it can also be included separately with out the rest of the CppAD.

Contents
thread_alloc.cppFast Multi-Threading Memory Allocator: Example and Test
ta_parallel_setupSetup thread_alloc For Use in Multi-Threading Environment
ta_num_threadsGet Number of Threads
ta_in_parallelIs The Current Execution in Parallel Mode
ta_thread_numGet the Current Thread Number
ta_get_memoryGet At Least A Specified Amount of Memory
ta_return_memoryReturn Memory to thread_alloc
ta_free_availableFree Memory Currently Available for Quick Use by a Thread
ta_hold_memoryControl When Thread Alloc Retains Memory For Future Use
ta_inuseAmount of Memory a Thread is Currently Using
ta_availableAmount of Memory Available for Quick Use by a Thread
ta_create_arrayAllocate An Array and Call Default Constructor for its Elements
ta_delete_arrayDeallocate An Array and Call Destructor for its Elements
ta_free_allFree All Memory That Was Allocated for Use by thread_alloc
Input File: omh/thread_alloc.omh cppad-20170000.3/doc/thread_alloc.cpp.xml0000644000175200017650000011133513057470507017127 0ustar coincoin-web Fast Multi-Threading Memory Allocator: Example and Test
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Fast Multi-Threading Memory Allocator: Example and Test
# include <cppad/utility/thread_alloc.hpp>
# include <cppad/utility/memory_leak.hpp>
# include <vector>
# include <limits>


namespace { // Begin empty namespace



bool raw_allocate(void)
{     bool ok = true;
     using CppAD::thread_alloc;
     size_t thread;

     // check that no memory is initilaly inuse
     ok &= thread_alloc::free_all();

     // amount of static memory used by thread zero
     size_t static_inuse = 0;

     // repeatedly allocate enough memory for at least two size_t values.
     size_t min_size_t = 2;
     size_t min_bytes  = min_size_t * sizeof(size_t);
     size_t n_outter   = 10;
     size_t n_inner    = 5;
     for(size_t i = 0; i < n_outter; i++)
     {     // Do not use CppAD::vector here because its use of thread_alloc
          // complicates the inuse and avaialble results.
          std::vector<void*> v_ptr(n_inner);
          // cap_bytes will be set by get_memory
          size_t cap_bytes = 0; // set here to avoid MSC warning
          for(size_t j = 0; j < n_inner; j++)
          {     // allocate enough memory for min_size_t size_t objects
               v_ptr[j]    = thread_alloc::get_memory(min_bytes, cap_bytes);
               size_t* ptr = reinterpret_cast<size_t*>(v_ptr[j]);
               // determine the number of size_t values we have obtained
               size_t  cap_size_t = cap_bytes / sizeof(size_t);
               ok                &= min_size_t <= cap_size_t;
               // use placement new to call the size_t copy constructor
               for(size_t k = 0; k < cap_size_t; k++)
                    new(ptr + k) size_t(i + j + k);
               // check that the constructor worked
               for(size_t k = 0; k < cap_size_t; k++)
                    ok &= ptr[k] == (i + j + k);
          }
          // check that n_inner * cap_bytes are inuse and none are available
          thread = thread_alloc::thread_num();
          ok &= thread_alloc::inuse(thread) == n_inner*cap_bytes + static_inuse;
          ok &= thread_alloc::available(thread) == 0;
          // return the memrory to thread_alloc
          for(size_t j = 0; j < n_inner; j++)
               thread_alloc::return_memory(v_ptr[j]);
          // check that now n_inner * cap_bytes are now available
          // and none are in use
          ok &= thread_alloc::inuse(thread) == static_inuse;
          ok &= thread_alloc::available(thread) == n_inner * cap_bytes;
     }
     thread_alloc::free_available(thread);

     // check that the tests have not held onto memory
     ok &= ! CppAD::memory_leak();

     return ok;
}

class my_char {
public:
     char ch_ ;
     my_char(void) : ch_(' ')
     { }
     my_char(const my_char& my_ch) : ch_(my_ch.ch_)
     { }
};

bool type_allocate(void)
{     bool ok = true;
     using CppAD::thread_alloc;
     size_t i;

     // check initial memory values
     size_t thread = thread_alloc::thread_num();
     ok &= thread == 0;
     ok &= thread_alloc::free_all();
     size_t static_inuse = 0;

     // initial allocation of an array
     size_t  size_min  = 3;
     size_t  size_one;
     my_char *array_one  =
          thread_alloc::create_array<my_char>(size_min, size_one);

     // check the values and change them to null 'x'
     for(i = 0; i < size_one; i++)
     {     ok &= array_one[i].ch_ == ' ';
          array_one[i].ch_ = 'x';
     }

     // now create a longer array
     size_t size_two;
     my_char *array_two =
          thread_alloc::create_array<my_char>(2 * size_min, size_two);

     // check the values in array one
     for(i = 0; i < size_one; i++)
          ok &= array_one[i].ch_ == 'x';

     // check the values in array two
     for(i = 0; i < size_two; i++)
          ok &= array_two[i].ch_ == ' ';

     // check the amount of inuse and available memory
     // (an extra size_t value is used for each memory block).
     size_t check = static_inuse + sizeof(my_char)*(size_one + size_two);
     ok   &= thread_alloc::inuse(thread) - check < sizeof(my_char);
     ok   &= thread_alloc::available(thread) == 0;

     // delete the arrays
     thread_alloc::delete_array(array_one);
     thread_alloc::delete_array(array_two);
     ok   &= thread_alloc::inuse(thread) == static_inuse;
     check = sizeof(my_char)*(size_one + size_two);
     ok   &= thread_alloc::available(thread) - check < sizeof(my_char);

     // free the memory for use by this thread
     thread_alloc::free_available(thread);

     // check that the tests have not held onto memory
     ok &= ! CppAD::memory_leak();

     return ok;
}

} // End empty namespace

bool check_alignment(void)
{     bool ok = true;
     using CppAD::thread_alloc;

     // number of binary digits in a size_t value
     size_t n_digit = std::numeric_limits<size_t>::digits;

     // must be a multiple of 8
     ok &= (n_digit % 8) == 0;

     // number of bytes in a size_t value
     size_t n_byte  = n_digit / 8;

     // check raw allocation -------------------------------------------------
     size_t min_bytes = 1;
     size_t cap_bytes;
     void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes);

     // convert to a size_t value
     size_t v_size_t = reinterpret_cast<size_t>(v_ptr);

     // check that it is aligned
     ok &= (v_size_t % n_byte) == 0;

     // return memory to available pool
     thread_alloc::return_memory(v_ptr);

     // check array allocation ----------------------------------------------
     size_t size_min = 1;
     size_t size_out;
     my_char *array_ptr =
          thread_alloc::create_array<my_char>(size_min, size_out);

     // convert to a size_t value
     size_t array_size_t = reinterpret_cast<size_t>(array_ptr);

     // check that it is aligned
     ok &= (array_size_t % n_byte) == 0;

     // return memory to avialable pool
     thread_alloc::delete_array(array_ptr);

     return ok;
}


bool thread_alloc(void)
{     bool ok  = true;
     using CppAD::thread_alloc;

     // check that there is only on thread
     ok  &= thread_alloc::num_threads() == 1;
     // so thread number must be zero
     ok  &= thread_alloc::thread_num() == 0;
     // and we are in sequential execution mode
     ok  &= thread_alloc::in_parallel() == false;

     // Instruct thread_alloc to hold onto memory.  This makes memory
     // allocation faster (especially when there are multiple threads).
     thread_alloc::hold_memory(true);

     // run raw allocation tests
     ok &= raw_allocate();

     // run typed allocation tests
     ok &= type_allocate();

     // check alignment
     ok &= check_alignment();

     // return allocator to its default mode
     thread_alloc::hold_memory(false);
     return ok;
}
Input File: example/thread_alloc.cpp cppad-20170000.3/doc/ta_parallel_setup.xml0000644000175200017650000002242713057470507017430 0ustar coincoin-web Setup thread_alloc For Use in Multi-Threading Environment
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Setup thread_alloc For Use in Multi-Threading Environment

Syntax
thread_alloc::parallel_setup(num_threads, in_parallel, thread_num)
Purpose
By default there is only one thread and all execution is in sequential mode, i.e., multiple threads are not sharing the same memory; i.e. not in parallel mode.

Speed
It should be faster, even when num_thread is equal to one, for thread_alloc to hold onto memory. This can be accomplished using the function call
     thread_alloc::hold_memory(true)
 see hold_memory .

num_threads
This argument has prototype
     size_t num_threads
 and must be greater than zero. It specifies the number of threads that are sharing memory. The case num_threads == 1 is a special case that is used to terminate a multi-threading environment.

in_parallel
This function has prototype
     bool in_parallel(void)
 It must return true if there is more than one thread currently executing. Otherwise it can return false.

In the special case where num_threads == 1 , the routine in_parallel is not used.

thread_num
This function has prototype
     size_t thread_num(void)
 It must return a thread number that uniquely identifies the currently executing thread. Furthermore
     0 <= thread_num() < num_threads
 . In the special case where num_threads == 1 , the routine thread_num is not used.

Note that this function is called by other routines so, as soon as a new thread is executing, one must be certain that thread_num() will work for that thread.

Restrictions
The function parallel_setup must be called before the program enters parallel execution mode. In addition, this function cannot be called while in parallel mode.

Example
The files simple_ad_openmp.cpp , simple_ad_bthread.cpp , and simple_ad_pthread.cpp , contain examples and tests that use this function.
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_num_threads.xml0000644000175200017650000001156013057470507016721 0ustar coincoin-web Get Number of Threads
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Get Number of Threads

Syntax
number = thread_alloc::num_threads()

Purpose
Determine the number of threads as set during parallel_setup .

number
The return value number has prototype
     size_t number
 and is equal to the value of num_threads in the previous call to parallel_setup . If there was no such previous call, the value one is returned.

Example
The example and test thread_alloc.cpp uses this routine.
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_in_parallel.xml0000644000175200017650000001136213057470507016672 0ustar coincoin-web Is The Current Execution in Parallel Mode
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Is The Current Execution in Parallel Mode

Syntax
flag = thread_alloc::in_parallel()

Purpose
Some of the thread_alloc allocation routines have different specifications for parallel (not sequential) execution mode. This routine enables you to determine if the current execution mode is sequential or parallel.

flag
The return value has prototype
     bool flag
 It is true if the current execution is in parallel mode (possibly multi-threaded) and false otherwise (sequential mode).

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_thread_num.xml0000644000175200017650000001117313057470507016536 0ustar coincoin-web Get the Current Thread Number
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Get the Current Thread Number

Syntax
thread = thread_alloc::thread_num()

Purpose
Some of the thread_alloc allocation routines have a thread number. This routine enables you to determine the current thread.

thread
The return value thread has prototype
     size_t thread
 and is the currently executing thread number.

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_get_memory.xml0000644000175200017650000001772213057470507016565 0ustar coincoin-web Get At Least A Specified Amount of Memory
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Get At Least A Specified Amount of Memory

Syntax
v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes)

Purpose
Use thread_alloc to obtain a minimum number of bytes of memory (for use by the current thread ).

min_bytes
This argument has prototype
     size_t min_bytes
 It specifies the minimum number of bytes to allocate. This value must be less than 
 
     std::numeric_limits<size_t>::max() / 2

cap_bytes
This argument has prototype
     size_t& cap_bytes
 It's input value does not matter. Upon return, it is the actual number of bytes (capacity) that have been allocated for use,
     min_bytes <= cap_bytes
v_ptr
The return value v_ptr has prototype
     void* v_ptr
 It is the location where the cap_bytes of memory that have been allocated for use begins.

Allocation Speed
This allocation should be faster if the following conditions hold:
  1. The memory allocated by a previous call to get_memory is currently available for use.
  2. The current min_bytes is between the previous min_bytes and previous cap_bytes .


Alignment
We call a memory allocation aligned if the address is a multiple of the number of bytes in a size_t value. If the system new allocator is aligned, then v_ptr pointer is also aligned.

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_return_memory.xml0000644000175200017650000001363213057470507017321 0ustar coincoin-web Return Memory to thread_alloc
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Return Memory to thread_alloc

Syntax
thread_alloc::return_memory(v_ptr)

Purpose
If hold_memory is false, the memory is returned to the system. Otherwise, the memory is retained by thread_alloc for quick future use by the thread that allocated to memory.

v_ptr
This argument has prototype
     void* v_ptr
 . It must be a pointer to memory that is currently in use; i.e. obtained by a previous call to get_memory and not yet returned.

Thread
Either the current thread must be the same as during the corresponding call to get_memory , or the current execution mode must be sequential (not parallel ).

NDEBUG
If NDEBUG is defined, v_ptr is not checked (this is faster). Otherwise, a list of in use pointers is searched to make sure that v_ptr is in the list.

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_free_available.xml0000644000175200017650000001342413057470507017332 0ustar coincoin-web Free Memory Currently Available for Quick Use by a Thread
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Free Memory Currently Available for Quick Use by a Thread

Syntax
thread_alloc::free_available(thread)

Purpose
Return to the system all the memory that is currently being held for quick use by the specified thread.

Extra Memory
In the case where thread > 0 , some extra memory is used to track allocations by the specified thread. If
     thread_alloc::inuse(thread) == 0
 the extra memory is also returned to the system.

thread
This argument has prototype
     size_t thread
 Either thread_num must be the same as thread , or the current execution mode must be sequential (not parallel ).

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_hold_memory.xml0000644000175200017650000001312413057470507016724 0ustar coincoin-web Control When Thread Alloc Retains Memory For Future Use
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Control When Thread Alloc Retains Memory For Future Use

Syntax
thread_alloc::hold_memory(value)

Purpose
It should be faster, even when num_thread is equal to one, for thread_alloc to hold onto memory. Calling hold_memory with value equal to true, instructs thread_alloc to hold onto memory, and put it in the available pool, after each call to return_memory .

value
If value is true, thread_alloc with hold onto memory for future quick use. If it is false, future calls to return_memory will return the corresponding memory to the system. By default (when hold_memory has not been called) thread_alloc does not hold onto memory.

free_available
Memory that is being held by thread_alloc can be returned to the system using free_available .
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_inuse.xml0000644000175200017650000001317413057470507015536 0ustar coincoin-web Amount of Memory a Thread is Currently Using
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Amount of Memory a Thread is Currently Using

Syntax
num_bytes = thread_alloc::inuse(thread)

Purpose
Memory being managed by thread_alloc has two states, currently in use by the specified thread, and quickly available for future use by the specified thread. This function informs the program how much memory is in use.

thread
This argument has prototype
     size_t thread
 Either thread_num must be the same as thread , or the current execution mode must be sequential (not parallel ).

num_bytes
The return value has prototype
     size_t num_bytes
 It is the number of bytes currently in use by the specified thread.

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_available.xml0000644000175200017650000001325213057470507016330 0ustar coincoin-web Amount of Memory Available for Quick Use by a Thread
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Amount of Memory Available for Quick Use by a Thread

Syntax
num_bytes = thread_alloc::available(thread)

Purpose
Memory being managed by thread_alloc has two states, currently in use by the specified thread, and quickly available for future use by the specified thread. This function informs the program how much memory is available.

thread
This argument has prototype
     size_t thread
 Either thread_num must be the same as thread , or the current execution mode must be sequential (not parallel ).

num_bytes
The return value has prototype
     size_t num_bytes
 It is the number of bytes currently available for use by the specified thread.

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_create_array.xml0000644000175200017650000002337013057470507017053 0ustar coincoin-web Allocate An Array and Call Default Constructor for its Elements
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Allocate An Array and Call Default Constructor for its Elements

Syntax
array = thread_alloc::create_array<Type>(size_min, size_out) .

Purpose
Create a new raw array using thread_alloc memory allocator (works well in a multi-threading environment) and call default constructor for each element.

Type
The type of the elements of the array.

size_min
This argument has prototype
     size_t size_min
 This is the minimum number of elements that there can be in the resulting array .

size_out
This argument has prototype
     size_t& size_out
 The input value of this argument does not matter. Upon return, it is the actual number of elements in array (  size_min <= size_out ).

array
The return value array has prototype
     Type* array
 It is array with size_out elements. The default constructor for Type is used to initialize the elements of array . Note that delete_array should be used to destroy the array when it is no longer needed.

Delta
The amount of memory inuse by the current thread, will increase delta where
     sizeof(Type) * (size_out + 1) > delta >= sizeof(Type) * size_out
 The available memory will decrease by delta , (and the allocation will be faster) if a previous allocation with size_min between its current value and size_out is available.

Alignment
We call a memory allocation aligned if the address is a multiple of the number of bytes in a size_t value. If the system new allocator is aligned, then array pointer is also aligned.

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_delete_array.xml0000644000175200017650000001547413057470507017060 0ustar coincoin-web Deallocate An Array and Call Destructor for its Elements
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Deallocate An Array and Call Destructor for its Elements

Syntax
thread_alloc::delete_array(array) .

Purpose
Returns memory corresponding to an array created by (create by create_array ) to the available memory pool for the current thread.

Type
The type of the elements of the array.

array
The argument array has prototype
     Type* array
 It is a value returned by create_array and not yet deleted. The Type destructor is called for each element in the array.

Thread
The current thread must be the same as when create_array returned the value array . There is an exception to this rule: when the current execution mode is sequential (not parallel ) the current thread number does not matter.

Delta
The amount of memory inuse will decrease by delta , and the available memory will increase by delta , where delta is the same as for the corresponding call to create_array.

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/ta_free_all.xml0000644000175200017650000001263613057470507016166 0ustar coincoin-web Free All Memory That Was Allocated for Use by thread_alloc
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Free All Memory That Was Allocated for Use by thread_alloc

Syntax
ok = thread_alloc::free_all() .

Purpose
Returns all memory that was used by thread_alloc to the system.

ok
The return value ok has prototype
     bool ok
 Its value will be true if all the memory can be freed. This requires that for all thread indices, there is no memory inuse ; i.e.,
     0 == thread_alloc::inuse(thread)
 Otherwise, the return value will be false.

Restrictions
This function cannot be called while in parallel mode.

Example
thread_alloc.cpp
Input File: cppad/utility/thread_alloc.hpp cppad-20170000.3/doc/index_sort.xml0000644000175200017650000002203613057470507016102 0ustar coincoin-web Returns Indices that Sort a Vector
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Returns Indices that Sort a Vector

Syntax
# include <cppad/utility/index_sort.hpp>
 index_sort(keys, ind)

keys
The argument keys has prototype
     const VectorKey& keys
 where VectorKey is a SimpleVector class with elements that support the < operation.

ind
The argument ind has prototype
     VectorSize& ind
 where VectorSize is a SimpleVector class with elements of type size_t. The routine CheckSimpleVector will generate an error message if this is not the case.

Input
The size of ind must be the same as the size of keys and the value of its input elements does not matter.

Return
Upon return, ind is a permutation of the set of indices that yields increasing order for keys . In other words, for all i != j ,
     ind[i] != ind[j]
 and for i = 0 , ... , size-2 ,
     ( keys[ ind[i+1] ] < keys[ ind[i] ] ) == false
Example
The file index_sort.cpp contains an example and test of this routine. It return true if it succeeds and false otherwise.
Input File: cppad/utility/index_sort.hpp cppad-20170000.3/doc/index_sort.cpp.xml0000644000175200017650000004220313057470507016661 0ustar coincoin-web Index Sort: Example and Test
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Index Sort: Example and Test
# include <cppad/utility/index_sort.hpp>
# include <cppad/utility/vector.hpp>
# include <valarray>
# include <vector>


namespace{
     // class that uses < to compare a pair of size_t values
     class Key {
     public:
          size_t first_;
          size_t second_;
          //
          Key(void)
          { }
          //
          Key(size_t first, size_t second)
          : first_(first), second_(second)
          { }
          //
          bool operator<(const Key& other) const
          {     if( first_ == other.first_ )
                    return second_ < other.second_;
               return first_ < other.first_;
          }
     };

     template <class VectorKey, class VectorSize>
     bool vector_case(void)
     {     bool ok = true;
          size_t i, j;
          size_t first[]  =  { 4, 4, 3, 3, 2, 2, 1, 1};
          size_t second[] = { 0, 1, 0, 1, 0, 1, 0, 1};
          size_t size     = sizeof(first) / sizeof(first[0]);

          VectorKey keys(size);
          for(i = 0; i < size; i++)
               keys[i] = Key(first[i], second[i]);

          VectorSize ind(size);
          CppAD::index_sort(keys, ind);

          // check that all the indices are different
          for(i = 0; i < size; i++)
          {     for(j = 0; j < size; j++)
                    ok &= (i == j) | (ind[i] != ind[j]);
          }

          // check for increasing order
          for(i = 0; i < size-1; i++)
          {     if( first[ ind[i] ] == first[ ind[i+1] ] )
                    ok &= second[ ind[i] ] <= second[ ind[i+1] ];
               else     ok &= first[ ind[i] ] < first[ ind[i+1] ];
          }

          return ok;
     }
}

bool index_sort(void)
{     bool ok = true;

     // some example simple vector template classes
     ok &= vector_case<  std::vector<Key>,  std::valarray<size_t> >();
     ok &= vector_case< std::valarray<Key>, CppAD::vector<size_t> >();
     ok &= vector_case< CppAD::vector<Key>,   std::vector<size_t> >();

     return ok;
}
Input File: example/index_sort.cpp cppad-20170000.3/doc/to_string.cpp.xml0000644000175200017650000004633513057470507016525 0ustar coincoin-web to_string: Example and Test
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to_string: Example and Test

// Examples with fundamental types
# include <cppad/utility/to_string.hpp>
namespace {
     template <class Integer>
     Integer string2int(const std::string& s)
     {     Integer result = 0;
          size_t index   = 0;
          if( s[0] == '-' )
               ++index;
          while( index < s.size() )
               result = 10 * result + Integer( s[index++] - '0');
          if( s[0] == '-' )
               return - result;
          return result;
     }
     template <class Integer>
     bool integer(void)
     {     bool ok = true;
          //
          Integer max    = std::numeric_limits<Integer>::max();
          std::string s  = CppAD::to_string(max);
          Integer check  = string2int<Integer>(s);
          ok            &= max == check;
          //
          Integer min       = std::numeric_limits<Integer>::min();
          s              = CppAD::to_string(min);
          check          = string2int<Integer>(s);
          ok            &= min == check;
          //
          return ok;
     }
     template <class Float>
     bool floating(void)
     {     bool  ok  = true;
          Float eps = std::numeric_limits<Float>::epsilon();
          Float pi  = 4.0 * std::atan(1.);
          //
          std::string s = CppAD::to_string( pi );
          Float check    = std::atof( s.c_str() );
          ok           &= std::fabs( check - pi ) <= 2.0 * eps;
          //
          return ok;
     }
}

// Examples with AD types
# include <cppad/cppad.hpp>
namespace {
     template <class Base>
     bool ad_floating(void)
     {     bool  ok  = true;
          Base eps = std::numeric_limits<Base>::epsilon();
          Base pi  = 4.0 * std::atan(1.);
          //
          std::string s = CppAD::to_string( CppAD::AD<Base>( pi ) );
          Base check    = std::atof( s.c_str() );
          ok           &= std::fabs( check - pi ) <= 2.0 * eps;
          //
          return ok;
     }
}

// Test driver
bool to_string(void)
{     bool ok = true;

     ok &= integer<unsigned short>();
     ok &= integer<signed int>();
     ok &= integer<unsigned long>();
# if CPPAD_USE_CPLUSPLUS_2011
     ok &= integer<signed long long>();
# endif
     //
     ok &= floating<float>();
     ok &= floating<double>();
     ok &= floating<long double>();
     //
     ok &= ad_floating<float>();
     ok &= ad_floating<double>();
     //
     return ok;
}
Input File: example/to_string.cpp cppad-20170000.3/doc/to_string.xml0000644000175200017650000002131313057470507015731 0ustar coincoin-web Convert Certain Types to a String
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Convert Certain Types to a String

Syntax
# include <cppad/utility/to_string.hpp>
 s = to_string(value) .

See Also
base_to_string , ad_to_string

Purpose
This routine is similar to the C++11 routine std::to_string with the following differences:
  1. It works with C++98.
  2. It has been extended to the fundamental floating point types.
  3. It has specifications for extending to an arbitrary type; see base_to_string .
  4. If <cppad/cppad.hpp> is included, and it has been extended to a Base type, it automatically extends to the AD types above Base .


value

Integer
The argument value can have the following prototype
     const Integer&  value
 where Integer is any of the fundamental integer types; e.g., short int and unsigned long. Note that if C++11 is supported by this compilation, unsigned long long is also a fundamental integer type.

Float
The argument value can have the following prototype
     const Float&  value
 where Float is any of the fundamental floating point types; i.e., float, double, and long double.

s
The return value has prototype
     std::string s
 and contains a representation of the specified value .

Integer
If value is an Integer , the representation is equivalent to os << value where os is an std::ostringstream.

Float
If value is a Float , enough digits are used in the representation so that the result is accurate to withing round off error.

Example
The file to_string.cpp contains an example and test of this routine. It returns true if it succeeds and false otherwise.
Input File: cppad/utility/to_string.hpp cppad-20170000.3/doc/set_union.xml0000644000175200017650000001406713057470507015734 0ustar coincoin-web Union of Standard Sets
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Union of Standard Sets

Syntax
result = set_union(left, right)

Purpose
This is a simplified (and restricted) interface to the std::union operation.

Element
This is the type of the elements of the sets.

left
This argument has prototype
     const std::set<Element>& left
right
This argument has prototype
     const std::set<Element>& right
result
The return value has prototype
     std::set<Element>& result
 It contains the union of left and right . Note that C++11 detects that the return value is a temporary and uses it for the result instead of making a separate copy.

Example
The file set_union.cpp contains an example and test of this operation. It returns true if the test passes and false otherwise.
Input File: cppad/utility/set_union.hpp cppad-20170000.3/doc/set_union.cpp.xml0000644000175200017650000001512413057470507016510 0ustar coincoin-web Set Union: Example and Test
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Set Union: Example and Test
# include <cppad/utility/set_union.hpp>

bool set_union(void)
{     bool ok = true;

     // create empty sets
     std::set<size_t> left, right, result;

     // set left = {1, 2}
     left.insert(1);
     left.insert(2);

     // set right = {2, 3}
     right.insert(2);
     right.insert(3);

     // set result = {1, 2} U {2, 3}
     result = CppAD::set_union(left, right);

     // expected result
     size_t check_vec[] = {1, 2, 3};
     std::set<size_t> check_set(check_vec, check_vec + 3);

     // check result
     ok &= result == check_set;

     return ok;
}
Input File: example/set_union.cpp cppad-20170000.3/doc/ipopt_solve.xml0000644000175200017650000011105013057470507016262 0ustar coincoin-web Use Ipopt to Solve a Nonlinear Programming Problem
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Use Ipopt to Solve a Nonlinear Programming Problem

Syntax
# include <cppad/ipopt/solve.hpp>
 ipopt::solve(
     options, xi, xl, xu, gl, gu, fg_eval, solution
)

Purpose
The function ipopt::solve solves nonlinear programming problems of the form minimize f ( x ) subject to gl ≤ g ( x ) ≤ gu xl ≤ x ≤ xu This is done using Ipopt optimizer and CppAD for the derivative and sparsity calculations.

Include File
Currently, this routine ipopt::solve is not included by the command
     # include <cppad/cppad.hpp>
 (Doing so would require the ipopt library to link the corresponding program (even if ipopt::solve) was not used.) For this reason, if you are using ipopt::solve you should use
     # include <cppad/ipopt/solve.hpp>
 which in turn will also include <cppad/cppad.hpp>.

Bvector
The type Bvector must be a SimpleVector class with elements of type bool.

Dvector
The type DVector must be a SimpleVector class with elements of type double.

options
The argument options has prototype
     const std::string options
 It contains a list of options. Each option, including the last option, is terminated by the '\n' character. Each line consists of two or three tokens separated by one or more spaces.

Retape
You can set the retape flag with the following syntax:
     Retape value
 If the value is true, ipopt::solve with retape the operation sequence for each new value of x . If the value is false, ipopt::solve will tape the operation sequence at the value of xi and use that sequence for the entire optimization process. The default value is false.

Sparse
You can set the sparse Jacobian and Hessian flag with the following syntax:
     Sparse value direction
 If the value is true, ipopt::solve will use a sparse matrix representation for the computation of Jacobians and Hessians. Otherwise, it will use a full matrix representation for these calculations. The default for value is false. If sparse is true, retape must be false.

It is unclear if sparse_jacobian would be faster user forward or reverse mode so you are able to choose the direction. If
     value == true && direction == forward
 the Jacobians will be calculated using SparseJacobianForward. If
     value == true && direction == reverse
 the Jacobians will be calculated using SparseJacobianReverse.

String
You can set any Ipopt string option using a line with the following syntax:
     String name value
 Here name is any valid Ipopt string option and value is its setting.

Numeric
You can set any Ipopt numeric option using a line with the following syntax:
     Numeric name value
 Here name is any valid Ipopt numeric option and value is its setting.

Integer
You can set any Ipopt integer option using a line with the following syntax:
     Integer name value
 Here name is any valid Ipopt integer option and value is its setting.

xi
The argument xi has prototype
     const Vector& xi
 and its size is equal to nx . It specifies the initial point where Ipopt starts the optimization process.

xl
The argument xl has prototype
     const Vector& xl
 and its size is equal to nx . It specifies the lower limits for the argument in the optimization problem.

xu
The argument xu has prototype
     const Vector& xu
 and its size is equal to nx . It specifies the upper limits for the argument in the optimization problem.

gl
The argument gl has prototype
     const Vector& gl
 and its size is equal to ng . It specifies the lower limits for the constraints in the optimization problem.

gu
The argument gu has prototype
     const Vector& gu
 and its size is equal to ng . It specifies the upper limits for the constraints in the optimization problem.

fg_eval
The argument fg_eval has prototype
     FG_eval fg_eval
 where the class FG_eval is unspecified except for the fact that it supports the syntax
     FG_eval::ADvector
     fg_eval(fg, x)
 The type ADvector and the arguments to fg , x have the following meaning:

ADvector
The type FG_eval::ADvector must be a SimpleVector class with elements of type AD<double>.

x
The fg_eval argument x has prototype
     const ADvector& x
 where nx = x.size() .

fg
The fg_eval argument fg has prototype
     ADvector& fg
 where 1 + ng = fg.size() . The input value of the elements of fg does not matter. Upon return from fg_eval ,
     fg[0] = f ( x )
and for i = 0 , … , ng -1 ,
     fg[1 + i] = g i ( x )

solution
The argument solution has prototype
     ipopt::solve_result<Dvector>& solution
 After the optimization process is completed, solution contains the following information:

status
The status field of solution has prototype
     ipopt::solve_result<Dvector>::status_type solution.status
 It is the final Ipopt status for the optimizer. Here is a list of the possible values for the status:
status Meaning
not_defined The optimizer did not return a final status for this problem.
unknown The status returned by the optimizer is not defined in the Ipopt documentation for finalize_solution.
success Algorithm terminated successfully at a point satisfying the convergence tolerances (see Ipopt options).
maxiter_exceeded The maximum number of iterations was exceeded (see Ipopt options).
stop_at_tiny_step Algorithm terminated because progress was very slow.
stop_at_acceptable_point Algorithm stopped at a point that was converged, not to the 'desired' tolerances, but to 'acceptable' tolerances (see Ipopt options).
local_infeasibility Algorithm converged to a non-feasible point (problem may have no solution).
user_requested_stop This return value should not happen.
diverging_iterates It the iterates are diverging.
restoration_failure Restoration phase failed, algorithm doesn't know how to proceed.
error_in_step_computation An unrecoverable error occurred while Ipopt tried to compute the search direction.
invalid_number_detected Algorithm received an invalid number (such as nan or inf) from the users function fg_info.eval or from the CppAD evaluations of its derivatives (see the Ipopt option check_derivatives_for_naninf).
internal_error An unknown Ipopt internal error occurred. Contact the Ipopt authors through the mailing list.

x
The x field of solution has prototype
     Vector solution.x
 and its size is equal to nx . It is the final x value for the optimizer.

zl
The zl field of solution has prototype
     Vector solution.zl
 and its size is equal to nx . It is the final Lagrange multipliers for the lower bounds on x .

zu
The zu field of solution has prototype
     Vector solution.zu
 and its size is equal to nx . It is the final Lagrange multipliers for the upper bounds on x .

g
The g field of solution has prototype
     Vector solution.g
 and its size is equal to ng . It is the final value for the constraint function g ( x ) .

lambda
The lambda field of solution has prototype
     Vector> solution.lambda
 and its size is equal to ng . It is the final value for the Lagrange multipliers corresponding to the constraint function.

obj_value
The obj_value field of solution has prototype
     double solution.obj_value
 It is the final value of the objective function f ( x ) .

Example
All the examples return true if it succeeds and false otherwise.

get_started
The file example/ipopt_solve/get_started.cpp is an example and test of ipopt::solve taken from the Ipopt manual.

retape
The file example/ipopt_solve/retape.cpp demonstrates when it is necessary to specify retape as true.

ode_inverse
The file example/ipopt_solve/ode_inverse.cpp demonstrates using Ipopt to solve for parameters in an ODE model.
Input File: cppad/ipopt/solve.hpp cppad-20170000.3/doc/ipopt_solve_retape.cpp.xml0000644000175200017650000004124213057470507020410 0ustar coincoin-web Nonlinear Programming Retaping: Example and Test
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Nonlinear Programming Retaping: Example and Test

Purpose
This example program demonstrates a case were the ipopt::solve argument retape should be true. 
# include <cppad/ipopt/solve.hpp>

namespace {
     using CppAD::AD;

     class FG_eval {
     public:
          typedef CPPAD_TESTVECTOR( AD<double> ) ADvector;
          void operator()(ADvector& fg, const ADvector& x)
          {     assert( fg.size() == 1 );
               assert( x.size()  == 1 );

               // compute the Huber function using a conditional
               // statement that depends on the value of x.
               double eps = 0.1;
               if( abs(x[0]) <= eps )
                    fg[0] = x[0] * x[0] / (2.0 * eps);
               else
                    fg[0] = abs(x[0]) - eps / 2.0;

               return;
          }
     };
}

bool retape(void)
{     bool ok = true;
     typedef CPPAD_TESTVECTOR( double ) Dvector;

     // number of independent variables (domain dimension for f and g)
     size_t nx = 1;
     // number of constraints (range dimension for g)
     size_t ng = 0;
     // initial value, lower and upper limits, for the independent variables
     Dvector xi(nx), xl(nx), xu(nx);
     xi[0] = 2.0;
     xl[0] = -1e+19;
     xu[0] = +1e+19;
     // lower and upper limits for g
     Dvector gl(ng), gu(ng);

     // object that computes objective and constraints
     FG_eval fg_eval;

     // options
     std::string options;
     // retape operation sequence for each new x
     options += "Retape  true\n";
     // turn off any printing
     options += "Integer print_level   0\n";
     options += "String  sb          yes\n";
     // maximum number of iterations
     options += "Integer max_iter      10\n";
     // approximate accuracy in first order necessary conditions;
     // see Mathematical Programming, Volume 106, Number 1,
     // Pages 25-57, Equation (6)
     options += "Numeric tol           1e-9\n";
     // derivative testing
     options += "String  derivative_test            second-order\n";
     // maximum amount of random pertubation; e.g.,
     // when evaluation finite diff
     options += "Numeric point_perturbation_radius  0.\n";

     // place to return solution
     CppAD::ipopt::solve_result<Dvector> solution;

     // solve the problem
     CppAD::ipopt::solve<Dvector, FG_eval>(
          options, xi, xl, xu, gl, gu, fg_eval, solution
     );
     //
     // Check some of the solution values
     //
     ok &= solution.status == CppAD::ipopt::solve_result<Dvector>::success;
     double rel_tol    = 1e-6;  // relative tolerance
     double abs_tol    = 1e-6;  // absolute tolerance
     ok &= CppAD::NearEqual( solution.x[0], 0.0,  rel_tol, abs_tol);

     return ok;
}
Input File: example/ipopt_solve/retape.cpp cppad-20170000.3/doc/_ipopt_solve_retape.cpp_xml.js0000644000175200017650000000275313057470507021247 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ipopt_solve.xml', 'ipopt_solve_retape.cpp.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'ipopt_solve_get_started.cpp.xml', 'ipopt_solve_retape.cpp.xml', 'ipopt_solve_ode_inverse.cpp.xml' ]; var list_current0 = [ 'ipopt_solve_retape.cpp.xml#Purpose' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/example.xml0000644000175200017650000000776613057470507015374 0ustar coincoin-web Examples
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Examples

Introduction
This section organizes the information related to the CppAD examples. Each CppAD operation has its own specific example, for example add.cpp is an example for addition . Some of the examples are of a more general nature (not connected of a specific feature of CppAD). In addition, there are some utility functions that are used by the examples.

Running Examples
The installation instructions show how the examples can be run on your system.

The CppAD Test Vector Template Class
Many of the examples use the CPPAD_TESTVECTOR preprocessor symbol to determine which SimpleVector template class is used with the examples.

Contents
Input File: omh/example.omh cppad-20170000.3/doc/_example_xml.js0000644000175200017650000000257113057470507016214 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'example.xml' ]; var list_down1 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down0 = [ 'general.xml', 'exampleutility.xml', 'listallexamples.xml', 'testvector.xml' ]; var list_current0 = [ 'example.xml#Introduction', 'example.xml#Running Examples', 'example.xml#The CppAD Test Vector Template Class', 'example.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/general.xml0000644000175200017650000001342613057470507015344 0ustar coincoin-web General Examples
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General Examples

Description
Most of the examples in CppAD are part of the documentation for a specific feature; for example, add.cpp is an example using the addition operator . The examples list in this section are of a more general nature.

Contents
ad_fun.cppCreating Your Own Interface to an ADFun Object
ad_in_c.cppExample and Test Linking CppAD to Languages Other than C++
conj_grad.cppDifferentiate Conjugate Gradient Algorithm: Example and Test
cppad_eigen.hppEnable Use of Eigen Linear Algebra Package with CppAD
hes_minor_det.cppGradient of Determinant Using Expansion by Minors: Example and Test
hes_lu_det.cppGradient of Determinant Using LU Factorization: Example and Test
interface2c.cppInterfacing to C: Example and Test
jac_minor_det.cppGradient of Determinant Using Expansion by Minors: Example and Test
jac_lu_det.cppGradient of Determinant Using Lu Factorization: Example and Test
mul_levelUsing Multiple Levels of AD
ode_stiff.cppA Stiff Ode: Example and Test
mul_level_ode.cppTaylor's Ode Solver: A Multi-Level AD Example and Test
mul_level_adolc_ode.cppTaylor's Ode Solver: A Multi-Level Adolc Example and Test
ode_taylor.cppTaylor's Ode Solver: An Example and Test
stack_machine.cppExample Differentiating a Stack Machine Interpreter
Input File: omh/example_list.omh cppad-20170000.3/doc/_general_xml.js0000644000175200017650000000346713057470507016203 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'example.xml', 'general.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'general.xml', 'exampleutility.xml', 'listallexamples.xml', 'testvector.xml' ]; var list_down0 = [ 'ad_fun.cpp.xml', 'ad_in_c.cpp.xml', 'conj_grad.cpp.xml', 'cppad_eigen.hpp.xml', 'hes_minor_det.cpp.xml', 'hes_lu_det.cpp.xml', 'interface2c.cpp.xml', 'jac_minor_det.cpp.xml', 'jac_lu_det.cpp.xml', 'mul_level.xml', 'ode_stiff.cpp.xml', 'mul_level_ode.cpp.xml', 'mul_level_adolc_ode.cpp.xml', 'ode_taylor.cpp.xml', 'stack_machine.cpp.xml' ]; var list_current0 = [ 'general.xml#Description', 'general.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/example.cpp.xml0000644000175200017650000031250713057470507016145 0ustar coincoin-web CppAD Examples and Tests
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CppAD Examples and Tests

Running Tests
To build this program and run its correctness tests see cmake_check . 

// system include files used for I/O
# include <iostream>

// C style asserts
# include <cassert>

// standard string
# include <string>

// memory utility
# include <cppad/utility/thread_alloc.hpp>

// prototype external compiled tests (this line expected by bin/new_test.sh)
extern bool abort_recording(void);
extern bool abs(void);
extern bool acosh(void);
extern bool acos(void);
extern bool ad_assign(void);
extern bool ad_ctor(void);
extern bool AddEq(void);
extern bool Add(void);
extern bool ad_fun(void);
extern bool ad_in_c(void);
extern bool ad_input(void);
extern bool ad_output(void);
extern bool asinh(void);
extern bool asin(void);
extern bool atan2(void);
extern bool atanh(void);
extern bool atan(void);
extern bool azmul(void);
extern bool base_require(void);
extern bool BenderQuad(void);
extern bool BoolFun(void);
extern bool bool_sparsity(void);
extern bool capacity_order(void);
extern bool change_param(void);
extern bool check_for_nan(void);
extern bool CheckNumericType(void);
extern bool CheckSimpleVector(void);
extern bool colpack_hes(void);
extern bool colpack_jac(void);
extern bool compare_change(void);
extern bool Compare(void);
extern bool complex_poly(void);
extern bool CondExp(void);
extern bool conj_grad(void);
extern bool Cosh(void);
extern bool Cos(void);
extern bool CppAD_vector(void);
extern bool dependency(void);
extern bool DivEq(void);
extern bool Div(void);
extern bool eigen_array(void);
extern bool eigen_det(void);
extern bool EqualOpSeq(void);
extern bool Erf(void);
extern bool ErrorHandler(void);
extern bool expm1(void);
extern bool exp(void);
extern bool ForOne(void);
extern bool for_sparse_hes(void);
extern bool ForSparseJac(void);
extern bool ForTwo(void);
extern bool forward_dir(void);
extern bool forward_order(void);
extern bool Forward(void);
extern bool fun_assign(void);
extern bool FunCheck(void);
extern bool HesLagrangian(void);
extern bool HesLuDet(void);
extern bool HesMinorDet(void);
extern bool Hessian(void);
extern bool HesTimesDir(void);
extern bool Independent(void);
extern bool index_sort(void);
extern bool Integer(void);
extern bool Interface2C(void);
extern bool interp_onetape(void);
extern bool interp_retape(void);
extern bool JacLuDet(void);
extern bool JacMinorDet(void);
extern bool Jacobian(void);
extern bool log10(void);
extern bool log1p(void);
extern bool log(void);
extern bool LuFactor(void);
extern bool LuInvert(void);
extern bool LuRatio(void);
extern bool LuSolve(void);
extern bool LuVecADOk(void);
extern bool MulEq(void);
extern bool mul_level_adolc_ode(void);
extern bool mul_level_adolc(void);
extern bool mul_level_ode(void);
extern bool mul_level(void);
extern bool Mul(void);
extern bool nan(void);
extern bool NearEqualExt(void);
extern bool Near_Equal(void);
extern bool number_skip(void);
extern bool NumericType(void);
extern bool num_limits(void);
extern bool OdeErrControl(void);
extern bool OdeErrMaxabs(void);
extern bool OdeGearControl(void);
extern bool OdeGear(void);
extern bool OdeStiff(void);
extern bool ode_taylor(void);
extern bool opt_val_hes(void);
extern bool ParVar(void);
extern bool Poly(void);
extern bool pow_int(void);
extern bool pow(void);
extern bool print_for(void);
extern bool reverse_any(void);
extern bool reverse_one(void);
extern bool reverse_three(void);
extern bool reverse_two(void);
extern bool RevOne(void);
extern bool rev_sparse_hes(void);
extern bool RevSparseJac(void);
extern bool RevTwo(void);
extern bool RombergMul(void);
extern bool RombergOne(void);
extern bool Rosen34(void);
extern bool runge_45_1(void);
extern bool runge_45_2(void);
extern bool seq_property(void);
extern bool set_union(void);
extern bool sign(void);
extern bool SimpleVector(void);
extern bool Sinh(void);
extern bool Sin(void);
extern bool sparse_hessian(void);
extern bool sparse_jacobian(void);
extern bool sparse_sub_hes(void);
extern bool sparsity_sub(void);
extern bool Sqrt(void);
extern bool StackMachine(void);
extern bool SubEq(void);
extern bool sub_sparse_hes(void);
extern bool Sub(void);
extern bool Tanh(void);
extern bool Tan(void);
extern bool TapeIndex(void);
extern bool thread_alloc(void);
extern bool to_string(void);
extern bool UnaryMinus(void);
extern bool UnaryPlus(void);
extern bool Value(void);
extern bool Var2Par(void);
extern bool vec_ad(void);
extern bool vectorBool(void);

namespace {
     // function that runs one test
     static size_t Run_ok_count    = 0;
     static size_t Run_error_count = 0;
     bool Run(bool TestOk(void), std::string name)
     {     bool ok      = true;
          std::streamsize width =  20;
          std::cout.width( width );
          std::cout.setf( std::ios_base::left );
          std::cout << name;
          //
          ok &= name.size() < size_t(width);
          ok &= TestOk();
          if( ok )
          {     std::cout << "OK" << std::endl;
               Run_ok_count++;
          }
          else
          {     std::cout << "Error" << std::endl;
               Run_error_count++;
          }
          return ok;
     }
}

// main program that runs all the tests
int main(void)
{     bool ok = true;

     // This line is used by test_one.sh

     // run external compiled tests (this line expected by bin/new_test.sh)
     ok &= Run( abort_recording,   "abort_recording"  );
     ok &= Run( abs,               "abs"              );
     ok &= Run( acos,              "acos"             );
     ok &= Run( acosh,             "acosh"            );
     ok &= Run( ad_assign,         "ad_assign"        );
     ok &= Run( ad_ctor,           "ad_ctor"          );
     ok &= Run( Add,               "Add"              );
     ok &= Run( AddEq,             "AddEq"            );
     ok &= Run( ad_fun,            "ad_fun"           );
     ok &= Run( ad_in_c,           "ad_in_c"          );
     ok &= Run( ad_input,          "ad_input"         );
     ok &= Run( ad_output,         "ad_output"        );
     ok &= Run( asin,              "asin"             );
     ok &= Run( asinh,             "asinh"            );
     ok &= Run( atan2,             "atan2"            );
     ok &= Run( atan,              "atan"             );
     ok &= Run( atanh,             "atanh"            );
     ok &= Run( azmul,             "azmul"            );
     ok &= Run( BenderQuad,        "BenderQuad"       );
     ok &= Run( BoolFun,           "BoolFun"          );
     ok &= Run( bool_sparsity,     "bool_sparsity"    );
     ok &= Run( capacity_order,    "capacity_order"   );
     ok &= Run( change_param,      "change_param"     );
     ok &= Run( check_for_nan,     "check_for_nan"    );
     ok &= Run( CheckNumericType,  "CheckNumericType" );
     ok &= Run( CheckSimpleVector, "CheckSimpleVector");
     ok &= Run( compare_change,    "compare_change"   );
     ok &= Run( Compare,           "Compare"          );
     ok &= Run( complex_poly,      "complex_poly"     );
     ok &= Run( CondExp,           "CondExp"          );
     ok &= Run( conj_grad,         "conj_grad"        );
     ok &= Run( Cos,               "Cos"              );
     ok &= Run( Cosh,              "Cosh"             );
     ok &= Run( CppAD_vector,      "CppAD_vector"     );
     ok &= Run( dependency,        "dependency"       );
     ok &= Run( Div,               "Div"              );
     ok &= Run( DivEq,             "DivEq"            );
     ok &= Run( EqualOpSeq,        "EqualOpSeq"       );
     ok &= Run( Erf,               "Erf"              );
     ok &= Run( ErrorHandler,      "ErrorHandler"     );
     ok &= Run( exp,               "exp"              );
     ok &= Run( expm1,             "expm1"            );
     ok &= Run( ForOne,            "ForOne"           );
     ok &= Run( for_sparse_hes,    "for_sparse_hes"   );
     ok &= Run( ForSparseJac,      "ForSparseJac"     );
     ok &= Run( ForTwo,            "ForTwo"           );
     ok &= Run( forward_dir,       "forward_dir"      );
     ok &= Run( Forward,           "Forward"          );
     ok &= Run( forward_order,     "forward_order"    );
     ok &= Run( fun_assign,        "fun_assign"       );
     ok &= Run( FunCheck,          "FunCheck"         );
     ok &= Run( HesLagrangian,     "HesLagrangian"    );
     ok &= Run( HesLuDet,          "HesLuDet"         );
     ok &= Run( HesMinorDet,       "HesMinorDet"      );
     ok &= Run( Hessian,           "Hessian"          );
     ok &= Run( HesTimesDir,       "HesTimesDir"      );
     ok &= Run( Independent,       "Independent"      );
     ok &= Run( index_sort,        "index_sort"       );
     ok &= Run( Integer,           "Integer"          );
     ok &= Run( Interface2C,       "Interface2C"      );
     ok &= Run( interp_onetape,    "interp_onetape"   );
     ok &= Run( interp_retape,     "interp_retape"    );
     ok &= Run( JacLuDet,          "JacLuDet"         );
     ok &= Run( JacMinorDet,       "JacMinorDet"      );
     ok &= Run( Jacobian,          "Jacobian"         );
     ok &= Run( log10,             "log10"            );
     ok &= Run( log1p,             "log1p"            );
     ok &= Run( log,               "log"              );
     ok &= Run( LuFactor,          "LuFactor"         );
     ok &= Run( LuInvert,          "LuInvert"         );
     ok &= Run( LuRatio,           "LuRatio"          );
     ok &= Run( LuSolve,           "LuSolve"          );
     ok &= Run( LuVecADOk,         "LuVecADOk"        );
     ok &= Run( MulEq,             "MulEq"            );
     ok &= Run( mul_level,         "mul_level"        );
     ok &= Run( mul_level_ode,     "mul_level_ode"    );
     ok &= Run( Mul,               "Mul"              );
     ok &= Run( nan,               "nan"              );
     ok &= Run( NearEqualExt,      "NearEqualExt"     );
     ok &= Run( Near_Equal,        "Near_Equal"       );
     ok &= Run( number_skip,       "number_skip"      );
     ok &= Run( NumericType,       "NumericType"      );
     ok &= Run( num_limits,        "num_limits"       );
     ok &= Run( OdeErrControl,     "OdeErrControl"    );
     ok &= Run( OdeErrMaxabs,      "OdeErrMaxabs"     );
     ok &= Run( OdeGearControl,    "OdeGearControl"   );
     ok &= Run( OdeGear,           "OdeGear"          );
     ok &= Run( OdeStiff,          "OdeStiff"         );
     ok &= Run( ode_taylor,        "ode_taylor"       );
     ok &= Run( opt_val_hes,       "opt_val_hes"      );
     ok &= Run( ParVar,            "ParVar"           );
     ok &= Run( Poly,              "Poly"             );
     ok &= Run( pow_int,           "pow_int"          );
     ok &= Run( pow,               "pow"              );
     ok &= Run( reverse_any,       "reverse_any"      );
     ok &= Run( reverse_one,       "reverse_one"      );
     ok &= Run( reverse_three,     "reverse_three"    );
     ok &= Run( reverse_two,       "reverse_two"      );
     ok &= Run( RevOne,            "RevOne"           );
     ok &= Run( rev_sparse_hes,    "rev_sparse_hes"   );
     ok &= Run( RevSparseJac,      "RevSparseJac"     );
     ok &= Run( RevTwo,            "RevTwo"           );
     ok &= Run( RombergMul,        "RombergMul"       );
     ok &= Run( RombergOne,        "RombergOne"       );
     ok &= Run( Rosen34,           "Rosen34"          );
     ok &= Run( runge_45_1,        "runge_45_1"       );
     ok &= Run( runge_45_2,        "runge_45_2"       );
     ok &= Run( seq_property,      "seq_property"     );
     ok &= Run( set_union,         "set_union"        );
     ok &= Run( sign,              "sign"             );
     ok &= Run( SimpleVector,      "SimpleVector"     );
     ok &= Run( Sinh,              "Sinh"             );
     ok &= Run( Sin,               "Sin"              );
     ok &= Run( sparse_hessian,    "sparse_hessian"   );
     ok &= Run( sparse_jacobian,   "sparse_jacobian"  );
     ok &= Run( sparse_sub_hes,    "sparse_sub_hes"   );
     ok &= Run( sparsity_sub,      "sparsity_sub"     );
     ok &= Run( Sqrt,              "Sqrt"             );
     ok &= Run( StackMachine,      "StackMachine"     );
     ok &= Run( SubEq,             "SubEq"            );
     ok &= Run( sub_sparse_hes,    "sub_sparse_hes"   );
     ok &= Run( Sub,               "Sub"              );
     ok &= Run( Tanh,              "Tanh"             );
     ok &= Run( Tan,               "Tan"              );
     ok &= Run( TapeIndex,         "TapeIndex"        );
     ok &= Run( thread_alloc,      "thread_alloc"     );
     ok &= Run( to_string,         "to_string"        );
     ok &= Run( UnaryMinus,        "UnaryMinus"       );
     ok &= Run( UnaryPlus,         "UnaryPlus"        );
     ok &= Run( Value,             "Value"            );
     ok &= Run( Var2Par,           "Var2Par"          );
     ok &= Run( vec_ad,            "vec_ad"           );
     ok &= Run( vectorBool,        "vectorBool"       );
# ifdef CPPAD_HAS_ADOLC
     ok &= Run( mul_level_adolc,      "mul_level_adolc"     );
     ok &= Run( mul_level_adolc_ode,  "mul_level_adolc_ode" );
# endif
# ifdef CPPAD_COLPACK_EXAMPLES
     ok &= Run( colpack_hes,       "colpack_hes"      );
     ok &= Run( colpack_jac,       "colpack_jac"      );
# endif
# ifdef CPPAD_HAS_EIGEN
     ok &= Run( eigen_array,       "eigen_array"      );
     ok &= Run( eigen_det,         "eigen_det"        );
# endif

     // check for errors
     using std::cout;
     using std::endl;
     assert( ok || (Run_error_count > 0) );
     if( CppAD::thread_alloc::free_all() )
     {     Run_ok_count++;
          cout << "OK:    " << "No memory leak detected" << endl;
     }
     else
     {     ok = false;
          Run_error_count++;
          cout << "Error: " << "memory leak detected" << endl;
     }
     // Run base_require after memory leak check because base_alloc.hpp uses
     // thread_alloc to allocate memory for static copies of nan.
     ok &= Run( base_require,      "base_require"     );
     // convert int(size_t) to avoid warning on _MSC_VER systems
     if( ok )
          cout << "All " << int(Run_ok_count) << " tests passed." << endl;
     else     cout << int(Run_error_count) << " tests failed." << endl;

     return static_cast<int>( ! ok );
}
Input File: example/example.cpp cppad-20170000.3/doc/testvector.xml0000644000175200017650000002250713057470507016131 0ustar coincoin-web Using The CppAD Test Vector Template Class
Prev Next testvector

Using The CppAD Test Vector Template Class

Syntax
CPPAD_TESTVECTOR(Scalar)
Introduction
Many of the CppAD examples and tests use the CPPAD_TESTVECTOR template class to pass information to CppAD. This is not a true template class because it's syntax uses (Scalar) instead of <Scalar> . This enables us to use
     Eigen::Matrix<Scalar, Eigen::Dynamic, 1>
 as one of the possible cases for this 'template class'.

CppAD::vector
If in the cmake command you specify cppad_testvector to be cppad, CPPAD_CPPADVECTOR will be true. In this case, CPPAD_TESTVECTOR is defined by the following source code: 

# if CPPAD_CPPADVECTOR
# define CPPAD_TESTVECTOR(Scalar) CppAD::vector< Scalar >
# endif
In this case CppAD will use its own vector for many of its examples and tests.

std::vector
If in the cmake command you specify cppad_testvector to be std, CPPAD_STDVECTOR will be true. In this case, CPPAD_TESTVECTOR is defined by the following source code: 
# if CPPAD_STDVECTOR
# include <vector>
# define CPPAD_TESTVECTOR(Scalar) std::vector< Scalar >
# endif
In this case CppAD will use standard vector for many of its examples and tests.

boost::numeric::ublas::vector
If in the cmake command you specify cppad_testvector to be boost, CPPAD_BOOSTVECTOR will be true. In this case, CPPAD_TESTVECTOR is defined by the following source code: 
# if CPPAD_BOOSTVECTOR
# include <boost/numeric/ublas/vector.hpp>
# define CPPAD_TESTVECTOR(Scalar) boost::numeric::ublas::vector< Scalar >
# endif
In this case CppAD will use this boost vector for many of its examples and tests.

Eigen Vectors
If in the cmake command you specify cppad_testvector to be eigen, CPPAD_EIGENVECTOR will be true. In this case, CPPAD_TESTVECTOR is defined by the following source code: 
# if CPPAD_EIGENVECTOR
# include <cppad/example/cppad_eigen.hpp>
# define CPPAD_TESTVECTOR(Scalar) Eigen::Matrix< Scalar , Eigen::Dynamic, 1>
# endif
In this case CppAD will use the Eigen vector for many of its examples and tests.
Input File: cppad/core/testvector.hpp cppad-20170000.3/doc/_speed_xml.js0000644000175200017650000000252513057470507015660 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml' ]; var list_down1 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down0 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_current0 = [ 'speed.xml#Purpose', 'speed.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/ad_in_c.cpp.xml0000644000175200017650000025603313057470507016067 0ustar coincoin-web Example and Test Linking CppAD to Languages Other than C++
Prev Next ad_in_c.cpp Headings

Example and Test Linking CppAD to Languages Other than C++
# include <cstdio>
# include <cppad/cppad.hpp>
# include <list>

namespace { // Begin empty namespace *****************************************

/*
void debug_print(const char *label, double d)
{     using std::printf;

     unsigned char *byte = reinterpret_cast<unsigned char *>(&d);
     size_t n_byte = sizeof(d);
     printf("%s", label);
     for(size_t i = 0; i < n_byte; i++)
          printf("%x", byte[i]);
     printf("\n");
}
*/

// type in C corresponding to an AD<double> object
typedef struct { void*  p_void; } cad;

// type in C corresponding to a an ADFun<double>
typedef struct { void* p_void; } cad_fun;

// type in C corresponding to a C AD binary operator
typedef enum { op_add, op_sub, op_mul, op_div } cad_binary_op;

// type in C corresponding to a C AD unary operator
typedef enum {
     op_abs, op_acos, op_asin, op_atan, op_cos, op_cosh,
     op_exp, op_log,  op_sin,  op_sinh, op_sqrt
} cad_unary_op;

// --------------------------------------------------------------------------
// helper code not intended for use by C code  ------------------------------
using CppAD::AD;
using CppAD::ADFun;
using CppAD::vector;
using CppAD::NearEqual;

void cad2vector(size_t n, cad* p_cad, vector< AD<double> >& v)
{     assert( n == v.size() );
     for(size_t j = 0; j < n; j++)
     {     AD<double>* p_ad =
               reinterpret_cast< AD<double>* > (p_cad[j].p_void);
          v[j] = *p_ad;
     }
}

void vector2cad(size_t n, vector< AD<double> >& v, cad* p_cad)
{     assert( n == v.size() );
     for(size_t j = 0; j < n; j++)
     {     AD<double>* p_ad =
               reinterpret_cast< AD<double>* > (p_cad[j].p_void);
          *p_ad = v[j];
     }
}

void double2vector(size_t n, double* p_dbl, vector<double>& v)
{     assert( n == v.size() );
     for(size_t j = 0; j < n; j++)
          v[j] = p_dbl[j];
}

void vector2double(size_t n, vector<double>& v, double *p_dbl)
{     assert( n == v.size() );
     for(size_t j = 0; j < n; j++)
          p_dbl[j] = v[j];
}

std::list<void*> allocated;
# ifdef NDEBUG
inline void push_allocated(void *p)
{ }
inline void pop_allocated(void *p)
{ }
# else
inline void push_allocated(void *p)
{     assert( p != 0 );
     allocated.push_front(p);
}
inline void pop_allocated(void *p)
{     std::list<void*>::iterator i;
     for(i = allocated.begin(); i != allocated.end(); ++i)
     {     if( *i == p )
          {     allocated.erase(i);
               return;
          }
     }
     assert( 0 );
}

# endif
// --------------------------------------------------------------------------
// Here is the code that links C to CppAD. You will have to add more
// functions and operators to make a complete language link.
//
extern "C"
bool cad_near_equal(double x, double y)
{     double eps = 10. * std::numeric_limits<double>::epsilon();
     return NearEqual(x, y, eps, 0.);
}

// create a C++ AD object
// value is the value that the C++ AD object will have
// p_cad->p_void: on input is 0, on output points to C++ AD object
extern "C"
void cad_new_ad(cad *p_cad, double value)
{     // make sure pointer is not currently allocated
     assert( p_cad->p_void == 0 );

     AD<double>* p_ad   = new AD<double>(value);
     p_cad->p_void      = reinterpret_cast<void*>(p_ad);

     // put in list of allocate pointers
     push_allocated( p_cad->p_void );
}

// delete a C++ AD object
// p_cad->value: not used
// p_cad->p_void: on input points to C++ AD object, on output is 0
extern "C"
void cad_del_ad(cad* p_cad)
{     // make sure that p_cad has been allocated
     pop_allocated( p_cad->p_void );

     AD<double>* p_ad   = reinterpret_cast< AD<double>* >( p_cad->p_void );
     delete p_ad;

     // special value for pointers that are not allocated
     p_cad->p_void = 0;
}

// extract the value from a C++ AD object
// extern "C"
double cad_value(cad* p_cad)
{     AD<double>* p_ad = reinterpret_cast< AD<double>* > (p_cad->p_void);
     return Value( Var2Par(*p_ad) );
}

// preform a C AD unary operation
extern "C"
void cad_unary(cad_unary_op op, cad* p_operand, cad* p_result)
{     AD<double> *operand, *result;
     result  = reinterpret_cast< AD<double>* > (p_result->p_void);
     operand = reinterpret_cast< AD<double>* > (p_operand->p_void);
     switch(op)
     {
          case op_abs:
          *result = abs( *operand );
          break;

          case op_acos:
          *result = acos( *operand );
          break;

          case op_asin:
          *result = asin( *operand );
          break;

          case op_atan:
          *result = atan( *operand );
          break;

          case op_cos:
          *result = cos( *operand );
          break;

          case op_cosh:
          *result = cosh( *operand );
          break;

          case op_exp:
          *result = exp( *operand );
          break;

          case op_log:
          *result = log( *operand );
          break;

          case op_sin:
          *result = sin( *operand );
          break;

          case op_sinh:
          *result = sinh( *operand );
          break;

          case op_sqrt:
          *result = sqrt( *operand );
          break;

          default:
          // not a unary operator
          assert(0);
          break;

     }
     return;
}

// perform a C AD binary operation
extern "C"
void cad_binary(cad_binary_op op, cad* p_left, cad* p_right, cad* p_result)
{     AD<double> *result, *left, *right;
     result = reinterpret_cast< AD<double>* > (p_result->p_void);
     left   = reinterpret_cast< AD<double>* > (p_left->p_void);
     right  = reinterpret_cast< AD<double>* > (p_right->p_void);
     assert( result != 0 );
     assert( left != 0 );
     assert( right != 0 );

     switch(op)
     {     case op_add:
          *result         = *left + (*right);
          break;

          case op_sub:
          *result         = *left - (*right);
          break;

          case op_mul:
          *result         = *left * (*right);
          break;

          case op_div:
          *result         = *left / (*right);
          break;

          default:
          // not a binary operator
          assert(0);
     }
     return;
}

// declare the independent variables in C++
extern "C"
void cad_independent(size_t n, cad* px_cad)
{     vector< AD<double> > x(n);
     cad2vector(n, px_cad, x);
     CppAD::Independent(x);
     vector2cad(n, x, px_cad);
}

// create an ADFun object in C++
extern "C"
cad_fun cad_new_fun(size_t n, size_t m, cad* px_cad, cad* py_cad)
{     cad_fun fun;

     ADFun<double>* p_adfun = new ADFun<double>;
     vector< AD<double> > x(n);
     vector< AD<double> > y(m);
     cad2vector(n, px_cad, x);
     cad2vector(m, py_cad, y);
     p_adfun->Dependent(x, y);

     fun.p_void = reinterpret_cast<void*>( p_adfun );

     // put in list of allocate pointers
     push_allocated( fun.p_void );

     return fun;
}

// delete an AD function object in C
extern "C"
void cad_del_fun(cad_fun *fun)
{     // make sure this pointer has been allocated
     pop_allocated( fun->p_void );

     ADFun<double>* p_adfun
          = reinterpret_cast< ADFun<double>* > (fun->p_void);
     delete p_adfun;

     // special value for pointers that are not allocated
     fun->p_void = 0;
}

// evaluate the Jacobian corresponding to a function object
extern "C"
void cad_jacobian(cad_fun fun,
     size_t n, size_t m, double* px, double* pjac )
{     assert( fun.p_void != 0 );

     ADFun<double>* p_adfun =
          reinterpret_cast< ADFun<double>* >(fun.p_void);
     vector<double> x(n), jac(n * m);

     double2vector(n, px, x);
     jac = p_adfun->Jacobian(x);
     vector2double(n * m, jac, pjac);
}

// forward mode
extern "C"
void cad_forward(cad_fun fun,
     size_t order, size_t n, size_t m, double* px, double* py )
{     assert( fun.p_void != 0 );

     ADFun<double>* p_adfun =
          reinterpret_cast< ADFun<double>* >(fun.p_void);
     vector<double> x(n), y(m);

     double2vector(n, px, x);
     y = p_adfun->Forward(order, x);
     vector2double(m, y, py);
}

// check that allocated list has been completely freed
extern "C"
bool cad_allocated_empty(void)
{     return allocated.empty();
}

} // End empty namespace ****************************************************

# include <math.h> // used to check results in c code below

# define N 2       // number of independent variables in example
# define M 5       // number of dependent variables in example

// -------------------------------------------------------------------------
// Here is the C code that uses the CppAD link above
bool ad_in_c(void)
{     // This routine is intentionally coded as if it were written in C
     // as an example of how you can link C, and other languages to CppAD
     bool ok = true;

     // x vector of AD objects in C
     double value;
     size_t j, n = N;
     cad X[N];
     for(j = 0; j < n; j++)
     {     value       = (double) (j+1) / (double) n;
          X[j].p_void = 0;
          cad_new_ad(X + j, value);
     }

     // y vector of AD objects in C
     size_t i, m = M;
     cad Y[M];
     for(i = 0; i < m; i++)
     {     value       = 0.; // required, but not used
          Y[i].p_void = 0;
          cad_new_ad(Y + i, value);
     }

     // declare X as the independent variable vector
     cad_independent(n, X);

     // y[0] = x[0] + x[1]
     cad_binary(op_add, X+0, X+1, Y+0);
     ok &= cad_near_equal( cad_value(Y+0), cad_value(X+0)+cad_value(X+1) );

     // y[1] = x[0] - x[1]
     cad_binary(op_sub, X+0, X+1, Y+1);
     ok &= cad_near_equal( cad_value(Y+1), cad_value(X+0)-cad_value(X+1) );

     // y[2] = x[0] * x[1]
     cad_binary(op_mul, X+0, X+1, Y+2);
     ok &= cad_near_equal( cad_value(Y+2), cad_value(X+0)*cad_value(X+1) );

     // y[3] = x[0] * x[1]
     cad_binary(op_div, X+0, X+1, Y+3);
     ok &= cad_near_equal( cad_value(Y+3), cad_value(X+0)/cad_value(X+1) );

     // y[4] = sin(x[0]) + asin(sin(x[0]))
     cad sin_x0 = { 0 };       // initialize p_void as zero
     cad_new_ad( &sin_x0, 0.);
     cad_unary(op_sin, X+0, &sin_x0);
     ok &= cad_near_equal(cad_value(&sin_x0), sin(cad_value(X+0)) );

     cad asin_sin_x0 = { 0 };  // initialize p_void as zero
     cad_new_ad( &asin_sin_x0, 0.);
     cad_unary(op_asin, &sin_x0, &asin_sin_x0);
     ok &= cad_near_equal(
          cad_value(&asin_sin_x0),
          asin( cad_value(&sin_x0) )
     );

     cad_binary(op_add, &sin_x0, &asin_sin_x0, Y+4);
     ok &= cad_near_equal(
          cad_value(Y+4),
          cad_value(&sin_x0) + cad_value(&asin_sin_x0)
     );

     // declare y as the dependent variable vector and stop recording
     // and store function object in f
     cad_fun f = cad_new_fun(n, m, X, Y);

     // now use the function object
     double x[N], jac[N * M];
     x[0] = 1.;
     x[1] = .5;

     // compute the Jacobian
     cad_jacobian(f, n, m, x, jac);

     // check the Jacobian values
     size_t k = 0;
     // partial y[0] w.r.t. x[0]
     ok &= cad_near_equal(jac[k++], 1.);
     // partial y[0] w.r.t. x[1]
     ok &= cad_near_equal(jac[k++], 1.);
     // partial y[1] w.r.t. x[0]
     ok &= cad_near_equal(jac[k++], 1.);
     // partial y[1] w.r.t. x[1]
     ok &= cad_near_equal(jac[k++], -1.);
     // partial y[2] w.r.t. x[0]
     ok &= cad_near_equal(jac[k++], x[1]);
     // partial y[2] w.r.t. x[1]
     ok &= cad_near_equal(jac[k++], x[0]);
     // partial y[3] w.r.t. x[0]
     ok &= cad_near_equal(jac[k++], 1./x[1]);
     // partial y[3] w.r.t. x[1]
     ok &= cad_near_equal(jac[k++], -x[0]/(x[1]*x[1]));
     // partial y[4] w.r.t x[0]
     ok &= cad_near_equal(jac[k++],  cos(x[0]) + 1.);
     // partial y[4] w.r.t x[1]
     ok &= cad_near_equal(jac[k++],  0.);

     // evaluate the function f at a different x
     size_t order = 0;
     double y[M];
     x[0] = .5;
     x[1] = 1.;
     cad_forward(f, order, n, m, x, y);

     // check the function values
     ok &= cad_near_equal(y[0] , x[0] + x[1] );
     ok &= cad_near_equal(y[1] , x[0] - x[1] );
     ok &= cad_near_equal(y[2] , x[0] * x[1] );
     ok &= cad_near_equal(y[3] , x[0] / x[1] );
     ok &= cad_near_equal(y[4] , sin(x[0]) + asin(sin(x[0])) );

     // delete All C++ copies of the AD objects
     cad_del_fun( &f );
     cad_del_ad( &sin_x0 );
     cad_del_ad( &asin_sin_x0 );
     for(j = 0; j < n; j++)
          cad_del_ad(X + j);
     for(i = 0; i < m; i++)
          cad_del_ad(Y + i);

     ok     &= cad_allocated_empty();
     return ok;
}
Input File: example/ad_in_c.cpp cppad-20170000.3/doc/conj_grad.cpp.xml0000644000175200017650000014405313057470507016437 0ustar coincoin-web Differentiate Conjugate Gradient Algorithm: Example and Test
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Differentiate Conjugate Gradient Algorithm: Example and Test

Purpose
The conjugate gradient algorithm is sparse linear solver and a good example where checkpointing can be applied (for each iteration). This example is a preliminary version of a new library routine for the conjugate gradient algorithm.

Algorithm
Given a positive definite matrix A ∈ R n × n , a vector b ∈ R n , and tolerance ε , the conjugate gradient algorithm finds an x ∈ R n such that ‖ A x - b ‖ 2 / n ≤ ε 2 (or it terminates at a specified maximum number of iterations).
  1. Input:
    The matrix A ∈ R n × n , the vector b ∈ R n , a tolerance ε ≥ 0 , a maximum number of iterations m , and the initial approximate solution x 0 ∈ R n (can use zero for x 0 ).
  2. Initialize:
    g 0 = A * x 0 - b , d 0 = - g 0 , s 0 = ( g 0 ) T g 0 , k = 0 .
  3. Convergence Check:
    if k = m or s k / n < ε , return k as the number of iterations and x k as the approximate solution.
  4. Next x :
    μ k + 1 = s k / [ ( d k ) T A d k ] , x k + 1 = x k + μ k + 1 d k .
  5. Next g :
    g k + 1 = g k + μ k + 1 A d k , s k + 1 = ( g k + 1 ) T g k + 1 .
  6. Next d :
    d k + 1 = - g k + ( s k + 1 / s k ) d k .
  7. Iterate:
    k = k + 1 , goto Convergence Check. 
# include <cppad/cppad.hpp>
# include <cstdlib>
# include <cmath>

namespace { // Begin empty namespace
     using CppAD::AD;

     // A simple matrix multiply c = a * b , where a has n columns
     // and b has n rows. This should be changed to a function so that
     // it can efficiently handle the case were A is large and sparse.
     template <class Vector> // a simple vector class
     void mat_mul(size_t n, const Vector& a, const Vector& b, Vector& c)
     {     typedef typename Vector::value_type scalar;

          size_t m, p;
          m = a.size() / n;
          p = b.size() / n;

          assert( m * n == a.size() );
          assert( n * p == b.size() );
          assert( m * p == c.size() );

          size_t i, j, k, ij;
          for(i = 0; i < m; i++)
          {     for(j = 0; j < p; j++)
               {     ij    = i * p + j;
                    c[ij] = scalar(0);
                    for(k = 0; k < n; k++)
                         c[ij] = c[ij] + a[i * m + k] * b[k * p + j];
               }
          }
          return;
     }

     // Solve A * x == b to tolerance epsilon or terminate at m interations.
     template <class Vector> // a simple vector class
     size_t conjugate_gradient(
          size_t         m       , // input
          double         epsilon , // input
          const Vector&  A       , // input
          const Vector&  b       , // input
          Vector&        x       ) // input / output
     {     typedef typename Vector::value_type scalar;
          scalar mu, s_previous;
          size_t i, k;

          size_t n = x.size();
          assert( A.size() == n * n );
          assert( b.size() == n );

          Vector g(n), d(n), s(1), Ad(n), dAd(1);

          // g = A * x
          mat_mul(n, A, x, g);
          for(i = 0; i < n; i++)
          {     // g = A * x - b
               g[i] = g[i] - b[i];

               // d = - g
               d[i] = -g[i];
          }
          // s = g^T * g
          mat_mul(n, g, g, s);

          for(k = 0; k < m; k++)
          {     s_previous = s[0];
               if( s_previous < epsilon )
                    return k;

               // Ad = A * d
               mat_mul(n, A, d, Ad);

               // dAd = d^T * A * d
               mat_mul(n, d, Ad, dAd);

               // mu = s / d^T * A * d
               mu = s_previous / dAd[0];

               // g = g + mu * A * d
               for(i = 0; i < n; i++)
               {     x[i] = x[i] + mu * d[i];
                    g[i] = g[i] + mu * Ad[i];
               }

               // s = g^T * g
               mat_mul(n, g, g, s);

               // d = - g + (s / s_previous) * d
               for(i = 0; i < n; i++)
                    d[i] = - g[i] + ( s[0] / s_previous) * d[i];
          }
          return m;
     }

} // End empty namespace

bool conj_grad(void)
{     bool ok = true;

     // ----------------------------------------------------------------------
     // Setup
     // ----------------------------------------------------------------------
     using CppAD::AD;
     using CppAD::NearEqual;
     using CppAD::vector;
     using std::cout;
     using std::endl;
     size_t i, j;


     // size of the vectors
     size_t n  = 40;
     vector<double> D(n * n), Dt(n * n), A(n * n), x(n), b(n), c(n);
     vector< AD<double> > a_A(n * n), a_x(n), a_b(n);

     // D = diagonally dominant matrix
     // c = vector of ones
     for(i = 0; i < n; i++)
     {     c[i] = 1.;
          double sum = 0;
          for(j = 0; j < n; j++) if( i != j )
          {     D[ i * n + j ] = std::rand() / double(RAND_MAX);
               Dt[j * n + i ] = D[i * n + j ];
               sum           += D[i * n + j ];
          }
          Dt[ i * n + i ] = D[ i * n + i ] = sum * 1.1;
     }

     // A = D^T * D
     mat_mul(n, Dt, D, A);

     // b = D^T * c
     mat_mul(n, Dt, c, b);

     // copy from double to AD<double>
     for(i = 0; i < n; i++)
     {     a_b[i] = b[i];
          for(j = 0; j < n; j++)
               a_A[ i * n + j ] = A[ i * n + j ];
     }

     // ---------------------------------------------------------------------
     // Record the function f : b -> x
     // ---------------------------------------------------------------------
     // Make b the independent variable vector
     Independent(a_b);

     // Solve A * x = b using conjugate gradient method
     double epsilon = 1e-7;
     for(i = 0; i < n; i++)
               a_x[i] = AD<double>(0);
     size_t m = n + 1;
     size_t k = conjugate_gradient(m, epsilon, a_A, a_b, a_x);

     // create f_cg: b -> x and stop tape recording
     CppAD::ADFun<double> f(a_b, a_x);

     // ---------------------------------------------------------------------
     // Check for correctness
     // ---------------------------------------------------------------------

     // conjugate gradient should converge with in n iterations
     ok &= (k <= n);

     // accuracy to which we expect values to agree
     double delta = 10. * epsilon * std::sqrt( double(n) );

     // copy x from AD<double> to double
     for(i = 0; i < n; i++)
          x[i] = Value( a_x[i] );

     // check c = A * x
     mat_mul(n, A, x, c);
     for(i = 0; i < n; i++)
          ok &= NearEqual(c[i] , b[i],  delta , delta);

     // forward computation of partials w.r.t. b[0]
     vector<double> db(n), dx(n);
     for(j = 0; j < n; j++)
          db[j] = 0.;
     db[0] = 1.;

     // check db = A * dx
     delta = 5. * delta;
     dx = f.Forward(1, db);
     mat_mul(n, A, dx, c);
     for(i = 0; i < n; i++)
          ok   &= NearEqual(c[i], db[i], delta, delta);

     return ok;
}
Input File: example/conj_grad.cpp cppad-20170000.3/doc/cppad_eigen.hpp.xml0000644000175200017650000005565313057470507016763 0ustar coincoin-web Enable Use of Eigen Linear Algebra Package with CppAD
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Enable Use of Eigen Linear Algebra Package with CppAD

Syntax
# include <cppad/example/cppad_eigen.hpp>

Purpose
Enables the use of the eigen linear algebra package with the type AD<Base> .

Example
The files eigen_array.cpp and eigen_det.cpp contain an example and test of this include file. It returns true if it succeeds and false otherwise.

Include Files
The file cppad_eigen.hpp includes both <cppad/cppad.hpp> and <Eigen/Core>. In addition, The file eigen_plugin.hpp is used to define value_type in the Eigen matrix class definition so its vectors are simple vectors . 

# define EIGEN_MATRIXBASE_PLUGIN <cppad/example/eigen_plugin.hpp>
# include <Eigen/Core>
# include <cppad/cppad.hpp>

Eigen NumTraits
Eigen needs the following definitions to work properly with AD<Base> scalars: 
namespace Eigen {
     template <class Base> struct NumTraits< CppAD::AD<Base> >
     {     // type that corresponds to the real part of an AD<Base> value
          typedef CppAD::AD<Base>   Real;
          // type for AD<Base> operations that result in non-integer values
          typedef CppAD::AD<Base>   NonInteger;
          // type for nested value inside an AD<Base> expression tree
          typedef CppAD::AD<Base>   Nested;

          enum {
               // does not support complex Base types
               IsComplex             = 0 ,
               // does not support integer Base types
               IsInteger             = 0 ,
               // only support signed Base types
               IsSigned              = 1 ,
               // must initialize an AD<Base> object
               RequireInitialization = 1 ,
               // computational cost of the corresponding operations
               ReadCost              = 1 ,
               AddCost               = 2 ,
               MulCost               = 2
          };

          // machine epsilon with type of real part of x
          // (use assumption that Base is not complex)
          static CppAD::AD<Base> epsilon(void)
          {     return CppAD::numeric_limits< CppAD::AD<Base> >::epsilon(); }

          // relaxed version of machine epsilon for comparison of different
          // operations that should result in the same value
          static CppAD::AD<Base> dummy_precision(void)
          {     return 100. *
                    CppAD::numeric_limits< CppAD::AD<Base> >::epsilon();
          }

          // minimum normalized positive value
          static CppAD::AD<Base> lowest(void)
          {     return CppAD::numeric_limits< CppAD::AD<Base> >::min(); }

          // maximum finite value
          static CppAD::AD<Base> highest(void)
          {     return CppAD::numeric_limits< CppAD::AD<Base> >::max(); }

     };
}

CppAD Namespace
Eigen also needs the following definitions to work properly with AD<Base> scalars: 
namespace CppAD {
          // functions that return references
          template <class Base> const AD<Base>& conj(const AD<Base>& x)
          {     return x; }
          template <class Base> const AD<Base>& real(const AD<Base>& x)
          {     return x; }

          // functions that return values (note abs is defined by cppad.hpp)
          template <class Base> AD<Base> imag(const AD<Base>& x)
          {     return CppAD::AD<Base>(0.); }
          template <class Base> AD<Base> abs2(const AD<Base>& x)
          {     return x * x; }
}

namespace Eigen {
     namespace internal {

          template<class Base>
          struct significant_decimals_default_impl< CppAD::AD<Base>, false>
          {     typedef CppAD::AD<Base> Scalar;

               typedef typename NumTraits<Scalar>::Real RealScalar;
               static inline int run()
               {     Scalar neg_log_eps = - log(
                         NumTraits<RealScalar>::epsilon()
                    );
                    int ceil_neg_log_eps = Integer( neg_log_eps );
                    if( Scalar(ceil_neg_log_eps) < neg_log_eps )
                         ceil_neg_log_eps++;
                    return ceil_neg_log_eps;
               }
          };
     }
}
Input File: cppad/example/cppad_eigen.hpp cppad-20170000.3/doc/eigen_plugin.hpp.xml0000644000175200017650000000554613057470507017166 0ustar coincoin-web Source Code for eigen_plugin.hpp
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Source Code for eigen_plugin.hpp

// Declaration needed so an Eigen vector is a simple vector
typedef Scalar value_type;
Input File: cppad/example/eigen_plugin.hpp cppad-20170000.3/doc/eigen_array.cpp.xml0000644000175200017650000003022013057470507016764 0ustar coincoin-web Using Eigen Arrays: Example and Test
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Using Eigen Arrays: Example and Test
# include <cppad/example/cppad_eigen.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <Eigen/Dense>

bool eigen_array(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     using Eigen::Matrix;
     using Eigen::Dynamic;
     //
     typedef Matrix< AD<double> , Dynamic, 1 > a_vector;
     //
     // some temporary indices
     size_t i, j;

     // domain and range space vectors
     size_t n  = 10, m = n;
     a_vector a_x(n), a_y(m);

     // set and declare independent variables and start tape recording
     for(j = 0; j < n; j++)
          a_x[j] = double(1 + j);
     CppAD::Independent(a_x);

     // evaluate a component wise function
     a_y = a_x.array() + a_x.array().sin();

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(a_x, a_y);

     // compute the derivative of y w.r.t x using CppAD
     CPPAD_TESTVECTOR(double) x(n);
     for(j = 0; j < n; j++)
          x[j] = double(j) + 1.0 / double(j+1);
     CPPAD_TESTVECTOR(double) jac = f.Jacobian(x);

     // check Jacobian
     double eps = 100. * CppAD::numeric_limits<double>::epsilon();
     for(i = 0; i < m; i++)
     {     for(j = 0; j < n; j++)
          {     double check = 1.0 + cos(x[i]);
               if( i != j )
                    check = 0.0;
               ok &= NearEqual(jac[i * n + j], check, eps, eps);
          }
     }

     return ok;
}
Input File: example/eigen_array.cpp cppad-20170000.3/doc/eigen_det.cpp.xml0000644000175200017650000004135213057470507016432 0ustar coincoin-web Using Eigen To Compute Determinant: Example and Test
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Using Eigen To Compute Determinant: Example and Test
# include <cppad/example/cppad_eigen.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <Eigen/Dense>

bool eigen_det(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     using Eigen::Matrix;
     using Eigen::Dynamic;
     //
     typedef Matrix< double     , Dynamic, Dynamic > matrix;
     typedef Matrix< AD<double> , Dynamic, Dynamic > a_matrix;
     //
     typedef Matrix< double ,     Dynamic , 1>       vector;
     typedef Matrix< AD<double> , Dynamic , 1>       a_vector;
     // some temporary indices
     size_t i, j;

     // domain and range space vectors
     size_t size = 3, n  = size * size, m = 1;
     a_vector a_x(n), a_y(m);
     vector x(n);

     // set and declare independent variables and start tape recording
     for(i = 0; i < size; i++)
     {     for(j = 0; j < size; j++)
          {     // lower triangular matrix
               a_x[i * size + j] = x[i * size + j] = 0.0;
               if( j <= i )
                    a_x[i * size + j] = x[i * size + j] = double(1 + i + j);
          }
     }
     CppAD::Independent(a_x);

     // copy independent variable vector to a matrix
     a_matrix a_X(size, size);
     matrix X(size, size);
     for(i = 0; i < size; i++)
     {     for(j = 0; j < size; j++)
          {     X(i, j)   = x[i * size + j];
               // If we used a_X(i, j) = X(i, j), a_X would not depend on a_x.
               a_X(i, j) = a_x[i * size + j];
          }
     }

     // Compute the log of determinant of X
     a_y[0] = log( a_X.determinant() );

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(a_x, a_y);

     // check function value
     double eps = 100. * CppAD::numeric_limits<double>::epsilon();
     CppAD::det_by_minor<double> det(size);
     ok &= NearEqual(Value(a_y[0]) , log(det(x)), eps, eps);

     // compute the derivative of y w.r.t x using CppAD
     vector jac = f.Jacobian(x);

     // check the derivative using the formula
     // d/dX log(det(X)) = transpose( inv(X) )
     matrix inv_X = X.inverse();
     for(i = 0; i < size; i++)
     {     for(j = 0; j < size; j++)
               ok &= NearEqual(jac[i * size + j], inv_X(j, i), eps, eps);
     }

     return ok;
}
Input File: example/eigen_det.cpp cppad-20170000.3/doc/hes_minor_det.cpp.xml0000644000175200017650000003250713057470507017330 0ustar coincoin-web Gradient of Determinant Using Expansion by Minors: Example and Test
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Gradient of Determinant Using Expansion by Minors: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <complex>

typedef std::complex<double>     Complex;
typedef CppAD::AD<Complex>       ADComplex;
typedef CPPAD_TESTVECTOR(ADComplex)   ADVector;

// ----------------------------------------------------------------------------

bool HesMinorDet(void)
{     bool ok = true;

     using namespace CppAD;

     size_t n = 2;

     // object for computing determinants
     det_by_minor<ADComplex> Det(n);

     // independent and dependent variable vectors
     CPPAD_TESTVECTOR(ADComplex)  X(n * n);
     CPPAD_TESTVECTOR(ADComplex)  D(1);

     // value of the independent variable
     size_t i;
     for(i = 0; i < n * n; i++)
          X[i] = Complex(int(i), -int(i));

     // set the independent variables
     Independent(X);

     // comupute the determinant
     D[0] = Det(X);

     // create the function object
     ADFun<Complex> f(X, D);

     // argument value
     CPPAD_TESTVECTOR(Complex)     x( n * n );
     for(i = 0; i < n * n; i++)
          x[i] = Complex(2 * i, i);

     // first derivative of the determinant
     CPPAD_TESTVECTOR(Complex) H( n * n * n * n);
     H = f.Hessian(x, 0);

     /*
     f(x)     = x[0] * x[3] - x[1] * x[2]
     f'(x)    = ( x[3], -x[2], -x[1], x[0] )
     */
     Complex zero(0., 0.);
     Complex one(1., 0.);
     Complex Htrue[]  = {
          zero, zero, zero,  one,
          zero, zero, -one, zero,
          zero, -one, zero, zero,
           one, zero, zero, zero
     };
     for( i = 0; i < n*n*n*n; i++)
          ok &= Htrue[i] == H[i];

     return ok;

}
Input File: example/hes_minor_det.cpp cppad-20170000.3/doc/hes_lu_det.cpp.xml0000644000175200017650000003136713057470507016627 0ustar coincoin-web Gradient of Determinant Using LU Factorization: Example and Test
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Gradient of Determinant Using LU Factorization: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_lu.hpp>

bool HesLuDet(void)
{     bool ok = true;

     using namespace CppAD;

     typedef std::complex<double> Complex;

     size_t n = 2;

     // object for computing determinants
     det_by_lu< AD<Complex> > Det(n);

     // independent and dependent variable vectors
     CPPAD_TESTVECTOR(AD<Complex>)  X(n * n);
     CPPAD_TESTVECTOR(AD<Complex>)  D(1);

     // value of the independent variable
     size_t i;
     for(i = 0; i < n * n; i++)
          X[i] = Complex(int(i), -int(i) );

     // set the independent variables
     Independent(X);

     D[0]  = Det(X);

     // create the function object
     ADFun<Complex> f(X, D);

     // argument value
     CPPAD_TESTVECTOR(Complex)     x( n * n );
     for(i = 0; i < n * n; i++)
          x[i] = Complex(2 * i, i);

     // first derivative of the determinant
     CPPAD_TESTVECTOR(Complex) H( n * n * n * n );
     H = f.Hessian(x, 0);

     /*
     f(x)     = x[0] * x[3] - x[1] * x[2]
     f'(x)    = ( x[3], -x[2], -x[1], x[0] )
     */
     Complex zero(0., 0.);
     Complex one(1., 0.);
     Complex Htrue[]  = {
          zero, zero, zero,  one,
          zero, zero, -one, zero,
          zero, -one, zero, zero,
           one, zero, zero, zero
     };
     for( i = 0; i < n*n*n*n; i++)
          ok &= NearEqual( Htrue[i], H[i], 1e-10 , 1e-10 );

     return ok;
}
Input File: example/hes_lu_det.cpp cppad-20170000.3/doc/interface2c.cpp.xml0000644000175200017650000006323213057470507016675 0ustar coincoin-web Interfacing to C: Example and Test
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Interfacing to C: Example and Test
# include <cppad/cppad.hpp>  // CppAD utilities
# include <cassert>        // assert macro

namespace { // Begin empty namespace
/*
Compute the value of a sum of Gaussians defined by a and evaluated at x
     y = sum_{i=1}^n a[3*i] exp( (x - a[3*i+1])^2 / a[3*i+2])^2 )
where the floating point type is a template parameter
*/
template <class Float>
Float sumGauss(const Float &x, const CppAD::vector<Float> &a)
{
     // number of components in a
     size_t na = a.size();

     // number of Gaussians
     size_t n = na / 3;

     // check the restricitons on na
     assert( na == n * 3 );

     // declare temporaries used inside of loop
     Float ex, arg;

     // initialize sum
     Float y = 0.;

     // loop with respect to Gaussians
     size_t i;
     for(i = 0; i < n; i++)
     {
          arg =   (x - a[3*i+1]) / a[3*i+2];
          ex  =   exp(-arg * arg);
          y  +=   a[3*i] * ex;
     }
     return y;
}
/*
Create a C function interface that computes both
     y = sum_{i=1}^n a[3*i] exp( (x - a[3*i+1])^2 / a[3*i+2])^2 )
and its derivative with respect to the parameter vector a.
*/
extern "C"
void sumGauss(float x, float a[], float *y, float dyda[], size_t na)
{     // Note that any simple vector could replace CppAD::vector;
     // for example, std::vector, std::valarray

     // check the restrictions on na
     assert( na % 3 == 0 );  // mod(na, 3) = 0

     // use the shorthand ADfloat for the type CppAD::AD<float>
     typedef CppAD::AD<float> ADfloat;

     // vector for indpendent variables
     CppAD::vector<ADfloat> A(na);      // used with template function above
     CppAD::vector<float>   acopy(na);  // used for derivative calculations

     // vector for the dependent variables (there is only one)
     CppAD::vector<ADfloat> Y(1);

     // copy the independent variables from C vector to CppAD vectors
     size_t i;
     for(i = 0; i < na; i++)
          A[i] = acopy[i] = a[i];

     // declare that A is the independent variable vector
     CppAD::Independent(A);

     // value of x as an ADfloat object
     ADfloat X = x;

     // Evaluate template version of sumGauss with ADfloat as the template
     // parameter. Set the independent variable to the resulting value
     Y[0] = sumGauss(X, A);

     // create the AD function object F : A -> Y
     CppAD::ADFun<float> F(A, Y);

     // use Value to convert Y[0] to float and return y = F(a)
     *y = CppAD::Value(Y[0]);

     // evaluate the derivative F'(a)
     CppAD::vector<float> J(na);
     J = F.Jacobian(acopy);

     // return the value of dyda = F'(a) as a C vector
     for(i = 0; i < na; i++)
          dyda[i] = J[i];

     return;
}
/*
Link CppAD::NearEqual so do not have to use namespace notation in Interface2C
*/
bool NearEqual(float x, float y, float r, float a)
{     return CppAD::NearEqual(x, y, r, a);
}

} // End empty namespace

bool Interface2C(void)
{     // This routine is intentionally coded as if it were a C routine
     // except for the fact that it uses the predefined type bool.
     bool ok = true;

     // declare variables
     float x, a[6], y, dyda[6], tmp[6];
     size_t na, i;

     // number of parameters (3 for each Gaussian)
     na = 6;

     // number of Gaussians: n  = na / 3;

     // value of x
     x = 1.;

     // value of the parameter vector a
     for(i = 0; i < na; i++)
          a[i] = (float) (i+1);

     // evaulate function and derivative
     sumGauss(x, a, &y, dyda, na);

     // compare dyda to central difference approximation for deriative
     for(i = 0; i < na; i++)
     {     // local variables
          float small, ai, yp, ym, dy_da;

          // We assume that the type float has at least 7 digits of
          // precision, so we choose small to be about pow(10., -7./2.).
          small  = (float) 3e-4;

          // value of this component of a
          ai    = a[i];

          // evaluate F( a + small * ei )
          a[i]  = ai + small;
          sumGauss(x, a, &yp, tmp, na);

          // evaluate F( a - small * ei )
          a[i]  = ai - small;
          sumGauss(x, a, &ym, tmp, na);

          // evaluate central difference approximates for partial
          dy_da = (yp - ym) / (2 * small);

          // restore this component of a
          a[i]  = ai;

          ok   &= NearEqual(dyda[i], dy_da, small, small);
     }
     return ok;
}
Input File: example/interface2c.cpp cppad-20170000.3/doc/jac_minor_det.cpp.xml0000644000175200017650000003041213057470507017277 0ustar coincoin-web Gradient of Determinant Using Expansion by Minors: Example and Test
Prev Next jac_minor_det.cpp Headings

Gradient of Determinant Using Expansion by Minors: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <complex>


typedef std::complex<double>     Complex;
typedef CppAD::AD<Complex>       ADComplex;
typedef CPPAD_TESTVECTOR(ADComplex)   ADVector;

// ----------------------------------------------------------------------------

bool JacMinorDet(void)
{     bool ok = true;

     using namespace CppAD;

     size_t n = 2;

     // object for computing determinant
     det_by_minor<ADComplex> Det(n);

     // independent and dependent variable vectors
     CPPAD_TESTVECTOR(ADComplex)  X(n * n);
     CPPAD_TESTVECTOR(ADComplex)  D(1);

     // value of the independent variable
     size_t i;
     for(i = 0; i < n * n; i++)
          X[i] = Complex(int(i), -int(i));

     // set the independent variables
     Independent(X);

     // comupute the determinant
     D[0] = Det(X);

     // create the function object
     ADFun<Complex> f(X, D);

     // argument value
     CPPAD_TESTVECTOR(Complex)     x( n * n );
     for(i = 0; i < n * n; i++)
          x[i] = Complex(2 * i, i);

     // first derivative of the determinant
     CPPAD_TESTVECTOR(Complex) J( n * n );
     J = f.Jacobian(x);

     /*
     f(x)     = x[0] * x[3] - x[1] * x[2]
     f'(x)    = ( x[3], -x[2], -x[1], x[0] )
     */
     Complex Jtrue[] = { x[3], -x[2], -x[1], x[0] };
     for(i = 0; i < n * n; i++)
          ok &= Jtrue[i] == J[i];

     return ok;

}
Input File: example/jac_minor_det.cpp cppad-20170000.3/doc/jac_lu_det.cpp.xml0000644000175200017650000002646413057470507016607 0ustar coincoin-web Gradient of Determinant Using Lu Factorization: Example and Test
Prev Next jac_lu_det.cpp Headings

Gradient of Determinant Using Lu Factorization: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_lu.hpp>

bool JacLuDet(void)
{     bool ok = true;

     using namespace CppAD;

     size_t n = 2;

     // object for computing determinants
     det_by_lu<ADComplex> Det(n);

     // independent and dependent variable vectors
     CPPAD_TESTVECTOR(ADComplex)  X(n * n);
     CPPAD_TESTVECTOR(ADComplex)  D(1);

     // value of the independent variable
     size_t i;
     for(i = 0; i < n * n; i++)
          X[i] = Complex(int(i), -int(i));

     // set the independent variables
     Independent(X);

     // compute the determinant
     D[0]  = Det(X);

     // create the function object
     ADFun<Complex> f(X, D);

     // argument value
     CPPAD_TESTVECTOR(Complex)     x( n * n );
     for(i = 0; i < n * n; i++)
          x[i] = Complex(2 * i, i);

     // first derivative of the determinant
     CPPAD_TESTVECTOR(Complex) J( n * n );
     J = f.Jacobian(x);

     /*
     f(x)     = x[0] * x[3] - x[1] * x[2]
     */
     Complex Jtrue[]  = { x[3], -x[2], -x[1], x[0] };
     for( i = 0; i < n*n; i++)
          ok &= NearEqual( Jtrue[i], J[i], 1e-10 , 1e-10 );

     return ok;
}
Input File: example/jac_lu_det.cpp cppad-20170000.3/doc/mul_level.xml0000644000175200017650000003414113057470507015710 0ustar coincoin-web Using Multiple Levels of AD
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Using Multiple Levels of AD

Background
If f is an ADFun<Base> object, the vectors returned by f.Forward , and f.Reverse , have values of type Base and not AD<Base> . This reflects the fact that operations used to calculate these function values are not recorded by the tape corresponding to AD<Base> operations.

Motivation
Suppose that you use derivatives of one or more inner functions as part of the operations needed to compute an outer function. For example, the derivatives returned by f.Forward might be used as part of Taylor's method for solving ordinary differential equations. In addition, we might want to differentiate the solution of a differential equation with respect to parameters in the equation. This can be accomplished in the following way:
  1. The function defining the differential equation could be calculated using the class AD< AD<double> > .
  2. The operations during the calculation of Taylor's method could be done using the AD<double> class.
  3. Derivatives of the solution of the differential equation could then be calculated using the double class.


Procedure

First Start AD<double>
If some of the parameters in the AD< AD<double> > recording depend on the variables in the AD<double> recording, we must first declaring these variables; i.e.,
     Independent(a1x)
 where a1x is a SimpleVector with elements of type AD<double> . This will start recording a new tape of operations performed using AD<double> class objects.

Start AD< AD<double> > Recording
The next step is to declare the independent variables using
     Independent(a2x)
 where a2x is a SimpleVector with elements of type AD< AD<double> > . This will start recording a new tape of operations performed using AD< AD<double> > class objects.

Inner Function
The next step is to calculation the inner function using AD< AD<double> > class objects. We then stop the recording using
     a1f.Dependent(a2x, a2y)
 where a2y is a SimpleVector with elements of type AD< AD<double> > and a1f is an ADFun< AD<double> > object.

Second Start AD< AD<double> >
If none of the parameters in the AD< AD<double> > recording depend on the variables in the AD<double> recording, it is preferred to delay declaring these variables to this point; i.e.,
     Independent(a1x)
 where a1x is a SimpleVector with elements of type AD<double> . This will start recording a new tape of operations performed using AD<double> class objects.

Outer Function
The next step is to calculation the outer function using AD<double> class objects. Note that derivatives of the inner function can be included in the calculation of the outer function using a1f . We then stop the recording of AD<double> operations using
     g.Dependent(a1x, a1y)
 where a1y is a SimpleVector with elements of type AD<double> and g is an ADFun<double> object.

Derivatives of Outer Function
The AD function object g can then be used to calculate the derivatives of the outer function.

Example
The files mul_level.cpp and change_param.cpp contain an examples and tests of this procedure. They return true if they succeed and false otherwise. The file mul_level_ode.cpp is a more complex example use of multiple tapes.
Input File: omh/mul_level.omh cppad-20170000.3/doc/mul_level.cpp.xml0000644000175200017650000005420213057470507016471 0ustar coincoin-web Multiple Level of AD: Example and Test
Prev Next mul_level.cpp

Multiple Level of AD: Example and Test

Purpose
In this example, we use AD< AD<double> > (level two taping), the compute values of the function f : R n → R where f ( x ) = 1 2 (x 0 2 + ⋯ + x n -1 2 ) We then use AD<double> (level one taping) to compute the directional derivative f ( 1 ) ( x ) * v = x 0 v 0 + ⋯ + x n -1 v n -1 . where v ∈ R n . We then use double (no taping) to compute d dx [f ( 1 ) ( x ) * v ] = v This is only meant as an example of multiple levels of taping. The example hes_times_dir.cpp computes the same value more efficiently by using the identity: d dx [f ( 1 ) ( x ) * v ] = f ( 2 ) ( x ) * v The example mul_level_adolc.cpp computes the same values using Adolc's type adouble and CppAD's type AD<adouble>.

Source 


# include <cppad/cppad.hpp>

namespace {
     // f(x) = |x|^2 / 2 = .5 * ( x[0]^2 + ... + x[n-1]^2 )
     template <class Type>
     Type f(const CPPAD_TESTVECTOR(Type)& x)
     {     Type sum;

          sum  = 0.;
          size_t i = size_t(x.size());
          for(i = 0; i < size_t(x.size()); i++)
               sum += x[i] * x[i];

          return .5 * sum;
     }
}

bool mul_level(void)
{     bool ok = true;                          // initialize test result

     typedef CppAD::AD<double>   a1type;    // for one level of taping
     typedef CppAD::AD<a1type>    a2type;    // for two levels of taping
     size_t n = 5;                           // dimension for example
     size_t j;                               // a temporary index variable

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     CPPAD_TESTVECTOR(double) x(n);
     CPPAD_TESTVECTOR(a1type)  a1x(n), a1v(n), a1dy(1) ;
     CPPAD_TESTVECTOR(a2type)  a2x(n), a2y(1);

     // Values for the independent variables while taping the function f(x)
     for(j = 0; j < n; j++)
          a2x[j] = a1x[j] = x[j] = double(j);
     // Declare the independent variable for taping f(x)
     CppAD::Independent(a2x);

     // Use AD< AD<double> > to tape the evaluation of f(x)
     a2y[0] = f(a2x);

     // Declare a1f as the corresponding ADFun< AD<double> >
     // (make sure we do not run zero order forward during constructor)
     CppAD::ADFun<a1type> a1f;
     a1f.Dependent(a2x, a2y);

     // Values for the independent variables while taping f'(x) * v
     // Declare the independent variable for taping f'(x) * v
     // (Note we did not have to tape the creationg of a1f.)
     CppAD::Independent(a1x);

     // set the argument value x for computing f'(x) * v
     a1f.Forward(0, a1x);
     // compute f'(x) * v
     for(j = 0; j < n; j++)
          a1v[j] = double(n - j);
     a1dy = a1f.Forward(1, a1v);

     // declare g as ADFun<double> function corresponding to f'(x) * v
     CppAD::ADFun<double> g;
     g.Dependent(a1x, a1dy);

     // optimize out operations not necessary for function f'(x) * v
     g.optimize();

     // Evaluate f'(x) * v
     g.Forward(0, x);

     // compute the d/dx of f'(x) * v = f''(x) * v = v
     CPPAD_TESTVECTOR(double) w(1);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0] = 1.;
     dw   = g.Reverse(1, w);

     for(j = 0; j < n; j++)
          ok &= CppAD::NearEqual(dw[j], a1v[j], eps, eps);

     return ok;
}
Input File: example/mul_level.cpp cppad-20170000.3/doc/change_param.cpp.xml0000644000175200017650000001372613057470507017120 0ustar coincoin-web Computing a Jacobian With Constants that Change
Prev Next change_param.cpp

Computing a Jacobian With Constants that Change

Purpose
In this example we use two levels of taping so that a derivative can have constant parameters that can be changed. To be specific, we consider the function f : R 2 → R 2 f ( x ) = p ( sin ( x 0 ) sin ( x 1 ) ) were p ∈ R is a parameter. The Jacobian of this function is g ( x , p ) = p ( cos ( x 0 ) 0 0 cos ( x 1 ) ) In this example we use two levels of AD to avoid computing the partial of f ( x ) with respect to p , but still allow for the evaluation of g ( x , p ) at different values of p .
Input File: example/change_param.cpp cppad-20170000.3/doc/ode_stiff.cpp.xml0000644000175200017650000012541013057470507016447 0ustar coincoin-web A Stiff Ode: Example and Test
Prev Next ode_stiff.cpp Headings

A Stiff Ode: Example and Test
Define x : R → R 2 by x 0 ( 0 ) = 1 x 1 ( 0 ) = 0 x 0 ′ ( t ) = - a 0 x 0 ( t ) x 1 ′ ( t ) = + a 0 x 0 ( t ) - a 1 x 1 ( t ) If a 0 ≫ a 1 > 0 , this is a stiff Ode and the analytic solution is x 0 ( t ) = exp ( - a 0 t ) x 1 ( t ) = a 0 [ exp ( - a 1 t ) - exp ( - a 0 t ) ] / ( a 0 - a 1 ) The example tests Rosen34 using the relations above: 

# include <cppad/cppad.hpp>

// To print the comparision, change the 0 to 1 on the next line.
# define CPPAD_ODE_STIFF_PRINT 0

namespace {
     // --------------------------------------------------------------
     class Fun {
     private:
          CPPAD_TESTVECTOR(double) a;
     public:
          // constructor
          Fun(const CPPAD_TESTVECTOR(double)& a_) : a(a_)
          { }
          // compute f(t, x)
          void Ode(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f)
          {     f[0]  = - a[0] * x[0];
               f[1]  = + a[0] * x[0] - a[1] * x[1];
          }
          // compute partial of f(t, x) w.r.t. t
          void Ode_ind(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f_t)
          {     f_t[0] = 0.;
               f_t[1] = 0.;
          }
          // compute partial of f(t, x) w.r.t. x
          void Ode_dep(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f_x)
          {     f_x[0] = -a[0];
               f_x[1] = 0.;
               f_x[2] = +a[0];
               f_x[3] = -a[1];
          }
     };
     // --------------------------------------------------------------
     class RungeMethod {
     private:
          Fun F;
     public:
          // constructor
          RungeMethod(const CPPAD_TESTVECTOR(double) &a_) : F(a_)
          { }
          void step(
               double                     ta ,
               double                     tb ,
               CPPAD_TESTVECTOR(double) &xa ,
               CPPAD_TESTVECTOR(double) &xb ,
               CPPAD_TESTVECTOR(double) &eb )
          {     xb = CppAD::Runge45(F, 1, ta, tb, xa, eb);
          }
          size_t order(void)
          {     return 5; }
     };
     class RosenMethod {
     private:
          Fun F;
     public:
          // constructor
          RosenMethod(const CPPAD_TESTVECTOR(double) &a_) : F(a_)
          { }
          void step(
               double                     ta ,
               double                     tb ,
               CPPAD_TESTVECTOR(double) &xa ,
               CPPAD_TESTVECTOR(double) &xb ,
               CPPAD_TESTVECTOR(double) &eb )
          {     xb = CppAD::Rosen34(F, 1, ta, tb, xa, eb);
          }
          size_t order(void)
          {     return 4; }
     };
}

bool OdeStiff(void)
{     bool ok = true;     // initial return value

     CPPAD_TESTVECTOR(double) a(2);
     a[0] = 1e3;
     a[1] = 1.;
     RosenMethod rosen(a);
     RungeMethod runge(a);
     Fun          gear(a);

     CPPAD_TESTVECTOR(double) xi(2);
     xi[0] = 1.;
     xi[1] = 0.;

     CPPAD_TESTVECTOR(double) eabs(2);
     eabs[0] = 1e-6;
     eabs[1] = 1e-6;

     CPPAD_TESTVECTOR(double) ef(2);
     CPPAD_TESTVECTOR(double) xf(2);
     CPPAD_TESTVECTOR(double) maxabs(2);
     size_t                nstep;

     size_t k;
     for(k = 0; k < 3; k++)
     {
          size_t M    = 5;
          double ti   = 0.;
          double tf   = 1.;
          double smin = 1e-7;
          double sini = 1e-7;
          double smax = 1.;
          double scur = .5;
          double erel = 0.;

          if( k == 0 )
          {     xf = CppAD::OdeErrControl(rosen, ti, tf,
               xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
          }
          else if( k == 1 )
          {     xf = CppAD::OdeErrControl(runge, ti, tf,
               xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
          }
          else if( k == 2 )
          {     xf = CppAD::OdeGearControl(gear, M, ti, tf,
               xi, smin, smax, sini, eabs, erel, ef, maxabs, nstep);
          }
          double x0 = exp(-a[0]*tf);
          ok &= CppAD::NearEqual(x0, xf[0], 0., eabs[0]);
          ok &= CppAD::NearEqual(0., ef[0], 0., eabs[0]);

          double x1 = a[0] *
               (exp(-a[1]*tf) - exp(-a[0]*tf))/(a[0] - a[1]);
          ok &= CppAD::NearEqual(x1, xf[1], 0., eabs[1]);
          ok &= CppAD::NearEqual(0., ef[1], 0., eabs[0]);
# if CPPAD_ODE_STIFF_PRINT
          const char* method[]={ "Rosen34", "Runge45", "Gear5" };
          std::cout << std::endl;
          std::cout << "method     = " << method[k] << std::endl;
          std::cout << "nstep      = " << nstep  << std::endl;
          std::cout << "x0         = " << x0 << std::endl;
          std::cout << "xf[0]      = " << xf[0] << std::endl;
          std::cout << "x0 - xf[0] = " << x0 - xf[0] << std::endl;
          std::cout << "ef[0]      = " << ef[0] << std::endl;
          std::cout << "x1         = " << x1 << std::endl;
          std::cout << "xf[1]      = " << xf[1] << std::endl;
          std::cout << "x1 - xf[1] = " << x1 - xf[1] << std::endl;
          std::cout << "ef[1]      = " << ef[1] << std::endl;
# endif
     }

     return ok;
}
Input File: example/ode_stiff.cpp cppad-20170000.3/doc/mul_level_ode.cpp.xml0000644000175200017650000015420613057470507017325 0ustar coincoin-web Taylor's Ode Solver: A Multi-Level AD Example and Test
Prev Next mul_level_ode.cpp

Taylor's Ode Solver: A Multi-Level AD Example and Test

Purpose
This is a realistic example using two levels of AD; see mul_level . The first level uses AD<double> to tape the solution of an ordinary differential equation. This solution is then differentiated with respect to a parameter vector. The second level uses AD< AD<double> > to take derivatives during the solution of the differential equation. These derivatives are used in the application of Taylor's method to the solution of the ODE. The example mul_level_adolc_ode.cpp computes the same values using Adolc's type adouble and CppAD's type AD<adouble>. The example ode_taylor.cpp is a simpler applications of Taylor's method for solving an ODE.

ODE
For this example the ODE's are defined by the function h : R n × R n → R n where h [ x , y ( t , x ) ] = ( x 0 x 1 y 0 ( t , x ) ⋮ x n -1 y n -2 ( t , x ) ) = ( ∂ t y 0 ( t , x ) ∂ t y 1 ( t , x ) ⋮ ∂ t y n -1 ( t , x ) ) and the initial condition y ( 0 , x ) = 0 . The value of x is fixed during the solution of the ODE and the function g : R n → R n is used to define the ODE where g ( y ) = ( x 0 x 1 y 0 ⋮ x n -1 y n -2 )
ODE Solution
The solution for this example can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain y ( t , x ) = ( x 0 t x 1 x 0 t 2 / 2 ⋮ x n -1 x n -2 … x 0 t n / n ! )
Derivative of ODE Solution
Differentiating the solution above, with respect to the parameter vector x , we notice that ∂ x y ( t , x ) = ( y 0 ( t , x ) / x 0 0 ⋯ 0 y 1 ( t , x ) / x 0 y 1 ( t , x ) / x 1 0 ⋮ ⋮ ⋮ ⋱ 0 y n -1 ( t , x ) / x 0 y n -1 ( t , x ) / x 1 ⋯ y n -1 ( t , x ) / x n -1 )

An m-th order Taylor method for approximating the solution of an ordinary differential equations is y ( t + Δ t , x ) ≈ ∑ k = 0 p ∂ t k y ( t , x ) Δ t k k ! = y ( 0 ) ( t , x ) + y ( 1 ) ( t , x ) Δ t + ⋯ + y ( p ) ( t , x ) Δ t p where the Taylor coefficients y ( k ) ( t , x ) are defined by y ( k ) ( t , x ) = ∂ t k y ( t , x ) / k ! We define the function z ( t , x ) by the equation z ( t , x ) = g [ y ( t , x ) ] = h [ x , y ( t , x ) ] It follows that ∂ t y ( t , x ) = z ( t , x ) ∂ t k + 1 y ( t , x ) = ∂ t k z ( t , x ) y ( k + 1 ) ( t , x ) = z ( k ) ( t , x ) / ( k + 1 ) where z ( k ) ( t , x ) is the k-th order Taylor coefficient for z ( t , x ) . In the example below, the Taylor coefficients y ( 0 ) ( t , x ) , … , y ( k ) ( t , x ) are used to calculate the Taylor coefficient z ( k ) ( t , x ) which in turn gives the value for y ( k + 1 ) y ( t , x ) .

Source 


# include <cppad/cppad.hpp>

// =========================================================================
// define types for each level
namespace { // BEGIN empty namespace
typedef CppAD::AD<double>   a1type;
typedef CppAD::AD<a1type>   a2type;

// -------------------------------------------------------------------------
// class definition for C++ function object that defines ODE
class Ode {
private:
     // copy of a that is set by constructor and used by g(y)
     CPPAD_TESTVECTOR(a1type) a1x_;
public:
     // constructor
     Ode(const CPPAD_TESTVECTOR(a1type)& a1x) : a1x_(a1x)
     { }
     // the function g(y) is evaluated with two levels of taping
     CPPAD_TESTVECTOR(a2type) operator()
     ( const CPPAD_TESTVECTOR(a2type)& a2y) const
     {     size_t n = a2y.size();
          CPPAD_TESTVECTOR(a2type) a2g(n);
          size_t i;
          a2g[0] = a1x_[0];
          for(i = 1; i < n; i++)
               a2g[i] = a1x_[i] * a2y[i-1];

          return a2g;
     }
};

// -------------------------------------------------------------------------
// Routine that uses Taylor's method to solve ordinary differential equaitons
// and allows for algorithmic differentiation of the solution.
CPPAD_TESTVECTOR(a1type) taylor_ode(
     Ode                            G       ,  // function that defines the ODE
     size_t                         order   ,  // order of Taylor's method used
     size_t                         nstep   ,  // number of steps to take
     const a1type&                  a1dt    ,  // Delta t for each step
     const CPPAD_TESTVECTOR(a1type)& a1y_ini)  // y(t) at the initial time
{
     // some temporary indices
     size_t i, k, ell;

     // number of variables in the ODE
     size_t n = a1y_ini.size();

     // copies of x and g(y) with two levels of taping
     CPPAD_TESTVECTOR(a2type)   a2y(n), a2z(n);

     // y, y^{(k)} , z^{(k)}, and y^{(k+1)}
     CPPAD_TESTVECTOR(a1type)  a1y(n), a1y_k(n), a1z_k(n), a1y_kp(n);

     // initialize x
     for(i = 0; i < n; i++)
          a1y[i] = a1y_ini[i];

     // loop with respect to each step of Taylors method
     for(ell = 0; ell < nstep; ell++)
     {     // prepare to compute derivatives using a1type
          for(i = 0; i < n; i++)
               a2y[i] = a1y[i];
          CppAD::Independent(a2y);

          // evaluate ODE in a2type
          a2z = G(a2y);

          // define differentiable version of a1g: y -> z
          // that computes its derivatives using a1type objects
          CppAD::ADFun<a1type> a1g(a2y, a2z);

          // Use Taylor's method to take a step
          a1y_k            = a1y;     // initialize y^{(k)}
          a1type   a1dt_kp = a1dt;  // initialize dt^(k+1)
          for(k = 0; k <= order; k++)
          {     // evaluate k-th order Taylor coefficient of y
               a1z_k = a1g.Forward(k, a1y_k);

               for(i = 0; i < n; i++)
               {     // convert to (k+1)-Taylor coefficient for x
                    a1y_kp[i] = a1z_k[i] / a1type(k + 1);

                    // add term for to this Taylor coefficient
                    // to solution for y(t, x)
                    a1y[i]    += a1y_kp[i] * a1dt_kp;
               }
               // next power of t
               a1dt_kp *= a1dt;
               // next Taylor coefficient
               a1y_k   = a1y_kp;
          }
     }
     return a1y;
}
} // END empty namespace
// ==========================================================================
// Routine that tests alogirhtmic differentiation of solutions computed
// by the routine taylor_ode.
bool mul_level_ode(void)
{     bool ok = true;
     double eps = 100. * std::numeric_limits<double>::epsilon();

     // number of components in differential equation
     size_t n = 4;

     // some temporary indices
     size_t i, j;

     // parameter vector in both double and a1type
     CPPAD_TESTVECTOR(double)  x(n);
     CPPAD_TESTVECTOR(a1type)  a1x(n);
     for(i = 0; i < n; i++)
          a1x[i] = x[i] = double(i + 1);

     // declare the parameters as the independent variable
     CppAD::Independent(a1x);

     // arguments to taylor_ode
     Ode G(a1x);                // function that defines the ODE
     size_t   order = n;      // order of Taylor's method used
     size_t   nstep = 2;      // number of steps to take
     a1type   a1dt  = double(1.);     // Delta t for each step
     // value of y(t, x) at the initial time
     CPPAD_TESTVECTOR(a1type) a1y_ini(n);
     for(i = 0; i < n; i++)
          a1y_ini[i] = 0.;

     // integrate the differential equation
     CPPAD_TESTVECTOR(a1type) a1y_final(n);
     a1y_final = taylor_ode(G, order, nstep, a1dt, a1y_ini);

     // define differentiable fucntion object f : x -> y_final
     // that computes its derivatives in double
     CppAD::ADFun<double> f(a1x, a1y_final);

     // check function values
     double check = 1.;
     double t     = nstep * Value(a1dt);
     for(i = 0; i < n; i++)
     {     check *= x[i] * t / double(i + 1);
          ok &= CppAD::NearEqual(Value(a1y_final[i]), check, eps, eps);
     }

     // evaluate the Jacobian of h at a
     CPPAD_TESTVECTOR(double) jac ( f.Jacobian(x) );
     // There appears to be a bug in g++ version 4.4.2 because it generates
     // a warning for the equivalent form
     // CPPAD_TESTVECTOR(double) jac = f.Jacobian(x);

     // check Jacobian
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     double jac_ij = jac[i * n + j];
               if( i < j )
                    check = 0.;
               else     check = Value( a1y_final[i] ) / x[j];
               ok &= CppAD::NearEqual(jac_ij, check, eps, eps);
          }
     }
     return ok;
}
Input File: example/mul_level_ode.cpp cppad-20170000.3/doc/ode_taylor.cpp.xml0000644000175200017650000007043213057470507016651 0ustar coincoin-web Taylor's Ode Solver: An Example and Test
Prev Next ode_taylor.cpp

Taylor's Ode Solver: An Example and Test

Purpose
This example solves an ordinary differential equation using Taylor's method; i.e., Z ( t + Δ t ) ≈ Z ( 0 ) ( t ) + Z ( 1 ) ( t ) 1 ! Δ t + ⋯ + Z ( p ) ( t ) p ! ( Δ t ) p )
ODE
The ODE is defined by the function h : R n → R n , which for this example is given by Z ( 1 ) ( t ) = H [ Z ( t ) ] = ( 1 Z 1 ( t ) ⋮ Z n -1 ( t ) ) and the initial condition is z ( 0 ) = 0 .

ODE Solution
The solution for this example can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain Z ( t ) = ( t t 2 / 2 ⋮ t n / n ! )
Forward Mode
Given the Taylor coefficients for k = 0 , … , K z ( k ) = Z ( k ) k ! ( t ) we note that Z ( 1 ) ( t ) = H ( z ( 0 ) + z ( 1 ) t + ⋯ + z ( K ) t K ) + O ( t K + 1 ) = h ( 0 ) + h ( 1 ) t + ⋯ + h ( K ) t K + O ( t K + 1 ) where h ( k ) is the k-th order Taylor coefficient for H ( Z ( t ) ) . Taking K-th order derivatives of both sides we obtain Z ( K + 1 ) ( t ) = K ! h ( K ) z ( K + 1 ) = h ( K ) / K The code below uses this relationship to implement Taylor's method for approximating the solution of an ODE. 

# include <cppad/cppad.hpp>

// =========================================================================
// define types for each level
namespace { // BEGIN empty namespace
     using CppAD::AD;

     CPPAD_TESTVECTOR( AD<double> ) ode(
          const CPPAD_TESTVECTOR( AD<double> )& Z )
     {     size_t n = Z.size();
          CPPAD_TESTVECTOR( AD<double> ) y(n);
          y[0] = 1;
          for(size_t k = 1; k < n; k++)
               y[k] = Z[k-1];
          return y;
     }

}

// -------------------------------------------------------------------------
// Example that uses Taylor's method to solve ordinary differential equaitons
bool ode_taylor(void)
{     // initialize the return value as true
     bool ok = true;

     // some temporary indices
     size_t i, j, k;

     // The ODE does not depend on the arugment values
     // so only tape once, also note that ode does not depend on t
     size_t n = 5;    // number of independent and dependent variables
     CPPAD_TESTVECTOR( AD<double> ) a_x(n), a_y(n);
     CppAD::Independent( a_x );
     a_y = ode(a_x);
     CppAD::ADFun<double> H(a_x, a_y);

     // initialize the solution vector at time zero
     CPPAD_TESTVECTOR( double ) z(n);
     for(j = 0; j < n; j++)
          z[j] = 0.0;

     size_t order   = n;   // order of the Taylor method
     size_t n_step  = 4;   // number of time steps
     double dt      = 0.5; // step size in time
     // Taylor coefficients of order k
     CPPAD_TESTVECTOR( double ) hk(n), zk(n);

     // loop with respect to each step of Taylor's method
     for(size_t i_step = 0; i_step < n_step; i_step++)
     {     // Use Taylor's method to take a step
          zk           = z;     // initialize z^{(k)}  for k = 0
          double dt_kp = dt;    // initialize dt^(k+1) for k = 0
          for(k = 0; k < order; k++)
          {     // evaluate k-th order Taylor coefficient of H
               hk = H.Forward(k, zk);

               for(j = 0; j < n; j++)
               {     // convert to (k+1)-Taylor coefficient for z
                    zk[j] = hk[j] / double(k + 1);

                    // add term for to this Taylor coefficient
                    // to solution for y(t, x)
                    z[j] += zk[j] * dt_kp;
               }
               // next power of t
               dt_kp *= dt;
          }
     }

     // check solution of the ODE,
     // Taylor's method should have no truncation error for this case
     double eps   = 100. * std::numeric_limits<double>::epsilon();
     double check = 1.;
     double t     = n_step * dt;
     for(i = 0; i < n; i++)
     {     check *= t / double(i + 1);
          ok &= CppAD::NearEqual(z[i], check, eps, eps);
     }

     return ok;
}
Input File: example/ode_taylor.cpp cppad-20170000.3/doc/_ode_taylor.cpp_xml.js0000644000175200017650000000406413057470507017502 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'example.xml', 'general.xml', 'ode_taylor.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'general.xml', 'exampleutility.xml', 'listallexamples.xml', 'testvector.xml' ]; var list_down1 = [ 'ad_fun.cpp.xml', 'ad_in_c.cpp.xml', 'conj_grad.cpp.xml', 'cppad_eigen.hpp.xml', 'hes_minor_det.cpp.xml', 'hes_lu_det.cpp.xml', 'interface2c.cpp.xml', 'jac_minor_det.cpp.xml', 'jac_lu_det.cpp.xml', 'mul_level.xml', 'ode_stiff.cpp.xml', 'mul_level_ode.cpp.xml', 'mul_level_adolc_ode.cpp.xml', 'ode_taylor.cpp.xml', 'stack_machine.cpp.xml' ]; var list_current0 = [ 'ode_taylor.cpp.xml#Purpose', 'ode_taylor.cpp.xml#ODE', 'ode_taylor.cpp.xml#ODE Solution', 'ode_taylor.cpp.xml#Forward Mode' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/stack_machine.cpp.xml0000644000175200017650000012100513057470507017272 0ustar coincoin-web Example Differentiating a Stack Machine Interpreter
Prev Next stack_machine.cpp Headings

Example Differentiating a Stack Machine Interpreter

# include <cstring>
# include <cstddef>
# include <cstdlib>
# include <cctype>
# include <cassert>
# include <stack>

# include <cppad/cppad.hpp>

namespace {
// Begin empty namespace ------------------------------------------------

bool is_number( const std::string &s )
{     char ch = s[0];
     bool number = (std::strchr("0123456789.", ch) != 0);
     return number;
}
bool is_binary( const std::string &s )
{     char ch = s[0];
     bool binary = (strchr("+-*/.", ch) != 0);
     return binary;
}
bool is_variable( const std::string &s )
{     char ch = s[0];
     bool variable = ('a' <= ch) & (ch <= 'z');
     return variable;
}

void StackMachine(
     std::stack< std::string >          &token_stack  ,
     CppAD::vector< CppAD::AD<double> > &variable     )
{     using std::string;
     using std::stack;

     using CppAD::AD;

     stack< AD<double> > value_stack;
     string              token;
     AD<double>          value_one;
     AD<double>          value_two;

     while( ! token_stack.empty() )
     {     string s = token_stack.top();
          token_stack.pop();

          if( is_number(s) )
          {     value_one = std::atof( s.c_str() );
               value_stack.push( value_one );
          }
          else if( is_variable(s) )
          {     value_one = variable[ size_t(s[0]) - size_t('a') ];
               value_stack.push( value_one );
          }
          else if( is_binary(s) )
          {     assert( value_stack.size() >= 2 );
               value_one = value_stack.top();
               value_stack.pop();
               value_two = value_stack.top();
               value_stack.pop();

               switch( s[0] )
               {
                    case '+':
                    value_stack.push(value_one + value_two);
                    break;

                    case '-':
                    value_stack.push(value_one - value_two);
                    break;

                    case '*':
                    value_stack.push(value_one * value_two);
                    break;

                    case '/':
                    value_stack.push(value_one / value_two);
                    break;

                    default:
                    assert(0);
               }
          }
          else if( s[0] == '=' )
          {     assert( value_stack.size() >= 1 );
               assert( token_stack.size() >= 1 );
               //
               s = token_stack.top();
               token_stack.pop();
               //
               assert( is_variable( s ) );
               value_one = value_stack.top();
               value_stack.pop();
               //
               variable[ size_t(s[0]) - size_t('a') ] = value_one;
          }
          else assert(0);
     }
     return;
}

// End empty namespace -------------------------------------------------------
}

bool StackMachine(void)
{     bool ok = true;

     using std::string;
     using std::stack;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::vector;

     // The users program in that stack machine language
     const char *program[] = {
          "1.0", "a", "+", "=", "b",  // b = a + 1
          "2.0", "b", "*", "=", "c",  // c = b * 2
          "3.0", "c", "-", "=", "d",  // d = c - 3
          "4.0", "d", "/", "=", "e"   // e = d / 4
     };
     size_t n_program = sizeof( program ) / sizeof( program[0] );

     // put the program in the token stack
     stack< string > token_stack;
     size_t i = n_program;
     while(i--)
          token_stack.push( program[i] );

     // domain space vector
     size_t n = 1;
     vector< AD<double> > X(n);
     X[0] = 0.;

     // declare independent variables and start tape recording
     CppAD::Independent(X);

     // x[0] corresponds to a in the stack machine
     vector< AD<double> > variable(26);
     variable[0] = X[0];

     // calculate the resutls of the program
     StackMachine( token_stack , variable);

     // range space vector
     size_t m = 4;
     vector< AD<double> > Y(m);
     Y[0] = variable[1];   // b = a + 1
     Y[1] = variable[2];   // c = (a + 1) * 2
     Y[2] = variable[3];   // d = (a + 1) * 2 - 3
     Y[3] = variable[4];   // e = ( (a + 1) * 2 - 3 ) / 4

     // create f : X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // use forward mode to evaluate function at different argument value
     size_t p = 0;
     vector<double> x(n);
     vector<double> y(m);
     x[0] = 1.;
     y    = f.Forward(p, x);

     // check function values
     ok &= (y[0] == x[0] + 1.);
     ok &= (y[1] == (x[0] + 1.) * 2.);
     ok &= (y[2] == (x[0] + 1.) * 2. - 3.);
     ok &= (y[3] == ( (x[0] + 1.) * 2. - 3.) / 4.);

     // Use forward mode (because x is shorter than y) to calculate Jacobian
     p = 1;
     vector<double> dx(n);
     vector<double> dy(m);
     dx[0] = 1.;
     dy    = f.Forward(p, dx);
     ok   &= NearEqual(dy[0], 1., eps99, eps99);
     ok   &= NearEqual(dy[1], 2., eps99, eps99);
     ok   &= NearEqual(dy[2], 2., eps99, eps99);
     ok   &= NearEqual(dy[3], .5, eps99, eps99);

     // Use Jacobian routine (which automatically decides which mode to use)
     dy = f.Jacobian(x);
     ok   &= NearEqual(dy[0], 1., eps99, eps99);
     ok   &= NearEqual(dy[1], 2., eps99, eps99);
     ok   &= NearEqual(dy[2], 2., eps99, eps99);
     ok   &= NearEqual(dy[3], .5, eps99, eps99);

     return ok;
}
Input File: example/stack_machine.cpp cppad-20170000.3/doc/exampleutility.xml0000644000175200017650000000550713057470507017007 0ustar coincoin-web Utility Routines used by CppAD Examples
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Utility Routines used by CppAD Examples

Contents
example.cppCppAD Examples and Tests
speed_example.cppRun the Speed Examples
lu_vec_ad.cppLu Factor and Solve with Recorded Pivoting
Input File: omh/example_list.omh cppad-20170000.3/doc/speed_example.cpp.xml0000644000175200017650000005063213057470507017323 0ustar coincoin-web Run the Speed Examples
Prev Next speed_example.cpp

Run the Speed Examples

Running Tests
To build this program and run its correctness tests see cmake_check . 

# include <cppad/cppad.hpp>

// various example routines
extern bool det_of_minor(void);
extern bool det_by_lu(void);
extern bool det_by_minor(void);
extern bool elapsed_seconds(void);
extern bool mat_sum_sq(void);
extern bool ode_evaluate(void);
extern bool sparse_hes_fun(void);
extern bool sparse_jac_fun(void);
extern bool speed_test(void);
extern bool time_test(void);

namespace {
     // function that runs one test
     size_t Run_ok_count    = 0;
     size_t Run_error_count = 0;
     const char* exception_list[] = {
          "elapsed_seconds",
          "speed_test",
          "time_test"
     };
     size_t n_exception = sizeof(exception_list) / sizeof(exception_list[0]);
     bool Run(bool TestOk(void), std::string name)
     {     bool ok               = true;
          std::streamsize width =  20;
          std::cout.width( width );
          std::cout.setf( std::ios_base::left );
          std::cout << name;
          bool exception = false;
          for(size_t i = 0; i < n_exception; i++)
               exception |= exception_list[i] == name;
          //
          ok &= name.size() < size_t(width);
          ok &= TestOk();
          if( ok )
          {     std::cout << "OK" << std::endl;
               Run_ok_count++;
          }
          else if ( exception )
          {     std::cout << "Error: perhaps too many other programs running";
               std::cout << std::endl;
               // no change to Run_ok_count
               ok = true;
          }
          else
          {     std::cout << "Error" << std::endl;
               Run_error_count++;
          }
          return ok;
     }
}

// main program that runs all the tests
int main(void)
{     bool ok = true;
     using std::cout;
     using std::endl;

     ok &= Run(det_of_minor,          "det_of_minor"   );
     ok &= Run(det_by_minor,         "det_by_minor"    );
     ok &= Run(det_by_lu,               "det_by_lu"    );
     ok &= Run(elapsed_seconds,   "elapsed_seconds"    );
     ok &= Run(mat_sum_sq,             "mat_sum_sq"    );
     ok &= Run(ode_evaluate,         "ode_evaluate"    );
     ok &= Run(sparse_hes_fun,    "sparse_hes_fun"     );
     ok &= Run(sparse_jac_fun,    "sparse_jac_fun"     );
     ok &= Run(speed_test,             "speed_test"    );
     ok &= Run(time_test,               "time_test"    );
     assert( ok || (Run_error_count > 0) );

     // check for memory leak in previous calculations
     if( ! CppAD::thread_alloc::free_all() )
     {     ok = false;
          cout << "Error: memroy leak detected" << endl;
     }

     if( ok )
     {     cout << "All " << int(Run_ok_count) << " tests passed ";
          cout << "(possibly excepting elapsed_seconds).";
     }
     else     cout << int(Run_error_count) << " tests failed.";
     cout << endl;


     return static_cast<int>( ! ok );
}
Input File: speed/example/example.cpp cppad-20170000.3/doc/lu_vec_ad.cpp.xml0000644000175200017650000003265113057470507016432 0ustar coincoin-web Lu Factor and Solve with Recorded Pivoting
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Lu Factor and Solve with Recorded Pivoting

Syntax
int LuVecAD(
     size_t n,
     size_t m,
     VecAD<double> &Matrix,
     VecAD<double> &Rhs,
     VecAD<double> &Result,
     AD<double> &logdet)

Purpose
Solves the linear equation Matrix * Result = Rhs where Matrix is an n × n matrix, Rhs is an n x m matrix, and Result is an n x m matrix.

The routine LuSolve uses an arbitrary vector type, instead of VecAD , to hold its elements. The pivoting operations for a ADFun object corresponding to an LuVecAD solution will change to be optimal for the matrix being factored.

It is often the case that LuSolve is faster than LuVecAD when LuSolve uses a simple vector class with elements of type double , but the corresponding ADFun objects have a fixed set of pivoting operations.

Storage Convention
The matrices stored in row major order. To be specific, if A contains the vector storage for an n x m matrix, i is between zero and n -1 , and j is between zero and m -1 , A i , j = A [ i * m + j ] (The length of A must be equal to n * m .)

n
is the number of rows in Matrix , Rhs , and Result .

m
is the number of columns in Rhs and Result . It is ok for m to be zero which is reasonable when you are only interested in the determinant of Matrix .

Matrix
On input, this is an n × n matrix containing the variable coefficients for the equation we wish to solve. On output, the elements of Matrix have been overwritten and are not specified.

Rhs
On input, this is an n × m matrix containing the right hand side for the equation we wish to solve. On output, the elements of Rhs have been overwritten and are not specified. If m is zero, Rhs is not used.

Result
On input, this is an n × m matrix and the value of its elements do not matter. On output, the elements of Rhs contain the solution of the equation we wish to solve (unless the value returned by LuVecAD is equal to zero). If m is zero, Result is not used.

logdet
On input, the value of logdet does not matter. On output, it has been set to the log of the determinant of Matrix (but not quite). To be more specific, if signdet is the value returned by LuVecAD, the determinant of Matrix is given by the formula det = signdet exp ( logdet ) This enables LuVecAD to use logs of absolute values.

Example
The file lu_vec_ad_ok.cpp contains an example and test of LuVecAD. It returns true if it succeeds and false otherwise.
Input File: example/lu_vec_ad.cpp cppad-20170000.3/doc/lu_vec_ad_ok.cpp.xml0000644000175200017650000006100613057470507017117 0ustar coincoin-web Lu Factor and Solve With Recorded Pivoting: Example and Test
Prev Next lu_vec_ad_ok.cpp Headings

Lu Factor and Solve With Recorded Pivoting: Example and Test

# include <cppad/cppad.hpp>
# include "lu_vec_ad.hpp"
# include <cppad/speed/det_by_minor.hpp>

bool LuVecADOk(void)
{     bool  ok = true;

     using namespace CppAD;
     typedef AD<double> ADdouble;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     size_t              n = 3;
     size_t              m = 2;
     double a1[] = {
          3., 0., 0., // (1,1) is first  pivot
          1., 2., 1., // (2,2) is second pivot
          1., 0., .5  // (3,3) is third  pivot
     };
     double a2[] = {
          1., 2., 1., // (1,2) is second pivot
          3., 0., 0., // (2,1) is first  pivot
          1., 0., .5  // (3,3) is third  pivot
     };
     double rhs[] = {
          1., 3.,
          2., 2.,
          3., 1.
     };

     VecAD<double>       Copy    (n * n);
     VecAD<double>       Rhs     (n * m);
     VecAD<double>       Result  (n * m);
     ADdouble            logdet;
     ADdouble            signdet;

     // routine for checking determinants using expansion by minors
     det_by_minor<ADdouble> Det(n);

     // matrix we are computing the determinant of
     CPPAD_TESTVECTOR(ADdouble) A(n * n);

     // dependent variable values
     CPPAD_TESTVECTOR(ADdouble) Y(1 + n * m);

     size_t  i;
     size_t  j;
     size_t  k;

     // Original matrix
     for(i = 0; i < n * n; i++)
          A[i] = a1[i];

     // right hand side
     for(j = 0; j < n; j++)
          for(k = 0; k < m; k++)
               Rhs[ j * m + k ] = rhs[ j * m + k ];

     // Declare independent variables
     Independent(A);

     // Copy the matrix
     ADdouble index(0);
     for(i = 0; i < n*n; i++)
     {     Copy[index] = A[i];
          index += 1.;
     }

     // Solve the equation
     signdet = LuVecAD(n, m, Copy, Rhs, Result, logdet);

     // Result is the first n * m dependent variables
     index = 0.;
     for(i = 0; i < n * m; i++)
     {     Y[i] = Result[index];
          index += 1.;
     }

     // Determinant is last component of the solution
     Y[ n * m ] = signdet * exp( logdet );

     // construct f: A -> Y
     ADFun<double> f(A, Y);

     // check determinant using minors routine
     ADdouble determinant = Det( A );
     ok &= NearEqual(Y[n * m], determinant, eps99, eps99);


     // Check solution of Rhs = A * Result
     double sum;
     for(k = 0; k < m; k++)
     {     for(i = 0; i < n; i++)
          {     sum = 0.;
               for(j = 0; j < n; j++)
                    sum += a1[i * n + j] * Value( Y[j * m + k] );
               ok &= NearEqual( rhs[i * m + k], sum, eps99, eps99);
          }
     }

     CPPAD_TESTVECTOR(double) y2(1 + n * m);
     CPPAD_TESTVECTOR(double) A2(n * n);
     for(i = 0; i < n * n; i++)
          A[i] = A2[i] = a2[i];


     y2          = f.Forward(0, A2);
     determinant = Det(A);
     ok &= NearEqual(y2[ n * m], Value(determinant), eps99, eps99);

     // Check solution of Rhs = A2 * Result
     for(k = 0; k < m; k++)
     {     for(i = 0; i < n; i++)
          {     sum = 0.;
               for(j = 0; j < n; j++)
                    sum += a2[i * n + j] * y2[j * m + k];
               ok &= NearEqual( rhs[i * m + k], sum, eps99, eps99);
          }
     }

     return ok;
}
Input File: example/lu_vec_ad_ok.cpp cppad-20170000.3/doc/listallexamples.xml0000644000175200017650000007471113057470507017136 0ustar coincoin-web List of All the CppAD Examples
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List of All the CppAD Examples
a11c_bthread.cpp A Simple Boost Thread Example and Test
a11c_openmp.cpp A Simple OpenMP Example and Test
a11c_pthread.cpp A Simple Parallel Pthread Example and Test
abort_recording.cpp Abort Current Recording: Example and Test
Abs.cpp AD Absolute Value Function: Example and Test
acos.cpp The AD acos Function: Example and Test
acosh.cpp The AD acosh Function: Example and Test
ad_assign.cpp AD Assignment: Example and Test
ad_ctor.cpp AD Constructors: Example and Test
add.cpp AD Binary Addition: Example and Test
AddEq.cpp AD Computed Assignment Addition: Example and Test
ad_fun.cpp Creating Your Own Interface to an ADFun Object
ad_in_c.cpp Example and Test Linking CppAD to Languages Other than C++
ad_input.cpp AD Output Operator: Example and Test
ad_output.cpp AD Output Operator: Example and Test
asin.cpp The AD asin Function: Example and Test
asinh.cpp The AD asinh Function: Example and Test
atan2.cpp The AD atan2 Function: Example and Test
atan.cpp The AD atan Function: Example and Test
atanh.cpp The AD atanh Function: Example and Test
atomic_eigen_cholesky.cpp Atomic Eigen Cholesky Factorization: Example and Test
atomic_eigen_cholesky.hpp Atomic Eigen Cholesky Factorization Class
atomic_eigen_mat_inv.cpp Atomic Eigen Matrix Inverse: Example and Test
atomic_eigen_mat_inv.hpp Atomic Eigen Matrix Inversion Class
atomic_eigen_mat_mul.cpp Atomic Eigen Matrix Multiply: Example and Test
atomic_eigen_mat_mul.hpp Atomic Eigen Matrix Multiply Class
checkpoint_extended_ode.cpp Checkpointing an Extended ODE Solver: Example and Test
atomic_for_sparse_hes.cpp Atomic Forward Hessian Sparsity: Example and Test
atomic_for_sparse_jac.cpp Atomic Forward Jacobian Sparsity: Example and Test
atomic_forward.cpp Atomic Forward: Example and Test
atomic_get_started.cpp Getting Started with Atomic Operations: Example and Test
atomic_mat_mul.cpp User Atomic Matrix Multiply: Example and Test
atomic_mat_mul.hpp Matrix Multiply as an Atomic Operation
atomic_mul_level.cpp Atomic Operations and Multiple-Levels of AD: Example and Test
atomic_norm_sq.cpp Atomic Euclidean Norm Squared: Example and Test
checkpoint_ode.cpp Checkpointing an ODE Solver: Example and Test
atomic_reciprocal.cpp Reciprocal as an Atomic Operation: Example and Test
atomic_reverse.cpp Atomic Reverse: Example and Test
atomic_rev_sparse_hes.cpp Atomic Reverse Hessian Sparsity: Example and Test
atomic_rev_sparse_jac.cpp Atomic Reverse Jacobian Sparsity: Example and Test
atomic_set_sparsity.cpp Atomic Sparsity with Set Patterns: Example and Test
atomic_tangent.cpp Tan and Tanh as User Atomic Operations: Example and Test
azmul.cpp AD Absolute Zero Multiplication: Example and Test
base_adolc.hpp Enable use of AD<Base> where Base is Adolc's adouble Type
base_alloc.hpp Example AD<Base> Where Base Constructor Allocates Memory
base_complex.hpp Enable use of AD<Base> where Base is std::complex<double>
base_require.cpp Using a User Defined AD Base Type: Example and Test
bender_quad.cpp BenderQuad: Example and Test
bool_fun.cpp AD Boolean Functions: Example and Test
bool_sparsity.cpp Using vectorBool Sparsity To Conserve Memory: Example and Test
capacity_order.cpp Controlling Taylor Coefficient Memory Allocation: Example and Test
change_param.cpp Computing a Jacobian With Constants that Change
check_for_nan.cpp ADFun Checking For Nan: Example and Test
check_numeric_type.cpp The CheckNumericType Function: Example and Test
checkpoint.cpp Simple Checkpointing: Example and Test
check_simple_vector.cpp The CheckSimpleVector Function: Example and Test
colpack_hes.cpp Using ColPack: Example and Test
colpack_jac.cpp Using ColPack: Example and Test
compare_change.cpp CompareChange and Re-Tape: Example and Test
compare.cpp AD Binary Comparison Operators: Example and Test
complex_poly.cpp Complex Polynomial: Example and Test
cond_exp.cpp Conditional Expressions: Example and Test
conj_grad.cpp Differentiate Conjugate Gradient Algorithm: Example and Test
cos.cpp The AD cos Function: Example and Test
cosh.cpp The AD cosh Function: Example and Test
cppad_eigen.hpp Enable Use of Eigen Linear Algebra Package with CppAD
cppad_vector.cpp CppAD::vector Template Class: Example and Test
dependency.cpp Computing Dependency: Example and Test
det_by_lu.cpp Determinant Using Lu Factorization: Example and Test
det_by_minor.cpp Determinant Using Expansion by Minors: Example and Test
det_of_minor.cpp Determinant of a Minor: Example and Test
div.cpp AD Binary Division: Example and Test
div_eq.cpp AD Computed Assignment Division: Example and Test
eigen_array.cpp Using Eigen Arrays: Example and Test
eigen_det.cpp Using Eigen To Compute Determinant: Example and Test
eigen_plugin.hpp Source Code for eigen_plugin.hpp
elapsed_seconds.cpp Elapsed Seconds: Example and Test
equal_op_seq.cpp EqualOpSeq: Example and Test
erf.cpp The AD erf Function: Example and Test
error_handler.cpp Replacing The CppAD Error Handler: Example and Test
example.cpp CppAD Examples and Tests
exp.cpp The AD exp Function: Example and Test
expm1.cpp The AD exp Function: Example and Test
expm1.cpp The AD exp Function: Example and Test
for_one.cpp First Order Partial Driver: Example and Test
for_sparse_hes.cpp Forward Mode Hessian Sparsity: Example and Test
for_sparse_jac.cpp Forward Mode Jacobian Sparsity: Example and Test
for_two.cpp Subset of Second Order Partials: Example and Test
forward.cpp Forward Mode: Example and Test
forward_dir.cpp Forward Mode: Example and Test of Multiple Directions
forward_order.cpp Forward Mode: Example and Test of Multiple Orders
fun_assign.cpp ADFun Assignment: Example and Test
fun_check.cpp ADFun Check and Re-Tape: Example and Test
get_started.cpp Getting Started Using CppAD to Compute Derivatives
harmonic.cpp Multi-Threaded Implementation of Summation of 1/i
harmonic_time.cpp Timing Test of Multi-Threaded Summation of 1/i
harmonic_work.cpp Multi-threading Sum of 1/i Utility Routines
hes_lagrangian.cpp Hessian of Lagrangian and ADFun Default Constructor: Example and Test
hes_lu_det.cpp Gradient of Determinant Using LU Factorization: Example and Test
hes_minor_det.cpp Gradient of Determinant Using Expansion by Minors: Example and Test
hessian.cpp Hessian: Example and Test
hes_times_dir.cpp Hessian Times Direction: Example and Test
independent.cpp Independent and ADFun Constructor: Example and Test
index_sort.cpp Index Sort: Example and Test
integer.cpp Convert From AD to Integer: Example and Test
interface2c.cpp Interfacing to C: Example and Test
interp_onetape.cpp Interpolation With Out Retaping: Example and Test
interp_retape.cpp Interpolation With Retaping: Example and Test
ipopt_solve_get_started.cpp Nonlinear Programming Using CppAD and Ipopt: Example and Test
ipopt_solve_ode_inverse.cpp ODE Inverse Problem Definitions: Source Code
ipopt_solve_retape.cpp Nonlinear Programming Retaping: Example and Test
jac_lu_det.cpp Gradient of Determinant Using Lu Factorization: Example and Test
jac_minor_det.cpp Gradient of Determinant Using Expansion by Minors: Example and Test
jacobian.cpp Jacobian: Example and Test
log10.cpp The AD log10 Function: Example and Test
log1p.cpp The AD log1p Function: Example and Test
log.cpp The AD log Function: Example and Test
lu_factor.cpp LuFactor: Example and Test
lu_invert.cpp LuInvert: Example and Test
lu_ratio.cpp LuRatio: Example and Test
lu_solve.cpp LuSolve With Complex Arguments: Example and Test
lu_vec_ad_ok.cpp Lu Factor and Solve With Recorded Pivoting: Example and Test
mat_sum_sq.cpp Sum of the Elements of the Square of a Matrix: Example and Test
mul.cpp AD Binary Multiplication: Example and Test
mul_eq.cpp AD Computed Assignment Multiplication: Example and Test
mul_level_adolc.cpp Using Adolc with Multiple Levels of Taping: Example and Test
mul_level_adolc_ode.cpp Taylor's Ode Solver: A Multi-Level Adolc Example and Test
mul_level.cpp Multiple Level of AD: Example and Test
mul_level_ode.cpp Taylor's Ode Solver: A Multi-Level AD Example and Test
multi_newton.cpp A Multi-Threaded Newton's Method
multi_newton_time.cpp Timing Test of Multi-Threaded Newton Method
multi_newton_work.cpp Multi-threading Newton Method Utility Routines
nan.cpp nan: Example and Test
near_equal.cpp NearEqual Function: Example and Test
near_equal_ext.cpp Compare AD with Base Objects: Example and Test
number_skip.cpp Number of Variables That Can be Skipped: Example and Test
numeric_type.cpp The NumericType: Example and Test
num_limits.cpp Numeric Limits: Example and Test
ode_err_control.cpp OdeErrControl: Example and Test
ode_err_maxabs.cpp OdeErrControl: Example and Test Using Maxabs Argument
ode_evaluate.cpp ode_evaluate: Example and test
ode_gear_control.cpp OdeGearControl: Example and Test
ode_gear.cpp OdeGear: Example and Test
ode_stiff.cpp A Stiff Ode: Example and Test
ode_taylor.cpp Taylor's Ode Solver: An Example and Test
optimize_compare_op.cpp Example Optimization and Comparison Operators
optimize_conditional_skip.cpp Example Optimization and Conditional Expressions
optimize_cumulative_sum.cpp Example Optimization and Cumulative Sum Operations
optimize_forward_active.cpp Example Optimization and Forward Activity Analysis
optimize_nest_conditional.cpp Example Optimization and Nested Conditional Expressions
optimize_print_for.cpp Example Optimization and Print Forward Operators
optimize_reverse_active.cpp Example Optimization and Reverse Activity Analysis
opt_val_hes.cpp opt_val_hes: Example and Test
par_var.cpp AD Parameter and Variable Functions: Example and Test
poly.cpp Polynomial Evaluation: Example and Test
pow.cpp The AD Power Function: Example and Test
pow_int.cpp The Pow Integer Exponent: Example and Test
print_for_cout.cpp Printing During Forward Mode: Example and Test
print_for_string.cpp Print During Zero Order Forward Mode: Example and Test
reverse_checkpoint.cpp Reverse Mode General Case (Checkpointing): Example and Test
reverse_one.cpp First Order Reverse Mode: Example and Test
reverse_three.cpp Third Order Reverse Mode: Example and Test
reverse_two.cpp Second Order Reverse ModeExample and Test
rev_one.cpp First Order Derivative Driver: Example and Test
rev_sparse_hes.cpp Reverse Mode Hessian Sparsity: Example and Test
rev_sparse_jac.cpp Reverse Mode Jacobian Sparsity: Example and Test
rev_two.cpp Second Partials Reverse Driver: Example and Test
Rombergmul.cpp One Dimensional Romberg Integration: Example and Test
romberg_one.cpp One Dimensional Romberg Integration: Example and Test
rosen_34.cpp Rosen34: Example and Test
runge45_1.cpp Runge45: Example and Test
runge45_2.cpp Runge45: Example and Test
seq_property.cpp ADFun Sequence Properties: Example and Test
set_union.cpp Set Union: Example and Test
simple_ad_bthread.cpp A Simple Boost Threading AD: Example and Test
simple_ad_openmp.cpp A Simple OpenMP AD: Example and Test
simple_ad_pthread.cpp A Simple pthread AD: Example and Test
simple_vector.cpp Simple Vector Template Class: Example and Test
sin.cpp The AD sin Function: Example and Test
sinh.cpp The AD sinh Function: Example and Test
sparse_hes_fun.cpp sparse_hes_fun: Example and test
sparse_hessian.cpp Sparse Hessian: Example and Test
sparse_jac_fun.cpp sparse_jac_fun: Example and test
sparse_jacobian.cpp Sparse Jacobian: Example and Test
sparse_sub_hes.cpp Sparse Hessian on Subset of Variables: Example and Test
sparsity_sub.cpp Sparsity Patterns For a Subset of Variables: Example and Test
speed_example.cpp Run the Speed Examples
speed_program.cpp Example Use of SpeedTest
speed_test.cpp speed_test: Example and test
sqrt.cpp The AD sqrt Function: Example and Test
stack_machine.cpp Example Differentiating a Stack Machine Interpreter
sub.cpp AD Binary Subtraction: Example and Test
sub_eq.cpp AD Computed Assignment Subtraction: Example and Test
sub_sparse_hes.cpp Computing Sparse Hessian for a Subset of Variables
tan.cpp The AD tan Function: Example and Test
tanh.cpp The AD tanh Function: Example and Test
tape_index.cpp Taping Array Index Operation: Example and Test
team_bthread.cpp Boost Thread Implementation of a Team of AD Threads
team_example.cpp Using a Team of AD Threads: Example and Test
team_openmp.cpp OpenMP Implementation of a Team of AD Threads
team_pthread.cpp Pthread Implementation of a Team of AD Threads
team_thread.hpp Specifications for A Team of AD Threads
thread_alloc.cpp Fast Multi-Threading Memory Allocator: Example and Test
thread_test.cpp Run Multi-Threading Examples and Speed Tests
time_test.cpp time_test: Example and test
to_string.cpp to_string: Example and Test
unary_minus.cpp AD Unary Minus Operator: Example and Test
unary_plus.cpp AD Unary Plus Operator: Example and Test
value.cpp Convert From AD to its Base Type: Example and Test
var2par.cpp Convert an AD Variable to a Parameter: Example and Test
vec_ad.cpp AD Vectors that Record Index Operations: Example and Test
vector_bool.cpp CppAD::vectorBool Class: Example and Test
Input File: omh/example_list.omh cppad-20170000.3/doc/speed.xml0000644000175200017650000000777313057470507015037 0ustar coincoin-web Speed Test an Operator Overloading AD Package
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Speed Test an Operator Overloading AD Package

Purpose
CppAD has a set of speed tests that are used to determine if certain changes improve its execution speed. These tests can also be used to compare the AD packages Adolc , CppAD , Fadbad and Sacado . The sections below explain how you can run these tests on your computer.

Contents
speed_mainRunning the Speed Test Program
speed_utilitySpeed Testing Utilities
speed_doubleSpeed Test of Functions in Double
speed_adolcSpeed Test of Derivatives Using Adolc
speed_cppadSpeed Test Derivatives Using CppAD
speed_fadbadSpeed Test Derivatives Using Fadbad
speed_sacadoSpeed Test Derivatives Using Sacado
Input File: omh/speed/speed.omh cppad-20170000.3/doc/speed_main.xml0000644000175200017650000006142313057470510016025 0ustar coincoin-web Running the Speed Test Program
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Running the Speed Test Program

Syntax
speed/package/speed_package test seed option_list

Purpose
A version of this program runs the correctness tests or the speed tests for one AD package identified by package .

package

AD Package
The command line argument package specifies one of the AD package. The CppAD distribution comes with support for the following packages: adolc , cppad , fadbad , sacado . You can extend this program to include other package. Such an extension need not include all the tests. For example, link_sparse_hessian just returns false for the fadbad and sacado packages.

double
The value package can be double in which case the function values (instead of derivatives) are computed using double precision operations. This enables one to compare the speed of computing function values in double to the speed of the derivative computations. (It is often useful to divide the speed of the derivative computation by the speed of the function evaluation in double.)

profile
In the special case where package is profile, the CppAD package is compiled and run with profiling to aid in determining where it is spending most of its time.

test
It the argument test specifies which test to run and has the following possible values: correct , speed , det_minor , det_lu , mat_mul , ode , poly , sparse_hessian , sparse_jacobian . You can experiment with changing the implementation of a particular test for a particular package.

correct
If test is equal to correct, all of the correctness tests are run.

speed
If test is equal to speed, all of the speed tests are run.

seed
The command line argument seed is a positive integer. The random number simulator uniform_01 is initialized with the call
     uniform_01(seed)
 before any of the testing routines (listed above) are called.

Global Options
This global variable has prototype 

     extern std::map<std::string, bool> global_option;
This is true for each option that follows seed . The order of the options does not matter and the list can be empty. Each option, must be separate command line argument to the main program. The documentation below specifics how CppAD uses these options, see the examples in speed_adolc for how another package might uses these options.

onetape
If the option onetape is present, 
 
     global_option["onetape"]
is true and otherwise it is false. If this external symbol is true, CppAD will use one taping of the operation sequence for all the repetitions of that speed test. Otherwise, the operation sequence will be retaped for each test repetition.

All of the tests, except det_lu , have a fixed operations sequence. The operation sequence for det_lu may be different for each repetition of the test because it depends on the matrix for which the determinant is being calculated. For this reason, the CppAD test cppad_det_lu.cpp returns false (indicating that the test not implemented) when global_onetape is true.

optimize
If the option optimize is present, 
 
     global_option["optimize"]
is true and otherwise it is false. If this external symbol is true, CppAD will optimize the operation sequence before doing computations. If it is false, this optimization will not be done.

atomic
If the option atomic is present, 
 
     global_option["atomic"]
is true and otherwise it is false. If this external symbol is true, CppAD will use its user defined atomic operation is used for the test. If no such atomic operation exists, and atomic is chosen, CppAD returns false for the test.

memory
If the option memory is present, 
 
     global_option["memory"]
is true and otherwise it is false. If it is true, the CppAD hold_memory routine will be called by the main program before any of the tests are executed. This should make the CppAD thread_alloc allocator faster. If it is false, CppAD will used standard memory allocation.

Sparsity Options
The following options only apply to the sparse_jacobian and sparse_hessian tests. The other tests will ignore these options:

boolsparsity
If the option boolsparsity is present, 
 
     global_option["boolsparsity"]
is true and otherwise it is false. If it is true, CppAD will use a vector of bool for its sparsity patterns. Otherwise it will use a vector of sets .

revsparsity
If the option revsparsity is present, 
 
     global_option["revsparsity"]
is true and otherwise it is false. If it is true, CppAD will use a ForSparseJac and ForSparseHes where possible for its sparsity patterns. Otherwise it will use RevSparseJac and RevSparseHes .

colpack
If the option colpack is present, 
 
     global_option["colpack"]
is true and otherwise it is false. If this external symbol is true, CppAD will use colpack to do the coloring for its Otherwise, it will use it's own coloring algorithm.

Correctness Results
One, but not both, of the following two output lines
     package_test_optionlist_available = false
     package_test_optionlist_ok = flag
 is generated for each correctness test where package and test are as above, optionlist are the options (in option_list ) separated by the underbar _ character (whereas they are separated by spaces in option_list ), and flag is true or false.

Speed Results
For each speed test, corresponds to three lines of the following form are generated:
     package_test_optionlist_ok   = flag
     package_test_size = [ size_1, ..., size_n ]
     package_test_rate = [ rate_1, ..., rate_n ]
 The values package , test , optionlist , and flag are as in the correctness results above. The values size_1 , ..., size_n are the size arguments used for the corresponding tests. The values rate_1 , ..., rate_n are the number of times per second that the corresponding size problem executed.

n_sweep
The sparse_jacobian and sparse_hessian tests has an extra output line with the following form
     package_sparse_test_n_sweep = [ n_sweep_1, ..., n_sweep_n ]
 were test is jacobian (hessian). The values n_sweep_1 , ..., n_sweep_n are the number of sweeps (colors) used for each sparse Jacobian (Hessian) calculation; see n_sweep for sparse_jacobian and sparse_hessian .

Link Functions
Each package defines it's own version of one of the link functions listed below. Each of these functions links this main program to the corresponding test:
link_det_lu Speed Testing Gradient of Determinant Using Lu Factorization
link_det_minor Speed Testing Gradient of Determinant by Minor Expansion
link_mat_mul Speed Testing Derivative of Matrix Multiply
link_ode Speed Testing the Jacobian of Ode Solution
link_poly Speed Testing Second Derivative of a Polynomial
link_sparse_hessian Speed Testing Sparse Hessian
link_sparse_jacobian Speed Testing Sparse Jacobian
Input File: speed/main.cpp cppad-20170000.3/doc/link_det_lu.xml0000644000175200017650000001701213057470510016205 0ustar coincoin-web Speed Testing Gradient of Determinant Using Lu Factorization
Prev Next link_det_lu

Speed Testing Gradient of Determinant Using Lu Factorization

Prototype
extern bool link_det_lu(
     size_t                 size      ,
     size_t                 repeat    ,
     CppAD::vector<double> &matrix    ,
     CppAD::vector<double> &gradient
);
Purpose
Each package must define a version of this routine as specified below. This is used by the speed_main program to run the corresponding speed and correctness tests.

Method
The same template routine det_by_lu is used by the different AD packages.

Return Value
If this speed test is not yet supported by a particular package , the corresponding return value for link_det_lu should be false.

size
The argument size is the number of rows and columns in the matrix.

repeat
The argument repeat is the number of different matrices that the gradient (or determinant) is computed for.

matrix
The argument matrix is a vector with size*size elements. The input value of its elements does not matter. The output value of its elements is the last matrix that the gradient (or determinant) is computed for.

gradient
The argument gradient is a vector with size*size elements. The input value of its elements does not matter. The output value of its elements is the gradient of the determinant of matrix with respect to its elements.

double
In the case where package is double, only the first element of gradient is used and it is actually the determinant value (the gradient value is not computed).
Input File: speed/src/link_det_lu.cpp cppad-20170000.3/doc/link_det_minor.xml0000644000175200017650000001702313057470510016713 0ustar coincoin-web Speed Testing Gradient of Determinant by Minor Expansion
Prev Next link_det_minor

Speed Testing Gradient of Determinant by Minor Expansion

Prototype
extern bool link_det_minor(
     size_t                 size      ,
     size_t                 repeat    ,
     CppAD::vector<double> &matrix    ,
     CppAD::vector<double> &gradient
);
Purpose
Each package must define a version of this routine as specified below. This is used by the speed_main program to run the corresponding speed and correctness tests.

Method
The same template class det_by_minor is used by the different AD packages.

Return Value
If this speed test is not yet supported by a particular package , the corresponding return value for link_det_minor should be false.

size
The argument size is the number of rows and columns in the matrix.

repeat
The argument repeat is the number of different matrices that the gradient (or determinant) is computed for.

matrix
The argument matrix is a vector with size*size elements. The input value of its elements does not matter. The output value of its elements is the last matrix that the gradient (or determinant) is computed for.

gradient
The argument gradient is a vector with size*size elements. The input value of its elements does not matter. The output value of its elements is the gradient of the determinant of matrix with respect to its elements.

double
In the case where package is double, only the first element of gradient is used and it is actually the determinant value (the gradient value is not computed).
Input File: speed/src/link_det_minor.cpp cppad-20170000.3/doc/link_mat_mul.xml0000644000175200017650000002601613057470510016373 0ustar coincoin-web Speed Testing Derivative of Matrix Multiply
Prev Next link_mat_mul

Speed Testing Derivative of Matrix Multiply

Prototype
extern bool link_mat_mul(
     size_t                         size    ,
     size_t                         repeat  ,
     CppAD::vector<double>&         x       ,
     CppAD::vector<double>&         z       ,
     CppAD::vector<double>&         dz
);
Purpose
Each package must define a version of this routine as specified below. This is used by the speed_main program to run the corresponding speed and correctness tests.

Return Value
If this speed test is not yet supported by a particular package , the corresponding return value for link_mat_mul should be false.

n
The argument n is the number of rows and columns in the square matrix x .

repeat
The argument repeat is the number of different argument values that the derivative of z (or just the value of z ) will be computed.

x
The argument x is a vector with x.size() = size * size elements. The input value of its elements does not matter. The output value of its elements is the last random matrix that is multiplied and then summed to form z ; x i , j = x [ i * s + j ] where s = size .

z
The argument z is a vector with one element. The input value of the element does not matter. The output of its element the sum of the elements of y = x * x ; i.e., y i , j = ∑ k = 0 s -1 x i , k x k , j z = ∑ i = 0 s -1 ∑ j = 0 s -1 y i , j
dz
The argument dz is a vector with dz.size() = size * size . The input values of its elements do not matter. The output value of its elements form the derivative of z with respect to x .
Input File: speed/src/link_mat_mul.cpp cppad-20170000.3/doc/link_ode.xml0000644000175200017650000002604613057470510015507 0ustar coincoin-web Speed Testing the Jacobian of Ode Solution
Prev Next link_ode

Speed Testing the Jacobian of Ode Solution

Prototype
extern bool link_ode(
     size_t                 size      ,
     size_t                 repeat    ,
     CppAD::vector<double> &x         ,
     CppAD::vector<double> &jacobian
);
Purpose
Each package must define a version of this routine as specified below. This is used by the speed_main program to run the corresponding speed and correctness tests.

Method
The same template routine ode_evaluate is used by th different AD packages.

f
The function f : R n → R n that is defined and computed by evaluating ode_evaluate with a call of the form
     ode_evaluate(x, p, fp)
 with p equal to zero. Calls with the value p equal to one are used to check the derivative values.

Return Value
If this speed test is not yet supported by a particular package , the corresponding return value for link_ode should be false.

size
The argument size is the number of variables in the ordinary differential equations which is also equal to n .

repeat
The argument repeat is the number of times the Jacobian is computed.

x
The argument x is a vector with n elements. The input value of the elements of x does not matter. On output, it has been set to the argument value for which the function, or its derivative, is being evaluated. The value of this vector must change with each repetition.

jacobian
The argument jacobian is a vector with n 2 elements. The input value of its elements does not matter. The output value of its elements is the Jacobian of the function f ( x ) that corresponds to output value of x . To be more specific, for i = 0 , … , n -1 and j = 0 , … , n -1 , ∂ f [ i ] ∂ x [ j ] ( x ) = jacobian [ i · n + j ]
double
In the case where package is double, only the first n element of jacobian are modified and they are to the function value f ( x ) corresponding to the output value of x .
Input File: speed/src/link_ode.cpp cppad-20170000.3/doc/link_poly.xml0000644000175200017650000001723313057470510015721 0ustar coincoin-web Speed Testing Second Derivative of a Polynomial
Prev Next link_poly

Speed Testing Second Derivative of a Polynomial

Prototype
extern bool link_poly(
     size_t                 size    ,
     size_t                 repeat  ,
     CppAD::vector<double> &a       ,
     CppAD::vector<double> &z       ,
     CppAD::vector<double> &ddp
);
Purpose
Each package must define a version of this routine as specified below. This is used by the speed_main program to run the corresponding speed and correctness tests.

Method
The same template routine Poly is used by the different AD packages.

Return Value
If this speed test is not yet supported by a particular package , the corresponding return value for link_poly should be false.

size
The argument size is the order of the polynomial (the number of coefficients in the polynomial).

repeat
The argument repeat is the number of different argument values that the second derivative (or just the polynomial) will be computed at.

a
The argument a is a vector with size elements. The input value of its elements does not matter. The output value of its elements is the coefficients of the polynomial that is differentiated (i-th element is coefficient of order i ).

z
The argument z is a vector with one element. The input value of the element does not matter. The output of its element is the polynomial argument value were the last second derivative (or polynomial value) was computed.

ddp
The argument ddp is a vector with one element. The input value of its element does not matter. The output value of its element is the second derivative of the polynomial with respect to it's argument value.

double
In the case where package is double, the output value of the element of ddp is the polynomial value (the second derivative is not computed).
Input File: speed/src/link_poly.cpp cppad-20170000.3/doc/link_sparse_jacobian.xml0000644000175200017650000004231313057470510020056 0ustar coincoin-web Speed Testing Sparse Jacobian
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Speed Testing Sparse Jacobian

Prototype
extern bool link_sparse_jacobian(
     size_t                       size      ,
     size_t                       repeat    ,
     size_t                       m         ,
     const CppAD::vector<size_t>& row       ,
     const CppAD::vector<size_t>& col       ,
           CppAD::vector<double>& x         ,
           CppAD::vector<double>& jacobian  ,
           size_t&                n_sweep
);
Method
Given a range space dimension m the row index vector row , and column index vector col , a corresponding function f : R n → R m is defined by sparse_jac_fun . The non-zero entries in the Jacobian of this function have the form ∂ f [ row [ k ] ] ∂ x [ col [ k ] ] ] for some k between zero and K = row.size()-1 . All the other terms of the Jacobian are zero.

size
The argument size , referred to as n below, is the dimension of the domain space for f ( x ) .

repeat
The argument repeat is the number of times to repeat the test (with a different value for x corresponding to each repetition).

m
Is the dimension of the range space for the function f ( x ) .

row
The size of the vector row defines the value K . All the elements of row are between zero and m -1 .

col
The argument col is a vector with size K . The input value of its elements does not matter. On output, it has been set the column index vector for the last repetition. All the elements of col are between zero and n -1 . There are no duplicate row and column entires; i.e., if j != k ,
     row[j] != row[k] || col[j] != col[k]
x
The argument x has prototype
        CppAD::vector<double>& x
 and its size is n ; i.e., x.size() == size . The input value of the elements of x does not matter. On output, it has been set to the argument value for which the function, or its derivative, is being evaluated and placed in jacobian . The value of this vector need not change with each repetition.

jacobian
The argument jacobian has prototype
        CppAD::vector<double>& jacobian
 and its size is K . The input value of its elements does not matter. The output value of its elements is the Jacobian of the function f ( x ) . To be more specific, for k = 0 , … , K - 1 , ∂ f [ row [ k ] ] ∂ x [ col [ k ] ] ( x ) = jacobian [ k ]
n_sweep
The input value of n_sweep does not matter. On output, it is the value n_sweep corresponding to the evaluation of jacobian . This is also the number of colors corresponding to the coloring method , which can be set to colpack , and is otherwise cppad.

double
In the case where package is double, only the first m elements of jacobian are used and they are set to the value of f ( x ) .
Input File: speed/src/link_sparse_jacobian.cpp cppad-20170000.3/doc/microsoft_timer.xml0000644000175200017650000001002613057470510017117 0ustar coincoin-web Microsoft Version of Elapsed Number of Seconds
Prev Next microsoft_timer

Microsoft Version of Elapsed Number of Seconds

Syntax
s = microsoft_timer()

Purpose
This routine is accurate to within .02 seconds (see elapsed_seconds which uses this routine when the preprocessor symbol _MSC_VER is defined). It does not necessary work for time intervals that are greater than a day. It uses ::GetSystemTime for timing.

s
is a double equal to the number of seconds since the first call to microsoft_timer.

Linking
The source code for this routine is located in speed/src/microsoft_timer.cpp. The preprocessor symbol _MSC_VER must be defined, or this routine is not compiled.
Input File: speed/src/microsoft_timer.cpp cppad-20170000.3/doc/_microsoft_timer_xml.js0000644000175200017650000000370113057470510017754 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_main.xml', 'microsoft_timer.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'link_det_lu.xml', 'link_det_minor.xml', 'link_mat_mul.xml', 'link_ode.xml', 'link_poly.xml', 'link_sparse_hessian.xml', 'link_sparse_jacobian.xml', 'microsoft_timer.xml' ]; var list_current0 = [ 'microsoft_timer.xml#Syntax', 'microsoft_timer.xml#Purpose', 'microsoft_timer.xml#s', 'microsoft_timer.xml#Linking' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/speed_utility.xml0000644000175200017650000001465213057470510016606 0ustar coincoin-web Speed Testing Utilities
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Speed Testing Utilities

Speed Main Program
speed_main Running the Speed Test Program

Speed Utility Routines
det_by_lu Determinant Using Expansion by Lu Factorization
det_by_minor Determinant Using Expansion by Minors
det_of_minor Determinant of a Minor
det_33 Check Determinant of 3 by 3 matrix
det_grad_33 Check Gradient of Determinant of 3 by 3 matrix
mat_sum_sq Sum Elements of a Matrix Times Itself
ode_evaluate Evaluate a Function Defined in Terms of an ODE
sparse_jac_fun Evaluate a Function That Has a Sparse Jacobian
sparse_hes_fun Evaluate a Function That Has a Sparse Hessian
uniform_01 Simulate a [0,1] Uniform Random Variate

Library Routines
LuFactor LU Factorization of A Square Matrix
LuInvert Invert an LU Factored Equation
LuSolve Compute Determinant and Solve Linear Equations
Poly Evaluate a Polynomial or its Derivative

Source Code
det_by_lu.hpp Source: det_by_lu
det_by_minor.hpp Source: det_by_minor
det_grad_33.hpp Source: det_grad_33
det_of_minor.hpp Source: det_of_minor
lu_factor.hpp Source: LuFactor
lu_invert.hpp Source: LuInvert
lu_solve.hpp Source: LuSolve
mat_sum_sq.hpp Source: mat_sum_sq
poly.hpp Source: Poly
sparse_jac_fun.hpp Source: sparse_jac_fun
sparse_hes_fun.hpp Source: sparse_hes_fun
uniform_01.hpp Source: uniform_01
Input File: omh/speed/speed_utility.omh cppad-20170000.3/doc/det_by_lu.xml0000644000175200017650000003151413057470510015665 0ustar coincoin-web Determinant Using Expansion by Lu Factorization
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Determinant Using Expansion by Lu Factorization

Syntax
# include <cppad/speed/det_by_lu.hpp>
 det_by_lu<Scalar> det(n)
 d = det(a)
Inclusion
The template class det_by_lu is defined in the CppAD namespace by including the file cppad/speed/det_by_lu.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

Constructor
The syntax
     det_by_lu<Scalar> det(n)
 constructs the object det which can be used for evaluating the determinant of n by n matrices using LU factorization.

Scalar
The type Scalar can be any NumericType

n
The argument n has prototype
     size_t n
det
The syntax
     d = det(a)
 returns the determinant of the matrix A using LU factorization.

a
The argument a has prototype
     const Vector &a
 It must be a Vector with length n * n and with It must be a Vector with length n * n and with elements of type Scalar . The elements of the n × n matrix A are defined, for i = 0 , … , n -1 and j = 0 , … , n -1 , by A i , j = a [ i * m + j ]
d
The return value d has prototype
     Scalar d
Vector
If y is a Vector object, it must support the syntax
     y[i]
 where i has type size_t with value less than n * n . This must return a Scalar value corresponding to the i-th element of the vector y . This is the only requirement of the type Vector .

Example
The file det_by_lu.cpp contains an example and test of det_by_lu.hpp. It returns true if it succeeds and false otherwise.

Source Code
The file det_by_lu.hpp contains the source for this template function.
Input File: cppad/speed/det_by_lu.hpp cppad-20170000.3/doc/det_by_lu.cpp.xml0000644000175200017650000002206013057470510016442 0ustar coincoin-web Determinant Using Lu Factorization: Example and Test
Prev Next det_by_lu.cpp Headings

Determinant Using Lu Factorization: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_lu.hpp>

bool det_by_lu()
{     bool ok = true;

     // dimension of the matrix
     size_t n = 3;

     // construct the determinat object
     CppAD::det_by_lu<double> Det(n);

     double  a[] = {
          1., 2., 3.,  // a[0] a[1] a[2]
          3., 2., 1.,  // a[3] a[4] a[5]
          2., 1., 2.   // a[6] a[7] a[8]
     };
     CPPAD_TESTVECTOR(double) A(9);
     size_t i;
     for(i = 0; i < 9; i++)
          A[i] = a[i];


     // evaluate the determinant
     double det = Det(A);

     double check;
     check = a[0]*(a[4]*a[8] - a[5]*a[7])
           - a[1]*(a[3]*a[8] - a[5]*a[6])
           + a[2]*(a[3]*a[7] - a[4]*a[6]);

     ok = CppAD::NearEqual(det, check, 1e-10, 1e-10);

     return ok;
}
Input File: speed/example/det_by_lu.cpp cppad-20170000.3/doc/det_by_lu.hpp.xml0000644000175200017650000002752413057470510016461 0ustar coincoin-web Source: det_by_lu
Prev Next det_by_lu.hpp Headings

Source: det_by_lu
# ifndef CPPAD_DET_BY_LU_HPP
# define CPPAD_DET_BY_LU_HPP 
# include <cppad/cppad.hpp>
# include <complex>

// BEGIN CppAD namespace
namespace CppAD {

// The AD complex case is used by examples by not used by speed tests
// Must define a specializatgion of LeqZero,AbsGeq for the ADComplex case
typedef std::complex<double>     Complex;
typedef CppAD::AD<Complex>     ADComplex;
CPPAD_BOOL_UNARY(Complex,  LeqZero )
CPPAD_BOOL_BINARY(Complex, AbsGeq )

template <class Scalar>
class det_by_lu {
private:
     const size_t m_;
     const size_t n_;
     CPPAD_TESTVECTOR(Scalar) A_;
     CPPAD_TESTVECTOR(Scalar) B_;
     CPPAD_TESTVECTOR(Scalar) X_;
public:
     det_by_lu(size_t n) : m_(0), n_(n), A_(n * n)
     {     }

     template <class Vector>
     inline Scalar operator()(const Vector &x)
     {
          using CppAD::exp;

          Scalar       logdet;
          Scalar       det;
          int          signdet;
          size_t       i;

          // copy matrix so it is not overwritten
          for(i = 0; i < n_ * n_; i++)
               A_[i] = x[i];

          // comput log determinant
          signdet = CppAD::LuSolve(
               n_, m_, A_, B_, X_, logdet);

/*
          // Do not do this for speed test because it makes floating
          // point operation sequence very simple.
          if( signdet == 0 )
               det = 0;
          else     det =  Scalar( signdet ) * exp( logdet );
*/

          // convert to determinant
          det     = Scalar( signdet ) * exp( logdet );

# ifdef FADBAD
          // Fadbad requires tempories to be set to constants
          for(i = 0; i < n_ * n_; i++)
               A_[i] = 0;
# endif

          return det;
     }
};
} // END CppAD namespace
# endif
Input File: omh/det_by_lu_hpp.omh cppad-20170000.3/doc/det_of_minor.xml0000644000175200017650000006346513057470510016375 0ustar coincoin-web Determinant of a Minor
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Determinant of a Minor

Syntax
# include <cppad/speed/det_of_minor.hpp>
 d = det_of_minor(a, m, n, r, c)

Inclusion
The template function det_of_minor is defined in the CppAD namespace by including the file cppad/speed/det_of_minor.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

Purpose
This template function returns the determinant of a minor of the matrix A using expansion by minors. The elements of the n × n minor M of the matrix A are defined, for i = 0 , … , n -1 and j = 0 , … , n -1 , by M i , j = A R ( i ) , C ( j ) where the functions R ( i ) is defined by the argument r and C ( j ) is defined by the argument c .

This template function is for example and testing purposes only. Expansion by minors is chosen as an example because it uses a lot of floating point operations yet does not require much source code (on the order of m factorial floating point operations and about 70 lines of source code including comments). This is not an efficient method for computing a determinant; for example, using an LU factorization would be better.

Determinant of A
If the following conditions hold, the minor is the entire matrix A and hence det_of_minor will return the determinant of A :
  1. n = m .
  2. for i = 0 , … , m -1 , r [ i ] = i + 1 , and r [ m ] = 0 .
  3. for j = 0 , … , m -1 , c [ j ] = j + 1 , and c [ m ] = 0 .


a
The argument a has prototype
     const std::vector<Scalar>& a
 and is a vector with size m * m (see description of Scalar below). The elements of the m × m matrix A are defined, for i = 0 , … , m -1 and j = 0 , … , m -1 , by A i , j = a [ i * m + j ]
m
The argument m has prototype
     size_t m
 and is the number of rows (and columns) in the square matrix A .

n
The argument n has prototype
     size_t n
 and is the number of rows (and columns) in the square minor M .

r
The argument r has prototype
     std::vector<size_t>& r
 and is a vector with m + 1 elements. This vector defines the function R ( i ) which specifies the rows of the minor M . To be specific, the function R ( i ) for i = 0 , … , n -1 is defined by R ( 0 ) = r [ m ] R ( i + 1 ) = r [ R ( i ) ] All the elements of r must have value less than or equal m . The elements of vector r are modified during the computation, and restored to their original value before the return from det_of_minor.

c
The argument c has prototype
     std::vector<size_t>& c
 and is a vector with m + 1 elements This vector defines the function C ( i ) which specifies the rows of the minor M . To be specific, the function C ( i ) for j = 0 , … , n -1 is defined by C ( 0 ) = c [ m ] C ( j + 1 ) = c [ C ( j ) ] All the elements of c must have value less than or equal m . The elements of vector c are modified during the computation, and restored to their original value before the return from det_of_minor.

d
The result d has prototype
     Scalar d
 and is equal to the determinant of the minor M .

Scalar
If x and y are objects of type Scalar and i is an object of type int, the Scalar must support the following operations:
Syntax Description Result Type
Scalar x default constructor for Scalar object.
x = i set value of x to current value of i
x = y set value of x to current value of y
x + y value of x plus y Scalar
x - y value of x minus y Scalar
x * y value of x times value of y Scalar

Example
The file det_of_minor.cpp contains an example and test of det_of_minor.hpp. It returns true if it succeeds and false otherwise.

Source Code
The file det_of_minor.hpp contains the source for this template function.
Input File: cppad/speed/det_of_minor.hpp cppad-20170000.3/doc/det_of_minor.cpp.xml0000644000175200017650000003025113057470510017141 0ustar coincoin-web Determinant of a Minor: Example and Test
Prev Next det_of_minor.cpp Headings

Determinant of a Minor: Example and Test
# include <vector>
# include <cstddef>
# include <cppad/speed/det_of_minor.hpp>

bool det_of_minor()
{     bool   ok = true;
     size_t i;

     // dimension of the matrix A
     size_t m = 3;
     // index vectors set so minor is the entire matrix A
     std::vector<size_t> r(m + 1);
     std::vector<size_t> c(m + 1);
     for(i= 0; i < m; i++)
     {     r[i] = i+1;
          c[i] = i+1;
     }
     r[m] = 0;
     c[m] = 0;
     // values in the matrix A
     double  data[] = {
          1., 2., 3.,
          3., 2., 1.,
          2., 1., 2.
     };
     // construct vector a with the values of the matrix A
     std::vector<double> a(data, data + 9);

     // evaluate the determinant of A
     size_t n   = m; // minor has same dimension as A
     double det = CppAD::det_of_minor(a, m, n, r, c);

     // check the value of the determinant of A
     ok &= (det == (double) (1*(2*2-1*1) - 2*(3*2-1*2) + 3*(3*1-2*2)) );

     // minor where row 0 and column 1 are removed
     r[m] = 1;  // skip row index 0 by starting at row index 1
     c[0] = 2;  // skip column index 1 by pointing from index 0 to index 2
     // evaluate determinant of the minor
     n   = m - 1; // dimension of the minor
     det = CppAD::det_of_minor(a, m, m-1, r, c);

     // check the value of the determinant of the minor
     ok &= (det == (double) (3*2-1*2) );

     return ok;
}
Input File: speed/example/det_of_minor.cpp cppad-20170000.3/doc/det_of_minor.hpp.xml0000644000175200017650000002526013057470510017152 0ustar coincoin-web Source: det_of_minor
Prev Next det_of_minor.hpp Headings

Source: det_of_minor
# ifndef CPPAD_DET_OF_MINOR_HPP
# define CPPAD_DET_OF_MINOR_HPP 
namespace CppAD { // BEGIN CppAD namespace
template <class Scalar>
Scalar det_of_minor(
     const std::vector<Scalar>& a  ,
     size_t                     m  ,
     size_t                     n  ,
     std::vector<size_t>&       r  ,
     std::vector<size_t>&       c  )
{
     const size_t R0 = r[m]; // R(0)
     size_t       Cj = c[m]; // C(j)    (case j = 0)
     size_t       Cj1 = m;   // C(j-1)  (case j = 0)

     // check for 1 by 1 case
     if( n == 1 ) return a[ R0 * m + Cj ];

     // initialize determinant of the minor M
     Scalar detM = Scalar(0);

     // initialize sign of factor for next sub-minor
     int s = 1;

     // remove row with index 0 in M from all the sub-minors of M
     r[m] = r[R0];

     // for each column of M
     for(size_t j = 0; j < n; j++)
     {     // element with index (0,j) in the minor M
          Scalar M0j = a[ R0 * m + Cj ];

          // remove column with index j in M to form next sub-minor S of M
          c[Cj1] = c[Cj];

          // compute determinant of the current sub-minor S
          Scalar detS = det_of_minor(a, m, n - 1, r, c);

          // restore column Cj to represenation of M as a minor of A
          c[Cj1] = Cj;

          // include this sub-minor term in the summation
          if( s > 0 )
               detM = detM + M0j * detS;
          else     detM = detM - M0j * detS;

          // advance to next column of M
          Cj1 = Cj;
          Cj  = c[Cj];
          s   = - s;
     }

     // restore row zero to the minor representation for M
     r[m] = R0;

     // return the determinant of the minor M
     return detM;
}
} // END CppAD namespace
# endif
Input File: omh/det_of_minor_hpp.omh cppad-20170000.3/doc/det_by_minor.xml0000644000175200017650000003132113057470510016365 0ustar coincoin-web Determinant Using Expansion by Minors
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Determinant Using Expansion by Minors

Syntax
# include <cppad/speed/det_by_minor.hpp>
 det_by_minor<Scalar> det(n)
 d = det(a)
Inclusion
The template class det_by_minor is defined in the CppAD namespace by including the file cppad/speed/det_by_minor.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

Constructor
The syntax
     det_by_minor<Scalar> det(n)
 constructs the object det which can be used for evaluating the determinant of n by n matrices using expansion by minors.

Scalar
The type Scalar must satisfy the same conditions as in the function det_of_minor .

n
The argument n has prototype
     size_t n
det
The syntax
     d = det(a)
 returns the determinant of the matrix A using expansion by minors.

a
The argument a has prototype
     const Vector &a
 It must be a Vector with length n * n and with elements of type Scalar . The elements of the n × n matrix A are defined, for i = 0 , … , n -1 and j = 0 , … , n -1 , by A i , j = a [ i * m + j ]
d
The return value d has prototype
     Scalar d
 It is equal to the determinant of A .

Vector
If y is a Vector object, it must support the syntax
     y[i]
 where i has type size_t with value less than n * n . This must return a Scalar value corresponding to the i-th element of the vector y . This is the only requirement of the type Vector .

Example
The file det_by_minor.cpp contains an example and test of det_by_minor.hpp. It returns true if it succeeds and false otherwise.

Source Code
The file det_by_minor.hpp contains the source for this template function.
Input File: cppad/speed/det_by_minor.hpp cppad-20170000.3/doc/det_by_minor.cpp.xml0000644000175200017650000002143713057470510017155 0ustar coincoin-web Determinant Using Expansion by Minors: Example and Test
Prev Next det_by_minor.cpp Headings

Determinant Using Expansion by Minors: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_minor.hpp>

bool det_by_minor()
{     bool ok = true;

     // dimension of the matrix
     size_t n = 3;

     // construct the determinat object
     CppAD::det_by_minor<double> Det(n);

     double  a[] = {
          1., 2., 3.,  // a[0] a[1] a[2]
          3., 2., 1.,  // a[3] a[4] a[5]
          2., 1., 2.   // a[6] a[7] a[8]
     };
     CPPAD_TESTVECTOR(double) A(9);
     size_t i;
     for(i = 0; i < 9; i++)
          A[i] = a[i];


     // evaluate the determinant
     double det = Det(A);

     double check;
     check = a[0]*(a[4]*a[8] - a[5]*a[7])
           - a[1]*(a[3]*a[8] - a[5]*a[6])
           + a[2]*(a[3]*a[7] - a[4]*a[6]);

     ok = det == check;

     return ok;
}
Input File: speed/example/det_by_minor.cpp cppad-20170000.3/doc/det_by_minor.hpp.xml0000644000175200017650000002277313057470510017166 0ustar coincoin-web Source: det_by_minor
Prev Next det_by_minor.hpp Headings

Source: det_by_minor
# ifndef CPPAD_DET_BY_MINOR_HPP
# define CPPAD_DET_BY_MINOR_HPP 
# include <cppad/cppad.hpp>
# include <cppad/speed/det_of_minor.hpp>

// BEGIN CppAD namespace
namespace CppAD {

template <class Scalar>
class det_by_minor {
private:
     size_t              m_;

     // made mutable because modified and then restored
     mutable std::vector<size_t> r_;
     mutable std::vector<size_t> c_;

     // make mutable because its value does not matter
     mutable std::vector<Scalar> a_;
public:
     det_by_minor(size_t m) : m_(m) , r_(m + 1) , c_(m + 1), a_(m * m)
     {
          size_t i;

          // values for r and c that correspond to entire matrix
          for(i = 0; i < m; i++)
          {     r_[i] = i+1;
               c_[i] = i+1;
          }
          r_[m] = 0;
          c_[m] = 0;
     }

     template <class Vector>
     inline Scalar operator()(const Vector &x) const
     {     size_t i = m_ * m_;
          while(i--)
               a_[i] = x[i];
          return det_of_minor(a_, m_, m_, r_, c_);
     }

};

} // END CppAD namespace
# endif
Input File: omh/det_by_minor_hpp.omh cppad-20170000.3/doc/det_33.xml0000644000175200017650000002155013057470510014777 0ustar coincoin-web Check Determinant of 3 by 3 matrix
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Check Determinant of 3 by 3 matrix

Syntax
# include <cppad/speed/det_33.hpp>
 ok = det_33(x, d)

Purpose
This routine can be used to check a method for computing the determinant of a matrix.

Inclusion
The template function det_33 is defined in the CppAD namespace by including the file cppad/speed/det_33.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

x
The argument x has prototype
     const Vector &x
 . It contains the elements of the matrix X in row major order; i.e., X i , j = x [ i * 3 + j ]
d
The argument d has prototype
     const Vector &d
 . It is tested to see if d[0] it is equal to det ( X ) .

Vector
If y is a Vector object, it must support the syntax
     y[i]
 where i has type size_t with value less than 9. This must return a double value corresponding to the i-th element of the vector y . This is the only requirement of the type Vector . (Note that only the first element of the vector d is used.)

ok
The return value ok has prototype
     bool ok
 It is true, if the determinant d[0] passes the test and false otherwise.

Source Code
The file det_33.hpp contains the source code for this template function.
Input File: cppad/speed/det_33.hpp cppad-20170000.3/doc/det_33.hpp.xml0000644000175200017650000001645313057470510015573 0ustar coincoin-web Source: det_33
Prev Next det_33.hpp Headings

Source: det_33
# ifndef CPPAD_DET_33_HPP
# define CPPAD_DET_33_HPP 
# include <cppad/utility/near_equal.hpp>
namespace CppAD {
template <class Vector>
     bool det_33(const Vector &x, const Vector &d)
     {     bool ok = true;

          // use expansion by minors to compute the determinant by hand
          double check = 0.;
          check += x[0] * ( x[4] * x[8] - x[5] * x[7] );
          check -= x[1] * ( x[3] * x[8] - x[5] * x[6] );
          check += x[2] * ( x[3] * x[7] - x[4] * x[6] );

          ok &= CppAD::NearEqual(check, d[0], 1e-10, 1e-10);

          return ok;
     }
}
# endif
Input File: omh/det_33_hpp.omh cppad-20170000.3/doc/det_grad_33.xml0000644000175200017650000002252413057470510015776 0ustar coincoin-web Check Gradient of Determinant of 3 by 3 matrix
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Check Gradient of Determinant of 3 by 3 matrix

Syntax
# include <cppad/speed/det_grad_33.hpp>
 ok = det_grad_33(x, g)

Purpose
This routine can be used to check a method for computing the gradient of the determinant of a matrix.

Inclusion
The template function det_grad_33 is defined in the CppAD namespace by including the file cppad/speed/det_grad_33.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

x
The argument x has prototype
     const Vector &x
 . It contains the elements of the matrix X in row major order; i.e., X i , j = x [ i * 3 + j ]
g
The argument g has prototype
     const Vector &g
 . It contains the elements of the gradient of det ( X ) in row major order; i.e., ∂ det ( X ) ∂ X ( i , j ) = g [ i * 3 + j ]
Vector
If y is a Vector object, it must support the syntax
     y[i]
 where i has type size_t with value less than 9. This must return a double value corresponding to the i-th element of the vector y . This is the only requirement of the type Vector .

ok
The return value ok has prototype
     bool ok
 It is true, if the gradient g passes the test and false otherwise.

Source Code
The file det_grad_33.hpp contains the source code for this template function.
Input File: cppad/speed/det_grad_33.hpp cppad-20170000.3/doc/det_grad_33.hpp.xml0000644000175200017650000003420513057470510016563 0ustar coincoin-web Source: det_grad_33
Prev Next det_grad_33.hpp Headings

Source: det_grad_33
# ifndef CPPAD_DET_GRAD_33_HPP
# define CPPAD_DET_GRAD_33_HPP 
# include <limits>
# include <cppad/utility/near_equal.hpp>
namespace CppAD {
template <class Vector>
     bool det_grad_33(const Vector &x, const Vector &g)
     {     bool ok = true;
          typedef typename Vector::value_type Float;
          Float eps = 10. * Float( std::numeric_limits<double>::epsilon() );

          // use expansion by minors to compute the derivative by hand
          double check[9];
          check[0] = + ( x[4] * x[8] - x[5] * x[7] );
          check[1] = - ( x[3] * x[8] - x[5] * x[6] );
          check[2] = + ( x[3] * x[7] - x[4] * x[6] );
          //
          check[3] = - ( x[1] * x[8] - x[2] * x[7] );
          check[4] = + ( x[0] * x[8] - x[2] * x[6] );
          check[5] = - ( x[0] * x[7] - x[1] * x[6] );
          //
          check[6] = + ( x[1] * x[5] - x[2] * x[4] );
          check[7] = - ( x[0] * x[5] - x[2] * x[3] );
          check[8] = + ( x[0] * x[4] - x[1] * x[3] );
          //
          for(size_t i = 0; i < 3 * 3; i++)
               ok &= CppAD::NearEqual(check[i], g[i], eps, eps);

          return ok;
     }
}
# endif
Input File: omh/det_grad_33_hpp.omh cppad-20170000.3/doc/mat_sum_sq.xml0000644000175200017650000003355413057470510016075 0ustar coincoin-web Sum Elements of a Matrix Times Itself
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Sum Elements of a Matrix Times Itself

Syntax
# include <cppad/speed/mat_sum_sq.hpp>
 mat_sum_sq(n, x, y, z)

Purpose
This routine is intended for use with the matrix multiply speed tests; to be specific, it computes y i , j = ∑ k = 0 n -1 x i , k x k , j z 0 = ∑ i = 0 n -1 ∑ j = 0 n -1 y i , j see link_mat_mul .

Inclusion
The template function mat_sum_sq is defined in the CppAD namespace by including the file cppad/speed/mat_sum_sq.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

n
This argument has prototype
     size_t n
 It specifies the size of the matrices.

x
The argument x has prototype
     const Vector &x
 and x.size() == n * n . It contains the elements of x in row major order; i.e., x i , j = x [ i * n + j ]
y
The argument y has prototype
     Vector& y
 and y.size() == n * n . The input value of its elements does not matter. Upon return, y i , j = ∑ k = 0 n -1 x i , k x k , j y [ i * n + j ] = y i , j
z
The argument d has prototype
     Vector& z
 . The input value of its element does not matter. Upon return z 0 = ∑ i = 0 n -1 ∑ j = 0 n y i , j z [ 0 ] = z 0
Vector
The type Vector is any SimpleVector , or it can be a raw pointer to the vector elements. The element type must support addition, multiplication, and assignment to both its own type and to a double value.

Example
The file mat_sum_sq.cpp contains an example and test of mat_sum_sq.hpp. It returns true if it succeeds and false otherwise.

Source Code
The file mat_sum_sq.hpp contains the source for this template function.
Input File: cppad/speed/mat_sum_sq.hpp cppad-20170000.3/doc/mat_sum_sq.cpp.xml0000644000175200017650000002321013057470510016642 0ustar coincoin-web Sum of the Elements of the Square of a Matrix: Example and Test
Prev Next mat_sum_sq.cpp Headings

Sum of the Elements of the Square of a Matrix: Example and Test
# include <vector>
# include <cstddef>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/mat_sum_sq.hpp>

bool mat_sum_sq()
{     bool   ok = true;
     double x_00, x_01, x_10, x_11, check;

     // dimension of the matrices x, y, and the result z
     size_t n = 2;
     CppAD::vector<double> x(n * n), y(n * n), z(1);

     // x = [ 1 2 ; 3 4 ]
     x[0] = x_00 = 1.;
     x[1] = x_01 = 2.;
     x[2] = x_10 = 3.;
     x[3] = x_11 = 4.;

     // compute y = x * x and z = sum of elements in y
     CppAD::mat_sum_sq(n, x, y, z);

     // check y_00
     check = x_00 * x_00 + x_01 * x_10;
     ok   &= (check == y[0]);

     // check y_01
     check = x_00 * x_01 + x_01 * x_11;
     ok   &= (check == y[1]);

     // check y_10
     check = x_10 * x_00 + x_11 * x_10;
     ok   &= (check == y[2]);

     // check y_11
     check = x_10 * x_01 + x_11 * x_11;
     ok   &= (check == y[3]);

     // check z
     check = y[0] + y[1] + y[2] + y[3];
     ok   &= (check == z[0]);

     return ok;
}
Input File: speed/example/mat_sum_sq.cpp cppad-20170000.3/doc/mat_sum_sq.hpp.xml0000644000175200017650000001715313057470510016660 0ustar coincoin-web Source: mat_sum_sq
Prev Next mat_sum_sq.hpp Headings

Source: mat_sum_sq
# ifndef CPPAD_MAT_SUM_SQ_HPP
# define CPPAD_MAT_SUM_SQ_HPP 
# include <cstddef>
//
namespace CppAD {
     template <class Vector>
     void mat_sum_sq(size_t n, Vector& x , Vector& y , Vector& z)
     {     size_t i, j, k;
          // Very simple computation of y = x * x for speed comparison
          for(i = 0; i < n; i++)
          {     for(j = 0; j < n; j++)
               {     y[i * n + j] = 0.;
                    for(k = 0; k < n; k++)
                         y[i * n + j] += x[i * n + k] * x[k * n + j];
               }
          }
          z[0] = 0.;
          for(i = 0; i < n; i++)
          {     for(j = 0; j < n; j++)
                    z[0] += y[i * n + j];
          }
          return;
     }

}
# endif
Input File: omh/mat_sum_sq_hpp.omh cppad-20170000.3/doc/ode_evaluate.xml0000644000175200017650000004001713057470510016352 0ustar coincoin-web Evaluate a Function Defined in Terms of an ODE
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Evaluate a Function Defined in Terms of an ODE

Syntax
# include <cppad/speed/ode_evaluate.hpp>
 ode_evaluate(x, p, fp)

Purpose
This routine evaluates a function f : R n → R n defined by f ( x ) = y ( x , 1 ) where y ( x , t ) solves the ordinary differential equation y ( x , 0 ) = x ∂ t y ( x , t ) = g [ y ( x , t ) , t ] where g : R n × R → R n is an unspecified function.

Inclusion
The template function ode_evaluate is defined in the CppAD namespace by including the file cppad/speed/ode_evaluate.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

Float

Operation Sequence
The type Float must be a NumericType . The Float operation sequence for this routine does not depend on the value of the argument x , hence it does not need to be retaped for each value of x .

fabs
If y and z are Float objects, the syntax
     y = fabs(z)
 must be supported. Note that it does not matter if the operation sequence for fabs depends on z because the corresponding results are not actually used by ode_evaluate; see fabs in Runge45 .

x
The argument x has prototype
     const CppAD::vector<Float>& x
 It contains he argument value for which the function, or its derivative, is being evaluated. The value n is determined by the size of the vector x .

p
The argument p has prototype
     size_t p
p == 0
In this case a numerical method is used to solve the ode and obtain an accurate approximation for y ( x , 1 ) . This numerical method has a fixed that does not depend on x .

p = 1
In this case an analytic solution for the partial derivative ∂ x y ( x , 1 ) is returned.

fp
The argument fp has prototype
     CppAD::vector<Float>& fp
 The input value of the elements of fp does not matter.

Function
If p is zero, fp has size equal to n and contains the value of y ( x , 1 ) .

Gradient
If p is one, fp has size equal to n^2 and for i = 0 , … and n -1 , j = 0 , … , n -1 ∂ y [ i ] ∂ x [ j ] ( x , 1 ) = fp [ i · n + j ]
Example
The file ode_evaluate.cpp contains an example and test of ode_evaluate.hpp. It returns true if it succeeds and false otherwise.

Source Code
The file ode_evaluate.hpp contains the source code for this template function.
Input File: cppad/speed/ode_evaluate.hpp cppad-20170000.3/doc/ode_evaluate.cpp.xml0000644000175200017650000002273413057470510017141 0ustar coincoin-web ode_evaluate: Example and test
Prev Next ode_evaluate.cpp Headings

ode_evaluate: Example and test
# include <cppad/speed/ode_evaluate.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/cppad.hpp>

bool ode_evaluate(void)
{     using CppAD::NearEqual;
     using CppAD::AD;

     bool ok = true;

     size_t n = 3;
     CppAD::vector<double>       x(n);
     CppAD::vector<double>       ym(n * n);
     CppAD::vector< AD<double> > X(n);
     CppAD::vector< AD<double> > Ym(n);

     // choose x
     size_t j;
     for(j = 0; j < n; j++)
     {     x[j] = double(j + 1);
          X[j] = x[j];
     }

     // declare independent variables
     Independent(X);

     // evaluate function
     size_t m = 0;
     CppAD::ode_evaluate(X, m, Ym);

     // evaluate derivative
     m = 1;
     CppAD::ode_evaluate(x, m, ym);

     // use AD to evaluate derivative
     CppAD::ADFun<double>   F(X, Ym);
     CppAD::vector<double>  dy(n * n);
     dy = F.Jacobian(x);

     size_t k;
     for(k = 0; k < n * n; k++)
          ok &= NearEqual(ym[k], dy[k] , 1e-7, 1e-7);

     return ok;
}
Input File: speed/example/ode_evaluate.cpp cppad-20170000.3/doc/ode_evaluate.hpp.xml0000644000175200017650000004226413057470510017146 0ustar coincoin-web Source: ode_evaluate
Prev Next ode_evaluate.hpp Headings

Source: ode_evaluate
# ifndef CPPAD_ODE_EVALUATE_HPP
# define CPPAD_ODE_EVALUATE_HPP 
# include <cppad/utility/vector.hpp>
# include <cppad/utility/ode_err_control.hpp>
# include <cppad/utility/runge_45.hpp>

namespace CppAD {

     template <class Float>
     class ode_evaluate_fun {
     public:
          // Given that y_i (0) = x_i,
          // the following y_i (t) satisfy the ODE below:
          // y_0 (t) = x[0]
          // y_1 (t) = x[1] + x[0] * t
          // y_2 (t) = x[2] + x[1] * t + x[0] * t^2/2
          // y_3 (t) = x[3] + x[2] * t + x[1] * t^2/2 + x[0] * t^3 / 3!
          // ...
          void Ode(
               const Float&                    t,
               const CppAD::vector<Float>&     y,
               CppAD::vector<Float>&           f)
          {     size_t n  = y.size();
               f[0]      = 0.;
               for(size_t k = 1; k < n; k++)
                    f[k] = y[k-1];
          }
     };
     //
     template <class Float>
     void ode_evaluate(
          const CppAD::vector<Float>& x  ,
          size_t                      p  ,
          CppAD::vector<Float>&       fp )
     {     using CppAD::vector;
          typedef vector<Float> VectorFloat;

          size_t n = x.size();
          CPPAD_ASSERT_KNOWN( p == 0 || p == 1,
               "ode_evaluate: p is not zero or one"
          );
          CPPAD_ASSERT_KNOWN(
               ((p==0) & (fp.size()==n)) || ((p==1) & (fp.size()==n*n)),
               "ode_evaluate: the size of fp is not correct"
          );
          if( p == 0 )
          {     // function that defines the ode
               ode_evaluate_fun<Float> F;

               // number of Runge45 steps to use
               size_t M = 10;

               // initial and final time
               Float ti = 0.0;
               Float tf = 1.0;

               // initial value for y(x, t); i.e. y(x, 0)
               // (is a reference to x)
               const VectorFloat& yi = x;

               // final value for y(x, t); i.e., y(x, 1)
               // (is a reference to fp)
               VectorFloat& yf = fp;

               // Use fourth order Runge-Kutta to solve ODE
               yf = CppAD::Runge45(F, M, ti, tf, yi);

               return;
          }
          /* Compute derivaitve of y(x, 1) w.r.t x
          y_0 (x, t) = x[0]
          y_1 (x, t) = x[1] + x[0] * t
          y_2 (x, t) = x[2] + x[1] * t + x[0] * t^2/2
          y_3 (x, t) = x[3] + x[2] * t + x[1] * t^2/2 + x[0] * t^3 / 3!
          ...
          */
          size_t i, j, k;
          for(i = 0; i < n; i++)
          {     for(j = 0; j < n; j++)
                    fp[ i * n + j ] = 0.0;
          }
          size_t factorial = 1;
          for(k = 0; k < n; k++)
          {     if( k > 1 )
                    factorial *= k;
               for(i = k; i < n; i++)
               {     // partial w.r.t x[i-k] of x[i-k] * t^k / k!
                    j = i - k;
                    fp[ i * n + j ] += 1.0 / Float(factorial);
               }
          }
     }
}
# endif
Input File: omh/ode_evaluate.omh cppad-20170000.3/doc/sparse_jac_fun.xml0000644000175200017650000005102513057470510016700 0ustar coincoin-web Evaluate a Function That Has a Sparse Jacobian
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Evaluate a Function That Has a Sparse Jacobian

Syntax
# include <cppad/speed/sparse_jac_fun.hpp>
 sparse_jac_fun(m, n, x, row, col, p, fp)

Purpose
This routine evaluates f ( x ) and f ( 1 ) ( x ) where the Jacobian f ( 1 ) ( x ) is sparse. The function f : R n → R m only depends on the size and contents of the index vectors row and col . The non-zero entries in the Jacobian of this function have one of the following forms: ∂ f [ row [ k ] ] ∂ x [ col [ k ] ] for some k between zero and K -1 . All the other terms of the Jacobian are zero.

Inclusion
The template function sparse_jac_fun is defined in the CppAD namespace by including the file cppad/speed/sparse_jac_fun.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

Float
The type Float must be a NumericType . In addition, if y and z are Float objects,
     y = exp(z)
 must set the y equal the exponential of z , i.e., the derivative of y with respect to z is equal to y .

FloatVector
The type FloatVector is any SimpleVector , or it can be a raw pointer, with elements of type Float .

n
The argument n has prototype
     size_t n
 It specifies the dimension for the domain space for f ( x ) .

m
The argument m has prototype
     size_t m
 It specifies the dimension for the range space for f ( x ) .

x
The argument x has prototype
     const FloatVector& x
 It contains the argument value for which the function, or its derivative, is being evaluated. We use n to denote the size of the vector x .

row
The argument row has prototype
      const CppAD::vector<size_t>& row
 It specifies indices in the range of f ( x ) for non-zero components of the Jacobian (see purpose above). The value K is defined by K = row.size() . All the elements of row must be between zero and m-1 .

col
The argument row has prototype
      const CppAD::vector<size_t>& col
 and its size must be K ; i.e., the same as for col . It specifies the component of x for the non-zero Jacobian terms. All the elements of col must be between zero and n-1 .

p
The argument p has prototype
     size_t p
 It is either zero or one and specifies the order of the derivative of f that is being evaluated, i.e., f ( p ) ( x ) is evaluated.

fp
The argument fp has prototype
     FloatVector& fp
 If p = 0 , it size is m otherwise its size is K . The input value of the elements of fp does not matter.

Function
If p is zero, fp has size m and (fp[0], ... , fp[m-1]) is the value of f ( x ) .

Jacobian
If p is one, fp has size K and for k = 0 , … , K -1 , ∂ f [ row [ i ] ] ∂ x [ col [ j ] ] = fp [ k ]
Example
The file sparse_jac_fun.cpp contains an example and test of sparse_jac_fun.hpp. It returns true if it succeeds and false otherwise.

Source Code
The file sparse_jac_fun.hpp contains the source code for this template function.
Input File: cppad/speed/sparse_jac_fun.hpp cppad-20170000.3/doc/sparse_jac_fun.hpp.xml0000644000175200017650000002475313057470510017476 0ustar coincoin-web Source: sparse_jac_fun
Prev Next sparse_jac_fun.hpp Headings

Source: sparse_jac_fun
# ifndef CPPAD_SPARSE_JAC_FUN_HPP
# define CPPAD_SPARSE_JAC_FUN_HPP 
# include <cppad/core/cppad_assert.hpp>
# include <cppad/utility/check_numeric_type.hpp>
# include <cppad/utility/vector.hpp>

// following needed by gcc under fedora 17 so that exp(double) is defined
# include <cppad/base_require.hpp>

namespace CppAD {
     template <class Float, class FloatVector>
     void sparse_jac_fun(
          size_t                       m    ,
          size_t                       n    ,
          const FloatVector&           x    ,
          const CppAD::vector<size_t>& row  ,
          const CppAD::vector<size_t>& col  ,
          size_t                       p    ,
          FloatVector&                 fp   )
     {
          // check numeric type specifications
          CheckNumericType<Float>();
          // check value of p
          CPPAD_ASSERT_KNOWN(
               p == 0 || p == 1,
               "sparse_jac_fun: p != 0 and p != 1"
          );
          size_t K = row.size();
          CPPAD_ASSERT_KNOWN(
               K >= m,
               "sparse_jac_fun: row.size() < m"
          );
          size_t i, j, k;

          if( p == 0 )
               for(i = 0; i < m; i++)
                    fp[i] = Float(0);

          Float t;
          for(k = 0; k < K; k++)
          {     i    = row[k];
               j    = col[k];
               t    = exp( x[j] * x[j] / 2.0 );
               switch(p)
               {
                    case 0:
                    fp[i] += t;
                    break;

                    case 1:
                    fp[k] = t * x[j];
                    break;
               }
          }
     }
}
# endif
Input File: omh/sparse_jac_fun.omh cppad-20170000.3/doc/sparse_hes_fun.xml0000644000175200017650000005534413057470510016732 0ustar coincoin-web Evaluate a Function That Has a Sparse Hessian
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Evaluate a Function That Has a Sparse Hessian

Syntax
# include <cppad/speed/sparse_hes_fun.hpp>
 sparse_hes_fun(n, x, row, col, p, fp)

Purpose
This routine evaluates f ( x ) , f ( 1 ) ( x ) , or f ( 2 ) ( x ) where the Hessian f ( 2 ) ( x ) is sparse. The function f : R n → R only depends on the size and contents of the index vectors row and col . The non-zero entries in the Hessian of this function have one of the following forms: ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ row [ k ] ] , ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ col [ k ] ] , ∂ 2 f ∂ x [ col [ k ] ] ∂ x [ row [ k ] ] , ∂ 2 f ∂ x [ col [ k ] ] ∂ x [ col [ k ] ] for some k between zero and K -1 . All the other terms of the Hessian are zero.

Inclusion
The template function sparse_hes_fun is defined in the CppAD namespace by including the file cppad/speed/sparse_hes_fun.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

Float
The type Float must be a NumericType . In addition, if y and z are Float objects,
     y = exp(z)
 must set the y equal the exponential of z , i.e., the derivative of y with respect to z is equal to y .

FloatVector
The type FloatVector is any SimpleVector , or it can be a raw pointer, with elements of type Float .

n
The argument n has prototype
     size_t n
 It specifies the dimension for the domain space for f ( x ) .

x
The argument x has prototype
     const FloatVector& x
 It contains the argument value for which the function, or its derivative, is being evaluated. We use n to denote the size of the vector x .

row
The argument row has prototype
      const CppAD::vector<size_t>& row
 It specifies one of the first index of x for each non-zero Hessian term (see purpose above). All the elements of row must be between zero and n-1 . The value K is defined by K = row.size() .

col
The argument col has prototype
      const CppAD::vector<size_t>& col
 and its size must be K ; i.e., the same as for col . It specifies the second index of x for the non-zero Hessian terms. All the elements of col must be between zero and n-1 . There are no duplicated entries requested, to be specific, if k1 != k2 then
     ( row[k1] , col[k1] ) != ( row[k2] , col[k2] )
p
The argument p has prototype
     size_t p
 It is either zero or two and specifies the order of the derivative of f that is being evaluated, i.e., f ( p ) ( x ) is evaluated.

fp
The argument fp has prototype
     FloatVector& fp
 The input value of the elements of fp does not matter.

Function
If p is zero, fp has size one and fp[0] is the value of f ( x ) .

Hessian
If p is two, fp has size K and for k = 0 , … , K -1 , ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ col [ k ] ] = fp [ k ]
Example
The file sparse_hes_fun.cpp contains an example and test of sparse_hes_fun.hpp. It returns true if it succeeds and false otherwise.

Source Code
The file sparse_hes_fun.hpp contains the source code for this template function.
Input File: cppad/speed/sparse_hes_fun.hpp cppad-20170000.3/doc/_sparse_hes_fun_xml.js0000644000175200017650000000453213057470510017556 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'sparse_hes_fun.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down0 = [ 'sparse_hes_fun.cpp.xml', 'sparse_hes_fun.hpp.xml' ]; var list_current0 = [ 'sparse_hes_fun.xml#Syntax', 'sparse_hes_fun.xml#Purpose', 'sparse_hes_fun.xml#Inclusion', 'sparse_hes_fun.xml#Float', 'sparse_hes_fun.xml#FloatVector', 'sparse_hes_fun.xml#n', 'sparse_hes_fun.xml#x', 'sparse_hes_fun.xml#row', 'sparse_hes_fun.xml#col', 'sparse_hes_fun.xml#p', 'sparse_hes_fun.xml#fp', 'sparse_hes_fun.xml#fp.Function', 'sparse_hes_fun.xml#fp.Hessian', 'sparse_hes_fun.xml#Example', 'sparse_hes_fun.xml#Source Code' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/sparse_hes_fun.hpp.xml0000644000175200017650000005130213057470510017506 0ustar coincoin-web Source: sparse_hes_fun
Prev Next sparse_hes_fun.hpp Headings

Source: sparse_hes_fun
# ifndef CPPAD_SPARSE_HES_FUN_HPP
# define CPPAD_SPARSE_HES_FUN_HPP 
# include <cppad/core/cppad_assert.hpp>
# include <cppad/utility/check_numeric_type.hpp>
# include <cppad/utility/vector.hpp>

// following needed by gcc under fedora 17 so that exp(double) is defined
# include <cppad/base_require.hpp>

namespace CppAD {
     template <class Float, class FloatVector>
     void sparse_hes_fun(
          size_t                       n    ,
          const FloatVector&           x    ,
          const CppAD::vector<size_t>& row  ,
          const CppAD::vector<size_t>& col  ,
          size_t                       p    ,
          FloatVector&                fp    )
     {
          // check numeric type specifications
          CheckNumericType<Float>();

          // check value of p
          CPPAD_ASSERT_KNOWN(
               p == 0 || p == 2,
               "sparse_hes_fun: p != 0 and p != 2"
          );

          size_t K = row.size();
          size_t i, j, k;
          if( p == 0 )
               fp[0] = Float(0);
          else
          {     for(k = 0; k < K; k++)
                    fp[k] = Float(0);
          }

          // determine which diagonal entries are present in row[k], col[k]
          CppAD::vector<size_t> diagonal(n);
          for(i = 0; i < n; i++)
               diagonal[i] = K;   // no diagonal entry for this row
          for(k = 0; k < K; k++)
          {     if( row[k] == col[k] )
               {     CPPAD_ASSERT_UNKNOWN( diagonal[row[k]] == K );
                    // index of the diagonal entry
                    diagonal[ row[k] ] = k;
               }
          }

          // determine which entries must be multiplied by a factor of two
          CppAD::vector<Float> factor(K);
          for(k = 0; k < K; k++)
          {     factor[k] = Float(1);
               for(size_t k1 = 0; k1 < K; k1++)
               {     bool reflected = true;
                    reflected &= k != k1;
                    reflected &= row[k] != col[k];
                    reflected &= row[k] == col[k1];
                    reflected &= col[k] == row[k1];
                    if( reflected )
                         factor[k] = Float(2);
               }
          }

          Float t;
          for(k = 0; k < K; k++)
          {     i    = row[k];
               j    = col[k];
               t    = exp( x[i] * x[j] );
               switch(p)
               {
                    case 0:
                    fp[0] += t;
                    break;

                    case 2:
                    if( i == j )
                    {     // dt_dxi = 2.0 * xi * t
                         fp[k] += ( Float(2) + Float(4) * x[i] * x[i] ) * t;
                    }
                    else
                    {     // dt_dxi = xj * t
                         fp[k] += factor[k] * ( Float(1) + x[i] * x[j] ) * t;
                         if( diagonal[i] != K )
                         {     size_t ki = diagonal[i];
                              fp[ki] += x[j] * x[j] * t;
                         }
                         if( diagonal[j] != K )
                         {     size_t kj = diagonal[j];
                              fp[kj] += x[i] * x[i] * t;
                         }
                    }
                    break;
               }
          }

     }
}
# endif
Input File: omh/sparse_hes_fun.omh cppad-20170000.3/doc/uniform_01.xml0000644000175200017650000002021213057470510015667 0ustar coincoin-web Simulate a [0,1] Uniform Random Variate
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Simulate a [0,1] Uniform Random Variate

Syntax
# include <cppad/speed/uniform_01.hpp>
 uniform_01(seed)
 uniform_01(n, x)

Purpose
This routine is used to create random values for speed testing purposes.

Inclusion
The template function uniform_01 is defined in the CppAD namespace by including the file cppad/speed/uniform_01.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

seed
The argument seed has prototype
     size_t seed
 It specifies a seed for the uniform random number generator.

n
The argument n has prototype
     size_t n
 It specifies the number of elements in the random vector x .

x
The argument x has prototype
     Vector &x
 . The input value of the elements of x does not matter. Upon return, the elements of x are set to values randomly sampled over the interval [0,1].

Vector
If y is a double value, the object x must support the syntax
     x[i] = y
 where i has type size_t with value less than or equal n -1 . This is the only requirement of the type Vector .

Source Code
The file uniform_01.hpp constraints the source code for this template function.
Input File: cppad/speed/uniform_01.hpp cppad-20170000.3/doc/_uniform_01_xml.js0000644000175200017650000000411413057470510016525 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'uniform_01.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down0 = [ 'uniform_01.hpp.xml' ]; var list_current0 = [ 'uniform_01.xml#Syntax', 'uniform_01.xml#Purpose', 'uniform_01.xml#Inclusion', 'uniform_01.xml#seed', 'uniform_01.xml#n', 'uniform_01.xml#x', 'uniform_01.xml#Vector', 'uniform_01.xml#Source Code' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/uniform_01.hpp.xml0000644000175200017650000001226613057470510016467 0ustar coincoin-web Source: uniform_01
Prev Next uniform_01.hpp Headings

Source: uniform_01
# ifndef CPPAD_UNIFORM_01_HPP
# define CPPAD_UNIFORM_01_HPP 
# include <cstdlib>

namespace CppAD {
     inline void uniform_01(size_t seed)
     {     std::srand( (unsigned int) seed); }

     template <class Vector>
     void uniform_01(size_t n, Vector &x)
     {     static double factor = 1. / double(RAND_MAX);
          while(n--)
               x[n] = std::rand() * factor;
     }
}
# endif
Input File: omh/uniform_01_hpp.omh cppad-20170000.3/doc/speed_double.xml0000644000175200017650000001164413057470510016353 0ustar coincoin-web Speed Test of Functions in Double
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Speed Test of Functions in Double

Purpose
CppAD has a set of speed tests for just calculating functions (in double precision instead of an AD type). This section links to the source code the function value speed tests.

Running Tests
To build these speed tests, and run their correctness tests, execute the following commands starting in the build directory :
     cd speed/double
     make check_speed_double VERBOSE=1
 You can then run the corresponding speed tests with the following command
     ./speed_double speed seed
 where seed is a positive integer. See speed_main for more options.

Contents
Input File: omh/speed/speed_double.omh cppad-20170000.3/doc/double_det_minor.cpp.xml0000644000175200017650000001736013057470510020015 0ustar coincoin-web Double Speed: Determinant by Minor Expansion
Prev Next double_det_minor.cpp

Double Speed: Determinant by Minor Expansion

Specifications
See link_det_minor .

Implementation 
# include <cppad/utility/vector.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_minor(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &det      )
{
     if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"])
          return false;
     // -----------------------------------------------------
     // setup
     CppAD::det_by_minor<double>   Det(size);
     size_t n = size * size; // number of independent variables

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, matrix);

          // computation of the determinant
          det[0] = Det(matrix);
     }
     return true;
}
Input File: speed/double/det_minor.cpp cppad-20170000.3/doc/double_det_lu.cpp.xml0000644000175200017650000001742313057470510017311 0ustar coincoin-web Double Speed: Determinant Using Lu Factorization
Prev Next double_det_lu.cpp

Double Speed: Determinant Using Lu Factorization

Specifications
See link_det_lu .

Implementation 
# include <cppad/utility/vector.hpp>
# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_lu(
     size_t                           size     ,
     size_t                           repeat   ,
     CppAD::vector<double>           &matrix   ,
     CppAD::vector<double>           &det      )
{
     if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"])
          return false;
     // -----------------------------------------------------
     // setup
     CppAD::det_by_lu<double>  Det(size);
     size_t n = size * size; // number of independent variables

     // ------------------------------------------------------

     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, matrix);

          // computation of the determinant
          det[0] = Det(matrix);
     }
     return true;
}
Input File: speed/double/det_lu.cpp cppad-20170000.3/doc/double_mat_mul.cpp.xml0000644000175200017650000001744213057470510017474 0ustar coincoin-web CppAD Speed: Matrix Multiplication (Double Version)
Prev Next double_mat_mul.cpp

CppAD Speed: Matrix Multiplication (Double Version)

Specifications
See link_mat_mul .

Implementation 
# include <cppad/cppad.hpp>
# include <cppad/speed/mat_sum_sq.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_mat_mul(
     size_t                           size     ,
     size_t                           repeat   ,
     CppAD::vector<double>&           x        ,
     CppAD::vector<double>&           z        ,
     CppAD::vector<double>&           dz
)
{
     if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"])
          return false;
     // -----------------------------------------------------
     size_t n = size * size; // number of independent variables
     CppAD::vector<double> y(n);

     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, x);

          // do computation
          mat_sum_sq(size, x, y, z);

     }
     return true;
}
Input File: speed/double/mat_mul.cpp cppad-20170000.3/doc/double_ode.cpp.xml0000644000175200017650000002116413057470510016601 0ustar coincoin-web Double Speed: Ode Solution
Prev Next double_ode.cpp

Double Speed: Ode Solution

Specifications
See link_ode .

Implementation 
# include <cstring>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/ode_evaluate.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_ode(
     size_t                     size       ,
     size_t                     repeat     ,
     CppAD::vector<double>      &x         ,
     CppAD::vector<double>      &jacobian
)
{
     if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"])
          return false;
     // -------------------------------------------------------------
     // setup
     assert( x.size() == size );

     size_t n = size;

     size_t m = 0;
     CppAD::vector<double> f(n);

     while(repeat--)
     {     // choose next x value
          uniform_01(n, x);

          // evaluate function
          CppAD::ode_evaluate(x, m, f);

     }
     size_t i;
     for(i = 0; i < n; i++)
          jacobian[i] = f[i];
     return true;
}
Input File: speed/double/ode.cpp cppad-20170000.3/doc/double_poly.cpp.xml0000644000175200017650000001737513057470510017026 0ustar coincoin-web Double Speed: Evaluate a Polynomial
Prev Next double_poly.cpp

Double Speed: Evaluate a Polynomial

Specifications
See link_poly .

Implementation 
# include <cppad/cppad.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_poly(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &a        ,  // coefficients of polynomial
     CppAD::vector<double>     &z        ,  // polynomial argument value
     CppAD::vector<double>     &p        )  // second derivative w.r.t z
{
     if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"])
          return false;
     // -----------------------------------------------------
     // setup

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next argument value
          CppAD::uniform_01(1, z);

          // evaluate the polynomial at the new argument value
          p[0] = CppAD::Poly(0, a, z[0]);
     }
     return true;
}
Input File: speed/double/poly.cpp cppad-20170000.3/doc/double_sparse_hessian.cpp.xml0000644000175200017650000002334613057470510021045 0ustar coincoin-web Double Speed: Sparse Hessian
Prev Next double_sparse_hessian.cpp

Double Speed: Sparse Hessian

Specifications
See link_sparse_hessian .

Implementation 
# include <cppad/utility/vector.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/speed/sparse_hes_fun.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_sparse_hessian(
     size_t                           size     ,
     size_t                           repeat   ,
     const CppAD::vector<size_t>&     row      ,
     const CppAD::vector<size_t>&     col      ,
     CppAD::vector<double>&           x        ,
     CppAD::vector<double>&           hessian  ,
     size_t&                          n_sweep  )
{
     if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]||global_option["boolsparsity"])
          return false;
     // -----------------------------------------------------
     // setup
     using CppAD::vector;
     size_t order = 0;          // derivative order corresponding to function
     size_t n     = size;       // argument space dimension
     size_t m     = 1;          // range space dimension
     vector<double> y(m);       // function value

     // choose a value for x
     CppAD::uniform_01(n, x);

     // ------------------------------------------------------

     while(repeat--)
     {
          // computation of the function
          CppAD::sparse_hes_fun<double>(n, x, row, col, order, y);
     }
     hessian[0] = y[0];

     return true;
}
Input File: speed/double/sparse_hessian.cpp cppad-20170000.3/doc/speed_adolc.xml0000644000175200017650000001305313057470510016157 0ustar coincoin-web Speed Test of Derivatives Using Adolc
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Speed Test of Derivatives Using Adolc

Purpose
CppAD has a set of speed tests that are used to compare Adolc with other AD packages. This section links to the source code the Adolc speed tests (any suggestions to make the Adolc results faster are welcome).

adolc_prefix
To run these tests, you must include the adolc_prefix in you cmake command .

Running Tests
To build these speed tests, and run their correctness tests, execute the following commands starting in the build directory :
     cd speed/adolc
     make check_speed_adolc VERBOSE=1
 You can then run the corresponding speed tests with the following command
     ./speed_adolc speed seed
 where seed is a positive integer. See speed_main for more options.

Contents
Input File: omh/speed/speed_adolc.omh cppad-20170000.3/doc/_speed_adolc_xml.js0000644000175200017650000000346513057470510017020 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_adolc.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down0 = [ 'adolc_det_minor.cpp.xml', 'adolc_det_lu.cpp.xml', 'adolc_mat_mul.cpp.xml', 'adolc_ode.cpp.xml', 'adolc_poly.cpp.xml', 'adolc_sparse_hessian.cpp.xml', 'adolc_sparse_jacobian.cpp.xml', 'adolc_alloc_mat.xml' ]; var list_current0 = [ 'speed_adolc.xml#Purpose', 'speed_adolc.xml#adolc_prefix', 'speed_adolc.xml#Running Tests', 'speed_adolc.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/adolc_det_minor.cpp.xml0000644000175200017650000005340013057470510017620 0ustar coincoin-web Adolc Speed: Gradient of Determinant by Minor Expansion
Prev Next adolc_det_minor.cpp

Adolc Speed: Gradient of Determinant by Minor Expansion

Specifications
See link_det_minor .

Implementation 
# include <adolc/adolc.h>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <cppad/speed/uniform_01.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_minor(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &gradient )
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     typedef adouble    ADScalar;
     typedef ADScalar*  ADVector;

     int tag  = 0;         // tape identifier
     int m    = 1;         // number of dependent variables
     int n    = size*size; // number of independent variables
     double f;             // function value
     int j;                // temporary index

     // set up for thread_alloc memory allocator (fast and checks for leaks)
     using CppAD::thread_alloc; // the allocator
     size_t capacity;           // capacity of an allocation

     // object for computing determinant
     CppAD::det_by_minor<ADScalar> Det(size);

     // AD value of determinant
     ADScalar   detA;

     // AD version of matrix
     ADVector A   = thread_alloc::create_array<ADScalar>(size_t(n), capacity);

     // vectors of reverse mode weights
     double* u    = thread_alloc::create_array<double>(size_t(m), capacity);
     u[0] = 1.;

     // vector with matrix value
     double* mat  = thread_alloc::create_array<double>(size_t(n), capacity);

     // vector to receive gradient result
     double* grad = thread_alloc::create_array<double>(size_t(n), capacity);

     // ----------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose a matrix
          CppAD::uniform_01(n, mat);

          // declare independent variables
          int keep = 1; // keep forward mode results
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               A[j] <<= mat[j];

          // AD computation of the determinant
          detA = Det(A);

          // create function object f : A -> detA
          detA >>= f;
          trace_off();

          // evaluate and return gradient using reverse mode
          fos_reverse(tag, m, n, u, grad);
     }
     else
     {
          // choose a matrix
          CppAD::uniform_01(n, mat);

          // declare independent variables
          int keep = 0; // do not keep forward mode results in buffer
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               A[j] <<= mat[j];

          // AD computation of the determinant
          detA = Det(A);

          // create function object f : A -> detA
          detA >>= f;
          trace_off();

          while(repeat--)
          {     // get the next matrix
               CppAD::uniform_01(n, mat);

               // evaluate the determinant at the new matrix value
               keep = 1; // keep this forward mode result
               zos_forward(tag, m, n, keep, mat, &f);

               // evaluate and return gradient using reverse mode
               fos_reverse(tag, m, n, u, grad);
          }
     }
     // --------------------------------------------------------------------

     // return matrix and gradient
     for(j = 0; j < n; j++)
     {     matrix[j] = mat[j];
          gradient[j] = grad[j];
     }

     // tear down
     thread_alloc::delete_array(grad);
     thread_alloc::delete_array(mat);
     thread_alloc::delete_array(u);
     thread_alloc::delete_array(A);
     return true;
}
Input File: speed/adolc/det_minor.cpp cppad-20170000.3/doc/adolc_det_lu.cpp.xml0000644000175200017650000004300513057470510017114 0ustar coincoin-web Adolc Speed: Gradient of Determinant Using Lu Factorization
Prev Next adolc_det_lu.cpp

Adolc Speed: Gradient of Determinant Using Lu Factorization

Specifications
See link_det_lu .

Implementation 
# include <adolc/adolc.h>

# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/track_new_del.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_lu(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &gradient )
{
     // speed test global option values
     if( global_option["onetape"] || global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     int tag  = 0;         // tape identifier
     int keep = 1;         // keep forward mode results in buffer
     int m    = 1;         // number of dependent variables
     int n    = size*size; // number of independent variables
     double f;             // function value
     int j;                // temporary index

     // set up for thread_alloc memory allocator (fast and checks for leaks)
     using CppAD::thread_alloc; // the allocator
     size_t size_min;           // requested number of elements
     size_t size_out;           // capacity of an allocation

     // object for computing determinant
     typedef adouble            ADScalar;
     typedef ADScalar*          ADVector;
     CppAD::det_by_lu<ADScalar> Det(size);

     // AD value of determinant
     ADScalar   detA;

     // AD version of matrix
     size_min    = n;
     ADVector A  = thread_alloc::create_array<ADScalar>(size_min, size_out);

     // vectors of reverse mode weights
     size_min    = m;
     double* u   = thread_alloc::create_array<double>(size_min, size_out);
     u[0] = 1.;

     // vector with matrix value
     size_min     = n;
     double* mat  = thread_alloc::create_array<double>(size_min, size_out);

     // vector to receive gradient result
     size_min     = n;
     double* grad = thread_alloc::create_array<double>(size_min, size_out);
     // ------------------------------------------------------
     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, mat);

          // declare independent variables
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               A[j] <<= mat[j];

          // AD computation of the determinant
          detA = Det(A);

          // create function object f : A -> detA
          detA >>= f;
          trace_off();

          // evaluate and return gradient using reverse mode
          fos_reverse(tag, m, n, u, grad);
     }
     // ------------------------------------------------------

     // return matrix and gradient
     for(j = 0; j < n; j++)
     {     matrix[j] = mat[j];
          gradient[j] = grad[j];
     }
     // tear down
     thread_alloc::delete_array(grad);
     thread_alloc::delete_array(mat);
     thread_alloc::delete_array(u);
     thread_alloc::delete_array(A);

     return true;
}
Input File: speed/adolc/det_lu.cpp cppad-20170000.3/doc/adolc_mat_mul.cpp.xml0000644000175200017650000005624513057470510017310 0ustar coincoin-web Adolc Speed: Matrix Multiplication
Prev Next adolc_mat_mul.cpp

Adolc Speed: Matrix Multiplication

Specifications
See link_mat_mul .

Implementation 
# include <adolc/adolc.h>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/mat_sum_sq.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/vector.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_mat_mul(
     size_t                           size     ,
     size_t                           repeat   ,
     CppAD::vector<double>&           x        ,
     CppAD::vector<double>&           z        ,
     CppAD::vector<double>&           dz       )
{
     // speed test global option values
     if( global_option["memory"] || global_option["atomic"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     typedef adouble    ADScalar;
     typedef ADScalar*  ADVector;

     int tag  = 0;         // tape identifier
     int m    = 1;         // number of dependent variables
     int n    = size*size; // number of independent variables
     double f;             // function value
     int j;                // temporary index

     // set up for thread_alloc memory allocator (fast and checks for leaks)
     using CppAD::thread_alloc; // the allocator
     size_t capacity;           // capacity of an allocation

     // AD domain space vector
     ADVector X = thread_alloc::create_array<ADScalar>(size_t(n), capacity);

     // Product matrix
     ADVector Y = thread_alloc::create_array<ADScalar>(size_t(n), capacity);

     // AD range space vector
     ADVector Z = thread_alloc::create_array<ADScalar>(size_t(m), capacity);

     // vector with matrix value
     double* mat = thread_alloc::create_array<double>(size_t(n), capacity);

     // vector of reverse mode weights
     double* u  = thread_alloc::create_array<double>(size_t(m), capacity);
     u[0] = 1.;

     // gradient
     double* grad = thread_alloc::create_array<double>(size_t(n), capacity);

     // ----------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose a matrix
          CppAD::uniform_01(n, mat);

          // declare independent variables
          int keep = 1; // keep forward mode results
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               X[j] <<= mat[j];

          // do computations
          CppAD::mat_sum_sq(size, X, Y, Z);

          // create function object f : X -> Z
          Z[0] >>= f;
          trace_off();

          // evaluate and return gradient using reverse mode
          fos_reverse(tag, m, n, u, grad);
     }
     else
     {     // choose a matrix
          CppAD::uniform_01(n, mat);

          // declare independent variables
          int keep = 0; // do not keep forward mode results
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               X[j] <<= mat[j];

          // do computations
          CppAD::mat_sum_sq(size, X, Y, Z);

          // create function object f : X -> Z
          Z[0] >>= f;
          trace_off();

          while(repeat--)
          {     // choose a matrix
               CppAD::uniform_01(n, mat);

               // evaluate the determinant at the new matrix value
               keep = 1; // keep this forward mode result
               zos_forward(tag, m, n, keep, mat, &f);

               // evaluate and return gradient using reverse mode
               fos_reverse(tag, m, n, u, grad);
          }
     }
     // return function, matrix, and gradient
     z[0] = f;
     for(j = 0; j < n; j++)
     {     x[j]  = mat[j];
          dz[j] = grad[j];
     }

     // tear down
     thread_alloc::delete_array(X);
     thread_alloc::delete_array(Y);
     thread_alloc::delete_array(Z);
     thread_alloc::delete_array(mat);
     thread_alloc::delete_array(u);
     thread_alloc::delete_array(grad);

     return true;
}
Input File: speed/adolc/mat_mul.cpp cppad-20170000.3/doc/adolc_ode.cpp.xml0000644000175200017650000005674413057470510016425 0ustar coincoin-web Adolc Speed: Ode
Prev Next adolc_ode.cpp

Adolc Speed: Ode

Specifications
See link_ode .

Implementation 
# include <adolc/adolc.h>

# include <cppad/utility/vector.hpp>
# include <cppad/speed/ode_evaluate.hpp>
# include <cppad/speed/uniform_01.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_ode(
     size_t                     size       ,
     size_t                     repeat     ,
     CppAD::vector<double>      &x         ,
     CppAD::vector<double>      &jac
)
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["optimize"] )
          return false;
     // -------------------------------------------------------------
     // setup
     assert( x.size() == size );
     assert( jac.size() == size * size );

     typedef CppAD::vector<adouble> ADVector;
     typedef CppAD::vector<double>  DblVector;

     size_t i, j;
     int tag    = 0;       // tape identifier
     int keep   = 0;       // do not keep forward mode results
     size_t p   = 0;       // use ode to calculate function values
     size_t n   = size;    // number of independent variables
     size_t m   = n;       // number of dependent variables
     ADVector  X(n), Y(m); // independent and dependent variables
     DblVector f(m);       // function value

     // set up for thread_alloc memory allocator (fast and checks for leaks)
     using CppAD::thread_alloc; // the allocator
     size_t size_min;           // requested number of elements
     size_t size_out;           // capacity of an allocation

     // raw memory for use with adolc
     size_min = n;
     double *x_raw   = thread_alloc::create_array<double>(size_min, size_out);
     size_min = m * n;
     double *jac_raw = thread_alloc::create_array<double>(size_min, size_out);
     size_min = m;
     double **jac_ptr = thread_alloc::create_array<double*>(size_min, size_out);
     for(i = 0; i < m; i++)
          jac_ptr[i] = jac_raw + i * n;

     // -------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose next x value
          uniform_01(n, x);

          // declare independent variables
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               X[j] <<= x[j];

          // evaluate function
          CppAD::ode_evaluate(X, p, Y);

          // create function object f : X -> Y
          for(i = 0; i < m; i++)
               Y[i] >>= f[i];
          trace_off();

          // evaluate the Jacobian
          for(j = 0; j < n; j++)
               x_raw[j] = x[j];
          jacobian(tag, m, n, x_raw, jac_ptr);
     }
     else
     {     // choose next x value
          uniform_01(n, x);

          // declare independent variables
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               X[j] <<= x[j];

          // evaluate function
          CppAD::ode_evaluate(X, p, Y);

          // create function object f : X -> Y
          for(i = 0; i < m; i++)
               Y[i] >>= f[i];
          trace_off();

          while(repeat--)
          {     // get next argument value
               uniform_01(n, x);
               for(j = 0; j < n; j++)
                    x_raw[j] = x[j];

               // evaluate jacobian
               jacobian(tag, m, n, x_raw, jac_ptr);
          }
     }
     // convert return value to a simple vector
     for(i = 0; i < m; i++)
     {     for(j = 0; j < n; j++)
               jac[i * n + j] = jac_ptr[i][j];
     }
     // ----------------------------------------------------------------------
     // tear down
     thread_alloc::delete_array(x_raw);
     thread_alloc::delete_array(jac_raw);
     thread_alloc::delete_array(jac_ptr);

     return true;
}
Input File: speed/adolc/ode.cpp cppad-20170000.3/doc/adolc_poly.cpp.xml0000644000175200017650000005664513057470510016641 0ustar coincoin-web Adolc Speed: Second Derivative of a Polynomial
Prev Next adolc_poly.cpp

Adolc Speed: Second Derivative of a Polynomial

Specifications
See link_poly .

Implementation 
# include <vector>
# include <adolc/adolc.h>

# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/poly.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/utility/thread_alloc.hpp>
# include "adolc_alloc_mat.hpp"

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_poly(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &a        ,  // coefficients of polynomial
     CppAD::vector<double>     &z        ,  // polynomial argument value
     CppAD::vector<double>     &ddp      )  // second derivative w.r.t z
{
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     size_t i;
     int tag  = 0;  // tape identifier
     int keep = 0;  // do not keep forward mode results in buffer
     int m    = 1;  // number of dependent variables
     int n    = 1;  // number of independent variables
     int d    = 2;  // highest derivative degree
     double f;      // function value

     // set up for thread_alloc memory allocator (fast and checks for leaks)
     using CppAD::thread_alloc; // the allocator
     size_t capacity;           // capacity of an allocation

     // choose a vector of polynomial coefficients
     CppAD::uniform_01(size, a);

     // AD copy of the polynomial coefficients
     std::vector<adouble> A(size);
     for(i = 0; i < size; i++)
          A[i] = a[i];

     // domain and range space AD values
     adouble Z, P;

     // allocate arguments to hos_forward
     double* x0 = thread_alloc::create_array<double>(size_t(n), capacity);
     double* y0 = thread_alloc::create_array<double>(size_t(m), capacity);
     double** x = adolc_alloc_mat(size_t(n), size_t(d));
     double** y = adolc_alloc_mat(size_t(m), size_t(d));

     // Taylor coefficient for argument
     x[0][0] = 1.;  // first order
     x[0][1] = 0.;  // second order

     // ----------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose an argument value
          CppAD::uniform_01(1, z);

          // declare independent variables
          trace_on(tag, keep);
          Z <<= z[0];

          // AD computation of the function value
          P = CppAD::Poly(0, A, Z);

          // create function object f : Z -> P
          P >>= f;
          trace_off();

          // set the argument value
          x0[0] = z[0];

          // evaluate the polynomial at the new argument value
          hos_forward(tag, m, n, d, keep, x0, x, y0, y);

          // second derivative is twice second order Taylor coef
          ddp[0] = 2. * y[0][1];
     }
     else
     {
          // choose an argument value
          CppAD::uniform_01(1, z);

          // declare independent variables
          trace_on(tag, keep);
          Z <<= z[0];

          // AD computation of the function value
          P = CppAD::Poly(0, A, Z);

          // create function object f : Z -> P
          P >>= f;
          trace_off();

          while(repeat--)
          {     // get the next argument value
               CppAD::uniform_01(1, z);
               x0[0] = z[0];

               // evaluate the polynomial at the new argument value
               hos_forward(tag, m, n, d, keep, x0, x, y0, y);

               // second derivative is twice second order Taylor coef
               ddp[0] = 2. * y[0][1];
          }
     }
     // ------------------------------------------------------
     // tear down
     adolc_free_mat(x);
     adolc_free_mat(y);
     thread_alloc::delete_array(x0);
     thread_alloc::delete_array(y0);

     return true;
}
Input File: speed/adolc/poly.cpp cppad-20170000.3/doc/adolc_sparse_hessian.cpp.xml0000644000175200017650000010065213057470510020651 0ustar coincoin-web Adolc Speed: Sparse Hessian
Prev Next adolc_sparse_hessian.cpp

Adolc Speed: Sparse Hessian

Specifications
See link_sparse_hessian .

Implementation 
# include <adolc/adolc.h>
# include <adolc/adolc_sparse.h>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/thread_alloc.hpp>
# include <cppad/speed/sparse_hes_fun.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_sparse_hessian(
     size_t                           size     ,
     size_t                           repeat   ,
     const CppAD::vector<size_t>&     row      ,
     const CppAD::vector<size_t>&     col      ,
     CppAD::vector<double>&           x_return ,
     CppAD::vector<double>&           hessian  ,
     size_t&                          n_sweep )
{
     if( global_option["atomic"] || (! global_option["colpack"]) )
          return false;
     if( global_option["memory"] || global_option["optimize"] || global_option["boolsparsity"] )
          return false;
     // -----------------------------------------------------
     // setup
     typedef unsigned int*    SizeVector;
     typedef double*          DblVector;
     typedef adouble          ADScalar;
     typedef ADScalar*        ADVector;


     size_t i, j, k;         // temporary indices
     size_t order = 0;    // derivative order corresponding to function
     size_t m = 1;        // number of dependent variables
     size_t n = size;     // number of independent variables

     // setup for thread_alloc memory allocator (fast and checks for leaks)
     using CppAD::thread_alloc; // the allocator
     size_t capacity;           // capacity of an allocation

     // tape identifier
     int tag  = 0;
     // AD domain space vector
     ADVector a_x = thread_alloc::create_array<ADScalar>(n, capacity);
     // AD range space vector
     ADVector a_y = thread_alloc::create_array<ADScalar>(m, capacity);
     // double argument value
     DblVector x = thread_alloc::create_array<double>(n, capacity);
     // double function value
     double f;

     // options that control sparse_hess
     int        options[2];
     options[0] = 0; // safe mode
     options[1] = 0; // indirect recovery

     // structure that holds some of the work done by sparse_hess
     int        nnz;                   // number of non-zero values
     SizeVector rind   = CPPAD_NULL;   // row indices
     SizeVector cind   = CPPAD_NULL;   // column indices
     DblVector  values = CPPAD_NULL;   // Hessian values

     // ----------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose a value for x
          CppAD::uniform_01(n, x);

          // declare independent variables
          int keep = 0; // keep forward mode results
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               a_x[j] <<= x[j];

          // AD computation of f (x)
          CppAD::sparse_hes_fun<ADScalar>(n, a_x, row, col, order, a_y);

          // create function object f : x -> y
          a_y[0] >>= f;
          trace_off();

          // is this a repeat call with the same sparsity pattern
          int same_pattern = 0;

          // calculate the hessian at this x
          rind   = CPPAD_NULL;
          cind   = CPPAD_NULL;
          values = CPPAD_NULL;
          sparse_hess(tag, int(n),
               same_pattern, x, &nnz, &rind, &cind, &values, options
          );
          // only needed last time through loop
          if( repeat == 0 )
          {     size_t K = row.size();
               for(int ell = 0; ell < nnz; ell++)
               {     i = size_t(rind[ell]);
                    j = size_t(cind[ell]);
                    for(k = 0; k < K; k++)
                    {     if( (row[k]==i && col[k]==j) || (row[k]==j && col[k]==i) )
                              hessian[k] = values[ell];
                    }
               }
          }

          // free raw memory allocated by sparse_hess
          free(rind);
          free(cind);
          free(values);
     }
     else
     {     // choose a value for x
          CppAD::uniform_01(n, x);

          // declare independent variables
          int keep = 0; // keep forward mode results
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               a_x[j] <<= x[j];

          // AD computation of f (x)
          CppAD::sparse_hes_fun<ADScalar>(n, a_x, row, col, order, a_y);

          // create function object f : x -> y
          a_y[0] >>= f;
          trace_off();

          // is this a repeat call at the same argument
          int same_pattern = 0;

          while(repeat--)
          {     // choose a value for x
               CppAD::uniform_01(n, x);

               // calculate the hessian at this x
               sparse_hess(tag, int(n),
                    same_pattern, x, &nnz, &rind, &cind, &values, options
               );
               same_pattern = 1;
          }
          size_t K = row.size();
          for(int ell = 0; ell < nnz; ell++)
          {     i = size_t(rind[ell]);
               j = size_t(cind[ell]);
               for(k = 0; k < K; k++)
               {     if( (row[k]==i && col[k]==j) || (row[k]==j && col[k]==i) )
                         hessian[k] = values[ell];
               }
          }
          // free raw memory allocated by sparse_hessian
          free(rind);
          free(cind);
          free(values);
     }
     // --------------------------------------------------------------------
     // return argument
     for(j = 0; j < n; j++)
          x_return[j] = x[j];

     // do not know how to return number of sweeps used
     n_sweep = 0;

     // tear down
     thread_alloc::delete_array(a_x);
     thread_alloc::delete_array(a_y);
     thread_alloc::delete_array(x);
     return true;

}
Input File: speed/adolc/sparse_hessian.cpp cppad-20170000.3/doc/adolc_sparse_jacobian.cpp.xml0000644000175200017650000010574213057470510020772 0ustar coincoin-web adolc Speed: Sparse Jacobian
Prev Next adolc_sparse_jacobian.cpp

adolc Speed: Sparse Jacobian

Specifications
See link_sparse_jacobian .

Implementation 
# include <adolc/adolc.h>
# include <adolc/adolc_sparse.h>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/speed/sparse_jac_fun.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_sparse_jacobian(
     size_t                           size     ,
     size_t                           repeat   ,
     size_t                           m        ,
     const CppAD::vector<size_t>&     row      ,
     const CppAD::vector<size_t>&     col      ,
           CppAD::vector<double>&     x_return ,
           CppAD::vector<double>&     jacobian ,
           size_t&                    n_sweep  )
{
     if( global_option["atomic"] || (! global_option["colpack"]) )
          return false;
     if( global_option["memory"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     typedef unsigned int*    SizeVector;
     typedef double*          DblVector;
     typedef adouble          ADScalar;
     typedef ADScalar*        ADVector;

     size_t i, j, k;            // temporary indices
     size_t n = size;           // number of independent variables
     size_t order = 0;          // derivative order corresponding to function

     // set up for thread_alloc memory allocator (fast and checks for leaks)
     using CppAD::thread_alloc; // the allocator
     size_t capacity;           // capacity of an allocation

     // tape identifier
     int tag  = 0;
     // AD domain space vector
     ADVector a_x = thread_alloc::create_array<ADScalar>(n, capacity);
     // AD range space vector
     ADVector a_y = thread_alloc::create_array<ADScalar>(m, capacity);
     // argument value in double
     DblVector x = thread_alloc::create_array<double>(n, capacity);
     // function value in double
     DblVector y = thread_alloc::create_array<double>(m, capacity);


     // options that control sparse_jac
     int        options[4];
     if( global_option["boolsparsity"] )
          options[0] = 1;  // sparsity by propagation of bit pattern
     else
          options[0] = 0;  // sparsity pattern by index domains
     options[1] = 0; // (0 = safe mode, 1 = tight mode)
     options[2] = 0; // see changing to -1 and back to 0 below
     options[3] = 0; // (0 = column compression, 1 = row compression)

     // structure that holds some of the work done by sparse_jac
     int        nnz;                   // number of non-zero values
     SizeVector rind   = CPPAD_NULL;   // row indices
     SizeVector cind   = CPPAD_NULL;   // column indices
     DblVector  values = CPPAD_NULL;   // Jacobian values

     // choose a value for x
     CppAD::uniform_01(n, x);

     // declare independent variables
     int keep = 0; // keep forward mode results
     trace_on(tag, keep);
     for(j = 0; j < n; j++)
          a_x[j] <<= x[j];

     // AD computation of f (x)
     CppAD::sparse_jac_fun<ADScalar>(m, n, a_x, row, col, order, a_y);

     // create function object f : x -> y
     for(i = 0; i < m; i++)
          a_y[i] >>= y[i];
     trace_off();

     // Retrieve n_sweep using undocumented feature of sparsedrivers.cpp
     int same_pattern = 0;
     options[2]       = -1;
     n_sweep = sparse_jac(tag, int(m), int(n),
          same_pattern, x, &nnz, &rind, &cind, &values, options
     );
     options[2]       = 0;
     // ----------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose a value for x
          CppAD::uniform_01(n, x);

          // declare independent variables
          trace_on(tag, keep);
          for(j = 0; j < n; j++)
               a_x[j] <<= x[j];

          // AD computation of f (x)
          CppAD::sparse_jac_fun<ADScalar>(m, n, a_x, row, col, order, a_y);

          // create function object f : x -> y
          for(i = 0; i < m; i++)
               a_y[i] >>= y[i];
          trace_off();

          // is this a repeat call with the same sparsity pattern
          same_pattern = 0;

          // calculate the jacobian at this x
          rind   = CPPAD_NULL;
          cind   = CPPAD_NULL;
          values = CPPAD_NULL;
          sparse_jac(tag, int(m), int(n),
               same_pattern, x, &nnz, &rind, &cind, &values, options
          );
          // only needed last time through loop
          if( repeat == 0 )
          {     size_t K = row.size();
               for(int ell = 0; ell < nnz; ell++)
               {     i = size_t(rind[ell]);
                    j = size_t(cind[ell]);
                    for(k = 0; k < K; k++)
                    {     if( row[k]==i && col[k]==j )
                              jacobian[k] = values[ell];
                    }
               }
          }

          // free raw memory allocated by sparse_jac
          free(rind);
          free(cind);
          free(values);
     }
     else
     {     while(repeat--)
          {     // choose a value for x
               CppAD::uniform_01(n, x);

               // calculate the jacobian at this x
               sparse_jac(tag, int(m), int(n),
                    same_pattern, x, &nnz, &rind, &cind, &values, options
               );
               same_pattern = 1;
          }
          size_t K = row.size();
          for(int ell = 0; ell < nnz; ell++)
          {     i = size_t(rind[ell]);
               j = size_t(cind[ell]);
               for(k = 0; k < K; k++)
               {     if( row[k]==i && col[k]==j )
                         jacobian[k] = values[ell];
               }
          }

          // free raw memory allocated by sparse_jac
          free(rind);
          free(cind);
          free(values);
     }
     // --------------------------------------------------------------------
     // return argument
     for(j = 0; j < n; j++)
          x_return[j] = x[j];

     // tear down
     thread_alloc::delete_array(a_x);
     thread_alloc::delete_array(a_y);
     thread_alloc::delete_array(x);
     thread_alloc::delete_array(y);
     return true;
}
Input File: speed/adolc/sparse_jacobian.cpp cppad-20170000.3/doc/adolc_alloc_mat.xml0000644000175200017650000001375413057470510017022 0ustar coincoin-web Adolc Test Utility: Allocate and Free Memory For a Matrix
Prev Next adolc_alloc_mat

Adolc Test Utility: Allocate and Free Memory For a Matrix

Syntax
mat = adolc_alloc_mat(m, n)
 adolc_free_mat(mat)
Purpose
Use the thread_alloc memory allocator to allocate and free memory that can be used as a matrix with the Adolc package.

m
Is the number of rows in the matrix.

n
Is the number of columns in the matrix.

mat
Is the matrix. To be specific, between a call to adolc_alloc_mat, and the corresponding call to adolc_free_mat, for i = 0 , ... , m-1 and j = 0 , ... , n-1 , mat[i][j] is the element in row i and column j .
Input File: speed/adolc/alloc_mat.cpp cppad-20170000.3/doc/speed_cppad.xml0000644000175200017650000001206413057470510016165 0ustar coincoin-web Speed Test Derivatives Using CppAD
Prev Next

Speed Test Derivatives Using CppAD

Purpose
CppAD has a set of speed tests that are used to determine if certain changes improve its execution speed (and to compare CppAD with other AD packages). This section links to the source code the CppAD speed tests (any suggestions to make the CppAD results faster are welcome).

Running Tests
To build these speed tests, and run their correctness tests, execute the following commands starting in the build directory :
     cd speed/cppad
     make check_speed_cppad VERBOSE=1
 You can then run the corresponding speed tests with the following command
     ./speed_cppad speed seed
 where seed is a positive integer. See speed_main for more options.

Contents
Input File: omh/speed/speed_cppad.omh cppad-20170000.3/doc/cppad_det_minor.cpp.xml0000644000175200017650000004517613057470510017640 0ustar coincoin-web CppAD Speed: Gradient of Determinant by Minor Expansion
Prev Next cppad_det_minor.cpp

CppAD Speed: Gradient of Determinant by Minor Expansion

Specifications
See link_det_minor .

Implementation 
# include <cppad/utility/vector.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_minor(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &gradient )
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;

     // optimization options: no conditional skips or compare operators
     std::string options="no_compare_op";
     // -----------------------------------------------------
     // setup

     // object for computing determinant
     typedef CppAD::AD<double>       ADScalar;
     typedef CppAD::vector<ADScalar> ADVector;
     CppAD::det_by_minor<ADScalar>   Det(size);

     size_t i;               // temporary index
     size_t m = 1;           // number of dependent variables
     size_t n = size * size; // number of independent variables
     ADVector   A(n);        // AD domain space vector
     ADVector   detA(m);     // AD range space vector

     // vectors of reverse mode weights
     CppAD::vector<double> w(1);
     w[0] = 1.;

     // the AD function object
     CppAD::ADFun<double> f;

     // ---------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {
          // choose a matrix
          CppAD::uniform_01(n, matrix);
          for( i = 0; i < size * size; i++)
               A[i] = matrix[i];

          // declare independent variables
          Independent(A);

          // AD computation of the determinant
          detA[0] = Det(A);

          // create function object f : A -> detA
          f.Dependent(A, detA);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // evaluate the determinant at the new matrix value
          f.Forward(0, matrix);

          // evaluate and return gradient using reverse mode
          gradient = f.Reverse(1, w);
     }
     else
     {
          // choose a matrix
          CppAD::uniform_01(n, matrix);
          for( i = 0; i < size * size; i++)
               A[i] = matrix[i];

          // declare independent variables
          Independent(A);

          // AD computation of the determinant
          detA[0] = Det(A);

          // create function object f : A -> detA
          f.Dependent(A, detA);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // ------------------------------------------------------
          while(repeat--)
          {     // get the next matrix
               CppAD::uniform_01(n, matrix);

               // evaluate the determinant at the new matrix value
               f.Forward(0, matrix);

               // evaluate and return gradient using reverse mode
               gradient = f.Reverse(1, w);
          }
     }
     return true;
}
Input File: speed/cppad/det_minor.cpp cppad-20170000.3/doc/cppad_det_lu.cpp.xml0000644000175200017650000003272413057470510017127 0ustar coincoin-web CppAD Speed: Gradient of Determinant Using Lu Factorization
Prev Next cppad_det_lu.cpp

CppAD Speed: Gradient of Determinant Using Lu Factorization

Specifications
See link_det_lu .

Implementation 
# include <cppad/utility/vector.hpp>
# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_lu(
     size_t                           size     ,
     size_t                           repeat   ,
     CppAD::vector<double>           &matrix   ,
     CppAD::vector<double>           &gradient )
{
     // speed test global option values
     if( global_option["onetape"] || global_option["atomic"] )
          return false;

     // optimization options: no conditional skips or compare operators
     std::string options="no_compare_op";
     // -----------------------------------------------------
     // setup
     typedef CppAD::AD<double>           ADScalar;
     typedef CppAD::vector<ADScalar>     ADVector;
     CppAD::det_by_lu<ADScalar>          Det(size);

     size_t i;               // temporary index
     size_t m = 1;           // number of dependent variables
     size_t n = size * size; // number of independent variables
     ADVector   A(n);        // AD domain space vector
     ADVector   detA(m);     // AD range space vector
     CppAD::ADFun<double> f; // AD function object

     // vectors of reverse mode weights
     CppAD::vector<double> w(1);
     w[0] = 1.;

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, matrix);
          for( i = 0; i < n; i++)
               A[i] = matrix[i];

          // declare independent variables
          Independent(A);

          // AD computation of the determinant
          detA[0] = Det(A);

          // create function object f : A -> detA
          f.Dependent(A, detA);
          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // evaluate and return gradient using reverse mode
          f.Forward(0, matrix);
          gradient = f.Reverse(1, w);
     }
     return true;
}
Input File: speed/cppad/det_lu.cpp cppad-20170000.3/doc/cppad_mat_mul.cpp.xml0000644000175200017650000006602013057470510017305 0ustar coincoin-web CppAD Speed, Matrix Multiplication
Prev Next cppad_mat_mul.cpp

CppAD Speed, Matrix Multiplication

Specifications
See link_mat_mul .

Implementation 
# include <cppad/cppad.hpp>
# include <cppad/speed/mat_sum_sq.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/example/mat_mul.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_mat_mul(
     size_t                           size     ,
     size_t                           repeat   ,
     CppAD::vector<double>&           x        ,
     CppAD::vector<double>&           z        ,
     CppAD::vector<double>&           dz
)
{
     // optimization options: no conditional skips or compare operators
     std::string options="no_compare_op";
     // -----------------------------------------------------
     // setup
     typedef CppAD::AD<double>           ADScalar;
     typedef CppAD::vector<ADScalar>     ADVector;

     size_t j;               // temporary index
     size_t m = 1;           // number of dependent variables
     size_t n = size * size; // number of independent variables
     ADVector   X(n);        // AD domain space vector
     ADVector   Y(n);        // Store product matrix
     ADVector   Z(m);        // AD range space vector
     CppAD::ADFun<double> f; // AD function object

     // vectors of reverse mode weights
     CppAD::vector<double> w(1);
     w[0] = 1.;

     // user atomic information
     CppAD::vector<ADScalar> ax(3 + 2 * n), ay(n);
     atomic_mat_mul atom_mul;
     //
     if( global_option["boolsparsity"] )
          atom_mul.option( CppAD::atomic_base<double>::pack_sparsity_enum );
     else
          atom_mul.option( CppAD::atomic_base<double>::set_sparsity_enum );
     // ------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, x);
          for( j = 0; j < n; j++)
               X[j] = x[j];

          // declare independent variables
          Independent(X);

          // do computations
          if( ! global_option["atomic"] )
               mat_sum_sq(size, X, Y, Z);
          else
          {     ax[0] = ADScalar( size ); // number of rows in left matrix
               ax[1] = ADScalar( size ); // rows in left and columns in right
               ax[2] = ADScalar( size ); // number of columns in right matrix
               for(j = 0; j < n; j++)
               {     ax[3 + j]     = X[j];
                    ax[3 + n + j] = X[j];
               }
               // Y = X * X
               atom_mul(ax, ay);
               Z[0] = 0.;
               for(j = 0; j < n; j++)
                    Z[0] += ay[j];
          }
          // create function object f : X -> Z
          f.Dependent(X, Z);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // evaluate and return gradient using reverse mode
          z  = f.Forward(0, x);
          dz = f.Reverse(1, w);
     }
     else
     {     // get a next matrix
          CppAD::uniform_01(n, x);
          for(j = 0; j < n; j++)
               X[j] = x[j];

          // declare independent variables
          Independent(X);

          // do computations
          if( ! global_option["atomic"] )
               mat_sum_sq(size, X, Y, Z);
          else
          {     for(j = 0; j < n; j++)
               {     ax[j]   = X[j];
                    ax[j+n] = X[j];
               }
               // Y = X * X
               atom_mul(ax, ay);
               Z[0] = 0.;
               for(j = 0; j < n; j++)
                    Z[0] += ay[j];
          }

          // create function object f : X -> Z
          f.Dependent(X, Z);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          while(repeat--)
          {     // get a next matrix
               CppAD::uniform_01(n, x);

               // evaluate and return gradient using reverse mode
               z  = f.Forward(0, x);
               dz = f.Reverse(1, w);
          }
     }
     // --------------------------------------------------------------------
     // Free temporary work space (any future atomic_mat_mul constructors
     // would create new temporary work space.)
     CppAD::user_atomic<double>::clear();

     return true;
}
Input File: speed/cppad/mat_mul.cpp cppad-20170000.3/doc/cppad_ode.cpp.xml0000644000175200017650000004150213057470510016414 0ustar coincoin-web CppAD Speed: Gradient of Ode Solution
Prev Next cppad_ode.cpp

CppAD Speed: Gradient of Ode Solution

Specifications
See link_ode .

Implementation 
# include <cppad/cppad.hpp>
# include <cppad/speed/ode_evaluate.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cassert>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_ode(
     size_t                     size       ,
     size_t                     repeat     ,
     CppAD::vector<double>      &x         ,
     CppAD::vector<double>      &jacobian
)
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;

     // optimization options: no conditional skips or compare operators
     std::string options="no_compare_op";
     // --------------------------------------------------------------------
     // setup
     assert( x.size() == size );
     assert( jacobian.size() == size * size );

     typedef CppAD::AD<double>       ADScalar;
     typedef CppAD::vector<ADScalar> ADVector;

     size_t j;
     size_t p = 0;              // use ode to calculate function values
     size_t n = size;           // number of independent variables
     size_t m = n;              // number of dependent variables
     ADVector  X(n), Y(m);      // independent and dependent variables
     CppAD::ADFun<double>  f;   // AD function

     // -------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose next x value
          uniform_01(n, x);
          for(j = 0; j < n; j++)
               X[j] = x[j];

          // declare the independent variable vector
          Independent(X);

          // evaluate function
          CppAD::ode_evaluate(X, p, Y);

          // create function object f : X -> Y
          f.Dependent(X, Y);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          jacobian = f.Jacobian(x);
     }
     else
     {     // an x value
          uniform_01(n, x);
          for(j = 0; j < n; j++)
               X[j] = x[j];

          // declare the independent variable vector
          Independent(X);

          // evaluate function
          CppAD::ode_evaluate(X, p, Y);

          // create function object f : X -> Y
          f.Dependent(X, Y);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          while(repeat--)
          {     // get next argument value
               uniform_01(n, x);

               // evaluate jacobian
               jacobian = f.Jacobian(x);
          }
     }
     return true;
}
Input File: speed/cppad/ode.cpp cppad-20170000.3/doc/cppad_poly.cpp.xml0000644000175200017650000005432213057470510016634 0ustar coincoin-web CppAD Speed: Second Derivative of a Polynomial
Prev Next cppad_poly.cpp

CppAD Speed: Second Derivative of a Polynomial

Specifications
See link_poly .

Implementation 
# include <cppad/cppad.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_poly(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &a        ,  // coefficients of polynomial
     CppAD::vector<double>     &z        ,  // polynomial argument value
     CppAD::vector<double>     &ddp      )  // second derivative w.r.t z
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;

     // optimization options: no conditional skips or compare operators
     std::string options="no_compare_op";
     // -----------------------------------------------------
     // setup
     typedef CppAD::AD<double>     ADScalar;
     typedef CppAD::vector<ADScalar> ADVector;

     size_t i;      // temporary index
     size_t m = 1;  // number of dependent variables
     size_t n = 1;  // number of independent variables
     ADVector Z(n); // AD domain space vector
     ADVector P(m); // AD range space vector

     // choose the polynomial coefficients
     CppAD::uniform_01(size, a);

     // AD copy of the polynomial coefficients
     ADVector A(size);
     for(i = 0; i < size; i++)
          A[i] = a[i];

     // forward mode first and second differentials
     CppAD::vector<double> p(1), dp(1), dz(1), ddz(1);
     dz[0]  = 1.;
     ddz[0] = 0.;

     // AD function object
     CppAD::ADFun<double> f;

     // --------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {
          // choose an argument value
          CppAD::uniform_01(1, z);
          Z[0] = z[0];

          // declare independent variables
          Independent(Z);

          // AD computation of the function value
          P[0] = CppAD::Poly(0, A, Z[0]);

          // create function object f : A -> detA
          f.Dependent(Z, P);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // pre-allocate memory for three forward mode calculations
          f.capacity_order(3);

          // evaluate the polynomial
          p = f.Forward(0, z);

          // evaluate first order Taylor coefficient
          dp = f.Forward(1, dz);

          // second derivative is twice second order Taylor coef
          ddp     = f.Forward(2, ddz);
          ddp[0] *= 2.;
     }
     else
     {
          // choose an argument value
          CppAD::uniform_01(1, z);
          Z[0] = z[0];

          // declare independent variables
          Independent(Z);

          // AD computation of the function value
          P[0] = CppAD::Poly(0, A, Z[0]);

          // create function object f : A -> detA
          f.Dependent(Z, P);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          while(repeat--)
          {     // sufficient memory is allocated by second repetition

               // get the next argument value
               CppAD::uniform_01(1, z);

               // evaluate the polynomial at the new argument value
               p = f.Forward(0, z);

               // evaluate first order Taylor coefficient
               dp = f.Forward(1, dz);

               // second derivative is twice second order Taylor coef
               ddp     = f.Forward(2, ddz);
               ddp[0] *= 2.;
          }
     }
     return true;
}
Input File: speed/cppad/poly.cpp cppad-20170000.3/doc/cppad_sparse_hessian.cpp.xml0000644000175200017650000011252513057470510020660 0ustar coincoin-web CppAD Speed: Sparse Hessian
Prev Next cppad_sparse_hessian.cpp

CppAD Speed: Sparse Hessian

Specifications
See link_sparse_hessian .

Implementation 
# include <cppad/cppad.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/speed/sparse_hes_fun.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

namespace {
     using CppAD::vector;
     typedef vector< std::set<size_t> >  SetVector;
     typedef vector<bool>                BoolVector;

     void calc_sparsity(SetVector& sparsity_set, CppAD::ADFun<double>& f)
     {     size_t n = f.Domain();
          size_t m = f.Range();
          CPPAD_ASSERT_UNKNOWN( m == 1 );
          //
          SetVector s_set(m);
          s_set[0].insert(0);
          //
          if( global_option["revsparsity"] )
          {     SetVector r_set(n);
               for(size_t i = 0; i < n; i++)
                    r_set[i].insert(i);
               f.ForSparseJac(n, r_set);
               sparsity_set = f.RevSparseHes(n, s_set);
          }
          else
          {     SetVector r_set(1);
               for(size_t i = 0; i < n; i++)
                    r_set[0].insert(i);
               sparsity_set = f.ForSparseHes(r_set, s_set);
          }
     }
     void calc_sparsity(BoolVector& sparsity_bool, CppAD::ADFun<double>& f)
     {     size_t n = f.Domain();
          size_t m = f.Range();
          CPPAD_ASSERT_UNKNOWN( m == 1 );
          //
          BoolVector s_bool(m);
          s_bool[0] = true;
          //
          if( global_option["revsparsity"] )
          {     BoolVector r_bool(n * n);
               for(size_t i = 0; i < n; i++)
               {     for(size_t j = 0; j < n; j++)
                         r_bool[ i * n + j] = i == j;
               }
               f.ForSparseJac(n, r_bool);
               sparsity_bool = f.RevSparseHes(n, s_bool);
          }
          else
          {     BoolVector r_bool(n);
               for(size_t i = 0; i < n; i++)
                    r_bool[i] = true;
               sparsity_bool = f.ForSparseHes(r_bool, s_bool);
          }
     }
}

bool link_sparse_hessian(
     size_t                           size     ,
     size_t                           repeat   ,
     const CppAD::vector<size_t>&     row      ,
     const CppAD::vector<size_t>&     col      ,
     CppAD::vector<double>&           x        ,
     CppAD::vector<double>&           hessian  ,
     size_t&                          n_sweep  )
{
     if( global_option["atomic"] )
          return false;
# if ! CPPAD_HAS_COLPACK
     if( global_option["colpack"] )
          return false;
# endif
     // optimization options: no conditional skips or compare operators
     std::string options="no_compare_op";
     // -----------------------------------------------------
     // setup
     typedef vector<double>              DblVector;
     typedef vector< std::set<size_t> >  SetVector;
     typedef CppAD::AD<double>           ADScalar;
     typedef vector<ADScalar>            ADVector;

     size_t j;
     size_t order = 0;         // derivative order corresponding to function
     size_t m = 1;             // number of dependent variables
     size_t n = size;          // number of independent variables
     ADVector   a_x(n);        // AD domain space vector
     ADVector   a_y(m);        // AD range space vector
     DblVector  w(m);          // double range space vector
     CppAD::ADFun<double> f;   // AD function object

     // weights for hessian calculation (only one component of f)
     w[0] = 1.;

     // declare sparsity pattern
     SetVector  set_sparsity(n);
     BoolVector bool_sparsity(n * n);

     // ------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose a value for x
          CppAD::uniform_01(n, x);
          for(j = 0; j < n; j++)
               a_x[j] = x[j];

          // declare independent variables
          Independent(a_x);

          // AD computation of f(x)
          CppAD::sparse_hes_fun<ADScalar>(n, a_x, row, col, order, a_y);

          // create function object f : X -> Y
          f.Dependent(a_x, a_y);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // calculate the Hessian sparsity pattern for this function
          if( global_option["boolsparsity"] )
               calc_sparsity(bool_sparsity, f);
          else
               calc_sparsity(set_sparsity, f);

          // structure that holds some of work done by SparseHessian
          CppAD::sparse_hessian_work work;
# if CPPAD_HAS_COLPACK
          if( global_option["colpack"] )
               work.color_method = "colpack.star";
# endif
          // calculate this Hessian at this x
          if( global_option["boolsparsity"]) n_sweep = f.SparseHessian(
               x, w, bool_sparsity, row, col, hessian, work
          );
          else n_sweep = f.SparseHessian(
                    x, w, set_sparsity, row, col, hessian, work
          );
     }
     else
     {     // choose a value for x
          CppAD::uniform_01(n, x);
          for(j = 0; j < n; j++)
               a_x[j] = x[j];

          // declare independent variables
          Independent(a_x);

          // AD computation of f(x)
          CppAD::sparse_hes_fun<ADScalar>(n, a_x, row, col, order, a_y);

          // create function object f : X -> Y
          f.Dependent(a_x, a_y);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // calculate the Hessian sparsity pattern for this function
          if( global_option["boolsparsity"])
               calc_sparsity(bool_sparsity, f);
          else
               calc_sparsity(set_sparsity, f);

          // declare structure that holds some of work done by SparseHessian
          CppAD::sparse_hessian_work work;
# if CPPAD_HAS_COLPACK
          if( global_option["colpack"] )
               work.color_method = "colpack.star";
# endif
          while(repeat--)
          {     // choose a value for x
               CppAD::uniform_01(n, x);

               // calculate hessian at this x
               if( global_option["boolsparsity"] ) n_sweep = f.SparseHessian(
                    x, w, bool_sparsity, row, col, hessian, work
               );
               else n_sweep = f.SparseHessian(
                    x, w, set_sparsity, row, col, hessian, work
               );
          }
     }
     return true;
}
Input File: speed/cppad/sparse_hessian.cpp cppad-20170000.3/doc/cppad_sparse_jacobian.cpp.xml0000644000175200017650000010175213057470510020774 0ustar coincoin-web CppAD Speed: Sparse Jacobian
Prev Next cppad_sparse_jacobian.cpp

CppAD Speed: Sparse Jacobian

Specifications
See link_sparse_jacobian .

Implementation 
# include <cppad/cppad.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/speed/sparse_jac_fun.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

namespace {
     using CppAD::vector;
     typedef vector< std::set<size_t> >  SetVector;
     typedef vector<bool>                BoolVector;

     void calc_sparsity(SetVector& sparsity_set, CppAD::ADFun<double>& f)
     {     bool reverse = global_option["revsparsity"];
          size_t q;
          if( reverse )
               q = f.Range();
          else
               q = f.Domain();
          //
          SetVector r_set(q);
          for(size_t j = 0; j < q; j++)
               r_set[j].insert(j);
          if( reverse )
               sparsity_set = f.RevSparseJac(q, r_set);
          else
               sparsity_set = f.ForSparseJac(q, r_set);
     }
     void calc_sparsity(BoolVector& sparsity_bool, CppAD::ADFun<double>& f)
     {     bool reverse = global_option["revsparsity"];
          size_t q;
          if( reverse )
               q = f.Range();
          else
               q = f.Domain();
          //
          BoolVector r_bool(q * q);
          for(size_t i = 0; i < q; i++)
          {     for(size_t j = 0; j < q; j++)
                    r_bool[ i * q + j] = i == j;
          }
          if( reverse )
               sparsity_bool = f.RevSparseJac(q, r_bool);
          else
               sparsity_bool = f.ForSparseJac(q, r_bool);
     }

}

bool link_sparse_jacobian(
     size_t                           size     ,
     size_t                           repeat   ,
     size_t                           m        ,
     const CppAD::vector<size_t>&     row      ,
     const CppAD::vector<size_t>&     col      ,
           CppAD::vector<double>&     x        ,
           CppAD::vector<double>&     jacobian ,
           size_t&                    n_sweep  )
{
     if( global_option["atomic"] )
          return false;
# if ! CPPAD_HAS_COLPACK
     if( global_option["colpack"] )
          return false;
# endif
     // optimization options: no conditional skips or compare operators
     std::string options="no_compare_op";
     // -----------------------------------------------------
     // setup
     typedef vector< std::set<size_t> >  SetVector;
     typedef CppAD::AD<double>           ADScalar;
     typedef CppAD::vector<ADScalar>     ADVector;

     size_t j;
     size_t order = 0;         // derivative order corresponding to function
     size_t n     = size;      // number of independent variables
     ADVector   a_x(n);        // AD domain space vector
     ADVector   a_y(m);        // AD range space vector y = g(x)
     CppAD::ADFun<double> f;   // AD function object

     // declare sparsity pattern
     SetVector  set_sparsity(m);
     BoolVector bool_sparsity(m * n);

     // ------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose a value for x
          CppAD::uniform_01(n, x);
          for(j = 0; j < n; j++)
               a_x[j] = x[j];

          // declare independent variables
          Independent(a_x);

          // AD computation of f (x)
          CppAD::sparse_jac_fun<ADScalar>(m, n, a_x, row, col, order, a_y);

          // create function object f : X -> Y
          f.Dependent(a_x, a_y);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // calculate the Jacobian sparsity pattern for this function
          if( global_option["boolsparsity"] )
               calc_sparsity(bool_sparsity, f);
          else
               calc_sparsity(set_sparsity, f);

          // structure that holds some of the work done by SparseJacobian
          CppAD::sparse_jacobian_work work;
# if CPPAD_HAS_COLPACK
          if( global_option["colpack"] )
               work.color_method = "colpack";
# endif
          // calculate the Jacobian at this x
          // (use forward mode because m > n ?)
          if( global_option["boolsparsity"]) n_sweep = f.SparseJacobianForward(
                    x, bool_sparsity, row, col, jacobian, work
          );
          else n_sweep = f.SparseJacobianForward(
                    x, set_sparsity, row, col, jacobian, work
          );
     }
     else
     {     // choose a value for x
          CppAD::uniform_01(n, x);
          for(j = 0; j < n; j++)
               a_x[j] = x[j];

          // declare independent variables
          Independent(a_x);

          // AD computation of f (x)
          CppAD::sparse_jac_fun<ADScalar>(m, n, a_x, row, col, order, a_y);

          // create function object f : X -> Y
          f.Dependent(a_x, a_y);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // calculate the Jacobian sparsity pattern for this function
          if( global_option["boolsparsity"] )
               calc_sparsity(bool_sparsity, f);
          else
               calc_sparsity(set_sparsity, f);

          // structure that holds some of the work done by SparseJacobian
          CppAD::sparse_jacobian_work work;
# if CPPAD_HAS_COLPACK
          if( global_option["colpack"] )
               work.color_method = "colpack";
# endif
          while(repeat--)
          {     // choose a value for x
               CppAD::uniform_01(n, x);

               // calculate the Jacobian at this x
               // (use forward mode because m > n ?)
               if( global_option["boolsparsity"] ) n_sweep = f.SparseJacobianForward(
                         x, bool_sparsity, row, col, jacobian, work
               );
               else n_sweep = f.SparseJacobianForward(
                         x, set_sparsity, row, col, jacobian, work
               );
          }
     }
     return true;
}
Input File: speed/cppad/sparse_jacobian.cpp cppad-20170000.3/doc/speed_fadbad.xml0000644000175200017650000001261213057470510016276 0ustar coincoin-web Speed Test Derivatives Using Fadbad
Prev Next

Speed Test Derivatives Using Fadbad

Purpose
CppAD has a set of speed tests that are used to compare Fadbad with other AD packages. This section links to the source code the Fadbad speed tests (any suggestions to make the Fadbad results faster are welcome).

fadbad_prefix
To run these tests, you must include the fadbad_prefix in you cmake command .

Running Tests
To build these speed tests, and run their correctness tests, execute the following commands starting in the build directory :
     cd speed/fadbad
     make check_speed_fadbad VERBOSE=1
 You can then run the corresponding speed tests with the following command
     ./speed_fadbad speed seed
 where seed is a positive integer. See speed_main for more options.

Contents
Input File: omh/speed/speed_fadbad.omh cppad-20170000.3/doc/fadbad_det_minor.cpp.xml0000644000175200017650000003054313057470510017742 0ustar coincoin-web Fadbad Speed: Gradient of Determinant by Minor Expansion
Prev Next fadbad_det_minor.cpp

Fadbad Speed: Gradient of Determinant by Minor Expansion

Specifications
See link_det_minor .

Implementation 
# include <FADBAD++/badiff.h>
# include <cppad/speed/det_by_minor.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/vector.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_minor(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &gradient )
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup

     // object for computing determinant
     typedef fadbad::B<double>       ADScalar;
     typedef CppAD::vector<ADScalar> ADVector;
     CppAD::det_by_minor<ADScalar>   Det(size);

     size_t i;                // temporary index
     size_t m = 1;            // number of dependent variables
     size_t n = size * size;  // number of independent variables
     ADScalar   detA;         // AD value of the determinant
     ADVector   A(n);         // AD version of matrix

     // ------------------------------------------------------
     while(repeat--)
       {     // get the next matrix
          CppAD::uniform_01(n, matrix);

          // set independent variable values
          for(i = 0; i < n; i++)
               A[i] = matrix[i];

          // compute the determinant
          detA = Det(A);

          // create function object f : A -> detA
          detA.diff(0, m);  // index 0 of m dependent variables

          // evaluate and return gradient using reverse mode
          for(i =0; i < n; i++)
               gradient[i] = A[i].d(0); // partial detA w.r.t A[i]
     }
     // ---------------------------------------------------------
     return true;
}
Input File: speed/fadbad/det_minor.cpp cppad-20170000.3/doc/fadbad_det_lu.cpp.xml0000644000175200017650000003070413057470510017235 0ustar coincoin-web Fadbad Speed: Gradient of Determinant Using Lu Factorization
Prev Next fadbad_det_lu.cpp

Fadbad Speed: Gradient of Determinant Using Lu Factorization

Specifications
See link_det_lu .

Implementation 
# include <FADBAD++/badiff.h>
# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/vector.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_lu(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &gradient )
{
     // speed test global option values
     if( global_option["onetape"] || global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     //
     // object for computing determinant
     typedef fadbad::B<double>       ADScalar;
     typedef CppAD::vector<ADScalar> ADVector;
     CppAD::det_by_lu<ADScalar>      Det(size);

     size_t i;                // temporary index
     size_t m = 1;            // number of dependent variables
     size_t n = size * size;  // number of independent variables
     ADScalar   detA;         // AD value of the determinant
     ADVector   A(n);         // AD version of matrix

     // ------------------------------------------------------
     while(repeat--)
       {     // get the next matrix
          CppAD::uniform_01(n, matrix);

          // set independent variable values
          for(i = 0; i < n; i++)
               A[i] = matrix[i];

          // compute the determinant
          detA = Det(A);

          // create function object f : A -> detA
          detA.diff(0, m);  // index 0 of m dependent variables

          // evaluate and return gradient using reverse mode
          for(i =0; i < n; i++)
               gradient[i] = A[i].d(0); // partial detA w.r.t A[i]
     }
     // ---------------------------------------------------------
     return true;
}
Input File: speed/fadbad/det_lu.cpp cppad-20170000.3/doc/fadbad_mat_mul.cpp.xml0000644000175200017650000003257413057470510017426 0ustar coincoin-web Fadbad Speed: Matrix Multiplication
Prev Next fadbad_mat_mul.cpp

Fadbad Speed: Matrix Multiplication

Specifications
See link_mat_mul .

Implementation 
# include <FADBAD++/badiff.h>
# include <cppad/speed/mat_sum_sq.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/vector.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_mat_mul(
     size_t                           size     ,
     size_t                           repeat   ,
     CppAD::vector<double>&           x        ,
     CppAD::vector<double>&           z        ,
     CppAD::vector<double>&           dz       )
{
     // speed test global option values
     if( global_option["memory"] || global_option["onetape"] || global_option["atomic"] || global_option["optimize"] )
          return false;
     // The correctness check for this test is failing, so abort (for now).
     return false;

     // -----------------------------------------------------
     // setup

     // object for computing determinant
     typedef fadbad::B<double>       ADScalar;
     typedef CppAD::vector<ADScalar> ADVector;

     size_t j;                // temporary index
     size_t m = 1;            // number of dependent variables
     size_t n = size * size;  // number of independent variables
     ADVector   X(n);         // AD domain space vector
     ADVector   Y(n);         // Store product matrix
     ADVector   Z(m);         // AD range space vector

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, x);

          // set independent variable values
          for(j = 0; j < n; j++)
               X[j] = x[j];

          // do the computation
          mat_sum_sq(size, X, Y, Z);

          // create function object f : X -> Z
          Z[0].diff(0, m);  // index 0 of m dependent variables

          // evaluate and return gradient using reverse mode
          for(j = 0; j < n; j++)
               dz[j] = X[j].d(0); // partial Z[0] w.r.t X[j]
     }
     // return function value
     z[0] = Z[0].x();

     // ---------------------------------------------------------
     return true;
}
Input File: speed/fadbad/mat_mul.cpp cppad-20170000.3/doc/fadbad_ode.cpp.xml0000644000175200017650000003473513057470510016540 0ustar coincoin-web Fadbad Speed: Ode
Prev Next fadbad_ode.cpp

Fadbad Speed: Ode

Specifications
See link_ode .

Implementation 
# include <FADBAD++/fadiff.h>
# include <algorithm>
# include <cassert>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/speed/ode_evaluate.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

namespace fadbad {
     // define fabs for use by ode_evaluate
     fadbad::F<double> fabs(const fadbad::F<double>& x)
     {     return std::max(-x, x); }
}

bool link_ode(
     size_t                     size       ,
     size_t                     repeat     ,
     CppAD::vector<double>      &x         ,
     CppAD::vector<double>      &jacobian
)
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] )
          return false;
     // -------------------------------------------------------------
     // setup
     assert( x.size() == size );
     assert( jacobian.size() == size * size );

     typedef fadbad::F<double>       ADScalar;
     typedef CppAD::vector<ADScalar> ADVector;

     size_t i, j;
     size_t p = 0;          // use ode to calculate function values
     size_t n = size;       // number of independent variables
     size_t m = n;          // number of dependent variables
     ADVector X(n), Y(m);   // independent and dependent variables

     // -------------------------------------------------------------
     while(repeat--)
     {     // choose next x value
          CppAD::uniform_01(n, x);
          for(j = 0; j < n; j++)
          {     // set value of x[j]
               X[j] = x[j];
               // set up for X as the independent variable vector
               X[j].diff(j, n);
          }

          // evaluate function
          CppAD::ode_evaluate(X, p, Y);

          // return values with Y as the dependent variable vector
          for(i = 0; i < m; i++)
          {     for(j = 0; j < n; j++)
                    jacobian[ i * n + j ] = Y[i].d(j);
          }
     }
     return true;
}
Input File: speed/fadbad/ode.cpp cppad-20170000.3/doc/fadbad_poly.cpp.xml0000644000175200017650000003106113057470510016741 0ustar coincoin-web Fadbad Speed: Second Derivative of a Polynomial
Prev Next fadbad_poly.cpp

Fadbad Speed: Second Derivative of a Polynomial

Specifications
See link_poly .

Implementation 
# include <cppad/utility/vector.hpp>
# include <cppad/utility/poly.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <FADBAD++/tadiff.h>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_poly(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &a        ,  // coefficients of polynomial
     CppAD::vector<double>     &z        ,  // polynomial argument value
     CppAD::vector<double>     &ddp      )  // second derivative w.r.t z
{
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     size_t i;             // temporary index
     fadbad::T<double>  Z; // domain space AD value
     fadbad::T<double>  P; // range space AD value

     // choose the polynomial coefficients
     CppAD::uniform_01(size, a);

     // AD copy of the polynomial coefficients
     CppAD::vector< fadbad::T<double> > A(size);
     for(i = 0; i < size; i++)
          A[i] = a[i];

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next argument value
          CppAD::uniform_01(1, z);

          // independent variable value
          Z    = z[0]; // argument value
          Z[1] = 1;    // argument first order Taylor coefficient

          // AD computation of the dependent variable
          P = CppAD::Poly(0, A, Z);

          // Taylor-expand P to degree one
          P.eval(2);

          // second derivative is twice second order Taylor coefficient
          ddp[0] = 2. * P[2];

          // Free DAG corresponding to P does not seem to improve speed.
          // Probably because it gets freed the next time P is assigned.
          // P.reset();
     }
     // ------------------------------------------------------
     return true;
}
Input File: speed/fadbad/poly.cpp cppad-20170000.3/doc/fadbad_sparse_hessian.cpp.xml0000644000175200017650000001104013057470510020760 0ustar coincoin-web Fadbad Speed: Sparse Hessian
Prev Next fadbad_sparse_hessian.cpp Headings

Fadbad Speed: Sparse Hessian
// A fadbad version of this test is not yet available
bool link_sparse_hessian(
        size_t                           size       ,
        size_t                           repeat     ,
        const CppAD::vector<size_t>&      row       ,
        const CppAD::vector<size_t>&      col       ,
        CppAD::vector<double>&            x         ,
        CppAD::vector<double>&            hessian   ,
        size_t&                           n_sweep
)
{
     return false;
}
Input File: speed/fadbad/sparse_hessian.cpp cppad-20170000.3/doc/fadbad_sparse_jacobian.cpp.xml0000644000175200017650000001117513057470510021105 0ustar coincoin-web fadbad Speed: sparse_jacobian
Prev Next fadbad_sparse_jacobian.cpp Headings

fadbad Speed: sparse_jacobian
// A fadbad version of this test is not yet available
bool link_sparse_jacobian(
     size_t                           size     ,
     size_t                           repeat   ,
     size_t                           m        ,
     const CppAD::vector<size_t>&     row      ,
     const CppAD::vector<size_t>&     col      ,
           CppAD::vector<double>&     x        ,
           CppAD::vector<double>&     jacobian ,
           size_t&                    n_sweep  )
{
     return false;
}
Input File: speed/fadbad/sparse_jacobian.cpp cppad-20170000.3/doc/speed_sacado.xml0000644000175200017650000001265713057470510016340 0ustar coincoin-web Speed Test Derivatives Using Sacado
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Speed Test Derivatives Using Sacado

Purpose
CppAD has a set of speed tests that are used to compare Sacado with other AD packages. This section links to the source code the Sacado speed tests (any suggestions to make the Sacado results faster are welcome).

sacado_prefix
To run these tests, you must include the sacado_prefix in you cmake command .

Running Tests
To build these speed tests, and run their correctness tests, execute the following commands starting in the build directory :
     cd speed/sacado
     make check_speed_sacado VERBOSE=1
 You can then run the corresponding speed tests with the following command
     ./speed_sacado speed seed
 where seed is a positive integer. See speed_main for more options.

Contents
Input File: omh/speed/speed_sacado.omh cppad-20170000.3/doc/sacado_det_minor.cpp.xml0000644000175200017650000002751713057470510020002 0ustar coincoin-web Sacado Speed: Gradient of Determinant by Minor Expansion
Prev Next sacado_det_minor.cpp

Sacado Speed: Gradient of Determinant by Minor Expansion

Specifications
See link_det_minor .

Implementation 
# include <Sacado.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/vector.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_minor(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &gradient )
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup

     // object for computing determinant
     typedef Sacado::Rad::ADvar<double>    ADScalar;
     typedef CppAD::vector<ADScalar>       ADVector;
     CppAD::det_by_minor<ADScalar>         Det(size);

     size_t i;                // temporary index
     size_t n = size * size;  // number of independent variables
     ADScalar   detA;         // AD value of the determinant
     ADVector   A(n);         // AD version of matrix

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, matrix);

          // set independent variable values
          for(i = 0; i < n; i++)
               A[i] = matrix[i];

          // compute the determinant
          detA = Det(A);

          // reverse mode compute gradient of last computed value; i.e., detA
          ADScalar::Gradcomp();

          // return gradient
          for(i =0; i < n; i++)
               gradient[i] = A[i].adj(); // partial detA w.r.t A[i]
     }
     // ---------------------------------------------------------
     return true;
}
Input File: speed/sacado/det_minor.cpp cppad-20170000.3/doc/sacado_det_lu.cpp.xml0000644000175200017650000002765113057470510017275 0ustar coincoin-web Sacado Speed: Gradient of Determinant Using Lu Factorization
Prev Next sacado_det_lu.cpp

Sacado Speed: Gradient of Determinant Using Lu Factorization

Specifications
See link_det_lu .

Implementation 
# include <Sacado.hpp>
# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/vector.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_lu(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &gradient )
{
     // speed test global option values
     if( global_option["onetape"] || global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     //
     // object for computing determinant
     typedef Sacado::Rad::ADvar<double>   ADScalar;
     typedef CppAD::vector<ADScalar>      ADVector;
     CppAD::det_by_lu<ADScalar>           Det(size);

     size_t i;                // temporary index
     size_t n = size * size;  // number of independent variables
     ADScalar   detA;         // AD value of the determinant
     ADVector   A(n);         // AD version of matrix

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, matrix);

          // set independent variable values
          for(i = 0; i < n; i++)
               A[i] = matrix[i];

          // compute the determinant
          detA = Det(A);

          // compute the gradient of detA
          ADScalar::Gradcomp();

          // evaluate and return gradient using reverse mode
          for(i =0; i < n; i++)
               gradient[i] = A[i].adj(); // partial detA w.r.t A[i]
     }
     // ---------------------------------------------------------
     return true;
}
Input File: speed/sacado/det_lu.cpp cppad-20170000.3/doc/sacado_mat_mul.cpp.xml0000644000175200017650000003200113057470510017440 0ustar coincoin-web Sacado Speed: Matrix Multiplication
Prev Next sacado_mat_mul.cpp

Sacado Speed: Matrix Multiplication

Specifications
See link_mat_mul .

Implementation 
# include <Sacado.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/mat_sum_sq.hpp>
# include <cppad/speed/uniform_01.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_mat_mul(
     size_t                           size     ,
     size_t                           repeat   ,
     CppAD::vector<double>&           x        ,
     CppAD::vector<double>&           z        ,
     CppAD::vector<double>&           dz       )
{
     // speed test global option values
     if( global_option["memory"] || global_option["onetape"] || global_option["atomic"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup

     // object for computing determinant
     typedef Sacado::Rad::ADvar<double>    ADScalar;
     typedef CppAD::vector<ADScalar>       ADVector;

     size_t j;                // temporary index
     size_t m = 1;            // number of dependent variables
     size_t n = size * size;  // number of independent variables
     ADVector   X(n);         // AD domain space vector
     ADVector   Y(n);         // Store product matrix
     ADVector   Z(m);         // AD range space vector
     ADScalar   f;

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next matrix
          CppAD::uniform_01(n, x);

          // set independent variable values
          for(j = 0; j < n; j++)
               X[j] = x[j];

          // do the computation
          mat_sum_sq(size, X, Y, Z);

          // create function object f : X -> Z
          f = Z[0];

          // reverse mode gradient of last ADvar computed value; i.e., f
          ADScalar::Gradcomp();

          // return gradient
          for(j = 0; j < n; j++)
               dz[j] = X[j].adj(); // partial f w.r.t X[j]
     }
     // return function value
     z[0] = f.val();

     // ---------------------------------------------------------
     return true;
}
Input File: speed/sacado/mat_mul.cpp cppad-20170000.3/doc/sacado_ode.cpp.xml0000644000175200017650000003252213057470510016561 0ustar coincoin-web Sacado Speed: Gradient of Ode Solution
Prev Next sacado_ode.cpp

Sacado Speed: Gradient of Ode Solution

Specifications
See link_ode .

Implementation 
# include <Sacado.hpp>
// # include <algorithm>
# include <cassert>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/speed/ode_evaluate.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_ode(
     size_t                     size       ,
     size_t                     repeat     ,
     CppAD::vector<double>      &x         ,
     CppAD::vector<double>      &jacobian
)
{
     // speed test global option values
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] )
          return false;
     // -------------------------------------------------------------
     // setup
     assert( x.size() == size );
     assert( jacobian.size() == size * size );

     typedef Sacado::Fad::DFad<double>  ADScalar;
     typedef CppAD::vector<ADScalar>    ADVector;

     size_t i, j;
     size_t p = 0;          // use ode to calculate function values
     size_t n = size;       // number of independent variables
     size_t m = n;          // number of dependent variables
     ADVector X(n), Y(m);   // independent and dependent variables

     // -------------------------------------------------------------
     while(repeat--)
     {     // choose next x value
          CppAD::uniform_01(n, x);
          for(j = 0; j < n; j++)
          {     // set up for X as the independent variable vector
               X[j] = ADScalar(int(n), int(j), x[j]);
          }

          // evaluate function
          CppAD::ode_evaluate(X, p, Y);

          // return values with Y as the dependent variable vector
          for(i = 0; i < m; i++)
          {     for(j = 0; j < n; j++)
                    jacobian[ i * n + j ] = Y[i].dx(j);
          }
     }
     return true;
}
Input File: speed/sacado/ode.cpp cppad-20170000.3/doc/sacado_poly.cpp.xml0000644000175200017650000003400413057470510016772 0ustar coincoin-web Sacado Speed: Second Derivative of a Polynomial
Prev Next sacado_poly.cpp

Sacado Speed: Second Derivative of a Polynomial

Specifications
See link_poly .

Implementation 
# include <cppad/utility/vector.hpp>
# include <cppad/utility/poly.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <Sacado.hpp>

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_poly(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &a        ,  // coefficients of polynomial
     CppAD::vector<double>     &z        ,  // polynomial argument value
     CppAD::vector<double>     &ddp      )  // second derivative w.r.t z
{
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     typedef Sacado::Tay::Taylor<double>  ADScalar;
     CppAD::vector<ADScalar>              A(size);

     size_t i;               // temporary index
     ADScalar   Z;           // domain space AD value
     ADScalar   P;           // range space AD value
     unsigned int order = 2; // order of Taylor coefficients
     Z.resize(order+1, false);
     P.resize(order+1, false);

     // choose the polynomial coefficients
     CppAD::uniform_01(size, a);

     // AD copy of the polynomial coefficients
     for(i = 0; i < size; i++)
          A[i] = a[i];

     // ------------------------------------------------------
     while(repeat--)
     {     // get the next argument value
          CppAD::uniform_01(1, z);

          // independent variable value
          Z.fastAccessCoeff(0)   = z[0]; // argument value
          Z.fastAccessCoeff(1)   = 1.;   // first order coefficient
          Z.fastAccessCoeff(2)   = 0.;   // second order coefficient

          // AD computation of the dependent variable
          P = CppAD::Poly(0, A, Z);

          // second derivative is twice second order Taylor coefficient
          ddp[0] = 2. * P.fastAccessCoeff(2);
     }
     // ------------------------------------------------------
     return true;
}
Input File: speed/sacado/poly.cpp cppad-20170000.3/doc/sacado_sparse_hessian.cpp.xml0000644000175200017650000001116413057470510021020 0ustar coincoin-web Sacado Speed: Sparse Hessian
Prev Next sacado_sparse_hessian.cpp Headings

Sacado Speed: Sparse Hessian
// A sacado version of this test is not yet implemented
extern bool link_sparse_hessian(
        size_t                           size       ,
        size_t                           repeat     ,
        const CppAD::vector<size_t>&      row       ,
        const CppAD::vector<size_t>&      col       ,
        CppAD::vector<double>&            x         ,
        CppAD::vector<double>&            hessian   ,
        size_t&                           n_sweep
)
{
     return false;
}
Input File: speed/sacado/sparse_hessian.cpp cppad-20170000.3/doc/sacado_sparse_jacobian.cpp.xml0000644000175200017650000001117113057470510021132 0ustar coincoin-web sacado Speed: sparse_jacobian
Prev Next sacado_sparse_jacobian.cpp Headings

sacado Speed: sparse_jacobian
// A sacado version of this test is not yet available
bool link_sparse_jacobian(
     size_t                           size     ,
     size_t                           repeat   ,
     size_t                           m        ,
     const CppAD::vector<size_t>&     row      ,
     const CppAD::vector<size_t>&     col      ,
           CppAD::vector<double>&     x        ,
           CppAD::vector<double>&     jacobian ,
           size_t&                    n_sweep  )
{
     return false;
}
Input File: speed/sacado/sparse_jacobian.cpp cppad-20170000.3/doc/appendix.xml0000644000175200017650000000671713057470510015536 0ustar coincoin-web Appendix
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Appendix

Contents
FaqFrequently Asked Questions and Answers
TheoryThe Theory of Derivative Calculations
glossaryGlossary
BibBibliography
wish_listThe CppAD Wish List
whats_newChanges and Additions to CppAD
deprecatedCppAD Deprecated API Features
compare_cCompare Speed of C and C++
numeric_adSome Numerical AD Utilities
addonCppAD Addons
LicenseYour License for the CppAD Software
Input File: omh/appendix.omh cppad-20170000.3/doc/_appendix_xml.js0000644000175200017650000000254413057470510016363 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'appendix.xml' ]; var list_down1 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down0 = [ 'faq.xml', 'theory.xml', 'glossary.xml', 'bib.xml', 'wish_list.xml', 'whats_new.xml', 'deprecated.xml', 'compare_c.xml', 'numeric_ad.xml', 'addon.xml', 'license.xml' ]; var list_current0 = [ 'appendix.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/faq.xml0000644000175200017650000004032013057470510014461 0ustar coincoin-web Frequently Asked Questions and Answers
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Frequently Asked Questions and Answers

Assignment and Independent
Why does the code sequence
     Independent(u);
     v = u[0];
 behave differently from the code sequence
     v = u[0];
     Independent(u);
 Before the call to Independent , u[0] is a parameter and after the call it is a variable. Thus in the first case, v is a variable and in the second case it is a parameter.

Bugs
What should I do if I suspect that there is a bug in CppAD ?

  1. The first step is to search this page for mention of some feature that perhaps you interpreting as a bug (and is not). If this does not solve your problem, continue to the next step.
  2. The second step is to check the whats_new messages from the date of the release that you are using to the current date. If the bug has been mentioned and fixed, then install the current version of CppAD. If this does not solve your problem, continue to the next step.
  3. Create a simple as possible demonstration of the bug; see the file bug/template.sh for a template that you can edit for that purpose. The smaller the program, the better the bug report.
  4. Send an e-mail message to the mailing list cppad@list.coin-or.org with a description of the bug. Attaching your program that demonstrates the bug.


CompareChange
If you attempt to use the CompareChange function when NDEBUG is true, you will get an error message stating that CompareChange is not a member of the ADFun template class.

Complex Types
Which of the following complex types is better:
     AD< std::complex<Base> >
     std::complex< AD<Base> >
 The complex abs function is differentiable with respect to its real and imaginary parts, but it is not complex differentiable. Thus one would prefer to use
     std::complex< AD<Base> >
 On the other hand, the C++ standard only specifies std::complex<Type> where Type is float, double, or lone double. The effect of instantiating the template complex for any other type is unspecified.

Exceptions
Why, in all the examples, do you pass back a boolean variable instead of throwing an exception ?

The examples are also used to test the correctness of CppAD and to check your installation. For these two uses, it is helpful to run all the tests and to know which ones failed. The actual code in CppAD uses the ErrorHandler utility to signal exceptions. Specifications for redefining this action are provided.

Independent Variables
Is it possible to evaluate the same tape recording with different values for the independent variables ?

Yes (see forward_zero ).

Matrix Inverse
Is it possible to differentiate (with respect to the matrix elements) the computation of the inverse of a matrix where the computation of the inverse uses pivoting ?

The example routine LuSolve can be used to do this because the inverse is a special case of the solution of linear equations. The examples jac_lu_det.cpp and hes_lu_det.cpp use LuSolve to compute derivatives of the determinant with respect to the components of the matrix.

Mode: Forward or Reverse
When evaluating derivatives, one always has a choice between forward and reverse mode. How does one decide which mode to use ?

In general, the best mode depends on the number of domain and range components in the function that your are differentiating. Each call to Forward computes the derivative of all the range directions with respect to one domain direction. Each call to Reverse computes the derivative of one range direction with respect to all the domain directions. The times required for (speed of) calls Forward and Reverse are about equal. The Parameter function can be used to quickly determine that some range directions have derivative zero.

Namespace

Test Vector Preprocessor Symbol
Why do you use CPPAD_TESTVECTOR instead of a namespace for the CppAD testvector class ?

The preprocessor symbol CPPAD_TESTVECTOR determines which SimpleVector template class is used for extensive testing. The default definition for CPPAD_TESTVECTOR is the CppAD::vector template class, but it can be changed. Note that all the preprocessor symbols that are defined or used by CppAD begin with either CPPAD (some old deprecated symbols begin with CppAD).

Using
Why do I have trouble when the following command 
 
     using namespace CppAD
is at the global level (not within a function or some other limited scope).

Some versions of # include <cmath> for gcc and Visual C++ define the standard math functions, (for example double sqrt(double x) ) at the global level. It is necessary to put your using commands within the scope of a function, or some other limited scope, in order to shadow these improper global definitions.

Speed
How do I get the best speed performance out of CppAD ?

NDEBUG
You should compile your code with optimization, without debugging, and with the preprocessor symbol NDEBUG defined. (The speed_cppad tests do this.) Note that defining NDEBUG will turn off all of the error checking and reporting that is done using ErrorHandler .

Optimize
It is also possible that preforming a tape optimization will improve the speed of evaluation more than the time required for the optimization.

Memory Allocation
You may also increase execution speed by calling hold_memory with value equal to true.

Tape Storage: Disk or Memory
Does CppAD store the tape on disk or in memory ?

CppAD uses memory to store a different tape for recording operations for each AD<Base> type that is used. If you have a very large number calculations that are recorded on a tape, the tape will keep growing to hold the necessary information. Eventually, virtual memory may be used to store the tape and the calculations may slow down because of necessary disk access.
Input File: omh/faq.omh cppad-20170000.3/doc/theory.xml0000644000175200017650000000552213057470510015231 0ustar coincoin-web The Theory of Derivative Calculations
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The Theory of Derivative Calculations

Contents
Input File: omh/theory/theory.omh cppad-20170000.3/doc/exp_forward.xml0000644000175200017650000003524613057470510016245 0ustar coincoin-web Exponential Function Forward Mode Theory
Prev Next exp_forward

Exponential Function Forward Mode Theory

Derivatives
If F ( x ) is exp ( x ) or expm 1 ( x ) the corresponding derivative satisfies the equation 1 * F ( 1 ) ( x ) - 1 * F ( x ) = d ( 0 ) = { 0 if F ( x ) = exp ( x ) 1 if F ( x ) = expm 1 ( x ) where the equation above defines d ( 0 ) . In the standard math function differential equation , A ( x ) = 1 , B ( x ) = 1 , and D ( x ) = d ( 0 ) . We use a , b , d , and z to denote the Taylor coefficients for A [ X ( t ) ] , B [ X ( t ) ] , D [ X ( t ) ] , and F [ X ( t ) ] respectively.

Taylor Coefficients Recursion
For orders j = 0 , 1 , … , z ( 0 ) = F ( x ( 0 ) ) e ( 0 ) = d ( 0 ) + z ( 0 ) e ( j + 1 ) = d ( j + 1 ) + ∑ k = 0 j + 1 a ( j + 1 - k ) * z ( k ) = z ( j + 1 ) z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 1 j + 1 k x ( k ) e ( j + 1 - k ) - ∑ k = 1 j k z ( k ) b ( j + 1 - k ) ) = x ( j + 1 ) d ( 0 ) + 1 j + 1 ∑ k = 1 j + 1 k x ( k ) z ( j + 1 - k )
Input File: omh/theory/exp_forward.omh cppad-20170000.3/doc/log_forward.xml0000644000175200017650000003551513057470510016231 0ustar coincoin-web Logarithm Function Forward Mode Theory
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Logarithm Function Forward Mode Theory

Derivatives
If F ( x ) is log ( x ) or log 1 p ( x ) the corresponding derivative satisfies the equation ( b ¯ + x ) * F ( 1 ) ( x ) - 0 * F ( x ) = 1 where b ¯ = { 0 if F ( x ) = log ( x ) 1 if F ( x ) = log 1 p ( x ) In the standard math function differential equation , A ( x ) = 0 , B ( x ) = b ¯ + x , and D ( x ) = 1 . We use a , b , d , and z to denote the Taylor coefficients for A [ X ( t ) ] , B [ X ( t ) ] , D [ X ( t ) ] , and F [ X ( t ) ] respectively.

Taylor Coefficients Recursion
For orders j = 0 , 1 , … , z ( 0 ) = F ( x ( 0 ) ) e ( j ) = d ( j ) + ∑ k = 0 j a ( j - k ) * z ( k ) = { 1 if j = 0 0 otherwise z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 1 j + 1 k x ( k ) e ( j + 1 - k ) - ∑ k = 1 j k z ( k ) b ( j + 1 - k ) ) = 1 j + 1 1 b ¯ + x ( 0 ) (( j + 1 ) x ( j + 1 ) - ∑ k = 1 j k z ( k ) x ( j + 1 - k ) )
Input File: omh/theory/log_forward.omh cppad-20170000.3/doc/sqrt_forward.xml0000644000175200017650000003077613057470510016445 0ustar coincoin-web Square Root Function Forward Mode Theory
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Square Root Function Forward Mode Theory
If F ( x ) = x F ( x ) * F ( 1 ) ( x ) - 0 * F ( x ) = 1 / 2 and in the standard math function differential equation , A ( x ) = 0 , B ( x ) = F ( x ) , and D ( x ) = 1 / 2 . We use a , b , d , and z to denote the Taylor coefficients for A [ X ( t ) ] , B [ X ( t ) ] , D [ X ( t ) ] , and F [ X ( t ) ] respectively. It now follows from the general Taylor coefficients recursion formula that for j = 0 , 1 , … , z ( 0 ) = x ( 0 ) e ( j ) = d ( j ) + ∑ k = 0 j a ( j - k ) * z ( k ) = { 1 / 2 if j = 0 0 otherwise z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 1 j + 1 k x ( k ) e ( j + 1 - k ) - ∑ k = 1 j k z ( k ) b ( j + 1 - k ) ) = 1 j + 1 1 z ( 0 ) (j + 1 2 x ( j + 1 ) - ∑ k = 1 j k z ( k ) z ( j + 1 - k ) )
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Trigonometric and Hyperbolic Sine and Cosine Forward Theory

Differential Equation
The standard math function differential equation is B ( u ) * F ( 1 ) ( u ) - A ( u ) * F ( u ) = D ( u ) In this sections we consider forward mode for the following choices:
     F ( u ) sin ( u ) cos ( u ) sinh ( u ) cosh ( u )
A ( u ) 0 0 0 0
B ( u ) 1 1 1 1
D ( u ) cos ( u ) - sin ( u ) cosh ( u ) sinh ( u )
We use a , b , d and f for the Taylor coefficients of A [ X ( t ) ] , B [ X ( t ) ] , D [ X ( t ) ] , and F [ X ( t ) ] respectively. It now follows from the general Taylor coefficients recursion formula that for j = 0 , 1 , … , f ( 0 ) = D ( x ( 0 ) ) e ( j ) = d ( j ) + ∑ k = 0 j a ( j - k ) * f ( k ) = d ( j ) f ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 1 j + 1 k x ( k ) e ( j + 1 - k ) - ∑ k = 1 j k f ( k ) b ( j + 1 - k ) ) = 1 j + 1 ∑ k = 1 j + 1 k x ( k ) d ( j + 1 - k ) The formula above generates the order j + 1 coefficient of F [ X ( t ) ] from the lower order coefficients for X ( t ) and D [ X ( t ) ] .
Input File: omh/theory/sin_cos_forward.omh cppad-20170000.3/doc/atan_forward.xml0000644000175200017650000004141513057470510016367 0ustar coincoin-web Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
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Inverse Tangent and Hyperbolic Tangent Forward Mode Theory

Derivatives atan ( 1 ) ( x ) = 1 / ( 1 + x * x ) atanh ( 1 ) ( x ) = 1 / ( 1 - x * x ) If F ( x ) is atan ( x ) or atanh ( x ) , the corresponding derivative satisfies the equation ( 1 ± x * x ) * F ( 1 ) ( x ) - 0 * F ( x ) = 1 and in the standard math function differential equation , A ( x ) = 0 , B ( x ) = 1 ± x * x , and D ( x ) = 1 . We use a , b , d and z to denote the Taylor coefficients for A [ X ( t ) ] , B [ X ( t ) ] , D [ X ( t ) ] , and F [ X ( t ) ] respectively.

Taylor Coefficients Recursion
For j = 0 , 1 , … , z ( 0 ) = F ( x ( 0 ) ) b ( j ) = { 1 ± x ( 0 ) * x ( 0 ) if j = 0 ± ∑ k = 0 j x ( k ) x ( j - k ) otherwise e ( j ) = d ( j ) + ∑ k = 0 j a ( j - k ) * z ( k ) = { 1 if j = 0 0 otherwise z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 0 j e ( k ) ( j + 1 - k ) x ( j + 1 - k ) - ∑ k = 1 j b ( k ) ( j + 1 - k ) z ( j + 1 - k ) ) z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (( j + 1 ) x ( j + 1 ) - ∑ k = 1 j k z ( k ) b ( j + 1 - k ) )
Input File: omh/theory/atan_forward.omh cppad-20170000.3/doc/asin_forward.xml0000644000175200017650000005163413057470510016402 0ustar coincoin-web Inverse Sine and Hyperbolic Sine Forward Mode Theory
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Inverse Sine and Hyperbolic Sine Forward Mode Theory

Derivatives asin ( 1 ) ( x ) = 1 / 1 - x * x asinh ( 1 ) ( x ) = 1 / 1 + x * x If F ( x ) is asin ( x ) or asinh ( x ) the corresponding derivative satisfies the equation 1 ∓ x * x * F ( 1 ) ( x ) - 0 * F ( u ) = 1 and in the standard math function differential equation , A ( x ) = 0 , B ( x ) = 1 ∓ x * x , and D ( x ) = 1 . We use a , b , d and z to denote the Taylor coefficients for A [ X ( t ) ] , B [ X ( t ) ] , D [ X ( t ) ] , and F [ X ( t ) ] respectively.

Taylor Coefficients Recursion
We define Q ( x ) = 1 ∓ x * x and let q be the corresponding Taylor coefficients for Q [ X ( t ) ] . It follows that q ( j ) = { 1 ∓ x ( 0 ) * x ( 0 ) if j = 0 ∓ ∑ k = 0 j x ( k ) x ( j - k ) otherwise It follows that B [ X ( t ) ] = Q [ X ( t ) ] and from the equations for the square root that for j = 0 , 1 , … , b ( 0 ) = q ( 0 ) b ( j + 1 ) = 1 j + 1 1 b ( 0 ) (j + 1 2 q ( j + 1 ) - ∑ k = 1 j k b ( k ) b ( j + 1 - k ) ) It now follows from the general Taylor coefficients recursion formula that for j = 0 , 1 , … , z ( 0 ) = F ( x ( 0 ) ) e ( j ) = d ( j ) + ∑ k = 0 j a ( j - k ) * z ( k ) = { 1 if j = 0 0 otherwise z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 0 j e ( k ) ( j + 1 - k ) x ( j + 1 - k ) - ∑ k = 1 j b ( k ) ( j + 1 - k ) z ( j + 1 - k ) ) z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (( j + 1 ) x ( j + 1 ) - ∑ k = 1 j k z ( k ) b ( j + 1 - k ) )
Input File: omh/theory/asin_forward.omh cppad-20170000.3/doc/acos_forward.xml0000644000175200017650000005270113057470510016371 0ustar coincoin-web Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
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Inverse Cosine and Hyperbolic Cosine Forward Mode Theory

Derivatives acos ( 1 ) ( x ) = - 1 / 1 - x * x acosh ( 1 ) ( x ) = + 1 / x * x - 1 If F ( x ) is acos ( x ) or acosh ( x ) the corresponding derivative satisfies the equation ∓ ( x * x - 1 ) * F ( 1 ) ( x ) - 0 * F ( u ) = ∓ 1 and in the standard math function differential equation , A ( x ) = 0 , B ( x ) = ∓ ( x * x - 1 ) , and D ( x ) = ∓ 1 . We use a , b , d and z to denote the Taylor coefficients for A [ X ( t ) ] , B [ X ( t ) ] , D [ X ( t ) ] , and F [ X ( t ) ] respectively.

Taylor Coefficients Recursion
We define Q ( x ) = ∓ ( x * x - 1 ) and let q be the corresponding Taylor coefficients for Q [ X ( t ) ] . It follows that q ( j ) = { ∓ ( x ( 0 ) * x ( 0 ) - 1 ) if j = 0 ∓ ∑ k = 0 j x ( k ) x ( j - k ) otherwise It follows that B [ X ( t ) ] = Q [ X ( t ) ] and from the equations for the square root that for j = 0 , 1 , … , b ( 0 ) = q ( 0 ) b ( j + 1 ) = 1 j + 1 1 b ( 0 ) (j + 1 2 q ( j + 1 ) - ∑ k = 1 j k b ( k ) b ( j + 1 - k ) ) It now follows from the general Taylor coefficients recursion formula that for j = 0 , 1 , … , z ( 0 ) = F ( x ( 0 ) ) e ( j ) = d ( j ) + ∑ k = 0 j a ( j - k ) * z ( k ) = { ∓ 1 if j = 0 0 otherwise z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 0 j e ( k ) ( j + 1 - k ) x ( j + 1 - k ) - ∑ k = 1 j b ( k ) ( j + 1 - k ) z ( j + 1 - k ) ) z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∓ ( j + 1 ) x ( j + 1 ) - ∑ k = 1 j k z ( k ) b ( j + 1 - k ) )
Input File: omh/theory/acos_forward.omh cppad-20170000.3/doc/tan_forward.xml0000644000175200017650000004172613057470510016233 0ustar coincoin-web Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
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Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory

Derivatives tan ( 1 ) ( u ) = [ cos ( u ) 2 + sin ( u ) 2 ] / cos ( u ) 2 = 1 + tan ( u ) 2 tanh ( 1 ) ( u ) = [ cosh ( u ) 2 - sinh ( u ) 2 ] / cosh ( u ) 2 = 1 - tanh ( u ) 2 If F ( u ) is tan ( u ) or tanh ( u ) the corresponding derivative is given by F ( 1 ) ( u ) = 1 ± F ( u ) 2 Given X ( t ) , we define the function Z ( t ) = F [ X ( t ) ] . It follows that Z ( 1 ) ( t ) = F ( 1 ) [ X ( t ) ] X ( 1 ) ( t ) = [ 1 ± Y ( t ) ] X ( 1 ) ( t ) where we define the function Y ( t ) = Z ( t ) 2 .

Taylor Coefficients Recursion
Suppose that we are given the Taylor coefficients up to order j for the function X ( t ) and up to order j -1 for the functions Y ( t ) and Z ( t ) . We need a formula that computes the coefficient of order j for Y ( t ) and Z ( t ) . Using the equation above for Z ( 1 ) ( t ) , we have ∑ k = 1 j k z ( k ) t k -1 = ∑ k = 1 j k x ( k ) t k -1 ± [∑ k = 0 j -1 y ( k ) t k ] [∑ k = 1 j k x ( k ) t k -1 ] + o ( t j -1 ) Setting the coefficients of t j -1 equal, we have j z ( j ) = j x ( j ) ± ∑ k = 1 j k x ( k ) y ( j - k ) z ( j ) = x ( j ) ± 1 j ∑ k = 1 j k x ( k ) y ( j - k ) Once we have computed z ( j ) , we can compute y ( j ) as follows: y ( j ) = ∑ k = 0 j z ( k ) z ( j - k )
Input File: omh/theory/tan_forward.omh cppad-20170000.3/doc/erf_forward.xml0000644000175200017650000002735613057470510016230 0ustar coincoin-web Error Function Forward Taylor Polynomial Theory
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Error Function Forward Taylor Polynomial Theory

Derivatives
Given X ( t ) , we define the function Z ( t ) = erf [ X ( t ) ] It follows that erf ( 1 ) ( u ) = ( 2 / π ) exp (- u 2 ) Z ( 1 ) ( t ) = erf ( 1 ) [ X ( t ) ] X ( 1 ) ( t ) = Y ( t ) X ( 1 ) ( t ) where we define the function Y ( t ) = 2 π exp [- X ( t ) 2 ]
Taylor Coefficients Recursion
Suppose that we are given the Taylor coefficients up to order j for the function X ( t ) and Y ( t ) . We need a formula that computes the coefficient of order j for Z ( t ) . Using the equation above for Z ( 1 ) ( t ) , we have ∑ k = 1 j k z ( k ) t k -1 = [∑ k = 0 j y ( k ) t k ] [∑ k = 1 j k x ( k ) t k -1 ] + o ( t j -1 ) Setting the coefficients of t j -1 equal, we have j z ( j ) = ∑ k = 1 j k x ( k ) y ( j - k ) z ( j ) = 1 j ∑ k = 1 j k x ( k ) y ( j - k )
Input File: omh/theory/erf_forward.omh cppad-20170000.3/doc/reversetheory.xml0000644000175200017650000012002513057470510016621 0ustar coincoin-web The Theory of Reverse Mode
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The Theory of Reverse Mode

Taylor Notation
In Taylor notation, each variable corresponds to a function of a single argument which we denote by t (see Section 10.2 of Evaluating Derivatives ). Here and below X ( t ) , Y ( t ) , and Z(t) are scalar valued functions and the corresponding p-th order Taylor coefficients row vectors are x , y and z ; i.e., X ( t ) = x ( 0 ) + x ( 1 ) * t + ⋯ + x ( p ) * t p + O ( t p + 1 ) Y ( t ) = y ( 0 ) + y ( 1 ) * t + ⋯ + y ( p ) * t p + O ( t p + 1 ) Z ( t ) = z ( 0 ) + z ( 1 ) * t + ⋯ + z ( p ) * t p + O ( t p + 1 ) For the purposes of this discussion, we are given the p-th order Taylor coefficient row vectors x , y , and z . In addition, we are given the partial derivatives of a scalar valued function G ( z ( j ) , … , z ( 0 ) , x , y ) We need to compute the partial derivatives of the scalar valued function H ( z ( j -1 ) , … , z ( 0 ) , x , y ) = G ( z ( j ) , z ( j -1 ) , … , z ( 0 ) , x , y ) where z ( j ) is expressed as a function of the j-1-th order Taylor coefficient row vector for Z and the vectors x , y ; i.e., z ( j ) above is a shorthand for z ( j ) ( z ( j -1 ) , … , z ( 0 ) , x , y ) If we do not provide a formula for a partial derivative of H , then that partial derivative has the same value as for the function G .

Binary Operators

Addition
The forward mode formula for addition is z ( j ) = x ( j ) + y ( j ) If follows that for k = 0 , … , j and l = 0 , … , j -1 ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( k ) ∂ H ∂ y ( k ) = ∂ G ∂ y ( k ) + ∂ G ∂ z ( k ) ∂ H ∂ z ( l ) = ∂ G ∂ z ( l )
Subtraction
The forward mode formula for subtraction is z ( j ) = x ( j ) - y ( j ) If follows that for k = 0 , … , j ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) - ∂ G ∂ z ( k ) ∂ H ∂ y ( k ) = ∂ G ∂ y ( k ) - ∂ G ∂ z ( k )
Multiplication
The forward mode formula for multiplication is z ( j ) = ∑ k = 0 j x ( j - k ) * y ( k ) If follows that for k = 0 , … , j and l = 0 , … , j -1 ∂ H ∂ x ( j - k ) = ∂ G ∂ x ( j - k ) + ∑ k = 0 j ∂ G ∂ z ( j ) y ( k ) ∂ H ∂ y ( k ) = ∂ G ∂ y ( k ) + ∑ k = 0 j ∂ G ∂ z ( j ) x ( j - k )
Division
The forward mode formula for division is z ( j ) = 1 y ( 0 ) (x ( j ) - ∑ k = 1 j z ( j - k ) y ( k ) ) If follows that for k = 1 , … , j ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) 1 y ( 0 ) ∂ H ∂ z ( j - k ) = ∂ G ∂ z ( j - k ) - ∂ G ∂ z ( j ) 1 y ( 0 ) y ( k ) ∂ H ∂ y ( k ) = ∂ G ∂ y ( k ) - ∂ G ∂ z ( j ) 1 y ( 0 ) z ( j - k ) ∂ H ∂ y ( 0 ) = ∂ G ∂ y ( 0 ) - ∂ G ∂ z ( j ) 1 y ( 0 ) 1 y ( 0 ) (x ( j ) - ∑ k = 1 j z ( j - k ) y ( k ) ) = ∂ G ∂ y ( 0 ) - ∂ G ∂ z ( j ) 1 y ( 0 ) z ( j )
Standard Math Functions
The standard math functions have only one argument. Hence we are given the partial derivatives of a scalar valued function G ( z ( j ) , … , z ( 0 ) , x ) We need to compute the partial derivatives of the scalar valued function H ( z ( j -1 ) , … , z ( 0 ) , x ) = G ( z ( j ) , z ( j -1 ) , … , z ( 0 ) , x ) where z ( j ) is expressed as a function of the j-1-th order Taylor coefficient row vector for Z and the vector x ; i.e., z ( j ) above is a shorthand for z ( j ) ( z ( j -1 ) , … , z ( 0 ) , x )
Contents
exp_reverseExponential Function Reverse Mode Theory
log_reverseLogarithm Function Reverse Mode Theory
sqrt_reverseSquare Root Function Reverse Mode Theory
sin_cos_reverseTrigonometric and Hyperbolic Sine and Cosine Reverse Theory
atan_reverseInverse Tangent and Hyperbolic Tangent Reverse Mode Theory
asin_reverseInverse Sine and Hyperbolic Sine Reverse Mode Theory
acos_reverseInverse Cosine and Hyperbolic Cosine Reverse Mode Theory
tan_reverseTangent and Hyperbolic Tangent Reverse Mode Theory
erf_reverseError Function Reverse Mode Theory
Input File: omh/theory/reverse_theory.omh cppad-20170000.3/doc/exp_reverse.xml0000644000175200017650000003077613057470510016257 0ustar coincoin-web Exponential Function Reverse Mode Theory
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Exponential Function Reverse Mode Theory
We use the reverse theory standard math function definition for the functions H and G . The zero order forward mode formula for the exponential is z ( 0 ) = F ( x ( 0 ) ) and for j > 0 , z ( j ) = x ( j ) d ( 0 ) + 1 j ∑ k = 1 j k x ( k ) z ( j - k ) where d ( 0 ) = { 0 if F ( x ) = exp ( x ) 1 if F ( x ) = expm 1 ( x ) For order j = 0 , 1 , … we note that ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ( d ( 0 ) + z ( 0 ) ) If j > 0 , then for k = 1 , … , j ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( j ) 1 j k z ( j - k ) ∂ H ∂ z ( j - k ) = ∂ G ∂ z ( j - k ) + ∂ G ∂ z ( j ) 1 j k x ( k )
Input File: omh/theory/exp_reverse.omh cppad-20170000.3/doc/log_reverse.xml0000644000175200017650000005216113057470510016234 0ustar coincoin-web Logarithm Function Reverse Mode Theory
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Logarithm Function Reverse Mode Theory
We use the reverse theory standard math function definition for the functions H and G . The zero order forward mode formula for the logarithm is z ( 0 ) = F ( x ( 0 ) ) and for j > 0 , z ( j ) = 1 b ¯ + x ( 0 ) 1 j (j x ( j ) - ∑ k = 1 j -1 k z ( k ) x ( j - k ) ) where b ¯ = { 0 if F ( x ) = log ( x ) 1 if F ( x ) = log 1 p ( x ) We note that for j > 0 ∂ z ( j ) ∂ x ( 0 ) = - 1 b ¯ + x ( 0 ) 1 b ¯ + x ( 0 ) 1 j (j x ( j ) - ∑ k = 1 j -1 k z ( k ) x ( j - k ) ) = - z ( j ) b ¯ + x ( 0 ) Removing the zero order partials are given by ∂ H ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ z ( 0 ) ∂ z ( 0 ) ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ z ( 0 ) 1 b ¯ + x ( 0 ) For orders j > 0 and for k = 1 , … , j -1 ∂ H ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) - ∂ G ∂ z ( j ) z ( j ) b ¯ + x ( 0 ) ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) 1 b ¯ + x ( 0 ) ∂ H ∂ x ( j - k ) = ∂ G ∂ x ( j - k ) - ∂ G ∂ z ( j ) 1 b ¯ + x ( 0 ) k j z ( k ) ∂ H ∂ z ( k ) = ∂ G ∂ z ( k ) - ∂ G ∂ z ( j ) 1 b ¯ + x ( 0 ) k j x ( j - k )
Input File: omh/theory/log_reverse.omh cppad-20170000.3/doc/sqrt_reverse.xml0000644000175200017650000003747513057470510016457 0ustar coincoin-web Square Root Function Reverse Mode Theory
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Square Root Function Reverse Mode Theory
We use the reverse theory standard math function definition for the functions H and G . The forward mode formulas for the square root function are z ( j ) = x ( 0 ) for the case j = 0 , and for j > 0 , z ( j ) = 1 j 1 z ( 0 ) (j 2 x ( j ) - ∑ ℓ = 1 j -1 ℓ z ( ℓ ) z ( j - ℓ ) ) If j = 0 , we have the relation ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( 0 ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) 1 2 z ( 0 ) If j > 0 , then for k = 1 , … , j -1 ∂ H ∂ z ( 0 ) = ∂ G ∂ z ( 0 ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ z ( 0 ) = ∂ G ∂ z ( 0 ) - ∂ G ∂ z ( j ) z ( j ) z ( 0 ) ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) 1 2 z ( 0 ) ∂ H ∂ z ( k ) = ∂ G ∂ z ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ z ( k ) = ∂ G ∂ z ( k ) - ∂ G ∂ z ( j ) z ( j - k ) z ( 0 )
Input File: omh/theory/sqrt_reverse.omh cppad-20170000.3/doc/sin_cos_reverse.xml0000644000175200017650000004474413057470510017120 0ustar coincoin-web Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
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Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
We use the reverse theory standard math function definition for the functions H and G . In addition, we use the following definitions for s and c and the integer ℓ
Coefficients s c ℓ
Trigonometric Case sin [ X ( t ) ] cos [ X ( t ) ] 1
Hyperbolic Case sinh [ X ( t ) ] cosh [ X ( t ) ] -1
We use the value z ( j ) = ( s ( j ) , c ( j ) ) in the definition for G and H . The forward mode formulas for the sine and cosine functions are s ( j ) = 1 + ℓ 2 sin ( x ( 0 ) ) + 1 - ℓ 2 sinh ( x ( 0 ) ) c ( j ) = 1 + ℓ 2 cos ( x ( 0 ) ) + 1 - ℓ 2 cosh ( x ( 0 ) ) for the case j = 0 , and for j > 0 , s ( j ) = 1 j ∑ k = 1 j k x ( k ) c ( j - k ) c ( j ) = ℓ 1 j ∑ k = 1 j k x ( k ) s ( j - k ) If j = 0 , we have the relation ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ s ( j ) c ( 0 ) + ℓ ∂ G ∂ c ( j ) s ( 0 ) If j > 0 , then for k = 1 , … , j -1 ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ s ( j ) 1 j k c ( j - k ) + ℓ ∂ G ∂ c ( j ) 1 j k s ( j - k ) ∂ H ∂ s ( j - k ) = ∂ G ∂ s ( j - k ) + ℓ ∂ G ∂ c ( j ) k x ( k ) ∂ H ∂ c ( j - k ) = ∂ G ∂ c ( j - k ) + ∂ G ∂ s ( j ) k x ( k )
Input File: omh/theory/sin_cos_reverse.omh cppad-20170000.3/doc/atan_reverse.xml0000644000175200017650000010343013057470510016372 0ustar coincoin-web Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
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Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
We use the reverse theory standard math function definition for the functions H and G . In addition, we use the forward mode notation in atan_forward for B ( t ) = 1 ± X ( t ) * X ( t ) We use b for the p-th order Taylor coefficient row vectors corresponding to B ( t ) and replace z ( j ) by ( z ( j ) , b ( j ) ) in the definition for G and H . The zero order forward mode formulas for the atan function are z ( 0 ) = F ( x ( 0 ) ) b ( 0 ) = 1 ± x ( 0 ) x ( 0 ) where F ( x ) = atan ( x ) for + and F ( x ) = atanh ( x ) for - . For orders j greater than zero we have b ( j ) = ± ∑ k = 0 j x ( k ) x ( j - k ) z ( j ) = 1 j 1 b ( 0 ) (j x ( j ) - ∑ k = 1 j -1 k z ( k ) b ( j - k ) ) If j = 0 , we note that F ( 1 ) ( x ( 0 ) ) = 1 / b ( 0 ) and hence ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( 0 ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ x ( 0 ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) 1 b ( 0 ) ± ∂ G ∂ b ( j ) 2 x ( 0 ) If j > 0 , then for k = 1 , … , j -1 ∂ H ∂ b ( 0 ) = ∂ G ∂ b ( 0 ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ b ( 0 ) = ∂ G ∂ b ( 0 ) - ∂ G ∂ z ( j ) z ( j ) b ( 0 ) ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( j ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) 1 b ( 0 ) ± ∂ G ∂ b ( j ) 2 x ( 0 ) ∂ H ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( 0 ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) ± ∂ G ∂ b ( j ) 2 x ( j ) ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ x ( k ) = ∂ G ∂ x ( k ) ± ∂ G ∂ b ( j ) 2 x ( j - k ) ∂ H ∂ z ( k ) = ∂ G ∂ z ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ z ( k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ z ( k ) = ∂ G ∂ z ( k ) - ∂ G ∂ z ( j ) k b ( j - k ) j b ( 0 ) ∂ H ∂ b ( j - k ) = ∂ G ∂ b ( j - k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ b ( j - k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ b ( j - k ) = ∂ G ∂ b ( j - k ) - ∂ G ∂ z ( j ) k z ( k ) j b ( 0 )
Input File: omh/theory/atan_reverse.omh cppad-20170000.3/doc/asin_reverse.xml0000644000175200017650000011711513057470510016406 0ustar coincoin-web Inverse Sine and Hyperbolic Sine Reverse Mode Theory
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Inverse Sine and Hyperbolic Sine Reverse Mode Theory
We use the reverse theory standard math function definition for the functions H and G . In addition, we use the forward mode notation in asin_forward for Q ( t ) = 1 ∓ X ( t ) * X ( t ) B ( t ) = Q ( t ) We use q and b for the p-th order Taylor coefficient row vectors corresponding to these functions and replace z ( j ) by ( z ( j ) , b ( j ) ) in the definition for G and H . The zero order forward mode formulas for the asin function are q ( 0 ) = 1 ∓ x ( 0 ) x ( 0 ) b ( 0 ) = q ( 0 ) z ( 0 ) = F ( x ( 0 ) ) where F ( x ) = asin ( x ) for - and F ( x ) = asinh ( x ) for + . For the orders j greater than zero we have q ( j ) = ∓ ∑ k = 0 j x ( k ) x ( j - k ) b ( j ) = 1 j 1 b ( 0 ) (j 2 q ( j ) - ∑ k = 1 j -1 k b ( k ) b ( j - k ) ) z ( j ) = 1 j 1 b ( 0 ) (j x ( j ) - ∑ k = 1 j -1 k z ( k ) b ( j - k ) ) If j = 0 , we note that F ( 1 ) ( x ( 0 ) ) = 1 / b ( 0 ) and hence ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( 0 ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ q ( 0 ) ∂ q ( 0 ) ∂ x ( 0 ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) 1 b ( 0 ) ∓ ∂ G ∂ b ( j ) x ( 0 ) b ( 0 ) If j > 0 , then for k = 1 , … , j -1 ∂ H ∂ b ( 0 ) = ∂ G ∂ b ( 0 ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ b ( 0 ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ b ( 0 ) = ∂ G ∂ b ( 0 ) - ∂ G ∂ z ( j ) z ( j ) b ( 0 ) - ∂ G ∂ b ( j ) b ( j ) b ( 0 ) ∂ H ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ q ( j ) ∂ q ( j ) ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) ∓ ∂ G ∂ b ( j ) x ( j ) b ( 0 ) ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( j ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ q ( j ) ∂ q ( j ) ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) 1 b ( 0 ) ∓ ∂ G ∂ b ( j ) x ( 0 ) b ( 0 ) ∂ H ∂ b ( j - k ) = ∂ G ∂ b ( j - k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ b ( j - k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ b ( j - k ) = ∂ G ∂ b ( j - k ) - ∂ G ∂ z ( j ) k z ( k ) j b ( 0 ) - ∂ G ∂ b ( j ) b ( k ) b ( 0 ) ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ q ( j ) ∂ q ( j ) ∂ x ( k ) = ∂ G ∂ x ( k ) ∓ ∂ G ∂ b ( j ) x ( j - k ) b ( 0 ) ∂ H ∂ z ( k ) = ∂ G ∂ z ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ z ( k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ z ( k ) = ∂ G ∂ z ( k ) - ∂ G ∂ z ( j ) k b ( j - k ) j b ( 0 )
Input File: omh/theory/asin_reverse.omh cppad-20170000.3/doc/acos_reverse.xml0000644000175200017650000011752713057470510016410 0ustar coincoin-web Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
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Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
We use the reverse theory standard math function definition for the functions H and G . In addition, we use the forward mode notation in acos_forward for Q ( t ) = ∓ ( X ( t ) * X ( t ) - 1 ) B ( t ) = Q ( t ) We use q and b for the p-th order Taylor coefficient row vectors corresponding to these functions and replace z ( j ) by ( z ( j ) , b ( j ) ) in the definition for G and H . The zero order forward mode formulas for the acos function are q ( 0 ) = ∓ ( x ( 0 ) x ( 0 ) - 1 ) b ( 0 ) = q ( 0 ) z ( 0 ) = F ( x ( 0 ) ) where F ( x ) = acos ( x ) for - and F ( x ) = acosh ( x ) for + . For orders j greater than zero we have q ( j ) = ∓ ∑ k = 0 j x ( k ) x ( j - k ) b ( j ) = 1 j 1 b ( 0 ) (j 2 q ( j ) - ∑ k = 1 j -1 k b ( k ) b ( j - k ) ) z ( j ) = 1 j 1 b ( 0 ) (∓ j x ( j ) - ∑ k = 1 j -1 k z ( k ) b ( j - k ) ) If j = 0 , we note that F ( 1 ) ( x ( 0 ) ) = ∓ 1 / b ( 0 ) and hence ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( 0 ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ q ( 0 ) ∂ q ( 0 ) ∂ x ( 0 ) = ∂ G ∂ x ( j ) ∓ ∂ G ∂ z ( j ) 1 b ( 0 ) ∓ ∂ G ∂ b ( j ) x ( 0 ) b ( 0 ) If j > 0 , then for k = 1 , … , j -1 ∂ H ∂ b ( 0 ) = ∂ G ∂ b ( 0 ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ b ( 0 ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ b ( 0 ) = ∂ G ∂ b ( 0 ) - ∂ G ∂ z ( j ) z ( j ) b ( 0 ) - ∂ G ∂ b ( j ) b ( j ) b ( 0 ) ∂ H ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ q ( j ) ∂ q ( j ) ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) ∓ ∂ G ∂ b ( j ) x ( j ) b ( 0 ) ∂ H ∂ x ( j ) = ∂ G ∂ x ( j ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( j ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ q ( j ) ∂ q ( j ) ∂ x ( j ) = ∂ G ∂ x ( j ) ∓ ∂ G ∂ z ( j ) 1 b ( 0 ) ∓ ∂ G ∂ b ( j ) x ( 0 ) b ( 0 ) ∂ H ∂ b ( j - k ) = ∂ G ∂ b ( j - k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ b ( j - k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ b ( j - k ) = ∂ G ∂ b ( j - k ) - ∂ G ∂ z ( j ) k z ( k ) j b ( 0 ) - ∂ G ∂ b ( j ) b ( k ) b ( 0 ) ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ q ( j ) ∂ q ( j ) ∂ x ( k ) = ∂ G ∂ x ( k ) ∓ ∂ G ∂ b ( j ) x ( j - k ) b ( 0 ) ∂ H ∂ z ( k ) = ∂ G ∂ z ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ z ( k ) + ∂ G ∂ b ( j ) ∂ b ( j ) ∂ z ( k ) = ∂ G ∂ z ( k ) - ∂ G ∂ z ( j ) k b ( j - k ) j b ( 0 )
Input File: omh/theory/acos_reverse.omh cppad-20170000.3/doc/tan_reverse.xml0000644000175200017650000005657013057470510016245 0ustar coincoin-web Tangent and Hyperbolic Tangent Reverse Mode Theory
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Tangent and Hyperbolic Tangent Reverse Mode Theory

Notation
We use the reverse theory standard math function definition for the functions H and G . In addition, we use the forward mode notation in tan_forward for X ( t ) , Y ( t ) and Z ( t ) .

Eliminating Y(t)
For j > 0 , the forward mode coefficients are given by y ( j -1 ) = ∑ k = 0 j -1 z ( k ) z ( j - k -1 ) Fix j > 0 and suppose that H is the same as G except that y ( j -1 ) is replaced as a function of the Taylor coefficients for Z ( t ) . To be specific, for k = 0 , … , j -1 , ∂ H ∂ z ( k ) = ∂ G ∂ z ( k ) + ∂ G ∂ y ( j -1 ) ∂ y ( j -1 ) ∂ z ( k ) = ∂ G ∂ z ( k ) + ∂ G ∂ y ( j -1 ) 2 z ( j - k -1 )
Positive Orders Z(t)
For order j > 0 , suppose that H is the same as G except that z ( j ) is expressed as a function of the coefficients for X ( t ) , and the lower order Taylor coefficients for Y ( t ) , Z ( t ) . z ( j ) = x ( j ) ± 1 j ∑ k = 1 j k x ( k ) y ( j - k ) For k = 1 , … , j , the partial of H with respect to x ( k ) is given by ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( j ) [δ ( j - k ) ± k j y ( j - k ) ] where δ ( j - k ) is one if j = k and zero otherwise. For k = 1 , … , j The partial of H with respect to y j - k , is given by ∂ H ∂ y ( j - k ) = ∂ G ∂ y ( j - k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ y ( j - k ) = ∂ G ∂ y ( j - k ) ± ∂ G ∂ z ( j ) k j x k
Order Zero Z(t)
The order zero coefficients for the tangent and hyperbolic tangent are z ( 0 ) = { tan ( x ( 0 ) ) tanh ( x ( 0 ) ) Suppose that H is the same as G except that z ( 0 ) is expressed as a function of the Taylor coefficients for X ( t ) . In this case, ∂ H ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ z ( 0 ) ∂ z ( 0 ) ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ z ( 0 ) ( 1 ± y ( 0 ) )
Input File: omh/theory/tan_reverse.omh cppad-20170000.3/doc/erf_reverse.xml0000644000175200017650000003324613057470510016232 0ustar coincoin-web Error Function Reverse Mode Theory
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Error Function Reverse Mode Theory

Notation
We use the reverse theory standard math function definition for the functions H and G .

Positive Orders Z(t)
For order j > 0 , suppose that H is the same as G . z ( j ) = 1 j ∑ k = 1 j k x ( k ) y ( j - k ) For k = 1 , … , j , the partial of H with respect to x ( k ) is given by ∂ H ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ x ( k ) = ∂ G ∂ x ( k ) + ∂ G ∂ z ( j ) k j y ( j - k ) For k = 1 , … , j The partial of H with respect to y j - k , is given by ∂ H ∂ y ( j - k ) = ∂ G ∂ y ( j - k ) + ∂ G ∂ z ( j ) ∂ z ( j ) ∂ y ( j - k ) = ∂ G ∂ y ( j - k ) + ∂ G ∂ z ( j ) k j x k
Order Zero Z(t)
The z ( 0 ) coefficient is expressed as a function of the Taylor coefficients for X ( t ) and Y ( t ) as follows: In this case, ∂ H ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ z ( 0 ) ∂ z ( 0 ) ∂ x ( 0 ) = ∂ G ∂ x ( 0 ) + ∂ G ∂ z ( 0 ) y ( 0 )
Input File: omh/theory/erf_reverse.omh cppad-20170000.3/doc/reverse_identity.xml0000644000175200017650000011075513057470510017310 0ustar coincoin-web An Important Reverse Mode Identity
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An Important Reverse Mode Identity
The theorem and the proof below is a restatement of the results on page 236 of Evaluating Derivatives .

Notation
Given a function f ( u , v ) where u ∈ B n we use the notation ∂ f ∂ u ( u , v ) = [∂ f ∂ u 1 ( u , v ) , ⋯ , ∂ f ∂ u n ( u , v ) ]
Reverse Sweep
When using reverse mode we are given a function F : B n → B m , a matrix of Taylor coefficients x ∈ B n × p , and a weight vector w ∈ B m . We define the functions X : B × B n × p → B n , W : B × B n × p → B , and W j : B n × p → B by X ( t , x ) = x ( 0 ) + x ( 1 ) t + ⋯ + x ( p -1 ) t p -1 W ( t , x ) = w 0 F 0 [ X ( t , x ) ] + ⋯ + w m -1 F m -1 [ X ( t , x ) ] W j ( x ) = 1 j ! ∂ j ∂ t j W ( 0 , x ) where x ( j ) is the j-th column of x ∈ B n × p . The theorem below implies that ∂ W j ∂ x ( i ) ( x ) = ∂ W j - i ∂ x ( 0 ) ( x ) A general reverse sweep calculates the values ∂ W p -1 ∂ x ( i ) ( x ) ( i = 0 , … , p -1 ) But the return values for a reverse sweep are specified in terms of the more useful values ∂ W j ∂ x ( 0 ) ( x ) ( j = 0 , … , p -1 )
Theorem
Suppose that F : B n → B m is a p times continuously differentiable function. Define the functions Z : B × B n × p → B n , Y : B × B n × p → B m , and y ( j ) : B n × p → B m by Z ( t , x ) = x ( 0 ) + x ( 1 ) t + ⋯ + x ( p -1 ) t p -1 Y ( t , x ) = F [ Z ( t , x ) ] y ( j ) ( x ) = 1 j ! ∂ j ∂ t j Y ( 0 , x ) where x ( j ) denotes the j-th column of x ∈ B n × p . It follows that for all i , j such that i ≤ j < p , ∂ y ( j ) ∂ x ( i ) ( x ) = ∂ y ( j - i ) ∂ x ( 0 ) ( x )
Proof
If follows from the definitions that ∂ y ( j ) ∂ x ( i ) ( x ) = 1 j ! ∂ ∂ x ( i ) [∂ j ∂ t j ( F ∘ Z ) ( t , x ) ] t = 0 = 1 j ! [∂ j ∂ t j ∂ ∂ x ( i ) ( F ∘ Z ) ( t , x ) ] t = 0 = 1 j ! {∂ j ∂ t j [t i ( F ( 1 ) ∘ Z ) ( t , x ) ] } t = 0 For k > i , the k-th partial of t i with respect to t is zero. Thus, the partial with respect to t is given by ∂ j ∂ t j [t i ( F ( 1 ) ∘ Z ) ( t , x ) ] = ∑ k = 0 i ( j k ) i ! ( i - k ) ! t i - k ∂ j - k ∂ t j - k ( F ( 1 ) ∘ Z ) ( t , x ) {∂ j ∂ t j [t i ( F ( 1 ) ∘ Z ) ( t , x ) ] } t = 0 = ( j i ) i ! ∂ j - i ∂ t j - i ( F ( 1 ) ∘ Z ) ( t , x ) = j ! ( j - i ) ! ∂ j - i ∂ t j - i ( F ( 1 ) ∘ Z ) ( t , x ) ∂ y ( j ) ∂ x ( i ) ( x ) = 1 ( j - i ) ! ∂ j - i ∂ t j - i ( F ( 1 ) ∘ Z ) ( t , x ) Applying this formula to the case where j is replaced by j - i and i is replaced by zero, we obtain ∂ y ( j - i ) ∂ x ( 0 ) ( x ) = 1 ( j - i ) ! ∂ j - i ∂ t j - i ( F ( 1 ) ∘ Z ) ( t , x ) = ∂ y ( j ) ∂ x ( i ) ( x ) which completes the proof
Input File: omh/theory/reverse_identity.omh cppad-20170000.3/doc/glossary.xml0000644000175200017650000011404313057470510015561 0ustar coincoin-web Glossary
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Glossary

AD Function
Given an ADFun object f there is a corresponding AD of Base operation sequence . This operation sequence defines a function F : B n → B m where B is the space corresponding to objects of type Base , n is the size of the domain space, and m is the size of the range space. We refer to F as the AD function corresponding to the operation sequence stored in the object f . (See the FunCheck discussion for possible differences between F ( x ) and the algorithm that defined the operation sequence.)

AD of Base
An object is called an AD of Base object its type is either AD<Base> (see the default and copy constructors or VecAD<Base>::reference (see VecAD ) for some Base type.

AD Type Above Base
If Base is a type, an AD type above Base is the following sequence of types:
     AD<Base> , AD< AD<Base> > , AD< AD< AD<Base> > > , ...
Base Function
A function f : B → B is referred to as a Base function, if Base is a C++ type that represent elements of the domain and range space of f ; i.e. elements of B .

Base Type
If x is an AD<Base> object, Base is referred to as the base type for x .

Elementary Vector
The j-th elementary vector e j ∈ B m is defined by e i j = { 1 if i = j 0 otherwise
Operation

Atomic
An atomic Type operation is an operation that has a Type result and is not made up of other more basic operations.

Sequence
A sequence of atomic Type operations is called a Type operation sequence. A sequence of atomic AD of Base operations is referred to as an AD of Base operation sequence. The abbreviated notation AD operation sequence is often used when it is not necessary to specify the base type.

Dependent
Suppose that x and y are Type objects and the result of
     x < y
 has type bool (where Type is not the same as bool). If one executes the following code
     if( x < y )
          y = cos(x);
     else y = sin(x);
 the choice above depends on the value of x and y and the two choices result in a different Type operation sequence. In this case, we say that the Type operation sequence depends on x and y .

Independent
Suppose that i and n are size_t objects, and x[i] , y are Type objects, where Type is different from size_t. The Type sequence of operations corresponding to
     y = Type(0);
     for(i = 0; i < n; i++)
          y += x[i];
 does not depend on the value of x or y . In this case, we say that the Type operation sequence is independent of y and the elements of x .

Parameter
All Base objects are parameters. An AD<Base> object u is currently a parameter if its value does not depend on the value of an Independent variable vector for an active tape . If u is a parameter, the function Parameter(u) returns true and Variable(u) returns false.

Sparsity Pattern
CppAD describes a sparse matrix as a vector of sets with each vector component corresponding to a row and the elements of the set corresponding to the possibly non-zero columns. A vector of bool can represent a vector of sets using one bit per element. (Some vectors of bool use one byte per element but vectorBool is an example class that uses one bit per element.) The problem is that this representation uses one bit for both the elements that are there and the ones that are not.

A vector of std::set<size_t> does not represent the elements that are not present, but it uses about three size_t values for each element that is present. For example, if size_t uses 32 bits, a vector of std::set<size_t> uses about 100 bits for each element that is present in the vector of sets. Thus, a vector of std::set<size_t> should be more efficient for very sparse matrix representations.

Vector of Boolean
Given a matrix A ∈ B m × n , a vector of bool B of length m × n is a sparsity pattern for A if for i = 0 , … , m -1 and j = 0 , … n -1 , A i , j ≠ 0 ⇒ B i * n + j = true Given two sparsity patterns B and C for a matrix A , we say that B is more efficient than C if B has fewer true elements than C . For example, if A is the identity matrix, B i * n + j = ( i = j ) defines an efficient sparsity pattern for A .

Vector of Sets
Given a matrix A ∈ B m × n , a vector of sets S of length m is a sparsity pattern for A if for i = 0 , … , m -1 A i , j ≠ 0 ⇒ j ∈ S i Given two sparsity patterns S and T for a matrix A , we say that S is more efficient than T if S has fewer elements than T . For example, if A is the identity matrix, S i = { i } defines an efficient sparsity pattern for A .

Tape

Active
A new tape is created and becomes active after each call of the form (see Independent )
     Independent(x)
 All operations that depend on the elements of x are recorded on this active tape.

Inactive
The operation sequence stored in a tape must be transferred to a function object using the syntax (see ADFun<Base> f(x, y) )
     ADFun<Base> f( x, y)
 or using the syntax (see f.Dependent(x, y) )
     f.Dependent( x, y)
 After such a transfer, the tape becomes inactive.

Independent Variable
While the tape is active, we refer to the elements of x as the independent variables for the tape. When the tape becomes inactive, the corresponding objects become parameters .

Dependent Variables
While the tape is active, we use the term dependent variables for the tape for any objects whose value depends on the independent variables for the tape. When the tape becomes inactive, the corresponding objects become parameters .

Taylor Coefficient
Suppose X : B → B n is a is p times continuously differentiable function in some neighborhood of zero. For k = 0 , … , p , we use the column vector x ( k ) ∈ B n for the k-th order Taylor coefficient corresponding to X which is defined by x ( k ) = 1 k ! ∂ k ∂ t k X ( 0 ) It follows that X ( t ) = x ( 0 ) + x ( 1 ) t + ⋯ + x ( p ) t p + R ( t ) where the remainder R ( t ) divided by t p converges to zero and t goes to zero.

Variable
An AD<Base> object u is a variable if its value depends on an independent variable vector for a currently active tape . If u is a variable, Variable(u) returns true and Parameter(u) returns false. For example, directly after the code sequence
     Independent(x);
     AD<double> u = x[0];
 the AD<double> object u is currently a variable. Directly after the code sequence
     Independent(x);
     AD<double> u = x[0];
     u = 5;
 u is currently a parameter (not a variable).

Note that we often drop the word currently and just refer to an AD<Base> object as a variable or parameter.
Input File: omh/glossary.omh cppad-20170000.3/doc/bib.xml0000644000175200017650000000707313057470510014456 0ustar coincoin-web Bibliography
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Bibliography

Abramowitz and Stegun
Handbook of Mathematical Functions, Dover, New York.

The C++ Programming Language
Bjarne Stroustrup, The C++ Programming Language, Special ed., AT&T, 2000

Evaluating Derivatives
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Andreas Griewank, SIAM, Philadelphia, 2000

Numerical Recipes
Numerical Recipes in Fortran: The Art of Scientific Computing, Second Edition, William H. Press, William T. Vetterling, Saul, A. Teukolsky, Brian R. Flannery, Cambridge University Press, 1992

Shampine, L.F.
Implementation of Rosenbrock Methods, ACM Transactions on Mathematical Software, Vol. 8, No. 2, June 1982.
Input File: omh/bib.omh cppad-20170000.3/doc/wish_list.xml0000644000175200017650000003310213057470510015717 0ustar coincoin-web The CppAD Wish List
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The CppAD Wish List

Optimization

Taping
Perhaps some of the optimization done while taping forward mode should be delayed to the optimization step.

Special Operators
Add special operators that can be implemented more efficiently, e.g.,
     square(x) = x * x
 and have the optimizer recognize when they should be used. (They could also be in the user API, but it would not be expected that the user would use them.)

checkpoint

Retape
Perhaps there should be a version of the checkpoint class that uses a tapeless AD package to compute the derivative values. This would allow for algorithms where the operations sequence depends on the independent variable values. There is a question as to how sparsity patterns would be determined in this case. Perhaps they would be passed into the constructor. If it was known to be constant, the user could compute the pattern using CppAD. Otherwise, the user could input a conservative estimate of the pattern that would be correct.

Testing
There should be some examples and tests for both speed and memory use that demonstrate that checkpointing is useful.

Sparsity Patterns
It may be that each set has a large overhead in a large and very sparse vector of sets representation of a sparsity pattern. The user API for this representation uses
     vector< std::set<size_t> >
 Perhaps CppAD's API should have a sparse matrix class with the following fields
     vector<size_t> row;
     vector<size_t> col;
     vector<Type> val;
 where the vectors are arbitrary simple vectors . If the val vector has size zero, this would just be a sparsity pattern (and row and col vectors would have the same size). Otherwise, it would be a sparse matrix with elements of type Type and val would have the same size as row and col .

check_finite
Sometimes one only gets infinite value during zero order forward and nan when computing corresponding derivatives. Change check_for_nan to check_finite (not infinite or nan) so that error detection happens during zero order forward instead of later.

Compilation Speed
Create a library corresponding to AD<double> so that one does not need to re-compile all the header files every time.

Base Requirements
Change the Base requirements to use template specialization instead of functions so that there is a default value for each function. The default would result in a known assert when the operation is used and not defined by the base class. An example of this type of template specialization can be found in the implementation of to_string .

Adolc
Create a documentation page that shows how to convert Adolc commands to CppAD commands.

Forward Mode Recomputation
If the results of forward_order have already been computed and are still stored in the ADFun object (see size_order ), then they do not need to be recomputed and the results can just be returned.

Iterator Interface
All of the CppAD simple vector interfaces should also have an iterator version for the following reasons:
  1. It would not be necessary to copy information to simple vectors when it was originally stored in a different type of container.
  2. It would not be necessary to reallocate memory for a result that is repeatedly calculated (because an iterator for the result container would be passed in).


Operation Sequence
It is possible to detect if the AD of Base operation sequence does not depend on any of the independent variable values. This could be returned as an extra seq_property .

Software Guidelines
The following is a list of some software guidelines taken from boost . These guidelines are not followed by the current CppAD source code, but perhaps they should be:
  1. Names (except as noted below) should be all lowercase, with words separated by underscores. For example, acronyms should be treated as ordinary names (xml_parser instead of XML_parser).
  2. Template parameter names should begin with an uppercase letter.
  3. Use spaces rather than tabs. Currently, CppAD uses a tabs stops at column multiples of 5. Five columns were chosen to avoid high levels of indenting and to allow for 
     
     if( expression )
          statement
     else statement
    with a tab after the else. Automatic conversion to actual spaces should be easy.


Tracing
Add tracing the operation sequence to the user API and documentation. Tracing the operation sequence is currently done by changing the CppAD source code. Use the command 
 
     grep '^# *define *CPPAD_.*_TRACE' cppad/local/*.hpp
to find all the possible tracing flags.

atan2
The atan2 function could be made faster by adding a special operator for it.

BenderQuad
See the problem with the current BenderQuad specifications.
Input File: omh/wish_list.omh cppad-20170000.3/doc/whats_new.xml0000644000175200017650000001131313057470510015711 0ustar coincoin-web Changes and Additions to CppAD
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Changes and Additions to CppAD

Introduction
The sections listed below contain a list of the changes to CppAD in reverse order by date. The purpose of these sections is to assist you in learning about changes between various versions of CppAD.

This Year
whats_new_16


whats_new_15 whats_new_14 whats_new_13 whats_new_12 whats_new_11 , whats_new_10 , whats_new_09 , whats_new_08 , whats_new_07 , whats_new_06 , whats_new_05 , whats_new_04 , whats_new_03 .
Input File: omh/whats_new/whats_new.omh cppad-20170000.3/doc/whats_new_16.xml0000644000175200017650000010072313057470510016223 0ustar coincoin-web Changes and Additions to CppAD During 2016
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Changes and Additions to CppAD During 2016

Introduction
The sections listed below contain a list of the changes to CppAD in reverse order by date. The purpose of these sections is to assist you in learning about changes between various versions of CppAD.

12-23
Added a way for the user to determine what tests options are available; see make check .

12-20
Change the optimize examples to use NearEqual for floating point tests (instead of exactly equal). There were some other exactly equal floating point tests that were failing on a mingw system. Theses have also been fixed.

12-18
Add the no_print_for_op to the optimize routine.

12-13
  1. Fix a bug in ForSparseHes . To be more specific, there was a bug in handling the cumulative summations operator in this routine. This could only come up when used an optimized f ,
  2. Add the nest_conditional.cpp example.


12-11
Improve the optimize documentation. This includes making examples that demonstrate specific aspects of the optimization; see forward_active.cpp , reverse_active.cpp , compare_op.cpp , conditional_skip.cpp , cumulative_sum.cpp .

12-09
The options argument was added to the optimize routine.

11-18
Move classes and functions that are part of the user API from the cppad/local directory to the cppad/core directory. The remaining symbols, in the cppad/local directory, are now in the CppAD::local namespace. Note that a class in the CppAD name space, may have a member function that is not part of the user API.

11-14
Increase the speed of the sparse_pack class. This improves the speed for vector of boolean sparsity pattern calculations.

11-13
Merged in the sparse branch which has const_iterator, instead of next_element for the sparse_list and sparse_pack classes. These classes are not part of the CppAD API and hence their specifications can change (as in this case). They can be used to get more efficient representations of sparsity patterns .

10-27
The optional optimize option was added to the checkpoint functions.

10-12
  1. Change elapsed_seconds to use std::chrono::steady_clock instead of std::chrono::high_resolution_clock.
  2. The test for C++11 features was failing on a Mac system because the elapsed time was returning as zero (between two events). This test has been made more robust by add a one millisecond sleep between the two clock accesses.


09-29
The multiple directions version of forward was missing erf function in the case where C++ 2011 was supported; see issue 16 . This has been fixed.

09-27
Change the implementation of atomic_eigen_cholesky.hpp so that the computation of M k exactly agrees with the corresponding theory .

09-26
  1. A possible bug in the optimize command was fixed. To be specific, a warning of the form indentations;
         warning: this 'if' clause does not guard... [-Wmisleading-indentation]
     using the gcc-6.2.1 compiler, was fixed and it may have fixed a bug.
  2. There was a problem with the sacado where the symbol HAS_C99_TR1_CMATH was being defined twice. This has been fixed by leaving it up to the sacado install to determine if this symbol should be defined.


09-16
Fix a problem using the colpack option to the speed_cppad program. (There was a problem whereby the speed_cppad program did not properly detect when colpack was available.)

09-13
Test third order and fix bug in atomic_eigen_cholesky.hpp for orders greater than or equal to three.

08-30
Add the atomic_eigen_cholesky.cpp example.

08-25
  1. Fix some missing include files in optimize.hpp and set_union.hpp (when compiling with MS Visual Studio 2015).
  2. Fix a warning in atanh.hpp (when compiling with MS Visual Studio 14).
  3. Fix a typo in the Reverse section of the eigen_mat_inv.hpp example.


07-17
Add documentation for only needing to compute a column subset of the sparsity pattern when computing a subset of a sparse Hessians. In addition, improve the corresponding example sparse_sub_hes.cpp .

07-14
Correct title in ForSparseHes (change Reverse to Forward).

06-30
Change the atomic_mat_mul.cpp example so that on atomic object works for matrices of any size.

06-29
Change the atomic_base examples so they do no longer use the deprecated atomic function interfaces to for_sparse_jac, rev_sparse_jac, for_sparse_hes, and rev_sparse_hes.

06-27
  1. Improve the atomic_eigen_mat_mul.hpp and atomic_eigen_mat_inv.hpp examples. Most importantly, one atomic object now works for matrices of any size.
  2. Add the vector x , that contains the parameters in an atomic function call to the user following atomic functions: for_sparse_jac , rev_sparse_jac , for_sparse_hes , rev_sparse_hes . This enables one to pass parameter information to these functions; e.g., the dimensions of matrices that the function operates on.


06-25
Add more entries to the optimization wish_list .

06-10
Add a check_finite wish list item.

05-05
  1. Add documentation for redirecting output for the PrintFor function.
  2. Change distributed version to build examples as debug instead of release version. (Was changed to release version while checking for compiler warnings; see 04-17 below).


04-17
Fix all some compiler warnings that occurred when compiling the examples with NDEBUG defined.

03-27
  1. Fix a bug in the calculation of the atomic_eigen_mat_inv.hpp reverse example.
  2. Use a very simple method (that over estimates variables) for calculating vy in the atomic_eigen_mat_inv.hpp forward example.


03-26
  1. Implement and test the atomic_eigen_mat_inv.cpp reverse is implemented.
  2. Fix a bug in the calculation of vy in the atomic_eigen_mat_inv.hpp forward example.


03-25
  1. Start construction of the atomic_eigen_mat_inv.cpp example, currently only forward is implemented and tested.
  2. More improvements to atomic_eigen_mat_mul.cpp example.


03-24
  1. Fix build of example/atomic.cpp when eigen_prefix is not available (bug introduced when atomic_eigen_mat_mul.cpp was added).
  2. Extend atomic_eigen_mat_mul.cpp example to include for_sparse_jac , rev_sparse_jac , for_sparse_hes , rev_sparse_hes .
  3. Fix a bug in the ForSparseHes routine.
  4. Edit atomic_rev_sparse_hes documentation.


03-23
  1. Fix bug in auto-tools file example/atomic/makefile.am (introduced on 03-22).
  2. Improve the atomic_eigen_mat_mul.cpp example and extend it to include reverse mode.


03-22
  1. Start construction of the atomic_eigen_mat_mul.cpp example.
  2. change atomic_ode.cpp to checkpoint_ode.cpp and atomic_extended_ode.cpp to checkpoint_extended_ode.cpp .


03-21
Change the atomic_mat_mul.hpp class name from mat_mul to atomic_mat_mul. This example use of the name mat_mul in the atomic_mat_mul.cpp example / test.

03-20
  1. Include the sub-directory name to the include guards in *.hpp files. For example, 
     
     # ifndef CPPAD_UTILITY_VECTOR_HPP
     # define CPPAD_UTILITY_VECTOR_HPP
    appears in the file cppad/utility/vector.hpp. This makes it easier to avoid conflicts when choosing addon names.
  2. Add the set_union utility and use it to simplify the atomic examples that use vector of sets sparsity patterns.


03-19
  1. Move atomic_mat_mul.cpp to atomic_mat_mul_xam.cpp (moved back on 03-21 .
  2. Move atomic_matrix_mul.hpp to atomic_mat_mul.hpp .


03-17
Add the atomic_ode.cpp and atomic_extended_ode.cpp examples.

03-12
  1. Move the example reverse_any.cpp to reverse_checkpoint.cpp .
  2. Add the atomic_mul_level.cpp example.


03-05
The following atomic function examples were added These examples are for a specific atomic operation. In addition, the domain and range dimensions for these examples are not one and not equal to each other: atomic_forward.cpp , atomic_reverse.cpp , atomic_for_sparse_jac.cpp , atomic_rev_sparse_jac.cpp , atomic_for_sparse_hes.cpp , atomic_rev_sparse_hes.cpp .

03-01
  1. Improve documentation of implementation requirements for the atomic rev_sparse_jac .
  2. Make some corrections to the atomic_for_sparse_hes documentation. and fix a bug in how CppAD used these functions.


02-29
  1. Merged sparse into master branch. This makes the ForSparseHes routine available for use.
  2. Changed the global options in the speed test main program to use one global variable with prototype 
    
     extern std::map<std::string, bool> global_option;

02-28
Fix a mistake in the old atomic example/sparsity/sparsity.cpp example. This example has since been changed to atomic_set_sparsity.cpp .

02-27
The --with-sparse_set and --with-sparse_set options were removed from the auto_tools install procedure.

02-26
The condition that the operation sequence in f is independent of the independent variables was added to the statement about the validity of the sparsity patterns; see x in ForSparseJac , RevSparseJac , and RevSparseHes .

02-25
The cmake command line argument cppad_sparse_list has been removed (because it is so much better than the other option).

02-23
A new version of the cppad_sparse_list class (not part of user API) uses reference counters to reduce the number of copies of sets that are equal. This improved the speed of sparsity pattern computations that use the vector of sets representation. For example, the results for the cppad_sparse_hessian.cpp test compare as follows: 
 
     sparse_hessian_size     = [  100,    400,   900,  1600, 2500 ]
     sparse_hessian_rate_old = [ 1480, 265.21, 93.33, 41.93, 0.86 ]
     sparse_hessian_rate_new = [ 1328, 241.61, 92.99, 40.51, 3.80 ]
Note that the improvement is only for large problems. In fact, for large problems, preliminary testing indicates that the new vector of sets representation preforms better than the vector of boolean representation.

01-21
Fix a valgrind warning about use of uninitialized memory in the test test_more/checkpoint.cpp (the problem was in the test).

01-20
  1. Fix a valgrind warning about use of uninitialized memory when using the adouble base type. This required an optional base_hash function and the special adouble hash_code implementation.
  2. The adouble to_string functions required a special implementation; see adouble to_string .
  3. Add the to_string and hash_code examples to the base_alloc.hpp example.


01-18
  1. Fix ambiguity between CppAD::sin and std::sin, and other standard math functions, when using 
     
     using namespace std;
     using namespace CppAD;
    This is OK for simple programs, but not generally recommended. See double version of base class definitions for Unary Standard Math for more details.
  2. Change Eigen array example eigen_array.cpp to use member function version of sin function (as per Eigen's array class documentation).
Input File: omh/whats_new/whats_new_16.omh cppad-20170000.3/doc/whats_new_15.xml0000644000175200017650000017422113057470510016226 0ustar coincoin-web CppAD Changes and Additions During 2015
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CppAD Changes and Additions During 2015

Introduction
This section contains a list of the changes to CppAD during 2015 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-31
The download instructions were modified to have more mention of using git and less mention of subversion .

12-29
Separate to_string from ad_to_string so that it can be used without the rest of CppAD; i.e., by including
     # include <cppad/utility/to_string.hpp>
12-28
  1. Add the to_string utility.
  2. Add base_to_string to the Base type requirements.
  3. A Base requirements item was added to the wish list.
  4. The wish_list item to reorganize the include directory has been removed. It was completed when the utilities was moved to cppad/utility; see 11-30 .


12-08
  1. A convention was included for addon library files .
  2. Change new utility specifications to allow for individual file includes; e.g., <cppad/utility/vector.hpp>.


12-01
Fix problem with auto_tools install handling of the deprecated files. This included changing the auto-tools --with-implicit_ctor option to --with-deprecated .

11-30
  1. The library section has been moved to the utilities section. In addition, the corresponding source code files in cppad have been moved to cppad/utility.
  2. The individual utility include files have been deprecated; see include_deprecated . For example, 
     
     # include <cppad/runge_45.hpp>
    You should us the utility include instead; i.e., 
     
     # include <cppad/utility.hpp>
  3. The numeric_ad routines where moved from the library the a separate documentation section.
  4. Change cmake_install_prefix to cppad_prefix and Change cmake_install_postfix to cppad_postfix .
  5. Change cppad_implicit_ctor_from_any_type to cppad_deprecated and change its specifications to refer to all deprecated features.


11-25
  1. CppAD now installs the object library 
     
     -lcppad_lib
    to be included when linking. Currently, it is only required when colpack_prefix is specified on the cmake command .
  2. It is no longer necessary to compile and link the file 
     
     cppad_colpack.cpp
    when colpack_prefix is specified during the install process; see cmake command . (It is included in cppad_lib).


11-24
  1. The check_for_nan output now includes the first dependent variable index that is nan in its error message.
  2. Change the deprecated include reference pow_int.h to pow_int.hpp in pow_int .


11-14
There was a bug in the new get_check_for_nan feature that writes independent variable values to a temporary file; see 11-06 below. This has been fixed.

11-08
  1. Fixed a bug in the RevSparseJac routine. To be specific, the argument r was transposed from what the documentation said. (This has no effect in the usual case where r is the identity.)
  2. Added the bool_sparsity.cpp examples which show how to conserve memory when computing sparsity patterns.
  3. Modified the ipopt_solve procedure to take advantage of the memory conserving sparsity pattern calculations when retape is false.
  4. Added the bit_per_unit function to the vectorBool class. (This aids the memory conservation mentioned above.)


11-06
It is often difficult to determine what cause a nan result during an operation with an ADFun object. The new feature get_check_for_nan was added to make this easier.

10-21
There was a mistake in the documentation for index_sort , the argument ind is not const.

10-16
Add a PrintFor optimization wish list item. This has been done, see no_print_for_op .

10-06
  1. Add CPPAD_USE_CPLUSPLUS_2011 , CPPAD_NUMERIC_LIMITS, and CPPAD_STANDARD_MATH_UNARY, to the preprocessor section. In addition, remove checking that all user API preprocessor symbols are in this section form the wish_list .
  2. Alphabetize and make some corrections to list of examples .
  3. The documentation for some of the deprecated features was missing the date when they were deprecated. This has been fixed; e.g., see Deprecated 2012-12-26 .


10-04
  1. base_require : Add the macro CPPAD_NUMERIC_LIMITS to aid in setting the numeric limits for a user defined Base class.
  2. base_require : The quiet_NaN function has been added to the CppAD numeric_limits. Note the reason for not using std::numeric_limits .
  3. The nan(zero) function computes a nan by dividing zero by zero which results in a warning when using some compilers. This function has been deprecated and the corresponding wish_list item has been removed.
  4. Move documentation for zdouble to deprecated section and documentation for numeric_limits to ADValued .
  5. Remove all uses of, and references to, zdouble from the examples .


10-03
base_require : It is no longer necessary to define the specialization for CppAD::epsilon<Base>() for each Base type.

10-02
There was a bug in test_more/azmul.cpp whereby the vector z had the wrong dimension (in two places). This has been fixed.

09-28
  1. Use the current atomic_option setting to determine which type of sparsity patterns to use for dependency calculations during optimize procedure. It used to be that the bool_sparsity_enum was used when pack_sparsity_enum was specified.
  2. It is not longer an error to take the derivative of the square root function, because the result may be the part of a conditional expression that is not used.
  3. Update the wish_list section.


09-27
  1. It is no longer necessary to use the zdouble class when computing with multiple levels of AD conditional expressions and reverse mode .
  2. The zdouble class has been deprecated. Use the azmul function for absolute zero (when it is needed).


09-25
base_require : absolute zero multiplication is now required for user defined base types. This makes it possible to combine conditional expression , multiple levels , reverse , and a base type that has standard ieee multiplication; e.g., double. In other words, not all multiplications will need to have an absolute zero (as is the case with the zdouble base class.

09-24
Fix some Visual Studio 2013 C++ level four /W4 warnings (previous warnings were are level 3). In addition, disable warning 4100 unreferenced formal parameter, and warning 4127 conditional expression is constant.

09-23
CppAD can optionally test its use with the external packages eigen , ipopt , and colpack . In addition, it can compare its speed with the external AD packages adolc , fadbad , and sacado . The scripts that download and install a local copy of these external packages have been modified to automatically skip installation when it has already been done.

09-21
Improve discussion of windows download and testing .

09-20
  1. Add the cppad_profile_flag to the list of possible cmake command arguments.
  2. More of the warnings generated by Visual Studio 2013 have been fixed. One remaining warning is about asctime and gmtime not being thread safe.


09-19
  1. There was a bug in the numeric_limits section of the example user defined base type. This has been fixed.
  2. There were some compile and link errors when running the tests using Visual Studio 2013. These have been fixed.
  3. Many of the warnings generated by Visual Studio 2013 have been fixed.


09-16
The conditional expressions, CondExp , were not working for the type < CppAD::AD<adouble> > where adouble is the ADOL-C AD type. This has been fixed by adding a call to CPPAD_COND_EXP_REL in base_adolc.hpp.

09-03
  1. There was a bug in the vectorBool assignment . To be specific, it not allow a size zero vector to be assigned using a vector any other size. This has been fixed.
  2. The addition of the pack option on 08-31 introduced a bug in the calculation of RevSparseHes . The checkpoint.cpp example was changed to demonstrate this problem and the bug was fixed.


09-02
The dependency pattern was not being computed correctly for the sign , Discrete , and VecAD operations. This has been fixed. This could have caused problems using checkpoint functions that used any of these operations.

08-31
  1. Mention the fact that using checkpoint functions can make recordings faster .
  2. Add the pack sparsity option for atomic_base operations.
  3. Add the pack sparsity option to checkpoint functions.
  4. Added the example/atomic/sparsity.cpp example.
  5. Remove mention of OpenMP from thread_alloc::thread_num (thread_alloc never was OpenMP specific).


08-30
  1. The sparsity argument was added to the atomic_base constructor and the checkpoint constructor.
  2. Make atomic_norm_sq.cpp an example with no set sparsity and atomic_reciprocal.cpp an example with no bool sparsity.
  3. Improve discussion of Independent and parallel mode .


08-29
Some asserts in the checkpoint implementation were not using the CppAD ErrorHandler . This has been fixed.

08-28
Free checkpoint function sparsity patters during forward operations that use its atomic operation. (They kept between sparsity calculations because they do not change.)

08-26
Fix a bug in RevSparseJac when used to compute sparsity pattern for a subset of the rows in a checkpoint function.

08-25
Reduce the amount of memory required for checkpoint functions (since sparsity patterns are now being held so they do not need to be recalculated).

08-20
Added an example that computes the sparsity pattern for a subset of the Jacobian and a subset of the Hessian .

08-17
  1. Do some optimization of the checkpoint feature so that sparsity patterns are stored and not recalculated.
  2. Fix a warning (introduced on 08-11) where the CppAD::vector data function was being shadowed by a local variable.
  3. The source code control for CppAD has a link to compile, instead of real file. This sometimes caused problems with the deprecated auto_tools install procedure and has been fixed.


08-16
  1. Improve the documentation for checkpoint functions. To be specific, change the syntax to use the name atom_fun . In addition, include the fact that atom_fun must not be destructed for as along as the corresponding atomic operations are used.
  2. Add the size_var function to the checkpoint objects.


08-09
Add the preservation of data to the specifications of a CppAD::vector during a resize when the capacity of the vector does not change. In addition, added and example of this to cppad_vector.cpp .

08-06
The zdouble numeric_limits were not being computed properly. This has been fixed.

07-31
Added the sparse_sub_hes.cpp example, a way to compute the sparsity for a subset of variables without using multiple levels of AD .

06-16
  1. There were some unknown asserts when the sparsity pattern p in sparse_jacobian and sparse_hessian was not properly dimensioned. These have been changed to known asserts to give better error reporting.
  2. In the special case where sparse Hessian work or sparse Jacobian work was specified and the set of elements to be computed was empty, the work vector is empty after the call (and it appears to need to be calculated on subsequent calls). This resulted in a bug when the sparsity pattern was not provided on subsequent calls (and has been fixed).


06-11
  1. Some C++11 features were not being taken advantage of after the change on 05-10 . To be specific, move semantics, the high resolution clock, and null pointers. This has been fixed.
  2. In the example zdouble.cpp , the vector a1z was not properly dimensioned. This has been fixed and the dimensions of all the variables have been clarified.


06-09
Add an abort_op_index item to the wish list. It has since been removed (domain errors may not affect the results due to conditional expressions ).

06-07
Add a absolute zero item and a numeric_limits item to the wish list. The absolute zero item has been completed and the numeric limit item was modified on implementation. Remove the multiple directions with list item.

05-26

cond_exp_1
There was a problem using conditional expressions with multiple levels of AD where the result of the conditional expression might not be determined during forward mode. This would generate an assert of the form:
     Error detected by false result for
          IdenticalPar(side)
    at line number in the file
          .../cppad/local/cskip_op.hpp
 where side was left or right and number was the line number of an assert in cskip_op.hpp. This has been fixed.

cond_exp_2
There was a problem with using conditional expressions and reverse mode with multiple levels of AD . This was problem was represented by the file bug/cond_exp_2.sh.
  1. The problem above has been fixed by adding the base type zdouble, see CppAD motivation for this new type. (It is no longer necessary to use zdouble to get an absolute zero because CppAD now uses azmul where an absolute zero is required.)
  2. The sections mul_level , change_param.cpp , mul_level.cpp , and mul_level_ode.cpp were changed to use zdouble .
  3. The adolc multi-level examples mul_level_adolc.cpp and mul_level_adolc_ode.cpp were changed to mention the limitations because Adolc does not have an absolute zero .
  4. The example above were also changed so that AD variable names that indicated the level of AD for the variable.
  5. base_require : The base type requirements were modified to include mention of absolute zero . In addition, the base type requirements API warning is now more informative.


05-11
Reorganize the unary_standard_math documentation.

05-10
  1. Add the exponential minus one function log1p .
  2. base_require : If you are defining your own base type, note that log1p was added to the base type requirements.
  3. Use the single preprocessor flag CPPAD_USE_CPLUSPLUS_2011 to signal that the functions erf, asinh, acosh, atanh, expm1, log1p are part of the base type requirements.


05-09
  1. Add the exponential minus one function expm1 . If you are defining your own base type, note that expm1 was added to the base type requirements.
  2. Fix some warnings about comparing signed and unsigned integers when using eigen for the CppAD test vector. (The eigen vector size() function returns an int instead of a size_t.)


05-08
  1. Add the inverse hyperbolic sine function atanh . If you are defining your own base type, note that atanh was added to the base type requirements.
  2. Fix a bug in the implementation of the acosh multiple direction forward mode forward_dir (when compiler has acosh ).


05-07
Add the inverse hyperbolic sine function acosh . If you are defining your own base type, note that acosh was added to the base type requirements.

05-05
Add the inverse hyperbolic sine function asinh . If you are defining your own base type, note that asinh was added to the base type requirements.

04-18
In the sparse jacobian and sparse hessian calculations, If work is present, and has already been computed, the sparsity pattern p is not used. This has been added to the documentation; see sparse jacobian and sparse hessian documentation for work and p .

03-13
Remove the syntax
     AD<Base> y = x
 for the AD constructor documentation because it does not work when the constructor is explicit . Also document the restriction that the constructor in the assignment must be implicit.

03-06
The developers of the TMB package reported that for large ADFun tapes, the optimize routine uses a large amount of memory because it allocates a standard set for each variable on the tape. These sets are only necessary for variables in conditional expressions that can be skipped once the independent variables have a set value. The problem has been reduced by using a NULL pointer for the empty set and similar changes. It still needs more work.

02-28
It used to be the case that the Reverse mode would propagate nan through the conditional expression case that is not used. For example, if 
 
     Independent(ax);
     AD<double> aeps = 1e-10;
     ay[0] = CondExpGt( ax[0], aeps, 1.0/ax[0], 1.0/aeps );
     ADFun<double> f(ax, ay);
The corresponding reverse mode calculation, at x[0] = 0.0, would result in 
 
     Error detected by false result for
     ! ( hasnan(value) && check_for_nan_ )
This has been fixed so that only the conditional expression case that is used affects the reverse mode results. The example cond_exp.cpp was changed to reflect this (a check for nan was changed to a check for zero). Note that this fix only works when IdenticalPar is true for the base type of the result in the conditional expression; e.g., one can still get a nan effect from the case that is not selected when using AD< AD<double> > conditional expressions.

02-18
If the compiler supports the c++11 feature std::chrono:high_resolution_clock then use it for the elapsed_seconds function.

02-16
The new example sub_sparse_hes.cpp shows one way to compute a Hessian for a subset of variables without having to compute the sparsity pattern for the entire functions.

02-14
Fix another bug in the derivative calculations for the c++11 version of the error function; see CPPAD_USE_CPLUSPLUS_2011 .

02-11
Fix a bug in the optimization of conditional expressions. To be specific, if NDEBUG is not defined, one could get an assert with the message: 
 
     Error detected by false result for
          var_index_ >= NumRes(op_)

02-10
The change on 2014-12-23 introduced a bug when the c++11 version of the error function was used with an optimized function. see CPPAD_USE_CPLUSPLUS_2011 . There was also a bug in the sparsity calculations for when this erf function was included. These bugs have been fixed.

02-09
The test test_more/optimize.cpp was failing on some systems because an exactly equality check should have been a near equal check. This has been fixed.

02-07
On some systems, the library corresponding to speed/src could not be found. This library is only used for testing and so has been changed to always be static (hence does not need to be found at run time).

02-06
There was a bug in the coloring method change on 2015-01-07 . To be specific, work.color_method was not being set to "cppad.symmetric" after work.color_method.clear() . This has been fixed.

02-04
  1. Enable the same install of CppAD to be used both with and without C++11 features; e.g., with both g++ --std=c++11 and with g++ --std=c++98. Previously if the cppad_cxx_flags specified C++11, then it could only be used in that way.
  2. The cmake command now requires the version of cmake to be greater than or equal 2.8 (due a bug in cmake version 2.6).


02-03
Improved the searching for the boost multi-threading library which is used for by the team_bthread.cpp case of the thread_test.cpp example and test.

02-02
Improve the documentation for the cmake command line options
     cmake_install_dir
 for dir equal to prefix, postfix, includedirs, libdirs, datadir, and docdir.

01-30
Fix bug in link_sparse_hessian speed test introduced on 01-09 below.

01-29
Fix some warnings generated by g++ 4.9.2.

01-26
The change of global variables to local in cppad/local/op_code.hpp on 2014-50-14 created a bug in parallel_ad (some local statics needed to be initialized). This has been fixed.

01-23
There was a bug in the cmake install detection of compiler features. One symptom of this bug was that on systems that had the gettimeofday function, the cmake install would sometimes report
     cppad_has_gettimeofday = 0
 This has been fixed.

01-21
The deprecated auto_tools procedure had a bug in the detection of when the size of an unsigned int was the same as the size of a size_t. This has been fixed.

01-20
  1. The new compare_change interface has been created and the old CompareChange function has been deprecated; see the compare_change.cpp example. This enables one to determine the source code during taping that corresponds to changes in the comparisons during zero order forward operations; see abort_op_index .
  2. This new compare_change interface can detect comparison changes even if NDEBUG is defined and even if f.optimize() has been called. The deprecated function CompareChange used to always return zero after
             f.optimize()
     and was not even defined when NDEBUG was defined. There was a resulting speed effect for this; see no_compare_op .
  3. The date when some features where deprecated has been added to the documentation. For example, see Deprecated 2006-12-17 .


01-09
  1. The change 01-07 below included (but did not mention) using a sparse, instead of full, structure for the Hessian in the test. This has also been done for the sparse Jacobian test.
  2. For both the sparse_jacobian and sparse_hessian tests, the sparse function is only chosen once (it used to be different for every repeat). This reduced the amount of computation not connected what is being tested. It also make the onetape a valid option for these tests.
  3. There was a bug in the multiple direction forward routine. Results for function values that are parameter were not being computed properly (all the derivatives are zero in this case). This has been fixed.


01-07
The following changes were merged in from the color_hes branch:
  1. Specify the type of coloring for the sparse hessian calculations. To be specific, instead of "cppad" and "colpack", the choices are "cppad.symmetric", "cppad.general", and "colpack.star". This is not compatible with the change on 01-02 , which was so recent that this should not be a problem.
  2. The n_sweep values were not being returned properly by cppad_sparse_hessian.cpp and adolc_sparse_hessian.cpp . The CppAD version has been fixed and the ADOL-C version has been set to zero.
  3. The link_sparse_hessian example case was to sparse for good testing (by mistake). This has been fixed.
  4. Add n_sweep to link_sparse_hessian and speed_main .
  5. Change the cppad sparse Hessian color_method to take advantage of the symmetry of the Hessian (in a similar fashion to the colpack coloring method).


01-02
Added to option to uses colpack for the sparse Hessian coloring method ; see the example colpack_hes.cpp .
Input File: omh/whats_new/whats_new_15.omh cppad-20170000.3/doc/whats_new_14.xml0000644000175200017650000007757413057470510016242 0ustar coincoin-web CppAD Changes and Additions During 2014
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CppAD Changes and Additions During 2014

Introduction
This section contains a list of the changes to CppAD during 2014 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-30
There was a bug in the cmake whereby it would sometimes mistakenly exit with the error message 
 
     cppad_max_num_threads is not an integer greater than or equal 4
This has been fixed.

12-29
The example not_complex_ad.cpp was using the type
     std::complex< CppAD::AD<double> >
 and was failing to compile with the clang complier. This example has been removed because it is not consistent with the C++ standard; see complex FAQ .

12-28
  1. Fix some warnings generated by clang 3.5 about local functions that were not being used; e.g., sub-tests that were not being executed.
  2. Fix cmake setting cppad_implicit_ctor_from_any_type Note that this cmake option has since been replaced by cppad_deprecated .
  3. The clang++ compiler was optimizing out the calculations in the time_test.cpp and speed_test.cpp examples. This caused these tests to hang while trying to determine how many times to repeat the test. This has been fixed.


12-27
More work on the bug in optimizing conditional expressions.

12-26
A minimal example for computing cross terms in atomic operation Hessian sparsity patterns atomic_rev_sparse_hes.cpp was added.

12-25
More work on the bug in optimizing conditional expressions.

12-23
The c++11 standard includes the error function erf in cmath. If the c++ compiler has the error function defined in cmath, the complier version of the error function is used and it corresponds to an atomic operation.

Fix typo in tangent reverse mode theory for Positive Orders .

12-22
There was a bug related to optimizing conditional expressions. This has been fixed.

12-17
Fix some compiler warnings and speed program names when using the deprecated auto-tools install procedure.

12-16
If the c++11 include file <cstdint> defines all the standard types, they can be used by to specify cppad_tape_addr_type and cppad_tape_id_type .

12-15
Correct the title and _index entries for forward_two from first to second order.

11-28
Improve the index and search using a new version of the omhelp documentation tool.

11-27
  1. Add alignment to the get_memory and create_array specifications and thread_alloc example .
  2. Advance the deprecated unix install utilities to autoconf-2.69 and automake-1.13.4.


09-28
Fix more bugs related to optimizing condition conditional expressions.
  1. Using old instead of new operator indices.
  2. Not properly following dependence back through atomic operations.
  3. Aborting during forward order zero, when skipping computation for a variable that was already completed (the skip is still useful for higher orders and for reverse mode).
  4. Reverse mode not properly handling the variable number of arguments in the conditional skip operation.
  5. Reverse mode tracing not properly handling the variable number of argument operations; i.e., conditional skip and cumulative summation.


09-27
Fix a bug that occurred when f.optimize was used with a function f that contained calls to user defined atomic operations and conditional expressions .

09-25
Fix a bug that occurred when f.optimize was used with a function f that contained discrete functions.

09-21
Fix a typo in documentation for any order reverse . To be specific, x ( k ) was changed to be u ( k ) .

05-28
  1. Change the boolsparsity so that it only affects the sparsity speed tests sparse_jacobian and sparse_hessian ; i.e., it is now ignored by the other tests.
  2. Improve the speed documentation page.


05-27
  1. The cppad_colpack.cpp file was not being copied to the specified directory. In addition, the specified directory was changed from an include directory to data directory because cppad_colpack.cpp is not an include file.
  2. If colpack_prefix was specified, the CppAD pkgconfig file was missing some information. This has been fixed.


05-23
The speed test instructions were converted from using the old auto-tools unix install instructions to use the cmake install instructions. These instructions should work on any system, not just unix.

05-22
  1. Add multiple direction for mode forward_dir and use it to speed up the forward version of sparse_jacobian . Below is an example run of cppad_sparse_jacobian.cpp results before this change: 
     
     cppad_sparse_jacobian_size = [ 100, 400, 900, 1600, 2500 ]
     cppad_sparse_jacobian_rate = [ 2973, 431.94, 142.25, 78.64, 26.87 ]
    and after this change: 
     
     cppad_sparse_jacobian_size = [ 100, 400, 900, 1600, 2500 ]
     cppad_sparse_jacobian_rate = [ 6389, 954.26, 314.04, 180.06, 56.95 ]
    Due to the success of this change, multiple direction items were added to the wish list (they were later removed).
  2. Improve the forward mode tracing of arguments to, and results from, user defined atomic operations.


05-20
  1. Move speed/adolc/alloc_mat.hpp to speed/adolc/adolc_alloc_mat.hpp so it has the same name is its # ifndef command.
  2. Fix # ifndef command in cppad/ipopt/solve_callback.hpp.
  3. Add # ifndef command to test_more/extern_value.hpp.


05-19
In the files cppad/local/asin_op.hpp and cppad/local/acos_op.hpp there were assignments of the form uj = 0. where u_j has type Base . These may have not be defined operations in certain cases and have been converted to uj = Base(0).

05-16
There was a mistake in printing the arguments for CSumOp and CSkipOp when using the undocumented TRACE option during forward mode (available in files of the form cppad/local/*sweep.hpp/ ). This has been fixed.

05-14
  1. There were some global variables in the file cppad/local/op_code.hpp that might have caused multiple definitions during link time for CppAD applications. These variables have been changed to be local so that this cannot happen.
  2. There was a mistaken assert that the number of arguments for the BeginOp was zero that caused an abort when using the undocumented TRACE option available in files of the form cppad/local/*sweep.hpp/ . This has been fixed.


03-18
  1. The size_taylor and capacity_taylor functions were deprecated; use size_order and capacity_order instead.
  2. The documentation for forward and the examples forward.cpp , forward_order.cpp , have been improved. To be more specific, forward_order now references the special cases forward_zero , forward_one and the new case forward_two .


03-17
The move semantics version of the CppAD::vector assignment statement was not checking vector sizes. This has been fixed so that things work the same with compilers that do not have move semantics. (Note that with move semantics, no extra memory allocation is done even if the target vector has a different size.)

03-09
The documentation links forwardzero, forwardone, and forwardany have been changed to forward_zero , forward_one , and forward_order respectively. This may affect links from other web pages to the CppAD documentation.

03-05
The names p and q in the forward , reverse , atomic_forward , and atomic_reverse functions were reverse so that p <= q . This is only a notational change to make the arguments easier to remember.

03-02
  1. In the output for the speed correct test, mention which tests are not available. Note that the set of available tests can depend on the list of options .
  2. In the documentation for n_sweep , mention that it is equal to the number of colors determined by the color_method .
  3. The speed_cppad tests were simplified by removing the printing of auxillary information related to the optimize option. Future auxillary information will be passed back in a manner similar to n_sweep for the sparse jacobian test.
  4. Move semantics were added to the CppAD::vector assignment operator.


03-01
  1. Change the prototype for row and col in the link_sparse_jacobian speed test to be const; i.e., they are not changed.
  2. Move x near end of link_sparse_hessian speed test parameter list, (as is the case for link_sparse_jacobian ).


02-28
The data function was added to the CppAD::vector template class.

02-27
The CppAD developer documentation for the subdirectory cppad/ipopt was not being built by the command bin/run_doxygen.sh. This has been fixed.

02-26
  1. The adolc and cppad sparse jacobian speed tests now print out n_sweep .
  2. The size of some of the speed test cases has been increased to test behavior for larger problems.
  3. A link to ode_evaluate was missing in the Speed Utility Routines table. This has been fixed.


02-23
The color_method option was added to the sparse Jacobian calculations. This enables one to use ColPack do color the rows or columns. The speed test colpack option was also added (but not yet implemented for sparse_hessian speed tests).

02-22
The program names in thread_test.cpp where changes from threading_test to multi_thread_threading where threading is openmp, pthread or bthread.

02-17
Fix ambiguous call to isnan during MS Visual Studio 2012 compilation.

02-15
  1. The boolsparsity option was added to the speed_main program.
  2. The retape option what changed to onetape so that the default is to retape (option not present). This was done because fadbad and sacado always retape.
  3. The documentation, and example source code, for all the speed options was improved (made clearer).
  4. Improve the success rate for speed_test.cpp and time_test.cpp .


01-26
The destination directory for the cppad documentation is now set separately from the data directory using the cmake option
     -D cmake_install_docdir=cmake_install_docdir
 This has increased the flexibility of the documentation installation and removed the need for the option
     -D cppad_documentation=yes_or_no
 which has been removed.

01-21
The destination directory for the cppad documentation used to be one of the following:
     prefix/datadir/doc/cppad-version
     prefix/datadir/doc/postfixcppad-version
 This has been changed by dropping the version number at the end of the directory name.

01-10
The change on 2013-12-27 caused a conversion error in atan2 when it was used with AD< AD<double> > arguments (and other similar cases). This has been fixed.
Input File: omh/whats_new/whats_new_14.omh cppad-20170000.3/doc/whats_new_13.xml0000644000175200017650000007213713057470510016227 0ustar coincoin-web CppAD Changes and Additions During 2013
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CppAD Changes and Additions During 2013

Introduction
This section contains a list of the changes to CppAD during 2013 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-29
  1. The include file cppad_eigen.hpp now automatically includes cppad.hpp.
  2. There was a problem with this automation when eigen was used for the cppad testvector . This has been fixed.
  3. There was a problem with deprecated auto_tools (created when optional implicit constructor from any type was added). This has been fixed by adding the --with-implicit_ctor option (later changed to --with-deprecated ).


12-27
The constructor from an arbitrary type to AD<Base> was implicit, but there was no specification to this effect. The caused problems when using CppAD with eigen 3.2 (scheduled to be fixed in 3.3). The default for this constructor has been changed to be explicit . In addition, other implicit constructors are now listed in the documentation.

If you get a compiler error on an constructor / assignment of the form
     AD<Base> x = y
 (that used to work) try changing the constructor call to
     AD<Base>( y )
 A deprecated alternative is to make this constructor implicit using the cppad_deprecated option during the install procedure.

12-26
Document fact that monthly versions of the CppAD compressed tar file last till the end of the year.

12-24
The interface to eigen defined a function
     NumTraits< CppAD::AD<Base> >::dummy_epsilon()
 that should have been named dummy_precision(). This has been fixed.

11-27
  1. Fix bug when using optimize with an ADFun object containing the sign function.
  2. Add atomic_norm_sq.cpp , an atomic function example with domain dimension two and range dimension one.


11-13
It used to be that one had to define the std::set version of atomic_rev_sparse_jac for each atomic function that was part of an ADFun object that was optimized . Now the current atomic_sparsity setting is used to determine if the bool or std::set version of rev_sparse_jac is used by the optimization process.

11-12
Error detection and reporting (when NDEBUG is not defined) has been added for the following case: Using optimize with atomic_base functions that have not defined rev_sparse_jac .

10-29
The optimization now handles nested conditional expressions. For example, give the code 
 
     x = CondExpLt(left_x, right_x, true_x, false_x)
     y = CondExpGt(left_y, right_y, true_y, false_y)
     z = CondExpEq(left_z, right_z, x, y)
only two of the conditional expressions will be evaluated (one will be skipped depending on the result of left_z == right_z). For more details, see optimize_nest_conditional.cpp .

10-23
  1. Fix a bug in the optimization of calls to atomic functions. This bug existed before recent change to optimizing conditional expressions. This required adding the dependency argument to the reverse Jacobian sparsity pattern calculation.
  2. Fix the deprecated autotools install (see auto_tools ) which was broken by the changes on 10-22. To be specific, the example for number_skip was not being included.


10-22
  1. Add optimization of conditional expressions; see CondExp .
  2. Add a phantom argument at the beginning of the operations sequence; size_op_arg and seq_property.cpp . (This helps with the optimization mentioned above.)
  3. Add the function number_skip to measure how much optimization of the conditional expressions there is.


10-16
Fix bug in Tracing atomic functions.

10-15
The documentation for the class vectorBool was improved.

10-14
The script get_adolc.sh was added (for downloading and installing ADOL-C ) in the build directory. Note that this local install of Adolc requires ColPack; see get_colpack.sh . In addition, the requirement that ColPack and Adolc are installed with the same prefix was added.

10-13
Make sure that all of the preprocessor symbols , that are not part of the CppAD API, are undefined when the <cppad/cppad.hpp> file concludes.

10-12
  1. Change get_eigen.sh so that it will reuse install information when it is present. In addition document reuse for get_eigen.sh , get_ipopt.sh , and get_sacado.sh .
  2. Fix following g++ error on OSX system: 
     
error: no match for 'operator|=' (operand types are
'std::vector<bool>::reference {aka std::_Bit_reference}' and 'bool')
    Check[i * n + j] |= F2[i * n + k] & r[ k * n + j];
                     ^

09-20
  1. Add lines for atomic_base function documentation to both the definition and use of each operation. This required adding sub-headings in the example usages corresponding to the function documentation sections. For example; see atomic forward examples .
  2. Improve the documentation for atomic_base_clear and remove its use from the atomic_base examples (because it is not needed).


09-19
Add links from the atomic_base functions documentation to the corresponding examples. This required adding headings in the examples that correspond to the function documentation sections. For example; see atomic forward examples .

09-18
  1. A segmentation fault would occur if an ADFun object used an atomic function that had been deleted. This has been fixed so that when NDEBUG is not defined, an error message is generated.
  2. A mistake in the documentation for Memory and Parallel Mode has been fixed. This corresponds to the change in the specifications for CppAD::vector::resize made on 2012-07-30
  3. There was a bug during the checking for nan during reverse mode. This has been fixed.
  4. It appears, from inspecting the Ipopt source file Ipopt/src/Algorithm/IpIpoptAlg.cpp that the option sb to yes suppress the printing of the Ipopt banner. The Ipopt examples and tests have been changed to use this option (although it is not in the ipopt documentation).
  5. Fix the a typo in the documentation for ipopt_solve Integer options (Numeric was changed to Integer).


09-07
There was a bug in the cumulative sum operator (which is used by optimize ) for Forward orders greater than zero. This was detected by the checkpoint tests when optimize was used to make the checkpoint functions faster. The bug has been fixed and the checkpoint functions now use optimize (and hence should be faster).

08-12
  1. The ability to turn on and off checking for nan in Forward mode results has been added; see check_for_nan .
  2. Use this option to remove the need to handel nan as a special case in checkpoint functions that atomic functions in within another function is optimized.
  3. Check reverse mode results when check_for_nan is true. (It used to be the case that only forward results were checked for nan.)


08-11
If an atomic function had arguments that did not affect the final dependent variables in f , f.optimize() would fail. This has been fixed. In addition, documentation about using optimize with atomic functions has been added.

08-06
Fix a case where the test test_more/num_limits.cpp failed because 
 
     double inf   = std::numeric_limits<double>::infinity();
     double check = std::complex<double>(inf) / std::complex<float>(1.)
can result in the imaginary part of check being - nan.

07-26
Allow for use of const::string& as a possible type for name in the atomic_base constructor.

05-28
Remove ok return flag from checkpoint algo and checkpoint atom_fun .

05-21
  1. Deprecate the old_atomic interface and replace it by the atomic_base and checkpoint interfaces.
  2. There was a problem with the cmake command if the cppad_cxx_flags was not specified. This has been fixed.


05-17
  1. Add the transpose option to ForSparseJac .
  2. Add the transpose option to RevSparseHes .


05-15
Change RevSparseJac parameter names to be closer to the ForSparseJac names so the difference is clearer.

05-14
  1. The checkpoint class has been added. This is a much easier way to do checkpointing than the old checkpoint example. The old checkpointing example is now the reverse_checkpoint.cpp example.
  2. Fix bug in RevSparseJac for case when q was not equal to m (range dimension) and sparsity pattern was a vector of bool.
  3. Add the transpose option to RevSparseJac .


05-12
The sparse hessian example in old_reciprocal.cpp was not being run. This has been fixed.

05-11
The old_atomic examples names were all changed to begin with user.

05-04
The option to compute multiple orders was added. The old_usead_2.cpp example shows the need for this. The problem is that a new atomic function interface needs to be designed with checkpointing as a particular application. Multiple order forward mode is the first step in this direction.

04-28
  1. The scripts get_eigen.sh and get_sacado.sh were added. If you are using Unix, and you do not have Eigen or Sacado installed on your system, you can use the corresponding script to download and install a local copy for use when testing CppAD.
  2. The code std::cout << X , would generate a compile error when X was an Eigen matrix with CppAD::AD<Base> elements. This has been fixed.


04-27
There was a problem using the output operator << with and eigen matrix of AD elements. This has been fixed using a template partial specialization of 
 
     template<typename Scalar, bool IsInteger>
     struct significant_decimals_default_impl
because the original template requires definition of a implicit conversion from the scalar type to an int and this is dangerous for AD types (note that Integer is used for explicit conversions).

04-26
  1. The example old_usead_2.cpp was completed. This is a more realistic, but also more complicated, example of using AD to computed derivatives inside an atomic function.
  2. The script get_fadbad.sh has been added. If you are using Unix, and you do not have FADBAD installed on your system, you can use this script to download and install a local copy for use when testing CppAD.
Input File: omh/whats_new/whats_new_13.omh cppad-20170000.3/doc/whats_new_12.xml0000644000175200017650000021376213057470510016227 0ustar coincoin-web CppAD Changes and Additions During 2012
Prev Next whats_new_12

CppAD Changes and Additions During 2012

Introduction
This section contains a list of the changes to CppAD during 2012 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-30
  1. Merge changes in branches/ipopt_solve to trunk, delete that branch, and advance version number to cppad-20121230.
  2. Remove cppad/configure.hpp from repository because it is built by the configuration process (even for MS Visual Studio, now that we are using cmake ).
  3. Add the AD<Base> input stream operator >> .


12-29
In branches/ipopt_solve:
  1. Complete implementation of sparse Jacobian and Hessian calculations and add options that allow to user to choose between forward and reverse sparse Jacobians.
  2. The ipopt_solve routine seems to be faster and simpler than cppad_ipopt_nlp . More speed comparisons would be good to have.
  3. All of the ADFun Drivers have added specifications for the zero order Taylor coefficients after the routine is called. For example, see Hessian uses forward .


12-28
In branches/ipopt_solve:
  1. Add the ipopt_solve_retape.cpp and ipopt_solve_ode_inverse.cpp examples.
  2. Use ipopt::solve options argument (and not a file) for all the Ipopt options. As well as allowing for adding ipopt::solve special options; e.g., retape .


12-27
In branches/ipopt_solve: Change documentation section names that begin with cppad_ipopt to begin with ipopt_nlp to distinguish them from CppAD::ipopt::solve .

12-26
In branches/ipopt_solve:
  1. Convert documentation most all documentation references from the deprecated auto_tools instructions to the new cmake instructions.
  2. Include the Introduction programs in the cmake_check built using cmake .
  3. Deprecate cppad_ipopt_nlp and replace it by ipopt_solve which is easier to use. This is a first version of ipopt_solve and its speed and memory use needs to be improved.


12-23
Copy development trunk to branches/ipopt_solve.

12-22
Define a doxygen module (group) for each file that has doxygen documentation.

12-20
  1. The install instructions were installing cppad/CMakeLists.txt and cppad/configure.hpp.in in the cppad include directory. This has been fixed so that only *.h and *.hpp files get installed in the cppad include directory.
  2. Advance the version number to cppad-20121220.


12-19
The files <stdbool.h> and <sys/time.h> do not exist for all C compilers, and this caused a problem when using the Windows compiler. This has been fixed by defining the type bool inside the compare_c/det_by_minor.c source code.

12-17
There was a mistake in a check for a valid op code in the file hash_code.hpp. This mistake could generate a C++ assertion with an unknown error source. It has been fixed.

12-15
  1. Advance version number from 20121120 to 20121215. Note that the CppAD version number no longer automatically advances with the date and is rather chosen to advance to the current date.
  2. The cmake installation was putting the cppad.pc pkgconfig file in
         cppad_prefix    /cmake_install_datadir/cppad.pc
     This has been fixed and is now
         cppad_prefix    /cmake_install_datadir/pkgconfig/cppad.pc
  3. The pkgconfig documentation has been improved.
  4. The command for running the adolc examples and eigen examples was fixed (changed from make check to make check_example).


12-14
  1. Fix the old auto_tools so that it works with the new cppad.pc.
  2. Fix the old installation --with-Documentation option (it was attempting to copy from the wrong directory).


12-13
  1. Include documentation for ipopt_prefix
  2. Fix the cppad.pc pkgconfig file so that it includes the necessary libraries and include commands when ipopt_prefix is specified; see pkgconfig usage .


11-28
Update the wish_list :
  1. Remove Microsoft compiler warning item that has been fixed.
  2. Remove faster sparse set operations item that was completed using cppad_sparse_list (not part of user API).
  3. Remove cmake items that have been completed.
  4. Remove CondExp items related to using AD< std::complex<double> > types because it is better to use std::complex< AD<double> >.
  5. Remove thread_alloc memory chunk item that has been completed.
  6. Remove VecAD item about slicing from floating point type to int (not important).
  7. Change an Ipopt item to a cppad_ipopt_nlp (which was removed because cppad_ipopt_nlp is now deprecated). Add new cppad_ipopt_sum item to the wish list. (This has been removed because checkpointing can now be used for this purpose.)
  8. Add new old_atomic wish_list item (since removed).


11-21
  1. Fix the version number in link to the current download files .
  2. Change the subversion download instructions to use the export instead of checkout command. This avoids downloading the source code control files.


11-20
  1. The cmake variables cmake_install_includedir and cmake_install_libdir were changed to cmake_install_includedirs and cmake_install_libdirs to signify the fact that they can now be a list of directories.
  2. Advance version number to cppad-20121120.


11-17
  1. Finish documenting the new cmake configuration instructions and deprecate the old unix instructions.
  2. Change the specifications for CPPAD_MAX_NUM_THREADS to allow for a value of one. This enables one to have more tapes during a program execution.
  3. Include the C versus C++ speed comparison in the cmake build.


11-16
Fix a warning that occurred in Rosen34 when it was compiled with the preprocessor symbol NDEBUG defined.

11-14
Advanced the CppAD version to cppad-20121114.
  1. Started documenting the cmake configuration procedure during installation. This included factoring out the download procedure as a separate section so that the same download instruction also apply to the unix install procedure.
  2. Changed example/compare_change.cpp to just return true when NDEBUG is defined. This enabled all the tests in the example directory to be compiled with NDEBUG is defined and to pass.
  3. In the case where NDEBUG is defined, removed detection of nan during forward mode from test_more/forward.cpp%. This enables all the tests in the test_more directory to be compiled with NDEBUG is defined and to pass.
  4. Started a wish list for CppAD's use of cmake . The wish list items were completed and removed.


11-09
The team_pthread.cpp was failing to link on Ubuntu 12.04 because the libraries were not at the end of the link line. This has been fixed.

11-06
  1. Remove some remaining references to the old licenses CPL-1.0 and GPL-2.0; see 10-24 .
  2. Remove out of date Microsoft project files from the distribution. The build system is being converted to use cmake which builds these files automatically and thereby keeps them up to date. This feature is not yet documented, but one can inspect the file bin/run_cmake.sh to see how to use cmake with CppAD.


11-04
Add missing return value to the example base_alloc CondExpOp function. This has been fixed and the comments for this example have been improved.

10-31
The CppAD profiling was not compiling the speed/src/*.cpp files with the profiling flag. This has been changes (only for the profiling speed test).

10-30
The fadbad_dir directory install instructions were changed. To be specific, FADBAD++ was changed to include/FADBAD++. This makes it more like the other optional packages.

10-25
The test runge45_1.cpp was failing when using gcc-4.5.2. This has been fixed by properly defining fabs(x) where x is a double (without the std in front).

10-24
Change the CppAD licenses from CPL-1.0 and GPL-2.0 to EPL-1.0 and GPL-3.0.

10-12
  1. Change all the multiple levels of AD examples to start with mul_level . To be specific, move ode_taylor.cpp to mul_level_ode.cpp and ode_taylor_adolc.cpp to mul_level_adolc_ode.cpp .
  2. Add ode_taylor.cpp as a example of Taylor's method for solving ODEs, (mul_level_ode.cpp is an application of this method to multi-level AD.)


10-04
  1. Change speed_main so that it outputs small rates (less than 1000) with two decimal points of precision (instead of as integers). In addition, flush result for each size when it finishes to give user more feedback about how things are progressing.
  2. Add the optional test_size argument to the time_test routine.


10-03
Change the hold_memory speed to option to just memory . In addition, in the speed test output, include all of the options that are present in the output variable name; see speed results .

10-02
Fix another problem with Debian's /bin/sh shell executing multi_thread/test.sh; see 03-17

09-24
Improve documentation for the old_atomic rev_hes_sparse argument v . In addition, add sparsity calculations to the old_reciprocal.cpp example.

09-11
Add user_simple.cpp, a simpler old_atomic example.

08-05
  1. A new type was added for the internal representation of vector of sets sparsity patterns; see the configure --with-sparse_option (since removed).
  2. A new speed test, compare_c , compares the speed of the same source code compiled with C and C++.


07-30
  1. The clear function was added to CppAD::vector.
  2. Warning !!: The CppAD::vector resize specifications were changed so that x.resize(0) no longer frees the corresponding memory (use x.clear() instead).
  3. Fix a bug in error checking during optimize procedure had the following valgrind symptom during the optimize.cpp example: 
     
     ==6344== Conditional jump or move depends on uninitialised value(s)
  4. Fix mistake in old_tan.cpp where w[2] = 0 was missing before the call 
     
          dw    = F.Reverse(1, w);

07-08
  1. Improve the documentation for pow and pow_int .
  2. Change all the example section names to be same as corresponding file names; e.g. change vectorBool.cpp to vector_bool.cpp for the example example/vector_bool.cpp.


07-07
Add the CPPAD_TAPE_ID_TYPE argument to the configure command line.

07-05
Deprecate CPPAD_TEST_VECTOR and use CPPAD_TESTVECTOR in its place. This fixes a problem introduced by changes on 07-03 whereby code that used CPPAD_TEST_VECTOR would no longer work.

07-04
  1. Replace the requirement that the SimpleVector size function return a size_t value to the requirement that it can be converted to a size_t value.
  2. The --with-eigenvector option was added to the configure command line.


07-03
Fix bug in old_atomic functions identification of variables that caused old_tan.cpp to fail with error message 
 
Error detected by false result for
    y_taddr > 0
at line 262 in the file cppad/local/dependent.hpp

07-02
Add eigen_plugin.hpp so that an Eigen vector can be used as a SimpleVector .

07-01
  1. Change cppad_eigen.hpp to match new specifications and example in eigen help files on customizing and extending eigen.
  2. Fix bug whereby a newly constructed VecAD object was a variable (instead of a parameter) directly after construction (when no previous ADFun object had been created).
  3. Change a ok != a == 0. to ok &= a == 0. in the example ad_ctor.cpp .
  4. Add the eigen_array.cpp example.


06-17
  1. Move epsilon to numeric_limits and add the functions min and max in CppAD::numeric_limits<Type> .
  2. Convert use of the deprecated epsilon in examples to use of numeric_limits epsilon .
  3. Complete cppad_eigen.hpp interface to lowest and highest functions for all non-complex AD types.


06-16
Add the example eigen_det.cpp that uses the Eigen linear algebra package.

06-15
Include the base_adolc.hpp as <cppad/example/base_adolc.hpp> under the prefix_dir directory.

06-12
Increase the size and of the sparse Jacobian speed tests .

06-10
  1. Add the hold_memory option to the speed test main program. This was changed to just memory; see 10-03 .
  2. In cppad_sparse_jacobian.cpp , change USE_BOOL_SPARSITY from true to false. In addition, change the number of non-zeros per row from about approximately three to approximately ten.


06-09
Change adolc_sparse_jacobian.cpp to use the sparse adolc Jacobian (instead of the full Jacobian) driver. This was also done for adolc_sparse_hessian.cpp , but there is a problem with the test that is being investigated.

06-08
Implement the matrix multiply speed test link_mat_mul for all packages (there is a problem with the fadbad_mat_mul.cpp implementation and it is being looked into).

06-07
Make all the speed tests implementations (for the specific packages) uniform by having a Specification and Implementation heading and similar indexing. For example, see adolc_det_minor.cpp , cppad_det_minor.cpp , double_det_minor.cpp , fadbad_det_minor.cpp , and sacado_det_minor.cpp .

06-05
Add the sacado_ode.cpp speed test.

06-04
  1. The specifications for Runge45 where changes so that it uses the fabs function instead of the < operation. This enabled the a more precise statement about its operation sequence .
  2. The fabs function as added to the CppAD standard math library (see abs ) and the base type requirements . This enables one to write code that works with AD<double> as well as double without having to define abs for double arguments (and similarly for float).
  3. Add the adolc_ode.cpp and fadbad_ode.cpp speed tests (and edit the cppad_ode.cpp test).


06-03
  1. The CppAD::vector class was extended to allow assignment with the target of size zero and the source of non-zero size; see check size .
  2. A memory leak and a bug in cppad_mat_mul.cpp were fixed (the bug was related to the change to CppAD::vector above).


06-02
  1. Remove the deprecated symbol CppADvector from the det_by_lu speed test source code det_by_lu.hpp .
  2. Include memory_leak in the list of deprecated features.
  3. Change the ode_evaluate speed test utility so that its operation sequence does not depend on the repetition; see p == 0 in its documentation.
  4. Use same argument for taping and derivative evaluation when retape speed test option is true.
  5. Implement the retape == false option in cppad_ode.cpp .
  6. Have cppad_det_lu.cpp , cppad_det_minor.cpp , and cppad_poly.cpp , return false when one of the specified options is not supported. Do the same for package_test.cpp for package equal to adolc, fadbad, and sacado and for test equal to det_lu, det_minor, poly.


06-01
Change cppad_sparse_hessian.cpp and cppad_sparse_jacobian.cpp to use the row , col interface to sparse_hessian . In addition, implement the speed test retape speed test option for these tests.

05-31
Add the cppad_print_optimize routine to so that the corresponding code does not need to be reproduced for all the speed_cppad tests. In addition, during CppAD speed tests, print out the optimization results for each test size.

05-30
Change specifications for link_sparse_hessian so that the row and column indices are inputs (instead of being chosen randomly by the test for each repetition). This enables use of the retape speed test option during sparse Hessian speed tests.

05-29
Add index_sort to the general purpose template utilities so that it can be used by the implementations of link_sparse_jacobian and link_sparse_hessian .

05-27
Split the sparse Jacobian and Hessian test function the separate function sparse_jac_fun and sparse_hes_fun (do not use sparse Hessian for both). In addition, change row and column indices from i and j to row and col .

05-24
Merged in changes from branches/sparse:
  1. A new interface was added to sparse_jacobian and sparse_hessian . This interface returns a sparse representation of the corresponding matrices using row and column index vectors.
  2. The examples sparse_jacobian.cpp and sparse_hessian.cpp were improved and extended to include the new interface.
  3. The definition of an AD function was improved to include definition of the corresponding n and m .


04-19
The BOOST_DIR configure command line value has been changed to be the corresponding prefix during the installation of boost. To be specific, it used to be that boost_dir/boost was the boost include directory, now boost_dir/include is the boost include directory. This make it the same as the other directory arguments on the configure command line. In addition, it fixes some bugs in the detection of the boost multi-threading library.

04-18
Add documentation and testing for not using free_all and old_atomic clear while in parallel mode.

04-17
Fix bug when using old_atomic functions with multi_threading .

04-10
Add control of the max_num_threads argument to the unix configure command.

04-06
  1. A change was made to the way that the tapes were managed to reduce false sharing during multi-threading . Because of this change, it is now suggest that the user call parallel_ad after the multi-threading section of the program.
  2. The routine ta_free_all was created to make it easier to manage memory and the routine memory_leak was deprecated.
  3. Add the -lteuchos flag to the link line for the speed_sacado tests. (This was not necessary for trilinos-10.8.3 but is necessary for trilinos-10.10.1)


04-05
The restriction was added that parallel_ad cannot be called while a tape is being recorded. This was necessary inorder to initialize some new statics in the tape.

04-01
Fixed a race condition when using CppAD with multi-threading . This has been fixed and the error message below no longer occurs. Suppose that you ran the CppAD configure command in the work directory. If you then edited the file work/multi_thread/makefile and changed 
 
     # AM_CXXFLAGS     = -g $(CXX_FLAGS)
     AM_CXXFLAGS = -DNDEBUG -O2 $(CXX_FLAGS)
to 
 
     AM_CXXFLAGS     = -g $(CXX_FLAGS)
     # AM_CXXFLAGS = -DNDEBUG -O2 $(CXX_FLAGS)
and then executed the commands 
 
     make clean
     make pthread_test
     valgrind --tool=helgrind ./pthread_test simple_ad
The following error message would result:
     ... snip ...
==7041== Possible data race during write of size 4 at 0x8077460 by thread #1
==7041==    at 0x804FE23: CppAD::AD<double>::tape_new() (tape_link.hpp:221)
     ... snip ...
03-27
Reduce the amount of memory allocation and copying of information during a Dependent operation or an ADFun sequence constructor .

03-26
Calling taylor_capacity, with to with capacity equal to zero, was not freeing memory . This has been fixed.

03-23
  1. Improve, the multi-threading examples simple_ad_openmp.cpp , simple_ad_bthread.cpp , and simple_ad_pthread.cpp . This includes separating generic code that can be used for all applications from problem specific code.
  2. Add initialization of statics in CheckSimpleVector during parallel_ad call. These statics are required to use CppAD::vector .
  3. Add a debugging check to make sure CheckSimpleVector is initialized in sequential mode.


03-21
Fix an incorrect error check in thread_alloc that did not allow ta_return_memory to return memory in sequential execution mode that was allocated by a different thread during parallel execution.

03-17
Debian recently converted the default shell corresponding to /bin/sh to dash (which caused multi_thread/test.sh to fail). This has been fixed. In general, Debian's policy is that bin/sh will be a Posix Shell .

03-11
There was a bug in thread_alloc where extra memory was held onto even if hold_memory was never called and only one thread was used by the program. This caused
valgrind --leak-check=full --show-reachable=yes
 to generate an error message. If multiple threads are used, one should free this extra memory for threads other than thread zero. If hold_memory is used, one should call free_available for all threads.

03-03
  1. Add the examples simple_ad_openmp.cpp , simple_ad_bthread.cpp and simple_ad_pthread.cpp .
  2. Fix bug in finding boost multi-threading library (due to fact that boost_dir is not the prefix during the boost installation).


03-02
  1. Change the name simple_ad.cpp to team_example.cpp
  2. The multi-threading team_example.cpp example was changed to use f ( x ) = x 2 instead of the function atan 2 [ sin ( x ) , cos ( x ) ] (both functions should behave like the identity function f ( x ) = x ). This enabled the removal of multi_thread/arc_tan.cpp.
  3. In team_example.cpp check that all of the threads pass their individual test; i.e. work_all_[thread_num].ok is true for all thread_num .


02-11
  1. The requirements in base_member were missing from the base_require documentation. In addition, the base_require.cpp example has been added.
The specifications for memory_leak where changes so that calling routine specifies the amount of static memory to add. In addition, it is now possible to call memory_leak when num_threads is greater than one (still can't be in parallel mode).

02-10
  1. Add the missing Base class requirements in the entire base_member section and under the Output Operator in the base_require section.
  2. Add the base_alloc.hpp example.


02-09
  1. Add the set_static to memory_leak . This is necessary for testing base types that allocate memory for each element.
  2. Fix memory allocation bug in cppad/local/pod_vector.hpp when each element of the Base type allocated memory.


01-30
Make another attempt to fix linking with boost threads where the wrong version of the library is in the system include directory; i.e., to have boost_dir override the default library.

01-27
There were some problems with configure's automatic detection of the boost multi-threading library. These have been fixed.

01-24
It used to be that thread_alloc did not hold onto memory when num_threads was one in the previous call to parallel_setup . Holding onto memory is now controlled by the separate routine hold_memory . This give the user more control over the memory allocator and the ability to obtain a speed up even when there is only one thread. To convert old code to the new interface, after each call to
thread_alloc::parallel_setup(num_threads, in_parallel, thread_num);
 put the following call
thread_alloc::hold_memory(num_threads > 1);
01-23
Change variable notation and use optimize in mul_level.cpp .

01-20
  1. Add the example change_param.cpp which shows how to compute derivatives of functions that have parameters that change, but derivatives are not computed with respect to these parameters.
  2. The documentation for machine epsilon has been improved. (The fact that it can be used for Base types was missing.)


01-19
  1. In cases where test.sh is trivial, put its operations in corresponding makefile.
  2. Fix problem compiling cppad/speed/sparse_evaluate.hpp under gcc on Fedora 17.
  3. Run multi_thread/test.sh from source directory (no need to copy to build directory).


01-16
The test program multi_thread/test.sh failed if the openmp_flags not present in the configure command. This has been fixed. In addition, this test.sh has been made faster by cycling through the available threading systems instead of doing every system for every test.

01-15
Fix make test so it works when configure is run in the distribution directory cppad-yyyymmdd (not just when it is run in a different directory).

01-12
The -lpthread library was missing from the multi_thread test program linker command. This has been fixed.

01-07
  1. A duplicated code block beginning with 
     
if( fabs( fcur ) <= epsilon_ )
    was removed from the routine multi_newton_worker, in the file multi_newton_work.cpp .
  2. The distance between solutions that are joined to one solution has been corrected from ( b - a ) / ( 2 n ) to ( b - a ) / n ; see xout . The correction was in the file multi_newton_work.cpp where sub_length_ / 2 was change to sub_length_.


01-02
  1. The thread_alloc memory allocator was changed to avoid certain false sharing situations (cases where two different thread were changing and using memory that is on the same page of cache). On one tests machine, the execution time for the 32 thread case for the test 
     
./openmp_test multi_newton 1 32 1000 4800 10 true
    improved from 0.0302 seconds to 0.0135 seconds.
  2. There was a problem with the correctness test section of the multi_newton_time.cpp test. The convergence criteria, and correctness criteria, needed to be scaled by the largest argument values. This was a problem with over a hundred zeros were included in the test (and the largest argument value was 100 π or more).
  3. There was a problem with the way that multi_newton_combine joined two solutions into one. It is possible that one of the solutions that needs to be joined is on the boundary and very close to a solution in the next (or previous interval) that is not on the boundary. In this case, the one with the smaller function value is chosen.
for the previous
Input File: omh/whats_new/whats_new_12.omh cppad-20170000.3/doc/whats_new_11.xml0000644000175200017650000020274213057470510016222 0ustar coincoin-web Changes and Additions to CppAD During 2011
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Changes and Additions to CppAD During 2011

Introduction
This section contains a list of the changes to CppAD during 2011 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-30
  1. There was a bug when using abs with an AD< AD<double> > argument, whereby the corresponding AD<double> operation sequence depended on the value of the argument to the abs function.
  2. Change the specifications for the derivative of the abs function to be the sign function instead of a directional derivative.
  3. Add the sign function to the AD<Base> list of available functions. In addition, add the sign function to the list of base type requirements .


12-28
The file time_test.hpp was not being included by cppad/cppad.hpp. This has been fixed.

12-21
The types SizeVector, NumberVector, ADNumber, and ADVector, were in the global namespace and this was causing warnings about the shadowing of these declarations. The cppad_ipopt namespace was created to avoid these problems. The simplest way to make old cppad_ipopt_nlp code work with this change is to use the command 
 
     using namespace cppad_ipopt;

12-20
  1. Change team_start to team_create and team_stop to team_destroy .
  2. Change NDEBUG mentions to include link to NDEBUG .
  3. Improve memory_leak documentation.


11-29
THe time_test routine was still executing the test at least twice, even if that was not necessary for the specified minimum time. This has been fixed.

11-27
Move multi_thread.cpp to thread_test.cpp and fix its running instructions.

11-24
Create preprocessor section with pointers to all the preprocessor symbols that are in the CppAD API.

11-21
Separate --with-boostvector for boost_dir . This enables one to specify boost_dir for team_bthread.cpp with out using boost vectors.

11-20
  1. Move sum_i_inv.cpp to harmonic.cpp .
  2. Include the date, time, CppAD version, and team_name in the thread_test.cpp output.


11-18
  1. The thread_test.cpp program was truncating test_time to the nearest integer. This has been fixed.
  2. The time_test routine has been made more efficient and now check for the case where only one execution of the test is necessary to achieve the desired test_time (it used to always run at least two).
  3. The sum_i_inv_time.cpp and multi_newton.cpp routines were calling the test an extra time at the end to check for correctness. The results of the last test are now cached and used for the correctness test so that an extra call is not necessary (to make the tests run faster when only a few repetitions are necessary).


11-17
  1. Create another speed testing routine time_test which is like speed_test but it returns the time instead of rate and as a double instead of a size_t. The use it for the timing tests in sum_i_inv_time.cpp and multi_newton_time.cpp .
  2. Add test_time as a command line argument to the multi-threading sum_i_inv and multi_newton timing tests.


11-09
Change thread_team.hpp to team_thread.hpp and do the same for all other names that ended in _team; e.g., team_openmp.cpp .

11-07
The users choice for test_vector was not actually changing the tests that the user ran. This have been fixed.

11-06
Make all the output generated by multi_newton.cpp valid matlab and octave input so it is easy to plot the results.

11-04
Use thread specific data to simplify team_openmp.cpp .

11-01
Make team_bthread.cpp more similar to team_pthread.cpp .

10-30
  1. Reorganize and improve the multi_thread section and its subsections.
  2. There was a bug in multi_newton_work.cpp that only showed up when the number of threads was greater than or equal 4. This has been fixed. In addition, CPPAD_MAX_NUM_THREADS was increased from 2 to 4 (to enable testing for this bug).
  3. The accuracy expected in the sum_i_inv.cpp results were failing when mega_sum was large. This check has been modified to include a correction for mega_sum .


10-29
The following changes were merged in from branches/thread:
  1. Move openmp to multi_thread/openmp. and create multi_thread/bthread, multi_thread/pthread with similar tests.
  2. Put multi-threading common code in multi_thread directory and threading system specific code in multi_thread/threading for threading equal to openmp, bthread, and pthread.
  3. Update the README file.
  4. Remove the bug/optimize.sh file (no longer a bug).
  5. Make arc_tan.cpp utility that can be used by multiple multi-threading tests.
  6. Create team_thread.hpp specifications, move OpenMP management to team_openmp.cpp , Boost thread management to team_bthread.cpp , and pthread management to team_pthread.cpp .
  7. All of the make files were modified so that the command 
     
     make test
    would run the tests for the current directory.
  8. Extend the multi-threading speed tests sum_i_inv.cpp and multi_newton.cpp so they run using Boost threads and pthreads (as well as OpenMP threads).


10-14
Fix some compiler warnings about shadowed variables that were detected by g++ version 4.6.1 20110908.

10-12
  1. The MAC version of the pthread library does not include the pthread_barrier_wait function; i.e., is not compliant with the IEEE Std 1003.1, 2004 Edition for pthread. This caused the pthread_simple_ad.cpp to fail to compile on the MAC. This has been fixed by not compiling the pthread examples unless pthread_barrier_wait is present.
  2. The cppad_ipopt_nlp routine has been changed to optimize the functions r k ( u ) such that retape(k) is false.


09-06
  1. Add the boost multi-threading examples a11c_bthread.cpp and bthread_simple_ad.cpp.
  2. Improve documentation for thread_num argument to parallel_setup.
  3. More simplification of bthread_simple_ad.cpp example.


09-05
Simply and fix some problems with pthread_simple_ad.cpp, including avoiding a Bug in Cygwin .

09-02
  1. The OpenMP speed test program openmp/run.cpp was not setting the number of threads for the one thread case (so dynamic thread adjustment was used). This has been fixed.
  2. The thread_alloc.cpp example was missing from the Microsoft example/example.vcproj file and a attempt was made to link to missing OpenMP routines (this has been fixed). In addition, some Microsoft compiler warning have been fixed; see the examples and tests in the Windows install instructions.
  3. There was an oversight, and CPPAD_MAX_NUM_THREAD was being set to 2 when _OPENMP was not defined. This has been fixed and CPPAD_MAX_NUM_THREADS has been documented and is now part of the CppAD API.
  4. The pthread_simple_ad.cpp test failed under cygwin. This was because the previous test openmp_ad.cpp was set up calls to OpenMP routines that were still in effect when pthread/simple_ad ran. This has been fixed by making num_threads == 1 a special case in parallel_setup .


09-01
  1. Modify the CppAD trunk using the changes from svn revision 2060 to revision 2081 in the branch 
     
     https://projects.coin-or.org/svn/CppAD/branches/pthread
    These changes are described below under the headings 08-21 through 08-31 .
  2. There was a bug in the old_atomic functions in the case where none of the elements of the argument to the function was a variable . This has been fixed. In addition, old_tan.cpp generated an assert for this case and this has also been fixed (in addition to including an example for this case).


08-31
  1. Move the sum_i_inv_time.cpp test from openmp/run.sh to openmp/run.cpp.
  2. Change --with-openmp to OPENMP_FLAGS=openmp_flags configure command line argument.


08-30
  1. Create the openmp/run.cpp program and move the openmp_multi_newton.cpp test from openmp/run.sh to openmp/run.cpp. This uses configure information for building the tests.
  2. Document the --with-openmp configure command line argument.
  3. Move openmp/multi_newton.hpp to openmp/newton_method.hpp and openmp/multi_newton.cpp to openmp/newton_example.cpp.


08-25
  1. Replace omp_alloc by thread_alloc in multi_thread , the section on how to use CppAD in parallel.
  2. Implement omp_alloc as links to corresponding thread_alloc sections.
  3. Create the pthread_simple_ad.cpp example that does AD using the pthread library. In addition, fix some problems in openmp_simple_ad.cpp
  4. Move openmp/example_a11c.cpp to example/a11c_openmp.cpp .
  5. Move openmp/parallel_ad.cpp to openmp_simple_ad.cpp.


08-23
Beginning steps in replacing omp_alloc by thread_alloc :
  1. Replace omp_alloc by thread_alloc in the utilities .
  2. move omp_alloc to the deprecated section of the documentation.
  3. Change all omp_alloc section names to begin with omp_, and change all thread_alloc section names to begin with new_.
  4. Convert CppAD_vector from using omp_alloc to using thread_alloc for memory allocation.
  5. Extend the memory_leak routine to also check the thread_alloc allocator.


08-21
Create the OpenMP and pthread examples a11c_openmp.cpp , a11c_pthread.cpp , and openmp_simple_ad.cpp. These OpenMP examples were originally in the openmp directory, and have been moved, and modified to conform, to the normal example directory.

08-11
Modify the CppAD trunk using the changes from svn revision 2044 to revision 2056 in the branch 
 
     https://projects.coin-or.org/svn/CppAD/branches/base_require
These changes are described below under the headings 08-04 through 08-10 .

08-10
  1. Add the output stream optional argument s in
             f.Forward(0, x, s)
     See zero order forward mode and PrintFor .
  2. Improve omp_alloc.cpp example.


08-09
  1. base_require : Add epsilon to the Base type requirements.
  2. Extend epsilon to AD types.


08-08
  1. Improve the base_require documentation for standard math functions .
  2. base_require : Add abs_geq to the requirements for a user defined Base type.
  3. Check that zero order forward mode results are approximately equal, instead of exactly equal, after an optimize operation. This fixes a bug in the optimize correctness check (The order of operations can be changed by optimize and hence the zero order forward mode results may not be exactly the same.)


08-07
Improve the base_require documentation for EqualOpSeq , Identical Integer , and Ordered operations.

08-06
Add the CondExpRel paragraph to the base requirements documentation. This was missing and are required for CondExp to work with AD<Base> arguments and a non-standard Base type.

08-04
  1. base_require : Change the include file name to base_require.hpp .
  2. Use base_float.hpp and base_double.hpp as additional examples for the CondExp Base requirements requirements.


08-03
Change PrintFor condition from less than or equal zero to not greater than zero;i.e., not positive. This makes nan print because it results in false for all comparisons.

08-02
  1. Change PrintFor so it no longer aborts execution when there is no operation sequence being recording; see start recording .
  2. Improve the print_for_cout.cpp example.


07-31
Add a conditional version of the PrintFor command
     PrintFor(text, y, z)
 which only prints when z <= 0 . This is useful for error reporting during forward mode; i.e., reporting when the argument to the log function is not valid.

07-29
  1. The routines set_max_num_threads and get_max_num_threads were created. User's will need to replace calls to max_num_threads by calls to set_max_num_threads.
  2. The functions omp_efficient was deprecated because it has not been shown to be useful.


07-28
  1. Change omp_return_memory so that if omp_max_num_threads is one (the default), omp_alloc does not hold onto memory (keep it available for the corresponding thread).
  2. Add files that were missing from the Microsoft Visual Studio example and test_more subdirectory project files.
  3. Fix some warnings generated by Microsoft Visual Studio 2010 build.


07-27
Make tan and tanh atomic operations; see tan_forward and tan_reverse .

07-25
Finish the old_atomic example old_tan.cpp . This is also a design and implementation of the routines necessary to make tan and tanh CppAD atomic operations.

07-18
The reverse mode formulas for Z ( t ) need to involve the lower order Taylor coefficients for Y ( t ) . This has been fixed in tan_reverse .

07-17
  1. Fix bug in old_atomic functions. To be specific, the Taylor coefficients for y , of order less than k , were not passed into the old_atomic forward callback function.
  2. Derive the theory for including the tangent and hyperbolic tangent as CppAD atomic operations tan_forward and tan_reverse ; see the wish list item Tan and Tanh.
  3. Implement and test forward mode calculation of derivative for the tangent and hyperbolic tangent functions; see the new old_atomic example old_tan.cpp .


07-14
  1. The auto_tools instructions for running the individual correctness and speed tests were out of date. This has been fixed; see example and tests .
  2. Move parallel_ad.cpp from example directory to openmp directory (and convert it from a function to a program).
  3. Simplify example_a11c.cpp by making it just a correctness test.
  4. Change openmp/run.sh so that it runs correctness tests with the compiler debugging flags.


07-13
  1. static hash code data that was begin used by multiple threads when recording AD<Base> operations omp_in_parallel execution mode. This has been fixed.
  2. Make the sparsity calculations safe for use during omp_in_parallel execution mode.
  3. Add the parallel_ad.cpp example.
  4. Change example_a11c.cpp example so that is just a correctness (not speed) test.


07-11
  1. Change the upper limit for omp_max_num_threads from 32 to 48.
  2. Add parallel documentation for, nan, Rosen34 , and Runge45 .
  3. Fix CheckNumericType and CheckSimpleVector so they work properly when used in parallel mode.


openmp/run.sh
The following changes were made to openmp/run.sh:
  2. Change to openmp/run.sh maximum number of threads instead of specifying the entire set of values to be tested.
  3. Change settings for newton_example so that n_gird is a multiple of the maximum number of threads.
  4. Report dynamic number of thread results as a separate result in the summary output line.
  5. Fix automatic removal of executables from openmp directory (was commented out).
  6. The documentation for openmp/run.sh was moved to the multi_thread section.


07-10
  1. Add link to Discrete AD Functions in multi_thread .
  2. Make use of the TrackNewDel routines omp_in_parallel execution mode an error (it never worked properly); see TrackNewDel multi-threading .
  3. Change memory_leak so that it checks for a leak in all threads. This is what openmp_newton_example.cpp and sum_i_inv_time.cpp assumed was being done.


07-09
All the OpenMP parallel execution requirements have been grouped in the section multi_thread .

07-07
Add the routine parallel_ad to fix bug when using AD<Base> in parallel execution mode.

06-23
  1. Fix a bug whereby the assert
         Error detected by false result for
              ! omp_in_parallel()
         at line     n in the file
             prefix/include/cppad/omp_alloc.hpp
     sometimes occurred.
  2. The routine omp_max_thread was deprecated, use the routine omp_max_num_threads instead.
  3. The deprecated routines have been grouped together in the deprecated section of the CppAD manual.


06-21
  1. The openmp/run.sh routine was changed to use zero, instead of automatic, for automatic choice of openmp/run.sh number of repeats and maximum number of threads.
  2. The output of each of the OpenMP examples / speed tests (run by openmp/run.sh) was changed to be valid matlab / octave assignment statements.
  3. In the case where OpenMP is enabled during compilation, a summary for the different number of threads as added at the end of the openmp/run.sh output.


06-18
  1. The tape_addr_type option was added to the configure command line.
  2. The function size_op_seq results uses sizeof(CppAD_TAPE_ADDR_TYPE) where it used to use sizeof(size_t).
  3. Remove cppad/config.h from CppAD distribution, (put the information in cppad/configure.hpp.) This removes the need to undefine symbols that were defined by cppad/config.h and that did not begin with CPPAD_.
  4. Change adolc library linkage so it works with version ADOL-C-2.2.0.


05-29
Fix bug (introduced on 05-22 ) whereby constructor might not be called (but required) when the base type is not plain old data.

05-28
  1. Add the omp_efficient routine to the omp_alloc system.
  2. Improve the omp_alloc tracing so it prints the same pointer as returned to the user (not an offset version of that pointer).


05-26
Fix Visual Studio project files that were broken during the change on 05-22. In addition, in the file cppad/omp_alloc.hpp, suppress the following Microsoft Visual Studio warning 
 
     warning C4345: behavior change: an object of POD type constructed with
     an initializer of the form () will be default-initialized

05-22
  1. The old memory tracking routines TrackNewDel have been deprecated. Their use should be replaced using the omp_alloc a memory allocator which is designed to work well in a multi-threading OpenMP environment; see purpose .
  2. The replacement of TrackNewDel by omp_alloc has been throughout the CppAD source code, including the examples that used TrackNewDel; namely, mul_level_adolc.cpp , mul_level_adolc_ode.cpp .
  3. The CppAD vector template class and the vectorBool class were modified to use the omp_alloc memory manager. This should improves its speed of memory allocation omp_in_parallel sections of a program.
  4. The speed_test argument size_vec call was by value, instead of by reference (as documented). This has been fixed and the call is now by reference.
  5. The capacity function has been added to the CppAD vector class.
  6. The simple vector element constructor and destructor description has been changed to explicitly specify that the default constructor is used to initialize elements of the array.
  7. The size_op_seq documentation has been improved to mention that the allocated memory may be larger.


05-11
  1. Avoid ambiguity in the definition of the complex isnan function.
  2. Errors during make test were not being detected. This has been fixed.


05-03
  1. If NDEBUG is not defined, the hasnan function is used to make sure that the results of any Forward operation does not contain a nan (not a number). If so, an error message is generated and the program terminates. This error message and termination can be caught; see ErrorHandler .
  2. In the event that the cppad_ipopt_nlp objective function, the constraints, or their derivatives are infinite, an error message is generated and the program terminates (proved that NDEBUG is not defined and the default error handler has not been replaced).


04-29
  1. The Microsoft Visual Studio 2003 project files for the Windows examples and tests no longer worked because the current version of CppAD uses local types in template instantiation; see Compiler Error C2918 . These project files were converted to Visual Studio 2008 where they do work (if you use a later version, Visual Studio should automatically convert them for you).
  2. The old speed test directory was moved to speed_cppad before the new speed test organization was created on 2006-12-11 (revision 715 of the repository). The old speed tests have not been used for years and so have been deleted.


04-20
The openmp/run.sh script what changed to take an argument that specifies which tests is run (it no longer runs all the tests). Also improve the openmp test program output formatting.

04-19
The use_ad option was added to the openmp_newton_example.cpp test case.

03-19
The subversion write protected directory bin/.svn was mistakenly part of the compressed tar file . It has been removed.

03-11
The vector of sets argument r to the old_atomic function rev_hes_sparse must have size greater than or equal to n . There was a check that its size was greater than or equal q . This was incorrect and has been fixed.

03-05
Add the conjugate gradient example.

02-22
Add the atomic option to the speed test program and use old_mat_mul.hpp during the cppad_mat_mul.cpp speed test when the atomic option is specified.

02-19
There was a bug when omp_max_thread was set to one, and NDEBUG was not defined, the thread corresponding to parameters was one, but the only valid thread number was zero (only one thread) and an CPPAD stopped with an assertion error. This has been fixed.

02-17
There was a mistake in openmp/run.sh where it attempted to remove a non-existent file in the case where openmp/run.sh openmp_flag was not "". This has been fixed.

02-15
A matrix multiply speed test has been added. So far, this has only implemented for the cppad and double cases. (For the time being this test is not available for the other speed comparison cases.)

02-09
A variable in old_atomic.hpp was declare of type Base when it should have been declared of type size_t. It caused the old_atomic feature to fail with some base types. This has been fixed.

The old_mat_mul.hpp example has been improved by caching the x variable information and using it during reverse Hessian sparsity calculations.

Some of the old_atomic documentation was extended to include more explanation.

02-06
The use can now define complex atomic operations and store them in a CppAD ADFun object. This item has been remove from the wish list .

The documentation for RevSparseHes had a dimension error. This has been fixed.

A faster set operations item was added to the wish list. This has since been satisfied by cppad_sparse_list choice during the install process (since removed).

02-02
The documentation for ForSparseJac had some formatting errors. The errors have been fix and the documentation has been improved.

02-01
The subversion install instructions were brought up to date. They have since been replaced by just separate subversion instructions.

01-19
The directory where the pkgconfig file cppad.pc is stored has been moved from prefixdir/lib/pkgconfig/cppad.pc to prefixdir/share/pkgconfig/cppad.pc ; see devel@lists.fedoraproject.org .

01-16
The following have been fixed:
  1. The install of the documentation failed when it was done from a directory other than the top source directory.
  2. The GPL distribution had the output of the configure command in it.
  3. Since the change on 01-09, the file omh/whats_new_11.omh has been required to build the documentation (and it has been missing from the distribution).
  4. Fadbad was generating warnings due to the -Wshadow flag with the g++ compiler. The Fadbad speed tests have a special flag with this warning removed from the cxx_flags .


01-09
There were some problems running make test in the releases
http://www.coin-or.org/download/source/CppAD/cppad-20110101.0.license.tgz
 where license is gpl or cpl.
  1. The version of automake used to build the corresponding makefile.in files did not define abs_top_builddir.
  2. The include file cppad_ipopt_nlp.hpp was always installed, even if ipopt_dir was not defined on the configure command line.
  3. The speed test library libspeed.a was being installed (it is only intended for testing).
These problems are fixed in the trunk and these fixes will be copied to the corresponding stable and release versions; i.e.,
http://www.coin-or.org/download/source/CppAD/cppad-20110101.1.license.tgz
 will not have this problem.
Input File: omh/whats_new/whats_new_11.omh cppad-20170000.3/doc/whats_new_10.xml0000644000175200017650000005410213057470510016214 0ustar coincoin-web Changes and Additions to CppAD During 2010
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Changes and Additions to CppAD During 2010

Introduction
This section contains a list of the changes to CppAD during 2010 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-31
  1. Add specifications for the CppAD pkgconfig files.
  2. Update the CppAD README file.
  3. Move most all CppAD development shell scripts to the bin subdirectory of the distribution directory.
  4. Fix warnings generated by the g++ compiler option -Wshadow; for example, sparse_pack.hpp:101:2: warning: declaration of 'end' shadows a member of 'this'


11-27
If NDEBUB was defined, the default CppAD error handler would return because its assert had no effect in this case. This has been fixed by placing a call to std::exit(1) after its assert.

09-26
There was a bug (introduced on 09-22) in make test when the configure command was executed from a directory other than the distribution directory (the cppad_ipopt_nlp did not build). This has been fixed.

09-22
Promote cppad_ipopt_nlp from an example to a library that gets installed (provided that the ipopt_dir is specified on the configure command line).

08-21
Fix problems with linking of cppad_ipopt_nlp test with both older and newer versions of ipopt.

07-14
The new versions of ipopt use pkg-config to record the location where its necessary libraries are stored on the system. The cppad configure command has been improved so that it can work both with versions of ipopt that use pkg-config and ones that don't.

07-11
Old versions of the ipopt library were located in ipopt_dir/lib/libipopt.* (see ipopt_dir ), but newer versions will be located in ipopt_dir/lib/coin/libipopt.* . The directory ipopt_dir/lib/coin has been added to the library search path so that the cppad_ipopt_nlp examples work with both old and new versions of ipopt.

06-01
In the case where the preprocessor symbol NDEBUG was defined (see speed ), the function
     CheckSimpleVector(const Scalar& x, const Scalar& y)
 was not defined; see bug report . This has been fixed.

04-28
Change the multi-level taping examples mul_level.cpp and mul_level_adolc.cpp to be more efficient.

04-26
Include Blas and Linpack libraries in makefile links for cppad_ipopt_nlp examples. This removes the need to use get.Blas when building Ipopt.

The speed test in cppad_ipopt/speed was missing a link to the library ../src/libcppad_ipopt.a. This has been fixed.

04-24
There was a bug in the error checking done by cppad/local/sub_op.hpp that caused the following improper abort:
Error detected by false result for
    arg[1] < i_z
at line 337 in the file
    .../include/cppad/local/sub_op.hpp
 This was fixed in the trunk. It was also fixed in the release with version number 20100101.3 which can be downloaded from the CppAD download directory .

04-01
Some of the speed_utility library (in speed/src) was being compiled for debugging. This has been changed and they are now compiled with debugging off and optimization on.

03-11
The old reverse_any example was moved to reverse_three.cpp , the old checkpoint example is now the general case reverse example, and a better checkpoint.cpp/ example was created.

03-10
The optimize routine would mistakenly remove some expressions that depended on the independent variables and that affected the result of certain CondExp operations. This has been fixed.

03-09
Extend reverse_any so that it can be used for checkpointing ; i.e., splitting reverse mode calculations at function composition points.

03-03
Fixed a bug in handling vector of boolean sparsity patterns. (when the number of elements per set was a multiple of sizeof(size_t)).

02-11
The speed directory has been reorganized and the common part of the link functions , as well as the microsoft_timer , have been moved to the subdirectory speed/src where a library is built.

02-08
A bug was introduced in the 02-05 change whereby the make command tried to build the libcppad_ipopt.a library even if IPOPT_DIR was not specified on the configure command line. This has been fixed.

02-06
The Microsoft project files for the speed tests were extended so that the worked properly for the Release (as well as the Debug) configuration. (This required conversion from Visual Studio Version 7 to Visual Studio 2008 format.)

Add an automated check for optimize bug fixed on 02-05. (Automatic checking for PrintFor bug was added on 02-05.)

02-05
  1. Simplify running all the tests by adding the make test command.
  2. Simplify the configure command by removing need for: --with-Speed, --with-Introduction, --with-Example, --with-TestMore, and --with-PrintFor.
  3. Add files that were missing in the Microsoft Visual Studio projects.
  4. Fix two significant bugs. One in the optimize command and the other in the PrintFor command.


02-03
Fix a mistakes in the test bender_quad.cpp . In addition, the optimize routine was used to reduce the tape before doing the calculations.

The routine opt_val_hes was added as an alternative to BenderQuad .

01-26
Another speed improvement was made to cppad_ipopt_nlp . To be specific, the Lagragian multipliers where checked and components that were zero were excluded form the Hessian evaluation.

01-24
It appears that in cppad_ipopt_nlp , when retape[k] was true, and L[k] > 1, it was possible to use the wrong operation sequence in the calculations (though a test case that demonstrated this could not be produced). This is because the argument value to r k ( u ) depends on the value of ℓ in the expression r k ∘ [ J k , ℓ ⊗ n ] ( x ) (even when the value of x does not change).

There was a bug in the ipopt_nlp_ode_check.cpp program, for a long time, that did not show up until now. Basically, the check had code of the was using an undefined value. This has been fixed.

01-23
Improve the sparsity patterns and reduce the amount of memory required for large sparse problems using cppad_ipopt_nlp . The speed test cppad_ipopt/speed showed significant improvement.

01-20
We plan to split up the ipopt_cppad/src/ipopt_cppad_nlp.hpp include file. In preparation, the example ipopt_cppad has been changed to cppad_ipopt. This will facilitate using CPPAD_IPOPT_* for the # ifdef commands in the new include files (note that they must begin with CPPAD).

01-18
The ipopt_cppad subdirectory of the distribution has been split into an src, example, and speed subdirectories. The example (speed) subdirectory is where one builds the ipopt_cppad_nlp examples (speed tests ).

01-04
The following items have been fulfilled and hence were removed for the wish_list :
  1. If an exception occurs before the call to the corresponding ADFun constructor or Dependent , the tape recording can be stopped using abort_recording .
  2. A speed test for ipopt_cppad_nlp was added; see ipopt_ode_speed.cpp .
  3. The optimize command uses hash coding to check when an expression is already in the tape and can be reused.
  4. The optimize command removes operations that are not used by any of the dependent variables.
  5. The ad_in_c.cpp example demonstrates how to connect CppAD to an arbitrary scripting language.
  6. The vector of sets option has been added to sparsity calculations; see sparsity pattern .
Input File: omh/whats_new/whats_new_10.omh cppad-20170000.3/doc/whats_new_09.xml0000644000175200017650000011115513057470510016226 0ustar coincoin-web Changes and Additions to CppAD During 2009
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Changes and Additions to CppAD During 2009

Introduction
This section contains a list of the changes to CppAD during 2009 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD. (Comments about developer documentation are only important if you are trying to read and understand the CppAD source code.)

12-23
The ADFun assignment operator was changed so that it now copies forward mode Taylor coefficients and sparsity pattern information. (This assignment operator was added on 10-24 .) You can use capacity_order to delete the Taylor coefficients before copying them. Two new functions were added so that you can query and delete the forward mode sparsity information; see size_forward_bool and size_forward_set .

12-22
Convert the optimization of a sequence of additions from multiple operators to one operator with a varying number of arguments. This improved the speed for forward and reverse mode computations of an optimized tape.

12-18
It turns out that detection of a sequence of additions makes the optimization longer. This was simplified and makes slightly faster by converting two jointly recursive routines to one non-recursive routine that uses a stack for the necessary information. More work is planned to make this optimization faster.

12-12
Detection of a sequence of additions that can be converted to one variable during the optimize process. This leads to a significant improvement in the tape size and speed.

12-04
Change hash coding of parameter values as part of operators during the optimize process. This should leads to more detection and removal of duplicate operations.

12-02
Fix minor grammatical error in the Purpose heading for conditional expressions .

Add the following functions: size_op , size_op_arg , and size_op_seq . In addition, improve and extend the seq_property.cpp example.

11-28
Fix bug in tape optimization with VecAD objects.

11-27
Remove duplicate expressions for the commutative binary operators; i.e., addition and multiplication.

11-26
Improve optimize command so that it removes some duplicate expressions from the tape (more of this is planned).

10-30
Make program that check Ipopt ODE example correctness a separate file ipopt_nlp_ode_check.cpp Split out Ipopt driver for ODE example ipopt_nlp_ode_run.hpp . Add the speed testing problem ipopt_cppad/ipopt_ode_speed.cpp.

10-29
Split out the ode inverse problem , its simple representation , and its fast representation , as a separate files; to be specific, ipopt_nlp_ode_problem.hpp , ipopt_nlp_ode_simple.hpp , ipopt_nlp_ode_fast.hpp , and ipopt_nlp_ode_check.cpp .

10-28
Improve the documentation for ipopt_nlp_ode_simple and ipopt_nlp_ode_fast .

10-27
Moved old ipopt_cppad_simple.cpp to ipopt_nlp_get_started.cpp , created the example ipopt_nlp_ode_simple.hpp , and split and ipopt_cppad_ode.cpp into ipopt_nlp_ode_fast.hpp and ipopt_nlp_ode_check.cpp .

10-24
Added the assignment operator to the ADFun object class. This makes a copy of the entire operation sequence in another function object. The intention is that the two functions objects can do calculations in parallel. In addition, CppAD now check for the ADFun copy constructor and generates an error message if it is used.

10-23
The sparse_hessian routine was extended so the user can now choose between vectors of sets and boolean vectors for representing sparsity patterns .

10-21
The CheckSimpleVector function was extended so that it can check simple vectors where the elements of the vector can not be assigned to integer values. This was done by adding the x, y arguments to CheckSimpleVector.

10-16
The sparse_jacobian routine was extended so the user can now choose between vectors of sets and boolean vectors for representing sparsity patterns .

10-14
The packed parameter for the sparsity routines ForSparseJac , RevSparseJac , and RevSparseHes (introduced on 09-26 ) has been removed. It has been replaced by changing the argument and return values to be more versatile. To be specific, they can now represent sparsity using vectors of std::set<size_t> instead of just as vectors of bool (see sparsity patterns ).

10-03
The Microsoft Visual Studio project files for examples and testing and for more correctness testing were not including some new tests in their builds. This has been fixed.

09-30
Added the cppad_sparse_jacobian.cpp speed test and increased the sizes used by link_sparse_hessian . Some mistakes were fixed in the documentation for speed tests link_sparse_hessian and sparse_hes_fun .

09-29
The documentation definition of the function H ( x ) in RevSparseHes was missing a factor of R . This has been fixed.

09-28
Changed RevSparseHes so that it uses a sparse representation when the corresponding call to ForSparseJac used a sparse representation. This should have been included with the change on 09-26 because Hessian sparsity patters after ForSparseJac with packed did not work. Thus, this could be considered a bug fix.

09-26
Added the packed parameter to ForSparseJac and RevSparseJac . If packed is false, a sparse instead of packed representation is used during the calculations of sparsity patterns. The sparse representation should be faster, and use less memory, for very large sparse Jacobians. The functions ForSparseJac and RevSparseJac return packed representations. The plan is to eventually provide new member functions that return sparse representations.

09-20
Fixed a bug in the Hessian Sparsity calculations that included use of VecAD objects.

09-19
Some more memory allocation improvements (related to those on 09-18) were made.

09-18
A bug was found in all the Sparsity calculations. The result was that eight times the necessary memory was being used during these calculations. This has been fixed.

08-25
Add ad_fun.cpp an example of how to create your own interface to an ADFun object.

08-14
Add ad_in_c.cpp an example of how to link CppAD to other languages.

08_13
Add an option to optimize an operation sequence.

Begin Merge
of changes from the directory branches/optimize in the CppAD subversion repository. The subheading dates below represent when the correspond change was made in branches/optimize.

08-13
An automatic check of the forward_zero results was added after each call to f.optimize() (this check is skipped when NDEBUG is defined). In addition, all of the speed/cppad/*.cpp tests now check and use the speed test optimize flag.

08-11
Change the speed test main program so that it uses a list of options instead of a boolean flag for each option. This will make it possible to add options in the future with out having to change all the existing tests because the options are now global variables instead of arguments to the speed test routines; for example, see retape speed test option.

08-10
The routine for optimizing the operation sequence has been added has been further tested using test_more/optimize.cpp. Some bugs have been fix and the routine can now be trusted to work correctly.

The function size_VecAD function was added so that the user could see the VecAD vectors and elements corresponding to an operation sequence.

08-09
A routine for optimizing the operation sequence has been added. This is a preliminary version and needs more testing before it can be trusted to work correctly.
End Merge

08-06
Add hash table coding to reduce the number of copies of the same parameter value necessary in a tape recording. In addition, add the function size_par was added so that the user could see the number of parameters corresponding to an operation sequence.

08-02
Fix bug in new version of how ForSparseJac handles VecAD objects.

Fix bug in overnight build where HTML version and entire documentation as one page versions of documentation were not being built.

Fix missing new line under Using Value heading for simple vector documentation.

08-01
Fix bug in reverse mode Jacobian sparsity for VecAD objects.

07-31
The forward and reverse sparse Jacobian routines have been improved so the resulting sparsity patterns are valid for all values of the independent variables (even if you use CondExp or VecAD ).

07-26
Convert developer documentation from forward and reverse mode sweep routines from OMhelp to doxygen.

07-25
Add developer documentation for PrintFor operations.

07-24
Add developer documentation for Discrete operations.

07-23
Add developer documentation for tape evaluation of VecAD store operations. (a store operation changes the value of a VecAD element).

Improve the vec_ad.cpp user example.

07-06
Fixed a bug in second or higher order reverse mode calculations that used VecAD . This bug was demonstrated by the test case SecondOrderReverse in the file test_more/vec_ad.cpp.

Add developer documentation for tape evaluation of the VecAD load operations (a load operation accesses an element of the vector but does not change it.)

Fix isnan undefined in example/cond_exp.cpp error introduced on 07-04 change.

07-04
Add developer documentation for the CompareChange operations during tape evaluation.

Begin Merge
of changes from the directory branches/sweep in the CppAD subversion repository. The subheading dates below represent when the correspond change was made in branches/sweep.

07-04
Fixed a bug in second or higher order reverse mode calculations that included conditional expressions . This bug was demonstrated by the test case SecondOrderReverse in the file test_more/cond_exp.cpp.

A simpler and useful example was provided for conditional expressions ; see cond_exp.cpp .

07-03
Some minor improvements were made to the documentation for CondExp . To be specific, a newer OMhelp option was used to change the formatting of the syntax, some of the argument names were changed to be more descriptive.

07-02
Add developer doxygen documentation of tape evaluation for power (exponentiation) operators.

07-01
Fix an example indexing error in introduction/exp_apx/exp_eps_for2.cpp (found by valgrind).

Add developer doxygen documentation of tape evaluation for multiplication and division operators.

06-30
Add developer doxygen documentation of tape evaluation for addition and subtraction operators.

06-29
Add developer doxygen documentation of tape evaluation for sin, sinh, cos, and cosh.

06-28
Add developer doxygen documentation of tape evaluation for atan, asin, acos, sqrt, log.
End Merge

06-25
The tarball for most recent release (of the subversion trunk for CppAD) was not being placed in the download directory. This has been fixed.

06-22
Fix compiler warnings during the openmp/run.sh test.

Changed speed_example.cpp to omit the speed_test from the correctness result. In stead, a message is printed explaining that timing tests need to be run without a lot of other demands on the system.

06-21
The configure instructions for ipopt_dir had the wrong path for IpIpoptApplication.hpp. This has been fixed.

06-20
Upgrade to from autoconf 2.61 to 2.63, and from automake 1.10.1 to 1.11.

Fix conflict between CppAD's use of config.h preprocessor symbols and other packages use of the same symbol names.

06-06
  1. Using complex of an AD type (instead of AD of complex) was not working correctly in not_complex_ad.cpp because the default constructor for an AD object has an unspecified value. This has been fixed for the complex type by changing the default constructor to use value zero. (The not_complex_ad.cpp example has been removed; see complex FAQ .)
  2. Fixing the not_complex_ad.cpp problem above also fixed a warning generated by valgrind . Now valgrind runs the CppAD example/example program with out any warning or error messages. In addition, a minor initialization error was fixed in the test_more/jacobian.cpp routine so now valgrind also runs the CppAD test_more/test_more program with out any warnings or error messages.


05-20
A change was make to the trunk on 05-19 (svn revision 1361) that broke the Unix install procedure. This was has been fixed (revision 1362).

03-24
Added cross references in the examples to occurrence of the following tokens: AD , ADFun , CPPAD_TEST_VECTOR , Forward , Independent , Jacobian NearEqual , Reverse .

02-20
Demonstrate using AD to compute the derivative of the solution of an ODE with respect to a parameter (in the runge45_2.cpp example).

02-15
Change the distribution compressed tar file to only contain one copy of the documentation. Link to the current Internet documentation for the other three copies.

02-01
Move the Prev and Next buttons at the top of the documentation to the beginning so that their position does not change between sections. This makes it easier to repeatedly select this links.

01-31
Modify cppad/local/op_code.hpp to avoid incorrect warning by g++ version 4.3.2 when building pycppad (a python interface to CppAD).

01-18
Sometimes an error occurs while taping AD operations. The abort_recording function has been added to make it easier to recover in such cases.

Previously, CppAD speed and comparison tests used Adolc-1.10.2. The version used in the tests has been upgraded to Adolc-2.0.0.

A discussion has been added to the documentation for Jacobian about its use of forward or reverse mode depending on which it estimates is more efficient.

A minor typo has been fixed in the description of W(t, u) in reverse_any . To be specific, o ( t p -1 ) * t 1 - p → 0 has been replaced by o ( t p -1 ) / t 1 - p → 0 .

01-06
Made some minor improvements to the documentation in FunConstruct .
Input File: omh/whats_new/whats_new_09.omh cppad-20170000.3/doc/whats_new_08.xml0000644000175200017650000010204613057470510016224 0ustar coincoin-web Changes and Additions to CppAD During 2008
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Changes and Additions to CppAD During 2008

Introduction
This section contains a list of the changes to CppAD during 2008 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-19
In the documentation for pow_int change the integer exponent from int y to const int &y . In the implementation for pow make the integer base case agree with the documentation; i.e., change from int x to const int &x .

12-14
Added another test of mul_level calculations (in the test_more directory).

12-04
Extensive explanation for the ipopt_cppad/ipopt_cppad_ode example was provided in the section ipopt_cppad_ode .

11-22
The CppAD interface to the Ipopt nonlinear programming solver cppad_ipopt_nlp has been moved from example/ipopt_cppad_nlp to ipopt_cppad/ipopt_cppad_nlp.

11-21
The Microsoft's Visual C++ Version 9.0 generates a warning of the form warning C4396:%...% for every template function that is declared as a both a friend and inline (it thinks it is only doing this for specializations of template functions). The warnings are no longer generated because these inline directives are converted to empty code when a Microsoft Visual C++ is used.

11-20
The function tanh(x) was added to the unary_standard_math functions. The abs and erf functions were removed from the Base requirements . The restrictions about the Base class were removed from abs , atan2 , LuRatio , erf .

Visual Studio Version 9.0 could not handle the large number of static constants in the CppAD erf function. This function was changed to a simpler representation that is much faster and that is differentiable at all points (not defined differently on subregions). The down side to this is that the new version is not as accurate.

10-27
Change prototypes for ipopt_cppad/ipopt_cppad_ode helper routines to use const (where appropriate).

10-17
Major improvements to the ipopt_cppad/ipopt_cppad_ode example.

10-16
Minor improvement to description of optimization argument in ipopt_cppad/ipopt_cppad_ode.

09-30
Add or modify some wish list entries; see cppad_ipopt_nlp (since removed), multiple argument forward (completed with forward_dir ), and sparsity patterns (sparsity patterns has been fulfilled).

09-26
Use parenthesis and brackets to group terms of the form m × I to make the documentation of ipopt_cppad_nlp easier to read. Changed ipopt_cppad/ipopt_cppad_ode to use y ( t ) for the solution of the ODE to distinguish it for x , the vector we are optimizing with respect to.

09-18
Changed ipopt_cppad/ipopt_cppad_ode to a case where x ( t ) is a pair of exponential functions instead of a linear and quadratic. Fixed some of the comments in this example and included the source code in the documentation (which was missing by mistake).

09-17
Changed ipopt_cppad/ipopt_cppad_ode to a case where there are two components in the ODE (instead of one). Also removed an initialization section that was only intended for tests with a specific initial value.

09-16
Add ipopt_cppad/ipopt_cppad_ode, an example and test that optimizes the solution of an ODE. Change r_eval to eval_r in ipopt_cppad_nlp . Fix a dimension of u_ad error in ipopt_cppad_nlp.

09-12
Converted from storing full Hessian and Jacobian to a sparse data structure in ipopt_cppad_nlp . This greatly reduced the memory requirements (and increased the speed) for sparse problems.

09-10
Fixed more indexing bugs in ipopt_cppad_nlp that effected cases where the domain index vector J k , ℓ was different for different values of k and ℓ .

In ipopt_cppad_nlp , combined fg_info->domain_index() and fg_info->range_index() into a single function called fg_info->index() . Also added more error checking (if NDEBUG is not defined).

09-09
Fixed an indexing bug in ipopt_cppad_nlp . (This effected cases where the domain index vector J k , ℓ was different for different values of k and ℓ .)

09-07
Change ipopt_cppad_nlp so that object and constraints are expressed as the double summation of simpler functions. This is more versatile that the single summation representation.

09-06
Checked in a major change to ipopt_cppad_nlp whereby the object and constraints can be expressed as the sum of simpler functions. This is the first step in what will eventually be a more versatile representation.

09-05
Fix bug in ipopt_cppad_nlp (not recording the function at the proper location. Here is the difference that occurred multiple places in the ipopt_cppad/ipopt_cppad_nlp.cpp source: 
 
     for(j = 0; j < n_; j++)
-         x_ad_vec[0] = x[j];
+         x_ad_vec[j] = x[j];
This did not show up in testing because there currently is no test of ipopt_cppad_nlp where the operation sequence depends on the value of x .

Changed eval_grad_f in ipopt_cppad_nlp.cpp to be more efficient.

09-04
The ipopt_cppad_nlp interface has been changed to use a derived class object instead of a pointer to a function.

09-03
The ipopt_cppad_nlp interface has been changed to use size_t instead of Ipopt::Index.

09-01
Back out the changes made to ipopt_cppad_nlp on 08-29 (because testing proved the change to be less efficient in the case that motivated the change).

08-29
The push_vector member function was missing from the vectorBool class. This has been fixed. In addition, it seems that for some cases (or compilers) the assignment
     x[i] = y[j]
 did not work properly when both x and y had type vectorBool. This has been fixed.

The ipopt_cppad_nlp example has been extended so that it allows for both scalar and vector evaluation of the objective and constraints; see the argument fg_vector in ipopt_cppad_nlp . In the case where there is not a lot of common terms between the functions, the scalar evaluation may be more efficient.

08-19
Add push of a vector to the CppAD::vector template class. This makes it easy to accumulate multiple scalars and simple vectors into one large CppAD::vector.

08-08
There was an indexing bug in the ipopt_cppad_nlp example that affected the retape equal to false case. This has been fixed. In addition, the missing retape documentation was added.

07-02
Extend configure command to check for extras libraries that are necessary for linking the ipopt example.

06-18
Add specifications for the Ipopt class ipopt_cppad_nlp . This is only an example class it may change with future versions of CppAD.

06-15
The nonlinear programming example ipopt_nlp_get_started.cpp was added. This is a preliminary version of this example.

06-11
The sparsity pattern for the Hessian was being calculated each time by SparseHessian . This is not efficient when the pattern does not change between calls to SparseHessian. An optional sparsity pattern argument was added to SparseHessian so that it need not be recalculated each time.

06-10
The sparsity pattern for the Jacobian was being calculated each time by SparseJacobian . This is not efficient when the pattern does not change between calls to SparseJacobian. An optional sparsity pattern argument was added to SparseJacobian so that it need not be recalculated each time.

05-08
The sparse_jacobian routine has been added.

The example in sparse_hessian pointed to hessian.cpp instead of sparse_hessian.cpp . This has been fixed.

05-03
The retape flag has been added to speed_main . In addition the routines link_det_minor , link_poly , and link_ode pass this flag along to the speed test implementations (because the corresponding tests have a fixed operation sequence). If this flag is false, a test implementation is allowed to just tape the operation sequence once and reuse it. The following tests use this flag: adolc_det_minor.cpp , cppad_det_minor.cpp , cppad_ode.cpp , adolc_poly.cpp , cppad_poly.cpp .

Create specialized zero order forward mode routine that should be faster, but does not test out as faster under cygwin g++ (GCC) 3.4.4.

04-20
Added the ode_evaluate speed test utility in preparation for having ode speed tests. Created ode speed test for the cppad and double cases; see speed_main . In addition, added the examples ode_evaluate.cpp and sparse_hessian.cpp .

Changed the speed_main routines defined for each package from compute_name to link_name . For example, in speed/cppad/det_minor.cpp, the function name compute_det_minor was changed to link_det_minor.

04-18
Fix a problem in the link_poly correctness test. Also add double_sparse_hessian.cpp to the set speed and correctness tests (now available).

04-10
Change all the Adolc speed examples to use TrackNewDel instead of using new and delete directly. This makes it easy to check for memory allocation errors and leaks (when NDEBUG is not defined). Also include in documentation sub functions that indicate the sparse_hessian speed test is not available for double_sparse_hessian.cpp , fadbad_sparse_hessian.cpp , and sacado_sparse_hessian.cpp .

04-06
The following wish list entry has been completed and removed from the list: "Change private member variables names (not part of the user interface) so that they all end with an underscore."

04-04
Fix a problem compiling the speed test main program with gcc 4.3.

03-27
Corrected cppad_sparse_hessian.cpp so that it uses the sparse case when USE_CPPAD_SPARSE_HESSIAN is 1. Also added a wish list sparsity pattern entry (the sparsity pattern entry has been fulfilled).

Change the name of speedtest.cpp to speed_program.cpp .

02-05
Change windows install instructions to use Unix formatted files (so only two instead of four tarballs are necessary for each version). The Microsoft project files for speed/cppad, speed/double, and speed/example were missing. This has also been fixed.

02-03
There was an ambiguity problem (detected by g++ 4.3) with the following operations
     x op y
 where x and y were AD<double> and op was a member operator of that class. This has been fixed by making all such member functions friends instead of members of AD<double>.

Remove computed assignment entry from wish list (it was fixed on 2007-05-26 ). Add an expression hashing entry to the wish_list (it has since been removed). Add Library and Scripting Languages to the wish list (this has since been fulfilled by the example ad_in_c.cpp ).

01-26
The LuFactor routine gave a misleading error message when the input matrix had not a number or infinity in it. This has been fixed.

01-24
The postfix_dir has been added to the configure command line options.

01-21
A sparse Hessian case was added to the speed tests; see sparse_hessian .

01-20
CppAD can now be installed using yum on Fedora operating systems.

01-11
The CppAD correctness tests assume that machine epsilon is less than 1e-13. A test for this has been added to the test_more/test_more program.

01-08
Added a sparse_hessian routine and extended Hessian to allow for a weight vector w instead of just one component l .
Input File: omh/whats_new/whats_new_08.omh cppad-20170000.3/doc/whats_new_07.xml0000644000175200017650000017644213057470510016236 0ustar coincoin-web Changes and Additions to CppAD During 2007
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Changes and Additions to CppAD During 2007

Introduction
This section contains a list of the changes to CppAD during 2007 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-29
License conversions missed the copyright message at the top in the following special cases: makefile.am, makefile.in, and omh/license.omh.

12-25
The install instructions have been improved.

12-21
The --with-Documentation option on the configure command line caused an error on some systems because it attempted to copy to many files. This has been fixed by copying the directory instead of the individual files.

12-08
By mistake, the documentation License statement for the GPL distribution was the same as for the CPL distribution. This has been fixed.

12-05
Change the name of the spec file from cppad-yyyymmdd.spec to cppad.spec.

12-04
Add the capability for the RPM spec file to use a different prefix directory.

12-03
This is the first version with the rpm spec file cppad.spec.

12-02
Add the DESTDIR=directory option on the make install command line.

11-29
The unary_standard_math function sqrt did not link properly when Base was AD<double>. This has been fixed.

11-23
The routines nan and isnan were failing for some systems because they use nan and or isnan as preprocessor symbols. This has been fixed; see macros . In addition, the example and test nan.cpp has been added.

11-18
Speed tests for tape_values branch were not better than trunk, so the good parts of that branch (but not all) were merged into the trunk.

The interface specifications for base type requirements have been changed so that CppAD would compile with gcc 4.1.1 (which requires more definitions before use in template functions). This changed of requirements is demonstrated by the base_complex.hpp and base_adolc.hpp examples.

The problem with newer C++ compilers requiring more definitions before use also required the user to know about float and double definitions for the standard math functions in the CppAD namespace; see base_std_math .

The example/test_one.sh and test_more/test_one.sh scripts were modified so that one only need specify the test file name (does not also need the test routine name). Some of the test routine declarations were changed from name() to name(void) to make this possible.

The program test_more/test_more was changed to always report the memory leak test results (same as example/example).

The PrintFor function was putting an unused variable in the tape. This has been fixed.

11-06
Added the -DRAD_EQ_ALIAS compiler flag to the Sacado speed tests . In addition, compiler flag documentation was included for Sacado and all the other speed tests.

11-05
MS project files have been added for running the cppad and double speed tests.

11-04
The cppad/config.h file was not compatible with the Windows install procedure and the Windows project's could not find a certain include file. This has been fixed.

The unix install procedure has been modified so that the one configure flag --with-Speed builds all the possible executables related to the speed testing.

11-03
Improve the speed_main documentation and output (as well as the title for other sections under speed ).

The subversion copy of the configure script was not executable. This has been fixed.

11-02
The instructions for downloading the current version using subversion have changed. The user should now directly edit the file 
 
     trunk/configure
in order to set the correct date for the installation and to build the corresponding documentation.

The speed section has been slightly reorganized (the main program and utilities have been separated).

Add speed_double for testing the speed of evaluating functions in double as apposed to gradients using AD types.

11-01
The instructions for downloading the current version using subversion have changed. The user must now execute the command 
 
     ./build.sh version
in order to set the correct version number for her (or his) installation.

Add the return status for all the correctness tests to the documentation; see make test.

10-30
The download instructions did not update current version number and this broke the links to the current tarballs. This has been fixed.

The documentation for det_by_minor and det_by_lu has been improved. The order of the elements in det_of_minor has been corrected (they were transposed but this did not really matter because determinants of transposes are equal).

The makefiles in the distribution have been changed so that one can run configure from a directory other than the distribution directory.

10-27
A subversion method for downloading CppAD has been added.

The installation was broken on some systems because the configure command tried to run the autoconf and automake programs. This has been fixed by adding AM_MAINTAINER_MODE to the autoconf input file.

Extend the subversion methods to include a full installation and old versions.

10-23
The cxx_flags environment variable has been changed from CPP_ERROR_WARN to CXX_FLAGS.

The command configure --help now prints a description of the environment variables ADOLC_DIR, FADBAD_DIR, SACADO_DIR, BOOST_DIR, and CXX_FLAGS. In addition, if the environment variables POSTFIX_DIR or CPP_ERROR_WARN are used, an message is printed saying that are not longer valid.

10-22
The correctness checks and speed test wrappers were moved from the individual package directories to speed_main . This way they do not have to be reproduced for each package. This makes it easier to add a new package, but it requires the prototype for compute_test_name to be the same for all packages.

The Sacado package was added to the list of speed tests. In addition, the discussion about how to run each of the speed tests was corrected to include the seed argument.

The postfix_dir option was removed on 2006-12-05 but it was not removed from the configure documentation. This has been fixed.

The routine CheckSimpleVector was changed. It used to require conversion of the form
     Scalar(i)
 where i was 0 or 1. This does not work with when Scalar is Sacado::Tay::Taylor<double>. This requirement has been changed (see restrictions ) to support of
     x = i
 where x has type Scalar and i has type int.

Fix include directives in speed_fadbad programs det_lu, det_minor, and poly, to use FADBAD++ instead of Fadbad++ directory.

Add ADOLC_DIR, FADBAD_DIR, SACADO_DIR, and BOOST_DIR to the configure help string.

10-16
Add seed argument and improve speed_main documentation.

10-13
Fix the title in adolc_det_lu.cpp . Add the package name to each test case result printed by speed_main .

10-05
Added and example using complex calculations for a function that is not complex differentiable not_complex_ad.cpp. (This example has been removed; see complex FAQ .)

10-02
Extend the pow function to work for any case where one argument is AD<Base> and the other is double (as do the binary operators).

09-06
If the method.step function returned nan (not a number), it was possible for OdeErrControl to drop into an infinite loop. This has been fixed.

08-09
Let user detect and handel the case where an ODE initial vector xi contains not a number nan (see Runge45 , Rosen34 , and OdeErrControl ).

Use the || operation instead of | operator in the nan function (The Ginac library seems to use an alias for the type bool and does not have | defined for this alias).

The file test_more/ode_err_control.cpp was using the wrong include file name since the change on 08/07. This has been fixed.

08-07
Sometimes an ODE solver takes to large a step and this results in invalid values for the variables being integrated. The ODE solvers Runge45 and Rosen34 have been modified to abort and return nan when it is returned by the differential equation evaluation. The solver OdeErrControl have been modified to try smaller steps when this happens.

Fix an Sequence Constructor referenced to Dependent in documentation (was using the FunDeprecated one argument syntax).

Add comment about mixing debug and non-debug versions of CppAD in TrackDelVec error message.

07-30
CppADCreateBinaryBool and CppADCreateUnaryBool have been replaced by CPPAD_BOOL_BINARY and CPPAD_BOOL_UNARY respectively. In addition, the wish_list item for conversion of all preprocessor macros to upper case been completed and removed.

07-29
The preprocessor macros CppADUsageError and CppADUnknownError have been replaced by CPPAD_ASSERT_KNOWN and CPPAD_ASSERT_UNKNOWN respectively. The meaning for these macros has been included in the cppad_assert section. In addition, the known argument to ErrorHandler was wrong for the unknown case.

The wish_list item for conversion of all preprocessor macros to upper case has been changes (to an item that was previous missing).

07-28
The preprocessor macro CPPAD_DISCRETE_FUNCTIOIN was defined as a replacement for CppADCreateDiscrete which has been deprecated.

07-26
Merge in changes made in branches/test_vector.

07-26
Change all occurrences of CppADvector, in the files test_more/*.cpp and speed/*/*.cpp , where changed to CPPAD_TEST_VECTOR. All occurrences of the CppADvector in the documentation were edited to reflect that fact that it has been deprecated. The documentation index and search for deprecated items has been improved.

07-25
Deprecate the preprocessor symbol CppADvector and start changing it to CPPAD_TEST_VECTOR .

Change all occurrences of CppADvector, in the example/*.cpp files, to CPPAD_TEST_VECTOR.

07-23
The TrackNewDel macros CppADTrackNewVec, CppADTrackDelVec, and CppADTrackExtend have been deprecated. The new macros names to use are CPPAD_TRACK_NEW_VEC, CPPAD_TRACK_DEL_VEC, and CPPAD_TRACK_EXTEND respectively. This item has been removed from the software guidelines section of the wish list.

The member variable software guideline wish list item has be brought up to date.

07-22
Minor improvements to the mul_level_adolc_ode.cpp example.

07-21
  1. The openmp/run.sh example programs example_a11c.cpp, openmp_newton_example.cpp, and sum_i_inv.cpp have been changed so that they run on more systems (are C++ standard compliant).
  2. base_require : The IdenticalEqual function, in the base_require specification, was changed to IdenticalEqualPar (note the API warning in the Base requirement specifications).
  3. Implementation of the base requirements for complex types were moved into the base_complex.hpp example.


07-20
The download for CppAD was still broken. It turned out that the copyright message was missing from the file base_adolc.hpp and this stopped the creation of the download files. This has been fixed. In addition, the automated testing procedure has been modified so that missing copyright messages and test program failures will be more obvious in the test log.

07-19
The download for CppAD has been broken since the example mul_level_adolc_ode.cpp was added because the example/example program was failing. This has been fixed.

07-18
A realistic example using Adolc with CppAD mul_level_adolc_ode.cpp was added. The documentation for TrackNewDel was improved.

07-14
Add a discussion at the beginning of mul_level_ode.cpp example (and improve the notation used in the example).

07-13
Separate the include file base_adolc.hpp from the mul_level_adolc.cpp example so that it can be used by other examples.

06-22
Add mul_level_adolc.cpp , an example that demonstrates using adouble and for the Base type.

The get_started.cpp example did not build when the --with-Introduction and BOOST_DIR options were included on the configure command line. In fact, some of the speed tests also had compilation errors when BOOST_DIR was include in the configure command. This has been fixed.

There was a namespace reference missing in the files that could have caused compilation errors in the files speed/cppad/det_minor.cpp and speed/cppad/det_lu.cpp. This has been fixed.

06-20
The MS project test_more/test_more.vcproj would not build because the file test_more/fun_check.cpp was missing; this has been fixed. In addition, fix warnings generated by the MS compiler when compiling the test_more/test_more.cpp file.

Add a section defining the Base type requirements . Remove the Base type restrictions from the Faq . Make all the prototype for the default Base types agree with the specifications in the Base type requirements.

Fix the description of the tan function in unary_standard_math .

06-14
The routine Rosen34 ( Runge45 ) had a division of a size_t ( int ) by a Scalar , where Scalar was any NumericType . Such an operation may not be valid for a particular numeric type. This has been fixed by explicitly converting the size_t to an int, then converting the int to a Scalar , and then preforming the division. (The conversion of an int to any numeric type must be valid.)

05-26
If the Base type is not double, the computed assignment operators did not always allow for double operands. For example, if x had type AD< AD<double> >
     x += .5;
 would slice the value .5 to an int and then convert it to an AD< AD<double> >. This has been fixed.

This slicing has also been fixed in the assignment operation. In addition, the assignment and copy operations have been grouped together in the documentation; see ad_ctor and ad_assign .

05-25
Document usage of double with binary arithmetic operators, and combine all those operators into one section (ad_binary ).

The documentation for all the computed assignment operators has been grouped together. In addition, a computed assignment wish list item has been added (it was completed and removed with the 05-26 update.)

05-24
Suppose that op is a binary operation and we have
     left op right
 where one of the operands was AD< AD<double> > and the other operand was double. There was a bug in this case that caused the double operand to be converted to int before being converted to AD< AD<double> >. This has been fixed.

05-22
The Microsoft examples and testing project file example/example.vcproj was missing a reference to the source code file example/reverse_two.cpp. This has been fixed.

05-08
Reverse mode does not work with the pow function when the base is less than or equal zero and the exponent is an integer. For this reason, the pow_int function is no longer deprecated (and is used by CppAD when the exponent has type int).

05-05
Third and fourth order derivatives were included in the routine test_more/sqrt.cpp that tests square roots.

The return value descriptions were improved for the introduction examples: exp_2_for1 , exp_2_for2 , exp_eps_for1 , and exp_eps_for2 .

The summation index in sqrt_reverse was changed from k to ℓ to make partial differentiation with respect to z ( k ) easier to understand. In addition, a sign error was corrected near the end of sqrt_reverse .

The dimension for the notation X in reverse_identity was corrected.

The word mega was added to the spelling exception list for openmp/run.sh.

04-19
Improve connection from reverse_identity theorem to reverse_any calculations.

Improve the openmp/run.sh script. It now runs all the test cases at once in addition to including multiple number of thread cases for each test.

Add the sum_i_inv_time.cpp OpenMP example case.

There was a typo in the second order discussion (found by Kipp Martin). It has been fixed.

04-17
Add a paragraph to reverse_identity explaining how it relates to reverse_any calculations. Add description of first and second order results in reverse_any .

04-14
Simplify the Reverse mode documentation by creating a separate reverse_two section for second order reverse, making major changes to the description in reverse_any , and creating a third order example reverse_checkpoint.cpp for reverse mode calculations.

Improve the reverse_identity proof.

04-11
Merge in changes made in branches/intro.

04-11
Add exp_eps_rev2 and its verification routine exp_eps_rev2.cpp .

04-10
Finished off exp_2_rev2 and added exp_2_rev2.cpp which verifies its calculations. Added second order calculations to exp_2_cppad . Added exp_eps_for2 and its verification routine.

04-07
Added a preliminary version of exp_2_rev2 (does not yet have verification or exercises).

04-06
Fixed a problem with the Microsoft Visual Studio project file introduction/exp_apx/exp_apx.vcproj (it did not track the file name changes of the form exp_apx/exp_2_for to exp_apx/exp_2_for1 on 04-05).

Added exp_2_for2 to introduction.

04-05
Use order expansions in introduction; e.g., the second order expansion for the exp_2 example.

03-31
Merge in changes made in branches/intro and remove the corresponding Introduction item from the wish list:

03-31
Create the a simpler exponential approximation in the introduction called exp_2 which has a different program variable for each variable in the operation sequence.

Simplify the exp_eps approximation using the v 1 , … , v 7 notation so that variables directly correspond to index in operation sequence (as with the exp_2 example).

03-30
The Microsoft project file introduction/exp_apx/exp_apx.vcproj was referencing exp_apx_ad.cpp which no longer exists. It has been changed to reference exp_apx_cppad.cpp which is the new name for that file.

03-29
Fixed entries in this file where the year was mistakenly used for the month. To be more specific, 07-dd was changed to 03-dd for some of the entries directly below.

Corrected some places where CppAD was used in stead of Adolc in the adolc_poly.cpp documentation.

Added an Introduction and Tracing entry to the wish list. (The Introduction item was completed on 03-31 .)

03-20
Example A.1.1c, example_a11c.cpp, from the OpenMP 2.5 standards document, was added to the tests that can be run using openmp/run.sh.

03-15
Included the changes from openmp branch so that so CppAD does not use the OpenMP threadprivate command (some systems do not support this command).

03-15
Add command line arguments to openmp_newton_example.cpp, and modified openmp/run.sh to allow for more flexible testing.

03-14
Fixed some Microsoft compiler warnings by explicitly converting from size_t to int.

In the Microsoft compiler case, the cppad/config.h file had the wrong setting of GETTIMEOFDAY. The setting is now overridden (and always false) when the _MSC_VER preprocessor symbol is defined.

Some minor changes were made in an effort to speed up the multi-threading case.

03-13
Started a new openmp branch and created a version of CppAD that does not use the OpenMP threadprivate command (not supported on some systems).

03-09
Included the changes from openmp branch so that OpenMP can be used with CppAD, see omp_max_thread . The changes dated between 02-15 and 03-28 below were made in the openmp branch and transferred to the trunk on 03-09.

03-28
The conditional include commands were missing on some include files; for example 
 
     # ifndef CPPAD_BENDER_QUAD_HPP
     # define CPPAD_BENDER_QUAD_HPP
was missing at the beginning of the BenderQuad include file. This has been fixed.

The speed_test routines timing was changed to use gettimeofday if it is available. (gettimeofday measures wall clock time which is better in a multi-threading environment).

Added the user multi-threading interface omp_max_thread along with its examples which are distributed in the directory openmp.

The speed/*.hpp files have been moved to cppad/speed/*.hpp and the corresponding wish list item has been removed.

The multiple tapes with the same base type wish list item have been removed (it's purpose was multi-threading which has been implemented).

02-27
The speed include files are currently being distributed above the cppad include directory. A fix this wish list item has been added.

Multiple active tapes required a lot of multi-threading access management for the tapes. This was made simpler (and faster) by having at most one tape per thread.

02-22
The include command in the speed_test documentation was 
 
     # include <speed/speed_test.hpp>
but it should have been 
 
     # include <cppad/speed_test.hpp>
This has been fixed.

02-17
An entry about optimizing the operation sequence in an ADFun object was added to the wish_list .

Change the argument syntax for Dependent and deprecate the old Dependent syntax .

02-16
Added VecAD<Base> as a valid argument type for the Parameter and Variable functions. In addition, size_t indexing is was extended to be allowed during taping so long as the VecAD object is a parameter.

02-15
Fixed the example/test_one.sh script (it was using its old name one_test).

02-06
The BenderQuad documentation was improved by adding the fact that the x and y arguments to the f.dy member function are equal to the x and y arguments to BenderQuad. Hence values depending on them can be stored as private objects in f and need not be recalculated.

02-04
The method for distributing the documentation needed to be changed in the top level makefile.am in order to be compatible with automake version 1.10.

02-03
The change on 02-01 had a new, saved as a static pointer, with no corresponding delete. This was not a bug, but it has been changed to avoid an error message when using CppAD with valgrind .

The change to the pow function on 06-12-10 did not include the necessary changes to the Sparsity calculations. This has been fixed.

02-02
Fix minor errors and improve profiling documentation. Also change the problem sizes used for the speed tests.

02-01
There seems to be a bug in the cygwin version of g++ version 3.4.4 with the -O2 flag whereby some static variables in static member functions sometimes do not get constructed before being used. This has been avoided by using a static pointer and the new operator in cppad/local/ad.hpp.

01-29
The copyright message was missing from some of the distribution files for some new files added on 06-12-15 . This resulted in the tarballs *.tgz and *.zip not existing for a period of time. The automated tests have been extended so that this should not happen again.
Input File: omh/whats_new/whats_new_07.omh cppad-20170000.3/doc/whats_new_06.xml0000644000175200017650000024244413057470511016232 0ustar coincoin-web Changes and Additions to CppAD During 2006
Prev Next whats_new_06

Changes and Additions to CppAD During 2006

Introduction
This section contains a list of the changes to CppAD during 2006 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions of CppAD.

12-24
Move exp_eps_ad to exp_eps_cppad and add exercises to the following sections: exp_eps_rev1 , exp_eps_cppad .

Add operation sequence indices to help track operations in exp_eps_for0 , exp_eps_for1 , exp_eps_rev1 .

12-23
Add exercises to the following sections: get_started.cpp , exp_eps , exp_eps_for0 , and exp_eps_for1 .

12-22
Move get_started.cpp below the introduction directory.

Move the exponential example to the subdirectory introduction/exp_apx and change the --with-Introduction unix configure option to build both the get_started.cpp and exp_apx_main.cpp example programs. (The --with-GetStarted configure command line option has been removed.)

12-21
Add the source code for Poly to the documentation and include Poly in the in the speed_utility section.

The get_started.cpp section has been moved into the Introduction and exercises were added to that section. In addition some sections has switched position between the top level CppAD and the Appendix .

12-19
Reorganize so that the source code is below the corresponding routine in the documentation tree (instead of at the same level) for the following routines: det_by_minor , det_grad_33 , uniform_01 , det_of_minor , det_by_lu , LuInvert , LuFactor , LuSolve .

Separate the specifications for the source in speed_utility and add cross reference to the following routine specification and implementations: det_by_minor , det_grad_33 , uniform_01 , det_of_minor , det_by_lu , LuInvert , LuFactor , LuSolve .

12-18
Make the speed source code easier to read.

Change the speed test output name det_poly to poly (as it should have been).

12-17
The speed test det_grad_33 was missing its documentation (this has been fixed). In addition, the titles and indexing for the speed test documentation has been improved.

Add to the specifications that each repeated test corresponds to a different matrix in det_lu and det_minor . In addition, modify all the speed tests so that they abide by this rule.

Change some references from the deprecated name CppAD.h to new name cppad.hpp.

Change adolc_det_minor.cpp and cppad_det_minor.cpp to tape once and reuse operation sequence for each repeated matrix in the test.

Add the poly speed test for all three packages. In addition, correct a missing include in poly routine.

12-15
The wish list item to simplify and better organize the speed tests been completed:
speed/ template functions that are speed tested
speed/example example usage of speed template functions
speed/adolc Adolc drivers for the template functions
speed/cppad CppAD drivers for the template functions
speed/fadbad Fadbad drivers for the template functions
speed/profile profiling version of CppAD drivers

12-13
Next step for the speed wish list item: remove speed_cppad from the documentation and replace it by speed/cppad, see speed_cppad for the new CppAD speed test routines.

12-12
Started the speed wish list item by move the adolc director to speed/adolc and fadbad to speed/fadbad.

12-11
Started the speed wish list item by creating the speed/example directory and moving the relevant examples from example/*.cpp and speed_example/*.cpp to speed/example/*.cpp . In addition, the relevant include files have been moved from example/*.hpp to speed/*.hpp .

A new speed_test routine was added to the library.

12-10
The pow function was changed to be a an AD<Base> atomic operation. This function used to return a nan if x is negative because it was implemented as
     pow(x, y) = exp( log(x) * y )
 This has been fixed so that the function and its derivatives are now calculated properly when x is less than zero. The pow documentation was improved and the pow.cpp example was changed to test more cases and to use the same variable names as in the documentation.

12-09
A speed wish list item was added to the wish list.

The prototype for int arguments in binary operations (for example addition ) was documented as const int & but was actually just plain int. This has been fixed. (Later changed to double.)

12-07
Fix bug in the subversion installation instructions; see bug report .

The some of the automatically generated makefile.in files had an improper license statement in the GPL license version. This has been fixed.

12-05
Add the unix installation --with-Documentation option and remove the postfix_dir option.

Create a fixed whats_new section above the section for each particular year. Also improve the CppAD distribution README file.

12-03
The include file directory CppAD was changed to be all lower case; i.e., cppad. If you are using a Unix system, see include_deprecated . This completes the following wish_list items (which were removed):
  1. File and directory names should only contain lowercase letters, numbers underscores and possibly one period. The leading character must be alphabetic.
  2. C++ header files should have the .hpp extension.


12-02
Put explanation of version numbering in the download instructions.

Correct some file name references under the Windows heading in speed_cppad .

12-01
All of the Makefile.am and Makefile files were changed to lower case; i.e., makefile.am and makefile.

Fix compiler warning while compiling cppad/RombergOne/ (mistake occurred during 11-20 change).

11-30
Cygwin packages, and other system packages, should not have a dash in the version number. See cygwin package file naming or, to quote the rpm file naming convention The only restriction placed on the version is that it cannot contain a dash "-". As per the acceptable package naming conventions for cygwin, CppAD version numbering has be changed from yy-mm-dd format to yyyymmdd ; i.e. cppad-06-11-30 was changed to cppad-20061130.

11-29
There was a problem using RombergOne with floating point types other than double. This has been fixed.

11-28
The installation download files were not being built because Makefile.am referenced Doc when it should have referenced doc. This has been fixed.

11-23
A Version Numbering entry was added to the wish_list (this was completed on 11-30 ).

11-18
The example routine that computes determinants using expansion by minors DetOfMinor was changed to det_of_minor , in preparation for more formal speed comparisons with other packages. To be specific, its documentation was improved, its dependence on the rest of CppAD was removed (it no longer includes CppAD.h ).

11-12
The example.cpp and test_more/test_more.cpp programs were changed to print out the number of tests that passed or failed instead of just "All the tests passed" or "At least one of the tests failed".

The windows project files for examples and testing should have been changes to use lower case file names on as part of the 11-08 change below. This has been fixed.

11-08
Move the Example directory to example and change all its files to use lower case names.

11-06
Move the TestMore directory to test_more and change all its files to use lower case names.

11-05
Remove references in the speed_cppad tests to the Memory and Size functions because they have been deprecated .

Correct some references to var_size that should have been size_var .

11-04
Put text written to standard output in the documentation for the get_started.cpp and print_for.cpp examples. (Now documentation can be built from a subversion checkout with out needing to execute automake.) The PrintFor.cpp and speedtest.cpp examples were missing in ListAllExamples (which has been fixed).

Move the Speed directory to speed and change all its files to use lower case names.

11-02
The print_for directory was referenced as PrintFor in the root CppAD Makefile.am this has been fixed.

The documentation for the Adolc helper routines AllocVec and AllocMat were not being included. This has been fixed.

Move the GetStarted directory to get_started and change all its files to use lower case names.

11-01
Move the PrintFor directory to print_for and change all its files to use lower case names.

10-31
Move the SpeedExample directory to speed_cppad_example and change all its files to use lower case names.

10-29
Move the Adolc directory to adolc and change all its files to use lower case names.

Change all the file in the omh directory to use lower case names.

The file Makefile.am in the distribution directory had the CPL copyright message in the GPL version. This has been fixed.

10-28
The copyright message in the script files example/OneTest and TestMore/OneTest were GPL (in the CPL distribution). This has been fixed by moving them to example/OneTest.sh and TestMore/OneTest.sh so that the distribution automatically edits the copyright message.

10-27
Change hes_lagrangian.cpp example so that it computes the Lagrangian two ways. One is simpler and the other can be used to avoid re-taping operation sequence.

10-26
Change hes_lagrangian.cpp example so that it modifies the independent variable vector between the call to Independent and the ADFun<Base> constructor .

10-25
A subversion install procedure was added to the documentation.

Fix definition of preprocessor symbol PACKAGE_STRING in Speed/Speed.cpp (broken by change on 10-18).

Added the example hes_lagrangian.cpp which computes the Hessian of a Lagrangian.

10-18
Document and fix possible conflicts for preprocessor symbols that do not begin with CppAD or CPPAD_.

Include a default value for the file cppad/config.h in the subversion repository.

10-16
Fix bug when using OdeErrControl with the type AD< AD<double> >.

10-10
Add the Var2Par function so it is possible to obtain the Value of a variable. Move the Discrete.cpp example to tape_index.cpp . Fix the Microsoft project file so that the Windows install examples and testing works properly (it was missing the stack_machine.cpp example).

09-30
These changes were grouped together because it took a while for Coin-Or to review the dual licensing version and because it was not possible to get the nightly build changed:
  1. Change shell scripts to use *.sh extension.
  2. Two versions, one with CPL and other with GPL license.
  3. Change subversion version of CppAD from GPL to CPL copyright.
  4. Change all files in cppad/local to use lower case and *.hpp extension.
  5. CppAD_vector.h was generating a warning on version 4 of gcc. This have been fixed.
  6. Change the preprocessor # define commands in cppad/local/*.hpp to use upper case names.
  7. Add the stack_machine.cpp example.


08-17
Some error message occurred while executing 
 
     valgrind --tool=memcheck example/example
     valgrind --tool=memcheck TestMore/TestMore
These were not really bugs, but they have been fixed to avoid this conflict between CppAD and valgrind .

07-14
Make some improvements were made to the Introduction , exp_eps.hpp and exp_eps_rev1 sections.

07-12
Use a drop down menu for the navigation links, instead of a separate frame for the navigation links, for each section in the documentation.

06-29
Newer versions of the gcc compiler generated an error because erf was using CondExp before it was defined. This was found by Kasper Kristensen and his fix has been included in the CppAD distribution.

06-22
The ADFun operation f(x, y) no longer executes a zero order Forward operation when a new operation sequence is stored in f . In addition, the syntax for this operation was changed to f.Dependent(y) (see Dependent ).

06-19
The changes listed under 06-17 and 06-18 were made in the branches/ADFun branch of the CppAD subversion repository. They did not get merged into the trunk and become part of the distribution until 06-19. This accomplished the following goal, which was removed from the wish_list :

"We would like to be able to erase the function values so that ADFun objects use less memory. We may even want to erase the AD operation sequence so that ADFun objects use even less memory and can be used for a subsequent AD operation sequence."

06-17
Added capacity_order which can be used to control the amount of memory used to store Forward results. Also deprecated taylor_size, and defined size_order in its place.

06-18
Added the ADFun default constructor and the ability to store a new operation sequence in an ADFun object with out having to use ADFun pointers together with new and delete.

06-17
The location where the distribution files are stored has changed and this broke the Download Current Version links for the unix and windows installation. This has been fixed.

The compiling instructions for the speed_cppad routines have been improved.

The Value function has been extended to allow for parameter arguments even if the corresponding tape is in the Recording state.

The BenderQuad documentation and example have been improved by changing Vector to BAvector to emphasize that it corresponds to a vector of Base objects.

06-15
Change BenderQuad to use Base instead of AD<Base> where every possible. This allows for more calculations to be done in the base type; i.e., is more efficient.

06-09
Add a size check (size one) for the function value argument, g in BenderQuad.

06-07
Some major changes were made to the notation in get_started.cpp (to make it easier to start using CppAD).

In the Introduction example, exp eps was changed to exp _ eps .

06-05
Change BenderQuad F y ( x , y ) to H ( x , y ) so applies in a more general setting. This was another change to the BenderQuad interface, fun.fy was changed to fun.h .

06-02
Newer versions of the gcc compiler generated a warning for possible use of an uninitialized pointer. This was found by Michael Tautschnig and his fix has been included in the CppAD distribution.

05-31
The interface to BenderQuad has been changed. Now all the function evaluation routines are member functions of one class object. This makes it easy for them to share common data.

05-29
Change statement of command syntax to be in the same browser frame as the command documentation (for all the commands with a syntax statement). Now when a user links to a specific heading in a command's documentation, the syntax for that command is automatically included. Before the user needed to follow another link to see to the command syntax.

05-27
Added BenderQuad for computing the Hessian of Bender's reduced objective function.

Added special specifications for resize(0) to CppAD_vector .

05-03
The g++ (GCC) 4.1.0 (Red Hat 4.1.0-3) compiler reported an error because certain functions were used before being defined (version 3.4.4 did not complain about this). This has been fixed.

04-29
Change all of the example and test driver programs so that they return error codes; i.e., zero for no error and one for an error.

Add more discussion and a reference for a gcc 3.4.4 -O2 bug (since been removed).

04-28
Improve the get_started.cpp example and move it so that it is visible at the too level of the documentation.

04-26
The programs in Introduction have been converted to automated test that return true or false with the driver program Introduction .

04-25
Add an Introduction section to the documentation (replaces old example that was part of the Theory section).

04-19
A discussion was added near the end of the FunCheck documentation. And the cross references to the CompareChange discussion were changed to the FunCheck discussion.

An operation sequence entry was added to the wish_list .

04-18
The new definitions for AD of Base and operation sequence have been used throughout the documentation.

Add the FunCheck section for checking that a sequence of operations is as intended.

04-17
The documentation for SpeedTest and Poly was improved.

Definitions were added for an atomic operation and for an operation sequence being dependent and independent of the values of specific operands.

The definition of AD sequence of operations was made abstract and moved to the glossary as Type operation sequence .

04-15
The mul_level example was moved from ADFun to General . The documentation for SpeedTest was improved.

04-14
Documentation and examples were improved for the following routines: ForTwo , RevTwo . In addition, the computation in RevTwo was made more efficient (it used to possibly calculate some first order partials that were not used).

04-13
Documentation and examples were improved for the following routines: Jacobian , ForOne , RevOne , and Hessian .

04-08
In the case where use_VecAD is true, the ForSparseJac calculation in only for the current independent variable values. In this case, the sparsity pattern can be (and has been) made more efficient; i.e., fewer true values (because it only applies to the current forward_zero ).

The conversion from VecAD<Base>::reference to AD gave a compile error (this has been fixed). Code example for this fix 
 
     VecAD<double> V(1);
     AD<double> zero = 0;
     V[zero] = 1.;
     static_cast< AD<double> > ( V[zero] );

04-06
The ForSparseJac , RevSparseJac , RevSparseHes sparsity results are now valid for all independent variable values (if the AD operation sequence does no use any VecAD<Base> operands). In addition, the ForSparseJac, RevSparseJac and RevSparseHes documentation and examples were improved.

The useVecAD member function was added to ADFun objects.

The var_size member function was changed to size_var (this is not backward compatible, but var_size was just added on 04-03 ).

04-05
The documentation and example for CompareChange were improved and moved to be part of the Forward section.

04-04
The documentation and examples for Reverse were improved and split into reverse_one and reverse_any .

04-03
Create separate sections for the zero and forward_one first order case of Forward mode.

The ADFun Size member function has been deprecated (use size_order instead).

The Reverse member function is now declared, and documented as, const; i.e., it does not effect the state of the ADFun object.

Change the examples that use Reverse to use the same return value notation as the documentation; i.e., dw.

04-02
The member functions of ADFun that return properties of AD of Base operation sequence have been grouped into the seq_property section. In addition, the seq_property.cpp example has been added.

The CompareChange function documentation was improved and moved to a separate section.

Group the documentation for the ADFun member functions that evaluate functions and derivative values .

Remove the old Fun.cpp example and extend independent.cpp so that it demonstrates using different choices for the SimpleVector type.

04-01
Move the ADFun Constructor to its own separate section, improve its documentation, and use independent.cpp for its example.

The following member functions of ADFun have been deprecated : Order, Memory.

The wish list entry for Memory usage was updated on 04-01. The request was implemented on 06-19 and the entry was removed from the wish list.

03-31
Add examples for the Parameter, Variable and Independent functions.

Move the Parameter and Variable functions from the ADFun section to the AD section.

In the examples for the AD sections, refer to the range space vector instead of the dependent variable vector because some of the components may not be variables .

03-30
Move the LuRatio section below LuDetAndSolve .

Move the definition of an AD of Base operation sequence from the glossary to the AD section.

Improve the definition of tape state.

Add mention of taping to Erf , BoolFun , NearEqualExt ,and Pow .

Change the definition for VecAD<Base>::reference so that it stands out of the text better.

03-29
Mention the VecAD<Base>::reference case in documentation and examples for abs , atan2 , erf , and pow .

Fix a bug derivative computation for abs(x) when x had type AD< AD<double> > and x had value zero.

Fix a bug using non-zero AD indices for VecAD vectors while the tape is in the empty state.

Extend erf to include float, double, and VecAD<Base>::reference .

03-28
Mention the VecAD<Base>::reference case in documentation and examples for UnaryPlus , UnaryMinus , ad_binary , compute_assign , and unary_standard_math

03-27
Extend and improve the VecAD exceptions .

Mention the VecAD<Base>::reference case and generally improve addition documentation and examples.

03-26
Improve documentation and examples for VecAD and change its element type from VecADelem<Base> to VecAD_reference<Base> (so that it looks more like VecAD<Base>::reference ).

Mention the VecAD<Base>::reference case and generally improve Value , ad_output and assignment documentation and examples.

Extend Integer and PrintFor to include the VecAD<Base>::reference case (and mention in documentation and examples).

03-24
Move VecAD and LuRatio from the old ExtendDomain section to AD .

03-23
Improve documentation and examples for CondExp and Discrete . Move both of these sections from ExtendDomain to ADValued .

03-22
The documentation sections under AD have been organized into a new set of sub-groups.

03-18
The documentation and example for PrintFor have been improved. The sections below AD in the documentation have been organized into subgroups.

03-17
The documentation and examples have been improved for the following functions: BoolFun , and NearEqualExt .

03-16
Improve the documentation and example for the pow function. This includes splitting out and generalizing the integer case pow_int .

The copies of the atan2 function were included in the CppAD namespace for the float and double types.

03-15
Improve the introduction to CppAD.

03-11
The file cppad/local/MathOther.h had a file name case error that prevented the documentation from building and tests from running (except under Cygwin which is not really case sensitive). This has been fixed.

The term AD of Base operation sequence has been defined. It will be used to improve the user's understanding of exactly how an ADFun object is related to the C++ algorithm.

03-10
The math functions that are not under unary_standard_math have been grouped under MathOther.

The documentation and examples have been improved for the following functions: abs , atan2 .

03-09
The examples cos.cpp , cosh.cpp , exp.cpp , log.cpp , log10.cpp , sin.cpp , sinh.cpp , sqrt.cpp have been improved.

03-07
The tan function has been added to CppAD.

The examples Acos.cpp , Asin.cpp and atan.cpp have been improved.

03-05
The AD standard math unary functions documentation has been grouped together with improved documentation in unary_standard_math .

02-28
The ad_output and Abs documentation and example have been improved. Minor improvements were also made to the lu_vec_ad.cpp documentation.

02-25
The Compare documentation and example have been improved.

02-24
The documentation and examples have been improved for the following sections: division , -= , *= , and /= .

02-23
The multiplication documentation and example have been improved.

02-21
The subtraction documentation and example have been improved.

There was a bug RevTwo that was not detected by the rev_two.cpp test. This bug was reported by Kasper Kristensen A test was added TestMore/rev_two.cpp that detects this problem and the problem has been fixed.

02-15
The += documentation and example have been improved.

02-14
The addition documentation and example have been improved.

02-13
Combine the old binary operator and computed assignment documentation into Arithmetic documentation.

The documentation and examples have been improved for the following sections: assignment , UnaryPlus , UnaryMinus .

02-11
The documentation and examples have been improved for the following sections: ad_ctor , ad_ctor and ad_assign , and Value .

02-10
This is the beginning of a pass to improve the documentation: The documentation sections The CopyBase (formerly FromBase and now part of ad_ctor and ad_assign ) and AD copy constructor (formerly Copy) documentation has been modified.

Some of the error messaging during ADFun construction has been improved.

02-04
There was a read memory access past the end of an array in CppAD::vector::push_back . This has been fixed and in addition TrackNewDel is now used to do and check the allocation in CppAD::vector.

The routines Runge45 and Rosen34 had static vectors to avoid recalculation on each call. These have been changed to be plain vectors to avoid memory leak detection by TrackCount .

01-20
Add software guidelines to the wish list.

01-18
Improve the definition for parameters and variables . Remove unnecessary reference to parameter and variable in documentation for Independent .

01-08
The aclocal program is part of the automake and autoconf system. It often generates warnings of the form:
     /usr/share/aclocal/...: warning: underquoted definition of
     ...
 The shell script file FixAclocal, which attempts to fix these warnings, was added to the distribution.

01-07
Change CppAD error handler from using the macros defined in cppad/CppADError.h to using a class defined in cppad/utility/error_handler.hpp . The macros CppADUnknownError and CppADUsageError have been deprecated (they are temporarily still available in the file cppad/local/CppADError.h).

01-02
Add the sed script Speed/gprof.sed to aid in the display of the profiling output.

Make the following source code files easier to understand: Add.h, Sub.h, Mul.h, Div.h (in the directory cppad/local).

01-05
Make the following source code files easier to understand: RevSparseHes.h, Reverse.h, Fun.h, Forward.h, ForSparseJac.h, RevSparseJac.h (in the directory cppad/local).
Input File: omh/whats_new/whats_new_06.omh cppad-20170000.3/doc/whats_new_05.xml0000644000175200017650000017226613057470511016235 0ustar coincoin-web Changes and Additions to CppAD During 2005
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Changes and Additions to CppAD During 2005

12-24
Fix a memory leak that could occur during the ForSparseJac calculations.

12-23
The buffers that are used to do RevSparseJac and RevSparseHes calculations are now freed directly after use.

The TrackNewDel.cpp example was missing from the Windows install examples and testing project file. This has been fixed.

12-22
The buffer that is are used to do Reverse mode calculations is now freed directly after use. This reduces the memory requirements attached to an ADFun object.

12-20
Buffers that are used to store the tape information corresponding to the AD<Base> type are now freed when the corresponding ADFun object is constructed. This reduces memory requirements and actually had better results with the speed_cppad tests.

The speed_cppad test program now outputs the version of CppAD at the top (to help when comparing output between different versions).

12-19
The TrackNewDel routines were added for track memory allocation and deletion with new[] and delete[]. This is in preparation for making CppAD more efficient in it's use of memory. The bug mentioned on 12-01 resurfaced and the corresponding routine was changed as follows: 
 
     static local::ADTape<Base> *Tape(void)
     {    // If we return &tape, instead of creating and returning ptr,
          // there seems to be a bug in g++ with -O2 option.
          static local::ADTape<Base> tape;
          static local::ADTape<Base> *ptr = &tape;
          return ptr;
     }

12-16
The NearEqual function documentation for the relative error case was changed to
     | x - y | <= r * ( |x| + |y| )
 so that there is no problem with division by zero when x and y are zero (the code was changed to that form also). The std::abs function replaced the direct computation of the complex norms (for the complex case in NearEqual). In addition, more extensive testing was done in near_equal.cpp .

12-15
Extend NearEqual and NearEqualExt to cover more cases while converting them from, a library function in lib/CppADlib.a and an utility in example/NearEqualExt.h, to a template functions in cppad/near_equal.hpp and cppad/local/NearEqualExt.h. This is another step along the way of removing the entire CppADlib.a library.

The change on 12-14 broke the Microsoft project files example/Example.sln and TestMore/TestMore.sln used during CppAD installation on Windows. This has been fixed.

Move lib/SpeedTest.cpp to cppad/speed_test.hpp. This was the last change necessary in order to remove the CppAD library, so remove all commands related to building and linking CppADlib.a. The corresponding entry has been removed from the wish_list .

One of the entries in the wish_list corresponded to the Integer function. It has also been removed (because it is already implemented).

12-14
Extend erf to cover more cases while converting it from a function in lib/CppADlib.a to a template function in cppad/local/Erf.h. This is one step along the way of removing the entire CppADlib.a library.

12-11
Group routines that extend the domain for which an ADFun object is useful into the ExtendDomain section.

Add an example of a C callable routine that computes derivatives using CppAD (see interface2c.cpp ).

12-08
Split out LuFactor with the ratio argument to a separate function called LuRatio . This needed to be done because LuRatio is more restrictive and should not be part of the general template utilities .

12-07
Improve CheckSimpleVector so that it tests element assignment. Change check_simple_vector.cpp so that it provides and example and test of a case where a simple vector returns a type different from the element type and the element assignment returns void.

12-06
The specifications for a SimpleVector template class were extended so that the return type of an element access is not necessarily the same as the type of the elements. This enables us to include std::vector<bool> which packs multiple elements into a single storage location and returns a special type on element access (not the same as bool). To be more specific, if x is a std::vector<bool> object and i has type size_t, x[i] does not have type bool.

Add a Home icon, that links to the CppAD home page , to the top left of the navigation frame (left frame) for each documentation section.

12-05
The RevSparseHes reverse mode Hessian sparsity calculation has been added.

The definition of a sparsity pattern has been corrected to properly correspond to the more efficient form mentioned under whats_new_05 below.

The dates in this file used to correspond to local time for when the change was checked into the subversion repository . From now on the dates in this file will correspond to the first version of CppAD where the change appears; i.e., the date in the unix and windows download file names CppAD-yy-mm-dd .

12-03
There was a bug in the RevSparseJac reverse mode sparsity patterns when used with VecAD calculations. This bug was fixed and the calculations were made more efficient (fewer true entries).

12-02
There was a bug in the ForSparseJac forward mode sparsity patterns when used with VecAD calculations. This bug was fixed and the calculations were made more efficient (fewer true entries).

12-01
The speed test of lu_vec_ad.cpp has been reinstated. It appears that there is some sort of bug in the gcc compiler with the -O2 option whereby the following member function 
 
     static local::ADTape<Base> *Tape(void)
     {    static local::ADTape<Base> tape;
          return &tape;
     }
(in cppad/local/AD.h) would sometimes return a null value (during VecAD operations). A speed improvement in cppad/local/ExtendBuffer.h seems to prevent this problem. This fix is not well understood; i.e., we should watch to see if this problem reoccurs.

The source code for lu_vec_ad_ok.cpp was mistakenly used for speed_cppad/LuSolveSpeed.cpp. This has been fixed.

11-23
The speed test of lu_vec_ad.cpp has been commented out because it sometimes generates a segmentation fault. Here is an explanation:

If X is a AD<Base> object, y is a Base object, X[y] uses pointer from the element back to the original vector. Optimizing compilers might reorder operations so that the vector is destroyed before the object is used. This can be avoided by changing the syntax for VecAD objects to use set and get member functions.

11-22
A much better example for using VecAD vectors has been provided. In addition, a bug in the computation of derivatives using VecAD vectors has been fixed.

CppAD now checks that the domain dimension during Independent and the range dimension during ADFun (provided that -DNDEBUG is not defined). If either of these is zero, the CppADUsageError macro is invoked.

11-20
The sparsity pattern routines ForSparseJac and RevSparseJac have been modified so that they are relative to the Jacobian at a single argument value. This enables us to return more efficient sparsity patterns .

An extra exception has been added to the use of VecAD elements. This makes VecAD some what more efficient.

11-19
Improve the output messages generated during execution of the configure command.

Put a try and catch block around all of the uses of new so that if a memory allocation error occurs, it will generate a CppADUsageError/ message.

The get_started.cpp example has been simplified so that it is easier to understand.

11-15
Fix a memory leak in both the ForSparseJac and RevSparseJac calculations.

11-12
Add reverse mode Jacobian sparsity calculation.

11-09
Add prototype documentation for logdet in the LuSolve function.

Add the optional ratio argument to the LuFactor routine. (This has since been moved to a separate routine called LuRatio .)

11-07
Remove some blank lines from the example files listed directly below (under 11-06). Comments for computing the entire Jacobian entire sparsity pattern was added.

11-06
The cases of std::vector, std::valarray, and CppAD::vector were folded into the standard example and tests format for the following cases: rev_two.cpp , rev_one.cpp , Reverse.cpp, hessian.cpp , jacobian.cpp , forward.cpp , for_two.cpp , for_one.cpp , Fun.cpp (Fun.cpp has since been replaced by independent.cpp , Reverse.cpp has since been replaced by reverse_one.cpp and reverse_checkpoint.cpp).

11-01
Add forward mode Jacobian sparsity calculation.

10-20
Add sparsity patterns to the whish list.

10-18
The Unix install configure command was missing the -- before of the prefix command line argument.

10-14
The template class CppAD_vector uses a try/catch block during the allocation of memory (for error reporting). This may be slow down memory allocation and hence it is now replaced by simple memory allocation when the preprocessor variable NDEBUG is defined.

The specialization of CppAD::vector<bool> was moved to vectorBool so that CppAD::vector<bool> does not pack one bit per value (which can be slow to access).

10-12
Change the configure script so that compilation of the get_started.cpp and print_for_cout.cpp examples are optional.

One of the dates in the Unix installation extraction discussion was out of date. This has been fixed.

10-06
Change the Unix install configure script so that is reports information using the same order and notation as its documentation .

Some compiler errors in the ode_gear_control.cpp and ode_stiff.cpp examples were fixed.

09-29
Add a specialization to CppAD_vector for the CppAD::vector<bool> case. A test for the push_back member function as well as a CheckSimpleVector test has been added to cppad_vector.cpp . The source code for this template vector class, cppad/vector.hpp, has been removed from the documentation.

09-27
Add the prefix_dir and postfix_dir ( postfix_dir has since been removed) options to the configure command line. This gives the user more control over the location where CppAD is installed.

09-24
The stiff Ode routines, OdeGear and OdeGearControl , were added to the utilities . A comparison various Ode solvers on a stiff problem ode_stiff.cpp was added. In addition, OdeGear and OdeGearControl were added to the utilities and the library was reorganized.

09-20
The Microsoft compiler project files example/Example.vcproj and TestMore/TestMore.vcproj were not up to date. This has been fixed. In addition, the example numeric_type.cpp has been added.

Make the building of the Example, TestMore, and Speed, directories optional during the configure command. The Unix installation instructions were overhauled to make the larger set of options easy to understand.

09-14
Added the NumericType concept and made the following library routines require this concept for their floating point template parameter type: LuSolve , LuFactor , RombergOne , RombergMul , Runge45 , Rosen34 , and OdeErrControl . This is more restrictive than the previous requirements for these routines but it enables future changes to the implementation of these routines (for optimization purposes) with out affecting their specifications.

09-09
Add the UnaryPlus operator and move the Neg examples and tests to UnaryMinus .

09-07
Change name of distribution files from CppAD.unix.tar.gz and CppAD.dos.tar.gz to CppAD-yy-mm-dd.tar.gz and CppAD-yy-mm-dd.zip (the *.zip file uses pkzip compression).

08-30
The maxabs argument has been added to the OdeErrControl function so that it can be used with relative errors where components of the ODE solution may be zero (some of the time). In addition, some of the rest of the OdeErrControl documentation has been improved.

The documentation for replacing defaults in CppAD error macros has been improved.

08-24
Changed Romberg to RombergOne and added RombergMul . In addition, added missing entries to ListAllExamples and reorganized utilities .

08-20
Backed out addition of Romberg integration routine (at this point uncertain of the interface that is most useful in the context of AD.)

08-19
Added a Romberg integration routine for where the argument types are template parameters (for use with AD types).

08-15
The Microsoft project files example/Example.vcproj and TestMore/TestMore.vcproj were missing some necessary routines. In addition, Speed/Speed.vcproj was generating a warning. This has been fixed.

08-14
An Integer conversion function as been added.

The value.cpp example has been improved and the old example has been moved into the TestMore directory.

08-13
The unary_standard_math functions sinh, and cosh have been added. In addition, more correctness testing has been added for the sin and cos functions.

The OdeErrControl routine could lock in an infinite loop. This has been fixed and a test case has been added to check for this problem.

08-07
The conditional expression function has been changed from just CondExp to CondExpLt, CondExpLe, CondExpEq, CondExpGe, CondExpGt. This should make code with conditional expressions easier to understand. In addition, it should reduce the number of tape operations because one need not create as many temporaries to do comparisons with. The old CondExp function has been deprecated.

07-21
Remove unnecessary no-op that was left in tape for the unary_standard_math functions acos, asin, atan, cos.

Improve the index entries in the documentation that corresponds to the cppad/local directory source code.

07-19
The wish_list and Bugs information were moved out of this section and into their own separate sections (the Bugs section has been removed; see the bug subdirectory instead).

A discussion of VecAD speed and memory was added as well as an entry in the wish_list to make it more efficient.

07-15
The BOOST_DIR and CPP_ERROR_WARN configure options were not properly implemented for compiling the lib sub-directory. This has been fixed.

Some compiler warnings in the file lib/ErrFun.cpp, which computes the erf function, have been fixed.

07-11
The push_back function has been added to the CppAD::vector template class.

It appears that the TestMore/Runge45.cpp file was missing an include of example/NearEqualExt.h. This has been fixed.

07-08
The documentation for Forward and Reverse has been improved.

07-05
The rosen_34.cpp example mixed the CppAD::vector and CppADvector vector types. This caused the compilation of the examples to fail when CppADvector was defined as something other than CppAD::vector (found by Jon Pearce). This has been fixed.

The CheckSimpleVector run time code has been improved so that it is only run once per case that is being checked.

Simple Vector concept checking (CheckSimpleVector ) was added to the routines: ForOne , ForTwo , Forward , ADFun , Hessian , Independent , Jacobian , RevOne , RevTwo , and Reverse .

07-04
Simple Vector concept checking (CheckSimpleVector ) was added to the routines: LuFactor , LuSolve , LuInvert , OdeErrControl , Runge45 , and Rosen34 .

The previous version of the routine OdeErrControl was mistakenly in the global namespace. It has been moved to the CppAD namespace (where all the other utilities routines are).

The previous distribution (version 05-07-02) was missing the file cppad/local/Default.h. This has been fixed.

07-03
Added CheckSimpleVector , a C++ concept checking utility that checks if a vector type has all the necessary conditions to be a SimpleVector class with a specific element type.

07-02
Version 7 of Microsoft's C++ compiler supports the standard declaration for a friend template function. Version 6 did not and CppAD used macros to substitute the empty string for <Base>, < AD<Base> >, and < VecAD<Base> > in these declarations. These macro substitutions have been removed because Version 6 of Microsoft's C++ compiler is no longer supported by CppAD.

The copy base section was split into the default constructor and the construction for the base type. The construction from base type has been extended to include any type that is convertible to the base type. As a special case, this provides the previous wish list item of a constructor from an arbitrary Base to a AD< AD<Base> > , AD< AD< AD<Base> > > etc.

07-01
The permissions were set as executable for many of the no-executable files in the distribution; for example, the README, file. This has been fixed.

06-25
Some improvements were made to the README, AUTHORS, COPYING, and INSTALL files. In addition, the file UWCopy040507.html which contains the University of Washington's copyright policy (see Section 2) was added to the distribution.

06-24
The List2Vector example utility is no longer used and has been removed.

06-18
CppAD is now supported by Microsoft Visual C++ version 7 or higher. The version 6 project files *.dsw and *.dsp have been replaced by the version 7 project files *.sln and *.vcproj .

06-14
A new CondExp example has been added and the old CondExp example has been moved to the TestMore directory (it is now only a test).

06-13
The changes made on 06-06 do not run under Microsoft Visual C++ version 6.0 (even though they are within the C++ standard). Preliminary testing under version 7 indicates that Microsoft has fixed this problem in later versions of their C++ compiler.

06-06
Converted the routines Forward and Reverse to allow for any SimpleVector instead of just CppADvector. In addition, separated the syntax of the function call from the prototype for each of the arguments. This was also done for all the easy to use Drivers as well as the Independent function and the ADFun constructor.

Add a section containing a list of all the examples .

05-19
A significant improvement in speed was obtained by moving the buffer extension to a separate function and then inline the rest of putting operators in the tape. For example, here is part of the speed test output before this change: 
 
     Tape of Expansion by Minors Determinant: Length = 350, Memory = 6792
     size = 5 rate = 230
     size = 4 rate = 1,055
     size = 3 rate = 3,408
     size = 2 rate = 7,571
     size = 1 rate = 13,642
and here is the same output after this change: 
 
     Tape of Expansion by Minors Determinant: Length = 350, Memory = 6792
     size = 5 rate = 448
     size = 4 rate = 2,004
     size = 3 rate = 5,761
     size = 2 rate = 10,221
     size = 1 rate = 14,734
Note that your results will vary depending on operating system and machine.

05-18
Change name of OdeControl to OdeErrControl and improve its documentation.

Correct the syntax for the Parameter and Variable functions.

05-16
Change OdeErrControl to have method return its order instead of having a separate argument to OdeErrControl.

Add the argument scur to OdeErrControl, improve OdeErrControl choice of step size and documentation.

05-12
Using profiling, the multiplication operator was show to take a significant amount of time. It was reorganized in order to make it faster. The profiling indicated an improvement so that same change was made to the ad_binary and compute_assign operators.

05-06
The documentation for SimpleVector and NearEqual were changed to use more syntax (what the user enters) and simpler prototypes (the compiler oriented description of the arguments). In addition, exercises were added at the end of the SimpleVector , CppAD_vector , and NearEqual documentation.

There was a undesired divide by zero case in the file TestMore/VecUnary.cpp that just happened to work in corresponding NearEqual check. The NearEqual routine has been changed to return false if either of the values being compared is infinite or not a number. In addition, the divide by zero has been removed from the TestMore/VecUnary.cpp test.

05-01
The doubly linked list was also removed from the VecAD internal data structure because this method of coding is simpler and it makes it more like the rest of CppAD.

04-21
The profiling indicated that the destructor for an AD object was using a significant amount of time. The internal data structure of an AD object had a doubly linked list that pointed to the current variables and this was modified when an AD object was destroyed. In order to speed AD operations in general, the internal data structure of an AD object has been changed so that this list is no longer necessary (a tape id number is used in its place)

During the process above, the function Variable was added.

04-20
Add profiling to the speed tests.

04-19
Remove an extra (not necessary) semi-colon from the file cppad/local/Operator.h.

03-26
The new routine OdeErrControl does automatic step size control for the ODE solvers.

03-23
The routine Rosen34 is an improved stiff integration method that has an optional error estimate in the calling sequence. You must change all your calls to OdeImplicit to use Rosen34 (but do not need to change other arguments because error estimate is optional).

03-22
The routine Runge45 is an improved Runge-Kutta method that has an optional error estimate in the calling sequence. You must change all your calls to OdeRunge to use Runge45 (but do not need to change other arguments because error estimate is optional).

03-09
Some extra semi-colons (empty statements) were generating warnings on some compilers. The ones that occurred after the macros CppADStandardMathBinaryFun, CppADCompareMember, CppADBinaryMember, and CppADFoldBinaryOperator have been removed.

03-04
An new multiple level of AD example mul_level was added.

03-01
An option that specifies error and warning flags for all the C++ compile commands, was added to the Unix installation instructions .

02-24
The routine LuSolve was split into LuFactor and LuInvert . This enables one to efficiently solve equations where the matrix does not change and the right hand side for one equation depends on the left hand side for a previous equation.

An extra requirement was added to the SimpleVector template class. There must be a typedef for value_type which is the type of elements in the vector

Under Mandrake Linux 10.1, some template friend declarations were failing because the corresponding operations were not declared before being indicated as friends (found by Jean-Pierre Dussault ). This has been fixed.

01-08
The erf function was added. The implementation of this function used conditional expressions (CondExp ) and some times the expression that was not valid in a region caused division by zero. For this reason, the check and abort on division by zero has been removed.
Input File: omh/whats_new/whats_new_05.omh cppad-20170000.3/doc/whats_new_04.xml0000644000175200017650000021201413057470511016216 0ustar coincoin-web Changes and Additions to CppAD During 2004
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Changes and Additions to CppAD During 2004

Introduction
This section contains a list of the changes plus future plans for CppAD during 2004 (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions.

12-11
The documentation for the CppAD error macros was improved. The package title in cppad was changed. The documentation for CppAD::vector was improved and the corresponding source code cppad/vector.hpp was included.

12-09
The LuSolve and OdeRunge source code was modified to make the more in line with the introduction to C++ AD book (OdeRunge has been replaced by Runge45 ). In addition, the examples OdeRunge.cpp and lu_solve.cpp were modified to make the simpler. (The more complex version of OdeRunge.cpp was moved to the TestMore directory.)

12-03
The Poly documentation and source code were modified to make them more in line with the introduction to C++ AD book.

11-17
Changing to Autoconf and Automake on 08-24 mistakenly forgot the -Wall compiler switch (all warnings). This has been added and the corresponding warnings have been fixed.

11-16
The 11-15 Debug version would not compile under Visual C++ version 7.0 because a declaration of LessThanOrZero was missing. This has been fixed.

11-15
The ForOne and RevOne easy to use drivers were added.

11-14
The notation in the ADFun sections was changed to make the Forward and Reverse routines easier to use.

11-13
The Taylor coefficient vector and matrix notation was folded into just Taylor coefficients .

11-12
If NDEBUG is not defined during compile time, all AD<Base> comparison operations are checked during zero order forward mode calculations. The CompareChange function returns the number of comparison operations that have changed.

11-10
The get_started.cpp example was changed to use the Jacobian driver. In addition, more index entries, that point to the easy to use drivers , were added.

11-04
The Microsoft Visual Studio project file example/Example.dsp/ was missing some new examples that needed to be linked in the install windows procedure. This has been fixed.

11-02
The unix installation required the user to touch the files to get the dates in proper order. This is no longer necessary.

11-01
Some of the dependency directories and files, for example PrintFor/.deps and PrintFor/.deps/PrintFor.Po had an extra ? at the end of their names. This seems to have been fixed by using a newer version of the autoconf and automake tools.

10-29
Add the example and test simple_vector.cpp to the SimpleVector documentation.

The specifications for preprocessor symbols state that all the CppAD preprocessor symbols begin with CppAD (so they do not conflict with other packages). Some preprocessor symbols in the file cppad/config.h did began with WITH_. This has been fixed.

10-28
The examples hes_lu_det.cpp , hes_minor_det.cpp , jac_lu_det.cpp , and jac_minor_det.cpp used the negative of a size_t value. The value has been changed to an int.

The CppAD::vector template class was converted into a library routine so it can be used separately from the rest of CppAD.

10-27
The PrintFor example was moved to its own directory because the conversion from VC 6.0 to VC 7.0 projects did not work when there were multiple executables in one project file. The install instructions were modified to reflect this change.

10-21
One declaration (for the Value function) was missing from the file cppad/local/Declare.h. This has been added and CppAD should now compile and run under both Microsoft VC 6.0 and 7.0.

10-19
The current version of CppAD has a problem compiling under Microsoft Visual C++ version 7.0 (it compiles and works under version 6.0). The problem appears to be due to a closer agreement between VC 7.0 and the C++ standard for declaring templates functions as friends. Some friend declarations were removed and others were made more specific in order to migrate the a version that will compile and run using VC 7.0.

10-16
The example compare.cpp displayed the text from bool_fun.cpp by mistake. This has been fixed.

The Compare operators have been extended to work with int operands.

10-06
The test TapeDetLu was added to speed_cppad/DetLuSpeed.cpp and TapeDetMinor was added to speed_cppad/DetMinorSpeed.cpp. These tests just tape the calculations without computing any derivatives. Using this, and the other tests, one can to separate the taping time from the derivative calculation time.

The windows installation steps do not build a config.h file. Hence a default config.h file was added to the distribution for use with Microsoft Visual Studio.

The Distribute section of the developer documentation was brought up to date.

Links to the ADOLC and FADBAD download pages were added to the unix installation instructions.

09-29
The include files for the utilities are now included by the root file cppad/cppad.hpp. They can still be included individually with out the rest of the CppAD package.

09-26
The routine OdeRunge was modified so that it will now integrate functions of a complex arguments. This was done by removing all uses of greater than and less than comparisons were removed. (OdeRunge has been replaced by Runge45 ).

The changes on 09-21 did not fix all the file date and time problems; i.e., automake was still running in response to the unix installation make command.

09-23
There was a reference to B that should have been X in the description of the X argument of LuSolve. This has been fixed.

09-21
The CondExp function has been modified so that it works properly for AD< AD<Base> > types; i.e., it now works for multiple levels of taping.

The date of the files aclocal.m4 and config.h.in were later than the date of top level Makefile.am. This caused the make command during the unix installation to try to run autoconf and this did not work on systems with very old versions of autoconf. This has been fixed.

09-13
The examples that are specific to an operation were moved to be below that operation in the documentation tree. For example add.cpp is below ad_binary in the documentation tree.

09-10
The version released on 04-09-09 did not have the new file PrintFor.h in cppad/local. This has been fixed.

The Base type requirements were simplified.

The Unix installation instructions were modified so just one make command was executed at the top level. This was necessary because the order of the makes is now important (as previously suggested, the makes did not work properly).

09-09
The PrintFor function was added so that users can debug the computation of function values at arguments that are different from those used when taping.

09-07
In the Unix installation instructions place ./ in front of current directory program names; for example, ./GetStarted instead of GetStarted (because some unix systems do not have the current directory in the default executable path).

09-04
A library containing the SpeedTest and NearEqual object files was added to the distribution.

All of the include files of the form <cppad/library/name.h> were moved to <cppad/name.h> .

09-02
Some more messages were added to the output of configure during the Unix installation .

The suggested compression program during Windows installation was changed from 7-zip to WinZip .

08-27
The error messages printed by the default version of the CppAD error macros had YY-MM-DD in place of the date for the current version. This has been fixed.

All the correctness tests are now compiled with the -g command line option (the speed tests are still compiled with -O2 -DNDEBUG).

The installation instructions for Unix and Windows were split into separate pages.

08-25
The installation now automates the replacement of CppAD::vector by either the std::vector or boost::numeric::ublas::vector.

08-24
This date marks the first release that uses the Gnu tools Autoconf and Automake. This automates the building of the make files for the installation and is the standard way to distribute open source software. This caused some organizational changes, for example, the GetStarted example now has its own directory and the distribution directory is named
     cppad-yy-mm-dd
 where yy-mm-dd is the year, month and date of the distribution. (Note the distribution directory is different from the directory where CppAD is finally installed.)

08-12
Move OdeExplicit into the cppad/library/ directory. In addition, change it so that the vector type was a template argument; i.e., works for any type of vector (not just CppADvector).

07-31
Move LuSolve into the cppad/library/ directory. In addition, change it so that the vector type was a template argument; i.e., works for any type of vector (not just CppADvector).

07-08
The file cppad/example/NearEqual.h has been moved to cppad/example/NearEqualExt.h because it contains extensions of the NearEqual routine to AD types.

07-07
The double and std::complex<double> cases for the NearEqual routine arguments has been moved to the general purpose utilities .

07-03
The CppAD error macros names CppADExternalAssert and CppADInternalAssert were changed to CppADUsageError and CppADUnknownError. The SpeedTest routine was changed to use CppADUsageError instead of a C assert.

07-02
The SpeedTest output was improved so that the columns of values line up. Previously, this was not the case when the number of digits in the size changed.

06-29
Added code to trap and report memory allocation errors during new operations.

06-25
A discussion of the order dependence of the assignment operator and the independent function was added to the Faq . In addition, a similar discussion was added to the documentation for the Independent function.

The definition of a parameter and variable were changed to reflect that fact that these are time dependent (current) properties of an AD<Base> object.

06-12
All of the arithmetic operators (except for the unary operators) can now accept int arguments. The documentation for these arguments has been changed to reflect this. In addition, the corresponding test cases have been changed to test this and to test high order derivative cases. The old versions of these tests were moved into the cppad/Test directory.

06-04
The atan2 function was added.

06-03
The asin and acos unary_standard_math functions were added.

There was a bug the reverse mode theory and calculation of derivatives of sqrt for fourth and higher orders. This has been fixed. In addition, the following examples have been changed so that they test derivative up to fifth order: asin , atan , cos , exp , log , sin , sqrt .

06-01
There was a bug in the atan function forward mode calculations for Taylor coefficient orders greater than two. This has been fixed.

05-30
The sin and cos examples were changed so that they tested higher order derivatives.

05-29
The forward mode recursion formulas for each of the standard math functions has been split into separate sections.

A roman (instead of italic) font was used for the name of for the name of each of the standard math functions in the assumption statements below the section for the standard math functions. For example, sin ( x ) instead of sin ( x ) .

05-26
In the documentation for Poly , the reference to example/Poly.h was corrected to cppad/library/Poly.h.

In the documentation for SpeedTest , the reference to Lib/SpeedTest.h was corrected to cppad/library/SpeedTest.h. In addition, the example case was corrected.

In Reverse , the definition for U ( t , u ) had t p -1 where it should have had t p -1 . This has been fixed.

05-25
The special case where the second argument to the pow function is an int has been added.

05-14
Change all of the include syntax
     # include "filename"
 to the syntax
     # include <filename>
 so that examples and other use better reflect how one would use CppAD after it was installed in a standard include directory; for example /usr/local/include/cppad.

The user documentation was moved from the directory cppad/User to the directory cppad/Doc.

The directory cppad/Lib was moved to cppad/library to reflect that fact that it is not what one expects in a standard lib directory or a standard include directory.

05-12
The string YY-MM-DD in the preprocessor symbol CppADVersion was not being replaced by the current date during distribution. This resulted in the CppADExternalAssert macro printing YY-MM-DD where is should have printed the date of distribution. This has been fixed.

All of the include commands of the form
     # include "include/name.h"
     # include "lib/name.h"
 have been changed to the form
     # include "cppad/include/name.h"
     # include "cppad/lib/name.h"
 This will avoid mistakenly loading a file from another package that is in the set of directories being searched by the compiler. It is therefore necessary to specify that the directory above the CppAD directory be searched by the compiler. For example, if CppAD is in /usr/local/cppad, you must specify that /usr/local be searched by the compiler. Note that if /usr/local/cppad/ is no longer searched, you will have to change 
 
     # include "cppad.hpp"
to 
 
     # include "cppad/cppad.hpp"
.

The window nmake file Speed/Speed.mak was out of date. This has been fixed.

05-09
Move Poly and SpeedTest into the cppad/Lib directory and the CppAD namespace.

05-07
The divide operator tests were extended to include a second order derivative calculation using reverse mode.

The Poly routine was modified to be more efficient in the derivative case. In addition, it was changed to use an arbitrary vector for the coefficients (not just a CppADvector).

05-04
A reloading of the data base caused the files include/atan.h and include/cos.h to be mistakenly started with lower case letters. These have been moved to include/Atan.h and include/Cos.h respectively.

05-03
The Reverse mode calculations for conditional expressions were mistakenly left out. This has been fixed.

04-29
The unary functions, such as sin and cos , were not defined for elements of an VecAD vector. This has been fixed.

04-28
The operator << was added to the default test_vector template class.

A FADBAD correctness and speed comparison with CppAD was added.

04-25
Factor out common sub-expressions in order to make lu_vec_ad.cpp faster.

Convert description from C++ Automatic Differentiation to C++ Algorithmic Differentiation.

04-24
The VecAD element class is no longer a derived class of the AD class. This enabled a decrease in tape memory and an increase in the speed for VecAD operations.

The log10 function was added.

04-22
Add CondExp and use it to speed up lu_vec_ad.cpp .

04-21
Use abs to speed up lu_vec_ad.cpp .

04-20
The absolute value function was added.

The value n for OdeExplicit and OdeImplicit is deduced from the argument x0 and is not passed as a separate argument. This documentation has been fixed to this effect.

04-19
The += operator did not function correctly when the left hand operand was a parameter and the right hand operand was a variable (found by Mike Dodds ). This has been fixed.

04-09
Adding special operators for using parameters to index VecAD objects increased the speed and reduced the memory requirements (by about 20%) for the VecAD case in the speed_cppad/LuSolveSpeed.cpp/ test.

The VecAD objects are not being handled correctly by the Reverse function. The VecAD test was extended to demonstrate the problem and the problem was fixed (it is now part of TestMore/VecAD).

04-08
The example lu_vec_ad_ok.cpp uses VecAD to executes different pivoting operations during the solution of linear equations with out having to retape.

The speed test speed_cppad/LuSolveSpeed.cpp/ has been added. It shows that the initial implementation of VecAD is slow (and uses a lot of memory.) In fact, it is faster to use LuSolve and retape for each set of equations than it is to use lu_vec_ad.cpp and not have to retape. This test will help us improve the speed of lu_vec_ad.cpp .

04-07
There were bugs in the assignment to VecAD elements during taping that have been fixed. In addition, an example of tapping the pivoting operations in an Lu factorization has been added.

04-03
Added size_t indexing to the VecAD class.

Fixed a bug connected to the VecAD class and erasing the tape.

04-02
Some memory savings is done with regard to equal parameter values being stored in the tape. There was a bug in this logic when parameter in an AD< AD<Base> > class had values that were variables in the AD<Base> class. This has been fixed.

04-01
The name of the class that tapes indexing operations was changed from ADVec to VecAD . This class was extended so that the value of elements in these vectors can be variables (need not be parameters ).

03-30
Do some simple searching of the parameter table during taping avoid multiple copies of parameters on tape (use less tape memory).

03-28
The version ADVec , a vector class that tapes indexing operations, is now available. It is currently restricted by the fact that all the values in the vector must be parameters .

03-25
The internal taping structure has been changed to have variable length instructions. This is to save memory on the tape. In addition, it may help in the implementation of the vector class that tracks indexing. (A now functioning version of this class is described in VecAD .)

03-18
A change was made to the way parameter values are stored on the tape. This resulted in a significant savings in the amount of memory required.

03-17
Change the return type for SpeedTest from const char * to std::string. The memory required for the largest test cases was added to the speed_cppad tests output.

03-15
The comparison between ADOLC and CppAD for the DetLuADOLC.cpp/ example was returning an error (because it was checking for exact equality of calculated derivatives instead of nearly equal). This has been fixed.

03-12
The user defined unary functions were removed and the user defined discrete functions were added. These discrete functions add the capability of conditional expressions (alternate calculations) being included in an ADFun object.

03-11
The classes det_by_minor and det_by_lu were added and used these to simplify the examples that compute determinants.

03-09
The routines Grad and Hess have been removed. You should use Jacobian and Hessian instead.

03-07
The driver routines Hessian and RevTwo has been added. These to compute specialized subsets of the second order partials.

Documentation errors in ForTwo and Reverse were fixed. The example documentation was reorganized.

03-06
The driver ForTwo has been added. It uses forward mode to compute a subset of the second order partials.

Split all of the "example" and "test" index entries that come from cppad/example/*.cpp into sorted subheadings.

03-05
The Grad routine, which only computed first derivatives of scalar valued functions, has been replaced by the Jacobian routine which computes the derivative of vector valued functions.

03-04
The bug reported on 02-17 was present in all the operators. These have all been fixed and tests for all the operators have been added to the cppad/Test directory.

The f.Parameter() function was added so that one can count how many components of the range space depend on the value of the domain space components. This helps when deciding whether to use forward or reverse mode.

03-03
Special operators were added to distinguish the cases where one of the operands is a parameter . This reduced the amount of branching that is necessary when executing Forward and Reverse calculations.

The Independent and Parameter functions were moved below ADFun in the documentation.

03-01
The DetLuADOLC.cpp, DetLu case was added to the ADOLC comparison tests.

02-29
Under certain optimization flag values, and on certain systems, an error was reported by the ADOLC correctness comparison. It turned out that CppAD was not initializing a particular index when debugging was turned off. This has been fixed.

02-28
A set of routines for comparing CppAD with ADOLC has been added to the distribution. In addition, documentation for compiling and linking the Examples and Speed Tests has been added.

02-21
If you use the user defined unary atomic functions there is a restriction on the order of the derivatives that can be calculated. This restriction was documented in the user defined unary function Forward and Reverse . (These unary functions were removed on 03-12 .)

02-20
A user interface to arbitrary order reverse mode calculations was implemented. In addition, the ADFun member functions Rev and RevTwo were removed because it is easier to use the uniform syntax below:
Old Syntax Uniform Syntax
r1 = f.Rev(v) r1 = f.Reverse(1, v)
q1 = f.RevTwo(v) r2 = f.Reverse(2, v)
q1[i] == r2[2 * i + 1]


The Theory section has been completely changed so that it corresponds to the arbitrary order calculations. (Some of this change was made when the arbitrary forward mode interface was added on 04-02-15 .

The directory cppad/Test has been added. It contains tests cases that are not intended as examples.

02-17
There was a bug in the way CppAD handled the parameters zero and one when they were variables on a lower level tape; i.e. x might be a parameter on an AD< AD<Base> > tape and a its value might be a variable on the AD<Base> tape. This bug in the multiply and divide routines has been fixed.

There was a bug that is some cases reported a divide by zero error when the numerator was zero. This has been fixed.

02-16
A bug in Forward prevented the calculation of derivatives with higher order than two. In addition, this checking for user errors in the use of Forward was also faulty. This has been fixed.

The Microsoft project file example\Example.dsp was out of date. This has been fixed.

The example that tapes derivative calculations has been changed to an application of Taylor's method for solving ordinary differential equations.

02-15
A user interface to arbitrary order forward mode calculations was implemented. In addition, the ADFun member functions Arg, For and ForTwo were removed because it is easier to use the uniform syntax below:
Old Syntax Uniform Syntax
v0 = f.Arg(u0) v0 = f.Forward(0, u0)
v1 = f.For(u1) v1 = f.Forward(1, u1)
v2 = f.For(u2) v2 = f.Forward(1, u2)

02-12
All of the derivative calculations are now done using arbitrary order Taylor arithmetic routines. The Theory section was changed to document this method of calculation.

02-01
The definition of a Taylor coefficient was changed to include the factorial factor. This change was also made to the output specifications for the FunForTwo routine.

01-29
There were some bugs in the FunArg function that were fixed.
  1. If one of the dependent variables was a parameter FunArg did not set it's value properly. (All its derivatives are zero and this was handled properly.)
  2. The user defined unary functions were not computed correctly.
The specifications for the usage and unknown CppAD error macros were modified so that they could be used with out side effects.

01-28
Some corrections and improvements were made to the documentation including: CppADvector was placed before its use, a reference to Ode_ind and Ode_dep was fixed in OdeImplicit.

01-22
The specifications for the routine FunForTwo was changed to use Taylor coefficients . This makes the interface to CppAD closer to the interface for ADOLC .
Input File: omh/whats_new/whats_new_04.omh cppad-20170000.3/doc/whats_new_03.xml0000644000175200017650000015174113057470511016226 0ustar coincoin-web Changes and Additions to CppAD During 2003
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Changes and Additions to CppAD During 2003

Introduction
This section contains a list of the changes plus for (in reverse order by date). The purpose of this section is to assist you in learning about changes between various versions.

12-24
Some references to double should have been references to the base type (in reverse mode and in the Grad/ and Hess functions). This has been fixed.

12-22
The preprocessor symbol WIN32 was being used to determine if one was using Microsoft's C++ compiler. This symbol is predefined by the MinGW version of the GNU C++ compiler and hence CppAD had errors during installation using MinGW. This has been fixed by using the preprocessor symbol _MSC_VER to determine if one is using the Microsoft C++ compiler.

12-14
The extended system solvers OdeOne and OdeTwo have been removed from the distribution. In addition, the interface to the ODE solvers have been simplified.

12-13
Remove the CppADCreateTape macro and have the tapes created and grow automatically.

12-12
The old method where one directly accesses the tape has been removed and the following functions are no longer available:
          size_t TapeName.Independent(AD<Base> &indvar)
          size_t TapeName.Record(size_t order)
          size_t TapeName.Stop(void)
          bool Dependent(const AD<Base> &var) const
          bool TapeName.Dependent(const AD<Base> &var) const
          size_t TapeName.Total(void) const
          size_t TapeName.Required(void) const
          size_t TapeName.Erase(void)
          TapeState TapeName.State(void) const
          size_t TapeName.Order(void) const
          size_t TapeName.Required(void) const
          bool Parameter(CppADvector< AD<Base> > &u)
          TapeName.Forward(indvar)
          TapeName.Reverse(var)
          TapeName.Partial(var)
          TapeName.ForwardTwo(indvar)
          TapeName.ReverseTwo(var)
          TapeName.PartialTwo(var)
12-10
The change on 12-01 make the taping process simpler if one does not directly access CppADCreateTape. The examples were changed to not use TapeName . The following examples were skipped because they document the functions that access TapeName : DefFun.cpp, For.cpp, for_two.cpp, Rev.cpp, and rev_two.cpp.

12-05
There was a bug in f.Rev and f.RevTwo and when two dependent variables were always equal and shared the same location in the tape. This has been fixed.

The ODE Example was changed to tape the solution (and not use OdeOne or OdeTwo). This is simpler to use and the resulting speed tests gave much faster results.

12-01
The following function has been added:
     void Independent(const CppADvector<Base> &x)
 which will declare the independent variables and begin recording AD<Base> operations (see Independent ). The ADFun constructor was modified so that it stops the recording and erases that tape as well as creates the ADFun object. In addition, the tape no longer needs to be specified in the constructor.

11-21
Add StiffZero to set of ODE solvers.

11-20
The AbsGeq and LeqZero in LuSolve were changed to template functions so they could have default definitions in the case where the <= and >= operators are defined. This made the double and AD<double> use of LuSolve simpler because the user need not worry about these functions. On the other hand, it made the std::complex and AD<std::complex> use of LuSolve more complex.

The member function names for the fun argument to ODE were changed from fun.f to fun.Ode and from fun.g to fun.Ode_ini .

11-16
The table of contents was reorganized to provide a better grouping of the documentation.

The LuSolve utility is now part of the distribution and not just an example; i.e., it is automatically included by cppad.hpp.

11-15
The ODE solver was modified so that it can be used with any type (not just an AD type. This was useful for the speed testing. It is also useful for determining how the integrator steps should be before starting the tape.

The template argument Type was changed to Base where ever it was the base type of an AD class.

11-14
An speed_cppad/OdeSpeed.cpp/ test was added and some changes were made to the ODE interface in order to make it faster. The most significant change was in the specifications for the ODE function object fun .

11-12
The user defined unary function example example/UnaryFun.cpp was incorrect. It has been corrected and extended.

11-11
The CppAD::vector template class is now used where the std::vector template class was previously used. You can replace the CppAD::vector class with a vector template class of your choosing during the Install procedure.

11-06
The documentation for taping derivative calculations was improved as well as the corresponding example. In order to make this simpler, the example tape name DoubleTape was changed to ADdoubleTape (and the other example tape names were also changed).

11-04
The ODE utility was changed from an example to part of the distribution. In addition, it was extended so that it now supports taping the solution of the differential equations (case order equal zero) or solving the extended set of differential equations for both first and second derivatives (cases order equal one and two). In addition, an initial condition that depends on the parameter values is also allowed.

11-02
It is now legal to differentiate a parameter with respect to an independent variable (parameter derivatives are always equal to zero). This is an extension of the Reverse, Partial, ReverseTwo, and PartialTwo functions.

10-21
All the CppAD include files, except cppad.hpp were moved into an include subdirectory.

10-16
The ADFun template class was added so that one can save a tape recording and use it as a differentiable function. The ADFun functions supports directional derivatives in both Forward and Reverse mode where as the tape only supports partial derivatives.

10-14
The sqrt function was added to the unary_standard_math functions. In addition, a definition of the power function for the types float and double was automatically included in the CppAD namespace.

The Value function was changed so that it can be called when the tape is in the Empty state.

10-10
The atan function was added to the unary_standard_math functions.

10-06
In the notation below, zero and one are parameters that are exactly equal to zero and one. If the variables z and x were related in any of the following ways, they share can share the same record on the tape because they will have the same derivatives.
     z = x + zero        z =  x * one
     z = zero + x        z =  one * x
     z = x - zero        z =  x / one
 Furthermore, in the following cases, the result z is a parameter (equal to zero) and need not be recorded in the tape:
     z = x * zero        z =  zero / x
     z = zero * x
 The arithmetic operators were all checked to make sure they did not add to the tape in these special cases. The total record count for the program in the Example directory was 552 before this change and 458 after.

10-05
The process of converting the tape to operators was completed. In order to make this conversion, the binary user defined functions were removed. (Bob Goddard suggested a very nice way to keep the unary functions.) Another significant change was made to the user interface during this procedure, the standard math library functions are now part of the CppAD distribution and not defined by the user.

The function TapeName.Total was added to make it easy to track how many tape records are used by the test suite. This will help with future optimization of the CppAD recording process.

There was a bug (found by Mike Dodds ) in the error checking of the TapeName.Erase function. If Erase was called twice in a row, and NDEBUG was false during compilation, the program would abort. This has been fixed.

09-30
A process of changing the tape from storing partial derivatives to storing operators has been started. This will make the tape smaller and it will enable the computation of higher derivatives with out having to tape the tape (see mul_level ). The Add, Subtract, Multiply and Divide operators have been converted. The user defined functions are presenting some difficulties, so this process has not yet been completed.

There was a bug in reverse mode when an dependent variable was exactly equal to an independent variable. In this case, it was possible for it to be located before other of the independent variables on the tape. These other independent variable partials were not initialized to zero before the reverse calculation and hence had what ever value was left by the previous mode calculation. This has been fixed and the Eq.cpp example has been changed to test for this case.

The following tape functions were changed to be declared const because they do not modify the tape in any way: State, Order, Required, Dependent, and Parameter .

09-20
The functions Grad and Hess were changed to use function objects instead of function pointers.

09-19
The higher order constructors (in standard valarray) were removed from the ODE example in order to avoid memory allocation of temporaries (and hence increase speed). In addition, the function objects in the ODE examples were changed to be const.

09-18
An ordinary differential equation solver was added. In addition, the extended system to differentiate the solution was included.

09-15
The linked list of AD variables was not being maintained correctly by the AD destructor. This was fixed by have the destructor use RemoveFromVarList to remove variables from the list. (RemoveFromVarList is a private AD member function not visible to the user.)

09-14
There is a new Faq question about evaluating derivatives at multiple values for the independent variables .

09-13
An example that uses AD< AD<double> > to compute higher derivatives was added.

The name GaussEliminate was changed to LuSolve to better reflect the solution method.

09-06
Changed the get_started.cpp and complex_poly.cpp examples so they use a template function with both base type and AD type arguments. (The resulting code is simpler and a good use of templates.)

09-05
A getting started example was added and the organization of the Examples was changed.

09-04
The AbsOfDoubleNotDefine flag is no longer used and it was removed from the Windows install instructions.

The 03-09-03 distribution did not have the proper date attached to it. The distribution script has been changed so that attaching the proper date is automated (i.e., this should not happen again).

A Frequently Asked Questions and Answers section was started.

09-03
Added the Value function which returns the base type value corresponding to an AD object.

08-23
A new version of Cygwin was installed on the development system (this may affect the timing tests reported in this document). In addition, LuSolve was changed to use back substitution instead of reduction to an identity matrix. This reduced the number of floating point operations corresponding to evaluation of the determinant. The following results correspond to the speed test of DetLu on a 9 by 9 matrix:
Version double Rate AD<double> Rate Gradient Rate Hessian Rate Tape Length
03-08-20 8,524 5,278 4,260 2,450 532
03-08-23 7,869 4,989 4,870 2,637 464

08-22
The unary minus operator was added to the AD operations.

08-19
The standard math function examples were extended to include the complex case.

The LuSolve routine what changed to use std::vector<Base> & arguments in place of Base * arguments. This removes the need to use new and delete with LuSolve.

When testing the speed of the change to using standard vector, it was noticed that the LuSolve routine was much slower. (see times for 03-08-16 below). This was do to computing the determinant instead of the log of the determinant. Converting back to the log of the determinant regained the high speeds. The following results correspond to the speed test of DetLu on a 9 by 9 matrix:
Version double Rate AD<double> Rate Gradient Rate Hessian Rate Tape Length
03-08-16 9,509 5,565 3,587 54 537
03-08-19 8,655 5,313 4,307 2,495 532

08-17
The macro CppADTapeOverflow was added so that CppAD can check for tape overflow even in the NDEBUG preprocessor flag is defined.

08-16
The LuSolve routine was extended to handle complex arguments. Because the complex absolute value function is nowhere differentiable, this required the allowing for user defined boolean valued functions with AD arguments . The examples lu_solve.cpp and GradLu.cpp were converted to a complex case.

08-11
The routine LuSolve was made more efficient so that it is more useful as a tool for differentiating linear algebra calculations. The following results correspond to the speed test of DetLu on a 9 by 9 matrix:
Version double Rate AD<double> Rate Gradient Rate Hessian Rate Tape Length
03-08-10 49,201 7,787 2,655 1,809 824
03-08-11 35,178 12,681 4,521 2,541 540
In addition the corresponding test case lu_solve.cpp was changed to a Hilbert matrix case.

08-10
A complex polynomial example was added.

The documentation and type conversion in LuSolve was improved.

The absolute value function was removed from the examples because some systems do not yet properly support double abs(double x) ,

08-07
Because the change to the multiplication operator had such a large positive effect, all of the arithmetic operators were modified to reduce the amount of information in the tape (where possible).

08-06
During Lu factorization, certain elements of the matrix are know to be zero or one and do not depend on the variables. The multiplication operator was modified to take advantage of this fact. This reduced the size of the tape and increased the speed for the calculation of the gradient and Hessian for the Lu determinant test of a 5 by 5 matrix as follows:
Version Tape Length Gradient Rate Hessian Rate
03-08-05 176 11,362 1,149
03-08-06 167 12,780 10,625

08-05
Fixed a mistake in the calculation of the sign of the determinant in the LuSolve example.

08-04
Added a the compiler flag 
 
     AbsOfDoubleNotDefined
to the make files so that it could be removed on systems where the function
     double abs(double x)
 was defined in math.h.

08-03
The Grad and Hess functions were modified to handel the case where the function does not depend on the independent variables.

The LuSolve example was added to show how on can differentiate linear algebra calculations. In addition, it was used to add another set of speed tests .

The standard Math functions were added both as examples of defining atomic operations and to support mathematical operations for the AD<double> case.

The << operator was added to the AD template class for output to streams.

08-01
The computed assignment operators were added to the AD template class.

The name of the Speed/SpeedTest program was changed to Speed/Speed . In addition, Speed/SpeedRun was changed to Speed/SpeedTest.

07-30
The assignment operator was changed so the it returns a reference to the target. This allows for statements of the form
     x = y = z;
 i.e., multiple assignments.

07-29
If the AD copy constructor constructor or assignment operator used an independent variable for its source value, the result was also an independent variable. This has been fixed so that the result is a dependent variable in these cases.

07-26
The AD<Base> data structure was changed to include a doubly linked list of variables. This enabled the AD copy constructor constructor and assignment operator to create multiple references to the same place in the tape. This reduced the size of the tape and increased the speed for the calculation of the gradient and Hessian for the determinant of a 5 by 5 matrix as follows:
Version Tape Length Gradient Rate Hessian Rate
03-07-22 1668 1,363 53
03-07-26 436 3,436 213

07-22
The facility was added so that the user can define binary functions together with their derivatives. (This facility has been removed because it is better to define binary functions using AD variables.)

The Windows version make file directive /I ..\.. in example\Example.mak and Speed\Speed.mak was changed to /I .. (as it should have been).

07-20
The facility was added so that the user can define unary functions, together with their derivatives. For example, the standard math functions such as exp are good candidates for such definitions. (This feature has been replaced by and the standard math functions are now part of the AD types, see AD .)

The first Alpha for the Windows installation was released.

07-18
Computing the determinant of a minor of a matrix det_of_minor was documented as a realistic example using CppAD.

07-16
Fixed some non-standard constructions that caused problems with the installation on other machines.

Compiled and ran the tests under Microsoft Windows. (The Windows release should not take much more work.)

07-14
First Alpha release of CppAD and is being released under the Gnu Public License . It is intended for use by a Unix system. A Microsoft release is intended in the near future.
Input File: omh/whats_new/whats_new_03.omh cppad-20170000.3/doc/deprecated.xml0000644000175200017650000001464613057470511016027 0ustar coincoin-web CppAD Deprecated API Features
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CppAD Deprecated API Features

Contents
include_deprecatedDeprecated Include Files
FunDeprecatedADFun Object Deprecated Member Functions
CompareChangeComparison Changes During Zero Order Forward Mode
omp_max_threadOpenMP Parallel Setup
TrackNewDelRoutines That Track Use of New and Delete
omp_allocA Quick OpenMP Memory Allocator Used by CppAD
memory_leakMemory Leak Detection
epsilonMachine Epsilon For AD Types
test_vectorChoosing The Vector Testing Template Class
cppad_ipopt_nlpNonlinear Programming Using the CppAD Interface to Ipopt
old_atomicUser Defined Atomic AD Functions
zdoublezdouble: An AD Base Type With Absolute Zero
CppADCreateUnaryBool AD Boolean Functions
CppADCreateDiscrete Discrete AD Functions
auto_tools Auto Tools Unix Test and Installation
nan(zero) nan(zero)

Atomic Functions
The following are links to deprecated atomic_base interfaces: for_sparse_jac , rev_sparse_jac , for_sparse_hes , rev_sparse_hes .
Input File: omh/deprecated/deprecated.omh cppad-20170000.3/doc/fundeprecated.xml0000644000175200017650000004330313057470511016530 0ustar coincoin-web ADFun Object Deprecated Member Functions
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ADFun Object Deprecated Member Functions

Syntax
f.Dependent(y)
 o = f.Order()
 m = f.Memory()
 s = f.Size()
 t = f.taylor_size()
 u = f.use_VecAD()
 v = f.size_taylor()
 w = f.capacity_taylor()
Purpose
The ADFun<Base> functions documented here have been deprecated; i.e., they are no longer approved of and may be removed from some future version of CppAD.

Dependent
A recording of and AD of Base operation sequence is started by a call of the form
     Independent(x)
 If there is only one such recording at the current time, you can use f.Dependent(y) in place of
     f.Dependent(x, y)
 See Dependent for a description of this operation.

Deprecated 2007-08-07
This syntax was deprecated when CppAD was extended to allow for more than one AD<Base> recording to be active at one time. This was necessary to allow for multiple threading applications.

Order
The result o has prototype
     size_t o
 and is the order of the previous forward operation using the function f . This is the highest order of the Taylor coefficients that are currently stored in f .

Deprecated 2006-03-31
Zero order corresponds to function values being stored in f . In the future, we would like to be able to erase the function values so that f uses less memory. In this case, the return value of Order would not make sense. Use size_order to obtain the number of Taylor coefficients currently stored in the ADFun object f (which is equal to the order plus one).

Memory
The result
     size_t m
 and is the number of memory units (sizeof) required for the information currently stored in f . This memory is returned to the system when the destructor for f is called.

Deprecated 2006-03-31
It used to be the case that an ADFun object just kept increasing its buffers to the maximum size necessary during its lifetime. It would then return the buffers to the system when its destructor was called. This is no longer the case, an ADFun object now returns memory when it no longer needs the values stored in that memory. Thus the Memory function is no longer well defined.

Size
The result s has prototype
     size_t s
 and is the number of variables in the operation sequence plus the following: one for a phantom variable with tape address zero, one for each component of the domain that is a parameter. The amount of work and memory necessary for computing function values and derivatives using f is roughly proportional to s .

Deprecated 2006-04-03
There are other sizes attached to an ADFun object, for example, the number of operations in the sequence. In order to avoid confusion with these other sizes, use size_var to obtain the number of variables in the operation sequence.

taylor_size
The result t has prototype
     size_t t
 and is the number of Taylor coefficient orders currently calculated and stored in the ADFun object f .

Deprecated 2006-06-17
This function has been replaced by size_order .

use_VecAD
The result u has prototype
     bool u
 If it is true, the AD of Base operation sequence stored in f contains VecAD operands. Otherwise u is false.

Deprecated 2006-04-08
You can instead use
     u = f.size_VecAD() > 0
size_taylor
The result v has prototype
     size_t v
 and is the number of Taylor coefficient orders currently calculated and stored in the ADFun object f .

Deprecated 2014-03-18
This function has been replaced by size_order .

capacity_taylor
The result w has prototype
     size_t w
 and is the number of Taylor coefficient orders currently allocated in the ADFun object f .

Deprecated 2014-03-18
This function has been replaced by capacity_order .
Input File: omh/deprecated/fun_deprecated.omh cppad-20170000.3/doc/_fundeprecated_xml.js0000644000175200017650000000517713057470511017372 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'appendix.xml', 'deprecated.xml', 'fundeprecated.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'faq.xml', 'theory.xml', 'glossary.xml', 'bib.xml', 'wish_list.xml', 'whats_new.xml', 'deprecated.xml', 'compare_c.xml', 'numeric_ad.xml', 'addon.xml', 'license.xml' ]; var list_down1 = [ 'include_deprecated.xml', 'fundeprecated.xml', 'comparechange.xml', 'omp_max_thread.xml', 'tracknewdel.xml', 'omp_alloc.xml', 'memory_leak.xml', 'epsilon.xml', 'test_vector.xml', 'cppad_ipopt_nlp.xml', 'old_atomic.xml', 'zdouble.xml' ]; var list_current0 = [ 'fundeprecated.xml#Syntax', 'fundeprecated.xml#Purpose', 'fundeprecated.xml#Dependent', 'fundeprecated.xml#Dependent.Deprecated 2007-08-07', 'fundeprecated.xml#Order', 'fundeprecated.xml#Order.Deprecated 2006-03-31', 'fundeprecated.xml#Memory', 'fundeprecated.xml#Memory.Deprecated 2006-03-31', 'fundeprecated.xml#Size', 'fundeprecated.xml#Size.Deprecated 2006-04-03', 'fundeprecated.xml#taylor_size', 'fundeprecated.xml#taylor_size.Deprecated 2006-06-17', 'fundeprecated.xml#use_VecAD', 'fundeprecated.xml#use_VecAD.Deprecated 2006-04-08', 'fundeprecated.xml#size_taylor', 'fundeprecated.xml#size_taylor.Deprecated 2014-03-18', 'fundeprecated.xml#capacity_taylor', 'fundeprecated.xml#capacity_taylor.Deprecated 2014-03-18' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/comparechange.xml0000644000175200017650000002126613057470511016517 0ustar coincoin-web Comparison Changes During Zero Order Forward Mode
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Comparison Changes During Zero Order Forward Mode

Syntax
c = f.CompareChange()
See Also FunCheck

Deprecated 2015-01-20
This routine has been deprecated, use compare_change instead.

Purpose
We use F : B n → B m to denote the AD function corresponding to f . This function may be not agree with the algorithm that was used to create the corresponding AD of Base operation sequence because of changes in AD comparison results. The CompareChange function can be used to detect these changes.

f
The object f has prototype
     const ADFun<Base> f
c
The result c has prototype
     size_t c
 It is the number of AD<Base> comparison operations, corresponding to the previous call to Forward
     f.Forward(0, x)
 that have a different result from when F was created by taping an algorithm.

Discussion
If c is not zero, the boolean values resulting from some of the comparison operations corresponding to x are different from when the AD of Base operation sequence was created. In this case, you may want to re-tape the algorithm with the independent variables equal to the values in x (so AD operation sequence properly represents the algorithm for this value of independent variables). On the other hand, re-taping the AD operation sequence usually takes significantly more time than evaluation using forward_zero . If the functions values have not changed (see FunCheck ) it may not be worth re-taping a new AD operation sequence.
Input File: omh/deprecated/compare_change.omh cppad-20170000.3/doc/omp_max_thread.xml0000644000175200017650000001450613057470511016711 0ustar coincoin-web OpenMP Parallel Setup
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OpenMP Parallel Setup

Deprecated 2011-06-23
Use thread_alloc::parallel_setup to set the number of threads.

Syntax
AD<Base>::omp_max_thread(number)
Purpose
By default, for each AD<Base> class there is only one tape that records AD of Base operations. This tape is a global variable and hence it cannot be used by multiple OpenMP threads at the same time. The omp_max_thread function is used to set the maximum number of OpenMP threads that can be active. In this case, there is a different tape corresponding to each AD<Base> class and thread pair.

number
The argument number has prototype
     size_t number
 It must be greater than zero and specifies the maximum number of OpenMp threads that will be active at one time.

Independent
Each call to Independent(x) creates a new active tape. All of the operations with the corresponding variables must be preformed by the same OpenMP thread. This includes the corresponding call to f.Dependent(x,y) or the ADFun f(x, y) during which the tape stops recording and the variables become parameters.

Restriction
No tapes can be active when this function is called.
Input File: cppad/core/omp_max_thread.hpp cppad-20170000.3/doc/tracknewdel.xml0000644000175200017650000005447413057470511016235 0ustar coincoin-web Routines That Track Use of New and Delete
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Routines That Track Use of New and Delete

Deprecated 2007-07-23
All these routines have been deprecated. You should use the thread_alloc memory allocator instead (which works better in both a single thread and properly in multi-threading environment).

Syntax
# include <cppad/utility/track_new_del.hpp>
 newptr = TrackNewVec(file, line, newlen, oldptr)
 TrackDelVec(file, line, oldptr)
 newptr = TrackExtend(file, line, newlen, ncopy, oldptr)
 count = TrackCount(file, line)

Purpose
These routines aid in the use of new[] and delete[] during the execution of a C++ program.

Include
The file cppad/track_new_del.hpp is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD include files.

file
The argument file has prototype
     const char *file
 It should be the source code file name where the call to TrackNew is located. The best way to accomplish this is the use the preprocessor symbol __FILE__ for this argument.

line
The argument line has prototype
     int line
 It should be the source code file line number where the call to TrackNew is located. The best way to accomplish this is the use the preprocessor symbol __LINE__ for this argument.

oldptr
The argument oldptr has prototype
     Type *oldptr
 This argument is used to identify the type Type .

newlen
The argument newlen has prototype
     size_t newlen
head newptr
The return value newptr has prototype
     Type *newptr
 It points to the newly allocated vector of objects that were allocated using
     new Type[newlen]
ncopy
The argument ncopy has prototype
        size_t ncopy
 This specifies the number of elements that are copied from the old array to the new array. The value of ncopy must be less than or equal newlen .

TrackNewVec
If NDEBUG is defined, this routine only sets
     newptr = Type new[newlen]
 The value of oldptr does not matter (except that it is used to identify Type ). If NDEBUG is not defined, TrackNewVec also tracks the this memory allocation. In this case, if memory cannot be allocated ErrorHandler is used to generate a message stating that there was not sufficient memory.

Macro
The preprocessor macro call
     CPPAD_TRACK_NEW_VEC(newlen, oldptr)
 expands to
     CppAD::TrackNewVec(__FILE__, __LINE__, newlen, oldptr)
Previously Deprecated
The preprocessor macro CppADTrackNewVec is the same as CPPAD_TRACK_NEW_VEC and was previously deprecated.

TrackDelVec
This routine is used to a vector of objects that have been allocated using TrackNew or TrackExtend. If NDEBUG is defined, this routine only frees memory with
     delete [] oldptr
 If NDEBUG is not defined, TrackDelete also checks that oldptr was allocated by TrackNew or TrackExtend and has not yet been freed. If this is not the case, ErrorHandler is used to generate an error message.

Macro
The preprocessor macro call
     CPPAD_TRACK_DEL_VEC(oldptr)
 expands to
     CppAD::TrackDelVec(__FILE__, __LINE__, oldptr)
Previously Deprecated
The preprocessor macro CppADTrackDelVec is the same as CPPAD_TRACK_DEL_VEC was previously deprecated.

TrackExtend
This routine is used to allocate a new vector (using TrackNewVec), copy ncopy elements from the old vector to the new vector. If ncopy is greater than zero, oldptr must have been allocated using TrackNewVec or TrackExtend. In this case, the vector pointed to by oldptr must be have at least ncopy elements and it will be deleted (using TrackDelVec). Note that the dependence of TrackExtend on NDEBUG is indirectly through the routines TrackNewVec and TrackDelVec.

Macro
The preprocessor macro call
     CPPAD_TRACK_EXTEND(newlen, ncopy, oldptr)
 expands to
     CppAD::TrackExtend(__FILE__, __LINE__, newlen, ncopy, oldptr)
Previously Deprecated
The preprocessor macro CppADTrackExtend is the same as CPPAD_TRACK_EXTEND and was previously deprecated.

TrackCount
The return value count has prototype
     size_t count
 If NDEBUG is defined, count will be zero. Otherwise, it will be the number of vectors that have been allocated (by TrackNewVec or TrackExtend) and not yet freed (by TrackDelete).

Macro
The preprocessor macro call
     CPPAD_TRACK_COUNT()
 expands to
     CppAD::TrackCount(__FILE__, __LINE__)
Previously Deprecated
The preprocessor macro CppADTrackCount is the same as CPPAD_TRACK_COUNT and was previously deprecated.

Multi-Threading
These routines cannot be used in_parallel execution mode. Use the thread_alloc routines instead.

Example
The file TrackNewDel.cpp contains an example and test of these functions. It returns true, if it succeeds, and false otherwise.
Input File: cppad/utility/track_new_del.hpp cppad-20170000.3/doc/tracknewdel.cpp.xml0000644000175200017650000002000413057470511016774 0ustar coincoin-web Tracking Use of New and Delete: Example and Test
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Tracking Use of New and Delete: Example and Test

# include <cppad/utility/track_new_del.hpp>

bool track_new_del(void)
{     bool ok = true;

     // initial count
     size_t count = CPPAD_TRACK_COUNT();

     // allocate an array of lenght 5
     double *ptr = CPPAD_NULL;
     size_t  newlen = 5;
     ptr = CPPAD_TRACK_NEW_VEC(newlen, ptr);

     // copy data into the array
     size_t ncopy = newlen;
     size_t i;
     for(i = 0; i < ncopy; i++)
          ptr[i] = double(i);

     // extend the buffer to be lenght 10
     newlen = 10;
     ptr    = CPPAD_TRACK_EXTEND(newlen, ncopy, ptr);

     // copy data into the new part of the array
     for(i = ncopy; i < newlen; i++)
          ptr[i] = double(i);

     // check the values in the array
     for(i = 0; i < newlen; i++)
          ok &= (ptr[i] == double(i));

     // free the memory allocated since previous call to TrackCount
     CPPAD_TRACK_DEL_VEC(ptr);

     // check for memory leak
     ok &= (count == CPPAD_TRACK_COUNT());

     return ok;
}
Input File: test_more/track_new_del.cpp cppad-20170000.3/doc/omp_alloc.xml0000644000175200017650000001655213057470511015672 0ustar coincoin-web A Quick OpenMP Memory Allocator Used by CppAD
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A Quick OpenMP Memory Allocator Used by CppAD

Syntax
# include <cppad/omp_alloc.hpp>

Purpose
The C++ new and delete operators are thread safe, but this means that a thread may have to wait for a lock on these operations. Once memory is obtained for a thread, the omp_alloc memory allocator keeps that memory omp_available for the thread so that it can be re-used without waiting for a lock. All the CppAD memory allocations use this utility. The omp_free_available function should be used to return memory to the system (once it is no longer required by a thread).

Include
The routines in sections below are defined by cppad/omp_alloc.hpp. This file is included by cppad/cppad.hpp, but it can also be included separately with out the rest of the CppAD.

Deprecated 2011-08-23
Use thread_alloc instead.

Contents
omp_max_num_threadsSet and Get Maximum Number of Threads for omp_alloc Allocator
omp_in_parallelIs The Current Execution in OpenMP Parallel Mode
omp_get_thread_numGet the Current OpenMP Thread Number
omp_get_memoryGet At Least A Specified Amount of Memory
omp_return_memoryReturn Memory to omp_alloc
omp_free_availableFree Memory Currently Available for Quick Use by a Thread
omp_inuseAmount of Memory a Thread is Currently Using
omp_availableAmount of Memory Available for Quick Use by a Thread
omp_create_arrayAllocate Memory and Create A Raw Array
omp_delete_arrayReturn A Raw Array to The Available Memory for a Thread
omp_efficientCheck If A Memory Allocation is Efficient for Another Use
old_max_num_threadsSet Maximum Number of Threads for omp_alloc Allocator
omp_alloc.cppOpenMP Memory Allocator: Example and Test
Input File: omh/deprecated/omp_alloc.omh cppad-20170000.3/doc/omp_max_num_threads.xml0000644000175200017650000001432113057470511017746 0ustar coincoin-web Set and Get Maximum Number of Threads for omp_alloc Allocator
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Set and Get Maximum Number of Threads for omp_alloc Allocator

Deprecated 2011-08-31
Use the functions thread_alloc::parallel_setup and thread_alloc:num_threads instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 omp_alloc::set_max_num_threads(number)
 number = omp_alloc::get_max_num_threads()
Purpose
By default there is only one thread and all execution is in sequential mode (not parallel ).

number
The argument and return value number has prototype
     size_t number
 and must be greater than zero.

set_max_num_threads
Informs omp_alloc of the maximum number of OpenMP threads.

get_max_num_threads
Returns the valued used in the previous call to set_max_num_threads. If there was no such previous call, the value one is returned (and only thread number zero can use omp_alloc ).

Restrictions
The function set_max_num_threads must be called before the program enters parallel execution mode. In addition, this function cannot be called while in parallel mode.
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_in_parallel.xml0000644000175200017650000001161113057470511017051 0ustar coincoin-web Is The Current Execution in OpenMP Parallel Mode
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Is The Current Execution in OpenMP Parallel Mode

Deprecated 2011-08-31
Use the function thread_alloc::in_parallel instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 flag = omp_alloc::in_parallel()

Purpose
Some of the omp_alloc allocation routines have different specifications for parallel (not sequential) execution mode. This routine enables you to determine if the current execution mode is sequential or parallel.

flag
The return value has prototype
     bool flag
 It is true if the current execution is in parallel mode (possibly multi-threaded) and false otherwise (sequential mode).

Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_get_thread_num.xml0000644000175200017650000001172213057470511017557 0ustar coincoin-web Get the Current OpenMP Thread Number
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Get the Current OpenMP Thread Number

Deprecated 2011-08-31
Use the function thread_alloc::thread_num instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 thread = omp_alloc::get_thread_num()

Purpose
Some of the omp_alloc allocation routines have a thread number. This routine enables you to determine the current thread.

thread
The return value thread has prototype
     size_t thread
 and is the currently executing thread number. If _OPENMP is not defined, thread is zero.

Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_get_memory.xml0000644000175200017650000001672413057470511016750 0ustar coincoin-web Get At Least A Specified Amount of Memory
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Get At Least A Specified Amount of Memory

Deprecated 2011-08-31
Use the function thread_alloc::get_memory instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 v_ptr = omp_alloc::get_memory(min_bytes, cap_bytes)

Purpose
Use omp_alloc to obtain a minimum number of bytes of memory (for use by the current thread ).

min_bytes
This argument has prototype
     size_t min_bytes
 It specifies the minimum number of bytes to allocate.

cap_bytes
This argument has prototype
     size_t& cap_bytes
 It's input value does not matter. Upon return, it is the actual number of bytes (capacity) that have been allocated for use,
     min_bytes <= cap_bytes
v_ptr
The return value v_ptr has prototype
     void* v_ptr
 It is the location where the cap_bytes of memory that have been allocated for use begins.

Allocation Speed
This allocation should be faster if the following conditions hold:
  1. The memory allocated by a previous call to get_memory is currently available for use.
  2. The current min_bytes is between the previous min_bytes and previous cap_bytes .


Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_return_memory.xml0000644000175200017650000001402513057470511017500 0ustar coincoin-web Return Memory to omp_alloc
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Return Memory to omp_alloc

Deprecated 2011-08-31
Use the function thread_alloc::return_memory instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 omp_alloc::return_memory(v_ptr)

Purpose
If omp_max_num_threads is one, the memory is returned to the system. Otherwise, the memory is retained by omp_alloc for quick future use by the thread that allocated to memory.

v_ptr
This argument has prototype
     void* v_ptr
 . It must be a pointer to memory that is currently in use; i.e. obtained by a previous call to omp_get_memory and not yet returned.

Thread
Either the current thread must be the same as during the corresponding call to omp_get_memory , or the current execution mode must be sequential (not parallel ).

NDEBUG
If NDEBUG is defined, v_ptr is not checked (this is faster). Otherwise, a list of in use pointers is searched to make sure that v_ptr is in the list.

Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_free_available.xml0000644000175200017650000001206113057470511017510 0ustar coincoin-web Free Memory Currently Available for Quick Use by a Thread
Prev Next omp_free_available

Free Memory Currently Available for Quick Use by a Thread

Deprecated 2011-08-31
Use the function thread_alloc::free_available instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 omp_alloc::free_available(thread)

Purpose
Free memory, currently available for quick use by a specific thread, for general future use.

thread
This argument has prototype
     size_t thread
 Either omp_get_thread_num must be the same as thread , or the current execution mode must be sequential (not parallel ).

Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_inuse.xml0000644000175200017650000001335613057470511015722 0ustar coincoin-web Amount of Memory a Thread is Currently Using
Prev Next omp_inuse

Amount of Memory a Thread is Currently Using

Deprecated 2011-08-31

Syntax
# include <cppad/utility/omp_alloc.hpp>
 num_bytes = omp_alloc::inuse(thread) Use the function thread_alloc::inuse instead.

Purpose
Memory being managed by omp_alloc has two states, currently in use by the specified thread, and quickly available for future use by the specified thread. This function informs the program how much memory is in use.

thread
This argument has prototype
     size_t thread
 Either omp_get_thread_num must be the same as thread , or the current execution mode must be sequential (not parallel ).

num_bytes
The return value has prototype
     size_t num_bytes
 It is the number of bytes currently in use by the specified thread.

Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_available.xml0000644000175200017650000001344613057470511016517 0ustar coincoin-web Amount of Memory Available for Quick Use by a Thread
Prev Next omp_available

Amount of Memory Available for Quick Use by a Thread

Deprecated 2011-08-31
Use the function thread_alloc::available instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 num_bytes = omp_alloc::available(thread)

Purpose
Memory being managed by omp_alloc has two states, currently in use by the specified thread, and quickly available for future use by the specified thread. This function informs the program how much memory is available.

thread
This argument has prototype
     size_t thread
 Either omp_get_thread_num must be the same as thread , or the current execution mode must be sequential (not parallel ).

num_bytes
The return value has prototype
     size_t num_bytes
 It is the number of bytes currently available for use by the specified thread.

Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_create_array.xml0000644000175200017650000002244513057470511017237 0ustar coincoin-web Allocate Memory and Create A Raw Array
Prev Next omp_create_array

Allocate Memory and Create A Raw Array

Deprecated 2011-08-31
Use the function thread_alloc::create_array instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 array = omp_alloc::create_array<Type>(size_min, size_out) .

Purpose
Create a new raw array using omp_alloc a fast memory allocator that works well in a multi-threading OpenMP environment.

Type
The type of the elements of the array.

size_min
This argument has prototype
     size_t size_min
 This is the minimum number of elements that there can be in the resulting array .

size_out
This argument has prototype
     size_t& size_out
 The input value of this argument does not matter. Upon return, it is the actual number of elements in array (  size_min <= size_out ).

array
The return value array has prototype
     Type* array
 It is array with size_out elements. The default constructor for Type is used to initialize the elements of array . Note that omp_delete_array should be used to destroy the array when it is no longer needed.

Delta
The amount of memory omp_inuse by the current thread, will increase delta where
     sizeof(Type) * (size_out + 1) > delta >= sizeof(Type) * size_out
 The omp_available memory will decrease by delta , (and the allocation will be faster) if a previous allocation with size_min between its current value and size_out is available.

Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_delete_array.xml0000644000175200017650000001571413057470511017237 0ustar coincoin-web Return A Raw Array to The Available Memory for a Thread
Prev Next omp_delete_array

Return A Raw Array to The Available Memory for a Thread

Deprecated 2011-08-31
Use the function thread_alloc::delete_array instead.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 omp_alloc::delete_array(array) .

Purpose
Returns memory corresponding to a raw array (create by omp_create_array ) to the omp_available memory pool for the current thread.

Type
The type of the elements of the array.

array
The argument array has prototype
     Type* array
 It is a value returned by omp_create_array and not yet deleted. The Type destructor is called for each element in the array.

Thread
The current thread must be the same as when omp_create_array returned the value array . There is an exception to this rule: when the current execution mode is sequential (not parallel ) the current thread number does not matter.

Delta
The amount of memory omp_inuse will decrease by delta , and the omp_available memory will increase by delta , where delta is the same as for the corresponding call to create_array.

Example
omp_alloc.cpp
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_efficient.xml0000644000175200017650000001721513057470511016531 0ustar coincoin-web Check If A Memory Allocation is Efficient for Another Use
Prev Next omp_efficient

Check If A Memory Allocation is Efficient for Another Use

Removed
This function has been removed because speed tests seem to indicate it is just as fast, or faster, to free and then reallocate the memory.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 flag = omp_alloc::efficient(v_ptr, num_bytes)

Purpose
Check if memory that is currently in use is an efficient allocation for a specified number of bytes.

v_ptr
This argument has prototype
     const void* v_ptr
 . It must be a pointer to memory that is currently in use; i.e. obtained by a previous call to omp_get_memory and not yet returned.

num_bytes
This argument has prototype
     size_t num_bytes
 It specifies the number of bytes of the memory allocated by v_ptr that we want to use.

flag
The return value has prototype
     bool flag
 It is true, a call to get_memory with min_bytes equal to num_bytes would result in a value for cap_bytes that is the same as when v_ptr was returned by get_memory; i.e., v_ptr is an efficient memory block for num_bytes bytes of information.

Thread
Either the current thread must be the same as during the corresponding call to omp_get_memory , or the current execution mode must be sequential (not parallel ).

NDEBUG
If NDEBUG is defined, v_ptr is not checked (this is faster). Otherwise, a list of in use pointers is searched to make sure that v_ptr is in the list.
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/old_max_num_threads.xml0000644000175200017650000001202713057470511017732 0ustar coincoin-web Set Maximum Number of Threads for omp_alloc Allocator
Prev Next old_max_num_threads

Set Maximum Number of Threads for omp_alloc Allocator

Removed
This function has been removed from the CppAD API. Use the function thread_alloc::parallel_setup in its place.

Syntax
# include <cppad/utility/omp_alloc.hpp>
 omp_alloc::max_num_threads(number)

Purpose
By default there is only one thread and all execution is in sequential mode (not parallel ).

number
The argument number has prototype
     size_t number
 It must be greater than zero and specifies the maximum number of OpenMP threads that will be active at one time.

Restrictions
This function must be called before the program enters parallel execution mode.
Input File: cppad/utility/omp_alloc.hpp cppad-20170000.3/doc/omp_alloc.cpp.xml0000644000175200017650000007546413057470511016462 0ustar coincoin-web OpenMP Memory Allocator: Example and Test
Prev Next omp_alloc.cpp

OpenMP Memory Allocator: Example and Test

Deprecated 2011-08-31
This example is only intended to help convert calls to omp_alloc to calls to thread_alloc . 
# include <cppad/utility/omp_alloc.hpp>
# include <cppad/utility/memory_leak.hpp>
# include <vector>

namespace { // Begin empty namespace

bool omp_alloc_bytes(void)
{     bool ok = true;
     using CppAD::omp_alloc;
     size_t thread;

     // check initial memory values
     ok &= ! CppAD::memory_leak();

     // amount of static memory used by thread zero
     size_t static_inuse = omp_alloc::inuse(0);

     // determine the currently executing thread
     // (should be zero because not in parallel mode)
     thread = omp_alloc::get_thread_num();

     // repeatedly allocate enough memory for at least two size_t values.
     size_t min_size_t = 2;
     size_t min_bytes  = min_size_t * sizeof(size_t);
     size_t n_outter   = 10;
     size_t n_inner    = 5;
     size_t cap_bytes(0), i, j, k;
     for(i = 0; i < n_outter; i++)
     {     // Do not use CppAD::vector here because its use of omp_alloc
          // complicates the inuse and avaialble results.
          std::vector<void*> v_ptr(n_inner);
          for( j = 0; j < n_inner; j++)
          {     // allocate enough memory for min_size_t size_t objects
               v_ptr[j]    = omp_alloc::get_memory(min_bytes, cap_bytes);
               size_t* ptr = reinterpret_cast<size_t*>(v_ptr[j]);
               // determine the number of size_t values we have obtained
               size_t  cap_size_t = cap_bytes / sizeof(size_t);
               ok                &= min_size_t <= cap_size_t;
               // use placement new to call the size_t copy constructor
               for(k = 0; k < cap_size_t; k++)
                    new(ptr + k) size_t(i + j + k);
               // check that the constructor worked
               for(k = 0; k < cap_size_t; k++)
                    ok &= ptr[k] == (i + j + k);
          }
          // check that n_inner * cap_bytes are inuse and none are available
          ok &= omp_alloc::inuse(thread) == n_inner*cap_bytes + static_inuse;
          ok &= omp_alloc::available(thread) == 0;
          // return the memrory to omp_alloc
          for(j = 0; j < n_inner; j++)
               omp_alloc::return_memory(v_ptr[j]);
          // check that now n_inner * cap_bytes are now available
          // and none are in use
          ok &= omp_alloc::inuse(thread) == static_inuse;
          ok &= omp_alloc::available(thread) == n_inner * cap_bytes;
     }
     // return all the available memory to the system
     omp_alloc::free_available(thread);
     ok &= ! CppAD::memory_leak();

     return ok;
}

class my_char {
public:
     char ch_ ;
     my_char(void) : ch_(' ')
     { }
     my_char(const my_char& my_ch) : ch_(my_ch.ch_)
     { }
};

bool omp_alloc_array(void)
{     bool ok = true;
     using CppAD::omp_alloc;
     size_t i;

     // check initial memory values
     size_t thread = omp_alloc::get_thread_num();
     ok &= thread == 0;
     ok &= ! CppAD::memory_leak();
     size_t static_inuse = omp_alloc::inuse(0);

     // initial allocation of an array
     size_t  size_min  = 3;
     size_t  size_one;
     my_char *array_one  =
          omp_alloc::create_array<my_char>(size_min, size_one);

     // check the values and change them to null 'x'
     for(i = 0; i < size_one; i++)
     {     ok &= array_one[i].ch_ == ' ';
          array_one[i].ch_ = 'x';
     }

     // now create a longer array
     size_t size_two;
     my_char *array_two =
          omp_alloc::create_array<my_char>(2 * size_min, size_two);

     // check the values in array one
     for(i = 0; i < size_one; i++)
          ok &= array_one[i].ch_ == 'x';

     // check the values in array two
     for(i = 0; i < size_two; i++)
          ok &= array_two[i].ch_ == ' ';

     // check the amount of inuse and available memory
     // (an extra size_t value is used for each memory block).
     size_t check = static_inuse + sizeof(my_char)*(size_one + size_two);
     ok   &= omp_alloc::inuse(thread) - check < sizeof(my_char);
     ok   &= omp_alloc::available(thread) == 0;

     // delete the arrays
     omp_alloc::delete_array(array_one);
     omp_alloc::delete_array(array_two);
     ok   &= omp_alloc::inuse(thread) == static_inuse;
     check = sizeof(my_char)*(size_one + size_two);
     ok   &= omp_alloc::available(thread) - check < sizeof(my_char);

     // free the memory for use by this thread
     omp_alloc::free_available(thread);
     ok &= ! CppAD::memory_leak();

     return ok;
}
} // End empty namespace

bool omp_alloc(void)
{     bool ok  = true;
     using CppAD::omp_alloc;

     // check initial state of allocator
     ok  &= omp_alloc::get_max_num_threads() == 1;

     // set the maximum number of threads greater than one
     // so that omp_alloc holds onto memory
     CppAD::omp_alloc::set_max_num_threads(2);
     ok  &= omp_alloc::get_max_num_threads() == 2;
     ok  &= ! CppAD::memory_leak();

     // now use memory allocator in state where it holds onto memory
     ok   &= omp_alloc_bytes();
     ok   &= omp_alloc_array();

     // check that the tests have not held onto memory
     ok  &= ! CppAD::memory_leak();

     // set the maximum number of threads back to one
     // so that omp_alloc no longer holds onto memory
     CppAD::omp_alloc::set_max_num_threads(1);

     return ok;
}
Input File: test_more/omp_alloc.cpp cppad-20170000.3/doc/memory_leak.xml0000644000175200017650000002275313057470511016231 0ustar coincoin-web Memory Leak Detection
Prev Next memory_leak

Memory Leak Detection

Deprecated 2012-04-06
This routine has been deprecated. You should instead use the routine ta_free_all .

Syntax
# include <cppad/utility/memory_leak.hpp>
 flag = memory_leak()
 flag = memory_leak(add_static)

Purpose
This routine checks that the are no memory leaks caused by improper use of thread_alloc memory allocator. The deprecated memory allocator TrackNewDel is also checked. Memory errors in the deprecated omp_alloc allocator are reported as being in thread_alloc.

thread
It is assumed that in_parallel() is false and thread_num is zero when memory_leak is called.

add_static
This argument has prototype
     size_t add_static
 and its default value is zero. Static variables hold onto memory forever. If the argument add_static is present (and non-zero), memory_leak adds this amount of memory to the inuse sum that corresponds to static variables in the program. A call with add_static should be make after a routine that has static variables which use get_memory to allocate memory. The value of add_static should be the difference of
     thread_alloc::inuse(0)
 before and after the call. Since multiple statics may be allocated in different places in the program, it is expected that there will be multiple calls that use this option.

flag
The return value flag has prototype
     bool flag
 If add_static is non-zero, the return value for memory_leak is false. Otherwise, the return value for memory_leak should be false (indicating that the only allocated memory corresponds to static variables).

inuse
It is assumed that, when memory_leak is called, there should not be any memory inuse or omp_inuse for any thread (except for inuse memory corresponding to static variables). If there is, a message is printed and memory_leak returns false.

available
It is assumed that, when memory_leak is called, there should not be any memory available or omp_available for any thread; i.e., it all has been returned to the system. If there is memory still available for any thread, memory_leak returns false.

TRACK_COUNT
It is assumed that, when memory_leak is called, TrackCount will return a zero value. If it returns a non-zero value, memory_leak returns false.

Error Message
If this is the first call to memory_leak, no message is printed. Otherwise, if it returns true, an error message is printed to standard output describing the memory leak that was detected.
Input File: cppad/utility/memory_leak.hpp cppad-20170000.3/doc/epsilon.xml0000644000175200017650000001174113057470511015371 0ustar coincoin-web Machine Epsilon For AD Types
Prev Next epsilon

Machine Epsilon For AD Types

Deprecated 2012-06-17
This routine has been deprecated. You should use the numeric_limits epsilon instead.

Syntax
eps = epsilon<Float>()

Purpose
Obtain the value of machine epsilon corresponding to the type Float .

Float
this type can either be AD<Base> , or it can be Base for any AD<Base> type.

eps
The result eps has prototype
     Float eps
Input File: cppad/core/epsilon.hpp cppad-20170000.3/doc/test_vector.xml0000644000175200017650000002610613057470511016262 0ustar coincoin-web Choosing The Vector Testing Template Class
Prev Next test_vector

Choosing The Vector Testing Template Class

Deprecated 2012-07-03
The CPPAD_TEST_VECTOR macro has been deprecated, use CPPAD_TESTVECTOR instead.

Syntax
CPPAD_TEST_VECTOR<Scalar>
Introduction
Many of the CppAD examples and tests use the CPPAD_TEST_VECTOR template class to pass information. The default definition for this template class is CppAD::vector .

MS Windows
The include path for boost is not defined in the Windows project files. If we are using Microsofts compiler, the following code overrides the setting of CPPAD_BOOSTVECTOR: 
// The next 7 lines are C++ source code.
# ifdef _MSC_VER
# if CPPAD_BOOSTVECTOR
# undef  CPPAD_BOOSTVECTOR
# define CPPAD_BOOSTVECTOR 0
# undef  CPPAD_CPPADVECTOR
# define CPPAD_CPPADVECTOR 1
# endif
# endif

CppAD::vector
By default CPPAD_CPPADVECTOR is true and CPPAD_TEST_VECTOR is defined by the following source code 
// The next 3 line are C++ source code.
# if CPPAD_CPPADVECTOR
# define CPPAD_TEST_VECTOR CppAD::vector
# endif
If you specify --with-eigenvector on the configure command line, CPPAD_EIGENVECTOR is true. This vector type cannot be supported by CPPAD_TEST_VECTOR (use CPPAD_TESTVECTOR for this support) so CppAD::vector is used in this case 
// The next 3 line are C++ source code.
# if CPPAD_EIGENVECTOR
# define CPPAD_TEST_VECTOR CppAD::vector
# endif

std::vector
If you specify --with-stdvector on the configure command line during CppAD installation, CPPAD_STDVECTOR is true and CPPAD_TEST_VECTOR is defined by the following source code 
// The next 4 lines are C++ source code.
# if CPPAD_STDVECTOR
# include <vector>
# define CPPAD_TEST_VECTOR std::vector
# endif
In this case CppAD will use std::vector for its examples and tests. Use of CppAD::vector, std::vector, and std::valarray with CppAD is always tested to some degree. Specifying --with-stdvector will increase the amount of std::vector testing.

boost::numeric::ublas::vector
If you specify a value for boost_dir on the configure command line during CppAD installation, CPPAD_BOOSTVECTOR is true and CPPAD_TEST_VECTOR is defined by the following source code 
// The next 4 lines are C++ source code.
# if CPPAD_BOOSTVECTOR
# include <boost/numeric/ublas/vector.hpp>
# define CPPAD_TEST_VECTOR boost::numeric::ublas::vector
# endif
In this case CppAD will use Ublas vectors for its examples and tests. Use of CppAD::vector, std::vector, and std::valarray with CppAD is always tested to some degree. Specifying boost_dir will increase the amount of Ublas vector testing.

CppADvector Deprecated 2007-07-28
The preprocessor symbol CppADvector is defined to have the same value as CPPAD_TEST_VECTOR but its use is deprecated: 

# define CppADvector CPPAD_TEST_VECTOR
Input File: cppad/core/test_vector.hpp cppad-20170000.3/doc/cppad_ipopt_nlp.xml0000644000175200017650000022164113057470511017075 0ustar coincoin-web Nonlinear Programming Using the CppAD Interface to Ipopt
Prev Next

Nonlinear Programming Using the CppAD Interface to Ipopt

Deprecated 2012-11-28
This interface to Ipopt is deprecated, use ipopt_solve instead.

Syntax
# include "cppad_ipopt_nlp.hpp"
 cppad_ipopt_solution solution;
 cppad_ipopt_nlp cppad_nlp(
     n, m, x_i, x_l, x_u, g_l, g_u, &fg_info, &solution
)
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:ipopt_library_paths

Purpose
The class cppad_ipopt_nlp is used to solve nonlinear programming problems of the form minimize f ( x ) subject to g l ≤ g ( x ) ≤ g u x l ≤ x ≤ x u This is done using Ipopt optimizer and CppAD Algorithmic Differentiation package.

cppad_ipopt namespace
All of the declarations for these routines are in the cppad_ipopt namespace (not the CppAD namespace). For example; SizeVector below actually denotes the type cppad_ipopt::SizeVector.

ipopt_library_paths
If you are linking to a shared version of the Ipopt library, you may have to add some paths the LD_LIBRARY_PATH shell variable using the export command in the syntax above. For example, if the file the ipopt library is
     ipopt_prefix/lib64/libipopt.a
 you will need to add the corresponding directory; e.g.,
     export LD_LIBRARY_PATH="ipopt_prefix/lib64:$LD_LIBRARY_PATH"
 see ipopt_prefix .

fg(x)
The function fg : R n → R m + 1 is defined by fg 0 ( x ) = f ( x ) fg 1 ( x ) = g 0 ( x ) ⋮ fg m ( x ) = g m -1 ( x )
Index Vector
We define an index vector as a vector of non-negative integers for which none of the values are equal; i.e., it is both a vector and a set. If I is an index vector | I | is used to denote the number of elements in I and ‖ I ‖ is used to denote the value of the maximum element in I .

Projection
Given an index vector J and a positive integer n where n > ‖ J ‖ , we use J ⊗ n for the mapping ( J ⊗ n ) : R n → R | J | defined by [ J ⊗ n ] ( x ) j = x J ( j ) for j = 0 , … | J | - 1 .

Injection
Given an index vector I and a positive integer m where m > ‖ I ‖ , we use m ⊗ I for the mapping ( m ⊗ I ) : R | I | → R m defined by [ m ⊗ I ] ( y ) i = { y k if i = I ( k ) for some k ∈ { 0 , ⋯ , | I | -1 } 0 otherwise
Representation
In many applications, each of the component functions of fg ( x ) only depend on a few of the components of x . In this case, expressing fg ( x ) in terms of simpler functions with fewer arguments can greatly reduce the amount of work required to compute its derivatives.

We use the functions r k : R q ( k ) → R p ( k ) for k = 0 , … , K to express our representation of fg ( x ) in terms of simpler functions as follows fg ( x ) = ∑ k = 0 K -1 ∑ ℓ = 0 L ( k ) - 1 [ ( m + 1 ) ⊗ I k , ℓ ] ∘ r k ∘ [ J k , ℓ ⊗ n ] ( x ) where ∘ represents function composition, for k = 0 , … , K - 1 , and ℓ = 0 , … , L ( k ) , I k , ℓ and J k , ℓ are index vectors with | J k , ℓ | = q ( k ) , ‖ J k , ℓ ‖ < n , | I k , ℓ | = p ( k ) , and ‖ I k , ℓ ‖ ≤ m .

Simple Representation
In the simple representation, r 0 ( x ) = fg ( x ) , K = 1 , q ( 0 ) = n , p ( 0 ) = m + 1 , L ( 0 ) = 1 , I 0 , 0 = ( 0 , … , m ) , and J 0 , 0 = ( 0 , … , n -1 ) .

SizeVector
The type SizeVector is defined by the cppad_ipopt_nlp.hpp include file to be a SimpleVector class with elements of type size_t.

NumberVector
The type NumberVector is defined by the cppad_ipopt_nlp.hpp include file to be a SimpleVector class with elements of type Ipopt::Number.

ADNumber
The type ADNumber is defined by the cppad_ipopt_nlp.hpp include file to be a an AD type that can be used to compute derivatives.

ADVector
The type ADVector is defined by the cppad_ipopt_nlp.hpp include file to be a SimpleVector class with elements of type ADNumber.

n
The argument n has prototype
     size_t n
 It specifies the dimension of the argument space; i.e., x ∈ R n .

m
The argument m has prototype
     size_t m
 It specifies the dimension of the range space for g ; i.e., g : R n → R m .

x_i
The argument x_i has prototype
     const NumberVector& x_i
 and its size is equal to n . It specifies the initial point where Ipopt starts the optimization process.

x_l
The argument x_l has prototype
     const NumberVector& x_l
 and its size is equal to n . It specifies the lower limits for the argument in the optimization problem; i.e., x l .

x_u
The argument x_u has prototype
     const NumberVector& x_u
 and its size is equal to n . It specifies the upper limits for the argument in the optimization problem; i.e., x u .

g_l
The argument g_l has prototype
     const NumberVector& g_l
 and its size is equal to m . It specifies the lower limits for the constraints in the optimization problem; i.e., g l .

g_u
The argument g_u has prototype
     const NumberVector& g_u
 and its size is equal to n . It specifies the upper limits for the constraints in the optimization problem; i.e., g u .

fg_info
The argument fg_info has prototype
     FG_info fg_info
 where the class FG_info is derived from the base class cppad_ipopt_fg_info. Certain virtual member functions of fg_info are used to compute the value of fg ( x ) . The specifications for these member functions are given below:

fg_info.number_functions
This member function has prototype
     virtual size_t cppad_ipopt_fg_info::number_functions(void)
 If K has type size_t, the syntax
     K = fg_info.number_functions()
 sets K to the number of functions used in the representation of fg ( x ) ; i.e., K in the representation above.

The cppad_ipopt_fg_info implementation of this function corresponds to the simple representation mentioned above; i.e. K = 1 .

fg_info.eval_r
This member function has the prototype
virtual ADVector cppad_ipopt_fg_info::eval_r(size_t k, const ADVector& u) = 0;
 Thus it is a pure virtual function and must be defined in the derived class FG_info .

This function computes the value of r k ( u ) used in the representation for fg ( x ) . If k in { 0 , … , K -1 } has type size_t, u is an ADVector of size q(k) and r is an ADVector of size p(k) the syntax
     r = fg_info.eval_r(k, u)
 set r to the vector r k ( u ) .

fg_info.retape
This member function has the prototype
     virtual bool cppad_ipopt_fg_info::retape(size_t k)
 If k in { 0 , … , K -1 } has type size_t, and retape has type bool, the syntax
        retape = fg_info.retape(k)
 sets retape to true or false. If retape is true, cppad_ipopt_nlp will retape the operation sequence corresponding to r k ( u ) for every value of u . An cppad_ipopt_nlp object should use much less memory and run faster if retape is false. You can test both the true and false cases to make sure the operation sequence does not depend on u .

The cppad_ipopt_fg_info implementation of this function sets retape to true (while slower it is also safer to always retape).

fg_info.domain_size
This member function has prototype
     virtual size_t cppad_ipopt_fg_info::domain_size(size_t k)
 If k in { 0 , … , K -1 } has type size_t, and q has type size_t, the syntax
     q = fg_info.domain_size(k)
 sets q to the dimension of the domain space for r k ( u ) ; i.e., q ( k ) in the representation above.

The cppad_ipopt_h_base implementation of this function corresponds to the simple representation mentioned above; i.e., q = n .

fg_info.range_size
This member function has prototype
     virtual size_t cppad_ipopt_fg_info::range_size(size_t k)
 If k in { 0 , … , K -1 } has type size_t, and p has type size_t, the syntax
     p = fg_info.range_size(k)
 sets p to the dimension of the range space for r k ( u ) ; i.e., p ( k ) in the representation above.

The cppad_ipopt_h_base implementation of this function corresponds to the simple representation mentioned above; i.e., p = m + 1 .

fg_info.number_terms
This member function has prototype
     virtual size_t cppad_ipopt_fg_info::number_terms(size_t k)
 If k in { 0 , … , K -1 } has type size_t, and L has type size_t, the syntax
     L = fg_info.number_terms(k)
 sets L to the number of terms in representation for this value of k ; i.e., L ( k ) in the representation above.

The cppad_ipopt_h_base implementation of this function corresponds to the simple representation mentioned above; i.e., L = 1 .

fg_info.index
This member function has prototype
     virtual void cppad_ipopt_fg_info::index(
          size_t k, size_t ell, SizeVector& I, SizeVector& J
     )
 The argument
     k
 has type size_t and is a value between zero and K -1 inclusive. The argument
     ell
 has type size_t and is a value between zero and L ( k ) -1 inclusive. The argument
     I
 is a SimpleVector with elements of type size_t and size greater than or equal to p ( k ) . The input value of the elements of I does not matter. The output value of the first p ( k ) elements of I must be the corresponding elements of I k , ell in the representation above. The argument
     J
 is a SimpleVector with elements of type size_t and size greater than or equal to q ( k ) . The input value of the elements of J does not matter. The output value of the first q ( k ) elements of J must be the corresponding elements of J k , ell in the representation above.

The cppad_ipopt_h_base implementation of this function corresponds to the simple representation mentioned above; i.e., for i = 0 , … , m , I[i] = i , and for j = 0 , … , n -1 , J[j] = j .

solution
After the optimization process is completed, solution contains the following information:

status
The status field of solution has prototype
     cppad_ipopt_solution::solution_status solution.status
 It is the final Ipopt status for the optimizer. Here is a list of the possible values for the status:
status Meaning
not_defined The optimizer did not return a final status to this cppad_ipopt_nlp object.
unknown The status returned by the optimizer is not defined in the Ipopt documentation for finalize_solution.
success Algorithm terminated successfully at a point satisfying the convergence tolerances (see Ipopt options).
maxiter_exceeded The maximum number of iterations was exceeded (see Ipopt options).
stop_at_tiny_step Algorithm terminated because progress was very slow.
stop_at_acceptable_point Algorithm stopped at a point that was converged, not to the 'desired' tolerances, but to 'acceptable' tolerances (see Ipopt options).
local_infeasibility Algorithm converged to a non-feasible point (problem may have no solution).
user_requested_stop This return value should not happen.
diverging_iterates It the iterates are diverging.
restoration_failure Restoration phase failed, algorithm doesn't know how to proceed.
error_in_step_computation An unrecoverable error occurred while Ipopt tried to compute the search direction.
invalid_number_detected Algorithm received an invalid number (such as nan or inf) from the users function fg_info.eval or from the CppAD evaluations of its derivatives (see the Ipopt option check_derivatives_for_naninf).
internal_error An unknown Ipopt internal error occurred. Contact the Ipopt authors through the mailing list.

x
The x field of solution has prototype
     NumberVector solution.x
 and its size is equal to n . It is the final x value for the optimizer.

z_l
The z_l field of solution has prototype
     NumberVector solution.z_l
 and its size is equal to n . It is the final Lagrange multipliers for the lower bounds on x .

z_u
The z_u field of solution has prototype
     NumberVector solution.z_u
 and its size is equal to n . It is the final Lagrange multipliers for the upper bounds on x .

g
The g field of solution has prototype
     NumberVector solution.g
 and its size is equal to m . It is the final value for the constraint function g ( x ) .

lambda
The lambda field of solution has prototype
     NumberVector solution.lambda
 and its size is equal to m . It is the final value for the Lagrange multipliers corresponding to the constraint function.

obj_value
The obj_value field of solution has prototype
     Number solution.obj_value
 It is the final value of the objective function f ( x ) .

Example
The file ipopt_nlp_get_started.cpp is an example and test of cppad_ipopt_nlp that uses the simple representation . It returns true if it succeeds and false otherwise. The section ipopt_nlp_ode discusses an example that uses a more complex representation.

Wish List
This is a list of possible future improvements to cppad_ipopt_nlp that would require changed to the user interface:
  1. The routine fg_info.eval_r(k, u) should also support NumberVector for the type of the argument u (this would certainly be more efficient when fg_info.retape(k) is true and L ( k ) > 1 ). It could be an option for the user to provide this as well as the necessary ADVector definition.
  2. There should a Discrete routine that the user can call to determine the value of ℓ during the evaluation of fg_info.eval_r(k, u) . This way data, which does not affect the derivative values, can be included in the function recording and evaluation.
Input File: cppad_ipopt/src/cppad_ipopt_nlp.hpp cppad-20170000.3/doc/ipopt_nlp_get_started.cpp.xml0000644000175200017650000007440713057470511021102 0ustar coincoin-web Nonlinear Programming Using CppAD and Ipopt: Example and Test
Prev Next ipopt_nlp_get_started.cpp

Nonlinear Programming Using CppAD and Ipopt: Example and Test

Purpose
This example program demonstrates how to use the class cppad_ipopt_nlp to solve the example problem in the Ipopt documentation; i.e., the problem minimize x 1 * x 4 * ( x 1 + x 2 + x 3 ) + x 3 subject to x 1 * x 2 * x 3 * x 4 ≥ 25 x 1 2 + x 2 2 + x 3 2 + x 4 2 = 40 1 ≤ x 1 , x 2 , x 3 , x 4 ≤ 5
Configuration Requirement
This example will be compiled and tested provided that a value for ipopt_prefix is specified on the cmake command line. 

# include <cppad_ipopt_nlp.hpp>

namespace {
     using namespace cppad_ipopt;

     class FG_info : public cppad_ipopt_fg_info
     {
     private:
          bool retape_;
     public:
          // derived class part of constructor
          FG_info(bool retape_in)
          : retape_ (retape_in)
          { }
          // Evaluation of the objective f(x), and constraints g(x)
          // using an Algorithmic Differentiation (AD) class.
          ADVector eval_r(size_t k, const ADVector&  x)
          {     ADVector fg(3);

               // Fortran style indexing
               ADNumber x1 = x[0];
               ADNumber x2 = x[1];
               ADNumber x3 = x[2];
               ADNumber x4 = x[3];
               // f(x)
               fg[0] = x1 * x4 * (x1 + x2 + x3) + x3;
               // g_1 (x)
               fg[1] = x1 * x2 * x3 * x4;
               // g_2 (x)
               fg[2] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4;
               return fg;
          }
          bool retape(size_t k)
          {     return retape_; }
     };
}

bool ipopt_get_started(void)
{     bool ok = true;
     size_t j;


     // number of independent variables (domain dimension for f and g)
     size_t n = 4;
     // number of constraints (range dimension for g)
     size_t m = 2;
     // initial value of the independent variables
     NumberVector x_i(n);
     x_i[0] = 1.0;
     x_i[1] = 5.0;
     x_i[2] = 5.0;
     x_i[3] = 1.0;
     // lower and upper limits for x
     NumberVector x_l(n);
     NumberVector x_u(n);
     for(j = 0; j < n; j++)
     {     x_l[j] = 1.0;
          x_u[j] = 5.0;
     }
     // lower and upper limits for g
     NumberVector g_l(m);
     NumberVector g_u(m);
     g_l[0] = 25.0;     g_u[0] = 1.0e19;
     g_l[1] = 40.0;     g_u[1] = 40.0;

     size_t icase;
     for(icase = 0; icase <= 1; icase++)
     {     // Should cppad_ipopt_nlp retape the operation sequence for
          // every new x. Can test both true and false cases because
          // the operation sequence does not depend on x (for this case).
          bool retape = icase != 0;

          // object in derived class
          FG_info fg_info(retape);

          // create the Ipopt interface
          cppad_ipopt_solution solution;
          Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new cppad_ipopt_nlp(
          n, m, x_i, x_l, x_u, g_l, g_u, &fg_info, &solution
          );

          // Create an instance of the IpoptApplication
          using Ipopt::IpoptApplication;
          Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();

          // turn off any printing
          app->Options()->SetIntegerValue("print_level", 0);
          app->Options()->SetStringValue("sb", "yes");

          // maximum number of iterations
          app->Options()->SetIntegerValue("max_iter", 10);

          // approximate accuracy in first order necessary conditions;
          // see Mathematical Programming, Volume 106, Number 1,
          // Pages 25-57, Equation (6)
          app->Options()->SetNumericValue("tol", 1e-9);

          // derivative testing
          app->Options()->
          SetStringValue("derivative_test", "second-order");
          app->Options()-> SetNumericValue(
               "point_perturbation_radius", 0.
          );

          // Initialize the IpoptApplication and process the options
          Ipopt::ApplicationReturnStatus status = app->Initialize();
          ok    &= status == Ipopt::Solve_Succeeded;

          // Run the IpoptApplication
          status = app->OptimizeTNLP(cppad_nlp);
          ok    &= status == Ipopt::Solve_Succeeded;

          /*
          Check some of the solution values
          */
          ok &= solution.status == cppad_ipopt_solution::success;
          //
          double check_x[]   = { 1.000000, 4.743000, 3.82115, 1.379408 };
          double check_z_l[] = { 1.087871, 0.,       0.,      0.       };
          double check_z_u[] = { 0.,       0.,       0.,      0.       };
          double rel_tol     = 1e-6;  // relative tolerance
          double abs_tol     = 1e-6;  // absolute tolerance
          for(j = 0; j < n; j++)
          {     ok &= CppAD::NearEqual(
               check_x[j],   solution.x[j],   rel_tol, abs_tol
               );
               ok &= CppAD::NearEqual(
               check_z_l[j], solution.z_l[j], rel_tol, abs_tol
               );
               ok &= CppAD::NearEqual(
               check_z_u[j], solution.z_u[j], rel_tol, abs_tol
               );
          }
     }

     return ok;
}
Input File: cppad_ipopt/example/get_started.cpp cppad-20170000.3/doc/ipopt_nlp_ode.xml0000644000175200017650000000733513057470511016557 0ustar coincoin-web Example Simultaneous Solution of Forward and Inverse Problem
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Example Simultaneous Solution of Forward and Inverse Problem

Contents
Input File: cppad_ipopt/example/ode1.omh cppad-20170000.3/doc/ipopt_nlp_ode_problem.xml0000644000175200017650000013405413057470511020276 0ustar coincoin-web An ODE Inverse Problem Example
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An ODE Inverse Problem Example

Notation
The table below contains the name of a variable, the meaning of the variable value, and the value for this particular example. If the value is not specified in the table below, the corresponding value in ipopt_nlp_ode_problem.hpp can be changed and the example should still run (with no other changes).
Name Meaning Value
Na number of parameters to fit 3
Ny number components in ODE 2
Nz number of measurements 4
N ( i ) number of grid points between i-1-th and i-th measurement
S ( i ) number of grid points up to an including the i-th measurement

Forward Problem
We consider the following ordinary differential equation: ∂ t y 0 ( t , a ) = - a 1 * y 0 ( t , a ) ∂ t y 1 ( t , a ) = + a 1 * y 0 ( t , a ) - a 2 * y 1 ( t , a ) with the initial conditions y 0 ( 0 , a ) = F ( a ) = ( a 0 0 ) where Na is the number of parameters, a ∈ R Na is an unknown parameter vector. The function and F : R Na → R Ny is defined by the equation above where Ny is the number of components in y ( t , a ) . Our forward problem is stated as follows: Given a ∈ R Na determine the value of y ( t , a ) , for t ∈ R , that solves the initial value problem above.

Measurements
We use Nz to denote the number of measurements. Suppose we are also given a measurement vector z ∈ R Nz and for i = 1 , … , Nz , we model z i by z i = y 1 ( s i , a ) + e i where s i ∈ R is the time for the i-th measurement, e i ∼ N ( 0 , σ 2 ) is the corresponding noise, and σ ∈ R + is the corresponding standard deviation.

Simulation Analytic Solution
The following analytic solution to the forward problem is used to simulate a data set: y 0 ( t , a ) = a 0 * exp ( - a 1 * t ) y 1 ( t , a ) = a 0 * a 1 * exp ( - a 2 * t ) - exp ( - a 1 * t ) a 1 - a 2
Simulation Parameter Values
a ¯ 0 = 1   initial value of y 0 ( t , a )
a ¯ 1 = 2   transfer rate from compartment zero to compartment one
a ¯ 2 = 1   transfer rate from compartment one to outside world
σ = 0   standard deviation of measurement noise
e i = 0   simulated measurement noise, i = 1 , … , Nz
s i = i * .5   time corresponding to the i-th measurement, i = 1 , … , Nz

Simulated Measurement Values
The simulated measurement values are given by the equation z i = e i + y 1 ( s i , a ¯ ) = e i + a ¯ 0 * a ¯ 1 * exp ( - a ¯ 2 * s i ) - exp ( - a ¯ 1 * s i ) a ¯ 1 - a ¯ 2 for k = 1 , … , Nz .

Inverse Problem
The maximum likelihood estimate for a given z solves the following inverse problem minimize ∑ i = 1 Nz H i [ y ( s i , a ) , a ] w . r . t a ∈ R Na where the functions H i : R Ny × R Na → R is defined by H i ( y , a ) = ( z i - y 1 ) 2
Trapezoidal Approximation
This example uses a trapezoidal approximation to solve the ODE. This approximation procedures starts with y 0 = y ( 0 , a ) = ( a 0 0 ) Given a time grid { t i } and an approximate value y i -1 for y ( t i -1 , a ) , the a trapezoidal method approximates y ( t i , a ) (denoted by y i ) by solving the equation y i = y i -1 + [G ( y i , a ) + G ( y i -1 , a ) ] * t i - t i -1 2 where G : R Ny × R Na → R Ny is the function representing this ODE; i.e. G ( y , a ) = ( - a 1 * y 0 + a 1 * y 0 - a 2 * y 1 ) This G ( y , a ) is linear with respect to y , hence the implicit equation defining y i can be solved inverting the a set of linear equations. In the general case, where G ( y , a ) is non-linear with respect to y , an iterative procedure is used to calculate y i from y i -1 .

Trapezoidal Time Grid
The discrete time grid, used for the trapezoidal approximation, is denoted by { t i } which is defined by: t 0 = 0 and for i = 1 , … , Nz and for j = 1 , … , N ( i ) , Δ t i = ( s i - s i -1 ) / N ( i ) t S ( i -1 ) + j = s i -1 + Δ t i * j where s 0 = 0 , N ( i ) is the number of time grid points between s i -1 and s i , S ( 0 ) = 0 , and S ( i ) = N ( 1 ) + … + N ( i ) . Note that for i = 0 , … , S ( Nz ) , y i denotes our approximation for y ( t i , a ) and t S ( i ) is equal to s i .

Black Box Method
A common approach to an inverse problem is to treat the forward problem as a black box (that we do not look inside of or try to understand). In this approach, for each value of the parameter vector a one uses the trapezoidal approximation (on a finer grid that { s i } ) to solve for y 1 ( s i , a ) for i = 1 , … , Nz .

Two levels of Iteration
As noted above, the trapezoidal approximation often requires an iterative procedure. Thus, in this approach, there are two levels of iterations, one with respect to the parameter values during the minimization and the other for solving the trapezoidal approximation equation.

Derivatives
In addition, in the black box approach, differentiating the ODE solution often involves differentiating an iterative procedure. Direct application of AD to compute these derivatives requires a huge amount of memory and calculations to differentiate the iterative procedure. (There are special techniques for applying AD to the solutions of iterative procedures, but that is outside the scope of this presentation).

Simultaneous Method
The simultaneous forward and inverse method uses constraints to include the solution of the forward problem in the inverse problem. To be specific for our example, minimize ∑ i = 1 Nz H i ( y N ( i ) , a ) w . r . t y 1 ∈ R Ny , … , y S ( Nz ) ∈ R Ny , a ∈ R Na subject to y j = y j -1 + [G ( y j -1 , a ) + G ( y j , a ) ] * t j - t j -1 2 for j = 1 , … , S ( Nz ) y 0 = F ( a ) where for i = 1 , … , Nz , N ( i ) is the number of time intervals between s i -1 and s i (with s 0 = 0 ) and S ( i ) = N ( 1 ) + … + N ( i ) . Note that, in this form, the iterations of the optimization procedure also solve the forward problem equations. In addition, the functions that need to be differentiated do not involve an iterative procedure.

Source
The file ipopt_nlp_ode_problem.hpp contains source code that defines the example values and functions defined above.
Input File: cppad_ipopt/example/ode2.omh cppad-20170000.3/doc/ipopt_nlp_ode_problem.hpp.xml0000644000175200017650000004122313057470511021057 0ustar coincoin-web ODE Inverse Problem Definitions: Source Code
Prev Next ipopt_nlp_ode_problem.hpp Headings

ODE Inverse Problem Definitions: Source Code
# include "../src/cppad_ipopt_nlp.hpp"

namespace {
     //------------------------------------------------------------------
     typedef Ipopt::Number Number;
     Number a0 = 1.;  // simulation value for a[0]
     Number a1 = 2.;  // simulation value for a[1]
     Number a2 = 1.;  // simulatioln value for a[2]

     // function used to simulate data
     Number y_one(Number t)
     {     Number y_1 =  a0*a1 * (exp(-a2*t) - exp(-a1*t)) / (a1 - a2);
          return y_1;
     }

     // time points were we have data (no data at first point)
     double s[] = { 0.0,        0.5,        1.0,        1.5,        2.0 };
     // Simulated data for case with no noise (first point is not used)
     double z[] = { 0.0,  y_one(0.5), y_one(1.0), y_one(1.5), y_one(2.0) };
     // Number of measurement values
     size_t Nz  = sizeof(z) / sizeof(z[0]) - 1;
     // Number of components in the function y(t, a)
     size_t Ny  = 2;
     // Number of components in the vectro a
     size_t Na  = 3;

     // Initial Condition function, F(a) = y(t, a) at t = 0
     // (for this particular example)
     template <class Vector>
     Vector eval_F(const Vector &a)
     {     Vector F(Ny);
          // y_0 (t) = a[0]*exp(-a[1] * t)
          F[0] = a[0];
          // y_1 (t) =
          // a[0]*a[1]*(exp(-a[2] * t) - exp(-a[1] * t))/(a[1] - a[2])
          F[1] = 0.;
          return F;
     }
     // G(y, a) =  \partial_t y(t, a); i.e. the differential equation
     // (for this particular example)
     template <class Vector>
     Vector eval_G(const Vector &y , const Vector &a)
     {     Vector G(Ny);
          // y_0 (t) = a[0]*exp(-a[1] * t)
          G[0] = -a[1] * y[0];
          // y_1 (t) =
          // a[0]*a[1]*(exp(-a[2] * t) - exp(-a[1] * t))/(a[1] - a[2])
          G[1] = +a[1] * y[0] - a[2] * y[1];
          return G;
     }
     // H(i, y, a) = contribution to objective at i-th data point
     // (for this particular example)
     template <class Scalar, class Vector>
     Scalar eval_H(size_t i, const Vector &y, const Vector &a)
     {     // This particular H is for a case where y_1 (t) is measured
          Scalar diff = z[i] - y[1];
          return diff * diff;
     }
     // function used to count the number of calls to eval_r
     size_t count_eval_r(void)
     {     static size_t count = 0;
          ++count;
          return count;
     }
}
Input File: cppad_ipopt/example/ode_problem.hpp cppad-20170000.3/doc/ipopt_nlp_ode_simple.hpp.xml0000644000175200017650000005406113057470511020714 0ustar coincoin-web ODE Fitting Using Simple Representation
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ODE Fitting Using Simple Representation
# include "ode_problem.hpp"

// define in the empty namespace
namespace {
     using namespace cppad_ipopt;

     class FG_simple : public cppad_ipopt_fg_info
     {
     private:
          bool       retape_;
          SizeVector N_;
          SizeVector S_;
     public:
          // derived class part of constructor
          FG_simple(bool retape_in, const SizeVector& N)
          : retape_ (retape_in), N_(N)
          {     assert( N_[0] == 0 );
               S_.resize( N.size() );
               S_[0] = 0;
               for(size_t i = 1; i < N_.size(); i++)
                    S_[i] = S_[i-1] + N_[i];
          }
          // Evaluation of the objective f(x), and constraints g(x)
          // using an Algorithmic Differentiation (AD) class.
          ADVector eval_r(size_t not_used, const ADVector&  x)
          {     count_eval_r();

               // temporary indices
               size_t i, j, k;
               // # of components of x corresponding to values for y
               size_t ny_inx = (S_[Nz] + 1) * Ny;
               // # of constraints (range dimension of g)
               size_t m = ny_inx;
               // # of components in x (domain dimension for f and g)
               assert ( x.size() == ny_inx + Na );
               // vector for return value
               ADVector fg(m + 1);
               // vector of parameters
               ADVector a(Na);
               for(j = 0; j < Na; j++)
                    a[j] = x[ny_inx + j];
               // vector for value of y(t)
               ADVector y(Ny);
               // objective function -------------------------------
               fg[0] = 0.;
               for(k = 0; k < Nz; k++)
               {     for(j = 0; j < Ny; j++)
                         y[j] = x[Ny*S_[k+1] + j];
                    fg[0] += eval_H<ADNumber>(k+1, y, a);
               }
               // initial condition ---------------------------------
               ADVector F = eval_F(a);
               for(j = 0; j < Ny; j++)
               {     y[j]    = x[j];
                    fg[1+j] = y[j] - F[j];
               }
               // trapezoidal approximation --------------------------
               ADVector ym(Ny), G(Ny), Gm(Ny);
               G = eval_G(y, a);
               ADNumber dy;
               for(k = 0; k < Nz; k++)
               {     // interval between data points
                    Number T  = s[k+1] - s[k];
                    // integration step size
                    Number dt = T / Number( N_[k+1] );
                    for(j = 0; j < N_[k+1]; j++)
                    {     size_t Index = (j + S_[k]) * Ny;
                         // y(t) at end of last step
                         ym = y;
                         // G(y, a) at end of last step
                         Gm = G;
                         // value of y(t) at end of this step
                         for(i = 0; i < Ny; i++)
                              y[i] = x[Ny + Index + i];
                         // G(y, a) at end of this step
                         G = eval_G(y, a);
                         // trapezoidal approximation residual
                         for(i = 0; i < Ny; i++)
                         {     dy = (G[i] + Gm[i]) * dt / 2;
                              fg[1+Ny+Index+i] =
                                   y[i] - ym[i] - dy;
                         }
                    }
               }
               return fg;
          }
          // The operations sequence for r_eval does not depend on u,
          // hence retape = false should work and be faster.
          bool retape(size_t k)
          {     return retape_; }
     };

}
Input File: cppad_ipopt/example/ode_simple.hpp cppad-20170000.3/doc/ipopt_nlp_ode_fast.hpp.xml0000644000175200017650000010766513057470511020371 0ustar coincoin-web ODE Fitting Using Fast Representation
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ODE Fitting Using Fast Representation
# include "ode_problem.hpp"

namespace {
     using namespace cppad_ipopt;

     class FG_fast : public cppad_ipopt_fg_info
     {
     private:
          bool       retape_;
          SizeVector N_;
          SizeVector S_;
     public:
          // derived class part of constructor
          FG_fast(bool retape_in, const SizeVector& N)
          : retape_ (retape_in), N_(N)
          {     assert( N_[0] == 0 );
               S_.resize( N_.size() );
               S_[0] = 0;
               for(size_t i = 1; i < N_.size(); i++)
                    S_[i] = S_[i-1] + N_[i];
          }
          // r^k for k = 0, 1, ..., Nz-1 used for measurements
          // r^k for k = Nz              use for initial condition
          // r^k for k = Nz+1, ..., 2*Nz used for trapezoidal approx
          size_t number_functions(void)
          {     return Nz + 1 + Nz; }
          ADVector eval_r(size_t k, const ADVector &u)
          {     count_eval_r();

               size_t j;
               ADVector y(Ny), a(Na);
               // objective function --------------------------------
               if( k < Nz )
               {     // used for measurement with index k+1
                    ADVector r(1); // return value is a scalar
                    // u is [y( s[k+1] ) , a]
                    for(j = 0; j < Ny; j++)
                         y[j] = u[j];
                    for(j = 0; j < Na; j++)
                         a[j] = u[Ny + j];
                    r[0] = eval_H<ADNumber>(k+1, y, a);
                    return r;
               }
               // initial condition ---------------------------------
               if( k == Nz )
               {     ADVector r(Ny), F(Ny);
                    // u is [y(t), a] at t = 0
                    for(j = 0; j < Ny; j++)
                         y[j] = u[j];
                    for(j = 0; j < Na; j++)
                         a[j] = u[Ny + j];
                    F    = eval_F(a);
                    for(j = 0; j < Ny; j++)
                         r[j]   = y[j] - F[j];
                    return  r;
               }
               // trapezoidal approximation -------------------------
               ADVector ym(Ny), G(Ny), Gm(Ny), r(Ny);
               // r^k for k = Nz+1, ... , 2*Nz
               // interval between data samples
               Number T = s[k-Nz] - s[k-Nz-1];
               // integration step size
               Number dt = T / Number( N_[k-Nz] );
               // u = [ y(t[i-1], a) , y(t[i], a), a )
               for(j = 0; j < Ny; j++)
               {     ym[j] = u[j];
                    y[j]  = u[Ny + j];
               }
               for(j = 0; j < Na; j++)
                    a[j] = u[2 * Ny + j];
               Gm  = eval_G(ym, a);
               G   = eval_G(y,  a);
               for(j = 0; j < Ny; j++)
                    r[j] = y[j] - ym[j] - (G[j] + Gm[j]) * dt / 2.;
               return r;
          }
          // The operations sequence for r_eval does not depend on u,
          // hence retape = false should work and be faster.
          bool retape(size_t k)
          {     return retape_; }
          // size of the vector u in eval_r
          size_t domain_size(size_t k)
          {     if( k < Nz )
                    return Ny + Na;   // objective function
               if( k == Nz )
                    return Ny + Na;  // initial value constraint
               return 2 * Ny + Na;      // trapezodial constraints
          }
          // size of the return value from eval_r
          size_t range_size(size_t k)
          {     if( k < Nz )
                    return 1;
               return Ny;
          }
          // number of terms that use this value of k
          size_t number_terms(size_t k)
          {     if( k <= Nz )
                    return 1;  // r^k used once for k <= Nz
               // r^k used N_[k-Nz] times for k > Nz
               return N_[k-Nz];
          }
          void index(size_t k, size_t ell, SizeVector& I, SizeVector& J)
          {     size_t i, j;
               // # of components of x corresponding to values for y
               size_t ny_inx = (S_[Nz] + 1) * Ny;
               // objective function -------------------------------
               if( k < Nz )
               {     // index in fg corresponding to objective
                    I[0] = 0;
                    // u = [ y(t, a) , a ]
                    // The first Ny components of u is y(t) at
                    //     t = s[k+1] = t[S_[k+1]]
                    // x indices corresponding to this value of y
                    for(j = 0; j < Ny; j++)
                         J[j] = S_[k + 1] * Ny + j;
                    // components of x correspondig to a
                    for(j = 0; j < Na; j++)
                         J[Ny + j] = ny_inx + j;
                    return;
               }
               // initial conditions --------------------------------
               if( k == Nz )
               {     // index in fg for inidial condition constraint
                    for(j = 0; j < Ny; j++)
                         I[j] = 1 + j;
                    // u = [ y(t, a) , a ] where t = 0
                    // x indices corresponding to this value of y
                    for(j = 0; j < Ny; j++)
                         J[j] = j;
                    // following that, u contains the vector a
                    for(j = 0; j < Na; j++)
                         J[Ny + j] = ny_inx + j;
                    return;
               }
               // trapoziodal approximation -------------------------
               // index of first grid point in this approximation
               i = S_[k - Nz - 1]  + ell;
               // There are Ny difference equations for each time
               // point.  Add one for the objective function, and Ny
               // for the initial value constraints.
               for(j = 0; j < Ny; j++)
                    I[j] = 1 + Ny + i * Ny + j;
               // u = [ y(t, a) , y(t+dt, a) , a ] at t = t[i]
               for(j = 0; j < Ny; j++)
               {     J[j]      = i * Ny  + j; // y^i indices
                    J[Ny + j] = J[j] + Ny;   // y^{i+1} indices
               }
               for(j = 0; j < Na; j++)
                    J[2 * Ny + j] = ny_inx + j; // a indices
          }
     };

}
Input File: cppad_ipopt/example/ode_fast.hpp cppad-20170000.3/doc/ipopt_nlp_ode_simple.xml0000644000175200017650000003117113057470511020123 0ustar coincoin-web ODE Fitting Using Simple Representation
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ODE Fitting Using Simple Representation

Purpose
In this section we represent the objective and constraint functions, (in the simultaneous forward and reverse optimization problem) using the simple representation in the sense of cppad_ipopt_nlp.

Argument Vector
The argument vector that we are optimizing with respect to ( x in cppad_ipopt_nlp ) has the following structure x = ( y 0 , ⋯ , y S ( Nz ) , a ) Note that x ∈ R S ( Nz ) + Na and y i = ( x Ny * i , … , x Ny * i + Ny - 1 ) a = ( x Ny * S ( Nz ) + Ny , … , x Ny * S ( Nz ) + Na - 1 )
Objective Function
The objective function ( fg 0 ( x ) in cppad_ipopt_nlp ) has the following representation, fg 0 ( x ) = ∑ i = 1 Nz H i ( y S ( i ) , a )
Initial Condition Constraint
For i = 1 , … , Ny , we define the component functions fg i ( x ) , and corresponding constraint equations, by 0 = fg i ( x ) = y i 0 - F i ( a )
Trapezoidal Approximation Constraint
For i = 1 , … , S ( Nz ) , and for j = 1 , … , Ny , we define the component functions fg Ny * i + j ( x ) , and corresponding constraint equations, by 0 = fg Ny * i + j = y j i - y j i -1 - [G j ( y i , a ) + G j ( y i -1 , a ) ] * t i - t i -1 2
Source
The file ipopt_nlp_ode_simple.hpp contains source code for this representation of the objective and constraints.
Input File: cppad_ipopt/example/ode2.omh cppad-20170000.3/doc/ipopt_nlp_ode_fast.xml0000644000175200017650000012107413057470511017571 0ustar coincoin-web ODE Fitting Using Fast Representation
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ODE Fitting Using Fast Representation

Purpose
In this section we represent a more complex representation of the simultaneous forward and reverse ODE fitting problem (described above). The representation defines the problem using simpler functions that are faster to differentiate (either by hand coding or by using AD).

Objective Function
We use the following representation for the objective function : For k = 0 , … , Nz - 1 , we define the function r k : R Ny + Na → R by fg 0 ( x ) = ∑ i = 1 Nz H i ( y S ( i ) , a ) fg 0 ( x ) = ∑ k = 0 Nz -1 r k ( u k , 0 ) where for k = 0 , … , Nz -1 , u k , 0 ∈ R Ny + Na is defined by u k , 0 = ( y S ( k + 1 ) , a )

Range Indices I(k,0)
For k = 0 , … , Nz - 1 , the range index in the vector fg ( x ) corresponding to r k ( u k , 0 ) is 0. Thus, the range indices are given by I ( k , 0 ) = { 0 } for k = 0 , … , Nz -1 .

Domain Indices J(k,0)
For k = 0 , … , Nz - 1 , the components of the vector x corresponding to the vector u k , 0 are u k , 0 = ( y S ( k + 1 , a ) = ( x Ny * S ( k + 1 ) , … , x Ny * S ( k + 1 ) + Ny - 1 , x Ny * S ( Nz ) + Ny , … , x Ny * S ( Nz ) + Ny + Na - 1 ) Thus, the domain indices are given by J ( k , 0 ) = { Ny * S ( k + 1 ) , … , Ny * S ( k + 1 ) + Ny - 1 , Ny * S ( Nz ) + Ny , … , Ny * S ( Nz ) + Ny + Na - 1 }
Initial Condition
We use the following representation for the initial condition constraint : For k = Nz we define the function r k : R Ny × R Na + Ny by 0 = fg i ( x ) = y i 0 - F i ( a ) 0 = r i -1 k ( u k , 0 ) = y i 0 - F i ( a ) where i = 1 , … , Ny and where u k , 0 ∈ R Ny + Na is defined by u k , 0 = ( y 0 , a ) .

Range Indices I(k,0)
For k = Nz , the range index in the vector fg ( x ) corresponding to r k ( u k , 0 ) are I ( k , 0 ) = { 1 , … , Ny } .

Domain Indices J(k,0)
For k = Nz , the components of the vector x corresponding to the vector u k , 0 are u k , 0 = ( y 0 , a ) = ( x 0 , … , x Ny -1 , x Ny * S ( Nz ) + Ny , … , x Ny * S ( Nz ) + Ny + Na - 1 ) Thus, the domain indices are given by J ( k , 0 ) = { 0 , … , Ny - 1 , Ny * S ( Nz ) + Ny , … , Ny * S ( Nz ) + Ny + Na - 1 }
Trapezoidal Approximation
We use the following representation for the trapezoidal approximation constraint : For k = 1 , … , Nz , we define the function r Nz + k : R 2 * Ny + Na → R Ny by r Nz + k ( y , w , a ) = y - w - [ G ( y , a ) + G ( w , a ) ] * Δ t k 2 For ℓ = 0 , … , N ( k ) -1 , using the notation i = Ny * S ( k -1 ) + ℓ + 1 , the corresponding trapezoidal approximation is represented by 0 = fg Ny + i ( x ) = y i - y i -1 - [G ( y i , a ) + G ( y i -1 , a ) ] * Δ t k 2 = r Nz + k ( u Nz + k , ℓ ) where u Nz + k , ℓ ∈ R 2 * Ny + Na is defined by u Nz + k , ℓ = ( y i -1 , y i , a ) .

Range Indices I(k,0)
For k = Nz + 1 , … , 2 * Nz , and ℓ = 0 , … , N ( k ) -1 , the range index in the vector fg ( x ) corresponding to r k ( u k , ℓ ) are I ( k , ℓ ) = { Ny + i , … , 2 * Ny + i - 1 } where i = Ny * S ( k -1 ) + ℓ + 1 .

Domain Indices J(k,0)
For k = Nz + 1 , … , 2 * Nz , and ℓ = 0 , … , N ( k ) -1 , define i = Ny * S ( k -1 ) + ℓ + 1 . The components of the vector x corresponding to the vector u k , ℓ are (and the function fg ( x ) in cppad_ipopt_nlp ) u k , ℓ = ( y i -1 , y i , a ) = ( x Ny * ( i -1 ) , … , x Ny * ( i + 1 ) - 1 , x Ny * S ( Nz ) + Ny , … , x Ny * S ( Nz ) + Ny + Na - 1 ) Thus, the domain indices are given by J ( k , ℓ ) = { Ny * ( i -1 ) , … , Ny * ( i + 1 ) - 1 , Ny * S ( Nz ) + Ny , … , Ny * S ( Nz ) + Ny + Na - 1 }
Source
The file ipopt_nlp_ode_fast.hpp contains source code for this representation of the objective and constraints.
Input File: cppad_ipopt/example/ode2.omh cppad-20170000.3/doc/ipopt_nlp_ode_run.hpp.xml0000644000175200017650000005227313057470511020232 0ustar coincoin-web Driver for Running the Ipopt ODE Example
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Driver for Running the Ipopt ODE Example
# include "ode_problem.hpp"

namespace { // BEGIN empty namespace -----------------------------------------
using namespace cppad_ipopt;

template <class FG_info>
void ipopt_ode_case(
     bool  retape        ,
     const SizeVector& N ,
     NumberVector&     x )
{     bool ok = true;
     size_t i, j;

     // compute the partial sums of the number of grid points
     assert( N.size() == Nz + 1);
     assert( N[0] == 0 );
     SizeVector S(Nz+1);
     S[0] = 0;
     for(i = 1; i <= Nz; i++)
          S[i] = S[i-1] + N[i];

     // number of components of x corresponding to values for y
     size_t ny_inx = (S[Nz] + 1) * Ny;
     // number of constraints (range dimension of g)
     size_t m      = ny_inx;
     // number of components in x (domain dimension for f and g)
     size_t n      = ny_inx + Na;
     // the argument vector for the optimization is
     // y(t) at t[0] , ... , t[S[Nz]] , followed by a
     NumberVector x_i(n), x_l(n), x_u(n);
     for(j = 0; j < ny_inx; j++)
     {     x_i[j] = 0.;       // initial y(t) for optimization
          x_l[j] = -1.0e19;  // no lower limit
          x_u[j] = +1.0e19;  // no upper limit
     }
     for(j = 0; j < Na; j++)
     {     x_i[ny_inx + j ] = .5;       // initiali a for optimization
          x_l[ny_inx + j ] =  -1.e19;  // no lower limit
          x_u[ny_inx + j ] =  +1.e19;  // no upper
     }
     // all of the difference equations are constrained to the value zero
     NumberVector g_l(m), g_u(m);
     for(i = 0; i < m; i++)
     {     g_l[i] = 0.;
          g_u[i] = 0.;
     }

     // object defining the objective f(x) and constraints g(x)
     FG_info fg_info(retape, N);

     // create the CppAD Ipopt interface
     cppad_ipopt_solution solution;
     Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new cppad_ipopt_nlp(
          n, m, x_i, x_l, x_u, g_l, g_u, &fg_info, &solution
     );

     // Create an Ipopt application
     using Ipopt::IpoptApplication;
     Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();

     // turn off any printing
     app->Options()->SetIntegerValue("print_level", 0);
     app->Options()->SetStringValue("sb", "yes");

     // maximum number of iterations
     app->Options()->SetIntegerValue("max_iter", 30);

     // approximate accuracy in first order necessary conditions;
     // see Mathematical Programming, Volume 106, Number 1,
     // Pages 25-57, Equation (6)
     app->Options()->SetNumericValue("tol", 1e-9);

     // Derivative testing is very slow for large problems
     // so comment this out if you use a large value for N[].
     app->Options()-> SetStringValue( "derivative_test", "second-order");
     app->Options()-> SetNumericValue( "point_perturbation_radius", 0.);

     // Initialize the application and process the options
     Ipopt::ApplicationReturnStatus status = app->Initialize();
     ok    &= status == Ipopt::Solve_Succeeded;

     // Run the application
     status = app->OptimizeTNLP(cppad_nlp);
     ok    &= status == Ipopt::Solve_Succeeded;

     // return the solution
     x.resize( solution.x.size() );
     for(j = 0; j < x.size(); j++)
          x[j] = solution.x[j];

     return;
}
} // END empty namespace ----------------------------------------------------
Input File: cppad_ipopt/example/ode_run.hpp cppad-20170000.3/doc/ipopt_nlp_ode_check.cpp.xml0000644000175200017650000005361213057470511020474 0ustar coincoin-web Correctness Check for Both Simple and Fast Representations
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Correctness Check for Both Simple and Fast Representations
# include "ode_run.hpp"

bool ode_check(const SizeVector& N, const NumberVector& x)
{     bool ok = true;
     size_t i, j;

     // number of components of x corresponding to values for y
     size_t ny_inx = x.size() - Na;

     // compute the partial sums of the number of grid points
     // and the maximum step size for the trapezoidal approximation
     SizeVector S(Nz+1);
     S[0] = 0;
     double max_step = 0.;
     for(i = 1; i <= Nz; i++)
     {     S[i] = S[i-1] + N[i];
          max_step = std::max(max_step, (s[i] - s[i-1]) / N[i] );
     }

     // split out return values
     NumberVector a(Na), y_0(Ny), y_1(Ny), y_2(Ny);
     for(j = 0; j < Na; j++)
          a[j] = x[ny_inx+j];
     for(j = 0; j < Ny; j++)
     {     y_0[j] = x[j];
          y_1[j] = x[Ny + j];
          y_2[j] = x[2 * Ny + j];
     }

     // Check some of the optimal a value
     Number rel_tol = max_step * max_step;
     Number abs_tol = rel_tol;
     Number check_a[] = {a0, a1, a2}; // see the y_one function
     for(j = 0; j < Na; j++)
     {
          ok &= CppAD::NearEqual(
               check_a[j], a[j], rel_tol, abs_tol
          );
     }

     // check accuarcy of constraint equations
     rel_tol = 1e-9;
     abs_tol = 1e-9;

     // check the initial value constraint
     NumberVector F = eval_F(a);
     for(j = 0; j < Ny; j++)
          ok &= CppAD::NearEqual(F[j], y_0[j], rel_tol, abs_tol);

     // check the first trapezoidal equation
     NumberVector G_0 = eval_G(y_0, a);
     NumberVector G_1 = eval_G(y_1, a);
     Number dt = (s[1] - s[0]) / Number(N[1]);
     Number check;
     for(j = 0; j < Ny; j++)
     {     check = y_1[j] - y_0[j] - (G_1[j]+G_0[j])*dt/2;
          ok &= CppAD::NearEqual( check, 0., rel_tol, abs_tol);
     }
     //
     // check the second trapezoidal equation
     NumberVector G_2 = eval_G(y_2, a);
     if( N[1] == 1 )
          dt = (s[2] - s[1]) / Number(N[2]);
     for(j = 0; j < Ny; j++)
     {     check = y_2[j] - y_1[j] - (G_2[j]+G_1[j])*dt/2;
          ok &= CppAD::NearEqual( check, 0., rel_tol, abs_tol);
     }
     //
     // check the objective function (specialized to this case)
     check = 0.;
     NumberVector y_i(Ny);
     for(size_t k = 0; k < Nz; k++)
     {     for(j = 0; j < Ny; j++)
               y_i[j] =  x[S[k+1] * Ny + j];
          check += eval_H<Number>(k + 1, y_i, a);
     }
     Number obj_value = 0.; // optimal object (no noise in simulation)
     ok &= CppAD::NearEqual(check, obj_value, rel_tol, abs_tol);

     // Use this empty namespace function to avoid warning that it is not used
     static size_t ode_check_count = 0;
     ode_check_count++;
     ok &= count_eval_r() == ode_check_count;

     return ok;
}
Input File: cppad_ipopt/example/ode_check.cpp cppad-20170000.3/doc/ipopt_ode_speed.cpp.xml0000644000175200017650000003647613057470511017657 0ustar coincoin-web Speed Test for Both Simple and Fast Representations
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Speed Test for Both Simple and Fast Representations
# include "../example/ode_run.hpp"
# include "../example/ode_simple.hpp"
# include "../example/ode_fast.hpp"
# include <cassert>
# include <cstring>

# if CPPAD_HAS_GETTIMEOFDAY & CPPAD_NO_MICROSOFT
# include <sys/time.h>
# else
# include <ctime>
# endif

namespace {
     double current_second(void)
     {
# if CPPAD_HAS_GETTIMEOFDAY & CPPAD_NOT_MICOROSOFT
          struct timeval value;
          gettimeofday(&value, 0);
          return double(value.tv_sec) + double(value.tv_usec) * 1e-6;
# else
          return (double) clock() / (double) CLOCKS_PER_SEC;
# endif
     }
}

double ode_speed(const char* name, size_t& count)
{
     // determine simple and retape flags
     bool simple = true, retape = true;
     if( std::strcmp(name, "simple_retape_no") == 0 )
     {     simple = true; retape = false; }
     else if( std::strcmp(name, "simple_retape_yes") == 0 )
     {     simple = true; retape = true; }
     else if( std::strcmp(name, "fast_retape_no") == 0 )
     {     simple = false; retape = false; }
     else if( std::strcmp(name, "fast_retape_yes") == 0 )
     {     simple = false; retape = true; }
     else     assert(false);

     size_t i;
        double s0, s1;
     size_t  c0, c1;

     // solution vector
     NumberVector x;

     // number of time grid intervals between measurement values
     SizeVector N(Nz + 1);
     N[0] = 0;
     for(i = 1; i <= Nz; i++)
     {     N[i] = 10;
          // n   += N[i] * Ny;
     }
     // n += Na;

     s0              = current_second();
     c0              = count_eval_r();
     if( simple )
          ipopt_ode_case<FG_simple>(retape, N, x);
     else     ipopt_ode_case<FG_fast>(retape, N, x);
     s1              = current_second();
     c1              = count_eval_r();
     count           = c1 - c0 - 1;
     return s1 - s0;
}
Input File: cppad_ipopt/speed/ode_speed.cpp cppad-20170000.3/doc/old_atomic.xml0000644000175200017650000037761713057470511016053 0ustar coincoin-web User Defined Atomic AD Functions
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User Defined Atomic AD Functions

Deprecated 2013-05-27
Using CPPAD_USER_ATOMIC has been deprecated. Use atomic_base instead.

Syntax Function
CPPAD_USER_ATOMIC(afun, Tvector, Base,
     forward, reverse, for_jac_sparse, rev_jac_sparse, rev_hes_sparse
)
Use Function
afun(id, ax, ay)
Callback Routines
ok = forward(id, k, n, m, vx, vy, tx, ty)
 ok = reverse(id, k, n, m, tx, ty, px, py)
 ok = for_jac_sparse(id, n, m, q, r, s)
 ok = rev_jac_sparse(id, n, m, q, r, s)
 ok = rev_hes_sparse(id, n, m, q, r, s, t, u, v)
Free Static Memory
user_atomic<Base>::clear()

Purpose
In some cases, the user knows how to compute the derivative of a function y = f ( x ) where f : B n → B m more efficiently than by coding it using AD<Base> atomic operations and letting CppAD do the rest. In this case, CPPAD_USER_ATOMIC can be used add the user code for f ( x ) , and its derivatives, to the set of AD<Base> atomic operations.

Another possible purpose is to reduce the size of the tape; see use AD

Partial Implementation
The routines forward , reverse , for_jac_sparse , rev_jac_sparse , and rev_hes_sparse , must be defined by the user. The forward the routine, for the case k = 0 , must be implemented. Functions with the correct prototype, that just return false, can be used for the other cases (unless they are required by your calculations). For example, you need not implement forward for the case k == 2 until you require forward mode calculation of second derivatives.

CPPAD_USER_ATOMIC
The macro
CPPAD_USER_ATOMIC(afun, Tvector, Base,
     forward, reverse, for_jac_sparse, rev_jac_sparse, rev_hes_sparse
)
 defines the AD<Base> routine afun . This macro can be placed within a namespace (not the CppAD namespace) but must be outside of any routine.

Tvector
The macro argument Tvector must be a simple vector template class . It determines the type of vectors used as arguments to the routine afun .

Base
The macro argument Base specifies the base type corresponding to AD<Base> operation sequences. Calling the routine afun will add the operator defined by this macro to an AD<Base> operation sequence.

ok
For all routines documented below, the return value ok has prototype
     bool ok
 If it is true, the corresponding evaluation succeeded, otherwise it failed.

id
For all routines documented below, the argument id has prototype
     size_t id
 Its value in all other calls is the same as in the corresponding call to afun . It can be used to store and retrieve extra information about a specific call to afun .

k
For all routines documented below, the argument k has prototype
     size_t k
 The value k is the order of the Taylor coefficient that we are evaluating (forward ) or taking the derivative of (reverse ).

n
For all routines documented below, the argument n has prototype
     size_t n
 It is the size of the vector ax in the corresponding call to afun(id, ax, ay) ; i.e., the dimension of the domain space for y = f ( x ) .

m
For all routines documented below, the argument m has prototype
     size_t m
 It is the size of the vector ay in the corresponding call to afun(id, ax, ay) ; i.e., the dimension of the range space for y = f ( x ) .

tx
For all routines documented below, the argument tx has prototype
     const CppAD::vector<Base>& tx
 and tx.size() >= (k + 1) * n . For j = 0 , … , n -1 and ℓ = 0 , … , k , we use the Taylor coefficient notation x j ℓ = tx [ j * ( k + 1 ) + ℓ ] X j ( t ) = x j 0 + x j 1 t 1 + ⋯ + x j k t k If tx.size() > (k + 1) * n , the other components of tx are not specified and should not be used. Note that superscripts represent an index for x j ℓ and an exponent for t ℓ . Also note that the Taylor coefficients for X ( t ) correspond to the derivatives of X ( t ) at t = 0 in the following way: x j ℓ = 1 ℓ ! X j ( ℓ ) ( 0 )
ty
In calls to forward , the argument ty has prototype
     CppAD::vector<Base>& ty
 while in calls to reverse it has prototype
     const CppAD::vector<Base>& ty
 For all calls, tx.size() >= (k + 1) * m . For i = 0 , … , m -1 and ℓ = 0 , … , k , we use the Taylor coefficient notation y i ℓ = ty [ i * ( k + 1 ) + ℓ ] Y i ( t ) = y i 0 + y i 1 t 1 + ⋯ + y i k t k + o ( t k ) where o ( t k ) / t k → 0 as t → 0 . If ty.size() > (k + 1) * m , the other components of ty are not specified and should not be used. Note that superscripts represent an index for y j ℓ and an exponent for t ℓ . Also note that the Taylor coefficients for Y ( t ) correspond to the derivatives of Y ( t ) at t = 0 in the following way: y j ℓ = 1 ℓ ! Y j ( ℓ ) ( 0 )
forward
In the case of forward , for i = 0 , … , m -1 , ty [ i * ( k + 1 ) + k ] is an output and all the other components of ty are inputs.

reverse
In the case of reverse , all the components of ty are inputs.

afun
The macro argument afun , is the name of the AD function corresponding to this atomic operation (as it is used in the source code). CppAD uses the other functions, where the arguments are vectors with elements of type Base , to implement the function
     afun(id, ax, ay)
 where the argument are vectors with elements of type AD<Base> .

ax
The afun argument ax has prototype
     const Tvector< AD<Base> >& ax
 It is the argument vector x ∈ B n at which the AD<Base> version of y = f ( x ) is to be evaluated. The dimension of the domain space for y = f ( x ) is specified by n = ax.size() , which must be greater than zero.

ay
The afun result ay has prototype
     Tvector< AD<Base> >& ay
 The input values of its elements are not specified (must not matter). Upon return, it is the AD<Base> version of the result vector y = f ( x ) . The dimension of the range space for y = f ( x ) is specified by m = ay.size() , which must be greater than zero.

Parallel Mode
The first call to
     afun(id, ax, ay)
 must not be in parallel mode. In addition, the old_atomic clear routine cannot be called while in parallel mode.

forward
The macro argument forward is a user defined function
     ok = forward(id, k, n, m, vx, vy, tx, ty)
 that computes results during a forward mode sweep. For this call, we are given the Taylor coefficients in tx form order zero through k , and the Taylor coefficients in ty with order less than k . The forward routine computes the k order Taylor coefficients for y using the definition Y ( t ) = f [ X ( t ) ] . For example, for i = 0 , … , m -1 , y i 0 = Y ( 0 ) = f i ( x 0 ) y i 1 = Y ( 1 ) ( 0 ) = f i ( 1 ) ( x 0 ) X ( 1 ) ( 0 ) = f i ( 1 ) ( x 0 ) x 1 y i 2 = 1 2 ! Y ( 2 ) ( 0 ) = 1 2 X ( 1 ) ( 0 ) T f i ( 2 ) ( x 0 ) X ( 1 ) ( 0 ) + 1 2 f i ( 1 ) ( x 0 ) X ( 2 ) ( 0 ) = 1 2 ( x 1 ) T f i ( 2 ) ( x 0 ) x 1 + f i ( 1 ) ( x 0 ) x 2 Then, for i = 0 , … , m -1 , it sets ty [ i * ( k + 1 ) + k ] = y i k The other components of ty must be left unchanged.

Usage
This routine is used, with vx.size() > 0 and k == 0 , by calls to afun . It is used, with vx.size() = 0 and k equal to the order of the derivative begin computed, by calls to forward .

vx
The forward argument vx has prototype
     const CppAD::vector<bool>& vx
 The case vx.size() > 0 occurs once for each call to afun , during the call, and before any of the other callbacks corresponding to that call. Hence such a call can be used to cache information attached to the corresponding id (such as the elements of vx ). If vx.size() > 0 then k == 0 , vx.size() >= n , and for j = 0 , … , n -1 , vx[j] is true if and only if ax[j] is a variable .

If vx.size() == 0 , then vy.size() == 0 and neither of these vectors should be used.

vy
The forward argument vy has prototype
     CppAD::vector<bool>& vy
 If vy.size() == 0 , it should not be used. Otherwise, k == 0 and vy.size() >= m . The input values of the elements of vy are not specified (must not matter). Upon return, for j = 0 , … , m -1 , vy[i] is true if and only if ay[j] is a variable. (CppAD uses vy to reduce the necessary computations.)

reverse
The macro argument reverse is a user defined function
     ok = reverse(id, k, n, m, tx, ty, px, py)
 that computes results during a reverse mode sweep. The input value of the vectors tx and ty contain Taylor coefficient, up to order k , for X ( t ) and Y ( t ) respectively. We use the { x j ℓ } and { y i ℓ } to denote these Taylor coefficients where the implicit range indices are i = 0 , … , m -1 , j = 0 , … , n -1 , ℓ = 0 , … , k . Using the calculations done by forward , the Taylor coefficients { y i ℓ } are a function of the Taylor coefficients for { x j ℓ } ; i.e., given y = f ( x ) we define the function F : B n × ( k + 1 ) → B m × ( k + 1 ) by y i ℓ = F i ℓ ( { x j ℓ } ) We use G : B m × ( k + 1 ) → B to denote an arbitrary scalar valued function of the Taylor coefficients for Y ( t ) and write z = G ( { y i ℓ } ) . The reverse routine is given the derivative of z with respect to { y i ℓ } and computes its derivative with respect to { x j ℓ } .

Usage
This routine is used, with k + 1 equal to the order of the derivative being calculated, by calls to reverse .

py
The reverse argument py has prototype
     const CppAD::vector<Base>& py
 and py.size() >= (k + 1) * m . For i = 0 , … , m -1 and ℓ = 0 , … , k , py [ i * ( k + 1 ) + ℓ ] = ∂ G / ∂ y i ℓ If py.size() > (k + 1) * m , the other components of py are not specified and should not be used.

px
We define the function H ( { x j ℓ } ) = G [ F ( { x j ℓ } ) ] The reverse argument px has prototype
     CppAD::vector<Base>& px
 and px.size() >= (k + 1) * n . The input values of the elements of px are not specified (must not matter). Upon return, for j = 0 , … , n -1 and p = 0 , … , k , px [ j * ( k + 1 ) + p ] = ∂ H / ∂ x j p = ( ∂ G / ∂ { y i ℓ } ) ( ∂ { y i ℓ } / ∂ x j p ) = ∑ i = 0 m -1 ∑ ℓ = 0 k ( ∂ G / ∂ y i ℓ ) ( ∂ y i ℓ / ∂ x j p ) = ∑ i = 0 m -1 ∑ ℓ = p k py [ i * ( k + 1 ) + ℓ ] ( ∂ F i ℓ / ∂ x j p ) Note that we have used the fact that for ℓ < p , ∂ F i ℓ / ∂ x j p = 0 . If px.size() > (k + 1) * n , the other components of px are not specified and should not be used.

for_jac_sparse
The macro argument for_jac_sparse is a user defined function
     ok = for_jac_sparse(id, n, m, q, r, s)
 that is used to compute results during a forward Jacobian sparsity sweep. For a fixed n × q matrix R , the Jacobian of f ( x + R * u ) with respect to u ∈ B q is S ( x ) = f ( 1 ) ( x ) * R Given a sparsity pattern for R , for_jac_sparse computes a sparsity pattern for S ( x ) .

Usage
This routine is used by calls to ForSparseJac .

q
The for_jac_sparse argument q has prototype
     size_t q
 It specifies the number of columns in R ∈ B n × q and the Jacobian S ( x ) ∈ B m × q .

r
The for_jac_sparse argument r has prototype
     const CppAD::vector< std::set<size_t> >& r
 and r.size() >= n . For j = 0 , … , n -1 , all the elements of r[j] are between zero and q-1 inclusive. This specifies a sparsity pattern for the matrix R .

s
The for_jac_sparse return value s has prototype
     CppAD::vector< std::set<size_t> >& s
 and s.size() >= m . The input values of its sets are not specified (must not matter). Upon return for i = 0 , … , m -1 , all the elements of s[i] are between zero and q-1 inclusive. This represents a sparsity pattern for the matrix S ( x ) .

rev_jac_sparse
The macro argument rev_jac_sparse is a user defined function
     ok = rev_jac_sparse(id, n, m, q, r, s)
 that is used to compute results during a reverse Jacobian sparsity sweep. For a fixed q × m matrix S , the Jacobian of S * f ( x ) with respect to x ∈ B n is R ( x ) = S * f ( 1 ) ( x ) Given a sparsity pattern for S , rev_jac_sparse computes a sparsity pattern for R ( x ) .

Usage
This routine is used by calls to RevSparseJac and to optimize .

q
The rev_jac_sparse argument q has prototype
     size_t q
 It specifies the number of rows in S ∈ B q × m and the Jacobian R ( x ) ∈ B q × n .

s
The rev_jac_sparse argument s has prototype
     const CppAD::vector< std::set<size_t> >& s
 and s.size() >= m . For i = 0 , … , m -1 , all the elements of s[i] are between zero and q-1 inclusive. This specifies a sparsity pattern for the matrix S T .

r
The rev_jac_sparse return value r has prototype
     CppAD::vector< std::set<size_t> >& r
 and r.size() >= n . The input values of its sets are not specified (must not matter). Upon return for j = 0 , … , n -1 , all the elements of r[j] are between zero and q-1 inclusive. This represents a sparsity pattern for the matrix R ( x ) T .

rev_hes_sparse
The macro argument rev_hes_sparse is a user defined function
     ok = rev_hes_sparse(id, n, m, q, r, s, t, u, v)
 There is an unspecified scalar valued function g : B m → B . Given a sparsity pattern for R and information about the function z = g ( y ) , this routine computes the sparsity pattern for V ( x ) = ( g ∘ f ) ( 2 ) ( x ) R
Usage
This routine is used by calls to RevSparseHes .

q
The rev_hes_sparse argument q has prototype
     size_t q
 It specifies the number of columns in the sparsity patterns.

r
The rev_hes_sparse argument r has prototype
     const CppAD::vector< std::set<size_t> >& r
 and r.size() >= n . For j = 0 , … , n -1 , all the elements of r[j] are between zero and q-1 inclusive. This specifies a sparsity pattern for the matrix R ∈ B n × q .

s
The rev_hes_sparse argument s has prototype
     const CppAD::vector<bool>& s
 and s.size() >= m . This specifies a sparsity pattern for the matrix S ( x ) = g ( 1 ) ( y ) ∈ B 1 × m .

t
The rev_hes_sparse argument t has prototype
     CppAD::vector<bool>& t
 and t.size() >= n . The input values of its elements are not specified (must not matter). Upon return it represents a sparsity pattern for the matrix T ( x ) ∈ B 1 × n defined by T ( x ) = ( g ∘ f ) ( 1 ) ( x ) = S ( x ) * f ( 1 ) ( x )
u
The rev_hes_sparse argument u has prototype
     const CppAD::vector< std::set<size_t> >& u
 and u.size() >= m . For i = 0 , … , m -1 , all the elements of u[i] are between zero and q-1 inclusive. This specifies a sparsity pattern for the matrix U ( x ) ∈ B m × q defined by U ( x ) = ∂ u { ∂ y g [ y + f ( 1 ) ( x ) R u ] } u = 0 = ∂ u { g ( 1 ) [ y + f ( 1 ) ( x ) R u ] } u = 0 = g ( 2 ) ( y ) f ( 1 ) ( x ) R
v
The rev_hes_sparse argument v has prototype
     CppAD::vector< std::set<size_t> >& v
 and v.size() >= n . The input values of its elements are not specified (must not matter). Upon return, for j = 0 , … , n -1 , all the elements of v[j] are between zero and q-1 inclusive. This represents a sparsity pattern for the matrix V ( x ) ∈ B n × q defined by V ( x ) = ∂ u [ ∂ x ( g ∘ f ) ( x + R u ) ] u = 0 = ∂ u [ ( g ∘ f ) ( 1 ) ( x + R u ) ] u = 0 = ( g ∘ f ) ( 2 ) ( x ) R = f ( 1 ) ( x ) T g ( 2 ) ( y ) f ( 1 ) ( x ) R + ∑ i = 1 m [ g ( 1 ) ( y ) ] i f i ( 2 ) ( x ) R = f ( 1 ) ( x ) T U ( x ) + ∑ i = 1 m S ( x ) i f i ( 2 ) ( x ) R
clear
User atomic functions hold onto static work space in order to increase speed by avoiding system memory allocation calls. The function call
     user_atomic<Base>::clear()
 makes to work space available to for other uses by the same thread. This should be called when you are done using the user atomic functions for a specific value of Base .

Restriction
The user atomic clear routine cannot be called while in parallel execution mode.

Example

Simple
The file old_reciprocal.cpp contains the simplest example and test of a user atomic operation.


The examples old_usead_1.cpp and old_usead_2.cpp use AD to compute the derivatives inside a user defined atomic function. This may have the advantage of reducing the size of the tape, because a repeated section of code would only be taped once.

Tangent Function
The file old_tan.cpp contains an example and test implementation of the tangent function as a user atomic operation.

Matrix Multiplication
The file old_mat_mul.cpp contains an example and test implementation of matrix multiplication a a user atomic operation.
Input File: cppad/core/old_atomic.hpp cppad-20170000.3/doc/old_reciprocal.cpp.xml0000644000175200017650000017554513057470511017477 0ustar coincoin-web Old Atomic Operation Reciprocal: Example and Test
Prev Next old_reciprocal.cpp

Old Atomic Operation Reciprocal: Example and Test

Deprecated 2013-05-27
This example has been deprecated; see atomic_reciprocal.cpp instead.

Theory
The example below defines the user atomic function f : R n → R m where n = 1 , m = 1 , and f ( x ) = 1 / x . 
# include <cppad/cppad.hpp>

namespace { // Begin empty namespace
     using CppAD::vector;
     // ----------------------------------------------------------------------
     // a utility to compute the union of two sets.
     using CppAD::set_union;

     // ----------------------------------------------------------------------
     // forward mode routine called by CppAD
     bool reciprocal_forward(
          size_t                   id ,
          size_t                    k ,
          size_t                    n ,
          size_t                    m ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {     assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );
          assert( k == 0 || vx.size() == 0 );
          bool ok = false;
          double f, fp, fpp;

          // Must always define the case k = 0.
          // Do not need case k if not using f.Forward(q, xp) for q >= k.
          switch(k)
          {     case 0:
               // this case must  be implemented
               if( vx.size() > 0 )
                    vy[0] = vx[0];
               // y^0 = f( x^0 ) = 1 / x^0
               ty[0] = 1. / tx[0];
               ok    = true;
               break;

               case 1:
               // needed if first order forward mode is used
               assert( vx.size() == 0 );
               // y^1 = f'( x^0 ) x^1
               f     = ty[0];
               fp    = - f / tx[0];
               ty[1] = fp * tx[1];
               ok    = true;
               break;

               case 2:
               // needed if second order forward mode is used
               assert( vx.size() == 0 );
               // Y''(t) = X'(t)^\R{T} f''[X(t)] X'(t) + f'[X(t)] X''(t)
               // 2 y^2  = x^1 * f''( x^0 ) x^1 + 2 f'( x^0 ) x^2
               f     = ty[0];
               fp    = - f / tx[0];
               fpp   = - 2.0 * fp / tx[0];
               ty[2] = tx[1] * fpp * tx[1] / 2.0 + fp * tx[2];
               ok    = true;
               break;
          }
          return ok;
     }
     // ----------------------------------------------------------------------
     // reverse mode routine called by CppAD
     bool reciprocal_reverse(
          size_t                   id ,
          size_t                    k ,
          size_t                    n ,
          size_t                    m ,
          const vector<double>&    tx ,
          const vector<double>&    ty ,
          vector<double>&          px ,
          const vector<double>&    py
     )
     {     // Do not need case k if not using f.Reverse(k+1, w).
          assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );
          bool ok = false;

          double f, fp, fpp, fppp;
          switch(k)
          {     case 0:
               // needed if first order reverse mode is used
               // reverse: F^0 ( tx ) = y^0 = f( x^0 )
               f     = ty[0];
               fp    = - f / tx[0];
               px[0] = py[0] * fp;;
               ok    = true;
               break;

               case 1:
               // needed if second order reverse mode is used
               // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1
               f      = ty[0];
               fp     = - f / tx[0];
               fpp    = - 2.0 * fp / tx[0];
               px[1]  = py[1] * fp;
               px[0]  = py[1] * fpp * tx[1];
               // reverse: F^0 ( tx ) = y^0 = f( x^0 );
               px[0] += py[0] * fp;

               ok     = true;
               break;

               case 2:
               // needed if third order reverse mode is used
               // reverse: F^2 ( tx ) = y^2 =
               //            = x^1 * f''( x^0 ) x^1 / 2 + f'( x^0 ) x^2
               f      = ty[0];
               fp     = - f / tx[0];
               fpp    = - 2.0 * fp / tx[0];
               fppp   = - 3.0 * fpp / tx[0];
               px[2]  = py[2] * fp;
               px[1]  = py[2] * fpp * tx[1];
               px[0]  = py[2] * tx[1] * fppp * tx[1] / 2.0 + fpp * tx[2];
               // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1
               px[1] += py[1] * fp;
               px[0] += py[1] * fpp * tx[1];
               // reverse: F^0 ( tx ) = y^0 = f( x^0 );
               px[0] += py[0] * fp;

               ok = true;
               break;
          }
          return ok;
     }
     // ----------------------------------------------------------------------
     // forward Jacobian sparsity routine called by CppAD
     bool reciprocal_for_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          vector< std::set<size_t> >&           s )
     {     // Can just return false if not using f.ForSparseJac
          assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );

          // sparsity for S(x) = f'(x) * R is same as sparsity for R
          s[0] = r[0];

          return true;
     }
     // ----------------------------------------------------------------------
     // reverse Jacobian sparsity routine called by CppAD
     bool reciprocal_rev_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          vector< std::set<size_t> >&           r ,
          const vector< std::set<size_t> >&     s )
     {     // Can just return false if not using RevSparseJac.
          assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );

          // sparsity for R(x) = S * f'(x) is same as sparsity for S
          for(size_t q = 0; q < p; q++)
               r[q] = s[q];

          return true;
     }
     // ----------------------------------------------------------------------
     // reverse Hessian sparsity routine called by CppAD
     bool reciprocal_rev_hes_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          const vector<bool>&                   s ,
                vector<bool>&                   t ,
          const vector< std::set<size_t> >&     u ,
                vector< std::set<size_t> >&     v )
     {     // Can just return false if not use RevSparseHes.
          assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );

          // sparsity for T(x) = S(x) * f'(x) is same as sparsity for S
          t[0] = s[0];

          // V(x) = [ f'(x)^T * g''(y) * f'(x) + g'(y) * f''(x) ] * R
          // U(x) = g''(y) * f'(x) * R
          // S(x) = g'(y)

          // back propagate the sparsity for U because derivative of
          // reciprocal may be non-zero
          v[0] = u[0];

          // convert forward Jacobian sparsity to Hessian sparsity
          // because second derivative of reciprocal may be non-zero
          if( s[0] )
               v[0] = set_union(v[0], r[0] );


          return true;
     }
     // ---------------------------------------------------------------------
     // Declare the AD<double> routine reciprocal(id, ax, ay)
     CPPAD_USER_ATOMIC(
          reciprocal                 ,
          CppAD::vector              ,
          double                     ,
          reciprocal_forward         ,
          reciprocal_reverse         ,
          reciprocal_for_jac_sparse  ,
          reciprocal_rev_jac_sparse  ,
          reciprocal_rev_hes_sparse
     )
} // End empty namespace

bool old_reciprocal(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // --------------------------------------------------------------------
     // Create the function f(x)
     //
     // domain space vector
     size_t n  = 1;
     double  x0 = 0.5;
     vector< AD<double> > ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     vector< AD<double> > ay(m);

     // call user function and store reciprocal(x) in au[0]
     vector< AD<double> > au(m);
     size_t id = 0;           // not used
     reciprocal(id, ax, au);     // u = 1 / x

     // call user function and store reciprocal(u) in ay[0]
     reciprocal(id, au, ay);     // y = 1 / u = x

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (ax, ay);  // f(x) = x

     // --------------------------------------------------------------------
     // Check forward mode results
     //
     // check function value
     double check = x0;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> x_q(n), y_q(m);
     q      = 0;
     x_q[0] = x0;
     y_q    = f.Forward(q, x_q);
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // check first order forward mode
     q      = 1;
     x_q[0] = 1;
     y_q    = f.Forward(q, x_q);
     check  = 1.;
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // check second order forward mode
     q      = 2;
     x_q[0] = 0;
     y_q    = f.Forward(q, x_q);
     check  = 0.;
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // --------------------------------------------------------------------
     // Check reverse mode results
     //
     // third order reverse mode
     q     = 3;
     vector<double> w(m), dw(n * q);
     w[0]  = 1.;
     dw    = f.Reverse(q, w);
     check = 1.;
     ok &= NearEqual(dw[0] , check,  eps, eps);
     check = 0.;
     ok &= NearEqual(dw[1] , check,  eps, eps);
     ok &= NearEqual(dw[2] , check,  eps, eps);

     // --------------------------------------------------------------------
     // forward mode sparstiy pattern
     size_t p = n;
     CppAD::vectorBool r1(n * p), s1(m * p);
     r1[0] = true;          // compute sparsity pattern for x[0]
     s1    = f.ForSparseJac(p, r1);
     ok  &= s1[0] == true;  // f[0] depends on x[0]

     // --------------------------------------------------------------------
     // reverse mode sparstiy pattern
     q = m;
     CppAD::vectorBool s2(q * m), r2(q * n);
     s2[0] = true;          // compute sparsity pattern for f[0]
     r2    = f.RevSparseJac(q, s2);
     ok  &= r2[0] == true;  // f[0] depends on x[0]

     // --------------------------------------------------------------------
     // Hessian sparsity (using previous ForSparseJac call)
     CppAD::vectorBool s3(m), h(p * n);
     s3[0] = true;        // compute sparsity pattern for f[0]
     h     = f.RevSparseHes(p, s3);
     ok  &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero

     // -----------------------------------------------------------------
     // Free all temporary work space associated with old_atomic objects.
     // (If there are future calls to user atomic functions, they will
     // create new temporary work space.)
     CppAD::user_atomic<double>::clear();

     return ok;
}
Input File: test_more/old_reciprocal.cpp cppad-20170000.3/doc/old_usead_1.cpp.xml0000644000175200017650000020140613057470511016657 0ustar coincoin-web Using AD to Compute Atomic Function Derivatives
Prev Next old_usead_1.cpp

Using AD to Compute Atomic Function Derivatives

Deprecated 2013-05-27
This example has been deprecated because it is easier to use the checkpoint class instead.

Purpose
Consider the case where an inner function is used repeatedly in the definition of an outer function. In this case, it may reduce the number of variables size_var , and hence the required memory.

Simple Case
This example is the same as old_reciprocal.cpp , except that it uses AD to compute the derivatives needed by an atomic function. This is a simple example of an inner function, and hence not really useful for the purpose above; see old_usead_2.cpp for a more complete example. 
# include <cppad/cppad.hpp>

namespace { // Begin empty namespace
     using CppAD::AD;
     using CppAD::ADFun;
     using CppAD::vector;

     // ----------------------------------------------------------------------
     // function that computes reciprocal
     ADFun<double>* r_ptr_;
     void create_r(void)
     {     vector< AD<double> > ax(1), ay(1);
          ax[0]  = 1;
          CppAD::Independent(ax);
          ay[0]  = 1.0 / ax[0];
          r_ptr_ = new ADFun<double>(ax, ay);
     }
     void destroy_r(void)
     {     delete r_ptr_;
          r_ptr_ = CPPAD_NULL;
     }

     // ----------------------------------------------------------------------
     // forward mode routine called by CppAD
     bool reciprocal_forward(
          size_t                   id ,
          size_t                    k ,
          size_t                    n ,
          size_t                    m ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {     assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );
          assert( k == 0 || vx.size() == 0 );
          bool ok = true;
          vector<double> x_q(1), y_q(1);

          // check for special case
          if( vx.size() > 0 )
               vy[0] = vx[0];

          // make sure r_ has proper lower order Taylor coefficients stored
          // then compute ty[k]
          for(size_t q = 0; q <= k; q++)
          {     x_q[0] = tx[q];
               y_q    = r_ptr_->Forward(q, x_q);
               if( q == k )
                    ty[k] = y_q[0];
               assert( q == k || ty[q] == y_q[0] );
          }
          return ok;
     }
     // ----------------------------------------------------------------------
     // reverse mode routine called by CppAD
     bool reciprocal_reverse(
          size_t                   id ,
          size_t                    k ,
          size_t                    n ,
          size_t                    m ,
          const vector<double>&    tx ,
          const vector<double>&    ty ,
          vector<double>&          px ,
          const vector<double>&    py
     )
     {     assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );
          bool ok = true;
          vector<double> x_q(1), w(k+1), dw(k+1);

          // make sure r_ has proper forward mode coefficients
          size_t q;
          for(q = 0; q <= k; q++)
          {     x_q[0] = tx[q];
# ifdef NDEBUG
               r_ptr_->Forward(q, x_q);
# else
               vector<double> y_q(1);
               y_q    = r_ptr_->Forward(q, x_q);
               assert( ty[q] == y_q[0] );
# endif
          }
          for(q = 0; q <=k; q++)
               w[q] = py[q];
          dw = r_ptr_->Reverse(k+1, w);
          for(q = 0; q <=k; q++)
               px[q] = dw[q];

          return ok;
     }
     // ----------------------------------------------------------------------
     // forward Jacobian sparsity routine called by CppAD
     bool reciprocal_for_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          vector< std::set<size_t> >&           s )
     {     assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );
          bool ok = true;

          vector< std::set<size_t> > R(1), S(1);
          R[0] = r[0];
          S = r_ptr_->ForSparseJac(p, R);
          s[0] = S[0];

          return ok;
     }
     // ----------------------------------------------------------------------
     // reverse Jacobian sparsity routine called by CppAD
     bool reciprocal_rev_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          vector< std::set<size_t> >&           r ,
          const vector< std::set<size_t> >&     s )
     {
          assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );
          bool ok = true;

          vector< std::set<size_t> > R(p), S(p);
          size_t q;
          for(q = 0; q < p; q++)
               S[q] = s[q];
          R = r_ptr_->RevSparseJac(p, S);
          for(q = 0; q < p; q++)
               r[q] = R[q];

          return ok;
     }
     // ----------------------------------------------------------------------
     // reverse Hessian sparsity routine called by CppAD
     bool reciprocal_rev_hes_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          const vector<bool>&                   s ,
          vector<bool>&                         t ,
          const vector< std::set<size_t> >&     u ,
          vector< std::set<size_t> >&           v )
     {     // Can just return false if not use RevSparseHes.
          assert( id == 0 );
          assert( n == 1 );
          assert( m == 1 );
          bool ok = true;

          // compute sparsity pattern for T(x) = S(x) * f'(x)
          vector<bool> T(1), S(1);
          S[0]   = s[0];
          T      = r_ptr_->RevSparseJac(1, S);
          t[0]   = T[0];

          // compute sparsity pattern for A(x) = U(x)^T * f'(x)
          vector<bool> Ut(p), A(p);
          size_t q;
          for(q = 0; q < p; q++)
               Ut[q] = false;
          std::set<size_t>::iterator itr;
          for(itr = u[0].begin(); itr != u[0].end(); itr++)
               Ut[*itr] = true;
          A = r_ptr_-> RevSparseJac(p, Ut);

          // compute sparsity pattern for H(x) = R^T * (S * F)''(x)
          vector<bool> H(p), R(n);
          for(q = 0; q < p; q++)
               R[q] = false;
          for(itr = r[0].begin(); itr != r[0].end(); itr++)
               R[*itr] = true;
          r_ptr_->ForSparseJac(p, R);
          H = r_ptr_->RevSparseHes(p, S);

          // compute sparsity pattern for V(x) = A(x)^T + H(x)^T
          v[0].clear();
          for(q = 0; q < p; q++)
               if( A[q] | H[q] )
                    v[0].insert(q);

          return ok;
     }
     // ---------------------------------------------------------------------
     // Declare the AD<double> routine reciprocal(id, ax, ay)
     CPPAD_USER_ATOMIC(
          reciprocal                 ,
          CppAD::vector              ,
          double                     ,
          reciprocal_forward         ,
          reciprocal_reverse         ,
          reciprocal_for_jac_sparse  ,
          reciprocal_rev_jac_sparse  ,
          reciprocal_rev_hes_sparse
     )
} // End empty namespace

bool old_usead_1(void)
{     bool ok = true;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // --------------------------------------------------------------------
     // Create the ADFun<doulbe> r_
     create_r();

     // --------------------------------------------------------------------
     // Create the function f(x)
     //
     // domain space vector
     size_t n  = 1;
     double  x0 = 0.5;
     vector< AD<double> > ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     vector< AD<double> > ay(m);

     // call user function and store reciprocal(x) in au[0]
     vector< AD<double> > au(m);
     size_t id = 0;           // not used
     reciprocal(id, ax, au);     // u = 1 / x

     // call user function and store reciprocal(u) in ay[0]
     reciprocal(id, au, ay);     // y = 1 / u = x

     // create f: x -> y and stop tape recording
     ADFun<double> f;
     f.Dependent(ax, ay);  // f(x) = x

     // --------------------------------------------------------------------
     // Check function value results
     //
     // check function value
     double check = x0;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);

     // check zero order forward mode
     size_t q;
     vector<double> x_q(n), y_q(m);
     q      = 0;
     x_q[0] = x0;
     y_q    = f.Forward(q, x_q);
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // check first order forward mode
     q      = 1;
     x_q[0] = 1;
     y_q    = f.Forward(q, x_q);
     check  = 1.;
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // check second order forward mode
     q      = 2;
     x_q[0] = 0;
     y_q    = f.Forward(q, x_q);
     check  = 0.;
     ok &= NearEqual(y_q[0] , check,  eps, eps);

     // --------------------------------------------------------------------
     // Check reverse mode results
     //
     // third order reverse mode
     q     = 3;
     vector<double> w(m), dw(n * q);
     w[0]  = 1.;
     dw    = f.Reverse(q, w);
     check = 1.;
     ok &= NearEqual(dw[0] , check,  eps, eps);
     check = 0.;
     ok &= NearEqual(dw[1] , check,  eps, eps);
     ok &= NearEqual(dw[2] , check,  eps, eps);

     // --------------------------------------------------------------------
     // forward mode sparstiy pattern
     size_t p = n;
     CppAD::vectorBool r1(n * p), s1(m * p);
     r1[0] = true;          // compute sparsity pattern for x[0]
     s1    = f.ForSparseJac(p, r1);
     ok  &= s1[0] == true;  // f[0] depends on x[0]

     // --------------------------------------------------------------------
     // reverse mode sparstiy pattern
     q = m;
     CppAD::vectorBool s2(q * m), r2(q * n);
     s2[0] = true;          // compute sparsity pattern for f[0]
     r2    = f.RevSparseJac(q, s2);
     ok  &= r2[0] == true;  // f[0] depends on x[0]

     // --------------------------------------------------------------------
     // Hessian sparsity (using previous ForSparseJac call)
     CppAD::vectorBool s3(m), h(p * n);
     s3[0] = true;        // compute sparsity pattern for f[0]
     h     = f.RevSparseJac(p, s3);
     ok  &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero

     // -----------------------------------------------------------------
     // Free all memory associated with the object r_ptr
     destroy_r();

     // -----------------------------------------------------------------
     // Free all temporary work space associated with old_atomic objects.
     // (If there are future calls to user atomic functions, they will
     // create new temporary work space.)
     CppAD::user_atomic<double>::clear();

     return ok;
}
Input File: test_more/old_usead_1.cpp cppad-20170000.3/doc/old_usead_2.cpp.xml0000644000175200017650000032266513057470511016673 0ustar coincoin-web Using AD to Compute Atomic Function Derivatives
Prev Next old_usead_2.cpp

Using AD to Compute Atomic Function Derivatives

Deprecated 2013-05-27
This example has been deprecated because it is easier to use the checkpoint class instead.

Purpose
Consider the case where an inner function is used repeatedly in the definition of an outer function. In this case, it may reduce the number of variables size_var , and hence the required memory. 
# include <cppad/cppad.hpp>

namespace { // Begin empty namespace
     using CppAD::AD;
     using CppAD::ADFun;
     using CppAD::vector;

     // ----------------------------------------------------------------------
     // ODE for [t, t^2 / 2 ] in form required by Runge45
     class Fun {
     public:
          void Ode(
               const AD<double>           &t,
               const vector< AD<double> > &z,
               vector< AD<double> >       &f)
          {     assert( z.size() == 2 );
               assert( f.size() == 2 );
               f[0] =  1.0;
               f[1] =  z[0];
          }
     };

     // ----------------------------------------------------------------------
     // Create function that takes on Runge45 step for the ODE above
     ADFun<double>* r_ptr_;
     void create_r(void)
     {     size_t n = 3, m = 2;
          vector< AD<double> > x(n), zi(m), y(m), e(m);
          // The value of x does not matter because the operation sequence
          // does not depend on x.
          x[0]  = 0.0;  // initial value z_0 (t) at t = ti
          x[1]  = 0.0;  // initial value z_1 (t) at t = ti
          x[2]  = 0.1;  // final time for this integration
          CppAD::Independent(x);
          zi[0]         = x[0];  // z_0 (t) at t = ti
          zi[1]         = x[1];  // z_1 (t) at t = ti
          AD<double> ti = 0.0;   // t does not appear in ODE so does not matter
          AD<double> tf = x[2];  // final time
          size_t M      = 3;     // number of Runge45 steps to take
          Fun F;
          y             = CppAD::Runge45(F, M, ti, tf, zi, e);
          r_ptr_        = new ADFun<double>(x, y);
     }
     void destroy_r(void)
     {     delete r_ptr_;
          r_ptr_ = CPPAD_NULL;
     }

     // ----------------------------------------------------------------------
     // forward mode routine called by CppAD
     bool solve_ode_forward(
          size_t                   id ,
          size_t                    k ,
          size_t                    n ,
          size_t                    m ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {     assert( id == 0 );
          assert( n == 3 );
          assert( m == 2 );
          assert( k == 0 || vx.size() == 0 );
          bool ok = true;
          vector<double> xp(n), yp(m);
          size_t i, j;

          // check for special case
          if( vx.size() > 0 )
          {     //Compute r, a Jacobian sparsity pattern.
               // Use reverse mode because m < n.
               vector< std::set<size_t> > s(m), r(m);
               for(i = 0; i < m; i++)
                    s[i].insert(i);
               r = r_ptr_->RevSparseJac(m, s);
               std::set<size_t>::const_iterator itr;
               for(i = 0; i < m; i++)
               {     vy[i] = false;
                    for(itr = s[i].begin(); itr != s[i].end(); itr++)
                    {     j = *itr;
                         assert( j < n );
                         // y[i] depends on the value of x[j]
                         // Visual Studio 2013 generates warning without bool below
                         vy[i] |= bool( vx[j] );
                    }
               }
          }
          // make sure r_ has proper lower order Taylor coefficients stored
          // then compute ty[k]
          for(size_t q = 0; q <= k; q++)
          {     for(j = 0; j < n; j++)
                    xp[j] = tx[j * (k+1) + q];
               yp    = r_ptr_->Forward(q, xp);
               if( q == k )
               {     for(i = 0; i < m; i++)
                         ty[i * (k+1) + q] = yp[i];
               }
# ifndef NDEBUG
               else
               {     for(i = 0; i < m; i++)
                         assert( ty[i * (k+1) + q] == yp[i] );
               }
# endif
          }
          // no longer need the Taylor coefficients in r_ptr_
          // (have to reconstruct them every time)
          r_ptr_->capacity_order(0);
          return ok;
     }
     // ----------------------------------------------------------------------
     // reverse mode routine called by CppAD
     bool solve_ode_reverse(
          size_t                   id ,
          size_t                    k ,
          size_t                    n ,
          size_t                    m ,
          const vector<double>&    tx ,
          const vector<double>&    ty ,
          vector<double>&          px ,
          const vector<double>&    py
     )
     {     assert( id == 0 );
          assert( n == 3 );
          assert( m == 2 );
          bool ok = true;
          vector<double> xp(n), w( (k+1) * m ), dw( (k+1) * n );

          // make sure r_ has proper forward mode coefficients
          size_t i, j, q;
          for(q = 0; q <= k; q++)
          {     for(j = 0; j < n; j++)
                    xp[j] = tx[j * (k+1) + q];
# ifdef NDEBUG
               r_ptr_->Forward(q, xp);
# else
               vector<double> yp(m);
               yp = r_ptr_->Forward(q, xp);
               for(i = 0; i < m; i++)
                    assert( ty[i * (k+1) + q] == yp[i] );
# endif
          }
          for(i = 0; i < m; i++)
          {     for(q = 0; q <=k; q++)
                    w[ i * (k+1) + q] = py[ i * (k+1) + q];
          }
          dw = r_ptr_->Reverse(k+1, w);
          for(j = 0; j < n; j++)
          {     for(q = 0; q <=k; q++)
                    px[ j * (k+1) + q] = dw[ j * (k+1) + q];
          }
          // no longer need the Taylor coefficients in r_ptr_
          // (have to reconstruct them every time)
          r_ptr_->capacity_order(0);

          return ok;
     }
     // ----------------------------------------------------------------------
     // forward Jacobian sparsity routine called by CppAD
     bool solve_ode_for_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          vector< std::set<size_t> >&           s )
     {     assert( id == 0 );
          assert( n == 3 );
          assert( m == 2 );
          bool ok = true;

          vector< std::set<size_t> > R(n), S(m);
          for(size_t j = 0; j < n; j++)
               R[j] = r[j];
          S = r_ptr_->ForSparseJac(p, R);
          for(size_t i = 0; i < m; i++)
               s[i] = S[i];

          // no longer need the forward mode sparsity pattern
          // (have to reconstruct them every time)
          r_ptr_->size_forward_set(0);

          return ok;
     }
     // ----------------------------------------------------------------------
     // reverse Jacobian sparsity routine called by CppAD
     bool solve_ode_rev_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          vector< std::set<size_t> >&           r ,
          const vector< std::set<size_t> >&     s )
     {
          assert( id == 0 );
          assert( n == 3 );
          assert( m == 2 );
          bool ok = true;

          vector< std::set<size_t> > R(p), S(p);
          std::set<size_t>::const_iterator itr;
          size_t i;
          // untranspose s
          for(i = 0; i < m; i++)
          {     for(itr = s[i].begin(); itr != s[i].end(); itr++)
                    S[*itr].insert(i);
          }
          R = r_ptr_->RevSparseJac(p, S);
          // transpose r
          for(i = 0; i < m; i++)
               r[i].clear();
          for(i = 0; i < p; i++)
          {     for(itr = R[i].begin(); itr != R[i].end(); itr++)
                    r[*itr].insert(i);
          }
          return ok;
     }
     // ----------------------------------------------------------------------
     // reverse Hessian sparsity routine called by CppAD
     bool solve_ode_rev_hes_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          const vector<bool>&                   s ,
          vector<bool>&                         t ,
          const vector< std::set<size_t> >&     u ,
          vector< std::set<size_t> >&           v )
     {     // Can just return false if not use RevSparseHes.
          assert( id == 0 );
          assert( n == 3 );
          assert( m == 2 );
          bool ok = true;
          std::set<size_t>::const_iterator itr;

          // compute sparsity pattern for T(x) = S(x) * f'(x)
          vector< std::set<size_t> > S(1);
          size_t i, j;
          S[0].clear();
          for(i = 0; i < m; i++)
               if( s[i] )
                    S[0].insert(i);
          t = r_ptr_->RevSparseJac(1, s);

          // compute sparsity pattern for A(x)^T = U(x)^T * f'(x)
          vector< std::set<size_t> > Ut(p), At(p);
          for(i = 0; i < m; i++)
          {     for(itr = u[i].begin(); itr != u[i].end(); itr++)
                    Ut[*itr].insert(i);
          }
          At = r_ptr_->RevSparseJac(p, Ut);

          // compute sparsity pattern for H(x)^T = R^T * (S * F)''(x)
          vector< std::set<size_t> > R(n), Ht(p);
          for(j = 0; j < n; j++)
               R[j] = r[j];
          r_ptr_->ForSparseJac(p, R);
          Ht = r_ptr_->RevSparseHes(p, S);

          // compute sparsity pattern for V(x) = A(x) + H(x)^T
          for(j = 0; j < n; j++)
               v[j].clear();
          for(i = 0; i < p; i++)
          {     for(itr = At[i].begin(); itr != At[i].end(); itr++)
                    v[*itr].insert(i);
               for(itr = Ht[i].begin(); itr != Ht[i].end(); itr++)
                    v[*itr].insert(i);
          }

          // no longer need the forward mode sparsity pattern
          // (have to reconstruct them every time)
          r_ptr_->size_forward_set(0);

          return ok;
     }
     // ---------------------------------------------------------------------
     // Declare the AD<double> routine solve_ode(id, ax, ay)
     CPPAD_USER_ATOMIC(
          solve_ode                 ,
          CppAD::vector             ,
          double                    ,
          solve_ode_forward         ,
          solve_ode_reverse         ,
          solve_ode_for_jac_sparse  ,
          solve_ode_rev_jac_sparse  ,
          solve_ode_rev_hes_sparse
     )
} // End empty namespace

bool old_usead_2(void)
{     bool ok = true;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // --------------------------------------------------------------------
     // Create the ADFun<doulbe> r_
     create_r();

     // --------------------------------------------------------------------
     // domain and range space vectors
     size_t n = 3, m = 2;
     vector< AD<double> > au(n), ax(n), ay(m);
     au[0]         = 0.0;        // value of z_0 (t) = t, at t = 0
     ax[1]         = 0.0;        // value of z_1 (t) = t^2/2, at t = 0
     au[2]         = 1.0;        // final t
     CppAD::Independent(au);
     size_t M      = 2;          // number of r steps to take
     ax[0]         = au[0];      // value of z_0 (t) = t, at t = 0
     ax[1]         = au[1];      // value of z_1 (t) = t^2/2, at t = 0
     AD<double> dt = au[2] / M;  // size of each r step
     ax[2]         = dt;
     for(size_t i_step = 0; i_step < M; i_step++)
     {     size_t id = 0;               // not used
          solve_ode(id, ax, ay);
          ax[0] = ay[0];
          ax[1] = ay[1];
     }

     // create f: u -> y and stop tape recording
     // y_0(t) = u_0 + t                   = u_0 + u_2
     // y_1(t) = u_1 + u_0 * t + t^2 / 2   = u_1 + u_0 * u_2 + u_2^2 / 2
     // where t = u_2
     ADFun<double> f;
     f.Dependent(au, ay);

     // --------------------------------------------------------------------
     // Check forward mode results
     //
     // zero order forward
     vector<double> up(n), yp(m);
     size_t q  = 0;
     double u0 = 0.5;
     double u1 = 0.25;
     double u2 = 0.75;
     double check;
     up[0]     = u0;
     up[1]     = u1;
     up[2]     = u2;
     yp        = f.Forward(q, up);
     check     = u0 + u2;
     ok       &= NearEqual( yp[0], check,  eps, eps);
     check     = u1 + u0 * u2 + u2 * u2 / 2.0;
     ok       &= NearEqual( yp[1], check,  eps, eps);
     //
     // forward mode first derivative w.r.t t
     q         = 1;
     up[0]     = 0.0;
     up[1]     = 0.0;
     up[2]     = 1.0;
     yp        = f.Forward(q, up);
     check     = 1.0;
     ok       &= NearEqual( yp[0], check,  eps, eps);
     check     = u0 + u2;
     ok       &= NearEqual( yp[1], check,  eps, eps);
     //
     // forward mode second order Taylor coefficient w.r.t t
     q         = 2;
     up[0]     = 0.0;
     up[1]     = 0.0;
     up[2]     = 0.0;
     yp        = f.Forward(q, up);
     check     = 0.0;
     ok       &= NearEqual( yp[0], check,  eps, eps);
     check     = 1.0 / 2.0;
     ok       &= NearEqual( yp[1], check,  eps, eps);
     // --------------------------------------------------------------------
     // reverse mode derivatives of \partial_t y_1 (t)
     vector<double> w(m * q), dw(n * q);
     w[0 * q + 0]  = 0.0;
     w[1 * q + 0]  = 0.0;
     w[0 * q + 1]  = 0.0;
     w[1 * q + 1]  = 1.0;
     dw        = f.Reverse(q, w);
     // derivative of y_1(u) = u_1 + u_0 * u_2 + u_2^2 / 2,  w.r.t. u
     // is equal deritative of \partial_u2 y_1(u) w.r.t \partial_u2 u
     check     = u2;
     ok       &= NearEqual( dw[0 * q + 1], check,  eps, eps);
     check     = 1.0;
     ok       &= NearEqual( dw[1 * q + 1], check,  eps, eps);
     check     = u0 + u2;
     ok       &= NearEqual( dw[2 * q + 1], check,  eps, eps);
     // derivative of \partial_t y_1 w.r.t u = u_0 + t,  w.r.t u
     check     = 1.0;
     ok       &= NearEqual( dw[0 * q + 0], check,  eps, eps);
     check     = 0.0;
     ok       &= NearEqual( dw[1 * q + 0], check,  eps, eps);
     check     = 1.0;
     ok       &= NearEqual( dw[2 * q + 0], check,  eps, eps);
     // --------------------------------------------------------------------
     // forward mode sparsity pattern for the Jacobian
     // f_u = [   1, 0,   1 ]
     //       [ u_2, 1, u_2 ]
     size_t i, j, p = n;
     CppAD::vectorBool r(n * p), s(m * p);
     // r = identity sparsity pattern
     for(i = 0; i < n; i++)
          for(j = 0; j < p; j++)
               r[i*n +j] = (i == j);
     s   = f.ForSparseJac(p, r);
     ok &= s[ 0 * p + 0] == true;
     ok &= s[ 0 * p + 1] == false;
     ok &= s[ 0 * p + 2] == true;
     ok &= s[ 1 * p + 0] == true;
     ok &= s[ 1 * p + 1] == true;
     ok &= s[ 1 * p + 2] == true;
     // --------------------------------------------------------------------
     // reverse mode sparsity pattern for the Jacobian
     q = m;
     s.resize(q * m);
     r.resize(q * n);
     // s = identity sparsity pattern
     for(i = 0; i < q; i++)
          for(j = 0; j < m; j++)
               s[i*m +j] = (i == j);
     r   = f.RevSparseJac(q, s);
     ok &= r[ 0 * n + 0] == true;
     ok &= r[ 0 * n + 1] == false;
     ok &= r[ 0 * n + 2] == true;
     ok &= r[ 1 * n + 0] == true;
     ok &= r[ 1 * n + 1] == true;
     ok &= r[ 1 * n + 2] == true;

     // --------------------------------------------------------------------
     // Hessian sparsity for y_1 (u) = u_1 + u_0 * u_2 + u_2^2 / 2
     s.resize(m);
     s[0] = false;
     s[1] = true;
     r.resize(n * n);
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               r[ i * n + j ] = (i == j);
     CppAD::vectorBool h(n * n);
     h   = f.RevSparseHes(n, s);
     ok &= h[0 * n + 0] == false;
     ok &= h[0 * n + 1] == false;
     ok &= h[0 * n + 2] == true;
     ok &= h[1 * n + 0] == false;
     ok &= h[1 * n + 1] == false;
     ok &= h[1 * n + 2] == false;
     ok &= h[2 * n + 0] == true;
     ok &= h[2 * n + 1] == false;
     ok &= h[2 * n + 2] == true;

     // --------------------------------------------------------------------
     destroy_r();

     // Free all temporary work space associated with old_atomic objects.
     // (If there are future calls to user atomic functions, they will
     // create new temporary work space.)
     CppAD::user_atomic<double>::clear();

     return ok;
}
Input File: test_more/old_usead_2.cpp cppad-20170000.3/doc/old_tan.cpp.xml0000644000175200017650000024106013057470511016120 0ustar coincoin-web Old Tan and Tanh as User Atomic Operations: Example and Test
Prev Next old_tan.cpp

Old Tan and Tanh as User Atomic Operations: Example and Test

Deprecated 2013-05-27
This example has not deprecated; see atomic_tangent.cpp instead.

Theory
The code below uses the tan_forward and tan_reverse to implement the tangent ( id == 0 ) and hyperbolic tangent ( id == 1 ) functions as user atomic operations. 
# include <cppad/cppad.hpp>

namespace { // Begin empty namespace
     using CppAD::vector;

     // a utility to compute the union of two sets.
     using CppAD::set_union;

     // ----------------------------------------------------------------------
     // forward mode routine called by CppAD
     bool old_tan_forward(
          size_t                   id ,
          size_t                order ,
          size_t                    n ,
          size_t                    m ,
          const vector<bool>&      vx ,
          vector<bool>&           vzy ,
          const vector<float>&     tx ,
          vector<float>&          tzy
     )
     {
          assert( id == 0 || id == 1 );
          assert( n == 1 );
          assert( m == 2 );
          assert( tx.size() >= (order+1) * n );
          assert( tzy.size() >= (order+1) * m );

          size_t n_order = order + 1;
          size_t j = order;
          size_t k;

          // check if this is during the call to old_tan(id, ax, ay)
          if( vx.size() > 0 )
          {     assert( vx.size() >= n );
               assert( vzy.size() >= m );

               // now setvzy
               vzy[0] = vx[0];
               vzy[1] = vx[0];
          }

          if( j == 0 )
          {     // z^{(0)} = tan( x^{(0)} ) or tanh( x^{(0)} )
               if( id == 0 )
                    tzy[0] = tan( tx[0] );
               else     tzy[0] = tanh( tx[0] );

               // y^{(0)} = z^{(0)} * z^{(0)}
               tzy[n_order + 0] = tzy[0] * tzy[0];
          }
          else
          {     float j_inv = 1.f / float(j);
               if( id == 1 )
                    j_inv = - j_inv;

               // z^{(j)} = x^{(j)} +- sum_{k=1}^j k x^{(k)} y^{(j-k)} / j
               tzy[j] = tx[j];
               for(k = 1; k <= j; k++)
                    tzy[j] += tx[k] * tzy[n_order + j-k] * k * j_inv;

               // y^{(j)} = sum_{k=0}^j z^{(k)} z^{(j-k)}
               tzy[n_order + j] = 0.;
               for(k = 0; k <= j; k++)
                    tzy[n_order + j] += tzy[k] * tzy[j-k];
          }

          // All orders are implemented and there are no possible errors
          return true;
     }
     // ----------------------------------------------------------------------
     // reverse mode routine called by CppAD
     bool old_tan_reverse(
          size_t                   id ,
          size_t                order ,
          size_t                    n ,
          size_t                    m ,
          const vector<float>&     tx ,
          const vector<float>&    tzy ,
          vector<float>&           px ,
          const vector<float>&    pzy
     )
     {
          assert( id == 0 || id == 1 );
          assert( n == 1 );
          assert( m == 2 );
          assert( tx.size() >= (order+1) * n );
          assert( tzy.size() >= (order+1) * m );
          assert( px.size() >= (order+1) * n );
          assert( pzy.size() >= (order+1) * m );

          size_t n_order = order + 1;
          size_t j, k;

          // copy because partials w.r.t. y and z need to change
          vector<float> qzy = pzy;

          // initialize accumultion of reverse mode partials
          for(k = 0; k < n_order; k++)
               px[k] = 0.;

          // eliminate positive orders
          for(j = order; j > 0; j--)
          {     float j_inv = 1.f / float(j);
               if( id == 1 )
                    j_inv = - j_inv;

               // H_{x^{(k)}} += delta(j-k) +- H_{z^{(j)} y^{(j-k)} * k / j
               px[j] += qzy[j];
               for(k = 1; k <= j; k++)
                    px[k] += qzy[j] * tzy[n_order + j-k] * k * j_inv;

               // H_{y^{j-k)} += +- H_{z^{(j)} x^{(k)} * k / j
               for(k = 1; k <= j; k++)
                    qzy[n_order + j-k] += qzy[j] * tx[k] * k * j_inv;

               // H_{z^{(k)}} += H_{y^{(j-1)}} * z^{(j-k-1)} * 2.
               for(k = 0; k < j; k++)
                    qzy[k] += qzy[n_order + j-1] * tzy[j-k-1] * 2.f;
          }

          // eliminate order zero
          if( id == 0 )
               px[0] += qzy[0] * (1.f + tzy[n_order + 0]);
          else
               px[0] += qzy[0] * (1.f - tzy[n_order + 0]);

          return true;
     }
     // ----------------------------------------------------------------------
     // forward Jacobian sparsity routine called by CppAD
     bool old_tan_for_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          vector< std::set<size_t> >&           s )
     {
          assert( n == 1 );
          assert( m == 2 );
          assert( id == 0 || id == 1 );
          assert( r.size() >= n );
          assert( s.size() >= m );

          // sparsity for z and y are the same as for x
          s[0] = r[0];
          s[1] = r[0];

          return true;
     }
     // ----------------------------------------------------------------------
     // reverse Jacobian sparsity routine called by CppAD
     bool old_tan_rev_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          vector< std::set<size_t> >&           r ,
          const vector< std::set<size_t> >&     s )
     {
          assert( n == 1 );
          assert( m == 2 );
          assert( id == 0 || id == 1 );
          assert( r.size() >= n );
          assert( s.size() >= m );

          // note that, if the users code only uses z, and not y,
          // we could just set r[0] = s[0]
          r[0] = set_union(s[0], s[1]);
          return true;
     }
     // ----------------------------------------------------------------------
     // reverse Hessian sparsity routine called by CppAD
     bool old_tan_rev_hes_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          const vector<bool>&                   s ,
          vector<bool>&                         t ,
          const vector< std::set<size_t> >&     u ,
          vector< std::set<size_t> >&           v )
     {
          assert( n == 1 );
          assert( m == 2 );
          assert( id == 0 || id == 1 );
          assert( r.size() >= n );
          assert( s.size() >= m );
          assert( t.size() >= n );
          assert( u.size() >= m );
          assert( v.size() >= n );

          // back propagate Jacobian sparsity. If users code only uses z,
          // we could just set t[0] = s[0];
          t[0] =  s[0] | s[1];

          // back propagate Hessian sparsity, ...
          v[0] = set_union(u[0], u[1]);

          // convert forward Jacobian sparsity to Hessian sparsity
          // because tan and tanh are nonlinear
          if( t[0] )
               v[0] = set_union(v[0], r[0]);

          return true;
     }
     // ---------------------------------------------------------------------
     // Declare the AD<float> routine old_tan(id, ax, ay)
     CPPAD_USER_ATOMIC(
          old_tan                 ,
          CppAD::vector           ,
          float                   ,
          old_tan_forward         ,
          old_tan_reverse         ,
          old_tan_for_jac_sparse  ,
          old_tan_rev_jac_sparse  ,
          old_tan_rev_hes_sparse
     )
} // End empty namespace

bool old_tan(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     float eps = 10.f * CppAD::numeric_limits<float>::epsilon();

     // domain space vector
     size_t n  = 1;
     float  x0 = 0.5;
     CppAD::vector< AD<float> > ax(n);
     ax[0]     = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 3;
     CppAD::vector< AD<float> > af(m);

     // temporary vector for old_tan computations
     // (old_tan computes tan or tanh and its square)
     CppAD::vector< AD<float> > az(2);

     // call user tan function and store tan(x) in f[0] (ignore tan(x)^2)
     size_t id = 0;
     old_tan(id, ax, az);
     af[0] = az[0];

     // call user tanh function and store tanh(x) in f[1] (ignore tanh(x)^2)
     id = 1;
     old_tan(id, ax, az);
     af[1] = az[0];

     // put a constant in f[2] = tanh(1.) (for sparsity pattern testing)
     CppAD::vector< AD<float> > one(1);
     one[0] = 1.;
     old_tan(id, one, az);
     af[2] = az[0];

     // create f: x -> f and stop tape recording
     CppAD::ADFun<float> F;
     F.Dependent(ax, af);

     // check function value
     float tan = std::tan(x0);
     ok &= NearEqual(af[0] , tan,  eps, eps);
     float tanh = std::tanh(x0);
     ok &= NearEqual(af[1] , tanh,  eps, eps);

     // check zero order forward
     CppAD::vector<float> x(n), f(m);
     x[0] = x0;
     f    = F.Forward(0, x);
     ok &= NearEqual(f[0] , tan,  eps, eps);
     ok &= NearEqual(f[1] , tanh,  eps, eps);

     // compute first partial of f w.r.t. x[0] using forward mode
     CppAD::vector<float> dx(n), df(m);
     dx[0] = 1.;
     df    = F.Forward(1, dx);

     // compute derivative of tan - tanh using reverse mode
     CppAD::vector<float> w(m), dw(n);
     w[0]  = 1.;
     w[1]  = 1.;
     w[2]  = 0.;
     dw    = F.Reverse(1, w);

     // tan'(x)   = 1 + tan(x)  * tan(x)
     // tanh'(x)  = 1 - tanh(x) * tanh(x)
     float tanp  = 1.f + tan * tan;
     float tanhp = 1.f - tanh * tanh;
     ok   &= NearEqual(df[0], tanp, eps, eps);
     ok   &= NearEqual(df[1], tanhp, eps, eps);
     ok   &= NearEqual(dw[0], w[0]*tanp + w[1]*tanhp, eps, eps);

     // compute second partial of f w.r.t. x[0] using forward mode
     CppAD::vector<float> ddx(n), ddf(m);
     ddx[0] = 0.;
     ddf    = F.Forward(2, ddx);

     // compute second derivative of tan - tanh using reverse mode
     CppAD::vector<float> ddw(2);
     ddw   = F.Reverse(2, w);

     // tan''(x)   = 2 *  tan(x) * tan'(x)
     // tanh''(x)  = - 2 * tanh(x) * tanh'(x)
     // Note that second order Taylor coefficient for u half the
     // corresponding second derivative.
     float two    = 2;
     float tanpp  =   two * tan * tanp;
     float tanhpp = - two * tanh * tanhp;
     ok   &= NearEqual(two * ddf[0], tanpp, eps, eps);
     ok   &= NearEqual(two * ddf[1], tanhpp, eps, eps);
     ok   &= NearEqual(ddw[0], w[0]*tanp  + w[1]*tanhp , eps, eps);
     ok   &= NearEqual(ddw[1], w[0]*tanpp + w[1]*tanhpp, eps, eps);

     // Forward mode computation of sparsity pattern for F.
     size_t p = n;
     // user vectorBool because m and n are small
     CppAD::vectorBool r1(p), s1(m * p);
     r1[0] = true;            // propagate sparsity for x[0]
     s1    = F.ForSparseJac(p, r1);
     ok  &= (s1[0] == true);  // f[0] depends on x[0]
     ok  &= (s1[1] == true);  // f[1] depends on x[0]
     ok  &= (s1[2] == false); // f[2] does not depend on x[0]

     // Reverse mode computation of sparsity pattern for F.
     size_t q = m;
     CppAD::vectorBool s2(q * m), r2(q * n);
     // Sparsity pattern for identity matrix
     size_t i, j;
     for(i = 0; i < q; i++)
     {     for(j = 0; j < m; j++)
               s2[i * q + j] = (i == j);
     }
     r2   = F.RevSparseJac(q, s2);
     ok  &= (r2[0] == true);  // f[0] depends on x[0]
     ok  &= (r2[1] == true);  // f[1] depends on x[0]
     ok  &= (r2[2] == false); // f[2] does not depend on x[0]

     // Hessian sparsity for f[0]
     CppAD::vectorBool s3(m), h(p * n);
     s3[0] = true;
     s3[1] = false;
     s3[2] = false;
     h    = F.RevSparseHes(p, s3);
     ok  &= (h[0] == true);  // Hessian is non-zero

     // Hessian sparsity for f[2]
     s3[0] = false;
     s3[2] = true;
     h    = F.RevSparseHes(p, s3);
     ok  &= (h[0] == false);  // Hessian is zero

     // check tanh results for a large value of x
     x[0]  = std::numeric_limits<float>::max() / two;
     f     = F.Forward(0, x);
     tanh  = 1.;
     ok   &= NearEqual(f[1], tanh, eps, eps);
     df    = F.Forward(1, dx);
     tanhp = 0.;
     ok   &= NearEqual(df[1], tanhp, eps, eps);

     // --------------------------------------------------------------------
     // Free all temporary work space associated with old_atomic objects.
     // (If there are future calls to user atomic functions, they will
     // create new temporary work space.)
     CppAD::user_atomic<float>::clear();

     return ok;
}
Input File: test_more/old_tan.cpp cppad-20170000.3/doc/old_mat_mul.cpp.xml0000644000175200017650000020203113057470511016767 0ustar coincoin-web Old Matrix Multiply as a User Atomic Operation: Example and Test
Prev Next

Old Matrix Multiply as a User Atomic Operation: Example and Test

Deprecated 2013-05-27
This example has been deprecated; use atomic_mat_mul.cpp instead.

Include File
This routine uses the include file old_mat_mul.hpp . 
# include <cppad/cppad.hpp>
# include "old_mat_mul.hpp"

bool old_mat_mul(void)
{     bool ok = true;
     using CppAD::AD;

     // matrix sizes for this test
     size_t nr_result = 2;
     size_t n_middle  = 2;
     size_t nc_result = 2;

     // declare the AD<double> vectors ax and ay and X
     size_t n = nr_result * n_middle + n_middle * nc_result;
     size_t m = nr_result * nc_result;
     CppAD::vector< AD<double> > X(4), ax(n), ay(m);
     size_t i, j;
     for(j = 0; j < X.size(); j++)
          X[j] = (j + 1);

     // X is the vector of independent variables
     CppAD::Independent(X);
     // left matrix
     ax[0]  = X[0];  // left[0,0]   = x[0] = 1
     ax[1]  = X[1];  // left[0,1]   = x[1] = 2
     ax[2]  = 5.;    // left[1,0]   = 5
     ax[3]  = 6.;    // left[1,1]   = 6
     // right matrix
     ax[4]  = X[2];  // right[0,0]  = x[2] = 3
     ax[5]  = 7.;    // right[0,1]  = 7
     ax[6]  = X[3];  // right[1,0]  = x[3] = 4
     ax[7]  = 8.;    // right[1,1]  = 8
     /*
     [ x0 , x1 ] * [ x2 , 7 ] = [ x0*x2 + x1*x3 , x0*7 + x1*8 ]
     [ 5  , 6 ]    [ x3 , 8 ]   [ 5*x2  + 6*x3  , 5*7 + 6*8 ]
     */

     // The call back routines need to know the dimensions of the matrices.
     // Store information about the matrix multiply for this call to mat_mul.
     call_info info;
     info.nr_result = nr_result;
     info.n_middle  = n_middle;
     info.nc_result = nc_result;
     // info.vx gets set by forward during call to mat_mul below
     assert( info.vx.size() == 0 );
     size_t id      = info_.size();
     info_.push_back(info);

     // user defined AD<double> version of matrix multiply
     mat_mul(id, ax, ay);
     //----------------------------------------------------------------------
     // check AD<double>  results
     ok &= ay[0] == (1*3 + 2*4); ok &= Variable( ay[0] );
     ok &= ay[1] == (1*7 + 2*8); ok &= Variable( ay[1] );
     ok &= ay[2] == (5*3 + 6*4); ok &= Variable( ay[2] );
     ok &= ay[3] == (5*7 + 6*8); ok &= Parameter( ay[3] );
     //----------------------------------------------------------------------
     // use mat_mul to define a function g : X -> ay
     CppAD::ADFun<double> G;
     G.Dependent(X, ay);
     // g(x) = [ x0*x2 + x1*x3 , x0*7 + x1*8 , 5*x2  + 6*x3  , 5*7 + 6*8 ]^T
     //----------------------------------------------------------------------
     // Test zero order forward mode evaluation of g(x)
     CppAD::vector<double> x( X.size() ), y(m);
     for(j = 0; j <  X.size() ; j++)
          x[j] = j + 2;
     y = G.Forward(0, x);
     ok &= y[0] == x[0] * x[2] + x[1] * x[3];
     ok &= y[1] == x[0] * 7.   + x[1] * 8.;
     ok &= y[2] == 5. * x[2]   + 6. * x[3];
     ok &= y[3] == 5. * 7.     + 6. * 8.;

     //----------------------------------------------------------------------
     // Test first order forward mode evaluation of g'(x) * [1, 2, 3, 4]^T
     // g'(x) = [ x2, x3, x0, x1 ]
     //         [ 7 ,  8,  0, 0  ]
     //         [ 0 ,  0,  5, 6  ]
     //         [ 0 ,  0,  0, 0  ]
     CppAD::vector<double> dx( X.size() ), dy(m);
     for(j = 0; j <  X.size() ; j++)
          dx[j] = j + 1;
     dy = G.Forward(1, dx);
     ok &= dy[0] == 1. * x[2] + 2. * x[3] + 3. * x[0] + 4. * x[1];
     ok &= dy[1] == 1. * 7.   + 2. * 8.   + 3. * 0.   + 4. * 0.;
     ok &= dy[2] == 1. * 0.   + 2. * 0.   + 3. * 5.   + 4. * 6.;
     ok &= dy[3] == 1. * 0.   + 2. * 0.   + 3. * 0.   + 4. * 0.;

     //----------------------------------------------------------------------
     // Test second order forward mode
     // g_0^2 (x) = [ 0, 0, 1, 0 ], g_0^2 (x) * [1] = [3]
     //             [ 0, 0, 0, 1 ]              [2]   [4]
     //             [ 1, 0, 0, 0 ]              [3]   [1]
     //             [ 0, 1, 0, 0 ]              [4]   [2]
     CppAD::vector<double> ddx( X.size() ), ddy(m);
     for(j = 0; j <  X.size() ; j++)
          ddx[j] = 0.;
     ddy = G.Forward(2, ddx);
     // [1, 2, 3, 4] * g_0^2 (x) * [1, 2, 3, 4]^T = 1*3 + 2*4 + 3*1 + 4*2
     ok &= 2. * ddy[0] == 1. * 3. + 2. * 4. + 3. * 1. + 4. * 2.;
     // for i > 0, [1, 2, 3, 4] * g_i^2 (x) * [1, 2, 3, 4]^T = 0
     ok &= ddy[1] == 0.;
     ok &= ddy[2] == 0.;
     ok &= ddy[3] == 0.;

     //----------------------------------------------------------------------
     // Test second order reverse mode
     CppAD::vector<double> w(m), dw(2 *  X.size() );
     for(i = 0; i < m; i++)
          w[i] = 0.;
     w[0] = 1.;
     dw = G.Reverse(2, w);
     // g_0'(x) = [ x2, x3, x0, x1 ]
     ok &= dw[0*2 + 0] == x[2];
     ok &= dw[1*2 + 0] == x[3];
     ok &= dw[2*2 + 0] == x[0];
     ok &= dw[3*2 + 0] == x[1];
     // g_0'(x)   * [1, 2, 3, 4]  = 1 * x2 + 2 * x3 + 3 * x0 + 4 * x1
     // g_0^2 (x) * [1, 2, 3, 4]  = [3, 4, 1, 2]
     ok &= dw[0*2 + 1] == 3.;
     ok &= dw[1*2 + 1] == 4.;
     ok &= dw[2*2 + 1] == 1.;
     ok &= dw[3*2 + 1] == 2.;

     //----------------------------------------------------------------------
     // Test forward and reverse Jacobian sparsity pattern
     /*
     [ x0 , x1 ] * [ x2 , 7 ] = [ x0*x2 + x1*x3 , x0*7 + x1*8 ]
     [ 5  , 6 ]    [ x3 , 8 ]   [ 5*x2  + 6*x3  , 5*7 + 6*8 ]
     so the sparsity pattern should be
     s[0] = {0, 1, 2, 3}
     s[1] = {0, 1}
     s[2] = {2, 3}
     s[3] = {}
     */
     CppAD::vector< std::set<size_t> > r( X.size() ), s(m);
     for(j = 0; j <  X.size() ; j++)
     {     assert( r[j].empty() );
          r[j].insert(j);
     }
     s = G.ForSparseJac( X.size() , r);
     for(j = 0; j <  X.size() ; j++)
     {     // s[0] = {0, 1, 2, 3}
          ok &= s[0].find(j) != s[0].end();
          // s[1] = {0, 1}
          if( j == 0 || j == 1 )
               ok &= s[1].find(j) != s[1].end();
          else     ok &= s[1].find(j) == s[1].end();
          // s[2] = {2, 3}
          if( j == 2 || j == 3 )
               ok &= s[2].find(j) != s[2].end();
          else     ok &= s[2].find(j) == s[2].end();
     }
     // s[3] == {}
     ok &= s[3].empty();

     //----------------------------------------------------------------------
     // Test reverse Jacobian sparsity pattern
     /*
     [ x0 , x1 ] * [ x2 , 7 ] = [ x0*x2 + x1*x3 , x0*7 + x1*8 ]
     [ 5  , 6 ]    [ x3 , 8 ]   [ 5*x2  + 6*x3  , 5*7 + 6*8 ]
     so the sparsity pattern should be
     r[0] = {0, 1, 2, 3}
     r[1] = {0, 1}
     r[2] = {2, 3}
     r[3] = {}
     */
     for(i = 0; i <  m; i++)
     {     s[i].clear();
          s[i].insert(i);
     }
     r = G.RevSparseJac(m, s);
     for(j = 0; j <  X.size() ; j++)
     {     // r[0] = {0, 1, 2, 3}
          ok &= r[0].find(j) != r[0].end();
          // r[1] = {0, 1}
          if( j == 0 || j == 1 )
               ok &= r[1].find(j) != r[1].end();
          else     ok &= r[1].find(j) == r[1].end();
          // r[2] = {2, 3}
          if( j == 2 || j == 3 )
               ok &= r[2].find(j) != r[2].end();
          else     ok &= r[2].find(j) == r[2].end();
     }
     // r[3] == {}
     ok &= r[3].empty();

     //----------------------------------------------------------------------
     /* Test reverse Hessian sparsity pattern
     g_0^2 (x) = [ 0, 0, 1, 0 ] and for i > 0, g_i^2 = 0
                 [ 0, 0, 0, 1 ]
                 [ 1, 0, 0, 0 ]
                 [ 0, 1, 0, 0 ]
     so for the sparsity pattern for the first component of g is
     h[0] = {2}
     h[1] = {3}
     h[2] = {0}
     h[3] = {1}
     */
     CppAD::vector< std::set<size_t> > h( X.size() ), t(1);
     t[0].clear();
     t[0].insert(0);
     h = G.RevSparseHes(X.size() , t);
     size_t check[] = {2, 3, 0, 1};
     for(j = 0; j <  X.size() ; j++)
     {     // h[j] = { check[j] }
          for(i = 0; i < n; i++)
          {     if( i == check[j] )
                    ok &= h[j].find(i) != h[j].end();
               else     ok &= h[j].find(i) == h[j].end();
          }
     }
     t[0].clear();
     for( j = 1; j < X.size(); j++)
               t[0].insert(j);
     h = G.RevSparseHes(X.size() , t);
     for(j = 0; j <  X.size() ; j++)
     {     // h[j] = { }
          for(i = 0; i < X.size(); i++)
               ok &= h[j].find(i) == h[j].end();
     }

     // --------------------------------------------------------------------
     // Free temporary work space. (If there are future calls to
     // old_mat_mul they would create new temporary work space.)
     CppAD::user_atomic<double>::clear();
     info_.clear();

     return ok;
}
Input File: test_more/old_mat_mul.cpp cppad-20170000.3/doc/old_mat_mul.hpp.xml0000644000175200017650000021231113057470511016776 0ustar coincoin-web Define Matrix Multiply as a User Atomic Operation
Prev Next old_mat_mul.hpp

Define Matrix Multiply as a User Atomic Operation

Syntax
This file is located in the example directory. It can be copied to the current working directory and included with the syntax
     # include "old_mat_mul.hpp"
Example
The file old_mat_mul.cpp contains an example use of old_mat_mul.hpp. It returns true if it succeeds and false otherwise.

Begin Source 

# include <cppad/cppad.hpp>      // Include CppAD definitions
namespace {                      // Begin empty namespace
     using CppAD::vector;        // Let vector denote CppAD::vector

Extra Call Information 
     // Information we will attach to each mat_mul call
     struct call_info {
          size_t nr_result;
          size_t n_middle;
          size_t nc_result;
          vector<bool>  vx;
     };
     vector<call_info> info_; // vector of call information

     // number of orders for this operation (k + 1)
     size_t n_order_ = 0;
     // number of rows in the result matrix
     size_t nr_result_ = 0;
     // number of columns in left matrix and number of rows in right matrix
     size_t n_middle_ = 0;
     // number of columns in the result matrix
     size_t nc_result_ = 0;
     // which components of x are variables
     vector<bool>* vx_ = CPPAD_NULL;

     // get the information corresponding to this call
     void get_info(size_t id, size_t k, size_t n, size_t m)
     {     n_order_   = k + 1;
          nr_result_ = info_[id].nr_result;
          n_middle_  = info_[id].n_middle;
          nc_result_ = info_[id].nc_result;
          vx_        = &(info_[id].vx);

          assert(n == nr_result_ * n_middle_ + n_middle_ * nc_result_);
          assert(m ==  nr_result_ * nc_result_);
     }
Matrix Indexing 
     // Convert left matrix index pair and order to a single argument index
     size_t left(size_t i, size_t j, size_t ell)
     {     assert( i < nr_result_ );
          assert( j < n_middle_ );
          return (i * n_middle_ + j) * n_order_ + ell;
     }
     // Convert right matrix index pair and order to a single argument index
     size_t right(size_t i, size_t j, size_t ell)
     {     assert( i < n_middle_ );
          assert( j < nc_result_ );
          size_t offset = nr_result_ * n_middle_;
          return (offset + i * nc_result_ + j) * n_order_ + ell;
     }
     // Convert result matrix index pair and order to a single result index
     size_t result(size_t i, size_t j, size_t ell)
     {     assert( i < nr_result_ );
          assert( j < nc_result_ );
          return (i * nc_result_ + j) * n_order_ + ell;
     }

One Matrix Multiply
Forward mode matrix multiply left times right and sum into result: 
     void multiply_and_sum(
          size_t                order_left ,
          size_t                order_right,
          const vector<double>&         tx ,
          vector<double>&               ty )
     {     size_t i, j;
          size_t order_result = order_left + order_right;
          for(i = 0; i < nr_result_; i++)
          {     for(j = 0; j < nc_result_; j++)
               {     double sum = 0.;
                    size_t middle, im_left, mj_right, ij_result;
                    for(middle = 0; middle < n_middle_; middle++)
                    {     im_left  = left(i, middle, order_left);
                         mj_right = right(middle, j, order_right);
                         sum     += tx[im_left] * tx[mj_right];
                    }
                    ij_result = result(i, j, order_result);
                    ty[ ij_result ] += sum;
               }
          }
          return;
     }

Reverse Partials One Order
Compute reverse mode partials for one order and sum into px: 
     void reverse_multiply(
          size_t                order_left ,
          size_t                order_right,
          const vector<double>&         tx ,
          const vector<double>&         ty ,
          vector<double>&               px ,
          const vector<double>&         py )
     {     size_t i, j;
          size_t order_result = order_left + order_right;
          for(i = 0; i < nr_result_; i++)
          {     for(j = 0; j < nc_result_; j++)
               {     size_t middle, im_left, mj_right, ij_result;
                    for(middle = 0; middle < n_middle_; middle++)
                    {     ij_result = result(i, j, order_result);
                         im_left   = left(i, middle, order_left);
                         mj_right  = right(middle, j, order_right);
                         // sum       += tx[im_left]  * tx[mj_right];
                         px[im_left]  += tx[mj_right] * py[ij_result];
                         px[mj_right] += tx[im_left]  * py[ij_result];
                    }
               }
          }
          return;
     }

Set Union 

     using CppAD::set_union;

CppAD User Atomic Callback Functions 
     // ----------------------------------------------------------------------
     // forward mode routine called by CppAD
     bool mat_mul_forward(
          size_t                   id ,
          size_t                    k ,
          size_t                    n ,
          size_t                    m ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {     size_t i, j, ell;
          get_info(id, k, n, m);

          // check if this is during the call to mat_mul(id, ax, ay)
          if( vx.size() > 0 )
          {     assert( k == 0 && vx.size() > 0 );

               // store the vx information in info_
               assert( vx_->size() == 0 );
               info_[id].vx.resize(n);
               for(j = 0; j < n; j++)
                    info_[id].vx[j] = vx[j];
               assert( vx_->size() == n );

               // now compute vy
               for(i = 0; i < nr_result_; i++)
               {     for(j = 0; j < nc_result_; j++)
                    {     // compute vy[ result(i, j, 0) ]
                         bool   var = false;
                         bool   nz_left, nz_right;
                         size_t middle, im_left, mj_right, ij_result;
                         for(middle = 0; middle < n_middle_; middle++)
                         {     im_left  = left(i, middle, k);
                              mj_right = right(middle, j, k);
                              nz_left  = vx[im_left]  | (tx[im_left] != 0.);
                              nz_right = vx[mj_right] | (tx[mj_right]!= 0.);
                              // if not multiplying by the constant zero
                              if( nz_left & nz_right )
                                   var |= (vx[im_left] | vx[mj_right]);
                         }
                         ij_result     = result(i, j, k);
                         vy[ij_result] = var;
                    }
               }
          }

          // initialize result as zero
          for(i = 0; i < nr_result_; i++)
          {     for(j = 0; j < nc_result_; j++)
                    ty[ result(i, j, k) ] = 0.;
          }
          // sum the product of proper orders
          for(ell = 0; ell <=k; ell++)
               multiply_and_sum(ell, k-ell, tx, ty);

          // All orders are implemented and there are no possible error
          // conditions, so always return true.
          return true;
     }
     // ----------------------------------------------------------------------
     // reverse mode routine called by CppAD
     bool mat_mul_reverse(
          size_t                   id ,
          size_t                    k ,
          size_t                    n ,
          size_t                    m ,
          const vector<double>&    tx ,
          const vector<double>&    ty ,
          vector<double>&          px ,
          const vector<double>&    py
     )
     {     get_info(id, k, n, m);

          size_t ell = n * n_order_;
          while(ell--)
               px[ell] = 0.;

          size_t order = n_order_;
          while(order--)
          {     // reverse sum the products for specified order
               for(ell = 0; ell <=order; ell++)
                    reverse_multiply(ell, order-ell, tx, ty, px, py);
          }

          // All orders are implemented and there are no possible error
          // conditions, so always return true.
          return true;
     }

     // ----------------------------------------------------------------------
     // forward Jacobian sparsity routine called by CppAD
     bool mat_mul_for_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          vector< std::set<size_t> >&           s )
     {     size_t i, j, k, im_left, middle, mj_right, ij_result;
          k = 0;
          get_info(id, k, n, m);

          for(i = 0; i < nr_result_; i++)
          {     for(j = 0; j < nc_result_; j++)
               {     ij_result = result(i, j, k);
                    s[ij_result].clear();
                    for(middle = 0; middle < n_middle_; middle++)
                    {     im_left   = left(i, middle, k);
                         mj_right  = right(middle, j, k);

                         // s[ij_result] = union( s[ij_result], r[im_left] )
                         s[ij_result] = set_union(s[ij_result], r[im_left]);

                         // s[ij_result] = union( s[ij_result], r[mj_right] )
                         s[ij_result] = set_union(s[ij_result], r[mj_right]);
                    }
               }
          }
          return true;
     }
     // ----------------------------------------------------------------------
     // reverse Jacobian sparsity routine called by CppAD
     bool mat_mul_rev_jac_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          vector< std::set<size_t> >&           r ,
          const vector< std::set<size_t> >&     s )
     {     size_t i, j, k, im_left, middle, mj_right, ij_result;
          k = 0;
          get_info(id, k, n, m);

          for(j = 0; j < n; j++)
               r[j].clear();

          for(i = 0; i < nr_result_; i++)
          {     for(j = 0; j < nc_result_; j++)
               {     ij_result = result(i, j, k);
                    for(middle = 0; middle < n_middle_; middle++)
                    {     im_left   = left(i, middle, k);
                         mj_right  = right(middle, j, k);

                         // r[im_left] = union( r[im_left], s[ij_result] )
                         r[im_left] = set_union(r[im_left], s[ij_result]);

                         // r[mj_right] = union( r[mj_right], s[ij_result] )
                         r[mj_right] = set_union(r[mj_right], s[ij_result]);
                    }
               }
          }
          return true;
     }
     // ----------------------------------------------------------------------
     // reverse Hessian sparsity routine called by CppAD
     bool mat_mul_rev_hes_sparse(
          size_t                               id ,
          size_t                                n ,
          size_t                                m ,
          size_t                                p ,
          const vector< std::set<size_t> >&     r ,
          const vector<bool>&                   s ,
          vector<bool>&                         t ,
          const vector< std::set<size_t> >&     u ,
          vector< std::set<size_t> >&           v )
     {     size_t i, j, k, im_left, middle, mj_right, ij_result;
          k = 0;
          get_info(id, k, n, m);

          for(j = 0; j < n; j++)
          {     t[j] = false;
               v[j].clear();
          }

          assert( vx_->size() == n );
          for(i = 0; i < nr_result_; i++)
          {     for(j = 0; j < nc_result_; j++)
               {     ij_result = result(i, j, k);
                    for(middle = 0; middle < n_middle_; middle++)
                    {     im_left   = left(i, middle, k);
                         mj_right  = right(middle, j, k);

                         // back propagate Jacobian sparsity
                         t[im_left]   = (t[im_left] | s[ij_result]);
                         t[mj_right]  = (t[mj_right] | s[ij_result]);
                         // Visual Studio C++ 2008 warns unsafe mix of int and
                         // bool if we use the following code directly above:
                         // t[im_left]  |= s[ij_result];
                         // t[mj_right] |= s[ij_result];

                         // back propagate Hessian sparsity
                         // v[im_left]  = union( v[im_left],  u[ij_result] )
                         // v[mj_right] = union( v[mj_right], u[ij_result] )
                         v[im_left] = set_union(v[im_left],  u[ij_result] );
                         v[mj_right] = set_union(v[mj_right], u[ij_result] );

                         // Check for case where the (i,j) result element
                         // is in reverse Jacobian and both left and right
                         // operands in multiplication are variables
                         if(s[ij_result] & (*vx_)[im_left] & (*vx_)[mj_right])
                         {     // v[im_left] = union( v[im_left], r[mj_right] )
                              v[im_left] = set_union(v[im_left], r[mj_right] );
                              // v[mj_right] = union( v[mj_right], r[im_left] )
                              v[mj_right] = set_union(v[mj_right], r[im_left] );
                         }
                    }
               }
          }
          return true;
     }

Declare mat_mul Function
Declare the AD<double> routine mat_mul(id, ax, ay) and end empty namespace (we could use any simple vector template class instead of CppAD::vector): 
     CPPAD_USER_ATOMIC(
          mat_mul                 ,
          CppAD::vector           ,
          double                  ,
          mat_mul_forward         ,
          mat_mul_reverse         ,
          mat_mul_for_jac_sparse  ,
          mat_mul_rev_jac_sparse  ,
          mat_mul_rev_hes_sparse
     )
} // End empty namespace
Input File: test_more/old_mat_mul.hpp cppad-20170000.3/doc/zdouble.xml0000644000175200017650000004160213057470511015363 0ustar coincoin-web zdouble: An AD Base Type With Absolute Zero
Prev Next

zdouble: An AD Base Type With Absolute Zero

Deprecated 2015-09-26
Use the function azmul instead.

Absolute Zero
The zdouble class acts like the double type with the added property that zero times any value is zero. This includes zero time nan and zero times infinity. In addition, zero divided by any value and any value times zero are also zero.

Syntax

Constructor and Assignment
    zdouble z
     zdouble z(x)
     z1 op x
 where x is a double or zdouble object and op is =, +=, -=, *= or /=-.

Comparison Operators
    b = z op x
     b = x op z
 where b is a bool object, z is a zdouble object, x is a double or zdouble object, and op is ==, !=, <=, >=, < or >.

Arithmetic Operators
    z2 = z1 op x
     z2 = x op z1
 where z1 , z2 are zdouble objects, x is a double or zdouble object, and op is +, -, * or /.

Standard Math
    z2 = fun(z1)
     z3 = pow(z1, z2)
 where z1 , z2 , z3 are zdouble objects and fun is a unary_standard_math function.

Nan
There is a specialization of nan so that
    z2 = nan(z1)
 returns 'not a number' when z1 has type zdouble. Note that this template function needs to be specialized because  zdouble(0.0) ==  zdouble(0.0) / zdouble(0.0)
Motivation

General
Often during computing (and more so in parallel computing) alternative values for an expression are computed and one of the alternatives is chosen using some boolean variable. This is often represented by
     result = flag * value_if_true + (1 - flag) * value_if_false
 where flag is one for true and zero for false. This representation does not work for double when the value being multiplied by zero is +inf, -inf, or nan.

CppAD
In CppAD one can use conditional expressions to achieve the representation
     result = flag * value_if_true + (1 - flag) * value_if_false
 This works fine except when there are multiple levels of AD ; e.g., when using AD< AD<double> > . In this case the corresponding AD function objects have type ADFun< AD<double> > . When these AD function objects compute derivatives using reverse mode, the conditional expressions are represented use zeros to multiply the expression that is not used. Using AD< AD<zdouble> > instead of AD< AD<double> > makes this representation work and fixes the problem.

Base Type Requirements
The type zdouble satisfies all of the CppAD base type requirements .

Example
The file zdouble.cpp contains an example and test of this class. It returns true if it succeeds and false otherwise.
Input File: cppad/core/zdouble.hpp cppad-20170000.3/doc/zdouble.cpp.xml0000644000175200017650000005325713057470511016155 0ustar coincoin-web zdouble: Example and Test
Prev Next zdouble.cpp Headings

zdouble: Example and Test
# include <cppad/cppad.hpp>

namespace {
     template <class Base> bool test(bool is_double)
     {     bool ok = true;
          Base eps = 10. * std::numeric_limits<double>::epsilon();

          typedef CppAD::AD<Base>   a1type;
          typedef CppAD::AD<a1type> a2type;

          // value during taping
          size_t n = 2;
          CPPAD_TESTVECTOR(Base) x(n);
          x[0] = 0.0;
          x[1] = 0.0;

          // declare independent variable
          CPPAD_TESTVECTOR(a2type) a2x(n);
          for (size_t j = 0; j < n; j++)
               a2x[j] = a2type( a1type(x[j]) );
          Independent(a2x);

          // zero and one as a2type values
          a2type a2zero = a2type(0.0);
          a2type a2one  = a2type(1.0);

          // h(x) = x[0] / x[1] if x[1] > x[0] else 1.0
          a2type h_x = CondExpGt(a2x[1], a2x[0], a2x[0] / a2x[1], a2one);

          // f(x) = h(x) if x[0] > 0.0 else 0.0
          //      = x[0] / x[1] if x[1] > x[0]  and x[0] > 0.0
          //      = 1.0         if x[0] >= x[1] and x[0] > 0.0
          //      = 0.0         if x[0] <= 0.0
          a2type f_x = CondExpGt(a2x[0], a2zero, h_x, a2one);

          // define the function f(x)
          size_t m = 1;
          CPPAD_TESTVECTOR(a2type) a2y(m);
          a2y[0] = f_x;
          CppAD::ADFun<a1type> af1;
          af1.Dependent(a2x, a2y);

          // Define function g(x) = gradient of f(x)
          CPPAD_TESTVECTOR(a1type) a1x(n), a1z(n), a1w(m);
          for (size_t j = 0; j < n; j++)
               a1x[j] = a1type(x[j]);
          a1w[0] = a1type(1.0);
          Independent(a1x);
          af1.Forward(0, a1x);
          a1z = af1.Reverse(1, a1w);
          CppAD::ADFun<Base> g;
          g.Dependent(a1x, a1z);

          // check result for a case where f(x) = 0.0;
          CPPAD_TESTVECTOR(Base) z(2);
          x[0] = 0.0;
          x[1] = 0.0;
          z    = g.Forward(0, x);
          ok &= z[0] == 0.0;
          ok &= z[1] == 0.0;

          // check result for a case where f(x) = 1.0;
          x[0] = 1.0;
          x[1] = 0.5;
          z    = g.Forward(0, x);
          ok &= z[0] == 0.0;
          ok &= z[1] == 0.0;

          // check result for a case where f(x) = x[0] / x[1];
          x[0] = 1.0;
          x[1] = 2.0;
          z    = g.Forward(0, x);
          ok &= CppAD::NearEqual(z[0], 1.0/x[1], eps, eps);
          ok &= CppAD::NearEqual(z[1], - x[0]/(x[1]*x[1]), eps, eps);

          return ok;
     }
}

bool zdouble(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     using CppAD::zdouble;
     //
     bool is_double = false;
     ok &= test<zdouble>(is_double);
     //
     is_double = true;
     ok &= test<double>(is_double);
     //
     return ok;
}
Input File: test_more/zdouble.cpp cppad-20170000.3/doc/compare_c.xml0000644000175200017650000001072113057470511015645 0ustar coincoin-web Compare Speed of C and C++
Prev Next

Compare Speed of C and C++

Syntax
compare_c/det_by_minor_c
 compare_c/det_by_minor_cpp

Purpose
Compares the speed of the exact same source code compiled using C versus C++.

Contents
det_of_minor_cDeterminant of a Minor
det_by_minor_cCompute Determinant using Expansion by Minors
uniform_01_cSimulate a [0,1] Uniform Random Variate
correct_det_by_minor_cCorrectness Test of det_by_minor Routine
repeat_det_by_minor_cRepeat det_by_minor Routine A Specified Number of Times
elapsed_seconds_cReturns Elapsed Number of Seconds
time_det_by_minor_cDetermine Amount of Time to Execute det_by_minor
main_compare_cMain Program For Comparing C and C++ Speed
Input File: compare_c/CMakeLists.txt cppad-20170000.3/doc/det_of_minor_c.xml0000644000175200017650000006544213057470511016675 0ustar coincoin-web Determinant of a Minor
Prev Next det_of_minor_c

Determinant of a Minor

Syntax
d = det_of_minor(a, m, n, r, c)

Purpose
returns the determinant of a minor of the matrix A using expansion by minors. The elements of the n × n minor M of the matrix A are defined, for i = 0 , … , n -1 and j = 0 , … , n -1 , by M i , j = A R ( i ) , C ( j ) where the functions R ( i ) is defined by the argument r and C ( j ) is defined by the argument c .

This function is for example and testing purposes only. Expansion by minors is chosen as an example because it uses a lot of floating point operations yet does not require much source code (on the order of m factorial floating point operations and about 70 lines of source code including comments). This is not an efficient method for computing a determinant; for example, using an LU factorization would be better.

Determinant of A
If the following conditions hold, the minor is the entire matrix A and hence det_of_minor will return the determinant of A :
  1. n = m .
  2. for i = 0 , … , m -1 , r [ i ] = i + 1 , and r [ m ] = 0 .
  3. for j = 0 , … , m -1 , c [ j ] = j + 1 , and c [ m ] = 0 .


a
The argument a has prototype
     const double* a
 and is a vector with size m * m . The elements of the m × m matrix A are defined, for i = 0 , … , m -1 and j = 0 , … , m -1 , by A i , j = a [ i * m + j ]
m
The argument m has prototype
     size_t m
 and is the size of the square matrix A .

n
The argument n has prototype
     size_t n
 and is the size of the square minor M .

r
The argument r has prototype
     size_t* r
 and is a vector with m + 1 elements. This vector defines the function R ( i ) which specifies the rows of the minor M . To be specific, the function R ( i ) for i = 0 , … , n -1 is defined by R ( 0 ) = r [ m ] R ( i + 1 ) = r [ R ( i ) ] All the elements of r must have value less than or equal m . The elements of vector r are modified during the computation, and restored to their original value before the return from det_of_minor.

c
The argument c has prototype
     size_t* c
 and is a vector with m + 1 elements This vector defines the function C ( i ) which specifies the rows of the minor M . To be specific, the function C ( i ) for j = 0 , … , n -1 is defined by C ( 0 ) = c [ m ] C ( j + 1 ) = c [ C ( j ) ] All the elements of c must have value less than or equal m . The elements of vector c are modified during the computation, and restored to their original value before the return from det_of_minor.

d
The result d has prototype
     double d
 and is equal to the determinant of the minor M .

Source Code 
double det_of_minor(
     const double*        a  ,
     size_t               m  ,
     size_t               n  ,
     size_t*              r  ,
     size_t*              c  )
{     size_t R0, Cj, Cj1, j;
     double detM, M0j, detS;
     int s;

     R0 = r[m]; /* R(0) */
     Cj = c[m]; /* C(j)    (case j = 0) */
     Cj1 = m;   /* C(j-1)  (case j = 0) */

     /* check for 1 by 1 case */
     if( n == 1 ) return a[ R0 * m + Cj ];

     /* initialize determinant of the minor M */
     detM = 0.;

     /* initialize sign of factor for neat sub-minor */
     s = 1;

     /* remove row with index 0 in M from all the sub-minors of M */
     r[m] = r[R0];

     /* for each column of M */
     for(j = 0; j < n; j++)
     {     /* element with index (0,j) in the minor M */
          M0j = a[ R0 * m + Cj ];

          /* remove column with index j in M to form next sub-minor S of M */
          c[Cj1] = c[Cj];

          /* compute determinant of the current sub-minor S */
          detS = det_of_minor(a, m, n - 1, r, c);

          /* restore column Cj to representation of M as a minor of A */
          c[Cj1] = Cj;

          /* include this sub-minor term in the summation */
          if( s > 0 )
               detM = detM + M0j * detS;
          else     detM = detM - M0j * detS;

          /* advance to neat column of M */
          Cj1 = Cj;
          Cj  = c[Cj];
          s   = - s;
     }

     /* restore row zero to the minor representation for M */
     r[m] = R0;

     /* return the determinant of the minor M */
     return detM;
}
Input File: compare_c/det_by_minor.c cppad-20170000.3/doc/det_by_minor_c.xml0000644000175200017650000003042713057470511016676 0ustar coincoin-web Compute Determinant using Expansion by Minors
Prev Next det_by_minor_c

Compute Determinant using Expansion by Minors

Syntax
d = det_by_minor(a, n)

Purpose
returns the determinant of the matrix A using expansion by minors. The elements of the n × n minor M of the matrix A are defined, for i = 0 , … , n -1 and j = 0 , … , n -1 , by M i , j = A i , j
a
The argument a has prototype
     const double* a
 and is a vector with size m * m . The elements of the m × m matrix A are defined, for i = 0 , … , m -1 and j = 0 , … , m -1 , by A i , j = a [ i * m + j ]
m
The argument m has prototype
     size_t m
 and is the number of rows (and columns) in the square matrix A .

Source Code 
double det_by_minor(double* a, size_t m)
{     size_t *r, *c, i;
     double value;

     r = (size_t*) malloc( (m+1) * sizeof(size_t) );
     c = (size_t*) malloc( (m+1) * sizeof(size_t) );

     assert(m <= 100);
     for(i = 0; i < m; i++)
     {     r[i] = i+1;
          c[i] = i+1;
     }
     r[m] = 0;
     c[m] = 0;

     value = det_of_minor(a, m, m, r, c);

     free(r);
     free(c);
     return value;
}
Input File: compare_c/det_by_minor.c cppad-20170000.3/doc/uniform_01_c.xml0000644000175200017650000001702213057470511016177 0ustar coincoin-web Simulate a [0,1] Uniform Random Variate
Prev Next uniform_01_c

Simulate a [0,1] Uniform Random Variate

Syntax
random_seed(seed)
 uniform_01(n, a)

Purpose
This routine is used to create random values for speed testing purposes.

seed
The argument seed has prototype
     size_t seed
 It specifies a seed for the uniform random number generator.

n
The argument n has prototype
     size_t n
 It specifies the number of elements in the random vector a .

a
The argument a has prototype
     double* a
 . The input value of the elements of a does not matter. Upon return, the elements of a are set to values randomly sampled over the interval [0,1].

Source Code 
void random_seed(size_t seed)
{     srand(seed); }
void uniform_01(unsigned n, double* a)
{     static double factor = 1. / (double) RAND_MAX;
     while(n--)
          a[n] = rand() * factor;
}
Input File: compare_c/det_by_minor.c cppad-20170000.3/doc/correct_det_by_minor_c.xml0000644000175200017650000002136313057470511020416 0ustar coincoin-web Correctness Test of det_by_minor Routine
Prev Next correct_det_by_minor_c

Correctness Test of det_by_minor Routine

Syntax
flag = correct_det_by_minor()

flag
The return value has prototype
     bool flag
 It value is 1 if the test passes and 0 otherwise.

Source Code 
bool correct_det_by_minor(void)
{     double a[9], det, check;

     random_seed(123);
     uniform_01(9, a);

     /* compute determinant using expansion by minors */
     det = det_by_minor(a, 3);

     /* use expansion by minors to hand code the determinant  */
     check = 0.;
     check += a[0] * ( a[4] * a[8] - a[5] * a[7] );
     check -= a[1] * ( a[3] * a[8] - a[5] * a[6] );
     check += a[2] * ( a[3] * a[7] - a[4] * a[6] );

     if( fabs(det / check - 1.0) < 1e-10 )
          return true;
     return false;
}
Input File: compare_c/det_by_minor.c cppad-20170000.3/doc/repeat_det_by_minor_c.xml0000644000175200017650000001507513057470511020240 0ustar coincoin-web Repeat det_by_minor Routine A Specified Number of Times
Prev Next repeat_det_by_minor_c

Repeat det_by_minor Routine A Specified Number of Times

Syntax
repeat_det_by_minor(repeat, size)

repeat
The argument has prototype
     size_t repeat
 It specifies the number of times to repeat the calculation.

size
The argument has prototype
     size_t size
 It specifies the number of rows (and columns) in the square matrix we are computing the determinant of.

Source Code 
void repeat_det_by_minor(size_t repeat, size_t size)
{     double *a;
     a = (double*) malloc( (size * size) * sizeof(double) );

     while(repeat--)
     {     uniform_01(size * size, a);
          det_by_minor(a, size);
     }

     free(a);
     return;
}
Input File: compare_c/det_by_minor.c cppad-20170000.3/doc/elapsed_seconds_c.xml0000644000175200017650000003335413057470511017361 0ustar coincoin-web Returns Elapsed Number of Seconds
Prev Next elapsed_seconds_c

Returns Elapsed Number of Seconds

Syntax
s = elapsed_seconds()

Purpose
This routine is accurate to within .02 seconds It does not necessary work for time intervals that are greater than a day.

s
is a double equal to the number of seconds since the first call to elapsed_seconds.

Source Code 
# if _MSC_VER
// ---------------------------------------------------------------------------
// Microsoft version of timer
# include <windows.h>
# include <cassert>
double elapsed_seconds(void)
{     static bool       first_  = true;
     static SYSTEMTIME st_;
     double hour, minute, second, milli, diff;
     SYSTEMTIME st;

     if( first_ )
     {     GetSystemTime(&st_);
          first_ = false;
          return 0.;
     }
     GetSystemTime(&st);

     hour   = (double) st.wHour         - (double) st_.wHour;
     minute = (double) st.wMinute       - (double) st_.wMinute;
     second = (double) st.wSecond       - (double) st_.wSecond;
     milli  = (double) st.wMilliseconds - (double) st_.wMilliseconds;

     diff   = 1e-3*milli + second + 60.*minute + 3600.*hour;
     if( diff < 0. )
          diff += 3600.*24.;
     assert( 0 <= diff && diff < 3600.*24. );

     return diff;
}
# else
// ---------------------------------------------------------------------------
// Unix version of timer
# include <sys/time.h>
double elapsed_seconds(void)
{     double sec, usec, diff;

     static bool first_ = true;
     static struct timeval tv_first;
     struct timeval        tv;
     if( first_ )
     {     gettimeofday(&tv_first, NULL);
          first_ = false;
          return 0.;
     }
     gettimeofday(&tv, NULL);
     assert( tv.tv_sec >= tv_first.tv_sec );

     sec  = (double)(tv.tv_sec -  tv_first.tv_sec);
     usec = (double)tv.tv_usec - (double)tv_first.tv_usec;
     diff = sec + 1e-6*usec;

     return diff;
}
# endif
Input File: compare_c/det_by_minor.c cppad-20170000.3/doc/time_det_by_minor_c.xml0000644000175200017650000002142013057470511017705 0ustar coincoin-web Determine Amount of Time to Execute det_by_minor
Prev Next time_det_by_minor_c

Determine Amount of Time to Execute det_by_minor

Syntax
time = time_test(size, time_min)

Purpose
reports the amount of wall clock time for det_by_minor to compute the determinant of a square matrix. The size has prototype
     size_t size
 It specifies the number of rows (and columns) in the square matrix that the determinant is being calculated for.

time_min
The argument time_min has prototype
     double time_min
 It specifies the minimum amount of time in seconds that the test routine should take. The calculations is repeated the necessary number of times so that this amount of execution time (or more) is reached.

time
The return value time has prototype
     double time
 and is the number of wall clock seconds that it took for det_by_minor to compute its determinant (plus overhead which includes choosing a random matrix).

Source Code 
double time_det_by_minor(size_t size, double time_min)
{     size_t repeat;
     double s0, s1, time;
     repeat = 0;
     s0     = elapsed_seconds();
     s1     = s0;
     while( s1 - s0 < time_min )
     {     if( repeat == 0 )
               repeat = 1;
          else     repeat = 2 * repeat;
          s0     = elapsed_seconds();
          repeat_det_by_minor(repeat, size);
          s1     = elapsed_seconds();
     }
     time = (s1 - s0) / (double) repeat;
     return time;
}
Input File: compare_c/det_by_minor.c cppad-20170000.3/doc/main_compare_c.xml0000644000175200017650000001630213057470511016652 0ustar coincoin-web Main Program For Comparing C and C++ Speed
Prev Next main_compare_c

Main Program For Comparing C and C++ Speed

Source Code 
int main(void)
{     bool flag;
     size_t i;

     random_seed(123);

     printf("correct_det_by_minor: ");
     flag = correct_det_by_minor();
     if( flag )
          printf("OK\n");
     else     printf("Error\n");

     for(i = 0; i < 5; i++)
     {     double time_min = 1.0;
          size_t size     = 2 + i * 2;
          int   i_size    = (int) size;
          printf("time_det_minor for %d x %d matrix = ", i_size, i_size);
          printf("%g\n", time_det_by_minor(size, time_min) );
     }

     if( flag )
          return 0;
     return 1;
}
Input File: compare_c/det_by_minor.c cppad-20170000.3/doc/numeric_ad.xml0000644000175200017650000000613613057470511016030 0ustar coincoin-web Some Numerical AD Utilities
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Some Numerical AD Utilities
The routines listed below are numerical utilities that are designed to work with CppAD in particular.

Contents
BenderQuadComputing Jacobian and Hessian of Bender's Reduced Objective
opt_val_hesJacobian and Hessian of Optimal Values
LuRatioLU Factorization of A Square Matrix and Stability Calculation
Input File: omh/numeric_ad.omh cppad-20170000.3/doc/benderquad.xml0000644000175200017650000011454113057470511016034 0ustar coincoin-web Computing Jacobian and Hessian of Bender's Reduced Objective
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Computing Jacobian and Hessian of Bender's Reduced Objective

Syntax

# include <cppad/cppad.hpp>
BenderQuad(x, y, fun, g, gx, gxx)

See Also
opt_val_hes

Problem
The type ADvector cannot be determined form the arguments above (currently the type ADvector must be CPPAD_TESTVECTOR(Base) .) This will be corrected in the future by requiring Fun to define Fun::vector_type which will specify the type ADvector .

Purpose
We are given the optimization problem minimize F ( x , y ) w . r . t . ( x , y ) ∈ R n × R m that is convex with respect to y . In addition, we are given a set of equations H ( x , y ) such that H [ x , Y ( x ) ] = 0 ⇒ F y [ x , Y ( x ) ] = 0 (In fact, it is often the case that H ( x , y ) = F y ( x , y ) .) Furthermore, it is easy to calculate a Newton step for these equations; i.e., dy = - [ ∂ y H ( x , y ) ] -1 H ( x , y ) The purpose of this routine is to compute the value, Jacobian, and Hessian of the reduced objective function G ( x ) = F [ x , Y ( x ) ] Note that if only the value and Jacobian are needed, they can be computed more quickly using the relations G ( 1 ) ( x ) = ∂ x F [ x , Y ( x ) ]
x
The BenderQuad argument x has prototype
     const BAvector &x
 (see BAvector below) and its size must be equal to n . It specifies the point at which we evaluating the reduced objective function and its derivatives.

y
The BenderQuad argument y has prototype
     const BAvector &y
 and its size must be equal to m . It must be equal to Y ( x ) ; i.e., it must solve the problem in y for this given value of x minimize F ( x , y ) w . r . t . y ∈ R m
fun
The BenderQuad object fun must support the member functions listed below. The AD<Base> arguments will be variables for a tape created by a call to Independent from BenderQuad (hence they can not be combined with variables corresponding to a different tape).

fun.f
The BenderQuad argument fun supports the syntax
     f = fun.f(x, y)
 The fun.f argument x has prototype
     const ADvector &x
 (see ADvector below) and its size must be equal to n . The fun.f argument y has prototype
     const ADvector &y
 and its size must be equal to m . The fun.f result f has prototype
     ADvector f
 and its size must be equal to one. The value of f is f = F ( x , y ) .

fun.h
The BenderQuad argument fun supports the syntax
     h = fun.h(x, y)
 The fun.h argument x has prototype
     const ADvector &x
 and its size must be equal to n . The fun.h argument y has prototype
     const BAvector &y
 and its size must be equal to m . The fun.h result h has prototype
     ADvector h
 and its size must be equal to m . The value of h is h = H ( x , y ) .

fun.dy
The BenderQuad argument fun supports the syntax
     dy = fun.dy(x, y, h)

x
 The fun.dy argument x has prototype
     const BAvector &x
 and its size must be equal to n . Its value will be exactly equal to the BenderQuad argument x and values depending on it can be stored as private objects in f and need not be recalculated.

y
 The fun.dy argument y has prototype
     const BAvector &y
 and its size must be equal to m . Its value will be exactly equal to the BenderQuad argument y and values depending on it can be stored as private objects in f and need not be recalculated.

h
 The fun.dy argument h has prototype
     const ADvector &h
 and its size must be equal to m .

dy
 The fun.dy result dy has prototype
     ADvector dy
 and its size must be equal to m . The return value dy is given by dy = - [ ∂ y H ( x , y ) ] -1 h Note that if h is equal to H ( x , y ) , dy is the Newton step for finding a zero of H ( x , y ) with respect to y ; i.e., y + dy is an approximate solution for the equation H ( x , y + dy ) = 0 .

g
The argument g has prototype
     BAvector &g
 and has size one. The input value of its element does not matter. On output, it contains the value of G ( x ) ; i.e., g [ 0 ] = G ( x )
gx
The argument gx has prototype
     BAvector &gx
 and has size n . The input values of its elements do not matter. On output, it contains the Jacobian of G ( x ) ; i.e., for j = 0 , … , n -1 , gx [ j ] = G ( 1 ) ( x ) j
gxx
The argument gx has prototype
     BAvector &gxx
 and has size n × n . The input values of its elements do not matter. On output, it contains the Hessian of G ( x ) ; i.e., for i = 0 , … , n -1 , and j = 0 , … , n -1 , gxx [ i * n + j ] = G ( 2 ) ( x ) i , j
BAvector
The type BAvector must be a SimpleVector class. We use Base to refer to the type of the elements of BAvector ; i.e.,
     BAvector::value_type
ADvector
The type ADvector must be a SimpleVector class with elements of type AD<Base> ; i.e.,
     ADvector::value_type
 must be the same type as
     AD< BAvector::value_type >
 .

Example
The file bender_quad.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/bender_quad.hpp cppad-20170000.3/doc/bender_quad.cpp.xml0000644000175200017650000012040313057470511016746 0ustar coincoin-web BenderQuad: Example and Test
Prev Next bender_quad.cpp Headings

BenderQuad: Example and Test
Define F : R × R → R by F ( x , y ) = 1 2 ∑ i = 1 N [ y * sin ( x * t i ) - z i ] 2 where z ∈ R N is a fixed vector. It follows that ∂ y F ( x , y ) = ∑ i = 1 N [ y * sin ( x * t i ) - z i ] sin ( x * t i ) ∂ y ∂ y F ( x , y ) = ∑ i = 1 N sin ( x t i ) 2 Furthermore if we define Y ( x ) as the argmin of F ( x , y ) with respect to y , Y ( x ) = y - [ ∂ y ∂ y F ( x , y ) ] -1 ∂ y F [ x , y ] = ∑ i = 1 N z i sin ( x t i ) / ∑ i = 1 N z i sin ( x * t i ) 2 

# include <cppad/cppad.hpp>

namespace {
     using CppAD::AD;
     typedef CPPAD_TESTVECTOR(double)         BAvector;
     typedef CPPAD_TESTVECTOR(AD<double>)   ADvector;

     class Fun {
     private:
          BAvector t_; // measurement times
          BAvector z_; // measurement values
     public:
          // constructor
          Fun(const BAvector &t, const BAvector &z)
          : t_(t), z_(z)
          { }
          // Fun.f(x, y) = F(x, y)
          ADvector f(const ADvector &x, const ADvector &y)
          {     size_t i;
               size_t N = size_t(z_.size());

               ADvector F(1);
               F[0] = 0.;

               AD<double> residual;
               for(i = 0; i < N; i++)
               {     residual = y[0] * sin( x[0] * t_[i] ) - z_[i];
                    F[0]    += .5 * residual * residual;
               }
               return F;
          }
          // Fun.h(x, y) = H(x, y) = F_y (x, y)
          ADvector h(const ADvector &x, const BAvector &y)
          {     size_t i;
               size_t N = size_t(z_.size());

               ADvector fy(1);
               fy[0] = 0.;

               AD<double> residual;
               for(i = 0; i < N; i++)
               {     residual = y[0] * sin( x[0] * t_[i] ) - z_[i];
                    fy[0]   += residual * sin( x[0] * t_[i] );
               }
               return fy;
          }
          // Fun.dy(x, y, h) = - H_y (x,y)^{-1} * h
          //                 = - F_yy (x, y)^{-1} * h
          ADvector dy(
               const BAvector &x ,
               const BAvector &y ,
               const ADvector &H )
          {     size_t i;
               size_t N = size_t(z_.size());

               ADvector Dy(1);
               AD<double> fyy = 0.;

               for(i = 0; i < N; i++)
               {     fyy += sin( x[0] * t_[i] ) * sin( x[0] * t_[i] );
               }
               Dy[0] = - H[0] / fyy;

               return Dy;
          }
     };

     // Used to test calculation of Hessian of G
     AD<double> G(const ADvector& x, const BAvector& t, const BAvector& z)
     {     // compute Y(x)
          AD<double> numerator = 0.;
          AD<double> denominator = 0.;
          size_t k;
          for(k = 0; k < size_t(t.size()); k++)
          {     numerator   += sin( x[0] * t[k] ) * z[k];
               denominator += sin( x[0] * t[k] ) * sin( x[0] * t[k] );
          }
          AD<double> y = numerator / denominator;

          // V(x) = F[x, Y(x)]
          AD<double> sum = 0;
          for(k = 0; k < size_t(t.size()); k++)
          {     AD<double> residual = y * sin( x[0] * t[k] ) - z[k];
               sum += .5 * residual * residual;
          }
          return sum;
     }
}

bool BenderQuad(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;

     // temporary indices
     size_t i, j;

     // x space vector
     size_t n = 1;
     BAvector x(n);
     x[0] = 2. * 3.141592653;

     // y space vector
     size_t m = 1;
     BAvector y(m);
     y[0] = 1.;

     // t and z vectors
     size_t N = 10;
     BAvector t(N);
     BAvector z(N);
     for(i = 0; i < N; i++)
     {     t[i] = double(i) / double(N);       // time of measurement
          z[i] = y[0] * sin( x[0] * t[i] );   // data without noise
     }

     // construct the function object
     Fun fun(t, z);

     // evaluate the G(x), G'(x) and G''(x)
     BAvector g(1), gx(n), gxx(n * n);
     CppAD::BenderQuad(x, y, fun, g, gx, gxx);


     // create ADFun object Gfun corresponding to G(x)
     ADvector a_x(n), a_g(1);
     for(j = 0; j < n; j++)
          a_x[j] = x[j];
     Independent(a_x);
     a_g[0] = G(a_x, t, z);
     CppAD::ADFun<double> Gfun(a_x, a_g);

     // accuracy for checks
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // check Jacobian
     BAvector check_gx = Gfun.Jacobian(x);
     for(j = 0; j < n; j++)
          ok &= NearEqual(gx[j], check_gx[j], eps, eps);

     // check Hessian
     BAvector check_gxx = Gfun.Hessian(x, 0);
     for(j = 0; j < n*n; j++)
          ok &= NearEqual(gxx[j], check_gxx[j], eps, eps);

     return ok;
}
Input File: example/bender_quad.cpp cppad-20170000.3/doc/opt_val_hes.xml0000644000175200017650000007777413057470511016245 0ustar coincoin-web Jacobian and Hessian of Optimal Values
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Jacobian and Hessian of Optimal Values

Syntax
signdet = opt_val_hes(x, y, fun, jac, hes)

See Also
BenderQuad

Reference
Algorithmic differentiation of implicit functions and optimal values, Bradley M. Bell and James V. Burke, Advances in Automatic Differentiation, 2008, Springer.

Purpose
We are given a function S : R n × R m → R ℓ and we define F : R n × R m → R and V : R n → R by F ( x , y ) = ∑ k = 0 ℓ -1 S k ( x , y ) V ( x ) = F [ x , Y ( x ) ] 0 = ∂ y F [ x , Y ( x ) ] We wish to compute the Jacobian and possibly also the Hessian, of V ( x ) .

BaseVector
The type BaseVector must be a SimpleVector class. We use Base to refer to the type of the elements of BaseVector ; i.e.,
     BaseVector::value_type
x
The argument x has prototype
     const BaseVector& x
 and its size must be equal to n . It specifies the point at which we evaluating the Jacobian V ( 1 ) ( x ) (and possibly the Hessian V ( 2 ) ( x ) ).

y
The argument y has prototype
     const BaseVector& y
 and its size must be equal to m . It must be equal to Y ( x ) ; i.e., it must solve the implicit equation 0 = ∂ y F ( x , y )
Fun
The argument fun is an object of type Fun which must support the member functions listed below. CppAD will may be recording operations of the type AD<Base> when these member functions are called. These member functions must not stop such a recording; e.g., they must not call AD<Base>::abort_recording .

Fun::ad_vector
The type Fun::ad_vector must be a SimpleVector class with elements of type AD<Base> ; i.e.
     Fun::ad_vector::value_type
 is equal to AD<Base> .

fun.ell
The type Fun must support the syntax
     ell = fun.ell()
 where ell has prototype
     size_t ell
 and is the value of ℓ ; i.e., the number of terms in the summation.

One can choose ell equal to one, and have S ( x , y ) the same as F ( x , y ) . Each of the functions S k ( x , y ) , (in the summation defining F ( x , y ) ) is differentiated separately using AD. For very large problems, breaking F ( x , y ) into the sum of separate simpler functions may reduce the amount of memory necessary for algorithmic differentiation and there by speed up the process.

fun.s
The type Fun must support the syntax
     s_k = fun.s(k, x, y)
 The fun.s argument k has prototype
     size_t k
 and is between zero and ell - 1 . The argument x to fun.s has prototype
     const Fun::ad_vector& x
 and its size must be equal to n . The argument y to fun.s has prototype
     const Fun::ad_vector& y
 and its size must be equal to m . The fun.s result s_k has prototype
     AD<Base> s_k
 and its value must be given by s k = S k ( x , y ) .

fun.sy
The type Fun must support the syntax
     sy_k = fun.sy(k, x, y)
 The argument k to fun.sy has prototype
     size_t k
 The argument x to fun.sy has prototype
     const Fun::ad_vector& x
 and its size must be equal to n . The argument y to fun.sy has prototype
     const Fun::ad_vector& y
 and its size must be equal to m . The fun.sy result sy_k has prototype
     Fun::ad_vector sy_k
 its size must be equal to m , and its value must be given by sy k = ∂ y S k ( x , y ) .

jac
The argument jac has prototype
     BaseVector& jac
 and has size n or zero. The input values of its elements do not matter. If it has size zero, it is not affected. Otherwise, on output it contains the Jacobian of V ( x ) ; i.e., for j = 0 , … , n -1 , jac [ j ] = V ( 1 ) ( x ) j where x is the first argument to opt_val_hes.

hes
The argument hes has prototype
     BaseVector& hes
 and has size n * n or zero. The input values of its elements do not matter. If it has size zero, it is not affected. Otherwise, on output it contains the Hessian of V ( x ) ; i.e., for i = 0 , … , n -1 , and j = 0 , … , n -1 , hes [ i * n + j ] = V ( 2 ) ( x ) i , j
signdet
If hes has size zero, signdet is not defined. Otherwise the return value signdet is the sign of the determinant for ∂ yy 2 F ( x , y ) . If it is zero, then the matrix is singular and the Hessian is not computed ( hes is not changed).

Example
The file opt_val_hes.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/opt_val_hes.hpp cppad-20170000.3/doc/opt_val_hes.cpp.xml0000644000175200017650000011620013057470511017000 0ustar coincoin-web opt_val_hes: Example and Test
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opt_val_hes: Example and Test
Fix z ∈ R ℓ and define the functions S k : R × R → R ℓ by and F : R × R → R by S k ( x , y ) = 1 2 [ y * sin ( x * t k ) - z k ] 2 F ( x , y ) = ∑ k = 0 ℓ -1 S k ( x , y ) It follows that ∂ y F ( x , y ) = ∑ k = 0 ℓ -1 [ y * sin ( x * t k ) - z k ] sin ( x * t k ) ∂ y ∂ y F ( x , y ) = ∑ k = 0 ℓ -1 sin ( x t k ) 2 Furthermore if we define Y ( x ) as solving the equation ∂ F [ x , Y ( x ) ] = 0 we have 0 = ∑ k = 0 ℓ -1 [ Y ( x ) * sin ( x * t k ) - z k ] sin ( x * t k ) Y ( x ) ∑ k = 0 ℓ -1 sin ( x * t k ) 2 - ∑ k = 0 ℓ -1 sin ( x * t k ) z k Y ( x ) = ∑ k = 0 ℓ -1 sin ( x * t k ) z k ∑ k = 0 ℓ -1 sin ( x * t k ) 2 

# include <limits>
# include <cppad/cppad.hpp>

namespace {
     using CppAD::AD;
     typedef CPPAD_TESTVECTOR(double)       BaseVector;
     typedef CPPAD_TESTVECTOR(AD<double>) ADVector;

     class Fun {
     private:
          const BaseVector t_;    // measurement times
          const BaseVector z_;    // measurement values
     public:
          typedef ADVector ad_vector;
          // constructor
          Fun(const BaseVector &t, const BaseVector &z)
          : t_(t) , z_(z)
          {     assert( t.size() == z.size() ); }
          // ell
          size_t ell(void) const
          {     return t_.size(); }
          // Fun.s
          AD<double> s(size_t k, const ad_vector& x, const ad_vector& y) const
          {
               AD<double> residual = y[0] * sin( x[0] * t_[k] ) - z_[k];
               AD<double> s_k      = .5 * residual * residual;

               return s_k;
          }
          // Fun.sy
          ad_vector sy(size_t k, const ad_vector& x, const ad_vector& y) const
          {     assert( y.size() == 1);
               ad_vector sy_k(1);

               AD<double> residual = y[0] * sin( x[0] * t_[k] ) - z_[k];
               sy_k[0] = residual * sin( x[0] * t_[k] );

               return sy_k;
          }
     };
     // Used to test calculation of Hessian of V
     AD<double> V(const ADVector& x, const BaseVector& t, const BaseVector& z)
     {     // compute Y(x)
          AD<double> numerator = 0.;
          AD<double> denominator = 0.;
          size_t k;
          for(k = 0; k < size_t(t.size()); k++)
          {     numerator   += sin( x[0] * t[k] ) * z[k];
               denominator += sin( x[0] * t[k] ) * sin( x[0] * t[k] );
          }
          AD<double> y = numerator / denominator;

          // V(x) = F[x, Y(x)]
          AD<double> sum = 0;
          for(k = 0; k < size_t(t.size()); k++)
          {     AD<double> residual = y * sin( x[0] * t[k] ) - z[k];
               sum += .5 * residual * residual;
          }
          return sum;
     }
}

bool opt_val_hes(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;

     // temporary indices
     size_t j, k;

     // x space vector
     size_t n = 1;
     BaseVector x(n);
     x[0] = 2. * 3.141592653;

     // y space vector
     size_t m = 1;
     BaseVector y(m);
     y[0] = 1.;

     // t and z vectors
     size_t ell = 10;
     BaseVector t(ell);
     BaseVector z(ell);
     for(k = 0; k < ell; k++)
     {     t[k] = double(k) / double(ell);       // time of measurement
          z[k] = y[0] * sin( x[0] * t[k] );     // data without noise
     }

     // construct the function object
     Fun fun(t, z);

     // evaluate the Jacobian and Hessian
     BaseVector jac(n), hes(n * n);
# ifndef NDEBUG
     int signdet =
# endif
     CppAD::opt_val_hes(x, y, fun, jac, hes);

     // we know that F_yy is positive definate for this case
     assert( signdet == 1 );

     // create ADFun object g corresponding to V(x)
     ADVector a_x(n), a_v(1);
     for(j = 0; j < n; j++)
          a_x[j] = x[j];
     Independent(a_x);
     a_v[0] = V(a_x, t, z);
     CppAD::ADFun<double> g(a_x, a_v);

     // accuracy for checks
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // check Jacobian
     BaseVector check_jac = g.Jacobian(x);
     for(j = 0; j < n; j++)
          ok &= NearEqual(jac[j], check_jac[j], eps, eps);

     // check Hessian
     BaseVector check_hes = g.Hessian(x, 0);
     for(j = 0; j < n*n; j++)
          ok &= NearEqual(hes[j], check_hes[j], eps, eps);

     return ok;
}
Input File: example/opt_val_hes.cpp cppad-20170000.3/doc/luratio.xml0000644000175200017650000007047413057470511015407 0ustar coincoin-web LU Factorization of A Square Matrix and Stability Calculation
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LU Factorization of A Square Matrix and Stability Calculation

Syntax
# include <cppad/cppad.hpp>
sign = LuRatio(ip, jp, LU, ratio)

Description
Computes an LU factorization of the matrix A where A is a square matrix. A measure of the numerical stability called ratio is calculated. This ratio is useful when the results of LuRatio are used as part of an ADFun object.

Include
This routine is designed to be used with AD objects and requires the cppad/cppad.hpp file to be included.

Matrix Storage
All matrices are stored in row major order. To be specific, if Y is a vector that contains a p by q matrix, the size of Y must be equal to p * q and for i = 0 , … , p -1 , j = 0 , … , q -1 , Y i , j = Y [ i * q + j ]
sign
The return value sign has prototype
     int sign
 If A is invertible, sign is plus or minus one and is the sign of the permutation corresponding to the row ordering ip and column ordering jp . If A is not invertible, sign is zero.

ip
The argument ip has prototype
     SizeVector &ip
 (see description of SizeVector below). The size of ip is referred to as n in the specifications below. The input value of the elements of ip does not matter. The output value of the elements of ip determine the order of the rows in the permuted matrix.

jp
The argument jp has prototype
     SizeVector &jp
 (see description of SizeVector below). The size of jp must be equal to n . The input value of the elements of jp does not matter. The output value of the elements of jp determine the order of the columns in the permuted matrix.

LU
The argument LU has the prototype
     ADvector &LU
 and the size of LU must equal n * n (see description of ADvector below).

A
We define A as the matrix corresponding to the input value of LU .

P
We define the permuted matrix P in terms of A by
     P(i, j) = A[ ip[i] * n + jp[j] ]
L
We define the lower triangular matrix L in terms of the output value of LU . The matrix L is zero above the diagonal and the rest of the elements are defined by
     L(i, j) = LU[ ip[i] * n + jp[j] ]
 for i = 0 , … , n -1 and j = 0 , … , i .

U
We define the upper triangular matrix U in terms of the output value of LU . The matrix U is zero below the diagonal, one on the diagonal, and the rest of the elements are defined by
     U(i, j) = LU[ ip[i] * n + jp[j] ]
 for i = 0 , … , n -2 and j = i + 1 , … , n -1 .

Factor
If the return value sign is non-zero,
     L * U = P
 If the return value of sign is zero, the contents of L and U are not defined.

Determinant
If the return value sign is zero, the determinant of A is zero. If sign is non-zero, using the output value of LU the determinant of the matrix A is equal to
sign * LU[ip[0], jp[0]] * ... * LU[ip[n-1], jp[n-1]]
ratio
The argument ratio has prototype
        AD<Base> &ratio
 On input, the value of ratio does not matter. On output it is a measure of how good the choice of pivots is. For p = 0 , … , n -1 , the p-th pivot element is the element of maximum absolute value of a ( n - p ) × ( n - p ) sub-matrix. The ratio of each element of sub-matrix divided by the pivot element is computed. The return value of ratio is the maximum absolute value of such ratios over with respect to all elements and all the pivots.

Purpose
Suppose that the execution of a call to LuRatio is recorded in the ADFun<Base> object F . Then a call to Forward of the form
     F.Forward(k, xk)
 with k equal to zero will revaluate this Lu factorization with the same pivots and a new value for A . In this case, the resulting ratio may not be one. If ratio is too large (the meaning of too large is up to you), the current pivots do not yield a stable LU factorization of A . A better choice for the pivots (for this value of A ) will be made if you recreate the ADFun object starting with the Independent variable values that correspond to the vector xk .

SizeVector
The type SizeVector must be a SimpleVector class with elements of type size_t . The routine CheckSimpleVector will generate an error message if this is not the case.

ADvector
The type ADvector must be a simple vector class with elements of type AD<Base> . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file lu_ratio.cpp contains an example and test of using LuRatio. It returns true if it succeeds and false otherwise.
Input File: cppad/core/lu_ratio.hpp cppad-20170000.3/doc/lu_ratio.cpp.xml0000644000175200017650000010406413057470511016320 0ustar coincoin-web LuRatio: Example and Test
Prev Next lu_ratio.cpp Headings

LuRatio: Example and Test
# include <cstdlib>               // for rand function
# include <cassert>
# include <cppad/cppad.hpp>

namespace { // Begin empty namespace

CppAD::ADFun<double> *NewFactor(
     size_t                           n ,
     const CPPAD_TESTVECTOR(double) &x ,
     bool                           &ok ,
     CPPAD_TESTVECTOR(size_t)      &ip ,
     CPPAD_TESTVECTOR(size_t)      &jp )
{     using CppAD::AD;
     using CppAD::ADFun;
     size_t i, j, k;

     // values for independent and dependent variables
     CPPAD_TESTVECTOR(AD<double>) Y(n*n+1), X(n*n);

     // values for the LU factor
     CPPAD_TESTVECTOR(AD<double>) LU(n*n);

     // record the LU factorization corresponding to this value of x
     AD<double> Ratio;
     for(k = 0; k < n*n; k++)
          X[k] = x[k];
     Independent(X);
     for(k = 0; k < n*n; k++)
          LU[k] = X[k];
     CppAD::LuRatio(ip, jp, LU, Ratio);
     for(k = 0; k < n*n; k++)
          Y[k] = LU[k];
     Y[n*n] = Ratio;

     // use a function pointer so can return ADFun object
     ADFun<double> *FunPtr = new ADFun<double>(X, Y);

     // check value of ratio during recording
     ok &= (Ratio == 1.);

     // check that ip and jp are permutations of the indices 0, ... , n-1
     for(i = 0; i < n; i++)
     {     ok &= (ip[i] < n);
          ok &= (jp[i] < n);
          for(j = 0; j < n; j++)
          {     if( i != j )
               {     ok &= (ip[i] != ip[j]);
                    ok &= (jp[i] != jp[j]);
               }
          }
     }
     return FunPtr;
}
bool CheckLuFactor(
     size_t                           n  ,
     const CPPAD_TESTVECTOR(double) &x  ,
     const CPPAD_TESTVECTOR(double) &y  ,
     const CPPAD_TESTVECTOR(size_t) &ip ,
     const CPPAD_TESTVECTOR(size_t) &jp )
{     bool     ok = true;

     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     double  sum;                          // element of L * U
     double  pij;                          // element of permuted x
     size_t  i, j, k;                      // temporary indices

     // L and U factors
     CPPAD_TESTVECTOR(double)  L(n*n), U(n*n);

     // Extract L from LU factorization
     for(i = 0; i < n; i++)
     {     // elements along and below the diagonal
          for(j = 0; j <= i; j++)
               L[i * n + j] = y[ ip[i] * n + jp[j] ];
          // elements above the diagonal
          for(j = i+1; j < n; j++)
               L[i * n + j] = 0.;
     }

     // Extract U from LU factorization
     for(i = 0; i < n; i++)
     {     // elements below the diagonal
          for(j = 0; j < i; j++)
               U[i * n + j] = 0.;
          // elements along the diagonal
          U[i * n + i] = 1.;
          // elements above the diagonal
          for(j = i+1; j < n; j++)
               U[i * n + j] = y[ ip[i] * n + jp[j] ];
     }

     // Compute L * U
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     // compute element (i,j) entry in L * U
               sum = 0.;
               for(k = 0; k < n; k++)
                    sum += L[i * n + k] * U[k * n + j];
               // element (i,j) in permuted version of A
               pij  = x[ ip[i] * n + jp[j] ];
               // compare
               ok  &= NearEqual(pij, sum, eps99, eps99);
          }
     }
     return ok;
}

} // end Empty namespace

bool LuRatio(void)
{     bool  ok = true;

     size_t  n = 2; // number rows in A
     double  ratio;

     // values for independent and dependent variables
     CPPAD_TESTVECTOR(double)  x(n*n), y(n*n+1);

     // pivot vectors
     CPPAD_TESTVECTOR(size_t) ip(n), jp(n);

     // set x equal to the identity matrix
     x[0] = 1.; x[1] = 0;
     x[2] = 0.; x[3] = 1.;

     // create a fnction object corresponding to this value of x
     CppAD::ADFun<double> *FunPtr = NewFactor(n, x, ok, ip, jp);

     // use function object to factor matrix
     y     = FunPtr->Forward(0, x);
     ratio = y[n*n];
     ok   &= (ratio == 1.);
     ok   &= CheckLuFactor(n, x, y, ip, jp);

     // set x so that the pivot ratio will be infinite
     x[0] = 0. ; x[1] = 1.;
     x[2] = 1. ; x[3] = 0.;

     // try to use old function pointer to factor matrix
     y     = FunPtr->Forward(0, x);
     ratio = y[n*n];

     // check to see if we need to refactor matrix
     ok &= (ratio > 10.);
     if( ratio > 10. )
     {     delete FunPtr; // to avoid a memory leak
          FunPtr = NewFactor(n, x, ok, ip, jp);
     }

     //  now we can use the function object to factor matrix
     y     = FunPtr->Forward(0, x);
     ratio = y[n*n];
     ok    &= (ratio == 1.);
     ok    &= CheckLuFactor(n, x, y, ip, jp);

     delete FunPtr;  // avoid memory leak
     return ok;
}
Input File: example/lu_ratio.cpp cppad-20170000.3/doc/addon.xml0000644000175200017650000002176613057470511015015 0ustar coincoin-web CppAD Addons
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CppAD Addons

Name
Each CppAD addon has a short name which we denote by name below, a longer name longer and a description :
name    longer    description
cg CppADCodeGen C++ Source Code Generation of CppAD Derivative Calculations
py pycppad A Python Interface to CppAD
tmb adcomp An R Interface to CppAD with Random Effects Modeling Utilities
mixed cppad_mixed A C++ Interface to Random Effects Laplace Approximation

Include Files
If includedir is the directory where the include files are installed, the file
     includedir/cppad/name.hpp
 and the directory
     includedir/cppad/name
 are reserved for use by the name addon.

Library Files
If libdir is the directory where CppAD library files are installed, files with the name
     libdir/libcppad_name.ext
     libdir/libcppad_name_anything.ext
 where anything and ext are arbitrary, are reserved for use by the name addon.

Preprocessor Symbols
C++ preprocessor symbols that begin with
     CPPAD_NAME_
 where NAME is a upper-case version of name , are reserved for use by the name addon.

Namespace
The C++ namespace
     CppAD::name
 is reserved for use by the name addon.
Input File: omh/addon.omh cppad-20170000.3/doc/license.xml0000644000175200017650000011210713057470511015340 0ustar coincoin-web Your License for the CppAD Software
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Your License for the CppAD Software


                    GNU GENERAL PUBLIC LICENSE
                       Version 3, 29 June 2007

 Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.

                            Preamble

  The GNU General Public License is a free, copyleft license for
software and other kinds of works.

  The licenses for most software and other practical works are designed
to take away your freedom to share and change the works.  By contrast,
the GNU General Public License is intended to guarantee your freedom to
share and change all versions of a program--to make sure it remains free
software for all its users.  We, the Free Software Foundation, use the
GNU General Public License for most of our software; it applies also to
any other work released this way by its authors.  You can apply it to
your programs, too.

  When we speak of free software, we are referring to freedom, not
price.  Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
them if you wish), that you receive source code or can get it if you
want it, that you can change the software or use pieces of it in new
free programs, and that you know you can do these things.

  To protect your rights, we need to prevent others from denying you
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you modify it: responsibilities to respect the freedom of others.

  For example, if you distribute copies of such a program, whether
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  Developers that use the GNU GPL protect your rights with two steps:
(1) assert copyright on the software, and (2) offer you this License
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  For the developers' and authors' protection, the GPL clearly explains
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  Some devices are designed to deny users access to install or run
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pattern of such abuse occurs in the area of products for individuals to
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  Finally, every program is threatened constantly by software patents.
States should not allow patents to restrict development and use of
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  The precise terms and conditions for copying, distribution and
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                       TERMS AND CONDITIONS

  0. Definitions.

  "This License" refers to version 3 of the GNU General Public License.

  "Copyright" also means copyright-like laws that apply to other kinds of
works, such as semiconductor masks.

  "The Program" refers to any copyrightable work licensed under this
License.  Each licensee is addressed as "you".  "Licensees" and
"recipients" may be individuals or organizations.

  To "modify" a work means to copy from or adapt all or part of the work
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earlier work or a work "based on" the earlier work.

  A "covered work" means either the unmodified Program or a work based
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  To "propagate" a work means to do anything with it that, without
permission, would make you directly or secondarily liable for
infringement under applicable copyright law, except executing it on a
computer or modifying a private copy.  Propagation includes copying,
distribution (with or without modification), making available to the
public, and in some countries other activities as well.

  To "convey" a work means any kind of propagation that enables other
parties to make or receive copies.  Mere interaction with a user through
a computer network, with no transfer of a copy, is not conveying.

  An interactive user interface displays "Appropriate Legal Notices"
to the extent that it includes a convenient and prominently visible
feature that (1) displays an appropriate copyright notice, and (2)
tells the user that there is no warranty for the work (except to the
extent that warranties are provided), that licensees may convey the
work under this License, and how to view a copy of this License.  If
the interface presents a list of user commands or options, such as a
menu, a prominent item in the list meets this criterion.

  1. Source Code.

  The "source code" for a work means the preferred form of the work
for making modifications to it.  "Object code" means any non-source
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  A "Standard Interface" means an interface that either is an official
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is widely used among developers working in that language.

  The "System Libraries" of an executable work include anything, other
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"Major Component", in this context, means a major essential component
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  The "Corresponding Source" for a work in object code form means all
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which are not part of the work.  For example, Corresponding Source
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the work, and the source code for shared libraries and dynamically
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such as by intimate data communication or control flow between those
subprograms and other parts of the work.

  The Corresponding Source need not include anything that users
can regenerate automatically from other parts of the Corresponding
Source.

  The Corresponding Source for a work in source code form is that
same work.

  2. Basic Permissions.

  All rights granted under this License are granted for the term of
copyright on the Program, and are irrevocable provided the stated
conditions are met.  This License explicitly affirms your unlimited
permission to run the unmodified Program.  The output from running a
covered work is covered by this License only if the output, given its
content, constitutes a covered work.  This License acknowledges your
rights of fair use or other equivalent, as provided by copyright law.

  You may make, run and propagate covered works that you do not
convey, without conditions so long as your license otherwise remains
in force.  You may convey covered works to others for the sole purpose
of having them make modifications exclusively for you, or provide you
with facilities for running those works, provided that you comply with
the terms of this License in conveying all material for which you do
not control copyright.  Those thus making or running the covered works
for you must do so exclusively on your behalf, under your direction
and control, on terms that prohibit them from making any copies of
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  Conveying under any other circumstances is permitted solely under
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  3. Protecting Users' Legal Rights From Anti-Circumvention Law.

  No covered work shall be deemed part of an effective technological
measure under any applicable law fulfilling obligations under article
11 of the WIPO copyright treaty adopted on 20 December 1996, or
similar laws prohibiting or restricting circumvention of such
measures.

  When you convey a covered work, you waive any legal power to forbid
circumvention of technological measures to the extent such circumvention
is effected by exercising rights under this License with respect to
the covered work, and you disclaim any intention to limit operation or
modification of the work as a means of enforcing, against the work's
users, your or third parties' legal rights to forbid circumvention of
technological measures.

  4. Conveying Verbatim Copies.

  You may convey verbatim copies of the Program's source code as you
receive it, in any medium, provided that you conspicuously and
appropriately publish on each copy an appropriate copyright notice;
keep intact all notices stating that this License and any
non-permissive terms added in accord with section 7 apply to the code;
keep intact all notices of the absence of any warranty; and give all
recipients a copy of this License along with the Program.

  You may charge any price or no price for each copy that you convey,
and you may offer support or warranty protection for a fee.

  5. Conveying Modified Source Versions.

  You may convey a work based on the Program, or the modifications to
produce it from the Program, in the form of source code under the
terms of section 4, provided that you also meet all of these conditions:

    a) The work must carry prominent notices stating that you modified
    it, and giving a relevant date.

    b) The work must carry prominent notices stating that it is
    released under this License and any conditions added under section
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    c) You must license the entire work, as a whole, under this
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    d) If the work has interactive user interfaces, each must display
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    work need not make them do so.

  A compilation of a covered work with other separate and independent
works, which are not by their nature extensions of the covered work,
and which are not combined with it such as to form a larger program,
in or on a volume of a storage or distribution medium, is called an
"aggregate" if the compilation and its resulting copyright are not
used to limit the access or legal rights of the compilation's users
beyond what the individual works permit.  Inclusion of a covered work
in an aggregate does not cause this License to apply to the other
parts of the aggregate.

  6. Conveying Non-Source Forms.

  You may convey a covered work in object code form under the terms
of sections 4 and 5, provided that you also convey the
machine-readable Corresponding Source under the terms of this License,
in one of these ways:

    a) Convey the object code in, or embodied in, a physical product
    (including a physical distribution medium), accompanied by the
    Corresponding Source fixed on a durable physical medium
    customarily used for software interchange.

    b) Convey the object code in, or embodied in, a physical product
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    written offer, valid for at least three years and valid for as
    long as you offer spare parts or customer support for that product
    model, to give anyone who possesses the object code either (1) a
    copy of the Corresponding Source for all the software in the
    product that is covered by this License, on a durable physical
    medium customarily used for software interchange, for a price no
    more than your reasonable cost of physically performing this
    conveying of source, or (2) access to copy the
    Corresponding Source from a network server at no charge.

    c) Convey individual copies of the object code with a copy of the
    written offer to provide the Corresponding Source.  This
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    d) Convey the object code by offering access from a designated
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    available for as long as needed to satisfy these requirements.

    e) Convey the object code using peer-to-peer transmission, provided
    you inform other peers where the object code and Corresponding
    Source of the work are being offered to the general public at no
    charge under subsection 6d.

  A separable portion of the object code, whose source code is excluded
from the Corresponding Source as a System Library, need not be
included in conveying the object code work.

  A "User Product" is either (1) a "consumer product", which means any
tangible personal property which is normally used for personal, family,
or household purposes, or (2) anything designed or sold for incorporation
into a dwelling.  In determining whether a product is a consumer product,
doubtful cases shall be resolved in favor of coverage.  For a particular
product received by a particular user, "normally used" refers to a
typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product.  A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.

  "Installation Information" for a User Product means any methods,
procedures, authorization keys, or other information required to install
and execute modified versions of a covered work in that User Product from
a modified version of its Corresponding Source.  The information must
suffice to ensure that the continued functioning of the modified object
code is in no case prevented or interfered with solely because
modification has been made.

  If you convey an object code work under this section in, or with, or
specifically for use in, a User Product, and the conveying occurs as
part of a transaction in which the right of possession and use of the
User Product is transferred to the recipient in perpetuity or for a
fixed term (regardless of how the transaction is characterized), the
Corresponding Source conveyed under this section must be accompanied
by the Installation Information.  But this requirement does not apply
if neither you nor any third party retains the ability to install
modified object code on the User Product (for example, the work has
been installed in ROM).

  The requirement to provide Installation Information does not include a
requirement to continue to provide support service, warranty, or updates
for a work that has been modified or installed by the recipient, or for
the User Product in which it has been modified or installed.  Access to a
network may be denied when the modification itself materially and
adversely affects the operation of the network or violates the rules and
protocols for communication across the network.

  Corresponding Source conveyed, and Installation Information provided,
in accord with this section must be in a format that is publicly
documented (and with an implementation available to the public in
source code form), and must require no special password or key for
unpacking, reading or copying.

  7. Additional Terms.

  "Additional permissions" are terms that supplement the terms of this
License by making exceptions from one or more of its conditions.
Additional permissions that are applicable to the entire Program shall
be treated as though they were included in this License, to the extent
that they are valid under applicable law.  If additional permissions
apply only to part of the Program, that part may be used separately
under those permissions, but the entire Program remains governed by
this License without regard to the additional permissions.

  When you convey a copy of a covered work, you may at your option
remove any additional permissions from that copy, or from any part of
it.  (Additional permissions may be written to require their own
removal in certain cases when you modify the work.)  You may place
additional permissions on material, added by you to a covered work,
for which you have or can give appropriate copyright permission.

  Notwithstanding any other provision of this License, for material you
add to a covered work, you may (if authorized by the copyright holders of
that material) supplement the terms of this License with terms:

    a) Disclaiming warranty or limiting liability differently from the
    terms of sections 15 and 16 of this License; or

    b) Requiring preservation of specified reasonable legal notices or
    author attributions in that material or in the Appropriate Legal
    Notices displayed by works containing it; or

    c) Prohibiting misrepresentation of the origin of that material, or
    requiring that modified versions of such material be marked in
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    d) Limiting the use for publicity purposes of names of licensors or
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    e) Declining to grant rights under trademark law for use of some
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    f) Requiring indemnification of licensors and authors of that
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  All other non-permissive additional terms are considered "further
restrictions" within the meaning of section 10.  If the Program as you
received it, or any part of it, contains a notice stating that it is
governed by this License along with a term that is a further
restriction, you may remove that term.  If a license document contains
a further restriction but permits relicensing or conveying under this
License, you may add to a covered work material governed by the terms
of that license document, provided that the further restriction does
not survive such relicensing or conveying.

  If you add terms to a covered work in accord with this section, you
must place, in the relevant source files, a statement of the
additional terms that apply to those files, or a notice indicating
where to find the applicable terms.

  Additional terms, permissive or non-permissive, may be stated in the
form of a separately written license, or stated as exceptions;
the above requirements apply either way.

  8. Termination.

  You may not propagate or modify a covered work except as expressly
provided under this License.  Any attempt otherwise to propagate or
modify it is void, and will automatically terminate your rights under
this License (including any patent licenses granted under the third
paragraph of section 11).

  However, if you cease all violation of this License, then your
license from a particular copyright holder is reinstated (a)
provisionally, unless and until the copyright holder explicitly and
finally terminates your license, and (b) permanently, if the copyright
holder fails to notify you of the violation by some reasonable means
prior to 60 days after the cessation.

  Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.

  Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License.  If your rights have been terminated and not permanently
reinstated, you do not qualify to receive new licenses for the same
material under section 10.

  9. Acceptance Not Required for Having Copies.

  You are not required to accept this License in order to receive or
run a copy of the Program.  Ancillary propagation of a covered work
occurring solely as a consequence of using peer-to-peer transmission
to receive a copy likewise does not require acceptance.  However,
nothing other than this License grants you permission to propagate or
modify any covered work.  These actions infringe copyright if you do
not accept this License.  Therefore, by modifying or propagating a
covered work, you indicate your acceptance of this License to do so.

  10. Automatic Licensing of Downstream Recipients.

  Each time you convey a covered work, the recipient automatically
receives a license from the original licensors, to run, modify and
propagate that work, subject to this License.  You are not responsible
for enforcing compliance by third parties with this License.

  An "entity transaction" is a transaction transferring control of an
organization, or substantially all assets of one, or subdividing an
organization, or merging organizations.  If propagation of a covered
work results from an entity transaction, each party to that
transaction who receives a copy of the work also receives whatever
licenses to the work the party's predecessor in interest had or could
give under the previous paragraph, plus a right to possession of the
Corresponding Source of the work from the predecessor in interest, if
the predecessor has it or can get it with reasonable efforts.

  You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License.  For example, you may
not impose a license fee, royalty, or other charge for exercise of
rights granted under this License, and you may not initiate litigation
(including a cross-claim or counterclaim in a lawsuit) alleging that
any patent claim is infringed by making, using, selling, offering for
sale, or importing the Program or any portion of it.

  11. Patents.

  A "contributor" is a copyright holder who authorizes use under this
License of the Program or a work on which the Program is based.  The
work thus licensed is called the contributor's "contributor version".

  A contributor's "essential patent claims" are all patent claims
owned or controlled by the contributor, whether already acquired or
hereafter acquired, that would be infringed by some manner, permitted
by this License, of making, using, or selling its contributor version,
but do not include claims that would be infringed only as a
consequence of further modification of the contributor version.  For
purposes of this definition, "control" includes the right to grant
patent sublicenses in a manner consistent with the requirements of
this License.

  Each contributor grants you a non-exclusive, worldwide, royalty-free
patent license under the contributor's essential patent claims, to
make, use, sell, offer for sale, import and otherwise run, modify and
propagate the contents of its contributor version.

  In the following three paragraphs, a "patent license" is any express
agreement or commitment, however denominated, not to enforce a patent
(such as an express permission to practice a patent or covenant not to
sue for patent infringement).  To "grant" such a patent license to a
party means to make such an agreement or commitment not to enforce a
patent against the party.

  If you convey a covered work, knowingly relying on a patent license,
and the Corresponding Source of the work is not available for anyone
to copy, free of charge and under the terms of this License, through a
publicly available network server or other readily accessible means,
then you must either (1) cause the Corresponding Source to be so
available, or (2) arrange to deprive yourself of the benefit of the
patent license for this particular work, or (3) arrange, in a manner
consistent with the requirements of this License, to extend the patent
license to downstream recipients.  "Knowingly relying" means you have
actual knowledge that, but for the patent license, your conveying the
covered work in a country, or your recipient's use of the covered work
in a country, would infringe one or more identifiable patents in that
country that you have reason to believe are valid.

  If, pursuant to or in connection with a single transaction or
arrangement, you convey, or propagate by procuring conveyance of, a
covered work, and grant a patent license to some of the parties
receiving the covered work authorizing them to use, propagate, modify
or convey a specific copy of the covered work, then the patent license
you grant is automatically extended to all recipients of the covered
work and works based on it.

  A patent license is "discriminatory" if it does not include within
the scope of its coverage, prohibits the exercise of, or is
conditioned on the non-exercise of one or more of the rights that are
specifically granted under this License.  You may not convey a covered
work if you are a party to an arrangement with a third party that is
in the business of distributing software, under which you make payment
to the third party based on the extent of your activity of conveying
the work, and under which the third party grants, to any of the
parties who would receive the covered work from you, a discriminatory
patent license (a) in connection with copies of the covered work
conveyed by you (or copies made from those copies), or (b) primarily
for and in connection with specific products or compilations that
contain the covered work, unless you entered into that arrangement,
or that patent license was granted, prior to 28 March 2007.

  Nothing in this License shall be construed as excluding or limiting
any implied license or other defenses to infringement that may
otherwise be available to you under applicable patent law.

  12. No Surrender of Others' Freedom.

  If conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License.  If you cannot convey a
covered work so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you may
not convey it at all.  For example, if you agree to terms that obligate you
to collect a royalty for further conveying from those to whom you convey
the Program, the only way you could satisfy both those terms and this
License would be to refrain entirely from conveying the Program.

  13. Use with the GNU Affero General Public License.

  Notwithstanding any other provision of this License, you have
permission to link or combine any covered work with a work licensed
under version 3 of the GNU Affero General Public License into a single
combined work, and to convey the resulting work.  The terms of this
License will continue to apply to the part which is the covered work,
but the special requirements of the GNU Affero General Public License,
section 13, concerning interaction through a network will apply to the
combination as such.

  14. Revised Versions of this License.

  The Free Software Foundation may publish revised and/or new versions of
the GNU General Public License from time to time.  Such new versions will
be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.

  Each version is given a distinguishing version number.  If the
Program specifies that a certain numbered version of the GNU General
Public License "or any later version" applies to it, you have the
option of following the terms and conditions either of that numbered
version or of any later version published by the Free Software
Foundation.  If the Program does not specify a version number of the
GNU General Public License, you may choose any version ever published
by the Free Software Foundation.

  If the Program specifies that a proxy can decide which future
versions of the GNU General Public License can be used, that proxy's
public statement of acceptance of a version permanently authorizes you
to choose that version for the Program.

  Later license versions may give you additional or different
permissions.  However, no additional obligations are imposed on any
author or copyright holder as a result of your choosing to follow a
later version.

  15. Disclaimer of Warranty.

  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

  16. Limitation of Liability.

  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.

  17. Interpretation of Sections 15 and 16.

  If the disclaimer of warranty and limitation of liability provided
above cannot be given local legal effect according to their terms,
reviewing courts shall apply local law that most closely approximates
an absolute waiver of all civil liability in connection with the
Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.

                     END OF TERMS AND CONDITIONS

            How to Apply These Terms to Your New Programs

  If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.

  To do so, attach the following notices to the program.  It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.

    <one line to give the program's name and a brief idea of what it does.>
    Copyright (C) <year>  <name of author>

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.

Also add information on how to contact you by electronic and paper mail.

  If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:

    <program>  Copyright (C) <year>  <name of author>
    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
    This is free software, and you are welcome to redistribute it
    under certain conditions; type `show c' for details.

The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License.  Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".

  You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<http://www.gnu.org/licenses/>.

  The GNU General Public License does not permit incorporating your program
into proprietary programs.  If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library.  If this is what you want to do, use the GNU Lesser General
Public License instead of this License.  But first, please read
<http://www.gnu.org/philosophy/why-not-lgpl.html>.

Input File: omh/license.omh cppad-20170000.3/doc/_reference.xml0000644000175200017650000027047413057470511016027 0ustar coincoin-web Alphabetic Listing of Cross Reference Tags
Prev Next _reference

Alphabetic Listing of Cross Reference Tags
A
a11c_bthread.cpp
 A Simple Boost Thread Example and Test
a11c_openmp.cpp
 A Simple OpenMP Example and Test
a11c_pthread.cpp
 A Simple Parallel Pthread Example and Test
abort_recording
 Abort Recording of an Operation Sequence
abort_recording.cpp
 Abort Current Recording: Example and Test
abs
 AD Absolute Value Functions: abs, fabs
abs.cpp
 AD Absolute Value Function: Example and Test
acos
 Inverse Sine Function: acos
acos.cpp
 The AD acos Function: Example and Test
acos_forward
 Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
acos_reverse
 Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
acosh
 The Inverse Hyperbolic Cosine Function: acosh
acosh.cpp
 The AD acosh Function: Example and Test
AD
 AD Objects
ad_assign
 AD Assignment Operator
ad_assign.cpp
 AD Assignment: Example and Test
ad_binary
 AD Binary Arithmetic Operators
ad_ctor
 AD Constructors
ad_ctor.cpp
 AD Constructors: Example and Test
ad_fun.cpp
 Creating Your Own Interface to an ADFun Object
ad_in_c.cpp
 Example and Test Linking CppAD to Languages Other than C++
ad_input
 AD Output Stream Operator
ad_input.cpp
 AD Output Operator: Example and Test
ad_output
 AD Output Stream Operator
ad_output.cpp
 AD Output Operator: Example and Test
ad_to_string
 Convert An AD or Base Type to String
add.cpp
 AD Binary Addition: Example and Test
AddEq.cpp
 AD Computed Assignment Addition: Example and Test
addon
 CppAD Addons
ADFun
 ADFun Objects
adolc_alloc_mat
 Adolc Test Utility: Allocate and Free Memory For a Matrix
adolc_det_lu.cpp
 Adolc Speed: Gradient of Determinant Using Lu Factorization
adolc_det_minor.cpp
 Adolc Speed: Gradient of Determinant by Minor Expansion
adolc_mat_mul.cpp
 Adolc Speed: Matrix Multiplication
adolc_ode.cpp
 Adolc Speed: Ode
adolc_poly.cpp
 Adolc Speed: Second Derivative of a Polynomial
adolc_prefix
 Including the ADOL-C Examples and Tests
adolc_sparse_hessian.cpp
 Adolc Speed: Sparse Hessian
adolc_sparse_jacobian.cpp
 adolc Speed: Sparse Jacobian
ADValued
 AD Valued Operations and Functions
Appendix
 Appendix
Arithmetic
 AD Arithmetic Operators and Computed Assignments
asin
 Inverse Sine Function: asin
asin.cpp
 The AD asin Function: Example and Test
asin_forward
 Inverse Sine and Hyperbolic Sine Forward Mode Theory
asin_reverse
 Inverse Sine and Hyperbolic Sine Reverse Mode Theory
asinh
 The Inverse Hyperbolic Sine Function: asinh
asinh.cpp
 The AD asinh Function: Example and Test
atan
 Inverse Tangent Function: atan
atan.cpp
 The AD atan Function: Example and Test
atan2
 AD Two Argument Inverse Tangent Function
atan2.cpp
 The AD atan2 Function: Example and Test
atan_forward
 Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
atan_reverse
 Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
atanh
 The Inverse Hyperbolic Tangent Function: atanh
atanh.cpp
 The AD atanh Function: Example and Test
atomic
 Atomic AD Functions
atomic_afun
 Using AD Version of Atomic Function
atomic_base
 User Defined Atomic AD Functions
atomic_base_clear
 Free Static Variables
atomic_ctor
 Atomic Function Constructor
atomic_eigen_cholesky.cpp
 Atomic Eigen Cholesky Factorization: Example and Test
atomic_eigen_cholesky.hpp
 Atomic Eigen Cholesky Factorization Class
atomic_eigen_mat_inv.cpp
 Atomic Eigen Matrix Inverse: Example and Test
atomic_eigen_mat_inv.hpp
 Atomic Eigen Matrix Inversion Class
atomic_eigen_mat_mul.cpp
 Atomic Eigen Matrix Multiply: Example and Test
atomic_eigen_mat_mul.hpp
 Atomic Eigen Matrix Multiply Class
atomic_for_sparse_hes
 Atomic Forward Hessian Sparsity Patterns
atomic_for_sparse_hes.cpp
 Atomic Forward Hessian Sparsity: Example and Test
atomic_for_sparse_jac
 Atomic Forward Jacobian Sparsity Patterns
atomic_for_sparse_jac.cpp
 Atomic Forward Jacobian Sparsity: Example and Test
atomic_forward
 Atomic Forward Mode
atomic_forward.cpp
 Atomic Forward: Example and Test
atomic_get_started.cpp
 Getting Started with Atomic Operations: Example and Test
atomic_mat_mul.cpp
 User Atomic Matrix Multiply: Example and Test
atomic_mat_mul.hpp
 Matrix Multiply as an Atomic Operation
atomic_mul_level.cpp
 Atomic Operations and Multiple-Levels of AD: Example and Test
atomic_norm_sq.cpp
 Atomic Euclidean Norm Squared: Example and Test
atomic_option
 Set Atomic Function Options
atomic_reciprocal.cpp
 Reciprocal as an Atomic Operation: Example and Test
atomic_rev_sparse_hes
 Atomic Reverse Hessian Sparsity Patterns
atomic_rev_sparse_hes.cpp
 Atomic Reverse Hessian Sparsity: Example and Test
atomic_rev_sparse_jac
 Atomic Reverse Jacobian Sparsity Patterns
atomic_rev_sparse_jac.cpp
 Atomic Reverse Jacobian Sparsity: Example and Test
atomic_reverse
 Atomic Reverse Mode
atomic_reverse.cpp
 Atomic Reverse: Example and Test
atomic_set_sparsity.cpp
 Atomic Sparsity with Set Patterns: Example and Test
atomic_tangent.cpp
 Tan and Tanh as User Atomic Operations: Example and Test
auto_tools
 Auto Tools Unix Test and Installation
azmul
 Absolute Zero Multiplication
azmul.cpp
 AD Absolute Zero Multiplication: Example and Test
B
base_adolc.hpp
 Enable use of AD<Base> where Base is Adolc's adouble Type
base_alloc.hpp
 Example AD<Base> Where Base Constructor Allocates Memory
base_complex.hpp
 Enable use of AD<Base> where Base is std::complex<double>
base_cond_exp
 Base Type Requirements for Conditional Expressions
base_double.hpp
 Enable use of AD<Base> where Base is double
base_example
 Example AD Base Types That are not AD<OtherBase>
base_float.hpp
 Enable use of AD<Base> where Base is float
base_hash
 Base Type Requirements for Hash Coding Values
base_identical
 Base Type Requirements for Identically Equal Comparisons
base_limits
 Base Type Requirements for Numeric Limits
base_member
 Required Base Class Member Functions
base_ordered
 Base Type Requirements for Ordered Comparisons
base_require
 AD<Base> Requirements for a CppAD Base Type
base_require.cpp
 Using a User Defined AD Base Type: Example and Test
base_std_math
 Base Type Requirements for Standard Math Functions
base_to_string
 Extending to_string To Another Floating Point Type
bender_quad.cpp
 BenderQuad: Example and Test
BenderQuad
 Computing Jacobian and Hessian of Bender's Reduced Objective
Bib
 Bibliography
binary_math
 The Binary Math Functions
bool_fun.cpp
 AD Boolean Functions: Example and Test
bool_sparsity.cpp
 Using vectorBool Sparsity To Conserve Memory: Example and Test
BoolFun
 AD Boolean Functions
BoolValued
 Bool Valued Operations and Functions with AD Arguments
C
capacity_order
 Controlling Taylor Coefficients Memory Allocation
capacity_order.cpp
 Controlling Taylor Coefficient Memory Allocation: Example and Test
change_param.cpp
 Computing a Jacobian With Constants that Change
check_for_nan
 Check an ADFun Object For Nan Results
check_for_nan.cpp
 ADFun Checking For Nan: Example and Test
check_numeric_type.cpp
 The CheckNumericType Function: Example and Test
check_simple_vector.cpp
 The CheckSimpleVector Function: Example and Test
CheckNumericType
 Check NumericType Class Concept
checkpoint
 Checkpointing Functions
checkpoint.cpp
 Simple Checkpointing: Example and Test
checkpoint_extended_ode.cpp
 Checkpointing an Extended ODE Solver: Example and Test
checkpoint_ode.cpp
 Checkpointing an ODE Solver: Example and Test
CheckSimpleVector
 Check Simple Vector Concept
cholesky_theory
 AD Theory for Cholesky Factorization
cmake
 Using CMake to Configure CppAD
cmake_check
 Checking the CppAD Examples and Tests
colpack_hes.cpp
 Using ColPack: Example and Test
colpack_jac.cpp
 Using ColPack: Example and Test
colpack_prefix
 Including the ColPack Sparsity Calculations
Compare
 AD Binary Comparison Operators
compare.cpp
 AD Binary Comparison Operators: Example and Test
compare_c
 Compare Speed of C and C++
compare_change
 Comparison Changes Between Taping and Zero Order Forward
compare_change.cpp
 CompareChange and Re-Tape: Example and Test
CompareChange
 Comparison Changes During Zero Order Forward Mode
complex_poly.cpp
 Complex Polynomial: Example and Test
compute_assign
 AD Computed Assignment Operators
cond_exp.cpp
 Conditional Expressions: Example and Test
CondExp
 AD Conditional Expressions
conj_grad.cpp
 Differentiate Conjugate Gradient Algorithm: Example and Test
Convert
 Conversion and I/O of AD Objects
correct_det_by_minor_c
 Correctness Test of det_by_minor Routine
cos
 The Cosine Function: cos
cos.cpp
 The AD cos Function: Example and Test
cosh
 The Hyperbolic Cosine Function: cosh
cosh.cpp
 The AD cosh Function: Example and Test
CppAD
 cppad-20170000.3: A Package for Differentiation of C++ Algorithms
cppad_assert
 CppAD Assertions During Execution
cppad_det_lu.cpp
 CppAD Speed: Gradient of Determinant Using Lu Factorization
cppad_det_minor.cpp
 CppAD Speed: Gradient of Determinant by Minor Expansion
cppad_eigen.hpp
 Enable Use of Eigen Linear Algebra Package with CppAD
cppad_ipopt_nlp
 Nonlinear Programming Using the CppAD Interface to Ipopt
cppad_mat_mul.cpp
 CppAD Speed, Matrix Multiplication
cppad_ode.cpp
 CppAD Speed: Gradient of Ode Solution
cppad_poly.cpp
 CppAD Speed: Second Derivative of a Polynomial
cppad_sparse_hessian.cpp
 CppAD Speed: Sparse Hessian
cppad_sparse_jacobian.cpp
 CppAD Speed: Sparse Jacobian
cppad_testvector
 Choosing the CppAD Test Vector Template Class
CppAD_vector
 The CppAD::vector Template Class
cppad_vector.cpp
 CppAD::vector Template Class: Example and Test
D
dependency.cpp
 Computing Dependency: Example and Test
Dependent
 Stop Recording and Store Operation Sequence
deprecated
 CppAD Deprecated API Features
det_33
 Check Determinant of 3 by 3 matrix
det_33.hpp
 Source: det_33
det_by_lu
 Determinant Using Expansion by Lu Factorization
det_by_lu.cpp
 Determinant Using Lu Factorization: Example and Test
det_by_lu.hpp
 Source: det_by_lu
det_by_minor
 Determinant Using Expansion by Minors
det_by_minor.cpp
 Determinant Using Expansion by Minors: Example and Test
det_by_minor.hpp
 Source: det_by_minor
det_by_minor_c
 Compute Determinant using Expansion by Minors
det_grad_33
 Check Gradient of Determinant of 3 by 3 matrix
det_grad_33.hpp
 Source: det_grad_33
det_of_minor
 Determinant of a Minor
det_of_minor.cpp
 Determinant of a Minor: Example and Test
det_of_minor.hpp
 Source: det_of_minor
det_of_minor_c
 Determinant of a Minor
Discrete
 Discrete AD Functions
div.cpp
 AD Binary Division: Example and Test
div_eq.cpp
 AD Computed Assignment Division: Example and Test
double_det_lu.cpp
 Double Speed: Determinant Using Lu Factorization
double_det_minor.cpp
 Double Speed: Determinant by Minor Expansion
double_mat_mul.cpp
 CppAD Speed: Matrix Multiplication (Double Version)
double_ode.cpp
 Double Speed: Ode Solution
double_poly.cpp
 Double Speed: Evaluate a Polynomial
double_sparse_hessian.cpp
 Double Speed: Sparse Hessian
double_sparse_jacobian.cpp
 Double Speed: Sparse Jacobian
download
 Download The CppAD Source Code
Drivers
 First and Second Derivatives: Easy Drivers
E
eigen_array.cpp
 Using Eigen Arrays: Example and Test
eigen_det.cpp
 Using Eigen To Compute Determinant: Example and Test
eigen_plugin.hpp
 Source Code for eigen_plugin.hpp
eigen_prefix
 Including the Eigen Examples and Tests
elapsed_seconds
 Returns Elapsed Number of Seconds
elapsed_seconds.cpp
 Elapsed Seconds: Example and Test
elapsed_seconds_c
 Returns Elapsed Number of Seconds
epsilon
 Machine Epsilon For AD Types
equal_op_seq.cpp
 EqualOpSeq: Example and Test
EqualOpSeq
 Check if Two Value are Identically Equal
erf
 The Error Function
erf.cpp
 The AD erf Function: Example and Test
erf_forward
 Error Function Forward Taylor Polynomial Theory
erf_reverse
 Error Function Reverse Mode Theory
error_handler.cpp
 Replacing The CppAD Error Handler: Example and Test
ErrorHandler
 Replacing the CppAD Error Handler
Example
 Examples
example.cpp
 CppAD Examples and Tests
ExampleUtility
 Utility Routines used by CppAD Examples
exp
 The Exponential Function: exp
exp.cpp
 The AD exp Function: Example and Test
exp_2
 Second Order Exponential Approximation
exp_2.cpp
 exp_2: Test
exp_2.hpp
 exp_2: Implementation
exp_2_cppad
 exp_2: CppAD Forward and Reverse Sweeps
exp_2_for0
 exp_2: Operation Sequence and Zero Order Forward Mode
exp_2_for0.cpp
 exp_2: Verify Zero Order Forward Sweep
exp_2_for1
 exp_2: First Order Forward Mode
exp_2_for1.cpp
 exp_2: Verify First Order Forward Sweep
exp_2_for2
 exp_2: Second Order Forward Mode
exp_2_for2.cpp
 exp_2: Verify Second Order Forward Sweep
exp_2_rev1
 exp_2: First Order Reverse Mode
exp_2_rev1.cpp
 exp_2: Verify First Order Reverse Sweep
exp_2_rev2
 exp_2: Second Order Reverse Mode
exp_2_rev2.cpp
 exp_2: Verify Second Order Reverse Sweep
exp_apx_main.cpp
 Correctness Tests For Exponential Approximation in Introduction
exp_eps
 An Epsilon Accurate Exponential Approximation
exp_eps.cpp
 exp_eps: Test of exp_eps
exp_eps.hpp
 exp_eps: Implementation
exp_eps_cppad
 exp_eps: CppAD Forward and Reverse Sweeps
exp_eps_for0
 exp_eps: Operation Sequence and Zero Order Forward Sweep
exp_eps_for0.cpp
 exp_eps: Verify Zero Order Forward Sweep
exp_eps_for1
 exp_eps: First Order Forward Sweep
exp_eps_for1.cpp
 exp_eps: Verify First Order Forward Sweep
exp_eps_for2
 exp_eps: Second Order Forward Mode
exp_eps_for2.cpp
 exp_eps: Verify Second Order Forward Sweep
exp_eps_rev1
 exp_eps: First Order Reverse Sweep
exp_eps_rev1.cpp
 exp_eps: Verify First Order Reverse Sweep
exp_eps_rev2
 exp_eps: Second Order Reverse Sweep
exp_eps_rev2.cpp
 exp_eps: Verify Second Order Reverse Sweep
exp_forward
 Exponential Function Forward Mode Theory
exp_reverse
 Exponential Function Reverse Mode Theory
expm1
 The Exponential Function Minus One: expm1
expm1.cpp
 The AD exp Function: Example and Test
F
fadbad_det_lu.cpp
 Fadbad Speed: Gradient of Determinant Using Lu Factorization
fadbad_det_minor.cpp
 Fadbad Speed: Gradient of Determinant by Minor Expansion
fadbad_mat_mul.cpp
 Fadbad Speed: Matrix Multiplication
fadbad_ode.cpp
 Fadbad Speed: Ode
fadbad_poly.cpp
 Fadbad Speed: Second Derivative of a Polynomial
fadbad_prefix
 Including the FADBAD Speed Tests
fadbad_sparse_hessian.cpp
 Fadbad Speed: Sparse Hessian
fadbad_sparse_jacobian.cpp
 fadbad Speed: sparse_jacobian
Faq
 Frequently Asked Questions and Answers
for_one.cpp
 First Order Partial Driver: Example and Test
for_sparse_hes.cpp
 Forward Mode Hessian Sparsity: Example and Test
for_sparse_jac.cpp
 Forward Mode Jacobian Sparsity: Example and Test
for_two.cpp
 Subset of Second Order Partials: Example and Test
ForOne
 First Order Partial Derivative: Driver Routine
ForSparseHes
 Hessian Sparsity Pattern: Forward Mode
ForSparseJac
 Jacobian Sparsity Pattern: Forward Mode
ForTwo
 Forward Mode Second Partial Derivative Driver
Forward
 Forward Mode
forward.cpp
 Forward Mode: Example and Test
forward_dir
 Multiple Directions Forward Mode
forward_dir.cpp
 Forward Mode: Example and Test of Multiple Directions
forward_one
 First Order Forward Mode: Derivative Values
forward_order
 Multiple Order Forward Mode
forward_order.cpp
 Forward Mode: Example and Test of Multiple Orders
forward_two
 Second Order Forward Mode: Derivative Values
forward_zero
 Zero Order Forward Mode: Function Values
ForwardTheory
 The Theory of Forward Mode
fun_assign.cpp
 ADFun Assignment: Example and Test
fun_check.cpp
 ADFun Check and Re-Tape: Example and Test
FunCheck
 Check an ADFun Sequence of Operations
FunConstruct
 Construct an ADFun Object and Stop Recording
FunDeprecated
 ADFun Object Deprecated Member Functions
FunEval
 Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
G
General
 General Examples
get_adolc.sh
 Download and Install Adolc in Build Directory
get_colpack.sh
 Download and Install ColPack in Build Directory
get_eigen.sh
 Download and Install Eigen in Build Directory
get_fadbad.sh
 Download and Install Fadbad in Build Directory
get_ipopt.sh
 Download and Install Ipopt in Build Directory
get_sacado.sh
 Download and Install Sacado in Build Directory
get_started.cpp
 Getting Started Using CppAD to Compute Derivatives
glossary
 Glossary
H
harmonic.cpp
 Multi-Threaded Implementation of Summation of 1/i
harmonic_time.cpp
 Timing Test of Multi-Threaded Summation of 1/i
harmonic_work.cpp
 Multi-threading Sum of 1/i Utility Routines
hes_lagrangian.cpp
 Hessian of Lagrangian and ADFun Default Constructor: Example and Test
hes_lu_det.cpp
 Gradient of Determinant Using LU Factorization: Example and Test
hes_minor_det.cpp
 Gradient of Determinant Using Expansion by Minors: Example and Test
hes_times_dir.cpp
 Hessian Times Direction: Example and Test
Hessian
 Hessian: Easy Driver
hessian.cpp
 Hessian: Example and Test
I
include_deprecated
 Deprecated Include Files
Independent
 Declare Independent Variables and Start Recording
independent.cpp
 Independent and ADFun Constructor: Example and Test
index_sort
 Returns Indices that Sort a Vector
index_sort.cpp
 Index Sort: Example and Test
Install
 CppAD Download, Test, and Install Instructions
Integer
 Convert From AD to Integer
integer.cpp
 Convert From AD to Integer: Example and Test
interface2c.cpp
 Interfacing to C: Example and Test
interp_onetape.cpp
 Interpolation With Out Retaping: Example and Test
interp_retape.cpp
 Interpolation With Retaping: Example and Test
Introduction
 An Introduction by Example to Algorithmic Differentiation
ipopt_nlp_get_started.cpp
 Nonlinear Programming Using CppAD and Ipopt: Example and Test
ipopt_nlp_ode
 Example Simultaneous Solution of Forward and Inverse Problem
ipopt_nlp_ode_check.cpp
 Correctness Check for Both Simple and Fast Representations
ipopt_nlp_ode_fast
 ODE Fitting Using Fast Representation
ipopt_nlp_ode_fast.hpp
 ODE Fitting Using Fast Representation
ipopt_nlp_ode_problem
 An ODE Inverse Problem Example
ipopt_nlp_ode_problem.hpp
 ODE Inverse Problem Definitions: Source Code
ipopt_nlp_ode_run.hpp
 Driver for Running the Ipopt ODE Example
ipopt_nlp_ode_simple
 ODE Fitting Using Simple Representation
ipopt_nlp_ode_simple.hpp
 ODE Fitting Using Simple Representation
ipopt_ode_speed.cpp
 Speed Test for Both Simple and Fast Representations
ipopt_prefix
 Including the cppad_ipopt Library and Tests
ipopt_solve
 Use Ipopt to Solve a Nonlinear Programming Problem
ipopt_solve_get_started.cpp
 Nonlinear Programming Using CppAD and Ipopt: Example and Test
ipopt_solve_ode_inverse.cpp
 ODE Inverse Problem Definitions: Source Code
ipopt_solve_retape.cpp
 Nonlinear Programming Retaping: Example and Test
J
jac_lu_det.cpp
 Gradient of Determinant Using Lu Factorization: Example and Test
jac_minor_det.cpp
 Gradient of Determinant Using Expansion by Minors: Example and Test
Jacobian
 Jacobian: Driver Routine
jacobian.cpp
 Jacobian: Example and Test
L
License
 Your License for the CppAD Software
link_det_lu
 Speed Testing Gradient of Determinant Using Lu Factorization
link_det_minor
 Speed Testing Gradient of Determinant by Minor Expansion
link_mat_mul
 Speed Testing Derivative of Matrix Multiply
link_ode
 Speed Testing the Jacobian of Ode Solution
link_poly
 Speed Testing Second Derivative of a Polynomial
link_sparse_hessian
 Speed Testing Sparse Hessian
link_sparse_jacobian
 Speed Testing Sparse Jacobian
ListAllExamples
 List of All the CppAD Examples
log
 The Exponential Function: log
log.cpp
 The AD log Function: Example and Test
log10
 The Base 10 Logarithm Function: log10
log10.cpp
 The AD log10 Function: Example and Test
log1p
 The Logarithm of One Plus Argument: log1p
log1p.cpp
 The AD log1p Function: Example and Test
log_forward
 Logarithm Function Forward Mode Theory
log_reverse
 Logarithm Function Reverse Mode Theory
lu_factor.cpp
 LuFactor: Example and Test
lu_factor.hpp
 Source: LuFactor
lu_invert.cpp
 LuInvert: Example and Test
lu_invert.hpp
 Source: LuInvert
lu_ratio.cpp
 LuRatio: Example and Test
lu_solve.cpp
 LuSolve With Complex Arguments: Example and Test
lu_solve.hpp
 Source: LuSolve
lu_vec_ad.cpp
 Lu Factor and Solve with Recorded Pivoting
lu_vec_ad_ok.cpp
 Lu Factor and Solve With Recorded Pivoting: Example and Test
LuDetAndSolve
 Compute Determinants and Solve Equations by LU Factorization
LuFactor
 LU Factorization of A Square Matrix
LuInvert
 Invert an LU Factored Equation
LuRatio
 LU Factorization of A Square Matrix and Stability Calculation
LuSolve
 Compute Determinant and Solve Linear Equations
M
main_compare_c
 Main Program For Comparing C and C++ Speed
mat_sum_sq
 Sum Elements of a Matrix Times Itself
mat_sum_sq.cpp
 Sum of the Elements of the Square of a Matrix: Example and Test
mat_sum_sq.hpp
 Source: mat_sum_sq
memory_leak
 Memory Leak Detection
microsoft_timer
 Microsoft Version of Elapsed Number of Seconds
mul.cpp
 AD Binary Multiplication: Example and Test
mul_eq.cpp
 AD Computed Assignment Multiplication: Example and Test
mul_level
 Using Multiple Levels of AD
mul_level.cpp
 Multiple Level of AD: Example and Test
mul_level_adolc.cpp
 Using Adolc with Multiple Levels of Taping: Example and Test
mul_level_adolc_ode.cpp
 Taylor's Ode Solver: A Multi-Level Adolc Example and Test
mul_level_ode.cpp
 Taylor's Ode Solver: A Multi-Level AD Example and Test
multi_newton.cpp
 A Multi-Threaded Newton's Method
multi_newton_time.cpp
 Timing Test of Multi-Threaded Newton Method
multi_newton_work.cpp
 Multi-threading Newton Method Utility Routines
multi_thread
 Using CppAD in a Multi-Threading Environment
N
nan
 Obtain Nan or Determine if a Value is Nan
nan.cpp
 nan: Example and Test
near_equal.cpp
 NearEqual Function: Example and Test
near_equal_ext.cpp
 Compare AD with Base Objects: Example and Test
NearEqual
 Determine if Two Values Are Nearly Equal
NearEqualExt
 Compare AD and Base Objects for Nearly Equal
num_limits.cpp
 Numeric Limits: Example and Test
number_skip
 Number of Variables that Can be Skipped
number_skip.cpp
 Number of Variables That Can be Skipped: Example and Test
numeric_ad
 Some Numerical AD Utilities
numeric_limits
 Numeric Limits For an AD and Base Types
numeric_type.cpp
 The NumericType: Example and Test
NumericType
 Definition of a Numeric Type
O
ode_err_control.cpp
 OdeErrControl: Example and Test
ode_err_maxabs.cpp
 OdeErrControl: Example and Test Using Maxabs Argument
ode_evaluate
 Evaluate a Function Defined in Terms of an ODE
ode_evaluate.cpp
 ode_evaluate: Example and test
ode_evaluate.hpp
 Source: ode_evaluate
ode_gear.cpp
 OdeGear: Example and Test
ode_gear_control.cpp
 OdeGearControl: Example and Test
ode_stiff.cpp
 A Stiff Ode: Example and Test
ode_taylor.cpp
 Taylor's Ode Solver: An Example and Test
OdeErrControl
 An Error Controller for ODE Solvers
OdeGear
 An Arbitrary Order Gear Method
OdeGearControl
 An Error Controller for Gear's Ode Solvers
old_atomic
 User Defined Atomic AD Functions
old_mat_mul.cpp
 Old Matrix Multiply as a User Atomic Operation: Example and Test
old_mat_mul.hpp
 Define Matrix Multiply as a User Atomic Operation
old_max_num_threads
 Set Maximum Number of Threads for omp_alloc Allocator
old_reciprocal.cpp
 Old Atomic Operation Reciprocal: Example and Test
old_tan.cpp
 Old Tan and Tanh as User Atomic Operations: Example and Test
old_usead_1.cpp
 Using AD to Compute Atomic Function Derivatives
old_usead_2.cpp
 Using AD to Compute Atomic Function Derivatives
omp_alloc
 A Quick OpenMP Memory Allocator Used by CppAD
omp_alloc.cpp
 OpenMP Memory Allocator: Example and Test
omp_available
 Amount of Memory Available for Quick Use by a Thread
omp_create_array
 Allocate Memory and Create A Raw Array
omp_delete_array
 Return A Raw Array to The Available Memory for a Thread
omp_efficient
 Check If A Memory Allocation is Efficient for Another Use
omp_free_available
 Free Memory Currently Available for Quick Use by a Thread
omp_get_memory
 Get At Least A Specified Amount of Memory
omp_get_thread_num
 Get the Current OpenMP Thread Number
omp_in_parallel
 Is The Current Execution in OpenMP Parallel Mode
omp_inuse
 Amount of Memory a Thread is Currently Using
omp_max_num_threads
 Set and Get Maximum Number of Threads for omp_alloc Allocator
omp_max_thread
 OpenMP Parallel Setup
omp_return_memory
 Return Memory to omp_alloc
opt_val_hes
 Jacobian and Hessian of Optimal Values
opt_val_hes.cpp
 opt_val_hes: Example and Test
optimize
 Optimize an ADFun Object Tape
optimize_compare_op.cpp
 Example Optimization and Comparison Operators
optimize_conditional_skip.cpp
 Example Optimization and Conditional Expressions
optimize_cumulative_sum.cpp
 Example Optimization and Cumulative Sum Operations
optimize_forward_active.cpp
 Example Optimization and Forward Activity Analysis
optimize_nest_conditional.cpp
 Example Optimization and Nested Conditional Expressions
optimize_print_for.cpp
 Example Optimization and Print Forward Operators
optimize_reverse_active.cpp
 Example Optimization and Reverse Activity Analysis
P
par_var.cpp
 AD Parameter and Variable Functions: Example and Test
parallel_ad
 Enable AD Calculations During Parallel Mode
ParVar
 Is an AD Object a Parameter or Variable
pkgconfig
 CppAD pkg-config Files
Poly
 Evaluate a Polynomial or its Derivative
poly.cpp
 Polynomial Evaluation: Example and Test
poly.hpp
 Source: Poly
pow
 The AD Power Function
pow.cpp
 The AD Power Function: Example and Test
pow_int
 The Integer Power Function
pow_int.cpp
 The Pow Integer Exponent: Example and Test
preprocessor
 CppAD API Preprocessor Symbols
print_for_cout.cpp
 Printing During Forward Mode: Example and Test
print_for_string.cpp
 Print During Zero Order Forward Mode: Example and Test
PrintFor
 Printing AD Values During Forward Mode
R
repeat_det_by_minor_c
 Repeat det_by_minor Routine A Specified Number of Times
rev_one.cpp
 First Order Derivative Driver: Example and Test
rev_sparse_hes.cpp
 Reverse Mode Hessian Sparsity: Example and Test
rev_sparse_jac.cpp
 Reverse Mode Jacobian Sparsity: Example and Test
rev_two.cpp
 Second Partials Reverse Driver: Example and Test
Reverse
 Reverse Mode
reverse_any
 Any Order Reverse Mode
reverse_checkpoint.cpp
 Reverse Mode General Case (Checkpointing): Example and Test
reverse_identity
 An Important Reverse Mode Identity
reverse_one
 First Order Reverse Mode
reverse_one.cpp
 First Order Reverse Mode: Example and Test
reverse_three.cpp
 Third Order Reverse Mode: Example and Test
reverse_two
 Second Order Reverse Mode
reverse_two.cpp
 Second Order Reverse ModeExample and Test
ReverseTheory
 The Theory of Reverse Mode
RevOne
 First Order Derivative: Driver Routine
RevSparseHes
 Hessian Sparsity Pattern: Reverse Mode
RevSparseJac
 Jacobian Sparsity Pattern: Reverse Mode
RevTwo
 Reverse Mode Second Partial Derivative Driver
romberg_one.cpp
 One Dimensional Romberg Integration: Example and Test
RombergMul
 Multi-dimensional Romberg Integration
Rombergmul.cpp
 One Dimensional Romberg Integration: Example and Test
RombergOne
 One DimensionalRomberg Integration
Rosen34
 A 3rd and 4th Order Rosenbrock ODE Solver
rosen_34.cpp
 Rosen34: Example and Test
Runge45
 An Embedded 4th and 5th Order Runge-Kutta ODE Solver
runge45_1.cpp
 Runge45: Example and Test
runge45_2.cpp
 Runge45: Example and Test
S
sacado_det_lu.cpp
 Sacado Speed: Gradient of Determinant Using Lu Factorization
sacado_det_minor.cpp
 Sacado Speed: Gradient of Determinant by Minor Expansion
sacado_mat_mul.cpp
 Sacado Speed: Matrix Multiplication
sacado_ode.cpp
 Sacado Speed: Gradient of Ode Solution
sacado_poly.cpp
 Sacado Speed: Second Derivative of a Polynomial
sacado_prefix
 Including the Sacado Speed Tests
sacado_sparse_hessian.cpp
 Sacado Speed: Sparse Hessian
sacado_sparse_jacobian.cpp
 sacado Speed: sparse_jacobian
seq_property
 ADFun Sequence Properties
seq_property.cpp
 ADFun Sequence Properties: Example and Test
set_union
 Union of Standard Sets
set_union.cpp
 Set Union: Example and Test
sign
 The Sign: sign
sign.cpp
 Sign Function: Example and Test
simple_ad_bthread.cpp
 A Simple Boost Threading AD: Example and Test
simple_ad_openmp.cpp
 A Simple OpenMP AD: Example and Test
simple_ad_pthread.cpp
 A Simple pthread AD: Example and Test
simple_vector.cpp
 Simple Vector Template Class: Example and Test
SimpleVector
 Definition of a Simple Vector
sin
 The Sine Function: sin
sin.cpp
 The AD sin Function: Example and Test
sin_cos_forward
 Trigonometric and Hyperbolic Sine and Cosine Forward Theory
sin_cos_reverse
 Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
sinh
 The Hyperbolic Sine Function: sinh
sinh.cpp
 The AD sinh Function: Example and Test
size_order
 Number Taylor Coefficient Orders Currently Stored
Sparse
 Calculating Sparsity Patterns
sparse_hes_fun
 Evaluate a Function That Has a Sparse Hessian
sparse_hes_fun.cpp
 sparse_hes_fun: Example and test
sparse_hes_fun.hpp
 Source: sparse_hes_fun
sparse_hessian
 Sparse Hessian: Easy Driver
sparse_hessian.cpp
 Sparse Hessian: Example and Test
sparse_jac_fun
 Evaluate a Function That Has a Sparse Jacobian
sparse_jac_fun.cpp
 sparse_jac_fun: Example and test
sparse_jac_fun.hpp
 Source: sparse_jac_fun
sparse_jacobian
 Sparse Jacobian: Easy Driver
sparse_jacobian.cpp
 Sparse Jacobian: Example and Test
sparse_sub_hes.cpp
 Sparse Hessian on Subset of Variables: Example and Test
sparsity_sub.cpp
 Sparsity Patterns For a Subset of Variables: Example and Test
speed
 Speed Test an Operator Overloading AD Package
speed_adolc
 Speed Test of Derivatives Using Adolc
speed_cppad
 Speed Test Derivatives Using CppAD
speed_double
 Speed Test of Functions in Double
speed_example.cpp
 Run the Speed Examples
speed_fadbad
 Speed Test Derivatives Using Fadbad
speed_main
 Running the Speed Test Program
speed_program.cpp
 Example Use of SpeedTest
speed_sacado
 Speed Test Derivatives Using Sacado
speed_test
 Run One Speed Test and Return Results
speed_test.cpp
 speed_test: Example and test
speed_utility
 Speed Testing Utilities
SpeedTest
 Run One Speed Test and Print Results
sqrt
 The Square Root Function: sqrt
sqrt.cpp
 The AD sqrt Function: Example and Test
sqrt_forward
 Square Root Function Forward Mode Theory
sqrt_reverse
 Square Root Function Reverse Mode Theory
stack_machine.cpp
 Example Differentiating a Stack Machine Interpreter
sub.cpp
 AD Binary Subtraction: Example and Test
sub_eq.cpp
 AD Computed Assignment Subtraction: Example and Test
sub_sparse_hes.cpp
 Computing Sparse Hessian for a Subset of Variables
T
ta_available
 Amount of Memory Available for Quick Use by a Thread
ta_create_array
 Allocate An Array and Call Default Constructor for its Elements
ta_delete_array
 Deallocate An Array and Call Destructor for its Elements
ta_free_all
 Free All Memory That Was Allocated for Use by thread_alloc
ta_free_available
 Free Memory Currently Available for Quick Use by a Thread
ta_get_memory
 Get At Least A Specified Amount of Memory
ta_hold_memory
 Control When Thread Alloc Retains Memory For Future Use
ta_in_parallel
 Is The Current Execution in Parallel Mode
ta_inuse
 Amount of Memory a Thread is Currently Using
ta_num_threads
 Get Number of Threads
ta_parallel_setup
 Setup thread_alloc For Use in Multi-Threading Environment
ta_return_memory
 Return Memory to thread_alloc
ta_thread_num
 Get the Current Thread Number
tan
 The Tangent Function: tan
tan.cpp
 The AD tan Function: Example and Test
tan_forward
 Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
tan_reverse
 Tangent and Hyperbolic Tangent Reverse Mode Theory
tanh
 The Hyperbolic Tangent Function: tanh
tanh.cpp
 The AD tanh Function: Example and Test
tape_index.cpp
 Taping Array Index Operation: Example and Test
team_bthread.cpp
 Boost Thread Implementation of a Team of AD Threads
team_example.cpp
 Using a Team of AD Threads: Example and Test
team_openmp.cpp
 OpenMP Implementation of a Team of AD Threads
team_pthread.cpp
 Pthread Implementation of a Team of AD Threads
team_thread.hpp
 Specifications for A Team of AD Threads
test_vector
 Choosing The Vector Testing Template Class
testvector
 Using The CppAD Test Vector Template Class
Theory
 The Theory of Derivative Calculations
thread_alloc
 A Fast Multi-Threading Memory Allocator
thread_alloc.cpp
 Fast Multi-Threading Memory Allocator: Example and Test
thread_test.cpp
 Run Multi-Threading Examples and Speed Tests
time_det_by_minor_c
 Determine Amount of Time to Execute det_by_minor
time_test
 Determine Amount of Time to Execute a Test
time_test.cpp
 time_test: Example and test
to_string
 Convert Certain Types to a String
to_string.cpp
 to_string: Example and Test
TrackNewDel
 Routines That Track Use of New and Delete
TrackNewDel.cpp
 Tracking Use of New and Delete: Example and Test
U
unary_minus.cpp
 AD Unary Minus Operator: Example and Test
unary_plus.cpp
 AD Unary Plus Operator: Example and Test
unary_standard_math
 The Unary Standard Math Functions
UnaryMinus
 AD Unary Minus Operator
UnaryPlus
 AD Unary Plus Operator
uniform_01
 Simulate a [0,1] Uniform Random Variate
uniform_01.hpp
 Source: uniform_01
uniform_01_c
 Simulate a [0,1] Uniform Random Variate
utility
 Some General Purpose Utilities
V
Value
 Convert From an AD Type to its Base Type
value.cpp
 Convert From AD to its Base Type: Example and Test
Var2Par
 Convert an AD Variable to a Parameter
var2par.cpp
 Convert an AD Variable to a Parameter: Example and Test
vec_ad.cpp
 AD Vectors that Record Index Operations: Example and Test
VecAD
 AD Vectors that Record Index Operations
vector_bool.cpp
 CppAD::vectorBool Class: Example and Test
W
whats_new
 Changes and Additions to CppAD
whats_new_03
 Changes and Additions to CppAD During 2003
whats_new_04
 Changes and Additions to CppAD During 2004
whats_new_05
 Changes and Additions to CppAD During 2005
whats_new_06
 Changes and Additions to CppAD During 2006
whats_new_07
 Changes and Additions to CppAD During 2007
whats_new_08
 Changes and Additions to CppAD During 2008
whats_new_09
 Changes and Additions to CppAD During 2009
whats_new_10
 Changes and Additions to CppAD During 2010
whats_new_11
 Changes and Additions to CppAD During 2011
whats_new_12
 CppAD Changes and Additions During 2012
whats_new_13
 CppAD Changes and Additions During 2013
whats_new_14
 CppAD Changes and Additions During 2014
whats_new_15
 CppAD Changes and Additions During 2015
whats_new_16
 Changes and Additions to CppAD During 2016
wish_list
 The CppAD Wish List
Z
zdouble
 zdouble: An AD Base Type With Absolute Zero
zdouble.cpp
 zdouble: Example and Test
cppad-20170000.3/doc/_index.xml0000644000175200017650000571300313057470513015175 0ustar coincoin-web Keyword Index
Prev Next _index

Keyword Index
!= AD Binary Comparison Operators
   AD Binary Comparison Operators: Example and Test
(checkpointing): Reverse Mode General Case (Checkpointing): Example and Test
(double CppAD Speed: Matrix Multiplication (Double Version)
* AD Binary Arithmetic Operators
  AD Computed Assignment Operators
  AD Binary Multiplication: Example and Test
*= AD Computed Assignment Multiplication: Example and Test
+ AD Computed Assignment Operators
  AD Binary Addition: Example and Test
  AD Unary Plus Operator
  AD Binary Arithmetic Operators
+= AD Computed Assignment Addition: Example and Test
- AD Computed Assignment Operators
  AD Binary Subtraction: Example and Test
  AD Binary Arithmetic Operators
  AD Unary Minus Operator
--with-deprecated Auto Tools Unix Test and Installation: --with-deprecated
--with-documentation Auto Tools Unix Test and Installation: --with-Documentation
--with-testvector Auto Tools Unix Test and Installation: --with-testvector
-= AD Computed Assignment Subtraction: Example and Test
/ AD Computed Assignment Operators
  AD Binary Division: Example and Test
  AD Binary Arithmetic Operators
/= AD Computed Assignment Division: Example and Test
0 Evaluate a Function Defined in Terms of an ODE: p.p == 0
  AD Theory for Cholesky Factorization: Reverse Mode.Case k > 0
  AD Theory for Cholesky Factorization: Reverse Mode.Case k = 0
01-02 Changes and Additions to CppAD During 2006: 01-02
      CppAD Changes and Additions During 2012: 01-02
      CppAD Changes and Additions During 2015: 01-02
01-04 Changes and Additions to CppAD During 2010: 01-04
01-05 Changes and Additions to CppAD During 2006: 01-05
01-06 Changes and Additions to CppAD During 2009: 01-06
01-07 Changes and Additions to CppAD During 2006: 01-07
      CppAD Changes and Additions During 2012: 01-07
      CppAD Changes and Additions During 2015: 01-07
01-08 Changes and Additions to CppAD During 2005: 01-08
      Changes and Additions to CppAD During 2006: 01-08
      Changes and Additions to CppAD During 2008: 01-08
01-09 Changes and Additions to CppAD During 2011: 01-09
      CppAD Changes and Additions During 2015: 01-09
01-10 CppAD Changes and Additions During 2014: 01-10
01-11 Changes and Additions to CppAD During 2008: 01-11
01-12 CppAD Changes and Additions During 2012: 01-12
01-15 CppAD Changes and Additions During 2012: 01-15
01-16 Changes and Additions to CppAD During 2011: 01-16
      CppAD Changes and Additions During 2012: 01-16
01-18 Changes and Additions to CppAD During 2006: 01-18
      Changes and Additions to CppAD During 2009: 01-18
      Changes and Additions to CppAD During 2010: 01-18
      Changes and Additions to CppAD During 2016: 01-18
01-19 Changes and Additions to CppAD During 2011: 01-19
      CppAD Changes and Additions During 2012: 01-19
01-20 Changes and Additions to CppAD During 2006: 01-20
      Changes and Additions to CppAD During 2008: 01-20
      Changes and Additions to CppAD During 2010: 01-20
      CppAD Changes and Additions During 2012: 01-20
      CppAD Changes and Additions During 2015: 01-20
      Changes and Additions to CppAD During 2016: 01-20
01-21 Changes and Additions to CppAD During 2008: 01-21
      CppAD Changes and Additions During 2014: 01-21
      CppAD Changes and Additions During 2015: 01-21
      Changes and Additions to CppAD During 2016: 01-21
01-22 Changes and Additions to CppAD During 2004: 01-22
01-23 Changes and Additions to CppAD During 2010: 01-23
      CppAD Changes and Additions During 2012: 01-23
      CppAD Changes and Additions During 2015: 01-23
01-24 Changes and Additions to CppAD During 2008: 01-24
      Changes and Additions to CppAD During 2010: 01-24
      CppAD Changes and Additions During 2012: 01-24
01-26 Changes and Additions to CppAD During 2008: 01-26
      Changes and Additions to CppAD During 2010: 01-26
      CppAD Changes and Additions During 2014: 01-26
      CppAD Changes and Additions During 2015: 01-26
01-27 CppAD Changes and Additions During 2012: 01-27
01-28 Changes and Additions to CppAD During 2004: 01-28
01-29 Changes and Additions to CppAD During 2004: 01-29
      Changes and Additions to CppAD During 2007: 01-29
      CppAD Changes and Additions During 2015: 01-29
01-30 CppAD Changes and Additions During 2012: 01-30
      CppAD Changes and Additions During 2015: 01-30
01-31 Changes and Additions to CppAD During 2009: 01-31
02-01 Changes and Additions to CppAD During 2004: 02-01
      Changes and Additions to CppAD During 2007: 02-01
      Changes and Additions to CppAD During 2009: 02-01
      Changes and Additions to CppAD During 2011: 02-01
02-02 Changes and Additions to CppAD During 2007: 02-02
      Changes and Additions to CppAD During 2011: 02-02
      CppAD Changes and Additions During 2015: 02-02
02-03 Changes and Additions to CppAD During 2007: 02-03
      Changes and Additions to CppAD During 2008: 02-03
      Changes and Additions to CppAD During 2010: 02-03
      CppAD Changes and Additions During 2015: 02-03
02-04 Changes and Additions to CppAD During 2006: 02-04
      Changes and Additions to CppAD During 2007: 02-04
      CppAD Changes and Additions During 2015: 02-04
02-05 Changes and Additions to CppAD During 2008: 02-05
      Changes and Additions to CppAD During 2010: 02-05
02-06 Changes and Additions to CppAD During 2007: 02-06
      Changes and Additions to CppAD During 2010: 02-06
      Changes and Additions to CppAD During 2011: 02-06
      CppAD Changes and Additions During 2015: 02-06
02-07 CppAD Changes and Additions During 2015: 02-07
02-08 Changes and Additions to CppAD During 2010: 02-08
02-09 Changes and Additions to CppAD During 2011: 02-09
      CppAD Changes and Additions During 2012: 02-09
      CppAD Changes and Additions During 2015: 02-09
02-10 Changes and Additions to CppAD During 2006: 02-10
      CppAD Changes and Additions During 2012: 02-10
      CppAD Changes and Additions During 2015: 02-10
02-11 Changes and Additions to CppAD During 2006: 02-11
      Changes and Additions to CppAD During 2010: 02-11
      CppAD Changes and Additions During 2012: 02-11
      CppAD Changes and Additions During 2015: 02-11
02-12 Changes and Additions to CppAD During 2004: 02-12
02-13 Changes and Additions to CppAD During 2006: 02-13
02-14 Changes and Additions to CppAD During 2006: 02-14
      CppAD Changes and Additions During 2015: 02-14
02-15 Changes and Additions to CppAD During 2004: 02-15
      Changes and Additions to CppAD During 2006: 02-15
      Changes and Additions to CppAD During 2007: 03-09.02-15
      Changes and Additions to CppAD During 2009: 02-15
      Changes and Additions to CppAD During 2011: 02-15
      CppAD Changes and Additions During 2014: 02-15
02-16 Changes and Additions to CppAD During 2004: 02-16
      Changes and Additions to CppAD During 2007: 03-09.02-16
      CppAD Changes and Additions During 2015: 02-16
02-17 Changes and Additions to CppAD During 2004: 02-17
      Changes and Additions to CppAD During 2007: 03-09.02-17
      Changes and Additions to CppAD During 2011: 02-17
      CppAD Changes and Additions During 2014: 02-17
02-18 CppAD Changes and Additions During 2015: 02-18
02-19 Changes and Additions to CppAD During 2011: 02-19
02-20 Changes and Additions to CppAD During 2004: 02-20
      Changes and Additions to CppAD During 2009: 02-20
02-21 Changes and Additions to CppAD During 2004: 02-21
      Changes and Additions to CppAD During 2006: 02-21
02-22 Changes and Additions to CppAD During 2007: 03-09.02-22
      Changes and Additions to CppAD During 2011: 02-22
      CppAD Changes and Additions During 2014: 02-22
02-23 Changes and Additions to CppAD During 2006: 02-23
      CppAD Changes and Additions During 2014: 02-23
      Changes and Additions to CppAD During 2016: 02-23
02-24 Changes and Additions to CppAD During 2005: 02-24
      Changes and Additions to CppAD During 2006: 02-24
02-25 Changes and Additions to CppAD During 2006: 02-25
      Changes and Additions to CppAD During 2016: 02-25
02-26 CppAD Changes and Additions During 2014: 02-26
      Changes and Additions to CppAD During 2016: 02-26
02-27 Changes and Additions to CppAD During 2007: 03-09.02-27
      CppAD Changes and Additions During 2014: 02-27
      Changes and Additions to CppAD During 2016: 02-27
02-28 Changes and Additions to CppAD During 2004: 02-28
      Changes and Additions to CppAD During 2006: 02-28
      CppAD Changes and Additions During 2014: 02-28
      CppAD Changes and Additions During 2015: 02-28
      Changes and Additions to CppAD During 2016: 02-28
02-29 Changes and Additions to CppAD During 2004: 02-29
      Changes and Additions to CppAD During 2016: 02-29
03-01 Changes and Additions to CppAD During 2004: 03-01
      Changes and Additions to CppAD During 2005: 03-01
      CppAD Changes and Additions During 2014: 03-01
      Changes and Additions to CppAD During 2016: 03-01
03-02 CppAD Changes and Additions During 2012: 03-02
      CppAD Changes and Additions During 2014: 03-02
03-03 Changes and Additions to CppAD During 2004: 03-03
      Changes and Additions to CppAD During 2010: 03-03
      CppAD Changes and Additions During 2012: 03-03
03-04 Changes and Additions to CppAD During 2004: 03-04
      Changes and Additions to CppAD During 2005: 03-04
03-05 Changes and Additions to CppAD During 2004: 03-05
      Changes and Additions to CppAD During 2006: 03-05
      Changes and Additions to CppAD During 2011: 03-05
      CppAD Changes and Additions During 2014: 03-05
      Changes and Additions to CppAD During 2016: 03-05
03-06 Changes and Additions to CppAD During 2004: 03-06
      CppAD Changes and Additions During 2015: 03-06
03-07 Changes and Additions to CppAD During 2004: 03-07
      Changes and Additions to CppAD During 2006: 03-07
03-09 Changes and Additions to CppAD During 2004: 03-09
      Changes and Additions to CppAD During 2005: 03-09
      Changes and Additions to CppAD During 2006: 03-09
      Changes and Additions to CppAD During 2007: 03-09
      Changes and Additions to CppAD During 2010: 03-09
      CppAD Changes and Additions During 2014: 03-09
03-10 Changes and Additions to CppAD During 2006: 03-10
      Changes and Additions to CppAD During 2010: 03-10
03-11 Changes and Additions to CppAD During 2004: 03-11
      Changes and Additions to CppAD During 2006: 03-11
      Changes and Additions to CppAD During 2010: 03-11
      Changes and Additions to CppAD During 2011: 03-11
      CppAD Changes and Additions During 2012: 03-11
03-12 Changes and Additions to CppAD During 2004: 03-12
      Changes and Additions to CppAD During 2016: 03-12
03-13 Changes and Additions to CppAD During 2007: 03-15.03-13
      CppAD Changes and Additions During 2015: 03-13
03-14 Changes and Additions to CppAD During 2007: 03-15.03-14
03-15 Changes and Additions to CppAD During 2004: 03-15
      Changes and Additions to CppAD During 2006: 03-15
      Changes and Additions to CppAD During 2007: 03-15.03-15
      Changes and Additions to CppAD During 2007: 03-15
03-16 Changes and Additions to CppAD During 2006: 03-16
03-17 Changes and Additions to CppAD During 2004: 03-17
      Changes and Additions to CppAD During 2006: 03-17
      CppAD Changes and Additions During 2012: 03-17
      CppAD Changes and Additions During 2014: 03-17
      Changes and Additions to CppAD During 2016: 03-17
03-18 Changes and Additions to CppAD During 2004: 03-18
      Changes and Additions to CppAD During 2006: 03-18
      CppAD Changes and Additions During 2014: 03-18
03-19 Changes and Additions to CppAD During 2011: 03-19
      Changes and Additions to CppAD During 2016: 03-19
03-20 Changes and Additions to CppAD During 2007: 03-20
      Changes and Additions to CppAD During 2016: 03-20
03-21 CppAD Changes and Additions During 2012: 03-21
      Changes and Additions to CppAD During 2016: 03-21
03-22 Changes and Additions to CppAD During 2005: 03-22
      Changes and Additions to CppAD During 2006: 03-22
      Changes and Additions to CppAD During 2016: 03-22
03-23 Changes and Additions to CppAD During 2005: 03-23
      Changes and Additions to CppAD During 2006: 03-23
      CppAD Changes and Additions During 2012: 03-23
      Changes and Additions to CppAD During 2016: 03-23
03-24 Changes and Additions to CppAD During 2006: 03-24
      Changes and Additions to CppAD During 2009: 03-24
      Changes and Additions to CppAD During 2016: 03-24
03-25 Changes and Additions to CppAD During 2004: 03-25
      Changes and Additions to CppAD During 2016: 03-25
03-26 Changes and Additions to CppAD During 2005: 03-26
      Changes and Additions to CppAD During 2006: 03-26
      CppAD Changes and Additions During 2012: 03-26
      Changes and Additions to CppAD During 2016: 03-26
03-27 Changes and Additions to CppAD During 2006: 03-27
      Changes and Additions to CppAD During 2008: 03-27
      CppAD Changes and Additions During 2012: 03-27
      Changes and Additions to CppAD During 2016: 03-27
03-28 Changes and Additions to CppAD During 2004: 03-28
      Changes and Additions to CppAD During 2006: 03-28
      Changes and Additions to CppAD During 2007: 03-09.03-28
03-29 Changes and Additions to CppAD During 2006: 03-29
      Changes and Additions to CppAD During 2007: 03-29
03-30 Changes and Additions to CppAD During 2004: 03-30
      Changes and Additions to CppAD During 2006: 03-30
      Changes and Additions to CppAD During 2007: 03-31.03-30
03-31 Changes and Additions to CppAD During 2006: 03-31
      Changes and Additions to CppAD During 2007: 03-31.03-31
      Changes and Additions to CppAD During 2007: 03-31
04-01 Changes and Additions to CppAD During 2004: 04-01
      Changes and Additions to CppAD During 2006: 04-01
      Changes and Additions to CppAD During 2010: 04-01
      CppAD Changes and Additions During 2012: 04-01
04-02 Changes and Additions to CppAD During 2004: 04-02
      Changes and Additions to CppAD During 2006: 04-02
04-03 Changes and Additions to CppAD During 2004: 04-03
      Changes and Additions to CppAD During 2006: 04-03
04-04 Changes and Additions to CppAD During 2006: 04-04
      Changes and Additions to CppAD During 2008: 04-04
04-05 Changes and Additions to CppAD During 2006: 04-05
      Changes and Additions to CppAD During 2007: 04-11.04-05
      CppAD Changes and Additions During 2012: 04-05
04-06 Changes and Additions to CppAD During 2006: 04-06
      Changes and Additions to CppAD During 2007: 04-11.04-06
      Changes and Additions to CppAD During 2008: 04-06
      CppAD Changes and Additions During 2012: 04-06
04-07 Changes and Additions to CppAD During 2004: 04-07
      Changes and Additions to CppAD During 2007: 04-11.04-07
04-08 Changes and Additions to CppAD During 2004: 04-08
      Changes and Additions to CppAD During 2006: 04-08
04-09 Changes and Additions to CppAD During 2004: 04-09
04-10 Changes and Additions to CppAD During 2007: 04-11.04-10
      Changes and Additions to CppAD During 2008: 04-10
      CppAD Changes and Additions During 2012: 04-10
04-11 Changes and Additions to CppAD During 2007: 04-11.04-11
      Changes and Additions to CppAD During 2007: 04-11
04-13 Changes and Additions to CppAD During 2006: 04-13
04-14 Changes and Additions to CppAD During 2006: 04-14
      Changes and Additions to CppAD During 2007: 04-14
04-15 Changes and Additions to CppAD During 2006: 04-15
04-17 Changes and Additions to CppAD During 2006: 04-17
      Changes and Additions to CppAD During 2007: 04-17
      CppAD Changes and Additions During 2012: 04-17
      Changes and Additions to CppAD During 2016: 04-17
04-18 Changes and Additions to CppAD During 2006: 04-18
      Changes and Additions to CppAD During 2008: 04-18
      CppAD Changes and Additions During 2012: 04-18
      CppAD Changes and Additions During 2015: 04-18
04-19 Changes and Additions to CppAD During 2004: 04-19
      Changes and Additions to CppAD During 2005: 04-19
      Changes and Additions to CppAD During 2006: 04-19
      Changes and Additions to CppAD During 2007: 04-19
      Changes and Additions to CppAD During 2011: 04-19
      CppAD Changes and Additions During 2012: 04-19
04-20 Changes and Additions to CppAD During 2004: 04-20
      Changes and Additions to CppAD During 2005: 04-20
      Changes and Additions to CppAD During 2008: 04-20
      Changes and Additions to CppAD During 2011: 04-20
04-21 Changes and Additions to CppAD During 2004: 04-21
      Changes and Additions to CppAD During 2005: 04-21
04-22 Changes and Additions to CppAD During 2004: 04-22
04-24 Changes and Additions to CppAD During 2004: 04-24
      Changes and Additions to CppAD During 2010: 04-24
04-25 Changes and Additions to CppAD During 2004: 04-25
      Changes and Additions to CppAD During 2006: 04-25
04-26 Changes and Additions to CppAD During 2006: 04-26
      Changes and Additions to CppAD During 2010: 04-26
      CppAD Changes and Additions During 2013: 04-26
04-27 CppAD Changes and Additions During 2013: 04-27
04-28 Changes and Additions to CppAD During 2004: 04-28
      Changes and Additions to CppAD During 2006: 04-28
      Changes and Additions to CppAD During 2010: 04-28
      CppAD Changes and Additions During 2013: 04-28
04-29 Changes and Additions to CppAD During 2004: 04-29
      Changes and Additions to CppAD During 2006: 04-29
      Changes and Additions to CppAD During 2011: 04-29
05-01 Changes and Additions to CppAD During 2005: 05-01
05-03 Changes and Additions to CppAD During 2004: 05-03
      Changes and Additions to CppAD During 2006: 05-03
      Changes and Additions to CppAD During 2008: 05-03
      Changes and Additions to CppAD During 2011: 05-03
05-04 Changes and Additions to CppAD During 2004: 05-04
      CppAD Changes and Additions During 2013: 05-04
05-05 Changes and Additions to CppAD During 2007: 05-05
      CppAD Changes and Additions During 2015: 05-05
      Changes and Additions to CppAD During 2016: 05-05
05-06 Changes and Additions to CppAD During 2005: 05-06
05-07 Changes and Additions to CppAD During 2004: 05-07
      CppAD Changes and Additions During 2015: 05-07
05-08 Changes and Additions to CppAD During 2007: 05-08
      Changes and Additions to CppAD During 2008: 05-08
      CppAD Changes and Additions During 2015: 05-08
05-09 Changes and Additions to CppAD During 2004: 05-09
      CppAD Changes and Additions During 2015: 05-09
05-10 CppAD Changes and Additions During 2015: 05-10
05-11 Changes and Additions to CppAD During 2011: 05-11
      CppAD Changes and Additions During 2013: 05-11
      CppAD Changes and Additions During 2015: 05-11
05-12 Changes and Additions to CppAD During 2004: 05-12
      Changes and Additions to CppAD During 2005: 05-12
      CppAD Changes and Additions During 2013: 05-12
05-14 Changes and Additions to CppAD During 2004: 05-14
      CppAD Changes and Additions During 2013: 05-14
      CppAD Changes and Additions During 2014: 05-14
05-15 CppAD Changes and Additions During 2013: 05-15
05-16 Changes and Additions to CppAD During 2005: 05-16
      CppAD Changes and Additions During 2014: 05-16
05-17 CppAD Changes and Additions During 2013: 05-17
05-18 Changes and Additions to CppAD During 2005: 05-18
05-19 Changes and Additions to CppAD During 2005: 05-19
      CppAD Changes and Additions During 2014: 05-19
05-20 Changes and Additions to CppAD During 2009: 05-20
      CppAD Changes and Additions During 2014: 05-20
05-21 CppAD Changes and Additions During 2013: 05-21
05-22 Changes and Additions to CppAD During 2007: 05-22
      Changes and Additions to CppAD During 2011: 05-22
      CppAD Changes and Additions During 2014: 05-22
05-23 CppAD Changes and Additions During 2014: 05-23
05-24 Changes and Additions to CppAD During 2007: 05-24
      CppAD Changes and Additions During 2012: 05-24
05-25 Changes and Additions to CppAD During 2004: 05-25
      Changes and Additions to CppAD During 2007: 05-25
05-26 Changes and Additions to CppAD During 2004: 05-26
      Changes and Additions to CppAD During 2007: 05-26
      Changes and Additions to CppAD During 2011: 05-26
      CppAD Changes and Additions During 2015: 05-26
05-27 Changes and Additions to CppAD During 2006: 05-27
      CppAD Changes and Additions During 2012: 05-27
      CppAD Changes and Additions During 2014: 05-27
05-28 Changes and Additions to CppAD During 2011: 05-28
      CppAD Changes and Additions During 2013: 05-28
      CppAD Changes and Additions During 2014: 05-28
05-29 Changes and Additions to CppAD During 2004: 05-29
      Changes and Additions to CppAD During 2006: 05-29
      Changes and Additions to CppAD During 2011: 05-29
      CppAD Changes and Additions During 2012: 05-29
05-30 Changes and Additions to CppAD During 2004: 05-30
      CppAD Changes and Additions During 2012: 05-30
05-31 Changes and Additions to CppAD During 2006: 05-31
      CppAD Changes and Additions During 2012: 05-31
06-01 Changes and Additions to CppAD During 2004: 06-01
      Changes and Additions to CppAD During 2010: 06-01
      CppAD Changes and Additions During 2012: 06-01
06-02 Changes and Additions to CppAD During 2006: 06-02
      CppAD Changes and Additions During 2012: 06-02
06-03 Changes and Additions to CppAD During 2004: 06-03
      CppAD Changes and Additions During 2012: 06-03
06-04 Changes and Additions to CppAD During 2004: 06-04
      CppAD Changes and Additions During 2012: 06-04
06-05 Changes and Additions to CppAD During 2006: 06-05
      CppAD Changes and Additions During 2012: 06-05
06-06 Changes and Additions to CppAD During 2005: 06-06
      Changes and Additions to CppAD During 2009: 06-06
06-07 Changes and Additions to CppAD During 2006: 06-07
      CppAD Changes and Additions During 2012: 06-07
      CppAD Changes and Additions During 2015: 06-07
06-08 CppAD Changes and Additions During 2012: 06-08
06-09 Changes and Additions to CppAD During 2006: 06-09
      CppAD Changes and Additions During 2012: 06-09
      CppAD Changes and Additions During 2015: 06-09
06-10 Changes and Additions to CppAD During 2008: 06-10
      CppAD Changes and Additions During 2012: 06-10
      Changes and Additions to CppAD During 2016: 06-10
06-11 Changes and Additions to CppAD During 2008: 06-11
      CppAD Changes and Additions During 2015: 06-11
06-12 Changes and Additions to CppAD During 2004: 06-12
      CppAD Changes and Additions During 2012: 06-12
06-13 Changes and Additions to CppAD During 2005: 06-13
06-14 Changes and Additions to CppAD During 2005: 06-14
      Changes and Additions to CppAD During 2007: 06-14
06-15 Changes and Additions to CppAD During 2006: 06-15
      Changes and Additions to CppAD During 2008: 06-15
      CppAD Changes and Additions During 2012: 06-15
06-16 CppAD Changes and Additions During 2012: 06-16
      CppAD Changes and Additions During 2015: 06-16
06-17 Changes and Additions to CppAD During 2006: 06-17
      Changes and Additions to CppAD During 2006: 06-19.06-17
      CppAD Changes and Additions During 2012: 06-17
06-18 Changes and Additions to CppAD During 2005: 06-18
      Changes and Additions to CppAD During 2006: 06-19.06-18
      Changes and Additions to CppAD During 2008: 06-18
      Changes and Additions to CppAD During 2011: 06-18
06-19 Changes and Additions to CppAD During 2006: 06-19
06-20 Changes and Additions to CppAD During 2007: 06-20
      Changes and Additions to CppAD During 2009: 06-20
06-21 Changes and Additions to CppAD During 2009: 06-21
      Changes and Additions to CppAD During 2011: 06-21
06-22 Changes and Additions to CppAD During 2006: 06-22
      Changes and Additions to CppAD During 2007: 06-22
      Changes and Additions to CppAD During 2009: 06-22
06-23 Changes and Additions to CppAD During 2011: 06-23
06-24 Changes and Additions to CppAD During 2005: 06-24
06-25 Changes and Additions to CppAD During 2004: 06-25
      Changes and Additions to CppAD During 2005: 06-25
      Changes and Additions to CppAD During 2009: 06-25
      Changes and Additions to CppAD During 2016: 06-25
06-27 Changes and Additions to CppAD During 2016: 06-27
06-28 Changes and Additions to CppAD During 2009: 07-04.06-28
06-29 Changes and Additions to CppAD During 2004: 06-29
      Changes and Additions to CppAD During 2006: 06-29
      Changes and Additions to CppAD During 2009: 07-04.06-29
      Changes and Additions to CppAD During 2016: 06-29
06-30 Changes and Additions to CppAD During 2009: 07-04.06-30
      Changes and Additions to CppAD During 2016: 06-30
07-01 Changes and Additions to CppAD During 2005: 07-01
      Changes and Additions to CppAD During 2009: 07-04.07-01
      CppAD Changes and Additions During 2012: 07-01
07-02 Changes and Additions to CppAD During 2004: 07-02
      Changes and Additions to CppAD During 2005: 07-02
      Changes and Additions to CppAD During 2008: 07-02
      Changes and Additions to CppAD During 2009: 07-04.07-02
      CppAD Changes and Additions During 2012: 07-02
07-03 Changes and Additions to CppAD During 2004: 07-03
      Changes and Additions to CppAD During 2005: 07-03
      Changes and Additions to CppAD During 2009: 07-04.07-03
      CppAD Changes and Additions During 2012: 07-03
07-04 Changes and Additions to CppAD During 2005: 07-04
      Changes and Additions to CppAD During 2009: 07-04.07-04
      Changes and Additions to CppAD During 2009: 07-04
      CppAD Changes and Additions During 2012: 07-04
07-05 Changes and Additions to CppAD During 2005: 07-05
      CppAD Changes and Additions During 2012: 07-05
07-06 Changes and Additions to CppAD During 2009: 07-23.07-06
07-07 Changes and Additions to CppAD During 2004: 07-07
      Changes and Additions to CppAD During 2011: 07-07
      CppAD Changes and Additions During 2012: 07-07
07-08 Changes and Additions to CppAD During 2004: 07-08
      Changes and Additions to CppAD During 2005: 07-08
      CppAD Changes and Additions During 2012: 07-08
07-09 Changes and Additions to CppAD During 2011: 07-09
07-10 Changes and Additions to CppAD During 2011: 07-10
07-11 Changes and Additions to CppAD During 2005: 07-11
      Changes and Additions to CppAD During 2010: 07-11
      Changes and Additions to CppAD During 2011: 07-11
07-12 Changes and Additions to CppAD During 2006: 07-12
07-13 Changes and Additions to CppAD During 2007: 07-13
      Changes and Additions to CppAD During 2011: 07-13
07-14 Changes and Additions to CppAD During 2003: 07-14
      Changes and Additions to CppAD During 2006: 07-14
      Changes and Additions to CppAD During 2007: 07-14
      Changes and Additions to CppAD During 2010: 07-14
      Changes and Additions to CppAD During 2011: 07-14
      Changes and Additions to CppAD During 2016: 07-14
07-15 Changes and Additions to CppAD During 2005: 07-15
07-16 Changes and Additions to CppAD During 2003: 07-16
07-17 Changes and Additions to CppAD During 2011: 07-17
      Changes and Additions to CppAD During 2016: 07-17
07-18 Changes and Additions to CppAD During 2003: 07-18
      Changes and Additions to CppAD During 2007: 07-18
      Changes and Additions to CppAD During 2011: 07-18
07-19 Changes and Additions to CppAD During 2005: 07-19
      Changes and Additions to CppAD During 2007: 07-19
07-20 Changes and Additions to CppAD During 2003: 07-20
      Changes and Additions to CppAD During 2007: 07-20
07-21 Changes and Additions to CppAD During 2005: 07-21
      Changes and Additions to CppAD During 2007: 07-21
07-22 Changes and Additions to CppAD During 2003: 07-22
      Changes and Additions to CppAD During 2007: 07-22
07-23 Changes and Additions to CppAD During 2007: 07-23
      Changes and Additions to CppAD During 2009: 07-23
07-24 Changes and Additions to CppAD During 2009: 07-24
07-25 Changes and Additions to CppAD During 2007: 07-26.07-25
      Changes and Additions to CppAD During 2009: 07-25
      Changes and Additions to CppAD During 2011: 07-25
07-26 Changes and Additions to CppAD During 2003: 07-26
      Changes and Additions to CppAD During 2007: 07-26.07-26
      Changes and Additions to CppAD During 2007: 07-26
      Changes and Additions to CppAD During 2009: 07-26
      CppAD Changes and Additions During 2013: 07-26
07-27 Changes and Additions to CppAD During 2011: 07-27
07-28 Changes and Additions to CppAD During 2007: 07-28
      Changes and Additions to CppAD During 2011: 07-28
07-29 Changes and Additions to CppAD During 2003: 07-29
      Changes and Additions to CppAD During 2007: 07-29
      Changes and Additions to CppAD During 2011: 07-29
07-30 Changes and Additions to CppAD During 2003: 07-30
      Changes and Additions to CppAD During 2007: 07-30
      CppAD Changes and Additions During 2012: 07-30
07-31 Changes and Additions to CppAD During 2004: 07-31
      Changes and Additions to CppAD During 2009: 07-31
      Changes and Additions to CppAD During 2011: 07-31
      CppAD Changes and Additions During 2015: 07-31
08-01 Changes and Additions to CppAD During 2003: 08-01
      Changes and Additions to CppAD During 2009: 08-01
08-02 Changes and Additions to CppAD During 2009: 08-02
      Changes and Additions to CppAD During 2011: 08-02
08-03 Changes and Additions to CppAD During 2003: 08-03
      Changes and Additions to CppAD During 2011: 08-03
08-04 Changes and Additions to CppAD During 2003: 08-04
      Changes and Additions to CppAD During 2011: 08-11.08-04
08-05 Changes and Additions to CppAD During 2003: 08-05
      CppAD Changes and Additions During 2012: 08-05
08-06 Changes and Additions to CppAD During 2003: 08-06
      Changes and Additions to CppAD During 2009: 08-06
      Changes and Additions to CppAD During 2011: 08-11.08-06
      CppAD Changes and Additions During 2013: 08-06
      CppAD Changes and Additions During 2015: 08-06
08-07 Changes and Additions to CppAD During 2003: 08-07
      Changes and Additions to CppAD During 2005: 08-07
      Changes and Additions to CppAD During 2007: 08-07
      Changes and Additions to CppAD During 2011: 08-11.08-07
08-08 Changes and Additions to CppAD During 2008: 08-08
      Changes and Additions to CppAD During 2011: 08-11.08-08
08-09 Changes and Additions to CppAD During 2007: 08-09
      Changes and Additions to CppAD During 2009: 08_13.08-09
      Changes and Additions to CppAD During 2011: 08-11.08-09
      CppAD Changes and Additions During 2015: 08-09
08-10 Changes and Additions to CppAD During 2003: 08-10
      Changes and Additions to CppAD During 2009: 08_13.08-10
      Changes and Additions to CppAD During 2011: 08-11.08-10
08-11 Changes and Additions to CppAD During 2003: 08-11
      Changes and Additions to CppAD During 2009: 08_13.08-11
      Changes and Additions to CppAD During 2011: 08-11
      CppAD Changes and Additions During 2013: 08-11
08-12 Changes and Additions to CppAD During 2004: 08-12
      CppAD Changes and Additions During 2013: 08-12
08-13 Changes and Additions to CppAD During 2005: 08-13
      Changes and Additions to CppAD During 2009: 08_13.08-13
08-14 Changes and Additions to CppAD During 2005: 08-14
      Changes and Additions to CppAD During 2009: 08-14
08-15 Changes and Additions to CppAD During 2005: 08-15
08-16 Changes and Additions to CppAD During 2003: 08-16
      CppAD Changes and Additions During 2015: 08-16
08-17 Changes and Additions to CppAD During 2003: 08-17
      Changes and Additions to CppAD During 2006: 08-17
      CppAD Changes and Additions During 2015: 08-17
08-19 Changes and Additions to CppAD During 2003: 08-19
      Changes and Additions to CppAD During 2005: 08-19
      Changes and Additions to CppAD During 2008: 08-19
08-20 Changes and Additions to CppAD During 2005: 08-20
      CppAD Changes and Additions During 2015: 08-20
08-21 Changes and Additions to CppAD During 2010: 08-21
      Changes and Additions to CppAD During 2011: 09-01.08-21
08-22 Changes and Additions to CppAD During 2003: 08-22
08-23 Changes and Additions to CppAD During 2003: 08-23
      Changes and Additions to CppAD During 2011: 09-01.08-23
08-24 Changes and Additions to CppAD During 2004: 08-24
      Changes and Additions to CppAD During 2005: 08-24
08-25 Changes and Additions to CppAD During 2004: 08-25
      Changes and Additions to CppAD During 2009: 08-25
      Changes and Additions to CppAD During 2011: 09-01.08-25
      CppAD Changes and Additions During 2015: 08-25
      Changes and Additions to CppAD During 2016: 08-25
08-26 CppAD Changes and Additions During 2015: 08-26
08-27 Changes and Additions to CppAD During 2004: 08-27
08-28 CppAD Changes and Additions During 2015: 08-28
08-29 Changes and Additions to CppAD During 2008: 08-29
      CppAD Changes and Additions During 2015: 08-29
08-30 Changes and Additions to CppAD During 2005: 08-30
      Changes and Additions to CppAD During 2011: 09-01.08-30
      CppAD Changes and Additions During 2015: 08-30
      Changes and Additions to CppAD During 2016: 08-30
08-31 Changes and Additions to CppAD During 2011: 09-01.08-31
      CppAD Changes and Additions During 2015: 08-31
08_13 Changes and Additions to CppAD During 2009: 08_13
09-01 Changes and Additions to CppAD During 2008: 09-01
      Changes and Additions to CppAD During 2011: 09-01
09-02 Changes and Additions to CppAD During 2004: 09-02
      Changes and Additions to CppAD During 2011: 09-02
      CppAD Changes and Additions During 2015: 09-02
09-03 Changes and Additions to CppAD During 2003: 09-03
      Changes and Additions to CppAD During 2008: 09-03
      CppAD Changes and Additions During 2015: 09-03
09-04 Changes and Additions to CppAD During 2003: 09-04
      Changes and Additions to CppAD During 2004: 09-04
      Changes and Additions to CppAD During 2008: 09-04
09-05 Changes and Additions to CppAD During 2003: 09-05
      Changes and Additions to CppAD During 2008: 09-05
      Changes and Additions to CppAD During 2011: 09-05
09-06 Changes and Additions to CppAD During 2003: 09-06
      Changes and Additions to CppAD During 2007: 09-06
      Changes and Additions to CppAD During 2008: 09-06
      Changes and Additions to CppAD During 2011: 09-06
09-07 Changes and Additions to CppAD During 2004: 09-07
      Changes and Additions to CppAD During 2005: 09-07
      Changes and Additions to CppAD During 2008: 09-07
      CppAD Changes and Additions During 2013: 09-07
09-09 Changes and Additions to CppAD During 2004: 09-09
      Changes and Additions to CppAD During 2005: 09-09
      Changes and Additions to CppAD During 2008: 09-09
09-10 Changes and Additions to CppAD During 2004: 09-10
      Changes and Additions to CppAD During 2008: 09-10
09-11 CppAD Changes and Additions During 2012: 09-11
09-12 Changes and Additions to CppAD During 2008: 09-12
09-13 Changes and Additions to CppAD During 2003: 09-13
      Changes and Additions to CppAD During 2004: 09-13
      Changes and Additions to CppAD During 2016: 09-13
09-14 Changes and Additions to CppAD During 2003: 09-14
      Changes and Additions to CppAD During 2005: 09-14
09-15 Changes and Additions to CppAD During 2003: 09-15
09-16 Changes and Additions to CppAD During 2008: 09-16
      CppAD Changes and Additions During 2015: 09-16
      Changes and Additions to CppAD During 2016: 09-16
09-17 Changes and Additions to CppAD During 2008: 09-17
09-18 Changes and Additions to CppAD During 2003: 09-18
      Changes and Additions to CppAD During 2008: 09-18
      Changes and Additions to CppAD During 2009: 09-18
      CppAD Changes and Additions During 2013: 09-18
09-19 Changes and Additions to CppAD During 2003: 09-19
      Changes and Additions to CppAD During 2009: 09-19
      CppAD Changes and Additions During 2013: 09-19
      CppAD Changes and Additions During 2015: 09-19
09-20 Changes and Additions to CppAD During 2003: 09-20
      Changes and Additions to CppAD During 2005: 09-20
      Changes and Additions to CppAD During 2009: 09-20
      CppAD Changes and Additions During 2013: 09-20
      CppAD Changes and Additions During 2015: 09-20
09-21 Changes and Additions to CppAD During 2004: 09-21
      CppAD Changes and Additions During 2014: 09-21
      CppAD Changes and Additions During 2015: 09-21
09-22 Changes and Additions to CppAD During 2010: 09-22
09-23 Changes and Additions to CppAD During 2004: 09-23
      CppAD Changes and Additions During 2015: 09-23
09-24 Changes and Additions to CppAD During 2005: 09-24
      CppAD Changes and Additions During 2012: 09-24
      CppAD Changes and Additions During 2015: 09-24
09-25 CppAD Changes and Additions During 2014: 09-25
      CppAD Changes and Additions During 2015: 09-25
09-26 Changes and Additions to CppAD During 2004: 09-26
      Changes and Additions to CppAD During 2008: 09-26
      Changes and Additions to CppAD During 2009: 09-26
      Changes and Additions to CppAD During 2010: 09-26
      Changes and Additions to CppAD During 2016: 09-26
09-27 Changes and Additions to CppAD During 2005: 09-27
      CppAD Changes and Additions During 2014: 09-27
      CppAD Changes and Additions During 2015: 09-27
      Changes and Additions to CppAD During 2016: 09-27
09-28 Changes and Additions to CppAD During 2009: 09-28
      CppAD Changes and Additions During 2014: 09-28
      CppAD Changes and Additions During 2015: 09-28
09-29 Changes and Additions to CppAD During 2004: 09-29
      Changes and Additions to CppAD During 2005: 09-29
      Changes and Additions to CppAD During 2009: 09-29
      Changes and Additions to CppAD During 2016: 09-29
09-30 Changes and Additions to CppAD During 2003: 09-30
      Changes and Additions to CppAD During 2006: 09-30
      Changes and Additions to CppAD During 2008: 09-30
      Changes and Additions to CppAD During 2009: 09-30
1 Evaluate a Function Defined in Terms of an ODE: p.p = 1
  AD Theory for Cholesky Factorization: Lemma 1
1/i Multi-threading Sum of 1/i Utility Routines
    Timing Test of Multi-Threaded Summation of 1/i
    Multi-Threaded Implementation of Summation of 1/i
10 The Base 10 Logarithm Function: log10
10-02 Changes and Additions to CppAD During 2007: 10-02
      CppAD Changes and Additions During 2012: 10-02
      CppAD Changes and Additions During 2015: 10-02
10-03 Changes and Additions to CppAD During 2009: 10-03
      CppAD Changes and Additions During 2012: 10-03
      CppAD Changes and Additions During 2015: 10-03
10-04 CppAD Changes and Additions During 2012: 10-04
      CppAD Changes and Additions During 2015: 10-04
10-05 Changes and Additions to CppAD During 2003: 10-05
      Changes and Additions to CppAD During 2007: 10-05
10-06 Changes and Additions to CppAD During 2003: 10-06
      Changes and Additions to CppAD During 2004: 10-06
      Changes and Additions to CppAD During 2005: 10-06
      CppAD Changes and Additions During 2015: 10-06
10-10 Changes and Additions to CppAD During 2003: 10-10
      Changes and Additions to CppAD During 2006: 10-10
10-12 Changes and Additions to CppAD During 2005: 10-12
      Changes and Additions to CppAD During 2011: 10-12
      CppAD Changes and Additions During 2012: 10-12
      CppAD Changes and Additions During 2013: 10-12
      Changes and Additions to CppAD During 2016: 10-12
10-13 Changes and Additions to CppAD During 2007: 10-13
      CppAD Changes and Additions During 2013: 10-13
10-14 Changes and Additions to CppAD During 2003: 10-14
      Changes and Additions to CppAD During 2005: 10-14
      Changes and Additions to CppAD During 2009: 10-14
      Changes and Additions to CppAD During 2011: 10-14
      CppAD Changes and Additions During 2013: 10-14
10-15 CppAD Changes and Additions During 2013: 10-15
10-16 Changes and Additions to CppAD During 2003: 10-16
      Changes and Additions to CppAD During 2004: 10-16
      Changes and Additions to CppAD During 2006: 10-16
      Changes and Additions to CppAD During 2007: 10-16
      Changes and Additions to CppAD During 2008: 10-16
      Changes and Additions to CppAD During 2009: 10-16
      CppAD Changes and Additions During 2013: 10-16
      CppAD Changes and Additions During 2015: 10-16
10-17 Changes and Additions to CppAD During 2008: 10-17
10-18 Changes and Additions to CppAD During 2005: 10-18
      Changes and Additions to CppAD During 2006: 10-18
10-19 Changes and Additions to CppAD During 2004: 10-19
10-20 Changes and Additions to CppAD During 2005: 10-20
10-21 Changes and Additions to CppAD During 2003: 10-21
      Changes and Additions to CppAD During 2004: 10-21
      Changes and Additions to CppAD During 2009: 10-21
      CppAD Changes and Additions During 2015: 10-21
10-22 Changes and Additions to CppAD During 2007: 10-22
      CppAD Changes and Additions During 2013: 10-22
10-23 Changes and Additions to CppAD During 2007: 10-23
      Changes and Additions to CppAD During 2009: 10-23
      CppAD Changes and Additions During 2013: 10-23
10-24 Changes and Additions to CppAD During 2009: 10-24
      CppAD Changes and Additions During 2012: 10-24
10-25 Changes and Additions to CppAD During 2006: 10-25
      CppAD Changes and Additions During 2012: 10-25
10-26 Changes and Additions to CppAD During 2006: 10-26
10-27 Changes and Additions to CppAD During 2004: 10-27
      Changes and Additions to CppAD During 2006: 10-27
      Changes and Additions to CppAD During 2007: 10-27
      Changes and Additions to CppAD During 2008: 10-27
      Changes and Additions to CppAD During 2009: 10-27
      Changes and Additions to CppAD During 2016: 10-27
10-28 Changes and Additions to CppAD During 2004: 10-28
      Changes and Additions to CppAD During 2006: 10-28
      Changes and Additions to CppAD During 2009: 10-28
10-29 Changes and Additions to CppAD During 2004: 10-29
      Changes and Additions to CppAD During 2006: 10-29
      Changes and Additions to CppAD During 2009: 10-29
      Changes and Additions to CppAD During 2011: 10-29
      CppAD Changes and Additions During 2013: 10-29
10-30 Changes and Additions to CppAD During 2007: 10-30
      Changes and Additions to CppAD During 2009: 10-30
      Changes and Additions to CppAD During 2011: 10-30
      CppAD Changes and Additions During 2012: 10-30
10-31 Changes and Additions to CppAD During 2006: 10-31
      CppAD Changes and Additions During 2012: 10-31
11-01 Changes and Additions to CppAD During 2004: 11-01
      Changes and Additions to CppAD During 2005: 11-01
      Changes and Additions to CppAD During 2006: 11-01
      Changes and Additions to CppAD During 2007: 11-01
      Changes and Additions to CppAD During 2011: 11-01
11-02 Changes and Additions to CppAD During 2003: 11-02
      Changes and Additions to CppAD During 2004: 11-02
      Changes and Additions to CppAD During 2006: 11-02
      Changes and Additions to CppAD During 2007: 11-02
11-03 Changes and Additions to CppAD During 2007: 11-03
11-04 Changes and Additions to CppAD During 2003: 11-04
      Changes and Additions to CppAD During 2004: 11-04
      Changes and Additions to CppAD During 2006: 11-04
      Changes and Additions to CppAD During 2007: 11-04
      Changes and Additions to CppAD During 2011: 11-04
      CppAD Changes and Additions During 2012: 11-04
11-05 Changes and Additions to CppAD During 2006: 11-05
      Changes and Additions to CppAD During 2007: 11-05
11-06 Changes and Additions to CppAD During 2003: 11-06
      Changes and Additions to CppAD During 2005: 11-06
      Changes and Additions to CppAD During 2006: 11-06
      Changes and Additions to CppAD During 2007: 11-06
      Changes and Additions to CppAD During 2011: 11-06
      CppAD Changes and Additions During 2012: 11-06
      CppAD Changes and Additions During 2015: 11-06
11-07 Changes and Additions to CppAD During 2005: 11-07
      Changes and Additions to CppAD During 2011: 11-07
11-08 Changes and Additions to CppAD During 2006: 11-08
      CppAD Changes and Additions During 2015: 11-08
11-09 Changes and Additions to CppAD During 2005: 11-09
      Changes and Additions to CppAD During 2011: 11-09
      CppAD Changes and Additions During 2012: 11-09
11-10 Changes and Additions to CppAD During 2004: 11-10
11-11 Changes and Additions to CppAD During 2003: 11-11
11-12 Changes and Additions to CppAD During 2003: 11-12
      Changes and Additions to CppAD During 2004: 11-12
      Changes and Additions to CppAD During 2005: 11-12
      Changes and Additions to CppAD During 2006: 11-12
      CppAD Changes and Additions During 2013: 11-12
11-13 Changes and Additions to CppAD During 2004: 11-13
      CppAD Changes and Additions During 2013: 11-13
      Changes and Additions to CppAD During 2016: 11-13
11-14 Changes and Additions to CppAD During 2003: 11-14
      Changes and Additions to CppAD During 2004: 11-14
      CppAD Changes and Additions During 2012: 11-14
      CppAD Changes and Additions During 2015: 11-14
      Changes and Additions to CppAD During 2016: 11-14
11-15 Changes and Additions to CppAD During 2003: 11-15
      Changes and Additions to CppAD During 2004: 11-15
      Changes and Additions to CppAD During 2005: 11-15
11-16 Changes and Additions to CppAD During 2003: 11-16
      Changes and Additions to CppAD During 2004: 11-16
      CppAD Changes and Additions During 2012: 11-16
11-17 Changes and Additions to CppAD During 2004: 11-17
      Changes and Additions to CppAD During 2011: 11-17
      CppAD Changes and Additions During 2012: 11-17
11-18 Changes and Additions to CppAD During 2006: 11-18
      Changes and Additions to CppAD During 2007: 11-18
      Changes and Additions to CppAD During 2011: 11-18
      Changes and Additions to CppAD During 2016: 11-18
11-19 Changes and Additions to CppAD During 2005: 11-19
11-20 Changes and Additions to CppAD During 2003: 11-20
      Changes and Additions to CppAD During 2005: 11-20
      Changes and Additions to CppAD During 2008: 11-20
      Changes and Additions to CppAD During 2011: 11-20
      CppAD Changes and Additions During 2012: 11-20
11-21 Changes and Additions to CppAD During 2003: 11-21
      Changes and Additions to CppAD During 2008: 11-21
      Changes and Additions to CppAD During 2011: 11-21
      CppAD Changes and Additions During 2012: 11-21
11-22 Changes and Additions to CppAD During 2005: 11-22
      Changes and Additions to CppAD During 2008: 11-22
11-23 Changes and Additions to CppAD During 2005: 11-23
      Changes and Additions to CppAD During 2006: 11-23
      Changes and Additions to CppAD During 2007: 11-23
11-24 Changes and Additions to CppAD During 2011: 11-24
      CppAD Changes and Additions During 2015: 11-24
11-25 CppAD Changes and Additions During 2015: 11-25
11-26 Changes and Additions to CppAD During 2009: 11-26
11-27 Changes and Additions to CppAD During 2009: 11-27
      Changes and Additions to CppAD During 2010: 11-27
      Changes and Additions to CppAD During 2011: 11-27
      CppAD Changes and Additions During 2013: 11-27
      CppAD Changes and Additions During 2014: 11-27
11-28 Changes and Additions to CppAD During 2006: 11-28
      Changes and Additions to CppAD During 2009: 11-28
      CppAD Changes and Additions During 2012: 11-28
      CppAD Changes and Additions During 2014: 11-28
11-29 Changes and Additions to CppAD During 2006: 11-29
      Changes and Additions to CppAD During 2007: 11-29
      Changes and Additions to CppAD During 2011: 11-29
11-30 Changes and Additions to CppAD During 2006: 11-30
      CppAD Changes and Additions During 2015: 11-30
12-01 Changes and Additions to CppAD During 2003: 12-01
      Changes and Additions to CppAD During 2005: 12-01
      Changes and Additions to CppAD During 2006: 12-01
      CppAD Changes and Additions During 2015: 12-01
12-02 Changes and Additions to CppAD During 2005: 12-02
      Changes and Additions to CppAD During 2006: 12-02
      Changes and Additions to CppAD During 2007: 12-02
      Changes and Additions to CppAD During 2009: 12-02
12-03 Changes and Additions to CppAD During 2004: 12-03
      Changes and Additions to CppAD During 2005: 12-03
      Changes and Additions to CppAD During 2006: 12-03
      Changes and Additions to CppAD During 2007: 12-03
12-04 Changes and Additions to CppAD During 2007: 12-04
      Changes and Additions to CppAD During 2008: 12-04
      Changes and Additions to CppAD During 2009: 12-04
12-05 Changes and Additions to CppAD During 2003: 12-05
      Changes and Additions to CppAD During 2005: 12-05
      Changes and Additions to CppAD During 2006: 12-05
      Changes and Additions to CppAD During 2007: 12-05
12-06 Changes and Additions to CppAD During 2005: 12-06
12-07 Changes and Additions to CppAD During 2005: 12-07
      Changes and Additions to CppAD During 2006: 12-07
12-08 Changes and Additions to CppAD During 2005: 12-08
      Changes and Additions to CppAD During 2007: 12-08
      CppAD Changes and Additions During 2015: 12-08
12-09 Changes and Additions to CppAD During 2004: 12-09
      Changes and Additions to CppAD During 2006: 12-09
      Changes and Additions to CppAD During 2016: 12-09
12-10 Changes and Additions to CppAD During 2003: 12-10
      Changes and Additions to CppAD During 2006: 12-10
12-11 Changes and Additions to CppAD During 2004: 12-11
      Changes and Additions to CppAD During 2005: 12-11
      Changes and Additions to CppAD During 2006: 12-11
      Changes and Additions to CppAD During 2016: 12-11
12-12 Changes and Additions to CppAD During 2003: 12-12
      Changes and Additions to CppAD During 2006: 12-12
      Changes and Additions to CppAD During 2009: 12-12
12-13 Changes and Additions to CppAD During 2003: 12-13
      Changes and Additions to CppAD During 2006: 12-13
      CppAD Changes and Additions During 2012: 12-13
      Changes and Additions to CppAD During 2016: 12-13
12-14 Changes and Additions to CppAD During 2003: 12-14
      Changes and Additions to CppAD During 2005: 12-14
      Changes and Additions to CppAD During 2008: 12-14
      CppAD Changes and Additions During 2012: 12-14
12-15 Changes and Additions to CppAD During 2005: 12-15
      Changes and Additions to CppAD During 2006: 12-15
      CppAD Changes and Additions During 2012: 12-15
      CppAD Changes and Additions During 2014: 12-15
12-16 Changes and Additions to CppAD During 2005: 12-16
      CppAD Changes and Additions During 2014: 12-16
12-17 Changes and Additions to CppAD During 2006: 12-17
      CppAD Changes and Additions During 2012: 12-17
      CppAD Changes and Additions During 2014: 12-17
12-18 Changes and Additions to CppAD During 2006: 12-18
      Changes and Additions to CppAD During 2009: 12-18
      Changes and Additions to CppAD During 2016: 12-18
12-19 Changes and Additions to CppAD During 2005: 12-19
      Changes and Additions to CppAD During 2006: 12-19
      Changes and Additions to CppAD During 2008: 12-19
      CppAD Changes and Additions During 2012: 12-19
12-20 Changes and Additions to CppAD During 2005: 12-20
      Changes and Additions to CppAD During 2011: 12-20
      CppAD Changes and Additions During 2012: 12-20
      Changes and Additions to CppAD During 2016: 12-20
12-21 Changes and Additions to CppAD During 2006: 12-21
      Changes and Additions to CppAD During 2007: 12-21
      Changes and Additions to CppAD During 2011: 12-21
12-22 Changes and Additions to CppAD During 2003: 12-22
      Changes and Additions to CppAD During 2005: 12-22
      Changes and Additions to CppAD During 2006: 12-22
      Changes and Additions to CppAD During 2009: 12-22
      CppAD Changes and Additions During 2012: 12-22
      CppAD Changes and Additions During 2014: 12-22
12-23 Changes and Additions to CppAD During 2005: 12-23
      Changes and Additions to CppAD During 2006: 12-23
      Changes and Additions to CppAD During 2009: 12-23
      CppAD Changes and Additions During 2012: 12-23
      CppAD Changes and Additions During 2014: 12-23
      Changes and Additions to CppAD During 2016: 12-23
12-24 Changes and Additions to CppAD During 2003: 12-24
      Changes and Additions to CppAD During 2005: 12-24
      Changes and Additions to CppAD During 2006: 12-24
      CppAD Changes and Additions During 2013: 12-24
12-25 Changes and Additions to CppAD During 2007: 12-25
      CppAD Changes and Additions During 2014: 12-25
12-26 CppAD Changes and Additions During 2012: 12-26
      CppAD Changes and Additions During 2013: 12-26
      CppAD Changes and Additions During 2014: 12-26
12-27 CppAD Changes and Additions During 2012: 12-27
      CppAD Changes and Additions During 2013: 12-27
      CppAD Changes and Additions During 2014: 12-27
12-28 Changes and Additions to CppAD During 2011: 12-28
      CppAD Changes and Additions During 2012: 12-28
      CppAD Changes and Additions During 2014: 12-28
      CppAD Changes and Additions During 2015: 12-28
12-29 Changes and Additions to CppAD During 2007: 12-29
      CppAD Changes and Additions During 2012: 12-29
      CppAD Changes and Additions During 2013: 12-29
      CppAD Changes and Additions During 2014: 12-29
      CppAD Changes and Additions During 2015: 12-29
12-30 Changes and Additions to CppAD During 2011: 12-30
      CppAD Changes and Additions During 2012: 12-30
      CppAD Changes and Additions During 2014: 12-30
12-31 Changes and Additions to CppAD During 2010: 12-31
      CppAD Changes and Additions During 2015: 12-31
1: CppAD Download, Test, and Install Instructions: Instructions.Step 1: Download
2 AD Theory for Cholesky Factorization: Lemma 2
2003 Changes and Additions to CppAD During 2003
2004 Changes and Additions to CppAD During 2004
2005 Changes and Additions to CppAD During 2005
2005-08-07 AD Conditional Expressions: Deprecate 2005-08-07
2006 Changes and Additions to CppAD During 2006
2006-03-31 ADFun Object Deprecated Member Functions: Memory.Deprecated 2006-03-31
           ADFun Object Deprecated Member Functions: Order.Deprecated 2006-03-31
2006-04-03 ADFun Object Deprecated Member Functions: Size.Deprecated 2006-04-03
2006-04-08 ADFun Object Deprecated Member Functions: use_VecAD.Deprecated 2006-04-08
2006-06-17 ADFun Object Deprecated Member Functions: taylor_size.Deprecated 2006-06-17
2006-12-17 Deprecated Include Files: Deprecated 2006-12-17
2007 Changes and Additions to CppAD During 2007
2007-07-23 Routines That Track Use of New and Delete: Deprecated 2007-07-23
2007-07-28 Choosing The Vector Testing Template Class: CppADvector Deprecated 2007-07-28
           Discrete AD Functions: CppADCreateDiscrete Deprecated 2007-07-28
2007-07-31 AD Boolean Functions: Deprecated 2007-07-31
2007-08-07 ADFun Object Deprecated Member Functions: Dependent.Deprecated 2007-08-07
2008 Changes and Additions to CppAD During 2008
2009 Changes and Additions to CppAD During 2009
2010 Changes and Additions to CppAD During 2010
2011 Changes and Additions to CppAD During 2011
2011-06-23 OpenMP Parallel Setup: Deprecated 2011-06-23
2011-08-23 A Quick OpenMP Memory Allocator Used by CppAD: Deprecated 2011-08-23
2011-08-31 OpenMP Memory Allocator: Example and Test: Deprecated 2011-08-31
           Return A Raw Array to The Available Memory for a Thread: Deprecated 2011-08-31
           Allocate Memory and Create A Raw Array: Deprecated 2011-08-31
           Amount of Memory Available for Quick Use by a Thread: Deprecated 2011-08-31
           Amount of Memory a Thread is Currently Using: Deprecated 2011-08-31
           Free Memory Currently Available for Quick Use by a Thread: Deprecated 2011-08-31
           Return Memory to omp_alloc: Deprecated 2011-08-31
           Get At Least A Specified Amount of Memory: Deprecated 2011-08-31
           Get the Current OpenMP Thread Number: Deprecated 2011-08-31
           Is The Current Execution in OpenMP Parallel Mode: Deprecated 2011-08-31
           Set and Get Maximum Number of Threads for omp_alloc Allocator: Deprecated 2011-08-31
2012 CppAD Changes and Additions During 2012
2012-04-06 Memory Leak Detection: Deprecated 2012-04-06
2012-06-17 Machine Epsilon For AD Types: Deprecated 2012-06-17
2012-07-03 Choosing The Vector Testing Template Class: Deprecated 2012-07-03
2012-11-28 Nonlinear Programming Using the CppAD Interface to Ipopt: Deprecated 2012-11-28
2012-12-26 Auto Tools Unix Test and Installation: Deprecated 2012-12-26
2013 CppAD Changes and Additions During 2013
2013-05-27 Old Matrix Multiply as a User Atomic Operation: Example and Test: Deprecated 2013-05-27
           Old Tan and Tanh as User Atomic Operations: Example and Test: Deprecated 2013-05-27
           Using AD to Compute Atomic Function Derivatives: Deprecated 2013-05-27
           Using AD to Compute Atomic Function Derivatives: Deprecated 2013-05-27
           Old Atomic Operation Reciprocal: Example and Test: Deprecated 2013-05-27
           User Defined Atomic AD Functions: Deprecated 2013-05-27
2013-12-31 AD Constructors: x.Deprecated 2013-12-31
2014 CppAD Changes and Additions During 2014
2014-03-18 ADFun Object Deprecated Member Functions: capacity_taylor.Deprecated 2014-03-18
           ADFun Object Deprecated Member Functions: size_taylor.Deprecated 2014-03-18
2015 CppAD Changes and Additions During 2015
2015-01-20 Comparison Changes During Zero Order Forward Mode: Deprecated 2015-01-20
2015-09-26 zdouble: An AD Base Type With Absolute Zero: Deprecated 2015-09-26
2015-10-04 Obtain Nan or Determine if a Value is Nan: nan(zero).Deprecated 2015-10-04
2015-11-30 Deprecated Include Files: Deprecated 2015-11-30
2016 Changes and Additions to CppAD During 2016
2016-06-27 Atomic Reverse Hessian Sparsity Patterns: Deprecated 2016-06-27
           Atomic Forward Hessian Sparsity Patterns: Deprecated 2016-06-27
           Atomic Reverse Jacobian Sparsity Patterns: Deprecated 2016-06-27
           Atomic Forward Jacobian Sparsity Patterns: Deprecated 2016-06-27
2: exp_eps: Second Order Reverse Sweep: Index 2: f_1
   exp_eps: First Order Reverse Sweep: Index 2: f_1
   exp_2: Second Order Reverse Mode: Index 2: f_1
   exp_2: First Order Reverse Mode: Index 2: f_1
   CppAD Download, Test, and Install Instructions: Instructions.Step 2: Cmake
3 Check Gradient of Determinant of 3 by 3 matrix
  Check Gradient of Determinant of 3 by 3 matrix
  Check Determinant of 3 by 3 matrix
  Check Determinant of 3 by 3 matrix
3: exp_eps: Second Order Reverse Sweep: Index 3: f_2
   exp_eps: First Order Reverse Sweep: Index 3: f_2
   exp_2: Second Order Reverse Mode: Index 3: f_2
   exp_2: First Order Reverse Mode: Index 3: f_2
   CppAD Download, Test, and Install Instructions: Instructions.Step 3: Check
3rd A 3rd and 4th Order Rosenbrock ODE Solver
4: exp_eps: Second Order Reverse Sweep: Index 4: f_3
   exp_eps: First Order Reverse Sweep: Index 4: f_3
   exp_2: Second Order Reverse Mode: Index 4: f_3
   exp_2: First Order Reverse Mode: Index 4: f_3
   CppAD Download, Test, and Install Instructions: Instructions.Step 4: Installation
4th A 3rd and 4th Order Rosenbrock ODE Solver
    An Embedded 4th and 5th Order Runge-Kutta ODE Solver
5: exp_eps: Second Order Reverse Sweep: Index 5: f_4
   exp_eps: First Order Reverse Sweep: Index 5: f_4
   exp_2: Second Order Reverse Mode: Index 5: f_4
   exp_2: First Order Reverse Mode: Index 5: f_4
5th An Embedded 4th and 5th Order Runge-Kutta ODE Solver
6: exp_eps: Second Order Reverse Sweep: Index 6: f_5
   exp_eps: First Order Reverse Sweep: Index 6: f_5
7: exp_eps: Second Order Reverse Sweep: Index 7: f_6
   exp_eps: First Order Reverse Sweep: Index 7: f_6
< AD Binary Comparison Operators: Example and Test
  AD Binary Comparison Operators
<< AD Output Operator: Example and Test
   AD Output Operator: Example and Test
   AD Output Stream Operator
<= AD Binary Comparison Operators: Example and Test
   AD Binary Comparison Operators
= Evaluate a Function Defined in Terms of an ODE: p.p = 1
  AD Theory for Cholesky Factorization: Reverse Mode.Case k = 0
== Evaluate a Function Defined in Terms of an ODE: p.p == 0
   AD Binary Comparison Operators: Example and Test
   AD Binary Comparison Operators
> Using Multiple Levels of AD: Procedure.Second Start AD< AD<double> >
  Using Multiple Levels of AD: Procedure.Start AD< AD<double> > Recording
  AD Binary Comparison Operators: Example and Test
  AD Binary Comparison Operators
  AD Theory for Cholesky Factorization: Reverse Mode.Case k > 0
>= AD Binary Comparison Operators: Example and Test
   AD Binary Comparison Operators
>> AD Output Stream Operator
[0
     1] Simulate a [0,1] Uniform Random Variate
     1] Simulate a [0,1] Uniform Random Variate
[] The CppAD::vector Template Class
   Definition of a Simple Vector
A
A.1.1c A Simple Parallel Pthread Example and Test
       A Simple Boost Thread Example and Test
       A Simple OpenMP Example and Test
AD Nonlinear Programming Using CppAD and Ipopt: Example and Test
   Nonlinear Programming Using the CppAD Interface to Ipopt
   Computing a Jacobian With Constants that Change
   Example and Test Linking CppAD to Languages Other than C++
   Nonlinear Programming Using CppAD and Ipopt: Example and Test
   Timing Test of Multi-Threaded Newton Method
   A Simple pthread AD: Example and Test
   A Simple Boost Threading AD: Example and Test
   A Simple OpenMP AD: Example and Test
   An Introduction by Example to Algorithmic Differentiation
   cppad-20170000.3: A Package for Differentiation of C++ Algorithms
ADFun Comparison Changes During Zero Order Forward Mode
      Comparison Changes Between Taping and Zero Order Forward
      Stop Recording and Store Operation Sequence
Adolc Auto Tools Unix Test and Installation
Automatic An Introduction by Example to Algorithmic Differentiation
a11c Run Multi-Threading Examples and Speed Tests: a11c
abort Abort Current Recording: Example and Test
      Abort Recording of an Operation Sequence
abort_op_index Declare Independent Variables and Start Recording: abort_op_index
above Glossary: AD Type Above Base
      The Theory of Forward Mode: Standard Math Functions.Cases that Apply Recursion Above
abramowitz Bibliography: Abramowitz and Stegun
abs Enable use of AD<Base> where Base is Adolc's adouble Type: abs
    AD Absolute Value Function: Example and Test
    AD Absolute Value Functions: abs, fabs
absgeq LU Factorization of A Square Matrix: AbsGeq
       Compute Determinant and Solve Linear Equations: AbsGeq
absolute zdouble: An AD Base Type With Absolute Zero: Absolute Zero
         zdouble: An AD Base Type With Absolute Zero
         Determine if Two Values Are Nearly Equal
         AD<Base> Requirements for a CppAD Base Type: Absolute Zero, azmul
         AD Absolute Zero Multiplication: Example and Test
         Absolute Zero Multiplication
         AD Absolute Value Function: Example and Test
         AD Absolute Value Functions: abs, fabs
access The CppAD::vector Template Class: Element Access
       Definition of a Simple Vector: Element Access
accurate An Epsilon Accurate Exponential Approximation
aclocal Changes and Additions to CppAD During 2006
acos Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
     Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
     The AD acos Function: Example and Test
     Inverse Sine Function: acos
acosh Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
      Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
      Enable use of AD<Base> where Base is Adolc's adouble Type: erf, asinh, acosh, atanh, expm1, log1p
      Example AD<Base> Where Base Constructor Allocates Memory: erf, asinh, acosh, atanh, expm1, log1p
      Base Type Requirements for Standard Math Functions: erf, asinh, acosh, atanh, expm1, log1p
      The AD acosh Function: Example and Test
      The Inverse Hyperbolic Cosine Function: acosh
active Glossary: Tape.Active
activity Example Optimization and Reverse Activity Analysis
         Example Optimization and Forward Activity Analysis
ad Some Numerical AD Utilities
   zdouble: An AD Base Type With Absolute Zero
   Using AD to Compute Atomic Function Derivatives
   Using AD to Compute Atomic Function Derivatives
   User Defined Atomic AD Functions: Example.Use AD
   User Defined Atomic AD Functions
   Machine Epsilon For AD Types
   Glossary: AD Type Above Base
   Glossary: AD of Base
   Glossary: AD Function
   Running the Speed Test Program: package.AD Package
   Speed Test an Operator Overloading AD Package
   Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Taylor's Method Using AD
   Taylor's Ode Solver: A Multi-Level AD Example and Test: Taylor's Method Using AD
   Taylor's Ode Solver: A Multi-Level AD Example and Test
   Using Multiple Levels of AD
   Pthread Implementation of a Team of AD Threads
   Boost Thread Implementation of a Team of AD Threads
   OpenMP Implementation of a Team of AD Threads
   Specifications for A Team of AD Threads
   Using a Team of AD Threads: Example and Test
   Enable AD Calculations During Parallel Mode
   Using CppAD in a Multi-Threading Environment: Parallel AD
   Using a User Defined AD Base Type: Example and Test
   Example AD Base Types That are not AD<OtherBase>
   AD Vectors that Record Index Operations: Example and Test
   AD Vectors that Record Index Operations: AD Indexing
   AD Vectors that Record Index Operations
   AD Parameter and Variable Functions: Example and Test
   Is an AD Object a Parameter or Variable
   AD Boolean Functions: Example and Test
   AD Boolean Functions
   Compare AD with Base Objects: Example and Test
   Compare AD and Base Objects for Nearly Equal
   AD Binary Comparison Operators: Example and Test
   AD Binary Comparison Operators
   Bool Valued Operations and Functions with AD Arguments
   AD Theory for Cholesky Factorization
   Using AD Version of Atomic Function
   User Defined Atomic AD Functions
   Checkpointing Functions: Purpose.Multiple Level AD
   Atomic AD Functions
   Numeric Limits For an AD and Base Types
   Discrete AD Functions: Create AD Version
   Discrete AD Functions
   AD Conditional Expressions
   AD Absolute Zero Multiplication: Example and Test
   The AD Power Function: Example and Test
   The AD Power Function
   The AD atan2 Function: Example and Test
   AD Two Argument Inverse Tangent Function
   The AD log1p Function: Example and Test
   The AD exp Function: Example and Test
   The AD erf Function: Example and Test
   The AD atanh Function: Example and Test
   The AD asinh Function: Example and Test
   The AD acosh Function: Example and Test
   AD Absolute Value Function: Example and Test
   AD Absolute Value Functions: abs, fabs
   The AD tanh Function: Example and Test
   The AD tan Function: Example and Test
   The AD sqrt Function: Example and Test
   The AD sinh Function: Example and Test
   The AD sin Function: Example and Test
   The AD log10 Function: Example and Test
   The AD log Function: Example and Test
   The AD exp Function: Example and Test
   The AD cosh Function: Example and Test
   The AD cos Function: Example and Test
   The AD atan Function: Example and Test
   The AD asin Function: Example and Test
   The AD acos Function: Example and Test
   AD Computed Assignment Division: Example and Test
   AD Computed Assignment Multiplication: Example and Test
   AD Computed Assignment Subtraction: Example and Test
   AD Computed Assignment Addition: Example and Test
   AD Computed Assignment Operators
   AD Binary Division: Example and Test
   AD Binary Multiplication: Example and Test
   AD Binary Subtraction: Example and Test
   AD Binary Addition: Example and Test
   AD Binary Arithmetic Operators
   AD Unary Minus Operator: Example and Test
   AD Unary Minus Operator
   AD Unary Plus Operator: Example and Test
   AD Unary Plus Operator
   AD Arithmetic Operators and Computed Assignments
   AD Valued Operations and Functions
   Convert an AD Variable to a Parameter: Example and Test
   Convert an AD Variable to a Parameter
   Printing AD Values During Forward Mode
   AD Output Operator: Example and Test
   AD Output Operator: Example and Test
   AD Output Stream Operator
   AD Output Stream Operator
   Convert An AD or Base Type to String
   Convert From AD to Integer: Example and Test
   Convert From AD to Integer: x.AD Types
   Convert From AD to Integer
   Convert From AD to its Base Type: Example and Test
   Convert From an AD Type to its Base Type
   Conversion and I/O of AD Objects
   AD Assignment: Example and Test
   AD Assignment Operator
   AD Constructors: Example and Test
   AD Constructors
   AD Objects
ad: Multiple Level of AD: Example and Test
    A Simple pthread AD: Example and Test
    A Simple Boost Threading AD: Example and Test
    A Simple OpenMP AD: Example and Test
    Atomic Operations and Multiple-Levels of AD: Example and Test
ad< Using Multiple Levels of AD: Procedure.Second Start AD< AD<double> >
    Using Multiple Levels of AD: Procedure.Start AD< AD<double> > Recording
ad<base> Enable use of AD<Base> where Base is std::complex<double>
         Enable use of AD<Base> where Base is double
         Enable use of AD<Base> where Base is float
         Enable use of AD<Base> where Base is Adolc's adouble Type
         Example AD<Base> Where Base Constructor Allocates Memory
         AD<Base> Requirements for a CppAD Base Type
         Absolute Zero Multiplication: AD<Base>
         The Unary Standard Math Functions: Possible Types.AD<Base>
ad<double> Using Multiple Levels of AD: Procedure.Second Start AD< AD<double> >
           Using Multiple Levels of AD: Procedure.Start AD< AD<double> > Recording
           Using Multiple Levels of AD: Procedure.First Start AD<double>
ad<otherbase> Example AD Base Types That are not AD<OtherBase>
add AD Computed Assignment Division: Example and Test
    AD Computed Assignment Multiplication: Example and Test
    AD Computed Assignment Subtraction: Example and Test
    AD Computed Assignment Addition: Example and Test
    AD Computed Assignment Operators
    AD Binary Addition: Example and Test
    AD Binary Arithmetic Operators
add_static Memory Leak Detection: add_static
addition The Theory of Reverse Mode: Binary Operators.Addition
         The Theory of Forward Mode: Binary Operators.Addition
         AD Computed Assignment Operators: Derivative.Addition
         AD Binary Arithmetic Operators: Derivative.Addition
addition: AD Computed Assignment Addition: Example and Test
          AD Binary Addition: Example and Test
additions Changes and Additions to CppAD During 2003
          Changes and Additions to CppAD During 2004
          Changes and Additions to CppAD During 2005
          Changes and Additions to CppAD During 2006
          Changes and Additions to CppAD During 2007
          Changes and Additions to CppAD During 2008
          Changes and Additions to CppAD During 2009
          Changes and Additions to CppAD During 2010
          Changes and Additions to CppAD During 2011
          CppAD Changes and Additions During 2012
          CppAD Changes and Additions During 2013
          CppAD Changes and Additions During 2014
          CppAD Changes and Additions During 2015
          Changes and Additions to CppAD During 2016
          Changes and Additions to CppAD
addons CppAD Addons
adfun ADFun Object Deprecated Member Functions
      Creating Your Own Interface to an ADFun Object
      ADFun Checking For Nan: Example and Test
      Check an ADFun Object For Nan Results
      Optimize an ADFun Object Tape
      ADFun Check and Re-Tape: Example and Test
      Check an ADFun Sequence of Operations
      Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
      Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
      ADFun Sequence Properties: Example and Test
      ADFun Sequence Properties
      ADFun Assignment: Example and Test
      Construct an ADFun Object and Stop Recording
      Independent and ADFun Constructor: Example and Test
      ADFun Objects
adnumber Nonlinear Programming Using the CppAD Interface to Ipopt: ADNumber
adol-c Including the ADOL-C Examples and Tests
adolc The CppAD Wish List: Adolc
      Adolc Test Utility: Allocate and Free Memory For a Matrix
      adolc Speed: Sparse Jacobian
      Adolc Speed: Sparse Hessian
      Adolc Speed: Second Derivative of a Polynomial
      Adolc Speed: Ode
      Adolc Speed: Matrix Multiplication
      Adolc Speed: Gradient of Determinant Using Lu Factorization
      Adolc Speed: Gradient of Determinant by Minor Expansion
      Speed Test of Derivatives Using Adolc
      Taylor's Ode Solver: A Multi-Level Adolc Example and Test
      Using Adolc with Multiple Levels of Taping: Example and Test
      Download and Install Adolc in Build Directory
      Including the ADOL-C Examples and Tests
adolc's Enable use of AD<Base> where Base is Adolc's adouble Type
adolc_alloc_mat Adolc Test Utility: Allocate and Free Memory For a Matrix
adolc_dir Auto Tools Unix Test and Installation: adolc_dir
adolc_prefix Speed Test of Derivatives Using Adolc: adolc_prefix
             Including the ADOL-C Examples and Tests: adolc_prefix
adouble Enable use of AD<Base> where Base is Adolc's adouble Type
advector LU Factorization of A Square Matrix and Stability Calculation: ADvector
         Computing Jacobian and Hessian of Bender's Reduced Objective: ADvector
         Nonlinear Programming Using the CppAD Interface to Ipopt: ADVector
         Use Ipopt to Solve a Nonlinear Programming Problem: fg_eval.ADvector
         Stop Recording and Store Operation Sequence: ADvector
         Using AD Version of Atomic Function: ADVector
         Checkpointing Functions: ADVector
after Printing AD Values During Forward Mode: after
afun User Defined Atomic AD Functions: afun
     Using AD Version of Atomic Function: afun
     Atomic Function Constructor: atomic_user.afun
algebra Enable Use of Eigen Linear Algebra Package with CppAD
algo Checkpointing Functions: algo
algorithm Differentiate Conjugate Gradient Algorithm: Example and Test: Algorithm
          Hessian Sparsity Pattern: Forward Mode: Algorithm
          An Epsilon Accurate Exponential Approximation
          Second Order Exponential Approximation
          cppad-20170000.3: A Package for Differentiation of C++ Algorithms
algorithm: Differentiate Conjugate Gradient Algorithm: Example and Test
algorithmic Example and Test Linking CppAD to Languages Other than C++
            An Introduction by Example to Algorithmic Differentiation: Preface.Algorithmic Differentiation
            An Introduction by Example to Algorithmic Differentiation
            cppad-20170000.3: A Package for Differentiation of C++ Algorithms
algorithms cppad-20170000.3: A Package for Differentiation of C++ Algorithms
alignment Allocate An Array and Call Default Constructor for its Elements: Alignment
          Get At Least A Specified Amount of Memory: Alignment
all List of All the CppAD Examples
    Free All Memory That Was Allocated for Use by thread_alloc
    Checking the CppAD Examples and Tests: Check All
alloc Adolc Test Utility: Allocate and Free Memory For a Matrix
      Control When Thread Alloc Retains Memory For Future Use
allocate Allocate Memory and Create A Raw Array
         Adolc Test Utility: Allocate and Free Memory For a Matrix
         Allocate An Array and Call Default Constructor for its Elements
         Get At Least A Specified Amount of Memory
allocated Free All Memory That Was Allocated for Use by thread_alloc
allocates Example AD<Base> Where Base Constructor Allocates Memory
allocation OpenMP Memory Allocator: Example and Test
           Check If A Memory Allocation is Efficient for Another Use
           Get At Least A Specified Amount of Memory: Allocation Speed
           A Quick OpenMP Memory Allocator Used by CppAD
           Frequently Asked Questions and Answers: Speed.Memory Allocation
           Get At Least A Specified Amount of Memory: Allocation Speed
           Fast Multi-Threading Memory Allocator: Example and Test
           A Fast Multi-Threading Memory Allocator
           Some General Purpose Utilities: Miscellaneous.Multi-Threading Memory Allocation
           Controlling Taylor Coefficients Memory Allocation
allocation: Controlling Taylor Coefficient Memory Allocation: Example and Test
allocator Set Maximum Number of Threads for omp_alloc Allocator
          Set and Get Maximum Number of Threads for omp_alloc Allocator
          A Quick OpenMP Memory Allocator Used by CppAD
          A Fast Multi-Threading Memory Allocator
allocator: OpenMP Memory Allocator: Example and Test
           Fast Multi-Threading Memory Allocator: Example and Test
also Jacobian and Hessian of Optimal Values: See Also
     Computing Jacobian and Hessian of Bender's Reduced Objective: See Also
     Convert Certain Types to a String: See Also
     The Integer Power Function: See Also
     Example Optimization and Nested Conditional Expressions: See Also
     Example Optimization and Conditional Expressions: See Also
     Example Optimization and Comparison Operators: See Also
     Sparse Hessian on Subset of Variables: Example and Test: See Also
     Computing Sparse Hessian for a Subset of Variables: See Also
     Sparsity Patterns For a Subset of Variables: Example and Test: See Also
     Reverse Mode General Case (Checkpointing): Example and Test: See Also
     Number of Variables that Can be Skipped: Syntax.See Also
     Controlling Taylor Coefficients Memory Allocation: Syntax.See Also
     Number Taylor Coefficient Orders Currently Stored: Syntax.See Also
     ADFun Sequence Properties: Syntax.See Also
     Matrix Multiply as an Atomic Operation: See Also
     User Atomic Matrix Multiply: Example and Test: See Also
     Atomic Eigen Matrix Multiply Class: See Also
     Checkpointing an Extended ODE Solver: Example and Test: See Also
     Checkpointing an ODE Solver: Example and Test: See Also
     Checkpointing Functions: See Also
     Interpolation With Retaping: Example and Test: See Also
     Interpolation With Out Retaping: Example and Test: See Also
     Conditional Expressions: Example and Test: See Also
     The AD Power Function: See Also
     Convert an AD Variable to a Parameter: See Also
     Convert An AD or Base Type to String: See Also
     Convert From an AD Type to its Base Type: See Also
alternative Printing AD Values During Forward Mode: Alternative
alternatives AD Vectors that Record Index Operations: Alternatives
amount Determine Amount of Time to Execute det_by_minor
       Amount of Memory Available for Quick Use by a Thread
       Amount of Memory a Thread is Currently Using
       Get At Least A Specified Amount of Memory
       Amount of Memory Available for Quick Use by a Thread
       Amount of Memory a Thread is Currently Using
       Get At Least A Specified Amount of Memory
       Determine Amount of Time to Execute a Test
analysis Example Optimization and Reverse Activity Analysis
         Example Optimization and Forward Activity Analysis
analytic An ODE Inverse Problem Example: Measurements.Simulation Analytic Solution
         ODE Inverse Problem Definitions: Source Code: Measurements.Simulation Analytic Solution
another Check If A Memory Allocation is Efficient for Another Use
        Extending to_string To Another Floating Point Type
answers Frequently Asked Questions and Answers
any Any Order Reverse Mode
    Multiple Order Forward Mode
api CppAD Deprecated API Features
    CppAD API Preprocessor Symbols
    AD<Base> Requirements for a CppAD Base Type: API Warning
appendix Appendix
apply The Theory of Forward Mode: Standard Math Functions.Cases that Apply Recursion Above
approximation ODE Fitting Using Fast Representation: Trapezoidal Approximation
              ODE Fitting Using Simple Representation: Trapezoidal Approximation Constraint
              An ODE Inverse Problem Example: Trapezoidal Approximation
              ODE Inverse Problem Definitions: Source Code: Trapezoidal Approximation
              Correctness Tests For Exponential Approximation in Introduction
              An Epsilon Accurate Exponential Approximation
              Second Order Exponential Approximation
arbitrary An Arbitrary Order Gear Method
archives Download The CppAD Source Code: Current Version.Compressed Archives
         Download The CppAD Source Code: Compressed Archives
are Determine if Two Values Are Nearly Equal
    Example AD Base Types That are not AD<OtherBase>
    Check if Two Value are Identically Equal
argument ODE Fitting Using Simple Representation: Argument Vector
         OdeErrControl: Example and Test Using Maxabs Argument
         AD Two Argument Inverse Tangent Function
argument: The Logarithm of One Plus Argument: log1p
arguments Bool Valued Operations and Functions with AD Arguments
arguments: LuSolve With Complex Arguments: Example and Test
arithmetic zdouble: An AD Base Type With Absolute Zero: Syntax.Arithmetic Operators
           AD Binary Arithmetic Operators
           AD Arithmetic Operators and Computed Assignments
array Return A Raw Array to The Available Memory for a Thread: array
      Return A Raw Array to The Available Memory for a Thread
      Allocate Memory and Create A Raw Array: array
      Allocate Memory and Create A Raw Array
      Using Eigen Arrays: Example and Test
      Deallocate An Array and Call Destructor for its Elements: array
      Deallocate An Array and Call Destructor for its Elements
      Allocate An Array and Call Default Constructor for its Elements: array
      Allocate An Array and Call Default Constructor for its Elements
      Taping Array Index Operation: Example and Test
arrays: Using Eigen Arrays: Example and Test
asin Inverse Sine and Hyperbolic Sine Reverse Mode Theory
     Inverse Sine and Hyperbolic Sine Forward Mode Theory
     The AD asin Function: Example and Test
     Inverse Sine Function: asin
asinh Inverse Sine and Hyperbolic Sine Reverse Mode Theory
      Inverse Sine and Hyperbolic Sine Forward Mode Theory
      Enable use of AD<Base> where Base is Adolc's adouble Type: erf, asinh, acosh, atanh, expm1, log1p
      Example AD<Base> Where Base Constructor Allocates Memory: erf, asinh, acosh, atanh, expm1, log1p
      Base Type Requirements for Standard Math Functions: erf, asinh, acosh, atanh, expm1, log1p
      The AD asinh Function: Example and Test
      The Inverse Hyperbolic Sine Function: asinh
asked Frequently Asked Questions and Answers
assert CppAD Assertions During Execution
       Replacing the CppAD Error Handler
assertions CppAD Assertions During Execution
assign AD Conditional Expressions
       AD Computed Assignment Division: Example and Test
       AD Computed Assignment Multiplication: Example and Test
       AD Computed Assignment Subtraction: Example and Test
       AD Computed Assignment Addition: Example and Test
       AD Assignment: Example and Test
       AD Assignment Operator
assignment zdouble: An AD Base Type With Absolute Zero: Syntax.Constructor and Assignment
           Frequently Asked Questions and Answers: Assignment and Independent
           The CppAD::vector Template Class: Assignment
           Definition of a Simple Vector: Element Access.Assignment
           Definition of a Simple Vector: Assignment
           Definition of a Numeric Type: Assignment
           ADFun Assignment: Example and Test
           Construct an ADFun Object and Stop Recording: Example.Assignment Operator
           Construct an ADFun Object and Stop Recording: Assignment Operator
           Example AD<Base> Where Base Constructor Allocates Memory: Computed Assignment Macro
           Required Base Class Member Functions: Assignment Operators
           AD Computed Assignment Division: Example and Test
           AD Computed Assignment Multiplication: Example and Test
           AD Computed Assignment Subtraction: Example and Test
           AD Computed Assignment Addition: Example and Test
           AD Computed Assignment Operators
           AD Assignment Operator
assignment: ADFun Assignment: Example and Test
            AD Assignment: Example and Test
assignments AD Arithmetic Operators and Computed Assignments
assumption AD Output Stream Operator: Assumption
assumptions AD Binary Comparison Operators: Assumptions
atan Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
     The AD atan Function: Example and Test
     Inverse Tangent Function: atan
atan2 The CppAD Wish List: atan2
      AD Conditional Expressions: Atan2
      The AD atan2 Function: Example and Test
      AD Two Argument Inverse Tangent Function
atanh Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
      Enable use of AD<Base> where Base is Adolc's adouble Type: erf, asinh, acosh, atanh, expm1, log1p
      Example AD<Base> Where Base Constructor Allocates Memory: erf, asinh, acosh, atanh, expm1, log1p
      Base Type Requirements for Standard Math Functions: erf, asinh, acosh, atanh, expm1, log1p
      The AD atanh Function: Example and Test
      The Inverse Hyperbolic Tangent Function: atanh
atom_fun Checkpointing Functions: atom_fun
atomic Define Matrix Multiply as a User Atomic Operation: CppAD User Atomic Callback Functions
       Define Matrix Multiply as a User Atomic Operation
       Old Matrix Multiply as a User Atomic Operation: Example and Test
       Old Tan and Tanh as User Atomic Operations: Example and Test
       Using AD to Compute Atomic Function Derivatives
       Using AD to Compute Atomic Function Derivatives
       Old Atomic Operation Reciprocal: Example and Test
       User Defined Atomic AD Functions
       CppAD Deprecated API Features: Atomic Functions
       Glossary: Operation.Atomic
       Running the Speed Test Program: Global Options.atomic
       Optimize an ADFun Object Tape: Atomic Functions
       Matrix Multiply as an Atomic Operation
       User Atomic Matrix Multiply: Example and Test: Use Atomic Function
       User Atomic Matrix Multiply: Example and Test
       Atomic Eigen Cholesky Factorization Class
       Atomic Eigen Cholesky Factorization: Example and Test: Use Atomic Function
       Atomic Eigen Cholesky Factorization: Example and Test
       Atomic Eigen Matrix Inversion Class
       Atomic Eigen Matrix Inverse: Example and Test: Use Atomic Function
       Atomic Eigen Matrix Inverse: Example and Test
       Atomic Eigen Matrix Multiply Class
       Atomic Eigen Matrix Multiply: Example and Test: Use Atomic Function
       Atomic Eigen Matrix Multiply: Example and Test
       Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function
       Tan and Tanh as User Atomic Operations: Example and Test
       Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function
       Atomic Sparsity with Set Patterns: Example and Test
       Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function
       Reciprocal as an Atomic Operation: Example and Test
       Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function
       Atomic Euclidean Norm Squared: Example and Test
       Getting Started with Atomic Operations: Example and Test: Use Atomic Function
       Getting Started with Atomic Operations: Example and Test
       Atomic Reverse Hessian Sparsity: Example and Test: Use Atomic Function
       Atomic Reverse Hessian Sparsity: Example and Test
       Atomic Forward Hessian Sparsity: Example and Test: Use Atomic Function
       Atomic Forward Hessian Sparsity: Example and Test
       Atomic Reverse Jacobian Sparsity: Example and Test: Use Atomic Function
       Atomic Reverse Jacobian Sparsity: Example and Test
       Atomic Forward Jacobian Sparsity: Example and Test: Use Atomic Function
       Atomic Forward Jacobian Sparsity: Example and Test
       Atomic Reverse: Example and Test: Use Atomic Function
       Atomic Reverse: Example and Test
       Atomic Forward: Example and Test: Use Atomic Function
       Atomic Forward: Example and Test
       Atomic Reverse Hessian Sparsity Patterns
       Atomic Forward Hessian Sparsity Patterns
       Atomic Reverse Jacobian Sparsity Patterns
       Atomic Forward Jacobian Sparsity Patterns
       Atomic Reverse Mode
       Atomic Forward Mode
       Using AD Version of Atomic Function
       Set Atomic Function Options
       Atomic Function Constructor
       User Defined Atomic AD Functions
       Atomic Operations and Multiple-Levels of AD: Example and Test
       Atomic AD Functions
       The Sign: sign: Atomic
       AD Absolute Value Functions: abs, fabs: Atomic
       The Hyperbolic Tangent Function: tanh: Atomic
       The Tangent Function: tan: Atomic
       The Square Root Function: sqrt: Atomic
       The Hyperbolic Sine Function: sinh: Atomic
       The Sine Function: sin: Atomic
       The Exponential Function: log: Atomic
       The Exponential Function: exp: Atomic
       The Hyperbolic Cosine Function: cosh: Atomic
       The Cosine Function: cos: Atomic
       Inverse Tangent Function: atan: Atomic
       Inverse Sine Function: asin: Atomic
       Inverse Sine Function: acos: Atomic
atomic_base Atomic Function Constructor: atomic_base
atomic_sparsity Set Atomic Function Options: atomic_sparsity
atomic_user Atomic Function Constructor: atomic_user
auto Auto Tools Unix Test and Installation
automatic Example and Test Linking CppAD to Languages Other than C++
          cppad-20170000.3: A Package for Differentiation of C++ Algorithms
available Memory Leak Detection: available
          Return A Raw Array to The Available Memory for a Thread
          Amount of Memory Available for Quick Use by a Thread
          Free Memory Currently Available for Quick Use by a Thread
          Amount of Memory Available for Quick Use by a Thread
          Free Memory Currently Available for Quick Use by a Thread
          Return Memory to thread_alloc
avoid Frequently Asked Questions and Answers
ax User Defined Atomic AD Functions: afun.ax
   Using AD Version of Atomic Function: ax
   Checkpointing Functions: ax
   Discrete AD Functions: ax
ay User Defined Atomic AD Functions: afun.ay
   Using AD Version of Atomic Function: ay
   Checkpointing Functions: ay
   Discrete AD Functions: ay
azmul Enable use of AD<Base> where Base is std::complex<double>: azmul
      Enable use of AD<Base> where Base is double: azmul
      Enable use of AD<Base> where Base is float: azmul
      Enable use of AD<Base> where Base is Adolc's adouble Type: azmul
      Example AD<Base> Where Base Constructor Allocates Memory: azmul
      AD<Base> Requirements for a CppAD Base Type: Absolute Zero, azmul
B
Base AD Assignment Operator
     AD Constructors
BenderQuad BenderQuad: Example and Test
           Computing Jacobian and Hessian of Bender's Reduced Objective
background Using Multiple Levels of AD: Background
base zdouble: An AD Base Type With Absolute Zero: Base Type Requirements
     zdouble: An AD Base Type With Absolute Zero
     User Defined Atomic AD Functions: CPPAD_USER_ATOMIC.Base
     The CppAD Wish List: Base Requirements
     Glossary: Base Type
     Glossary: Base Function
     Glossary: AD Type Above Base
     Glossary: AD of Base
     Enable use of AD<Base> where Base is std::complex<double>
     Enable use of AD<Base> where Base is double
     Enable use of AD<Base> where Base is float
     Enable use of AD<Base> where Base is Adolc's adouble Type
     Using a User Defined AD Base Type: Example and Test
     Example AD<Base> Where Base Constructor Allocates Memory
     Example AD Base Types That are not AD<OtherBase>
     Base Type Requirements for Hash Coding Values
     Extending to_string To Another Floating Point Type: Base Requirement
     Base Type Requirements for Numeric Limits
     Base Type Requirements for Standard Math Functions
     Base Type Requirements for Ordered Comparisons
     Base Type Requirements for Identically Equal Comparisons
     Base Type Requirements for Conditional Expressions
     Required Base Class Member Functions
     AD<Base> Requirements for a CppAD Base Type: Standard Base Types
     AD<Base> Requirements for a CppAD Base Type
     Compare AD with Base Objects: Example and Test
     Compare AD and Base Objects for Nearly Equal
     Atomic Function Constructor: atomic_base.Base
     Checkpointing Functions: Base
     Numeric Limits For an AD and Base Types
     Discrete AD Functions: Base
     Absolute Zero Multiplication: Base
     The Base 10 Logarithm Function: log10
     The Unary Standard Math Functions: Possible Types.Base
     AD Computed Assignment Operators: Base
     AD Binary Arithmetic Operators: Base
     AD Unary Minus Operator: Base
     Convert An AD or Base Type to String
     Convert From AD to its Base Type: Example and Test
     Convert From an AD Type to its Base Type
     AD Objects: Base Type Requirements
base_adolc.hpp Taylor's Ode Solver: A Multi-Level Adolc Example and Test: base_adolc.hpp
basevector Jacobian and Hessian of Optimal Values: BaseVector
bavector Computing Jacobian and Hessian of Bender's Reduced Objective: BAvector
be Number of Variables That Can be Skipped: Example and Test
   Number of Variables that Can be Skipped
before Printing AD Values During Forward Mode: before
begin Define Matrix Multiply as a User Atomic Operation: Begin Source
bender's Computing Jacobian and Hessian of Bender's Reduced Objective
benderquad The CppAD Wish List: BenderQuad
benderquad: BenderQuad: Example and Test
between Comparison Changes Between Taping and Zero Order Forward
bibliography Bibliography
binary The Theory of Reverse Mode: Binary Operators
       The Theory of Forward Mode: Binary Operators
       Example AD<Base> Where Base Constructor Allocates Memory: Binary Operator Macro
       Required Base Class Member Functions: Binary Operators
       AD Boolean Functions: Create Binary
       AD Binary Comparison Operators: Example and Test
       AD Binary Comparison Operators
       The Binary Math Functions
       AD Binary Division: Example and Test
       AD Binary Multiplication: Example and Test
       AD Binary Subtraction: Example and Test
       AD Binary Addition: Example and Test
       AD Binary Arithmetic Operators
binary_name AD Boolean Functions: binary_name
bit_per_unit The CppAD::vector Template Class: vectorBool.bit_per_unit
black An ODE Inverse Problem Example: Black Box Method
bool CppAD::vectorBool Class: Example and Test
     Required Base Class Member Functions: Bool Operators
     AD Boolean Functions: Example and Test
     AD Boolean Functions
     Bool Valued Operations and Functions with AD Arguments
bool_sparsity_enum Atomic Euclidean Norm Squared: Example and Test
                   Set Atomic Function Options: atomic_sparsity.bool_sparsity_enum
boolean Glossary: Sparsity Pattern.Vector of Boolean
        Example AD<Base> Where Base Constructor Allocates Memory: Boolean Operator Macro
        AD Boolean Functions: Example and Test
        AD Boolean Functions
boolsparsity Running the Speed Test Program: Sparsity Options.boolsparsity
boost Fast Multi-Threading Memory Allocator: Example and Test
      Boost Thread Implementation of a Team of AD Threads
      A Simple Boost Threading AD: Example and Test
      A Simple Boost Thread Example and Test
      Auto Tools Unix Test and Installation
      Choosing the CppAD Test Vector Template Class: boost
boost::numeric::ublas::vector Choosing The Vector Testing Template Class: boost::numeric::ublas::vector
                              Using The CppAD Test Vector Template Class: boost::numeric::ublas::vector
boost_dir Auto Tools Unix Test and Installation: boost_dir
both Speed Test for Both Simple and Fast Representations
     Correctness Check for Both Simple and Fast Representations
     Atomic Reverse Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Forward Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Reverse Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Forward Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
box An ODE Inverse Problem Example: Black Box Method
bthread Boost Thread Implementation of a Team of AD Threads
        Run Multi-Threading Examples and Speed Tests
bug Pthread Implementation of a Team of AD Threads: Bug in Cygwin
bugs Frequently Asked Questions and Answers: Bugs
build Download and Install Sacado in Build Directory
      Download and Install Ipopt in Build Directory
      Download and Install Fadbad in Build Directory
      Download and Install Eigen in Build Directory
      Download and Install ColPack in Build Directory
      Download and Install Adolc in Build Directory
      Using CMake to Configure CppAD: CMake Command.Build Directory
building Download The CppAD Source Code: No Documentation.Building Documentation
bvector Use Ipopt to Solve a Nonlinear Programming Problem: Bvector
C
C Interfacing to C: Example and Test
  Example and Test Linking CppAD to Languages Other than C++
     compare speed with C++ Compare Speed of C and C++
C++ cppad-20170000.3: A Package for Differentiation of C++ Algorithms
     compare speed with C Compare Speed of C and C++
CheckNumericType Check NumericType Class Concept
CheckSimpleVector Check Simple Vector Concept
CompareChange Comparison Changes During Zero Order Forward Mode
CondExp Base Type Requirements for Conditional Expressions
CPPAD_ CppAD API Preprocessor Symbols
CPPAD_ASSERT_KNOWN CppAD Assertions During Execution
CPPAD_ASSERT_UNKNOWN CppAD Assertions During Execution
CPPAD_BOOL_BINARY AD Boolean Functions
CPPAD_BOOL_UNARY AD Boolean Functions
CPPAD_COND_EXP_REL Base Type Requirements for Conditional Expressions
CPPAD_DISCRETE_FUNCTION Discrete AD Functions
CPPAD_TEST_VECTOR Choosing The Vector Testing Template Class
CPPAD_TESTVECTOR Frequently Asked Questions and Answers
                 Using The CppAD Test Vector Template Class
CPPAD_TRACK_COUNT Routines That Track Use of New and Delete
CPPAD_TRACK_DEL_VEC Routines That Track Use of New and Delete
CPPAD_TRACK_EXTEND Routines That Track Use of New and Delete
CPPAD_TRACK_NEW_VEC Routines That Track Use of New and Delete
CppAD CppAD::vectorBool Class: Example and Test
      CppAD::vector Template Class: Example and Test
      The CppAD::vector Template Class
      cppad-20170000.3: A Package for Differentiation of C++ Algorithms
CppADTrackDelVec Routines That Track Use of New and Delete
CppADTrackExtend Routines That Track Use of New and Delete
CppADTrackNewVec Routines That Track Use of New and Delete
c Main Program For Comparing C and C++ Speed
  Determinant of a Minor: c
  Compare Speed of C and C++
  Comparison Changes During Zero Order Forward Mode: c
  Determinant of a Minor: c
  Controlling Taylor Coefficients Memory Allocation: c
c++ Main Program For Comparing C and C++ Speed
    Compare Speed of C and C++
    Bibliography: The C++ Programming Language
    Example and Test Linking CppAD to Languages Other than C++
    Some General Purpose Utilities: C++ Concepts
    cppad-20170000.3: A Package for Differentiation of C++ Algorithms
c++11 Using CMake to Configure CppAD: cppad_cxx_flags.C++11
c: Interfacing to C: Example and Test
calculating Calculating Sparsity Patterns
calculation LU Factorization of A Square Matrix and Stability Calculation
calculations The Theory of Derivative Calculations
             Enable AD Calculations During Parallel Mode
             Including the ColPack Sparsity Calculations
call Define Matrix Multiply as a User Atomic Operation: Extra Call Information
     Deallocate An Array and Call Destructor for its Elements
     Allocate An Array and Call Default Constructor for its Elements
     Replacing the CppAD Error Handler: Call
callback Define Matrix Multiply as a User Atomic Operation: CppAD User Atomic Callback Functions
         User Defined Atomic AD Functions: Syntax Function.Callback Routines
         Atomic Forward Mode
can Number of Variables That Can be Skipped: Example and Test
    Number of Variables that Can be Skipped
cap_bytes Get At Least A Specified Amount of Memory: cap_bytes
          Get At Least A Specified Amount of Memory: cap_bytes
capacity The CppAD::vector Template Class: capacity
capacity_order Controlling Taylor Coefficient Memory Allocation: Example and Test
               Controlling Taylor Coefficients Memory Allocation
               Number Taylor Coefficient Orders Currently Stored: capacity_order
capacity_taylor ADFun Object Deprecated Member Functions: capacity_taylor
case Using AD to Compute Atomic Function Derivatives: Simple Case
     Reverse Mode General Case (Checkpointing): Example and Test
     Second Order Forward Mode: Derivative Values: Special Case
     First Order Forward Mode: Derivative Values: Special Case
     Zero Order Forward Mode: Function Values: Special Case
     Base Type Requirements for Identically Equal Comparisons: EqualOpSeq.The Simple Case
     AD Theory for Cholesky Factorization: Reverse Mode.Case k > 0
     AD Theory for Cholesky Factorization: Reverse Mode.Case k = 0
     User Defined Atomic AD Functions: General Case
cases The Theory of Forward Mode: Standard Math Functions.Special Cases
      The Theory of Forward Mode: Standard Math Functions.Cases that Apply Recursion Above
      Base Type Requirements for Identically Equal Comparisons: EqualOpSeq.More Complicated Cases
central Interfacing to C: Example and Test
certain Convert Certain Types to a String
change Computing a Jacobian With Constants that Change
       CompareChange and Re-Tape: Example and Test
changes Comparison Changes During Zero Order Forward Mode
        Changes and Additions to CppAD During 2003
        Changes and Additions to CppAD During 2004
        Changes and Additions to CppAD During 2005
        Changes and Additions to CppAD During 2006
        Changes and Additions to CppAD During 2007
        Changes and Additions to CppAD During 2008
        Changes and Additions to CppAD During 2009
        Changes and Additions to CppAD During 2010
        Changes and Additions to CppAD During 2011
        CppAD Changes and Additions During 2012
        CppAD Changes and Additions During 2013
        CppAD Changes and Additions During 2014
        CppAD Changes and Additions During 2015
        Changes and Additions to CppAD During 2016
        Changes and Additions to CppAD
        Comparison Changes Between Taping and Zero Order Forward
check Correctness Check for Both Simple and Fast Representations
      Memory Leak Detection
      Check If A Memory Allocation is Efficient for Another Use
      Check Gradient of Determinant of 3 by 3 matrix
      Check Determinant of 3 by 3 matrix
      The CppAD::vector Template Class: Assignment.Check Size
      The CheckSimpleVector Function: Example and Test
      Check Simple Vector Concept
      The CheckNumericType Function: Example and Test
      Check NumericType Class Concept
      Check an ADFun Object For Nan Results
      ADFun Check and Re-Tape: Example and Test
      Check an ADFun Sequence of Operations
      Check if Two Value are Identically Equal
      Checking the CppAD Examples and Tests: Check All
      Using CMake to Configure CppAD: make check
      CppAD Download, Test, and Install Instructions: Instructions.Step 3: Check
check_finite The CppAD Wish List: check_finite
checking ADFun Checking For Nan: Example and Test
         Optimize an ADFun Object Tape: Checking Optimization
         Checking the CppAD Examples and Tests
checknumerictype The CheckNumericType Function: Example and Test
checkpoint Using AD to Compute Atomic Function Derivatives
           Using AD to Compute Atomic Function Derivatives
           The CppAD Wish List: checkpoint
checkpointing Checkpointing an Extended ODE Solver: Example and Test
              Checkpointing an ODE Solver: Example and Test
              Checkpointing Functions
checkpointing: Simple Checkpointing: Example and Test
checksimplevector The CheckSimpleVector Function: Example and Test
                  Enable AD Calculations During Parallel Mode: CheckSimpleVector
cholesky Atomic Eigen Cholesky Factorization Class
         AD Theory for Cholesky Factorization: Notation.Cholesky Factor
         AD Theory for Cholesky Factorization
         Atomic Eigen Cholesky Factorization: Example and Test
choosing Choosing The Vector Testing Template Class
         Choosing the CppAD Test Vector Template Class
class Choosing The Vector Testing Template Class
      Using The CppAD Test Vector Template Class
      Examples: The CppAD Test Vector Template Class
      The CppAD::vector Template Class
      Definition of a Simple Vector: Template Class Requirements
      Check NumericType Class Concept
      Some General Purpose Utilities: Miscellaneous.Simple Vector Template Class
      Example AD<Base> Where Base Constructor Allocates Memory: Class Definition
      Required Base Class Member Functions
      Matrix Multiply as an Atomic Operation: End Class Definition
      Matrix Multiply as an Atomic Operation: Start Class Definition
      User Atomic Matrix Multiply: Example and Test: Class Definition
      Atomic Eigen Cholesky Factorization Class: End Class Definition
      Atomic Eigen Cholesky Factorization Class: Start Class Definition
      Atomic Eigen Cholesky Factorization Class
      Atomic Eigen Matrix Inversion Class: End Class Definition
      Atomic Eigen Matrix Inversion Class: Start Class Definition
      Atomic Eigen Matrix Inversion Class
      Atomic Eigen Matrix Inverse: Example and Test: Class Definition
      Atomic Eigen Matrix Multiply Class: End Class Definition
      Atomic Eigen Matrix Multiply Class: Start Class Definition
      Atomic Eigen Matrix Multiply Class
      Atomic Eigen Matrix Multiply: Example and Test: Class Definition
      Tan and Tanh as User Atomic Operations: Example and Test: End Class Definition
      Tan and Tanh as User Atomic Operations: Example and Test: Start Class Definition
      Atomic Sparsity with Set Patterns: Example and Test: End Class Definition
      Atomic Sparsity with Set Patterns: Example and Test: Start Class Definition
      Reciprocal as an Atomic Operation: Example and Test: End Class Definition
      Reciprocal as an Atomic Operation: Example and Test: Start Class Definition
      Atomic Euclidean Norm Squared: Example and Test: End Class Definition
      Atomic Euclidean Norm Squared: Example and Test: Start Class Definition
      Getting Started with Atomic Operations: Example and Test: End Class Definition
      Getting Started with Atomic Operations: Example and Test: Start Class Definition
      Atomic Reverse Hessian Sparsity: Example and Test: Start Class Definition
      Atomic Forward Hessian Sparsity: Example and Test: Start Class Definition
      Atomic Reverse Jacobian Sparsity: Example and Test: Start Class Definition
      Atomic Forward Jacobian Sparsity: Example and Test: Start Class Definition
      Atomic Reverse: Example and Test: Start Class Definition
      Atomic Forward: Example and Test: Start Class Definition
      Choosing the CppAD Test Vector Template Class
class: CppAD::vectorBool Class: Example and Test
       CppAD::vector Template Class: Example and Test
       Simple Vector Template Class: Example and Test
clear User Defined Atomic AD Functions: clear
      The CppAD::vector Template Class: clear
      Free Static Variables
      Checkpointing Functions: clear
cmake Using CMake to Configure CppAD: CMake Command
      Using CMake to Configure CppAD: The CMake Program
      Using CMake to Configure CppAD
      CppAD Download, Test, and Install Instructions: Instructions.Step 2: Cmake
cmake_install_datadir Using CMake to Configure CppAD: cmake_install_datadir
cmake_install_docdir Using CMake to Configure CppAD: cmake_install_docdir
cmake_install_includedirs Using CMake to Configure CppAD: cmake_install_includedirs
cmake_install_libdirs Using CMake to Configure CppAD: cmake_install_libdirs
cmake_verbose_makefile Using CMake to Configure CppAD: cmake_verbose_makefile
code Main Program For Comparing C and C++ Speed: Source Code
     Determine Amount of Time to Execute det_by_minor: Source Code
     Returns Elapsed Number of Seconds: Source Code
     Repeat det_by_minor Routine A Specified Number of Times: Source Code
     Correctness Test of det_by_minor Routine: Source Code
     Simulate a [0,1] Uniform Random Variate: Source Code
     Compute Determinant using Expansion by Minors: Source Code
     Determinant of a Minor: Source Code
     ODE Inverse Problem Definitions: Source Code
     Simulate a [0,1] Uniform Random Variate: Source Code
     Evaluate a Function That Has a Sparse Hessian: Source Code
     Evaluate a Function That Has a Sparse Jacobian: Source Code
     Evaluate a Function Defined in Terms of an ODE: Source Code
     Sum Elements of a Matrix Times Itself: Source Code
     Check Gradient of Determinant of 3 by 3 matrix: Source Code
     Check Determinant of 3 by 3 matrix: Source Code
     Determinant Using Expansion by Minors: Source Code
     Determinant of a Minor: Source Code
     Determinant Using Expansion by Lu Factorization: Source Code
     Speed Testing Utilities: Source Code
     Source Code for eigen_plugin.hpp
     ODE Inverse Problem Definitions: Source Code
     An Error Controller for Gear's Ode Solvers: Source Code
     An Arbitrary Order Gear Method: Source Code
     An Error Controller for ODE Solvers: Source Code
     A 3rd and 4th Order Rosenbrock ODE Solver: Source Code
     An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Source Code
     Multi-dimensional Romberg Integration: Source Code
     One DimensionalRomberg Integration: Source Code
     Using a Team of AD Threads: Example and Test: Source Code
     A Simple pthread AD: Example and Test: Source Code
     A Simple Boost Threading AD: Example and Test: Source Code
     A Simple OpenMP AD: Example and Test: Source Code
     A Simple Parallel Pthread Example and Test: Source Code
     A Simple Boost Thread Example and Test: Source Code
     A Simple OpenMP Example and Test: Source Code
     Base Type Requirements for Hash Coding Values: code
     Printing During Forward Mode: Example and Test: Source Code
     exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence.Code
     exp_2: Operation Sequence and Zero Order Forward Mode: Operation Sequence.Code
     Download The CppAD Source Code
coding Base Type Requirements for Hash Coding Values
coefficient Glossary: Taylor Coefficient
            Controlling Taylor Coefficient Memory Allocation: Example and Test
            Number Taylor Coefficient Orders Currently Stored
            AD Theory for Cholesky Factorization: Notation.Taylor Coefficient
coefficients Error Function Forward Taylor Polynomial Theory: Taylor Coefficients Recursion
             Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory: Taylor Coefficients Recursion
             Inverse Cosine and Hyperbolic Cosine Forward Mode Theory: Taylor Coefficients Recursion
             Inverse Sine and Hyperbolic Sine Forward Mode Theory: Taylor Coefficients Recursion
             Inverse Tangent and Hyperbolic Tangent Forward Mode Theory: Taylor Coefficients Recursion
             Logarithm Function Forward Mode Theory: Taylor Coefficients Recursion
             Exponential Function Forward Mode Theory: Taylor Coefficients Recursion
             The Theory of Forward Mode: Standard Math Functions.Taylor Coefficients Recursion Formula
             Third Order Reverse Mode: Example and Test: Taylor Coefficients
             Controlling Taylor Coefficients Memory Allocation
             Construct an ADFun Object and Stop Recording: Assignment Operator.Taylor Coefficients
coin Download The CppAD Source Code: Release Versions.Coin
col Evaluate a Function That Has a Sparse Hessian: col
    Evaluate a Function That Has a Sparse Jacobian: col
    Speed Testing Sparse Jacobian: col
    Speed Testing Sparse Hessian: col
    Sparse Hessian: Easy Driver: row, col
    Sparse Jacobian: Easy Driver: row, col
color_method Sparse Hessian: Easy Driver: work.color_method
             Sparse Jacobian: Easy Driver: work.color_method
colpack Running the Speed Test Program: Sparsity Options.colpack
        Download and Install ColPack in Build Directory
        Using ColPack: Example and Test
        Using ColPack: Example and Test
        Including the ColPack Sparsity Calculations
colpack: Using ColPack: Example and Test
         Using ColPack: Example and Test
colpack_prefix Including the ColPack Sparsity Calculations: colpack_prefix
column Sparse Hessian: Easy Driver: p.Column Subset
combine Multi-threading Newton Method Utility Routines
        Multi-threading Sum of 1/i Utility Routines
command Using CMake to Configure CppAD: CMake Command
commands Deprecated Include Files: Linking New Files to Deprecated Commands
compare Compare Speed of C and C++
        CompareChange and Re-Tape: Example and Test
        Compare AD with Base Objects: Example and Test
        Compare AD and Base Objects for Nearly Equal
        AD Binary Comparison Operators: Example and Test
        AD Binary Comparison Operators
     speed C and C++ Compare Speed of C and C++
compare_change Comparison Changes Between Taping and Zero Order Forward
comparechange Frequently Asked Questions and Answers: CompareChange
              CompareChange and Re-Tape: Example and Test
compareop Base Type Requirements for Conditional Expressions: CompareOp
comparing Main Program For Comparing C and C++ Speed
comparison zdouble: An AD Base Type With Absolute Zero: Syntax.Comparison Operators
           Comparison Changes During Zero Order Forward Mode
           Example Optimization and Comparison Operators
           Comparison Changes Between Taping and Zero Order Forward
           AD Binary Comparison Operators: Example and Test
           AD Binary Comparison Operators
comparisons Base Type Requirements for Ordered Comparisons
            Base Type Requirements for Identically Equal Comparisons
            exp_eps: Operation Sequence and Zero Order Forward Sweep: Comparisons
compilation The CppAD Wish List: Compilation Speed
compile Auto Tools Unix Test and Installation
        Using CMake to Configure CppAD
complex Frequently Asked Questions and Answers: Complex Types
        LuSolve With Complex Arguments: Example and Test
        Complex Polynomial: Example and Test
        AD Absolute Value Functions: abs, fabs: Complex Types
        Convert From AD to Integer: x.Complex Types
complicated Base Type Requirements for Identically Equal Comparisons: EqualOpSeq.More Complicated Cases
compressed Download The CppAD Source Code: Current Version.Compressed Archives
           Download The CppAD Source Code: Compressed Archives
compute Compute Determinant using Expansion by Minors
        Using AD to Compute Atomic Function Derivatives
        Using AD to Compute Atomic Function Derivatives
        Using Eigen To Compute Determinant: Example and Test
        Compute Determinant and Solve Linear Equations
        Compute Determinants and Solve Equations by LU Factorization
        Getting Started Using CppAD to Compute Derivatives
computed Example AD<Base> Where Base Constructor Allocates Memory: Computed Assignment Macro
         AD Computed Assignment Division: Example and Test
         AD Computed Assignment Multiplication: Example and Test
         AD Computed Assignment Subtraction: Example and Test
         AD Computed Assignment Addition: Example and Test
         AD Computed Assignment Operators
         AD Arithmetic Operators and Computed Assignments
computing Computing Jacobian and Hessian of Bender's Reduced Objective
          Computing a Jacobian With Constants that Change
          Computing Sparse Hessian for a Subset of Variables
          Computing Dependency: Example and Test
concept Check Simple Vector Concept
        Check NumericType Class Concept
concepts Some General Purpose Utilities: C++ Concepts
cond_exp_1 CppAD Changes and Additions During 2015: 05-26.cond_exp_1
cond_exp_2 CppAD Changes and Additions During 2015: 05-26.cond_exp_2
condexpop Enable use of AD<Base> where Base is std::complex<double>: CondExpOp
          Enable use of AD<Base> where Base is double: CondExpOp
          Enable use of AD<Base> where Base is float: CondExpOp
          Enable use of AD<Base> where Base is Adolc's adouble Type: CondExpOp
          Example AD<Base> Where Base Constructor Allocates Memory: CondExpOp
condexprel Enable use of AD<Base> where Base is std::complex<double>: CondExpRel
           Enable use of AD<Base> where Base is double: CondExpRel
           Enable use of AD<Base> where Base is float: CondExpRel
           Enable use of AD<Base> where Base is Adolc's adouble Type: CondExpRel
           Example AD<Base> Where Base Constructor Allocates Memory: CondExpRel
           Base Type Requirements for Conditional Expressions: CondExpRel
condexptemplate Base Type Requirements for Conditional Expressions: CondExpTemplate
condition ODE Fitting Using Fast Representation: Initial Condition
          ODE Fitting Using Simple Representation: Initial Condition Constraint
          Number of Variables That Can be Skipped: Example and Test
conditional Example Optimization and Nested Conditional Expressions
            Example Optimization and Conditional Expressions
            Number of Variables That Can be Skipped: Example and Test
            Base Type Requirements for Conditional Expressions
            Conditional Expressions: Example and Test
            AD Conditional Expressions
configuration Nonlinear Programming Using CppAD and Ipopt: Example and Test: Configuration Requirement
              Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Configuration Requirement
              Nonlinear Programming Using CppAD and Ipopt: Example and Test: Configuration Requirement
              Using Adolc with Multiple Levels of Taping: Example and Test: Configuration Requirement
              CppAD pkg-config Files: CppAD Configuration Files
configure Auto Tools Unix Test and Installation: Configure
          Using CMake to Configure CppAD
conjugate Differentiate Conjugate Gradient Algorithm: Example and Test
conserve Using vectorBool Sparsity To Conserve Memory: Example and Test
constants Computing a Jacobian With Constants that Change
constraint ODE Fitting Using Simple Representation: Trapezoidal Approximation Constraint
           ODE Fitting Using Simple Representation: Initial Condition Constraint
construct Construct an ADFun Object and Stop Recording
constructor zdouble: An AD Base Type With Absolute Zero: Syntax.Constructor and Assignment
            Determinant Using Expansion by Minors: Constructor
            Determinant Using Expansion by Lu Factorization: Constructor
            Allocate An Array and Call Default Constructor for its Elements
            Definition of a Simple Vector: Element Constructor and Destructor
            Definition of a Simple Vector: Copy Constructor
            Definition of a Simple Vector: Sizing Constructor
            Definition of a Simple Vector: Default Constructor
            Definition of a Numeric Type: Copy Constructor
            Definition of a Numeric Type: Constructor From Integer
            Definition of a Numeric Type: Default Constructor
            Replacing the CppAD Error Handler: Constructor
            Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
            Number Taylor Coefficient Orders Currently Stored: Constructor
            Construct an ADFun Object and Stop Recording: Example.Default Constructor
            Construct an ADFun Object and Stop Recording: Example.Sequence Constructor
            Construct an ADFun Object and Stop Recording: Copy Constructor
            Construct an ADFun Object and Stop Recording: Sequence Constructor
            Construct an ADFun Object and Stop Recording: Default Constructor
            Example AD<Base> Where Base Constructor Allocates Memory
            Required Base Class Member Functions: Copy Constructor
            Required Base Class Member Functions: Double Constructor
            Required Base Class Member Functions: Default Constructor
            AD Vectors that Record Index Operations: Constructor
            Matrix Multiply as an Atomic Operation: Constructor
            User Atomic Matrix Multiply: Example and Test: Use Atomic Function.Constructor
            Atomic Eigen Cholesky Factorization Class: Public.Constructor
            Atomic Eigen Cholesky Factorization: Example and Test: Use Atomic Function.Constructor
            Atomic Eigen Matrix Inversion Class: Public.Constructor
            Atomic Eigen Matrix Inverse: Example and Test: Use Atomic Function.Constructor
            Atomic Eigen Matrix Multiply Class: Public.Constructor
            Atomic Eigen Matrix Multiply: Example and Test: Use Atomic Function.Constructor
            Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.Constructor
            Tan and Tanh as User Atomic Operations: Example and Test: Constructor
            Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function.Constructor
            Atomic Sparsity with Set Patterns: Example and Test: Constructor
            Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function.Constructor
            Reciprocal as an Atomic Operation: Example and Test: Constructor
            Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function.Constructor
            Atomic Euclidean Norm Squared: Example and Test: Constructor
            Getting Started with Atomic Operations: Example and Test: Use Atomic Function.Constructor
            Getting Started with Atomic Operations: Example and Test: Constructor
            Atomic Reverse Hessian Sparsity: Example and Test: Constructor
            Atomic Forward Hessian Sparsity: Example and Test: Constructor
            Atomic Reverse Jacobian Sparsity: Example and Test: Constructor
            Atomic Forward Jacobian Sparsity: Example and Test: Constructor
            Atomic Reverse: Example and Test: Constructor
            Atomic Forward: Example and Test: Constructor
            Atomic Function Constructor: Example.Use Constructor
            Atomic Function Constructor: Example.Define Constructor
            Atomic Function Constructor
            Checkpointing Functions: constructor
            AD Constructors: Example and Test
constructor: Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
             Independent and ADFun Constructor: Example and Test
constructors AD Constructors
constructors: AD Constructors: Example and Test
control Control When Thread Alloc Retains Memory For Future Use
        Controlling Taylor Coefficients Memory Allocation
controller An Error Controller for Gear's Ode Solvers
           An Error Controller for ODE Solvers
controlling Controlling Taylor Coefficient Memory Allocation: Example and Test
            Controlling Taylor Coefficients Memory Allocation
convention Lu Factor and Solve with Recorded Pivoting: Storage Convention
conversion Conversion and I/O of AD Objects
convert Convert Certain Types to a String
        Convert an AD Variable to a Parameter: Example and Test
        Convert an AD Variable to a Parameter
        Convert An AD or Base Type to String
        Convert From AD to Integer: Example and Test
        Convert From AD to Integer
        Convert From AD to its Base Type: Example and Test
        Convert From an AD Type to its Base Type
        Conversion and I/O of AD Objects
        AD Constructors
copy Definition of a Simple Vector: Copy Constructor
     Definition of a Numeric Type: Copy Constructor
     Construct an ADFun Object and Stop Recording: Copy Constructor
     Required Base Class Member Functions: Copy Constructor
correct Check Gradient of Determinant of 3 by 3 matrix
        Check Determinant of 3 by 3 matrix
        Running the Speed Test Program: test.correct
correctness Correctness Test of det_by_minor Routine
            Correctness Check for Both Simple and Fast Representations
            Running the Speed Test Program: Correctness Results
            Correctness Tests For Exponential Approximation in Introduction
cos Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
    Trigonometric and Hyperbolic Sine and Cosine Forward Theory
    The AD cos Function: Example and Test
    The Cosine Function: cos
cosh Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
     Trigonometric and Hyperbolic Sine and Cosine Forward Theory
     The AD cosh Function: Example and Test
     The Hyperbolic Cosine Function: cosh
cosine Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
       Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
       Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
       Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
       Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
       Trigonometric and Hyperbolic Sine and Cosine Forward Theory
       The Inverse Hyperbolic Cosine Function: acosh
       The Hyperbolic Cosine Function: cosh
       The Cosine Function: cos
count Comparison Changes Between Taping and Zero Order Forward: count
      An Introduction by Example to Algorithmic Differentiation: Preface.Operation Count
cppad Your License for the CppAD Software
      CppAD Addons
      zdouble: An AD Base Type With Absolute Zero: Motivation.CppAD
      Define Matrix Multiply as a User Atomic Operation: CppAD User Atomic Callback Functions
      Nonlinear Programming Using CppAD and Ipopt: Example and Test
      Nonlinear Programming Using the CppAD Interface to Ipopt
      A Quick OpenMP Memory Allocator Used by CppAD
      CppAD Deprecated API Features
      Changes and Additions to CppAD During 2003
      Changes and Additions to CppAD During 2004
      Changes and Additions to CppAD During 2005
      Changes and Additions to CppAD During 2006
      Changes and Additions to CppAD During 2007
      Changes and Additions to CppAD During 2008
      Changes and Additions to CppAD During 2009
      Changes and Additions to CppAD During 2010
      Changes and Additions to CppAD During 2011
      CppAD Changes and Additions During 2012
      CppAD Changes and Additions During 2013
      CppAD Changes and Additions During 2014
      CppAD Changes and Additions During 2015
      Changes and Additions to CppAD During 2016
      Changes and Additions to CppAD
      The CppAD Wish List
      CppAD Speed: Sparse Jacobian
      CppAD Speed: Sparse Hessian
      CppAD Speed: Second Derivative of a Polynomial
      CppAD Speed: Gradient of Ode Solution
      CppAD Speed, Matrix Multiplication
      CppAD Speed: Gradient of Determinant Using Lu Factorization
      CppAD Speed: Gradient of Determinant by Minor Expansion
      Speed Test Derivatives Using CppAD
      CppAD Speed: Matrix Multiplication (Double Version)
      Running the Speed Test Program
      Using The CppAD Test Vector Template Class
      CppAD Examples and Tests
      Enable Use of Eigen Linear Algebra Package with CppAD: CppAD Namespace
      Enable Use of Eigen Linear Algebra Package with CppAD
      Example and Test Linking CppAD to Languages Other than C++
      List of All the CppAD Examples
      Utility Routines used by CppAD Examples
      Examples: The CppAD Test Vector Template Class
      Nonlinear Programming Using CppAD and Ipopt: Example and Test
      CppAD Assertions During Execution
      Replacing The CppAD Error Handler: Example and Test
      Replacing the CppAD Error Handler
      Using CppAD in a Multi-Threading Environment
      CppAD API Preprocessor Symbols
      AD<Base> Requirements for a CppAD Base Type
      exp_eps: CppAD Forward and Reverse Sweeps
      exp_2: CppAD Forward and Reverse Sweeps
      Getting Started Using CppAD to Compute Derivatives
      Auto Tools Unix Test and Installation: Profiling CppAD
      CppAD pkg-config Files: CppAD Configuration Files
      CppAD pkg-config Files
      Checking the CppAD Examples and Tests
      Choosing the CppAD Test Vector Template Class: cppad
      Choosing the CppAD Test Vector Template Class
      Including the cppad_ipopt Library and Tests
      Using CMake to Configure CppAD
      Download The CppAD Source Code
      CppAD Download, Test, and Install Instructions
cppad-20170000.3: cppad-20170000.3: A Package for Differentiation of C++ Algorithms
cppad.hpp cppad-20170000.3: A Package for Differentiation of C++ Algorithms
cppad::numeric_limits Base Type Requirements for Numeric Limits: CppAD::numeric_limits
                      Numeric Limits For an AD and Base Types: CppAD::numeric_limits
cppad::vector Choosing The Vector Testing Template Class: CppAD::vector
              Using The CppAD Test Vector Template Class: CppAD::vector
              CppAD::vector Template Class: Example and Test
              The CppAD::vector Template Class
cppad::vectorbool CppAD::vectorBool Class: Example and Test
cppad_cxx_flags Using CMake to Configure CppAD: cppad_cxx_flags
cppad_deprecated Using CMake to Configure CppAD: cppad_deprecated
cppad_ipopt Nonlinear Programming Using the CppAD Interface to Ipopt: cppad_ipopt namespace
            Including the cppad_ipopt Library and Tests
cppad_ipopt_nlp ODE Fitting Using Fast Representation
                ODE Fitting Using Simple Representation
                ODE Fitting Using Simple Representation
cppad_lib Including the ColPack Sparsity Calculations: cppad_lib
cppad_max_num_threads Using CppAD in a Multi-Threading Environment: CPPAD_MAX_NUM_THREADS
                      Using CMake to Configure CppAD: cppad_max_num_threads
cppad_null CppAD API Preprocessor Symbols: Documented Here.CPPAD_NULL
cppad_numeric_limits Base Type Requirements for Numeric Limits: CPPAD_NUMERIC_LIMITS
cppad_package_string CppAD API Preprocessor Symbols: Documented Here.CPPAD_PACKAGE_STRING
cppad_postfix Using CMake to Configure CppAD: cppad_postfix
cppad_prefix Using CMake to Configure CppAD: cppad_prefix
cppad_profile_flag Using CMake to Configure CppAD: cppad_profile_flag
cppad_standard_math_unary Base Type Requirements for Standard Math Functions: CPPAD_STANDARD_MATH_UNARY
cppad_tape_addr_type Using CMake to Configure CppAD: cppad_tape_addr_type
cppad_tape_id_type Using CMake to Configure CppAD: cppad_tape_id_type
cppad_testvector Using CMake to Configure CppAD: cppad_testvector
cppad_to_string Extending to_string To Another Floating Point Type: CPPAD_TO_STRING
cppad_use_cplusplus_2011 CppAD API Preprocessor Symbols: Documented Here.CPPAD_USE_CPLUSPLUS_2011
                         The Logarithm of One Plus Argument: log1p: CPPAD_USE_CPLUSPLUS_2011
                         The Exponential Function Minus One: expm1: CPPAD_USE_CPLUSPLUS_2011
                         The Error Function: CPPAD_USE_CPLUSPLUS_2011
                         The Inverse Hyperbolic Tangent Function: atanh: CPPAD_USE_CPLUSPLUS_2011
                         The Inverse Hyperbolic Sine Function: asinh: CPPAD_USE_CPLUSPLUS_2011
                         The Inverse Hyperbolic Cosine Function: acosh: CPPAD_USE_CPLUSPLUS_2011
cppad_user_atomic User Defined Atomic AD Functions: CPPAD_USER_ATOMIC
cppadcreatediscrete Discrete AD Functions: CppADCreateDiscrete Deprecated 2007-07-28
cppadvector Choosing The Vector Testing Template Class: CppADvector Deprecated 2007-07-28
create Allocate Memory and Create A Raw Array
       AD Boolean Functions: Create Binary
       AD Boolean Functions: Create Unary
       Discrete AD Functions: Create AD Version
create_array Allocate Memory and Create A Raw Array
             Allocate An Array and Call Default Constructor for its Elements
creating Creating Your Own Interface to an ADFun Object
criteria An Error Controller for Gear's Ode Solvers: Error Criteria Discussion
         An Error Controller for ODE Solvers: Error Criteria Discussion
cstdint Using CMake to Configure CppAD: cppad_tape_addr_type.cstdint
        Using CMake to Configure CppAD: cppad_tape_id_type.cstdint
ctor Auto Tools Unix Test and Installation
     Using CMake to Configure CppAD
ctor_arg_list Atomic Function Constructor: atomic_user.ctor_arg_list
cumulative Example Optimization and Cumulative Sum Operations
current Get the Current OpenMP Thread Number
        Is The Current Execution in OpenMP Parallel Mode
        Get the Current Thread Number
        Is The Current Execution in Parallel Mode
        Abort Current Recording: Example and Test
        Download The CppAD Source Code: Current Version
currently Amount of Memory a Thread is Currently Using
          Free Memory Currently Available for Quick Use by a Thread
          Amount of Memory a Thread is Currently Using
          Free Memory Currently Available for Quick Use by a Thread
          Number Taylor Coefficient Orders Currently Stored
cxx_flags Auto Tools Unix Test and Installation: cxx_flags
cygwin Pthread Implementation of a Team of AD Threads: Bug in Cygwin
       Auto Tools Unix Test and Installation: adolc_dir.Cygwin
       Including the ADOL-C Examples and Tests: Cygwin
D
Dependent ADFun Check and Re-Tape: Example and Test
          Stop Recording and Store Operation Sequence
Domain ADFun Sequence Properties: Example and Test
daily Download The CppAD Source Code: Daily Versions
data The CppAD::vector Template Class: vectorBool.data
     The CppAD::vector Template Class: data
datadir Using CMake to Configure CppAD
ddp Speed Testing Second Derivative of a Polynomial: ddp
ddw Reverse Mode Second Partial Derivative Driver: ddw
ddy Forward Mode Second Partial Derivative Driver: ddy
deallocate Deallocate An Array and Call Destructor for its Elements
debug Printing AD Values During Forward Mode
debugging Check an ADFun Object For Nan Results: Debugging
declare Define Matrix Multiply as a User Atomic Operation: Declare mat_mul Function
        Declare Independent Variables and Start Recording
default Allocate An Array and Call Default Constructor for its Elements
        Definition of a Simple Vector: Default Constructor
        Definition of a Numeric Type: Default Constructor
        Check an ADFun Object For Nan Results: Default
        Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
        Construct an ADFun Object and Stop Recording: Example.Default Constructor
        Construct an ADFun Object and Stop Recording: Default Constructor
        Base Type Requirements for Hash Coding Values: Default
        Required Base Class Member Functions: Default Constructor
define Define Matrix Multiply as a User Atomic Operation
       Atomic Function Constructor: Example.Define Constructor
defined User Defined Atomic AD Functions
        Evaluate a Function Defined in Terms of an ODE
        Using a User Defined AD Base Type: Example and Test
        User Defined Atomic AD Functions
        CppAD pkg-config Files: Defined Fields
definition Definition of a Simple Vector
           Definition of a Numeric Type
           Example AD<Base> Where Base Constructor Allocates Memory: Class Definition
           Matrix Multiply as an Atomic Operation: End Class Definition
           Matrix Multiply as an Atomic Operation: Start Class Definition
           User Atomic Matrix Multiply: Example and Test: Class Definition
           Atomic Eigen Cholesky Factorization Class: End Class Definition
           Atomic Eigen Cholesky Factorization Class: Start Class Definition
           Atomic Eigen Matrix Inversion Class: End Class Definition
           Atomic Eigen Matrix Inversion Class: Start Class Definition
           Atomic Eigen Matrix Inverse: Example and Test: Class Definition
           Atomic Eigen Matrix Multiply Class: End Class Definition
           Atomic Eigen Matrix Multiply Class: Start Class Definition
           Atomic Eigen Matrix Multiply: Example and Test: Class Definition
           Tan and Tanh as User Atomic Operations: Example and Test: End Class Definition
           Tan and Tanh as User Atomic Operations: Example and Test: Start Class Definition
           Atomic Sparsity with Set Patterns: Example and Test: End Class Definition
           Atomic Sparsity with Set Patterns: Example and Test: Start Class Definition
           Reciprocal as an Atomic Operation: Example and Test: End Class Definition
           Reciprocal as an Atomic Operation: Example and Test: Start Class Definition
           Atomic Euclidean Norm Squared: Example and Test: End Class Definition
           Atomic Euclidean Norm Squared: Example and Test: Start Class Definition
           Getting Started with Atomic Operations: Example and Test: End Class Definition
           Getting Started with Atomic Operations: Example and Test: Start Class Definition
           Atomic Reverse Hessian Sparsity: Example and Test: Start Class Definition
           Atomic Forward Hessian Sparsity: Example and Test: Start Class Definition
           Atomic Reverse Jacobian Sparsity: Example and Test: Start Class Definition
           Atomic Forward Jacobian Sparsity: Example and Test: Start Class Definition
           Atomic Reverse: Example and Test: Start Class Definition
           Atomic Forward: Example and Test: Start Class Definition
definitions: ODE Inverse Problem Definitions: Source Code
             ODE Inverse Problem Definitions: Source Code
delete Tracking Use of New and Delete: Example and Test
       Routines That Track Use of New and Delete
delete: Tracking Use of New and Delete: Example and Test
delete_array Return A Raw Array to The Available Memory for a Thread
             Deallocate An Array and Call Destructor for its Elements
delta Return A Raw Array to The Available Memory for a Thread: Delta
      Allocate Memory and Create A Raw Array: Delta
      Deallocate An Array and Call Destructor for its Elements: Delta
      Allocate An Array and Call Default Constructor for its Elements: Delta
dependency Computing Dependency: Example and Test: Dependency Pattern
           Jacobian Sparsity Pattern: Reverse Mode: dependency
           Jacobian Sparsity Pattern: Forward Mode: dependency
dependency: Computing Dependency: Example and Test
dependent ADFun Object Deprecated Member Functions: Dependent
          Glossary: Tape.Dependent Variables
          Glossary: Operation.Dependent
deprecate AD Conditional Expressions: Deprecate 2005-08-07
deprecated zdouble: An AD Base Type With Absolute Zero: Deprecated 2015-09-26
           Old Matrix Multiply as a User Atomic Operation: Example and Test: Deprecated 2013-05-27
           Old Tan and Tanh as User Atomic Operations: Example and Test: Deprecated 2013-05-27
           Using AD to Compute Atomic Function Derivatives: Deprecated 2013-05-27
           Using AD to Compute Atomic Function Derivatives: Deprecated 2013-05-27
           Old Atomic Operation Reciprocal: Example and Test: Deprecated 2013-05-27
           User Defined Atomic AD Functions: Deprecated 2013-05-27
           Nonlinear Programming Using the CppAD Interface to Ipopt: Deprecated 2012-11-28
           Choosing The Vector Testing Template Class: CppADvector Deprecated 2007-07-28
           Choosing The Vector Testing Template Class: Deprecated 2012-07-03
           Machine Epsilon For AD Types: Deprecated 2012-06-17
           Memory Leak Detection: Deprecated 2012-04-06
           OpenMP Memory Allocator: Example and Test: Deprecated 2011-08-31
           Return A Raw Array to The Available Memory for a Thread: Deprecated 2011-08-31
           Allocate Memory and Create A Raw Array: Deprecated 2011-08-31
           Amount of Memory Available for Quick Use by a Thread: Deprecated 2011-08-31
           Amount of Memory a Thread is Currently Using: Deprecated 2011-08-31
           Free Memory Currently Available for Quick Use by a Thread: Deprecated 2011-08-31
           Return Memory to omp_alloc: Deprecated 2011-08-31
           Get At Least A Specified Amount of Memory: Deprecated 2011-08-31
           Get the Current OpenMP Thread Number: Deprecated 2011-08-31
           Is The Current Execution in OpenMP Parallel Mode: Deprecated 2011-08-31
           Set and Get Maximum Number of Threads for omp_alloc Allocator: Deprecated 2011-08-31
           A Quick OpenMP Memory Allocator Used by CppAD: Deprecated 2011-08-23
           Routines That Track Use of New and Delete: TrackCount.Previously Deprecated
           Routines That Track Use of New and Delete: TrackExtend.Previously Deprecated
           Routines That Track Use of New and Delete: TrackDelVec.Previously Deprecated
           Routines That Track Use of New and Delete: TrackNewVec.Previously Deprecated
           Routines That Track Use of New and Delete: Deprecated 2007-07-23
           OpenMP Parallel Setup: Deprecated 2011-06-23
           Comparison Changes During Zero Order Forward Mode: Deprecated 2015-01-20
           ADFun Object Deprecated Member Functions: capacity_taylor.Deprecated 2014-03-18
           ADFun Object Deprecated Member Functions: size_taylor.Deprecated 2014-03-18
           ADFun Object Deprecated Member Functions: use_VecAD.Deprecated 2006-04-08
           ADFun Object Deprecated Member Functions: taylor_size.Deprecated 2006-06-17
           ADFun Object Deprecated Member Functions: Size.Deprecated 2006-04-03
           ADFun Object Deprecated Member Functions: Memory.Deprecated 2006-03-31
           ADFun Object Deprecated Member Functions: Order.Deprecated 2006-03-31
           ADFun Object Deprecated Member Functions: Dependent.Deprecated 2007-08-07
           ADFun Object Deprecated Member Functions
           Deprecated Include Files: Linking New Files to Deprecated Commands
           Deprecated Include Files: Deprecated 2006-12-17
           Deprecated Include Files: Deprecated 2015-11-30
           Deprecated Include Files
           CppAD Deprecated API Features
           Obtain Nan or Determine if a Value is Nan: nan(zero).Deprecated 2015-10-04
           CppAD API Preprocessor Symbols: Deprecated
           AD Boolean Functions: Deprecated 2007-07-31
           Atomic Reverse Hessian Sparsity Patterns: u.x
           Atomic Reverse Hessian Sparsity Patterns: Deprecated 2016-06-27
           Atomic Forward Hessian Sparsity Patterns: Implementation.x
           Atomic Forward Hessian Sparsity Patterns: Deprecated 2016-06-27
           Atomic Reverse Jacobian Sparsity Patterns: Implementation.x
           Atomic Reverse Jacobian Sparsity Patterns: Deprecated 2016-06-27
           Atomic Forward Jacobian Sparsity Patterns: Implementation.x
           Atomic Forward Jacobian Sparsity Patterns: Deprecated 2016-06-27
           Discrete AD Functions: CppADCreateDiscrete Deprecated 2007-07-28
           AD Constructors: x.Deprecated 2013-12-31
           Auto Tools Unix Test and Installation: Deprecated 2012-12-26
derivative The Theory of Derivative Calculations
           Sacado Speed: Second Derivative of a Polynomial
           Fadbad Speed: Second Derivative of a Polynomial
           CppAD Speed: Second Derivative of a Polynomial
           Adolc Speed: Second Derivative of a Polynomial
           Speed Testing Second Derivative of a Polynomial
           Speed Testing Derivative of Matrix Multiply
           Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Derivative of ODE Solution
           Taylor's Ode Solver: A Multi-Level AD Example and Test: Derivative of ODE Solution
           Evaluate a Polynomial or its Derivative
           Reverse Mode Second Partial Derivative Driver
           Forward Mode Second Partial Derivative Driver
           Hessian: Easy Driver
           First Order Derivative Driver: Example and Test
           First Order Derivative: Driver Routine
           Jacobian: Driver Routine
           Any Order Reverse Mode
           Second Order Reverse Mode
           First Order Reverse Mode
           Multiple Order Forward Mode: Purpose.Derivative Values
           Second Order Forward Mode: Derivative Values
           First Order Forward Mode: Derivative Values
           The Sign: sign: Derivative
           AD Absolute Value Functions: abs, fabs: Derivative
           The Hyperbolic Tangent Function: tanh: Derivative
           The Tangent Function: tan: Derivative
           The Square Root Function: sqrt: Derivative
           The Hyperbolic Sine Function: sinh: Derivative
           The Sine Function: sin: Derivative
           The Exponential Function: log: Derivative
           The Exponential Function: exp: Derivative
           The Hyperbolic Cosine Function: cosh: Derivative
           The Cosine Function: cos: Derivative
           Inverse Tangent Function: atan: Derivative
           Inverse Sine Function: asin: Derivative
           Inverse Sine Function: acos: Derivative
           AD Computed Assignment Operators: Derivative
           AD Binary Arithmetic Operators: Derivative
           AD Unary Minus Operator: Derivative
           AD Unary Plus Operator: Derivative
           exp_eps: Second Order Forward Mode: Operation Sequence.Derivative
           exp_eps: First Order Forward Sweep: Operation Sequence.Derivative
           exp_2: Second Order Forward Mode: Operation Sequence.Derivative
           exp_2: First Order Forward Mode: Operation Sequence.Derivative
           Getting Started Using CppAD to Compute Derivatives: Derivative
           cppad-20170000.3: A Package for Differentiation of C++ Algorithms
derivative: First Order Derivative: Driver Routine
            First Order Partial Derivative: Driver Routine
derivatives Using AD to Compute Atomic Function Derivatives
            Using AD to Compute Atomic Function Derivatives
            An ODE Inverse Problem Example: Black Box Method.Derivatives
            Bibliography: Evaluating Derivatives
            Error Function Forward Taylor Polynomial Theory: Derivatives
            Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory: Derivatives
            Inverse Cosine and Hyperbolic Cosine Forward Mode Theory: Derivatives
            Inverse Sine and Hyperbolic Sine Forward Mode Theory: Derivatives
            Inverse Tangent and Hyperbolic Tangent Forward Mode Theory: Derivatives
            Logarithm Function Forward Mode Theory: Derivatives
            Exponential Function Forward Mode Theory: Derivatives
            Speed Test Derivatives Using Sacado
            Speed Test Derivatives Using Fadbad
            Speed Test Derivatives Using CppAD
            Speed Test of Derivatives Using Adolc
            Using Multiple Levels of AD: Procedure.Derivatives of Outer Function
            Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
            Discrete AD Functions: Derivatives
            Getting Started Using CppAD to Compute Derivatives
derivatives: First and Second Derivatives: Easy Drivers
description LU Factorization of A Square Matrix and Stability Calculation: Description
            General Examples: Description
            The CppAD::vector Template Class: Description
            An Error Controller for ODE Solvers: Description
            A 3rd and 4th Order Rosenbrock ODE Solver: Description
            Multi-dimensional Romberg Integration: Description
            One DimensionalRomberg Integration: Description
            Invert an LU Factored Equation: Description
            LU Factorization of A Square Matrix: Description
            Compute Determinant and Solve Linear Equations: Description
            Evaluate a Polynomial or its Derivative: Description
            Atomic Eigen Cholesky Factorization: Example and Test: Description
            Atomic Eigen Matrix Inverse: Example and Test: Description
            Atomic Eigen Matrix Multiply: Example and Test: Description
            Conditional Expressions: Example and Test: Description
            The Sign: sign: Description
            The Logarithm of One Plus Argument: log1p: Description
            The Exponential Function Minus One: expm1: Description
            The Error Function: Description
            The Inverse Hyperbolic Tangent Function: atanh: Description
            The Inverse Hyperbolic Sine Function: asinh: Description
            The Inverse Hyperbolic Cosine Function: acosh: Description
destructor Deallocate An Array and Call Destructor for its Elements
           Definition of a Simple Vector: Element Constructor and Destructor
det Determinant Using Expansion by Minors: det
    Determinant Using Expansion by Lu Factorization: det
det_33 Source: det_33
       Check Determinant of 3 by 3 matrix
det_by_lu Source: det_by_lu
          Determinant Using Expansion by Lu Factorization
det_by_minor Determine Amount of Time to Execute det_by_minor
             Repeat det_by_minor Routine A Specified Number of Times
             Correctness Test of det_by_minor Routine
             Source: det_by_minor
det_grad_33 Source: det_grad_33
            Check Gradient of Determinant of 3 by 3 matrix
det_of_minor Source: det_of_minor
             Determinant of a Minor: Example and Test
             Determinant of a Minor
detection Memory Leak Detection
determinant LU Factorization of A Square Matrix and Stability Calculation: LU.Determinant
            Compute Determinant using Expansion by Minors
            Determinant of a Minor: Determinant of A
            Determinant of a Minor
            Sacado Speed: Gradient of Determinant Using Lu Factorization
            Sacado Speed: Gradient of Determinant by Minor Expansion
            Fadbad Speed: Gradient of Determinant Using Lu Factorization
            Fadbad Speed: Gradient of Determinant by Minor Expansion
            CppAD Speed: Gradient of Determinant Using Lu Factorization
            CppAD Speed: Gradient of Determinant by Minor Expansion
            Adolc Speed: Gradient of Determinant Using Lu Factorization
            Adolc Speed: Gradient of Determinant by Minor Expansion
            Double Speed: Determinant Using Lu Factorization
            Double Speed: Determinant by Minor Expansion
            Check Gradient of Determinant of 3 by 3 matrix
            Check Determinant of 3 by 3 matrix
            Determinant Using Expansion by Minors: Example and Test
            Determinant Using Expansion by Minors
            Determinant of a Minor: Example and Test
            Determinant of a Minor: Determinant of A
            Determinant of a Minor
            Determinant Using Lu Factorization: Example and Test
            Determinant Using Expansion by Lu Factorization
            Speed Testing Gradient of Determinant by Minor Expansion
            Speed Testing Gradient of Determinant Using Lu Factorization
            Lu Factor and Solve with Recorded Pivoting
            Gradient of Determinant Using Lu Factorization: Example and Test
            Gradient of Determinant Using Expansion by Minors: Example and Test
            Gradient of Determinant Using LU Factorization: Example and Test
            Gradient of Determinant Using Expansion by Minors: Example and Test
            Using Eigen To Compute Determinant: Example and Test
            LU Factorization of A Square Matrix: LU.Determinant
            Compute Determinant and Solve Linear Equations
determinant: Using Eigen To Compute Determinant: Example and Test
determinants Compute Determinants and Solve Equations by LU Factorization
determine Determine Amount of Time to Execute det_by_minor
          Obtain Nan or Determine if a Value is Nan
          Determine Amount of Time to Execute a Test
          Determine if Two Values Are Nearly Equal
difference Interfacing to C: Example and Test
           Determine if Two Values Are Nearly Equal
differential Trigonometric and Hyperbolic Sine and Cosine Forward Theory: Differential Equation
             The Theory of Forward Mode: Standard Math Functions.Differential Equation
             An Error Controller for Gear's Ode Solvers
             An Arbitrary Order Gear Method
             An Error Controller for ODE Solvers
             A 3rd and 4th Order Rosenbrock ODE Solver
             An Embedded 4th and 5th Order Runge-Kutta ODE Solver
differentiate Differentiate Conjugate Gradient Algorithm: Example and Test
differentiating Example Differentiating a Stack Machine Interpreter
differentiation Example and Test Linking CppAD to Languages Other than C++
                An Introduction by Example to Algorithmic Differentiation: Preface.Algorithmic Differentiation
                An Introduction by Example to Algorithmic Differentiation
                cppad-20170000.3: A Package for Differentiation of C++ Algorithms
                cppad-20170000.3: A Package for Differentiation of C++ Algorithms
dimension Multi-dimensional Romberg Integration
dimensional One Dimensional Romberg Integration: Example and Test
            Multi-dimensional Romberg Integration
            One Dimensional Romberg Integration: Example and Test
dimensionalromberg One DimensionalRomberg Integration
dimensions Matrix Multiply as an Atomic Operation: Matrix Dimensions
           Atomic Eigen Matrix Inversion Class: Matrix Dimensions
           Atomic Eigen Matrix Multiply Class: Matrix Dimensions
direction Hessian Times Direction: Example and Test
          Second Order Reverse Mode: Hessian Times Direction
direction: Hessian Times Direction: Example and Test
directions Reverse Mode: Multiple Directions
           Forward Mode: Example and Test of Multiple Directions
           Multiple Directions Forward Mode
directories Using CMake to Configure CppAD
directory Auto Tools Unix Test and Installation: Work Directory
          Auto Tools Unix Test and Installation: Distribution Directory
          Download and Install Sacado in Build Directory: Prefix Directory
          Download and Install Sacado in Build Directory: External Directory
          Download and Install Sacado in Build Directory: Distribution Directory
          Download and Install Sacado in Build Directory
          Download and Install Ipopt in Build Directory: Prefix Directory
          Download and Install Ipopt in Build Directory: External Directory
          Download and Install Ipopt in Build Directory: Distribution Directory
          Download and Install Ipopt in Build Directory
          Download and Install Fadbad in Build Directory: Prefix Directory
          Download and Install Fadbad in Build Directory: External Directory
          Download and Install Fadbad in Build Directory: Distribution Directory
          Download and Install Fadbad in Build Directory
          Download and Install Eigen in Build Directory: Prefix Directory
          Download and Install Eigen in Build Directory: External Directory
          Download and Install Eigen in Build Directory: Distribution Directory
          Download and Install Eigen in Build Directory
          Download and Install ColPack in Build Directory: Prefix Directory
          Download and Install ColPack in Build Directory: External Directory
          Download and Install ColPack in Build Directory: Distribution Directory
          Download and Install ColPack in Build Directory
          Download and Install Adolc in Build Directory: Prefix Directory
          Download and Install Adolc in Build Directory: External Directory
          Download and Install Adolc in Build Directory: Distribution Directory
          Download and Install Adolc in Build Directory
          Using CMake to Configure CppAD: CMake Command.Build Directory
          Download The CppAD Source Code: Distribution Directory
discrete Discrete AD Functions
discussion Comparison Changes During Zero Order Forward Mode: Discussion
           An Error Controller for Gear's Ode Solvers: Error Criteria Discussion
           An Error Controller for ODE Solvers: Error Criteria Discussion
           Enable AD Calculations During Parallel Mode: Discussion
           Check an ADFun Sequence of Operations: Discussion
           Computing Dependency: Example and Test: Discussion
           Comparison Changes Between Taping and Zero Order Forward: number.Discussion
           Atomic Forward Mode: Discussion
           Checkpointing an Extended ODE Solver: Example and Test: Discussion
           Atomic Operations and Multiple-Levels of AD: Example and Test: Discussion
           Printing AD Values During Forward Mode: Discussion
disk Frequently Asked Questions and Answers: Tape Storage: Disk or Memory
distribution Auto Tools Unix Test and Installation: Distribution Directory
             Download and Install Sacado in Build Directory: Distribution Directory
             Download and Install Ipopt in Build Directory: Distribution Directory
             Download and Install Fadbad in Build Directory: Distribution Directory
             Download and Install Eigen in Build Directory: Distribution Directory
             Download and Install ColPack in Build Directory: Distribution Directory
             Download and Install Adolc in Build Directory: Distribution Directory
             Download The CppAD Source Code: Distribution Directory
divide AD Computed Assignment Division: Example and Test
       AD Computed Assignment Operators
       AD Binary Division: Example and Test
       AD Binary Arithmetic Operators
division The Theory of Reverse Mode: Binary Operators.Division
         The Theory of Forward Mode: Binary Operators.Division
         AD Computed Assignment Operators: Derivative.Division
         AD Binary Arithmetic Operators: Derivative.Division
division: AD Computed Assignment Division: Example and Test
          AD Binary Division: Example and Test
documentation Using CMake to Configure CppAD
              Download The CppAD Source Code: No Documentation.Building Documentation
              Download The CppAD Source Code: No Documentation
documented CppAD API Preprocessor Symbols: Documented Elsewhere
           CppAD API Preprocessor Symbols: Documented Here
domain ODE Fitting Using Fast Representation: Trapezoidal Approximation.Domain Indices J(k,0)
       ODE Fitting Using Fast Representation: Initial Condition.Domain Indices J(k,0)
       ODE Fitting Using Fast Representation: Objective Function.Domain Indices J(k,0)
       ADFun Sequence Properties: Domain
double Double Speed: Sparse Jacobian
       Double Speed: Sparse Hessian
       Double Speed: Evaluate a Polynomial
       Double Speed: Ode Solution
       Double Speed: Determinant Using Lu Factorization
       Double Speed: Determinant by Minor Expansion
       Speed Test of Functions in Double
       Speed Testing Sparse Jacobian: n_sweep.double
       Speed Testing Sparse Hessian: n_sweep.double
       Speed Testing Second Derivative of a Polynomial: ddp.double
       Speed Testing the Jacobian of Ode Solution: jacobian.double
       Speed Testing Gradient of Determinant by Minor Expansion: gradient.double
       Speed Testing Gradient of Determinant Using Lu Factorization: gradient.double
       Running the Speed Test Program: package.double
       Enable use of AD<Base> where Base is double
       Required Base Class Member Functions: Double Constructor
download Download and Install Sacado in Build Directory
         Download and Install Ipopt in Build Directory
         Download and Install Fadbad in Build Directory
         Download and Install Eigen in Build Directory
         Download and Install ColPack in Build Directory
         Download and Install Adolc in Build Directory
         Download The CppAD Source Code
         CppAD Download, Test, and Install Instructions: Instructions.Step 1: Download
         CppAD Download, Test, and Install Instructions
     install eigen Download and Install Eigen in Build Directory
     install fadbad Download and Install Fadbad in Build Directory
     install ipopt Download and Install Ipopt in Build Directory
     install sacado Download and Install Sacado in Build Directory
driver Driver for Running the Ipopt ODE Example
       Sparse Hessian: Easy Driver
       Sparse Jacobian: Easy Driver
       Reverse Mode Second Partial Derivative Driver
       Forward Mode Second Partial Derivative Driver
       Hessian: Easy Driver
       First Order Derivative: Driver Routine
       First Order Partial Derivative: Driver Routine
       Jacobian: Driver Routine
driver: Second Partials Reverse Driver: Example and Test
        First Order Derivative Driver: Example and Test
        First Order Partial Driver: Example and Test
drivers First and Second Derivatives: Easy Drivers
during Comparison Changes During Zero Order Forward Mode
       Changes and Additions to CppAD During 2003
       Changes and Additions to CppAD During 2004
       Changes and Additions to CppAD During 2005
       Changes and Additions to CppAD During 2006
       Changes and Additions to CppAD During 2007
       Changes and Additions to CppAD During 2008
       Changes and Additions to CppAD During 2009
       Changes and Additions to CppAD During 2010
       Changes and Additions to CppAD During 2011
       CppAD Changes and Additions During 2012
       CppAD Changes and Additions During 2013
       CppAD Changes and Additions During 2014
       CppAD Changes and Additions During 2015
       Changes and Additions to CppAD During 2016
       CppAD Assertions During Execution
       Enable AD Calculations During Parallel Mode
       Convert an AD Variable to a Parameter: Example and Test
       Convert an AD Variable to a Parameter
       Print During Zero Order Forward Mode: Example and Test
       Printing During Forward Mode: Example and Test
       Printing AD Values During Forward Mode
dvector Use Ipopt to Solve a Nonlinear Programming Problem: Dvector
dw First Order Derivative: Driver Routine: dw
   Any Order Reverse Mode: dw
   Second Order Reverse Mode: dw
   First Order Reverse Mode: dw
dy First Order Partial Derivative: Driver Routine: dy
dz Speed Testing Derivative of Matrix Multiply: dz
E
EqualOpSeq EqualOpSeq: Example and Test
           Check if Two Value are Identically Equal
ErrorHandler Frequently Asked Questions and Answers
             Replacing the CppAD Error Handler
e An Arbitrary Order Gear Method: e
  A 3rd and 4th Order Rosenbrock ODE Solver: e
  An Embedded 4th and 5th Order Runge-Kutta ODE Solver: e
  Multi-dimensional Romberg Integration: e
  One DimensionalRomberg Integration: e
eabs An Error Controller for Gear's Ode Solvers: eabs
     An Error Controller for ODE Solvers: eabs
easy Sparse Hessian: Easy Driver
     Sparse Jacobian: Easy Driver
     Reverse Mode Second Partial Derivative Driver
     Forward Mode Second Partial Derivative Driver
     Hessian: Easy Driver
     First Order Derivative: Driver Routine
     First Order Partial Derivative: Driver Routine
     First and Second Derivatives: Easy Drivers
ef An Error Controller for Gear's Ode Solvers: ef
   An Error Controller for ODE Solvers: ef
efficiency Optimize an ADFun Object Tape: Efficiency
           An Introduction by Example to Algorithmic Differentiation: Preface.Efficiency
efficient Check If A Memory Allocation is Efficient for Another Use
          Glossary
eigen Using The CppAD Test Vector Template Class: Eigen Vectors
      Using Eigen To Compute Determinant: Example and Test
      Using Eigen Arrays: Example and Test
      Enable Use of Eigen Linear Algebra Package with CppAD: Eigen NumTraits
      Enable Use of Eigen Linear Algebra Package with CppAD
      Atomic Eigen Cholesky Factorization Class
      Atomic Eigen Cholesky Factorization: Example and Test
      Atomic Eigen Matrix Inversion Class
      Atomic Eigen Matrix Inverse: Example and Test
      Atomic Eigen Matrix Multiply Class
      Atomic Eigen Matrix Multiply: Example and Test
      Auto Tools Unix Test and Installation
      Choosing the CppAD Test Vector Template Class: eigen
      Download and Install Eigen in Build Directory
      Including the Eigen Examples and Tests
      Using CMake to Configure CppAD: cppad_profile_flag.Eigen and Fadbad
     download and install Download and Install Eigen in Build Directory
eigen_dir Auto Tools Unix Test and Installation: eigen_dir
eigen_plugin.hpp Source Code for eigen_plugin.hpp
eigen_prefix Including the Eigen Examples and Tests: eigen_prefix
elapsed Returns Elapsed Number of Seconds
        Microsoft Version of Elapsed Number of Seconds
        Elapsed Seconds: Example and Test
        Returns Elapsed Number of Seconds
elapsed_seconds Returns Elapsed Number of Seconds
element Union of Standard Sets: Element
        The CppAD::vector Template Class: vectorBool.Element Type
        The CppAD::vector Template Class: Element Access
        Definition of a Simple Vector: Element Access
        Definition of a Simple Vector: Element Constructor and Destructor
        Matrix Multiply as an Atomic Operation: Result Element Index
        Matrix Multiply as an Atomic Operation: Right Operand Element Index
        Matrix Multiply as an Atomic Operation: Left Operand Element Index
elementary Glossary: Elementary Vector
elements Sum of the Elements of the Square of a Matrix: Example and Test
         Sum Elements of a Matrix Times Itself
         Deallocate An Array and Call Destructor for its Elements
         Allocate An Array and Call Default Constructor for its Elements
         Definition of a Simple Vector: Elements of Specified Type
eliminating Tangent and Hyperbolic Tangent Reverse Mode Theory: Eliminating Y(t)
elsewhere CppAD API Preprocessor Symbols: Documented Elsewhere
embedded An Embedded 4th and 5th Order Runge-Kutta ODE Solver
enable Enable Use of Eigen Linear Algebra Package with CppAD
       Enable AD Calculations During Parallel Mode
       Enable use of AD<Base> where Base is std::complex<double>
       Enable use of AD<Base> where Base is double
       Enable use of AD<Base> where Base is float
       Enable use of AD<Base> where Base is Adolc's adouble Type
end Matrix Multiply as an Atomic Operation: End Class Definition
    Atomic Eigen Cholesky Factorization Class: End Class Definition
    Atomic Eigen Matrix Inversion Class: End Class Definition
    Atomic Eigen Matrix Multiply Class: End Class Definition
    Tan and Tanh as User Atomic Operations: Example and Test: End Class Definition
    Atomic Sparsity with Set Patterns: Example and Test: End Class Definition
    Reciprocal as an Atomic Operation: Example and Test: End Class Definition
    Atomic Euclidean Norm Squared: Example and Test: End Class Definition
    Getting Started with Atomic Operations: Example and Test: End Class Definition
entire Hessian Sparsity Pattern: Reverse Mode: Entire Sparsity Pattern
       Jacobian Sparsity Pattern: Reverse Mode: Entire Sparsity Pattern
       Jacobian Sparsity Pattern: Forward Mode: Entire Sparsity Pattern
environment Setup thread_alloc For Use in Multi-Threading Environment
            Using CppAD in a Multi-Threading Environment
eps Machine Epsilon For AD Types: eps
epsilon Machine Epsilon For AD Types
        Multi-threading Newton Method Utility Routines: xlow.epsilon
        A Multi-Threaded Newton's Method: epsilon
        Numeric Limits For an AD and Base Types: epsilon
        exp_eps: Second Order Reverse Sweep: epsilon
        exp_eps: First Order Reverse Sweep: epsilon
        An Epsilon Accurate Exponential Approximation: epsilon
        An Epsilon Accurate Exponential Approximation
equal Determine if Two Values Are Nearly Equal
      Base Type Requirements for Identically Equal Comparisons
      Check if Two Value are Identically Equal
      Compare AD and Base Objects for Nearly Equal
equalopseq Enable use of AD<Base> where Base is std::complex<double>: EqualOpSeq
           Enable use of AD<Base> where Base is double: EqualOpSeq
           Enable use of AD<Base> where Base is float: EqualOpSeq
           Enable use of AD<Base> where Base is Adolc's adouble Type: EqualOpSeq
           Example AD<Base> Where Base Constructor Allocates Memory: EqualOpSeq
           Base Type Requirements for Identically Equal Comparisons: EqualOpSeq
equalopseq: EqualOpSeq: Example and Test
equation LU Factorization of A Square Matrix and Stability Calculation
         Trigonometric and Hyperbolic Sine and Cosine Forward Theory: Differential Equation
         The Theory of Forward Mode: Standard Math Functions.Differential Equation
         Lu Factor and Solve with Recorded Pivoting
         An Error Controller for Gear's Ode Solvers
         An Arbitrary Order Gear Method
         An Error Controller for ODE Solvers
         A 3rd and 4th Order Rosenbrock ODE Solver
         An Embedded 4th and 5th Order Runge-Kutta ODE Solver
         Invert an LU Factored Equation
         LU Factorization of A Square Matrix
equations Compute Determinant and Solve Linear Equations
          Compute Determinants and Solve Equations by LU Factorization
erel An Error Controller for Gear's Ode Solvers: erel
     An Error Controller for ODE Solvers: erel
erf Changes and Additions to CppAD During 2008
    Error Function Reverse Mode Theory
    Error Function Forward Taylor Polynomial Theory
    Enable use of AD<Base> where Base is Adolc's adouble Type: erf, asinh, acosh, atanh, expm1, log1p
    Example AD<Base> Where Base Constructor Allocates Memory: erf, asinh, acosh, atanh, expm1, log1p
    Base Type Requirements for Standard Math Functions: erf, asinh, acosh, atanh, expm1, log1p
    The AD erf Function: Example and Test
error Memory Leak Detection: Error Message
      Error Function Reverse Mode Theory
      Error Function Forward Taylor Polynomial Theory
      An Error Controller for Gear's Ode Solvers: Error Criteria Discussion
      An Error Controller for Gear's Ode Solvers
      An Error Controller for ODE Solvers: Error Criteria Discussion
      An Error Controller for ODE Solvers
      CppAD Assertions During Execution: Error Handler
      Replacing The CppAD Error Handler: Example and Test
      Replacing the CppAD Error Handler
      Some General Purpose Utilities: Miscellaneous.Error Handler
      Check an ADFun Object For Nan Results: Error Message
      The Error Function
errors Run One Speed Test and Print Results: Errors
euclidean Atomic Euclidean Norm Squared: Example and Test
evaluate Double Speed: Evaluate a Polynomial
         Evaluate a Function That Has a Sparse Hessian
         Evaluate a Function That Has a Sparse Jacobian
         Evaluate a Function Defined in Terms of an ODE
         Evaluate a Polynomial or its Derivative
         Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
evaluating Bibliography: Evaluating Derivatives
evaluation: Polynomial Evaluation: Example and Test
example LuRatio: Example and Test
        LU Factorization of A Square Matrix and Stability Calculation: Example
        opt_val_hes: Example and Test
        Jacobian and Hessian of Optimal Values: Example
        BenderQuad: Example and Test
        Computing Jacobian and Hessian of Bender's Reduced Objective: Example
        zdouble: Example and Test
        zdouble: An AD Base Type With Absolute Zero: Example
        Define Matrix Multiply as a User Atomic Operation: Example
        Old Matrix Multiply as a User Atomic Operation: Example and Test
        Old Tan and Tanh as User Atomic Operations: Example and Test
        Old Atomic Operation Reciprocal: Example and Test
        User Defined Atomic AD Functions: Example
        Driver for Running the Ipopt ODE Example
        ODE Fitting Using Fast Representation
        ODE Fitting Using Simple Representation
        ODE Inverse Problem Definitions: Source Code
        An ODE Inverse Problem Example
        Example Simultaneous Solution of Forward and Inverse Problem
        Nonlinear Programming Using CppAD and Ipopt: Example and Test
        Nonlinear Programming Using the CppAD Interface to Ipopt: Example
        OpenMP Memory Allocator: Example and Test
        Return A Raw Array to The Available Memory for a Thread: Example
        Allocate Memory and Create A Raw Array: Example
        Amount of Memory Available for Quick Use by a Thread: Example
        Amount of Memory a Thread is Currently Using: Example
        Free Memory Currently Available for Quick Use by a Thread: Example
        Return Memory to omp_alloc: Example
        Get At Least A Specified Amount of Memory: Example
        Get the Current OpenMP Thread Number: Example
        Is The Current Execution in OpenMP Parallel Mode: Example
        Tracking Use of New and Delete: Example and Test
        Routines That Track Use of New and Delete: Example
        sparse_hes_fun: Example and test
        Evaluate a Function That Has a Sparse Hessian: Example
        sparse_jac_fun: Example and test
        Evaluate a Function That Has a Sparse Jacobian: Example
        ode_evaluate: Example and test
        Evaluate a Function Defined in Terms of an ODE: Example
        Sum of the Elements of the Square of a Matrix: Example and Test
        Sum Elements of a Matrix Times Itself: Example
        Determinant Using Expansion by Minors: Example and Test
        Determinant Using Expansion by Minors: Example
        Determinant of a Minor: Example and Test
        Determinant of a Minor: Example
        Determinant Using Lu Factorization: Example and Test
        Determinant Using Expansion by Lu Factorization: Example
        Lu Factor and Solve With Recorded Pivoting: Example and Test
        Lu Factor and Solve with Recorded Pivoting: Example
        Example Differentiating a Stack Machine Interpreter
        Taylor's Ode Solver: An Example and Test
        Taylor's Ode Solver: A Multi-Level Adolc Example and Test
        Taylor's Ode Solver: A Multi-Level AD Example and Test
        A Stiff Ode: Example and Test
        Multiple Level of AD: Example and Test
        Using Multiple Levels of AD: Example
        Gradient of Determinant Using Lu Factorization: Example and Test
        Gradient of Determinant Using Expansion by Minors: Example and Test
        Interfacing to C: Example and Test
        Gradient of Determinant Using LU Factorization: Example and Test
        Gradient of Determinant Using Expansion by Minors: Example and Test
        Using Eigen To Compute Determinant: Example and Test
        Using Eigen Arrays: Example and Test
        Enable Use of Eigen Linear Algebra Package with CppAD: Example
        Differentiate Conjugate Gradient Algorithm: Example and Test
        Example and Test Linking CppAD to Languages Other than C++
        Creating Your Own Interface to an ADFun Object
        ODE Inverse Problem Definitions: Source Code
        Nonlinear Programming Retaping: Example and Test
        Nonlinear Programming Using CppAD and Ipopt: Example and Test
        Use Ipopt to Solve a Nonlinear Programming Problem: Example
        Set Union: Example and Test
        Union of Standard Sets: Example
        to_string: Example and Test
        Convert Certain Types to a String: Example
        Index Sort: Example and Test
        Returns Indices that Sort a Vector: Example
        Free All Memory That Was Allocated for Use by thread_alloc: Example
        Deallocate An Array and Call Destructor for its Elements: Example
        Allocate An Array and Call Default Constructor for its Elements: Example
        Amount of Memory Available for Quick Use by a Thread: Example
        Amount of Memory a Thread is Currently Using: Example
        Free Memory Currently Available for Quick Use by a Thread: Example
        Return Memory to thread_alloc: Example
        Get At Least A Specified Amount of Memory: Example
        Get the Current Thread Number: Example
        Is The Current Execution in Parallel Mode: Example
        Get Number of Threads: Example
        Setup thread_alloc For Use in Multi-Threading Environment: Example
        Fast Multi-Threading Memory Allocator: Example and Test
        CppAD::vectorBool Class: Example and Test
        CppAD::vector Template Class: Example and Test
        The CppAD::vector Template Class: Example
        OdeGearControl: Example and Test
        An Error Controller for Gear's Ode Solvers: Example
        OdeGear: Example and Test
        An Arbitrary Order Gear Method: Example
        OdeErrControl: Example and Test Using Maxabs Argument
        OdeErrControl: Example and Test
        An Error Controller for ODE Solvers: Example
        Rosen34: Example and Test
        A 3rd and 4th Order Rosenbrock ODE Solver: Example
        Runge45: Example and Test
        Runge45: Example and Test
        An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Example
        One Dimensional Romberg Integration: Example and Test
        Multi-dimensional Romberg Integration: Example
        One Dimensional Romberg Integration: Example and Test
        One DimensionalRomberg Integration: Example
        LuInvert: Example and Test
        Invert an LU Factored Equation: Example
        LuFactor: Example and Test
        LU Factorization of A Square Matrix: Example
        LuSolve With Complex Arguments: Example and Test
        Compute Determinant and Solve Linear Equations: Example
        Polynomial Evaluation: Example and Test
        Evaluate a Polynomial or its Derivative: Example
        The Pow Integer Exponent: Example and Test
        The Integer Power Function: Example
        nan: Example and Test
        Obtain Nan or Determine if a Value is Nan: Example
        The CheckSimpleVector Function: Example and Test
        Check Simple Vector Concept: Example
        Simple Vector Template Class: Example and Test
        Definition of a Simple Vector: Example
        The CheckNumericType Function: Example and Test
        Check NumericType Class Concept: Example
        The NumericType: Example and Test
        Definition of a Numeric Type: Example
        time_test: Example and test
        Elapsed Seconds: Example and Test
        Returns Elapsed Number of Seconds: Example
        Determine Amount of Time to Execute a Test: Example
        Example Use of SpeedTest
        speed_test: Example and test
        Run One Speed Test and Print Results: Example
        Run One Speed Test and Return Results: Example
        NearEqual Function: Example and Test
        Determine if Two Values Are Nearly Equal: Example
        Replacing The CppAD Error Handler: Example and Test
        Replacing the CppAD Error Handler: Example
        Specifications for A Team of AD Threads: Example Implementation
        Specifications for A Team of AD Threads: Example Use
        Using a Team of AD Threads: Example and Test
        A Simple pthread AD: Example and Test
        A Simple Boost Threading AD: Example and Test
        A Simple OpenMP AD: Example and Test
        A Simple Parallel Pthread Example and Test
        A Simple Boost Thread Example and Test
        A Simple OpenMP Example and Test
        Enable AD Calculations During Parallel Mode: Example
        ADFun Checking For Nan: Example and Test
        Check an ADFun Object For Nan Results: Example
        Example Optimization and Cumulative Sum Operations
        Example Optimization and Nested Conditional Expressions
        Example Optimization and Conditional Expressions
        Example Optimization and Print Forward Operators
        Example Optimization and Comparison Operators
        Example Optimization and Reverse Activity Analysis
        Example Optimization and Forward Activity Analysis
        ADFun Check and Re-Tape: Example and Test
        Check an ADFun Sequence of Operations: Example
        Sparse Hessian on Subset of Variables: Example and Test
        Computing Sparse Hessian for a Subset of Variables: Example
        Sparse Hessian: Example and Test
        Sparse Hessian: Easy Driver: Example
        Sparse Jacobian: Example and Test
        Sparse Jacobian: Easy Driver: Example
        Second Partials Reverse Driver: Example and Test
        Subset of Second Order Partials: Example and Test
        Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
        Hessian: Example and Test
        Hessian: Easy Driver: Example
        First Order Derivative Driver: Example and Test
        First Order Derivative: Driver Routine: Example
        First Order Partial Driver: Example and Test
        First Order Partial Derivative: Driver Routine: Example
        Jacobian: Example and Test
        Jacobian: Driver Routine: Example
        Using vectorBool Sparsity To Conserve Memory: Example and Test
        Forward Mode Hessian Sparsity: Example and Test
        Hessian Sparsity Pattern: Forward Mode: Example
        Sparsity Patterns For a Subset of Variables: Example and Test
        Reverse Mode Hessian Sparsity: Example and Test
        Hessian Sparsity Pattern: Reverse Mode: Example
        Computing Dependency: Example and Test
        Reverse Mode Jacobian Sparsity: Example and Test
        Jacobian Sparsity Pattern: Reverse Mode: Example
        Forward Mode Jacobian Sparsity: Example and Test
        Jacobian Sparsity Pattern: Forward Mode: Example
        Reverse Mode General Case (Checkpointing): Example and Test
        Third Order Reverse Mode: Example and Test
        Any Order Reverse Mode: Example
        Hessian Times Direction: Example and Test
        Second Order Reverse ModeExample and Test
        Second Order Reverse Mode: Example
        First Order Reverse Mode: Example and Test
        First Order Reverse Mode: Example
        Number of Variables That Can be Skipped: Example and Test
        Number of Variables that Can be Skipped: Example
        Controlling Taylor Coefficient Memory Allocation: Example and Test
        Controlling Taylor Coefficients Memory Allocation: Example
        CompareChange and Re-Tape: Example and Test
        Comparison Changes Between Taping and Zero Order Forward: Example
        Number Taylor Coefficient Orders Currently Stored: Example
        Forward Mode: Example and Test of Multiple Directions
        Multiple Directions Forward Mode: Example
        Forward Mode: Example and Test of Multiple Orders
        Forward Mode: Example and Test
        Multiple Order Forward Mode: Example
        Second Order Forward Mode: Derivative Values: Example
        First Order Forward Mode: Derivative Values: Example
        Zero Order Forward Mode: Function Values: Example
        ADFun Sequence Properties: Example and Test
        ADFun Sequence Properties: Example
        Abort Current Recording: Example and Test
        Abort Recording of an Operation Sequence: Example
        Stop Recording and Store Operation Sequence: Example
        ADFun Assignment: Example and Test
        Construct an ADFun Object and Stop Recording: Example
        Independent and ADFun Constructor: Example and Test
        Declare Independent Variables and Start Recording: Example
        Complex Polynomial: Example and Test
        Enable use of AD<Base> where Base is std::complex<double>: Example
        Using Adolc with Multiple Levels of Taping: Example and Test
        Enable use of AD<Base> where Base is Adolc's adouble Type: Example
        Using a User Defined AD Base Type: Example and Test
        Example AD<Base> Where Base Constructor Allocates Memory
        Example AD Base Types That are not AD<OtherBase>
        Base Type Requirements for Hash Coding Values: Example
        Required Base Class Member Functions: Example
        AD Vectors that Record Index Operations: Example and Test
        AD Vectors that Record Index Operations: Example
        EqualOpSeq: Example and Test
        Check if Two Value are Identically Equal: Example
        AD Parameter and Variable Functions: Example and Test
        Is an AD Object a Parameter or Variable: Example
        AD Boolean Functions: Example and Test
        AD Boolean Functions: Example
        Compare AD with Base Objects: Example and Test
        Compare AD and Base Objects for Nearly Equal: Example
        AD Binary Comparison Operators: Example and Test
        AD Binary Comparison Operators: Example
        User Atomic Matrix Multiply: Example and Test
        Atomic Eigen Cholesky Factorization: Example and Test
        Atomic Eigen Matrix Inverse: Example and Test
        Atomic Eigen Matrix Multiply: Example and Test
        Tan and Tanh as User Atomic Operations: Example and Test
        Atomic Sparsity with Set Patterns: Example and Test
        Reciprocal as an Atomic Operation: Example and Test
        Atomic Euclidean Norm Squared: Example and Test
        Getting Started with Atomic Operations: Example and Test
        Atomic Reverse Hessian Sparsity: Example and Test
        Atomic Forward Hessian Sparsity: Example and Test
        Atomic Reverse Jacobian Sparsity: Example and Test
        Atomic Forward Jacobian Sparsity: Example and Test
        Atomic Reverse: Example and Test
        Atomic Forward: Example and Test
        Atomic Function Constructor: Example
        Checkpointing an Extended ODE Solver: Example and Test
        Checkpointing an ODE Solver: Example and Test
        Atomic Operations and Multiple-Levels of AD: Example and Test
        Simple Checkpointing: Example and Test
        Checkpointing Functions: Example
        Numeric Limits: Example and Test
        Numeric Limits For an AD and Base Types: Example
        Interpolation With Retaping: Example and Test
        Interpolation With Out Retaping: Example and Test
        Taping Array Index Operation: Example and Test
        Discrete AD Functions: Example
        Conditional Expressions: Example and Test
        AD Conditional Expressions: Example
        AD Absolute Zero Multiplication: Example and Test
        Absolute Zero Multiplication: Example
        The AD Power Function: Example and Test
        The AD Power Function: Example
        The AD atan2 Function: Example and Test
        AD Two Argument Inverse Tangent Function: Example
        Sign Function: Example and Test
        The Sign: sign: Example
        The AD log1p Function: Example and Test
        The Logarithm of One Plus Argument: log1p: Example
        The AD exp Function: Example and Test
        The Exponential Function Minus One: expm1: Example
        The AD erf Function: Example and Test
        The Error Function: Example
        The AD atanh Function: Example and Test
        The Inverse Hyperbolic Tangent Function: atanh: Example
        The AD asinh Function: Example and Test
        The Inverse Hyperbolic Sine Function: asinh: Example
        The AD acosh Function: Example and Test
        The Inverse Hyperbolic Cosine Function: acosh: Example
        AD Absolute Value Function: Example and Test
        AD Absolute Value Functions: abs, fabs: Example
        The AD tanh Function: Example and Test
        The AD tan Function: Example and Test
        The AD sqrt Function: Example and Test
        The AD sinh Function: Example and Test
        The AD sin Function: Example and Test
        The AD log10 Function: Example and Test
        The AD log Function: Example and Test
        The AD exp Function: Example and Test
        The AD cosh Function: Example and Test
        The AD cos Function: Example and Test
        The AD atan Function: Example and Test
        The AD asin Function: Example and Test
        The AD acos Function: Example and Test
        The Hyperbolic Tangent Function: tanh: Example
        The Tangent Function: tan: Example
        The Square Root Function: sqrt: Example
        The Hyperbolic Sine Function: sinh: Example
        The Sine Function: sin: Example
        The Base 10 Logarithm Function: log10: Example
        The Exponential Function: log: Example
        The Exponential Function: exp: Example
        The Hyperbolic Cosine Function: cosh: Example
        The Cosine Function: cos: Example
        Inverse Tangent Function: atan: Example
        Inverse Sine Function: asin: Example
        Inverse Sine Function: acos: Example
        AD Computed Assignment Division: Example and Test
        AD Computed Assignment Multiplication: Example and Test
        AD Computed Assignment Subtraction: Example and Test
        AD Computed Assignment Addition: Example and Test
        AD Computed Assignment Operators: Example
        AD Binary Division: Example and Test
        AD Binary Multiplication: Example and Test
        AD Binary Subtraction: Example and Test
        AD Binary Addition: Example and Test
        AD Binary Arithmetic Operators: Example
        AD Unary Minus Operator: Example and Test
        AD Unary Minus Operator: Example
        AD Unary Plus Operator: Example and Test
        AD Unary Plus Operator: Example
        Convert an AD Variable to a Parameter: Example and Test
        Convert an AD Variable to a Parameter: Example
        Print During Zero Order Forward Mode: Example and Test
        Printing During Forward Mode: Example and Test
        Printing AD Values During Forward Mode: Example
        AD Output Operator: Example and Test
        AD Output Operator: Example and Test
        AD Output Stream Operator: Example
        AD Output Stream Operator: Example
        Convert An AD or Base Type to String: Example
        Convert From AD to Integer: Example and Test
        Convert From AD to Integer: Example
        Convert From AD to its Base Type: Example and Test
        Convert From an AD Type to its Base Type: Example
        AD Assignment: Example and Test
        AD Assignment Operator: Example
        AD Constructors: Example and Test
        AD Constructors: Example
        exp_eps: Operation Sequence and Zero Order Forward Sweep
        An Epsilon Accurate Exponential Approximation
        exp_2: Operation Sequence and Zero Order Forward Mode
        Second Order Exponential Approximation
        Getting Started Using CppAD to Compute Derivatives
        An Introduction by Example to Algorithmic Differentiation
        Using ColPack: Example and Test
        Using ColPack: Example and Test
        Including the ColPack Sparsity Calculations: Example
        cppad-20170000.3: A Package for Differentiation of C++ Algorithms: Example
examples Run the Speed Examples
         CppAD Examples and Tests
         List of All the CppAD Examples
         Utility Routines used by CppAD Examples
         General Examples
         Examples: Running Examples
         Examples
         Run Multi-Threading Examples and Speed Tests
         Optimize an ADFun Object Tape: Examples
         Reverse Mode Second Partial Derivative Driver: Examples
         Forward Mode Second Partial Derivative Driver: Examples
         Base Type Requirements for Identically Equal Comparisons: Identical.Examples
         Atomic Reverse Hessian Sparsity Patterns: Examples
         Atomic Forward Hessian Sparsity Patterns: Examples
         Atomic Reverse Jacobian Sparsity Patterns: Examples
         Atomic Forward Jacobian Sparsity Patterns: Examples
         Atomic Reverse Mode: Examples
         Atomic Forward Mode: Examples
         Using AD Version of Atomic Function: Examples
         User Defined Atomic AD Functions: Examples
         Auto Tools Unix Test and Installation: make.Examples and Tests
         Checking the CppAD Examples and Tests
         Including the cppad_ipopt Library and Tests: Examples and Tests
         Including the Eigen Examples and Tests: Examples
         Including the Eigen Examples and Tests
         Including the ADOL-C Examples and Tests: Examples
         Including the ADOL-C Examples and Tests
exception Replacing the CppAD Error Handler
exceptions Frequently Asked Questions and Answers: Exceptions
           AD Vectors that Record Index Operations: VecAD<Base>::reference.Exceptions
execute Determine Amount of Time to Execute det_by_minor
        Determine Amount of Time to Execute a Test
execution Is The Current Execution in OpenMP Parallel Mode
          Is The Current Execution in Parallel Mode
          CppAD Assertions During Execution
          Using CppAD in a Multi-Threading Environment
exercise The CppAD::vector Template Class: Exercise
         Definition of a Simple Vector: Exercise
         Definition of a Numeric Type: Exercise
         Determine if Two Values Are Nearly Equal: Exercise
exercises exp_eps: CppAD Forward and Reverse Sweeps: Exercises
          exp_eps: Second Order Reverse Sweep: Exercises
          exp_eps: Second Order Forward Mode: Exercises
          exp_eps: First Order Reverse Sweep: Exercises
          exp_eps: First Order Forward Sweep: Exercises
          exp_eps: Operation Sequence and Zero Order Forward Sweep: Exercises
          An Epsilon Accurate Exponential Approximation: Exercises
          exp_2: CppAD Forward and Reverse Sweeps: Exercises
          exp_2: Second Order Reverse Mode: Exercises
          exp_2: Second Order Forward Mode: Exercises
          exp_2: First Order Reverse Mode: Exercises
          exp_2: First Order Forward Mode: Exercises
          exp_2: Operation Sequence and Zero Order Forward Mode: Exercises
          Second Order Exponential Approximation: Exercises
          Getting Started Using CppAD to Compute Derivatives: Exercises
exp Exponential Function Reverse Mode Theory
    Exponential Function Forward Mode Theory
    CppAD Assertions During Execution: Exp
    Replacing the CppAD Error Handler: exp
    The AD exp Function: Example and Test
    The AD exp Function: Example and Test
    The Exponential Function: exp
exp_2 exp_eps: Verify Second Order Forward Sweep
      exp_eps: Verify First Order Forward Sweep
      exp_2: Verify Second Order Reverse Sweep
      exp_2: Verify Second Order Forward Sweep
      exp_2: Verify First Order Reverse Sweep
      exp_2: Verify First Order Forward Sweep
      exp_2: Verify Zero Order Forward Sweep
      exp_2: Implementation
      Second Order Exponential Approximation
exp_2: exp_2: CppAD Forward and Reverse Sweeps
       exp_2: Verify Second Order Reverse Sweep
       exp_2: Verify Second Order Forward Sweep
       exp_2: Verify First Order Reverse Sweep
       exp_2: Verify First Order Forward Sweep
       exp_2: Verify Zero Order Forward Sweep
       exp_2: Second Order Reverse Mode
       exp_2: Second Order Forward Mode
       exp_2: First Order Reverse Mode
       exp_2: First Order Forward Mode
       exp_2: Operation Sequence and Zero Order Forward Mode
       exp_2: Test
       exp_2: Implementation
exp_apx Correctness Tests For Exponential Approximation in Introduction
exp_eps exp_eps: Verify Second Order Reverse Sweep
        exp_eps: Verify First Order Reverse Sweep
        exp_eps: Verify Zero Order Forward Sweep
        exp_eps: Test of exp_eps
        exp_eps: Implementation
        An Epsilon Accurate Exponential Approximation
exp_eps: exp_eps: CppAD Forward and Reverse Sweeps
         exp_eps: Verify Second Order Reverse Sweep
         exp_eps: Verify Second Order Forward Sweep
         exp_eps: Verify First Order Reverse Sweep
         exp_eps: Verify First Order Forward Sweep
         exp_eps: Verify Zero Order Forward Sweep
         exp_eps: Second Order Reverse Sweep
         exp_eps: Second Order Forward Mode
         exp_eps: First Order Reverse Sweep
         exp_eps: First Order Forward Sweep
         exp_eps: Operation Sequence and Zero Order Forward Sweep
         exp_eps: Test of exp_eps
         exp_eps: Implementation
expansion Compute Determinant using Expansion by Minors
          Sacado Speed: Gradient of Determinant by Minor Expansion
          Fadbad Speed: Gradient of Determinant by Minor Expansion
          CppAD Speed: Gradient of Determinant by Minor Expansion
          Adolc Speed: Gradient of Determinant by Minor Expansion
          Double Speed: Determinant by Minor Expansion
          Determinant Using Expansion by Minors: Example and Test
          Determinant Using Expansion by Minors
          Determinant Using Expansion by Lu Factorization
          Speed Testing Gradient of Determinant by Minor Expansion
          Gradient of Determinant Using Expansion by Minors: Example and Test
          Gradient of Determinant Using Expansion by Minors: Example and Test
          exp_eps: Second Order Forward Mode: Second Order Expansion
          exp_eps: First Order Forward Sweep: First Order Expansion
          exp_2: Second Order Forward Mode: Second Order Expansion
          exp_2: First Order Forward Mode: First Order Expansion
          exp_2: Operation Sequence and Zero Order Forward Mode: Zero Order Expansion
explicit AD Constructors: x.explicit
         Auto Tools Unix Test and Installation
         Using CMake to Configure CppAD
expm1 Exponential Function Reverse Mode Theory
      Exponential Function Forward Mode Theory
      Enable use of AD<Base> where Base is Adolc's adouble Type: erf, asinh, acosh, atanh, expm1, log1p
      Example AD<Base> Where Base Constructor Allocates Memory: erf, asinh, acosh, atanh, expm1, log1p
      Base Type Requirements for Standard Math Functions: erf, asinh, acosh, atanh, expm1, log1p
      The Exponential Function Minus One: expm1
exponent The Integer Power Function
         The AD Power Function
exponent: The Pow Integer Exponent: Example and Test
exponential Exponential Function Reverse Mode Theory
            Exponential Function Forward Mode Theory
            The Exponential Function Minus One: expm1
            The Exponential Function: log
            The Exponential Function: exp
            Correctness Tests For Exponential Approximation in Introduction
            An Epsilon Accurate Exponential Approximation
            Second Order Exponential Approximation
expression Number of Variables That Can be Skipped: Example and Test
expressions Example Optimization and Nested Conditional Expressions
            Example Optimization and Conditional Expressions
            Base Type Requirements for Conditional Expressions
            AD Conditional Expressions
expressions: Conditional Expressions: Example and Test
extended Checkpointing an Extended ODE Solver: Example and Test
extending Extending to_string To Another Floating Point Type
external Download and Install Sacado in Build Directory: External Directory
         Download and Install Ipopt in Build Directory: External Directory
         Download and Install Fadbad in Build Directory: External Directory
         Download and Install Eigen in Build Directory: External Directory
         Download and Install ColPack in Build Directory: External Directory
         Download and Install Adolc in Build Directory: External Directory
extra Define Matrix Multiply as a User Atomic Operation: Extra Call Information
      Free Memory Currently Available for Quick Use by a Thread: Purpose.Extra Memory
extraction Download The CppAD Source Code: Windows File Extraction and Testing
F
FAQ Frequently Asked Questions and Answers
Fadbad Auto Tools Unix Test and Installation
ForSparseHes Forward Mode Hessian Sparsity: Example and Test
ForSparseJac Forward Mode Jacobian Sparsity: Example and Test
Forward Controlling Taylor Coefficients Memory Allocation
FunCheck ADFun Check and Re-Tape: Example and Test
f.forward(0 Printing AD Values During Forward Mode: f.Forward(0, x)
f_1 exp_eps: Second Order Reverse Sweep: Index 2: f_1
    exp_eps: First Order Reverse Sweep: Index 2: f_1
    exp_2: Second Order Reverse Mode: Index 2: f_1
    exp_2: First Order Reverse Mode: Index 2: f_1
f_2 exp_eps: Second Order Reverse Sweep: Index 3: f_2
    exp_eps: First Order Reverse Sweep: Index 3: f_2
    exp_2: Second Order Reverse Mode: Index 3: f_2
    exp_2: First Order Reverse Mode: Index 3: f_2
f_3 exp_eps: Second Order Reverse Sweep: Index 4: f_3
    exp_eps: First Order Reverse Sweep: Index 4: f_3
    exp_2: Second Order Reverse Mode: Index 4: f_3
    exp_2: First Order Reverse Mode: Index 4: f_3
f_4 exp_eps: Second Order Reverse Sweep: Index 5: f_4
    exp_eps: First Order Reverse Sweep: Index 5: f_4
    exp_2: Second Order Reverse Mode: Index 5: f_4
    exp_2: First Order Reverse Mode: Index 5: f_4
f_5 exp_eps: Second Order Reverse Sweep: Index 6: f_5
    exp_eps: First Order Reverse Sweep: Index 6: f_5
    exp_2: Second Order Reverse Mode: f_5
    exp_2: First Order Reverse Mode: f_5
f_6 exp_eps: Second Order Reverse Sweep: Index 7: f_6
    exp_eps: First Order Reverse Sweep: Index 7: f_6
f_7 exp_eps: Second Order Reverse Sweep: f_7
    exp_eps: First Order Reverse Sweep: f_7
f_t A 3rd and 4th Order Rosenbrock ODE Solver: Fun.f_t
f_x An Error Controller for Gear's Ode Solvers: Fun.f_x
    An Arbitrary Order Gear Method: Fun.f_x
    A 3rd and 4th Order Rosenbrock ODE Solver: Fun.f_x
fabs Evaluate a Function Defined in Terms of an ODE: Float.fabs
     An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Scalar.fabs
     AD Absolute Value Function: Example and Test
     AD Absolute Value Functions: abs, fabs
factor LU Factorization of A Square Matrix and Stability Calculation: LU.Factor
       Sacado Speed: Gradient of Determinant Using Lu Factorization
       Fadbad Speed: Gradient of Determinant Using Lu Factorization
       CppAD Speed: Gradient of Determinant Using Lu Factorization
       Adolc Speed: Gradient of Determinant Using Lu Factorization
       Double Speed: Determinant Using Lu Factorization
       Determinant Using Expansion by Lu Factorization
       Lu Factor and Solve With Recorded Pivoting: Example and Test
       Lu Factor and Solve with Recorded Pivoting
       LU Factorization of A Square Matrix: LU.Factor
       Compute Determinant and Solve Linear Equations: Factor and Invert
       Compute Determinants and Solve Equations by LU Factorization
       AD Theory for Cholesky Factorization: Notation.Cholesky Factor
factored Invert an LU Factored Equation
factorization LU Factorization of A Square Matrix and Stability Calculation
              Sacado Speed: Gradient of Determinant Using Lu Factorization
              Fadbad Speed: Gradient of Determinant Using Lu Factorization
              CppAD Speed: Gradient of Determinant Using Lu Factorization
              Adolc Speed: Gradient of Determinant Using Lu Factorization
              Double Speed: Determinant Using Lu Factorization
              Determinant Using Expansion by Lu Factorization
              Speed Testing Gradient of Determinant Using Lu Factorization
              LU Factorization of A Square Matrix
              Compute Determinants and Solve Equations by LU Factorization
              Atomic Eigen Cholesky Factorization Class
              AD Theory for Cholesky Factorization
factorization: Determinant Using Lu Factorization: Example and Test
               Gradient of Determinant Using Lu Factorization: Example and Test
               Gradient of Determinant Using LU Factorization: Example and Test
               Atomic Eigen Cholesky Factorization: Example and Test
fadbad fadbad Speed: sparse_jacobian
       Fadbad Speed: Sparse Hessian
       Fadbad Speed: Second Derivative of a Polynomial
       Fadbad Speed: Ode
       Fadbad Speed: Matrix Multiplication
       Fadbad Speed: Gradient of Determinant Using Lu Factorization
       Fadbad Speed: Gradient of Determinant by Minor Expansion
       Speed Test Derivatives Using Fadbad
       Download and Install Fadbad in Build Directory
       Including the FADBAD Speed Tests
       Using CMake to Configure CppAD: cppad_profile_flag.Eigen and Fadbad
     download and install Download and Install Fadbad in Build Directory
fadbad_dir Auto Tools Unix Test and Installation: fadbad_dir
fadbad_prefix Speed Test Derivatives Using Fadbad: fadbad_prefix
              Including the FADBAD Speed Tests: fadbad_prefix
false Hessian Sparsity Pattern: Reverse Mode: h.transpose false
      Jacobian Sparsity Pattern: Reverse Mode: s.transpose false
      Jacobian Sparsity Pattern: Reverse Mode: r.transpose false
      Jacobian Sparsity Pattern: Forward Mode: s.transpose false
      Jacobian Sparsity Pattern: Forward Mode: r.transpose false
      The Logarithm of One Plus Argument: log1p: CPPAD_USE_CPLUSPLUS_2011.false
      The Exponential Function Minus One: expm1: CPPAD_USE_CPLUSPLUS_2011.false
      The Error Function: CPPAD_USE_CPLUSPLUS_2011.false
      The Inverse Hyperbolic Tangent Function: atanh: CPPAD_USE_CPLUSPLUS_2011.false
      The Inverse Hyperbolic Sine Function: asinh: CPPAD_USE_CPLUSPLUS_2011.false
      The Inverse Hyperbolic Cosine Function: acosh: CPPAD_USE_CPLUSPLUS_2011.false
fast Speed Test for Both Simple and Fast Representations
     Correctness Check for Both Simple and Fast Representations
     ODE Fitting Using Fast Representation
     ODE Fitting Using Fast Representation
     Fast Multi-Threading Memory Allocator: Example and Test
     A Fast Multi-Threading Memory Allocator
faster Checkpointing Functions: Purpose.Faster Recording
features CppAD Deprecated API Features
fg Use Ipopt to Solve a Nonlinear Programming Problem: fg_eval.fg
fg(x) Nonlinear Programming Using the CppAD Interface to Ipopt: fg(x)
fg_eval Use Ipopt to Solve a Nonlinear Programming Problem: fg_eval
fg_info Nonlinear Programming Using the CppAD Interface to Ipopt: fg_info
fg_info.domain_size Nonlinear Programming Using the CppAD Interface to Ipopt: fg_info.fg_info.domain_size
fg_info.eval_r Nonlinear Programming Using the CppAD Interface to Ipopt: fg_info.fg_info.eval_r
fg_info.index Nonlinear Programming Using the CppAD Interface to Ipopt: fg_info.fg_info.index
fg_info.number_functions Nonlinear Programming Using the CppAD Interface to Ipopt: fg_info.fg_info.number_functions
fg_info.number_terms Nonlinear Programming Using the CppAD Interface to Ipopt: fg_info.fg_info.number_terms
fg_info.range_size Nonlinear Programming Using the CppAD Interface to Ipopt: fg_info.fg_info.range_size
fg_info.retape Nonlinear Programming Using the CppAD Interface to Ipopt: fg_info.fg_info.retape
fields CppAD pkg-config Files: Defined Fields
file Old Matrix Multiply as a User Atomic Operation: Example and Test: Include File
     Routines That Track Use of New and Delete: file
     Use Ipopt to Solve a Nonlinear Programming Problem: Include File
     NearEqual Function: Example and Test: File Name
     Replacing the CppAD Error Handler: file
     Check an ADFun Object For Nan Results: get_check_for_nan.file
     Example AD<Base> Where Base Constructor Allocates Memory: Include File
     Download The CppAD Source Code: Windows File Extraction and Testing
     cppad-20170000.3: A Package for Differentiation of C++ Algorithms: Include File
file_name Check an ADFun Object For Nan Results: Error Message.file_name
files CppAD Addons: Library Files
      CppAD Addons: Include Files
      Deprecated Include Files: Linking New Files to Deprecated Commands
      Deprecated Include Files
      Enable Use of Eigen Linear Algebra Package with CppAD: Include Files
      Determine if Two Values Are Nearly Equal: Include Files
      Enable use of AD<Base> where Base is Adolc's adouble Type: Include Files
      CppAD pkg-config Files: CppAD Configuration Files
      CppAD pkg-config Files
first Using Multiple Levels of AD: Procedure.First Start AD<double>
      Run One Speed Test and Print Results: first
      First Order Derivative Driver: Example and Test
      First Order Derivative: Driver Routine
      First Order Partial Driver: Example and Test
      First Order Partial Derivative: Driver Routine
      Jacobian: Driver Routine
      First and Second Derivatives: Easy Drivers
      Any Order Reverse Mode: First Order
      Second Order Reverse Mode: dw.First Order Partials
      First Order Reverse Mode: Example and Test
      First Order Reverse Mode
      Multiple Order Forward Mode: First Order
      First Order Forward Mode: Derivative Values
      exp_eps: Verify Second Order Forward Sweep
      exp_eps: Verify First Order Reverse Sweep
      exp_eps: Verify First Order Forward Sweep
      exp_eps: Second Order Forward Mode: Operation Sequence.First
      exp_eps: First Order Reverse Sweep
      exp_eps: First Order Forward Sweep: Operation Sequence.First Order
      exp_eps: First Order Forward Sweep: First Order Expansion
      exp_eps: First Order Forward Sweep
      exp_2: Verify First Order Reverse Sweep
      exp_2: Verify First Order Forward Sweep
      exp_2: Second Order Forward Mode: Operation Sequence.First
      exp_2: First Order Reverse Mode
      exp_2: First Order Forward Mode: Operation Sequence.First Order
      exp_2: First Order Forward Mode: First Order Expansion
      exp_2: First Order Forward Mode
fitting ODE Fitting Using Fast Representation
        ODE Fitting Using Simple Representation
        ODE Fitting Using Fast Representation
        ODE Fitting Using Simple Representation
flag Correctness Test of det_by_minor Routine: flag
     Memory Leak Detection: flag
     Check If A Memory Allocation is Efficient for Another Use: flag
     Is The Current Execution in OpenMP Parallel Mode: flag
     Is The Current Execution in Parallel Mode: flag
flags Auto Tools Unix Test and Installation
      Using CMake to Configure CppAD
float Machine Epsilon For AD Types: Float
      Evaluate a Function That Has a Sparse Hessian: Float
      Evaluate a Function That Has a Sparse Jacobian: Float
      Evaluate a Function Defined in Terms of an ODE: Float
      Convert Certain Types to a String: s.Float
      Convert Certain Types to a String: value.Float
      Multi-dimensional Romberg Integration: Float
      One DimensionalRomberg Integration: Float
      LU Factorization of A Square Matrix: Float
      Compute Determinant and Solve Linear Equations: Float
      Enable use of AD<Base> where Base is float
      Numeric Limits For an AD and Base Types: Float
floating Extending to_string To Another Floating Point Type
floatvector Evaluate a Function That Has a Sparse Hessian: FloatVector
            Evaluate a Function That Has a Sparse Jacobian: FloatVector
            Multi-dimensional Romberg Integration: FloatVector
            LU Factorization of A Square Matrix: FloatVector
            Compute Determinant and Solve Linear Equations: FloatVector
for_jac_sparse User Defined Atomic AD Functions: for_jac_sparse
for_sparse_hes Atomic Eigen Matrix Multiply Class: Private.for_sparse_hes
               Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function.for_sparse_hes
               Atomic Sparsity with Set Patterns: Example and Test: for_sparse_hes
               Atomic Forward Hessian Sparsity: Example and Test: for_sparse_hes
for_sparse_jac Matrix Multiply as an Atomic Operation: for_sparse_jac
               User Atomic Matrix Multiply: Example and Test: Use Atomic Function.for_sparse_jac
               Atomic Eigen Matrix Multiply Class: Private.for_sparse_jac
               Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.for_sparse_jac
               Tan and Tanh as User Atomic Operations: Example and Test: for_sparse_jac
               Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function.for_sparse_jac
               Atomic Sparsity with Set Patterns: Example and Test: for_sparse_jac
               Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function.for_sparse_jac
               Reciprocal as an Atomic Operation: Example and Test: for_sparse_jac
               Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function.for_sparse_jac
               Atomic Euclidean Norm Squared: Example and Test: for_sparse_jac
               Atomic Reverse Hessian Sparsity: Example and Test: for_sparse_jac
               Atomic Forward Hessian Sparsity: Example and Test: for_sparse_jac
               Atomic Forward Jacobian Sparsity: Example and Test: for_sparse_jac
form exp_eps: Second Order Reverse Sweep: Mathematical Form
     exp_eps: Second Order Forward Mode: Mathematical Form
     exp_eps: First Order Reverse Sweep: Mathematical Form
     exp_eps: First Order Forward Sweep: Mathematical Form
     exp_eps: Operation Sequence and Zero Order Forward Sweep: Mathematical Form
     exp_2: Second Order Reverse Mode: Mathematical Form
     exp_2: Second Order Forward Mode: Mathematical Form
     exp_2: First Order Reverse Mode: Mathematical Form
     exp_2: First Order Forward Mode: Mathematical Form
     exp_2: Operation Sequence and Zero Order Forward Mode: Mathematical Form
     Second Order Exponential Approximation: Mathematical Form
formula The Theory of Forward Mode: Standard Math Functions.Taylor Coefficients Recursion Formula
forone First Order Partial Derivative: Driver Routine: ForOne Uses Forward
forsparsejac Sparsity Patterns For a Subset of Variables: Example and Test: ForSparseJac
fortwo Forward Mode Second Partial Derivative Driver: ForTwo Uses Forward
forward User Defined Atomic AD Functions: forward
        User Defined Atomic AD Functions: ty.forward
        An ODE Inverse Problem Example: Forward Problem
        Example Simultaneous Solution of Forward and Inverse Problem
        Comparison Changes During Zero Order Forward Mode
        The CppAD Wish List: Forward Mode Recomputation
        Error Function Forward Taylor Polynomial Theory
        Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
        Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
        Inverse Sine and Hyperbolic Sine Forward Mode Theory
        Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
        Trigonometric and Hyperbolic Sine and Cosine Forward Theory
        Square Root Function Forward Mode Theory
        Logarithm Function Forward Mode Theory
        Exponential Function Forward Mode Theory
        The Theory of Forward Mode
        Frequently Asked Questions and Answers: Mode: Forward or Reverse
        Taylor's Ode Solver: An Example and Test: Forward Mode
        ODE Inverse Problem Definitions: Source Code: Forward Problem
        Example Optimization and Print Forward Operators
        Example Optimization and Forward Activity Analysis
        Check an ADFun Sequence of Operations: FunCheck Uses Forward
        Sparse Hessian: Easy Driver: Uses Forward
        Sparse Jacobian: Easy Driver: Uses Forward
        Reverse Mode Second Partial Derivative Driver: RevTwo Uses Forward
        Forward Mode Second Partial Derivative Driver: ForTwo Uses Forward
        Forward Mode Second Partial Derivative Driver
        Hessian: Easy Driver: Hessian Uses Forward
        First Order Derivative: Driver Routine: RevOne Uses Forward
        First Order Partial Derivative: Driver Routine: ForOne Uses Forward
        Jacobian: Driver Routine: Forward or Reverse
        First and Second Derivatives: Easy Drivers
        Forward Mode Hessian Sparsity: Example and Test
        Hessian Sparsity Pattern: Forward Mode
        Forward Mode Jacobian Sparsity: Example and Test
        Jacobian Sparsity Pattern: Forward Mode
        Comparison Changes Between Taping and Zero Order Forward
        Number Taylor Coefficient Orders Currently Stored: Forward
        Forward Mode: Example and Test of Multiple Directions
        Multiple Directions Forward Mode
        Forward Mode: Example and Test of Multiple Orders
        Forward Mode: Example and Test
        Multiple Order Forward Mode
        Second Order Forward Mode: Derivative Values
        First Order Forward Mode: Derivative Values
        Zero Order Forward Mode: Function Values
        Forward Mode
        Stop Recording and Store Operation Sequence: Forward
        Matrix Multiply as an Atomic Operation: forward
        Matrix Multiply as an Atomic Operation: Forward Matrix Multiply
        User Atomic Matrix Multiply: Example and Test: Use Atomic Function.forward
        Atomic Eigen Cholesky Factorization Class: Private.forward
        AD Theory for Cholesky Factorization: Forward Mode
        Atomic Eigen Matrix Inversion Class: Private.forward
        Atomic Eigen Matrix Inversion Class: Theory.Forward
        Atomic Eigen Matrix Multiply Class: Private.forward
        Atomic Eigen Matrix Multiply Class: Theory.Forward
        Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.forward
        Tan and Tanh as User Atomic Operations: Example and Test: forward
        Atomic Sparsity with Set Patterns: Example and Test: forward
        Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function.forward
        Reciprocal as an Atomic Operation: Example and Test: forward
        Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function.forward
        Atomic Euclidean Norm Squared: Example and Test: forward
        Getting Started with Atomic Operations: Example and Test: Use Atomic Function.forward
        Getting Started with Atomic Operations: Example and Test: forward
        Atomic Reverse Hessian Sparsity: Example and Test: forward
        Atomic Forward Hessian Sparsity: Example and Test: forward
        Atomic Forward Hessian Sparsity: Example and Test
        Atomic Reverse Jacobian Sparsity: Example and Test: forward
        Atomic Forward Jacobian Sparsity: Example and Test: forward
        Atomic Forward Jacobian Sparsity: Example and Test
        Atomic Reverse: Example and Test: forward
        Atomic Forward: Example and Test: forward
        Atomic Forward Hessian Sparsity Patterns
        Atomic Forward Jacobian Sparsity Patterns
        Atomic Forward Mode
        Checkpointing Functions: Purpose.Repeating Forward
        Print During Zero Order Forward Mode: Example and Test
        Printing During Forward Mode: Example and Test
        Printing AD Values During Forward Mode
        exp_eps: CppAD Forward and Reverse Sweeps
        exp_eps: Verify Second Order Forward Sweep
        exp_eps: Verify First Order Forward Sweep
        exp_eps: Verify Zero Order Forward Sweep
        exp_eps: Second Order Forward Mode
        exp_eps: First Order Forward Sweep
        exp_eps: Operation Sequence and Zero Order Forward Sweep
        exp_2: CppAD Forward and Reverse Sweeps
        exp_2: Verify Second Order Forward Sweep
        exp_2: Verify First Order Forward Sweep
        exp_2: Verify Zero Order Forward Sweep
        exp_2: Second Order Forward Mode
        exp_2: First Order Forward Mode
        exp_2: Operation Sequence and Zero Order Forward Mode
        An Introduction by Example to Algorithmic Differentiation: Preface.Forward Mode
forward: Atomic Forward: Example and Test
fp Evaluate a Function That Has a Sparse Hessian: fp
   Evaluate a Function That Has a Sparse Jacobian: fp
   Evaluate a Function Defined in Terms of an ODE: fp
free User Defined Atomic AD Functions: Syntax Function.Free Static Memory
     Free Memory Currently Available for Quick Use by a Thread
     Adolc Test Utility: Allocate and Free Memory For a Matrix
     Free All Memory That Was Allocated for Use by thread_alloc
     Free Memory Currently Available for Quick Use by a Thread
     Free Static Variables
free_available Free Memory Currently Available for Quick Use by a Thread
               Control When Thread Alloc Retains Memory For Future Use: free_available
               Free Memory Currently Available for Quick Use by a Thread
freeing Controlling Taylor Coefficients Memory Allocation: c.Freeing Memory
frequently Frequently Asked Questions and Answers
from Definition of a Numeric Type: Constructor From Integer
     Convert an AD Variable to a Parameter
     Convert From AD to Integer: Example and Test
     Convert From AD to Integer
     Convert From AD to its Base Type: Example and Test
     Convert From an AD Type to its Base Type
     Conversion and I/O of AD Objects
fun Jacobian and Hessian of Optimal Values: Fun
    Computing Jacobian and Hessian of Bender's Reduced Objective: fun
    An Error Controller for Gear's Ode Solvers: Fun
    An Arbitrary Order Gear Method: Fun
    A 3rd and 4th Order Rosenbrock ODE Solver: Fun
    An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Fun
    Multi-threading Newton Method Utility Routines: multi_newton_setup.fun
    A Multi-Threaded Newton's Method: fun
    The Unary Standard Math Functions: fun
fun.dy Computing Jacobian and Hessian of Bender's Reduced Objective: fun.fun.dy
fun.ell Jacobian and Hessian of Optimal Values: Fun.fun.ell
fun.f Computing Jacobian and Hessian of Bender's Reduced Objective: fun.fun.f
fun.h Computing Jacobian and Hessian of Bender's Reduced Objective: fun.fun.h
fun.s Jacobian and Hessian of Optimal Values: Fun.fun.s
fun.sy Jacobian and Hessian of Optimal Values: Fun.fun.sy
fun::ad_vector Jacobian and Hessian of Optimal Values: Fun.Fun::ad_vector
funcheck Check an ADFun Sequence of Operations: FunCheck Uses Forward
function Define Matrix Multiply as a User Atomic Operation: Declare mat_mul Function
         Using AD to Compute Atomic Function Derivatives
         Using AD to Compute Atomic Function Derivatives
         User Defined Atomic AD Functions: Example.Tangent Function
         User Defined Atomic AD Functions: Syntax Function.Use Function
         User Defined Atomic AD Functions: Syntax Function
         ODE Fitting Using Fast Representation: Objective Function
         ODE Fitting Using Simple Representation: Objective Function
         Glossary: Base Function
         Glossary: AD Function
         Error Function Reverse Mode Theory
         Square Root Function Reverse Mode Theory
         Logarithm Function Reverse Mode Theory
         Exponential Function Reverse Mode Theory
         Error Function Forward Taylor Polynomial Theory
         Square Root Function Forward Mode Theory
         Logarithm Function Forward Mode Theory
         Exponential Function Forward Mode Theory
         Frequently Asked Questions and Answers
         Evaluate a Function That Has a Sparse Hessian: fp.Function
         Evaluate a Function That Has a Sparse Hessian
         Evaluate a Function That Has a Sparse Jacobian: fp.Function
         Evaluate a Function That Has a Sparse Jacobian
         Evaluate a Function Defined in Terms of an ODE: fp.Function
         Evaluate a Function Defined in Terms of an ODE
         Using Multiple Levels of AD: Procedure.Derivatives of Outer Function
         Using Multiple Levels of AD: Procedure.Outer Function
         Using Multiple Levels of AD: Procedure.Inner Function
         The Integer Power Function
         Computing Sparse Hessian for a Subset of Variables: Function
         Multiple Order Forward Mode: Purpose.Function Values
         Zero Order Forward Mode: Function Values
         User Atomic Matrix Multiply: Example and Test: Use Atomic Function
         Atomic Eigen Cholesky Factorization: Example and Test: Use Atomic Function
         Atomic Eigen Matrix Inverse: Example and Test: Use Atomic Function
         Atomic Eigen Matrix Multiply: Example and Test: Use Atomic Function
         Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function
         Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function
         Atomic Sparsity with Set Patterns: Example and Test: function
         Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function
         Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function
         Getting Started with Atomic Operations: Example and Test: Use Atomic Function
         Atomic Reverse Hessian Sparsity: Example and Test: Use Atomic Function
         Atomic Reverse Hessian Sparsity: Example and Test: function
         Atomic Forward Hessian Sparsity: Example and Test: Use Atomic Function
         Atomic Forward Hessian Sparsity: Example and Test: function
         Atomic Reverse Jacobian Sparsity: Example and Test: Use Atomic Function
         Atomic Reverse Jacobian Sparsity: Example and Test: function
         Atomic Forward Jacobian Sparsity: Example and Test: Use Atomic Function
         Atomic Forward Jacobian Sparsity: Example and Test: function
         Atomic Reverse: Example and Test: Use Atomic Function
         Atomic Reverse: Example and Test: function
         Atomic Forward: Example and Test: Use Atomic Function
         Atomic Forward: Example and Test: function
         Using AD Version of Atomic Function
         Set Atomic Function Options
         Atomic Function Constructor
         User Defined Atomic AD Functions: Examples.Scalar Function
         The AD Power Function
         AD Two Argument Inverse Tangent Function
         The Exponential Function Minus One: expm1
         The Error Function
         An Epsilon Accurate Exponential Approximation: Mathematical Function
         Getting Started Using CppAD to Compute Derivatives: Function
function: The CheckSimpleVector Function: Example and Test
          The CheckNumericType Function: Example and Test
          NearEqual Function: Example and Test
          The AD Power Function: Example and Test
          The AD atan2 Function: Example and Test
          Sign Function: Example and Test
          The AD log1p Function: Example and Test
          The AD exp Function: Example and Test
          The AD erf Function: Example and Test
          The AD atanh Function: Example and Test
          The Inverse Hyperbolic Tangent Function: atanh
          The AD asinh Function: Example and Test
          The Inverse Hyperbolic Sine Function: asinh
          The AD acosh Function: Example and Test
          The Inverse Hyperbolic Cosine Function: acosh
          AD Absolute Value Function: Example and Test
          The AD tanh Function: Example and Test
          The AD tan Function: Example and Test
          The AD sqrt Function: Example and Test
          The AD sinh Function: Example and Test
          The AD sin Function: Example and Test
          The AD log10 Function: Example and Test
          The AD log Function: Example and Test
          The AD exp Function: Example and Test
          The AD cosh Function: Example and Test
          The AD cos Function: Example and Test
          The AD atan Function: Example and Test
          The AD asin Function: Example and Test
          The AD acos Function: Example and Test
          The Hyperbolic Tangent Function: tanh
          The Tangent Function: tan
          The Square Root Function: sqrt
          The Hyperbolic Sine Function: sinh
          The Sine Function: sin
          The Base 10 Logarithm Function: log10
          The Exponential Function: log
          The Exponential Function: exp
          The Hyperbolic Cosine Function: cosh
          The Cosine Function: cos
          Inverse Tangent Function: atan
          Inverse Sine Function: asin
          Inverse Sine Function: acos
functions Define Matrix Multiply as a User Atomic Operation: CppAD User Atomic Callback Functions
          User Defined Atomic AD Functions
          ADFun Object Deprecated Member Functions
          CppAD Deprecated API Features: Atomic Functions
          The Theory of Reverse Mode: Standard Math Functions
          The Theory of Forward Mode: Standard Math Functions
          Speed Test of Functions in Double
          Running the Speed Test Program: Link Functions
          Optimize an ADFun Object Tape: Atomic Functions
          Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
          Base Type Requirements for Standard Math Functions
          Base Type Requirements for Identically Equal Comparisons: Identical.Identical Functions
          Required Base Class Member Functions
          AD Boolean Functions
          Bool Valued Operations and Functions with AD Arguments
          User Defined Atomic AD Functions: Virtual Functions
          User Defined Atomic AD Functions
          Checkpointing Functions
          Atomic AD Functions
          Discrete AD Functions
          The Binary Math Functions
          The Unary Standard Math Functions
          AD Valued Operations and Functions
functions: AD Parameter and Variable Functions: Example and Test
           AD Boolean Functions: Example and Test
           AD Absolute Value Functions: abs, fabs
future Control When Thread Alloc Retains Memory For Future Use
       Free Static Variables: Future Use
G
Gear An Error Controller for Gear's Ode Solvers
g Computing Jacobian and Hessian of Bender's Reduced Objective: g
  Nonlinear Programming Using the CppAD Interface to Ipopt: solution.g
  Check Gradient of Determinant of 3 by 3 matrix: g
  Use Ipopt to Solve a Nonlinear Programming Problem: solution.g
  Check an ADFun Sequence of Operations: g
  Atomic Reverse Mode: G, H
g_l Nonlinear Programming Using the CppAD Interface to Ipopt: g_l
g_u Nonlinear Programming Using the CppAD Interface to Ipopt: g_u
gear An Arbitrary Order Gear Method
gear's An Error Controller for Gear's Ode Solvers
       An Arbitrary Order Gear Method: Gear's Method
general zdouble: An AD Base Type With Absolute Zero: Motivation.General
        General Examples
        Some General Purpose Utilities: General Numerical Routines
        Some General Purpose Utilities
        Reverse Mode General Case (Checkpointing): Example and Test
        User Defined Atomic AD Functions: General Case
generator Using CMake to Configure CppAD: generator
get Get At Least A Specified Amount of Memory
    Get the Current OpenMP Thread Number
    Set and Get Maximum Number of Threads for omp_alloc Allocator
    Get At Least A Specified Amount of Memory
    Get the Current Thread Number
    Get Number of Threads
    Including the Sacado Speed Tests
    Including the cppad_ipopt Library and Tests
    Including the FADBAD Speed Tests
    Including the Eigen Examples and Tests
    Including the ColPack Sparsity Calculations
    Including the ADOL-C Examples and Tests
get_adolc Including the ADOL-C Examples and Tests: get_adolc
get_check_for_nan Check an ADFun Object For Nan Results: get_check_for_nan
get_colpack Including the ColPack Sparsity Calculations: get_colpack
get_eigen Including the Eigen Examples and Tests: get_eigen
get_fadbad Including the FADBAD Speed Tests: get_fadbad
get_ipopt Including the cppad_ipopt Library and Tests: get_ipopt
get_max_num_threads Set and Get Maximum Number of Threads for omp_alloc Allocator: get_max_num_threads
get_sacado Including the Sacado Speed Tests: get_sacado
get_started Use Ipopt to Solve a Nonlinear Programming Problem: Example.get_started
get_thread_num Get the Current OpenMP Thread Number
getting Getting Started with Atomic Operations: Example and Test
        User Defined Atomic AD Functions: Examples.Getting Started
        Getting Started Using CppAD to Compute Derivatives
git Download The CppAD Source Code: Current Version.Git
github Download The CppAD Source Code: Release Versions.github
gl Use Ipopt to Solve a Nonlinear Programming Problem: gl
global Running the Speed Test Program: Global Options
gradient Sacado Speed: Gradient of Ode Solution
         Sacado Speed: Gradient of Determinant Using Lu Factorization
         Sacado Speed: Gradient of Determinant by Minor Expansion
         Fadbad Speed: Gradient of Determinant Using Lu Factorization
         Fadbad Speed: Gradient of Determinant by Minor Expansion
         CppAD Speed: Gradient of Ode Solution
         CppAD Speed: Gradient of Determinant Using Lu Factorization
         CppAD Speed: Gradient of Determinant by Minor Expansion
         Adolc Speed: Gradient of Determinant Using Lu Factorization
         Adolc Speed: Gradient of Determinant by Minor Expansion
         Evaluate a Function Defined in Terms of an ODE: fp.Gradient
         Check Gradient of Determinant of 3 by 3 matrix
         Speed Testing Gradient of Determinant by Minor Expansion: gradient
         Speed Testing Gradient of Determinant by Minor Expansion
         Speed Testing Gradient of Determinant Using Lu Factorization: gradient
         Speed Testing Gradient of Determinant Using Lu Factorization
         Gradient of Determinant Using Lu Factorization: Example and Test
         Gradient of Determinant Using Expansion by Minors: Example and Test
         Gradient of Determinant Using LU Factorization: Example and Test
         Gradient of Determinant Using Expansion by Minors: Example and Test
         Differentiate Conjugate Gradient Algorithm: Example and Test
grid An ODE Inverse Problem Example: Trapezoidal Approximation.Trapezoidal Time Grid
gu Use Ipopt to Solve a Nonlinear Programming Problem: gu
guidelines The CppAD Wish List: Software Guidelines
gx Computing Jacobian and Hessian of Bender's Reduced Objective: gx
gxx Computing Jacobian and Hessian of Bender's Reduced Objective: gxx
H
HesLagrangian Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
Hessian Sparse Hessian: Example and Test
        Hessian: Example and Test
h Hessian Sparsity Pattern: Forward Mode: h
  Hessian Sparsity Pattern: Reverse Mode: h
  Atomic Forward Hessian Sparsity Patterns: Implementation.h
  Atomic Reverse Mode: G, H
handler CppAD Assertions During Execution: Error Handler
        Replacing The CppAD Error Handler: Example and Test
        Replacing the CppAD Error Handler: handler
        Replacing the CppAD Error Handler
        Some General Purpose Utilities: Miscellaneous.Error Handler
handler: Replacing The CppAD Error Handler: Example and Test
harmonic Multi-Threaded Implementation of Summation of 1/i
         Run Multi-Threading Examples and Speed Tests: harmonic
harmonic_combine Multi-threading Sum of 1/i Utility Routines: harmonic_combine
harmonic_setup Multi-threading Sum of 1/i Utility Routines: harmonic_setup
harmonic_time Timing Test of Multi-Threaded Summation of 1/i
harmonic_work Multi-threading Sum of 1/i Utility Routines
harmonic_worker Multi-threading Sum of 1/i Utility Routines: harmonic_worker
has Evaluate a Function That Has a Sparse Hessian
    Evaluate a Function That Has a Sparse Jacobian
hash Base Type Requirements for Hash Coding Values
hash_code Enable use of AD<Base> where Base is Adolc's adouble Type: hash_code
          Example AD<Base> Where Base Constructor Allocates Memory: hash_code
hasnan Obtain Nan or Determine if a Value is Nan: hasnan
head Routines That Track Use of New and Delete: head newptr
here CppAD API Preprocessor Symbols: Documented Here
hes Jacobian and Hessian of Optimal Values: hes
    Sparse Hessian: Easy Driver: hes
    Hessian: Easy Driver: hes
hessian Jacobian and Hessian of Optimal Values
        Computing Jacobian and Hessian of Bender's Reduced Objective
        Sacado Speed: Sparse Hessian
        Fadbad Speed: Sparse Hessian
        CppAD Speed: Sparse Hessian
        Adolc Speed: Sparse Hessian
        Double Speed: Sparse Hessian
        Evaluate a Function That Has a Sparse Hessian: fp.Hessian
        Evaluate a Function That Has a Sparse Hessian
        Speed Testing Sparse Hessian: hessian
        Speed Testing Sparse Hessian
        Sparse Hessian on Subset of Variables: Example and Test
        Computing Sparse Hessian for a Subset of Variables
        Sparse Hessian: Easy Driver: Subset Hessian
        Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
        Hessian: Easy Driver: Hessian Uses Forward
        Forward Mode Hessian Sparsity: Example and Test
        Hessian Sparsity Pattern: Forward Mode
        Reverse Mode Hessian Sparsity: Example and Test
        Hessian Sparsity Pattern: Reverse Mode
        Hessian Times Direction: Example and Test
        Second Order Reverse Mode: Hessian Times Direction
        Atomic Reverse Hessian Sparsity: Example and Test
        Atomic Forward Hessian Sparsity: Example and Test
        Atomic Reverse Hessian Sparsity Patterns
        Atomic Forward Hessian Sparsity Patterns
        User Defined Atomic AD Functions: Examples.Hessian Sparsity Patterns
        Using ColPack: Example and Test
hessian: Sparse Hessian: Example and Test
         Sparse Hessian: Easy Driver
         Hessian: Example and Test
         Hessian: Easy Driver
hold Control When Thread Alloc Retains Memory For Future Use
hold_memory Using CppAD in a Multi-Threading Environment: hold_memory
hyperbolic Tangent and Hyperbolic Tangent Reverse Mode Theory
           Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
           Inverse Sine and Hyperbolic Sine Reverse Mode Theory
           Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
           Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
           Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
           Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
           Inverse Sine and Hyperbolic Sine Forward Mode Theory
           Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
           Trigonometric and Hyperbolic Sine and Cosine Forward Theory
           The Inverse Hyperbolic Tangent Function: atanh
           The Inverse Hyperbolic Sine Function: asinh
           The Inverse Hyperbolic Cosine Function: acosh
           The Hyperbolic Tangent Function: tanh
           The Hyperbolic Sine Function: sinh
           The Hyperbolic Cosine Function: cosh
I
Integer Convert From AD to Integer: Example and Test
Ipopt Auto Tools Unix Test and Installation
i(k
     0) ODE Fitting Using Fast Representation: Trapezoidal Approximation.Range Indices I(k,0)
     0) ODE Fitting Using Fast Representation: Initial Condition.Range Indices I(k,0)
     0) ODE Fitting Using Fast Representation: Objective Function.Range Indices I(k,0)
i/o Conversion and I/O of AD Objects
id User Defined Atomic AD Functions: id
identical Enable use of AD<Base> where Base is std::complex<double>: Identical
          Enable use of AD<Base> where Base is double: Identical
          Enable use of AD<Base> where Base is float: Identical
          Enable use of AD<Base> where Base is Adolc's adouble Type: Identical
          Example AD<Base> Where Base Constructor Allocates Memory: Identical
          Base Type Requirements for Identically Equal Comparisons: Identical.Identical Functions
          Base Type Requirements for Identically Equal Comparisons: Identical
identically Base Type Requirements for Identically Equal Comparisons
            Check if Two Value are Identically Equal
identicalpar Base Type Requirements for Identically Equal Comparisons: Identical.IdenticalPar
identity An Important Reverse Mode Identity
if Check If A Memory Allocation is Efficient for Another Use
   Obtain Nan or Determine if a Value is Nan
   Determine if Two Values Are Nearly Equal
   Check if Two Value are Identically Equal
if_false AD Conditional Expressions: if_false
if_true AD Conditional Expressions: if_true
implementation User Defined Atomic AD Functions: Partial Implementation
               Sacado Speed: Second Derivative of a Polynomial: Implementation
               Sacado Speed: Gradient of Ode Solution: Implementation
               Sacado Speed: Matrix Multiplication: Implementation
               Sacado Speed: Gradient of Determinant Using Lu Factorization: Implementation
               Sacado Speed: Gradient of Determinant by Minor Expansion: Implementation
               Fadbad Speed: Second Derivative of a Polynomial: Implementation
               Fadbad Speed: Ode: Implementation
               Fadbad Speed: Matrix Multiplication: Implementation
               Fadbad Speed: Gradient of Determinant Using Lu Factorization: Implementation
               Fadbad Speed: Gradient of Determinant by Minor Expansion: Implementation
               CppAD Speed: Sparse Jacobian: Implementation
               CppAD Speed: Sparse Hessian: Implementation
               CppAD Speed: Second Derivative of a Polynomial: Implementation
               CppAD Speed: Gradient of Ode Solution: Implementation
               CppAD Speed, Matrix Multiplication: Implementation
               CppAD Speed: Gradient of Determinant Using Lu Factorization: Implementation
               CppAD Speed: Gradient of Determinant by Minor Expansion: Implementation
               adolc Speed: Sparse Jacobian: Implementation
               Adolc Speed: Sparse Hessian: Implementation
               Adolc Speed: Second Derivative of a Polynomial: Implementation
               Adolc Speed: Ode: Implementation
               Adolc Speed: Matrix Multiplication: Implementation
               Adolc Speed: Gradient of Determinant Using Lu Factorization: Implementation
               Adolc Speed: Gradient of Determinant by Minor Expansion: Implementation
               Double Speed: Sparse Jacobian: Implementation
               Double Speed: Sparse Hessian: Implementation
               Double Speed: Evaluate a Polynomial: Implementation
               Double Speed: Ode Solution: Implementation
               CppAD Speed: Matrix Multiplication (Double Version): Implementation
               Double Speed: Determinant Using Lu Factorization: Implementation
               Double Speed: Determinant by Minor Expansion: Implementation
               Pthread Implementation of a Team of AD Threads
               Boost Thread Implementation of a Team of AD Threads
               OpenMP Implementation of a Team of AD Threads
               Specifications for A Team of AD Threads: Speed Test of Implementation
               Specifications for A Team of AD Threads: Example Implementation
               Multi-Threaded Implementation of Summation of 1/i
               Atomic Reverse Hessian Sparsity Patterns: Implementation
               Atomic Forward Hessian Sparsity Patterns: Implementation
               Atomic Reverse Jacobian Sparsity Patterns: Implementation
               Atomic Forward Jacobian Sparsity Patterns: Implementation
               Atomic Reverse Mode: Implementation
               Atomic Forward Mode: Implementation
               Atomic Function Constructor: atomic_user.Implementation
               exp_eps: Implementation
               An Epsilon Accurate Exponential Approximation: Implementation
               exp_2: Implementation
               Second Order Exponential Approximation: Implementation
implementations Run Multi-Threading Examples and Speed Tests: Team Implementations
implicit AD Constructors: x.implicit
         Auto Tools Unix Test and Installation
         Using CMake to Configure CppAD
important An Important Reverse Mode Identity
in_parallel Is The Current Execution in OpenMP Parallel Mode
            Setup thread_alloc For Use in Multi-Threading Environment: in_parallel
inactive Glossary: Tape.Inactive
inc Run One Speed Test and Print Results: inc
include CppAD Addons: Include Files
        LU Factorization of A Square Matrix and Stability Calculation: Include
        Old Matrix Multiply as a User Atomic Operation: Example and Test: Include File
        A Quick OpenMP Memory Allocator Used by CppAD: Include
        Routines That Track Use of New and Delete: Include
        Deprecated Include Files
        Enable Use of Eigen Linear Algebra Package with CppAD: Include Files
        Use Ipopt to Solve a Nonlinear Programming Problem: Include File
        A Fast Multi-Threading Memory Allocator: Include
        The CppAD::vector Template Class: Include
        An Error Controller for Gear's Ode Solvers: Include
        An Arbitrary Order Gear Method: Include
        An Error Controller for ODE Solvers: Include
        A 3rd and 4th Order Rosenbrock ODE Solver: Include
        An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Include
        Multi-dimensional Romberg Integration: Include
        One DimensionalRomberg Integration: Include
        Invert an LU Factored Equation: Include
        LU Factorization of A Square Matrix: Include
        Compute Determinant and Solve Linear Equations: Include
        Evaluate a Polynomial or its Derivative: Include
        The Integer Power Function: Include
        Obtain Nan or Determine if a Value is Nan: Include
        Check Simple Vector Concept: Include
        Check NumericType Class Concept: Include
        Determine Amount of Time to Execute a Test: Include
        Run One Speed Test and Print Results: Include
        Run One Speed Test and Return Results: Include
        Determine if Two Values Are Nearly Equal: Include Files
        Enable use of AD<Base> where Base is std::complex<double>: Include Order
        Enable use of AD<Base> where Base is Adolc's adouble Type: Include Files
        Example AD<Base> Where Base Constructor Allocates Memory: Include File
        AD<Base> Requirements for a CppAD Base Type: Include Order
        An Epsilon Accurate Exponential Approximation: include
        Second Order Exponential Approximation: include
        Using CMake to Configure CppAD
        cppad-20170000.3: A Package for Differentiation of C++ Algorithms: Include File
including Including the Sacado Speed Tests
          Including the cppad_ipopt Library and Tests
          Including the FADBAD Speed Tests
          Including the Eigen Examples and Tests
          Including the ColPack Sparsity Calculations
          Including the ADOL-C Examples and Tests
inclusion Simulate a [0,1] Uniform Random Variate: Inclusion
          Evaluate a Function That Has a Sparse Hessian: Inclusion
          Evaluate a Function That Has a Sparse Jacobian: Inclusion
          Evaluate a Function Defined in Terms of an ODE: Inclusion
          Sum Elements of a Matrix Times Itself: Inclusion
          Check Gradient of Determinant of 3 by 3 matrix: Inclusion
          Check Determinant of 3 by 3 matrix: Inclusion
          Determinant Using Expansion by Minors: Inclusion
          Determinant of a Minor: Inclusion
          Determinant Using Expansion by Lu Factorization: Inclusion
ind Returns Indices that Sort a Vector: ind
independent OpenMP Parallel Setup: Independent
            Glossary: Tape.Independent Variable
            Glossary: Operation.Independent
            Frequently Asked Questions and Answers: Independent Variables
            Frequently Asked Questions and Answers: Assignment and Independent
            Independent and ADFun Constructor: Example and Test
            Declare Independent Variables and Start Recording
index Nonlinear Programming Using the CppAD Interface to Ipopt: fg(x).Index Vector
      Index Sort: Example and Test
      Check an ADFun Object For Nan Results: Error Message.index
      AD Vectors that Record Index Operations: Example and Test
      AD Vectors that Record Index Operations
      Matrix Multiply as an Atomic Operation: Result Element Index
      Matrix Multiply as an Atomic Operation: Right Operand Element Index
      Matrix Multiply as an Atomic Operation: Left Operand Element Index
      Taping Array Index Operation: Example and Test
      exp_eps: Second Order Reverse Sweep: Index 2: f_1
      exp_eps: Second Order Reverse Sweep: Index 3: f_2
      exp_eps: Second Order Reverse Sweep: Index 4: f_3
      exp_eps: Second Order Reverse Sweep: Index 5: f_4
      exp_eps: Second Order Reverse Sweep: Index 6: f_5
      exp_eps: Second Order Reverse Sweep: Index 7: f_6
      exp_eps: Second Order Forward Mode: Operation Sequence.Index
      exp_eps: First Order Reverse Sweep: Index 2: f_1
      exp_eps: First Order Reverse Sweep: Index 3: f_2
      exp_eps: First Order Reverse Sweep: Index 4: f_3
      exp_eps: First Order Reverse Sweep: Index 5: f_4
      exp_eps: First Order Reverse Sweep: Index 6: f_5
      exp_eps: First Order Reverse Sweep: Index 7: f_6
      exp_eps: First Order Forward Sweep: Operation Sequence.Index
      exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence.Index
      exp_2: Second Order Reverse Mode: Index 2: f_1
      exp_2: Second Order Reverse Mode: Index 3: f_2
      exp_2: Second Order Reverse Mode: Index 4: f_3
      exp_2: Second Order Reverse Mode: Index 5: f_4
      exp_2: Second Order Forward Mode: Operation Sequence.Index
      exp_2: First Order Reverse Mode: Index 2: f_1
      exp_2: First Order Reverse Mode: Index 3: f_2
      exp_2: First Order Reverse Mode: Index 4: f_3
      exp_2: First Order Reverse Mode: Index 5: f_4
      exp_2: First Order Forward Mode: Operation Sequence.Index
      exp_2: Operation Sequence and Zero Order Forward Mode: Operation Sequence.Index
index_sort Index Sort: Example and Test
           Returns Indices that Sort a Vector
indexing Define Matrix Multiply as a User Atomic Operation: Matrix Indexing
         AD Vectors that Record Index Operations: AD Indexing
         AD Vectors that Record Index Operations: size_t Indexing
indices ODE Fitting Using Fast Representation: Trapezoidal Approximation.Domain Indices J(k,0)
        ODE Fitting Using Fast Representation: Trapezoidal Approximation.Range Indices I(k,0)
        ODE Fitting Using Fast Representation: Initial Condition.Domain Indices J(k,0)
        ODE Fitting Using Fast Representation: Initial Condition.Range Indices I(k,0)
        ODE Fitting Using Fast Representation: Objective Function.Domain Indices J(k,0)
        ODE Fitting Using Fast Representation: Objective Function.Range Indices I(k,0)
        Returns Indices that Sort a Vector
        Some General Purpose Utilities: Miscellaneous.Sorting Indices
info Replacing the CppAD Error Handler: info
information Define Matrix Multiply as a User Atomic Operation: Extra Call Information
initial ODE Fitting Using Fast Representation: Initial Condition
        ODE Fitting Using Simple Representation: Initial Condition Constraint
initialization Using CppAD in a Multi-Threading Environment: Initialization
initialize Setup thread_alloc For Use in Multi-Threading Environment
injection Nonlinear Programming Using the CppAD Interface to Ipopt: fg(x).Injection
inline Base Type Requirements for Hash Coding Values: inline
inner Using Multiple Levels of AD: Procedure.Inner Function
input Returns Indices that Sort a Vector: ind.Input
      AD Output Operator: Example and Test
      AD Output Stream Operator
inside Using AD to Compute Atomic Function Derivatives
       Using AD to Compute Atomic Function Derivatives
install Auto Tools Unix Test and Installation: make install
        Download and Install Sacado in Build Directory
        Download and Install Ipopt in Build Directory
        Download and Install Fadbad in Build Directory
        Download and Install Eigen in Build Directory
        Download and Install ColPack in Build Directory
        Download and Install Adolc in Build Directory
        Using CMake to Configure CppAD
        Download The CppAD Source Code: Install Instructions
        CppAD Download, Test, and Install Instructions
     eigen Download and Install Eigen in Build Directory
     fadbad Download and Install Fadbad in Build Directory
     ipopt Download and Install Ipopt in Build Directory
     sacado Download and Install Sacado in Build Directory
installation Auto Tools Unix Test and Installation
             CppAD Download, Test, and Install Instructions: Instructions.Step 4: Installation
instructions Download The CppAD Source Code: Install Instructions
             CppAD Download, Test, and Install Instructions: Instructions
             CppAD Download, Test, and Install Instructions
int The Pow Integer Exponent: Example and Test
    Definition of a Numeric Type
integer Use Ipopt to Solve a Nonlinear Programming Problem: options.Integer
        Convert Certain Types to a String: s.Integer
        Convert Certain Types to a String: value.Integer
        The Pow Integer Exponent: Example and Test
        The Integer Power Function
        Definition of a Numeric Type: Constructor From Integer
        Enable use of AD<Base> where Base is std::complex<double>: Integer
        Enable use of AD<Base> where Base is double: Integer
        Enable use of AD<Base> where Base is float: Integer
        Enable use of AD<Base> where Base is Adolc's adouble Type: Integer
        Example AD<Base> Where Base Constructor Allocates Memory: Integer
        AD<Base> Requirements for a CppAD Base Type: Integer
        Convert From AD to Integer
integer: Convert From AD to Integer: Example and Test
integrate Multi-dimensional Romberg Integration
          One DimensionalRomberg Integration
integration Multi-dimensional Romberg Integration
            One DimensionalRomberg Integration
integration: One Dimensional Romberg Integration: Example and Test
             One Dimensional Romberg Integration: Example and Test
interface Nonlinear Programming Using the CppAD Interface to Ipopt
          The CppAD Wish List: Iterator Interface
          Interfacing to C: Example and Test
          Creating Your Own Interface to an ADFun Object
interfacing Interfacing to C: Example and Test
internal Auto Tools Unix Test and Installation
         Using CMake to Configure CppAD
interpolate Interpolation With Retaping: Example and Test
            Interpolation With Out Retaping: Example and Test
interpolation Interpolation With Retaping: Example and Test
              Interpolation With Out Retaping: Example and Test
interpreter Example Differentiating a Stack Machine Interpreter
introduction Choosing The Vector Testing Template Class: Introduction
             Changes and Additions to CppAD During 2003: Introduction
             Changes and Additions to CppAD During 2004: Introduction
             Changes and Additions to CppAD During 2006: Introduction
             Changes and Additions to CppAD During 2007: Introduction
             Changes and Additions to CppAD During 2008: Introduction
             Changes and Additions to CppAD During 2009: Introduction
             Changes and Additions to CppAD During 2010: Introduction
             Changes and Additions to CppAD During 2011: Introduction
             CppAD Changes and Additions During 2012: Introduction
             CppAD Changes and Additions During 2013: Introduction
             CppAD Changes and Additions During 2014: Introduction
             CppAD Changes and Additions During 2015: Introduction
             Changes and Additions to CppAD During 2016: Introduction
             Changes and Additions to CppAD: Introduction
             Using The CppAD Test Vector Template Class: Introduction
             Examples: Introduction
             Correctness Tests For Exponential Approximation in Introduction
             An Introduction by Example to Algorithmic Differentiation
             cppad-20170000.3: A Package for Differentiation of C++ Algorithms: Introduction
inuse Memory Leak Detection: inuse
      Amount of Memory a Thread is Currently Using
      Amount of Memory a Thread is Currently Using
invalid Enable use of AD<Base> where Base is std::complex<double>: Invalid Unary Math
inverse ODE Inverse Problem Definitions: Source Code
        An ODE Inverse Problem Example: Inverse Problem
        An ODE Inverse Problem Example
        Example Simultaneous Solution of Forward and Inverse Problem
        Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
        Inverse Sine and Hyperbolic Sine Reverse Mode Theory
        Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
        Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
        Inverse Sine and Hyperbolic Sine Forward Mode Theory
        Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
        Frequently Asked Questions and Answers: Matrix Inverse
        ODE Inverse Problem Definitions: Source Code: Inverse Problem
        ODE Inverse Problem Definitions: Source Code
        AD Two Argument Inverse Tangent Function
        The Inverse Hyperbolic Tangent Function: atanh
        The Inverse Hyperbolic Sine Function: asinh
        The Inverse Hyperbolic Cosine Function: acosh
        Inverse Tangent Function: atan
        Inverse Sine Function: asin
        Inverse Sine Function: acos
inverse: Atomic Eigen Matrix Inverse: Example and Test
inversion Atomic Eigen Matrix Inversion Class
invert Invert an LU Factored Equation
       Compute Determinant and Solve Linear Equations: Factor and Invert
ip LU Factorization of A Square Matrix and Stability Calculation: ip
   Invert an LU Factored Equation: ip
   LU Factorization of A Square Matrix: ip
ipopt Driver for Running the Ipopt ODE Example
      Nonlinear Programming Using CppAD and Ipopt: Example and Test
      Nonlinear Programming Using the CppAD Interface to Ipopt
      Nonlinear Programming Using CppAD and Ipopt: Example and Test
      Use Ipopt to Solve a Nonlinear Programming Problem
      Download and Install Ipopt in Build Directory
      Including the cppad_ipopt Library and Tests
     download and install Download and Install Ipopt in Build Directory
ipopt: Nonlinear Programming Using CppAD and Ipopt: Example and Test
       Nonlinear Programming Using CppAD and Ipopt: Example and Test
ipopt_cppad_nlp Changes and Additions to CppAD During 2008
ipopt_dir Auto Tools Unix Test and Installation: ipopt_dir
ipopt_library_paths Nonlinear Programming Using the CppAD Interface to Ipopt: ipopt_library_paths
ipopt_prefix Including the cppad_ipopt Library and Tests: ipopt_prefix
ipopt_solve Nonlinear Programming Retaping: Example and Test
is Check If A Memory Allocation is Efficient for Another Use
   Amount of Memory a Thread is Currently Using
   Is The Current Execution in OpenMP Parallel Mode
   Amount of Memory a Thread is Currently Using
   Is The Current Execution in Parallel Mode
   Obtain Nan or Determine if a Value is Nan
   Enable use of AD<Base> where Base is std::complex<double>
   Enable use of AD<Base> where Base is double
   Enable use of AD<Base> where Base is float
   Enable use of AD<Base> where Base is Adolc's adouble Type
   Is an AD Object a Parameter or Variable
   AD Output Stream Operator: is
isnan Obtain Nan or Determine if a Value is Nan: isnan
      Enable use of AD<Base> where Base is std::complex<double>: isnan
      Base Type Requirements for Standard Math Functions: isnan
iteration An ODE Inverse Problem Example: Black Box Method.Two levels of Iteration
iterator The CppAD Wish List: Iterator Interface
its Deallocate An Array and Call Destructor for its Elements
    Allocate An Array and Call Default Constructor for its Elements
    Evaluate a Polynomial or its Derivative
    Convert From AD to its Base Type: Example and Test
    Convert From an AD Type to its Base Type
itself Sum Elements of a Matrix Times Itself
J
Jacobian Sparse Jacobian: Example and Test
         Jacobian: Example and Test
         Jacobian: Driver Routine
j Reverse Mode Second Partial Derivative Driver: j
  Forward Mode Second Partial Derivative Driver: j
  First Order Partial Derivative: Driver Routine: j
j(k
     0) ODE Fitting Using Fast Representation: Trapezoidal Approximation.Domain Indices J(k,0)
     0) ODE Fitting Using Fast Representation: Initial Condition.Domain Indices J(k,0)
     0) ODE Fitting Using Fast Representation: Objective Function.Domain Indices J(k,0)
jac Jacobian and Hessian of Optimal Values: jac
    Sparse Jacobian: Easy Driver: jac
    Jacobian: Driver Routine: jac
jacobian Jacobian and Hessian of Optimal Values
         Computing Jacobian and Hessian of Bender's Reduced Objective
         CppAD Speed: Sparse Jacobian
         adolc Speed: Sparse Jacobian
         Double Speed: Sparse Jacobian
         Evaluate a Function That Has a Sparse Jacobian: fp.Jacobian
         Evaluate a Function That Has a Sparse Jacobian
         Speed Testing Sparse Jacobian: jacobian
         Speed Testing Sparse Jacobian
         Speed Testing the Jacobian of Ode Solution: jacobian
         Speed Testing the Jacobian of Ode Solution
         Computing a Jacobian With Constants that Change
         Reverse Mode Jacobian Sparsity: Example and Test
         Jacobian Sparsity Pattern: Reverse Mode
         Forward Mode Jacobian Sparsity: Example and Test
         Jacobian Sparsity Pattern: Forward Mode
         Atomic Reverse Jacobian Sparsity: Example and Test
         Atomic Forward Jacobian Sparsity: Example and Test
         Atomic Reverse Jacobian Sparsity Patterns
         Atomic Forward Jacobian Sparsity Patterns
         Using ColPack: Example and Test
jacobian: Sparse Jacobian: Example and Test
          Sparse Jacobian: Easy Driver
          Jacobian: Example and Test
          Jacobian: Driver Routine
jp LU Factorization of A Square Matrix and Stability Calculation: jp
   Invert an LU Factored Equation: jp
   LU Factorization of A Square Matrix: jp
K
Kutta An Embedded 4th and 5th Order Runge-Kutta ODE Solver
k User Defined Atomic AD Functions: k
  Evaluate a Polynomial or its Derivative: k
  Forward Mode Second Partial Derivative Driver: k
  AD Theory for Cholesky Factorization: Reverse Mode.Case k > 0
  AD Theory for Cholesky Factorization: Reverse Mode.Case k = 0
keys Returns Indices that Sort a Vector: keys
known CppAD Assertions During Execution: Known
      Replacing the CppAD Error Handler: known
L
Lu Compute Determinant and Solve Linear Equations
LuFactor LuFactor: Example and Test
         LU Factorization of A Square Matrix
LuInvert LuInvert: Example and Test
         Invert an LU Factored Equation
LuRatio LuRatio: Example and Test
        LU Factorization of A Square Matrix and Stability Calculation
LuSolve Compute Determinant and Solve Linear Equations
LuVecAD Lu Factor and Solve with Recorded Pivoting
l LU Factorization of A Square Matrix and Stability Calculation: LU.L
  Invert an LU Factored Equation: LU.L
  LU Factorization of A Square Matrix: LU.L
  Hessian: Easy Driver: l
l.f. Bibliography: Shampine, L.F.
lagrangian Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
lambda Nonlinear Programming Using the CppAD Interface to Ipopt: solution.lambda
       Use Ipopt to Solve a Nonlinear Programming Problem: solution.lambda
language Bibliography: The C++ Programming Language
languages Example and Test Linking CppAD to Languages Other than C++
large Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.Large x Values
last Run One Speed Test and Print Results: last
leak Memory Leak Detection
least Get At Least A Specified Amount of Memory
      Get At Least A Specified Amount of Memory
left Union of Standard Sets: left
     Matrix Multiply as an Atomic Operation: Left Operand Element Index
     AD Conditional Expressions: left
lemma AD Theory for Cholesky Factorization: Lemma 2
      AD Theory for Cholesky Factorization: Lemma 1
leqzero Compute Determinant and Solve Linear Equations: LeqZero
level Computing a Jacobian With Constants that Change
      Multiple Level of AD: Example and Test
      Checkpointing Functions: Purpose.Multiple Level AD
levels An ODE Inverse Problem Example: Black Box Method.Two levels of Iteration
       Using Multiple Levels of AD
       Using Adolc with Multiple Levels of Taping: Example and Test
lib Using CMake to Configure CppAD
library CppAD Addons: Library Files
        Speed Testing Utilities: Library Routines
        Including the cppad_ipopt Library and Tests
license Your License for the CppAD Software
limits Base Type Requirements for Numeric Limits
       Numeric Limits For an AD and Base Types
limits: Numeric Limits: Example and Test
line Routines That Track Use of New and Delete: line
     Replacing the CppAD Error Handler: line
linear LU Factorization of A Square Matrix and Stability Calculation
       Lu Factor and Solve with Recorded Pivoting
       Enable Use of Eigen Linear Algebra Package with CppAD
       Invert an LU Factored Equation
       LU Factorization of A Square Matrix
       Compute Determinant and Solve Linear Equations
       Compute Determinants and Solve Equations by LU Factorization
link Running the Speed Test Program: Link Functions
     Example and Test Linking CppAD to Languages Other than C++
link_det_lu Sacado Speed: Gradient of Determinant Using Lu Factorization
            Fadbad Speed: Gradient of Determinant Using Lu Factorization
            CppAD Speed: Gradient of Determinant Using Lu Factorization
            Adolc Speed: Gradient of Determinant Using Lu Factorization
            Double Speed: Determinant Using Lu Factorization
            Speed Testing Gradient of Determinant Using Lu Factorization
link_det_minor Sacado Speed: Gradient of Determinant by Minor Expansion
               Fadbad Speed: Gradient of Determinant by Minor Expansion
               CppAD Speed: Gradient of Determinant by Minor Expansion
               Adolc Speed: Gradient of Determinant by Minor Expansion
               Double Speed: Determinant by Minor Expansion
               Speed Testing Gradient of Determinant by Minor Expansion
link_mat_mul Sacado Speed: Matrix Multiplication
             Fadbad Speed: Matrix Multiplication
             CppAD Speed, Matrix Multiplication
             Adolc Speed: Matrix Multiplication
             CppAD Speed: Matrix Multiplication (Double Version)
             Speed Testing Derivative of Matrix Multiply
link_ode Sacado Speed: Gradient of Ode Solution
         Fadbad Speed: Ode
         CppAD Speed: Gradient of Ode Solution
         Adolc Speed: Ode
         Double Speed: Ode Solution
         Speed Testing the Jacobian of Ode Solution
link_poly Sacado Speed: Second Derivative of a Polynomial
          Fadbad Speed: Second Derivative of a Polynomial
          CppAD Speed: Second Derivative of a Polynomial
          Adolc Speed: Second Derivative of a Polynomial
          Double Speed: Evaluate a Polynomial
          Speed Testing Second Derivative of a Polynomial
link_sparse_hessian CppAD Speed: Sparse Hessian
                    Adolc Speed: Sparse Hessian
                    Double Speed: Sparse Hessian
                    Speed Testing Sparse Hessian
link_sparse_jacobian CppAD Speed: Sparse Jacobian
                     adolc Speed: Sparse Jacobian
                     Double Speed: Sparse Jacobian
                     Speed Testing Sparse Jacobian
linking Deprecated Include Files: Linking New Files to Deprecated Commands
        Microsoft Version of Elapsed Number of Seconds: Linking
        Example and Test Linking CppAD to Languages Other than C++
linux Auto Tools Unix Test and Installation: adolc_dir.Linux
list Nonlinear Programming Using the CppAD Interface to Ipopt: Wish List
     The CppAD Wish List
     List of All the CppAD Examples
log The AD log Function: Example and Test
    The Exponential Function: log
log10 The AD log10 Function: Example and Test
      The Base 10 Logarithm Function: log10
log1p Logarithm Function Reverse Mode Theory
      Logarithm Function Forward Mode Theory
      Enable use of AD<Base> where Base is Adolc's adouble Type: erf, asinh, acosh, atanh, expm1, log1p
      Example AD<Base> Where Base Constructor Allocates Memory: erf, asinh, acosh, atanh, expm1, log1p
      Base Type Requirements for Standard Math Functions: erf, asinh, acosh, atanh, expm1, log1p
      The AD log1p Function: Example and Test
      The Logarithm of One Plus Argument: log1p
logarithm Logarithm Function Reverse Mode Theory
          Logarithm Function Forward Mode Theory
          The Logarithm of One Plus Argument: log1p
          The Base 10 Logarithm Function: log10
logdet Lu Factor and Solve with Recorded Pivoting: logdet
       Compute Determinant and Solve Linear Equations: logdet
lower Multiple Directions Forward Mode: Non-Zero Lower Orders
      AD Theory for Cholesky Factorization: Notation.Lower Triangular Part
lu LU Factorization of A Square Matrix and Stability Calculation: LU
   LU Factorization of A Square Matrix and Stability Calculation
   Sacado Speed: Gradient of Determinant Using Lu Factorization
   Fadbad Speed: Gradient of Determinant Using Lu Factorization
   CppAD Speed: Gradient of Determinant Using Lu Factorization
   Adolc Speed: Gradient of Determinant Using Lu Factorization
   Double Speed: Determinant Using Lu Factorization
   Determinant Using Lu Factorization: Example and Test
   Determinant Using Expansion by Lu Factorization
   Speed Testing Gradient of Determinant Using Lu Factorization
   Lu Factor and Solve With Recorded Pivoting: Example and Test
   Lu Factor and Solve with Recorded Pivoting
   Gradient of Determinant Using Lu Factorization: Example and Test
   Gradient of Determinant Using LU Factorization: Example and Test
   Invert an LU Factored Equation: LU
   Invert an LU Factored Equation
   LU Factorization of A Square Matrix: LU
   LU Factorization of A Square Matrix
   Compute Determinants and Solve Equations by LU Factorization
lufactor Source: LuFactor
lufactor: LuFactor: Example and Test
luinvert Source: LuInvert
luinvert: LuInvert: Example and Test
luratio: LuRatio: Example and Test
lusolve Source: LuSolve
        LuSolve With Complex Arguments: Example and Test
M
m Compute Determinant using Expansion by Minors: m
  Determinant of a Minor: m
  User Defined Atomic AD Functions: m
  Nonlinear Programming Using the CppAD Interface to Ipopt: m
  Adolc Test Utility: Allocate and Free Memory For a Matrix: m
  Evaluate a Function That Has a Sparse Jacobian: m
  Determinant of a Minor: m
  Speed Testing Sparse Jacobian: m
  Lu Factor and Solve with Recorded Pivoting: m
  An Error Controller for Gear's Ode Solvers: M
  An Arbitrary Order Gear Method: m
  A 3rd and 4th Order Rosenbrock ODE Solver: M
  An Embedded 4th and 5th Order Runge-Kutta ODE Solver: M
  Multi-dimensional Romberg Integration: m
  Compute Determinant and Solve Linear Equations: m
  Multiple Directions Forward Mode: Notation.m
  Multiple Order Forward Mode: Notation.m
machine Machine Epsilon For AD Types
        Example Differentiating a Stack Machine Interpreter
macro Routines That Track Use of New and Delete: TrackCount.Macro
      Routines That Track Use of New and Delete: TrackExtend.Macro
      Routines That Track Use of New and Delete: TrackDelVec.Macro
      Routines That Track Use of New and Delete: TrackNewVec.Macro
      CppAD Assertions During Execution
      Example AD<Base> Where Base Constructor Allocates Memory: Boolean Operator Macro
      Example AD<Base> Where Base Constructor Allocates Memory: Binary Operator Macro
      Example AD<Base> Where Base Constructor Allocates Memory: Computed Assignment Macro
macros Obtain Nan or Determine if a Value is Nan: Include.Macros
main Main Program For Comparing C and C++ Speed
     Speed Testing Utilities: Speed Main Program
     Correctness Tests For Exponential Approximation in Introduction
main.cpp Correctness Tests For Exponential Approximation in Introduction: main.cpp
make Auto Tools Unix Test and Installation: make install
     Auto Tools Unix Test and Installation: make
     Using CMake to Configure CppAD: make check
makefile Using CMake to Configure CppAD
management Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Memory Management
           Using Adolc with Multiple Levels of Taping: Example and Test: Memory Management
mat Adolc Test Utility: Allocate and Free Memory For a Matrix: mat
mat_mul Define Matrix Multiply as a User Atomic Operation: Declare mat_mul Function
mat_sum_sq Source: mat_sum_sq
           Sum of the Elements of the Square of a Matrix: Example and Test
           Sum Elements of a Matrix Times Itself
math zdouble: An AD Base Type With Absolute Zero: Syntax.Standard Math
     The Theory of Reverse Mode: Standard Math Functions
     The Theory of Forward Mode: Standard Math Functions
     Frequently Asked Questions and Answers
     Enable use of AD<Base> where Base is std::complex<double>: Invalid Unary Math
     Enable use of AD<Base> where Base is std::complex<double>: Valid Unary Math
     Enable use of AD<Base> where Base is double: Unary Standard Math
     Enable use of AD<Base> where Base is float: Unary Standard Math
     Enable use of AD<Base> where Base is Adolc's adouble Type: Unary Standard Math
     Example AD<Base> Where Base Constructor Allocates Memory: Unary Standard Math
     Base Type Requirements for Standard Math Functions: Unary Standard Math
     Base Type Requirements for Standard Math Functions
     The Binary Math Functions
     The Unary Standard Math Functions
mathematical exp_eps: Second Order Reverse Sweep: Mathematical Form
             exp_eps: Second Order Forward Mode: Mathematical Form
             exp_eps: First Order Reverse Sweep: Mathematical Form
             exp_eps: First Order Forward Sweep: Mathematical Form
             exp_eps: Operation Sequence and Zero Order Forward Sweep: Mathematical Form
             An Epsilon Accurate Exponential Approximation: Mathematical Function
             exp_2: Second Order Reverse Mode: Mathematical Form
             exp_2: Second Order Forward Mode: Mathematical Form
             exp_2: First Order Reverse Mode: Mathematical Form
             exp_2: First Order Forward Mode: Mathematical Form
             exp_2: Operation Sequence and Zero Order Forward Mode: Mathematical Form
             Second Order Exponential Approximation: Mathematical Form
matrices Atomic Eigen Matrix Inversion Class: Theory.Product of Three Matrices
         Atomic Eigen Matrix Multiply Class: Theory.Product of Two Matrices
matrix LU Factorization of A Square Matrix and Stability Calculation: Matrix Storage
       LU Factorization of A Square Matrix and Stability Calculation
       Define Matrix Multiply as a User Atomic Operation: One Matrix Multiply
       Define Matrix Multiply as a User Atomic Operation: Matrix Indexing
       Define Matrix Multiply as a User Atomic Operation
       Old Matrix Multiply as a User Atomic Operation: Example and Test
       User Defined Atomic AD Functions: Example.Matrix Multiplication
       Frequently Asked Questions and Answers: Matrix Inverse
       Sacado Speed: Matrix Multiplication
       Sacado Speed: Gradient of Determinant Using Lu Factorization
       Fadbad Speed: Matrix Multiplication
       Fadbad Speed: Gradient of Determinant Using Lu Factorization
       CppAD Speed, Matrix Multiplication
       CppAD Speed: Gradient of Determinant Using Lu Factorization
       Adolc Test Utility: Allocate and Free Memory For a Matrix
       Adolc Speed: Matrix Multiplication
       Adolc Speed: Gradient of Determinant Using Lu Factorization
       CppAD Speed: Matrix Multiplication (Double Version)
       Double Speed: Determinant Using Lu Factorization
       Sum Elements of a Matrix Times Itself
       Check Gradient of Determinant of 3 by 3 matrix
       Check Determinant of 3 by 3 matrix
       Determinant of a Minor
       Speed Testing Derivative of Matrix Multiply
       Speed Testing Gradient of Determinant by Minor Expansion: matrix
       Speed Testing Gradient of Determinant Using Lu Factorization: matrix
       Lu Factor and Solve with Recorded Pivoting: Matrix
       Invert an LU Factored Equation: Matrix Storage
       LU Factorization of A Square Matrix: Matrix Storage
       LU Factorization of A Square Matrix
       Compute Determinant and Solve Linear Equations: Matrix Storage
       Compute Determinants and Solve Equations by LU Factorization
       Matrix Multiply as an Atomic Operation: Reverse Matrix Multiply
       Matrix Multiply as an Atomic Operation: Forward Matrix Multiply
       Matrix Multiply as an Atomic Operation: Matrix Dimensions
       Matrix Multiply as an Atomic Operation
       User Atomic Matrix Multiply: Example and Test
       Atomic Eigen Matrix Inversion Class: Matrix Dimensions
       Atomic Eigen Matrix Inversion Class
       Atomic Eigen Matrix Inverse: Example and Test
       Atomic Eigen Matrix Multiply Class: Matrix Dimensions
       Atomic Eigen Matrix Multiply Class
       Atomic Eigen Matrix Multiply: Example and Test
matrix: Sum of the Elements of the Square of a Matrix: Example and Test
max Numeric Limits For an AD and Base Types: max
max_itr Multi-threading Newton Method Utility Routines: max_itr
        A Multi-Threaded Newton's Method: max_itr
max_num_threads Set Maximum Number of Threads for omp_alloc Allocator
                Auto Tools Unix Test and Installation: max_num_threads
max_threads Run Multi-Threading Examples and Speed Tests: multi_newton.max_threads
            Run Multi-Threading Examples and Speed Tests: harmonic.max_threads
maxabs An Error Controller for Gear's Ode Solvers: maxabs
       OdeErrControl: Example and Test Using Maxabs Argument
       An Error Controller for ODE Solvers: maxabs
maximum Set Maximum Number of Threads for omp_alloc Allocator
        Set and Get Maximum Number of Threads for omp_alloc Allocator
        Using CppAD in a Multi-Threading Environment
        Using CMake to Configure CppAD
measurement An ODE Inverse Problem Example: Measurements.Simulated Measurement Values
            ODE Inverse Problem Definitions: Source Code: Measurements.Simulated Measurement Values
measurements An ODE Inverse Problem Example: Measurements
             ODE Inverse Problem Definitions: Source Code: Measurements
mega_sum Timing Test of Multi-Threaded Summation of 1/i: mega_sum
         Run Multi-Threading Examples and Speed Tests: harmonic.mega_sum
member ADFun Object Deprecated Member Functions
       Required Base Class Member Functions
memory User Defined Atomic AD Functions: Syntax Function.Free Static Memory
       Memory Leak Detection
       OpenMP Memory Allocator: Example and Test
       Check If A Memory Allocation is Efficient for Another Use
       Return A Raw Array to The Available Memory for a Thread
       Allocate Memory and Create A Raw Array
       Amount of Memory Available for Quick Use by a Thread
       Amount of Memory a Thread is Currently Using
       Free Memory Currently Available for Quick Use by a Thread
       Return Memory to omp_alloc
       Get At Least A Specified Amount of Memory
       A Quick OpenMP Memory Allocator Used by CppAD
       Routines That Track Use of New and Delete
       ADFun Object Deprecated Member Functions: Memory
       Frequently Asked Questions and Answers: Tape Storage: Disk or Memory
       Frequently Asked Questions and Answers: Speed.Memory Allocation
       Adolc Test Utility: Allocate and Free Memory For a Matrix
       Running the Speed Test Program: Global Options.memory
       Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Memory Management
       Free All Memory That Was Allocated for Use by thread_alloc
       Amount of Memory Available for Quick Use by a Thread
       Amount of Memory a Thread is Currently Using
       Control When Thread Alloc Retains Memory For Future Use
       Free Memory Currently Available for Quick Use by a Thread: Purpose.Extra Memory
       Free Memory Currently Available for Quick Use by a Thread
       Return Memory to thread_alloc
       Get At Least A Specified Amount of Memory
       Fast Multi-Threading Memory Allocator: Example and Test
       A Fast Multi-Threading Memory Allocator
       The CppAD::vector Template Class: Memory and Parallel Mode
       The CppAD::vector Template Class: vectorBool.Memory
       Some General Purpose Utilities: Miscellaneous.Multi-Threading Memory Allocation
       Optimize an ADFun Object Tape
       Controlling Taylor Coefficient Memory Allocation: Example and Test
       Controlling Taylor Coefficients Memory Allocation: c.Freeing Memory
       Controlling Taylor Coefficients Memory Allocation: c.Pre-Allocating Memory
       Controlling Taylor Coefficients Memory Allocation
       Using Adolc with Multiple Levels of Taping: Example and Test: Memory Management
       Example AD<Base> Where Base Constructor Allocates Memory
       AD Vectors that Record Index Operations: Speed and Memory
       Checkpointing Functions: Purpose.Reduce Memory
       Auto Tools Unix Test and Installation
       Using CMake to Configure CppAD
memory: Using vectorBool Sparsity To Conserve Memory: Example and Test
memory_leak Memory Leak Detection
message Memory Leak Detection: Error Message
        Check an ADFun Object For Nan Results: Error Message
method An ODE Inverse Problem Example: Simultaneous Method
       An ODE Inverse Problem Example: Black Box Method
       Speed Testing Sparse Jacobian: Method
       Speed Testing Sparse Hessian: Method
       Speed Testing Second Derivative of a Polynomial: Method
       Speed Testing the Jacobian of Ode Solution: Method
       Speed Testing Gradient of Determinant by Minor Expansion: Method
       Speed Testing Gradient of Determinant Using Lu Factorization: Method
       Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Taylor's Method Using AD
       Taylor's Ode Solver: A Multi-Level AD Example and Test: Taylor's Method Using AD
       ODE Inverse Problem Definitions: Source Code: Solution Method
       An Arbitrary Order Gear Method: Gear's Method
       An Arbitrary Order Gear Method
       An Error Controller for ODE Solvers: Method
       Multi-threading Newton Method Utility Routines
       Timing Test of Multi-Threaded Newton Method
       A Multi-Threaded Newton's Method: Method
       A Multi-Threaded Newton's Method
       Checkpointing Functions: Method
       The Base 10 Logarithm Function: log10: Method
microsoft Microsoft Version of Elapsed Number of Seconds
          Returns Elapsed Number of Seconds: Microsoft Systems
min Numeric Limits For an AD and Base Types: min
min_bytes Get At Least A Specified Amount of Memory: min_bytes
          Get At Least A Specified Amount of Memory: min_bytes
minor Determinant of a Minor
      Sacado Speed: Gradient of Determinant by Minor Expansion
      Fadbad Speed: Gradient of Determinant by Minor Expansion
      CppAD Speed: Gradient of Determinant by Minor Expansion
      Adolc Speed: Gradient of Determinant by Minor Expansion
      Double Speed: Determinant by Minor Expansion
      Determinant of a Minor
      Speed Testing Gradient of Determinant by Minor Expansion
minor: Determinant of a Minor: Example and Test
minors Compute Determinant using Expansion by Minors
       Determinant Using Expansion by Minors: Example and Test
       Determinant Using Expansion by Minors
       Determinant Using Lu Factorization: Example and Test
       Gradient of Determinant Using Expansion by Minors: Example and Test
       Gradient of Determinant Using Expansion by Minors: Example and Test
minors: Determinant Using Expansion by Minors: Example and Test
        Gradient of Determinant Using Expansion by Minors: Example and Test
        Gradient of Determinant Using Expansion by Minors: Example and Test
minus The Exponential Function Minus One: expm1
      AD Computed Assignment Operators
      AD Binary Subtraction: Example and Test
      AD Binary Arithmetic Operators
      AD Unary Minus Operator: Example and Test
      AD Unary Minus Operator
miscellaneous Some General Purpose Utilities: Miscellaneous
mode User Defined Atomic AD Functions: afun.Parallel Mode
     Is The Current Execution in OpenMP Parallel Mode
     Comparison Changes During Zero Order Forward Mode
     The CppAD Wish List: Forward Mode Recomputation
     An Important Reverse Mode Identity
     Error Function Reverse Mode Theory
     Tangent and Hyperbolic Tangent Reverse Mode Theory
     Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
     Inverse Sine and Hyperbolic Sine Reverse Mode Theory
     Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
     Square Root Function Reverse Mode Theory
     Logarithm Function Reverse Mode Theory
     Exponential Function Reverse Mode Theory
     The Theory of Reverse Mode
     Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
     Inverse Sine and Hyperbolic Sine Forward Mode Theory
     Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
     Square Root Function Forward Mode Theory
     Logarithm Function Forward Mode Theory
     Exponential Function Forward Mode Theory
     The Theory of Forward Mode
     Frequently Asked Questions and Answers
     Taylor's Ode Solver: An Example and Test: Forward Mode
     Is The Current Execution in Parallel Mode
     The CppAD::vector Template Class: Memory and Parallel Mode
     A 3rd and 4th Order Rosenbrock ODE Solver: Parallel Mode
     An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Parallel Mode
     Check Simple Vector Concept: Parallel Mode
     Check NumericType Class Concept: Parallel Mode
     Replacing the CppAD Error Handler: Constructor.Parallel Mode
     Enable AD Calculations During Parallel Mode
     Using CppAD in a Multi-Threading Environment
     Reverse Mode Second Partial Derivative Driver
     Forward Mode Second Partial Derivative Driver
     Forward Mode Hessian Sparsity: Example and Test
     Hessian Sparsity Pattern: Forward Mode
     Reverse Mode Hessian Sparsity: Example and Test
     Hessian Sparsity Pattern: Reverse Mode
     Reverse Mode Jacobian Sparsity: Example and Test
     Jacobian Sparsity Pattern: Reverse Mode
     Forward Mode Jacobian Sparsity: Example and Test
     Jacobian Sparsity Pattern: Forward Mode
     Reverse Mode General Case (Checkpointing): Example and Test
     Any Order Reverse Mode
     Second Order Reverse Mode
     First Order Reverse Mode
     Reverse Mode
     Multiple Directions Forward Mode: Reverse Mode
     Multiple Directions Forward Mode
     Multiple Order Forward Mode
     Forward Mode
     Stop Recording and Store Operation Sequence: Parallel Mode
     Construct an ADFun Object and Stop Recording: Parallel Mode
     Declare Independent Variables and Start Recording: Parallel Mode
     AD Theory for Cholesky Factorization: Reverse Mode
     AD Theory for Cholesky Factorization: Forward Mode
     Atomic Reverse Mode
     Atomic Forward Mode
     Discrete AD Functions: Parallel Mode
     Printing During Forward Mode: Example and Test
     Printing AD Values During Forward Mode
     exp_eps: Second Order Forward Mode
     exp_eps: First Order Reverse Sweep
     exp_2: Verify Second Order Reverse Sweep
     exp_2: Verify First Order Reverse Sweep
     exp_2: Second Order Reverse Mode
     exp_2: Second Order Forward Mode
     exp_2: First Order Reverse Mode
     exp_2: First Order Forward Mode
     exp_2: Operation Sequence and Zero Order Forward Mode
     An Introduction by Example to Algorithmic Differentiation: Preface.Reverse Mode
     An Introduction by Example to Algorithmic Differentiation: Preface.Forward Mode
mode: Frequently Asked Questions and Answers: Mode: Forward or Reverse
      Third Order Reverse Mode: Example and Test
      First Order Reverse Mode: Example and Test
      Forward Mode: Example and Test of Multiple Directions
      Forward Mode: Example and Test of Multiple Orders
      Forward Mode: Example and Test
      Second Order Forward Mode: Derivative Values
      First Order Forward Mode: Derivative Values
      Zero Order Forward Mode: Function Values
      Print During Zero Order Forward Mode: Example and Test
      Printing During Forward Mode: Example and Test
modeexample Second Order Reverse ModeExample and Test
monthly Download The CppAD Source Code: Monthly Versions
more Base Type Requirements for Identically Equal Comparisons: EqualOpSeq.More Complicated Cases
motivation zdouble: An AD Base Type With Absolute Zero: Motivation
           Using Multiple Levels of AD: Motivation
           Determine Amount of Time to Execute a Test: Motivation
           Run One Speed Test and Print Results: Motivation
           Run One Speed Test and Return Results: Motivation
           Check if Two Value are Identically Equal: Motivation
move The CppAD::vector Template Class: Assignment.Move Semantics
ms Choosing The Vector Testing Template Class: MS Windows
msg CppAD Assertions During Execution: Msg
    Replacing the CppAD Error Handler: msg
mul_level
     checkpoint Checkpointing an Extended ODE Solver: Example and Test
multi OpenMP Memory Allocator: Example and Test
      Routines That Track Use of New and Delete
      Multi-dimensional Romberg Integration
      Run Multi-Threading Examples and Speed Tests
multi-dimensional Multi-dimensional Romberg Integration
multi-level Taylor's Ode Solver: A Multi-Level Adolc Example and Test
            Taylor's Ode Solver: A Multi-Level AD Example and Test
multi-thread Fast Multi-Threading Memory Allocator: Example and Test
multi-threaded Timing Test of Multi-Threaded Newton Method
               A Multi-Threaded Newton's Method
               Timing Test of Multi-Threaded Summation of 1/i
               Multi-Threaded Implementation of Summation of 1/i
multi-threading A Quick OpenMP Memory Allocator Used by CppAD
                Routines That Track Use of New and Delete: Multi-Threading
                Setup thread_alloc For Use in Multi-Threading Environment
                Fast Multi-Threading Memory Allocator: Example and Test
                A Fast Multi-Threading Memory Allocator
                Some General Purpose Utilities: Miscellaneous.Multi-Threading Memory Allocation
                Multi-threading Newton Method Utility Routines
                A Multi-Threaded Newton's Method
                Multi-threading Sum of 1/i Utility Routines
                Run Multi-Threading Examples and Speed Tests
                Using CppAD in a Multi-Threading Environment
multi_newton A Multi-Threaded Newton's Method
             Run Multi-Threading Examples and Speed Tests: multi_newton
multi_newton_combine Multi-threading Newton Method Utility Routines: multi_newton_combine
multi_newton_setup Multi-threading Newton Method Utility Routines: multi_newton_setup
multi_newton_time Timing Test of Multi-Threaded Newton Method
multi_newton_work Multi-threading Newton Method Utility Routines
multi_newton_worker Multi-threading Newton Method Utility Routines: multi_newton_worker
multi_thread Timing Test of Multi-Threaded Newton Method
             Timing Test of Multi-Threaded Summation of 1/i
             Multi-Threaded Implementation of Summation of 1/i
multiple Speed Testing Derivative of Matrix Multiply
         Computing a Jacobian With Constants that Change
         Multiple Level of AD: Example and Test
         Using Multiple Levels of AD
         Reverse Mode: Multiple Directions
         Forward Mode: Example and Test of Multiple Directions
         Multiple Directions Forward Mode
         Forward Mode: Example and Test of Multiple Orders
         Multiple Order Forward Mode: yq.Multiple Orders
         Multiple Order Forward Mode: xq.Multiple Orders
         Multiple Order Forward Mode
         Using Adolc with Multiple Levels of Taping: Example and Test
         Checkpointing Functions: Purpose.Multiple Level AD
         AD Computed Assignment Operators
multiple-levels Atomic Operations and Multiple-Levels of AD: Example and Test
multiplication User Defined Atomic AD Functions: Example.Matrix Multiplication
               The Theory of Reverse Mode: Binary Operators.Multiplication
               The Theory of Forward Mode: Binary Operators.Multiplication
               Sacado Speed: Matrix Multiplication
               Fadbad Speed: Matrix Multiplication
               CppAD Speed, Matrix Multiplication
               Adolc Speed: Matrix Multiplication
               CppAD Speed: Matrix Multiplication (Double Version)
               Absolute Zero Multiplication
               AD Computed Assignment Operators: Derivative.Multiplication
               AD Binary Arithmetic Operators: Derivative.Multiplication
multiplication: AD Absolute Zero Multiplication: Example and Test
                AD Computed Assignment Multiplication: Example and Test
                AD Binary Multiplication: Example and Test
multiply Define Matrix Multiply as a User Atomic Operation: One Matrix Multiply
         Define Matrix Multiply as a User Atomic Operation
         Old Matrix Multiply as a User Atomic Operation: Example and Test
         Sacado Speed: Matrix Multiplication
         Fadbad Speed: Matrix Multiplication
         CppAD Speed, Matrix Multiplication
         Adolc Speed: Matrix Multiplication
         CppAD Speed: Matrix Multiplication (Double Version)
         Sum Elements of a Matrix Times Itself
         Speed Testing Derivative of Matrix Multiply
         Matrix Multiply as an Atomic Operation: Reverse Matrix Multiply
         Matrix Multiply as an Atomic Operation: Forward Matrix Multiply
         Matrix Multiply as an Atomic Operation
         Atomic Eigen Matrix Multiply Class
         AD Computed Assignment Multiplication: Example and Test
         AD Computed Assignment Operators
         AD Binary Multiplication: Example and Test
         AD Binary Arithmetic Operators
multiply: User Atomic Matrix Multiply: Example and Test
          Atomic Eigen Matrix Multiply: Example and Test
N
NDEBUG Routines That Track Use of New and Delete
       Definition of a Simple Vector
       Optimize an ADFun Object Tape
NearEqual Determine if Two Values Are Nearly Equal
          Compare AD and Base Objects for Nearly Equal
NearEqualExt Compare AD with Base Objects: Example and Test
NULL CppAD API Preprocessor Symbols
NumericType The CheckNumericType Function: Example and Test
            The NumericType: Example and Test
n_sweep Speed Testing Sparse Jacobian: n_sweep
        Speed Testing Sparse Hessian: n_sweep
        Running the Speed Test Program: Speed Results.n_sweep
        Sparse Hessian: Easy Driver: n_sweep
        Sparse Jacobian: Easy Driver: n_sweep
name CppAD Addons: Name
     Run One Speed Test and Print Results: Test.name
     NearEqual Function: Example and Test: File Name
     Atomic Function Constructor: atomic_base.name
     Checkpointing Functions: name
     Discrete AD Functions: name
namespace CppAD Addons: Namespace
          Nonlinear Programming Using the CppAD Interface to Ipopt: cppad_ipopt namespace
          Frequently Asked Questions and Answers: Namespace
          Enable Use of Eigen Linear Algebra Package with CppAD: CppAD Namespace
          cppad-20170000.3: A Package for Differentiation of C++ Algorithms: Namespace
nan zdouble: An AD Base Type With Absolute Zero: Syntax.Nan
    OdeErrControl: Example and Test: Nan
    An Error Controller for ODE Solvers: Method.Nan
    A 3rd and 4th Order Rosenbrock ODE Solver: Fun.Nan
    Obtain Nan or Determine if a Value is Nan
    Obtain Nan or Determine if a Value is Nan
    Check an ADFun Object For Nan Results
    Optimize an ADFun Object Tape: Atomic Functions.nan
nan(zero) Obtain Nan or Determine if a Value is Nan: nan(zero)
nan: nan: Example and Test
     ADFun Checking For Nan: Example and Test
ncopy Routines That Track Use of New and Delete: ncopy
ndebug Check If A Memory Allocation is Efficient for Another Use: NDEBUG
       Return Memory to omp_alloc: NDEBUG
       Frequently Asked Questions and Answers: Speed.NDEBUG
       Return Memory to thread_alloc: NDEBUG
       CppAD Assertions During Execution: NDEBUG
near Determine if Two Values Are Nearly Equal
nearequal NearEqual Function: Example and Test
nearly Determine if Two Values Are Nearly Equal
       Compare AD and Base Objects for Nearly Equal
nested Example Optimization and Nested Conditional Expressions
new Tracking Use of New and Delete: Example and Test
    Routines That Track Use of New and Delete
    Deprecated Include Files: Linking New Files to Deprecated Commands
newlen Routines That Track Use of New and Delete: newlen
newptr Routines That Track Use of New and Delete: head newptr
newton Multi-threading Newton Method Utility Routines
       Timing Test of Multi-Threaded Newton Method
newton's A Multi-Threaded Newton's Method
no Download The CppAD Source Code: No Documentation
no_compare_op Optimize an ADFun Object Tape: options.no_compare_op
no_conditional_skip Optimize an ADFun Object Tape: options.no_conditional_skip
no_print_for_op Optimize an ADFun Object Tape: options.no_print_for_op
non-zero Multiple Directions Forward Mode: Non-Zero Lower Orders
nonlinear Nonlinear Programming Using CppAD and Ipopt: Example and Test
          Nonlinear Programming Using the CppAD Interface to Ipopt
          Nonlinear Programming Retaping: Example and Test
          Nonlinear Programming Using CppAD and Ipopt: Example and Test
          Use Ipopt to Solve a Nonlinear Programming Problem
norm Atomic Euclidean Norm Squared: Example and Test
not Example AD Base Types That are not AD<OtherBase>
    Base Type Requirements for Ordered Comparisons: Not Ordered
    Base Type Requirements for Conditional Expressions: CondExpTemplate.Not Ordered
notation An ODE Inverse Problem Example: Notation
         An Important Reverse Mode Identity: Notation
         Error Function Reverse Mode Theory: Notation
         Tangent and Hyperbolic Tangent Reverse Mode Theory: Notation
         The Theory of Reverse Mode: Taylor Notation
         The Theory of Forward Mode: Taylor Notation
         An Error Controller for Gear's Ode Solvers: Notation
         An Error Controller for ODE Solvers: Notation
         Any Order Reverse Mode: Notation
         Multiple Directions Forward Mode: Notation
         Multiple Order Forward Mode: Notation
         Required Base Class Member Functions: Notation
         AD Theory for Cholesky Factorization: Notation
nstep An Error Controller for Gear's Ode Solvers: nstep
      An Error Controller for ODE Solvers: nstep
num_bytes Check If A Memory Allocation is Efficient for Another Use: num_bytes
          Amount of Memory Available for Quick Use by a Thread: num_bytes
          Amount of Memory a Thread is Currently Using: num_bytes
          Amount of Memory Available for Quick Use by a Thread: num_bytes
          Amount of Memory a Thread is Currently Using: num_bytes
num_sub Multi-threading Newton Method Utility Routines: multi_newton_setup.num_sub
        Timing Test of Multi-Threaded Newton Method: num_sub
        A Multi-Threaded Newton's Method: num_sub
        Run Multi-Threading Examples and Speed Tests: multi_newton.num_sub
num_sum Timing Test of Multi-Threaded Newton Method: num_sum
        Multi-threading Sum of 1/i Utility Routines: harmonic_setup.num_sum
        Multi-Threaded Implementation of Summation of 1/i: num_sum
        Run Multi-Threading Examples and Speed Tests: multi_newton.num_sum
num_threads Setup thread_alloc For Use in Multi-Threading Environment: num_threads
            Multi-threading Newton Method Utility Routines: max_itr.num_threads
            Timing Test of Multi-Threaded Newton Method: num_threads
            A Multi-Threaded Newton's Method: num_threads
            Multi-threading Sum of 1/i Utility Routines: harmonic_setup.num_threads
            Timing Test of Multi-Threaded Summation of 1/i: num_threads
            Multi-Threaded Implementation of Summation of 1/i: num_threads
num_zero Timing Test of Multi-Threaded Newton Method: num_zero
         Run Multi-Threading Examples and Speed Tests: multi_newton.num_zero
number Returns Elapsed Number of Seconds
       Repeat det_by_minor Routine A Specified Number of Times
       Set Maximum Number of Threads for omp_alloc Allocator: number
       Set Maximum Number of Threads for omp_alloc Allocator
       Get the Current OpenMP Thread Number
       Set and Get Maximum Number of Threads for omp_alloc Allocator: number
       Set and Get Maximum Number of Threads for omp_alloc Allocator
       OpenMP Parallel Setup: number
       Microsoft Version of Elapsed Number of Seconds
       Get the Current Thread Number
       Get Number of Threads: number
       Get Number of Threads
       Returns Elapsed Number of Seconds
       Using CppAD in a Multi-Threading Environment
       Number of Variables That Can be Skipped: Example and Test
       Number of Variables that Can be Skipped
       Comparison Changes Between Taping and Zero Order Forward: number
       Number Taylor Coefficient Orders Currently Stored
       Using CMake to Configure CppAD
number_skip Number of Variables That Can be Skipped: Example and Test
            Number of Variables that Can be Skipped
numbervector Nonlinear Programming Using the CppAD Interface to Ipopt: NumberVector
numeric Use Ipopt to Solve a Nonlinear Programming Problem: options.Numeric
        Check NumericType Class Concept
        Definition of a Numeric Type
        Base Type Requirements for Numeric Limits
        AD<Base> Requirements for a CppAD Base Type: Numeric Type
        Numeric Limits: Example and Test
        Numeric Limits For an AD and Base Types
numeric_limits Enable use of AD<Base> where Base is std::complex<double>: numeric_limits
               Enable use of AD<Base> where Base is double: numeric_limits
               Enable use of AD<Base> where Base is float: numeric_limits
               Enable use of AD<Base> where Base is Adolc's adouble Type: numeric_limits
               Example AD<Base> Where Base Constructor Allocates Memory: numeric_limits
numerical Some Numerical AD Utilities
          Bibliography: Numerical Recipes
          Some General Purpose Utilities: General Numerical Routines
numerictype Check NumericType Class Concept
numerictype: The NumericType: Example and Test
numtraits Enable Use of Eigen Linear Algebra Package with CppAD: Eigen NumTraits
O
Ode An Arbitrary Order Gear Method
OdeErrControl OdeErrControl: Example and Test Using Maxabs Argument
              An Error Controller for ODE Solvers
OdeGear OdeGear: Example and Test
        An Arbitrary Order Gear Method
OdeGearControl OdeGearControl: Example and Test
               An Error Controller for Gear's Ode Solvers
OpenMP A Simple Parallel Pthread Example and Test
       Auto Tools Unix Test and Installation
obj_value Nonlinear Programming Using the CppAD Interface to Ipopt: solution.obj_value
          Use Ipopt to Solve a Nonlinear Programming Problem: solution.obj_value
object ADFun Object Deprecated Member Functions
       Creating Your Own Interface to an ADFun Object
       Check an ADFun Object For Nan Results
       Optimize an ADFun Object Tape
       Construct an ADFun Object and Stop Recording
       Is an AD Object a Parameter or Variable
       AD Assignment: Example and Test
       AD Constructors: Example and Test
objective Computing Jacobian and Hessian of Bender's Reduced Objective
          ODE Fitting Using Fast Representation: Objective Function
          ODE Fitting Using Simple Representation: Objective Function
objects ADFun Objects
        Compare AD and Base Objects for Nearly Equal
        Conversion and I/O of AD Objects
        AD Objects
objects: Compare AD with Base Objects: Example and Test
obtain Obtain Nan or Determine if a Value is Nan
       Convert an AD Variable to a Parameter
ode Driver for Running the Ipopt ODE Example
    ODE Fitting Using Fast Representation
    ODE Fitting Using Simple Representation
    ODE Inverse Problem Definitions: Source Code
    ODE Fitting Using Fast Representation
    ODE Fitting Using Simple Representation
    An ODE Inverse Problem Example
    Sacado Speed: Gradient of Ode Solution
    Fadbad Speed: Ode
    CppAD Speed: Gradient of Ode Solution
    Adolc Speed: Ode
    Double Speed: Ode Solution
    Evaluate a Function Defined in Terms of an ODE
    Speed Testing the Jacobian of Ode Solution
    Taylor's Ode Solver: An Example and Test: ODE Solution
    Taylor's Ode Solver: An Example and Test: ODE
    Taylor's Ode Solver: An Example and Test
    Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Derivative of ODE Solution
    Taylor's Ode Solver: A Multi-Level Adolc Example and Test: ODE Solution
    Taylor's Ode Solver: A Multi-Level Adolc Example and Test: ODE
    Taylor's Ode Solver: A Multi-Level Adolc Example and Test
    Taylor's Ode Solver: A Multi-Level AD Example and Test: Derivative of ODE Solution
    Taylor's Ode Solver: A Multi-Level AD Example and Test: ODE Solution
    Taylor's Ode Solver: A Multi-Level AD Example and Test: ODE
    Taylor's Ode Solver: A Multi-Level AD Example and Test
    A Stiff Ode: Example and Test
    ODE Inverse Problem Definitions: Source Code
    An Error Controller for Gear's Ode Solvers
    An Error Controller for ODE Solvers
    A 3rd and 4th Order Rosenbrock ODE Solver
    An Embedded 4th and 5th Order Runge-Kutta ODE Solver
    Checkpointing an Extended ODE Solver: Example and Test: ODE
    Checkpointing an Extended ODE Solver: Example and Test: ODE Solver
    Checkpointing an Extended ODE Solver: Example and Test
    Checkpointing an ODE Solver: Example and Test: ODE
    Checkpointing an ODE Solver: Example and Test: ODE Solver
    Checkpointing an ODE Solver: Example and Test
ode: A Stiff Ode: Example and Test
ode_evaluate Source: ode_evaluate
             ode_evaluate: Example and test
             Evaluate a Function Defined in Terms of an ODE
ode_evaluate: ode_evaluate: Example and test
ode_inverse Use Ipopt to Solve a Nonlinear Programming Problem: Example.ode_inverse
odeerrcontrol: OdeErrControl: Example and Test Using Maxabs Argument
               OdeErrControl: Example and Test
odegear: OdeGear: Example and Test
odegearcontrol: OdeGearControl: Example and Test
ok User Defined Atomic AD Functions: ok
   Check Gradient of Determinant of 3 by 3 matrix: ok
   Check Determinant of 3 by 3 matrix: ok
   Free All Memory That Was Allocated for Use by thread_alloc: ok
   Specifications for A Team of AD Threads: ok
   Timing Test of Multi-Threaded Newton Method: ok
   A Multi-Threaded Newton's Method: ok
   Timing Test of Multi-Threaded Summation of 1/i: ok
   Multi-Threaded Implementation of Summation of 1/i: ok
   Check an ADFun Sequence of Operations: ok
   Atomic Reverse Jacobian Sparsity Patterns: ok
   Atomic Forward Jacobian Sparsity Patterns: ok
   Atomic Reverse Mode: ok
   Atomic Forward Mode: ok
old Old Matrix Multiply as a User Atomic Operation: Example and Test
    Old Tan and Tanh as User Atomic Operations: Example and Test
    Old Atomic Operation Reciprocal: Example and Test
old_atomic Define Matrix Multiply as a User Atomic Operation
           User Defined Atomic AD Functions
old_mat_mul Define Matrix Multiply as a User Atomic Operation
oldptr Routines That Track Use of New and Delete: oldptr
omp_alloc Set Maximum Number of Threads for omp_alloc Allocator
          Return Memory to omp_alloc
          Set and Get Maximum Number of Threads for omp_alloc Allocator
omp_max_thread OpenMP Parallel Setup
on Sparse Hessian on Subset of Variables: Example and Test
one Define Matrix Multiply as a User Atomic Operation: Reverse Partials One Order
    Define Matrix Multiply as a User Atomic Operation: One Matrix Multiply
    One Dimensional Romberg Integration: Example and Test
    One Dimensional Romberg Integration: Example and Test
    One DimensionalRomberg Integration
    Run One Speed Test and Print Results
    Run One Speed Test and Return Results
    Multiple Order Forward Mode: yq.One Order
    Multiple Order Forward Mode: xq.One Order
    Multiple Order Forward Mode: One Order
    First Order Forward Mode: Derivative Values
    The Logarithm of One Plus Argument: log1p
one: The Exponential Function Minus One: expm1
onetape Running the Speed Test Program: Global Options.onetape
op AD Binary Comparison Operators: Op
   Atomic Eigen Cholesky Factorization Class: Public.op
   Atomic Eigen Matrix Inversion Class: Public.op
   Atomic Eigen Matrix Multiply Class: Public.op
   AD Computed Assignment Operators: Op
   AD Binary Arithmetic Operators: Op
op_index Comparison Changes Between Taping and Zero Order Forward: op_index
openmp OpenMP Memory Allocator: Example and Test
       Get the Current OpenMP Thread Number
       Is The Current Execution in OpenMP Parallel Mode
       A Quick OpenMP Memory Allocator Used by CppAD
       OpenMP Parallel Setup
       Fast Multi-Threading Memory Allocator: Example and Test
       OpenMP Implementation of a Team of AD Threads
       A Simple OpenMP AD: Example and Test
       A Simple OpenMP Example and Test
       Run Multi-Threading Examples and Speed Tests
openmp/run.sh Changes and Additions to CppAD During 2011: 07-11.openmp/run.sh
openmp_flags Auto Tools Unix Test and Installation: openmp_flags
operand Matrix Multiply as an Atomic Operation: Right Operand Element Index
        Matrix Multiply as an Atomic Operation: Left Operand Element Index
operation Define Matrix Multiply as a User Atomic Operation
          Old Atomic Operation Reciprocal: Example and Test
          User Defined Atomic AD Functions
          The CppAD Wish List: Operation Sequence
          Glossary: Operation
          Evaluate a Function Defined in Terms of an ODE: Float.Operation Sequence
          An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Operation Sequence
          Evaluate a Polynomial or its Derivative: Operation Sequence
          The Integer Power Function: Operation Sequence
          Abort Recording of an Operation Sequence
          Stop Recording and Store Operation Sequence
          Check if Two Value are Identically Equal
          Is an AD Object a Parameter or Variable: Operation Sequence
          AD Boolean Functions: Operation Sequence
          Compare AD and Base Objects for Nearly Equal: Operation Sequence
          AD Binary Comparison Operators: Operation Sequence
          Matrix Multiply as an Atomic Operation
          Tan and Tanh as User Atomic Operations: Example and Test
          Atomic AD Functions
          Taping Array Index Operation: Example and Test
          Discrete AD Functions: Operation Sequence
          AD Conditional Expressions: Operation Sequence
          The AD Power Function: Operation Sequence
          AD Two Argument Inverse Tangent Function: Operation Sequence
          AD Computed Assignment Operators: Operation Sequence
          AD Binary Arithmetic Operators: Operation Sequence
          AD Unary Minus Operator: Operation Sequence
          AD Unary Plus Operator: Operation Sequence
          AD Output Stream Operator: Operation Sequence
          AD Output Stream Operator: Operation Sequence
          Convert From AD to Integer: Operation Sequence
          Convert From an AD Type to its Base Type: Operation Sequence
          exp_eps: Second Order Forward Mode: Operation Sequence.Operation
          exp_eps: Second Order Forward Mode: Operation Sequence
          exp_eps: First Order Forward Sweep: Operation Sequence.Operation
          exp_eps: First Order Forward Sweep: Operation Sequence
          exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence.Operation
          exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence
          exp_eps: Operation Sequence and Zero Order Forward Sweep
          exp_2: Second Order Forward Mode: Operation Sequence.Operation
          exp_2: Second Order Forward Mode: Operation Sequence
          exp_2: First Order Forward Mode: Operation Sequence.Operation
          exp_2: First Order Forward Mode: Operation Sequence
          exp_2: Operation Sequence and Zero Order Forward Mode: Operation Sequence.Operation
          exp_2: Operation Sequence and Zero Order Forward Mode: Operation Sequence
          exp_2: Operation Sequence and Zero Order Forward Mode
          An Introduction by Example to Algorithmic Differentiation: Preface.Operation Count
operation: Old Matrix Multiply as a User Atomic Operation: Example and Test
           Reciprocal as an Atomic Operation: Example and Test
           Taping Array Index Operation: Example and Test
operations Evaluate a Polynomial or its Derivative: Type.Operations
           Example Optimization and Cumulative Sum Operations
           Optimize an ADFun Object Tape
           Check an ADFun Sequence of Operations
           AD Vectors that Record Index Operations
           Bool Valued Operations and Functions with AD Arguments
           Atomic Operations and Multiple-Levels of AD: Example and Test
           AD Valued Operations and Functions
operations: Old Tan and Tanh as User Atomic Operations: Example and Test
            AD Vectors that Record Index Operations: Example and Test
            Tan and Tanh as User Atomic Operations: Example and Test
            Getting Started with Atomic Operations: Example and Test
operator Frequently Asked Questions and Answers
         Speed Test an Operator Overloading AD Package
         Construct an ADFun Object and Stop Recording: Example.Assignment Operator
         Construct an ADFun Object and Stop Recording: Assignment Operator
         Example AD<Base> Where Base Constructor Allocates Memory: Output Operator
         Example AD<Base> Where Base Constructor Allocates Memory: Boolean Operator Macro
         Example AD<Base> Where Base Constructor Allocates Memory: Binary Operator Macro
         AD<Base> Requirements for a CppAD Base Type: Output Operator
         AD Unary Minus Operator
         AD Unary Plus Operator
         AD Output Stream Operator
         AD Output Stream Operator
         AD Assignment Operator
operator: AD Unary Minus Operator: Example and Test
          AD Unary Plus Operator: Example and Test
          AD Output Operator: Example and Test
          AD Output Operator: Example and Test
operators zdouble: An AD Base Type With Absolute Zero: Syntax.Arithmetic Operators
          zdouble: An AD Base Type With Absolute Zero: Syntax.Comparison Operators
          The CppAD Wish List: Optimization.Special Operators
          The Theory of Reverse Mode: Binary Operators
          The Theory of Forward Mode: Binary Operators
          Definition of a Numeric Type: Operators
          Example Optimization and Print Forward Operators
          Example Optimization and Comparison Operators
          Required Base Class Member Functions: Bool Operators
          Required Base Class Member Functions: Binary Operators
          Required Base Class Member Functions: Assignment Operators
          Required Base Class Member Functions: Unary Operators
          AD Binary Comparison Operators
          AD Computed Assignment Operators
          AD Binary Arithmetic Operators
          AD Arithmetic Operators and Computed Assignments
operators: AD Binary Comparison Operators: Example and Test
opt_val_hes opt_val_hes: Example and Test
            Jacobian and Hessian of Optimal Values
opt_val_hes: opt_val_hes: Example and Test
optimal Jacobian and Hessian of Optimal Values
optimization The CppAD Wish List: Optimization
             A 3rd and 4th Order Rosenbrock ODE Solver: Fun.Optimization
             Example Optimization and Cumulative Sum Operations
             Example Optimization and Nested Conditional Expressions
             Example Optimization and Conditional Expressions
             Example Optimization and Print Forward Operators
             Example Optimization and Comparison Operators
             Example Optimization and Reverse Activity Analysis
             Example Optimization and Forward Activity Analysis
             Optimize an ADFun Object Tape: Checking Optimization
optimize Frequently Asked Questions and Answers: Speed.Optimize
         Running the Speed Test Program: Global Options.optimize
         Optimize an ADFun Object Tape
         Number of Variables That Can be Skipped: Example and Test
         Checkpointing Functions: optimize
         AD Conditional Expressions: Optimize
option User Atomic Matrix Multiply: Example and Test: Use Atomic Function.option
       Checkpointing Functions: option
options Running the Speed Test Program: Sparsity Options
        Running the Speed Test Program: Global Options
        Use Ipopt to Solve a Nonlinear Programming Problem: options
        Optimize an ADFun Object Tape: options
        Set Atomic Function Options
order Define Matrix Multiply as a User Atomic Operation: Reverse Partials One Order
      Comparison Changes During Zero Order Forward Mode
      ADFun Object Deprecated Member Functions: Order
      Error Function Reverse Mode Theory: Order Zero Z(t)
      Tangent and Hyperbolic Tangent Reverse Mode Theory: Order Zero Z(t)
      An Arbitrary Order Gear Method
      An Error Controller for ODE Solvers: Method.order
      A 3rd and 4th Order Rosenbrock ODE Solver
      An Embedded 4th and 5th Order Runge-Kutta ODE Solver
      Reverse Mode Second Partial Derivative Driver
      Subset of Second Order Partials: Example and Test
      Forward Mode Second Partial Derivative Driver
      First Order Derivative Driver: Example and Test
      First Order Derivative: Driver Routine
      First Order Partial Driver: Example and Test
      First Order Partial Derivative: Driver Routine
      Third Order Reverse Mode: Example and Test
      Any Order Reverse Mode: Second Order
      Any Order Reverse Mode: First Order
      Any Order Reverse Mode
      Second Order Reverse ModeExample and Test
      Second Order Reverse Mode: dw.Second Order Partials
      Second Order Reverse Mode: dw.First Order Partials
      Second Order Reverse Mode
      First Order Reverse Mode: Example and Test
      First Order Reverse Mode
      Comparison Changes Between Taping and Zero Order Forward
      Forward Mode: Example and Test of Multiple Directions
      Multiple Directions Forward Mode: Zero Order
      Multiple Order Forward Mode: Second Order
      Multiple Order Forward Mode: First Order
      Multiple Order Forward Mode: Zero Order
      Multiple Order Forward Mode: yq.One Order
      Multiple Order Forward Mode: xq.One Order
      Multiple Order Forward Mode: One Order
      Multiple Order Forward Mode
      Second Order Forward Mode: Derivative Values
      First Order Forward Mode: Derivative Values
      Zero Order Forward Mode: Function Values
      Enable use of AD<Base> where Base is std::complex<double>: Include Order
      AD<Base> Requirements for a CppAD Base Type: Include Order
      Print During Zero Order Forward Mode: Example and Test
      exp_eps: Verify Second Order Reverse Sweep
      exp_eps: Verify Second Order Forward Sweep
      exp_eps: Verify First Order Reverse Sweep
      exp_eps: Verify First Order Forward Sweep
      exp_eps: Verify Zero Order Forward Sweep
      exp_eps: Second Order Reverse Sweep
      exp_eps: Second Order Forward Mode: Second Order Expansion
      exp_eps: Second Order Forward Mode
      exp_eps: First Order Reverse Sweep
      exp_eps: First Order Forward Sweep: Operation Sequence.First Order
      exp_eps: First Order Forward Sweep: Operation Sequence.Zero Order
      exp_eps: First Order Forward Sweep: First Order Expansion
      exp_eps: First Order Forward Sweep
      exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence.Zero Order
      exp_eps: Operation Sequence and Zero Order Forward Sweep
      exp_2: Verify Second Order Reverse Sweep
      exp_2: Verify Second Order Forward Sweep
      exp_2: Verify First Order Reverse Sweep
      exp_2: Verify First Order Forward Sweep
      exp_2: Verify Zero Order Forward Sweep
      exp_2: Second Order Reverse Mode
      exp_2: Second Order Forward Mode: Second Order Expansion
      exp_2: Second Order Forward Mode
      exp_2: First Order Reverse Mode
      exp_2: First Order Forward Mode: Operation Sequence.First Order
      exp_2: First Order Forward Mode: Operation Sequence.Zero Order
      exp_2: First Order Forward Mode: First Order Expansion
      exp_2: First Order Forward Mode
      exp_2: Operation Sequence and Zero Order Forward Mode: Operation Sequence.Zero Order
      exp_2: Operation Sequence and Zero Order Forward Mode: Zero Order Expansion
      exp_2: Operation Sequence and Zero Order Forward Mode
      Second Order Exponential Approximation
ordered Enable use of AD<Base> where Base is std::complex<double>: Ordered
        Enable use of AD<Base> where Base is double: Ordered
        Enable use of AD<Base> where Base is float: Ordered
        Enable use of AD<Base> where Base is Adolc's adouble Type: Ordered
        Example AD<Base> Where Base Constructor Allocates Memory: Ordered
        Base Type Requirements for Ordered Comparisons: Not Ordered
        Base Type Requirements for Ordered Comparisons: Ordered Type
        Base Type Requirements for Ordered Comparisons
        Base Type Requirements for Conditional Expressions: CondExpTemplate.Not Ordered
        Base Type Requirements for Conditional Expressions: CondExpTemplate.Ordered Type
orders Error Function Reverse Mode Theory: Positive Orders Z(t)
       Tangent and Hyperbolic Tangent Reverse Mode Theory: Positive Orders Z(t)
       Number Taylor Coefficient Orders Currently Stored
       Forward Mode: Example and Test of Multiple Directions
       Multiple Directions Forward Mode: Non-Zero Lower Orders
       Forward Mode: Example and Test of Multiple Orders
       Multiple Order Forward Mode: yq.Multiple Orders
       Multiple Order Forward Mode: xq.Multiple Orders
original Controlling Taylor Coefficients Memory Allocation: Original State
os AD Output Stream Operator: os
other Example and Test Linking CppAD to Languages Other than C++
out Interpolation With Out Retaping: Example and Test
outer Using Multiple Levels of AD: Procedure.Derivatives of Outer Function
      Using Multiple Levels of AD: Procedure.Outer Function
outline An Introduction by Example to Algorithmic Differentiation: Outline
output The CppAD::vector Template Class: vectorBool.Output
       The CppAD::vector Template Class: Output
       Example Use of SpeedTest: Output
       Example AD<Base> Where Base Constructor Allocates Memory: Output Operator
       AD<Base> Requirements for a CppAD Base Type: Output Operator
       Printing During Forward Mode: Example and Test: Output
       Printing AD Values During Forward Mode: Redirecting Output
       Printing AD Values During Forward Mode
       AD Output Operator: Example and Test
       AD Output Operator: Example and Test
       AD Output Stream Operator
       AD Output Stream Operator
       Getting Started Using CppAD to Compute Derivatives: Output
overloading Speed Test an Operator Overloading AD Package
own Creating Your Own Interface to an ADFun Object
P
Parameter ADFun Sequence Properties: Example and Test
Poly Evaluate a Polynomial or its Derivative
p LU Factorization of A Square Matrix and Stability Calculation: LU.P
  Evaluate a Function That Has a Sparse Hessian: p
  Evaluate a Function That Has a Sparse Jacobian: p
  Evaluate a Function Defined in Terms of an ODE: p.p = 1
  Evaluate a Function Defined in Terms of an ODE: p.p == 0
  Evaluate a Function Defined in Terms of an ODE: p
  Multi-dimensional Romberg Integration: p
  One DimensionalRomberg Integration: p
  Invert an LU Factored Equation: LU.P
  LU Factorization of A Square Matrix: LU.P
  Evaluate a Polynomial or its Derivative: p
  Sparse Hessian: Easy Driver: work.p
  Sparse Hessian: Easy Driver: p
  Sparse Jacobian: Easy Driver: work.p
  Sparse Jacobian: Easy Driver: p
  Atomic Forward Mode: p
pack_sparsity_enum Set Atomic Function Options: atomic_sparsity.pack_sparsity_enum
package Running the Speed Test Program: package.AD Package
        Running the Speed Test Program: package
        Speed Test an Operator Overloading AD Package
        Enable Use of Eigen Linear Algebra Package with CppAD
        Using CMake to Configure CppAD
        cppad-20170000.3: A Package for Differentiation of C++ Algorithms
package_prefix Using CMake to Configure CppAD: package_prefix
parallel User Defined Atomic AD Functions: afun.Parallel Mode
         Is The Current Execution in OpenMP Parallel Mode
         OpenMP Parallel Setup
         Is The Current Execution in Parallel Mode
         Setup thread_alloc For Use in Multi-Threading Environment
         The CppAD::vector Template Class: Memory and Parallel Mode
         A 3rd and 4th Order Rosenbrock ODE Solver: Parallel Mode
         An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Parallel Mode
         Check Simple Vector Concept: Parallel Mode
         Check NumericType Class Concept: Parallel Mode
         Replacing the CppAD Error Handler: Constructor.Parallel Mode
         A Simple Parallel Pthread Example and Test
         Enable AD Calculations During Parallel Mode
         Using CppAD in a Multi-Threading Environment: Parallel Prohibited
         Using CppAD in a Multi-Threading Environment: Parallel AD
         Stop Recording and Store Operation Sequence: Parallel Mode
         Construct an ADFun Object and Stop Recording: Parallel Mode
         Declare Independent Variables and Start Recording: Parallel Mode
         Discrete AD Functions: Parallel Mode
parallel_setup Using CppAD in a Multi-Threading Environment: parallel_setup
parameter An ODE Inverse Problem Example: Measurements.Simulation Parameter Values
          Glossary: Parameter
          ODE Inverse Problem Definitions: Source Code: Measurements.Simulation Parameter Values
          ADFun Sequence Properties: Parameter
          AD Parameter and Variable Functions: Example and Test
          Is an AD Object a Parameter or Variable
          Atomic Reverse Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
          Atomic Forward Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
          Atomic Reverse Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
          Atomic Forward Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
          Convert an AD Variable to a Parameter
          exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence.Parameter
parameter: Convert an AD Variable to a Parameter: Example and Test
part AD Theory for Cholesky Factorization: Notation.Lower Triangular Part
partial User Defined Atomic AD Functions: Partial Implementation
        Reverse Mode Second Partial Derivative Driver
        Subset of Second Order Partials: Example and Test
        Forward Mode Second Partial Derivative Driver
        First Order Partial Driver: Example and Test
        First Order Partial Derivative: Driver Routine
partials Define Matrix Multiply as a User Atomic Operation: Reverse Partials One Order
         Second Partials Reverse Driver: Example and Test
         Second Order Reverse Mode: dw.Second Order Partials
         Second Order Reverse Mode: dw.First Order Partials
partials: Subset of Second Order Partials: Example and Test
pattern Glossary: Sparsity Pattern
        Hessian Sparsity Pattern: Reverse Mode: Entire Sparsity Pattern
        Computing Dependency: Example and Test: Dependency Pattern
        Jacobian Sparsity Pattern: Reverse Mode: Entire Sparsity Pattern
        Jacobian Sparsity Pattern: Forward Mode: Entire Sparsity Pattern
pattern: Hessian Sparsity Pattern: Forward Mode
         Hessian Sparsity Pattern: Reverse Mode
         Jacobian Sparsity Pattern: Reverse Mode
         Jacobian Sparsity Pattern: Forward Mode
patterns The CppAD Wish List: Sparsity Patterns
         Sparsity Patterns For a Subset of Variables: Example and Test
         Calculating Sparsity Patterns
         Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
         Construct an ADFun Object and Stop Recording: Assignment Operator.Sparsity Patterns
         Atomic Reverse Hessian Sparsity Patterns
         Atomic Forward Hessian Sparsity Patterns
         Atomic Reverse Jacobian Sparsity Patterns
         Atomic Forward Jacobian Sparsity Patterns
         User Defined Atomic AD Functions: Examples.Hessian Sparsity Patterns
patterns: Atomic Sparsity with Set Patterns: Example and Test
pc CppAD pkg-config Files
pivot Lu Factor and Solve With Recorded Pivoting: Example and Test
pivoting Lu Factor and Solve with Recorded Pivoting
pivoting: Lu Factor and Solve With Recorded Pivoting: Example and Test
pkg-config CppAD pkg-config Files
plus The Logarithm of One Plus Argument: log1p
     AD Computed Assignment Division: Example and Test
     AD Computed Assignment Multiplication: Example and Test
     AD Computed Assignment Subtraction: Example and Test
     AD Computed Assignment Addition: Example and Test
     AD Computed Assignment Operators
     AD Binary Addition: Example and Test
     AD Binary Arithmetic Operators
     AD Unary Plus Operator: Example and Test
     AD Unary Plus Operator
point Extending to_string To Another Floating Point Type
pointer CppAD API Preprocessor Symbols
poly Source: Poly
     Complex Polynomial: Example and Test: Poly
     Getting Started Using CppAD to Compute Derivatives: Poly
polynomial Error Function Forward Taylor Polynomial Theory
           Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
           Sacado Speed: Second Derivative of a Polynomial
           Fadbad Speed: Second Derivative of a Polynomial
           CppAD Speed: Second Derivative of a Polynomial
           Adolc Speed: Second Derivative of a Polynomial
           Double Speed: Evaluate a Polynomial
           Speed Testing Second Derivative of a Polynomial
           Polynomial Evaluation: Example and Test
           Evaluate a Polynomial or its Derivative
           Complex Polynomial: Example and Test
polynomial: Complex Polynomial: Example and Test
pos Printing AD Values During Forward Mode: pos
positive Error Function Reverse Mode Theory: Positive Orders Z(t)
         Tangent and Hyperbolic Tangent Reverse Mode Theory: Positive Orders Z(t)
possible The Unary Standard Math Functions: Possible Types
postfix Auto Tools Unix Test and Installation
        Using CMake to Configure CppAD
postfix_dir Auto Tools Unix Test and Installation: postfix_dir
pow The Pow Integer Exponent: Example and Test
    The Integer Power Function
    Enable use of AD<Base> where Base is std::complex<double>: pow
    Enable use of AD<Base> where Base is double: pow
    Enable use of AD<Base> where Base is float: pow
    Enable use of AD<Base> where Base is Adolc's adouble Type: pow
    Example AD<Base> Where Base Constructor Allocates Memory: pow
    Base Type Requirements for Standard Math Functions: pow
    The AD Power Function
power The Integer Power Function
      The AD Power Function: Example and Test
      The AD Power Function
pre-allocating Controlling Taylor Coefficients Memory Allocation: c.Pre-Allocating Memory
preface An Introduction by Example to Algorithmic Differentiation: Preface
prefix Auto Tools Unix Test and Installation
       Download and Install Sacado in Build Directory: Prefix Directory
       Including the Sacado Speed Tests
       Download and Install Ipopt in Build Directory: Prefix Directory
       Including the cppad_ipopt Library and Tests
       Download and Install Fadbad in Build Directory: Prefix Directory
       Including the FADBAD Speed Tests
       Download and Install Eigen in Build Directory: Prefix Directory
       Including the Eigen Examples and Tests
       Download and Install ColPack in Build Directory: Prefix Directory
       Including the ColPack Sparsity Calculations
       Download and Install Adolc in Build Directory: Prefix Directory
       Including the ADOL-C Examples and Tests
       Using CMake to Configure CppAD
prefix_dir Auto Tools Unix Test and Installation: prefix_dir
preprocessor CppAD Addons: Preprocessor Symbols
             Frequently Asked Questions and Answers: Namespace.Test Vector Preprocessor Symbol
             CppAD API Preprocessor Symbols
             cppad-20170000.3: A Package for Differentiation of C++ Algorithms: Preprocessor Symbols
previous Changes and Additions to CppAD: Previous Years
previously Routines That Track Use of New and Delete: TrackCount.Previously Deprecated
           Routines That Track Use of New and Delete: TrackExtend.Previously Deprecated
           Routines That Track Use of New and Delete: TrackDelVec.Previously Deprecated
           Routines That Track Use of New and Delete: TrackNewVec.Previously Deprecated
print Run One Speed Test and Print Results
      Example Optimization and Print Forward Operators
      Print During Zero Order Forward Mode: Example and Test
      Printing During Forward Mode: Example and Test
      Printing AD Values During Forward Mode
printing Printing During Forward Mode: Example and Test
         Printing AD Values During Forward Mode
private Atomic Eigen Cholesky Factorization Class: Private
        Atomic Eigen Matrix Inversion Class: Private
        Atomic Eigen Matrix Multiply Class: Private
problem Computing Jacobian and Hessian of Bender's Reduced Objective: Problem
        ODE Inverse Problem Definitions: Source Code
        An ODE Inverse Problem Example: Inverse Problem
        An ODE Inverse Problem Example: Forward Problem
        An ODE Inverse Problem Example
        Example Simultaneous Solution of Forward and Inverse Problem
        ODE Inverse Problem Definitions: Source Code: Inverse Problem
        ODE Inverse Problem Definitions: Source Code: Forward Problem
        ODE Inverse Problem Definitions: Source Code
        Use Ipopt to Solve a Nonlinear Programming Problem
        Checkpointing an Extended ODE Solver: Example and Test: Problem
        Checkpointing an ODE Solver: Example and Test: Problem
procedure Using Multiple Levels of AD: Procedure
processing Reverse Mode General Case (Checkpointing): Example and Test: Processing Steps
product Atomic Eigen Matrix Inversion Class: Theory.Product of Three Matrices
        Atomic Eigen Matrix Multiply Class: Theory.Product of Two Matrices
profile Running the Speed Test Program: package.profile
        Auto Tools Unix Test and Installation
        Using CMake to Configure CppAD
profiling Auto Tools Unix Test and Installation: Profiling CppAD
program Main Program For Comparing C and C++ Speed
        Speed Testing Utilities: Speed Main Program
        Running the Speed Test Program
        Run the Speed Examples
        Example Use of SpeedTest: Program
        Example Use of SpeedTest: Running This Program
        Getting Started Using CppAD to Compute Derivatives: Program
        Using CMake to Configure CppAD: The CMake Program
programming Nonlinear Programming Using CppAD and Ipopt: Example and Test
            Nonlinear Programming Using the CppAD Interface to Ipopt
            Bibliography: The C++ Programming Language
            Nonlinear Programming Retaping: Example and Test
            Nonlinear Programming Using CppAD and Ipopt: Example and Test
            Use Ipopt to Solve a Nonlinear Programming Problem
prohibited Using CppAD in a Multi-Threading Environment: Parallel Prohibited
projection Nonlinear Programming Using the CppAD Interface to Ipopt: fg(x).Projection
proof An Important Reverse Mode Identity: Proof
      AD Theory for Cholesky Factorization: Lemma 1.Proof
properties ADFun Sequence Properties
properties: ADFun Sequence Properties: Example and Test
prototype Speed Testing Sparse Jacobian: Prototype
          Speed Testing Sparse Hessian: Prototype
          Speed Testing Second Derivative of a Polynomial: Prototype
          Speed Testing the Jacobian of Ode Solution: Prototype
          Speed Testing Derivative of Matrix Multiply: Prototype
          Speed Testing Gradient of Determinant by Minor Expansion: Prototype
          Speed Testing Gradient of Determinant Using Lu Factorization: Prototype
prototypes Base Type Requirements for Identically Equal Comparisons: Identical.Prototypes
pthread Fast Multi-Threading Memory Allocator: Example and Test
        Pthread Implementation of a Team of AD Threads
        A Simple pthread AD: Example and Test
        A Simple Parallel Pthread Example and Test
        Run Multi-Threading Examples and Speed Tests
pthread_exit Pthread Implementation of a Team of AD Threads
public Atomic Eigen Cholesky Factorization Class: Public
       Atomic Eigen Matrix Inversion Class: Public
       Atomic Eigen Matrix Multiply Class: Public
purpose LU Factorization of A Square Matrix and Stability Calculation: ratio.Purpose
        Jacobian and Hessian of Optimal Values: Purpose
        Computing Jacobian and Hessian of Bender's Reduced Objective: Purpose
        Determine Amount of Time to Execute det_by_minor: Purpose
        Returns Elapsed Number of Seconds: Purpose
        Simulate a [0,1] Uniform Random Variate: Purpose
        Compute Determinant using Expansion by Minors: Purpose
        Determinant of a Minor: Purpose
        Compare Speed of C and C++: Purpose
        Using AD to Compute Atomic Function Derivatives: Purpose
        Using AD to Compute Atomic Function Derivatives: Purpose
        User Defined Atomic AD Functions: Purpose
        ODE Fitting Using Fast Representation: Purpose
        ODE Fitting Using Simple Representation: Purpose
        Nonlinear Programming Using CppAD and Ipopt: Example and Test: Purpose
        Nonlinear Programming Using the CppAD Interface to Ipopt: Purpose
        Machine Epsilon For AD Types: Purpose
        Memory Leak Detection: Purpose
        Set Maximum Number of Threads for omp_alloc Allocator: Purpose
        Check If A Memory Allocation is Efficient for Another Use: Purpose
        Return A Raw Array to The Available Memory for a Thread: Purpose
        Allocate Memory and Create A Raw Array: Purpose
        Amount of Memory Available for Quick Use by a Thread: Purpose
        Amount of Memory a Thread is Currently Using: Purpose
        Free Memory Currently Available for Quick Use by a Thread: Purpose
        Return Memory to omp_alloc: Purpose
        Get At Least A Specified Amount of Memory: Purpose
        Get the Current OpenMP Thread Number: Purpose
        Is The Current Execution in OpenMP Parallel Mode: Purpose
        Set and Get Maximum Number of Threads for omp_alloc Allocator: Purpose
        A Quick OpenMP Memory Allocator Used by CppAD: Purpose
        Routines That Track Use of New and Delete: Purpose
        OpenMP Parallel Setup: Purpose
        Comparison Changes During Zero Order Forward Mode: Purpose
        ADFun Object Deprecated Member Functions: Purpose
        Speed Test Derivatives Using Sacado: Purpose
        Speed Test Derivatives Using Fadbad: Purpose
        Speed Test Derivatives Using CppAD: Purpose
        Adolc Test Utility: Allocate and Free Memory For a Matrix: Purpose
        Speed Test of Derivatives Using Adolc: Purpose
        Speed Test of Functions in Double: Purpose
        Simulate a [0,1] Uniform Random Variate: Purpose
        Evaluate a Function That Has a Sparse Hessian: Purpose
        Evaluate a Function That Has a Sparse Jacobian: Purpose
        Evaluate a Function Defined in Terms of an ODE: Purpose
        Sum Elements of a Matrix Times Itself: Purpose
        Check Gradient of Determinant of 3 by 3 matrix: Purpose
        Check Determinant of 3 by 3 matrix: Purpose
        Determinant of a Minor: Purpose
        Microsoft Version of Elapsed Number of Seconds: Purpose
        Speed Testing Second Derivative of a Polynomial: Purpose
        Speed Testing the Jacobian of Ode Solution: Purpose
        Speed Testing Derivative of Matrix Multiply: Purpose
        Speed Testing Gradient of Determinant by Minor Expansion: Purpose
        Speed Testing Gradient of Determinant Using Lu Factorization: Purpose
        Running the Speed Test Program: Purpose
        Speed Test an Operator Overloading AD Package: Purpose
        Lu Factor and Solve with Recorded Pivoting: Purpose
        Taylor's Ode Solver: An Example and Test: Purpose
        Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Purpose
        Taylor's Ode Solver: A Multi-Level AD Example and Test: Purpose
        Computing a Jacobian With Constants that Change: Purpose
        Multiple Level of AD: Example and Test: Purpose
        Enable Use of Eigen Linear Algebra Package with CppAD: Purpose
        Differentiate Conjugate Gradient Algorithm: Example and Test: Purpose
        ODE Inverse Problem Definitions: Source Code: Purpose
        Nonlinear Programming Retaping: Example and Test: Purpose
        Nonlinear Programming Using CppAD and Ipopt: Example and Test: Purpose
        Use Ipopt to Solve a Nonlinear Programming Problem: Purpose
        Union of Standard Sets: Purpose
        Convert Certain Types to a String: Purpose
        Free All Memory That Was Allocated for Use by thread_alloc: Purpose
        Deallocate An Array and Call Destructor for its Elements: Purpose
        Allocate An Array and Call Default Constructor for its Elements: Purpose
        Amount of Memory Available for Quick Use by a Thread: Purpose
        Amount of Memory a Thread is Currently Using: Purpose
        Control When Thread Alloc Retains Memory For Future Use: Purpose
        Free Memory Currently Available for Quick Use by a Thread: Purpose
        Return Memory to thread_alloc: Purpose
        Get At Least A Specified Amount of Memory: Purpose
        Get the Current Thread Number: Purpose
        Is The Current Execution in Parallel Mode: Purpose
        Get Number of Threads: Purpose
        Setup thread_alloc For Use in Multi-Threading Environment: Purpose
        A Fast Multi-Threading Memory Allocator: Purpose
        An Error Controller for Gear's Ode Solvers: Purpose
        An Arbitrary Order Gear Method: Purpose
        An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Purpose
        The Integer Power Function: Purpose
        Obtain Nan or Determine if a Value is Nan: Purpose
        Check Simple Vector Concept: Purpose
        Check NumericType Class Concept: Purpose
        Returns Elapsed Number of Seconds: Purpose
        Determine Amount of Time to Execute a Test: Purpose
        Run One Speed Test and Print Results: Purpose
        Run One Speed Test and Return Results: Purpose
        Determine if Two Values Are Nearly Equal: Purpose
        CppAD Assertions During Execution: Purpose
        Some General Purpose Utilities
        Specifications for A Team of AD Threads: Purpose
        Multi-threading Newton Method Utility Routines: Purpose
        Timing Test of Multi-Threaded Newton Method: Purpose
        A Multi-Threaded Newton's Method: Purpose
        Multi-threading Sum of 1/i Utility Routines: Purpose
        Timing Test of Multi-Threaded Summation of 1/i: Purpose
        Using a Team of AD Threads: Example and Test: Purpose
        A Simple pthread AD: Example and Test: Purpose
        A Simple Boost Threading AD: Example and Test: Purpose
        A Simple OpenMP AD: Example and Test: Purpose
        A Simple Parallel Pthread Example and Test: Purpose
        A Simple Boost Thread Example and Test: Purpose
        A Simple OpenMP Example and Test: Purpose
        Run Multi-Threading Examples and Speed Tests: Purpose
        Enable AD Calculations During Parallel Mode: Purpose
        Using CppAD in a Multi-Threading Environment: Purpose
        CppAD API Preprocessor Symbols: Purpose
        Optimize an ADFun Object Tape: Purpose
        Check an ADFun Sequence of Operations: Purpose
        Sparse Hessian on Subset of Variables: Example and Test: Purpose
        Computing Sparse Hessian for a Subset of Variables: Purpose
        Sparse Hessian: Easy Driver: p.Purpose
        Sparse Hessian: Easy Driver: Purpose
        Sparse Jacobian: Easy Driver: Purpose
        Reverse Mode Second Partial Derivative Driver: Purpose
        Forward Mode Second Partial Derivative Driver: Purpose
        Hessian: Easy Driver: Purpose
        First Order Derivative: Driver Routine: Purpose
        First Order Partial Derivative: Driver Routine: Purpose
        Jacobian: Driver Routine: Purpose
        Using vectorBool Sparsity To Conserve Memory: Example and Test: Purpose
        Hessian Sparsity Pattern: Forward Mode: Purpose
        Hessian Sparsity Pattern: Reverse Mode: Purpose
        Jacobian Sparsity Pattern: Reverse Mode: Purpose
        Jacobian Sparsity Pattern: Forward Mode: Purpose
        Reverse Mode General Case (Checkpointing): Example and Test: Purpose
        Any Order Reverse Mode: Purpose
        Second Order Reverse Mode: Purpose
        First Order Reverse Mode: Purpose
        Number of Variables that Can be Skipped: Purpose
        Controlling Taylor Coefficients Memory Allocation: Purpose
        Comparison Changes Between Taping and Zero Order Forward: op_index.Purpose
        Comparison Changes Between Taping and Zero Order Forward: Purpose
        Number Taylor Coefficient Orders Currently Stored: Purpose
        Multiple Directions Forward Mode: Purpose
        Multiple Order Forward Mode: Purpose
        Second Order Forward Mode: Derivative Values: Purpose
        First Order Forward Mode: Derivative Values: Purpose
        Zero Order Forward Mode: Function Values: Purpose
        ADFun Sequence Properties: Purpose
        Abort Recording of an Operation Sequence: Purpose
        Stop Recording and Store Operation Sequence: Purpose
        Construct an ADFun Object and Stop Recording: Purpose
        Declare Independent Variables and Start Recording: Purpose
        ADFun Objects: Purpose
        Using Adolc with Multiple Levels of Taping: Example and Test: Purpose
        Using a User Defined AD Base Type: Example and Test: Purpose
        Example AD<Base> Where Base Constructor Allocates Memory: Purpose
        Base Type Requirements for Hash Coding Values: Purpose
        Base Type Requirements for Standard Math Functions: Purpose
        Base Type Requirements for Ordered Comparisons: Purpose
        Base Type Requirements for Conditional Expressions: Purpose
        AD<Base> Requirements for a CppAD Base Type: Purpose
        AD Vectors that Record Index Operations: Purpose
        Check if Two Value are Identically Equal: Purpose
        Is an AD Object a Parameter or Variable: Purpose
        AD Boolean Functions: Purpose
        Compare AD and Base Objects for Nearly Equal: Purpose
        AD Binary Comparison Operators: Purpose
        Atomic Eigen Cholesky Factorization Class: Purpose
        Atomic Eigen Matrix Inversion Class: Purpose
        Atomic Eigen Matrix Multiply Class: Purpose
        Getting Started with Atomic Operations: Example and Test: Purpose
        Atomic Reverse Hessian Sparsity: Example and Test: Purpose
        Atomic Forward Hessian Sparsity: Example and Test: Purpose
        Atomic Reverse Jacobian Sparsity: Example and Test: Purpose
        Atomic Forward Jacobian Sparsity: Example and Test: Purpose
        Atomic Reverse: Example and Test: Purpose
        Atomic Forward: Example and Test: Purpose
        Free Static Variables: Purpose
        Atomic Reverse Hessian Sparsity Patterns: Purpose
        Atomic Forward Hessian Sparsity Patterns: Purpose
        Atomic Reverse Jacobian Sparsity Patterns: Purpose
        Atomic Forward Jacobian Sparsity Patterns: Purpose
        Atomic Reverse Mode: Purpose
        Atomic Forward Mode: Purpose
        Using AD Version of Atomic Function: Purpose
        User Defined Atomic AD Functions: Purpose
        Checkpointing an ODE Solver: Example and Test: Purpose
        Simple Checkpointing: Example and Test: Purpose
        Checkpointing Functions: Purpose
        Discrete AD Functions: Purpose
        AD Conditional Expressions: Purpose
        Absolute Zero Multiplication: Purpose
        The AD Power Function: Purpose
        AD Two Argument Inverse Tangent Function: Purpose
        The Unary Standard Math Functions: Purpose
        AD Computed Assignment Operators: Purpose
        AD Binary Arithmetic Operators: Purpose
        AD Unary Minus Operator: Purpose
        AD Unary Plus Operator: Purpose
        Convert an AD Variable to a Parameter: Purpose
        Printing AD Values During Forward Mode: Purpose
        AD Output Stream Operator: Purpose
        AD Output Stream Operator: Purpose
        Convert From AD to Integer: Purpose
        Convert From an AD Type to its Base Type: Purpose
        AD Assignment Operator: Purpose
        AD Constructors: Purpose
        AD Objects: Purpose
        exp_eps: CppAD Forward and Reverse Sweeps: Purpose
        exp_eps: Second Order Reverse Sweep: Purpose
        exp_eps: Second Order Forward Mode: Purpose
        exp_eps: First Order Reverse Sweep: Purpose
        An Epsilon Accurate Exponential Approximation: Purpose
        exp_2: CppAD Forward and Reverse Sweeps: Purpose
        exp_2: Second Order Reverse Mode: Purpose
        exp_2: Second Order Forward Mode: Purpose
        exp_2: First Order Reverse Mode: Purpose
        exp_2: First Order Forward Mode: Purpose
        Second Order Exponential Approximation: Purpose
        Getting Started Using CppAD to Compute Derivatives: Purpose
        An Introduction by Example to Algorithmic Differentiation: Purpose
        CppAD pkg-config Files: Purpose
        Checking the CppAD Examples and Tests: Purpose
        Choosing the CppAD Test Vector Template Class: Purpose
        Download and Install Sacado in Build Directory: Purpose
        Including the Sacado Speed Tests: Purpose
        Download and Install Ipopt in Build Directory: Purpose
        Including the cppad_ipopt Library and Tests: Purpose
        Download and Install Fadbad in Build Directory: Purpose
        Including the FADBAD Speed Tests: Purpose
        Download and Install Eigen in Build Directory: Purpose
        Including the Eigen Examples and Tests: Purpose
        Download and Install ColPack in Build Directory: Purpose
        Including the ColPack Sparsity Calculations: Purpose
        Download and Install Adolc in Build Directory: Purpose
        Including the ADOL-C Examples and Tests: Purpose
        Download The CppAD Source Code: Purpose
push The CppAD::vector Template Class
push_back The CppAD::vector Template Class: push_back
push_vector The CppAD::vector Template Class: push_vector
px User Defined Atomic AD Functions: reverse.px
   Atomic Reverse Mode: py.px
py User Defined Atomic AD Functions: reverse.py
   Atomic Reverse Mode: py
Q
q User Defined Atomic AD Functions: rev_hes_sparse.q
  User Defined Atomic AD Functions: rev_jac_sparse.q
  User Defined Atomic AD Functions: for_jac_sparse.q
  Hessian Sparsity Pattern: Reverse Mode: q
  Jacobian Sparsity Pattern: Reverse Mode: q
  Jacobian Sparsity Pattern: Forward Mode: q
  Any Order Reverse Mode: q
  Multiple Directions Forward Mode: q
  Multiple Order Forward Mode: q
  Atomic Reverse Hessian Sparsity Patterns: Implementation.q
  Atomic Reverse Jacobian Sparsity Patterns: Implementation.q
  Atomic Forward Jacobian Sparsity Patterns: Implementation.q
  Atomic Reverse Mode: q
  Atomic Forward Mode: q
questions Frequently Asked Questions and Answers
quick Amount of Memory Available for Quick Use by a Thread
      Free Memory Currently Available for Quick Use by a Thread
      A Quick OpenMP Memory Allocator Used by CppAD
      Amount of Memory Available for Quick Use by a Thread
      Free Memory Currently Available for Quick Use by a Thread
quiet_nan Numeric Limits For an AD and Base Types: quiet_NaN
quotient AD Binary Division: Example and Test
R
Range ADFun Sequence Properties: Example and Test
RevSparseHes Reverse Mode Hessian Sparsity: Example and Test
RevSparseJac Reverse Mode Jacobian Sparsity: Example and Test
             Jacobian Sparsity Pattern: Reverse Mode
Romberg One DimensionalRomberg Integration
Rosen34 Rosen34: Example and Test
        A 3rd and 4th Order Rosenbrock ODE Solver
Runge An Embedded 4th and 5th Order Runge-Kutta ODE Solver
Runge45 Runge45: Example and Test
        Runge45: Example and Test
        An Embedded 4th and 5th Order Runge-Kutta ODE Solver
random Simulate a [0,1] Uniform Random Variate
       Simulate a [0,1] Uniform Random Variate
range ODE Fitting Using Fast Representation: Trapezoidal Approximation.Range Indices I(k,0)
      ODE Fitting Using Fast Representation: Initial Condition.Range Indices I(k,0)
      ODE Fitting Using Fast Representation: Objective Function.Range Indices I(k,0)
      ADFun Sequence Properties: Range
      User Defined Atomic AD Functions: Examples.Vector Range
rate Run One Speed Test and Print Results: rate
rate_vec Run One Speed Test and Return Results: rate_vec
ratio LU Factorization of A Square Matrix and Stability Calculation: ratio
raw Return A Raw Array to The Available Memory for a Thread
    Allocate Memory and Create A Raw Array
re-tape CompareChange and Re-Tape: Example and Test
re-tape: ADFun Check and Re-Tape: Example and Test
         CompareChange and Re-Tape: Example and Test
real Convert From AD to Integer: x.Real Types
realistic General Examples
recipes Bibliography: Numerical Recipes
reciprocal Reciprocal as an Atomic Operation: Example and Test
reciprocal: Old Atomic Operation Reciprocal: Example and Test
recomputation The CppAD Wish List: Forward Mode Recomputation
record Frequently Asked Questions and Answers
       Lu Factor and Solve With Recorded Pivoting: Example and Test
       AD Vectors that Record Index Operations: Example and Test
       AD Vectors that Record Index Operations
       Convert From AD to its Base Type: Example and Test
recorded Lu Factor and Solve With Recorded Pivoting: Example and Test
         Lu Factor and Solve with Recorded Pivoting
recording Using Multiple Levels of AD: Procedure.Start AD< AD<double> > Recording
          Abort Current Recording: Example and Test
          Abort Recording of an Operation Sequence
          Stop Recording and Store Operation Sequence
          Construct an ADFun Object and Stop Recording
          Declare Independent Variables and Start Recording: Stop Recording
          Declare Independent Variables and Start Recording: Start Recording
          Declare Independent Variables and Start Recording
          User Atomic Matrix Multiply: Example and Test: Use Atomic Function.Recording
          Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.Recording
          Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function.Recording
          Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function.Recording
          Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function.Recording
          Getting Started with Atomic Operations: Example and Test: Use Atomic Function.Recording
          Checkpointing Functions: Purpose.Faster Recording
recording: Abort Current Recording: Example and Test
recursion Error Function Forward Taylor Polynomial Theory: Taylor Coefficients Recursion
          Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory: Taylor Coefficients Recursion
          Inverse Cosine and Hyperbolic Cosine Forward Mode Theory: Taylor Coefficients Recursion
          Inverse Sine and Hyperbolic Sine Forward Mode Theory: Taylor Coefficients Recursion
          Inverse Tangent and Hyperbolic Tangent Forward Mode Theory: Taylor Coefficients Recursion
          Logarithm Function Forward Mode Theory: Taylor Coefficients Recursion
          Exponential Function Forward Mode Theory: Taylor Coefficients Recursion
          The Theory of Forward Mode: Standard Math Functions.Cases that Apply Recursion Above
          The Theory of Forward Mode: Standard Math Functions.Taylor Coefficients Recursion Formula
redirecting Printing AD Values During Forward Mode: Redirecting Output
reduce Checkpointing Functions: Purpose.Reduce Memory
reduced Computing Jacobian and Hessian of Bender's Reduced Objective
reference Jacobian and Hessian of Optimal Values: Reference
          The CppAD::vector Template Class: Assignment.Return Reference
          AD Vectors that Record Index Operations
          AD Theory for Cholesky Factorization: Reference
          An Introduction by Example to Algorithmic Differentiation: Reference
rel AD Conditional Expressions: Rel
relative Determine if Two Values Are Nearly Equal
release Download The CppAD Source Code: Release Versions
removed Set Maximum Number of Threads for omp_alloc Allocator: Removed
        Check If A Memory Allocation is Efficient for Another Use: Removed
repeat Repeat det_by_minor Routine A Specified Number of Times: repeat
       Repeat det_by_minor Routine A Specified Number of Times
       Speed Testing Sparse Jacobian: repeat
       Speed Testing Sparse Hessian: repeat
       Speed Testing Second Derivative of a Polynomial: repeat
       Speed Testing the Jacobian of Ode Solution: repeat
       Speed Testing Derivative of Matrix Multiply: repeat
       Speed Testing Gradient of Determinant by Minor Expansion: repeat
       Speed Testing Gradient of Determinant Using Lu Factorization: repeat
       Determine Amount of Time to Execute a Test: test.repeat
       Run One Speed Test and Print Results: Test.repeat
       Run One Speed Test and Return Results: test.repeat
repeating Checkpointing Functions: Purpose.Repeating Forward
replace Replacing the CppAD Error Handler
replacing Replacing The CppAD Error Handler: Example and Test
          Replacing the CppAD Error Handler
reporting Frequently Asked Questions and Answers
representation ODE Fitting Using Fast Representation
               ODE Fitting Using Simple Representation
               ODE Fitting Using Fast Representation
               ODE Fitting Using Simple Representation
               Nonlinear Programming Using the CppAD Interface to Ipopt: Simple Representation
               Nonlinear Programming Using the CppAD Interface to Ipopt: fg(x).Representation
representations Speed Test for Both Simple and Fast Representations
                Correctness Check for Both Simple and Fast Representations
require Base Type Requirements for Identically Equal Comparisons
        Base Type Requirements for Conditional Expressions
        AD Objects
required Required Base Class Member Functions
requirement Nonlinear Programming Using CppAD and Ipopt: Example and Test: Configuration Requirement
            Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Configuration Requirement
            Nonlinear Programming Using CppAD and Ipopt: Example and Test: Configuration Requirement
            Using Adolc with Multiple Levels of Taping: Example and Test: Configuration Requirement
            Extending to_string To Another Floating Point Type: Base Requirement
requirements zdouble: An AD Base Type With Absolute Zero: Base Type Requirements
             The CppAD Wish List: Base Requirements
             Definition of a Simple Vector: Template Class Requirements
             Definition of a Numeric Type: Type Requirements
             Base Type Requirements for Hash Coding Values
             Base Type Requirements for Numeric Limits
             Base Type Requirements for Standard Math Functions
             Base Type Requirements for Ordered Comparisons
             Base Type Requirements for Identically Equal Comparisons
             Base Type Requirements for Conditional Expressions
             AD<Base> Requirements for a CppAD Base Type
             AD Objects: Base Type Requirements
             Download and Install Adolc in Build Directory: Requirements
resize The CppAD::vector Template Class: resize
       Definition of a Simple Vector: Resize
restriction User Defined Atomic AD Functions: clear.Restriction
            OpenMP Parallel Setup: Restriction
            CppAD Assertions During Execution: Restriction
            Enable AD Calculations During Parallel Mode: Restriction
            Free Static Variables: Restriction
            Checkpointing Functions: clear.Restriction
            Checkpointing Functions: Purpose.Restriction
            Convert From an AD Type to its Base Type: Restriction
restrictions Set Maximum Number of Threads for omp_alloc Allocator: Restrictions
             Set and Get Maximum Number of Threads for omp_alloc Allocator: Restrictions
             Free All Memory That Was Allocated for Use by thread_alloc: Restrictions
             Setup thread_alloc For Use in Multi-Threading Environment: Restrictions
             Check Simple Vector Concept: Restrictions
             Specifications for A Team of AD Threads: Restrictions
             Sparse Hessian: Easy Driver: VectorSet.Restrictions
             Sparse Jacobian: Easy Driver: VectorSet.Restrictions
             Multiple Order Forward Mode: xq.Restrictions
             Atomic Function Constructor: atomic_base.Restrictions
result Lu Factor and Solve with Recorded Pivoting: Result
       Union of Standard Sets: result
       Matrix Multiply as an Atomic Operation: Result Element Index
       Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function.Test Result
       AD Conditional Expressions: result
       AD Computed Assignment Operators: Result
       AD Output Stream Operator: Result
       AD Output Stream Operator: Result
results Running the Speed Test Program: Speed Results
        Running the Speed Test Program: Correctness Results
        Run One Speed Test and Print Results
        Run One Speed Test and Return Results
        Check an ADFun Object For Nan Results
retains Control When Thread Alloc Retains Memory For Future Use
retape The CppAD Wish List: checkpoint.Retape
       Nonlinear Programming Retaping: Example and Test
       Use Ipopt to Solve a Nonlinear Programming Problem: Example.retape
       Use Ipopt to Solve a Nonlinear Programming Problem: options.Retape
       Interpolation With Retaping: Example and Test
       Interpolation With Out Retaping: Example and Test
retaping: Nonlinear Programming Retaping: Example and Test
          Interpolation With Retaping: Example and Test
          Interpolation With Out Retaping: Example and Test
return Return A Raw Array to The Available Memory for a Thread
       Return Memory to omp_alloc
       Speed Testing Second Derivative of a Polynomial: Return Value
       Speed Testing the Jacobian of Ode Solution: Return Value
       Speed Testing Derivative of Matrix Multiply: Return Value
       Speed Testing Gradient of Determinant by Minor Expansion: Return Value
       Speed Testing Gradient of Determinant Using Lu Factorization: Return Value
       Returns Indices that Sort a Vector: ind.Return
       Return Memory to thread_alloc
       The CppAD::vector Template Class: Assignment.Return Reference
       Run One Speed Test and Return Results
       exp_eps: Second Order Forward Mode: Return Value
       exp_eps: First Order Forward Sweep: Return Value
       exp_eps: Operation Sequence and Zero Order Forward Sweep: Return Value
       exp_2: Second Order Forward Mode: Return Value
       exp_2: First Order Forward Mode: Return Value
       exp_2: Operation Sequence and Zero Order Forward Mode: Return Value
return_memory Return Memory to omp_alloc
              Return Memory to thread_alloc
returns Returns Elapsed Number of Seconds
        Returns Indices that Sort a Vector
        Returns Elapsed Number of Seconds
reuse Download and Install Sacado in Build Directory: Reuse
      Download and Install Ipopt in Build Directory: Reuse
      Download and Install Eigen in Build Directory: Reuse
      Download and Install ColPack in Build Directory: Reuse
      Download and Install Adolc in Build Directory: Reuse
rev_hes_sparse User Defined Atomic AD Functions: rev_hes_sparse
rev_jac_sparse User Defined Atomic AD Functions: rev_jac_sparse
rev_sparse_hes Matrix Multiply as an Atomic Operation: rev_sparse_hes
               User Atomic Matrix Multiply: Example and Test: Use Atomic Function.rev_sparse_hes
               Atomic Eigen Matrix Multiply Class: Private.rev_sparse_hes
               Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.rev_sparse_hes
               Tan and Tanh as User Atomic Operations: Example and Test: rev_sparse_hes
               Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function.rev_sparse_hes
               Atomic Sparsity with Set Patterns: Example and Test: rev_sparse_hes
               Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function.rev_sparse_hes
               Reciprocal as an Atomic Operation: Example and Test: rev_sparse_hes
               Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function.rev_sparse_hes
               Atomic Euclidean Norm Squared: Example and Test: rev_sparse_hes
               Atomic Reverse Hessian Sparsity: Example and Test: rev_sparse_hes
rev_sparse_jac Optimize an ADFun Object Tape: Atomic Functions.rev_sparse_jac
               Matrix Multiply as an Atomic Operation: rev_sparse_jac
               User Atomic Matrix Multiply: Example and Test: Use Atomic Function.rev_sparse_jac
               Atomic Eigen Matrix Multiply Class: Private.rev_sparse_jac
               Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.rev_sparse_jac
               Tan and Tanh as User Atomic Operations: Example and Test: rev_sparse_jac
               Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function.rev_sparse_jac
               Atomic Sparsity with Set Patterns: Example and Test: rev_sparse_jac
               Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function.rev_sparse_jac
               Reciprocal as an Atomic Operation: Example and Test: rev_sparse_jac
               Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function.rev_sparse_jac
               Atomic Euclidean Norm Squared: Example and Test: rev_sparse_jac
               Atomic Reverse Hessian Sparsity: Example and Test: rev_sparse_jac
               Atomic Forward Hessian Sparsity: Example and Test: rev_sparse_jac
               Atomic Reverse Jacobian Sparsity: Example and Test: rev_sparse_jac
reverse Define Matrix Multiply as a User Atomic Operation: Reverse Partials One Order
        User Defined Atomic AD Functions: reverse
        User Defined Atomic AD Functions: ty.reverse
        An Important Reverse Mode Identity: Reverse Sweep
        An Important Reverse Mode Identity
        Error Function Reverse Mode Theory
        Tangent and Hyperbolic Tangent Reverse Mode Theory
        Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
        Inverse Sine and Hyperbolic Sine Reverse Mode Theory
        Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
        Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
        Square Root Function Reverse Mode Theory
        Logarithm Function Reverse Mode Theory
        Exponential Function Reverse Mode Theory
        The Theory of Reverse Mode
        Frequently Asked Questions and Answers: Mode: Forward or Reverse
        Example Optimization and Reverse Activity Analysis
        Second Partials Reverse Driver: Example and Test
        Reverse Mode Second Partial Derivative Driver
        Jacobian: Driver Routine: Forward or Reverse
        First and Second Derivatives: Easy Drivers
        Reverse Mode Hessian Sparsity: Example and Test
        Hessian Sparsity Pattern: Reverse Mode
        Reverse Mode Jacobian Sparsity: Example and Test
        Jacobian Sparsity Pattern: Reverse Mode
        Reverse Mode General Case (Checkpointing): Example and Test
        Third Order Reverse Mode: Example and Test
        Any Order Reverse Mode
        Second Order Reverse ModeExample and Test
        Second Order Reverse Mode
        First Order Reverse Mode: Example and Test
        First Order Reverse Mode
        Reverse Mode
        Multiple Directions Forward Mode: Reverse Mode
        Matrix Multiply as an Atomic Operation: reverse
        Matrix Multiply as an Atomic Operation: Reverse Matrix Multiply
        User Atomic Matrix Multiply: Example and Test: Use Atomic Function.reverse
        Atomic Eigen Cholesky Factorization Class: Private.reverse
        AD Theory for Cholesky Factorization: Reverse Mode
        Atomic Eigen Matrix Inversion Class: Private.reverse
        Atomic Eigen Matrix Inversion Class: Theory.Reverse
        Atomic Eigen Matrix Multiply Class: Private.reverse
        Atomic Eigen Matrix Multiply Class: Theory.Reverse
        Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.reverse
        Tan and Tanh as User Atomic Operations: Example and Test: reverse
        Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function.reverse
        Reciprocal as an Atomic Operation: Example and Test: reverse
        Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function.reverse
        Atomic Euclidean Norm Squared: Example and Test: reverse
        Atomic Reverse Hessian Sparsity: Example and Test
        Atomic Reverse Jacobian Sparsity: Example and Test
        Atomic Reverse: Example and Test: reverse
        Atomic Reverse Hessian Sparsity Patterns
        Atomic Reverse Jacobian Sparsity Patterns
        Atomic Reverse Mode
        exp_eps: CppAD Forward and Reverse Sweeps
        exp_eps: Verify Second Order Reverse Sweep
        exp_eps: Verify First Order Reverse Sweep
        exp_eps: Second Order Reverse Sweep
        exp_eps: First Order Reverse Sweep
        exp_2: CppAD Forward and Reverse Sweeps
        exp_2: Verify Second Order Reverse Sweep
        exp_2: Verify First Order Reverse Sweep
        exp_2: Second Order Reverse Mode
        exp_2: First Order Reverse Mode
        An Introduction by Example to Algorithmic Differentiation: Preface.Reverse Mode
reverse: Atomic Reverse: Example and Test
revone First Order Derivative: Driver Routine: RevOne Uses Forward
revsparsehes Sparsity Patterns For a Subset of Variables: Example and Test: RevSparseHes
revsparsity Running the Speed Test Program: Sparsity Options.revsparsity
revtwo Reverse Mode Second Partial Derivative Driver: RevTwo Uses Forward
rhs Lu Factor and Solve with Recorded Pivoting: Rhs
right Union of Standard Sets: right
      Matrix Multiply as an Atomic Operation: Right Operand Element Index
      AD Conditional Expressions: right
romberg One Dimensional Romberg Integration: Example and Test
        Multi-dimensional Romberg Integration
        One Dimensional Romberg Integration: Example and Test
root Square Root Function Reverse Mode Theory
     Square Root Function Forward Mode Theory
     The Square Root Function: sqrt
rosen34: Rosen34: Example and Test
rosenbrock A 3rd and 4th Order Rosenbrock ODE Solver
routine Repeat det_by_minor Routine A Specified Number of Times
        Correctness Test of det_by_minor Routine
        First Order Derivative: Driver Routine
        First Order Partial Derivative: Driver Routine
        Jacobian: Driver Routine
routines User Defined Atomic AD Functions: Syntax Function.Callback Routines
         Routines That Track Use of New and Delete
         Speed Testing Utilities: Library Routines
         Speed Testing Utilities: Speed Utility Routines
         Utility Routines used by CppAD Examples
         Some General Purpose Utilities: General Numerical Routines
         Multi-threading Newton Method Utility Routines
         Multi-threading Sum of 1/i Utility Routines
row Evaluate a Function That Has a Sparse Hessian: row
    Evaluate a Function That Has a Sparse Jacobian: row
    Speed Testing Sparse Jacobian: row
    Speed Testing Sparse Hessian: row
    Sparse Hessian: Easy Driver: row, col
    Sparse Jacobian: Easy Driver: row, col
rt Atomic Reverse Jacobian Sparsity Patterns: Implementation.rt
run Run the Speed Examples
    Run One Speed Test and Print Results
    Run One Speed Test and Return Results
    Run Multi-Threading Examples and Speed Tests
    Correctness Tests For Exponential Approximation in Introduction
runge-kutta An Embedded 4th and 5th Order Runge-Kutta ODE Solver
runge45: Runge45: Example and Test
         Runge45: Example and Test
running Driver for Running the Ipopt ODE Example
        Speed Test Derivatives Using Sacado: Running Tests
        Speed Test Derivatives Using Fadbad: Running Tests
        Speed Test Derivatives Using CppAD: Running Tests
        Speed Test of Derivatives Using Adolc: Running Tests
        Speed Test of Functions in Double: Running Tests
        Running the Speed Test Program
        Run the Speed Examples: Running Tests
        CppAD Examples and Tests: Running Tests
        Examples: Running Examples
        Example Use of SpeedTest: Running This Program
        Run Multi-Threading Examples and Speed Tests: Running Tests
        Printing During Forward Mode: Example and Test: Running
        Correctness Tests For Exponential Approximation in Introduction: Running Tests
        Getting Started Using CppAD to Compute Derivatives: Running
S
Sacado Auto Tools Unix Test and Installation
SimpleVector The CheckSimpleVector Function: Example and Test
SparseHessian Sparse Hessian: Easy Driver
SparseJacobian Sparse Jacobian: Easy Driver
SpeedTest Run One Speed Test and Print Results
sacado sacado Speed: sparse_jacobian
       Sacado Speed: Sparse Hessian
       Sacado Speed: Second Derivative of a Polynomial
       Sacado Speed: Gradient of Ode Solution
       Sacado Speed: Matrix Multiplication
       Sacado Speed: Gradient of Determinant Using Lu Factorization
       Sacado Speed: Gradient of Determinant by Minor Expansion
       Speed Test Derivatives Using Sacado
       Download and Install Sacado in Build Directory
       Including the Sacado Speed Tests
     download and install Download and Install Sacado in Build Directory
sacado_dir Auto Tools Unix Test and Installation: sacado_dir
sacado_prefix Speed Test Derivatives Using Sacado: sacado_prefix
              Including the Sacado Speed Tests: sacado_prefix
same Using CppAD in a Multi-Threading Environment: Same Thread
scalar Determinant Using Expansion by Minors: Scalar
       Determinant of a Minor: Scalar
       Determinant Using Expansion by Lu Factorization: Scalar
       An Error Controller for Gear's Ode Solvers: Scalar
       An Arbitrary Order Gear Method: Scalar
       An Error Controller for ODE Solvers: Scalar
       A 3rd and 4th Order Rosenbrock ODE Solver: Scalar
       An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Scalar
       Obtain Nan or Determine if a Value is Nan: Scalar
       User Defined Atomic AD Functions: Examples.Scalar Function
scur An Error Controller for ODE Solvers: scur
second Sacado Speed: Second Derivative of a Polynomial
       Fadbad Speed: Second Derivative of a Polynomial
       CppAD Speed: Second Derivative of a Polynomial
       Adolc Speed: Second Derivative of a Polynomial
       Speed Testing Second Derivative of a Polynomial
       Using Multiple Levels of AD: Procedure.Second Start AD< AD<double> >
       Second Partials Reverse Driver: Example and Test
       Reverse Mode Second Partial Derivative Driver
       Subset of Second Order Partials: Example and Test
       Forward Mode Second Partial Derivative Driver
       Hessian: Easy Driver
       First and Second Derivatives: Easy Drivers
       Any Order Reverse Mode: Second Order
       Second Order Reverse ModeExample and Test
       Second Order Reverse Mode: dw.Second Order Partials
       Second Order Reverse Mode
       Multiple Order Forward Mode: Second Order
       Second Order Forward Mode: Derivative Values
       exp_eps: Verify Second Order Reverse Sweep
       exp_eps: Verify Second Order Forward Sweep
       exp_eps: Second Order Reverse Sweep
       exp_eps: Second Order Forward Mode: Operation Sequence.Second
       exp_eps: Second Order Forward Mode: Second Order Expansion
       exp_eps: Second Order Forward Mode
       exp_2: Verify Second Order Reverse Sweep
       exp_2: Verify Second Order Forward Sweep
       exp_2: Second Order Reverse Mode
       exp_2: Second Order Forward Mode: Operation Sequence.Second
       exp_2: Second Order Forward Mode: Second Order Expansion
       exp_2: Second Order Forward Mode
       Second Order Exponential Approximation
seconds Returns Elapsed Number of Seconds
        Microsoft Version of Elapsed Number of Seconds
        Elapsed Seconds: Example and Test
        Returns Elapsed Number of Seconds
seconds: Elapsed Seconds: Example and Test
see Jacobian and Hessian of Optimal Values: See Also
    Computing Jacobian and Hessian of Bender's Reduced Objective: See Also
    Convert Certain Types to a String: See Also
    The Integer Power Function: See Also
    Example Optimization and Nested Conditional Expressions: See Also
    Example Optimization and Conditional Expressions: See Also
    Example Optimization and Comparison Operators: See Also
    Sparse Hessian on Subset of Variables: Example and Test: See Also
    Computing Sparse Hessian for a Subset of Variables: See Also
    Sparsity Patterns For a Subset of Variables: Example and Test: See Also
    Reverse Mode General Case (Checkpointing): Example and Test: See Also
    Number of Variables that Can be Skipped: Syntax.See Also
    Controlling Taylor Coefficients Memory Allocation: Syntax.See Also
    Number Taylor Coefficient Orders Currently Stored: Syntax.See Also
    ADFun Sequence Properties: Syntax.See Also
    Matrix Multiply as an Atomic Operation: See Also
    User Atomic Matrix Multiply: Example and Test: See Also
    Atomic Eigen Matrix Multiply Class: See Also
    Checkpointing an Extended ODE Solver: Example and Test: See Also
    Checkpointing an ODE Solver: Example and Test: See Also
    Checkpointing Functions: See Also
    Interpolation With Retaping: Example and Test: See Also
    Interpolation With Out Retaping: Example and Test: See Also
    Conditional Expressions: Example and Test: See Also
    The AD Power Function: See Also
    Convert an AD Variable to a Parameter: See Also
    Convert An AD or Base Type to String: See Also
    Convert From an AD Type to its Base Type: See Also
seed Simulate a [0,1] Uniform Random Variate: seed
     Simulate a [0,1] Uniform Random Variate: seed
     Running the Speed Test Program: seed
semantics The CppAD::vector Template Class: Assignment.Move Semantics
sequence The CppAD Wish List: Operation Sequence
         Glossary: Operation.Sequence
         Evaluate a Function Defined in Terms of an ODE: Float.Operation Sequence
         An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Operation Sequence
         Evaluate a Polynomial or its Derivative: Operation Sequence
         The Integer Power Function: Operation Sequence
         Optimize an ADFun Object Tape
         Check an ADFun Sequence of Operations
         ADFun Sequence Properties: Example and Test
         ADFun Sequence Properties
         Abort Recording of an Operation Sequence
         Stop Recording and Store Operation Sequence
         Construct an ADFun Object and Stop Recording: Example.Sequence Constructor
         Construct an ADFun Object and Stop Recording: Sequence Constructor
         Check if Two Value are Identically Equal
         Is an AD Object a Parameter or Variable: Operation Sequence
         AD Boolean Functions: Operation Sequence
         Compare AD and Base Objects for Nearly Equal: Operation Sequence
         AD Binary Comparison Operators: Operation Sequence
         Discrete AD Functions: Operation Sequence
         AD Conditional Expressions: Operation Sequence
         The AD Power Function: Operation Sequence
         AD Two Argument Inverse Tangent Function: Operation Sequence
         AD Computed Assignment Operators: Operation Sequence
         AD Binary Arithmetic Operators: Operation Sequence
         AD Unary Minus Operator: Operation Sequence
         AD Unary Plus Operator: Operation Sequence
         AD Output Stream Operator: Operation Sequence
         AD Output Stream Operator: Operation Sequence
         Convert From AD to Integer: Operation Sequence
         Convert From an AD Type to its Base Type: Operation Sequence
         exp_eps: Second Order Forward Mode: Operation Sequence
         exp_eps: First Order Forward Sweep: Operation Sequence
         exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence
         exp_eps: Operation Sequence and Zero Order Forward Sweep
         exp_2: Second Order Forward Mode: Operation Sequence
         exp_2: First Order Forward Mode: Operation Sequence
         exp_2: Operation Sequence and Zero Order Forward Mode: Operation Sequence
         exp_2: Operation Sequence and Zero Order Forward Mode
sequential Is The Current Execution in Parallel Mode
set Define Matrix Multiply as a User Atomic Operation: Set Union
    Set Maximum Number of Threads for omp_alloc Allocator
    Set and Get Maximum Number of Threads for omp_alloc Allocator
    Set Union: Example and Test
    Atomic Sparsity with Set Patterns: Example and Test
    Set Atomic Function Options
set_max_num_threads Set and Get Maximum Number of Threads for omp_alloc Allocator: set_max_num_threads
set_sparsity_enum Atomic Sparsity with Set Patterns: Example and Test: set_sparsity_enum
                  Reciprocal as an Atomic Operation: Example and Test
                  Set Atomic Function Options: atomic_sparsity.set_sparsity_enum
set_union Some General Purpose Utilities: Miscellaneous.set_union
sets Glossary: Sparsity Pattern.Vector of Sets
     Union of Standard Sets
     Auto Tools Unix Test and Installation
     Using CMake to Configure CppAD
setup OpenMP Parallel Setup
      Setup thread_alloc For Use in Multi-Threading Environment
      Multi-threading Newton Method Utility Routines
      Multi-threading Sum of 1/i Utility Routines
shampine Bibliography: Shampine, L.F.
sign LU Factorization of A Square Matrix and Stability Calculation: sign
     LU Factorization of A Square Matrix: sign
     Enable use of AD<Base> where Base is double: sign
     Enable use of AD<Base> where Base is float: sign
     Enable use of AD<Base> where Base is Adolc's adouble Type: sign
     Example AD<Base> Where Base Constructor Allocates Memory: sign
     Base Type Requirements for Standard Math Functions: sign
     Sign Function: Example and Test
     The Sign: sign
sign: The Sign: sign
signdet Jacobian and Hessian of Optimal Values: signdet
        Compute Determinant and Solve Linear Equations: signdet
simple Using AD to Compute Atomic Function Derivatives: Simple Case
       User Defined Atomic AD Functions: Example.Simple
       Speed Test for Both Simple and Fast Representations
       Correctness Check for Both Simple and Fast Representations
       ODE Fitting Using Simple Representation
       ODE Fitting Using Simple Representation
       Nonlinear Programming Using the CppAD Interface to Ipopt: Simple Representation
       Check Simple Vector Concept
       Simple Vector Template Class: Example and Test
       Definition of a Simple Vector
       Some General Purpose Utilities: Miscellaneous.Simple Vector Template Class
       A Simple pthread AD: Example and Test
       A Simple Boost Threading AD: Example and Test
       A Simple OpenMP AD: Example and Test
       A Simple Parallel Pthread Example and Test
       A Simple Boost Thread Example and Test
       A Simple OpenMP Example and Test
       Base Type Requirements for Identically Equal Comparisons: EqualOpSeq.The Simple Case
       Simple Checkpointing: Example and Test
       Getting Started Using CppAD to Compute Derivatives
simple_ad Run Multi-Threading Examples and Speed Tests: simple_ad
simulate Simulate a [0,1] Uniform Random Variate
         Simulate a [0,1] Uniform Random Variate
simulated An ODE Inverse Problem Example: Measurements.Simulated Measurement Values
          ODE Inverse Problem Definitions: Source Code: Measurements.Simulated Measurement Values
simulation An ODE Inverse Problem Example: Measurements.Simulation Parameter Values
           An ODE Inverse Problem Example: Measurements.Simulation Analytic Solution
           ODE Inverse Problem Definitions: Source Code: Measurements.Simulation Parameter Values
           ODE Inverse Problem Definitions: Source Code: Measurements.Simulation Analytic Solution
simultaneous An ODE Inverse Problem Example: Simultaneous Method
             Example Simultaneous Solution of Forward and Inverse Problem
sin Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
    Trigonometric and Hyperbolic Sine and Cosine Forward Theory
    The AD sin Function: Example and Test
    The Sine Function: sin
sine Inverse Sine and Hyperbolic Sine Reverse Mode Theory
     Inverse Sine and Hyperbolic Sine Reverse Mode Theory
     Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
     Inverse Sine and Hyperbolic Sine Forward Mode Theory
     Inverse Sine and Hyperbolic Sine Forward Mode Theory
     Trigonometric and Hyperbolic Sine and Cosine Forward Theory
     The Inverse Hyperbolic Sine Function: asinh
     The Hyperbolic Sine Function: sinh
     The Sine Function: sin
     Inverse Sine Function: asin
     Inverse Sine Function: acos
sinh Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
     Trigonometric and Hyperbolic Sine and Cosine Forward Theory
     The AD sinh Function: Example and Test
     The Hyperbolic Sine Function: sinh
sini An Error Controller for Gear's Ode Solvers: sini
size Repeat det_by_minor Routine A Specified Number of Times: size
     ADFun Object Deprecated Member Functions: Size
     Speed Testing Sparse Jacobian: size
     Speed Testing Sparse Hessian: size
     Speed Testing Second Derivative of a Polynomial: size
     Speed Testing the Jacobian of Ode Solution: size
     Speed Testing Gradient of Determinant by Minor Expansion: size
     Speed Testing Gradient of Determinant Using Lu Factorization: size
     The CppAD::vector Template Class: Assignment.Check Size
     Definition of a Simple Vector: Size
     Determine Amount of Time to Execute a Test: test.size
     Run One Speed Test and Print Results: Test.size
     Run One Speed Test and Return Results: test.size
     AD Vectors that Record Index Operations: size
size_forward_bool Jacobian Sparsity Pattern: Forward Mode: f.size_forward_bool
size_forward_set Jacobian Sparsity Pattern: Forward Mode: f.size_forward_set
size_min Allocate Memory and Create A Raw Array: size_min
         Allocate An Array and Call Default Constructor for its Elements: size_min
size_op ADFun Sequence Properties: size_op
size_op_arg ADFun Sequence Properties: Example and Test
            ADFun Sequence Properties: size_op_arg
size_op_seq ADFun Sequence Properties: size_op_seq
size_out Allocate Memory and Create A Raw Array: size_out
         Allocate An Array and Call Default Constructor for its Elements: size_out
size_par ADFun Sequence Properties: Example and Test
         ADFun Sequence Properties: size_par
size_t AD Vectors that Record Index Operations: size_t Indexing
size_taylor ADFun Object Deprecated Member Functions: size_taylor
size_text ADFun Sequence Properties: size_text
size_VecAD ADFun Sequence Properties: Example and Test
size_var ADFun Sequence Properties: Example and Test
         ADFun Sequence Properties: size_var
         Checkpointing Functions: size_var
size_vec Run One Speed Test and Return Results: size_vec
size_vecad ADFun Sequence Properties: size_VecAD
sizevector LU Factorization of A Square Matrix and Stability Calculation: SizeVector
           Nonlinear Programming Using the CppAD Interface to Ipopt: SizeVector
           LU Factorization of A Square Matrix: SizeVector
sizing Definition of a Simple Vector: Sizing Constructor
skipped Number of Variables that Can be Skipped
skipped: Number of Variables That Can be Skipped: Example and Test
smax An Error Controller for Gear's Ode Solvers: smax
     An Error Controller for ODE Solvers: smax
smin An Error Controller for Gear's Ode Solvers: smin
     An Error Controller for ODE Solvers: smin
software Your License for the CppAD Software
         The CppAD Wish List: Software Guidelines
solution An ODE Inverse Problem Example: Measurements.Simulation Analytic Solution
         Example Simultaneous Solution of Forward and Inverse Problem
         Nonlinear Programming Using the CppAD Interface to Ipopt: solution
         Sacado Speed: Gradient of Ode Solution
         CppAD Speed: Gradient of Ode Solution
         Double Speed: Ode Solution
         Speed Testing the Jacobian of Ode Solution
         Taylor's Ode Solver: An Example and Test: ODE Solution
         Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Derivative of ODE Solution
         Taylor's Ode Solver: A Multi-Level Adolc Example and Test: ODE Solution
         Taylor's Ode Solver: A Multi-Level AD Example and Test: Derivative of ODE Solution
         Taylor's Ode Solver: A Multi-Level AD Example and Test: ODE Solution
         ODE Inverse Problem Definitions: Source Code: Solution Method
         ODE Inverse Problem Definitions: Source Code: Measurements.Simulation Analytic Solution
         Use Ipopt to Solve a Nonlinear Programming Problem: solution
         Checkpointing an Extended ODE Solver: Example and Test: Solution
         Checkpointing an ODE Solver: Example and Test: Solution
solve LU Factorization of A Square Matrix and Stability Calculation
      Lu Factor and Solve With Recorded Pivoting: Example and Test
      Lu Factor and Solve with Recorded Pivoting
      Use Ipopt to Solve a Nonlinear Programming Problem
      A 3rd and 4th Order Rosenbrock ODE Solver
      An Embedded 4th and 5th Order Runge-Kutta ODE Solver
      LU Factorization of A Square Matrix
      Compute Determinant and Solve Linear Equations
      Compute Determinants and Solve Equations by LU Factorization
solver A 3rd and 4th Order Rosenbrock ODE Solver
       An Embedded 4th and 5th Order Runge-Kutta ODE Solver
       Checkpointing an Extended ODE Solver: Example and Test: ODE Solver
       Checkpointing an ODE Solver: Example and Test: ODE Solver
solver: Taylor's Ode Solver: An Example and Test
        Taylor's Ode Solver: A Multi-Level Adolc Example and Test
        Taylor's Ode Solver: A Multi-Level AD Example and Test
        Checkpointing an Extended ODE Solver: Example and Test
        Checkpointing an ODE Solver: Example and Test
solvers An Error Controller for Gear's Ode Solvers
        An Error Controller for ODE Solvers
some Some Numerical AD Utilities
     Some General Purpose Utilities
sort Returns Indices that Sort a Vector
sort: Index Sort: Example and Test
sorting Some General Purpose Utilities: Miscellaneous.Sorting Indices
source Main Program For Comparing C and C++ Speed: Source Code
       Determine Amount of Time to Execute det_by_minor: Source Code
       Returns Elapsed Number of Seconds: Source Code
       Repeat det_by_minor Routine A Specified Number of Times: Source Code
       Correctness Test of det_by_minor Routine: Source Code
       Simulate a [0,1] Uniform Random Variate: Source Code
       Compute Determinant using Expansion by Minors: Source Code
       Determinant of a Minor: Source Code
       Define Matrix Multiply as a User Atomic Operation: Begin Source
       ODE Fitting Using Fast Representation
       ODE Fitting Using Simple Representation
       ODE Inverse Problem Definitions: Source Code
       ODE Fitting Using Fast Representation: Source
       ODE Fitting Using Simple Representation: Source
       An ODE Inverse Problem Example: Source
       Source: uniform_01
       Simulate a [0,1] Uniform Random Variate: Source Code
       Source: sparse_hes_fun
       Evaluate a Function That Has a Sparse Hessian: Source Code
       Source: sparse_jac_fun
       Evaluate a Function That Has a Sparse Jacobian: Source Code
       Source: ode_evaluate
       Evaluate a Function Defined in Terms of an ODE: Source Code
       Source: mat_sum_sq
       Sum Elements of a Matrix Times Itself: Source Code
       Source: det_grad_33
       Check Gradient of Determinant of 3 by 3 matrix: Source Code
       Source: det_33
       Check Determinant of 3 by 3 matrix: Source Code
       Source: det_by_minor
       Determinant Using Expansion by Minors: Source Code
       Source: det_of_minor
       Determinant of a Minor: Source Code
       Source: det_by_lu
       Determinant Using Expansion by Lu Factorization: Source Code
       Speed Testing Utilities: Source Code
       Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Source
       Taylor's Ode Solver: A Multi-Level AD Example and Test: Source
       Multiple Level of AD: Example and Test: Source
       Source Code for eigen_plugin.hpp
       ODE Inverse Problem Definitions: Source Code: Source
       ODE Inverse Problem Definitions: Source Code
       An Error Controller for Gear's Ode Solvers: Source Code
       An Arbitrary Order Gear Method: Source Code
       An Error Controller for ODE Solvers: Source Code
       A 3rd and 4th Order Rosenbrock ODE Solver: Source Code
       An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Source Code
       Multi-dimensional Romberg Integration: Source Code
       One DimensionalRomberg Integration: Source Code
       Source: LuInvert
       Invert an LU Factored Equation: Source
       Source: LuFactor
       LU Factorization of A Square Matrix: Source
       Source: LuSolve
       Compute Determinant and Solve Linear Equations: Source
       Source: Poly
       Evaluate a Polynomial or its Derivative: Source
       Specifications for A Team of AD Threads: Source
       Multi-threading Newton Method Utility Routines: Source
       Timing Test of Multi-Threaded Newton Method: Source
       A Multi-Threaded Newton's Method: Source
       Multi-threading Sum of 1/i Utility Routines: Source
       Timing Test of Multi-Threaded Summation of 1/i: Source
       Multi-Threaded Implementation of Summation of 1/i: Source
       Using a Team of AD Threads: Example and Test: Source Code
       A Simple pthread AD: Example and Test: Source Code
       A Simple Boost Threading AD: Example and Test: Source Code
       A Simple OpenMP AD: Example and Test: Source Code
       A Simple Parallel Pthread Example and Test: Source Code
       A Simple Boost Thread Example and Test: Source Code
       A Simple OpenMP Example and Test: Source Code
       Run Multi-Threading Examples and Speed Tests: Source
       Using Adolc with Multiple Levels of Taping: Example and Test: Source
       Printing During Forward Mode: Example and Test: Source Code
       Download The CppAD Source Code
source: Source: uniform_01
        Source: sparse_hes_fun
        Source: sparse_jac_fun
        Source: ode_evaluate
        Source: mat_sum_sq
        Source: det_grad_33
        Source: det_33
        Source: det_by_minor
        Source: det_of_minor
        Source: det_by_lu
        Source: LuInvert
        Source: LuFactor
        Source: LuSolve
        Source: Poly
spare Sparse Hessian: Example and Test
      Sparse Jacobian: Example and Test
sparse Sacado Speed: Sparse Hessian
       Fadbad Speed: Sparse Hessian
       CppAD Speed: Sparse Jacobian
       CppAD Speed: Sparse Hessian
       adolc Speed: Sparse Jacobian
       Adolc Speed: Sparse Hessian
       Double Speed: Sparse Jacobian
       Double Speed: Sparse Hessian
       Evaluate a Function That Has a Sparse Hessian
       Evaluate a Function That Has a Sparse Jacobian
       Speed Testing Sparse Jacobian
       Speed Testing Sparse Hessian
       Use Ipopt to Solve a Nonlinear Programming Problem: options.Sparse
       Sparse Hessian on Subset of Variables: Example and Test
       Computing Sparse Hessian for a Subset of Variables
       Sparse Hessian: Example and Test
       Sparse Hessian: Easy Driver
       Sparse Jacobian: Example and Test
       Sparse Jacobian: Easy Driver
       Jacobian Sparsity Pattern: Reverse Mode
       Auto Tools Unix Test and Installation
       Using ColPack: Example and Test
       Using ColPack: Example and Test
sparse_hes_fun Source: sparse_hes_fun
               sparse_hes_fun: Example and test
               Evaluate a Function That Has a Sparse Hessian
sparse_hes_fun: sparse_hes_fun: Example and test
sparse_jac_fun Source: sparse_jac_fun
               sparse_jac_fun: Example and test
               Evaluate a Function That Has a Sparse Jacobian
sparse_jac_fun: sparse_jac_fun: Example and test
sparse_jacobian sacado Speed: sparse_jacobian
                fadbad Speed: sparse_jacobian
sparsity The CppAD Wish List: Sparsity Patterns
         Glossary: Sparsity Pattern
         Running the Speed Test Program: Sparsity Options
         Using vectorBool Sparsity To Conserve Memory: Example and Test
         Forward Mode Hessian Sparsity: Example and Test
         Hessian Sparsity Pattern: Forward Mode
         Sparsity Patterns For a Subset of Variables: Example and Test
         Reverse Mode Hessian Sparsity: Example and Test
         Hessian Sparsity Pattern: Reverse Mode: Entire Sparsity Pattern
         Hessian Sparsity Pattern: Reverse Mode
         Reverse Mode Jacobian Sparsity: Example and Test
         Jacobian Sparsity Pattern: Reverse Mode: Entire Sparsity Pattern
         Jacobian Sparsity Pattern: Reverse Mode
         Forward Mode Jacobian Sparsity: Example and Test
         Jacobian Sparsity Pattern: Forward Mode: Entire Sparsity Pattern
         Jacobian Sparsity Pattern: Forward Mode
         Calculating Sparsity Patterns
         Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
         Construct an ADFun Object and Stop Recording: Assignment Operator.Sparsity Patterns
         Tan and Tanh as User Atomic Operations: Example and Test: sparsity
         Atomic Sparsity with Set Patterns: Example and Test
         Reciprocal as an Atomic Operation: Example and Test: sparsity
         Atomic Euclidean Norm Squared: Example and Test: sparsity
         Atomic Reverse Hessian Sparsity Patterns
         Atomic Forward Hessian Sparsity Patterns
         Atomic Reverse Jacobian Sparsity Patterns
         Atomic Forward Jacobian Sparsity Patterns
         Atomic Function Constructor: atomic_base.sparsity
         User Defined Atomic AD Functions: Examples.Hessian Sparsity Patterns
         Checkpointing Functions: sparsity
         Including the ColPack Sparsity Calculations
         Using CMake to Configure CppAD
sparsity: Forward Mode Hessian Sparsity: Example and Test
          Reverse Mode Hessian Sparsity: Example and Test
          Reverse Mode Jacobian Sparsity: Example and Test
          Forward Mode Jacobian Sparsity: Example and Test
          Atomic Reverse Hessian Sparsity: Example and Test
          Atomic Forward Hessian Sparsity: Example and Test
          Atomic Reverse Jacobian Sparsity: Example and Test
          Atomic Forward Jacobian Sparsity: Example and Test
special The CppAD Wish List: Optimization.Special Operators
        The Theory of Forward Mode: Standard Math Functions.Special Cases
        Second Order Forward Mode: Derivative Values: Special Case
        First Order Forward Mode: Derivative Values: Special Case
        Zero Order Forward Mode: Function Values: Special Case
specifications Sacado Speed: Second Derivative of a Polynomial: Specifications
               Sacado Speed: Gradient of Ode Solution: Specifications
               Sacado Speed: Matrix Multiplication: Specifications
               Sacado Speed: Gradient of Determinant Using Lu Factorization: Specifications
               Sacado Speed: Gradient of Determinant by Minor Expansion: Specifications
               Fadbad Speed: Second Derivative of a Polynomial: Specifications
               Fadbad Speed: Ode: Specifications
               Fadbad Speed: Matrix Multiplication: Specifications
               Fadbad Speed: Gradient of Determinant Using Lu Factorization: Specifications
               Fadbad Speed: Gradient of Determinant by Minor Expansion: Specifications
               CppAD Speed: Sparse Jacobian: Specifications
               CppAD Speed: Sparse Hessian: Specifications
               CppAD Speed: Second Derivative of a Polynomial: Specifications
               CppAD Speed: Gradient of Ode Solution: Specifications
               CppAD Speed, Matrix Multiplication: Specifications
               CppAD Speed: Gradient of Determinant Using Lu Factorization: Specifications
               CppAD Speed: Gradient of Determinant by Minor Expansion: Specifications
               adolc Speed: Sparse Jacobian: Specifications
               Adolc Speed: Sparse Hessian: Specifications
               Adolc Speed: Second Derivative of a Polynomial: Specifications
               Adolc Speed: Ode: Specifications
               Adolc Speed: Matrix Multiplication: Specifications
               Adolc Speed: Gradient of Determinant Using Lu Factorization: Specifications
               Adolc Speed: Gradient of Determinant by Minor Expansion: Specifications
               Double Speed: Sparse Jacobian: Specifications
               Double Speed: Sparse Hessian: Specifications
               Double Speed: Evaluate a Polynomial: Specifications
               Double Speed: Ode Solution: Specifications
               CppAD Speed: Matrix Multiplication (Double Version): Specifications
               Double Speed: Determinant Using Lu Factorization: Specifications
               Double Speed: Determinant by Minor Expansion: Specifications
               Specifications for A Team of AD Threads
specified Repeat det_by_minor Routine A Specified Number of Times
          Get At Least A Specified Amount of Memory
          Get At Least A Specified Amount of Memory
          Definition of a Simple Vector: Elements of Specified Type
speed Main Program For Comparing C and C++ Speed
      Compare Speed of C and C++
      Speed Test for Both Simple and Fast Representations
      Get At Least A Specified Amount of Memory: Allocation Speed
      The CppAD Wish List: Compilation Speed
      Frequently Asked Questions and Answers: Speed
      Sacado Speed: Second Derivative of a Polynomial
      Sacado Speed: Gradient of Ode Solution
      Sacado Speed: Matrix Multiplication
      Sacado Speed: Gradient of Determinant Using Lu Factorization
      Sacado Speed: Gradient of Determinant by Minor Expansion
      Speed Test Derivatives Using Sacado
      Fadbad Speed: Second Derivative of a Polynomial
      Fadbad Speed: Ode
      Fadbad Speed: Matrix Multiplication
      Fadbad Speed: Gradient of Determinant Using Lu Factorization
      Fadbad Speed: Gradient of Determinant by Minor Expansion
      Speed Test Derivatives Using Fadbad
      CppAD Speed: Sparse Jacobian
      CppAD Speed: Sparse Hessian
      CppAD Speed: Second Derivative of a Polynomial
      CppAD Speed: Gradient of Ode Solution
      CppAD Speed, Matrix Multiplication
      CppAD Speed: Gradient of Determinant Using Lu Factorization
      CppAD Speed: Gradient of Determinant by Minor Expansion
      Speed Test Derivatives Using CppAD
      adolc Speed: Sparse Jacobian
      Adolc Speed: Sparse Hessian
      Adolc Speed: Second Derivative of a Polynomial
      Adolc Speed: Ode
      Adolc Speed: Matrix Multiplication
      Adolc Speed: Gradient of Determinant Using Lu Factorization
      Adolc Speed: Gradient of Determinant by Minor Expansion
      Speed Test of Derivatives Using Adolc
      Double Speed: Sparse Jacobian
      Double Speed: Sparse Hessian
      Double Speed: Evaluate a Polynomial
      Double Speed: Ode Solution
      CppAD Speed: Matrix Multiplication (Double Version)
      Double Speed: Determinant Using Lu Factorization
      Double Speed: Determinant by Minor Expansion
      Speed Test of Functions in Double
      Sum Elements of a Matrix Times Itself
      Speed Testing Utilities: Speed Utility Routines
      Speed Testing Utilities: Speed Main Program
      Speed Testing Utilities
      Speed Testing Sparse Jacobian
      Speed Testing Sparse Hessian
      Speed Testing Second Derivative of a Polynomial
      Speed Testing the Jacobian of Ode Solution
      Speed Testing Derivative of Matrix Multiply
      Speed Testing Gradient of Determinant by Minor Expansion
      Speed Testing Gradient of Determinant Using Lu Factorization
      Running the Speed Test Program: Speed Results
      Running the Speed Test Program: test.speed
      Running the Speed Test Program
      Speed Test an Operator Overloading AD Package
      Run the Speed Examples
      Get At Least A Specified Amount of Memory: Allocation Speed
      Setup thread_alloc For Use in Multi-Threading Environment: Speed
      Determine Amount of Time to Execute a Test
      Example Use of SpeedTest
      Run One Speed Test and Print Results
      Run One Speed Test and Return Results
      Specifications for A Team of AD Threads: Speed Test of Implementation
      Timing Test of Multi-Threaded Newton Method
      Timing Test of Multi-Threaded Summation of 1/i
      Run Multi-Threading Examples and Speed Tests
      Optimize an ADFun Object Tape: Speed Testing
      Optimize an ADFun Object Tape
      Comparison Changes Between Taping and Zero Order Forward: count.Speed
      AD Vectors that Record Index Operations: Speed and Memory
      Auto Tools Unix Test and Installation
      Including the Sacado Speed Tests: Speed Tests
      Including the Sacado Speed Tests
      Including the FADBAD Speed Tests: Speed Tests
      Including the FADBAD Speed Tests
      Including the ADOL-C Examples and Tests: Speed Tests
     compare C and C++ Compare Speed of C and C++
speed: sacado Speed: sparse_jacobian
       Sacado Speed: Sparse Hessian
       Sacado Speed: Second Derivative of a Polynomial
       Sacado Speed: Gradient of Ode Solution
       Sacado Speed: Matrix Multiplication
       Sacado Speed: Gradient of Determinant Using Lu Factorization
       Sacado Speed: Gradient of Determinant by Minor Expansion
       fadbad Speed: sparse_jacobian
       Fadbad Speed: Sparse Hessian
       Fadbad Speed: Second Derivative of a Polynomial
       Fadbad Speed: Ode
       Fadbad Speed: Matrix Multiplication
       Fadbad Speed: Gradient of Determinant Using Lu Factorization
       Fadbad Speed: Gradient of Determinant by Minor Expansion
       CppAD Speed: Sparse Jacobian
       CppAD Speed: Sparse Hessian
       CppAD Speed: Second Derivative of a Polynomial
       CppAD Speed: Gradient of Ode Solution
       CppAD Speed: Gradient of Determinant Using Lu Factorization
       CppAD Speed: Gradient of Determinant by Minor Expansion
       adolc Speed: Sparse Jacobian
       Adolc Speed: Sparse Hessian
       Adolc Speed: Second Derivative of a Polynomial
       Adolc Speed: Ode
       Adolc Speed: Matrix Multiplication
       Adolc Speed: Gradient of Determinant Using Lu Factorization
       Adolc Speed: Gradient of Determinant by Minor Expansion
       Double Speed: Sparse Jacobian
       Double Speed: Sparse Hessian
       Double Speed: Evaluate a Polynomial
       Double Speed: Ode Solution
       CppAD Speed: Matrix Multiplication (Double Version)
       Double Speed: Determinant Using Lu Factorization
       Double Speed: Determinant by Minor Expansion
speed_test speed_test: Example and test
           Run One Speed Test and Return Results
speed_test: speed_test: Example and test
speedtest Example Use of SpeedTest
sqrt Square Root Function Reverse Mode Theory
     Square Root Function Forward Mode Theory
     The AD sqrt Function: Example and Test
     The Square Root Function: sqrt
square LU Factorization of A Square Matrix and Stability Calculation
       Square Root Function Reverse Mode Theory
       Square Root Function Forward Mode Theory
       Sum of the Elements of the Square of a Matrix: Example and Test
       LU Factorization of A Square Matrix
       The Square Root Function: sqrt
squared: Atomic Euclidean Norm Squared: Example and Test
st Atomic Reverse Jacobian Sparsity Patterns: Implementation.st
stability LU Factorization of A Square Matrix and Stability Calculation
stack Example Differentiating a Stack Machine Interpreter
standard zdouble: An AD Base Type With Absolute Zero: Syntax.Standard Math
         The Theory of Reverse Mode: Standard Math Functions
         The Theory of Forward Mode: Standard Math Functions
         Frequently Asked Questions and Answers
         Union of Standard Sets
         Enable use of AD<Base> where Base is double: Unary Standard Math
         Enable use of AD<Base> where Base is float: Unary Standard Math
         Enable use of AD<Base> where Base is Adolc's adouble Type: Unary Standard Math
         Example AD<Base> Where Base Constructor Allocates Memory: Unary Standard Math
         Base Type Requirements for Standard Math Functions: Unary Standard Math
         Base Type Requirements for Standard Math Functions
         AD<Base> Requirements for a CppAD Base Type: Standard Base Types
         The Unary Standard Math Functions
start Using Multiple Levels of AD: Procedure.Second Start AD< AD<double> >
      Using Multiple Levels of AD: Procedure.Start AD< AD<double> > Recording
      Using Multiple Levels of AD: Procedure.First Start AD<double>
      Declare Independent Variables and Start Recording: Start Recording
      Declare Independent Variables and Start Recording
      Matrix Multiply as an Atomic Operation: Start Class Definition
      Atomic Eigen Cholesky Factorization Class: Start Class Definition
      Atomic Eigen Matrix Inversion Class: Start Class Definition
      Atomic Eigen Matrix Multiply Class: Start Class Definition
      Tan and Tanh as User Atomic Operations: Example and Test: Start Class Definition
      Atomic Sparsity with Set Patterns: Example and Test: Start Class Definition
      Reciprocal as an Atomic Operation: Example and Test: Start Class Definition
      Atomic Euclidean Norm Squared: Example and Test: Start Class Definition
      Getting Started with Atomic Operations: Example and Test: Start Class Definition
      Atomic Reverse Hessian Sparsity: Example and Test: Start Class Definition
      Atomic Forward Hessian Sparsity: Example and Test: Start Class Definition
      Atomic Reverse Jacobian Sparsity: Example and Test: Start Class Definition
      Atomic Forward Jacobian Sparsity: Example and Test: Start Class Definition
      Atomic Reverse: Example and Test: Start Class Definition
      Atomic Forward: Example and Test: Start Class Definition
      Getting Started Using CppAD to Compute Derivatives
started Getting Started with Atomic Operations: Example and Test
        User Defined Atomic AD Functions: Examples.Getting Started
        Getting Started Using CppAD to Compute Derivatives
state Controlling Taylor Coefficients Memory Allocation: Original State
static User Defined Atomic AD Functions: Syntax Function.Free Static Memory
       Memory Leak Detection
       Free Static Variables
status Nonlinear Programming Using the CppAD Interface to Ipopt: solution.status
       Use Ipopt to Solve a Nonlinear Programming Problem: solution.status
std Auto Tools Unix Test and Installation
    Choosing the CppAD Test Vector Template Class: std
std::complex<double> Enable use of AD<Base> where Base is std::complex<double>
std::numeric_limits Numeric Limits For an AD and Base Types: std::numeric_limits
std::vector Choosing The Vector Testing Template Class: std::vector
            Using The CppAD Test Vector Template Class: std::vector
stegun Bibliography: Abramowitz and Stegun
step An Error Controller for ODE Solvers: Method.step
     CppAD Download, Test, and Install Instructions: Instructions.Step 4: Installation
     CppAD Download, Test, and Install Instructions: Instructions.Step 3: Check
     CppAD Download, Test, and Install Instructions: Instructions.Step 2: Cmake
     CppAD Download, Test, and Install Instructions: Instructions.Step 1: Download
steps Reverse Mode General Case (Checkpointing): Example and Test: Processing Steps
stiff A Stiff Ode: Example and Test
      An Arbitrary Order Gear Method
      A 3rd and 4th Order Rosenbrock ODE Solver
stop Stop Recording and Store Operation Sequence
     Construct an ADFun Object and Stop Recording
     Declare Independent Variables and Start Recording: Stop Recording
storage LU Factorization of A Square Matrix and Stability Calculation: Matrix Storage
        Frequently Asked Questions and Answers
        Lu Factor and Solve with Recorded Pivoting: Storage Convention
        Invert an LU Factored Equation: Matrix Storage
        LU Factorization of A Square Matrix: Matrix Storage
        Compute Determinant and Solve Linear Equations: Matrix Storage
storage: Frequently Asked Questions and Answers: Tape Storage: Disk or Memory
store Stop Recording and Store Operation Sequence
stored Number Taylor Coefficient Orders Currently Stored
stream AD Output Stream Operator
       AD Output Stream Operator
string Use Ipopt to Solve a Nonlinear Programming Problem: options.String
       Convert Certain Types to a String
       Convert An AD or Base Type to String
structure Using CMake to Configure CppAD
subset Sparse Hessian on Subset of Variables: Example and Test
       Computing Sparse Hessian for a Subset of Variables: Subset
       Computing Sparse Hessian for a Subset of Variables
       Sparse Hessian: Easy Driver: Subset Hessian
       Sparse Hessian: Easy Driver: p.Column Subset
       Subset of Second Order Partials: Example and Test
       Sparsity Patterns For a Subset of Variables: Example and Test
subsets Checking the CppAD Examples and Tests: Subsets
subtract AD Computed Assignment Subtraction: Example and Test
         AD Computed Assignment Operators
         AD Binary Subtraction: Example and Test
         AD Binary Arithmetic Operators
subtraction The Theory of Reverse Mode: Binary Operators.Subtraction
            The Theory of Forward Mode: Binary Operators.Subtraction
            AD Computed Assignment Operators: Derivative.Subtraction
            AD Binary Arithmetic Operators: Derivative.Subtraction
subtraction: AD Computed Assignment Subtraction: Example and Test
             AD Binary Subtraction: Example and Test
subversion Download The CppAD Source Code: Current Version.Subversion
suggestion AD<Base> Requirements for a CppAD Base Type: Integer.Suggestion
sum Sum of the Elements of the Square of a Matrix: Example and Test
    Sum Elements of a Matrix Times Itself
    Multi-threading Sum of 1/i Utility Routines
    Multi-Threaded Implementation of Summation of 1/i: sum
    Example Optimization and Cumulative Sum Operations
summation Timing Test of Multi-Threaded Summation of 1/i
          Multi-Threaded Implementation of Summation of 1/i: Summation
          Multi-Threaded Implementation of Summation of 1/i
sweep An Important Reverse Mode Identity: Reverse Sweep
      exp_eps: Verify Second Order Reverse Sweep
      exp_eps: Verify Second Order Forward Sweep
      exp_eps: Verify First Order Reverse Sweep
      exp_eps: Verify First Order Forward Sweep
      exp_eps: Verify Zero Order Forward Sweep
      exp_eps: Second Order Reverse Sweep
      exp_eps: Second Order Forward Mode: Operation Sequence.Sweep
      exp_eps: First Order Reverse Sweep
      exp_eps: First Order Forward Sweep: Operation Sequence.Sweep
      exp_eps: First Order Forward Sweep
      exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence.Sweep
      exp_eps: Operation Sequence and Zero Order Forward Sweep
      exp_2: Verify Second Order Reverse Sweep
      exp_2: Verify Second Order Forward Sweep
      exp_2: Verify First Order Reverse Sweep
      exp_2: Verify First Order Forward Sweep
      exp_2: Verify Zero Order Forward Sweep
      exp_2: Second Order Forward Mode: Operation Sequence.Sweep
      exp_2: First Order Forward Mode: Operation Sequence.Sweep
      exp_2: Operation Sequence and Zero Order Forward Mode: Operation Sequence.Sweep
sweeps exp_eps: CppAD Forward and Reverse Sweeps
       exp_2: CppAD Forward and Reverse Sweeps
symbol Frequently Asked Questions and Answers: Namespace.Test Vector Preprocessor Symbol
symbols CppAD Addons: Preprocessor Symbols
        CppAD API Preprocessor Symbols
        cppad-20170000.3: A Package for Differentiation of C++ Algorithms: Preprocessor Symbols
syntax LU Factorization of A Square Matrix and Stability Calculation: Syntax
       Jacobian and Hessian of Optimal Values: Syntax
       Computing Jacobian and Hessian of Bender's Reduced Objective: Syntax
       Determine Amount of Time to Execute det_by_minor: Syntax
       Returns Elapsed Number of Seconds: Syntax
       Repeat det_by_minor Routine A Specified Number of Times: Syntax
       Correctness Test of det_by_minor Routine: Syntax
       Simulate a [0,1] Uniform Random Variate: Syntax
       Compute Determinant using Expansion by Minors: Syntax
       Determinant of a Minor: Syntax
       Compare Speed of C and C++: Syntax
       zdouble: An AD Base Type With Absolute Zero: Syntax
       Define Matrix Multiply as a User Atomic Operation: Syntax
       User Defined Atomic AD Functions: Syntax Function
       Nonlinear Programming Using the CppAD Interface to Ipopt: Syntax
       Choosing The Vector Testing Template Class: Syntax
       Machine Epsilon For AD Types: Syntax
       Memory Leak Detection: Syntax
       Set Maximum Number of Threads for omp_alloc Allocator: Syntax
       Check If A Memory Allocation is Efficient for Another Use: Syntax
       Return A Raw Array to The Available Memory for a Thread: Syntax
       Allocate Memory and Create A Raw Array: Syntax
       Amount of Memory Available for Quick Use by a Thread: Syntax
       Amount of Memory a Thread is Currently Using: Syntax
       Free Memory Currently Available for Quick Use by a Thread: Syntax
       Return Memory to omp_alloc: Syntax
       Get At Least A Specified Amount of Memory: Syntax
       Get the Current OpenMP Thread Number: Syntax
       Is The Current Execution in OpenMP Parallel Mode: Syntax
       Set and Get Maximum Number of Threads for omp_alloc Allocator: Syntax
       A Quick OpenMP Memory Allocator Used by CppAD: Syntax
       Routines That Track Use of New and Delete: Syntax
       OpenMP Parallel Setup: Syntax
       Comparison Changes During Zero Order Forward Mode: Syntax
       ADFun Object Deprecated Member Functions: Syntax
       Adolc Test Utility: Allocate and Free Memory For a Matrix: Syntax
       Simulate a [0,1] Uniform Random Variate: Syntax
       Evaluate a Function That Has a Sparse Hessian: Syntax
       Evaluate a Function That Has a Sparse Jacobian: Syntax
       Evaluate a Function Defined in Terms of an ODE: Syntax
       Sum Elements of a Matrix Times Itself: Syntax
       Check Gradient of Determinant of 3 by 3 matrix: Syntax
       Check Determinant of 3 by 3 matrix: Syntax
       Determinant Using Expansion by Minors: Syntax
       Determinant of a Minor: Syntax
       Determinant Using Expansion by Lu Factorization: Syntax
       Microsoft Version of Elapsed Number of Seconds: Syntax
       Running the Speed Test Program: Syntax
       Using The CppAD Test Vector Template Class: Syntax
       Lu Factor and Solve with Recorded Pivoting: Syntax
       Enable Use of Eigen Linear Algebra Package with CppAD: Syntax
       Use Ipopt to Solve a Nonlinear Programming Problem: Syntax
       Union of Standard Sets: Syntax
       Convert Certain Types to a String: Syntax
       Returns Indices that Sort a Vector: Syntax
       Free All Memory That Was Allocated for Use by thread_alloc: Syntax
       Deallocate An Array and Call Destructor for its Elements: Syntax
       Allocate An Array and Call Default Constructor for its Elements: Syntax
       Amount of Memory Available for Quick Use by a Thread: Syntax
       Amount of Memory a Thread is Currently Using: Syntax
       Control When Thread Alloc Retains Memory For Future Use: Syntax
       Free Memory Currently Available for Quick Use by a Thread: Syntax
       Return Memory to thread_alloc: Syntax
       Get At Least A Specified Amount of Memory: Syntax
       Get the Current Thread Number: Syntax
       Is The Current Execution in Parallel Mode: Syntax
       Get Number of Threads: Syntax
       Setup thread_alloc For Use in Multi-Threading Environment: Syntax
       A Fast Multi-Threading Memory Allocator: Syntax
       The CppAD::vector Template Class: Syntax
       An Error Controller for Gear's Ode Solvers: Syntax
       An Arbitrary Order Gear Method: Syntax
       An Error Controller for ODE Solvers: Syntax
       A 3rd and 4th Order Rosenbrock ODE Solver: Syntax
       An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Syntax
       Multi-dimensional Romberg Integration: Syntax
       One DimensionalRomberg Integration: Syntax
       Invert an LU Factored Equation: Syntax
       LU Factorization of A Square Matrix: Syntax
       Compute Determinant and Solve Linear Equations: Syntax
       Evaluate a Polynomial or its Derivative: Syntax
       The Integer Power Function: Syntax
       Obtain Nan or Determine if a Value is Nan: nan(zero).Syntax
       Obtain Nan or Determine if a Value is Nan: Syntax
       Check Simple Vector Concept: Syntax
       Check NumericType Class Concept: Syntax
       Returns Elapsed Number of Seconds: Syntax
       Determine Amount of Time to Execute a Test: Syntax
       Run One Speed Test and Print Results: Syntax
       Run One Speed Test and Return Results: Syntax
       Determine if Two Values Are Nearly Equal: Syntax
       CppAD Assertions During Execution: Syntax
       Replacing the CppAD Error Handler: Syntax
       Specifications for A Team of AD Threads: Syntax
       Multi-threading Newton Method Utility Routines: Syntax
       Timing Test of Multi-Threaded Newton Method: Syntax
       A Multi-Threaded Newton's Method: Syntax
       Multi-threading Sum of 1/i Utility Routines: Syntax
       Timing Test of Multi-Threaded Summation of 1/i: Syntax
       Multi-Threaded Implementation of Summation of 1/i: Syntax
       Run Multi-Threading Examples and Speed Tests: Syntax
       Enable AD Calculations During Parallel Mode: Syntax
       Check an ADFun Object For Nan Results: Syntax
       Optimize an ADFun Object Tape: Syntax
       Check an ADFun Sequence of Operations: Syntax
       Sparse Hessian: Easy Driver: Syntax
       Sparse Jacobian: Easy Driver: Syntax
       Reverse Mode Second Partial Derivative Driver: Syntax
       Forward Mode Second Partial Derivative Driver: Syntax
       Hessian: Easy Driver: Syntax
       First Order Derivative: Driver Routine: Syntax
       First Order Partial Derivative: Driver Routine: Syntax
       Jacobian: Driver Routine: Syntax
       Hessian Sparsity Pattern: Forward Mode: Syntax
       Hessian Sparsity Pattern: Reverse Mode: Syntax
       Jacobian Sparsity Pattern: Reverse Mode: Syntax
       Jacobian Sparsity Pattern: Forward Mode: Syntax
       Any Order Reverse Mode: Syntax
       Second Order Reverse Mode: Syntax
       First Order Reverse Mode: Syntax
       Number of Variables that Can be Skipped: Syntax
       Controlling Taylor Coefficients Memory Allocation: Syntax
       Comparison Changes Between Taping and Zero Order Forward: Syntax
       Number Taylor Coefficient Orders Currently Stored: Syntax
       Multiple Directions Forward Mode: Syntax
       Multiple Order Forward Mode: Syntax
       Second Order Forward Mode: Derivative Values: Syntax
       First Order Forward Mode: Derivative Values: Syntax
       Zero Order Forward Mode: Function Values: Syntax
       ADFun Sequence Properties: Syntax
       Abort Recording of an Operation Sequence: Syntax
       Stop Recording and Store Operation Sequence: Syntax
       Construct an ADFun Object and Stop Recording: Syntax
       Declare Independent Variables and Start Recording: Syntax
       Enable use of AD<Base> where Base is Adolc's adouble Type: Syntax
       Base Type Requirements for Hash Coding Values: Syntax
       AD<Base> Requirements for a CppAD Base Type: Syntax
       AD Vectors that Record Index Operations: Syntax
       Check if Two Value are Identically Equal: Syntax
       Is an AD Object a Parameter or Variable: Syntax
       AD Boolean Functions: Syntax
       Compare AD and Base Objects for Nearly Equal: Syntax
       AD Binary Comparison Operators: Syntax
       Free Static Variables: Syntax
       Atomic Reverse Hessian Sparsity Patterns: Syntax
       Atomic Forward Hessian Sparsity Patterns: Syntax
       Atomic Reverse Jacobian Sparsity Patterns: Syntax
       Atomic Forward Jacobian Sparsity Patterns: Syntax
       Atomic Reverse Mode: Syntax
       Atomic Forward Mode: Syntax
       Using AD Version of Atomic Function: Syntax
       Set Atomic Function Options: Syntax
       Atomic Function Constructor: Syntax
       User Defined Atomic AD Functions: Syntax
       Checkpointing Functions: Syntax
       Numeric Limits For an AD and Base Types: Syntax
       Discrete AD Functions: Syntax
       AD Conditional Expressions: Syntax
       Absolute Zero Multiplication: Syntax
       The AD Power Function: Syntax
       AD Two Argument Inverse Tangent Function: Syntax
       The Sign: sign: Syntax
       The Logarithm of One Plus Argument: log1p: Syntax
       The Exponential Function Minus One: expm1: Syntax
       The Error Function: Syntax
       The Inverse Hyperbolic Tangent Function: atanh: Syntax
       The Inverse Hyperbolic Sine Function: asinh: Syntax
       The Inverse Hyperbolic Cosine Function: acosh: Syntax
       AD Absolute Value Functions: abs, fabs: Syntax
       The Hyperbolic Tangent Function: tanh: Syntax
       The Tangent Function: tan: Syntax
       The Square Root Function: sqrt: Syntax
       The Hyperbolic Sine Function: sinh: Syntax
       The Sine Function: sin: Syntax
       The Base 10 Logarithm Function: log10: Syntax
       The Exponential Function: log: Syntax
       The Exponential Function: exp: Syntax
       The Hyperbolic Cosine Function: cosh: Syntax
       The Cosine Function: cos: Syntax
       Inverse Tangent Function: atan: Syntax
       Inverse Sine Function: asin: Syntax
       Inverse Sine Function: acos: Syntax
       The Unary Standard Math Functions: Syntax
       AD Computed Assignment Operators: Syntax
       AD Binary Arithmetic Operators: Syntax
       AD Unary Minus Operator: Syntax
       AD Unary Plus Operator: Syntax
       Convert an AD Variable to a Parameter: Syntax
       Printing AD Values During Forward Mode: Syntax
       AD Output Stream Operator: Syntax
       AD Output Stream Operator: Syntax
       Convert An AD or Base Type to String: Syntax
       Convert From AD to Integer: Syntax
       Convert From an AD Type to its Base Type: Syntax
       AD Assignment Operator: Syntax
       AD Constructors: Syntax
       An Epsilon Accurate Exponential Approximation: Syntax
       Second Order Exponential Approximation: Syntax
       Download and Install Sacado in Build Directory: Syntax
       Download and Install Ipopt in Build Directory: Syntax
       Download and Install Fadbad in Build Directory: Syntax
       Download and Install Eigen in Build Directory: Syntax
       Download and Install ColPack in Build Directory: Syntax
       Download and Install Adolc in Build Directory: Syntax
       cppad-20170000.3: A Package for Differentiation of C++ Algorithms: Syntax
systems Returns Elapsed Number of Seconds: Microsoft Systems
T
Taylor Taylor's Ode Solver: An Example and Test
tan Old Tan and Tanh as User Atomic Operations: Example and Test
    Tangent and Hyperbolic Tangent Reverse Mode Theory
    Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
    Tan and Tanh as User Atomic Operations: Example and Test
    AD Two Argument Inverse Tangent Function
    The AD tan Function: Example and Test
    The Tangent Function: tan
tangent User Defined Atomic AD Functions: Example.Tangent Function
        Tangent and Hyperbolic Tangent Reverse Mode Theory
        Tangent and Hyperbolic Tangent Reverse Mode Theory
        Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
        Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
        Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
        Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
        Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
        Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
        Tan and Tanh as User Atomic Operations: Example and Test
        AD Two Argument Inverse Tangent Function
        The Inverse Hyperbolic Tangent Function: atanh
        The Hyperbolic Tangent Function: tanh
        The Tangent Function: tan
        Inverse Tangent Function: atan
tanh Old Tan and Tanh as User Atomic Operations: Example and Test
     Tan and Tanh as User Atomic Operations: Example and Test
     The AD tanh Function: Example and Test
     The Hyperbolic Tangent Function: tanh
tape Glossary: Tape
     Frequently Asked Questions and Answers: Tape Storage: Disk or Memory
     Optimize an ADFun Object Tape
     Abort Recording of an Operation Sequence
     Stop Recording and Store Operation Sequence
     Construct an ADFun Object and Stop Recording
     AD Vectors that Record Index Operations
     Interpolation With Retaping: Example and Test
     Interpolation With Out Retaping: Example and Test
     Taping Array Index Operation: Example and Test
     Auto Tools Unix Test and Installation
     Using CMake to Configure CppAD
tape_addr_type Auto Tools Unix Test and Installation: tape_addr_type
tape_id_type Auto Tools Unix Test and Installation: tape_id_type
taping The CppAD Wish List: Optimization.Taping
       Frequently Asked Questions and Answers
       Comparison Changes Between Taping and Zero Order Forward
       Stop Recording and Store Operation Sequence: Taping
       Taping Array Index Operation: Example and Test
       Convert an AD Variable to a Parameter: Example and Test
       Convert an AD Variable to a Parameter
taping: Using Adolc with Multiple Levels of Taping: Example and Test
taylor Glossary: Taylor Coefficient
       The Theory of Reverse Mode: Taylor Notation
       Error Function Forward Taylor Polynomial Theory: Taylor Coefficients Recursion
       Error Function Forward Taylor Polynomial Theory
       Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory: Taylor Coefficients Recursion
       Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
       Inverse Cosine and Hyperbolic Cosine Forward Mode Theory: Taylor Coefficients Recursion
       Inverse Sine and Hyperbolic Sine Forward Mode Theory: Taylor Coefficients Recursion
       Inverse Tangent and Hyperbolic Tangent Forward Mode Theory: Taylor Coefficients Recursion
       Logarithm Function Forward Mode Theory: Taylor Coefficients Recursion
       Exponential Function Forward Mode Theory: Taylor Coefficients Recursion
       The Theory of Forward Mode: Standard Math Functions.Taylor Coefficients Recursion Formula
       The Theory of Forward Mode: Taylor Notation
       Third Order Reverse Mode: Example and Test: Taylor Coefficients
       Controlling Taylor Coefficient Memory Allocation: Example and Test
       Controlling Taylor Coefficients Memory Allocation
       Number Taylor Coefficient Orders Currently Stored
       Construct an ADFun Object and Stop Recording: Assignment Operator.Taylor Coefficients
       AD Theory for Cholesky Factorization: Notation.Taylor Coefficient
taylor's Taylor's Ode Solver: An Example and Test
         Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Taylor's Method Using AD
         Taylor's Ode Solver: A Multi-Level Adolc Example and Test
         Taylor's Ode Solver: A Multi-Level AD Example and Test: Taylor's Method Using AD
         Taylor's Ode Solver: A Multi-Level AD Example and Test
taylor_size ADFun Object Deprecated Member Functions: taylor_size
team Pthread Implementation of a Team of AD Threads
     Boost Thread Implementation of a Team of AD Threads
     OpenMP Implementation of a Team of AD Threads
     Specifications for A Team of AD Threads
     Using a Team of AD Threads: Example and Test
     Run Multi-Threading Examples and Speed Tests: Team Implementations
team_create Specifications for A Team of AD Threads: team_create
team_destroy Specifications for A Team of AD Threads: team_destroy
team_example Run Multi-Threading Examples and Speed Tests: team_example
team_name Specifications for A Team of AD Threads: team_name
team_work Specifications for A Team of AD Threads: team_work
template Choosing The Vector Testing Template Class
         Using The CppAD Test Vector Template Class
         Examples: The CppAD Test Vector Template Class
         CppAD::vector Template Class: Example and Test
         The CppAD::vector Template Class
         Evaluate a Polynomial or its Derivative
         Simple Vector Template Class: Example and Test
         Definition of a Simple Vector: Template Class Requirements
         Some General Purpose Utilities: Miscellaneous.Simple Vector Template Class
         Choosing the CppAD Test Vector Template Class
terms Evaluate a Function Defined in Terms of an ODE
test LuRatio: Example and Test
     opt_val_hes: Example and Test
     BenderQuad: Example and Test
     Correctness Test of det_by_minor Routine
     zdouble: Example and Test
     Define Matrix Multiply as a User Atomic Operation
     Old Matrix Multiply as a User Atomic Operation: Example and Test
     Old Tan and Tanh as User Atomic Operations: Example and Test
     Old Atomic Operation Reciprocal: Example and Test
     Speed Test for Both Simple and Fast Representations
     Nonlinear Programming Using CppAD and Ipopt: Example and Test
     Choosing The Vector Testing Template Class
     OpenMP Memory Allocator: Example and Test
     Tracking Use of New and Delete: Example and Test
     Frequently Asked Questions and Answers: Namespace.Test Vector Preprocessor Symbol
     Speed Test Derivatives Using Sacado
     Speed Test Derivatives Using Fadbad
     Speed Test Derivatives Using CppAD
     Adolc Test Utility: Allocate and Free Memory For a Matrix
     Speed Test of Derivatives Using Adolc
     Speed Test of Functions in Double
     sparse_hes_fun: Example and test
     sparse_jac_fun: Example and test
     ode_evaluate: Example and test
     Sum of the Elements of the Square of a Matrix: Example and Test
     Sum Elements of a Matrix Times Itself
     Determinant Using Expansion by Minors: Example and Test
     Determinant of a Minor: Example and Test
     Determinant Using Lu Factorization: Example and Test
     Speed Testing Sparse Jacobian
     Speed Testing Sparse Hessian
     Speed Testing Second Derivative of a Polynomial
     Speed Testing the Jacobian of Ode Solution
     Speed Testing Derivative of Matrix Multiply
     Speed Testing Gradient of Determinant by Minor Expansion
     Speed Testing Gradient of Determinant Using Lu Factorization
     Running the Speed Test Program: test
     Running the Speed Test Program
     Speed Test an Operator Overloading AD Package
     Using The CppAD Test Vector Template Class
     Lu Factor and Solve With Recorded Pivoting: Example and Test
     Example Differentiating a Stack Machine Interpreter
     Taylor's Ode Solver: An Example and Test
     Taylor's Ode Solver: A Multi-Level Adolc Example and Test
     Taylor's Ode Solver: A Multi-Level AD Example and Test
     A Stiff Ode: Example and Test
     Multiple Level of AD: Example and Test
     Gradient of Determinant Using Lu Factorization: Example and Test
     Gradient of Determinant Using Expansion by Minors: Example and Test
     Interfacing to C: Example and Test
     Gradient of Determinant Using LU Factorization: Example and Test
     Gradient of Determinant Using Expansion by Minors: Example and Test
     Using Eigen To Compute Determinant: Example and Test
     Using Eigen Arrays: Example and Test
     Differentiate Conjugate Gradient Algorithm: Example and Test
     Example and Test Linking CppAD to Languages Other than C++
     Creating Your Own Interface to an ADFun Object
     Examples: The CppAD Test Vector Template Class
     Nonlinear Programming Retaping: Example and Test
     Nonlinear Programming Using CppAD and Ipopt: Example and Test
     Set Union: Example and Test
     to_string: Example and Test
     Index Sort: Example and Test
     Fast Multi-Threading Memory Allocator: Example and Test
     CppAD::vectorBool Class: Example and Test
     CppAD::vector Template Class: Example and Test
     OdeGearControl: Example and Test
     OdeGear: Example and Test
     OdeErrControl: Example and Test Using Maxabs Argument
     OdeErrControl: Example and Test
     Rosen34: Example and Test
     Runge45: Example and Test
     Runge45: Example and Test
     One Dimensional Romberg Integration: Example and Test
     One Dimensional Romberg Integration: Example and Test
     LuInvert: Example and Test
     LuFactor: Example and Test
     LuSolve With Complex Arguments: Example and Test
     Polynomial Evaluation: Example and Test
     The Pow Integer Exponent: Example and Test
     nan: Example and Test
     The CheckSimpleVector Function: Example and Test
     Simple Vector Template Class: Example and Test
     The CheckNumericType Function: Example and Test
     The NumericType: Example and Test
     time_test: Example and test
     Elapsed Seconds: Example and Test
     Determine Amount of Time to Execute a Test: test
     Determine Amount of Time to Execute a Test
     Example Use of SpeedTest
     speed_test: Example and test
     Run One Speed Test and Print Results: Test
     Run One Speed Test and Print Results
     Run One Speed Test and Return Results: test
     Run One Speed Test and Return Results
     NearEqual Function: Example and Test
     Replacing The CppAD Error Handler: Example and Test
     Specifications for A Team of AD Threads: Speed Test of Implementation
     Timing Test of Multi-Threaded Newton Method
     Timing Test of Multi-Threaded Summation of 1/i
     Using a Team of AD Threads: Example and Test
     A Simple pthread AD: Example and Test
     A Simple Boost Threading AD: Example and Test
     A Simple OpenMP AD: Example and Test
     A Simple Parallel Pthread Example and Test
     A Simple Boost Thread Example and Test
     A Simple OpenMP Example and Test
     ADFun Checking For Nan: Example and Test
     ADFun Check and Re-Tape: Example and Test
     Sparse Hessian on Subset of Variables: Example and Test
     Sparse Hessian: Example and Test
     Sparse Jacobian: Example and Test
     Second Partials Reverse Driver: Example and Test
     Subset of Second Order Partials: Example and Test
     Hessian of Lagrangian and  ADFun Default Constructor: Example and Test
     Hessian: Example and Test
     First Order Derivative Driver: Example and Test
     First Order Partial Driver: Example and Test
     Jacobian: Example and Test
     Using vectorBool Sparsity To Conserve Memory: Example and Test
     Forward Mode Hessian Sparsity: Example and Test
     Sparsity Patterns For a Subset of Variables: Example and Test
     Reverse Mode Hessian Sparsity: Example and Test
     Computing Dependency: Example and Test
     Reverse Mode Jacobian Sparsity: Example and Test
     Forward Mode Jacobian Sparsity: Example and Test
     Reverse Mode General Case (Checkpointing): Example and Test
     Third Order Reverse Mode: Example and Test
     Hessian Times Direction: Example and Test
     Second Order Reverse ModeExample and Test
     First Order Reverse Mode: Example and Test
     Number of Variables That Can be Skipped: Example and Test
     Controlling Taylor Coefficient Memory Allocation: Example and Test
     CompareChange and Re-Tape: Example and Test
     Forward Mode: Example and Test of Multiple Directions
     Forward Mode: Example and Test of Multiple Orders
     Forward Mode: Example and Test
     ADFun Sequence Properties: Example and Test
     Abort Current Recording: Example and Test
     ADFun Assignment: Example and Test
     Independent and ADFun Constructor: Example and Test
     Complex Polynomial: Example and Test
     Using Adolc with Multiple Levels of Taping: Example and Test
     Using a User Defined AD Base Type: Example and Test
     AD Vectors that Record Index Operations: Example and Test
     EqualOpSeq: Example and Test
     AD Parameter and Variable Functions: Example and Test
     AD Boolean Functions: Example and Test
     Compare AD with Base Objects: Example and Test
     AD Binary Comparison Operators: Example and Test
     User Atomic Matrix Multiply: Example and Test
     Atomic Eigen Cholesky Factorization: Example and Test
     Atomic Eigen Matrix Inverse: Example and Test
     Atomic Eigen Matrix Multiply: Example and Test
     Tan and Tanh as User Atomic Operations: Example and Test
     Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function.Test Result
     Atomic Sparsity with Set Patterns: Example and Test: Test Atomic Function
     Atomic Sparsity with Set Patterns: Example and Test
     Reciprocal as an Atomic Operation: Example and Test
     Atomic Euclidean Norm Squared: Example and Test
     Getting Started with Atomic Operations: Example and Test
     Atomic Reverse Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Reverse Hessian Sparsity: Example and Test
     Atomic Forward Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Forward Hessian Sparsity: Example and Test
     Atomic Reverse Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Reverse Jacobian Sparsity: Example and Test
     Atomic Forward Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Forward Jacobian Sparsity: Example and Test
     Atomic Reverse: Example and Test
     Atomic Forward: Example and Test
     Checkpointing an Extended ODE Solver: Example and Test
     Checkpointing an ODE Solver: Example and Test
     Atomic Operations and Multiple-Levels of AD: Example and Test
     Simple Checkpointing: Example and Test
     Numeric Limits: Example and Test
     Interpolation With Retaping: Example and Test
     Interpolation With Out Retaping: Example and Test
     Taping Array Index Operation: Example and Test
     Conditional Expressions: Example and Test
     AD Conditional Expressions: Test
     AD Absolute Zero Multiplication: Example and Test
     The AD Power Function: Example and Test
     The AD atan2 Function: Example and Test
     Sign Function: Example and Test
     The AD log1p Function: Example and Test
     The AD exp Function: Example and Test
     The AD erf Function: Example and Test
     The AD atanh Function: Example and Test
     The AD asinh Function: Example and Test
     The AD acosh Function: Example and Test
     AD Absolute Value Function: Example and Test
     The AD tanh Function: Example and Test
     The AD tan Function: Example and Test
     The AD sqrt Function: Example and Test
     The AD sinh Function: Example and Test
     The AD sin Function: Example and Test
     The AD log10 Function: Example and Test
     The AD log Function: Example and Test
     The AD exp Function: Example and Test
     The AD cosh Function: Example and Test
     The AD cos Function: Example and Test
     The AD atan Function: Example and Test
     The AD asin Function: Example and Test
     The AD acos Function: Example and Test
     AD Computed Assignment Division: Example and Test
     AD Computed Assignment Multiplication: Example and Test
     AD Computed Assignment Subtraction: Example and Test
     AD Computed Assignment Addition: Example and Test
     AD Binary Division: Example and Test
     AD Binary Multiplication: Example and Test
     AD Binary Subtraction: Example and Test
     AD Binary Addition: Example and Test
     AD Unary Minus Operator: Example and Test
     AD Unary Plus Operator: Example and Test
     Convert an AD Variable to a Parameter: Example and Test
     Print During Zero Order Forward Mode: Example and Test
     Printing During Forward Mode: Example and Test
     AD Output Operator: Example and Test
     AD Output Operator: Example and Test
     Convert From AD to Integer: Example and Test
     Convert From AD to its Base Type: Example and Test
     AD Assignment: Example and Test
     AD Constructors: Example and Test
     exp_eps: Test of exp_eps
     An Epsilon Accurate Exponential Approximation: Test
     exp_2: Test
     Second Order Exponential Approximation: Test
     Auto Tools Unix Test and Installation
     Choosing the CppAD Test Vector Template Class
     Including the Eigen Examples and Tests: Test Vector
     Using ColPack: Example and Test
     Using ColPack: Example and Test
     CppAD Download, Test, and Install Instructions
test_size Determine Amount of Time to Execute a Test: test_size
test_time Timing Test of Multi-Threaded Newton Method: test_time
          Timing Test of Multi-Threaded Summation of 1/i: test_time
          Run Multi-Threading Examples and Speed Tests: multi_newton.test_time
          Run Multi-Threading Examples and Speed Tests: harmonic.test_time
testing Choosing The Vector Testing Template Class
        The CppAD Wish List: checkpoint.Testing
        Speed Testing Utilities
        Speed Testing Sparse Jacobian
        Speed Testing Sparse Hessian
        Speed Testing Second Derivative of a Polynomial
        Speed Testing the Jacobian of Ode Solution
        Speed Testing Derivative of Matrix Multiply
        Speed Testing Gradient of Determinant by Minor Expansion
        Speed Testing Gradient of Determinant Using Lu Factorization
        Some General Purpose Utilities: Testing
        Optimize an ADFun Object Tape: Speed Testing
        Download The CppAD Source Code: Windows File Extraction and Testing
tests Speed Test Derivatives Using Sacado: Running Tests
      Speed Test Derivatives Using Fadbad: Running Tests
      Speed Test Derivatives Using CppAD: Running Tests
      Speed Test of Derivatives Using Adolc: Running Tests
      Speed Test of Functions in Double: Running Tests
      Run the Speed Examples: Running Tests
      CppAD Examples and Tests: Running Tests
      CppAD Examples and Tests
      Run Multi-Threading Examples and Speed Tests: Running Tests
      Run Multi-Threading Examples and Speed Tests
      Correctness Tests For Exponential Approximation in Introduction: Running Tests
      Correctness Tests For Exponential Approximation in Introduction
      Auto Tools Unix Test and Installation: make.Examples and Tests
      Checking the CppAD Examples and Tests
      Including the Sacado Speed Tests: Speed Tests
      Including the Sacado Speed Tests
      Including the cppad_ipopt Library and Tests: Examples and Tests
      Including the cppad_ipopt Library and Tests
      Including the FADBAD Speed Tests: Speed Tests
      Including the FADBAD Speed Tests
      Including the Eigen Examples and Tests
      Including the ADOL-C Examples and Tests: Speed Tests
      Including the ADOL-C Examples and Tests
text Printing AD Values During Forward Mode
tf An Error Controller for Gear's Ode Solvers: tf
   An Error Controller for ODE Solvers: tf
   A 3rd and 4th Order Rosenbrock ODE Solver: tf
   An Embedded 4th and 5th Order Runge-Kutta ODE Solver: tf
than Example and Test Linking CppAD to Languages Other than C++
that Routines That Track Use of New and Delete
     The Theory of Forward Mode: Standard Math Functions.Cases that Apply Recursion Above
     Evaluate a Function That Has a Sparse Hessian
     Evaluate a Function That Has a Sparse Jacobian
     Computing a Jacobian With Constants that Change
     Returns Indices that Sort a Vector
     Free All Memory That Was Allocated for Use by thread_alloc
     Number of Variables That Can be Skipped: Example and Test
     Number of Variables that Can be Skipped
     Example AD Base Types That are not AD<OtherBase>
     AD Vectors that Record Index Operations: Example and Test
     AD Vectors that Record Index Operations
the Your License for the CppAD Software
    Driver for Running the Ipopt ODE Example
    Nonlinear Programming Using the CppAD Interface to Ipopt
    Choosing The Vector Testing Template Class
    Return A Raw Array to The Available Memory for a Thread
    Get the Current OpenMP Thread Number
    Is The Current Execution in OpenMP Parallel Mode
    The CppAD Wish List
    Bibliography: The C++ Programming Language
    The Theory of Reverse Mode
    The Theory of Forward Mode
    The Theory of Derivative Calculations
    Sum of the Elements of the Square of a Matrix: Example and Test
    Sum of the Elements of the Square of a Matrix: Example and Test
    Speed Testing the Jacobian of Ode Solution
    Running the Speed Test Program
    Using The CppAD Test Vector Template Class
    Run the Speed Examples
    List of All the CppAD Examples
    Examples: The CppAD Test Vector Template Class
    Get the Current Thread Number
    Is The Current Execution in Parallel Mode
    The CppAD::vector Template Class
    The Pow Integer Exponent: Example and Test
    The Integer Power Function
    The CheckSimpleVector Function: Example and Test
    The CheckNumericType Function: Example and Test
    The NumericType: Example and Test
    Replacing The CppAD Error Handler: Example and Test
    Replacing the CppAD Error Handler
    Base Type Requirements for Identically Equal Comparisons: EqualOpSeq.The Simple Case
    The AD Power Function: Example and Test
    The AD Power Function
    The AD atan2 Function: Example and Test
    The Sign: sign
    The AD log1p Function: Example and Test
    The Logarithm of One Plus Argument: log1p
    The AD exp Function: Example and Test
    The Exponential Function Minus One: expm1
    The AD erf Function: Example and Test
    The Error Function
    The AD atanh Function: Example and Test
    The Inverse Hyperbolic Tangent Function: atanh
    The AD asinh Function: Example and Test
    The Inverse Hyperbolic Sine Function: asinh
    The AD acosh Function: Example and Test
    The Inverse Hyperbolic Cosine Function: acosh
    The AD tanh Function: Example and Test
    The AD tan Function: Example and Test
    The AD sqrt Function: Example and Test
    The AD sinh Function: Example and Test
    The AD sin Function: Example and Test
    The AD log10 Function: Example and Test
    The AD log Function: Example and Test
    The AD exp Function: Example and Test
    The AD cosh Function: Example and Test
    The AD cos Function: Example and Test
    The AD atan Function: Example and Test
    The AD asin Function: Example and Test
    The AD acos Function: Example and Test
    The Hyperbolic Tangent Function: tanh
    The Tangent Function: tan
    The Square Root Function: sqrt
    The Hyperbolic Sine Function: sinh
    The Sine Function: sin
    The Base 10 Logarithm Function: log10
    The Exponential Function: log
    The Exponential Function: exp
    The Hyperbolic Cosine Function: cosh
    The Cosine Function: cos
    The Binary Math Functions
    The Unary Standard Math Functions
    Checking the CppAD Examples and Tests
    Choosing the CppAD Test Vector Template Class
    Including the Sacado Speed Tests
    Including the cppad_ipopt Library and Tests
    Including the FADBAD Speed Tests
    Including the Eigen Examples and Tests
    Including the ColPack Sparsity Calculations
    Including the ADOL-C Examples and Tests
    Using CMake to Configure CppAD: The CMake Program
    Download The CppAD Source Code
theorem An Important Reverse Mode Identity: Theorem
theory Old Tan and Tanh as User Atomic Operations: Example and Test: Theory
       Old Atomic Operation Reciprocal: Example and Test: Theory
       Error Function Reverse Mode Theory
       Tangent and Hyperbolic Tangent Reverse Mode Theory
       Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
       Inverse Sine and Hyperbolic Sine Reverse Mode Theory
       Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
       Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
       Square Root Function Reverse Mode Theory
       Logarithm Function Reverse Mode Theory
       Exponential Function Reverse Mode Theory
       The Theory of Reverse Mode
       Error Function Forward Taylor Polynomial Theory
       Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
       Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
       Inverse Sine and Hyperbolic Sine Forward Mode Theory
       Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
       Trigonometric and Hyperbolic Sine and Cosine Forward Theory
       Square Root Function Forward Mode Theory
       Logarithm Function Forward Mode Theory
       Exponential Function Forward Mode Theory
       The Theory of Forward Mode
       The Theory of Derivative Calculations
       An Error Controller for Gear's Ode Solvers: Theory
       An Arbitrary Order Gear Method: Theory
       An Error Controller for ODE Solvers: Theory
       AD Theory for Cholesky Factorization
       Atomic Eigen Matrix Inversion Class: Theory
       Atomic Eigen Matrix Multiply Class: Theory
       Tan and Tanh as User Atomic Operations: Example and Test: Theory
       Reciprocal as an Atomic Operation: Example and Test: Theory
       Atomic Euclidean Norm Squared: Example and Test: Theory
theta AD Two Argument Inverse Tangent Function: theta
third Third Order Reverse Mode: Example and Test
this Changes and Additions to CppAD: This Year
     Example Use of SpeedTest: Running This Program
thread Memory Leak Detection: thread
       OpenMP Memory Allocator: Example and Test
       Check If A Memory Allocation is Efficient for Another Use: Thread
       Return A Raw Array to The Available Memory for a Thread: Thread
       Return A Raw Array to The Available Memory for a Thread
       Amount of Memory Available for Quick Use by a Thread: thread
       Amount of Memory Available for Quick Use by a Thread
       Amount of Memory a Thread is Currently Using: thread
       Amount of Memory a Thread is Currently Using
       Free Memory Currently Available for Quick Use by a Thread: thread
       Free Memory Currently Available for Quick Use by a Thread
       Return Memory to omp_alloc: Thread
       Get the Current OpenMP Thread Number: thread
       Get the Current OpenMP Thread Number
       Routines That Track Use of New and Delete
       Deallocate An Array and Call Destructor for its Elements: Thread
       Amount of Memory Available for Quick Use by a Thread: thread
       Amount of Memory Available for Quick Use by a Thread
       Amount of Memory a Thread is Currently Using: thread
       Amount of Memory a Thread is Currently Using
       Control When Thread Alloc Retains Memory For Future Use
       Free Memory Currently Available for Quick Use by a Thread: thread
       Free Memory Currently Available for Quick Use by a Thread
       Return Memory to thread_alloc: Thread
       Get the Current Thread Number: thread
       Get the Current Thread Number
       Boost Thread Implementation of a Team of AD Threads
       A Multi-Threaded Newton's Method
       Using a Team of AD Threads: Example and Test
       A Simple Boost Threading AD: Example and Test
       A Simple Parallel Pthread Example and Test
       A Simple Boost Thread Example and Test
       A Simple OpenMP Example and Test
       Using CppAD in a Multi-Threading Environment: Same Thread
thread_alloc Free All Memory That Was Allocated for Use by thread_alloc
             Return Memory to thread_alloc
             Setup thread_alloc For Use in Multi-Threading Environment
             The CppAD::vector Template Class
thread_num Setup thread_alloc For Use in Multi-Threading Environment: thread_num
thread_team Using a Team of AD Threads: Example and Test: thread_team
thread_test Run Multi-Threading Examples and Speed Tests
threading A Multi-Threaded Newton's Method
          A Simple Boost Threading AD: Example and Test
          Run Multi-Threading Examples and Speed Tests: Running Tests.threading
threads Set Maximum Number of Threads for omp_alloc Allocator
        Set and Get Maximum Number of Threads for omp_alloc Allocator
        Get Number of Threads
        Pthread Implementation of a Team of AD Threads
        Boost Thread Implementation of a Team of AD Threads
        OpenMP Implementation of a Team of AD Threads
        Specifications for A Team of AD Threads
        Using CMake to Configure CppAD
threads: Using a Team of AD Threads: Example and Test
three Atomic Eigen Matrix Inversion Class: Theory.Product of Three Matrices
ti An Error Controller for Gear's Ode Solvers: ti
   An Error Controller for ODE Solvers: ti
   A 3rd and 4th Order Rosenbrock ODE Solver: ti
   An Embedded 4th and 5th Order Runge-Kutta ODE Solver: ti
time Determine Amount of Time to Execute det_by_minor: time
     Determine Amount of Time to Execute det_by_minor
     An ODE Inverse Problem Example: Trapezoidal Approximation.Trapezoidal Time Grid
     Returns Elapsed Number of Seconds
     Determine Amount of Time to Execute a Test: time
     Determine Amount of Time to Execute a Test
time_min Determine Amount of Time to Execute det_by_minor: time_min
         Determine Amount of Time to Execute a Test: time_min
         Run One Speed Test and Return Results: time_min
time_out Timing Test of Multi-Threaded Newton Method: time_out
         Timing Test of Multi-Threaded Summation of 1/i: time_out
time_test time_test: Example and test
          Determine Amount of Time to Execute a Test
time_test: time_test: Example and test
timer Elapsed Seconds: Example and Test
times Repeat det_by_minor Routine A Specified Number of Times
      Sum Elements of a Matrix Times Itself
      Hessian Times Direction: Example and Test
      Second Order Reverse Mode: Hessian Times Direction
      AD Computed Assignment Operators
      AD Binary Multiplication: Example and Test
      AD Binary Arithmetic Operators
timing Determine Amount of Time to Execute a Test: Timing
       Run One Speed Test and Return Results: Timing
       Timing Test of Multi-Threaded Newton Method
       Timing Test of Multi-Threaded Summation of 1/i
to_string Some General Purpose Utilities: Miscellaneous.to_string
          Enable use of AD<Base> where Base is std::complex<double>: to_string
          Enable use of AD<Base> where Base is double: to_string
          Enable use of AD<Base> where Base is float: to_string
          Enable use of AD<Base> where Base is Adolc's adouble Type: to_string
          Example AD<Base> Where Base Constructor Allocates Memory: to_string
          Extending to_string To Another Floating Point Type
to_string: to_string: Example and Test
tools Auto Tools Unix Test and Installation
tracing The CppAD Wish List: Tracing
track Routines That Track Use of New and Delete
track_count Memory Leak Detection: TRACK_COUNT
trackcount Routines That Track Use of New and Delete: TrackCount
trackdelvec Routines That Track Use of New and Delete: TrackDelVec
trackextend Routines That Track Use of New and Delete: TrackExtend
tracking Tracking Use of New and Delete: Example and Test
tracknewvec Routines That Track Use of New and Delete: TrackNewVec
transpose Hessian Sparsity Pattern: Reverse Mode: h.transpose true
          Hessian Sparsity Pattern: Reverse Mode: h.transpose false
          Hessian Sparsity Pattern: Reverse Mode: transpose
          Jacobian Sparsity Pattern: Reverse Mode: s.transpose true
          Jacobian Sparsity Pattern: Reverse Mode: s.transpose false
          Jacobian Sparsity Pattern: Reverse Mode: r.transpose true
          Jacobian Sparsity Pattern: Reverse Mode: r.transpose false
          Jacobian Sparsity Pattern: Reverse Mode: transpose
          Jacobian Sparsity Pattern: Forward Mode: s.transpose true
          Jacobian Sparsity Pattern: Forward Mode: s.transpose false
          Jacobian Sparsity Pattern: Forward Mode: r.transpose true
          Jacobian Sparsity Pattern: Forward Mode: r.transpose false
          Jacobian Sparsity Pattern: Forward Mode: transpose
trapezoidal ODE Fitting Using Fast Representation: Trapezoidal Approximation
            ODE Fitting Using Simple Representation: Trapezoidal Approximation Constraint
            An ODE Inverse Problem Example: Trapezoidal Approximation.Trapezoidal Time Grid
            An ODE Inverse Problem Example: Trapezoidal Approximation
            ODE Inverse Problem Definitions: Source Code: Trapezoidal Approximation
triangular AD Theory for Cholesky Factorization: Notation.Lower Triangular Part
trigonometric Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
              Trigonometric and Hyperbolic Sine and Cosine Forward Theory
true Hessian Sparsity Pattern: Reverse Mode: h.transpose true
     Jacobian Sparsity Pattern: Reverse Mode: s.transpose true
     Jacobian Sparsity Pattern: Reverse Mode: r.transpose true
     Jacobian Sparsity Pattern: Forward Mode: s.transpose true
     Jacobian Sparsity Pattern: Forward Mode: r.transpose true
     The Logarithm of One Plus Argument: log1p: CPPAD_USE_CPLUSPLUS_2011.true
     The Exponential Function Minus One: expm1: CPPAD_USE_CPLUSPLUS_2011.true
     The Error Function: CPPAD_USE_CPLUSPLUS_2011.true
     The Inverse Hyperbolic Tangent Function: atanh: CPPAD_USE_CPLUSPLUS_2011.true
     The Inverse Hyperbolic Sine Function: asinh: CPPAD_USE_CPLUSPLUS_2011.true
     The Inverse Hyperbolic Cosine Function: acosh: CPPAD_USE_CPLUSPLUS_2011.true
tvector User Defined Atomic AD Functions: CPPAD_USER_ATOMIC.Tvector
two An ODE Inverse Problem Example: Black Box Method.Two levels of Iteration
    Determine if Two Values Are Nearly Equal
    Second Order Forward Mode: Derivative Values
    Check if Two Value are Identically Equal
    Atomic Eigen Matrix Multiply Class: Theory.Product of Two Matrices
    AD Two Argument Inverse Tangent Function
tx User Defined Atomic AD Functions: tx
   Atomic Reverse Mode: tx
   Atomic Forward Mode: tx
ty User Defined Atomic AD Functions: ty
   Atomic Reverse Mode: ty
   Atomic Forward Mode: ty
type zdouble: An AD Base Type With Absolute Zero: Base Type Requirements
     zdouble: An AD Base Type With Absolute Zero
     Return A Raw Array to The Available Memory for a Thread: Type
     Allocate Memory and Create A Raw Array: Type
     Glossary: Base Type
     Glossary: AD Type Above Base
     Deallocate An Array and Call Destructor for its Elements: Type
     Allocate An Array and Call Default Constructor for its Elements: Type
     The CppAD::vector Template Class: vectorBool.Element Type
     Evaluate a Polynomial or its Derivative: Type
     The Integer Power Function: Type
     Definition of a Simple Vector: Value Type
     Definition of a Simple Vector: Elements of Specified Type
     Definition of a Numeric Type: Type Requirements
     Definition of a Numeric Type
     Determine if Two Values Are Nearly Equal: Type
     Enable use of AD<Base> where Base is Adolc's adouble Type
     Using a User Defined AD Base Type: Example and Test
     Base Type Requirements for Hash Coding Values
     Extending to_string To Another Floating Point Type
     Base Type Requirements for Numeric Limits
     Base Type Requirements for Standard Math Functions
     Base Type Requirements for Ordered Comparisons: Ordered Type
     Base Type Requirements for Ordered Comparisons
     Base Type Requirements for Identically Equal Comparisons
     Base Type Requirements for Conditional Expressions: CondExpTemplate.Ordered Type
     Base Type Requirements for Conditional Expressions
     AD<Base> Requirements for a CppAD Base Type: Numeric Type
     AD<Base> Requirements for a CppAD Base Type
     Compare AD and Base Objects for Nearly Equal: Type
     AD Conditional Expressions: Type
     Convert An AD or Base Type to String
     Convert From an AD Type to its Base Type
     Convert From an AD Type to its Base Type
     AD Objects: Base Type Requirements
     An Epsilon Accurate Exponential Approximation: Type
     Second Order Exponential Approximation: Type
type: Using a User Defined AD Base Type: Example and Test
      Convert From AD to its Base Type: Example and Test
types Machine Epsilon For AD Types
      Frequently Asked Questions and Answers: Complex Types
      Convert Certain Types to a String
      Example AD Base Types That are not AD<OtherBase>
      AD<Base> Requirements for a CppAD Base Type: Standard Base Types
      Atomic Eigen Cholesky Factorization Class: Public.Types
      Atomic Eigen Matrix Inversion Class: Public.Types
      Atomic Eigen Matrix Multiply Class: Public.Types
      Numeric Limits For an AD and Base Types
      AD Absolute Value Functions: abs, fabs: Complex Types
      The Unary Standard Math Functions: Possible Types
      Convert From AD to Integer: x.AD Types
      Convert From AD to Integer: x.Complex Types
      Convert From AD to Integer: x.Real Types
U
u LU Factorization of A Square Matrix and Stability Calculation: LU.U
  User Defined Atomic AD Functions: rev_hes_sparse.u
  Invert an LU Factored Equation: LU.U
  LU Factorization of A Square Matrix: LU.U
  AD Boolean Functions: u
  Atomic Reverse Hessian Sparsity Patterns: u
u) Any Order Reverse Mode: Notation.Y(t, u)
   Any Order Reverse Mode: Notation.X(t, u)
u^(k) Any Order Reverse Mode: Notation.u^(k)
unary Enable use of AD<Base> where Base is std::complex<double>: Invalid Unary Math
      Enable use of AD<Base> where Base is std::complex<double>: Valid Unary Math
      Enable use of AD<Base> where Base is double: Unary Standard Math
      Enable use of AD<Base> where Base is float: Unary Standard Math
      Enable use of AD<Base> where Base is Adolc's adouble Type: Unary Standard Math
      Example AD<Base> Where Base Constructor Allocates Memory: Unary Standard Math
      Base Type Requirements for Standard Math Functions: Unary Standard Math
      Required Base Class Member Functions: Unary Operators
      AD Boolean Functions: Create Unary
      The Unary Standard Math Functions
      AD Unary Minus Operator: Example and Test
      AD Unary Minus Operator
      AD Unary Plus Operator: Example and Test
      AD Unary Plus Operator
unary_name AD Boolean Functions: unary_name
uniform Simulate a [0,1] Uniform Random Variate
        Simulate a [0,1] Uniform Random Variate
uniform_01 Source: uniform_01
           Simulate a [0,1] Uniform Random Variate
           Running the Speed Test Program
union Define Matrix Multiply as a User Atomic Operation: Set Union
      Union of Standard Sets
union: Set Union: Example and Test
unix Auto Tools Unix Test and Installation
     Including the ADOL-C Examples and Tests: Unix
unknown CppAD Assertions During Execution: Unknown
usage User Defined Atomic AD Functions: rev_hes_sparse.Usage
      User Defined Atomic AD Functions: rev_jac_sparse.Usage
      User Defined Atomic AD Functions: for_jac_sparse.Usage
      User Defined Atomic AD Functions: reverse.Usage
      User Defined Atomic AD Functions: forward.Usage
      Auto Tools Unix Test and Installation
      CppAD pkg-config Files: Usage
      Using CMake to Configure CppAD
use User Defined Atomic AD Functions: Example.Use AD
    User Defined Atomic AD Functions: Syntax Function.Use Function
    Check If A Memory Allocation is Efficient for Another Use
    Amount of Memory Available for Quick Use by a Thread
    Free Memory Currently Available for Quick Use by a Thread
    Tracking Use of New and Delete: Example and Test
    Routines That Track Use of New and Delete
    Enable Use of Eigen Linear Algebra Package with CppAD
    Use Ipopt to Solve a Nonlinear Programming Problem
    Free All Memory That Was Allocated for Use by thread_alloc
    Amount of Memory Available for Quick Use by a Thread
    Control When Thread Alloc Retains Memory For Future Use
    Free Memory Currently Available for Quick Use by a Thread
    Setup thread_alloc For Use in Multi-Threading Environment
    Example Use of SpeedTest
    Specifications for A Team of AD Threads: Example Use
    Enable use of AD<Base> where Base is std::complex<double>
    Enable use of AD<Base> where Base is double
    Enable use of AD<Base> where Base is float
    Enable use of AD<Base> where Base is Adolc's adouble Type
    User Atomic Matrix Multiply: Example and Test: Use Atomic Function
    Atomic Eigen Cholesky Factorization: Example and Test: Use Atomic Function
    Atomic Eigen Matrix Inverse: Example and Test: Use Atomic Function
    Atomic Eigen Matrix Multiply: Example and Test: Use Atomic Function
    Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function
    Reciprocal as an Atomic Operation: Example and Test: Use Atomic Function
    Atomic Euclidean Norm Squared: Example and Test: Use Atomic Function
    Getting Started with Atomic Operations: Example and Test: Use Atomic Function
    Atomic Reverse Hessian Sparsity: Example and Test: Use Atomic Function
    Atomic Forward Hessian Sparsity: Example and Test: Use Atomic Function
    Atomic Reverse Jacobian Sparsity: Example and Test: Use Atomic Function
    Atomic Forward Jacobian Sparsity: Example and Test: Use Atomic Function
    Atomic Reverse: Example and Test: Use Atomic Function
    Atomic Forward: Example and Test: Use Atomic Function
    Free Static Variables: Future Use
    Atomic Function Constructor: Example.Use Constructor
use_ad Timing Test of Multi-Threaded Newton Method: use_ad
       Run Multi-Threading Examples and Speed Tests: multi_newton.use_ad
use_vecad ADFun Object Deprecated Member Functions: use_VecAD
used A Quick OpenMP Memory Allocator Used by CppAD
     Utility Routines used by CppAD Examples
user Define Matrix Multiply as a User Atomic Operation: CppAD User Atomic Callback Functions
     Define Matrix Multiply as a User Atomic Operation
     Old Matrix Multiply as a User Atomic Operation: Example and Test
     Old Tan and Tanh as User Atomic Operations: Example and Test
     Using AD to Compute Atomic Function Derivatives
     Using AD to Compute Atomic Function Derivatives
     User Defined Atomic AD Functions
     Using a User Defined AD Base Type: Example and Test
     User Atomic Matrix Multiply: Example and Test
     Tan and Tanh as User Atomic Operations: Example and Test
     User Defined Atomic AD Functions
uses Check an ADFun Sequence of Operations: FunCheck Uses Forward
     Sparse Hessian: Easy Driver: Uses Forward
     Sparse Jacobian: Easy Driver: Uses Forward
     Reverse Mode Second Partial Derivative Driver: RevTwo Uses Forward
     Forward Mode Second Partial Derivative Driver: ForTwo Uses Forward
     Hessian: Easy Driver: Hessian Uses Forward
     First Order Derivative: Driver Routine: RevOne Uses Forward
     First Order Partial Derivative: Driver Routine: ForOne Uses Forward
using Compute Determinant using Expansion by Minors
      Using AD to Compute Atomic Function Derivatives
      Using AD to Compute Atomic Function Derivatives
      ODE Fitting Using Fast Representation
      ODE Fitting Using Simple Representation
      ODE Fitting Using Fast Representation
      ODE Fitting Using Simple Representation
      Nonlinear Programming Using CppAD and Ipopt: Example and Test
      Nonlinear Programming Using the CppAD Interface to Ipopt
      Amount of Memory a Thread is Currently Using
      Frequently Asked Questions and Answers: Namespace.Using
      Sacado Speed: Gradient of Determinant Using Lu Factorization
      Speed Test Derivatives Using Sacado
      Fadbad Speed: Gradient of Determinant Using Lu Factorization
      Speed Test Derivatives Using Fadbad
      CppAD Speed: Gradient of Determinant Using Lu Factorization
      Speed Test Derivatives Using CppAD
      Adolc Speed: Gradient of Determinant Using Lu Factorization
      Speed Test of Derivatives Using Adolc
      Double Speed: Determinant Using Lu Factorization
      Determinant Using Expansion by Minors: Example and Test
      Determinant Using Expansion by Minors
      Determinant Using Lu Factorization: Example and Test
      Determinant Using Expansion by Lu Factorization
      Speed Testing Gradient of Determinant Using Lu Factorization
      Using The CppAD Test Vector Template Class
      Taylor's Ode Solver: A Multi-Level Adolc Example and Test: Taylor's Method Using AD
      Taylor's Ode Solver: A Multi-Level AD Example and Test: Taylor's Method Using AD
      Using Multiple Levels of AD
      Gradient of Determinant Using Lu Factorization: Example and Test
      Gradient of Determinant Using Expansion by Minors: Example and Test
      Gradient of Determinant Using LU Factorization: Example and Test
      Gradient of Determinant Using Expansion by Minors: Example and Test
      Using Eigen To Compute Determinant: Example and Test
      Using Eigen Arrays: Example and Test
      Nonlinear Programming Using CppAD and Ipopt: Example and Test
      Amount of Memory a Thread is Currently Using
      OdeErrControl: Example and Test Using Maxabs Argument
      Definition of a Simple Vector: Element Access.Using Value
      Using a Team of AD Threads: Example and Test
      Using CppAD in a Multi-Threading Environment
      Using vectorBool Sparsity To Conserve Memory: Example and Test
      Using Adolc with Multiple Levels of Taping: Example and Test
      Using a User Defined AD Base Type: Example and Test
      Using AD Version of Atomic Function
      Getting Started Using CppAD to Compute Derivatives
      Using ColPack: Example and Test
      Using ColPack: Example and Test
      Using CMake to Configure CppAD
utilities Some Numerical AD Utilities
          Speed Testing Utilities
          Some General Purpose Utilities
utility Speed Testing Utilities: Speed Utility Routines
        Utility Routines used by CppAD Examples
        Multi-threading Newton Method Utility Routines
        Multi-threading Sum of 1/i Utility Routines
utility: Adolc Test Utility: Allocate and Free Memory For a Matrix
V
Value Convert an AD Variable to a Parameter: Example and Test
      Convert From AD to its Base Type: Example and Test
      Convert From an AD Type to its Base Type
Var2Par Convert an AD Variable to a Parameter: Example and Test
        Convert an AD Variable to a Parameter
VecAD AD Vectors that Record Index Operations: Example and Test
      AD Vectors that Record Index Operations
      AD Assignment Operator
      AD Constructors
VecAD<Base> AD Vectors that Record Index Operations
v User Defined Atomic AD Functions: rev_hes_sparse.v
  Obtain Nan or Determine if a Value is Nan: hasnan.v
  AD Vectors that Record Index Operations: Constructor.v
  AD Boolean Functions: v
  Atomic Reverse Hessian Sparsity Patterns: u.v
v_ptr Check If A Memory Allocation is Efficient for Another Use: v_ptr
      Return Memory to omp_alloc: v_ptr
      Get At Least A Specified Amount of Memory: v_ptr
      Return Memory to thread_alloc: v_ptr
      Get At Least A Specified Amount of Memory: v_ptr
valid Enable use of AD<Base> where Base is std::complex<double>: Valid Unary Math
value Speed Testing Second Derivative of a Polynomial: Return Value
      Speed Testing the Jacobian of Ode Solution: Return Value
      Speed Testing Derivative of Matrix Multiply: Return Value
      Speed Testing Gradient of Determinant by Minor Expansion: Return Value
      Speed Testing Gradient of Determinant Using Lu Factorization: Return Value
      Convert Certain Types to a String: value
      Control When Thread Alloc Retains Memory For Future Use: value
      Obtain Nan or Determine if a Value is Nan
      Definition of a Simple Vector: Element Access.Using Value
      Definition of a Simple Vector: Value Type
      Check if Two Value are Identically Equal
      AD Absolute Value Function: Example and Test
      AD Absolute Value Functions: abs, fabs
      Convert An AD or Base Type to String: value
      exp_eps: Second Order Forward Mode: Return Value
      exp_eps: First Order Forward Sweep: Return Value
      exp_eps: Operation Sequence and Zero Order Forward Sweep: Return Value
      exp_2: Second Order Forward Mode: Return Value
      exp_2: First Order Forward Mode: Return Value
      exp_2: Operation Sequence and Zero Order Forward Mode: Return Value
      Getting Started Using CppAD to Compute Derivatives: Value
value_ Convert an AD Variable to a Parameter
value_type Definition of a Simple Vector
valued Bool Valued Operations and Functions with AD Arguments
       AD Valued Operations and Functions
values Jacobian and Hessian of Optimal Values
       An ODE Inverse Problem Example: Measurements.Simulated Measurement Values
       An ODE Inverse Problem Example: Measurements.Simulation Parameter Values
       ODE Inverse Problem Definitions: Source Code: Measurements.Simulated Measurement Values
       ODE Inverse Problem Definitions: Source Code: Measurements.Simulation Parameter Values
       Determine if Two Values Are Nearly Equal
       Multiple Order Forward Mode: Purpose.Derivative Values
       Multiple Order Forward Mode: Purpose.Function Values
       Second Order Forward Mode: Derivative Values
       First Order Forward Mode: Derivative Values
       Zero Order Forward Mode: Function Values
       Base Type Requirements for Hash Coding Values
       Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.Large x Values
       Printing AD Values During Forward Mode
var Printing AD Values During Forward Mode: var
variable Glossary: Variable
         Glossary: Tape.Independent Variable
         AD Parameter and Variable Functions: Example and Test
         Is an AD Object a Parameter or Variable
         Atomic Reverse Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
         Atomic Forward Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
         Atomic Reverse Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
         Atomic Forward Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
         Convert an AD Variable to a Parameter: Example and Test
         Convert an AD Variable to a Parameter
         exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence.Variable
variables Glossary: Tape.Dependent Variables
          Frequently Asked Questions and Answers: Independent Variables
          Computing Sparse Hessian for a Subset of Variables
          Number of Variables That Can be Skipped: Example and Test
          Number of Variables that Can be Skipped
          Declare Independent Variables and Start Recording
          Atomic Eigen Cholesky Factorization Class: Private.Variables
          Atomic Eigen Matrix Inversion Class: Private.Variables
          Atomic Eigen Matrix Multiply Class: Private.Variables
          Free Static Variables
variables: Sparse Hessian on Subset of Variables: Example and Test
           Sparsity Patterns For a Subset of Variables: Example and Test
variate Simulate a [0,1] Uniform Random Variate
        Simulate a [0,1] Uniform Random Variate
vec Check an ADFun Object For Nan Results: get_check_for_nan.vec
vec_ad.cpp AD Vectors that Record Index Operations: Example and Test
vecad<base> Absolute Zero Multiplication: VecAD<Base>
            The Unary Standard Math Functions: Possible Types.VecAD<Base>
vecad<base>::reference AD Vectors that Record Index Operations: VecAD<Base>::reference
vector ODE Fitting Using Simple Representation: Argument Vector
       Nonlinear Programming Using the CppAD Interface to Ipopt: fg(x).Index Vector
       Choosing The Vector Testing Template Class
       Glossary: Sparsity Pattern.Vector of Sets
       Glossary: Sparsity Pattern.Vector of Boolean
       Glossary: Elementary Vector
       Frequently Asked Questions and Answers: Namespace.Test Vector Preprocessor Symbol
       Simulate a [0,1] Uniform Random Variate: Vector
       Sum Elements of a Matrix Times Itself: Vector
       Check Gradient of Determinant of 3 by 3 matrix: Vector
       Check Determinant of 3 by 3 matrix: Vector
       Determinant Using Expansion by Minors: Vector
       Determinant Using Expansion by Lu Factorization: Vector
       Using The CppAD Test Vector Template Class
       Examples: The CppAD Test Vector Template Class
       Returns Indices that Sort a Vector
       CppAD::vector Template Class: Example and Test
       The CppAD::vector Template Class
       An Error Controller for Gear's Ode Solvers: Vector
       An Arbitrary Order Gear Method: Vector
       An Error Controller for ODE Solvers: Vector
       A 3rd and 4th Order Rosenbrock ODE Solver: Vector
       An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Vector
       Evaluate a Polynomial or its Derivative: Vector
       Obtain Nan or Determine if a Value is Nan: Vector
       Check Simple Vector Concept
       Simple Vector Template Class: Example and Test
       Definition of a Simple Vector
       Run One Speed Test and Return Results: Vector
       Some General Purpose Utilities: Miscellaneous.Simple Vector Template Class
       Check an ADFun Sequence of Operations: Vector
       Hessian: Easy Driver: Vector
       First Order Derivative: Driver Routine: Vector
       First Order Partial Derivative: Driver Routine: Vector
       Jacobian: Driver Routine: Vector
       Any Order Reverse Mode: Vector
       Second Order Reverse Mode: Vector
       First Order Reverse Mode: Vector
       Multiple Directions Forward Mode: Vector
       Multiple Order Forward Mode: Vector
       Second Order Forward Mode: Derivative Values: Vector
       First Order Forward Mode: Derivative Values: Vector
       Zero Order Forward Mode: Function Values: Vector
       User Defined Atomic AD Functions: Examples.Vector Range
       Auto Tools Unix Test and Installation
       Choosing the CppAD Test Vector Template Class
       Including the Eigen Examples and Tests: Test Vector
       Using CMake to Configure CppAD
vector_size Check an ADFun Object For Nan Results: Error Message.vector_size
vectorad Construct an ADFun Object and Stop Recording: VectorAD
         Declare Independent Variables and Start Recording: VectorAD
vectorBool CppAD::vectorBool Class: Example and Test
vectorbase Sparse Hessian: Easy Driver: VectorBase
           Sparse Jacobian: Easy Driver: VectorBase
           Reverse Mode Second Partial Derivative Driver: VectorBase
           Forward Mode Second Partial Derivative Driver: VectorBase
vectorbool The CppAD::vector Template Class: vectorBool
           Using vectorBool Sparsity To Conserve Memory: Example and Test
vectors Using The CppAD Test Vector Template Class: Eigen Vectors
        AD Vectors that Record Index Operations: Example and Test
        AD Vectors that Record Index Operations
vectorset Sparse Hessian: Easy Driver: VectorSet
          Sparse Jacobian: Easy Driver: VectorSet
          Hessian Sparsity Pattern: Forward Mode: VectorSet
          Hessian Sparsity Pattern: Reverse Mode: VectorSet
          Jacobian Sparsity Pattern: Reverse Mode: VectorSet
          Jacobian Sparsity Pattern: Forward Mode: VectorSet
vectorsize Sparse Hessian: Easy Driver: VectorSize
           Sparse Jacobian: Easy Driver: VectorSize
vectorsize_t Reverse Mode Second Partial Derivative Driver: VectorSize_t
             Forward Mode Second Partial Derivative Driver: VectorSize_t
verification exp_eps: Second Order Reverse Sweep: Verification
             exp_eps: Second Order Forward Mode: Verification
             exp_eps: First Order Reverse Sweep: Verification
             exp_eps: First Order Forward Sweep: Verification
             exp_eps: Operation Sequence and Zero Order Forward Sweep: Verification
             exp_2: Second Order Reverse Mode: Verification
             exp_2: Second Order Forward Mode: Verification
             exp_2: First Order Reverse Mode: Verification
             exp_2: First Order Forward Mode: Verification
             exp_2: Operation Sequence and Zero Order Forward Mode: Verification
verify exp_eps: Verify Second Order Reverse Sweep
       exp_eps: Verify Second Order Forward Sweep
       exp_eps: Verify First Order Reverse Sweep
       exp_eps: Verify First Order Forward Sweep
       exp_eps: Verify Zero Order Forward Sweep
       exp_2: Verify Second Order Reverse Sweep
       exp_2: Verify Second Order Forward Sweep
       exp_2: Verify First Order Reverse Sweep
       exp_2: Verify First Order Forward Sweep
       exp_2: Verify Zero Order Forward Sweep
version Microsoft Version of Elapsed Number of Seconds
        Using AD Version of Atomic Function
        Discrete AD Functions: Create AD Version
        Download The CppAD Source Code: Current Version
        cppad-20170000.3: A Package for Differentiation of C++ Algorithms
version) CppAD Speed: Matrix Multiplication (Double Version)
versions Download The CppAD Source Code: Daily Versions
         Download The CppAD Source Code: Monthly Versions
         Download The CppAD Source Code: Release Versions
virtual Atomic Forward Mode
        User Defined Atomic AD Functions: Virtual Functions
vx User Defined Atomic AD Functions: forward.vx
   Atomic Reverse Hessian Sparsity Patterns: Implementation.vx
   Atomic Forward Hessian Sparsity Patterns: Implementation.vx
   Atomic Forward Mode: vx
vy User Defined Atomic AD Functions: forward.vy
   Atomic Forward Mode: vy
W
w Sparse Hessian: Easy Driver: w
  Hessian: Easy Driver: w
  Any Order Reverse Mode: w
  Second Order Reverse Mode: w
  Second Order Reverse Mode: W
  First Order Reverse Mode: w
w(u) Any Order Reverse Mode: Notation.W(u)
w^(k) Any Order Reverse Mode: Notation.w^(k)
warning An Error Controller for Gear's Ode Solvers: Fun.Warning
        An Arbitrary Order Gear Method: Fun.Warning
        A 3rd and 4th Order Rosenbrock ODE Solver: Fun.Warning
        An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Fun.Warning
        AD<Base> Requirements for a CppAD Base Type: API Warning
was Free All Memory That Was Allocated for Use by thread_alloc
when Control When Thread Alloc Retains Memory For Future Use
where Enable use of AD<Base> where Base is std::complex<double>
      Enable use of AD<Base> where Base is double
      Enable use of AD<Base> where Base is float
      Enable use of AD<Base> where Base is Adolc's adouble Type
      Example AD<Base> Where Base Constructor Allocates Memory
windows Choosing The Vector Testing Template Class: MS Windows
        Checking the CppAD Examples and Tests: Check All.Windows
        Download The CppAD Source Code: Windows File Extraction and Testing
wish Nonlinear Programming Using the CppAD Interface to Ipopt: Wish List
     The CppAD Wish List
with zdouble: An AD Base Type With Absolute Zero
     Lu Factor and Solve With Recorded Pivoting: Example and Test
     Lu Factor and Solve with Recorded Pivoting
     Computing a Jacobian With Constants that Change
     Enable Use of Eigen Linear Algebra Package with CppAD
     LuSolve With Complex Arguments: Example and Test
     Using Adolc with Multiple Levels of Taping: Example and Test
     Compare AD with Base Objects: Example and Test
     Compare AD and Base Objects for Nearly Equal
     Bool Valued Operations and Functions with AD Arguments
     Atomic Sparsity with Set Patterns: Example and Test
     Getting Started with Atomic Operations: Example and Test
     Atomic Reverse Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Forward Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Reverse Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Atomic Forward Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
     Interpolation With Retaping: Example and Test
     Interpolation With Out Retaping: Example and Test
work Sparse Hessian: Easy Driver: work
     Sparse Hessian: Easy Driver: p.work
     Sparse Jacobian: Easy Driver: work
     Auto Tools Unix Test and Installation: Work Directory
worker Multi-threading Newton Method Utility Routines
       Multi-threading Sum of 1/i Utility Routines
write AD Output Stream Operator
X
x Jacobian and Hessian of Optimal Values: x
  Computing Jacobian and Hessian of Bender's Reduced Objective: x
  Nonlinear Programming Using the CppAD Interface to Ipopt: solution.x
  Simulate a [0,1] Uniform Random Variate: x
  Evaluate a Function That Has a Sparse Hessian: x
  Evaluate a Function That Has a Sparse Jacobian: x
  Evaluate a Function Defined in Terms of an ODE: x
  Sum Elements of a Matrix Times Itself: x
  Check Gradient of Determinant of 3 by 3 matrix: x
  Check Determinant of 3 by 3 matrix: x
  Speed Testing Sparse Jacobian: x
  Speed Testing Sparse Hessian: x
  Speed Testing the Jacobian of Ode Solution: x
  Speed Testing Derivative of Matrix Multiply: x
  Use Ipopt to Solve a Nonlinear Programming Problem: solution.x
  Use Ipopt to Solve a Nonlinear Programming Problem: fg_eval.x
  An Error Controller for Gear's Ode Solvers: Fun.x
  An Arbitrary Order Gear Method: X
  An Arbitrary Order Gear Method: Fun.x
  A 3rd and 4th Order Rosenbrock ODE Solver: Fun.x
  An Embedded 4th and 5th Order Runge-Kutta ODE Solver: Fun.x
  Invert an LU Factored Equation: X
  Compute Determinant and Solve Linear Equations: X
  The Integer Power Function: x
  Check Simple Vector Concept: x, y
  Determine if Two Values Are Nearly Equal: x
  Check an ADFun Sequence of Operations: x
  Check an ADFun Sequence of Operations: g.x
  Sparse Hessian: Easy Driver: x
  Sparse Jacobian: Easy Driver: x
  Reverse Mode Second Partial Derivative Driver: x
  Forward Mode Second Partial Derivative Driver: x
  Hessian: Easy Driver: x
  First Order Derivative: Driver Routine: x
  First Order Partial Derivative: Driver Routine: x
  Jacobian: Driver Routine: x
  Hessian Sparsity Pattern: Forward Mode: x
  Hessian Sparsity Pattern: Reverse Mode: x
  Jacobian Sparsity Pattern: Reverse Mode: x
  Jacobian Sparsity Pattern: Forward Mode: x
  First Order Reverse Mode: x
  Stop Recording and Store Operation Sequence: x
  Construct an ADFun Object and Stop Recording: x
  Declare Independent Variables and Start Recording: x
  Base Type Requirements for Hash Coding Values: x
  AD Vectors that Record Index Operations: AD Indexing.x
  Check if Two Value are Identically Equal: x
  Is an AD Object a Parameter or Variable: x
  AD Boolean Functions: x
  Compare AD and Base Objects for Nearly Equal: x
  AD Binary Comparison Operators: x
  Tan and Tanh as User Atomic Operations: Example and Test: Use Atomic Function.Large x Values
  Atomic Reverse Hessian Sparsity Patterns: u.x
  Atomic Forward Hessian Sparsity Patterns: Implementation.x
  Atomic Reverse Jacobian Sparsity Patterns: Implementation.x
  Atomic Forward Jacobian Sparsity Patterns: Implementation.x
  Discrete AD Functions: x
  The AD Power Function: x
  AD Two Argument Inverse Tangent Function: x
  The Sign: sign: x, y
  The Logarithm of One Plus Argument: log1p: x, y
  The Exponential Function Minus One: expm1: x, y
  The Error Function: x, y
  The Inverse Hyperbolic Tangent Function: atanh: x, y
  The Inverse Hyperbolic Sine Function: asinh: x, y
  The Inverse Hyperbolic Cosine Function: acosh: x, y
  AD Absolute Value Functions: abs, fabs: x, y
  The Hyperbolic Tangent Function: tanh: x, y
  The Tangent Function: tan: x, y
  The Square Root Function: sqrt: x, y
  The Hyperbolic Sine Function: sinh: x, y
  The Sine Function: sin: x, y
  The Base 10 Logarithm Function: log10: x, y
  The Exponential Function: log: x, y
  The Exponential Function: exp: x, y
  The Hyperbolic Cosine Function: cosh: x, y
  The Cosine Function: cos: x, y
  Inverse Tangent Function: atan: x, y
  Inverse Sine Function: asin: x, y
  Inverse Sine Function: acos: x, y
  AD Computed Assignment Operators: x
  AD Binary Arithmetic Operators: x
  AD Unary Minus Operator: x
  AD Unary Plus Operator: x
  Convert an AD Variable to a Parameter: x
  AD Output Stream Operator: x
  AD Output Stream Operator: x
  Convert From AD to Integer: x
  Convert From an AD Type to its Base Type: x
  AD Assignment Operator: x
  AD Constructors: x
  An Epsilon Accurate Exponential Approximation: x
  Second Order Exponential Approximation: x
x(t Any Order Reverse Mode: Notation.X(t, u)
x(t) Multiple Directions Forward Mode: X(t)
     Multiple Order Forward Mode: X(t)
x) Printing AD Values During Forward Mode: f.Forward(0, x)
x0 Second Order Forward Mode: Derivative Values: x0
   First Order Forward Mode: Derivative Values: x0
   Zero Order Forward Mode: Function Values: x0
x1 Second Order Forward Mode: Derivative Values: x1
   First Order Forward Mode: Derivative Values: x1
x2 Second Order Forward Mode: Derivative Values: x2
x^(k) Second Order Reverse Mode: x^(k)
x_1 Atomic Reverse Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
    Atomic Forward Hessian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
    Atomic Reverse Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
    Atomic Forward Jacobian Sparsity: Example and Test: Test with x_1 Both a Variable and a Parameter
x_i Nonlinear Programming Using the CppAD Interface to Ipopt: x_i
x_l Nonlinear Programming Using the CppAD Interface to Ipopt: x_l
x_u Nonlinear Programming Using the CppAD Interface to Ipopt: x_u
xf An Error Controller for Gear's Ode Solvers: xf
   An Error Controller for ODE Solvers: xf
   A 3rd and 4th Order Rosenbrock ODE Solver: xf
   An Embedded 4th and 5th Order Runge-Kutta ODE Solver: xf
xi Use Ipopt to Solve a Nonlinear Programming Problem: xi
   An Error Controller for Gear's Ode Solvers: xi
   An Error Controller for ODE Solvers: xi
   A 3rd and 4th Order Rosenbrock ODE Solver: xi
   An Embedded 4th and 5th Order Runge-Kutta ODE Solver: xi
xl Use Ipopt to Solve a Nonlinear Programming Problem: xl
xlow Multi-threading Newton Method Utility Routines: xlow
     A Multi-Threaded Newton's Method: xlow
xout Multi-threading Newton Method Utility Routines: multi_newton_combine.xout
     A Multi-Threaded Newton's Method: xout
xq Multiple Directions Forward Mode: xq
   Multiple Order Forward Mode: xq
xu Use Ipopt to Solve a Nonlinear Programming Problem: xu
xup Multi-threading Newton Method Utility Routines: xlow.xup
    A Multi-Threaded Newton's Method: xup
Y
y(t Any Order Reverse Mode: Notation.Y(t, u)
y(t) Tangent and Hyperbolic Tangent Reverse Mode Theory: Eliminating Y(t)
     Multiple Directions Forward Mode: Y(t)
     Multiple Order Forward Mode: Y(t)
y0 Zero Order Forward Mode: Function Values: y0
y2 Second Order Forward Mode: Derivative Values: y2
year Changes and Additions to CppAD: This Year
years Changes and Additions to CppAD: Previous Years
your Your License for the CppAD Software
     Creating Your Own Interface to an ADFun Object
yq Multiple Directions Forward Mode: yq
   Multiple Order Forward Mode: yq
Z
z Sum Elements of a Matrix Times Itself: z
  Speed Testing Second Derivative of a Polynomial: z
  Speed Testing Derivative of Matrix Multiply: z
  Evaluate a Polynomial or its Derivative: z
  The Integer Power Function: z
  Obtain Nan or Determine if a Value is Nan: nan(zero).z
  The AD Power Function: z
  AD Binary Arithmetic Operators: z
z(t) Error Function Reverse Mode Theory: Order Zero Z(t)
     Error Function Reverse Mode Theory: Positive Orders Z(t)
     Tangent and Hyperbolic Tangent Reverse Mode Theory: Order Zero Z(t)
     Tangent and Hyperbolic Tangent Reverse Mode Theory: Positive Orders Z(t)
z_l Nonlinear Programming Using the CppAD Interface to Ipopt: solution.z_l
z_u Nonlinear Programming Using the CppAD Interface to Ipopt: solution.z_u
zdouble: zdouble: Example and Test
         zdouble: An AD Base Type With Absolute Zero
zero zdouble: An AD Base Type With Absolute Zero: Absolute Zero
     zdouble: An AD Base Type With Absolute Zero
     Comparison Changes During Zero Order Forward Mode
     Error Function Reverse Mode Theory: Order Zero Z(t)
     Tangent and Hyperbolic Tangent Reverse Mode Theory: Order Zero Z(t)
     Comparison Changes Between Taping and Zero Order Forward
     Multiple Directions Forward Mode: Zero Order
     Multiple Order Forward Mode: Zero Order
     Zero Order Forward Mode: Function Values
     AD<Base> Requirements for a CppAD Base Type: Absolute Zero, azmul
     AD Absolute Zero Multiplication: Example and Test
     Absolute Zero Multiplication
     Print During Zero Order Forward Mode: Example and Test
     exp_eps: Verify Zero Order Forward Sweep
     exp_eps: Second Order Forward Mode: Operation Sequence.Zero
     exp_eps: First Order Forward Sweep: Operation Sequence.Zero Order
     exp_eps: Operation Sequence and Zero Order Forward Sweep: Operation Sequence.Zero Order
     exp_eps: Operation Sequence and Zero Order Forward Sweep
     exp_2: Verify Zero Order Forward Sweep
     exp_2: Second Order Forward Mode: Operation Sequence.Zero
     exp_2: First Order Forward Mode: Operation Sequence.Zero Order
     exp_2: Operation Sequence and Zero Order Forward Mode: Operation Sequence.Zero Order
     exp_2: Operation Sequence and Zero Order Forward Mode: Zero Order Expansion
     exp_2: Operation Sequence and Zero Order Forward Mode
zl Use Ipopt to Solve a Nonlinear Programming Problem: solution.zl
zu Use Ipopt to Solve a Nonlinear Programming Problem: solution.zu
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cppad-20170000.3: A Package for Differentiation of C++ Algorithms

Syntax
# include <cppad/cppad.hpp>

Introduction
We refer to the step by step conversion from an algorithm that computes function values to an algorithm that computes derivative values as Algorithmic Differentiation (often referred to as Automatic Differentiation.) Given a C++ algorithm that computes function values, CppAD generates an algorithm that computes its derivative values. A brief introduction to Algorithmic Differentiation can be found in wikipedia . The web site autodiff.org is dedicated to research about, and promoting the use of, AD.
  1. CppAD uses operator overloading to compute derivatives of algorithms defined in C++. It is distributed by the COIN-OR Foundation with the Eclipse Public License EPL-1.0 or the GNU General Public License GPL-3.0 . Testing and installation is supported for Unix, Microsoft, and Apple operating systems. Extensive user and developer documentation is included.
  2. An AD of Base operation sequence is stored as an AD function object which can evaluate function values and derivatives. Arbitrary order forward and reverse mode derivative calculations can be preformed on the operation sequence. Logical comparisons can be included in an operation sequence using AD conditional expressions . Evaluation of user defined unary discrete functions can also be included in the sequence of operations; i.e., functions that depend on the independent variables but which have identically zero derivatives (e.g., a step function).
  3. Derivatives of functions that are defined in terms of other derivatives can be computed using multiple levels of AD; see mul_level.cpp for a simple example and mul_level_ode.cpp for a more realistic example. To this end, CppAD can also be used with other AD types; for example see mul_level_adolc_ode.cpp .
  4. A set of programs for doing speed comparisons between Adolc , CppAD, Fadbad , and Sacado are included.
  5. Includes a set of C++ utilities that are useful for general operator overloaded numerical method. Allows for replacement of the testvector template vector class which is used for extensive testing; for example, you can do your testing with the uBlas template vector class.
  6. See whats_new for a list of recent extensions and bug fixes.
You can find out about other algorithmic differentiation tools and about algorithmic differentiation in general at the following web sites: wikipedia , autodiff.org .

Example
The file get_started.cpp contains an example and test of using CppAD to compute the derivative of a polynomial. There are many other examples .

Include File
The following include directive
     # include <cppad/cppad.hpp>
includes the CppAD package for the rest of the current compilation unit.

Preprocessor Symbols
All the preprocessor symbols used by CppAD begin with eight CppAD or CPPAD_.

Namespace
All of the functions and objects defined by CppAD are in the CppAD namespace; for example, you can access the AD types as
     size_t n = 2;
     CppAD::vector< CppAD::AD<Base> > x(n)
You can abbreviate access to one object or function a using command of the form
     using CppAD::AD
     CppAD::vector< AD<Base> > x(n)
You can abbreviate access to all CppAD objects and functions with a command of the form
     using namespace CppAD
     vector< AD<Base> > x(n)
If you include other namespaces in a similar manner, this can cause naming conflicts.

Contents
_contentsTable of Contents
InstallCppAD Download, Test, and Install Instructions
IntroductionAn Introduction by Example to Algorithmic Differentiation
ADAD Objects
ADFunADFun Objects
preprocessorCppAD API Preprocessor Symbols
multi_threadUsing CppAD in a Multi-Threading Environment
utilitySome General Purpose Utilities
ipopt_solveUse Ipopt to Solve a Nonlinear Programming Problem
ExampleExamples
speedSpeed Test an Operator Overloading AD Package
AppendixAppendix
_referenceAlphabetic Listing of Cross Reference Tags
_indexKeyword Index
_searchSearch This Web Site
_externalExternal Internet References
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Table of Contents

cppad-20170000.3: A Package for Differentiation of C++ Algorithms
cppad-20170000.3: A Package for Differentiation of C++ Algorithms
    Table of Contents
     CppAD Download, Test, and Install Instructions
    CppAD Download, Test, and Install Instructions
        Download The CppAD Source Code
         Using CMake to Configure CppAD
        Using CMake to Configure CppAD
             Including the ADOL-C Examples and Tests
            Including the ADOL-C Examples and Tests
                Download and Install Adolc in Build Directory
             Including the ColPack Sparsity Calculations
            Including the ColPack Sparsity Calculations
                Using ColPack: Example and Test
                Using ColPack: Example and Test
                Download and Install ColPack in Build Directory
             Including the Eigen Examples and Tests
            Including the Eigen Examples and Tests
                Download and Install Eigen in Build Directory
             Including the FADBAD Speed Tests
            Including the FADBAD Speed Tests
                Download and Install Fadbad in Build Directory
             Including the cppad_ipopt Library and Tests
            Including the cppad_ipopt Library and Tests
                Download and Install Ipopt in Build Directory
             Including the Sacado Speed Tests
            Including the Sacado Speed Tests
                Download and Install Sacado in Build Directory
            Choosing the CppAD Test Vector Template Class
        Checking the CppAD Examples and Tests
        CppAD pkg-config Files
        Auto Tools Unix Test and Installation
     An Introduction by Example to Algorithmic Differentiation
    An Introduction by Example to Algorithmic Differentiation
        Getting Started Using CppAD to Compute Derivatives
         Second Order Exponential Approximation
        Second Order Exponential Approximation
            exp_2: Implementation
            exp_2: Test
             exp_2: Operation Sequence and Zero Order Forward Mode
            exp_2: Operation Sequence and Zero Order Forward Mode
                exp_2: Verify Zero Order Forward Sweep
             exp_2: First Order Forward Mode
            exp_2: First Order Forward Mode
                exp_2: Verify First Order Forward Sweep
             exp_2: First Order Reverse Mode
            exp_2: First Order Reverse Mode
                exp_2: Verify First Order Reverse Sweep
             exp_2: Second Order Forward Mode
            exp_2: Second Order Forward Mode
                exp_2: Verify Second Order Forward Sweep
             exp_2: Second Order Reverse Mode
            exp_2: Second Order Reverse Mode
                exp_2: Verify Second Order Reverse Sweep
            exp_2: CppAD Forward and Reverse Sweeps
         An Epsilon Accurate Exponential Approximation
        An Epsilon Accurate Exponential Approximation
            exp_eps: Implementation
            exp_eps: Test of exp_eps
             exp_eps: Operation Sequence and Zero Order Forward Sweep
            exp_eps: Operation Sequence and Zero Order Forward Sweep
                exp_eps: Verify Zero Order Forward Sweep
             exp_eps: First Order Forward Sweep
            exp_eps: First Order Forward Sweep
                exp_eps: Verify First Order Forward Sweep
             exp_eps: First Order Reverse Sweep
            exp_eps: First Order Reverse Sweep
                exp_eps: Verify First Order Reverse Sweep
             exp_eps: Second Order Forward Mode
            exp_eps: Second Order Forward Mode
                exp_eps: Verify Second Order Forward Sweep
             exp_eps: Second Order Reverse Sweep
            exp_eps: Second Order Reverse Sweep
                exp_eps: Verify Second Order Reverse Sweep
            exp_eps: CppAD Forward and Reverse Sweeps
        Correctness Tests For Exponential Approximation in Introduction
     AD Objects
    AD Objects
         AD Constructors
        AD Constructors
            AD Constructors: Example and Test
         AD Assignment Operator
        AD Assignment Operator
            AD Assignment: Example and Test
         Conversion and I/O of AD Objects
        Conversion and I/O of AD Objects
             Convert From an AD Type to its Base Type
            Convert From an AD Type to its Base Type
                Convert From AD to its Base Type: Example and Test
             Convert From AD to Integer
            Convert From AD to Integer
                Convert From AD to Integer: Example and Test
            Convert An AD or Base Type to String
             AD Output Stream Operator
            AD Output Stream Operator
                AD Output Operator: Example and Test
             AD Output Stream Operator
            AD Output Stream Operator
                AD Output Operator: Example and Test
             Printing AD Values During Forward Mode
            Printing AD Values During Forward Mode
                Printing During Forward Mode: Example and Test
                Print During Zero Order Forward Mode: Example and Test
             Convert an AD Variable to a Parameter
            Convert an AD Variable to a Parameter
                Convert an AD Variable to a Parameter: Example and Test
         AD Valued Operations and Functions
        AD Valued Operations and Functions
             AD Arithmetic Operators and Computed Assignments
            AD Arithmetic Operators and Computed Assignments
                 AD Unary Plus Operator
                AD Unary Plus Operator
                    AD Unary Plus Operator: Example and Test
                 AD Unary Minus Operator
                AD Unary Minus Operator
                    AD Unary Minus Operator: Example and Test
                 AD Binary Arithmetic Operators
                AD Binary Arithmetic Operators
                    AD Binary Addition: Example and Test
                    AD Binary Subtraction: Example and Test
                    AD Binary Multiplication: Example and Test
                    AD Binary Division: Example and Test
                 AD Computed Assignment Operators
                AD Computed Assignment Operators
                    AD Computed Assignment Addition: Example and Test
                    AD Computed Assignment Subtraction: Example and Test
                    AD Computed Assignment Multiplication: Example and Test
                    AD Computed Assignment Division: Example and Test
             The Unary Standard Math Functions
            The Unary Standard Math Functions
                 Inverse Sine Function: acos
                Inverse Sine Function: acos
                    The AD acos Function: Example and Test
                 Inverse Sine Function: asin
                Inverse Sine Function: asin
                    The AD asin Function: Example and Test
                 Inverse Tangent Function: atan
                Inverse Tangent Function: atan
                    The AD atan Function: Example and Test
                 The Cosine Function: cos
                The Cosine Function: cos
                    The AD cos Function: Example and Test
                 The Hyperbolic Cosine Function: cosh
                The Hyperbolic Cosine Function: cosh
                    The AD cosh Function: Example and Test
                 The Exponential Function: exp
                The Exponential Function: exp
                    The AD exp Function: Example and Test
                 The Exponential Function: log
                The Exponential Function: log
                    The AD log Function: Example and Test
                 The Base 10 Logarithm Function: log10
                The Base 10 Logarithm Function: log10
                    The AD log10 Function: Example and Test
                 The Sine Function: sin
                The Sine Function: sin
                    The AD sin Function: Example and Test
                 The Hyperbolic Sine Function: sinh
                The Hyperbolic Sine Function: sinh
                    The AD sinh Function: Example and Test
                 The Square Root Function: sqrt
                The Square Root Function: sqrt
                    The AD sqrt Function: Example and Test
                 The Tangent Function: tan
                The Tangent Function: tan
                    The AD tan Function: Example and Test
                 The Hyperbolic Tangent Function: tanh
                The Hyperbolic Tangent Function: tanh
                    The AD tanh Function: Example and Test
                 AD Absolute Value Functions: abs, fabs
                AD Absolute Value Functions: abs, fabs
                    AD Absolute Value Function: Example and Test
                 The Inverse Hyperbolic Cosine Function: acosh
                The Inverse Hyperbolic Cosine Function: acosh
                    The AD acosh Function: Example and Test
                 The Inverse Hyperbolic Sine Function: asinh
                The Inverse Hyperbolic Sine Function: asinh
                    The AD asinh Function: Example and Test
                 The Inverse Hyperbolic Tangent Function: atanh
                The Inverse Hyperbolic Tangent Function: atanh
                    The AD atanh Function: Example and Test
                 The Error Function
                The Error Function
                    The AD erf Function: Example and Test
                 The Exponential Function Minus One: expm1
                The Exponential Function Minus One: expm1
                    The AD exp Function: Example and Test
                 The Logarithm of One Plus Argument: log1p
                The Logarithm of One Plus Argument: log1p
                    The AD log1p Function: Example and Test
                 The Sign: sign
                The Sign: sign
                    Sign Function: Example and Test
             The Binary Math Functions
            The Binary Math Functions
                 AD Two Argument Inverse Tangent Function
                AD Two Argument Inverse Tangent Function
                    The AD atan2 Function: Example and Test
                 The AD Power Function
                The AD Power Function
                    The AD Power Function: Example and Test
                 Absolute Zero Multiplication
                Absolute Zero Multiplication
                    AD Absolute Zero Multiplication: Example and Test
             AD Conditional Expressions
            AD Conditional Expressions
                Conditional Expressions: Example and Test
             Discrete AD Functions
            Discrete AD Functions
                Taping Array Index Operation: Example and Test
                Interpolation With Out Retaping: Example and Test
                Interpolation With Retaping: Example and Test
             Numeric Limits For an AD and Base Types
            Numeric Limits For an AD and Base Types
                Numeric Limits: Example and Test
             Atomic AD Functions
            Atomic AD Functions
                 Checkpointing Functions
                Checkpointing Functions
                    Simple Checkpointing: Example and Test
                    Atomic Operations and Multiple-Levels of AD: Example and Test
                    Checkpointing an ODE Solver: Example and Test
                    Checkpointing an Extended ODE Solver: Example and Test
                 User Defined Atomic AD Functions
                User Defined Atomic AD Functions
                    Atomic Function Constructor
                    Set Atomic Function Options
                    Using AD Version of Atomic Function
                     Atomic Forward Mode
                    Atomic Forward Mode
                        Atomic Forward: Example and Test
                     Atomic Reverse Mode
                    Atomic Reverse Mode
                        Atomic Reverse: Example and Test
                     Atomic Forward Jacobian Sparsity Patterns
                    Atomic Forward Jacobian Sparsity Patterns
                        Atomic Forward Jacobian Sparsity: Example and Test
                     Atomic Reverse Jacobian Sparsity Patterns
                    Atomic Reverse Jacobian Sparsity Patterns
                        Atomic Reverse Jacobian Sparsity: Example and Test
                     Atomic Forward Hessian Sparsity Patterns
                    Atomic Forward Hessian Sparsity Patterns
                        Atomic Forward Hessian Sparsity: Example and Test
                     Atomic Reverse Hessian Sparsity Patterns
                    Atomic Reverse Hessian Sparsity Patterns
                        Atomic Reverse Hessian Sparsity: Example and Test
                    Free Static Variables
                    Getting Started with Atomic Operations: Example and Test
                    Atomic Euclidean Norm Squared: Example and Test
                    Reciprocal as an Atomic Operation: Example and Test
                    Atomic Sparsity with Set Patterns: Example and Test
                    Tan and Tanh as User Atomic Operations: Example and Test
                     Atomic Eigen Matrix Multiply: Example and Test
                    Atomic Eigen Matrix Multiply: Example and Test
                        Atomic Eigen Matrix Multiply Class
                     Atomic Eigen Matrix Inverse: Example and Test
                    Atomic Eigen Matrix Inverse: Example and Test
                        Atomic Eigen Matrix Inversion Class
                     Atomic Eigen Cholesky Factorization: Example and Test
                    Atomic Eigen Cholesky Factorization: Example and Test
                        AD Theory for Cholesky Factorization
                        Atomic Eigen Cholesky Factorization Class
                     User Atomic Matrix Multiply: Example and Test
                    User Atomic Matrix Multiply: Example and Test
                        Matrix Multiply as an Atomic Operation
         Bool Valued Operations and Functions with AD Arguments
        Bool Valued Operations and Functions with AD Arguments
             AD Binary Comparison Operators
            AD Binary Comparison Operators
                AD Binary Comparison Operators: Example and Test
             Compare AD and Base Objects for Nearly Equal
            Compare AD and Base Objects for Nearly Equal
                Compare AD with Base Objects: Example and Test
             AD Boolean Functions
            AD Boolean Functions
                AD Boolean Functions: Example and Test
             Is an AD Object a Parameter or Variable
            Is an AD Object a Parameter or Variable
                AD Parameter and Variable Functions: Example and Test
             Check if Two Value are Identically Equal
            Check if Two Value are Identically Equal
                EqualOpSeq: Example and Test
         AD Vectors that Record Index Operations
        AD Vectors that Record Index Operations
            AD Vectors that Record Index Operations: Example and Test
         AD<Base> Requirements for a CppAD Base Type
        AD<Base> Requirements for a CppAD Base Type
            Required Base Class Member Functions
            Base Type Requirements for Conditional Expressions
            Base Type Requirements for Identically Equal Comparisons
            Base Type Requirements for Ordered Comparisons
            Base Type Requirements for Standard Math Functions
            Base Type Requirements for Numeric Limits
            Extending to_string To Another Floating Point Type
            Base Type Requirements for Hash Coding Values
             Example AD Base Types That are not AD<OtherBase>
            Example AD Base Types That are not AD<OtherBase>
                Example AD<Base> Where Base Constructor Allocates Memory
                Using a User Defined AD Base Type: Example and Test
                 Enable use of AD<Base> where Base is Adolc's adouble Type
                Enable use of AD<Base> where Base is Adolc's adouble Type
                    Using Adolc with Multiple Levels of Taping: Example and Test
                Enable use of AD<Base> where Base is float
                Enable use of AD<Base> where Base is double
                 Enable use of AD<Base> where Base is std::complex<double>
                Enable use of AD<Base> where Base is std::complex<double>
                    Complex Polynomial: Example and Test
     ADFun Objects
    ADFun Objects
         Declare Independent Variables and Start Recording
        Declare Independent Variables and Start Recording
            Independent and ADFun Constructor: Example and Test
         Construct an ADFun Object and Stop Recording
        Construct an ADFun Object and Stop Recording
            ADFun Assignment: Example and Test
        Stop Recording and Store Operation Sequence
         Abort Recording of an Operation Sequence
        Abort Recording of an Operation Sequence
            Abort Current Recording: Example and Test
         ADFun Sequence Properties
        ADFun Sequence Properties
            ADFun Sequence Properties: Example and Test
         Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
        Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
             Forward Mode
            Forward Mode
                Zero Order Forward Mode: Function Values
                First Order Forward Mode: Derivative Values
                Second Order Forward Mode: Derivative Values
                 Multiple Order Forward Mode
                Multiple Order Forward Mode
                    Forward Mode: Example and Test
                    Forward Mode: Example and Test of Multiple Orders
                 Multiple Directions Forward Mode
                Multiple Directions Forward Mode
                    Forward Mode: Example and Test of Multiple Directions
                Number Taylor Coefficient Orders Currently Stored
                 Comparison Changes Between Taping and Zero Order Forward
                Comparison Changes Between Taping and Zero Order Forward
                    CompareChange and Re-Tape: Example and Test
                 Controlling Taylor Coefficients Memory Allocation
                Controlling Taylor Coefficients Memory Allocation
                    Controlling Taylor Coefficient Memory Allocation: Example and Test
                 Number of Variables that Can be Skipped
                Number of Variables that Can be Skipped
                    Number of Variables That Can be Skipped: Example and Test
             Reverse Mode
            Reverse Mode
                 First Order Reverse Mode
                First Order Reverse Mode
                    First Order Reverse Mode: Example and Test
                 Second Order Reverse Mode
                Second Order Reverse Mode
                    Second Order Reverse ModeExample and Test
                    Hessian Times Direction: Example and Test
                 Any Order Reverse Mode
                Any Order Reverse Mode
                    Third Order Reverse Mode: Example and Test
                    Reverse Mode General Case (Checkpointing): Example and Test
             Calculating Sparsity Patterns
            Calculating Sparsity Patterns
                 Jacobian Sparsity Pattern: Forward Mode
                Jacobian Sparsity Pattern: Forward Mode
                    Forward Mode Jacobian Sparsity: Example and Test
                 Jacobian Sparsity Pattern: Reverse Mode
                Jacobian Sparsity Pattern: Reverse Mode
                    Reverse Mode Jacobian Sparsity: Example and Test
                Computing Dependency: Example and Test
                 Hessian Sparsity Pattern: Reverse Mode
                Hessian Sparsity Pattern: Reverse Mode
                    Reverse Mode Hessian Sparsity: Example and Test
                    Sparsity Patterns For a Subset of Variables: Example and Test
                 Hessian Sparsity Pattern: Forward Mode
                Hessian Sparsity Pattern: Forward Mode
                    Forward Mode Hessian Sparsity: Example and Test
                Using vectorBool Sparsity To Conserve Memory: Example and Test
         First and Second Derivatives: Easy Drivers
        First and Second Derivatives: Easy Drivers
             Jacobian: Driver Routine
            Jacobian: Driver Routine
                Jacobian: Example and Test
             First Order Partial Derivative: Driver Routine
            First Order Partial Derivative: Driver Routine
                First Order Partial Driver: Example and Test
             First Order Derivative: Driver Routine
            First Order Derivative: Driver Routine
                First Order Derivative Driver: Example and Test
             Hessian: Easy Driver
            Hessian: Easy Driver
                Hessian: Example and Test
                Hessian of Lagrangian and ADFun Default Constructor: Example and Test
             Forward Mode Second Partial Derivative Driver
            Forward Mode Second Partial Derivative Driver
                Subset of Second Order Partials: Example and Test
             Reverse Mode Second Partial Derivative Driver
            Reverse Mode Second Partial Derivative Driver
                Second Partials Reverse Driver: Example and Test
             Sparse Jacobian: Easy Driver
            Sparse Jacobian: Easy Driver
                Sparse Jacobian: Example and Test
             Sparse Hessian: Easy Driver
            Sparse Hessian: Easy Driver
                Sparse Hessian: Example and Test
                Computing Sparse Hessian for a Subset of Variables
                Sparse Hessian on Subset of Variables: Example and Test
         Check an ADFun Sequence of Operations
        Check an ADFun Sequence of Operations
            ADFun Check and Re-Tape: Example and Test
         Optimize an ADFun Object Tape
        Optimize an ADFun Object Tape
            Example Optimization and Forward Activity Analysis
            Example Optimization and Reverse Activity Analysis
            Example Optimization and Comparison Operators
            Example Optimization and Print Forward Operators
            Example Optimization and Conditional Expressions
            Example Optimization and Nested Conditional Expressions
            Example Optimization and Cumulative Sum Operations
         Check an ADFun Object For Nan Results
        Check an ADFun Object For Nan Results
            ADFun Checking For Nan: Example and Test
    CppAD API Preprocessor Symbols
     Using CppAD in a Multi-Threading Environment
    Using CppAD in a Multi-Threading Environment
        Enable AD Calculations During Parallel Mode
         Run Multi-Threading Examples and Speed Tests
        Run Multi-Threading Examples and Speed Tests
            A Simple OpenMP Example and Test
            A Simple Boost Thread Example and Test
            A Simple Parallel Pthread Example and Test
            A Simple OpenMP AD: Example and Test
            A Simple Boost Threading AD: Example and Test
            A Simple pthread AD: Example and Test
            Using a Team of AD Threads: Example and Test
             Multi-Threaded Implementation of Summation of 1/i
            Multi-Threaded Implementation of Summation of 1/i
                Timing Test of Multi-Threaded Summation of 1/i
                Multi-threading Sum of 1/i Utility Routines
             A Multi-Threaded Newton's Method
            A Multi-Threaded Newton's Method
                Timing Test of Multi-Threaded Newton Method
                Multi-threading Newton Method Utility Routines
             Specifications for A Team of AD Threads
            Specifications for A Team of AD Threads
                OpenMP Implementation of a Team of AD Threads
                Boost Thread Implementation of a Team of AD Threads
                Pthread Implementation of a Team of AD Threads
     Some General Purpose Utilities
    Some General Purpose Utilities
         Replacing the CppAD Error Handler
        Replacing the CppAD Error Handler
            Replacing The CppAD Error Handler: Example and Test
            CppAD Assertions During Execution
         Determine if Two Values Are Nearly Equal
        Determine if Two Values Are Nearly Equal
            NearEqual Function: Example and Test
         Run One Speed Test and Return Results
        Run One Speed Test and Return Results
            speed_test: Example and test
         Run One Speed Test and Print Results
        Run One Speed Test and Print Results
            Example Use of SpeedTest
         Determine Amount of Time to Execute a Test
        Determine Amount of Time to Execute a Test
             Returns Elapsed Number of Seconds
            Returns Elapsed Number of Seconds
                Elapsed Seconds: Example and Test
            time_test: Example and test
         Definition of a Numeric Type
        Definition of a Numeric Type
            The NumericType: Example and Test
         Check NumericType Class Concept
        Check NumericType Class Concept
            The CheckNumericType Function: Example and Test
         Definition of a Simple Vector
        Definition of a Simple Vector
            Simple Vector Template Class: Example and Test
         Check Simple Vector Concept
        Check Simple Vector Concept
            The CheckSimpleVector Function: Example and Test
         Obtain Nan or Determine if a Value is Nan
        Obtain Nan or Determine if a Value is Nan
            nan: Example and Test
         The Integer Power Function
        The Integer Power Function
            The Pow Integer Exponent: Example and Test
         Evaluate a Polynomial or its Derivative
        Evaluate a Polynomial or its Derivative
            Polynomial Evaluation: Example and Test
            Source: Poly
         Compute Determinants and Solve Equations by LU Factorization
        Compute Determinants and Solve Equations by LU Factorization
             Compute Determinant and Solve Linear Equations
            Compute Determinant and Solve Linear Equations
                LuSolve With Complex Arguments: Example and Test
                Source: LuSolve
             LU Factorization of A Square Matrix
            LU Factorization of A Square Matrix
                LuFactor: Example and Test
                Source: LuFactor
             Invert an LU Factored Equation
            Invert an LU Factored Equation
                LuInvert: Example and Test
                Source: LuInvert
         One DimensionalRomberg Integration
        One DimensionalRomberg Integration
            One Dimensional Romberg Integration: Example and Test
         Multi-dimensional Romberg Integration
        Multi-dimensional Romberg Integration
            One Dimensional Romberg Integration: Example and Test
         An Embedded 4th and 5th Order Runge-Kutta ODE Solver
        An Embedded 4th and 5th Order Runge-Kutta ODE Solver
            Runge45: Example and Test
            Runge45: Example and Test
         A 3rd and 4th Order Rosenbrock ODE Solver
        A 3rd and 4th Order Rosenbrock ODE Solver
            Rosen34: Example and Test
         An Error Controller for ODE Solvers
        An Error Controller for ODE Solvers
            OdeErrControl: Example and Test
            OdeErrControl: Example and Test Using Maxabs Argument
         An Arbitrary Order Gear Method
        An Arbitrary Order Gear Method
            OdeGear: Example and Test
         An Error Controller for Gear's Ode Solvers
        An Error Controller for Gear's Ode Solvers
            OdeGearControl: Example and Test
         The CppAD::vector Template Class
        The CppAD::vector Template Class
            CppAD::vector Template Class: Example and Test
            CppAD::vectorBool Class: Example and Test
         A Fast Multi-Threading Memory Allocator
        A Fast Multi-Threading Memory Allocator
            Fast Multi-Threading Memory Allocator: Example and Test
            Setup thread_alloc For Use in Multi-Threading Environment
            Get Number of Threads
            Is The Current Execution in Parallel Mode
            Get the Current Thread Number
            Get At Least A Specified Amount of Memory
            Return Memory to thread_alloc
            Free Memory Currently Available for Quick Use by a Thread
            Control When Thread Alloc Retains Memory For Future Use
            Amount of Memory a Thread is Currently Using
            Amount of Memory Available for Quick Use by a Thread
            Allocate An Array and Call Default Constructor for its Elements
            Deallocate An Array and Call Destructor for its Elements
            Free All Memory That Was Allocated for Use by thread_alloc
         Returns Indices that Sort a Vector
        Returns Indices that Sort a Vector
            Index Sort: Example and Test
         Convert Certain Types to a String
        Convert Certain Types to a String
            to_string: Example and Test
         Union of Standard Sets
        Union of Standard Sets
            Set Union: Example and Test
     Use Ipopt to Solve a Nonlinear Programming Problem
    Use Ipopt to Solve a Nonlinear Programming Problem
        Nonlinear Programming Using CppAD and Ipopt: Example and Test
        Nonlinear Programming Retaping: Example and Test
        ODE Inverse Problem Definitions: Source Code
     Examples
    Examples
         General Examples
        General Examples
            Creating Your Own Interface to an ADFun Object
            Example and Test Linking CppAD to Languages Other than C++
            Differentiate Conjugate Gradient Algorithm: Example and Test
             Enable Use of Eigen Linear Algebra Package with CppAD
            Enable Use of Eigen Linear Algebra Package with CppAD
                Source Code for eigen_plugin.hpp
                Using Eigen Arrays: Example and Test
                Using Eigen To Compute Determinant: Example and Test
            Gradient of Determinant Using Expansion by Minors: Example and Test
            Gradient of Determinant Using LU Factorization: Example and Test
            Interfacing to C: Example and Test
            Gradient of Determinant Using Expansion by Minors: Example and Test
            Gradient of Determinant Using Lu Factorization: Example and Test
             Using Multiple Levels of AD
            Using Multiple Levels of AD
                Multiple Level of AD: Example and Test
                Computing a Jacobian With Constants that Change
            A Stiff Ode: Example and Test
            Taylor's Ode Solver: A Multi-Level AD Example and Test
            Taylor's Ode Solver: A Multi-Level Adolc Example and Test
            Taylor's Ode Solver: An Example and Test
            Example Differentiating a Stack Machine Interpreter
         Utility Routines used by CppAD Examples
        Utility Routines used by CppAD Examples
            CppAD Examples and Tests
            Run the Speed Examples
             Lu Factor and Solve with Recorded Pivoting
            Lu Factor and Solve with Recorded Pivoting
                Lu Factor and Solve With Recorded Pivoting: Example and Test
        List of All the CppAD Examples
        Using The CppAD Test Vector Template Class
     Speed Test an Operator Overloading AD Package
    Speed Test an Operator Overloading AD Package
         Running the Speed Test Program
        Running the Speed Test Program
            Speed Testing Gradient of Determinant Using Lu Factorization
            Speed Testing Gradient of Determinant by Minor Expansion
            Speed Testing Derivative of Matrix Multiply
            Speed Testing the Jacobian of Ode Solution
            Speed Testing Second Derivative of a Polynomial
            Speed Testing Sparse Hessian
            Speed Testing Sparse Jacobian
            Microsoft Version of Elapsed Number of Seconds
         Speed Testing Utilities
        Speed Testing Utilities
             Determinant Using Expansion by Lu Factorization
            Determinant Using Expansion by Lu Factorization
                Determinant Using Lu Factorization: Example and Test
                Source: det_by_lu
             Determinant of a Minor
            Determinant of a Minor
                Determinant of a Minor: Example and Test
                Source: det_of_minor
             Determinant Using Expansion by Minors
            Determinant Using Expansion by Minors
                Determinant Using Expansion by Minors: Example and Test
                Source: det_by_minor
             Check Determinant of 3 by 3 matrix
            Check Determinant of 3 by 3 matrix
                Source: det_33
             Check Gradient of Determinant of 3 by 3 matrix
            Check Gradient of Determinant of 3 by 3 matrix
                Source: det_grad_33
             Sum Elements of a Matrix Times Itself
            Sum Elements of a Matrix Times Itself
                Sum of the Elements of the Square of a Matrix: Example and Test
                Source: mat_sum_sq
             Evaluate a Function Defined in Terms of an ODE
            Evaluate a Function Defined in Terms of an ODE
                ode_evaluate: Example and test
                Source: ode_evaluate
             Evaluate a Function That Has a Sparse Jacobian
            Evaluate a Function That Has a Sparse Jacobian
                sparse_jac_fun: Example and test
                Source: sparse_jac_fun
             Evaluate a Function That Has a Sparse Hessian
            Evaluate a Function That Has a Sparse Hessian
                sparse_hes_fun: Example and test
                Source: sparse_hes_fun
             Simulate a [0,1] Uniform Random Variate
            Simulate a [0,1] Uniform Random Variate
                Source: uniform_01
         Speed Test of Functions in Double
        Speed Test of Functions in Double
            Double Speed: Determinant by Minor Expansion
            Double Speed: Determinant Using Lu Factorization
            CppAD Speed: Matrix Multiplication (Double Version)
            Double Speed: Ode Solution
            Double Speed: Evaluate a Polynomial
            Double Speed: Sparse Hessian
            Double Speed: Sparse Jacobian
         Speed Test of Derivatives Using Adolc
        Speed Test of Derivatives Using Adolc
            Adolc Speed: Gradient of Determinant by Minor Expansion
            Adolc Speed: Gradient of Determinant Using Lu Factorization
            Adolc Speed: Matrix Multiplication
            Adolc Speed: Ode
            Adolc Speed: Second Derivative of a Polynomial
            Adolc Speed: Sparse Hessian
            adolc Speed: Sparse Jacobian
            Adolc Test Utility: Allocate and Free Memory For a Matrix
         Speed Test Derivatives Using CppAD
        Speed Test Derivatives Using CppAD
            CppAD Speed: Gradient of Determinant by Minor Expansion
            CppAD Speed: Gradient of Determinant Using Lu Factorization
            CppAD Speed, Matrix Multiplication
            CppAD Speed: Gradient of Ode Solution
            CppAD Speed: Second Derivative of a Polynomial
            CppAD Speed: Sparse Hessian
            CppAD Speed: Sparse Jacobian
         Speed Test Derivatives Using Fadbad
        Speed Test Derivatives Using Fadbad
            Fadbad Speed: Gradient of Determinant by Minor Expansion
            Fadbad Speed: Gradient of Determinant Using Lu Factorization
            Fadbad Speed: Matrix Multiplication
            Fadbad Speed: Ode
            Fadbad Speed: Second Derivative of a Polynomial
            Fadbad Speed: Sparse Hessian
            fadbad Speed: sparse_jacobian
         Speed Test Derivatives Using Sacado
        Speed Test Derivatives Using Sacado
            Sacado Speed: Gradient of Determinant by Minor Expansion
            Sacado Speed: Gradient of Determinant Using Lu Factorization
            Sacado Speed: Matrix Multiplication
            Sacado Speed: Gradient of Ode Solution
            Sacado Speed: Second Derivative of a Polynomial
            Sacado Speed: Sparse Hessian
            sacado Speed: sparse_jacobian
     Appendix
    Appendix
        Frequently Asked Questions and Answers
         The Theory of Derivative Calculations
        The Theory of Derivative Calculations
             The Theory of Forward Mode
            The Theory of Forward Mode
                Exponential Function Forward Mode Theory
                Logarithm Function Forward Mode Theory
                Square Root Function Forward Mode Theory
                Trigonometric and Hyperbolic Sine and Cosine Forward Theory
                Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
                Inverse Sine and Hyperbolic Sine Forward Mode Theory
                Inverse Cosine and Hyperbolic Cosine Forward Mode Theory
                Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
                Error Function Forward Taylor Polynomial Theory
             The Theory of Reverse Mode
            The Theory of Reverse Mode
                Exponential Function Reverse Mode Theory
                Logarithm Function Reverse Mode Theory
                Square Root Function Reverse Mode Theory
                Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
                Inverse Tangent and Hyperbolic Tangent Reverse Mode Theory
                Inverse Sine and Hyperbolic Sine Reverse Mode Theory
                Inverse Cosine and Hyperbolic Cosine Reverse Mode Theory
                Tangent and Hyperbolic Tangent Reverse Mode Theory
                Error Function Reverse Mode Theory
            An Important Reverse Mode Identity
        Glossary
        Bibliography
        The CppAD Wish List
         Changes and Additions to CppAD
        Changes and Additions to CppAD
            Changes and Additions to CppAD During 2016
            CppAD Changes and Additions During 2015
            CppAD Changes and Additions During 2014
            CppAD Changes and Additions During 2013
            CppAD Changes and Additions During 2012
            Changes and Additions to CppAD During 2011
            Changes and Additions to CppAD During 2010
            Changes and Additions to CppAD During 2009
            Changes and Additions to CppAD During 2008
            Changes and Additions to CppAD During 2007
            Changes and Additions to CppAD During 2006
            Changes and Additions to CppAD During 2005
            Changes and Additions to CppAD During 2004
            Changes and Additions to CppAD During 2003
         CppAD Deprecated API Features
        CppAD Deprecated API Features
            Deprecated Include Files
            ADFun Object Deprecated Member Functions
            Comparison Changes During Zero Order Forward Mode
            OpenMP Parallel Setup
             Routines That Track Use of New and Delete
            Routines That Track Use of New and Delete
                Tracking Use of New and Delete: Example and Test
             A Quick OpenMP Memory Allocator Used by CppAD
            A Quick OpenMP Memory Allocator Used by CppAD
                Set and Get Maximum Number of Threads for omp_alloc Allocator
                Is The Current Execution in OpenMP Parallel Mode
                Get the Current OpenMP Thread Number
                Get At Least A Specified Amount of Memory
                Return Memory to omp_alloc
                Free Memory Currently Available for Quick Use by a Thread
                Amount of Memory a Thread is Currently Using
                Amount of Memory Available for Quick Use by a Thread
                Allocate Memory and Create A Raw Array
                Return A Raw Array to The Available Memory for a Thread
                Check If A Memory Allocation is Efficient for Another Use
                Set Maximum Number of Threads for omp_alloc Allocator
                OpenMP Memory Allocator: Example and Test
            Memory Leak Detection
            Machine Epsilon For AD Types
            Choosing The Vector Testing Template Class
             Nonlinear Programming Using the CppAD Interface to Ipopt
            Nonlinear Programming Using the CppAD Interface to Ipopt
                Nonlinear Programming Using CppAD and Ipopt: Example and Test
                 Example Simultaneous Solution of Forward and Inverse Problem
                Example Simultaneous Solution of Forward and Inverse Problem
                     An ODE Inverse Problem Example
                    An ODE Inverse Problem Example
                        ODE Inverse Problem Definitions: Source Code
                     ODE Fitting Using Simple Representation
                    ODE Fitting Using Simple Representation
                        ODE Fitting Using Simple Representation
                     ODE Fitting Using Fast Representation
                    ODE Fitting Using Fast Representation
                        ODE Fitting Using Fast Representation
                    Driver for Running the Ipopt ODE Example
                    Correctness Check for Both Simple and Fast Representations
                Speed Test for Both Simple and Fast Representations
             User Defined Atomic AD Functions
            User Defined Atomic AD Functions
                Old Atomic Operation Reciprocal: Example and Test
                Using AD to Compute Atomic Function Derivatives
                Using AD to Compute Atomic Function Derivatives
                Old Tan and Tanh as User Atomic Operations: Example and Test
                 Old Matrix Multiply as a User Atomic Operation: Example and Test
                Old Matrix Multiply as a User Atomic Operation: Example and Test
                    Define Matrix Multiply as a User Atomic Operation
             zdouble: An AD Base Type With Absolute Zero
            zdouble: An AD Base Type With Absolute Zero
                zdouble: Example and Test
         Compare Speed of C and C++
        Compare Speed of C and C++
            Determinant of a Minor
            Compute Determinant using Expansion by Minors
            Simulate a [0,1] Uniform Random Variate
            Correctness Test of det_by_minor Routine
            Repeat det_by_minor Routine A Specified Number of Times
            Returns Elapsed Number of Seconds
            Determine Amount of Time to Execute det_by_minor
            Main Program For Comparing C and C++ Speed
         Some Numerical AD Utilities
        Some Numerical AD Utilities
             Computing Jacobian and Hessian of Bender's Reduced Objective
            Computing Jacobian and Hessian of Bender's Reduced Objective
                BenderQuad: Example and Test
             Jacobian and Hessian of Optimal Values
            Jacobian and Hessian of Optimal Values
                opt_val_hes: Example and Test
             LU Factorization of A Square Matrix and Stability Calculation
            LU Factorization of A Square Matrix and Stability Calculation
                LuRatio: Example and Test
        CppAD Addons
        Your License for the CppAD Software
    Alphabetic Listing of Cross Reference Tags
    Keyword Index
    Search This Web Site
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Including the ADOL-C Examples and Tests

Purpose
CppAD includes examples and tests that can use the AD package ADOL-C . The includes speed comparison with other AD packages; see speed_adolc . It also includes examples that combine ADOL-C with CppAD; see
base_adolc.hpp Enable use of AD<Base> where Base is Adolc's adouble Type
mul_level_adolc.cpp Using Adolc with Multiple Levels of Taping: Example and Test
mul_level_adolc_ode.cpp Taylor's Ode Solver: A Multi-Level Adolc Example and Test

adolc_prefix
If ADOL-C is installed on your system, you can specify a value for its install adolc_prefix on the cmake command line. The value of adolc_prefix must be such that, for one of the directories dir in cmake_install_includedirs ,
     adolc_prefix/dir/adolc/adouble.h
 is a valid way to reference to the include file adouble.h; Note that CppAD assumes ADOL-C has been configured with its sparse matrix computations enabled; i.e, using
     --with-colpack=adolc_prefix
 In other words ColPack is installed and with the same prefix as ACOL-C; see get_colpack.sh .

Examples
If you include adolc_prefix on the cmake command line, you will be able to run the ADOL-C examples listed above by executing the following commands starting in the distribution directory :
     cd build/example
     make check_example
 If you do this, you will see an indication that the examples mul_level_adolc and mul_level_adolc_ode have passed their correctness check.

Speed Tests
If you include adolc_prefix on the cmake command line, you will be able to run the ADOL-C speed correctness tests by executing the following commands starting in the distribution directory :
     cd build/speed/adolc
     make check_speed_adolc
 After executing make check_speed_adolc, you can run a specific ADOL-C speed tests by executing the command ./speed_adolc; see speed_main for the meaning of the command line options to this program.

Unix
If you are using Unix, you may have to add adolc_prefix to LD_LIBRARY_PATH. For example, if you use the bash shell to run your programs, you could include
     LD_LIBRARY_PATH=adolc_prefix/lib:${LD_LIBRARY_PATH}
     export LD_LIBRARY_PATH
 in your $HOME/.bashrc file.

Cygwin
If you are using Cygwin, you may have to add to following lines to the file .bashrc in your home directory:
     PATH=adolc_prefix/bin:${PATH}
     export PATH
 in order for ADOL-C to run properly. If adolc_prefix begins with a disk specification, you must use the Cygwin format for the disk specification. For example, if d:/adolc_base is the proper directory, /cygdrive/d/adolc_base should be used for adolc_prefix .

get_adolc
If you are using Unix, you can download and install a copy of Adolc using get_adolc.sh . The corresponding adolc_prefix would be build/prefix.
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function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_get_sacado.sh_xml.js0000644000175200017650000000350113057470504017252 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cppad_testvector_xml.js0000644000175200017650000000362213057470504020125 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'install.xml', 'cmake.xml', 'cppad_testvector.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; 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} function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cmake_check_xml.js0000644000175200017650000000303513057470504016767 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'install.xml', 'cmake_check.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'download.xml', 'cmake.xml', 'cmake_check.xml', 'pkgconfig.xml', 'auto_tools.xml' ]; 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} cppad-20170000.3/doc/auto_tools.xml0000644000175200017650000011615113057470504016113 0ustar coincoin-web Auto Tools Unix Test and Installation
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Auto Tools Unix Test and Installation

Deprecated 2012-12-26
These install instructions have been deprecated and no improvements have been added since 2012. For example, this install procedure will not detect any of the c++11 extensions. You should use the cmake instructions to install CppAD.

Distribution Directory
You must first obtain a copy of the CppAD distribution directory using the download instructions. The install instructions below correspond to the current version which has distribution directory cppad-20121230.

Work Directory
Create the directory cppad-20121230/build, which will be referred to as the build directory below.

Configure
Execute the following command in the build directory:
./configure                                  \
     --prefix=prefix_dir                    \
     --with-Documentation                     \
     --with-testvector                      \
     --with-deprecated                        \
     MAX_NUM_THREADS=max_num_threads         \
     CXX_FLAGS=cxx_flags                     \
     OPENMP_FLAGS=openmp_flags               \
     POSTFIX_DIR=postfix_dir                 \
     ADOLC_DIR=adolc_dir                     \
     BOOST_DIR=boost_dir                     \
     EIGEN_DIR=eigen_dir                     \
     FADBAD_DIR=fadbad_dir                   \
     SADADO_DIR=sacado_dir                   \
     IPOPT_DIR=ipopt_dir                     \
     TAPE_ADDR_TYPE=tape_addr_type           \
     TAPE_ID_TYPE=tape_id_type
 where only the configure line need appear; i.e., the entries in all of the other lines are optional. The text in italic is replaced values that you choose; see discussion below.

make
CppAD has some object libraries that are used for its correctness tests. (Currently, none of these libraries get installed.) You can build these libraries by executing the command
     make
 in the build directory.

Examples and Tests
Once you have executed the make command, you can run the correctness and speed tests.

The following command will build all the correctness and speed tests. In addition, it will run all the correctness tests: 
 
     make test


The following links describe how to build and run subsets of these tests:
get_started Getting Started Using CppAD to Compute Derivatives
exp_apx_main Correctness Tests For Exponential Approximation in Introduction
example CppAD Examples and Tests
print_for_cout Printing During Forward Mode: Example and Test
speed_example Run the Speed Examples
speed_double Speed Test of Functions in Double
speed_adolc Speed Test of Derivatives Using Adolc
speed_cppad Speed Test Derivatives Using CppAD
speed_fadbad Speed Test Derivatives Using Fadbad
speed_sacado Speed Test Derivatives Using Sacado
In addition, you can run a large subset of correctness tests (that are not intended to be examples) by executing the following commands starting in the build directory:
     cd test_more
     make test
Profiling CppAD
The CppAD derivative speed tests mentioned above can be profiled. You can test that the results computed during this profiling are correct by executing the following commands starting in the build directory:
     cd speed/profile
     make test
 After executing make test, you can run a profile speed test by executing the command ./profile; see speed_main for the meaning of the command line options to this program.

After you have run a profiling speed test, you can then obtain the profiling results with
     gprof -b profile
 If you are using a windows operating system with Cygwin or MinGW, you may have to replace profile by profile.exe in the gprof command above; i.e., 
 
     gprof -b profile.exe
In C++, template parameters and argument types become part of a routines's name. This can make the gprof output hard to read (the routine names can be very long). You can remove the template parameters and argument types from the routine names by executing the following command 
 
     gprof -b profile | sed -f gprof.sed
If you are using a windows operating system with Cygwin or MinGW, you would need to use 
 
     gprof -b profile.exe | sed -f gprof.sed

prefix_dir
The default value for prefix directory is $HOME i.e., by default the CppAD include files will install below $HOME. If you want to install elsewhere, you will have to use this option. As an example of using the --prefix=prefix_dir option, if you specify 
 
     ./configure --prefix=/usr/local
the CppAD include files will be installed in the directory
     /usr/local/include/cppad
 If --with-Documentation is specified, the CppAD documentation files will be installed in the directory
     /usr/local/share/doc/cppad-20121230
--with-Documentation
If the command line argument --with-Documentation is specified, the CppAD documentation HTML and XML files are copied to the directory
     prefix_dir/share/doc/postfix_dir/cppad-20121230
 (see postfix_dir ). The top of the CppAD HTML documentation tree (with mathematics displayed as LaTex command) will be located at
     prefix_dir/share/doc/postfix_dir/cppad-20121230/cppad.htm
 and the top of the XML documentation tree (with mathematics displayed as MathML) will be located at
     prefix_dir/share/doc/postfix_dir/cppad-20121230/cppad.xml
--with-testvector
The CPPAD_TESTVECTOR template class is used for many of the CppAD examples and tests. The default for this template class is CppAD::vector<Scalar> . If one, and only one, of the following command line arguments is specified: 
 
     --with-stdvector
     --with-boostvector
     --with-eigenvector
the corresponding of the following template classes is used
     std::vector<Scalar>
     boost::numeric::ublas::vector<Scalar>
     Eigen::matrix<Scalar, Eigen::Dynamic, 1>
 See also, boost_dir and eigen_dir .

--with-deprecated
If this configure argument is present, then all the deprecated features are included in the install. Otherwise, they are not included.

max_num_threads
this specifies the value for the default value for the preprocessor symbol CPPAD_MAX_NUM_THREADS . It must be greater than or equal to four; i.e., max_num_threads >= 4 .

cxx_flags
If the command line argument CompilerFlags is present, it specifies compiler flags. For example,
     CXX_FLAGS="-Wall -ansi"
 would specify that warning flags -Wall and -ansi should be included in all the C++ compile commands. The error and warning flags chosen must be valid options for the C++ compiler. The default value for CompilerFlags is the empty string.

openmp_flags
If the command line argument OpenmpFlags is present, it specifies the necessary flags so that the compiler will properly interpret OpenMP directives. For example, when using the GNU g++ compiler, the following setting includes the OpenMP tests:
     OPENMP_FLAGS=-fopenmp
 If you specify configure command, the CppAD OpenMP correctness and speed tests will be built; see threading multi-threading tests.

postfix_dir
By default, the postfix directory is empty; i.e., there is no postfix directory. As an example of using the POSTFIX_DIR=postfix_dir option, if you specify 
 
     ./configure --prefix=/usr/local POSTFIX_DIR=coin
the CppAD include files will be installed in the directory
     /usr/local/include/coin/cppad
 If --with-Documentation is specified, the CppAD documentation files will be installed in the directory
     /usr/local/share/doc/coin/cppad-20121230
adolc_dir
If you have ADOL-C installed on your system, you can specify a value for adolc_dir in the configure command line. The value of adolc_dir must be such that
     adolc_dir/include/adolc/adouble.h
 is a valid way to reference adouble.h. In this case, you can run the Adolc speed correctness tests by executing the following commands starting in the build directory:
     cd speed/adolc
     make test
 After executing make test, you can run an Adolc speed tests by executing the command ./adolc; see speed_main for the meaning of the command line options to this program. Note that these speed tests assume Adolc has been configure with its sparse matrix computations enabled using
     --with-colpack=colpack_dir
Linux
If you are using Linux, you will have to add adolc_dir/lib to LD_LIBRARY_PATH. For example, if you use the bash shell to run your programs, you could include
     LD_LIBRARY_PATH=adolc_dir/lib:${LD_LIBRARY_PATH}
     export LD_LIBRARY_PATH
 in your $HOME/.bash_profile file.

Cygwin
If you are using Cygwin, you will have to add to following lines to the file .bash_profile in your home directory:
     PATH=adolc_dir/bin:${PATH}
     export PATH
 in order for Adolc to run properly. If adolc_dir begins with a disk specification, you must use the Cygwin format for the disk specification. For example, if d:/adolc_base is the proper directory, /cygdrive/d/adolc_base should be used for adolc_dir .

boost_dir
If the command line argument
     BOOST_DIR=boost_dir
 is present, it must be such that files
     boost_dir/include/boost/numeric/ublas/vector.hpp
     boost_dir/include/boost/thread.hpp
 are present. In this case, these files will be used by CppAD. See also, --with-boostvector

eigen_dir
If you have Eigen installed on your system, you can specify a value for eigen_dir . It must be such that
     eigen_dir/include/Eigen/Core
 is a valid include file. In this case CppAD will compile and test the Eigen examples; e.g., eigen_array.cpp . See also, --with-eigenvector

fadbad_dir
If you have Fadbad 2.1 installed on your system, you can specify a value for fadbad_dir . It must be such that
     fadbad_dir/include/FADBAD++/badiff.h
 is a valid reference to badiff.h. In this case, you can run the Fadbad speed correctness tests by executing the following commands starting in the build directory:
     cd speed/fadbad
     make test
 After executing make test, you can run a Fadbad speed tests by executing the command ./fadbad; see speed_main for the meaning of the command line options to this program.

ipopt_dir
If you have Ipopt installed on your system, you can specify a value for ipopt_dir . It must be such that
     ipopt_dir/include/coin/IpIpoptApplication.hpp
 is a valid reference to IpIpoptApplication.hpp. In this case, the CppAD interface to Ipopt examples can be built and tested by executing the following commands starting in the build directory:
     make
     #
     cd cppad_ipopt/example
     make test
     #
     cd ../test
     make test
     #
     cd ../speed
     make test
 Once this has been done, you can execute the program ./speed in the build/cppad_ipopt/speed directory; see ipopt_ode_speed.cpp .

sacado_dir
If you have Sacado installed on your system, you can specify a value for sacado_dir . It must be such that
     sacado_dir/include/Sacado.hpp
 is a valid reference to Sacado.hpp. In this case, you can run the Sacado speed correctness tests by executing the following commands starting in the build directory:
     cd speed/sacado
     make test
 After executing make test, you can run a Sacado speed tests by executing the command ./sacado; see speed_main for the meaning of the command line options to this program.

tape_addr_type
If the command line argument tape_addr_type is present, it specifies the type used for address in the AD recordings (tapes). The valid values for this argument are unsigned short int, unsigned int, size_t. The smaller the value of sizeof(tape_addr_type) , the less memory is used. On the other hand, the value
     std::numeric_limits<tape_addr_type>::max()
 must be larger than any of the following: size_op , size_op_arg , size_par , size_par , size_par .

tape_id_type
If the command line argument tape_id_type is present, it specifies the type used for identifying tapes. The valid values for this argument are unsigned short int, unsigned int, size_t. The smaller the value of sizeof(tape_id_type) , the less memory is used. On the other hand, the value
     std::numeric_limits<tape_id_type>::max()
 must be larger than the maximum number of tapes per thread times max_num_threads .

make install
Once you are satisfied that the tests are giving correct results, you can install CppAD into easy to use directories by executing the command 
 
     make install
This will install CppAD in the location specified by prefix_dir . You must have permission to write in the prefix_dir directory to execute this command. You may optionally specify a destination directory for the install; i.e.,
     make install DESTDIR=DestinationDirectory
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} function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_2_rev1.cpp_xml.js0000644000175200017650000000312213057470504017302 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'introduction.xml', 'exp_2.xml', 'exp_2_rev1.xml', 'exp_2_rev1.cpp.xml' ]; var list_down3 = [ 'get_started.cpp.xml', 'exp_2.xml', 'exp_eps.xml', 'exp_apx_main.cpp.xml' ]; var list_down2 = [ 'exp_2.hpp.xml', 'exp_2.cpp.xml', 'exp_2_for0.xml', 'exp_2_for1.xml', 'exp_2_rev1.xml', 'exp_2_for2.xml', 'exp_2_rev2.xml', 'exp_2_cppad.xml' ]; var list_down1 = [ 'exp_2_rev1.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_2_for2_xml.js0000644000175200017650000000446513057470504016527 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_2_rev2_xml.js0000644000175200017650000000404413057470504016526 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'introduction.xml', 'exp_2.xml', 'exp_2_rev2.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; 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} function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_2_rev2.cpp_xml.js0000644000175200017650000000312213057470504017303 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'introduction.xml', 'exp_2.xml', 'exp_2_rev2.xml', 'exp_2_rev2.cpp.xml' ]; var list_down3 = [ 'get_started.cpp.xml', 'exp_2.xml', 'exp_eps.xml', 'exp_apx_main.cpp.xml' ]; 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if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_2_cppad_xml.js0000644000175200017650000000344713057470504016745 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'introduction.xml', 'exp_2.xml', 'exp_2_cppad.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'get_started.cpp.xml', 'exp_2.xml', 'exp_eps.xml', 'exp_apx_main.cpp.xml' ]; var list_down1 = [ 'exp_2.hpp.xml', 'exp_2.cpp.xml', 'exp_2_for0.xml', 'exp_2_for1.xml', 'exp_2_rev1.xml', 'exp_2_for2.xml', 'exp_2_rev2.xml', 'exp_2_cppad.xml' ]; var list_current0 = [ 'exp_2_cppad.xml#Purpose', 'exp_2_cppad.xml#Exercises' ]; 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function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_eps.hpp_xml.js0000644000175200017650000000335113057470504017004 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_eps.cpp_xml.js0000644000175200017650000000335113057470504016777 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'introduction.xml', 'exp_eps.xml', 'exp_eps.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'get_started.cpp.xml', 'exp_2.xml', 'exp_eps.xml', 'exp_apx_main.cpp.xml' ]; var list_down1 = [ 'exp_eps.hpp.xml', 'exp_eps.cpp.xml', 'exp_eps_for0.xml', 'exp_eps_for1.xml', 'exp_eps_rev1.xml', 'exp_eps_for2.xml', 'exp_eps_rev2.xml', 'exp_eps_cppad.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_eps_for0_xml.js0000644000175200017650000000450613057470504017147 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'introduction.xml', 'exp_eps.xml', 'exp_eps_for0.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'get_started.cpp.xml', 'exp_2.xml', 'exp_eps.xml', 'exp_apx_main.cpp.xml' ]; var list_down1 = [ 'exp_eps.hpp.xml', 'exp_eps.cpp.xml', 'exp_eps_for0.xml', 'exp_eps_for1.xml', 'exp_eps_rev1.xml', 'exp_eps_for2.xml', 'exp_eps_rev2.xml', 'exp_eps_cppad.xml' ]; 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} function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_value_xml.js0000644000175200017650000000367213057470504015675 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'convert.xml', 'value.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; 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Prev Next ad_output.cpp Headings

AD Output Operator: Example and Test

# include <cppad/cppad.hpp>

# include <sstream>  // std::ostringstream
# include <string>   // std::string
# include <iomanip>  // std::setprecision, setw, setfill, right

namespace {
     template <class S>
     void set_ostream(S &os)
     {     os
          << std::setprecision(4) // 4 digits of precision
          << std::setw(6)         // 6 characters per field
          << std::setfill(' ')    // fill with spaces
          << std::right;          // adjust value to the right
     }
}

bool ad_output(void)
{     bool ok = true;

     // This output stream is an ostringstream for testing purposes.
     // You can use << with other types of streams; i.e., std::cout.
     std::ostringstream stream;

     // ouput an AD<double> object
     CppAD::AD<double>  pi = 4. * atan(1.); // 3.1415926536
     set_ostream(stream);
     stream << pi;

     // ouput a VecAD<double>::reference object
     CppAD::VecAD<double> v(1);
     CppAD::AD<double> zero(0);
     v[zero]   = exp(1.);                  // 2.7182818285
     set_ostream(stream);
     stream << v[zero];

     // convert output from stream to string
     std::string str = stream.str();

     // check the output
     ok      &= (str == " 3.142 2.718");

     return ok;
}
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item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_printfor_xml.js0000644000175200017650000000411513057470504016415 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'convert.xml', 'printfor.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; 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if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_print_for_cout.cpp_xml.js0000644000175200017650000000336513057470504020375 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'convert.xml', 'printfor.xml', 'print_for_cout.cpp.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; 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var list_current0 = [ 'advalued.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_arithmetic_xml.js0000644000175200017650000000357413057470504016713 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_unary_plus.cpp_xml.js0000644000175200017650000000311713057470504017535 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'unaryplus.xml', 'unary_plus.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'unary_plus.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_unaryminus_xml.js0000644000175200017650000000365013057470504016767 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'unaryminus.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down0 = [ 'unary_minus.cpp.xml' ]; var list_current0 = [ 'unaryminus.xml#Syntax', 'unaryminus.xml#Purpose', 'unaryminus.xml#Base', 'unaryminus.xml#x', 'unaryminus.xml#y', 'unaryminus.xml#Operation Sequence', 'unaryminus.xml#Derivative', 'unaryminus.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_unary_minus.cpp_xml.js0000644000175200017650000000312213057470504017701 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'unaryminus.xml', 'unary_minus.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'unary_minus.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_ad_binary_xml.js0000644000175200017650000000421013057470504016476 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'ad_binary.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down0 = [ 'add.cpp.xml', 'sub.cpp.xml', 'mul.cpp.xml', 'div.cpp.xml' ]; var list_current0 = [ 'ad_binary.xml#Syntax', 'ad_binary.xml#Purpose', 'ad_binary.xml#Op', 'ad_binary.xml#Base', 'ad_binary.xml#x', 'ad_binary.xml#y', 'ad_binary.xml#z', 'ad_binary.xml#Operation Sequence', 'ad_binary.xml#Example', 'ad_binary.xml#Derivative', 'ad_binary.xml#Derivative.Addition', 'ad_binary.xml#Derivative.Subtraction', 'ad_binary.xml#Derivative.Multiplication', 'ad_binary.xml#Derivative.Division' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_add.cpp_xml.js0000644000175200017650000000315613057470504016067 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'ad_binary.xml', 'add.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'add.cpp.xml', 'sub.cpp.xml', 'mul.cpp.xml', 'div.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sub.cpp_xml.js0000644000175200017650000000315613057470504016130 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'ad_binary.xml', 'sub.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'add.cpp.xml', 'sub.cpp.xml', 'mul.cpp.xml', 'div.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_mul.cpp_xml.js0000644000175200017650000000315613057470504016134 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'ad_binary.xml', 'mul.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'add.cpp.xml', 'sub.cpp.xml', 'mul.cpp.xml', 'div.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_div.cpp_xml.js0000644000175200017650000000315613057470505016122 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'ad_binary.xml', 'div.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'add.cpp.xml', 'sub.cpp.xml', 'mul.cpp.xml', 'div.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_compute_assign_xml.js0000644000175200017650000000434313057470505017576 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'compute_assign.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down0 = [ 'addeq.cpp.xml', 'sub_eq.cpp.xml', 'mul_eq.cpp.xml', 'div_eq.cpp.xml' ]; var list_current0 = [ 'compute_assign.xml#Syntax', 'compute_assign.xml#Purpose', 'compute_assign.xml#Op', 'compute_assign.xml#Base', 'compute_assign.xml#x', 'compute_assign.xml#y', 'compute_assign.xml#Result', 'compute_assign.xml#Operation Sequence', 'compute_assign.xml#Example', 'compute_assign.xml#Derivative', 'compute_assign.xml#Derivative.Addition', 'compute_assign.xml#Derivative.Subtraction', 'compute_assign.xml#Derivative.Multiplication', 'compute_assign.xml#Derivative.Division' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_addeq.cpp_xml.js0000644000175200017650000000320013057470505016404 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'compute_assign.xml', 'addeq.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'addeq.cpp.xml', 'sub_eq.cpp.xml', 'mul_eq.cpp.xml', 'div_eq.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sub_eq.cpp_xml.js0000644000175200017650000000320113057470505016605 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'compute_assign.xml', 'sub_eq.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'addeq.cpp.xml', 'sub_eq.cpp.xml', 'mul_eq.cpp.xml', 'div_eq.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_mul_eq.cpp_xml.js0000644000175200017650000000320113057470505016611 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'compute_assign.xml', 'mul_eq.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'addeq.cpp.xml', 'sub_eq.cpp.xml', 'mul_eq.cpp.xml', 'div_eq.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_div_eq.cpp_xml.js0000644000175200017650000000320113057470505016576 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'arithmetic.xml', 'compute_assign.xml', 'div_eq.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'unaryplus.xml', 'unaryminus.xml', 'ad_binary.xml', 'compute_assign.xml' ]; var list_down1 = [ 'addeq.cpp.xml', 'sub_eq.cpp.xml', 'mul_eq.cpp.xml', 'div_eq.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_unary_standard_math_xml.js0000644000175200017650000000451513057470505020606 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; 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} function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_acos.cpp_xml.js0000644000175200017650000000337013057470505016263 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'acos.xml', 'acos.cpp.xml' ]; 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} function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_asin_xml.js0000644000175200017650000000375113057470505015512 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'asin.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; 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} function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_asin.cpp_xml.js0000644000175200017650000000337013057470505016270 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'asin.xml', 'asin.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'asin.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cos_xml.js0000644000175200017650000000374213057470505015344 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cos.cpp_xml.js0000644000175200017650000000336513057470505016126 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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} function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cosh.cpp_xml.js0000644000175200017650000000337013057470505016272 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'cosh.xml', 'cosh.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'cosh.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_exp_xml.js0000644000175200017650000000374213057470505015354 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'exp.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'exp.cpp.xml' ]; var list_current0 = [ 'exp.xml#Syntax', 'exp.xml#x, y', 'exp.xml#Atomic', 'exp.xml#Derivative', 'exp.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_log_xml.js0000644000175200017650000000374213057470505015341 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'log.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'log.cpp.xml' ]; var list_current0 = [ 'log.xml#Syntax', 'log.xml#x, y', 'log.xml#Atomic', 'log.xml#Derivative', 'log.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_log.cpp_xml.js0000644000175200017650000000336513057470505016123 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'log.xml', 'log.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; 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} function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_log10_xml.js0000644000175200017650000000373013057470505015477 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'log10.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'log10.cpp.xml' ]; var list_current0 = [ 'log10.xml#Syntax', 'log10.xml#x, y', 'log10.xml#Method', 'log10.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_log10.cpp_xml.js0000644000175200017650000000337313057470505016263 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'log10.xml', 'log10.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'log10.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sin_xml.js0000644000175200017650000000374213057470505015351 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'sin.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'sin.cpp.xml' ]; var list_current0 = [ 'sin.xml#Syntax', 'sin.xml#x, y', 'sin.xml#Atomic', 'sin.xml#Derivative', 'sin.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sin.cpp_xml.js0000644000175200017650000000336513057470505016133 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sinh_xml.js0000644000175200017650000000375113057470505015521 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'sinh.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'sinh.cpp.xml' ]; var list_current0 = [ 'sinh.xml#Syntax', 'sinh.xml#x, y', 'sinh.xml#Atomic', 'sinh.xml#Derivative', 'sinh.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sinh.cpp_xml.js0000644000175200017650000000337013057470505016277 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'sinh.xml', 'sinh.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'sinh.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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var list_down1 = [ 'tanh.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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} function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_asinh_xml.js0000644000175200017650000000413213057470505015654 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'asinh.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_asinh.cpp_xml.js0000644000175200017650000000337313057470505016443 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'asinh.xml', 'asinh.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'asinh.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_atanh_xml.js0000644000175200017650000000413213057470505015645 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'atanh.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'atanh.cpp.xml' ]; var list_current0 = [ 'atanh.xml#Syntax', 'atanh.xml#Description', 'atanh.xml#x, y', 'atanh.xml#CPPAD_USE_CPLUSPLUS_2011', 'atanh.xml#CPPAD_USE_CPLUSPLUS_2011.true', 'atanh.xml#CPPAD_USE_CPLUSPLUS_2011.false', 'atanh.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_atanh.cpp_xml.js0000644000175200017650000000337313057470505016434 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'atanh.xml', 'atanh.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'atanh.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_erf_xml.js0000644000175200017650000000411013057470505015322 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'erf.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'erf.cpp.xml' ]; var list_current0 = [ 'erf.xml#Syntax', 'erf.xml#Description', 'erf.xml#x, y', 'erf.xml#CPPAD_USE_CPLUSPLUS_2011', 'erf.xml#CPPAD_USE_CPLUSPLUS_2011.true', 'erf.xml#CPPAD_USE_CPLUSPLUS_2011.false', 'erf.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_erf.cpp_xml.js0000644000175200017650000000336513057470505016116 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'erf.xml', 'erf.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'erf.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_expm1_xml.js0000644000175200017650000000413213057470505015604 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'expm1.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'expm1.cpp.xml' ]; var list_current0 = [ 'expm1.xml#Syntax', 'expm1.xml#Description', 'expm1.xml#x, y', 'expm1.xml#CPPAD_USE_CPLUSPLUS_2011', 'expm1.xml#CPPAD_USE_CPLUSPLUS_2011.true', 'expm1.xml#CPPAD_USE_CPLUSPLUS_2011.false', 'expm1.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_expm1.cpp_xml.js0000644000175200017650000000337313057470505016373 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'expm1.xml', 'expm1.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'expm1.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_log1p_xml.js0000644000175200017650000000413213057470505015574 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'log1p.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down0 = [ 'log1p.cpp.xml' ]; var list_current0 = [ 'log1p.xml#Syntax', 'log1p.xml#Description', 'log1p.xml#x, y', 'log1p.xml#CPPAD_USE_CPLUSPLUS_2011', 'log1p.xml#CPPAD_USE_CPLUSPLUS_2011.true', 'log1p.xml#CPPAD_USE_CPLUSPLUS_2011.false', 'log1p.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_log1p.cpp_xml.js0000644000175200017650000000337313057470505016363 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'log1p.xml', 'log1p.cpp.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; var list_down1 = [ 'log1p.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sign_xml.js0000644000175200017650000000400113057470505015505 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'unary_standard_math.xml', 'sign.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'acos.xml', 'asin.xml', 'atan.xml', 'cos.xml', 'cosh.xml', 'exp.xml', 'log.xml', 'log10.xml', 'sin.xml', 'sinh.xml', 'sqrt.xml', 'tan.xml', 'tanh.xml', 'abs.xml', 'acosh.xml', 'asinh.xml', 'atanh.xml', 'erf.xml', 'expm1.xml', 'log1p.xml', 'sign.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/binary_math.xml0000644000175200017650000000603313057470505016216 0ustar coincoin-web The Binary Math Functions
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The Binary Math Functions

Contents
atan2AD Two Argument Inverse Tangent Function
powThe AD Power Function
azmulAbsolute Zero Multiplication
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} cppad-20170000.3/doc/cond_exp.cpp.xml0000644000175200017650000005407613057470505016313 0ustar coincoin-web Conditional Expressions: Example and Test
Prev Next cond_exp.cpp

Conditional Expressions: Example and Test

See Also
optimize_conditional_skip.cpp

Description
Use CondExp to compute f ( x ) = ∑ j = 0 m -1 x j log ( x j ) and its derivative at various argument values ( where x j ≥ 0 ) with out having to re-tape; i.e., using only one ADFun object. Note that x j log ( x j ) → 0 as x j ↓ 0 and we need to handle the case x j = 0 in a special way to avoid multiplying zero by infinity. 

# include <cppad/cppad.hpp>
# include <limits>

bool CondExp(void)
{     bool ok = true;

     using CppAD::isnan;
     using CppAD::AD;
     using CppAD::NearEqual;
     using CppAD::log;
     using CppAD::abs;
     double eps  = 100. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 5;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     size_t j;
     for(j = 0; j < n; j++)
          ax[j] = 1.;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     AD<double> asum  = 0.;
     AD<double> azero = 0.;
     for(j = 0; j < n; j++)
     {     // if x_j > 0, add x_j * log( x_j ) to the sum
          asum += CppAD::CondExpGt(ax[j], azero, ax[j] * log(ax[j]), azero);
     }

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = asum;

     // create f: x -> ay and stop tape recording
     CppAD::ADFun<double> f(ax, ay);

     // vectors for arguments to the function object f
     CPPAD_TESTVECTOR(double) x(n);   // argument values
     CPPAD_TESTVECTOR(double) y(m);   // function values
     CPPAD_TESTVECTOR(double) w(m);   // function weights
     CPPAD_TESTVECTOR(double) dw(n);  // derivative of weighted function

     // a case where x[j] > 0 for all j
     double check  = 0.;
     for(j = 0; j < n; j++)
     {     x[j]   = double(j + 1);
          check += x[j] * log( x[j] );
     }

     // function value
     y  = f.Forward(0, x);
     ok &= NearEqual(y[0], check, eps, eps);

     // compute derivative of y[0]
     w[0] = 1.;
     dw   = f.Reverse(1, w);
     for(j = 0; j < n; j++)
          ok &= NearEqual(dw[j], log(x[j]) + 1., eps, eps);

     // a case where x[3] is equal to zero
     check -= x[3] * log( x[3] );
     x[3]   = 0.;

     // function value
     y   = f.Forward(0, x);
     ok &= NearEqual(y[0], check, eps, eps);

     // check derivative of y[0]
     f.check_for_nan(false);
     w[0] = 1.;
     dw   = f.Reverse(1, w);
     for(j = 0; j < n; j++)
     {     if( x[j] > 0 )
               ok &= NearEqual(dw[j], log(x[j]) + 1., eps, eps);
          else
          {     // Note that in case where dw has type AD<double> and is a variable
               // this dw[j] can be nan (zero times nan is not zero).
               ok &= NearEqual(dw[j], 0.0, eps, eps);
          }
     }

     return ok;
}
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Prev Next tape_index.cpp Headings

Taping Array Index Operation: Example and Test
# include <cppad/cppad.hpp>

namespace {
     double Array(const double &index)
     {     static double array[] = {
               5.,
               4.,
               3.,
               2.,
               1.
          };
          static size_t number = sizeof(array) / sizeof(array[0]);
          if( index < 0. )
               return array[0];

          size_t i = static_cast<size_t>(index);
          if( i >= number )
               return array[number-1];

          return array[i];
     }
     // in empty namespace and outside any other routine
     CPPAD_DISCRETE_FUNCTION(double, Array)
}

bool TapeIndex(void)
{     bool ok = true;
     using CppAD::AD;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) X(n);
     X[0] = 2.;   // array index value
     X[1] = 3.;   // multiplier of array index value

     // declare independent variables and start tape recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y[0] = X[1] * Array( X[0] );

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // vectors for arguments to the function object f
     CPPAD_TESTVECTOR(double) x(n);   // argument values
     CPPAD_TESTVECTOR(double) y(m);   // function values
     CPPAD_TESTVECTOR(double) w(m);   // function weights
     CPPAD_TESTVECTOR(double) dw(n);  // derivative of weighted function

     // check function value
     x[0] = Value(X[0]);
     x[1] = Value(X[1]);
     y[0] = Value(Y[0]);
     ok  &= y[0] == x[1] * Array(x[0]);

     // evaluate f where x has different values
     x[0] = x[0] + 1.;  // new array index value
     x[1] = x[1] + 1.;  // new multiplier value
     y    = f.Forward(0, x);
     ok  &= y[0] == x[1] * Array(x[0]);

     // evaluate derivaitve of y[0]
     w[0] = 1.;
     dw   = f.Reverse(1, w);
     ok   &= dw[0] == 0.;              // partial w.r.t array index
     ok   &= dw[1] == Array(x[0]);     // partial w.r.t multiplier

     return ok;
}
Input File: example/tape_index.cpp cppad-20170000.3/doc/_tape_index.cpp_xml.js0000644000175200017650000000322713057470505017457 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'discrete.xml', 'tape_index.cpp.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'tape_index.cpp.xml', 'interp_onetape.cpp.xml', 'interp_retape.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/interp_onetape.cpp.xml0000644000175200017650000007120413057470505017520 0ustar coincoin-web Interpolation With Out Retaping: Example and Test
Prev Next interp_onetape.cpp

Interpolation With Out Retaping: Example and Test

See Also
interp_retape.cpp 

# include <cppad/cppad.hpp>
# include <cassert>
# include <cmath>

namespace {
     double ArgumentValue[] = {
          .0 ,
          .2 ,
          .4 ,
          .8 ,
          1.
     };
     double FunctionValue[] = {
          std::sin( ArgumentValue[0] ) ,
          std::sin( ArgumentValue[1] ) ,
          std::sin( ArgumentValue[2] ) ,
          std::sin( ArgumentValue[3] ) ,
          std::sin( ArgumentValue[4] )
     };
     size_t TableLength = 5;

     size_t Index(const double &x)
     {     // determine the index j such that x is between
          // ArgumentValue[j] and ArgumentValue[j+1]
          static size_t j = 0;
          while ( x < ArgumentValue[j] && j > 0 )
               j--;
          while ( x > ArgumentValue[j+1] && j < TableLength - 2)
               j++;
          // assert conditions that must be true given logic above
          assert( j >= 0 && j < TableLength - 1 );
          return j;
     }

     double Argument(const double &x)
     {     size_t j = Index(x);
          return ArgumentValue[j];
     }
     double Function(const double &x)
     {     size_t j = Index(x);
          return FunctionValue[j];
     }

     double Slope(const double &x)
     {     size_t j  = Index(x);
          double dx = ArgumentValue[j+1] - ArgumentValue[j];
          double dy = FunctionValue[j+1] - FunctionValue[j];
          return dy / dx;
     }
     CPPAD_DISCRETE_FUNCTION(double, Argument)
     CPPAD_DISCRETE_FUNCTION(double, Function)
     CPPAD_DISCRETE_FUNCTION(double, Slope)
}


bool interp_onetape(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 1;
     CPPAD_TESTVECTOR(AD<double>) X(n);
     X[0] = .4 * ArgumentValue[1] + .6 * ArgumentValue[2];

     // declare independent variables and start tape recording
     CppAD::Independent(X);

     // evaluate piecewise linear interpolant at X[0]
     AD<double> A = Argument(X[0]);
     AD<double> F = Function(X[0]);
     AD<double> S = Slope(X[0]);
     AD<double> I = F + (X[0] - A) * S;

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) Y(m);
     Y[0] = I;

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // vectors for arguments to the function object f
     CPPAD_TESTVECTOR(double) x(n);   // argument values
     CPPAD_TESTVECTOR(double) y(m);   // function values
     CPPAD_TESTVECTOR(double) dx(n);  // differentials in x space
     CPPAD_TESTVECTOR(double) dy(m);  // differentials in y space

     // to check function value we use the fact that X[0] is between
     // ArgumentValue[1] and ArgumentValue[2]
     x[0]          = Value(X[0]);
     double delta  = ArgumentValue[2] - ArgumentValue[1];
     double check  = FunctionValue[2] * (x[0] - ArgumentValue[1]) / delta
                   + FunctionValue[1] * (ArgumentValue[2] - x[0]) / delta;
     ok  &= NearEqual(Y[0], check, eps99, eps99);

     // evaluate f where x has different value
     x[0]   = .7 * ArgumentValue[2] + .3 * ArgumentValue[3];
     y      = f.Forward(0, x);

     // check function value
     delta  = ArgumentValue[3] - ArgumentValue[2];
     check  = FunctionValue[3] * (x[0] - ArgumentValue[2]) / delta
                   + FunctionValue[2] * (ArgumentValue[3] - x[0]) / delta;
     ok  &= NearEqual(y[0], check, eps99, eps99);

     // evaluate partials w.r.t. x[0]
     dx[0] = 1.;
     dy    = f.Forward(1, dx);

     // check that the derivative is the slope
     check = (FunctionValue[3] - FunctionValue[2])
           / (ArgumentValue[3] - ArgumentValue[2]);
     ok   &= NearEqual(dy[0], check, eps99, eps99);

     return ok;
}
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var list_current0 = [ 'nan.xml#Syntax', 'nan.xml#Purpose', 'nan.xml#Include', 'nan.xml#Include.Macros', 'nan.xml#isnan', 'nan.xml#isnan.s', 'nan.xml#isnan.b', 'nan.xml#hasnan', 'nan.xml#hasnan.v', 'nan.xml#hasnan.b', 'nan.xml#nan(zero)', 'nan.xml#nan(zero).Deprecated 2015-10-04', 'nan.xml#nan(zero).Syntax', 'nan.xml#nan(zero).z', 'nan.xml#nan(zero).s', 'nan.xml#Scalar', 'nan.xml#Vector', 'nan.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_interp_onetape.cpp_xml.js0000644000175200017650000000332613057470505020353 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'discrete.xml', 'interp_onetape.cpp.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'tape_index.cpp.xml', 'interp_onetape.cpp.xml', 'interp_retape.cpp.xml' ]; var list_current0 = [ 'interp_onetape.cpp.xml#See Also' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_numeric_limits_xml.js0000644000175200017650000000412013057470505017572 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'numeric_limits.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down1 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down0 = [ 'num_limits.cpp.xml' ]; var list_current0 = [ 'numeric_limits.xml#Syntax', 'numeric_limits.xml#CppAD::numeric_limits', 'numeric_limits.xml#std::numeric_limits', 'numeric_limits.xml#Float', 'numeric_limits.xml#epsilon', 'numeric_limits.xml#min', 'numeric_limits.xml#max', 'numeric_limits.xml#quiet_NaN', 'numeric_limits.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_num_limits.cpp_xml.js0000644000175200017650000000315213057470505017514 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'numeric_limits.xml', 'num_limits.cpp.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down1 = [ 'num_limits.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/checkpoint.xml0000644000175200017650000006523113057470505016055 0ustar coincoin-web Checkpointing Functions
Prev Next

Checkpointing Functions

Syntax
checkpoint<Base> atom_fun(
     name, algo, ax, ay, sparsity, optimize
)
sv = atom_fun.size_var()
atom_fun.option(option_value)
algo(ax, ay)
atom_fun(ax, ay)
checkpoint<Base>::clear()

See Also
reverse_checkpoint.cpp

Purpose

Reduce Memory
You can reduce the size of the tape and memory required for AD by checkpointing functions of the form y = f ( x ) where f : B n → B m .

Faster Recording
It may also reduce the time to make a recording the same function for different values of the independent variable. Note that the operation sequence for a recording that uses f ( x ) may depend on its independent variables.

Repeating Forward
Normally, CppAD store forward mode results until they freed using capacity_order or the corresponding ADFun object is deleted. This is not true for checkpoint functions because a checkpoint function may be used repeatedly with different arguments in the same tape. Thus, forward mode results are recomputed each time a checkpoint function is used during a forward or reverse mode sweep.

Restriction
The operation sequence representing f ( x ) cannot depend on the value of x . The approach in the reverse_checkpoint.cpp example case be applied when the operation sequence depends on x .


If Base is an AD type, it is possible to record Base operations. Note that atom_fun will treat algo as an atomic operation while recording AD<Base> operations, but not while recording Base operations. See the atomic_mul_level.cpp example.

Method
The checkpoint class is derived from atomic_base and makes this easy. It implements all the atomic_base virtual functions and hence its source code cppad/core/checkpoint.hpp provides an example implementation of atomic_base . The difference is that checkpoint.hpp uses AD instead of user provided derivatives.

constructor
The syntax for the checkpoint constructor is
     checkpoint<Base> atom_fun(name, algo, ax, ay)
  1. This constructor cannot be called in parallel mode.
  2. You cannot currently be recording AD<Base> operations when the constructor is called.
  3. This object atom_fun must not be destructed for as long as any ADFun<Base> object uses its atomic operation.
  4. This class is implemented as a derived class of atomic_base and hence some of its error message will refer to atomic_base.


Base
The type Base specifies the base type for AD operations.

ADVector
The type ADVector must be a simple vector class with elements of type AD<Base> .

name
This checkpoint constructor argument has prototype
     const char* name
 It is the name used for error reporting. The suggested value for name is atom_fun ; i.e., the same name as used for the object being constructed.

ax
This argument has prototype
     const ADVector& ax
 and size must be equal to n . It specifies vector x ∈ B n at which an AD<Base> version of y = f ( x ) is to be evaluated.

ay
This argument has prototype
     ADVector& ay
 Its input size must be equal to m and does not change. The input values of its elements do not matter. Upon return, it is an AD<Base> version of y = f ( x ) .

sparsity
This argument has prototype
     atomic_base<Base>::option_enum sparsity
 It specifies sparsity in the atomic_base constructor and must be either atomic_base<Base>::pack_sparsity_enum , atomic_base<Base>::bool_sparsity_enum , or atomic_base<Base>::set_sparsity_enum . This argument is optional and its default value is unspecified.

optimize
This argument has prototype
     bool optimize
 It specifies if the recording corresponding to the atomic function should be optimized . One expects to use a checkpoint function many times, so it should be worth the time to optimize its operation sequence. For debugging purposes, it may be useful to use the original operation sequence (before optimization) because it corresponds more closely to algo . This argument is optional and its default value is true.

size_var
This size_var member function return value has prototype
     size_t sv
 It is the size_var for the ADFun<Base> object is used to store the operation sequence corresponding to algo .

option
The option syntax can be used to set the type of sparsity pattern used by atom_fun . This is an atomic_base<Base> function and its documentation can be found at atomic_option .

algo
The type of algo is arbitrary, except for the fact that the syntax
     algo(ax, ay)
 must evaluate the function y = f ( x ) using AD<Base> operations. In addition, we assume that the operation sequence does not depend on the value of ax .

atom_fun
Given ax it computes the corresponding value of ay using the operation sequence corresponding to algo . If AD<Base> operations are being recorded, it enters the computation as single operation in the recording see start recording . (Currently each use of atom_fun actually corresponds to m+n+2 operations and creates m new variables, but this is not part of the CppAD specifications and my change.)

clear
The atomic_base class holds onto static work space in order to increase speed by avoiding system memory allocation calls. This call makes to work space available to for other uses by the same thread. This should be called when you are done using the user atomic functions for a specific value of Base .

Restriction
The clear routine cannot be called while in parallel execution mode.

Example
The file checkpoint.cpp contains an example and test of these operations. It returns true if it succeeds and false if it fails.
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Prev Next atomic_mul_level.cpp

Atomic Operations and Multiple-Levels of AD: Example and Test

Discussion
One can use checkpoint or atomic_base to code an AD<Base> operation as atomic. This means that derivative computations that use the type Base will call the corresponding atomic_base member functions. On the other hand, if Base is AD<Other> the operations recorded at the Base level will not be atomic. This is demonstrated in this example. 

# include <cppad/cppad.hpp>

namespace {
     using CppAD::AD;
     typedef AD<double>                      a1double;
     typedef AD<a1double>                    a2double;
     typedef CPPAD_TESTVECTOR(a1double)      a1vector;
     typedef CPPAD_TESTVECTOR(a2double)      a2vector;

     void f_algo(const a2vector& x, a2vector& y)
     {     size_t n = x.size();
          y[0] = 0.0;
          for(size_t j = 1; j < n; j++)
               y[0] += x[j-1] * x[j];
          return;
     }
}
//
bool mul_level(void)
{     bool ok = true;
     using CppAD::checkpoint;
     using CppAD::ADFun;
     using CppAD::Independent;

     // domain dimension for this problem
     size_t n = 10;
     size_t m = 1;

     // checkpoint version of the function F(x)
     a2vector a2x(n), a2y(m);
     for(size_t j = 0; j < n; j++)
          a2x[j] = a2double(j + 1);
     //
     // could also use bool_sparsity_enum or set_sparsity_enum
     checkpoint<a1double> atom_f("atom_f", f_algo, a2x, a2y);
     //
     // Record a version of y = f(x) without checkpointing
     Independent(a2x);
     f_algo(a2x, a2y);
     ADFun<a1double> check_not(a2x, a2y);
     //
     // number of variables in a tape of f_algo that does not use checkpointing
     size_t size_not = check_not.size_var();
     //
     // Record a version of y = f(x) with checkpointing
     Independent(a2x);
     atom_f(a2x, a2y);
     ADFun<a1double> check_yes(a2x, a2y);
     //
     // f_algo is represented by one atomic operation in this tape
     ok &= check_yes.size_var() < size_not;
     //
     // now record operations at a1double level
     a1vector a1x(n), a1y(m);
     for(size_t j = 0; j < n; j++)
          a1x[j] = a1double(j + 1);
     //
     // without checkpointing
     Independent(a1x);
     a1y = check_not.Forward(0, a1x);
     ADFun<double> with_not(a1x, a1y);
     //
     // should have the same size
     ok &= with_not.size_var() == size_not;
     //
     // with checkpointing
     Independent(a1x);
     a1y = check_yes.Forward(0, a1x);
     ADFun<double> with_yes(a1x, a1y);
     //
     // f_algo is nolonger represented by one atomic operation in this tape
     ok &= with_yes.size_var() == size_not;
     //
     return ok;
}
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Prev Next atomic_reverse.cpp

Atomic Reverse: Example and Test

Purpose
This example demonstrates reverse mode derivative calculation using an atomic operation.

function
For this example, the atomic function f : R 3 → R 2 is defined by f ( x ) = ( x 2 * x 2 x 0 * x 1 ) The corresponding Jacobian is f ( 1 ) ( x ) = ( 0 0 2 x 2 x 1 x 0 0 ) The Hessians of the component functions are f 0 ( 2 ) ( x ) = ( 0 0 0 0 0 0 0 0 2 ) , f 1 ( 2 ) ( x ) = ( 0 1 0 1 0 0 0 0 0 )
Start Class Definition 
# include <cppad/cppad.hpp>
namespace {          // isolate items below to this file
using CppAD::vector; // abbreviate as vector
//
class atomic_reverse : public CppAD::atomic_base<double> {

Constructor 
public:
     // constructor (could use const char* for name)
     atomic_reverse(const std::string& name) :
     // this example does not use sparsity patterns
     CppAD::atomic_base<double>(name)
     { }
private:

forward 
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                    p ,
          size_t                    q ,
          const vector<bool>&      vx ,
          vector<bool>&            vy ,
          const vector<double>&    tx ,
          vector<double>&          ty
     )
     {
          size_t q1 = q + 1;
# ifndef NDEBUG
          size_t n = tx.size() / q1;
          size_t m = ty.size() / q1;
# endif
          assert( n == 3 );
          assert( m == 2 );
          assert( p <= q );

          // this example only implements up to first order forward mode
          bool ok = q <= 1;
          if( ! ok )
               return ok;

          // check for defining variable information
          // This case must always be implemented
          if( vx.size() > 0 )
          {     vy[0] = vx[2];
               vy[1] = vx[0] || vx[1];
          }
          // ------------------------------------------------------------------
          // Zero forward mode.
          // This case must always be implemented
          // f(x) = [ x_2 * x_2 ]
          //        [ x_0 * x_1 ]
          // y^0  = f( x^0 )
          if( p <= 0 )
          {     // y_0^0 = x_2^0 * x_2^0
               ty[0 * q1 + 0] = tx[2 * q1 + 0] * tx[2 * q1 + 0];
               // y_1^0 = x_0^0 * x_1^0
               ty[1 * q1 + 0] = tx[0 * q1 + 0] * tx[1 * q1 + 0];
          }
          if( q <= 0 )
               return ok;
          // ------------------------------------------------------------------
          // First order one forward mode.
          // This case is needed if first order forward mode is used.
          // f'(x) = [   0,   0, 2 * x_2 ]
          //         [ x_1, x_0,       0 ]
          // y^1 =  f'(x^0) * x^1
          if( p <= 1 )
          {     // y_0^1 = 2 * x_2^0 * x_2^1
               ty[0 * q1 + 1] = 2.0 * tx[2 * q1 + 0] * tx[2 * q1 + 1];

               // y_1^1 = x_1^0 * x_0^1 + x_0^0 * x_1^1
               ty[1 * q1 + 1]  = tx[1 * q1 + 0] * tx[0 * q1 + 1];
               ty[1 * q1 + 1] += tx[0 * q1 + 0] * tx[1 * q1 + 1];
          }
          return ok;
     }

reverse 
     // reverse mode routine called by CppAD
     virtual bool reverse(
          size_t                   q ,
          const vector<double>&    tx ,
          const vector<double>&    ty ,
          vector<double>&          px ,
          const vector<double>&    py
     )
     {
          size_t q1 = q + 1;
          size_t n = tx.size() / q1;
# ifndef NDEBUG
          size_t m = ty.size() / q1;
# endif
          assert( n == 3 );
          assert( m == 2 );

          // this example only implements up to second order reverse mode
          bool ok = q1 <= 2;
          if( ! ok )
               return ok;
          //
          // initalize summation as zero
          for(size_t j = 0; j < n; j++)
               for(size_t k = 0; k < q; k++)
                    px[j * q1 + k] = 0.0;
          //
          if( q1 == 2 )
          {     // --------------------------------------------------------------
               // Second order reverse first compute partials of first order
               // We use the notation pf_ij^k for partial of F_i^1 w.r.t. x_j^k
               //
               // y_0^1    = 2 * x_2^0 * x_2^1
               // pf_02^0  = 2 * x_2^1
               // pf_02^1  = 2 * x_2^0
               //
               // y_1^1    = x_1^0 * x_0^1 + x_0^0 * x_1^1
               // pf_10^0  = x_1^1
               // pf_11^0  = x_0^1
               // pf_10^1  = x_1^0
               // pf_11^1  = x_0^0
               //
               // px_0^0 += py_0^1 * pf_00^0 + py_1^1 * pf_10^0
               //        += py_1^1 * x_1^1
               px[0 * q1 + 0] += py[1 * q1 + 1] * tx[1 * q1 + 1];
               //
               // px_0^1 += py_0^1 * pf_00^1 + py_1^1 * pf_10^1
               //        += py_1^1 * x_1^0
               px[0 * q1 + 1] += py[1 * q1 + 1] * tx[1 * q1 + 0];
               //
               // px_1^0 += py_0^1 * pf_01^0 + py_1^1 * pf_11^0
               //        += py_1^1 * x_0^1
               px[1 * q1 + 0] += py[1 * q1 + 1] * tx[0 * q1 + 1];
               //
               // px_1^1 += py_0^1 * pf_01^1 + py_1^1 * pf_11^1
               //        += py_1^1 * x_0^0
               px[1 * q1 + 1] += py[1 * q1 + 1] * tx[0 * q1 + 0];
               //
               // px_2^0 += py_0^1 * pf_02^0 + py_1^1 * pf_12^0
               //        += py_0^1 * 2 * x_2^1
               px[2 * q1 + 0] += py[0 * q1 + 1] * 2.0 * tx[2 * q1 + 1];
               //
               // px_2^1 += py_0^1 * pf_02^1 + py_1^1 * pf_12^1
               //        += py_0^1 * 2 * x_2^0
               px[2 * q1 + 1] += py[0 * q1 + 1] * 2.0 * tx[2 * q1 + 0];
          }
          // --------------------------------------------------------------
          // First order reverse computes partials of zero order coefficients
          // We use the notation pf_ij for partial of F_i^0 w.r.t. x_j^0
          //
          // y_0^0 = x_2^0 * x_2^0
          // pf_00 = 0,     pf_01 = 0,  pf_02 = 2 * x_2^0
          //
          // y_1^0 = x_0^0 * x_1^0
          // pf_10 = x_1^0, pf_11 = x_0^0,  pf_12 = 0
          //
          // px_0^0 += py_0^0 * pf_00 + py_1^0 * pf_10
          //        += py_1^0 * x_1^0
          px[0 * q1 + 0] += py[1 * q1 + 0] * tx[1 * q1 + 0];
          //
          // px_1^0 += py_1^0 * pf_01 + py_1^0 * pf_11
          //        += py_1^0 * x_0^0
          px[1 * q1 + 0] += py[1 * q1 + 0] * tx[0 * q1 + 0];
          //
          // px_2^0 += py_1^0 * pf_02 + py_1^0 * pf_12
          //        += py_0^0 * 2.0 * x_2^0
          px[2 * q1 + 0] += py[0 * q1 + 0] * 2.0 * tx[2 * q1 + 0];
          // --------------------------------------------------------------
          return ok;
     }
};
}  // End empty namespace

Use Atomic Function 
bool reverse(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     //
     // Create the atomic_reverse object
     atomic_reverse afun("atomic_reverse");
     //
     // Create the function f(u)
     //
     // domain space vector
     size_t n  = 3;
     double x_0 = 1.00;
     double x_1 = 2.00;
     double x_2 = 3.00;
     vector< AD<double> > au(n);
     au[0] = x_0;
     au[1] = x_1;
     au[2] = x_2;

     // declare independent variables and start tape recording
     CppAD::Independent(au);

     // range space vector
     size_t m = 2;
     vector< AD<double> > ay(m);

     // call user function
     vector< AD<double> > ax = au;
     afun(ax, ay);

     // create f: u -> y and stop tape recording
     CppAD::ADFun<double> f;
     f.Dependent (au, ay);  // y = f(u)
     //
     // check function value
     double check = x_2 * x_2;
     ok &= NearEqual( Value(ay[0]) , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual( Value(ay[1]) , check,  eps, eps);

     // --------------------------------------------------------------------
     // zero order forward
     //
     vector<double> x0(n), y0(m);
     x0[0] = x_0;
     x0[1] = x_1;
     x0[2] = x_2;
     y0   = f.Forward(0, x0);
     check = x_2 * x_2;
     ok &= NearEqual(y0[0] , check,  eps, eps);
     check = x_0 * x_1;
     ok &= NearEqual(y0[1] , check,  eps, eps);
     // --------------------------------------------------------------------
     // first order reverse
     //
     // value of Jacobian of f
     double check_jac[] = {
          0.0, 0.0, 2.0 * x_2,
          x_1, x_0,       0.0
     };
     vector<double> w(m), dw(n);
     //
     // check derivative of f_0 (x)
     for(size_t i = 0; i < m; i++)
     {     w[i]   = 1.0;
          w[1-i] = 0.0;
          dw = f.Reverse(1, w);
          for(size_t j = 0; j < n; j++)
          {     // compute partial in j-th component direction
               ok &= NearEqual(dw[j], check_jac[i * n + j], eps, eps);
          }
     }
     // --------------------------------------------------------------------
     // second order reverse
     //
     // value of Hessian of f_0
     double check_hes_0[] = {
          0.0, 0.0, 0.0,
          0.0, 0.0, 0.0,
          0.0, 0.0, 2.0
     };
     //
     // value of Hessian of f_1
     double check_hes_1[] = {
          0.0, 1.0, 0.0,
          1.0, 0.0, 0.0,
          0.0, 0.0, 0.0
     };
     vector<double> x1(n), dw2( 2 * n );
     for(size_t j = 0; j < n; j++)
     {     for(size_t j1 = 0; j1 < n; j1++)
               x1[j1] = 0.0;
          x1[j] = 1.0;
          // first order forward
          f.Forward(1, x1);
          w[0] = 1.0;
          w[1] = 0.0;
          dw2  = f.Reverse(2, w);
          for(size_t i = 0; i < n; i++)
               ok &= NearEqual(dw2[i * 2 + 1], check_hes_0[i * n + j], eps, eps);
          w[0] = 0.0;
          w[1] = 1.0;
          dw2  = f.Reverse(2, w);
          for(size_t i = 0; i < n; i++)
               ok &= NearEqual(dw2[i * 2 + 1], check_hes_1[i * n + j], eps, eps);
     }
     // --------------------------------------------------------------------
     return ok;
}
Input File: example/atomic/reverse.cpp cppad-20170000.3/doc/_atomic_reverse.cpp_xml.js0000644000175200017650000000434613057470505020351 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'atomic.xml', 'atomic_base.xml', 'atomic_reverse.xml', 'atomic_reverse.cpp.xml' ]; var list_down3 = [ 'checkpoint.xml', 'atomic_base.xml' ]; var list_down2 = [ 'atomic_ctor.xml', 'atomic_option.xml', 'atomic_afun.xml', 'atomic_forward.xml', 'atomic_reverse.xml', 'atomic_for_sparse_jac.xml', 'atomic_rev_sparse_jac.xml', 'atomic_for_sparse_hes.xml', 'atomic_rev_sparse_hes.xml', 'atomic_base_clear.xml', 'atomic_get_started.cpp.xml', 'atomic_norm_sq.cpp.xml', 'atomic_reciprocal.cpp.xml', 'atomic_set_sparsity.cpp.xml', 'atomic_tangent.cpp.xml', 'atomic_eigen_mat_mul.cpp.xml', 'atomic_eigen_mat_inv.cpp.xml', 'atomic_eigen_cholesky.cpp.xml', 'atomic_mat_mul.cpp.xml' ]; var list_down1 = [ 'atomic_reverse.cpp.xml' ]; var list_current0 = [ 'atomic_reverse.cpp.xml#Purpose', 'atomic_reverse.cpp.xml#function', 'atomic_reverse.cpp.xml#Start Class Definition', 'atomic_reverse.cpp.xml#Constructor', 'atomic_reverse.cpp.xml#forward', 'atomic_reverse.cpp.xml#reverse', 'atomic_reverse.cpp.xml#Use Atomic Function' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_atomic_for_sparse_jac_xml.js0000644000175200017650000000501213057470505021064 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'atomic.xml', 'atomic_base.xml', 'atomic_for_sparse_jac.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; var list_down2 = [ 'checkpoint.xml', 'atomic_base.xml' ]; var list_down1 = [ 'atomic_ctor.xml', 'atomic_option.xml', 'atomic_afun.xml', 'atomic_forward.xml', 'atomic_reverse.xml', 'atomic_for_sparse_jac.xml', 'atomic_rev_sparse_jac.xml', 'atomic_for_sparse_hes.xml', 'atomic_rev_sparse_hes.xml', 'atomic_base_clear.xml', 'atomic_get_started.cpp.xml', 'atomic_norm_sq.cpp.xml', 'atomic_reciprocal.cpp.xml', 'atomic_set_sparsity.cpp.xml', 'atomic_tangent.cpp.xml', 'atomic_eigen_mat_mul.cpp.xml', 'atomic_eigen_mat_inv.cpp.xml', 'atomic_eigen_cholesky.cpp.xml', 'atomic_mat_mul.cpp.xml' ]; 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if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_atomic_rev_sparse_jac.cpp_xml.js0000644000175200017650000000460213057470505021657 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'atomic.xml', 'atomic_base.xml', 'atomic_rev_sparse_jac.xml', 'atomic_rev_sparse_jac.cpp.xml' ]; var list_down3 = [ 'checkpoint.xml', 'atomic_base.xml' ]; var list_down2 = [ 'atomic_ctor.xml', 'atomic_option.xml', 'atomic_afun.xml', 'atomic_forward.xml', 'atomic_reverse.xml', 'atomic_for_sparse_jac.xml', 'atomic_rev_sparse_jac.xml', 'atomic_for_sparse_hes.xml', 'atomic_rev_sparse_hes.xml', 'atomic_base_clear.xml', 'atomic_get_started.cpp.xml', 'atomic_norm_sq.cpp.xml', 'atomic_reciprocal.cpp.xml', 'atomic_set_sparsity.cpp.xml', 'atomic_tangent.cpp.xml', 'atomic_eigen_mat_mul.cpp.xml', 'atomic_eigen_mat_inv.cpp.xml', 'atomic_eigen_cholesky.cpp.xml', 'atomic_mat_mul.cpp.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_atomic_base_clear_xml.js0000644000175200017650000000426413057470505020174 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'advalued.xml', 'atomic.xml', 'atomic_base.xml', 'atomic_base_clear.xml' ]; var list_down3 = [ 'arithmetic.xml', 'unary_standard_math.xml', 'binary_math.xml', 'condexp.xml', 'discrete.xml', 'numeric_limits.xml', 'atomic.xml' ]; 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function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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} function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_atomic_reciprocal.cpp_xml.js0000644000175200017650000000566013057470505021021 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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} cppad-20170000.3/doc/_base_complex.hpp_xml.js0000644000175200017650000000453513057470506020011 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'base_require.xml', 'base_example.xml', 'base_complex.hpp.xml' ]; var list_down3 = [ 'ad_ctor.xml', 'ad_assign.xml', 'convert.xml', 'advalued.xml', 'boolvalued.xml', 'vecad.xml', 'base_require.xml' ]; var list_down2 = [ 'base_member.xml', 'base_cond_exp.xml', 'base_identical.xml', 'base_ordered.xml', 'base_std_math.xml', 'base_limits.xml', 'base_to_string.xml', 'base_hash.xml', 'base_example.xml' ]; var list_down1 = [ 'base_alloc.hpp.xml', 'base_require.cpp.xml', 'base_adolc.hpp.xml', 'base_float.hpp.xml', 'base_double.hpp.xml', 'base_complex.hpp.xml' ]; var list_down0 = [ 'complex_poly.cpp.xml' ]; var list_current0 = [ 'base_complex.hpp.xml#Example', 'base_complex.hpp.xml#Include Order', 'base_complex.hpp.xml#CondExpOp', 'base_complex.hpp.xml#CondExpRel', 'base_complex.hpp.xml#EqualOpSeq', 'base_complex.hpp.xml#Identical', 'base_complex.hpp.xml#Ordered', 'base_complex.hpp.xml#Integer', 'base_complex.hpp.xml#azmul', 'base_complex.hpp.xml#isnan', 'base_complex.hpp.xml#Valid Unary Math', 'base_complex.hpp.xml#Invalid Unary Math', 'base_complex.hpp.xml#pow', 'base_complex.hpp.xml#numeric_limits', 'base_complex.hpp.xml#to_string' ]; 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} cppad-20170000.3/doc/_complex_poly.cpp_xml.js0000644000175200017650000000340613057470506020051 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ad.xml', 'base_require.xml', 'base_example.xml', 'base_complex.hpp.xml', 'complex_poly.cpp.xml' ]; var list_down3 = [ 'base_member.xml', 'base_cond_exp.xml', 'base_identical.xml', 'base_ordered.xml', 'base_std_math.xml', 'base_limits.xml', 'base_to_string.xml', 'base_hash.xml', 'base_example.xml' ]; var list_down2 = [ 'base_alloc.hpp.xml', 'base_require.cpp.xml', 'base_adolc.hpp.xml', 'base_float.hpp.xml', 'base_double.hpp.xml', 'base_complex.hpp.xml' ]; var list_down1 = [ 'complex_poly.cpp.xml' ]; var list_current0 = [ 'complex_poly.cpp.xml#Poly' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/independent.xml0000644000175200017650000002775113057470506016231 0ustar coincoin-web Declare Independent Variables and Start Recording
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Declare Independent Variables and Start Recording

Syntax
Independent(x)
 Independent(x, abort_op_index)
Purpose
Start recording AD of Base operations with x as the independent variable vector. Once the operation sequence is completed, it must be transferred to a function object; see below.

Start Recording
An operation sequence recording is started by the commands
     Independent(x)
     Independent(x, abort_op_index)
Stop Recording
The recording is stopped, and the operation sequence is transferred to the AD function object f , using either the function constructor
     ADFun<Base> f(x, y)
 or the dependent variable specifier
     f.Dependent(x, y)
 The only other way to stop a recording is using abort_recording . Between when the recording is started and when it stopped, we refer to the elements of x , and the values that depend on the elements of x , as AD<Base> variables.

x
The vector x has prototype
     VectorAD &x
 (see VectorAD below). The size of the vector x , must be greater than zero, and is the number of independent variables for this AD operation sequence.

abort_op_index
It specifies the operator index at which the execution is be aborted by calling the CppAD error handler . When this error handler leads to an assert, the user can inspect the call stack to see the source code corresponding to this operator index; see purpose . No abort will occur if abort_op_index is zero, of if NDEBUG is defined.

VectorAD
The type VectorAD must be a SimpleVector class with elements of type AD<Base> . The routine CheckSimpleVector will generate an error message if this is not the case.

Parallel Mode
Each thread can have one, and only one, active recording. A call to Independent starts the recording for the current thread. The recording must be stopped by a corresponding call to
     ADFun<Base> f( x, y)
 or
     f.Dependent( x, y)
 or abort_recording preformed by the same thread; i.e., thread_alloc::thread_num must be the same.

Example
The file independent.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/independent.hpp cppad-20170000.3/doc/_independent_xml.js0000644000175200017650000000347313057470506017057 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'independent.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'independent.cpp.xml' ]; var list_current0 = [ 'independent.xml#Syntax', 'independent.xml#Purpose', 'independent.xml#Start Recording', 'independent.xml#Stop Recording', 'independent.xml#x', 'independent.xml#abort_op_index', 'independent.xml#VectorAD', 'independent.xml#Parallel Mode', 'independent.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_independent.cpp_xml.js0000644000175200017650000000331513057470506017633 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'independent.xml', 'independent.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'independent.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_funconstruct_xml.js0000644000175200017650000000422513057470506017313 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funconstruct.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'fun_assign.cpp.xml' ]; var list_current0 = [ 'funconstruct.xml#Syntax', 'funconstruct.xml#Purpose', 'funconstruct.xml#x', 'funconstruct.xml#y', 'funconstruct.xml#VectorAD', 'funconstruct.xml#Default Constructor', 'funconstruct.xml#Sequence Constructor', 'funconstruct.xml#Copy Constructor', 'funconstruct.xml#Assignment Operator', 'funconstruct.xml#Assignment Operator.Taylor Coefficients', 'funconstruct.xml#Assignment Operator.Sparsity Patterns', 'funconstruct.xml#Parallel Mode', 'funconstruct.xml#Example', 'funconstruct.xml#Example.Sequence Constructor', 'funconstruct.xml#Example.Default Constructor', 'funconstruct.xml#Example.Assignment Operator' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_fun_assign.cpp_xml.js0000644000175200017650000000331413057470506017471 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funconstruct.xml', 'fun_assign.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'fun_assign.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/abort_recording.xml0000644000175200017650000000753513057470506017075 0ustar coincoin-web Abort Recording of an Operation Sequence
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Abort Recording of an Operation Sequence

Syntax
AD<Base>::abort_recording()

Purpose
Sometimes it is necessary to abort the recording of an operation sequence that started with a call of the form
     Independent(x)
 If such a recording is currently in progress, abort_recording will stop the recording and delete the corresponding information. Otherwise, abort_recording has no effect.

Example
The file abort_recording.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: cppad/core/abort_recording.hpp cppad-20170000.3/doc/_abort_recording_xml.js0000644000175200017650000000322613057470506017721 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'abort_recording.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'abort_recording.cpp.xml' ]; var list_current0 = [ 'abort_recording.xml#Syntax', 'abort_recording.xml#Purpose', 'abort_recording.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_abort_recording.cpp_xml.js0000644000175200017650000000333113057470506020477 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'abort_recording.xml', 'abort_recording.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'abort_recording.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_seq_property_xml.js0000644000175200017650000000374713057470506017322 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'seq_property.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down0 = [ 'seq_property.cpp.xml' ]; var list_current0 = [ 'seq_property.xml#Syntax', 'seq_property.xml#Syntax.See Also', 'seq_property.xml#Purpose', 'seq_property.xml#f', 'seq_property.xml#Domain', 'seq_property.xml#Range', 'seq_property.xml#Parameter', 'seq_property.xml#size_var', 'seq_property.xml#size_par', 'seq_property.xml#size_op', 'seq_property.xml#size_op_arg', 'seq_property.xml#size_text', 'seq_property.xml#size_VecAD', 'seq_property.xml#size_op_seq', 'seq_property.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; 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} cppad-20170000.3/doc/forward_zero.xml0000644000175200017650000004155013057470506016430 0ustar coincoin-web Zero Order Forward Mode: Function Values
Prev Next forward_zero

Zero Order Forward Mode: Function Values

Syntax
y0 = f.Forward(0, x0)
 y0 = f.Forward(0, x0, s)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The result of the syntax above is y 0 = F ( x 0 ) See the FunCheck discussion for possible differences between F ( x ) and the algorithm that defined the operation sequence.

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const. After this call to Forward, the value returned by
     f.size_order()
 will be equal to one (see size_order ).

x0
The argument x0 has prototype
     const Vector& x0
 (see Vector below) and its size must be equal to n , the dimension of the domain space for f .

s
If the argument s is not present, std::cout is used in its place. Otherwise, this argument has prototype
     std::ostream& s
 It specifies where the output corresponding to PrintFor , and this zero order forward mode call, will be written.

y0
The result y0 has prototype
     Vector y0
 (see Vector below) and its value is F ( x ) at x = x0 . The size of y0 is equal to m , the dimension of the range space for f .

Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file forward.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.

Special Case
This is special case of forward_order where Y ( t ) = F [ X ( t ) ] X ( t ) = x ( 0 ) t 0 + x ( 1 ) * t 1 + ⋯ , + x ( q ) * t q + o ( t q ) Y ( t ) = y ( 0 ) t 0 + y ( 1 ) * t 1 + ⋯ , + y ( q ) * t q + o ( t q ) and o ( t q ) * t - q → 0 as t → 0 . For this special case, q = 0 , x ( 0 ) = x0 , X ( t ) = x ( 0 ) , and y ( 0 ) = Y ( t ) = F [ X ( t ) ] = F ( x ( 0 ) ) which agrees with the specifications for y0 in the purpose above.
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} cppad-20170000.3/doc/_compare_change_xml.js0000644000175200017650000000416013057470506017507 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'forward.xml', 'compare_change.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down1 = [ 'forward_zero.xml', 'forward_one.xml', 'forward_two.xml', 'forward_order.xml', 'forward_dir.xml', 'size_order.xml', 'compare_change.xml', 'capacity_order.xml', 'number_skip.xml' ]; var list_down0 = [ 'compare_change.cpp.xml' ]; var list_current0 = [ 'compare_change.xml#Syntax', 'compare_change.xml#Purpose', 'compare_change.xml#f', 'compare_change.xml#count', 'compare_change.xml#count.Speed', 'compare_change.xml#number', 'compare_change.xml#number.Discussion', 'compare_change.xml#op_index', 'compare_change.xml#op_index.Purpose', 'compare_change.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_compare_change.cpp_xml.js0000644000175200017650000000315513057470506020273 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'forward.xml', 'compare_change.xml', 'compare_change.cpp.xml' ]; var list_down3 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down2 = [ 'forward_zero.xml', 'forward_one.xml', 'forward_two.xml', 'forward_order.xml', 'forward_dir.xml', 'size_order.xml', 'compare_change.xml', 'capacity_order.xml', 'number_skip.xml' ]; var list_down1 = [ 'compare_change.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_capacity_order_xml.js0000644000175200017650000000413713057470506017550 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'forward.xml', 'capacity_order.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down1 = [ 'forward_zero.xml', 'forward_one.xml', 'forward_two.xml', 'forward_order.xml', 'forward_dir.xml', 'size_order.xml', 'compare_change.xml', 'capacity_order.xml', 'number_skip.xml' ]; var list_down0 = [ 'capacity_order.cpp.xml' ]; var list_current0 = [ 'capacity_order.xml#Syntax', 'capacity_order.xml#Syntax.See Also', 'capacity_order.xml#Purpose', 'capacity_order.xml#f', 'capacity_order.xml#c', 'capacity_order.xml#c.Pre-Allocating Memory', 'capacity_order.xml#c.Freeing Memory', 'capacity_order.xml#Original State', 'capacity_order.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_capacity_order.cpp_xml.js0000644000175200017650000000315513057470506020330 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'forward.xml', 'capacity_order.xml', 'capacity_order.cpp.xml' ]; var list_down3 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down2 = [ 'forward_zero.xml', 'forward_one.xml', 'forward_two.xml', 'forward_order.xml', 'forward_dir.xml', 'size_order.xml', 'compare_change.xml', 'capacity_order.xml', 'number_skip.xml' ]; var list_down1 = [ 'capacity_order.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_number_skip_xml.js0000644000175200017650000000371513057470506017077 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'forward.xml', 'number_skip.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down1 = [ 'forward_zero.xml', 'forward_one.xml', 'forward_two.xml', 'forward_order.xml', 'forward_dir.xml', 'size_order.xml', 'compare_change.xml', 'capacity_order.xml', 'number_skip.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_number_skip.cpp_xml.js0000644000175200017650000000314413057470506017654 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'forward.xml', 'number_skip.xml', 'number_skip.cpp.xml' ]; var list_down3 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down2 = [ 'forward_zero.xml', 'forward_one.xml', 'forward_two.xml', 'forward_order.xml', 'forward_dir.xml', 'size_order.xml', 'compare_change.xml', 'capacity_order.xml', 'number_skip.xml' ]; var list_down1 = [ 'number_skip.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/reverse_one.xml0000644000175200017650000003156213057470506016243 0ustar coincoin-web First Order Reverse Mode
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First Order Reverse Mode

Syntax
dw = f.Reverse(1, w)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . The function W : B n → B is defined by W ( x ) = w 0 * F 0 ( x ) + ⋯ + w m -1 * F m -1 ( x ) The result of this operation is the derivative dw = W ( 1 ) ( x ) ; i.e., dw = w 0 * F 0 ( 1 ) ( x ) + ⋯ + w m -1 * F m -1 ( 1 ) ( x ) Note that if w is the i-th elementary vector , dw = F i ( 1 ) ( x ) .

f
The object f has prototype
     const ADFun<Base> f
 Before this call to Reverse, the value returned by
     f.size_order()
 must be greater than or equal one (see size_order ).

x
The vector x in expression for dw above corresponds to the previous call to forward_zero using this ADFun object f ; i.e.,
     f.Forward(0, x)
 If there is no previous call with the first argument zero, the value of the independent variables during the recording of the AD sequence of operations is used for x .

w
The argument w has prototype
     const Vector &w
 (see Vector below) and its size must be equal to m , the dimension of the range space for f .

dw
The result dw has prototype
     Vector dw
 (see Vector below) and its value is the derivative W ( 1 ) ( x ) . The size of dw is equal to n , the dimension of the domain space for f .

Vector
The type Vector must be a SimpleVector class with elements of type Base . The routine CheckSimpleVector will generate an error message if this is not the case.

Example
The file reverse_one.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.
Input File: omh/reverse/reverse_one.omh cppad-20170000.3/doc/_reverse_one_xml.js0000644000175200017650000000356513057470506017100 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'reverse.xml', 'reverse_one.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down1 = [ 'reverse_one.xml', 'reverse_two.xml', 'reverse_any.xml' ]; var list_down0 = [ 'reverse_one.cpp.xml' ]; var list_current0 = [ 'reverse_one.xml#Syntax', 'reverse_one.xml#Purpose', 'reverse_one.xml#f', 'reverse_one.xml#x', 'reverse_one.xml#w', 'reverse_one.xml#dw', 'reverse_one.xml#Vector', 'reverse_one.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_reverse_one.cpp_xml.js0000644000175200017650000000275213057470506017656 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'reverse.xml', 'reverse_one.xml', 'reverse_one.cpp.xml' ]; var list_down3 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down2 = [ 'reverse_one.xml', 'reverse_two.xml', 'reverse_any.xml' ]; var list_down1 = [ 'reverse_one.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_reverse_two_xml.js0000644000175200017650000000405113057470506017117 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funeval.xml', 'reverse.xml', 'reverse_two.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'forward.xml', 'reverse.xml', 'sparse.xml' ]; var list_down1 = [ 'reverse_one.xml', 'reverse_two.xml', 'reverse_any.xml' ]; var list_down0 = [ 'reverse_two.cpp.xml', 'hes_times_dir.cpp.xml' ]; var list_current0 = [ 'reverse_two.xml#Syntax', 'reverse_two.xml#Purpose', 'reverse_two.xml#x^(k)', 'reverse_two.xml#W', 'reverse_two.xml#f', 'reverse_two.xml#w', 'reverse_two.xml#dw', 'reverse_two.xml#dw.First Order Partials', 'reverse_two.xml#dw.Second Order Partials', 'reverse_two.xml#Vector', 'reverse_two.xml#Hessian Times Direction', 'reverse_two.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; 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Jacobian Sparsity Pattern: Forward Mode

Syntax
s = f.ForSparseJac(q, r)
 s = f.ForSparseJac(q, r, transpose, dependency)

Purpose
We use F : B n → B m to denote the AD function corresponding to f . For a fixed n × q matrix R , the Jacobian of F [ x + R * u ] with respect to u at u = 0 is S ( x ) = F ( 1 ) ( x ) * R Given a sparsity pattern for R , ForSparseJac returns a sparsity pattern for the S ( x ) .

f
The object f has prototype
     ADFun<Base> f
 Note that the ADFun object f is not const. After a call to ForSparseJac, the sparsity pattern for each of the variables in the operation sequence is held in f (for possible later use by RevSparseHes ). These sparsity patterns are stored with elements of type bool or elements of type std::set<size_t> (see VectorSet below).

size_forward_bool
After ForSparseJac, if k is a size_t object,
     k = f.size_forward_bool()
 sets k to the amount of memory (in unsigned character units) used to store the sparsity pattern with elements of type bool in the function object f . If the sparsity patterns for the previous ForSparseJac used elements of type bool, the return value for size_forward_bool will be non-zero. Otherwise, its return value will be zero. This sparsity pattern is stored for use by RevSparseHes and when it is not longer needed, it can be deleted (and the corresponding memory freed) using
     f.size_forward_bool(0)
 After this call, f.size_forward_bool() will return zero.

size_forward_set
After ForSparseJac, if k is a size_t object,
     k = f.size_forward_set()
 sets s to the total number of elements in all the sets corresponding to the sparsity pattern stored in the function object f . If the sparsity patterns for this operation use elements of type bool, the return value for size_forward_set will be zero. Otherwise, its return value will be non-zero (unless the entire sparsity pattern is false). This sparsity pattern is stored for use by RevSparseHes and when it is not longer needed, it can be deleted (and the corresponding memory freed) using
     f.size_forward_set(0)
 After this call, f.size_forward_set() will return zero.

x
If the operation sequence in f is independent of the independent variables in x ∈ B n , the sparsity pattern is valid for all values of (even if it has CondExp or VecAD operations).

q
The argument q has prototype
     size_t q
 It specifies the number of columns in R ∈ B n × q and the Jacobian S ( x ) ∈ B m × q .

transpose
The argument transpose has prototype
     bool transpose
 The default value false is used when transpose is not present.

dependency
The argument dependency has prototype
     bool dependency
 If dependency is true, the dependency pattern (instead of sparsity pattern) is computed.

r
The argument r has prototype
     const VectorSet& r
 see VectorSet below.

transpose false
If r has elements of type bool, its size is n * q . If it has elements of type std::set<size_t>, its size is n and all the set elements must be between zero and q-1 inclusive. It specifies a sparsity pattern for the matrix R ∈ B n × q .

transpose true
If r has elements of type bool, its size is q * n . If it has elements of type std::set<size_t>, its size is q and all the set elements must be between zero and n-1 inclusive. It specifies a sparsity pattern for the matrix R T ∈ B q × n .

s
The return value s has prototype
     VectorSet s
 see VectorSet below.

transpose false
If s has elements of type bool, its size is m * q . If it has elements of type std::set<size_t>, its size is m and all its set elements are between zero and q-1 inclusive. It specifies a sparsity pattern for the matrix S ( x ) ∈ B m × q .

transpose true
If s has elements of type bool, its size is q * m . If it has elements of type std::set<size_t>, its size is q and all its set elements are between zero and m-1 inclusive. It specifies a sparsity pattern for the matrix S ( x ) T ∈ B q × m .

VectorSet
The type VectorSet must be a SimpleVector class with elements of type bool or std::set<size_t>; see sparsity pattern for a discussion of the difference.

Entire Sparsity Pattern
Suppose that q = n and R is the n × n identity matrix. In this case, the corresponding value for s is a sparsity pattern for the Jacobian S ( x ) = F ( 1 ) ( x ) .

Example
The file for_sparse_jac.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise. The file sparsity_sub.cpp contains an example and test of using ForSparseJac to compute the sparsity pattern for a subset of the Jacobian.
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Jacobian: Example and Test

# include <cppad/cppad.hpp>
namespace { // ---------------------------------------------------------
// define the template function JacobianCases<Vector> in empty namespace
template <typename Vector>
bool JacobianCases()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::exp;
     using CppAD::sin;
     using CppAD::cos;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     X[0] = 1.;
     X[1] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(X);

     // a calculation between the domain and range values
     AD<double> Square = X[0] * X[0];

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>)  Y(m);
     Y[0] = Square * exp( X[1] );
     Y[1] = Square * sin( X[1] );
     Y[2] = Square * cos( X[1] );

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // new value for the independent variable vector
     Vector x(n);
     x[0] = 2.;
     x[1] = 1.;

     // compute the derivative at this x
     Vector jac( m * n );
     jac = f.Jacobian(x);

     /*
     F'(x) = [ 2 * x[0] * exp(x[1]) ,  x[0] * x[0] * exp(x[1]) ]
             [ 2 * x[0] * sin(x[1]) ,  x[0] * x[0] * cos(x[1]) ]
             [ 2 * x[0] * cos(x[1]) , -x[0] * x[0] * sin(x[i]) ]
     */
     ok &=  NearEqual( 2.*x[0]*exp(x[1]), jac[0*n+0], eps99, eps99);
     ok &=  NearEqual( 2.*x[0]*sin(x[1]), jac[1*n+0], eps99, eps99);
     ok &=  NearEqual( 2.*x[0]*cos(x[1]), jac[2*n+0], eps99, eps99);

     ok &=  NearEqual( x[0] * x[0] *exp(x[1]), jac[0*n+1], eps99, eps99);
     ok &=  NearEqual( x[0] * x[0] *cos(x[1]), jac[1*n+1], eps99, eps99);
     ok &=  NearEqual(-x[0] * x[0] *sin(x[1]), jac[2*n+1], eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool Jacobian(void)
{     bool ok = true;
     // Run with Vector equal to three different cases
     // all of which are Simple Vectors with elements of type double.
     ok &= JacobianCases< CppAD::vector  <double> >();
     ok &= JacobianCases< std::vector    <double> >();
     ok &= JacobianCases< std::valarray  <double> >();
     return ok;
}
Input File: example/jacobian.cpp cppad-20170000.3/doc/_jacobian.cpp_xml.js0000644000175200017650000000324713057470506017110 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'jacobian.xml', 'jacobian.cpp.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down1 = [ 'jacobian.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/for_one.cpp.xml0000644000175200017650000004301313057470506016131 0ustar coincoin-web First Order Partial Driver: Example and Test
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First Order Partial Driver: Example and Test
# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------
// define the template function ForOneCases<Vector> in empty namespace
template <typename Vector>
bool ForOneCases()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::exp;
     using CppAD::sin;
     using CppAD::cos;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     X[0] = 1.;
     X[1] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>)  Y(m);
     Y[0] = X[0] * exp( X[1] );
     Y[1] = X[0] * sin( X[1] );
     Y[2] = X[0] * cos( X[1] );

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // new value for the independent variable vector
     Vector x(n);
     x[0] = 2.;
     x[1] = 1.;

     // compute partial of y w.r.t x[0]
     Vector dy(m);
     dy  = f.ForOne(x, 0);
     ok &= NearEqual( dy[0], exp(x[1]), eps99, eps99); // for y[0]
     ok &= NearEqual( dy[1], sin(x[1]), eps99, eps99); // for y[1]
     ok &= NearEqual( dy[2], cos(x[1]), eps99, eps99); // for y[2]

     // compute partial of F w.r.t x[1]
     dy  = f.ForOne(x, 1);
     ok &= NearEqual( dy[0],  x[0]*exp(x[1]), eps99, eps99);
     ok &= NearEqual( dy[1],  x[0]*cos(x[1]), eps99, eps99);
     ok &= NearEqual( dy[2], -x[0]*sin(x[1]), eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool ForOne(void)
{     bool ok = true;
     // Run with Vector equal to three different cases
     // all of which are Simple Vectors with elements of type double.
     ok &= ForOneCases< CppAD::vector  <double> >();
     ok &= ForOneCases< std::vector    <double> >();
     ok &= ForOneCases< std::valarray  <double> >();
     return ok;
}
Input File: example/for_one.cpp cppad-20170000.3/doc/_for_one.cpp_xml.js0000644000175200017650000000324313057470506016765 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'forone.xml', 'for_one.cpp.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down1 = [ 'for_one.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/rev_one.cpp.xml0000644000175200017650000004361713057470506016151 0ustar coincoin-web First Order Derivative Driver: Example and Test
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First Order Derivative Driver: Example and Test
# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------
// define the template function RevOneCases<Vector> in empty namespace
template <typename Vector>
bool RevOneCases()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::exp;
     using CppAD::sin;
     using CppAD::cos;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     X[0] = 1.;
     X[1] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(X);

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>)  Y(m);
     Y[0] = X[0] * exp( X[1] );
     Y[1] = X[0] * sin( X[1] );
     Y[2] = X[0] * cos( X[1] );

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // new value for the independent variable vector
     Vector x(n);
     x[0] = 2.;
     x[1] = 1.;

     // compute and check derivative of y[0]
     Vector dw(n);
     dw  = f.RevOne(x, 0);
     ok &= NearEqual(dw[0],      exp(x[1]), eps99, eps99); // w.r.t x[0]
     ok &= NearEqual(dw[1], x[0]*exp(x[1]), eps99, eps99); // w.r.t x[1]

     // compute and check derivative of y[1]
     dw  = f.RevOne(x, 1);
     ok &= NearEqual(dw[0],      sin(x[1]), eps99, eps99);
     ok &= NearEqual(dw[1], x[0]*cos(x[1]), eps99, eps99);

     // compute and check derivative of y[2]
     dw  = f.RevOne(x, 2);
     ok &= NearEqual(dw[0],        cos(x[1]), eps99, eps99);
     ok &= NearEqual(dw[1], - x[0]*sin(x[1]), eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool RevOne(void)
{     bool ok = true;
     // Run with Vector equal to three different cases
     // all of which are Simple Vectors with elements of type double.
     ok &= RevOneCases< CppAD::vector  <double> >();
     ok &= RevOneCases< std::vector    <double> >();
     ok &= RevOneCases< std::valarray  <double> >();
     return ok;
}
Input File: example/rev_one.cpp cppad-20170000.3/doc/_rev_one.cpp_xml.js0000644000175200017650000000324313057470506016773 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'revone.xml', 'rev_one.cpp.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down1 = [ 'rev_one.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/hessian.cpp.xml0000644000175200017650000004255113057470506016142 0ustar coincoin-web Hessian: Example and Test
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Hessian: Example and Test

# include <cppad/cppad.hpp>
namespace { // ---------------------------------------------------------
// define the template function HessianCases<Vector> in empty namespace
template <typename Vector>
bool HessianCases()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::exp;
     using CppAD::sin;
     using CppAD::cos;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     X[0] = 1.;
     X[1] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(X);

     // a calculation between the domain and range values
     AD<double> Square = X[0] * X[0];

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>)  Y(m);
     Y[0] = Square * exp( X[1] );
     Y[1] = Square * sin( X[1] );
     Y[2] = Square * cos( X[1] );

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // new value for the independent variable vector
     Vector x(n);
     x[0] = 2.;
     x[1] = 1.;

     // second derivative of y[1]
     Vector hes( n * n );
     hes = f.Hessian(x, 1);
     /*
     F_1       = x[0] * x[0] * sin(x[1])

     F_1^{(1)} = [ 2 * x[0] * sin(x[1]) , x[0] * x[0] * cos(x[1]) ]

     F_1^{(2)} = [        2 * sin(x[1]) ,      2 * x[0] * cos(x[1]) ]
                 [ 2 * x[0] * cos(x[1]) , - x[0] * x[0] * sin(x[1]) ]
     */
     ok &=  NearEqual(          2.*sin(x[1]), hes[0*n+0], eps99, eps99);
     ok &=  NearEqual(     2.*x[0]*cos(x[1]), hes[0*n+1], eps99, eps99);
     ok &=  NearEqual(     2.*x[0]*cos(x[1]), hes[1*n+0], eps99, eps99);
     ok &=  NearEqual( - x[0]*x[0]*sin(x[1]), hes[1*n+1], eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool Hessian(void)
{     bool ok = true;
     // Run with Vector equal to three different cases
     // all of which are Simple Vectors with elements of type double.
     ok &= HessianCases< CppAD::vector  <double> >();
     ok &= HessianCases< std::vector    <double> >();
     ok &= HessianCases< std::valarray  <double> >();
     return ok;
}
Input File: example/hessian.cpp cppad-20170000.3/doc/_hessian.cpp_xml.js0000644000175200017650000000327613057470506016776 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'hessian.xml', 'hessian.cpp.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down1 = [ 'hessian.cpp.xml', 'hes_lagrangian.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_hes_lagrangian.cpp_xml.js0000644000175200017650000000330513057470506020277 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'hessian.xml', 'hes_lagrangian.cpp.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down1 = [ 'hessian.cpp.xml', 'hes_lagrangian.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/for_two.cpp.xml0000644000175200017650000005517713057470506016177 0ustar coincoin-web Subset of Second Order Partials: Example and Test
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Subset of Second Order Partials: Example and Test
# include <cppad/cppad.hpp>
namespace { // -----------------------------------------------------
// define the template function in empty namespace
// bool ForTwoCases<VectorBase, VectorSize_t>(void)
template <class VectorBase, class VectorSize_t>
bool ForTwoCases()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::exp;
     using CppAD::sin;
     using CppAD::cos;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     X[0] = 1.;
     X[1] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(X);

     // a calculation between the domain and range values
     AD<double> Square = X[0] * X[0];

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>)  Y(m);
     Y[0] = Square * exp( X[1] );
     Y[1] = Square * sin( X[1] );
     Y[2] = Square * cos( X[1] );

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // new value for the independent variable vector
     VectorBase x(n);
     x[0] = 2.;
     x[1] = 1.;

     // set j and k to compute specific second partials of y
     size_t p = 2;
     VectorSize_t j(p);
     VectorSize_t k(p);
     j[0] = 0; k[0] = 0; // for second partial w.r.t. x[0] and x[0]
     j[1] = 0; k[1] = 1; // for second partial w.r.t x[0] and x[1]

     // compute the second partials
     VectorBase ddy(m * p);
     ddy = f.ForTwo(x, j, k);
     /*
     partial of y w.r.t x[0] is
     [ 2 * x[0] * exp(x[1]) ]
     [ 2 * x[0] * sin(x[1]) ]
     [ 2 * x[0] * cos(x[1]) ]
     */
     // second partial of y w.r.t x[0] and x[1]
     ok &=  NearEqual( 2.*exp(x[1]), ddy[0*p+0], eps99, eps99);
     ok &=  NearEqual( 2.*sin(x[1]), ddy[1*p+0], eps99, eps99);
     ok &=  NearEqual( 2.*cos(x[1]), ddy[2*p+0], eps99, eps99);

     // second partial of F w.r.t x[0] and x[1]
     ok &=  NearEqual( 2.*x[0]*exp(x[1]), ddy[0*p+1], eps99, eps99);
     ok &=  NearEqual( 2.*x[0]*cos(x[1]), ddy[1*p+1], eps99, eps99);
     ok &=  NearEqual(-2.*x[0]*sin(x[1]), ddy[2*p+1], eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool ForTwo(void)
{     bool ok = true;
        // Run with VectorBase equal to three different cases
        // all of which are Simple Vectors with elements of type double.
     ok &= ForTwoCases< CppAD::vector <double>, std::vector<size_t> >();
     ok &= ForTwoCases< std::vector   <double>, std::vector<size_t> >();
     ok &= ForTwoCases< std::valarray <double>, std::vector<size_t> >();

        // Run with VectorSize_t equal to two other cases
        // which are Simple Vectors with elements of type size_t.
     ok &= ForTwoCases< std::vector <double>, CppAD::vector<size_t> >();
     ok &= ForTwoCases< std::vector <double>, std::valarray<size_t> >();

     return ok;
}
Input File: example/for_two.cpp cppad-20170000.3/doc/_for_two.cpp_xml.js0000644000175200017650000000324313057470506017015 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'fortwo.xml', 'for_two.cpp.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down1 = [ 'for_two.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/rev_two.cpp.xml0000644000175200017650000005157413057470506016202 0ustar coincoin-web Second Partials Reverse Driver: Example and Test
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Second Partials Reverse Driver: Example and Test
# include <cppad/cppad.hpp>
namespace { // -----------------------------------------------------
// define the template function in empty namespace
// bool RevTwoCases<VectorBase, VectorSize_t>(void)
template <class VectorBase, class VectorSize_t>
bool RevTwoCases()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::exp;
     using CppAD::sin;
     using CppAD::cos;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     X[0] = 1.;
     X[1] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(X);

     // a calculation between the domain and range values
     AD<double> Square = X[0] * X[0];

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>)  Y(m);
     Y[0] = Square * exp( X[1] );
     Y[1] = Square * sin( X[1] );
     Y[2] = Square * cos( X[1] );

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // new value for the independent variable vector
     VectorBase x(n);
     x[0] = 2.;
     x[1] = 1.;

     // set i and j to compute specific second partials of y
     size_t p = 2;
     VectorSize_t i(p);
     VectorSize_t j(p);
     i[0] = 0; j[0] = 0; // for partials y[0] w.r.t x[0] and x[k]
     i[1] = 1; j[1] = 1; // for partials y[1] w.r.t x[1] and x[k]

     // compute the second partials
     VectorBase ddw(n * p);
     ddw = f.RevTwo(x, i, j);

     // partials of y[0] w.r.t x[0] is 2 * x[0] * exp(x[1])
     // check partials of y[0] w.r.t x[0] and x[k] for k = 0, 1
     ok &=  NearEqual(      2.*exp(x[1]), ddw[0*p+0], eps99, eps99);
     ok &=  NearEqual( 2.*x[0]*exp(x[1]), ddw[1*p+0], eps99, eps99);

     // partials of y[1] w.r.t x[1] is x[0] * x[0] * cos(x[1])
     // check partials of F_1 w.r.t x[1] and x[k] for k = 0, 1
     ok &=  NearEqual(    2.*x[0]*cos(x[1]), ddw[0*p+1], eps99, eps99);
     ok &=  NearEqual( -x[0]*x[0]*sin(x[1]), ddw[1*p+1], eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool RevTwo(void)
{     bool ok = true;
        // Run with VectorBase equal to three different cases
        // all of which are Simple Vectors with elements of type double.
     ok &= RevTwoCases< CppAD::vector <double>, std::vector<size_t> >();
     ok &= RevTwoCases< std::vector   <double>, std::vector<size_t> >();
     ok &= RevTwoCases< std::valarray <double>, std::vector<size_t> >();

        // Run with VectorSize_t equal to two other cases
        // which are Simple Vectors with elements of type size_t.
     ok &= RevTwoCases< std::vector <double>, CppAD::vector<size_t> >();
     ok &= RevTwoCases< std::vector <double>, std::valarray<size_t> >();

     return ok;
}
Input File: example/rev_two.cpp cppad-20170000.3/doc/_rev_two.cpp_xml.js0000644000175200017650000000324313057470506017023 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'drivers.xml', 'revtwo.xml', 'rev_two.cpp.xml' ]; var list_down3 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down2 = [ 'jacobian.xml', 'forone.xml', 'revone.xml', 'hessian.xml', 'fortwo.xml', 'revtwo.xml', 'sparse_jacobian.xml', 'sparse_hessian.xml' ]; var list_down1 = [ 'rev_two.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/fun_check.cpp.xml0000644000175200017650000005320113057470506016427 0ustar coincoin-web ADFun Check and Re-Tape: Example and Test
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ADFun Check and Re-Tape: Example and Test
# include <cppad/cppad.hpp>

namespace { // -----------------------------------------------------------
// define the template function object Fun<Type,Vector> in empty namespace
template <class Type, class Vector>
class Fun {
private:
     size_t n;
public:
     // function constructor
     Fun(size_t n_) : n(n_)
     { }
     // function evaluator
     Vector operator() (const Vector &x)
     {     Vector y(n);
          size_t i;
          for(i = 0; i < n; i++)
          {     // This operaiton sequence depends on x
               if( x[i] >= 0 )
                    y[i] = exp(x[i]);
               else     y[i] = exp(-x[i]);
          }
          return y;
     }
};
// template function FunCheckCases<Vector, ADVector> in empty namespace
template <class Vector, class ADVector>
bool FunCheckCases(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::ADFun;
     using CppAD::Independent;

     // use the ADFun default constructor
     ADFun<double> f;

     // domain space vector
     size_t n = 2;
     ADVector X(n);
     X[0] = -1.;
     X[1] = 1.;

     // declare independent variables and starting recording
     Independent(X);

     // create function object to use with AD<double>
     Fun< AD<double>, ADVector > G(n);

     // range space vector
     size_t m = n;
     ADVector Y(m);
     Y = G(X);

     // stop tape and store operation sequence in f : X -> Y
     f.Dependent(X, Y);
     ok &= (f.size_order() == 0);  // no implicit forward operation

     // create function object to use with double
     Fun<double, Vector> g(n);

     // function values should agree when the independent variable
     // values are the same as during recording
     Vector x(n);
     size_t j;
     for(j = 0; j < n; j++)
          x[j] = Value(X[j]);
     double r = 1e-10;
     double a = 1e-10;
     ok      &= FunCheck(f, g, x, a, r);

     // function values should not agree when the independent variable
     // values are the negative of values during recording
     for(j = 0; j < n; j++)
          x[j] = - Value(X[j]);
     ok      &= ! FunCheck(f, g, x, a, r);

     // re-tape to obtain the new AD of double operation sequence
     for(j = 0; j < n; j++)
          X[j] = x[j];
     Independent(X);
     Y = G(X);

     // stop tape and store operation sequence in f : X -> Y
     f.Dependent(X, Y);
     ok &= (f.size_order() == 0);  // no implicit forward with this x

     // function values should agree now
     ok      &= FunCheck(f, g, x, a, r);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool FunCheck(void)
{     bool ok = true;
     typedef CppAD::vector<double>                Vector1;
     typedef CppAD::vector< CppAD::AD<double> > ADVector1;
     typedef   std::vector<double>                Vector2;
     typedef   std::vector< CppAD::AD<double> > ADVector2;
     typedef std::valarray<double>                Vector3;
     typedef std::valarray< CppAD::AD<double> > ADVector3;
     // Run with Vector and ADVector equal to three different cases
     // all of which are Simple Vectors with elements of type
     // double and AD<double> respectively.
     ok &= FunCheckCases< Vector1, ADVector2 >();
     ok &= FunCheckCases< Vector2, ADVector3 >();
     ok &= FunCheckCases< Vector3, ADVector1 >();
     return ok;
}
Input File: example/fun_check.cpp cppad-20170000.3/doc/_fun_check.cpp_xml.js0000644000175200017650000000330613057470506017263 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'adfun.xml', 'funcheck.xml', 'fun_check.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'independent.xml', 'funconstruct.xml', 'dependent.xml', 'abort_recording.xml', 'seq_property.xml', 'funeval.xml', 'drivers.xml', 'funcheck.xml', 'optimize.xml', 'check_for_nan.xml' ]; var list_down1 = [ 'fun_check.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/optimize_forward_active.cpp.xml0000644000175200017650000006070613057470506021431 0ustar coincoin-web Example Optimization and Forward Activity Analysis
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Example Optimization and Forward Activity Analysis
# include <cppad/cppad.hpp>
namespace {
     struct tape_size { size_t n_var; size_t n_op; };

     template <class Vector> void fun(
          const Vector& x, Vector& y, tape_size& before, tape_size& after
     )
     {     typedef typename Vector::value_type scalar;

          // phantom variable with index 0 and independent variables
          // begin operator, independent variable operators and end operator
          before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
          after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

          // adding the constant zero does not take any operations
          scalar zero   = 0.0 + x[0];
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;

          // multiplication by the constant one does not take any operations
          scalar one    = 1.0 * x[1];
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;

          // multiplication by the constant zero does not take any operations
          // and results in the constant zero.
          scalar two    = 0.0 * x[0];

          // operations that only involve constants do not take any operations
          scalar three  = (1.0 + two) * 3.0;
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;

          // The optimizer will reconize that zero + one = one + zero
          // for all values of x.
          scalar four   = zero + one;
          scalar five   = one  + zero;
          before.n_var += 2; before.n_op  += 2;
          after.n_var  += 1; after.n_op   += 1;

          // The optimizer will reconize that sin(x[3]) = sin(x[3])
          // for all values of x. Note that, for computation of derivatives,
          // sin(x[3]) and cos(x[3]) are stored on the tape as a pair.
          scalar six    = sin(x[2]);
          scalar seven  = sin(x[2]);
          before.n_var += 4; before.n_op  += 2;
          after.n_var  += 2; after.n_op   += 1;

          // If we used addition here, five + seven = zero + one + seven
          // which would get converted to a cumulative summation operator.
          scalar eight = five * seven;
          before.n_var += 1; before.n_op  += 1;
          after.n_var  += 1; after.n_op   += 1;

          // results for this operation sequence
          y[0] = eight;
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;
     }
}

bool forward_active(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 3;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.5;
     ax[1] = 1.5;
     ax[2] = 2.0;

     // declare independent variables and start tape recording
     CppAD::Independent(ax);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     tape_size before, after;
     fun(ax, ay, before, after);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);
     ok &= f.size_var() == before.n_var;
     ok &= f.size_op()  == before.n_op;

     // Optimize the operation sequence
     // Note that, for this case, all the optimization was done during
     // the recording and there is no benifit to the optimization.
     f.optimize();
     ok &= f.size_var() == after.n_var;
     ok &= f.size_op()  == after.n_op;

     // check zero order forward with different argument value
     CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
     for(size_t i = 0; i < n; i++)
          x[i] = double(i + 2);
     y    = f.Forward(0, x);
     fun(x, check, before, after);
     ok &= NearEqual(y[0], check[0], eps10, eps10);

     return ok;
}
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} function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_nearequal_xml.js0000644000175200017650000000406713057470507016540 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'nearequal.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down0 = [ 'near_equal.cpp.xml' ]; var list_current0 = [ 'nearequal.xml#Syntax', 'nearequal.xml#Purpose', 'nearequal.xml#x', 'nearequal.xml#y', 'nearequal.xml#r', 'nearequal.xml#a', 'nearequal.xml#b', 'nearequal.xml#Type', 'nearequal.xml#Include Files', 'nearequal.xml#Example', 'nearequal.xml#Exercise' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_near_equal.cpp_xml.js0000644000175200017650000000402113057470507017446 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'nearequal.xml', 'near_equal.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down1 = [ 'near_equal.cpp.xml' ]; var list_current0 = [ 'near_equal.cpp.xml#File Name' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; 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var list_down0 = [ 'speed_test.cpp.xml' ]; var list_current0 = [ 'speed_test.xml#Syntax', 'speed_test.xml#Purpose', 'speed_test.xml#Motivation', 'speed_test.xml#Include', 'speed_test.xml#Vector', 'speed_test.xml#test', 'speed_test.xml#test.size', 'speed_test.xml#test.repeat', 'speed_test.xml#size_vec', 'speed_test.xml#time_min', 'speed_test.xml#rate_vec', 'speed_test.xml#Timing', 'speed_test.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_speed_test.cpp_xml.js0000644000175200017650000000373213057470507017501 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'speed_test.xml', 'speed_test.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down1 = [ 'speed_test.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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var list_current0 = [ 'speedtest.xml#Syntax', 'speedtest.xml#Purpose', 'speedtest.xml#Motivation', 'speedtest.xml#Include', 'speedtest.xml#Test', 'speedtest.xml#Test.size', 'speedtest.xml#Test.repeat', 'speedtest.xml#Test.name', 'speedtest.xml#first', 'speedtest.xml#last', 'speedtest.xml#inc', 'speedtest.xml#rate', 'speedtest.xml#Errors', 'speedtest.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_speed_program.cpp_xml.js0000644000175200017650000000414613057470507020171 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'speedtest.xml', 'speed_program.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down1 = [ 'speed_program.cpp.xml' ]; var list_current0 = [ 'speed_program.cpp.xml#Running This Program', 'speed_program.cpp.xml#Program', 'speed_program.cpp.xml#Output' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_time_test_xml.js0000644000175200017650000000420513057470507016552 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'time_test.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down0 = [ 'elapsed_seconds.xml', 'time_test.cpp.xml' ]; var list_current0 = [ 'time_test.xml#Syntax', 'time_test.xml#Purpose', 'time_test.xml#Motivation', 'time_test.xml#Include', 'time_test.xml#test', 'time_test.xml#test.size', 'time_test.xml#test.repeat', 'time_test.xml#time_min', 'time_test.xml#test_size', 'time_test.xml#time', 'time_test.xml#Timing', 'time_test.xml#Example' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_elapsed_seconds_xml.js0000644000175200017650000000432613057470507017714 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'time_test.xml', 'elapsed_seconds.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; 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function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_lu_factor.hpp_xml.js0000644000175200017650000000357713057470507017334 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'ludetandsolve.xml', 'lufactor.xml', 'lu_factor.hpp.xml' ]; var list_down3 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down2 = [ 'lusolve.xml', 'lufactor.xml', 'luinvert.xml' ]; var list_down1 = [ 'lu_factor.cpp.xml', 'lu_factor.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_luinvert_xml.js0000644000175200017650000000457713057470507016441 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'ludetandsolve.xml', 'luinvert.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down1 = [ 'lusolve.xml', 'lufactor.xml', 'luinvert.xml' ]; var list_down0 = [ 'lu_invert.cpp.xml', 'lu_invert.hpp.xml' ]; var list_current0 = [ 'luinvert.xml#Syntax', 'luinvert.xml#Description', 'luinvert.xml#Include', 'luinvert.xml#Matrix Storage', 'luinvert.xml#ip', 'luinvert.xml#jp', 'luinvert.xml#LU', 'luinvert.xml#LU.L', 'luinvert.xml#LU.U', 'luinvert.xml#LU.P', 'luinvert.xml#LU.A', 'luinvert.xml#X', 'luinvert.xml#Example', 'luinvert.xml#Source' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_lu_invert.cpp_xml.js0000644000175200017650000000357713057470507017360 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'ludetandsolve.xml', 'luinvert.xml', 'lu_invert.cpp.xml' ]; var list_down3 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down2 = [ 'lusolve.xml', 'lufactor.xml', 'luinvert.xml' ]; var list_down1 = [ 'lu_invert.cpp.xml', 'lu_invert.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_lu_invert.hpp_xml.js0000644000175200017650000000357713057470507017365 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'ludetandsolve.xml', 'luinvert.xml', 'lu_invert.hpp.xml' ]; var list_down3 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down2 = [ 'lusolve.xml', 'lufactor.xml', 'luinvert.xml' ]; var list_down1 = [ 'lu_invert.cpp.xml', 'lu_invert.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_rombergone_xml.js0000644000175200017650000000415613057470507016721 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'rombergone.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down0 = [ 'romberg_one.cpp.xml' ]; var list_current0 = [ 'rombergone.xml#Syntax', 'rombergone.xml#Description', 'rombergone.xml#Include', 'rombergone.xml#r', 'rombergone.xml#F', 'rombergone.xml#a', 'rombergone.xml#b', 'rombergone.xml#n', 'rombergone.xml#p', 'rombergone.xml#e', 'rombergone.xml#Float', 'rombergone.xml#Example', 'rombergone.xml#Source Code' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_romberg_one.cpp_xml.js0000644000175200017650000000373413057470507017642 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'rombergone.xml', 'romberg_one.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down1 = [ 'romberg_one.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_rombergmul_xml.js0000644000175200017650000000423713057470507016735 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'rombergmul.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down0 = [ 'rombergmul.cpp.xml' ]; var list_current0 = [ 'rombergmul.xml#Syntax', 'rombergmul.xml#Description', 'rombergmul.xml#Include', 'rombergmul.xml#m', 'rombergmul.xml#r', 'rombergmul.xml#F', 'rombergmul.xml#a', 'rombergmul.xml#b', 'rombergmul.xml#n', 'rombergmul.xml#p', 'rombergmul.xml#e', 'rombergmul.xml#Float', 'rombergmul.xml#FloatVector', 'rombergmul.xml#Example', 'rombergmul.xml#Source Code' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_rombergmul.cpp_xml.js0000644000175200017650000000373213057470507017515 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'rombergmul.xml', 'rombergmul.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down1 = [ 'rombergmul.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_runge45_xml.js0000644000175200017650000000444413057470507016053 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'runge45.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; var list_down0 = [ 'runge45_1.cpp.xml', 'runge45_2.cpp.xml' ]; 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} function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_ta_thread_num_xml.js0000644000175200017650000000460213057470507017370 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'thread_alloc.xml', 'ta_thread_num.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; 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function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_ta_hold_memory_xml.js0000644000175200017650000000461513057470507017564 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'thread_alloc.xml', 'ta_hold_memory.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; 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} function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_ta_inuse_xml.js0000644000175200017650000000460313057470507016366 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'thread_alloc.xml', 'ta_inuse.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'errorhandler.xml', 'nearequal.xml', 'speed_test.xml', 'speedtest.xml', 'time_test.xml', 'numerictype.xml', 'checknumerictype.xml', 'simplevector.xml', 'checksimplevector.xml', 'nan.xml', 'pow_int.xml', 'poly.xml', 'ludetandsolve.xml', 'rombergone.xml', 'rombergmul.xml', 'runge45.xml', 'rosen34.xml', 'odeerrcontrol.xml', 'odegear.xml', 'odegearcontrol.xml', 'cppad_vector.xml', 'thread_alloc.xml', 'index_sort.xml', 'to_string.xml', 'set_union.xml' ]; 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if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_ta_create_array_xml.js0000644000175200017650000000504513057470507017705 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'utility.xml', 'thread_alloc.xml', 'ta_create_array.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; 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Nonlinear Programming Using CppAD and Ipopt: Example and Test

Purpose
This example program demonstrates how to use ipopt_solve to solve the example problem in the Ipopt documentation; i.e., the problem minimize x 1 * x 4 * ( x 1 + x 2 + x 3 ) + x 3 subject to x 1 * x 2 * x 3 * x 4 ≥ 25 x 1 2 + x 2 2 + x 3 2 + x 4 2 = 40 1 ≤ x 1 , x 2 , x 3 , x 4 ≤ 5
Configuration Requirement
This example will be compiled and tested provided that ipopt_prefix is specified on the cmake command line. 
# include <cppad/ipopt/solve.hpp>

namespace {
     using CppAD::AD;

     class FG_eval {
     public:
          typedef CPPAD_TESTVECTOR( AD<double> ) ADvector;
          void operator()(ADvector& fg, const ADvector& x)
          {     assert( fg.size() == 3 );
               assert( x.size()  == 4 );

               // Fortran style indexing
               AD<double> x1 = x[0];
               AD<double> x2 = x[1];
               AD<double> x3 = x[2];
               AD<double> x4 = x[3];
               // f(x)
               fg[0] = x1 * x4 * (x1 + x2 + x3) + x3;
               // g_1 (x)
               fg[1] = x1 * x2 * x3 * x4;
               // g_2 (x)
               fg[2] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4;
               //
               return;
          }
     };
}

bool get_started(void)
{     bool ok = true;
     size_t i;
     typedef CPPAD_TESTVECTOR( double ) Dvector;

     // number of independent variables (domain dimension for f and g)
     size_t nx = 4;
     // number of constraints (range dimension for g)
     size_t ng = 2;
     // initial value of the independent variables
     Dvector xi(nx);
     xi[0] = 1.0;
     xi[1] = 5.0;
     xi[2] = 5.0;
     xi[3] = 1.0;
     // lower and upper limits for x
     Dvector xl(nx), xu(nx);
     for(i = 0; i < nx; i++)
     {     xl[i] = 1.0;
          xu[i] = 5.0;
     }
     // lower and upper limits for g
     Dvector gl(ng), gu(ng);
     gl[0] = 25.0;     gu[0] = 1.0e19;
     gl[1] = 40.0;     gu[1] = 40.0;

     // object that computes objective and constraints
     FG_eval fg_eval;

     // options
     std::string options;
     // turn off any printing
     options += "Integer print_level  0\n";
     options += "String  sb           yes\n";
     // maximum number of iterations
     options += "Integer max_iter     10\n";
     // approximate accuracy in first order necessary conditions;
     // see Mathematical Programming, Volume 106, Number 1,
     // Pages 25-57, Equation (6)
     options += "Numeric tol          1e-6\n";
     // derivative testing
     options += "String  derivative_test            second-order\n";
     // maximum amount of random pertubation; e.g.,
     // when evaluation finite diff
     options += "Numeric point_perturbation_radius  0.\n";

     // place to return solution
     CppAD::ipopt::solve_result<Dvector> solution;

     // solve the problem
     CppAD::ipopt::solve<Dvector, FG_eval>(
          options, xi, xl, xu, gl, gu, fg_eval, solution
     );
     //
     // Check some of the solution values
     //
     ok &= solution.status == CppAD::ipopt::solve_result<Dvector>::success;
     //
     double check_x[]  = { 1.000000, 4.743000, 3.82115, 1.379408 };
     double check_zl[] = { 1.087871, 0.,       0.,      0.       };
     double check_zu[] = { 0.,       0.,       0.,      0.       };
     double rel_tol    = 1e-6;  // relative tolerance
     double abs_tol    = 1e-6;  // absolute tolerance
     for(i = 0; i < nx; i++)
     {     ok &= CppAD::NearEqual(
               check_x[i],  solution.x[i],   rel_tol, abs_tol
          );
          ok &= CppAD::NearEqual(
               check_zl[i], solution.zl[i], rel_tol, abs_tol
          );
          ok &= CppAD::NearEqual(
               check_zu[i], solution.zu[i], rel_tol, abs_tol
          );
     }

     return ok;
}
Input File: example/ipopt_solve/get_started.cpp cppad-20170000.3/doc/_ipopt_solve_get_started.cpp_xml.js0000644000175200017650000000306213057470507022266 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ipopt_solve.xml', 'ipopt_solve_get_started.cpp.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'ipopt_solve_get_started.cpp.xml', 'ipopt_solve_retape.cpp.xml', 'ipopt_solve_ode_inverse.cpp.xml' ]; var list_current0 = [ 'ipopt_solve_get_started.cpp.xml#Purpose', 'ipopt_solve_get_started.cpp.xml#Configuration Requirement' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/ipopt_solve_ode_inverse.cpp.xml0000644000175200017650000020023513057470507021431 0ustar coincoin-web ODE Inverse Problem Definitions: Source Code
Prev Next ipopt_solve_ode_inverse.cpp

ODE Inverse Problem Definitions: Source Code

Purpose
This example demonstrates how to invert for parameters in a ODE where the solution of the ODE is numerically approximated.

Forward Problem
We consider the following ordinary differential equation: ∂ t y 0 ( t , a ) = - a 1 * y 0 ( t , a ) ∂ t y 1 ( t , a ) = + a 1 * y 0 ( t , a ) - a 2 * y 1 ( t , a ) with the initial conditions y 0 ( 0 , a ) = ( a 0 , 0 ) T Our forward problem is stated as follows: Given a ∈ R 3 determine the value of y ( t , a ) , for t ∈ R , that solves the initial value problem above.

Measurements
Suppose we are also given measurement times s ∈ R 5 and a measurement vector z ∈ R 4 and for i = 0 , … , 3 , we model z i by z i = y 1 ( s i + 1 , a ) + e i where e i -1 ∼ N ( 0 , σ 2 ) is the measurement noise, and σ > 0 is the standard deviation of the noise.

Simulation Analytic Solution
The following analytic solution to the forward problem is used to simulate a data set: y 0 ( t , a ) = a 0 * exp ( - a 1 * t ) y 1 ( t , a ) = a 0 * a 1 * exp ( - a 2 * t ) - exp ( - a 1 * t ) a 1 - a 2
Simulation Parameter Values
a ¯ 0 = 1   initial value of y 0 ( t , a )
a ¯ 1 = 2   transfer rate from compartment zero to compartment one
a ¯ 2 = 1   transfer rate from compartment one to outside world
σ = 0   standard deviation of measurement noise
e i = 0   simulated measurement noise, i = 1 , … , Nz
s i = i * .5   time corresponding to the i-th measurement, i = 0 , … , 3

Simulated Measurement Values
The simulated measurement values are given by the equation z i = e i + y 1 ( s i + 1 , a ¯ ) = a ¯ 0 * a ¯ 1 * exp ( - a ¯ 2 * s i ) - exp ( - a ¯ 1 * s i ) a ¯ 1 - a ¯ 2 for i = 0 , … , 3 .

Inverse Problem
The maximum likelihood estimate for a given z solves the following optimization problem minimize ∑ i = 0 3 ( z i - y 1 ( s i + 1 , a ) ) 2 w . r . t a ∈ R 3
Trapezoidal Approximation
We are given a number of approximation points per measurement interval np and define the time grid t ∈ R 4 · np + 1 as follows: t 0 = s 0 and for i = 0 , 1 , 2 , 3 , j = 1 , … , np t i · np + j = s i + ( s i + 1 - s i ) i np We note that for i = 1 , … , 4 , t i · np = s i . This example uses a trapezoidal approximation to solve the ODE. Given a ∈ R 3 and y k -1 ≈ y ( t k -1 , a ) , the a trapezoidal method approximates y ( t j , a ) by the value y k ∈ R 2 ) that solves the equation y k = y k -1 + G ( y k , a ) + G ( y k -1 , a ) 2 * ( t k - t k -1 ) where G : R 2 × R 3 → R 2 is defined by G 0 ( y , a ) = - a 1 * y 0 G 1 ( y , a ) = + a 1 * y 0 - a 2 * y 1
Solution Method
We use constraints to embed the forward problem in the inverse problem. To be specific, we solve the optimization problem minimize ∑ i = 0 3 ( z i - y 1 ( i + 1 ) · np ) 2 w . r . t a ∈ R 3 y 0 ∈ R 2 , … , y 3 · np -1 ∈ R 2 subject to 0 = y 0 - ( a 0 , 0 ) T 0 = y k - y k -1 - G ( y k , a ) + G ( y k -1 , a ) 2 ( t k - t k -1 ) for k = 1 , … , 4 · np The code below we using the notation x ∈ 3 + ( 4 · np + 1 ) · 2 defined by x = (a 0 , a 1 , a 2 , y 0 0 , y 1 0 , … , y 0 4 · np , y 1 4 ⋯ np )
Source
The following source code implements the ODE inversion method proposed above: 
# include <cppad/ipopt/solve.hpp>

namespace {
     using CppAD::AD;

     // value of a during simulation a[0], a[1], a[2]
     double a_[] =                   {2.0,  1.0, 0.5};
     // number of components in a
     size_t na_ = sizeof(a_) / sizeof(a_[0]);

     // function used to simulate data
     double yone(double t)
     {     return
               a_[0]*a_[1] * (exp(-a_[2]*t) - exp(-a_[1]*t)) / (a_[1] - a_[2]);
     }

     // time points were we have data (no data at first point)
     double s_[] = {0.0,   0.5,        1.0,          1.5,         2.0 };

     // Simulated data for case with no noise (first point is not used)
     double z_[] = {yone(s_[1]), yone(s_[2]), yone(s_[3]), yone(s_[4])};
     size_t nz_  = sizeof(z_) / sizeof(z_[0]);

     // number of trapozoidal approximation points per measurement interval
     size_t np_  = 40;


     class FG_eval
     {
     private:
     public:
          // derived class part of constructor
          typedef CPPAD_TESTVECTOR( AD<double> ) ADvector;

          // Evaluation of the objective f(x), and constraints g(x)
          void operator()(ADvector& fg, const ADvector& x)
          {     CPPAD_TESTVECTOR( AD<double> ) a(na_);
               size_t i, j, k;

               // extract the vector a
               for(i = 0; i < na_; i++)
                    a[i] = x[i];

               // compute the object f(x)
               fg[0] = 0.0;
               for(i = 0; i < nz_; i++)
               {     k = (i + 1) * np_;
                    AD<double> y_1 = x[na_ + 2 * k + 1];
                    AD<double> dif = z_[i] - y_1;
                    fg[0]         += dif * dif;
               }

               // constraint corresponding to initial value y(0, a)
               // Note that this constraint is invariant with size of dt
               fg[1] = x[na_+0] - a[0];
               fg[2] = x[na_+1] - 0.0;

               // constraints corresponding to trapozoidal approximation
               for(i = 0; i < nz_; i++)
               {     // spacing between grid point
                    double dt = (s_[i+1] - s_[i]) / static_cast<double>(np_);
                    for(j = 1; j <= np_; j++)
                    {     k = i * np_ + j;
                         // compute derivative at y^k
                         AD<double> y_0  = x[na_ + 2 * k + 0];
                         AD<double> y_1  = x[na_ + 2 * k + 1];
                         AD<double> G_0  = - a[1] * y_0;
                         AD<double> G_1  = + a[1] * y_0 - a[2] * y_1;

                         // compute derivative at y^{k-1}
                         AD<double> ym_0  = x[na_ + 2 * (k-1) + 0];
                         AD<double> ym_1  = x[na_ + 2 * (k-1) + 1];
                         AD<double> Gm_0  = - a[1] * ym_0;
                         AD<double> Gm_1  = + a[1] * ym_0 - a[2] * ym_1;

                         // constraint should be zero
                         fg[1 + 2*k ] = y_0  - ym_0 - dt*(G_0 + Gm_0)/2.;
                         fg[2 + 2*k ] = y_1  - ym_1 - dt*(G_1 + Gm_1)/2.;

                         // scale g(x) so it has similar size as f(x)
                         fg[1 + 2*k ] /= dt;
                         fg[2 + 2*k ] /= dt;
                    }
               }
          }
     };
}
bool ode_inverse(void)
{     bool ok = true;
     size_t i;
     typedef CPPAD_TESTVECTOR( double ) Dvector;

     // number of components in the function g
     size_t ng = (np_ * nz_ + 1) * 2;
     // number of independent variables
     size_t nx = na_ + ng;
     // initial vlaue for the variables we are optimizing w.r.t
     Dvector xi(nx), xl(nx), xu(nx);
     for(i = 0; i < nx; i++)
     {     xi[i] =   0.0; // initial value
          xl[i] = -1e19; // no lower limit
          xu[i] = +1e19; // no upper limit
     }
     for(i = 0; i < na_; i++)
          xi[0] = 1.5;   // initial value for a

     // all the difference equations are constrainted to be zero
     Dvector gl(ng), gu(ng);
     for(i = 0; i < ng; i++)
     {     gl[i] = 0.0;
          gu[i] = 0.0;
     }
     // object defining both f(x) and g(x)
     FG_eval fg_eval;

     // options
     std::string options;
     // Use sparse matrices for calculation of Jacobians and Hessians
     // with forward mode for Jacobian (seems to be faster for this case).
     options += "Sparse  true        forward\n";
     // turn off any printing
     options += "Integer print_level 0\n";
     options += "String  sb        yes\n";
     // maximum number of iterations
     options += "Integer max_iter    30\n";
     // approximate accuracy in first order necessary conditions;
     // see Mathematical Programming, Volume 106, Number 1,
     // Pages 25-57, Equation (6)
     options += "Numeric tol         1e-6\n";

     // place to return solution
     CppAD::ipopt::solve_result<Dvector> solution;

     // solve the problem
     CppAD::ipopt::solve<Dvector, FG_eval>(
          options, xi, xl, xu, gl, gu, fg_eval, solution
     );
     //
     // Check some of the solution values
     //
     ok &= solution.status == CppAD::ipopt::solve_result<Dvector>::success;
     //
     double rel_tol    = 1e-4;  // relative tolerance
     double abs_tol    = 1e-4;  // absolute tolerance
     for(i = 0; i < na_; i++)
          ok &= CppAD::NearEqual( a_[i],  solution.x[i],   rel_tol, abs_tol);

     return ok;
}
Input File: example/ipopt_solve/ode_inverse.cpp cppad-20170000.3/doc/_ipopt_solve_ode_inverse.cpp_xml.js0000644000175200017650000000401313057470507022260 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'ipopt_solve.xml', 'ipopt_solve_ode_inverse.cpp.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'ipopt_solve_get_started.cpp.xml', 'ipopt_solve_retape.cpp.xml', 'ipopt_solve_ode_inverse.cpp.xml' ]; var list_current0 = [ 'ipopt_solve_ode_inverse.cpp.xml#Purpose', 'ipopt_solve_ode_inverse.cpp.xml#Forward Problem', 'ipopt_solve_ode_inverse.cpp.xml#Measurements', 'ipopt_solve_ode_inverse.cpp.xml#Measurements.Simulation Analytic Solution', 'ipopt_solve_ode_inverse.cpp.xml#Measurements.Simulation Parameter Values', 'ipopt_solve_ode_inverse.cpp.xml#Measurements.Simulated Measurement Values', 'ipopt_solve_ode_inverse.cpp.xml#Inverse Problem', 'ipopt_solve_ode_inverse.cpp.xml#Trapezoidal Approximation', 'ipopt_solve_ode_inverse.cpp.xml#Solution Method', 'ipopt_solve_ode_inverse.cpp.xml#Source' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/ad_fun.cpp.xml0000644000175200017650000005722413057470507015750 0ustar coincoin-web Creating Your Own Interface to an ADFun Object
Prev Next ad_fun.cpp Headings

Creating Your Own Interface to an ADFun Object

# include <cppad/cppad.hpp>

namespace {

     // This class is an example of a different interface to an AD function object
     template <class Base>
     class my_ad_fun {

     private:
          CppAD::ADFun<Base> f;

     public:
          // default constructor
          my_ad_fun(void)
          { }

          // destructor
          ~ my_ad_fun(void)
          { }

          // Construct an my_ad_fun object with an operation sequence.
          // This is the same as for ADFun<Base> except that no zero
          // order forward sweep is done. Note Hessian and Jacobian do
          // their own zero order forward mode sweep.
          template <class ADvector>
          my_ad_fun(const ADvector& x, const ADvector& y)
          {     f.Dependent(x, y); }

          // same as ADFun<Base>::Jacobian
          template <class VectorBase>
          VectorBase jacobian(const VectorBase& x)
          {     return f.Jacobian(x); }

          // same as ADFun<Base>::Hessian
             template <typename VectorBase>
          VectorBase hessian(const VectorBase &x, const VectorBase &w)
          {     return f.Hessian(x, w); }
     };

} // End empty namespace

bool ad_fun(void)
{     // This example is similar to example/jacobian.cpp, except that it
     // uses my_ad_fun instead of ADFun.

     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::exp;
     using CppAD::sin;
     using CppAD::cos;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     X[0] = 1.;
     X[1] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(X);

     // a calculation between the domain and range values
     AD<double> Square = X[0] * X[0];

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>)  Y(m);
     Y[0] = Square * exp( X[1] );
     Y[1] = Square * sin( X[1] );
     Y[2] = Square * cos( X[1] );

     // create f: X -> Y and stop tape recording
     my_ad_fun<double> f(X, Y);

     // new value for the independent variable vector
     CPPAD_TESTVECTOR(double) x(n);
     x[0] = 2.;
     x[1] = 1.;

     // compute the derivative at this x
     CPPAD_TESTVECTOR(double) jac( m * n );
     jac = f.jacobian(x);

     /*
     F'(x) = [ 2 * x[0] * exp(x[1]) ,  x[0] * x[0] * exp(x[1]) ]
             [ 2 * x[0] * sin(x[1]) ,  x[0] * x[0] * cos(x[1]) ]
             [ 2 * x[0] * cos(x[1]) , -x[0] * x[0] * sin(x[i]) ]
     */
     ok &=  NearEqual( 2.*x[0]*exp(x[1]), jac[0*n+0], eps99, eps99);
     ok &=  NearEqual( 2.*x[0]*sin(x[1]), jac[1*n+0], eps99, eps99);
     ok &=  NearEqual( 2.*x[0]*cos(x[1]), jac[2*n+0], eps99, eps99);

     ok &=  NearEqual( x[0] * x[0] *exp(x[1]), jac[0*n+1], eps99, eps99);
     ok &=  NearEqual( x[0] * x[0] *cos(x[1]), jac[1*n+1], eps99, eps99);
     ok &=  NearEqual(-x[0] * x[0] *sin(x[1]), jac[2*n+1], eps99, eps99);

     return ok;
}
Input File: example/ad_fun.cpp cppad-20170000.3/doc/_ad_fun.cpp_xml.js0000644000175200017650000000363213057470507016575 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'example.xml', 'general.xml', 'ad_fun.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'general.xml', 'exampleutility.xml', 'listallexamples.xml', 'testvector.xml' ]; var list_down1 = [ 'ad_fun.cpp.xml', 'ad_in_c.cpp.xml', 'conj_grad.cpp.xml', 'cppad_eigen.hpp.xml', 'hes_minor_det.cpp.xml', 'hes_lu_det.cpp.xml', 'interface2c.cpp.xml', 'jac_minor_det.cpp.xml', 'jac_lu_det.cpp.xml', 'mul_level.xml', 'ode_stiff.cpp.xml', 'mul_level_ode.cpp.xml', 'mul_level_adolc_ode.cpp.xml', 'ode_taylor.cpp.xml', 'stack_machine.cpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; 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Prev Next mul_level_adolc_ode.cpp

Taylor's Ode Solver: A Multi-Level Adolc Example and Test

Purpose
This is a realistic example using two levels of AD; see mul_level . The first level uses Adolc's adouble type to tape the solution of an ordinary differential equation. This solution is then differentiated with respect to a parameter vector. The second level uses CppAD's type AD<adouble> to take derivatives during the solution of the differential equation. These derivatives are used in the application of Taylor's method to the solution of the ODE. The example mul_level_ode.cpp computes the same values using AD<double> and AD< AD<double> >. The example ode_taylor.cpp is a simpler applications of Taylor's method for solving an ODE.

ODE
For this example the ODE's are defined by the function h : R n × R n → R n where h [ x , y ( t , x ) ] = ( x 0 x 1 y 0 ( t , x ) ⋮ x n -1 y n -2 ( t , x ) ) = ( ∂ t y 0 ( t , x ) ∂ t y 1 ( t , x ) ⋮ ∂ t y n -1 ( t , x ) ) and the initial condition y ( 0 , x ) = 0 . The value of x is fixed during the solution of the ODE and the function g : R n → R n is used to define the ODE where g ( y ) = ( x 0 x 1 y 0 ⋮ x n -1 y n -2 )
ODE Solution
The solution for this example can be calculated by starting with the first row and then using the solution for the first row to solve the second and so on. Doing this we obtain y ( t , x ) = ( x 0 t x 1 x 0 t 2 / 2 ⋮ x n -1 x n -2 … x 0 t n / n ! )
Derivative of ODE Solution
Differentiating the solution above, with respect to the parameter vector x , we notice that ∂ x y ( t , x ) = ( y 0 ( t , x ) / x 0 0 ⋯ 0 y 1 ( t , x ) / x 0 y 1 ( t , x ) / x 1 0 ⋮ ⋮ ⋮ ⋱ 0 y n -1 ( t , x ) / x 0 y n -1 ( t , x ) / x 1 ⋯ y n -1 ( t , x ) / x n -1 )

An m-th order Taylor method for approximating the solution of an ordinary differential equations is y ( t + Δ t , x ) ≈ ∑ k = 0 p ∂ t k y ( t , x ) Δ t k k ! = y ( 0 ) ( t , x ) + y ( 1 ) ( t , x ) Δ t + ⋯ + y ( p ) ( t , x ) Δ t p where the Taylor coefficients y ( k ) ( t , x ) are defined by y ( k ) ( t , x ) = ∂ t k y ( t , x ) / k ! We define the function z ( t , x ) by the equation z ( t , x ) = g [ y ( t , x ) ] = h [ x , y ( t , x ) ] It follows that ∂ t y ( t , x ) = z ( t , x ) ∂ t k + 1 y ( t , x ) = ∂ t k z ( t , x ) y ( k + 1 ) ( t , x ) = z ( k ) ( t , x ) / ( k + 1 ) where z ( k ) ( t , x ) is the k-th order Taylor coefficient for z ( t , x ) . In the example below, the Taylor coefficients y ( 0 ) ( t , x ) , … , y ( k ) ( t , x ) are used to calculate the Taylor coefficient z ( k ) ( t , x ) which in turn gives the value for y ( k + 1 ) y ( t , x ) .

base_adolc.hpp
The file base_adolc.hpp is implements the Base type requirements where Base is adolc.

Memory Management
Adolc uses raw memory arrays that depend on the number of dependent and independent variables. The thread_alloc memory management utilities create_array and delete_array are used to manage this memory allocation.

Configuration Requirement
This example will be compiled and tested provided that the value ipopt_prefix is specified on the cmake command line.

Source 

# include <adolc/adouble.h>
# include <adolc/taping.h>
# include <adolc/drivers/drivers.h>

// definitions not in Adolc distribution and required to use CppAD::AD<adouble>
# include <cppad/example/base_adolc.hpp>

# include <cppad/cppad.hpp>
// ==========================================================================
namespace { // BEGIN empty namespace
// define types for each level
typedef adouble           a1type;
typedef CppAD::AD<a1type> a2type;

// -------------------------------------------------------------------------
// class definition for C++ function object that defines ODE
class Ode {
private:
     // copy of a that is set by constructor and used by g(y)
     CPPAD_TESTVECTOR(a1type) a1x_;
public:
     // constructor
     Ode(const CPPAD_TESTVECTOR(a1type)& a1x) : a1x_(a1x)
     { }
     // the function g(y) is evaluated with two levels of taping
     CPPAD_TESTVECTOR(a2type) operator()
     ( const CPPAD_TESTVECTOR(a2type)& a2y) const
     {     size_t n = a2y.size();
          CPPAD_TESTVECTOR(a2type) a2g(n);
          size_t i;
          a2g[0] = a1x_[0];
          for(i = 1; i < n; i++)
               a2g[i] = a1x_[i] * a2y[i-1];

          return a2g;
     }
};

// -------------------------------------------------------------------------
// Routine that uses Taylor's method to solve ordinary differential equaitons
// and allows for algorithmic differentiation of the solution.
CPPAD_TESTVECTOR(a1type) taylor_ode_adolc(
     Ode                            G       ,  // function that defines the ODE
     size_t                         order   ,  // order of Taylor's method used
     size_t                         nstep   ,  // number of steps to take
     const a1type                   &a1dt   ,  // Delta t for each step
     const CPPAD_TESTVECTOR(a1type) &a1y_ini)  // y(t) at the initial time
{
     // some temporary indices
     size_t i, k, ell;

     // number of variables in the ODE
     size_t n = a1y_ini.size();

     // copies of x and g(y) with two levels of taping
     CPPAD_TESTVECTOR(a2type)   a2y(n), Z(n);

     // y, y^{(k)} , z^{(k)}, and y^{(k+1)}
     CPPAD_TESTVECTOR(a1type)  a1y(n), a1y_k(n), a1z_k(n), a1y_kp(n);

     // initialize x
     for(i = 0; i < n; i++)
          a1y[i] = a1y_ini[i];

     // loop with respect to each step of Taylors method
     for(ell = 0; ell < nstep; ell++)
     {     // prepare to compute derivatives using a1type
          for(i = 0; i < n; i++)
               a2y[i] = a1y[i];
          CppAD::Independent(a2y);

          // evaluate ODE using a2type
          Z = G(a2y);

          // define differentiable version of g: X -> Y
          // that computes its derivatives using a1type
          CppAD::ADFun<a1type> a1g(a2y, Z);

          // Use Taylor's method to take a step
          a1y_k            = a1y;     // initialize y^{(k)}
          a1type dt_kp = a1dt;    // initialize dt^(k+1)
          for(k = 0; k <= order; k++)
          {     // evaluate k-th order Taylor coefficient of y
               a1z_k = a1g.Forward(k, a1y_k);

               for(i = 0; i < n; i++)
               {     // convert to (k+1)-Taylor coefficient for x
                    a1y_kp[i] = a1z_k[i] / a1type(k + 1);

                    // add term for to this Taylor coefficient
                    // to solution for y(t, x)
                    a1y[i]    += a1y_kp[i] * dt_kp;
               }
               // next power of t
               dt_kp *= a1dt;
               // next Taylor coefficient
               a1y_k   = a1y_kp;
          }
     }
     return a1y;
}
} // END empty namespace
// ==========================================================================
// Routine that tests algorithmic differentiation of solutions computed
// by the routine taylor_ode.
bool mul_level_adolc_ode(void)
{     bool ok = true;
     double eps = 100. * std::numeric_limits<double>::epsilon();

     // number of components in differential equation
     size_t n = 4;

     // some temporary indices
     size_t i, j;

     // set up for thread_alloc memory allocator
     using CppAD::thread_alloc; // the allocator
     size_t capacity;           // capacity of an allocation

     // the vector x with lenght n (or greater) in double
     double* x = thread_alloc::create_array<double>(n, capacity);

     // the vector x with lenght n in a1type
     CPPAD_TESTVECTOR(a1type) a1x(n);
     for(i = 0; i < n; i++)
          a1x[i] = x[i] = double(i + 1);

     // declare the parameters as the independent variable
     int tag = 0;                     // Adolc setup
     int keep = 1;
     trace_on(tag, keep);
     for(i = 0; i < n; i++)
          a1x[i] <<= double(i + 1);  // a1x is independent for adouble type

     // arguments to taylor_ode_adolc
     Ode G(a1x);                // function that defines the ODE
     size_t   order = n;      // order of Taylor's method used
     size_t   nstep = 2;      // number of steps to take
     a1type   a1dt  = 1.;     // Delta t for each step
     // value of y(t, x) at the initial time
     CPPAD_TESTVECTOR(a1type) a1y_ini(n);
     for(i = 0; i < n; i++)
          a1y_ini[i] = 0.;

     // integrate the differential equation
     CPPAD_TESTVECTOR(a1type) a1y_final(n);
     a1y_final = taylor_ode_adolc(G, order, nstep, a1dt, a1y_ini);

     // declare the differentiable fucntion f : x -> y_final
     // (corresponding to the tape of adouble operations)
     double* y_final = thread_alloc::create_array<double>(n, capacity);
     for(i = 0; i < n; i++)
          a1y_final[i] >>= y_final[i];
     trace_off();

     // check function values
     double check = 1.;
     double t     = nstep * a1dt.value();
     for(i = 0; i < n; i++)
     {     check *= x[i] * t / double(i + 1);
          ok &= CppAD::NearEqual(y_final[i], check, eps, eps);
     }

     // memory where Jacobian will be returned
     double* jac_ = thread_alloc::create_array<double>(n * n, capacity);
     double** jac = thread_alloc::create_array<double*>(n, capacity);
     for(i = 0; i < n; i++)
          jac[i] = jac_ + i * n;

     // evaluate Jacobian of h at a
     size_t m = n;              // # dependent variables
     jacobian(tag, int(m), int(n), x, jac);

     // check Jacobian
     for(i = 0; i < n; i++)
     {     for(j = 0; j < n; j++)
          {     if( i < j )
                    check = 0.;
               else     check = y_final[i] / x[j];
               ok &= CppAD::NearEqual(jac[i][j], check, eps, eps);
          }
     }

     // make memroy avaiable for other use by this thread
     thread_alloc::delete_array(x);
     thread_alloc::delete_array(y_final);
     thread_alloc::delete_array(jac_);
     thread_alloc::delete_array(jac);
     return ok;
}
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} function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/link_sparse_hessian.xml0000644000175200017650000004620113057470510017742 0ustar coincoin-web Speed Testing Sparse Hessian
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Speed Testing Sparse Hessian

Prototype
extern bool link_sparse_hessian(
     size_t                        size      ,
     size_t                        repeat    ,
     CppAD::vector<double>&        x         ,
     const CppAD::vector<size_t>&  row       ,
     const CppAD::vector<size_t>&  col       ,
     CppAD::vector<double>&        hessian   ,
     size_t                        n_sweep
);
Method
Given a row index vector row and a second column vector col , the corresponding function f : R n → R is defined by sparse_hes_fun . The non-zero entries in the Hessian of this function have one of the following forms: ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ row [ k ] ] , ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ col [ k ] ] , ∂ 2 f ∂ x [ col [ k ] ] ∂ x [ row [ k ] ] , ∂ 2 f ∂ x [ col [ k ] ] ∂ x [ col [ k ] ] for some k between zero and K -1 . All the other terms of the Hessian are zero.

size
The argument size , referred to as n below, is the dimension of the domain space for f ( x ) .

repeat
The argument repeat is the number of times to repeat the test (with a different value for x corresponding to each repetition).

x
The argument x has prototype
        CppAD::vector<double>& x
 and its size is n ; i.e., x.size() == size . The input value of the elements of x does not matter. On output, it has been set to the argument value for which the function, or its derivative, is being evaluated. The value of this vector need not change with each repetition.

row
The argument row has prototype
     const CppAD::vector<size_t> row
 Its size defines the value K . It contains the row indices for the corresponding function f ( x ) . All the elements of row are between zero and n -1 .

col
The argument col has prototype
     const CppAD::vector<size_t> col
 Its size must be the same as row ; i.e., K . It contains the column indices for the corresponding function f ( x ) . All the elements of col are between zero and n -1 . There are no duplicated entries requested, to be specific, if k1 != k2 then
     ( row[k1] , col[k1] ) != ( row[k2] , col[k2] )
hessian
The argument hessian has prototype
     CppAD::vector<double>&  hessian
 and its size is K . The input value of its elements does not matter. The output value of its elements is the Hessian of the function f ( x ) . To be more specific, for k = 0 , … , K -1 , ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ col [ k ] ] = hessian [ k ]
n_sweep
The input value of n_sweep does not matter. On output, it is the value n_sweep corresponding to the evaluation of hessian . This is also the number of colors corresponding to the coloring method , which can be set to colpack , and is otherwise cppad.

double
In the case where package is double, only the first element of hessian is used and it is actually the value of f ( x ) (derivatives are not computed).
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item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_det_grad_33.hpp_xml.js0000644000175200017650000000330313057470510017411 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'det_grad_33.xml', 'det_grad_33.hpp.xml' ]; var list_down3 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down2 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down1 = [ 'det_grad_33.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; 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item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_mat_sum_sq.cpp_xml.js0000644000175200017650000000332613057470510017503 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_mat_sum_sq.hpp_xml.js0000644000175200017650000000332613057470510017510 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'mat_sum_sq.xml', 'mat_sum_sq.hpp.xml' ]; var list_down3 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down2 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down1 = [ 'mat_sum_sq.cpp.xml', 'mat_sum_sq.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_ode_evaluate_xml.js0000644000175200017650000000452613057470510017212 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'ode_evaluate.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down0 = [ 'ode_evaluate.cpp.xml', 'ode_evaluate.hpp.xml' ]; var list_current0 = [ 'ode_evaluate.xml#Syntax', 'ode_evaluate.xml#Purpose', 'ode_evaluate.xml#Inclusion', 'ode_evaluate.xml#Float', 'ode_evaluate.xml#Float.Operation Sequence', 'ode_evaluate.xml#Float.fabs', 'ode_evaluate.xml#x', 'ode_evaluate.xml#p', 'ode_evaluate.xml#p.p == 0', 'ode_evaluate.xml#p.p = 1', 'ode_evaluate.xml#fp', 'ode_evaluate.xml#fp.Function', 'ode_evaluate.xml#fp.Gradient', 'ode_evaluate.xml#Example', 'ode_evaluate.xml#Source Code' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_ode_evaluate.cpp_xml.js0000644000175200017650000000333613057470510017771 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'ode_evaluate.xml', 'ode_evaluate.cpp.xml' ]; var list_down3 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_ode_evaluate.hpp_xml.js0000644000175200017650000000333613057470510017776 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'ode_evaluate.xml', 'ode_evaluate.hpp.xml' ]; var list_down3 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down2 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down1 = [ 'ode_evaluate.cpp.xml', 'ode_evaluate.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sparse_jac_fun_xml.js0000644000175200017650000000456313057470510017540 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'sparse_jac_fun.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down0 = [ 'sparse_jac_fun.cpp.xml', 'sparse_jac_fun.hpp.xml' ]; var list_current0 = [ 'sparse_jac_fun.xml#Syntax', 'sparse_jac_fun.xml#Purpose', 'sparse_jac_fun.xml#Inclusion', 'sparse_jac_fun.xml#Float', 'sparse_jac_fun.xml#FloatVector', 'sparse_jac_fun.xml#n', 'sparse_jac_fun.xml#m', 'sparse_jac_fun.xml#x', 'sparse_jac_fun.xml#row', 'sparse_jac_fun.xml#col', 'sparse_jac_fun.xml#p', 'sparse_jac_fun.xml#fp', 'sparse_jac_fun.xml#fp.Function', 'sparse_jac_fun.xml#fp.Jacobian', 'sparse_jac_fun.xml#Example', 'sparse_jac_fun.xml#Source Code' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/sparse_jac_fun.cpp.xml0000644000175200017650000002767413057470510017476 0ustar coincoin-web sparse_jac_fun: Example and test
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sparse_jac_fun: Example and test
# include <cppad/speed/sparse_jac_fun.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/cppad.hpp>

bool sparse_jac_fun(void)
{     using CppAD::NearEqual;
     using CppAD::AD;

     bool ok = true;

     size_t j, k;
     double eps = CppAD::numeric_limits<double>::epsilon();
     size_t n   = 3;
     size_t m   = 4;
     size_t K   = 5;
     CppAD::vector<size_t>       row(K), col(K);
     CppAD::vector<double>       x(n),   yp(K);
     CppAD::vector< AD<double> > a_x(n), a_y(m);

     // choose x
     for(j = 0; j < n; j++)
          a_x[j] = x[j] = double(j + 1);

     // choose row, col
     for(k = 0; k < K; k++)
     {     row[k] = k % m;
          col[k] = (K - k) % n;
     }

     // declare independent variables
     Independent(a_x);

     // evaluate function
     size_t order = 0;
     CppAD::sparse_jac_fun< AD<double> >(m, n, a_x, row, col, order, a_y);

     // evaluate derivative
     order = 1;
     CppAD::sparse_jac_fun<double>(m, n, x, row, col, order, yp);

     // use AD to evaluate derivative
     CppAD::ADFun<double>   f(a_x, a_y);
     CppAD::vector<double>  jac(m * n);
     jac = f.Jacobian(x);

     for(k = 0; k < K; k++)
     {     size_t index = row[k] * n + col[k];
          ok &= NearEqual(jac[index], yp[k] , eps, eps);
     }
     return ok;
}
Input File: speed/example/sparse_jac_fun.cpp cppad-20170000.3/doc/_sparse_jac_fun.cpp_xml.js0000644000175200017650000000334613057470510020317 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'sparse_jac_fun.xml', 'sparse_jac_fun.cpp.xml' ]; var list_down3 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down2 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down1 = [ 'sparse_jac_fun.cpp.xml', 'sparse_jac_fun.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sparse_jac_fun.hpp_xml.js0000644000175200017650000000334613057470510020324 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'sparse_jac_fun.xml', 'sparse_jac_fun.hpp.xml' ]; var list_down3 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down2 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down1 = [ 'sparse_jac_fun.cpp.xml', 'sparse_jac_fun.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/sparse_hes_fun.cpp.xml0000644000175200017650000003313313057470510017503 0ustar coincoin-web sparse_hes_fun: Example and test
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sparse_hes_fun: Example and test
# include <cppad/speed/sparse_hes_fun.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/cppad.hpp>

bool sparse_hes_fun(void)
{     using CppAD::NearEqual;
     bool ok = true;

     typedef CppAD::AD<double> ADScalar;

     size_t j, k;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     size_t n   = 5;
     size_t m   = 1;
     size_t K   = 2 * n;
     CppAD::vector<size_t>       row(K),  col(K);
     CppAD::vector<double>       x(n),    ypp(K);
     CppAD::vector<ADScalar>     a_x(n),  a_y(m);

     // choose x
     for(j = 0; j < n; j++)
          a_x[j] = x[j] = double(j + 1);

     // choose row, col
     for(k = 0; k < K; k++)
     {     row[k] = k % 3;
          col[k] = k / 3;
     }
     for(k = 0; k < K; k++)
     {     for(size_t k1 = 0; k1 < K; k1++)
               assert( k == k1 || row[k] != row[k1] || col[k] != col[k1] );
     }

     // declare independent variables
     Independent(a_x);

     // evaluate function
     size_t order = 0;
     CppAD::sparse_hes_fun<ADScalar>(n, a_x, row, col, order, a_y);

     // evaluate Hessian
     order = 2;
     CppAD::sparse_hes_fun<double>(n, x, row, col, order, ypp);

     // use AD to evaluate Hessian
     CppAD::ADFun<double>   f(a_x, a_y);
     CppAD::vector<double>  hes(n * n);
     // compoute Hessian of f_0 (x)
     hes = f.Hessian(x, 0);

     for(k = 0; k < K; k++)
     {     size_t index = row[k] * n + col[k];
          ok &= NearEqual(hes[index], ypp[k] , eps, eps);
     }
     return ok;
}
Input File: speed/example/sparse_hes_fun.cpp cppad-20170000.3/doc/_sparse_hes_fun.cpp_xml.js0000644000175200017650000000334613057470510020341 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_utility.xml', 'sparse_hes_fun.xml', 'sparse_hes_fun.cpp.xml' ]; var list_down3 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down2 = [ 'det_by_lu.xml', 'det_of_minor.xml', 'det_by_minor.xml', 'det_33.xml', 'det_grad_33.xml', 'mat_sum_sq.xml', 'ode_evaluate.xml', 'sparse_jac_fun.xml', 'sparse_hes_fun.xml', 'uniform_01.xml' ]; var list_down1 = [ 'sparse_hes_fun.cpp.xml', 'sparse_hes_fun.hpp.xml' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_sparse_hes_fun.hpp_xml.js0000644000175200017650000000334613057470510020346 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_double_det_lu.cpp_xml.js0000644000175200017650000000366313057470510020145 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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} function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_double_mat_mul.cpp_xml.js0000644000175200017650000000366613057470510020332 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_double.xml', 'double_mat_mul.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'double_det_minor.cpp.xml', 'double_det_lu.cpp.xml', 'double_mat_mul.cpp.xml', 'double_ode.cpp.xml', 'double_poly.cpp.xml', 'double_sparse_hessian.cpp.xml', 'double_sparse_jacobian.cpp.xml' ]; var list_current0 = [ 'double_mat_mul.cpp.xml#Specifications', 'double_mat_mul.cpp.xml#Implementation' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_double_ode.cpp_xml.js0000644000175200017650000000365213057470510017436 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_double.xml', 'double_ode.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'double_det_minor.cpp.xml', 'double_det_lu.cpp.xml', 'double_mat_mul.cpp.xml', 'double_ode.cpp.xml', 'double_poly.cpp.xml', 'double_sparse_hessian.cpp.xml', 'double_sparse_jacobian.cpp.xml' ]; var list_current0 = [ 'double_ode.cpp.xml#Specifications', 'double_ode.cpp.xml#Implementation' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_double_poly.cpp_xml.js0000644000175200017650000000365513057470510017655 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_double.xml', 'double_poly.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; 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} function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_double_sparse_hessian.cpp_xml.js0000644000175200017650000000371313057470510021674 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_double.xml', 'double_sparse_hessian.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'double_det_minor.cpp.xml', 'double_det_lu.cpp.xml', 'double_mat_mul.cpp.xml', 'double_ode.cpp.xml', 'double_poly.cpp.xml', 'double_sparse_hessian.cpp.xml', 'double_sparse_jacobian.cpp.xml' ]; var list_current0 = [ 'double_sparse_hessian.cpp.xml#Specifications', 'double_sparse_hessian.cpp.xml#Implementation' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/double_sparse_jacobian.cpp.xml0000644000175200017650000002377213057470510021164 0ustar coincoin-web Double Speed: Sparse Jacobian
Prev Next double_sparse_jacobian.cpp

Double Speed: Sparse Jacobian

Specifications
See link_sparse_jacobian .

Implementation 
# include <cppad/utility/vector.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/speed/sparse_jac_fun.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_sparse_jacobian(
     size_t                           size     ,
     size_t                           repeat   ,
     size_t                           m        ,
     const CppAD::vector<size_t>&     row      ,
     const CppAD::vector<size_t>&     col      ,
           CppAD::vector<double>&     x        ,
           CppAD::vector<double>&     jacobian ,
           size_t&                    n_sweep  )
{
     if(global_option["onetape"]||global_option["atomic"]||global_option["optimize"]||global_option["boolsparsity"])
          return false;
     // -----------------------------------------------------
     // setup
     using CppAD::vector;
     size_t i;
     size_t order = 0;          // order for computing function value
     size_t n     = size;       // argument space dimension
     vector<double> yp(m);      // function value yp = f(x)

     // ------------------------------------------------------
     while(repeat--)
     {     // choose a value for x
          CppAD::uniform_01(n, x);

          // computation of the function
          CppAD::sparse_jac_fun<double>(m, n, x, row, col, order, yp);
     }
     for(i = 0; i < m; i++)
          jacobian[i] = yp[i];

     return true;
}
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item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cppad_det_lu.cpp_xml.js0000644000175200017650000000365013057470510017756 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_cppad.xml', 'cppad_det_lu.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down1 = [ 'cppad_det_minor.cpp.xml', 'cppad_det_lu.cpp.xml', 'cppad_mat_mul.cpp.xml', 'cppad_ode.cpp.xml', 'cppad_poly.cpp.xml', 'cppad_sparse_hessian.cpp.xml', 'cppad_sparse_jacobian.cpp.xml' ]; var list_current0 = [ 'cppad_det_lu.cpp.xml#Specifications', 'cppad_det_lu.cpp.xml#Implementation' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cppad_ode.cpp_xml.js0000644000175200017650000000363713057470510017256 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; 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} function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cppad_poly.cpp_xml.js0000644000175200017650000000364213057470510017466 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_cppad.xml', 'cppad_poly.cpp.xml' ]; 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item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cppad_sparse_hessian.cpp_xml.js0000644000175200017650000000370013057470510021505 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_cppad.xml', 'cppad_sparse_hessian.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; 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} function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_cppad_sparse_jacobian.cpp_xml.js0000644000175200017650000000370313057470510021624 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_cppad.xml', 'cppad_sparse_jacobian.cpp.xml' ]; var list_down3 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down2 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; 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} function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; } cppad-20170000.3/doc/_speed_fadbad_xml.js0000644000175200017650000000345313057470510017134 0ustar coincoin-webvar list_across0 = [ '_contents_xml.htm', '_reference.xml', '_index.xml', '_search_xml.htm', '_external.xml' ]; var list_up0 = [ 'cppad.xml', 'speed.xml', 'speed_fadbad.xml' ]; var list_down2 = [ 'install.xml', 'introduction.xml', 'ad.xml', 'adfun.xml', 'preprocessor.xml', 'multi_thread.xml', 'utility.xml', 'ipopt_solve.xml', 'example.xml', 'speed.xml', 'appendix.xml' ]; var list_down1 = [ 'speed_main.xml', 'speed_utility.xml', 'speed_double.xml', 'speed_adolc.xml', 'speed_cppad.xml', 'speed_fadbad.xml', 'speed_sacado.xml' ]; var list_down0 = [ 'fadbad_det_minor.cpp.xml', 'fadbad_det_lu.cpp.xml', 'fadbad_mat_mul.cpp.xml', 'fadbad_ode.cpp.xml', 'fadbad_poly.cpp.xml', 'fadbad_sparse_hessian.cpp.xml', 'fadbad_sparse_jacobian.cpp.xml' ]; var list_current0 = [ 'speed_fadbad.xml#Purpose', 'speed_fadbad.xml#fadbad_prefix', 'speed_fadbad.xml#Running Tests', 'speed_fadbad.xml#Contents' ]; function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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function choose_across0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_across0[index-1]; } function choose_up0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_up0[index-1]; } function choose_down3(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down3[index-1]; } function choose_down2(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down2[index-1]; } function choose_down1(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down1[index-1]; } function choose_down0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_down0[index-1]; } function choose_current0(item) { var index = item.selectedIndex; item.selectedIndex = 0; if(index > 0) document.location = list_current0[index-1]; 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The Theory of Forward Mode

Taylor Notation
In Taylor notation, each variable corresponds to a function of a single argument which we denote by t (see Section 10.2 of Evaluating Derivatives ). Here and below X ( t ) , Y ( t ) , and Z(t) are scalar valued functions and the corresponding p-th order Taylor coefficients row vectors are x , y and z ; i.e., X ( t ) = x ( 0 ) + x ( 1 ) * t + ⋯ + x ( p ) * t p + o ( t p ) Y ( t ) = y ( 0 ) + y ( 1 ) * t + ⋯ + y ( p ) * t p + o ( t p ) Z ( t ) = z ( 0 ) + z ( 1 ) * t + ⋯ + z ( p ) * t p + o ( t p ) For the purposes of this section, we are given x and y and need to determine z .

Binary Operators

Addition Z ( t ) = X ( t ) + Y ( t ) ∑ j = 0 p z ( j ) * t j = ∑ j = 0 p x ( j ) * t j + ∑ j = 0 p y ( j ) * t j + o ( t p ) z ( j ) = x ( j ) + y ( j )
Subtraction Z ( t ) = X ( t ) - Y ( t ) ∑ j = 0 p z ( j ) * t j = ∑ j = 0 p x ( j ) * t j - ∑ j = 0 p y ( j ) * t j + o ( t p ) z ( j ) = x ( j ) - y ( j )
Multiplication Z ( t ) = X ( t ) * Y ( t ) ∑ j = 0 p z ( j ) * t j = (∑ j = 0 p x ( j ) * t j ) * (∑ j = 0 p y ( j ) * t j ) + o ( t p ) z ( j ) = ∑ k = 0 j x ( j - k ) * y ( k )
Division Z ( t ) = X ( t ) / Y ( t ) x = z * y ∑ j = 0 p x ( j ) * t j = (∑ j = 0 p z ( j ) * t j ) * (∑ j = 0 p y ( j ) * t j ) + o ( t p ) x ( j ) = ∑ k = 0 j z ( j - k ) y ( k ) z ( j ) = 1 y ( 0 ) (x ( j ) - ∑ k = 1 j z ( j - k ) y ( k ) )
Standard Math Functions
Suppose that F is a standard math function and Z ( t ) = F [ X ( t ) ]
Differential Equation
All of the standard math functions satisfy a differential equation of the form B ( u ) * F ( 1 ) ( u ) - A ( u ) * F ( u ) = D ( u ) We use a , b and d to denote the p-th order Taylor coefficient row vectors for A [ X ( t ) ] , B [ X ( t ) ] and D [ X ( t ) ] respectively. We assume that these coefficients are known functions of x , the p-th order Taylor coefficients for X ( t ) .

Taylor Coefficients Recursion Formula
Our problem here is to express z , the p-th order Taylor coefficient row vector for Z ( t ) , in terms of these other known coefficients. It follows from the formulas above that Z ( 1 ) ( t ) = F ( 1 ) [ X ( t ) ] * X ( 1 ) ( t ) B [ X ( t ) ] * Z ( 1 ) ( t ) = { D [ X ( t ) ] + A [ X ( t ) ] * Z ( t ) } * X ( 1 ) ( t ) B [ X ( t ) ] * Z ( 1 ) ( t ) = E ( t ) * X ( 1 ) ( t ) where we define E ( t ) = D [ X ( t ) ] + A [ X ( t ) ] * Z ( t ) We can compute the value of z ( 0 ) using the formula z ( 0 ) = F ( x ( 0 ) ) Suppose by induction (on j ) that we are given the Taylor coefficients of E ( t ) up to order j -1 ; i.e., e ( k ) for k = 0 , … , j -1 and the coefficients z ( k ) for k = 0 , … , j . We can compute e ( j ) using the formula e ( j ) = d ( j ) + ∑ k = 0 j a ( j - k ) * z ( k ) We need to complete the induction by finding formulas for z ( j + 1 ) . It follows for the formula for the multiplication operator that (∑ k = 0 j b ( k ) t k ) * (∑ k = 1 j + 1 k z ( k ) * t k -1 ) = (∑ k = 0 j e ( k ) * t k ) * (∑ k = 1 j + 1 k x ( k ) * t k -1 ) + o ( t p ) z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 0 j e ( k ) ( j + 1 - k ) x ( j + 1 - k ) - ∑ k = 1 j b ( k ) ( j + 1 - k ) z ( j + 1 - k ) ) z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 1 j + 1 k x ( k ) e ( j + 1 - k ) - ∑ k = 1 j k z ( k ) b ( j + 1 - k ) ) This completes the induction that computes e ( j ) and z ( j + 1 ) .

Cases that Apply Recursion Above
exp_forward Exponential Function Forward Mode Theory
log_forward Logarithm Function Forward Mode Theory
sqrt_forward Square Root Function Forward Mode Theory
sin_cos_forward Trigonometric and Hyperbolic Sine and Cosine Forward Theory
atan_forward Inverse Tangent and Hyperbolic Tangent Forward Mode Theory
asin_forward Inverse Sine and Hyperbolic Sine Forward Mode Theory
acos_forward Inverse Cosine and Hyperbolic Cosine Forward Mode Theory

Special Cases
tan_forward Tangent and Hyperbolic Tangent Forward Taylor Polynomial Theory
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Prev Next include_deprecated

Deprecated Include Files

Deprecated 2015-11-30
The utility individual include files have been deprecated; e.g., 
 
     # include <cppad/runge_45.hpp>
You should instead use 
 
     # include <cppad/utility.hpp>

Deprecated 2006-12-17
The following is a list of deprecated include file names and the corresponding names that should be used. For example, if your program uses the deprecated preprocessor command 
 
     # include <CppAD/CppAD.h>
you should change it to the command 
 
     # include <cppad/cppad.hpp>

Linking New Files to Deprecated Commands
On Unix systems, references in your source code of the from
     # include <CppAD/name.h>
 will refer to the older versions of CppAD unless you preform the following steps (this only needs to be done once, not for every install):
     cp prefix_dir/include
     sudo mv CppAD CppAD.old
     sudo ln -s cppad CppAD
 where prefix_dir is the prefix directory corresponding to your Unix installation . This will link form the deprecated commands to the commands that should be used:
Deprecated    Should Use    Documentation
CppAD/CheckNumericType.h    cppad/check_numeric_type.hpp    CheckNumericType
CppAD/CheckSimpleVector.h    cppad/check_simple_vector.hpp    CheckSimpleVector
CppAD/CppAD.h    cppad/cppad.hpp    CppAD
CppAD/CppAD_vector.h    cppad/vector.hpp    CppAD_vector
CppAD/ErrorHandler.h    cppad/error_handler.hpp    ErrorHandler
CppAD/LuFactor.h    cppad/lu_factor.hpp    LuFactor
CppAD/LuInvert.h    cppad/lu_invert.hpp    LuInvert
CppAD/LuSolve.h    cppad/lu_solve.hpp    LuSolve
CppAD/NearEqual.h    cppad/near_equal.hpp    NearEqual
CppAD/OdeErrControl.h    cppad/ode_err_control.hpp    OdeErrControl
CppAD/OdeGear.h    cppad/ode_gear.hpp    OdeGear
CppAD/OdeGearControl.h    cppad/ode_gear_control.hpp    OdeGearControl
CppAD/Poly.h    cppad/poly.hpp    Poly
CppAD/PowInt.h    cppad/pow_int.hpp    pow_int
CppAD/RombergMul.h    cppad/romberg_mul.hpp    RombergMul
CppAD/RombergOne.h    cppad/romberg_one.hpp    RombergOne
CppAD/Rosen34.h    cppad/rosen_34.hpp    Rosen34
CppAD/Runge45.h    cppad/runge_45.hpp    Runge45
CppAD/SpeedTest.h    cppad/speed_test.hpp    SpeedTest
CppAD/TrackNewDel.h    cppad/track_new_del.hpp    TrackNewDel
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